POLYAMIDOAMINE CATIONIC COLLECTORS

AND METHODS FOR MAKING AND USING SAME

CROSS-REFERENCE TO RELATED APPLICATION

[0001] This application claims priority to U.S. Provisional Patent Application No. 62/067,688, filed on October 23, 2014, which is incorporated by reference herein.

BACKGROUND

Field

[0002] Embodiments described generally relate to compositions that include a polyamidoamine and an organic acid and methods for making and using same. More particularly, such embodiments relate to compositions that include a polyamidoamine and an organic acid, aqueous mixtures that include the composition and an ore, and methods for making and using same.

Description of the Related Art

[0003] Froth flotation is a method that uses the differences in the hydrophobicity of the mineral particles to be separated or purified from aqueous slurries containing the mineral particles and one or more impurities. Certain heteropolar or nonpolar chemicals called collectors are typically added to the aqueous slurries to enhance or form water repellencies on the surfaces of these mineral particles. These collectors are designed to selectively attach to one or more of the mineral particles to be separated and form a hydrophobic monolayer on the surfaces of the mineral particles. The formation of the hydrophobic monolayer lowers the surface energy of the mineral particles, which increases the chance that the particles will bind with air bubbles passing through in the slurry. The density of the combined air bubble and mineral particles is less than the displaced mass of the aqueous slurry, which causes the air bubble and mineral particles to float to the surface of the slurry. A mineral-rich froth is formed by the collection of the floating air bubble and mineral particles at the surface of the slurry that can be skimmed off from the surface, while other minerals or material, e.g., impurities, remain submerged and/or flocculated in the slurry. The flotation of minerals with a negative surface charge, such as silica, silicates, feldspar, mica, clays, chrysocolla, potash and others, from an aqueous slurry can be achieved using cationic collectors. [0004] In reverse flotation, impurities are floated out of and away from the unpurified or crude material to be beneficiated or otherwise purified. In particular, phosphate minerals, iron ore, copper ores, and other minerals and/or ores are frequently beneficiated in this manner. In many cases, silicate is the main component of the mineral impurities that cause quality reductions in the purified product. The minerals containing silicates or other silicon oxides include quartz, sand, mica, feldspar, muscovite, and biotite. A high silicate content lowers the quality of the phosphate or other purified material.

[0005] Phosphorous ores generally contain impurities and phosphate materials, e.g., calcium phosphate that can be represented by the general chemical formula Ca5(P0 ₄ )3(X), where X can be fluoride, chloride, and/or hydroxide. Phosphate materials, such as calcium phosphate, generally have a polar, hydrophilic surface. Many of the impurities, e.g., silicates, in the phosphorous ore also have polar, hydrophilic surfaces and are not easy to selectively separate from the phosphate material. Conventional collectors used for silicate flotation in phosphate beneficiation generally exhibit inadequate results with respect to selectivity and yield of phosphate relative to the impurities.

[0006] Monoamidoamines have been used in phosphate beneficiation, but are difficult to handle and use as a collector due to generally being highly viscous liquids or waxy solids at room temperature, e.g., about 25°C. Monoamidoamines also exhibit inadequate selectivity of silicate over phosphate and, therefore, provide a phosphate product with a higher impurity content than other conventional collectors. In addition to lower purity, phosphate products recovered with monoamidoamines generally are recovered in lower yields relative to other conventional collectors.

[0007] There is a need, therefore, for improved collectors and methods for making and using same.

SUMMARY

[0008] Compositions, aqueous mixtures that include the composition and an ore, and methods for making and using same are provided. In one or more embodiments, the composition can include an organic acid and a polyamidoamine having the chemical formula:

1 d R 2

[0009] In the chemical formula (A): R an can independently be a saturated or unsaturated, substituted or unsubstituted, linear or branched, cyclic, heterocyclic, or aromatic hydrocarbyl group, R ³ and R ⁴ can independently be hydrogen or a saturated or unsaturated, substituted or unsubstituted, linear or branched, cyclic, heterocyclic, or aromatic hydrocarbyl group, each m can be an integer of 1 to 5, and n can be an integer of 2 to 8. .

[0010] In one or more embodiments, the aqueous mixture can include an ore; water; an organic acid; and a polyamidoamine having the chemical formula (A). In the chemical formula (A): R ¹ and R can independently be a saturated or unsaturated, substituted or unsubstituted, linear or branched, cyclic, heterocyclic, or aromatic hydrocarbyl group, R ³ and R ⁴ can independently be hydrogen or a saturated or unsaturated, substituted or unsubstituted, linear or branched, cyclic, heterocyclic, or aromatic hydrocarbyl group, each m can be an integer of 1 to 5, and n can be an integer of 2 to 8.

[0011] In one or more embodiments, a method for purifying an ore can include combining an ore, water, an organic acid, and a polyamidoamine to produce an aqueous mixture. The ore can include an impurity. The polyamidoamine can have the chemical formula (A). In the chemical

1 2

formula (A): R and R are independently a saturated or unsaturated, substituted or unsubstituted, linear or branched, cyclic, heterocyclic, or aromatic hydrocarbyl group, R ³ and R ⁴ are independently hydrogen or a saturated or unsaturated, substituted or unsubstituted, linear or branched, cyclic, heterocyclic, or aromatic hydrocarbyl group, each m is an integer of 1 to 5, and n is an integer of 2 to 8. A purified ore having a reduced concentration of the impurity relative to the ore can be collected from the aqueous mixture.

DETAILED DESCRIPTION

[0012] It has been surprisingly and unexpectedly discovered that compositions containing one or more polyamidoamines and one or more organic acids, e.g., acetic acid, provide high yields and/or selectivity by impurity, e.g., silicate, flotation in an aqueous mixture for the purification or beneficiation of one or more ores. For example, the compositions containing the polyamidoamme and organic acid, e.g., acetic acid, surprisingly and unexpectedly perform better, e.g., greater yield and/or selectivity, in phosphate beneficiation than blends of monoamidoamines and acetic acid. Without wishing to be bound by theory, it is believed that the mixture of the polyamidoamme and organic acid, e.g., acetic acid, provides enhanced adhesion to the surfaces of impurities, e.g., silicate particles and other gangue material, which lowers the surface energy of the impurities. This reduced surface energy increases the likelihood for the impurities to bind or otherwise attract to air bubbles and thus increases the buoyancy of the impurities. The purified phosphate or other purified materials can be collected or removed from the aqueous mixture, for example, after settling toward or on a bottom of a separation vessel. Accordingly, the compositions can be used as cationic collectors.

[0013] It has also been surprisingly and unexpectedly discovered that combining the polyamidoamme, e.g., diamidoamines and/or triamidoamines, and the organic acid, e.g., acetic acid, produces a free flowing, homogeneous solution at room temperature, e.g., about 25°C. For example, a mixture of the polyamidoamme and organic acid, e.g., acetic acid, surprisingly and unexpectedly produces a composition that has a lower viscosity and is freer flowing at a temperature of about 25°C than monoamidoamines or polyamidoamines free of the organic acid, which are often solids, waxy solids, or highly viscous liquids at a temperature of about 25°C.

[0014] The composition or cationic collector can include one or more polyamidoamines and one or more organic acids, e.g., acetic acid. The polyamidoamme can be or include one or more amidoamines having the chemical formula (A):

1 2

[0015] where R and R can independently be a saturated or unsaturated, substituted or unsubstituted, linear or branched, cyclic, heterocyclic, or aromatic hydrocarbyl group, R ³ and R ⁴ can independently be hydrogen or a saturated or unsaturated, substituted or unsubstituted, linear or branched, cyclic, heterocyclic, or aromatic hydrocarbyl group, each m can be an integer of 1, 2, 3, 4, 5, 6, 7, 8, or greater, and n can be an integer of 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, or

1 2

greater. In one example, R and R can be the same saturated or unsaturated, substituted or unsubstituted, linear or branched, cyclic, heterocyclic, or aromatic hydrocarbyl group. In another

1 2

example, R and R can be different and can be selected from a saturated or unsaturated, substituted or unsubstituted, linear or branched, cyclic, heterocyclic, or aromatic hydrocarbyl group.

[0016] In some examples, R ¹ , R ² , R ³ , and R ⁴ can independently be an alkyl, an alkenyl, an alkynyl, an aryl, an alkoxyl, a carboxylic acid, an amino, an amido, a saturated and/or an unsaturated fatty acid group, and/or isomers thereof. In some examples, R ¹ , R ² , R ³ , and R ⁴ can independently be a hydrocarbyl group with 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 25, 30, or more carbon atoms. For example, R ¹ , R ² , R ³ , and R ⁴ can independently be a C4 to C30 chain, a C8 to C24 chain, a C9 to C30 chain, a C9 to C24 chain, a C9 to C21 chain, a C9 to C20 chain, a C9 to C19 chain, a C9 to CI 8 chain, a C9 to C17 chain, a C9 to C15 chain, a CIO to C24 chain, a CIO to C20 chain, a CIO to C18 chain, a CI 1 to C21 chain, a CI 1 to C19 chain, a CI 1 to C17 chain, a C12 to C20 chain, a C14 to C20 chain, a C14 to C19 chain, a C14 to C18 chain, a C14 to C17 chain, a C14 to C16 chain, a C14 to C15 chain, a C15 to C20 chain, a C15 to C19 chain, a C15 to C18 chain, a C15 to C17 chain, or a C15 to C16 chain.

[0017] In one or more examples, R ¹ , R ² , R ³ , and R ⁴ can independently be derived from one or more fatty acid sources. Illustrative fatty acid sources can be or include, but are not limited to, one or more fatty acids, tall oil fatty acids (TOFA), rosin acids, crude tall oils (CTO), distilled tall oils (DTO), tall oil pitches, portions thereof, fractions thereof, or any mixture thereof. Other illustrative fatty acid sources can be or include lauric acid, stearic acid, isostearic acid, naphthenic acid, oleic acid, linoleic acid, linolenic acid, palmitic acid, salts thereof, isomers thereof, or any mixture thereof. In some examples, R ³ and R ⁴ can be hydrogen and R ¹ and R ² can independently be derived from lauric acid, stearic acid, isostearic acid, naphthenic acid, oleic acid, linoleic acid, linolenic acid, palmitic acid, other fatty acids, isomers thereof, or any mixture thereof.

[0018] In some examples of the polyamidoamines, each R ¹ , R ² , R ³ , and R ⁴ can have all saturated bonds, such as saturated fatty acid groups, and therefore no unsaturated bonds. In other examples of the polyamidoamines, R ¹ , R ² , R ³ , and R ⁴ can independently have one or more unsaturated bonds, such as unsaturated fatty acid groups. For example, R ¹ , R ² , R ³ , and R ⁴ can independently have 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 15, 20, or more unsaturated bonds. In some examples, R ¹ , R ² , R ³ , and R ⁴ can independently have less than 10 unsaturated bonds, less than 8 unsaturated bonds, less than 6 unsaturated bonds, or less than 5 unsaturated bonds, such as, for example, 0, 1, 2, 3, or 4 unsaturated bonds. n some examples, R 1 and R 2

[0019] I can independently be a C6 to C24 chain having 0, 1, 2, 3, 4,

1 2

5, or more unsaturated bonds. For example, R and R can independently be a C8 to C24 chain

1 2 having 0 to 5, 0 to 4, 0 to 3, or 0 to 2 unsaturated bonds. In other examples, R and R can independently be a C10 to C18 chain having 0 to 3 unsaturated bonds. In other examples, R ¹ and R ² can independently be C ₉ Hi ₉ , C ₉ Hi ₇ , C ₉ Hi ₅ , C ₉ Hi ₃ , CnH ₂₃ , C _n H ₂₁ , Ci ₅ H ₃₃ , Ci ₅ H ₃ i, Ci ₅ H ₂₉ , Ci ₇ H ₃₅ , Ci ₇ H ₃₃ , Ci ₇ H ₃ i, Ci ₇ H ₂₉ , Ci ₉ H ₃₇ , Ci ₉ H ₃₅ , Ci ₉ H ₃₃ , Ci ₉ H ₃ i, Ci ₉ H ₂₉ , isomers thereof,

1 2

combinations thereof, or any mixture thereof. In some examples, R and R can independently be the -CH ₂ CH ₂ (C5Hg)CH ₂ CFl ₃ hydrocarbyl, such as derived from naphthenic acid. R ³ and R ⁴ can independently be hydrogen or a C6 to C24 chain having 0, 1, 2, 3, 4, 5, or more unsaturated bonds. For example, R ³ and R ⁴ can independently be hydrogen. In other examples, R ³ and R ⁴ can independently be a C8 to C24 chain having 0 to 3 unsaturated bonds. In other examples, R and R ⁴ can independently be hydrogen, an amino, an amido, or a C10 to C18 chain having 0 to 3 unsaturated bonds.

[0020] The value of m defines number of carbon atoms, i.e., the carbon chain length, of the organic diyl group having the N(R )(CH ₂ ) _m portion of the chemical formula (A). In one or more examples, each m can independently be 1, 2, 3, 4, 5, 6, 7, 8, or greater. In some examples, each m can independently be 1 to 8, 1 to 7, 1 to 6, 1 to 5, 1 to 4, 1 to 3, or 1 to 2. For example, each m can independently be 1, 2, 3, 4, 5, 6, 7, or 8, and the organic diyl group having the N(R )(CH ₂ ) _m portion of the chemical formula (A) can be or include methanediyl (-CH ₂ -), ethanediyl (-CH2CH2-), propanediyl (-CH ₂ CH ₂ CH ₂ -), butanediyl (-CH ₂ (CH ₂ ) ₂ CH ₂ -), pentanediyl (-CH ₂ (CH ₂ ) ₃ CH ₂ -), hexanediyl (-CH ₂ (CH ₂ ) ₄ CH ₂ -), heptanediyl (-CH ₂ (CH ₂ ) ₅ CH ₂ -), octanediyl (-CH ₂ (CH ₂ ) ₆ CH ₂ -), or isomers thereof, respectively. In some specific examples, each m can independently be 1, 2, 3, or 4, and the organic diyl group having the N(R )(CH ₂ ) _m portion of the chemical formula (A) can include methylene, ethylene, propylene, or butylene, respectively. [0021] The value of n defines number of organic diyl groups having the N(R )(CH2) _m portion of the chemical formula (A). In one or more examples, n can be 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, or greater. In some examples, n can be 1 to 12, 1 to 10, 1 to 8, 1 to 6, 1 to 5, 1 to 4, 1 to 3, 1 to 2, 2 to 12, 2 to 10, 2 to 8, 2 to 6, 2 to 5, 2 to 4, or 2 to 3. For example, n can be 2, 3, 4, or 5 and the polyamidoamines can be or include diamidomonoamines, diamidodiamines, diamidotriamines, or diamidotetraamines, respectively. In other examples, the polyamidoamines can be or include triamidomonoamines, triamidodiamines, triamidotriamines, or triamidotetraamines.

3 3

[0022] In one example, R in each of the organic diyl groups having the N(R )(CH2) _m portion of the chemical formula (A) contained in a single polyamidoamine molecule can be the same group or can independently be different groups. Therefore, each of the R groups can independently be hydrogen or a saturated or unsaturated, substituted or unsubstituted, linear or branched, cyclic, heterocyclic, or aromatic hydrocarbyl group. Similarly, each m can independently be selected for each organic diyl group. For example, if n is 2, then the organic diyl groups having the N(R ³ )(CH ₂ ) _m portion is N(R ³ )(CH ₂ ) _m N(R ³ )(CH ₂ ) _m , and the polyamidoamine can include N(H)(CH ₂ ) _m N(H)(CH ₂ ) _m (if both R ^3, s are hydrogen), N(CH3)(CH ₂ ) _m N(CH3)(CH ₂ ) _m (if both R ^3, s

3 3

are methyl), N(H)(CH2) _m N(CH3)(CH ₂ ) _m (if one R is hydrogen and one R is methyl), or any other permutation.

[0023] In another example, R ¹ , R ² , R ³ , and R ⁴ can independently be or include one or more amino groups, one or more amido groups, or one or more amidoamino groups. For example, R ¹ ,

2 3 4

R R , and R" can independently be or include one or more amido groups and the polyamidoamines can include triamidoamines, tetraamidoamines, pentamidoamines, or higher polyamidoamines.

[0024] In some examples, the polyamidoamines can be or include one or more amidoamines,

1 2 3 where R and R can independently be a C8 to C24 chain having 0 to 3 unsaturated bonds, R and R ⁴ can be hydrogen, each m can be an integer of 2 to 4, and n can be an integer of 2 to 5.

1 2

For example, each R and R can independently be C9H19, C9H17, C9H15, C9H13, C11H23, CnH ₂₁ , C15H33, C15H31, C15H29, C17H35, C17H33, C17H31, C17H29, C19H37, C19H35, C19H33, C19H31, or C19H29. In other examples, the polyamidoamines can be or include one or more amidoamines

1 2 3 where R and R can independently be a C10 to C18 chain having 0 to 3 unsaturated bonds, R and R ⁴ can be hydrogen, each m can be an integer of 2 or 3, and n can be an integer of 2, 3, or 4. 1 2

For example, each R and R can independently be C11H23, CnH ₂₁ , C15H33, C15H31, C15H29, C17H35, C17H33, C17H31, or C17H29, and n can be 2.

[0025] In some illustrative polyamidoammes, m can be 2, where the organic diyl group having the N(R )(CH2) _m portion of the chemical formula (A) can include an ethanediyl or ethylene group. These polyamidoammes can be referred to as polyethylenepolyamidoammes and can have the chemical formula (B):

[0026] where R ¹ , R ² , R ³ , R ⁴ , and n are defined as above for the chemical formula (A).

[0027] Polyethylene polyamidoammes can include polyethylene diamidoamines, polyethylene triamidoamines, and polyethylene polyamidoammes with four or more amido groups. In some examples of polyamidoammes having the chemical formula 1 2

(B), R and R can independently be a C8 to C24 chain having 0 to 5 or 0 to 3 unsaturated bonds or a C10 to C18 chain having 0 to 5 or 0 to 3 unsaturated bonds. In other examples of polyamidoammes having the chemical formula

1 2

(B), each R and R can independently be or include C9H19, C9H17, C9H15, C9H13, CnH ₂ 3, CnH ₂₁ , C15H33, C15H31, C15H29, C17H35, C17H33, C17H31, C17H29, C19H37, C19H35, C19H33, C19H31, or C19H29. In some examples of polyamidoammes having the chemical formula (B), R ³ and R ⁴ can independently be hydrogen, an amino, an amido, or a C10 to C18 chain having 0 to 3 unsaturated bonds. In some examples of polyamidoammes having the chemical formula (B), n can be 1, 2, 3, 4, 5, 6, 7, or 8. For example, n can be 2 to 8, 2 to 5, 2 to 4, or 2 to 3.

[0028] In some specific examples, the polyamidoammes can have the chemical formula (B), where each R ¹ and R ² can independently be a C8 to C24 chain, R ³ and R ⁴ can be hydrogen, and n can be 2, 3, 4, or 5. In other specific examples, the polyamidoammes can have the chemical formula (B), where each R ¹ and R ² can independently be a C10 to C18 chain, R ³ and R ⁴ can be hydrogen, and n can be 2, 3, or 4. [0029] In other illustrative polyamidoammes, R ³ and R ⁴ can be hydrogen in the chemical formula (A). The polyamidoammes, therefore, can be or include one or more amidoamines having the chemical formula (C):

1 2

[0030] where R , R , m, and n are defined as above for the chemical formula (A).

[0031] In some specific examples, the polyamidoammes can have the chemical formula (C), where each R 1 and R 2 can independently be a C8 to C24 chain, each m can be 2, 3, or 4, and n can be 2, 3, 4, or 5. In other specific examples, the polyamidoammes can have the chemical formula (C), where each R 1 and R 2 can independently be a C10 to C18 chain, each m can be 2 or 3, and n can be 2, 3, or 4.

[0032] In other illustrative polyamidoammes, R ³ and R ⁴ can be hydrogen and m can be 2, where the organic diyl group having the N(R )(CH2) _m portion of the chemical formula (A) can include an ethanediyl or ethylene group. These polyethylenepolyamidoamines can have the chemical formula (D):

1 2

[0033] where R , R , and n are defined as above for the chemical formula (A).

[0034] In some specific examples, the polyamidoammes can have the chemical formula (D), where each R 1 and R 2 can independently be a C8 to C24 chain and n can be 2, 3, 4, or 5. In other specific examples, the polyamidoammes can have the chemical formula (D), where each R ¹ and

R can independently be C ₉ Hi ₉ , C ₉ Hi ₇ , C ₉ Hi ₅ , C ₉ Hi ₃ , CnH ₂₃ , CnH ₂₁ , Ci ₅ H ₃₃ , Ci ₅ H ₃ i, Ci ₅ H 29, C17H35, C17H33, C17H31, C17H29, C19H37, C19H35, C19H33, C19H31, or C19H29 and n can be 2, 3, or 4. In other specific examples, the polyamidoammes can have the chemical formula (D), where each R ¹ and R ² can independently be C ₉ Hi ₅ , C9H13, CnH ₂₃ , C _n H ₂₁ , Ci ₅ H ₃₃ , Ci ₅ H ₃ i, Ci ₅ H ₂₉ , Ci ₇ H ₃₅ , C17H33, C17H31, or C17H29 and n can be 2, 3, or 4.

[0035] In other examples, the polyamidoammes can have the chemical formula (A), where R and R ⁴ can be hydrogen, m can be 2, and n can be 2, 3, or 4, thereby providing polyethylenepolyamidoammes having the chemical formulas (E), (F), and (G), respectively:

[0036] where R and R are defined as above for the chemical formula (A). In some examples of

1 2

polyamidoammes having the chemical formulas (E)-(G), each R and R can independently be a C8 to C24 chain having 0 to 3 unsaturated bonds or a C10 to C18 chain having 0 to 3 unsaturated bonds. In other examples of polyamidoammes having the chemical formulas (E)-(G), each R ¹ and R can independently be or include C9H19, C9H17, C9H15, C9H13, C11H23, CnH ₂₁ , C15H33, C15H31, C15H29, C17H35, C17H33, C17H31, C17H29, C19H37, C19H35, C19H33, C19H31, or C19H29. In

1 2 other examples of polyamidoammes having the chemical formulas (E)-(G), each R and R can independently be or include C ₉ Hi ₅ , C9H13, CnH ₂₃ , C _U H ₂₁ , Ci ₅ H ₃₃ , Ci ₅ H ₃ i, Ci ₅ H ₂₉ , Ci ₇ H ₃₅ , C17H33, C17H31, or C17H29.

[0037] In one or more examples, m can be 2 in the chemical formula (A), and the polyamidoammes can be or include one or more polyethylenepolyamidoammes having the chemical formula (H):

[0038] where R ¹ , R ² , R ³ , R ⁴ , and n are defined as above for the chemical formula (A), and where each R ⁵ can be hydrogen or a saturated or unsaturated, substituted or unsubstituted, linear or branched, cyclic, heterocyclic, or aromatic hydrocarbyl group. In some examples, each R ⁵ can be or include hydrogen or any hydrocarbyl group disclosed for R ¹ , R ² , R ³ , or R ⁴ . For example, R ³ , R ⁴ , and each R ⁵ can independently be hydrogen or a saturated or unsaturated, substituted or unsubstituted, linear or branched, cyclic, heterocyclic, or aromatic hydrocarbyl group. In some examples, R ³ , R ⁴ , and each R ⁵ can all be hydrogen. In other examples, R ¹ , R ² , R ³ , R ⁴ , and each R ⁵ can independently be a hydrocarbyl group that can be or include one or more alkyl, alkenyl, alkynyl, aryl, alkoxyl, carboxylic acid, amino, amido, saturated and/or unsaturated fatty acid group, isomers thereof, combinations thereof, or any mixture thereof.

[0039] In some examples, R ³ , R ⁴ , and each R ⁵ can be hydrogen in the chemical formula (H), and the polyamidoammes can be or include one or more polyethylenepolyamidoammes having the chemical formula (I): o o

H

H H (I),

[0040] where R 1 , R 2 , and n are defined as above for the chemical formula (H).

[0041] In some examples of the polyethylenepolyamidoamines having the chemical formula (I), n can be 1, 2, 3, 4, 5, 6, 7, 8, or greater. For example, the polyamidoamines can have the chemical formula (I), where n can be 1, 2, or 3, thereby providing the above chemical formulas (E), (F), and (G), respectively.

[0042] In one or more examples, any of the polyamidoamines having the chemical formulas (A)- (I) can be combined, mixed, and/or reacted with one or more reagents to form salts, complexes, adducts, hydrates, or other forms of the polyamidoamines. For example, one or more polyamidoamines can be reacted with one or more acids to form one or more polyamidoaminates. The polyamidoamines can be reacted with the one or more reagents, such as acid, before being combined with other components to form or produce the composition or cationic collector. Alternatively, the polyamidoamines and the one or more reagents can be combined as separate components, at the same time or at different times, to form or produce the composition or cationic collector.

[0043] In one example, one or more organic acids can be mixed, blended, or otherwise combined with the one or more polyamidoamines. Combining the organic acid with the polyamidoamine can make, form, or otherwise produce one or more salts of the polyamidoamines, e.g., polyamidoaminates. Illustrative organic acid sources or organic acids can include, but are not limited to, acetic acid, glycolic acid, lactic acid, pyruvic acid, formic acid, propionic acid, butyric acid, valeric acid (pentanoic acid), oxalic acid, malonic acid, caproic acid, enanthic acid, caprylic acid, pelargonic acid, capric acid, undecylic acid, lauric acid, isomers thereof, hydrates thereof, salts thereof, complexes thereof, adducts thereof, or any mixture thereof. In some examples, the one or more organic acids can be or include acetic acid. In other example, the one or more organic acids can be or include glacial acetic acid. [0044] In some examples, the polyamidoamines can be or include one or more polyamidoaminates and/or complexes of the amidoamines having the chemical formula (J):

[0045] where R ¹ , R ² , R ³ , R ⁴ , m, and n are defined as above for the chemical formula (A), and where A can be hydrogen, one or more alkali metals, one or more alkaline earth metals, ammonium, alkylammonium compounds, one or more hydrocarbyl groups, or one or more cationic species, X can be one or more conjugate bases, halides, e.g., F, CI, Br, or I anions, hydroxide, or other anionic species, and each y and z can independently be about 0.1 to about 8, such as, for example, about 1 to about 8 or about 1 to about 4.

[0046] The A can be hydrogen, lithium, sodium, potassium, cesium, magnesium, calcium, ammonium, monoalkylammonium, dialkylammonium, trialkylammonium, tetraalkylammonium, adducts thereof, complexed salts thereof, hydrates thereof, or mixtures thereof. In some examples, the A can be bonded to the nitrogen atom of the N(R )(CH ₂ ) _m portion to produce a cationic [N(A)(R 3 )(CH ₂ ) _m ] ^" I- portion of the polyamidoamine, such as a quaternary ammonium cation. The X can be one or more one or more anionic species coordinated with the cationic

3 ^" I-

[N(A)(R )(CH ₂ ) _m ] portion of the polyamidoamine. In some examples, the X can be one or more conjugate bases, such as organic conjugate bases, inorganic conjugate bases, or a mixture thereof. The X can be, for example, but not limited to, one or more organic conjugate bases of monocarboxylic acids, dicarboxylic acids, tricarboxylic or higher acids, amino acids, sugars, isomers thereof, hydrates thereof, salts thereof, complexes thereof, adducts thereof, or any mixture thereof. Illustrative conjugate bases can be or include, but are not limited to, acetate, glycolate, lactate, pyruvate, formate, propionate, butyrate, valerate (pentanoate), oxalate, malonate, malonate, caproate, enanthate, caprylate, pelargonate, caprate, undecylate, laurate, malonic acid, caproic acid, enanthic acid, caprylic acid, pelargonic acid, capric acid, undecylic acid, lauric acid, alkyl derivatives thereof, isomers thereof, or salts thereof. [0047] The A and X groups in the polyamidoamines or polyamidoaminates can vary depending on the one or more reagents used to complex the polyamidoamines. Therefore, the values of y and z can also vary relative to the particular reagent combined with the polyamidoamine. For example, acetic acid is a monoprotic acid that provides one proton, e.g., H ⁺ , and one conjugate base, e.g., AcO ^" , while oxalic acid is a diprotic acid that provides two protons, e.g., 2H ⁺ , and one conjugate base, e.g., C ₂ O ₄ ^" . In various compositions of the polyamidoamines or polyamidoaminates, y and z can be equal or substantially to each other, y can be greater than z, or z can be greater than y.

[0048] In some examples of the polyamidoamines or polyamidoaminates, y and/or z can be integers, such as 1, 2, 3, 4, 5, 6, 7, 8, 9, or 10. Alternatively, in other examples of the polyamidoamines or polyamidoaminates, y and/or z can be non-integers or fractions which can indicate a mixture of molecules which are partially cationic and/or anionic functionalized. Each y and z can independently be about 0.1, about 0.2, about 0.3, about 0.4, about 0.5, about 0.6, about 0.7, about 0.8, about 0.9, about 1, about 1.1, about 1.2, about 1.3, about 1.4, about 1.5, about 1.6, about 1.7, about 1.8, about 1.9, about 2, about 2.5, about 3, about 3.5, about 4, about 4.5, about 5, about 5.5, about 6, about 6.5, about 7, about 7.5, about 8, about 8.5, about 9, about 9.5, about 10, or greater. In some examples, each y and z can independently be about 0.1 to about 8, about 0.5 to about 8, about 1 to about 8, about 1 to about 4. In other examples, each y and z can independently be 1 to 8, 1 to 7, 1 to 6, 1 to 5, 1 to 4, 1 to 3, or 1 to 2.

[0049] In one or more examples, illustrative polyamidoaminates can be or include one or more polyethylene polyamidoaminates having the chemical formula (K):

[0050] where R ¹ , R ² , R ³ , R ⁴ , each R ⁵ , and n are defined as above for the chemical formula (H), and where A and X are defined as above for the chemical formula (J). In some examples, A can be hydrogen or a saturated or unsaturated, substituted or unsubstituted, linear or branched, cyclic, heterocyclic, or aromatic hydrocarbyl group. [0051] In some illustrative polyethylene polyamidoaminates having chemical formula (K), each

1 2

R and R can independently be a saturated or unsaturated, substituted or unsubstituted, linear or branched, cyclic, heterocyclic, or aromatic hydrocarbyl group, R ³ , R ⁴ , and each R ⁵ can independently be hydrogen or a saturated or unsaturated, substituted or unsubstituted, linear or branched, cyclic, heterocyclic, or aromatic hydrocarbyl group, n can be an integer of 1 to 8, A can be hydrogen, one or more alkali metals, one or more alkaline earth metals, ammonium, alkylammonium compounds, or one or more other cationic species, and X can be one or more conjugate bases, halides, e.g., F, CI, Br, or I anions, hydroxide, or other anionic species. examples, R 1 and R 2

[0052] In some can independently be alkyl, alkenyl, alkynyl, aryl, alkoxyl, carboxylic acid, amino, amido, saturated and/or unsaturated fatty acid group, isomers thereof, combinations thereof, or mixtures thereof, R ³ , R ⁴ , and each R ⁵ can independently be hydrogen, n can be 1, 2, 3, 4, or 5, A can be hydrogen, and X can be or include one or more conjugate bases which include acetate, glycolate, lactate, pyruvate, formate, propionate, butyrate, valerate, oxalate, alkyl derivatives thereof, isomers thereof, or mixtures thereof.

[0053] For example, R ³ , R ⁴ , and each R ⁵ can be hydrogen in the chemical formula (K), and the polyamidoaminates can be or include one or more polyethylene polyamidoaminates having the chemical formula (L):

where R 1 , R 2

[0054] , n, A, and X are defined as above for the chemical formula (K).

[0055] In one or more examples, A can be hydrogen and X can be acetate in the chemical formula (L), and the polyethylene polyamidoaminates can be or include one or more polyethylene polyamidoamine acetates having the chemical formulas (M) and (N):

1 2

[0056] where R , R , and n are defined as above for the chemical formula (K). In some examples, n can be 1 for the polyethylene polyamidoamine acetates having the chemical formula (M) to provide illustrative diethylene polyamidoamine acetates which have the chemical formula (N). In other illustrative polyethylene polyamidoamine acetates having the chemical formula (M), n can be 2, 3, 4, 5, or greater, for example, triethylene polyamidoamine acetate (n = 2), tetraethylene polyamidoamine acetate (n = 3), or pentaethylene polyamidoamine acetate (n = 4).

[0057] In one or more examples, the polyamidoamines can be made, formed, synthesized, or otherwise produced by reacting one or more polyamines and one or more fatty acids or other carboxylic acids. The polyamidoamines can be produced by combining and reacting greater than one molar equivalent of the fatty acids with one molar equivalent of the polyamines. In some examples, the polyamidoamines can be produced by combining and reacting greater than 1, about 1.1, about 1.2, about 1.3, about 1.4, about 1.5, about 1.6, about 1.7, about 1.8, about 1.9, about 2, about 2.1, about 2.2, about 2.3, about 2.4, about 2.5, about 2.6, about 2.7, about 2.8, about 2.9, about 3, about 3.1, about 3.2, about 3.3, about 3.4, about 3.5, about 3.6, about 3.7, about 3.8, about 3.9, about 4, about 4.5, or about 5 molar equivalents of the fatty acid with one molar equivalent of the polyamine. Processes that can be used to produce the polyamidoamines from polyamine and fatty acid are discussed and described in, for example, U.S. Patent Nos. 2,857,331; 2,927,692; and 3,166,548.

[0058] The one or more polyamines and one or more fatty acids or other carboxylic acids can be reacted to form the polyamidoamines at a temperature of about 0°C, about 10°C, about 20°C, about 25°C, about 30°C, about 40°C, about 50°C, about 60°C, about 70°C, about 80°C, about 90°C, about 100°C, about 110°C, about 120°C, about 130°C, about 140°C, about 150°C, about 160°C, about 170°C, about 180°C, about 190°C, about 200°C, about 250°C, or about 300°C. For example, the one or more polyamines and one or more fatty acids or other carboxylic acids can be reacted to form the polyamidoamines at a temperature of about 0°C to about 300°C, about 10°C to about 250°C, about 20°C to about 225°C, about 20°C to about 200°C, about 20°C to about 190°C, about 20°C to about 180°C, about 20°C to about 175°C, about 20°C to about 165°C, about 20°C to about 150°C, about 50°C to about 225°C, about 50°C to about 500°C, about 50°C to about 190°C, about 50°C to about 180°C, about 50°C to about 175°C, about 50°C to about 165°C, about 50°C to about 150°C, about 100°C to about 225°C, about 100°C to about 1000°C, about 100°C to about 190°C, about 100°C to about 180°C, about 100°C to about 175°C, about 100°C to about 165°C, about 100°C to about 150°C, about 120°C to about 225°C, about 120°C to about 1200°C, about 120°C to about 190°C, about 120°C to about 180°C, about 120°C to about 175°C, about 120°C to about 165°C, or about 120°C to about 150°C. The one or more polyamines and one or more fatty acids or other carboxylic acids can be reacted to form the polyamidoamines for about 10 min to about 24 hr, about 0.5 hr to about 12 hr, about 0.75 hr to about 10 hr, about 1 hr to about 5 hr, about 2 hr to about 4 hr, or about 3 hr.

[0059] In one or more examples, the composition or cationic collector can include one or more polyamidoamines that can be derived, formed, or otherwise produced from one or more polyamines or polyamine sources. The one or more polyamines or polyamine sources can be reacted with one or more fatty acids to produce or otherwise form the one or more polyamidoamines. Illustrative polyamines can include, but are not limited to, dimethylenetriamine, trimethylenetetramine, tetramethylenepentamine, pentamethylenehexamine, diethylenetriamine (DETA), triethylenetetramine (TETA), tetraethylenepentamine (TEPA), pentaethylenehexamine (PEHA), dipropylenetriamine, tripropylenetetramine, tetrapropylenepentamine, pentapropylenehexamine, dibutylenetriamine, tributylenetetramine, tetrabutylenepentamine, pentabutylenehexamine, aminoethylpiperazine, dipropylenetriamine, spermine, spermidine, heavy polyamine X (HPA X), tallow amines, isomers thereof, salts thereof, complexes thereof, adducts thereof, or any mixture thereof. In some examples, the polyamine can be or include a mixture of linear, branched, and/or cyclic ethyleneamines and/or other alkyleneamines, polyethylene polyamines, pentaethylenehexamine mixtures, tetraethylenepentamine mixtures, triethylenetetramine mixtures, isomers thereof, salts thereof, or any mixture thereof. For example, such polyamine can be or include heavy polyamine X (HPA X), commercially available from Dow Chemical Company, and can have components that contain six or more nitrogen atoms per molecule. Polyamine sources can be or include salts, adducts, complexes, or other forms of polyamines or other compounds which provide a source of polyamines which can be used to make polyamidoamines. Polyamine sources can produce polyamines, for example, but not limited to, upon heating, adjusting the pH or concentration, or reacting with other reagents or compounds.

[0060] In one or more examples, the composition or cationic collector can include one or more polyamidoamines that can be derived, formed, or otherwise produced, in part, from one or more fatty acids or fatty acid sources. The one or more fatty acids or fatty acid sources can be reacted with one or more polyamines to produce or otherwise form the one or more polyamidoamines. Illustrative fatty acids or fatty acid sources can be or include one or more fatty acids, TOFA, rosin acids, CTO, DTO, tall oil pitches, portions thereof, fractions thereof, or any mixture thereof. In some specific examples, the fatty acids or fatty acid sources can be or include TOFA, lauric acid, stearic acid, isostearic acid, naphthenic acid, oleic acid, linoleic acid, linolenic acid, palmitic acid, coconut oil fatty acid, isomers thereof, or any mixture thereof.

[0061] In one or more examples, the fatty acids or fatty acid sources can be or include coconut oil fatty acids. Illustrative coconut oil fatty acids can include lauric acid, myristic acid, palmitic acid, capric acid, caprylic acid, oleic acid, stearic acid, palmitoleic acid, linoleic acid, caproic acid, arachidic acid, one or more other fatty acids, isomers thereof, or any mixture thereof. The composition or cationic collector can include one or more polyamidoamines that can be derived, formed, or otherwise produced from at least 6, at least 7, at least 8, at least 9, at least 10, or at least 11 fatty acids selected from lauric acid, myristic acid, palmitic acid, capric acid, caprylic acid, oleic acid, stearic acid, palmitoleic acid, linoleic acid, caproic acid, arachidic acid, one or more other fatty acids, isomers thereof, or any mixture thereof. For example, the one or more polyamidoamines can be derived, formed, or otherwise produced from about 6 to about 10, about 7 to about 10, about 8 to about 10, about 6 to about 11, about 7 to about 11, about 8 to about 11, about 9 to about 11, or about 10 to about 11 fatty acids selected from lauric acid, myristic acid, palmitic acid, capric acid, caprylic acid, oleic acid, stearic acid, palmitoleic acid, linoleic acid, caproic acid, arachidic acid, one or more other fatty acids, isomers thereof, or any mixture thereof. In some examples, the coconut oil fatty acids can include about 40 wt% to about 55 wt% of lauric acid, about 10 wt% to about 25 wt% of myristic acid, about 5 wt% to about 15 wt% of palmitic acid, about 4 wt% to about 15 wt% of capric acid, about 3 wt% to about 12 wt% of caprylic acid, about 3 wt% to about 12 wt% of oleic acid, about 0.5 wt% to about 5 wt% of stearic acid, about 0.01 wt% to about 5 wt% of palmitoleic acid, about 0.01 wt% to about 3 wt% of linoleic acid, about 0.01 wt% to about 2.5 wt% of caproic acid, about 0.01 wt% to about 2.5 wt% of arachidic acid, isomers thereof, or any mixture thereof. In other examples, the coconut oil fatty acids can include about 44 wt% to about 52 wt% of lauric acid, about 13 wt% to about 19 wt% of myristic acid, about 8 wt% to about 11 wt% of palmitic acid, about 6 wt% to about 10 wt% of capric acid, about 5 wt% to about 9 wt% of caprylic acid, about 5 wt% to about 8 wt% of oleic acid, about 1 wt% to about 3 wt% of stearic acid, about 0.01 wt% to about 2.5 wt% of palmitoleic acid, about 0.01 wt% to about 1 wt% of linoleic acid, about 0.01 wt% to about 0.8 wt% of caproic acid, about 0.01 wt% to about 0.5 wt% of arachidic acid, isomers thereof, or any mixture thereof.

[0062] In one example, CTO can be made or produced as an acidified byproduct in the kraft or sulfate processing of wood. Crude tall oil, prior to refining, can include a mixture of rosin acids, fatty acids, sterols, high-molecular weight alcohols, and other alkyl chain materials. The components of CTO can depend on a variety of factors, such as the particular species of the wood being processed (wood type), the geographical location of the wood source, the age of the wood, the particular season that the wood is harvested, and others. Thus, depending on the particular source, CTO can contain about 20 wt% to about 75 wt% of fatty acids, e.g., about 30 wt% to about 60 wt% of fatty acids, about 20 wt% to about 65 wt% of rosin acids, e.g., about 30 wt% to about 60 wt% of rosin acids, and the balance being neutral and non-saponifiable components. In some examples, the CTO can include at least 8 wt% or about 10 wt% of neutral materials or non-saponifiable components.

[0063] Distillation of CTO can be used to recover a mixture of fatty acids, referred to as DTO or DTO fraction, which can have about 16 carbon atoms to about 20 carbon atoms. In some examples, these fatty acids can be included with the polyamines to produce or otherwise form the polyamidoamines. Fatty acids found in tall oils can include, but are not limited to, oleic acid, linoleic acid, stearic acid, and palmitic acid. Rosin acids found in tall oils, include, but are not limited to, abietic acid, dehydroabietic acid, isopimaric acid, and pimaric acid. [0064] The DTO fraction can have a fatty acids and/or esters of fatty acids concentration of about 55 wt%, about 60 wt%, or about 65 wt% to about 85 wt%, about 90 wt%, or about 95 wt%. The DTO fraction can have a rosin acids or rosins concentration of about 5 wt%, about 10 wt%, or about 15 wt% to about 30 wt%, about 35 wt%, or about 40 wt%. The DTO fraction can have a neutrals concentration of about 0.1 wt%, about 1 wt%, or about 1.5 wt% to about 2 wt%, about 3.5 wt%, or about 5 wt%. The DTO fraction can have an acid value of about 20, about 25, or about 30 to about 40, about 45, or about 50. The DTO fraction can have a viscosity (centipoise at 85°C) of about 10 cP, about 20 cP, about 30 cP, or about 40 cP to about 100 cP, about 120 cP, about 135 cP, or about 150 cP. The distilled tall oil can have a density of about 840 g/L, about 860 g/L, or about 880 g/L to about 900 g/L, about 920 g/L, or about 935 g/L. The DTO fraction can have a saponification number of about 180, about 185, or about 190 to about 200, about 205, or about 210. The DTO fraction can have an iodine value of about 115, about 117, or about 120 to about 130, about 135, or about 140.

[0065] The rosin acids derived from CTO are also an intermediate fraction that can be produced from the distillation of CTO. The tall oil rosin can have a concentration of rosin acids of about 80 wt%, about 85 wt%, or about 90 wt% to about 93 wt%, about 95 wt%, or about 99 wt%. The tall oil rosin can have a concentration of abietic acid of about 35 wt%, about 40 wt%, or about 43 wt% to about 50 wt%, about 55 wt%, or about 60 wt%. The tall oil rosin can have a concentration of dehydroabietic acid of about 10 wt%, about 13 wt%, or about 15 wt% to about 20 wt%, about 23 wt%, or about 25 wt%. The tall oil rosin can have a concentration of isopimaric acid of about 10 wt% or less, about 8 wt% or less, about 5 wt% or less, or about 3 wt% or less. The tall oil rosin can have a concentration of pimaric acid of about 10 wt% or less, about 8 wt% or less, about 5 wt% or less, or about 3 wt% or less. The tall oil rosin can have a fatty acids concentration of about 0.5 wt%, about 1 wt%, or about 2 wt% to about 3 wt%, about 5 wt%, or about 10 wt%. The tall oil rosin can have a concentration of neutral materials of about 0.5 wt%, about 1 wt%, or about 2 wt% to about 3 wt%, about 5 wt%, or about 10 wt%. The tall oil rosin can have a density of about 960 g/L, about 970 g/L, or about 980 g/L to about 1,000 g/L, about 1,010 g/L, or about 1,020 g/L. The tall oil rosin can have an acid value of about 150, about 160, or about 165 to about 170, about 175, or about 180.

[0066] Representative tall oil products, which can be fatty acid sources used to form the polyamidoamines, can be or include, but are not limited to, saturated and unsaturated fatty acids in the C ₁₆ -C ₁₈ range, as well as minor amounts of rosin acids, and can include XTOL 100, XTOL ^® 300, and XTOL ^® 304, XTOL ^® 520, and LYTOR ^® 100, all of which are commercially available from Georgia-Pacific Chemicals LLC, Atlanta, GA. XTOL ^® 100 includes about 1.6 wt% of palmitic acid, about 2.5 wt% of stearic acid, about 37.9 wt% of oleic acid, about 26.3 wt% of linoleic acid, about 0.3 wt% of linolenic acid, about 2.9 wt% of linoleic isomers, about 0.2 wt% of arachidic acid, about 3.6 wt% eicosatrienoic acid, about 1.4 wt% of pimaric acid, <0.16 wt% of sandarocopimaric, <0.16 wt% of isopimaric acid, <0.16 wt% of dehydroabietic acid, about 0.2 wt% of abietic acid, with the balance being neutrals and high molecular weight species. LYTOR ^® 100 includes <0.16 wt% of palmitic acid, <0.16 wt% of stearic acid, about 0.2 wt% of oleic acid, about 0.2 wt% of arachidic acid, about 0.2 wt% eicosatrienoic acid, about 2.2 wt% of pimaric acid, about 0.6 wt% of sandarocopimaric, about 8.5 wt% of palustric acid, about 1.6 wt% of levopimaric acid, about 2.8 wt% of isopimaric acid, about 15.3 wt% of dehydroabietic acid, about 51.4 wt% of abietic acid, about 2.4 wt% of neoabietic acid, with the balance being neutrals and high molecular weight species. XTOL ^® 520 DTO includes about 0.2 wt% of palmitic acid, about 3.3 wt% of stearic acid, about 37.9 wt% of oleic acid, about 26.3 wt% of linoleic acid, about 0.3 wt% of linolenic acid, about 2.9 wt% of linoleic isomers, about 0.2 wt% of arachidic acid, about 3.6 wt% eicosatrienoic acid, about 1.4 wt% of pimaric acid, <0.16 wt% wt% of sandarocopimaric, <0.16 wt% of isopimaric acid, <0.16 wt% of dehydroabietic acid, about 0.2 wt% of abietic acid, with the balance being neutrals and high molecular weight species. Such tall oil products can be used in the reaction with the polyamine or a mixture of polyamines. Other fatty acids and mixtures of fatty acids, including oxidized and/or dimerized tall oil, such those discussed below can also be employed.

[0067] In one or more examples, illustrative fatty acid sources can be or include a fatty acid, a mixture of fatty acids, a fatty acid ester, a mixture of fatty acid esters, or a mixture of one or more fatty acids and one or more fatty acid esters. The fatty acid sources or fatty acids can be combined with the tall oils and one or more polyamines, and subsequently reacted to produce or otherwise form the one or more polyamidoamines. In other examples, the fatty acid sources or fatty acids can be used instead of the tall oils, therefore, the fatty acids can be reacted with one or more polyamines to produce or otherwise form the one or more polyamidoamines. Illustrative fatty acid sources or fatty acids can be or include, but are not limited to, oleic acid, lauric acid, linoleic acid, linolenic acid, palmitic acid, stearic acid, isostearic acid, ricinoleic acid, myristic acid, arachidic acid, behenic acid, capric acid, caprylic acid, caproic acid, palmitoleic acid, isomers thereof, or any mixture thereof.

[0068] In some examples, fatty acid sources or fatty acids which can be reacted with one or more polyamines to produce or otherwise form the one or more polyamidoamines can include fatty acids from various plant and/or vegetable oil sources. Illustrative plant or vegetable oils that can be used as the fatty acids can include, but are not limited to, safflower oil, grapeseed oil, sunflower oil, walnut oil, soybean oil, cottonseed oil, coconut oil, corn oil, olive oil, palm oil, palm olein, peanut oil, rapeseed oil, canola oil, sesame oil, hazelnut oil, almond oil, beech nut oil, cashew oil, macadamia oil, mongongo nut oil, pecan oil, pine nut oil, pistachio oil, grapefruit seed oil, lemon oil, orange oil, watermelon seed oil, bitter gourd oil, buffalo gourd oil, butternut squash seed oil, egusi seed oil, pumpkin seed oil, borage seed oil, blackcurrant seed oil, evening primrose oil, acai oil, black seed oil, flaxseed oil, carob pod oil, amaranth oil, apricot oil, apple seed oil, argan oil, avocado oil, babassu oil, ben oil, borneo tallow nut oil, cape chestnut, algaroba oil, cocoa butter, cocklebur oil, poppyseed oil, cohune oil, coriander seed oil, date seed oil, dika oil, false flax oil, hemp oil, kapok seed oil, kenaf seed oil, lallemantia oil, mafura oil, marula oil, meadowfoam seed oil, mustard oil, okra seed oil, papaya seed oil, perilla seed oil, persimmon seed oil, pequi oil, pili nut oil, pomegranate seed oil, prune kernel oil, quinoa oil, queef oil, ramtil oil, rice bran oil, royle oil, shea nut oil, sacha inchi oil, sapote oil, seje oil, taramira oil, tea seed oil, thistle oil, tigernut oil, tobacco seed oil, tomato seed oil, wheat germ oil, castor oil, colza oil, flax oil, radish oil, salicornia oil, tung oil, honge oil, jatropha oil, jojoba oil, nahor oil, paradise oil, petroleum nut oil, dammar oil, linseed oil, stillingia oil, vernonia oil, amur cork tree fruit oil, artichoke oil, balanos oil, bladderpod oil, brucea javanica oil, burdock oil, candlenut oil, carrot seed oil, chaulmoogra oil, crambe oil, croton oil, cuphea oil, honesty oil, mango oil, neem oil, oojon oil, rose hip seed oil, rubber seed oil, sea buckthorn oil, sea rocket seed oil, snowball seed oil, tall oil, tamanu oil, tonka bean oil, ucuhuba seed oil, or any mixture thereof. Illustrative animal fats or oils that can be used as the fatty acids can include, but are not limited to, fatty acids from animal sources, such as cows, pigs, lambs, chickens, turkeys, ducks, geese, and other animals, as well as dairy products such as milk, butter, or cheese. Illustrative fatty acids from animal sources can include palmitic acid, stearic acid, myristic acid, oleic acid, palmitoleic acid, linoleic acid, or any mixture thereof. [0069] If the fatty acid source includes two or more fatty acids, each fatty acid can be present in the same amount or different amounts with respect to one another. For example, a first fatty acid can be present with respect to another or "second" fatty acid contained therein in a weight ratio of about 10,000: 1, about 9,000: 1, about 8,000: 1, about 7,000: 1, about 6,000: 1, about 5,000: 1, about 4,000:1, about 3,000:1, about 2,000:1, about 1,000:1, about 900: 1, about 800:1, about 700: 1, about 600:1, about 500:1, about 400: 1, about 300: 1, about 200: 1, about 150:1, about 100: 1, about 99: 1, about 90: 10, about 80:20, about 70:30, about 60:40, about 50:50, about 40:60, about 30:70, about 20:80, about 10:90, about 1 :99, about 1 :100, about 1 : 150, about 1 :200, about 1 :300, about 1 :400, about 1 :500, about 1 :600, about 1 :700, about 1 :800, about 1 :900, about 1,000, about 2,000, about 1 :3,000, about 1 :4,000, about 1 :5,000, about 1 :6,000, about 1 :7,000, about 1 :8,000, about 1 :9,000, or about 1 :10,000. Similarly, if three or more fatty acids are mixed, the three or more fatty acids can be present in any ratio. Therefore, the two or more fatty acids can be reacted with one or more polyamines to produce or otherwise form

1 2

polyamidoamines with different R and R groups in any of the chemical formulas (A)-(M).

[0070] In some examples, one or more organic acid sources or organic acids can be combined with one or more fatty acid sources or fatty acids and one or more polyamines, and subsequently reacted to produce or otherwise form the one or more polyamidoamines. In other examples, organic acid sources or organic acids can be used instead of the fatty acid sources or fatty acids, therefore, the organic acid sources or organic acids can be reacted with one or more polyamines to produce or otherwise form the one or more polyamidoamines. Illustrative organic acid sources or organic acids can include, but are not limited to, glycolic acid, lactic acid, pyruvic acid, formic acid, acetic acid, propionic acid, butyric acid, valeric acid, oxalic acid, malonic acid, caproic acid, enanthic acid, caprylic acid, pelargonic acid, capric acid, undecylic acid, lauric acid, isomers thereof, hydrates thereof, salts thereof, complexes thereof, adducts thereof, or any mixture thereof.

[0071] In some specific examples, the polyamines that can be reacted with the fatty acids to produce the polyamidoamines can be or include diethylenetriamine, triethylenetetramine, tetraethylenepentamine, or a mixture thereof, and the fatty acids that can be reacted with the polyamines to produce the polyamidoamines can be or include tall oil fatty acids, lauric acid, stearic acid, isostearic acid, naphthenic acid, isomers thereof, or any mixture thereof. [0072] The polyamidoamine can have a total amine value (TAV) of about 50, about 60, about 70, about 80, about 90, about 100, about 110, about 120, about 130, about 140, about 150, about 160, about 170, about 180, about 190, about 200, about 210, about 220, about 230, about 240, about 250, about 260, about 270, about 280, about 290, or about 300, based on mg of KOH per g of polyamidoamine. In some examples, the polyamidoamine can have a TAV of about 50 to about 300, about 50 to about 200, about 50 to about 100, about 80 to about 120, about 180 to about 300, about 200 to about 300, about 220 to about 280, about 230 to about 270, about 240 to about 260, or about 245 to about 255, based on mg of KOH per g of polyamidoamine.

[0073] In one or more examples, a critical micelle concentration (CMG) of a polyamidoamine

1 2

(having any one of the chemical formulas (A)-(M)) can be increased where R and R are or include different hydrocarbyl groups, relative to a polyamidoamine, having the same chemical

1 2

formula except where R and R are or include the same hydrocarbyl group. Disorder in

1 2

chemical structure, such as branching or irregularities in the R and R hydrocarbyl groups, can inhibit formation of micelles in the aqueous solutions or slurries. In some examples, preventing or minimizing micelle formation can provide more available polyamidoamine for adhering to mineral particles in the aqueous solutions or slurries. In other aspects, the irregularities in structure can also provide lower melting points for the polyamidoamine and/or the composition or cationic collector, which in turn can be increase the utility of the polyamidoamine or the composition or cationic collector in cold-weather applications.

[0074] In other examples, the composition or cationic collector having a polyamidoamine with

1 2

varying carbon chain lengths in the R and R hydrocarbyl groups can be prepared to have a desired collecting power based on mineral particle size in the aqueous solutions or slurries. In

1 2

some examples, if the R and R hydrocarbyl groups include long carbon chains, such as a CI 8 to C24 chain, then the polyamidoamine can favor collecting particles having a particle size of greater than 150 μιη, such as greater than 150 μιη to about 750 μιη. Alternatively, in other

1 2

examples, if the R and R hydrocarbyl groups include short carbon chains, such as a C6 to C12 chain, then the polyamidoamine can favor collecting particles having a particle size of less than 75 μιη, such as less than 75 μιη to about 5 μιη. In some examples, diamidoamines, triamidoamines, and other polyamidoamines having intermediate sized carbon chain lengths, such as a C6 to C24 chain, can be produced or otherwise formed from mixed fatty acids with varying carbon chain lengths, then the polyamidoamine can favor collecting particles having a particle size of about 75 μηι to about 150 μηι.

[0075] In one or more examples, a hydrophilic-lipophilic balance (HLB) value of the polyamidoamine can be tuned or otherwise selected, at least in part, by varying the carbon chain

1 2

lengths of the R and R hydrocarbyl groups. Polyamidoamines having an intermediate HLB value can be produced which would not be obtained from synthesis with a single fatty acid. The HLB value of the polyamidoamine can be determined by the Davies' Method that assigns a value to different functional groups based on polarity and also uses the following equation:

HLB = 7 + mH _h + nHi ,

[0076] where "¾" is the value assigned to each specific hydrophilic functional group, "m" is the numerical amount of the specified hydrophilic functional groups, "Hi" is the value assigned to each specific lipophilic group, and "n" is the numerical amount of the specified lipophilic groups. For example, ¾ can have an amine value of 10 and an amide value of 4, and Hi can have a CH _n value of -0.475. The HLB value and the equation for determining the HLB value by the Davies' Method are discussed and described in, for example, Davies, J. T., "A Quantitative Kinetic Theory of Emulsion Type, I. Physical Chemistry of the Emulsifying Agent," Gas/Liquid and Liquid/Liquid Interfaces, Proceedings of the 2 ^nd International Congress Surface Activity, Butterworths, London, pgs. 426-438, 1957.

[0077] In one or more examples, the polyamidoamines can generally have an HLB of about 2, about 5, about 8, about 10, about 12, about 15, about 18, about 20, about 25, about 30, about 35, about 40, about 45, or about 50, based on the Davies' Method for hydrophilic-lipophilic balance. For example, the polyamidoamines can generally have an HLB of about 2 to about 50, about 5 to about 50, about 5 to about 20, about 5 to about 15, about 10 to about 25, about 10 to about 20, about 20 to about 35, about 20 to about 30, about 25 to about 35, about 25 to about 30, or about 30 to about 35, based on the Davies' Method for hydrophilic-lipophilic balance.

[0078] In some examples, the polyamidoamines can be or include one or more amidoamines having chemical formula (A), where n can be 2 and the polyamidoamine can have an HLB of about 7.5 to about 12, n can be 3 and the polyamidoamine can have an HLB of about 16.5 to about 21, or n can be 4 and the polyamidoamine can have an HLB of about 25.5 to about 30, based on the Davies' Method for hydrophilic-lipophilic balance. In other examples, the polyamidoamines can be or include one or more amidoamines having chemical formula (A), where n can be 2 and the polyamidoamme can have an HLB of about 8.5 to about 11, n can be 3 and the polyamidoamme can have an HLB of about 17.5 to about 20, or n can be 4 and the polyamidoamme can have an HLB of about 26 to about 29, based on the Davies' Method for hydrophilic-lipophilic balance. In other examples, the polyamidoamines can be or include one or more amidoamines having chemical formula (A), where n can be 2 and the polyamidoamme can have an HLB of about 9 to about 10.5, n can be 3 and the polyamidoamme can have an HLB of about 18 to about 19.5, or n can be 4 and the polyamidoamme can have an HLB of about 26.5 to about 28.5 or about 27 to about 28, based on the Davies' Method for hydrophilic-lipophilic balance.

[0079] In some examples, a mixture of two, three, or more polyamidoamines having any one of the chemical formulas (A)-(D) can have an HLB of about 7.5 to about 30 and can include one or more polyamidoamines having any one of the chemical formulas (A)-(D) where n is 2, one or more polyamidoamines having any one of the chemical formulas (A)-(D) where n is 3, one or more polyamidoamines having any one of the chemical formulas (A)-(D) where n is 4 or 5, or any mixture thereof. In other examples, a mixture of two, three, or more polyethylenepolyamidoammes can have an HLB of about 7.5 to about 30 and can include one or more polyethylenepolyamidoammes having the chemical formula (E), one or more polyethylenepolyamidoammes having the chemical formula (F), one or more polyethylenepolyamidoammes having the chemical formula (G), or any mixture thereof.

[0080] In one or more examples, the polyamidoamines can be or include a mixture of three or more polyamidoamines having any one of the chemical formulas (A)-(M), where the mixture can include at least a first diamidoamine, a second diamidoamine, and a third diamidoamine. The

1 2

first diamidoamine can have R and R as the same hydrocarbyl group, a second diamidoamine

1 2

can have R and R as the same hydrocarbyl group, but different hydrocarbyl groups as the first

1 2

diamidoamine, and the third diamidoamine can have R and R as different hydrocarbyl groups,

1 1 2 such that the R hydrocarbyl group in the third diamidoamine is the same as the R and R hydrocarbyl groups in the first diamidoamine and the R hydrocarbyl group in the third

1 2

diamidoamine is the same as the R and R hydrocarbyl groups in the second diamidoamine. For

1 2 1

example, the R and R hydrocarbyl groups in the first diamidoamine and the R hydrocarbyl

1 2

group in the third diamidoamine can be same hydrocarbyl group, and the R and R hydrocarbyl 2

groups in the second diamidoamine and the R hydrocarbyl group in the third diamidoamine can

1 2

be same hydrocarbyl group, but different than the R and R hydrocarbyl groups in the first diamidoamine and the R ¹ hydrocarbyl group in the third diamidoamine.

[0081] In one or more examples, the polyamidoamines can be or include a mixture of two, three, or more polyamidoamines having any one of the chemical formulas (A)-(M), where the mixture can include polyamidoamines of different amounts of amido groups and/or amine groups. For example, the mixture of polyamidoamines can include a first polyamidoamine having any one of the chemical formulas (A)-(D) where n is 2 and a second polyamidoamine having any one of the chemical formulas (A)-(D) where n is 3, 4, or 5. In another example, the mixture of polyamidoamines can include a first polyamidoamine having any one of the chemical formulas (A)-(D) where n is 2, a second polyamidoamine having any one of the chemical formulas (A)- (D) where n is 3, and a third polyamidoamine having any one of the chemical formulas (A)-(D) where n is 4 or 5. In some examples, the mixture of polyamidoamines can be or include a mixture of polyethylenepolyamidoammes, such as, but is not limited to, the polyethylenepolyamidoammes having the chemical formulas (E), (F), and (G). For example, the mixture of polyethylenepolyamidoammes can include a first polyethylenepolyamidoamine having the chemical formula (E) and a second polyethylenepolyamidoamine having the chemical formula (F) or (G). In another example, the mixture of polyethylenepolyamidoammes can include a first polyethylenepolyamidoamine having the chemical formula (E), a second polyethylenepolyamidoamine having the chemical formula (F), and a third polyethylenepolyamidoamine having the chemical formula (G).

[0082] In one or more examples, an aqueous mixture can include an ore, e.g., a phosphorous ore, one or more polyamidoamines, optionally acetic acid and/or other organic acid, and water, where the polyamidoamine can be or include one or more amidoamines having any one of the chemical formulas (A)-(M). In some examples, an aqueous mixture of a phosphorous containing material can include one or more phosphorous ores, one or more polyamidoamines, optionally acetic acid and/or other organic acid, and water, where the polyamidoamines can be or include one or more amidoamines having any one of the chemical formulas (A)-(M).

[0083] In some examples, the polyamidoamines can be or include one or more amidoamines having chemical formula (A), where each R 1 and R 2 can independently be a saturated or unsaturated, substituted or unsubstituted, linear or branched, cyclic, heterocyclic, or aromatic hydrocarbyl group, R ³ and R ⁴ can independently be hydrogen or a saturated or unsaturated, substituted or unsubstituted, linear or branched, cyclic, heterocyclic, or aromatic hydrocarbyl group, each m can independently be an integer of 1 to 5, and n can be an integer of 2 to 8. In other examples, the polyamidoamines can be or include one or more amidoamines having the chemical formula (B), where each R 1 and R 2 can independently be C9H19, C9H17, C9H15, C9H13, C11H23, C11H21 , C15H33, C15H31, C15H29, C17H35, C17H33, C17H31 , C17H29, C19H37, C19H35, C19H33, C19H31, or C19H29, and n can be an integer of 2, 3, or 4.

[0084] In one example, the polyamidoamine in the composition or cationic collector can be or include one or more products formed by reacting a polyamine and a fatty acid, where the polyamine can be or include diethylenetriamine, triethylenetetramine, tetraethylenepentamme, pentaethylenehexamme, or any mixture thereof, and the fatty acid can be or include tall oil fatty acids, coconut oil fatty acids, lauric acid, stearic acid, isostearic acid, naphthenic acid, oleic acid, linoleic acid, linolenic acid, palmitic acid, isomers thereof, or any mixture thereof. In some specific examples, the polyamine can be or include one or more diethylenetriamine, triethylenetetramine, tetraethylenepentamme, or any mixture thereof, and the fatty acid can be or include one or more tall oil fatty acids, lauric acid, stearic acid, isostearic acid, naphthenic acid, isomers thereof, or any mixture thereof. In other examples, a mixture of fatty acids can be used to make or form the polyamidoamines. The mixture of fatty acids can be or include at least 2, 3, 4, 5, 6, 7, 8, 9, or 10 fatty acids selected from lauric acid, myristic acid, palmitic acid, capric acid, caprylic acid, oleic acid, stearic acid, palmitoleic acid, linoleic acid, caproic acid, arachidic acid, isomers thereof, or any mixture thereof.

[0085] In another example, one or more organic acids can be combined with one or more polyamidoamines to make, form, or otherwise produce the composition or cationic collector, the aqueous mixture, and/or other compositions. In some examples, the one or more organic acids can be combined with the polyamidoamine and subsequently added with other components to make, form, or otherwise produce the composition or cationic collector, the aqueous mixture, and/or other compositions. In other examples, the one or more organic acids and the polyamidoamine can independently be combined with one or more components to make, form, or otherwise produce the composition or cationic collector, the aqueous mixture, and/or other compositions. When the one or more organic acids and the polyamidoamine are independently combined with one or more components, the organic acid and the polyamidoamme can be combined at the same time, the organic acid can be added before the polyamidoamme, or the polyamidoamme can be added before the organic acid. Illustrative organic acid sources or organic acids can include glycolic acid, lactic acid, pyruvic acid, formic acid, acetic acid, propionic acid, butyric acid, valeric acid, oxalic acid, malonic acid, caproic acid, enanthic acid, caprylic acid, pelargonic acid, capric acid, undecylic acid, lauric acid, isomers thereof, hydrates thereof, salts thereof, complexes thereof, adducts thereof, or any mixture thereof.

[0086] In some examples, one or more ores, e.g., phosphorous ores, can be purified by agitating, blending, mixing, or otherwise combining ore, one or more polyamidoamines, one or more organic acids, e.g., acetic acid, and water to produce an aqueous mixture. In some examples, any or all of the phosphorous ore, the polyamidoamme, the acetic acid and/or other organic acids, and water can be combined with one another, in any order, to produce the aqueous mixture. In other examples, phosphorous ore, the polyamidoamme, organic acid, and water can be separately combined with one another, in any order, to produce the aqueous mixture. In some examples, the polyamidoamme and organic acid can be combined with one another to produce a first mixture and the phosphorous ore and water can be combined with one another to produce a second mixture and the first and second mixtures can be combined to produce the aqueous mixture. In some examples, the one or more polyamidoamines and organic acid can be combined with one another to produce the composition or cationic collector, and subsequently, the composition or cationic collector can be combined with the phosphorous ore and water to produce the aqueous mixture. In other examples, the one or more polyamidoamines, organic acid, and water can be combined with one another to produce the composition or cationic collector, and subsequently, the composition or cationic collector can be added or combined with the phosphorous ore and if desired additional water to produce the aqueous mixture.

[0087] In some examples, an ore, e.g., a phosphorous ore, can be purified by combining one or more ores, one or more polyamidoamines, one or more organic acids, e.g., acetic acid, and water to produce an aqueous mixture and collecting or recovering a purified ore from the aqueous mixture. In other examples, a phosphorous containing material can be purified by combining one or more phosphorous ores, one or more polyamidoamines, one or more organic acids, e.g., acetic acid, and water to produce an aqueous mixture and collecting a phosphate material from the aqueous mixture. Generally, in some examples, silicates, silicon oxides, and/or other gangue materials can be floated away from the aqueous mixture or slurry providing the beneficiation or purification of the ore. The polyamidoamines can be or include one or more amidoamines having any one of the chemical formulas (A)-(M). In some examples, the method can include the use of the amidoamines having any one of the chemical formulas (A)-(M), where each R ¹ and R can independently be a saturated or unsaturated, substituted or unsubstituted, linear or branched, cyclic, heterocyclic, or aromatic hydrocarbyl group.

[0088] In some examples, the purification or beneficiation of the ore, e.g., a phosphorous ore,

1 2 can include the use of the amidoamines having the chemical formula (A), where each R and R can independently be a saturated or unsaturated, substituted or unsubstituted, linear or branched, cyclic, heterocyclic, or aromatic hydrocarbyl group, R ³ and R ⁴ can independently be hydrogen or a saturated or unsaturated, substituted or unsubstituted, linear or branched, cyclic, heterocyclic, or aromatic hydrocarbyl group, each m can independently be an integer of 1 to 5, and n can be an integer of 2 to 8. In some examples, the methods can include the use of the amidoamines having the chemical formula (A), where each R 1 and R 2 can independently be a CIO to C18 chain having 0 to 3 unsaturated bonds, R ³ and R ⁴ can be hydrogen, each m can independently be an integer of 2 or 3, and n can be an integer of 2, 3, or 4.

[0089] In some examples, the purification or beneficiation of the ore, e.g., a phosphorous ore,

1 2 can include the use of the amidoamines having the chemical formula (B), where each R and R can independently be a saturated or unsaturated, substituted or unsubstituted, linear or branched, cyclic, heterocyclic, or aromatic hydrocarbyl group, R ³ and R ⁴ can independently be hydrogen or a saturated or unsaturated, substituted or unsubstituted, linear or branched, cyclic, heterocyclic, or aromatic hydrocarbyl group, and n can be an integer of 2 to 8.

[0090] The polyamidoamines can be produced by reacting one or more polyamines and one or more fatty acids, where the polyamines can be or include diethylenetriamine, triethylenetetramine, tetraethylenepentamine, pentaethylenehexamine, or any mixture thereof, and the fatty acids can be or include tall oil fatty acids, lauric acid, stearic acid, isostearic acid, naphthenic acid, oleic acid, linoleic acid, linolenic acid, palmitic acid, isomers thereof, or any mixture thereof.

[0091] In some examples, the purification or beneficiation of the ore, e.g., phosphorous ore, can include combining the organic acid, e.g., acetic acid, and the polyamidoamine to produce the composition or cationic collector and combining the composition or cationic collector and the ore to produce the aqueous mixture. The acetic acid can be glacial acetic acid. The composition or cationic collector can include about 10 wt% to about 60 wt% of the acetic acid and about 40 wt% to about 95 wt% of the polyamidoamine, based on the combined weight of the polyamidoamine and the acetic acid. The composition or cationic collector can also include about 2 wt% to about 50 wt% of water, based on the combined weight of the polyamidoamine, the acetic acid, and the water.

[0092] The aqueous mixture can be contacted with a gas, e.g., air. For example, the aqueous mixture can be agitated by passing air bubbles or other gas bubbles through the aqueous mixture, mechanically stirring, e.g., impeller, paddle, stirrer, shaking, directing sound waves, e.g., ultrasonic sound waves, into the aqueous mixture, or otherwise moving the aqueous mixture, or any combination thereof. The aqueous mixture can be an aqueous solution, slurry, suspension, dispersion, or the like.

[0093] The composition or cationic collector that can include the polyamidoamine and the purification or beneficiation methods that can use the composition or cationic collector can be used to recover, collect, or otherwise purify one or more materials from less pure mixtures, such as, ores and/or minerals. The composition or cationic collector can be used in froth flotation processes for the beneficiation of a wide variety of materials. The ore can generally be or include an aggregate of minerals and gangue from which one or more metals and/or oxides thereof can be separated or extracted. Illustrative ores that can be purified can be or include, but are not limited to, minerals, elements, and/or metals. Illustrative metals can be or include, but are not limited to, phosphorous such as phosphate or other phosphorous oxides, iron, copper, aluminum, nickel, gold, silver, platinum, palladium, titanium, chromium, molybdenum, tungsten, manganese, magnesium, lead, zinc, potassium such as potash, sodium, calcium, graphite, uranium, cerium, dysprosium, erbium, europium, gadolinium, holmium, lanthanum, lutetium, neodymium, praseodymium, promethium, samarium, scandium, terbium, thulium, ytterbium, yttrium, potash, feldspar, bauxite, other precious metals thereof, oxides thereof, ores thereof, or any mixture thereof. In one or more examples, the ore, such as a crude mineral ore to be beneficiated and produce a purified mineral ore or material, can be or include a phosphorous ore, an iron ore, an aluminum ore, a potassium ore, a sodium ore, a calcium ore, potash, feldspar, bauxite, any mixture thereof. The raw materials to be purified and recovered generally contains or includes gangue. The gangue can be or include one or more silicates, sand, quartz, clay, rocks, other materials, or any mixture thereof. The composition or cationic collector can be selective toward the gangue, and especially selective toward silicates, sand, quartz, and other silicon oxide materials.

[0094] In one or more examples, the composition or cationic collector that can include the polyamidoamine and the organic acid, e.g., acetic acid, can be used in froth flotation processes for the beneficiation of phosphorous containing materials, such as phosphate. The phosphorous or phosphate containing ores, rocks, minerals, or other materials, as well as the recovered or collected phosphate materials can include one or more tribasic phosphate salts. The tribasic phosphate salts can include alkaline earth metals, alkali metals, adducts thereof, complexed salts thereof, hydrates thereof, or mixtures thereof. For example, the phosphorous ore or the phosphate material can include calcium phosphate.

[0095] In one or more examples, the amount of the polyamidoamine in the composition or cationic collector can be about 20 wt%, about 30 wt%, about 40 wt%, about 50 wt%, about 55 wt%, about 60 wt%, about 65 wt%, about 70 wt%, about 75 wt%, about 80 wt%, about 85 wt%, about 90 wt%, about 91 wt%, about 92 wt%, about 93 wt%, about 94 wt%, about 95 wt%, about 96 wt%, about 97 wt%, about 97.5 wt%, about 98 wt%, about 98.5 wt%, about 99 wt%, about 99.3 wt%, or about 99.5 wt%, based on the combined weight of the polyamidoamine and the organic acid, e.g., acetic acid. In some examples, the amount of the polyamidoamine in the composition or cationic collector can be about 20 wt% to about 99 wt%, about 30 wt% to about

98 wt%, about 30 wt% to about 95 wt%, about 30 wt% to about 90 wt%, about 40 wt% to about

99 wt%, about 40 wt% to about 95 wt%, about 50 wt% to about 98 wt%, or about 50 wt% to about 95 wt%, based on the combined weight of the polyamidoamine and the organic acid. In one or more examples, the organic acid can be or include acetic acid in the composition or cationic collector.

[0096] The amount of the organic acid, e.g., acetic acid, in the composition or cationic collector can be about 5 wt%, about 10 wt%, about 15 wt%, about 20 wt%, about 25 wt%, about 30 wt%, about 35 wt%, about 40 wt%, about 45 wt%, about 50 wt%, about 55 wt%, about 60 wt%, about 65 wt%, about 70 wt%, about 75 wt%, about 80 wt%, about 85 wt%, or about 90 wt%, based on the combined weight of the polyamidoamine and the organic acid. In some examples, the amount of the organic acid in the composition or cationic collector can be about 5 wt% to about 90 wt%, about 5 wt% to about 80 wt%, about 5 wt% to about 70 wt%, about 5 wt% to about 60 wt%, about 5 wt% to about 50 wt%, about 5 wt% to about 40 wt%, about 5 wt% to about 30 wt%, about 5 wt% to about 20 wt%, about 10 wt% to about 90 wt%, about 10 wt% to about 80 wt%, about 10 wt% to about 70 wt%, about 10 wt% to about 60 wt%, about 10 wt% to about 50 wt%, about 10 wt% to about 40 wt%, about 10 wt% to about 30 wt%, about 10 wt% to about 20 wt%, about 20 wt% to about 90 wt%, about 20 wt% to about 80 wt%, about 20 wt% to about 70 wt%, about 20 wt% to about 60 wt%, about 20 wt% to about 50 wt%, or about 20 wt% to about 40 wt%, based on the combined weight of the polyamidoamme and the organic acid.

[0097] In one specific example, the composition or cationic collector can include about 10 wt% to about 60 wt% of the organic acid, e.g. , acetic acid, and about 40 wt% to about 90 wt% of the polyamidoamme, based on the combined weight of the polyamidoamme and the organic acid. In another specific example, the composition or cationic collector can include about 20 wt% to about 50 wt% of the organic acid and about 50 wt% to about 80 wt% of the polyamidoamme, based on the combined weight of the polyamidoamme and the organic acid. In another specific example, the composition or cationic collector can include about 40 wt% to about 60 wt% of the organic acid and about 60 wt% to about 40 wt% of the polyamidoamme, based on the combined weight of the polyamidoamme and the organic acid. In another specific example, the composition or cationic collector can include about 10 wt% to about 45 wt% of the organic acid and about 55 wt% to about 90 wt% of the polyamidoamme, based on the combined weight of the polyamidoamme and the organic acid.

[0098] In another example, the amount of the polyamidoamme in the composition or cationic collector can be about 5 wt%, about 10 wt%, about 20 wt%, about 30 wt%, about 40 wt%, about 50 wt%, about 55 wt%, about 60 wt%, about 65 wt%, about 70 wt%, about 75 wt%, about 80 wt%, about 85 wt%, about 90 wt%, about 91 wt%, about 92 wt%, about 93 wt%, about 94 wt%, about 95 wt%, about 96 wt%, about 97 wt%, about 97.5 wt%, about 98 wt%, about 98.5 wt%, about 99 wt%, about 99.3 wt%, or about 99.5 wt%, based on the combined weight of the polyamidoamme, the organic acid, e.g., acetic acid, and the water. In some examples, the amount of the polyamidoamme in the composition or cationic collector can be about 5 wt% to about 99 wt%, about 10 wt% to about 98 wt%, about 20 wt% to about 99 wt%, about 30 wt% to about 98 wt%, about 30 wt% to about 95 wt%, about 30 wt% to about 90 wt%, about 40 wt% to about 99 wt%, about 40 wt% to about 95 wt%, about 50 wt% to about 98 wt%, or about 50 wt% to about 95 wt%, based on the combined weight of the polyamidoamme, the organic acid, and the water. In one or more examples, the organic acid can be or include acetic acid in the composition or cationic collector.

[0099] The amount of the organic acid, e.g., acetic acid, in the composition or cationic collector can be about 1 wt%, about 2 wt%, about 3 wt%, about 4 wt%, about 5 wt%, about 6 wt%, about 7 wt%, about 8 wt%, about 9 wt%, about 10 wt%, about 12 wt%, about 15 wt%, about 20 wt%, about 25 wt%, about 30 wt%, about 35 wt%, about 40 wt%, about 45 wt%, about 50 wt%, about 55 wt%, about 60 wt%, about 65 wt%, about 70 wt%, about 75 wt%, about 80 wt%, about 85 wt%, or about 90 wt%, based on the combined weight of the polyamidoamme, the organic acid, and the water. In some examples, the amount of the organic acid in the composition or cationic collector can be about 1 wt% to about 90 wt%, about 2 wt% to about 80 wt%, about 3 wt% to about 70 wt%, about 4 wt% to about 70 wt%, about 5 wt% to about 70 wt%, about 5 wt% to about 90 wt%, about 5 wt% to about 80 wt%, about 5 wt% to about 70 wt%, about 5 wt% to about 60 wt%, about 5 wt% to about 50 wt%, about 5 wt% to about 40 wt%, about 5 wt% to about 30 wt%, about 5 wt% to about 20 wt%, about 10 wt% to about 90 wt%, about 10 wt% to about 80 wt%, about 10 wt% to about 70 wt%, about 10 wt% to about 60 wt%, about 10 wt% to about 50 wt%, about 10 wt% to about 40 wt%, about 10 wt% to about 30 wt%, about 10 wt% to about 20 wt%, about 20 wt% to about 90 wt%, about 20 wt% to about 80 wt%, about 20 wt% to about 70 wt%, about 20 wt% to about 60 wt%, about 20 wt% to about 50 wt%, or about 20 wt% to about 40 wt%, based on the combined weight of the polyamidoamme, the organic acid, and the water.

[00100] The amount of the water in the composition or cationic collector can be about 1 wt%, about 2 wt%, about 3 wt%, about 4 wt%, about 5 wt%, about 6 wt%, about 7 wt%, about 8 wt%, about 9 wt%, about 10 wt%, about 12 wt%, about 15 wt%, about 20 wt%, about 25 wt%, about 30 wt%, about 35 wt%, about 40 wt%, about 45 wt%, about 50 wt%, about 55 wt%, about 60 wt%, about 65 wt%, about 70 wt%, about 75 wt%, about 80 wt%, about 85 wt%, or about 90 wt%, based on the combined weight of the polyamidoamme, the organic acid, e.g., acetic acid, and the water. In some examples, the amount of the water in the composition or cationic collector can be about 1 wt% to about 90 wt%, about 2 wt% to about 80 wt%, about 3 wt% to about 70 wt%, about 4 wt% to about 70 wt%, about 5 wt% to about 70 wt%, about 5 wt% to about 90 wt%, about 5 wt% to about 80 wt%, about 5 wt% to about 70 wt%, about 5 wt% to about 60 wt%, about 5 wt% to about 50 wt%, about 5 wt% to about 40 wt%, about 5 wt% to about 30 wt%, about 5 wt% to about 20 wt%, about 10 wt% to about 90 wt%, about 10 wt% to about 80 wt%, about 10 wt% to about 70 wt%, about 10 wt% to about 60 wt%, about 10 wt% to about 50 wt%, about 10 wt% to about 40 wt%, about 10 wt% to about 30 wt%, about 10 wt% to about 20 wt%, about 20 wt% to about 90 wt%, about 20 wt% to about 80 wt%, about 20 wt% to about 70 wt%, about 20 wt% to about 60 wt%, about 20 wt% to about 50 wt%, or about 20 wt% to about 40 wt%, based on the combined weight of the polyamidoamme, the organic acid, and the water.

[00101] In one specific example, the composition or cationic collector can include about 2 wt% to about 50 wt% of the organic acid, e.g., acetic acid, about 2 wt% to about 50 wt% of water, and about 30 wt% to about 95 wt% of the polyamidoamme, based on the combined weight of the polyamidoamme, the organic acid, and the water. In another specific example, the composition or cationic collector can include about 5 wt% to about 45 wt% of the organic acid, about 5 wt% to about 45 wt% of water, and about 40 wt% to about 90 wt% of the polyamidoamme, based on the combined weight of the polyamidoamme, the organic acid, and the water. In another specific example, the composition or cationic collector can include about 10 wt% to about 40 wt% of the organic acid, about 10 wt% to about 40 wt% of water, and about 40 wt% to about 90 wt% of the polyamidoamme, based on the combined weight of the polyamidoamme, the organic acid, and the water. In another specific example, the composition or cationic collector can include about 20 wt% to about 60 wt% of the organic acid, about 20 wt% to about 60 wt% of water, and about 30 wt% to about 80 wt% of the polyamidoamme, based on the combined weight of the polyamidoamme, the organic acid, and the water.

[00102] In one or more examples, the composition or cationic collector can include one or more polyamidoamines which can be or include one or more polyalkylene polyamidoamines. Illustrative polyalkylene polyamidoamines can include, but are not limited to, polyethylene polyamidoamines, polypropylene polyamidoamines, polybutylene polyamidoamines, or any combination thereof. In some examples, the composition or cationic collector can include one or more polyamidoamines which can be or include one or more polyethylene polyamidoamines. Illustrative polyethylene polyamidoamines can include, but are not limited to, polyethylene diamidoamines, polyethylene triamidoamines, polyethylene polyamidoamines with four or more amido groups, or any mixture thereof. In some examples, the composition or cationic collector can include one or more polyamidoamines which can be or include one or more mixtures of polyethylene diamidoamines and polyethylene triamidoamines.

[00103] The mixture of polyethylene diamidoamines and polyethylene triamidoamines can include about 0.5 mol%, about 1 mol%, about 2 mol%, about 3 mol%, about 4 mol%, about 5 mol%, about 6 mol%, about 7 mol%, about 8 mol%, about 9 mol%, about 10 mol%, about 11 mol%, about 12 mol%, about 13 mol%, about 14 mol%, about 15 mol%, about 16 mol%, about 17 mol%, about 18 mol%, about 19 mol%, about 20 mol%, about 25 mol%, about 30 mol%, about 35 mol%, about 40 mol%, about 45 mol%, about 50 mol%, about 55 mol%, about 60 mol%, about 65 mol%, about 70 mol%, about 75 mol%, about 80 mol%, about 81 mol%, about 82 mol%, about 83 mol%, about 84 mol%, about 85 mol%, about 86 mol%, about 87 mol%, about 88 mol%, about 89 mol%, about 91 mol%, about 92 mol%, about 93 mol%, about 94 mol%, about 95 mol%, about 96 mol%, about 97 mol%, about 98 mol%, about 99 mol%, about 99.1 mol%, about 99.2 mol%, about 99.3 mol%, about 99.4 mol%, about 99.5 mol%, about 99.6 mol%, about 99.7 mol%, about 99.8 mol%, or about 99.9 mol% of the polyethylene diamidoamines, based on the combined moles of the polyethylene diamidoamines and the polyethylene triamidoamines. For example, the mixture of polyethylene diamidoamines and polyethylene triamidoamines can include about 5 mol% to about 99.5 mol%, about 10 mol% to about 99 mol%, about 20 mol% to about 95 mol%, about 30 mol% to about 95 mol%, about 40 mol% to about 95 mol%, about 50 mol% to about 95 mol%, about 60 mol% to about 95 mol%, about 70 mol% to about 95 mol%, about 80 mol% to about 95 mol%, about 90 mol% to about 95 mol%, about 60 mol% to about 90 mol%, about 70 mol% to about 90 mol%, about 80 mol% to about 90 mol%, about 85 mol% to about 99.5 mol%, about 86 mol% to about 99.5 mol%, about 87 mol% to about 99.5 mol%, about 88 mol% to about 99.5 mol%, about 89 mol% to about 99.5 mol%, about 90 mol% to about 99.5 mol%, about 91 mol% to about 99.5 mol%, about 92 mol% to about 99.5 mol%, about 93 mol% to about 99.5 mol%, about 94 mol% to about 99.5 mol%, about 95 mol% to about 99.5 mol%, about 96 mol% to about 99.5 mol%, about 97 mol% to about 99.5 mol%, about 98 mol% to about 99.5 mol%, or about 99 mol% to about 99.5 mol% of the polyethylene diamidoamines, based on the combined moles of the polyethylene diamidoamines and the polyethylene triamidoamines. [00104] The mixture of polyethylene diamidoamines and polyethylene triamidoamines can include about 0.1 mol%, about 0.2 mol%, about 0.3 mol%, about 0.4 mol%, about 0.5 mol%, about 0.6 mol%, about 0.7 mol%, about 0.8 mol%, about 0.9 mol%, about 1 mol%, about 2 mol%, about 3 mol%, about 4 mol%, about 5 mol%, about 6 mol%, about 7 mol%, about 8 mol%, about 9 mol%, about 10 mol%, about 11 mol%, about 12 mol%, about 13 mol%, about 14 mol%, about 15 mol%, about 16 mol%, about 17 mol%, about 18 mol%, about 19 mol%, about 20 mol%, about 25 mol%, about 30 mol%, about 35 mol%, about 40 mol%, about 45 mol%, about 50 mol%, about 55 mol%, about 60 mol%, about 65 mol%, about 70 mol%, about 75 mol%, about 80 mol%, about 85 mol%, about 90 mol%, or about 95 mol% of the polyethylene triamidoamines, based on the combined moles of the polyethylene diamidoamines and the polyethylene triamidoamines. For example, the mixture of polyethylene diamidoamines and polyethylene triamidoamines can include about 0.5 mol% to about 95 mol%, about 1 mol% to about 90 mol%, about 1 mol% to about 80 mol%, about 1 mol% to about 70 mol%, about 1 mol% to about 60 mol%, about 1 mol% to about 50 mol%, about 1 mol% to about 40 mol%, about 1 mol% to about 30 mol%, about 1 mol% to about 20 mol%, about 1 mol% to about 10 mol%, about 5 mol% to about 90 mol%, about 5 mol% to about 80 mol%, about 5 mol% to about 70 mol%, about 5 mol% to about 60 mol%, about 5 mol% to about 50 mol%, about 5 mol% to about 40 mol%, about 5 mol% to about 30 mol%, about 5 mol% to about 20 mol%, about 5 mol% to about 10 mol%, about 0.5 mol% to about 30 mol%, about 0.5 mol% to about 25 mol%, about 0.5 mol% to about 20 mol%, about 0.5 mol% to about 19 mol%, about 0.5 mol% to about 18 mol%, about 0.5 mol% to about 17 mol%, about 0.5 mol% to about 16 mol%, about 0.5 mol% to about 15 mol%, about 0.5 mol% to about 14 mol%, about 0.5 mol% to about 13 mol%, about 0.5 mol% to about 12 mol%, about 0.5 mol% to about 11 mol%, about 0.5 mol% to about 10 mol%, about 0.5 mol% to about 9 mol%, about 0.5 mol% to about 8 mol%, about 0.5 mol% to about 7 mol%, about 0.5 mol% to about 6 mol%, about 0.5 mol% to about 5 mol%, about 0.5 mol% to about 4 mol%, about 0.5 mol% to about 3 mol%, about 0.5 mol% to about 2 mol%, or about 0.5 mol% to about 1 mol% of the polyethylene triamidoamines, based on the combined moles of the polyethylene diamidoamines and the polyethylene triamidoamines.

[00105] In some examples, the mixtures of polyethylene diamidoamines and polyethylene triamidoamines can include about 70 mol% to about 99.5 mol% of the polyethylene triamidoamines and about 0.5 mol% to about 30 mol% of the polyethylene triamidoamines, based on the combined weight of the polyethylene diamidoamines and the polyethylene triamido amines. In other examples, the mixtures of polyethylene diamidoamines and polyethylene triamidoamines can include about 80 mol% to about 99.5 mol% of the polyethylene triamido amines and about 0.5 mol% to about 20 mol% of the polyethylene triamidoamines, based on the combined weight of the polyethylene diamidoamines and the polyethylene triamidoamines. In other examples, the mixtures of polyethylene diamidoamines and polyethylene triamidoamines can include about 90 mol% to about 99.5 mol% of the polyethylene triamidoamines and about 0.5 mol% to about 10 mol% of the polyethylene triamidoamines, based on the combined weight of the polyethylene diamidoamines and the polyethylene triamidoamines.

[00106] In one or more examples, the composition or cationic collector can include one, two, three, or more polyamidoaminates and have a free flowing viscosity. The composition or cationic collector can have a viscosity of about 10 cP, about 20 cP, about 30 cP, about 40 cP, about 50 cP, about 60 cP, about 70 cP, about 80 cP, about 90 cP, about 100 cP, about 110 cP, about 120 cP, about 130 cP, about 140 cP, about 150 cP, about 160 cP, about 170 cP, about 180 cP, about 190 cP, about 200 cP, about 210 cP, about 220 cP, about 230 cP, about 240 cP, about 250 cP, about 260 cP, about 270 cP, about 280 cP, about 290 cP, about 300 cP to about 350 cP, about 400 cP, about 450 cP, about 500 cP, about 600 cP, about 700 cP, or about 800 cP at a temperature of about 25°C. For example, the composition or cationic collector can have a viscosity of about 10 cP to about 500 cP, about 10 cP to about 450 cP, about 10 cP to about 400 cP, about 10 cP to about 350 cP, about 10 cP to about 300 cP, about 10 cP to about 250 cP, about 10 cP to about 200 cP, about 10 cP to about 150 cP, about 10 cP to about 125 cP, about 10 cP to about 100 cP, about 10 cP to about 80 cP, about 30 cP to about 500 cP, about 30 cP to about 450 cP, about 30 cP to about 400 cP, about 30 cP to about 350 cP, about 30 cP to about 300 cP, about 30 cP to about 250 cP, about 30 cP to about 200 cP, about 30 cP to about 150 cP, about 30 cP to about 125 cP, about 30 cP to about 100 cP, about 30 cP to about 80 cP, about 50 cP to about 500 cP, about 50 cP to about 450 cP, about 50 cP to about 400 cP, about 50 cP to about 350 cP, about 50 cP to about 300 cP, about 50 cP to about 250 cP, about 50 cP to about 200 cP, about 50 cP to about 150 cP, about 50 cP to about 125 cP, about 50 cP to about 100 cP, or about 50 cP to about 80 cP at a temperature of about 25°C. In some examples, the composition or cationic collector can have a viscosity of about 10 cP to less than 500 cP, about 10 cP to less than 400 cP, about 10 cP to less than 300 cP, about 10 cP to less than 250 cP, about 10 cP to less than 200 cP, about 10 cP to less than 150 cP, about 10 cP to less than 125 cP, about 10 cP to less than 100 cP, about 10 cP to less than 80 cP, about 50 cP to less than 500 cP, about 50 cP to less than 400 cP, about 50 cP to less than 300 cP, about 50 cP to less than 250 cP, about 50 cP to less than 200 cP, about 50 cP to less than 150 cP, about 50 cP to less than 125 cP, about 50 cP to less than 100 cP, or about 50 cP to about 80 cP at a temperature of about 25°C. In other examples, the composition or cationic collector can have a viscosity of about 400 cP to about 5,000 cP, about 400 cP to about 4,500 cP, about 400 cP to about 4,000 cP, about 400 cP to about 3,500 cP, about 400 cP to about 3,000 cP, about 400 cP to about 2,500 cP, about 400 cP to about 2,000 cP, about 400 cP to about 1,500 cP, about 400 cP to about 1,250 cP, about 400 cP to about 1 ,000 cP, about 400 cP to about 800 cP, about 500 cP to about 5,000 cP, about 500 cP to about 4,500 cP, about 500 cP to about 4,000 cP, about 500 cP to about 3,500 cP, about 500 cP to about 3,000 cP, about 500 cP to about 2,500 cP, about 500 cP to about 2,000 cP, about 500 cP to about 1,500 cP, about 500 cP to about 1,250 cP, about 500 cP to about 1,000 cP, about 500 cP to about 800 cP, about 700 cP to about 5,000 cP, about 700 cP to about 4,500 cP, about 700 cP to about 4,000 cP, about 700 cP to about 3,500 cP, about 700 cP to about 3,000 cP, about 700 cP to about 2,500 cP, about 700 cP to about 2,000 cP, about 700 cP to about 1,500 cP, about 700 cP to about 1,250 cP, about 700 cP to about 1,000 cP, or about 700 cP to about 800 cP at a temperature of about 25°C.

[00107] The composition or cationic collector can have a viscosity of about 10 cP, about 20 cP, or about 30 cP, to about 40 cP, about 50 cP, about 60 cP, about 70 cP, about 80 cP, about 90 cP, about 100 cP, about 110 cP, about 120 cP, about 130 cP, about 140 cP, about 150 cP, about 160 cP, about 170 cP, about 180 cP, about 190 cP, about 200 cP, about 210 cP, about 220 cP, about 230 cP, about 240 cP, about 250 cP, about 260 cP, about 270 cP, about 280 cP, about 290 cP, or about 300 cP at a temperature of about 80°C. For example, the composition or cationic collector can have a viscosity of about 10 cP to about 300 cP, about 10 cP to about 250 cP, about 10 cP to about 200 cP, about 10 cP to about 150 cP, about 10 cP to about 125 cP, about 10 cP to about 100 cP, about 10 cP to about 80 cP, about 10 cP to about 60 cP, about 10 cP to about 50 cP, about 20 cP to about 300 cP, about 20 cP to about 250 cP, about 20 cP to about 200 cP, about 20 cP to about 150 cP, about 20 cP to about 125 cP, about 20 cP to about 100 cP, about 20 cP to about 80 cP, about 20 cP to about 60 cP, about 20 cP to about 50 cP, about 30 cP to about 300 cP, about 30 cP to about 250 cP, about 30 cP to about 200 cP, about 30 cP to about 150 cP, about 30 cP to about 125 cP, about 30 cP to about 100 cP, about 30 cP to about 80 cP, about 30 cP to about 60 cP, or about 30 cP to about 50 cP at a temperature of about 80°C. In some examples, the composition or cationic collector can have a viscosity of about 10 cP to less than 300 cP, about 10 cP to less than 250 cP, about 10 cP to less than 200 cP, about 10 cP to less than 150 cP, about 10 cP to less than 125 cP, about 10 cP to less than 100 cP, about 10 cP to less than 80 cP, about 10 cP to less than 60 cP, or about 10 cP to less than 50 cP at a temperature of about 80°C.

[00108] In other examples, the composition or cationic collector can have a viscosity of about 10 cP, about 20 cP, about 30 cP, about 40 cP, about 50 cP, about 60 cP, about 70 cP, about 80 cP, about 90 cP, about 100 cP, about 110 cP, about 120 cP, about 130 cP, about 140 cP, about 150 cP, about 160 cP, about 170 cP, about 180 cP, about 190 cP, about 200 cP, about 210 cP, about 220 cP, about 230 cP, about 240 cP, about 250 cP, about 260 cP, about 270 cP, about 280 cP, about 290 cP, about 300 cP to about 350 cP, about 400 cP, about 450 cP, about 500 cP, about 600 cP, about 700 cP, or about 800 cP at a temperature of about 25°C when the composition or cationic collector includes about 2 wt% to about 50 wt% of the organic acid, e.g., acetic acid, about 2 wt% to about 50 wt% of water, and about 30 wt% to about 95 wt% of the polyamidoamme, based on the combined weight of the polyamidoamme, the organic acid, and the water. In other examples, the composition or cationic collector can have a viscosity of about 10 cP, about 20 cP, about 30 cP, about 40 cP, about 50 cP, about 60 cP, about 70 cP, about 80 cP, about 90 cP, about 100 cP, about 110 cP, about 120 cP, about 130 cP, about 140 cP, about 150 cP, about 160 cP, about 170 cP, about 180 cP, about 190 cP, about 200 cP, about 210 cP, about 220 cP, about 230 cP, about 240 cP, about 250 cP, about 260 cP, about 270 cP, about 280 cP, about 290 cP, about 300 cP to about 350 cP, about 400 cP, about 450 cP, about 500 cP, about 600 cP, about 700 cP, or about 800 cP at a temperature of about 25°C when the composition or cationic collector includes about 20 wt% to about 60 wt% of the organic acid, about 20 wt% to about 60 wt% of water, and about 30 wt% to about 80 wt% of the polyamidoamme, based on the combined weight of the polyamidoamme, the organic acid, and the water.

[00109] The viscosity of the various compositions discussed and described herein can be determined using a viscometer at a specified temperature, such as about 25°C or about 80°C. For example, a viscometer, Model DV-II+, commercially available from the Brookfield Company, with a small sample adapter with, for example, a number 3 spindle, can be used. The small sample adapter can allow the sample to be cooled or heated by the chamber jacket to maintain the temperature of the sample surrounding the spindle at a temperature of about 25°C (unless otherwise noted).

[00110] In one or more examples, the amount of the composition or cationic collector in the aqueous mixture can be about 0.0005 wt%, about 0.001 wt%, about 0.005 wt%, about 0.01 wt%, about 0.02 wt%, about 0.03 wt%, about 0.04 wt%, about 0.05 wt%, about 0.06 wt%, about 0.07 wt%, about 0.08 wt%, about 0.09 wt%, about 0.1 wt%, about 0.11 wt%, about 0.12 wt%, about 0.13 wt%, about 0.14 wt%, about 0.15 wt%, about 0.16 wt%, about 0.17 wt%, about 0.18 wt%, about 0.19 wt%, about 0.2 wt%, about 0.25 wt%, about 0.3 wt%, about 0.35 wt%, about 0.4 wt%, about 0.5 wt%, about 0.6 wt%, about 0.7 wt%, about 0.8 wt%, about 0.9 wt%, about 1 wt%, about 1.5 wt%, about 2 wt%, about 2.5 wt%, about 3 wt%, about 3.5 wt%, about 4 wt%, about 4.5 wt%, about 5 wt%, about 6 wt%, about 7 wt%, about 8 wt%, about 9 wt%, or about 10 wt%, based on the weight of the ore, e.g., phosphorous ore. In some examples, the amount of the composition or cationic collector in the aqueous mixture can be about 0.001 wt% to about 10 wt%, about 0.005 wt% to about 5 wt%, about 0.005 wt% to about 2 wt%, about 0.005 wt% to about 1 wt%, about 0.005 wt% to about 0.5 wt%, about 0.005 wt% to about 0.1 wt%, about 0.005 wt% to about 0.09 wt%, or about 0.005 wt% to about 0.05 wt%, based on the weight of the ore, e.g., phosphorous ore. In other examples, the amount of the composition or cationic collector in the aqueous mixture can be greater than 0.001 wt% to about 10 wt%, greater than 0.005 wt% to about 5 wt%, greater than 0.005 wt% to about 2 wt%, greater than 0.005 wt% to about 1 wt%, greater than 0.005 wt% to about 0.5 wt%, greater than 0.005 wt% to about 0.1 wt%, greater than 0.005 wt% to about 0.09 wt%, or greater than 0.005 wt% to about 0.05 wt%, based on the weight of the ore, e.g., phosphorous ore. In other examples, the amount of the composition or cationic collector in the aqueous mixture can be about 0.001 wt% to less than 10 wt%, about 0.005 wt% to less than 5 wt%, about 0.005 wt% to less than 2 wt%, about 0.005 wt% to less than 1 wt%, about 0.005 wt% to less than 0.5 wt%, about 0.005 wt% to less than 0.1 wt%, about 0.005 wt% to less than 0.09 wt%, or about 0.005 wt% to less than 0.05 wt%, based on the weight of the phosphorous ore.

[00111] In one or more examples, the amount of the polyamidoamine in the aqueous mixture can be about 0.0001 wt%, about 0.0005 wt%, about 0.001 wt%, about 0.005 wt%, about 0.01 wt%, about 0.02 wt%, about 0.03 wt%, about 0.04 wt%, about 0.05 wt%, about 0.06 wt%, about 0.07 wt%, about 0.08 wt%, about 0.09 wt%, about 0.1 wt%, about 0.11 wt%, about 0.12 wt%, about 0.13 wt%, about 0.14 wt%, about 0.15 wt%, about 0.16 wt%, about 0.17 wt%, about 0.18 wt%, about 0.19 wt%, about 0.2 wt%, about 0.25 wt%, about 0.3 wt%, about 0.35 wt%, about 0.4 wt%, about 0.5 wt%, about 0.6 wt%, about 0.7 wt%, about 0.8 wt%, about 0.9 wt%, about 1 wt%, about 1.5 wt%, about 2 wt%, about 2.5 wt%, about 3 wt%, about 3.5 wt%, about 4 wt%, about 4.5 wt%, about 5 wt%, based on the weight of the ore, e.g., phosphorous ore. In some examples, the amount of the polyamidoamine in the aqueous mixture can be about 0.0001 wt% to about 2 wt%, about 0.0005 wt% to about 1 wt%, about 0.001 wt% to about 1 wt%, about 0.005 wt% to about 1 wt%, about 0.005 wt% to about 0.5 wt%, about 0.005 wt% to about 0.1 wt%, about 0.005 wt% to about 0.09 wt%, or about 0.005 wt% to about 0.05 wt%, based on the weight of the ore, e.g., phosphorous ore. In other examples, the amount of the polyamidoamine in the aqueous mixture can be greater than 0.0001 wt% to about 2 wt%, greater than 0.0005 wt% to about 1 wt%, greater than 0.001 wt% to about 1 wt%, greater than 0.005 wt% to about 1 wt%, greater than 0.005 wt% to about 0.5 wt%, greater than 0.005 wt% to about 0.1 wt%, greater than 0.005 wt% to about 0.09 wt%, or greater than 0.005 wt% to about 0.05 wt%, based on the weight of the ore, e.g., phosphorous ore. In other examples, the amount of the polyamidoamine in the aqueous mixture can be about 0.0001 wt% to less than 2 wt%, about 0.0005 wt% to less than 1 wt%, about 0.001 wt% to less than 1 wt%, about 0.005 wt% to less than 1 wt%, about 0.005 wt% to less than 0.5 wt%, about 0.005 wt% to less than 0.1 wt%, about 0.005 wt% to less than 0.09 wt%, or about 0.005 wt% to less than 0.05 wt%, based on the weight of the phosphorous ore.

[00112] In one or more examples, the amount of the organic acid, e.g., acetic acid, in the aqueous mixture can be about 0.0001 wt%, about 0.0005 wt%, about 0.001 wt%, about 0.005 wt%, about 0.01 wt%, about 0.02 wt%, about 0.03 wt%, about 0.04 wt%, about 0.05 wt%, about 0.06 wt%, about 0.07 wt%, about 0.08 wt%, about 0.09 wt%, about 0.1 wt%, about 0.11 wt%, about 0.12 wt%, about 0.13 wt%, about 0.14 wt%, about 0.15 wt%, about 0.16 wt%, about 0.17 wt%, about 0.18 wt%, about 0.19 wt%, about 0.2 wt%, about 0.25 wt%, about 0.3 wt%, about 0.35 wt%, about 0.4 wt%, about 0.5 wt%, about 0.6 wt%, about 0.7 wt%, about 0.8 wt%, about 0.9 wt%, about 1 wt%, about 1.5 wt%, about 2 wt%, about 2.5 wt%, about 3 wt%, about 3.5 wt%, about 4 wt%, about 4.5 wt%, about 5 wt%, based on the weight of the ore, e.g., phosphorous ore. In some examples, the amount of the organic acid in the aqueous mixture can be about 0.0001 wt% to about 2 wt%, about 0.0005 wt% to about 1 wt%, about 0.001 wt% to about 1 wt%, about 0.005 wt% to about 1 wt%, about 0.005 wt% to about 0.5 wt%, about 0.005 wt% to about 0.1 wt%, about 0.005 wt% to about 0.09 wt%, or about 0.005 wt% to about 0.05 wt%, based on the weight of the ore, e.g., phosphorous ore. In some examples, the amount of the organic acid in the aqueous mixture can be greater than 0.0001 wt% to about 2 wt%, greater than 0.0005 wt% to about 1 wt%, greater than 0.001 wt% to about 1 wt%, greater than 0.005 wt% to about 1 wt%, greater than 0.005 wt% to about 0.5 wt%, greater than 0.005 wt% to about 0.1 wt%, greater than 0.005 wt% to about 0.09 wt%, or greater than 0.005 wt% to about 0.05 wt%, based on the weight of the ore, e.g., phosphorous ore. In some examples, the amount of the organic acid in the aqueous mixture can be about 0.0001 wt% to less than 2 wt%, about 0.0005 wt% to less than 1 wt%, about 0.001 wt% to less than 1 wt%, about 0.005 wt% to less than 1 wt%, about 0.005 wt% to less than 0.5 wt%, about 0.005 wt% to less than 0.1 wt%, about 0.005 wt% to less than 0.09 wt%, or about 0.005 wt% to less than 0.05 wt%, based on the weight of the phosphorous ore. In one or more examples, the organic acid can be or include acetic acid.

[00113] The aqueous mixtures which can include water, one or more ores, e.g., phosphorous ores or phosphate materials, one or more polyamidoamines, and one or more organic acids, e.g., acetic acid, including aqueous suspensions, dispersions, slurries, solutions, or mixtures, can be conditioned for a given time period during and between steps of combining components. Conditioning the aqueous mixture upon the addition of water, one or more ores, one or more polyamidoamines, and one or more organic acids can facilitate contact between the components. Conditioning can include, but is not limited to, agitating the aqueous mixture for a given time period prior to subjecting the aqueous mixture to separation or collection techniques. For example, the aqueous mixtures can be stirred, blended, mixed, air or gas bubbled, or otherwise agitated for a time of about 30 seconds, about 1 minute, about 2 minutes, about 3 minutes, about 4 minutes, about 5 minutes, about 6 minutes, about 7 minutes, about 8 minutes, about 9 minutes, about 10 minutes, about 12 minutes, about 15 minutes, about 20 minutes, about 30 minutes, about 1 hour, or about 24 hours. Conditioning the aqueous mixture can also include heating (or cooling) mixture to a temperature of about 15°C, about 20°C, about 25°C, about 30°C, about 35°C, about 60°C, about 80°C, or about 95°C.

[00114] Conditioning the aqueous mixture can also include adjusting the pH values of any of portions of and including the aqueous mixtures. The aqueous mixture containing the ore, e.g., phosphorous ore, the polyamidoamine, the organic acid, e.g., acetic acid, and water can be maintained at or adjusted to have a pH value of greater than 7, such as about 7.5, about 8, about 8.5, about 9, about 9.5, about 10, about 10.5, about 11, about 11.5, about 12, about 12.5, or about 13. In one or more examples, the pH value of the aqueous mixture can be or can be adjusted to about 8.5 to about 10.5, about 9 to about 10, about 9.2 to about 9.8, or about 9.5. In other examples, the pH value of the aqueous mixture can be or can be adjusted to about 8.5 to about 10.5, about 9 to about 10, about 9.2 to about 9.8, or about 9.5. Any one or combination of acid and/or base compounds can be combined with the mixtures to adjust the pH values thereof.

[00115] Illustrative acid compounds that can be used to maintain or adjust the pH value of any of the aqueous mixtures can include, but are not limited to, one or more mineral acids, one or more organic acids, one or more acid salts, or any mixture thereof. Illustrative mineral acids can include, but are not limited to, hydrochloric acid, nitric acid, phosphoric acid, sulfuric acid, or any mixture thereof. Illustrative organic acids can include, but are not limited to, acetic acid, formic acid, citric acid, oxalic acid, uric acid, lactic acid, or any mixture thereof. Illustrative acid salts can include, but are not limited to, ammonium sulfate, sodium bisulfate, sodium metabisulfite, or any mixture thereof.

[00116] Illustrative base compounds that can be used to maintain or adjust the pH value of any of the aqueous mixtures can include, but are not limited to, hydroxides, carbonates, ammonia, amines, or any mixture thereof. Illustrative hydroxides can include, but are not limited to, sodium hydroxide, potassium hydroxide, ammonium hydroxide, e.g., aqueous ammonia, lithium hydroxide, and cesium hydroxide. Illustrative carbonates can include, but are not limited to, sodium carbonate, sodium bicarbonate, potassium carbonate, and ammonium carbonate. Illustrative amines can include, but are not limited to, trimethylamine, triethylamine, triethanolamine, diisopropylethylamine (Hunig's base), pyridine, 4-dimethylaminopyridine (DMAP), and l,4-diazabicyclo[2.2.2]octane (DABCO).

[00117] In one or more examples, the aqueous mixture or slurry can be aerated in a conventional flotation machine or bank of rougher cells to float phosphates or other phosphorous containing materials. Any conventional flotation unit can be employed. The composition or cationic collector can be used to separate a wide variety of contaminants from a liquid, e.g., water. For example, the composition or cationic collector can be used to separate siliceous contaminants such as sand, clay, and/or ash from aqueous liquid suspensions or slurries containing one or more of these siliceous contaminants. Aqueous mixtures can therefore be treated with the composition or cationic collector allowing for the effective separation of at least a portion of the contaminants, in a contaminant-rich fraction, to provide a purified liquid. The contaminant-rich fraction contains a higher percentage of solid contaminants than originally present in the aqueous mixture. Conversely, the purified liquid has a lower percentage of solid contaminants than originally present in the aqueous mixture.

[00118] The treatment can involve adding an effective amount of the composition or cationic collector to interact with and either coagulate or flocculate one or more solid contaminants into larger agglomerates. An effective amount can be readily determined depending, at least in part, on a number of variables, e.g., the type and concentration of contaminant. In other examples, the treatment can involve contacting the aqueous mixture or slurry continuously with a fixed bed of the composition or cationic collector, in solid form.

[00119] During or after the treatment of the aqueous mixture or slurry with the composition or cationic collector, the coagulated or flocculated solid contaminant (which can now be, for example, in the form of larger, agglomerated particles or flocs) can be removed. Removal can be effected by flotation (with or without the use of rising air bubbles, such as in a froth flotation. Filtration or straining can also be an effective means for removing the agglomerated flocs of solid particulates on the surface of the aqueous mixture or slurry.

[00120] Considering froth flotation in more detail, froth flotation is a separation process based on differences in the tendency of various materials to associate with rising air bubbles. The composition or cationic collector and optionally a dispersant, a depressant, and/or other additives can be combined with water and an ore that includes one or more contaminants to produce an aqueous slurry or other mixture. A gas, e.g., air, can be flowed, forced, or otherwise passed through the mixture. Some materials (e.g., value minerals) will, relative to others (e.g., contaminants), exhibit preferential affinity for air bubbles, causing them to rise to the surface of the aqueous slurry, where they can be collected in a froth concentrate. A degree of separation is thereby provided. In "reverse" froth flotation, it is the contaminant that can preferentially float and concentrated at the surface, with the ore and/or other value material concentrated in the bottoms. The relatively hydrophobic fraction of the material can have a selective affinity for the rising bubbles and can float to the surface, where it can be skimmed off and recovered. The relatively hydrophilic fraction of the material can flow or otherwise move toward the bottom of the aqueous mixture and can be recovered as a bottoms fraction. Froth flotation is a separation process well known to those skilled in the art.

[00121] As used herein, the term "purifying" broadly refers to any process for beneficiation, upgrading, and/or recovering, a value material as described herein, such as phosphates or other phosphorous containing materials. In some examples, the aqueous mixture or slurry can include the clay-containing aqueous suspensions or brines, which accompany ore refinement processes, including those described above. The production of purified phosphate from mined calcium phosphate rock, for example, generally relies on multiple separations of solid particulates from aqueous media, whereby such separations can be improved using the composition or cationic collector. In the overall process, calcium phosphate can be mined from deposits and the phosphate rock can be initially recovered in a matrix containing sand and clay impurities. The matrix can be mixed with water to form a slurry, which after mechanical agitation, can be screened to retain phosphate pebbles and to allow fine clay particles to pass through as a clay slurry effluent with large amounts of water.

[00122] These clay-containing effluents can have high flow rates and generally carry less than 10 wt% of solids, e.g., about 1 wt% to about 5 wt% of solids. The dewatering, e.g., by settling or filtration, of this waste clay, which allows for recycle of the water, poses a significant challenge for reclamation. The time required to dewater the clay, however, can be decreased through treatment of the clay slurry effluent, obtained in the production of phosphate, with the composition or cationic collector. Reduction in the clay settling time allows for efficient re-use of the purified water, obtained from clay dewatering, in the phosphate production operation. In one example of the purification method, where the aqueous mixture or slurry is a clay-containing effluent slurry from a phosphate production facility, the purified liquid can contain less than 1 wt% solids after a settling or dewatering time of less than 1 month.

[00123] In addition to the phosphate pebbles and clay slurry effluent that can be produced by screening the slurry of the matrix that can contain sand and clay impurities described above, a mixture of sand and finer particles of phosphate can also be obtained in the initial processing of mined phosphate matrix. The sand and phosphate can be separated by froth flotation which, as described above, can be improved using the composition or cationic collector as a depressant for the sand. [00124] In one or more examples, the phosphate material that can be collected, recovered or otherwise purified from the aqueous mixture due to the composition or cationic collector can be compared to the initial or total amount of the phosphate material contained in the phosphorous ore. For example, the collected or recovered phosphate material can be about 90 wt%, about 91 wt%, about 92 wt%, about 93 wt%, about 94 wt%, about 95 wt%, about 96 wt%, about 97 wt%, about 97.1 wt%, about 97.2 wt%, about 97.3 wt%, about 97.4 wt%, about 97.5 wt%, about 97.6 wt%, about 97.7 wt%, about 97.8 wt%, or about 97.9 wt%, about 98 wt%, about 98.1 wt%, about

98.2 wt%, about 98.3 wt%, about 98.4 wt%, about 98.5 wt%, about 98.6 wt%, about 98.7 wt%, about 98.8 wt%, about 98.9 wt%, about 99 wt%, about 99.1 wt%, about 99.2 wt%, about 99.3 wt%, about 99.4 wt%, about 99.5 wt%, about 99.6 wt%, about 99.7 wt%, about 99.8 wt%, or about 99.9 wt% of the total phosphate material contained in the phosphorous ore. In other examples, the collected or recovered phosphate material can be about 90 wt% to about 99.9 wt%, about 91 wt% to about 99.9 wt%, about 92 wt% to about 99.9 wt%, about 93 wt% to about 99.9 wt%, about 94 wt% to about 99.9 wt%, about 95 wt% to about 99.9 wt%, about 96 wt% to about 99.9 wt%, about 97 wt% to about 99.9 wt%, about 98 wt% to about 99.9 wt%, about 99 wt% to about 99.9 wt%, about 99.1 wt% to about 99.9 wt%, about 99.2 wt% to about 99.9 wt%, about

99.3 wt% to about 99.9 wt%, about 99.4 wt% to about 99.9 wt%, about 99.5 wt% to about 99.9 wt%, about 99.6 wt% to about 99.9 wt%, about 99.7 wt% to about 99.9 wt%, about 95 wt% to about 99.7 wt%, about 96 wt% to about 99.7 wt%, about 97 wt% to about 99.7 wt%, about 98 wt% to about 99.7 wt%, about 99 wt% to about 99.7 wt%, about 95 wt% to about 99.5 wt%, about 96 wt% to about 99.5 wt%, about 97 wt% to about 99.5 wt%, about 98 wt% to about 99.5 wt%, or about 99 wt% to about 99.5 wt% of the total phosphate material contained in the phosphorous ore. In one specific example, the collected phosphate material can be about 98 wt% to about 99.9 wt% of the total phosphate material contained in the phosphorous ore.

[00125] In some examples, a tail material can be submerged, flocculated, sunk, suspended, or otherwise rejected or not floated at the top of the aqueous mixture or slurry. The tail material can include acid insoluble materials and/or other impurities formerly contained in the phosphorous or phosphate containing ores, rocks, minerals, or other materials. The tail material flocculated in the aqueous mixture can be collected or otherwise recovered, separately from the recovered phosphate material. The tail material can generally be less than 99 wt% of the total acid insolubles (AI) contained in the phosphorous ore. For example, the tail material can be less than 97 wt%, less than 95 wt%, less than 90 wt%, less than 85 wt%, less than 80 wt%, less than 75 wt%, less than 70 wt%, less than 65 wt%, less than 60 wt%, less than 65 wt%, less than 50 wt% to about 40 wt%, about 30 wt%, about 20 wt%, about 10 wt%, about 5 wt%, or less, based on the total acid insolubles contained in the phosphorous ore. In some examples, the acid insolubles can be about 10 wt% to less than 97 wt%, about 25 wt% to less than 95 wt%, about 40 wt% to less than 95 wt%, about 50 wt% to less than 95 wt%, about 60 wt% to less than 95 wt%, about 70 wt% to less than 95 wt%, about 80 wt% to less than 95 wt%, about 90 wt% to less than 95 wt%, about 50 wt% to about 90 wt%, about 60 wt% to about 90 wt%, about 70 wt% to about 90 wt%, or about 80 wt% to about 90 wt%, based on the total acid insolubles contained in the phosphorous ore. In one specific example, a tail material can be collected or recovered that can be flocculated on the bottom of the aqueous mixture, where the tail material can include acid insolubles, and the acid insolubles can be about 70 wt% to about 90 wt% of the total acid insolubles contained in the phosphorous ore.

[00126] The separation efficiency is defined as E _s = Rpo - RAI, where Rpo is the ratio of the total weight of the recovered phosphate material over the total weight of the phosphate material contained in the phosphorous ore and RAI is the ratio of the total weight of the recovered acid insolubles over the total weight of the phosphorous ore. The composition or cationic collector can provide a separation efficiency for purified materials, including phosphate, of about 50 wt% of greater, such as about 55 wt%, about 60 wt%, about 65 wt%, about 70 wt%, about 75 wt%, about 80 wt%, about 81 wt%, about 82 wt%, about 83 wt%, about 84 wt%, about 85 wt%, about 86 wt%, about 87 wt%, about 88 wt%, about 89 wt%, about 90 wt%, about 91 wt%, about 92 wt%, about 93 wt%, about 94 wt%, about 95 wt%, about 96 wt%, about 97 wt%, about 98 wt%, or about 99 wt%.

[00127] In one or more examples, compositions or cationic collectors having one or more polyamidoamines that incorporate at least one naphthenate group can be used to increase the flotation of silicate materials, such as sand. The polyamidoamine can be formed by reacting one or more polyamines with naphthenic acid and optionally one or more other fatty acids or other carboxylic acids. For example, the polyamidoamine can be formed by reacting DETA, TETA, TEPA, and/or PEHA with naphthenic acid and one or more of lauric acid, isostearic acid, oleic acid, linoleic acid, TOFA, and/or other fatty acids. [00128] In one example, the polyamidoamines having the chemical formula (D) where R is a naphthenate group, can be or include one or more amidoamines having the chemical formula (O):

[00129] where R ¹ and n are defined as above for the chemical formula (D). Naphthenic acid can generally include mixtures of carboxylic acid compounds having cyclopentyl, cyclohexyl cyclic, and/or other cyclic motifs with C6 to C24 chains, e.g., backbone chains or carboxylic acid chains, such as C9 to C20 chains, C9 to C19 chains, and/or CIO to C16 chains. Naphthenic acids and naphthenate groups can include one or more cyclopentyl carboxylic acids or one or more cyclohexyl carboxylic acids that have one or more C9 to C20 chains, C9 to C19 chains, and/or CIO to C 16 chains as backbone chains or carboxylic acid chains.

[00130] In some specific examples, the polyamidoamines can have the chemical formula (O), where R ¹ can be a C6 to C24 chain or a C8 to C24 chain and n can be 2, 3, 4, or 5. In other examples, the polyamidoamines can have the chemical formula (O), where R ¹ can be a CIO to C24 chain having 0 to 2 unsaturated bonds and n can be 2, 3, or 4. In other examples, the polyamidoamines can have the chemical formula (O), where R can be C9H 9, C9H 7, C9H 5, C9H13, C11H23, C11H21, C15H33, C15H31, C15H29, C17H35, C17H33, C17H31, C17H29, C19H37, C19H35, C19H33, C19H31, or C19H29 and n can be 2, 3, or 4. In other examples, the polyamidoamines can have the chemical formula (O), where R ¹ can be a laurate group, a stearate group, an isostearate group, an oleate group, a linoleate group, isomers thereof, or any mixture thereof and n can be 2, 3, or 4. Examples

[00131] In order to provide a better understanding of the foregoing discussion, the following non- limiting examples are offered. Although the examples can be directed to specific examples, they are not to be viewed as limiting the invention in any specific respect.

[00132] The compositions or cationic collectors contained polyamidoamines with varying types of hydrocarbyl groups on the amido groups and varying amounts and types of amine groups between the amido groups. The synergetic effects for selective phosphate flotation were due, at least in part, to these novel polyamidoamines to form the cationic collectors as highlighted by the results of Examples 1A-10B, summarized below in Table 1.

[00133] The synergetic effects for viscosity and homogeneity of the cationic collectors were due, at least in part, to the combination of the polyamidoamines, e.g., diamidoamines or triamidoamines, and acetic acid as highlighted by the results of Examples 11-41, summarized below in Tables 2 and 3. The cationic collectors contained varying amounts of acetic acid and water (when present) relative to a constant amount of polyamidoamines, and also contained varying polyamidoamine compositions within different cationic collectors. The synergetic effects for selective phosphate flotation were due, at least in part, to the combination of the diamidoamines and the acetic acid to form the cationic collectors as highlighted by the results of Examples 42A-47D, summarized below in Table 4.

[00134] Beneficiation Procedure: The following phosphate beneficiation procedure was used for Examples 1A-10B and 42A-45D. About 500 g of phosphate rougher concentrate and about 214 g of water were added to a 2 L capacity stainless steel beaker equipped with a cruciform impeller. The concentrate and water were stirred for about 0.5 min and maintained at a pH value of about 7 (if needed, 1 N NaOH solution was added to adjust the pH value) to produce a mixture of about 70 wt% solids. For each of the Examples 1A-10B and 42A-45D, the listed polyamidoamine at the respective dosage was added to the mixture and stirred at about 400 rpm for about 5 min. The mixture was transferred to stainless steel flotation cell. About 1,300 g of water was added to the mixture that was stirred for about 0.5 min to produce a mixture of about 25 wt% solids. An air injection valve on the flotation cell was opened and frothing ensued as air was introduced into the mixture. After about 2 min, the froth was collected from the flotation cell. The froth concentrate and the tailings remaining in the flotation cell were separately filtered, dewatered, and weighed. The dried froth concentrate and the tailings were separately analyzed for phosphate (Bone Phosphate of Lime, BPL) content using inductively coupled plasma (ICP) and for acid insoluble content using an acid digestion.

[00135] Examples 1A-1B: The TOFA-DETA polyamidoamine was made by the following: To a 40 mL scintillation vial equipped with a magnetic stir bar, about 20 g of tall oil fatty acid was added under an air atmosphere. The mixture was stirred and warmed to about 80°C, and about 3.68 g of DETA was added over about 4 min. The mixture exothermed to a temperature of about 105°C to about 110°C, and then the mixture was heated for about 15 min to reach a temperature of about 165°C. As the reaction mixture neared 165°C, bubbling commenced, indicating reaction progress. The mixture was maintained at about 165°C for about 3 hr, at which point, bubbling ceased. The mixture cooled to room temperature, e.g., about 25°C, and slowly formed a waxy substance.

[00136] Examples 2A-2B: The lauric acid-TOFA-DETA polyamidoamine was made by the following: To a 40 mL scintillation vial equipped with a magnetic stir bar, about 10 g of tall oil fatty acid and about 6.95 g of lauric acid were added under an air atmosphere. The mixture was stirred and warmed to about 80°C, and about 3.7 g of DETA was added over about 4 min. The mixture exothermed to a temperature of about 105°C to about 110°C, and then the mixture was heated for about 15 min to reach a temperature of about 165°C. As the reaction mixture neared 165°C, bubbling commenced, indicating reaction progress. The mixture was maintained at about 165°C for about 3 hr, at which point, bubbling ceased. The mixture cooled to room temperature, e.g., about 25°C, and slowly formed a waxy substance.

[00137] Examples 3A-3B: The naphthenic acid-TOFA-DETA polyamidoamine was made by the following: To a 40 mL scintillation vial equipped with a magnetic stir bar, about 10 g of tall oil fatty acid and about 8.125 g of naphthenic acid were added under an air atmosphere. The mixture was stirred and warmed to about 80°C, and about 3.7 g of DETA was added over about 4 min. The mixture exothermed to a temperature of about 105°C to about 110°C, and then the mixture was heated for about 15 min to reach a temperature of about 165°C. As the reaction mixture neared 165°C, bubbling commenced, indicating reaction progress. The mixture was maintained at about 165°C for about 3 hr, at which point, bubbling ceased. The mixture cooled to room temperature, e.g., about 25°C, and slowly formed a waxy substance. [00138] Examples 4A-4B: The isostearic acid-TOFA-DETA polyamidoamine was made by the following: To a 40 mL scintillation vial equipped with a magnetic stir bar, about 10 g of tall oil fatty acid and about 10.32 g of isostearic acid were added under an air atmosphere. The mixture was stirred and warmed to about 80°C, and about 3.7 g of DETA was added over about 4 min. The mixture exothermed to a temperature of about 105°C to about 110°C, and then the mixture was heated for about 15 min to reach a temperature of about 165°C. As the reaction mixture neared 165°C, bubbling commenced, indicating reaction progress. The mixture was maintained at about 165°C for about 3 hr, at which point, bubbling ceased. The mixture cooled to room temperature, e.g., about 25°C, and slowly formed a waxy substance.

[00139] Examples 5A-5B: The LNI-TOFA-DETA polyamidoamine was made by the following: To a 40 mL scintillation vial equipped with a magnetic stir bar, about 12.5 g of tall oil fatty acid, about 1.74 g of lauric acid, about 2.22 g of naphthenic acid, and about 2.57 g of isostearic acid were added under an air atmosphere. The mixture was stirred and warmed to about 80°C, and about 3.68 g of DETA was added over about 4 min. The mixture exothermed to a temperature of about 105°C to about 110°C, and then the mixture was heated for about 15 min to reach a temperature of about 165°C. As the reaction mixture neared 165°C, bubbling commenced, indicating reaction progress. The mixture was maintained at about 165°C for about 3 hr, at which point, bubbling ceased. The mixture cooled to room temperature, e.g., about 25°C, and slowly formed a waxy substance.

[00140] Examples 6A-6B: The TOFA-TEPA polyamidoamine was made by the following: To a 2 L reactor equipped with a mechanical stirrer, thermocouple, and Barrett trap/condenser, about 600 g of tall oil fatty acid was added under an air atmosphere. The mixture was stirred and warmed to about 80°C, and about 202 g of TEPA was added over about 4 min. The mixture exothermed to a temperature of about 105°C to about 110°C, and then the mixture was heated for about 15 min to reach a temperature of about 165°C. The mixture was maintained at about 165°C for about 3 hr, at which point, the Barrett trap had collected about 23 mL of water. The mixture cooled to room temperature, e.g., about 25°C, and slowly formed a waxy yellow substance.

[00141] Examples 7A-7B: The lauric acid-TOFA-TEPA polyamidoamine was made by the following: To a 40 mL scintillation vial equipped with a magnetic stir bar, about 10 g of tall oil fatty acid and about 6.95 g of lauric acid were added under an air atmosphere. The mixture was stirred and warmed to about 80°C, and about 7.12 g of TEPA was added over about 4 min. The mixture exothermed to a temperature of about 105°C to about 110°C, and then the mixture was heated for about 15 min to reach a temperature of about 165°C. As the reaction mixture neared 165°C, bubbling commenced, indicating reaction progress. The mixture was maintained at about 165°C for about 3 hr, at which point, bubbling ceased. The mixture cooled to room temperature, e.g., about 25°C, and slowly formed a waxy substance.

[00142] Examples 8A-8B: The naphthenic acid-TOFA-TEPA polyamidoamine was made by the following: To a 40 mL scintillation vial equipped with a magnetic stir bar, about 10 g of tall oil fatty acid and about 8.125 g of naphthenic acid were added under an air atmosphere. The mixture was stirred and warmed to about 80°C, and about 7.12 g of TEPA was added over about 4 min. The mixture exothermed to a temperature of about 105°C to about 110°C, and then the mixture was heated for about 15 min to reach a temperature of about 165°C. As the reaction mixture neared 165°C, bubbling commenced, indicating reaction progress. The mixture was maintained at about 165°C for about 3 hr, at which point, bubbling ceased. The mixture cooled to room temperature, e.g., about 25°C, and slowly formed a waxy substance.

[00143] Examples 9A-9B: The isostearic acid-TOFA-TEPA polyamidoamine was made by the following: To a 40 mL scintillation vial equipped with a magnetic stir bar, about 10 g of tall oil fatty acid and about 10.32 g of isostearic acid were added under an air atmosphere. The mixture was stirred and warmed to about 80°C, and about 7.12 g of TEPA was added over about 4 min. The mixture exothermed to a temperature of about 105°C to about 110°C, and then the mixture was heated for about 15 min to reach a temperature of about 165°C. As the reaction mixture neared 165°C, bubbling commenced, indicating reaction progress. The mixture was maintained at about 165°C for about 3 hr, at which point, bubbling ceased. The mixture cooled to room temperature, e.g., about 25°C, and slowly formed a waxy substance.

[00144] Examples 10A-10B: The LNI-TOFA-TEPA polyamidoamine was made by the following: To a 40 mL scintillation vial equipped with a magnetic stir bar, about 12.5 g of tall oil fatty acid, about 1.74 g of lauric acid, about 2.22 g of naphthenic acid, and about 2.57 g of isostearic acid were added under an air atmosphere. The mixture was stirred and warmed to about 80°C, and about 7.12 g of TEPA was added over about 4 min. The mixture exothermed to a temperature of about 105°C to about 110°C, and then the mixture was heated for about 15 min to reach a temperature of about 165°C. As the reaction mixture neared 165°C, bubbling commenced, indicating reaction progress. The mixture was maintained at about 165°C for about 3 hr, at which point, bubbling ceased. The mixture cooled to room temperature, e.g., about 25°C, and slowly formed a waxy substance.

[00145] In Examples 1A-10B, the flotation results listed in Table 1, demonstrates the effectiveness of collectors having diamidoamines used to remove impurities, such as acid insoluble, e.g., sand or silicate, from phosphate ore. The low acid insoluble values indicate removal of gangue from the crude phosphate mineral ore. The use of a mixed acid amidoamine system (a collector containing the amidoamines having the chemical formulas (E) and (G), where

1 2

R and R were different hydrocarbyl groups, provided the low recovery of acid insoluble content in the phosphate concentrate. In both DETA and TEPA-based collectors, incorporation of naphthenic acid (or the naphthenate group) increased flotation of silicates, as shown in Table 1 for Examples 3A, 3B, 5A, 5B, 8A, 8B, 10A, and 10B. Surprisingly, these results indicate that the collectors can provide a technical and an economic benefit by removing impurities at lower dosages than does the traditional purely TOFA based system.

6B TOFA-TEPA 2 [1] 97.95 8.57 91.38

lauric acid-TOFA-

7A 1 [0.5] 98.54 53.28 45.26

TEPA

lauric acid-TOFA-

7B 2 [1] 99.02 17.61 81.41

TEPA

naphthenic acid-

8A 1 [0.5] 99.75 86.54 13.21

TOFA-TEPA

naphthenic acid-

8B 2 [1] 94.99 7.23 87.76

TOFA-TEPA

isostearic acid-

9A 1 [0.5] 99.8 78.69 21.11

TOFA-TEPA

isostearic acid-

9B 2 [1] 98.64 10.12 88.52

TOFA-TEPA

10A LNI-TOFA-TEPA 1 [0.5] 99.45 30.69 68.76

10B LNI-TOFA-TEPA 2 [1] 94.97 7.1 87.87

"LNI" is laurate, isostearate, and naphthenate groups

[00146] The TOFA-DETA polyamidoamines and the TOFA-TEPA polyamidoamines prepared in Examples 1A-1B and 6A-6B, were used in Examples 11-16 and 17-23, respectively.

[00147] Example 11 : The TOFA-DETA polyamidoamme acetate was prepared as follows: About 1 g of TOFA-DETA polyamidoamme was added to a 20 mL scintillation vial, then stirred and heated to about 80°C. About 0.093 g of glacial acetic acid was added over a period of about 2 min. The reaction mixture reached a temperature of about 100°C, then the heating source was removed and the mixture was cooled to about 25°C.

[00148] Example 12: The TOFA-DETA polyamidoamme acetate was prepared as follows: About 1 g of TOFA-DETA polyamidoamme was added to a 20 mL scintillation vial, then stirred and heated to about 80°C. About 0.19 g of glacial acetic acid was added over a period of about 2 min. The reaction mixture reached a temperature of about 100°C, then the heating source was removed and the mixture was cooled to about 25°C.

[00149] Example 13: The TOFA-DETA polyamidoamme acetate was prepared as follows: About 1 g of TOFA-DETA polyamidoamme was added to a 20 mL scintillation vial, then stirred and heated to about 80°C. About 0.28 g of glacial acetic acid was added over a period of about 2 min. The reaction mixture reached a temperature of about 100°C, then the heating source was removed and the mixture was cooled to about 25°C. [00150] Example 14: The TOFA-DETA polyamidoamme acetate was prepared as follows: About 1 g of TOFA-DETA polyamidoamme was added to a 20 mL scintillation vial, then stirred and heated to about 80°C. About 0.37 g of glacial acetic acid was added over a period of about 2 min. The reaction mixture reached a temperature of about 100°C, then the heating source was removed and the mixture was cooled to about 25°C.

[00151] Example 15: The TOFA-DETA polyamidoamme acetate was prepared as follows: About 1 g of TOFA-DETA polyamidoamme was added to a 20 mL scintillation vial, then stirred and heated to about 80°C. About 0.37 g of glacial acetic acid and about 0.1 g of water were added over a period of about 2 min. The reaction mixture reached a temperature of about 100°C, then the heating source was removed and the mixture was cooled to about 25°C.

[00152] Example 16: The TOFA-DETA polyamidoamme acetate was prepared as follows: About 1 g of TOFA-DETA polyamidoamme was added to a 20 mL scintillation vial, then stirred and heated to about 80°C. About 0.37 g of glacial acetic acid and about 0.2 g of water were added over a period of about 2 min. The reaction mixture reached a temperature of about 100°C, then the heating source was removed and the mixture was cooled to about 25°C.

[00153] Example 17: The TOFA-TEPA polyamidoamme acetate was prepared as follows: About 1 g of TOFA-TEPA polyamidoamme was added to a 20 mL scintillation vial, then stirred and heated to about 80°C. About 0.23 g of glacial acetic acid was added over a period of about 2 min. The reaction mixture reached a temperature of about 100°C, then the heating source was removed and the mixture was cooled to about 25°C.

[00154] Example 18: The TOFA-TEPA polyamidoamme acetate was prepared as follows: About 1 g of TOFA-TEPA polyamidoamme was added to a 20 mL scintillation vial, then stirred and heated to about 80°C. About 0.23 g of glacial acetic acid and about 0.25 g of water were added over a period of about 2 min. The reaction mixture reached a temperature of about 100°C, then the heating source was removed and the mixture was cooled to about 25°C.

[00155] Example 19: The TOFA-TEPA polyamidoamme acetate was prepared as follows: About 1 g of TOFA-TEPA polyamidoamme was added to a 20 mL scintillation vial, then stirred and heated to about 80°C. About 0.23 g of glacial acetic acid and about 0.5 g of water were added over a period of about 2 min. The reaction mixture reached a temperature of about 100°C, then the heating source was removed and the mixture was cooled to about 25°C. [00156] Example 20: The TOFA-TEPA polyamidoamine acetate was prepared as follows: About 1 g of TOFA-TEPA polyamidoamine was added to a 20 mL scintillation vial, then stirred and heated to about 80°C. About 0.23 g of glacial acetic acid and about 0.75 g of water were added over a period of about 2 min. The reaction mixture reached a temperature of about 100°C, then the heating source was removed and the mixture was cooled to about 25°C.

[00157] Example 21 : The TOFA-TEPA polyamidoamine acetate was prepared as follows: About 1 g of TOFA-TEPA polyamidoamine was added to a 20 mL scintillation vial, then stirred and heated to about 80°C. About 0.44 g of glacial acetic acid was added over a period of about 2 min. The reaction mixture reached a temperature of about 100°C, then the heating source was removed and the mixture was cooled to about 25°C.

[00158] Example 22: The TOFA-TEPA polyamidoamine acetate was prepared as follows: About 1 g of TOFA-TEPA polyamidoamine was added to a 20 mL scintillation vial, then stirred and heated to about 80°C. About 0.44 g of glacial acetic acid and about 0.25 g of water were added over a period of about 2 min. The reaction mixture reached a temperature of about 100°C, then the heating source was removed and the mixture was cooled to about 25°C.

[00159] Example 23: The TOFA-TEPA polyamidoamine acetate was prepared as follows: About 1 g of TOFA-TEPA polyamidoamine was added to a 20 mL scintillation vial, then stirred and heated to about 80°C. About 0.9 g of glacial acetic acid was added over a period of about 2 min. The reaction mixture reached a temperature of about 100°C, then the heating source was removed and the mixture was cooled to about 25°C.

"PS" is phase separates

[00160] Example 24: The LNI-TOFA-DETA polyamidoamme acetate was prepared as follows: About 1 g of LNI-TOFA-DETA polyamidoamme was added to a 20 mL scintillation vial, then stirred and heated to about 80°C. About 0.11 g of glacial acetic acid was added over a period of about 2 min. The reaction mixture reached a temperature of about 100°C, then the heating source was removed and the mixture was cooled to about 25°C.

[00161] Example 25: The LNI-TOFA-DETA polyamidoamme acetate was prepared as follows: About 1 g of LNI-TOFA-DETA polyamidoamme was added to a 20 mL scintillation vial, then stirred and heated to about 80°C. About 0.21 g of glacial acetic acid was added over a period of about 2 min. The reaction mixture reached a temperature of about 100°C, then the heating source was removed and the mixture was cooled to about 25°C.

[00162] Example 26: The LNI-TOFA-DETA polyamidoamme acetate was prepared as follows: About 1 g of LNI-TOFA-DETA polyamidoamme was added to a 20 mL scintillation vial, then stirred and heated to about 80°C. About 0.32 g of glacial acetic acid was added over a period of about 2 min. The reaction mixture reached a temperature of about 100°C, then the heating source was removed and the mixture was cooled to about 25°C.

[00163] Example 27: The LNI-TOFA-DETA polyamidoamme acetate was prepared as follows: About 1 g of LNI-TOFA-DETA polyamidoamme was added to a 20 mL scintillation vial, then stirred and heated to about 80°C. About 0.42 g of glacial acetic acid was added over a period of about 2 min. The reaction mixture reached a temperature of about 100°C, then the heating source was removed and the mixture was cooled to about 25°C.

[00164] Example 28: The LNI-TOFA-DETA polyamidoamme acetate was prepared as follows: About 1 g of LNI-TOFA-DETA polyamidoamme was added to a 20 mL scintillation vial, then stirred and heated to about 80°C. About 0.42 g of glacial acetic acid and about 0.1 g of water were added over a period of about 2 min. The reaction mixture reached a temperature of about 100°C, then the heating source was removed and the mixture was cooled to about 25°C.

[00165] Example 29: The LNI-TOFA-DETA polyamidoamme acetate was prepared as follows: About 1 g of LNI-TOFA-DETA polyamidoamme was added to a 20 mL scintillation vial, then stirred and heated to about 80°C. About 0.42 g of glacial acetic acid and about 0.2 g of water were added over a period of about 2 min. The reaction mixture reached a temperature of about 100°C, then the heating source was removed and the mixture was cooled to about 25°C.

[00166] Example 30: The LNI-TOFA-TEPA polyamidoamme acetate was prepared as follows: About 1 g of LNI-TOFA-TEPA polyamidoamme was added to a 20 mL scintillation vial, then stirred and heated to about 80°C. About 0.26 g of glacial acetic acid was added over a period of about 2 min. The reaction mixture reached a temperature of about 100°C, then the heating source was removed and the mixture was cooled to about 25°C.

[00167] Example 31 : The LNI-TOFA-TEPA polyamidoamme acetate was prepared as follows: About 1 g of LNI-TOFA-TEPA polyamidoamme was added to a 20 mL scintillation vial, then stirred and heated to about 80°C. About 0.37 g of glacial acetic acid was added over a period of about 2 min. The reaction mixture reached a temperature of about 100°C, then the heating source was removed and the mixture was cooled to about 25°C.

[00168] Example 32: The LNI-TOFA-TEPA polyamidoamme acetate was prepared as follows: About 1 g of LNI-TOFA-TEPA polyamidoamme was added to a 20 mL scintillation vial, then stirred and heated to about 80°C. About 0.52 g of glacial acetic acid was added over a period of about 2 min. The reaction mixture reached a temperature of about 100°C, then the heating source was removed and the mixture was cooled to about 25°C. [00169] Example 33: The LNI-TOFA-TEPA polyamidoamine acetate was prepared as follows: About 1 g of LNI-TOFA-TEPA polyamidoamine was added to a 20 mL scintillation vial, then stirred and heated to about 80°C. About 0.52 g of glacial acetic acid and about 0.25 g of water were added over a period of about 2 min. The reaction mixture reached a temperature of about 100°C, then the heating source was removed and the mixture was cooled to about 25°C.

[00170] Example 34: The lauric acid-TOFA-TEPA polyamidoamine acetate was prepared as follows: About 1 g of LNI-TOFA-TEPA polyamidoamine was added to a 20 mL scintillation vial, then stirred and heated to about 80°C. About 0.52 g of glacial acetic acid and about 1 g of water were added over a period of about 2 min. The reaction mixture reached a temperature of about 100°C, then the heating source was removed and the mixture was cooled to about 25°C.

[00171] Example 35: The lauric acid-TOFA-TEPA polyamidoamine acetate was prepared as follows: About 1 g of lauric acid-TOFA-TEPA polyamidoamine was added to a 20 mL scintillation vial, then stirred and heated to about 80°C. About 0.53 g of glacial acetic acid was added over a period of about 2 min. The reaction mixture reached a temperature of about 100°C, then the heating source was removed and the mixture was cooled to about 25°C.

[00172] Example 36: The lauric acid-TOFA-TEPA polyamidoamine acetate was prepared as follows: About 1 g of lauric acid-TOFA-TEPA polyamidoamine was added to a 20 mL scintillation vial, then stirred and heated to about 80°C. About 0.53 g of glacial acetic acid and about 0.1 g of water were added over a period of about 2 min. The reaction mixture reached a temperature of about 100°C, then the heating source was removed and the mixture was cooled to about 25°C.

[00173] Example 37: The lauric acid-TOFA-TEPA polyamidoamine acetate was prepared as follows: About 1 g of lauric acid-TOFA-TEPA polyamidoamine was added to a 20 mL scintillation vial, then stirred and heated to about 80°C. About 0.53 g of glacial acetic acid and about 0.25 g of water were added over a period of about 2 min. The reaction mixture reached a temperature of about 100°C, then the heating source was removed and the mixture was cooled to about 25°C.

[00174] Example 38: The lauric acid-TOFA-TEPA polyamidoamine acetate was prepared as follows: About 1 g of lauric acid-TOFA-TEPA polyamidoamine was added to a 20 mL scintillation vial, then stirred and heated to about 80°C. About 0.53 g of glacial acetic acid and about 1 g of water were added over a period of about 2 min. The reaction mixture reached a temperature of about 100°C, then the heating source was removed and the mixture was cooled to about 25°C.

[00175] Example 39: The naphthenic acid-TOFA-TEPA polyamidoamine acetate was prepared as follows: About 1 g of naphthenic acid-TOFA-TEPA polyamidoamine was added to a 20 mL scintillation vial, then stirred and heated to about 80°C. About 0.53 g of glacial acetic acid and about 0.25 g of water were added over a period of about 2 min. The reaction mixture reached a temperature of about 100°C, then the heating source was removed and the mixture was cooled to about 25°C.

[00176] Example 40: The isostearic acid-TOFA-TEPA polyamidoamine acetate was prepared as follows: About 1 g of isostearic acid-TOFA-TEPA polyamidoamine was added to a 20 mL scintillation vial, then stirred and heated to about 80°C. About 0.42 g of glacial acetic acid and about 0.25 g of water were added over a period of about 2 min. The reaction mixture reached a temperature of about 100°C, then the heating source was removed and the mixture was cooled to about 25°C.

[00177] Example 41 : The isostearic acid-TOFA-TEPA polyamidoamine acetate was prepared as follows: About 1 g of isostearic acid-TOFA-TEPA polyamidoamine was added to a 20 mL scintillation vial, then stirred and heated to about 80°C. About 0.53 g of glacial acetic acid and about 0.25 g of water were added over a period of about 2 min. The reaction mixture reached a temperature of about 100°C, then the heating source was removed and the mixture was cooled to about 25°C.

v scous; s no ow; s p ase separates

[00178] Examples 42A-42C: The TOFA-TEPA polyamidoamine acetate was prepared was prepared as follows: To a 2 L reactor, about 779 g of the TOFA-TEPA polyamidoamine was added, stirred, and heated to about 80°C. About 553 g of glacial acetic acid was added over a period of about 6 min. The reaction mixture reached a temperature of about 100°C, then the heating source was removed and the mixture was cooled to about 25°C.

[00179] Examples 43A-43D: The TOFA-TEPA polyamidoamine acetate was prepared was prepared as follows: To a 2 L reactor, about 779 g of the TOFA-TEPA polyamidoamine was added, stirred, and heated to about 80°C. About 138 g of glacial acetic acid was added over a period of about 6 min. The reaction mixture reached a temperature of about 100°C, then the heating source was removed and the mixture was cooled to about 25°C. [00180] Examples 44A-44D: The lauric acid-TOFA-TEPA polyamidoamine acetate was prepared was prepared as follows: To a 2 L reactor, about 600 g of the lauric acid-TOFA-TEPA polyamidoamine was added, stirred, and heated to about 80°C. About 308 g of glacial acetic acid and 147 g of water were added over a period of about 6 min. The reaction mixture reached a temperature of about 100°C, then the heating source was removed and the mixture was cooled to about 25°C.

[00181] Examples 45A-45D: The LNI-TOFA-TEPA polyamidoamine acetate was prepared was prepared as follows: To a 2 L reactor, about 600 g of the LNI-TOFA-TEPA polyamidoamine was added, stirred, and heated to about 80°C. About 299 g of glacial acetic acid and 143 g water were added over a period of about 6 min. The reaction mixture reached a temperature of about 100°C, then the heating source was removed and the mixture was cooled to about 25°C.

[00182] Examples 46A-46D: The TOFA-DETA monoamidoamine acetate was prepared was prepared as follows: To a 2 L reactor, about 600 g of the TOFA-DETA monoamidoamine was added, stirred, and heated to about 80°C. About 210 g of glacial acetic acid, 600 g water, and 210 g Flomin 663 frother were added over a period of about 6 min. The reaction mixture reached a temperature of about 100°C, then the heating source was removed and the mixture was cooled to about 25°C.

[00183] Examples 47A-47D: The cocoamine acetate was prepared was prepared as follows: To a 2 L reactor, about 600 g of the cocoamine was added, stirred, and heated to about 80°C. About 35.2 g of glacial acetic acid and 473 g water were added over a period of about 6 min. The reaction mixture reached a temperature of about 100°C, then the heating source was removed and the mixture was cooled to about 25°C.

lauric acid-TOFA-

44A 30 1 [0.5] 99.86 98.29 1.57

TEPA

lauric acid-TOFA-

44B 30 1.5 [0.75] 99.54 41.75 57.79

TEPA

lauric acid-TOFA-

44C 30 2 [1] 98.84 13.48 85.36

TEPA

lauric acid-TOFA-

44D 30 2.5 [1.25] 97.85 8.32 89.53

TEPA

45A LNI-TOFA-TEPA 30 1 [0.5] 99.55 47.79 51.76

45B LNI-TOFA-TEPA 30 1.5 [0.75] 99.46 43.17 56.29

45C LNI-TOFA-TEPA 30 2 [1] 96.73 7.84 88.89

45D LNI-TOFA-TEPA 30 2.5 [1.25] 94.91 9.18 85.73

Monoamidoamine

TOFA-DETA

46A 13 1 [0.5] 99.53 64.45 35.09 monoamidoamine

TOFA-DETA

46B 13 1.5 [0.75] 98.28 32.02 66.26 monoamidoamine

TOFA-DETA

46C 13 2 [1] 97.87 25.71 72.16 monoamidoamine

TOFA-DETA

46D 13 2.5 [1.25] 97.02 20.32 76.70 monoamidoamine

47A cocoamine acetate 6 1 [0.5] 98.94 28.80 70.14

47B cocoamine acetate 6 1.5 [0.75] 97.88 20.21 77.67

47C cocoamine acetate 6 2 [1] 96.60 14.51 82.09

47D cocoamine acetate 6 2.5 [1.25] 95.32 12.91 82.41

* HO Ac wt% values are based on the total weight of the polyamidoamine and the acetic acid.

[00184] Embodiments of the present disclosure further relate to any one or more of the following paragraphs:

[00185] 1. A cationic collector, comprising: an organic acid; and a polyamidoamine, wherein the polyamidoamine comprises one or more amidoamines having the chemical formula (A),wherein:

1 2

R and R are each independently a saturated or unsaturated, substituted or unsubstituted, linear or branched, cyclic, heterocyclic, or aromatic hydrocarbyl group, each R ³ and R ⁴ are each independently hydrogen or a saturated or unsaturated, substituted or unsubstituted, linear or branched, cyclic, heterocyclic, or aromatic hydrocarbyl group, each m is an integer of 1 to 5, and n is an integer of 2 to 8.

[00186] 2. A cationic collector, comprising: acetic acid; and a polyamidoamine, wherein the polyamidoamine comprises one or more amidoamines having the chemical formula (A),

1 2

wherein: R and R are each independently a saturated or unsaturated, substituted or unsubstituted, linear or branched, cyclic, heterocyclic, or aromatic hydrocarbyl group, each R and R ⁴ are each independently hydrogen or a saturated or unsaturated, substituted or unsubstituted, linear or branched, cyclic, heterocyclic, or aromatic hydrocarbyl group, each m is an integer of 1 to 5, and n is an integer of 2 to 8.

1 2

[00187] 3. The cationic collector according to paragraph 1 or 2, wherein R and R are each independently a C8 to C24 chain having 0 to 5 unsaturated bonds, each R ³ and R ⁴ are hydrogen, each m is 2, 3, or 4, and n is 2, 3, 4, or 5.

1 2

[00188] 4. The cationic collector according to any one of paragraphs 1 to 3, wherein R and R are each independently a CIO to C20 chain having 0 to 3 unsaturated bonds, each R ³ and R ⁴ are hydrogen, each m is 2 or 3, and n is 2, 3, or 4.

1 2

[00189] 5. The cationic collector according to any one of paragraphs 1 to 4, wherein R and R are each independently C ₉ Hi ₉ , C ₉ H _i7 , C ₉ Hi ₅ , C ₉ Hi ₃ , CnH ₂₃ , C _n H ₂₁ , Ci ₅ H ₃₃ , Ci ₅ H ₃ i, Ci ₅ H ₂₉ , Ci ₇ H ₃ 5, Ci ₇ H ₃₃ , Ci ₇ H ₃ i, Ci ₇ H ₂₉ , Ci ₉ H ₃₇ , Ci ₉ H ₃ 5 , Ci ₉ H ₃₃ , Ci ₉ H ₃ i, or Ci ₉ H ₂₉ , and wherein n is 2.

1 2

[00190] 6. The cationic collector according to any one of paragraphs 1 to 5, wherein R and R are each independently derived from lauric acid, stearic acid, isostearic acid, naphthenic acid, oleic acid, linoleic acid, linolenic acid, palmitic acid, or isomers thereof.

1 2

[00191] 7. The cationic collector according to any one of paragraphs 1 to 5, wherein R and R are each independently derived from one or more fatty acids, tall oil fatty acids, rosin acids, crude tall oils, distilled tall oils, tall oil pitches, or any mixture thereof.

[00192] 8. The cationic collector according to any one of paragraphs 1 to 7, wherein each R and R ⁴ are each independently hydrogen, an amino, an amido, or a C10 to C18 chain having 0 to 3 unsaturated bonds.

[00193] 9. The cationic collector according to any one of paragraphs 1 to 8, wherein the organic acid comprises glacial acetic acid.

[00194] 10. The cationic collector according to any one of paragraphs 1 to 9, wherein the cationic collector comprises the organic acid in an amount of about 10 wt% to about 60 wt% and the polyamidoamine in an amount of about 40 wt% to about 90 wt%, based on the combined weight of the polyamidoamine and the organic acid. [00195] 1 1. The cationic collector according to any one of paragraphs 1 to 10, further comprising water, wherein the cationic collector comprises about 2 wt% to about 50 wt% of water, based on the combined weight of the polyamidoamme, the organic acid, and the water.

[00196] 12. The cationic collector according to any one of paragraphs 1 to 1 1 , wherein the polyamidoamme comprises a product formed by reacting a polyamine and a fatty acid, wherein the polyamine comprises diethylenetriamine, triethylenetetramine, tetraethylenepentamine, pentaethylenehexamine, or any mixture thereof, and wherein the fatty acid comprises tall oil fatty acids, lauric acid, stearic acid, isostearic acid, naphthenic acid, oleic acid, linoleic acid, linolenic acid, palmitic acid, isomers thereof, or any mixture thereof.

[00197] 13. The cationic collector according to any one of paragraphs 1 to 12, wherein the polyamine comprises diethylenetriamine, tetraethylenepentamine, or a mixture thereof, and wherein the fatty acid comprises tall oil fatty acids, lauric acid, stearic acid, isostearic acid, naphthenic acid, isomers thereof, or any mixture thereof.

[00198] 14. The cationic collector according to any one of paragraphs 1 to 13, wherein the cationic collector has a viscosity of about 30 cP to about 200 cP at 25°C.

[00199] 15. The cationic collector according to any one of paragraphs 1 to 14, wherein the cationic collector has a viscosity of about 10 cP to about 125 cP at 80°C.

[00200] 16. The cationic collector according to any one of paragraphs 1 to 15, wherein the polyamidoamme comprises diamidoamines, triamidoamines, or a mixture thereof.

[00201] 17. The cationic collector according to any one of paragraphs 1 to 16, wherein the polyamidoamme comprises one or more amidoamines having the chemical formula (D), wherein R ¹ and R ² are each independently CnH ₂ 3, CnH ₂₁ , C15H33, C15H31, Ci ₅ H ₂₉ , C17H35, C17H33, C17H31, or Ci ₇ H ₂₉ , and n is an integer of 2, 3, or 4.

[00202] 18. A method for purifying a phosphorous containing material, comprising combining phosphorous ore, water, an organic acid, and a polyamidoamme to produce an aqueous mixture, wherein the polyamidoamme comprises one or more amidoamines having the chemical formula

1 2

(A), wherein R and R are each independently a saturated or unsaturated, substituted or unsubstituted, linear or branched, cyclic, heterocyclic, or aromatic hydrocarbyl group, each R and R ⁴ are each independently hydrogen or a saturated or unsaturated, substituted or unsubstituted, linear or branched, cyclic, heterocyclic, or aromatic hydrocarbyl group, each m is an integer of 1 to 5, and n is an integer of 2 to 8, and collecting a phosphate material from the aqueous mixture.

[00203] 19. A method for purifying a phosphorous containing material, comprising combining phosphorous ore, water, acetic acid, and a polyamidoamine to produce an aqueous mixture, wherein the polyamidoamine comprises one or more amidoamines having the chemical formula

1 2

(B), wherein R and R are each independently a saturated or unsaturated, substituted or unsubstituted, linear or branched, cyclic, heterocyclic, or aromatic hydrocarbyl group, each R and R ⁴ are each independently selected from hydrogen or a saturated or unsaturated, substituted or unsubstituted, linear or branched, cyclic, heterocyclic, or aromatic hydrocarbyl group, and n is an integer of 2 to 8, collecting a phosphate material from in the aqueous mixture.

[00204] 20. The method according to paragraph 18 or 19, wherein the cationic collector further comprises about 2 wt% to about 50 wt% of water, based on the combined weight of the polyamidoamine, the acetic acid, and the water.

[00205] 21. The method according to any one of paragraphs 18 to 20, further comprising combining the organic acid and the polyamidoamine to produce a cationic collector, wherein the organic acid is acetic acid, and combining the cationic collector, the phosphorous ore, and water to produce the aqueous mixture.

[00206] 22. The method according to any one of paragraphs 18 to 21, wherein the acetic acid is glacial acetic acid, and wherein the cationic collector comprises about 10 wt% to about 60 wt% of the acetic acid and about 40 wt% to about 90 wt% of the polyamidoamine, based on the combined weight of the polyamidoamine and the acetic acid.

[00207] 23. The method according to any one of paragraphs 18 to 22, wherein the collected phosphate material is about 95 wt% to about 99.99 wt% of the total phosphate material contained

1 2

in the phosphorous ore, and wherein R and R are each independently a CIO to C20 chain having 0 to 5 unsaturated bonds, each R ³ and R ⁴ are hydrogen, each m is 2 or 3, and n is 2, 3, or 4.

[00208] 24. The method according to any one of paragraphs 18 to 23, further comprising producing the polyamidoamine by reacting a polyamine and a fatty acid, wherein the polyamine comprises diethylenetriamine, triethylenetetramine, tetraethylenepentamine, pentaethylenehexamme, or any mixture thereof, and wherein the fatty acid comprises tall oil fatty acids, lauric acid, stearic acid, isostearic acid, naphthenic acid, oleic acid, linoleic acid, linolenic acid, palmitic acid, isomers thereof, or any mixture thereof.

[00209] 25. An aqueous mixture of a phosphorous containing material, comprising a phosphorous ore, water, an organic acid, and a polyamidoamine, wherein the polyamidoamine

1 2 comprises one or more amidoamines having the chemical formula (A), wherein R and R are each independently a saturated or unsaturated, substituted or unsubstituted, linear or branched, cyclic, heterocyclic, or aromatic hydrocarbyl group, each R ³ and R ⁴ are each independently hydrogen or a saturated or unsaturated, substituted or unsubstituted, linear or branched, cyclic, heterocyclic, or aromatic hydrocarbyl group, each m is an integer of 1 to 5, and n is an integer of 2 to 8.

[00210] 26. An aqueous mixture of a phosphorous containing material, comprising a phosphorous ore, water, acetic acid, and a polyamidoamine, wherein the polyamidoamine

1 2 comprises one or more amidoamines having the chemical formula (A), wherein R and R are each independently a saturated or unsaturated, substituted or unsubstituted, linear or branched, cyclic, heterocyclic, or aromatic hydrocarbyl group, each R ³ and R ⁴ are each independently hydrogen or a saturated or unsaturated, substituted or unsubstituted, linear or branched, cyclic, heterocyclic, or aromatic hydrocarbyl group, each m is an integer of 1 to 5, and n is an integer of 2 to 8.

[00211] 27. An aqueous mixture of a collector and an ore mineral, comprising an ore, water, and a polyamidoaminate having the chemical formula (K), wherein R 1 and R 2 are each independently a saturated or unsaturated, substituted or unsubstituted, linear or branched, cyclic, heterocyclic, or aromatic hydrocarbyl group, each R ³ , R ⁴ , and R ⁵ are each independently selected from hydrogen or a saturated or unsaturated, substituted or unsubstituted, linear or branched, cyclic, heterocyclic, or aromatic hydrocarbyl group, A is hydrogen or a hydrocarbyl group, X is a conjugate base, a halide, or a hydroxide, and n is an integer of 2 to 8. 28. The aqueous mixture according to paragraph 27, wherein R 1 and R 2

[00212] are each independently a saturated or unsaturated, substituted or unsubstituted, linear or branched, cyclic, heterocyclic, or aromatic hydrocarbyl group, each R ³ , R ⁴ , and R ⁵ are each hydrogen, A is hydrogen, X is a conjugate base, wherein the conjugate base is acetate, glycolate, lactate, pyruvate, formate, propionate, butyrate, valerate, oxalate, alkyl derivatives thereof, isomers thereof, or mixtures thereof, and n is 1, 2, 3, or 4.

[00213] 29. The aqueous mixture according to any one of paragraphs 25 to 28, wherein the polyamidoamine comprises one or more amidoamines having the chemical formula (D), wherein

1 2

R and R are each independently C9H15, C9H13, C11H23, CnH ₂₁ , C15H33, C15H31, C15H29, C17H35, C17H33, C17H31, or C17H29, and n is 2, 3, or 4.

1 2

[00214] 30. The aqueous mixture according to any one of paragraphs 25 to 29, wherein R and R are each independently derived from lauric acid, stearic acid, isostearic acid, naphthenic acid, oleic acid, linoleic acid, linolenic acid, palmitic acid, or isomers thereof.

[00215] 31. A cationic collector, comprising water, and one or more polyethylene polyamidoamine acetates having the chemical formula (M), wherein R 1 and R 2 are each independently a saturated or unsaturated, substituted or unsubstituted, linear or branched, cyclic, heterocyclic, or aromatic hydrocarbyl group, and n is 1, 2, 3, or 4.

[00216] 32. A composition, comprising: an organic acid; and a polyamidoamine having the

chemical formula: , wherein: R and R are independently a saturated or unsaturated, substituted or unsubstituted, linear or branched, cyclic, heterocyclic, or aromatic hydrocarbyl group, R ³ and R ⁴ are independently hydrogen or a saturated or unsaturated, substituted or unsubstituted, linear or branched, cyclic, heterocyclic, or aromatic hydrocarbyl group, each m is an integer of 1 to 5, and n is an integer of 2 to 8.

[00217] 33. A cationic collector for purifying an ore, comprising: an organic acid; and a polyamidoamine having the chemical formula (A), wherein: R 1 and R 2 are independently a saturated or unsaturated, substituted or unsubstituted, linear or branched, cyclic, heterocyclic, or aromatic hydrocarbyl group, each R is independently hydrogen or a saturated or unsaturated, substituted or unsubstituted, linear or branched, cyclic, heterocyclic, or aromatic hydrocarbyl group, R is hydrogen or a saturated or unsaturated, substituted or unsubstituted, linear or branched, cyclic, heterocyclic, or aromatic hydrocarbyl group, each m is independently an integer of 1 to 5, and n is an integer of 2 to 8.

[00218] 34. An aqueous mixture, comprising: an ore; water; an organic acid; and a

polyamidoamine having the chemical formula: ,

1 2

wherein: R and R are independently a saturated or unsaturated, substituted or unsubstituted, linear or branched, cyclic, heterocyclic, or aromatic hydrocarbyl group, R ³ and R ⁴ are independently hydrogen or a saturated or unsaturated, substituted or unsubstituted, linear or branched, cyclic, heterocyclic, or aromatic hydrocarbyl group, each m is an integer of 1 to 5, and n is an integer of 2 to 8.

[00219] 35. An aqueous mixture, comprising: an ore; water; an organic acid; and a polyamidoamine having the chemical formula (A), wherein R 1 and R 2 are independently a saturated or unsaturated, substituted or unsubstituted, linear or branched, cyclic, heterocyclic, or aromatic hydrocarbyl group, each R is independently hydrogen or a saturated or unsaturated, substituted or unsubstituted, linear or branched, cyclic, heterocyclic, or aromatic hydrocarbyl group, R ⁴ is hydrogen or a saturated or unsaturated, substituted or unsubstituted, linear or branched, cyclic, heterocyclic, or aromatic hydrocarbyl group, each m is independently an integer of 1 to 5, and n is an integer of 2 to 8.

[00220] 36. A method for purifying an ore, comprising: combining an ore, water, an organic acid, and a polyamidoamine to produce an aqueous mixture, wherein the ore comprises an impurity, and wherein the polyamidoamine has the chemical formula:

wherein: R 1 and R 2 are independently a saturated or unsaturated, substituted or unsubstituted, linear or branched, cyclic, heterocyclic, or aromatic hydrocarbyl group, R ³ and R ⁴ are independently hydrogen or a saturated or unsaturated, substituted or unsubstituted, linear or branched, cyclic, heterocyclic, or aromatic hydrocarbyl group, each m is an integer of 1 to 5, and n is an integer of 2 to 8; and collecting a purified ore having a reduced concentration of the impurity relative to the ore from the aqueous mixture.

[00221] 37. A method for purifying a phosphorous containing material, comprising: combining a phosphorous ore, water, an organic acid, and a polyamidoamine to produce an aqueous mixture, wherein the polyamidoamine has the chemical formula (A), wherein: R 1 and R 2 are independently a saturated or unsaturated, substituted or unsubstituted, linear or branched, cyclic, heterocyclic, or aromatic hydrocarbyl group, each R is independently hydrogen or a saturated or unsaturated, substituted or unsubstituted, linear or branched, cyclic, heterocyclic, or aromatic hydrocarbyl group, R ⁴ is hydrogen or a saturated or unsaturated, substituted or unsubstituted, linear or branched, cyclic, heterocyclic, or aromatic hydrocarbyl group, each m is independently an integer of 1 to 5, and n is an integer of 2 to 8; and collecting a phosphate material from the aqueous mixture.

[00222] 38. A method for purifying an ore, comprising: combining an ore, water, an organic acid, and a polyamidoamine to produce an aqueous mixture, wherein the polyamidoamine has the chemical formula (A), wherein: R 1 and R 2 are independently a saturated or unsaturated, substituted or unsubstituted, linear or branched, cyclic, heterocyclic, or aromatic hydrocarbyl group, each R is independently hydrogen or a saturated or unsaturated, substituted or unsubstituted, linear or branched, cyclic, heterocyclic, or aromatic hydrocarbyl group, R ⁴ is hydrogen or a saturated or unsaturated, substituted or unsubstituted, linear or branched, cyclic, heterocyclic, or aromatic hydrocarbyl group, each m is independently an integer of 1 to 5, and n is an integer of 2 to 8; and recovering a purified ore product from the aqueous mixture.

[00223] 39. The composition, cationic collector, aqueous mixture, or method according to any one of paragraphs 32 to 38, wherein: R 1 and R 2 are independently a C8 to C24 chain having 0 to 5 unsaturated bonds, R ³ and R ⁴ are hydrogen, each m is an integer of 2, 3, or 4, and n is an integer of 2, 3, 4, or 5.

[00224] 40. The composition, cationic collector, aqueous mixture, or method according to any

1 2

one of paragraphs 32 to 38, wherein: R and R are independently a C9 to C20 chain having 0 to 3 unsaturated bonds, R ³ and R ⁴ are hydrogen, each m is an integer of 2 or 3, and n is an integer of 2, 3, or 4.

[00225] 41. The composition, cationic collector, aqueous mixture, or method according to paragraph 40, wherein R 1 and R 2 are independently C H19, C9H17, C9H15, C9H13, CnH ₂ 3, CnH ₂₁ , C15H33, C15H31, Ci ₅ H ₂ 9, C17H35, C17H33, C17H31, C ₁₇ H ₂ 9, C19H37, C19H35, C19H33, C19H31, or Ci9¾9, and wherein n is 2.

[00226] 42. The composition, cationic collector, aqueous mixture, or method according to any

1 2

one of paragraphs 32 to 38, wherein R and R are independently derived from lauric acid, stearic acid, isostearic acid, naphthenic acid, oleic acid, linoleic acid, linolenic acid, palmitic acid, or isomers thereof.

[00227] 43. The composition, cationic collector, aqueous mixture, or method according to any one of paragraphs 32 to 38, wherein R ³ and R ⁴ are independently hydrogen, an amino, an amido, or a C10 to C18 chain having 0 to 3 unsaturated bonds.

[00228] 44. The composition, cationic collector, aqueous mixture, or method according to any one of paragraphs 32 to 38, wherein: R 1 and R 2 are independently C9H15, C9H13, CnH ₂₃ , CnH ₂₁ , Ci ₅ H ₃₃ , C ₁₅ H ₃₁ , Ci ₅ H ₂₉ , Ci ₇ H ₃₅ , Ci ₇ H ₃₃ , C ₁₇ H ₃₁ , or Ci ₇ H ₂₉ , R ³ and R ⁴ are hydrogen, m is an integer of 2, and n is an integer of 2, 3, or 4.

[00229] 45. The composition, cationic collector, aqueous mixture, or method according to any one of paragraphs 32 to 44, wherein the organic acid comprises glacial acetic acid.

[00230] 46. The composition or cationic collector according to any one of paragraphs 32, 33, or 39 to 45, wherein the composition or the cationic collector comprises about 10 wt% to about 60 wt% of the organic acid and about 40 wt% to about 90 wt% of the polyamidoamine, based on a combined weight of the polyamidoamine and the organic acid.

[00231] 47. The composition or cationic collector according to any one of paragraphs 32, 33, or 39 to 46, further comprising about 2 wt% to about 50 wt% of water, based on a combined weight of the polyamidoamine, the organic acid, and the water, wherein the organic acid comprises acetic acid.

[00232] 48. The composition, cationic collector, aqueous mixture, or method according to any one of paragraphs 32 to 47, wherein the polyamidoamine comprises a product formed by reacting a polyamine and a fatty acid, wherein the polyamine comprises diethylenetriamine, triethylenetetramine, tetraethylenepentamine, pentaethylenehexamine, or any mixture thereof, and wherein the fatty acid comprises tall oil fatty acids, lauric acid, stearic acid, isostearic acid, naphthenic acid, oleic acid, linoleic acid, linolenic acid, palmitic acid, isomers thereof, or any mixture thereof.

[00233] 49. The composition, cationic collector, aqueous mixture, or method according to paragraph 48, wherein the polyamine comprises diethylenetriamine, tetraethylenepentamine, or a mixture thereof, and wherein the fatty acid comprises tall oil fatty acids, lauric acid, stearic acid, isostearic acid, naphthenic acid, isomers thereof, or any mixture thereof.

[00234] 50. The composition, cationic collector, aqueous mixture, or method according to any one of paragraphs 32 or 39 to 49, wherein the composition has a viscosity of about 30 cP to about 200 cP at a temperature of 25°C.

[00235] 51. The composition , cationic collector, aqueous mixture, or method according to any one of paragraphs 32 to 50, wherein the organic acid comprises acetic acid, glycolic acid, lactic acid, pyruvic acid, formic acid, propionic acid, butyric acid, valeric acid (pentanoic acid), oxalic acid, malonic acid, caproic acid, enanthic acid, caprylic acid, pelargonic acid, capric acid, undecylic acid, lauric acid, isomers thereof, hydrates thereof, salts thereof, complexes thereof, adducts thereof, or any mixture thereof.

[00236] 52. The composition, cationic collector, aqueous mixture, or method according to any one of paragraphs 32 to 51, wherein the polyamidoamine comprises a product formed by reacting a polyamine and a fatty acid at a temperature of about 10°C to about 300°C.

[00237] 53. The composition, cationic collector, aqueous mixture, or method according to any one of paragraphs 32 to 44 or 46 to 52, wherein the organic acid comprises acetic acid.

[00238] 54. The composition or cationic collector according to any one of paragraphs 32, 33, or 39 to 53, wherein the composition or the cationic collector has a viscosity of about 10 cP to about 800 cP at a temperature of 25°C.

[00239] 55. The composition or cationic collector according to any one of paragraphs 32, 33, or 39 to 53, wherein the composition or the cationic collector has a viscosity of about 10 cP to about 160 cP at a temperature of 25°C. [00240] 56. The composition or cationic collector according to any one of paragraphs 32, 33, or 39 to 53, wherein the composition or the cationic collector has a viscosity of about 30 cP to about 200 cP at a temperature of 25°C.

[00241] 57. The composition or cationic collector according to any one of paragraphs 32, 33, or 39 to 53, wherein the composition or the cationic collector has a viscosity of about 10 cP to about 140 cP at a temperature of 25°C.

[00242] 58. The composition or cationic collector according to any one of paragraphs 32, 33, or 39 to 57, wherein the composition or the cationic collector has a viscosity of about 10 cP to about 300 cP at a temperature of 80°C.

[00243] 59. The composition or cationic collector according to any one of paragraphs 32, 33, or 39 to 57, wherein the composition or the cationic collector has a viscosity of about 10 cP to about 100 cP at a temperature of 80°C.

[00244] 60 The composition or cationic collector according to any one of paragraphs 32, 33, or 39 to 59, wherein the composition or the cationic collector further comprises water, and wherein the composition or the cationic collector has a viscosity of about 10 cP to about 800 cP at a temperature of 25°C when the composition or the cationic collector includes about 2 wt% to about 50 wt% of the organic acid, about 2 wt% to about 50 wt% of water, and about 30 wt% to about 95 wt% of the polyamidoamine, based on the combined weight of the polyamidoamine, the organic acid, and the water.

[00245] 61. The composition or cationic collector according to any one of paragraphs 32, 33, or 39 to 59, wherein the composition or the cationic collector further comprises water, and wherein the composition or the cationic collector has a viscosity of about 10 cP to about 800 cP at a temperature of 25°C when the composition or the cationic collector includes about 20 wt% to about 60 wt% of the organic acid, about 20 wt% to about 60 wt% of water, and about 30 wt% to about 80 wt% of the polyamidoamine, based on the combined weight of the polyamidoamine, the organic acid, and the water.

[00246] 62. The aqueous mixture or method according to any one of paragraphs 34 to 36 or 38 to 61, wherein the ore is a phosphorous ore, an iron ore, an aluminum ore, a potassium ore, a sodium ore, a calcium ore, potash, feldspar, bauxite, any mixture thereof. [00247] 63. The aqueous mixture or method according to any one of paragraphs 34 to 36 or 38 to 61, wherein the ore is a phosphorous ore.

[00248] 64. The aqueous mixture or method according to any one of paragraphs 34 to 63, wherein the aqueous mixture comprises about 2 wt% to about 50 wt% of water, based on a combined weight of the polyamidoamine, the organic acid, and the water.

[00249] 65. The method according to any one of paragraphs 36 to 45, 48 to 53, or 62 to 64, further comprising: combining the organic acid and the polyamidoamine to produce a cationic collector, and combining the cationic collector, the ore, and water to produce the aqueous mixture.

[00250] 66. The method according to paragraph 65, wherein the organic acid is acetic acid.

[00251] 67. The method according to paragraph 66, wherein the cationic collector comprises about 10 wt% to about 60 wt% of the acetic acid and about 40 wt% to about 90 wt% of the polyamidoamine, based on a combined weight of the polyamidoamine and the acetic acid.

[00252] 68. The method according to any one of paragraphs 65 to 67, wherein the ore is a phosphorous ore, an iron ore, an aluminum ore, a potassium ore, a sodium ore, a calcium ore, potash, feldspar, bauxite, or any mixture thereof.

[00253] 69. The aqueous mixture or method according to any one of paragraphs 34 to 45, 48 to 53, or 62 to 68, wherein the aqueous mixture comprises about 0.0001 wt% to about 2 wt% of the polyamidoamine, based on the weight of the ore.

[00254] 70. The aqueous mixture or method according to any one of paragraphs 34 to 45, 48 to 53, or 62 to 69, wherein the aqueous mixture comprises about 0.0001 wt% to about 2 wt% of the organic acid, based on the weight of the ore. The method according to any one of paragraphs 65 to 70, wherein R 1 and R 2

[00255] 71. are each independently a C9 to C20 chain having 0 to 5 unsaturated bonds, R ³ and R ⁴ are hydrogen, each m is an integer of 2 or 3, and n is an integer of 2, 3, or 4.

[00256] 72. The method according to paragraph 65, wherein the cationic collector comprises about 10 wt% to about 60 wt% of the acetic acid and about 40 wt% to about 90 wt% of the polyamidoamine, based on a combined weight of the polyamidoamine and the acetic acid, wherein the ore comprises a phosphorus ore, wherein the purified ore comprises a phosphate material, wherein the phosphate material comprises about 95 wt% to about 99.99 wt% of a total

1 2 phosphate material contained in the phosphorous ore, and wherein: R and R are each independently a C9 to C20 chain having 0 to 5 unsaturated bonds, R ³ and R ⁴ are hydrogen, each m is 2 or 3, and n is 2, 3, or 4.

[00257] 73. The method according to any one of paragraphs 36, 38 to 45, 48 to 53, or 64 to 72, wherein the ore is a phosphorous ore.

[00258] 74. The method according to any one of paragraphs 36, 38 to 45, 48 to 53, or 64 to 73, wherein the impurity comprises a silicate material.

[00259] 75. The aqueous mixture or method according to any one of paragraphs 34 to 45, 48 to 53, or 62 to 74, wherein the aqueous mixture comprises about 0.0001 wt% to about 2 wt% of the polyamidoamine, based on the weight of the ore.

[00260] 76. The aqueous mixture or method according to any one of paragraphs 34 to 45, 48 to 53, or 62 to 75, wherein the aqueous mixture comprises about 0.0001 wt% to about 2 wt% of the organic acid, based on the weight of the ore.

[00261] Certain embodiments and features have been described using a set of numerical upper limits and a set of numerical lower limits. It should be appreciated that ranges including the combination of any two values, e.g., the combination of any lower value with any upper value, the combination of any two lower values, and/or the combination of any two upper values are contemplated unless otherwise indicated. Certain lower limits, upper limits and ranges appear in one or more claims below. All numerical values are "about" or "approximately" the indicated value, and take into account experimental error and variations that would be expected by a person having ordinary skill in the art.

[00262] Various terms have been defined above. To the extent a term used in a claim is not defined above, it should be given the broadest definition persons in the pertinent art have given that term as reflected in at least one printed publication or issued patent. Furthermore, all patents, test procedures, and other documents cited in this application are fully incorporated by reference to the extent such disclosure is not inconsistent with this application and for all jurisdictions in which such incorporation is permitted. [00263] While the foregoing is directed to embodiments, other and further embodiments of the invention can be devised without departing from the basic scope thereof, and the scope thereof is determined by the claims that follow.