The present invention provides a process for preparing advanced epoxy resin containing triazine or both triazine and oxazoline groups.

Epoxy resins are the reaction product of a diphenol or polyphenol with an epihalohydrin and a basic-acting material. Said reaction generally involves two distinct steps: coupling reaction of the epihalohydrin and diphenol or polyphenol to provide a halohydrin intermediate and dehydrohalogenation reaction of the halohydrin intermediate to provide the glycidyl ether product.

It is known, for example, as taught by Bender et al in U.S. Patent 2,506,486 that epoxy resins can be reacted with, diphenols. Said reaction involves etherification of hydroxyl groups via reaction with epoxide groups. This reaction is designated as an advancement reaction and the product thereof is an advanced epoxy resin.

The advanced epoxy resin prepared by the process of the present invention contain triazine groups or both triazine and oxazoline groups are derived by reaction of the respective triazine-containing or triazine-containing and oxazoline-containing hydroxyaromatic oligomers with an epoxy resin.

The present invention pertains to a process- for preparing advanced epoxy resins containing triazine groups or both triazine and oxazoline groups characterized by reacting (A) (1) at least one hydroxyaromatic oligomer containing at least one triazine group, or (2) at least one hydroxyaromatic oligomer containing both at least one triazine group and at least one oxazoline group, or (3) a mixture of (1) and (2) with (B) at least one material having an average of more than one 1,2-epoxy group per molecule wherein the components are employed in proportions which provide a ratio of hydroxyl groups to epoxy groups of from 0.1:1 to 1:1, preferably from 0.1:1 to 0.5:1.

Suitable materials having an average of more than one aromatic hydroxyl group per molecule which can be employed to prepare the cyanate mixture precursor to the triazine functional oligomers or the triazine and oxazoline functional oligomers include, for example, those represented by the formulas:

OH

wherein A is a divalent hydrocarbon g oup having from 1 to 12, preferably from 1 to 6

O O

II I! If carbon atoms, -S-, -S-S- -s- •s- ^■ c- -0-C-0-, -O-,

II

O

is a divalent

hydrocarbon group having from 1 to 3, pre erably 1, carbon atoms; each R is independently hydrogen, halogen, preferably chlorine or bromine, a hydrocarbyl group havxng from 1 to 6 carbon atoms or a hydroxyl group; each R' is independently hydrogen or a

_ _π G...PI

hydrocarbyl group having from 1 to 6 carbon atoms or a halogen, preferably chlorine or bromine; m has a value from zero to 2; m' has a value from 1 to 100, preferably from 1 to 10; n has a value of zero or 1 and n' has a value from 1.01 to 6.

Particularly suitable aromatic hydroxyl- -containing compounds include, for example, o-, m- and p-dihydroxybenzene, 2-tert butyl hydroquinone, 2,4-dimethyl resorcinol, 2,5-di-tert butyl hydroquinone, tetramethyl hydroquinone, 2,4,6-trimethyl resorcinol, 4-chlororesorcinol, 4-tert butyl pyrocatechol, 1,1-bis( -hydroxyphenyl)ethane; 2,2-bis(4-hydroxyphenyl)- propane; 2,2-bis(4-hydroxyphenylJpentane; bis(4,4'-dihydroxyphenyl)methane; 4,4'-dihydroxydiphenyl, 2,2'-dihydroxydiphenyl, 3,3' ,5,5*-tetramethyl- -4,4'-dihydroxydiphenyl, 3,3' ,5,5 ^■ -tetrachloro- -4,4*-dihydroxydiphenyl, 3,3 ^• ,5,5*-tetrachloro- -2,2'-dihydroxydiphenyl, 2,2 ^• ,6,6'-tetrachloro- -4,4'-dihydroxydiphenyl, 4,4'-bis((3-hydroxy)phenoxy)- -diphenyl, 4,4'-bis((4-hydroxy)phenox )-diphenyl, 2,2'-dihydroxy-1,1'-binaphthyl, and other dihydroxydiphenyls; 4,4'-dihydroxydiphenyl ether, 3,3' ,5,5 ^f -tetramethyl-4,4'-dihydroxydiphenyl ether, 3,3' ,5,5'-tetrachloro-4,4 ^• -hydroxydiphenyl ether, 4,4'-bis(p-hydroxyphenoxy)-diphenyl ether,

4,4'-bis(p-hydroxyphenyl isopropyl)-diphenyl ether, 4,4'-bis(p-hydroxyphenox )-benzene, 4,4'-bis(p-hydroxy¬ phenoxy)-diphenyl ether, 4,4'-bis(4(4-hydroxyphenoxy)- -phenyl sulfone)-diphenyl ether, and other dihydroxy- diphenyl ethers; 4,4'-dihydroxydiphenyl sulfone,

3,3' ,5,5'-tetramethyl-4,4*-dihydroxydiphenyl sulfone,

_ C-/PI

3,3•5,5•-tetrachloro-4,4'-dihydroxydiphenyl sulfone, 4,4'-bis(p-hydroxyphenyl isopropyl)-diphenyl sulfone, 4,4'-bis((4-hydroxy)-phenoxy)-diphenyl sulfone, 4,4'-bis((3-hydroxy)-phenoxy)-diphenyl sulfone, 4,4'-bis(4-(4-hydroxyphenyl-isopropyl)-phenoxy)-diphenyl sulfone, 4, '-bis(4(4-hydroxy)diphenoxy)-diphenyl sulfone, and other diphenyl sulfones; 4,4'-dihydroxy¬ diphenyl methane, 4,4'-bis(p-hydroxyphenyl)-diphenyl methane, 2,2'-bis(p-hydroxyphenyl)-propane, 3,3' ,5,5'-tetramethyl-2,2'-bis(p-hydroxyphenyl)-propane, 3,3' ,5,5, ^■ -tetrachloro-2,2'-bis(p-hydroxyphenyl)-propane, 1,1-bis(p-hydroxyphenyl)-cyclohexane, bis-(2-hydroxy- -1-naphthyl)-methane, 1,2-bis(p-hydroxyphenyl)- -1,1,2,2-tetramethyl ethane, 4,4'-dihydroxybenzophenone, 4,4'-bis(4-hydroxy)phenoxy-benzophenone,

1,4-bis(p-hydroxyphenyl isopropyl)-benzene, phloroglucinol, pyrogallol, 2,2' ,5,5'-tetrahydroxy- -diphenyl sulfone, other dihydroxydiphenyl alkanes, and mixtures thereof.

Suitable cyanogen halides which can be employed to prepare the cyanate mixture precursor include, for example, cyanogen chloride, cyanogen bromide, mixtures thereof.

If desired, the method reported in Organic Synthesis, Vol. 61, page 35-37 (1983), published by John Wiley & Sons, may be used to generate the required amount of cyanogen halide in situ, although this is less preferred than using neat cyanogen halide.

Suitable base materials which can be employed to prepare the cyanate mixture precursor include both inorganic bases and tertiary amines, such as, for example, sodium hydroxide, potassium hydroxide,

O PI

triethyla ine, pyridine, lutidine, and mixtures thereof. The tertiary amines are most preferred as the base material.

Suitable trimerization catalysts which can be employed for conversion of the cyanate mixture to triazine functional oligomers include, for example, metal salts of carboxylic acids, such as, for example, lead octoate, zinc stearate,' zinc acetylacetonate, at concentrations of 0.001 to 5 percent. Most preferred catalysts are cobalt naphthenate and cobalt octoate, ^' mixtures thereof and the like. The aforementioned catalysts are also employed for co-oligomerization of the cyanate mixture with an epoxy resin to provide oligomers containing both triazine and oxazoline groups.

Suitable epoxy resins for co-oligomerization with the cyanate mixture are those represented by the following formulas:

wherein A, R', m ¹ and n are as herein before defined, R" is independently hydrogen or a hydrocarbyl group having from 1 to 3 carbon atoms, x has a value of from 0 to 4 and n" has a value of from 0 to 100, preferably from 0 to 5.

Although the co-oligomerization of the cyanate mixture with an epoxy resin provides both triazine and oxazoline functionality in the oligomer product, it is felt that other reactions may also be occurring. Unreacted phenolic groups may copolymerize with a portion of the epoxide groups of the epoxy resin during the co-oligomerization reaction. Unreacted phenolic groups may react with cyanate groups to form iminocarbonate linkages ^' which may in turn react with remaining epoxide groups.

Reaction to provide the cyanate mixture is usually conducted at a temperature of from -40°C to 60°C, preferably from -20°C to 25°C for from 10 minutes (600 s) to 120 minutes (7200 s), preferably ^" from 10 minutes (600 s) to 60 minutes (3600 s).

If desired, the reaction to provide the cyanate mixture can be conducted in the presence of an inert solvent reaction medium. Suitable such solvents include, for example, water, chlorinated hydrocarbons, ketones, and mixtures thereof.

The trimerization or co-oligomerization reactions are both usually conducted at a temperature of from 70°C to 250°C, preferably from 70°C to 200°C for a period of from 15 minutes (900 s) to 120 minutes (7200 s), preferably from 30 minutes (1800 s) to 75

minutes (4500 s). These reactions are preferably performed in the presence of the aforementioned catalyst(s).

Suitable epoxy resins for advancement reaction with the hydroxyaromatic oligomers containing triazine group(s) or triazine and oxazoline groups are represented by Formlas IV, V and VI above. The advancement reaction is optionally, although preferably, performed in the presence of 0.01 to 2.0 percent by weight of a suitable catalyst. Suitable catalysts include bases, basic acting materials, acids and the like.

Preferred catalysts are the quarternary ammonium salts and phosphonium salts. A most preferred catalyst is benzyltri ethy1ammonium chloride. Reaction times and temperatures vary depending on the composition of the epoxy resin reactant used; the amount and type of catalyst used, if any; the presence of inert solvent, if any. Typically, the advancement reaction when catalyzed is conducted at a temperature of from 50°C to 150°C, preferably from 90°C to 120°C for from 15 minutes (900 s) to 240 minutes (14400 s), preferably from 30 minutes (1800 s) to 90 minutes (5400 s) . Advancement reaction times and temperatures are generally longer and higher, respectively, for the non-catalyzed reaction.

Suitable curing agents and/or catalysts for curing and/or preparing epoxy resins are described in the Handbook of Epoxy Resins by Lee and Neville, McGraw-Hill, (1967), as well as U.S. Patents 3,477,990, 3,948,855 and 4,366,295. Preferred curing agents

and/or catalysts are aromatic amines, such as, for example, methylenedianiline.

The cured advanced epoxy resins of this invention possess improvements in one or more physical or mechanical properties such as tensile strength, flexural strength, percent elongation and/or heat distortion temperature. Furthermore, the invention allows for incorporation of triazine or both triazine and oxazoline groups into an epoxy resin without having to epoxidize (i.e., react with an epihalohydrin followed by dehydrohalogenation) the hydroxy aromatic oligomers containing triazine or triazine and oxazoline groups.

The epoxy resins of the present invention can be used to prepare castings, coatings, laminates, or encapsulations, and are especially suited for use in applications requiring high mechanical strength.

The following examples are illustrative of the invention, but are not to be construed as to limiting the scope thereof in any manner.

EXAMPLE 1

A. Preparation of Diphenol Cyanate Mixture

Cyanogen bromide ^' (1.10 mole, 116.52 grams) was added to a reactor containing a stirred solution of bisphenol A (2.00 moles, 456.60 grams) in acetone (1050 milliliters) cooled to -5°C under a nitrogen atmosphere. The stirred solution was allowed to equilibrate at -5°C. Triethylamine (1.00 mole, 101.19 grams) was then added to the reactor over a 17 minute (1020 s) period so as to maintain the reaction temperature at -2° to -5°C. After completion of the

triethylamine addition, the reactor was maintained at

-2° to 5°C for an additional 30 minutes (1800 s), followed by addition of the reaction product to chilled water (1.5 gallons, 5.7 liters) with agitation. After 5 minutes (300 s), the water and product mixture was subjected to multiple extractions with three 800 milliliter portions of methylene chloride. The combined methylene chloride extracts were sequentially washed with 500 milliliters of dilute 5% aqueous' hydrochloric acid, 1000 milliliters of water and then dried over anhydrous sodium sulfate. The dry methylene chloride extract was filtered and solvent removed by rotary evaporation under vacuum. The diphenol cyanate mixture was recovered (416.0 grams) as a light yellow colored solid at room temperature (25°C). Infrared spectrophotometric analysis demonstrated the presence of the nitrile groups as well as unreacted hydroxyl groups. Liquid chromatographic analysis demonstrated the presence of 56.00 area percent bisphenol A, 34.89 area percent bisphenol A monocyanate, and 9.11 area percent bisphenol A dicyanate.

B. Trimerization of Diphenol Cyanate Mixture

A portion of the diphenol cyanate mixture (415.0 grams) from A above and 6.0 percent cobalt naphthenate (0.10 percent by weight, 0.42 gram) were thoroughly mixed and placed in a glass tray. The tray was then placed in a forced-air, convection-type oven and maintained for 1.25 hours (4500 s) at 177°C. The hydroxyaromatic oligomers containing triazine groups were recovered in quantitative yield as a transparent, brittle solid at room temperature (25°C). The oligomers had a greenish-colored cast due to the catalyst. At the 177°C temperature, the oligomers were totally fluid. Infrared spectrophotometric analysis

demonstrated complete disappearance of the nitrile groups, appearance of the triazine groups, and the presence of unreacted hydroxyl groups.

C. Epoxy Resin Advancement with Hydroxyaromatic Oligomers _ Containing Triazine Groups

A portion (15.92 grams, 0.10 hydroxyl equivalent) of the hydroxyaromatic oligomers containing triazine groups from B above, a diglycidyl ether of bisphenol A (219.60 grams, 1.2 equiv. ) having an 0 epoxide equivalent weight (EEW) of 183 and 60 percent aqueous benzyltrimethylammonium chloride (0.236 gram) catalyst were added to a reactor and heated to 120°C with stirring under a nitrogen atmosphere. After 60 minutes (3600 s) at the 120°C reaction temperature, the 5 reactor was cooled and the epoxy resin advanced with oligomers containing triazine groups was recovered as a transparent, light yellow colored liquid. Epoxide titration revealed the resin to contain 18.28 percent epoxide (235.23 EEW).

0 . D. Curing of Epoxy Resin Advanced with Hydroxyaromatic Oligomers Containing Triazine Groups

A portion (230.31 grams, 0.9791 epoxide equivalent) of the epoxy resin advanced with hydroxyaromatic oligomers containing triazine groups 5 from C above was heated to 75°C and blended with methylenedianiline (48.47 grams, 0.2448 mole) which also was heated to 75°C. This mixture was used to prepare a clear, unfilled 1/8 inch (0.3175 cm) casting for heat distortion temperature (264 psi, 1820 kPa), 0 tensile and flexural strength, flexural modulus, percent elongation and average Barcol Hardness (934-1 scale) determinations. The casting was cured at 75°C for 2.0 hours (7200 s),- followed by post curing at

^{O τ}

125°C for 2.0 hours (7200 s), 175°C for 2.0 hours (7200 s), then 200°C for 2.0 hours (7200 s). Mechanical properties of tensile (8) and flexural (6) test pieces were determined using an Instron machine with standard test methods (ASTM D-638 and D-790). Heat distortion temperature of clear casting test pieces (2) was determined using an Aminco Plastic Deflection Test (American Instrument Co. ) with standard test methods (ASTM D-648 modified). The results are given in Table I.

EXAMPLE 2

A. Epoxy Resin Advancement with Hydroxyaromatic Oligomers Containing Triazine Groups

A portion (31.84 grams, 0.20 hydroxyl equiv. ) of the hydroxyaromatic oligomers containing triazine groups from Example 1-B, a diglycidyl ether of bisphenol A (219.60 grams, 1.2 equiv.) having an EEW of

183 and 60 percent aqueous benzyltrimethylammonium chloride (0.251 gram) catalyst were added to a reactor and heated to 120°C with stirring under a nitrogen atmosphere. After 60 minutes (3600 s) at the 120°C reaction temperature, the reactor was cooled and the epoxy resin advanced with oligomers containing triazine groups was recovered as a transparent yellow colored liquid. Epoxide titration revealed the resin to contain 15.38 percent epoxide (279.58 EEW).

B. Curing of Epoxy Resin Advanced with Hydroxyaromatic Oligomers Containing Triazine Groups

A portion (241.13 grams, 0.8374 epoxide equiv. ) of the epoxy resin advanced with hydroxyaromatic oligomers containing triazine groups from A above was heated to 100°C and blended with methylenedianiline

(41.45 grams, 0.2093 mole) which also was heated to

OMP

100°C. This mixture was used to prepare a clear, unfilled casting using the method of Example 1-D. Mechanical properties were evaluated using the method of Example 1-D. The results are given in Table I.

EXAMPLE 3

A. Preparation of Diphenol Cyanate Mixture

Cyanogen bromide (1.10 mole, 116.52 grams) was added to a reactor containing a stirred solution of bisphenol A (2.00 moles, 456.60 grams) in acetone (1050 milliliters) cooled to -5°C under a nitrogen atmosphere. The stirred solution was allowed to equilibrate at -5°C. Triethylamine (1.00 mole, 101.19 grams) was added to the reactor over an 18 minute (1080 s) period so as to maintain the reaction temperature at 0° to -5°C. After completion of the triethylamine addition, the reactor was maintained at 0° to 5°C for an additional 30 minutes (1800 s) followed by addition of the reaction product to chilled water (1.5 gallons, 5.7 1) with agitation. After 5 minutes (300 s), the water and product mixture was subjected to multiple extractions with three 800 milliliter portions of methylene chloride. The combined methylene chloride extracts were sequentially washed with 500 milliliters of dilute hydrochloric acid (5 percent aqueous), 1000 milliliters of water and then dried over anhydrous sodium sulfate. The dry methylene chloride extract was filtered and solvent removed by rotary evaporation under vacuum. The resultant diphenol cyanate mixture was recovered (398.0 grams) as a light yellow colored solid at room temperature (25°C) . Infrared spectrophotometric analysis demonstrated the presence of the nitrile groups as well as unreacted hydroxyl groups. Liquid chromatographic analysis demonstrated the presence of 57.11 area

percent bisphenol A, 35.33 area percent bisphenol A monocyanate, and 7.56 area percent bisphenol A dicyanate.

B. Co-oligomerization of Diphenol Cyanate Mixture and ^• an Epoxy Resin

A portion of the diphenol cyanate mixture

(388.7 grams) from A above, an epoxy resin (25.64 grams), and 6.0 percent cobalt naphthenate (0.10 percent by weight, 0.41 gram) were thoroughly mixed and placed in a glass tray. The epoxy resin had an epoxide equivalent weight (EEW) of 340.4 and was prepared by reaction of a diglycidyl ether of bisphenol A (EEW = 183, 0.8 equiv., 146.4 grams) with bisphenol A (0.4 equiv., 45.66 grams) and benzyltrime hy1ammonium chloride catalyst (60 percent, aqueous, 0.19 gram) at 120°C for 50 minutes (3000 s). The tray was then placed in a forced-air, convection-type oven and maintained for 1.25 hours (4500 s) at 177°C. The hydroxyaromatic co-oligomerization product containing triazine and oxazoline groups was recovered in quantitative yield as a transparent, light amber-colored, brittle solid at room temperature (25°C). Infrared spectrophotometric analysis demonstrated complete disappearance of the nitrile groups, appearance of the triazine groups, appearance of the oxazoline groups and the presence of unreacted hydroxyl groups.

C. Epoxy Resin Advancement with Hydroxyaromatic Oligomers Containing Triazine and Oxazoline Groups A portion (16.62 grams, 0.10 hydroxyl equiv.) of the hydroxyaromatic oligomers containing triazine and oxazoline groups from B above, a diglycidyl ether of bisphenol A (219.60 grams, 1.2 equiv.) having an EEW

__OM?I ^"

of 183 and 60 percent aqueous benzyltrimethylammonium chloride (0.236 gram) catalyst were added to a reactor and heated to 120°C with stirring under a nitrogen atmosphere. After 60 minutes (3600 s) at the 120°C reaction temperature, the reactor was cooled and the epoxy resin advanced with oligomers containing triazine and oxazoline groups was recovered as a transparent light yellow colored liquid. Epoxide titration revealed the resin to contain 18.28 percent epoxide (235.23 EEW).

D. Curing of Epoxy Resin Advanced with Hydroxyaromatic Oligomers Containing Triazine and Oxazoline Groups

A portion (231.64 grams, 0.9847 epoxide equiv. ) of the epoxy resin advanced with hydroxyaromatic oligomers containing triazine and oxazoline groups from C above was heated to 75°C and blended with methylenedianiline (48.75 grams, 0.2462 mole) which was also heated to 75°C. This mixture was used to prepare a clear, unfilled casting using the method of Example 1-D. Mechanical properties were evaluated using the method of Example 1-D. The results are given in Table I.

EXAMPLE 4

A. Epoxy Resin Advancement with Hydroxyaromatic Oligomers Containing Triazine and Oxazoline Groups

A portion (33.24 grams, 0.20 hydroxyl equiv.) of the hydroxyaromatic oligomers containing triazine and oxazoline groups from Example 3-B, a diglycidyl ether of bisphenol A (219.60 grams, 1.2 equiv.) having an EEW of 183 and 60 percent aqueous benzyltrimethyl-

-ammonium chloride (0.253 gram) catalyst were added to a reactor and heated to 120°C with stirring under a

nitrogen atmosphere. After 60 minutes (3600 s) at the 120°C reaction temperature, the reactor was cooled and the epoxy resin advanced with oligomers containing triazine and oxazoline groups was recovered as a transparent yellow colored liquid. Epoxide titration revealed the resin to contain 15.32 percent epoxide (280.68 EEW).

B. Curing of Epoxy Resin Advanced with Hydroxyaromatic Oligomers Containing Triazine and Oxazoline Groups A portion (238.64 grams, 0.8502 epoxide equiv. ) of the epoxy resin advanced with hydroxyaromatic oligomers containing triazine and oxazoline groups from A above was heated to 100°C and blended with methylene-dianiline (42.09 grams, 0.2126 mole) which was also heated to 100°C. This mixture was used to prepare a clear, unfilled casting using the method of Example 1-D. Mechanical properties were evaluated using the method of Example 1-D. The results are given in Table I.

COMPARATIVE EXPERIMENT A

A. Preparation of Advanced Epoxy Resin Free of Triazine and Oxazoline Groups

A diglycidyl ether of bisphenol A (292.80 grams, 1.6 equiv.) having an EEW of 183 was reacted with bisphenol A (30.44 grams, 0.2666 equiv.) to provide an advanced epoxy resin. The diglycidyl ether of bisphenol A, bisphenol A and 60 percent aqueous benzyltrimethylammonium chloride (0.32 gram) catalyst were added to a reactor and heated to 120°C with stirring under a nitrogen atmosphere. After 60 minutes (3600 s) at the 120°C reaction temperature, the reactor was cooled and the epoxy resin advanced with bisphenol A was recovered as a transparent, light yellow colored

C2-.PI

liquid. Epoxide titration revealed the resin to contain 17.04 percent epoxide (252.35 EEW).

B. Curing of the Advanced Epoxy Resin Free of Triazine and Oxazoline Groups A portion (250.0 grams, 0.9907 epoxide equiv. ) of the epoxy resin advanced with bisphenol A from A above was heated to 75°C and blended with methylenedianiline (49.04 grams, 0.2477 mole) which was also heated to 75°C. This mixture was used to prepare a clear, unfilled casting using the method of Example

1-D. Mechanical properties were evaluated using the method of Example 1-D. The results are given in Table

I.

EXAMPLE 5 A. Epoxy Resin Advancement with Hydroxyaromatic Oligomers Containing Triazine Groups

A portion (46.42 grams, 0.30 hydroxyl equiv.) of hydroxyaromatic oligomers containing triazine groups prepared in the manner of Example 1-A and 1-B, a diglycidyl ether of bisphenol A (219.60 grams, 1.2 equiv. ) having an EEW of 183 and 60 percent aqueous benzyltrimethylammonium chloride (0.27 gram) catalyst were added to a reactor and heated to 120°C with stirring under a nitrogen atmosphere. After 60 minutes (3600 s) at the 120°C reaction temperature, the reactor was cooled and the epoxy resin advanced with oligomers containing triazine groups was recovered as a transparent yellow colored solid. Epoxide titration revealed the resin to contain 12.73 percent epoxide groups (337.78 EEW).

B. Curing of Epoxy Resin Advanced with Hydroxyaromatic Oligomers Containing Triazine Groups

A portion (252.60 grams, 0.7478 epoxide equiv. ) of the epoxy resin advanced with hydroxyaromatic oligomers containing triazine groups from A above was heated to 100°C and blended with methylenedianiline (37.02 grams, 0.1870 mole) which was also heated to 100°C. This mixture was used to prepare a clear, unfilled casting using the method of Example 1-D. Mechanical properties were evaluated using the method of Example 1-D. The results are given in

Table I.