22SHPP0066-WO-PCT (SS290012PCT) METHOD OF CONVERTING POLY(ETHYLENE TEREPHTHALATE) TO TEREPHTHALIC ACID BACKGROUND OF THE INVENTION [0001] Poly(ethylene terephthalate) (PET) is the most commonly recycled plastic. Many processes exist to convert poly(ethylene terephthalate) to its component monomers, ethylene glycol and terephthalic acid (or terephthalic acid esters), so that they can be reused. Some methods utilize glycolysis with ethylene glycol to yield bis(hydroxyethyl) terephthalate and additional ethylene glycol. See, e.g., S. Ugduler et al., “Towards closed-loop recycling of multilayer and coloured PET plastic waste by alkaline hydrolysis,” Green Chemistry, 2020, volume 22, pages 5376–5394 (Table 2, citing R. Lopez-Fonseca et al., “A kinetic study of the depolymerization of poly(ethylene terephthalate) by phase transfer catalysed alkaline hydrolysis,” Journal of Chemical Technology and Biotechnology, 2009, volume 84, pages 92- 99). However, such processes either fail to approach complete depolymerization of PET in a reasonable time or require high pressures and/or high temperatures to do so. Other methods utilize base-catalyzed hydrolysis to yield ethylene glycol and salts of terephthalic acid. See, e.g., J. Harvie et al., US Patent No.5,886,057, issued 23 March 1999; and S. Ugduler et al., “Towards closed-loop recycling of multilayer and coloured PET plastic waste by alkaline hydrolysis,” Green Chemistry, 2020, volume 22, pages 5376–5394. But such methods require either high pressures or organic solvents other than ethylene glycol. Still other methods utilize a combination of glycolysis and hydrolysis. See, e.g., J. Harvie et al., US Patent No.5,886,057, issued 23 March 1999; and Czechoslovakia Patent No. CZ 299244 B6 of Sirek et al., published 28 May 2008. But these methods, too, require high pressures and/or high temperatures in the glycolysis, hydrolysis, or combined glycolysis/hydrolysis steps. There is therefore a desire for a method of depolymerizing PET to terephthalic acid in high yield, the method being conducted at temperatures less than the 260 °C melting point of poly(ethylene terephthalate) and at ambient or near-ambient pressure. Preferably, the method would also avoid the use of organic solvents other than ethylene glycol. BRIEF SUMMARY OF EMBODIMENTS OF THE INVENTION [0002] One embodiment is a method of converting poly(ethylene terephthalate) to terephthalic acid, comprising: reacting poly(ethylene terephthalate) with ethylene glycol in the presence of a catalyst at a temperature of 150 to 230 °C and an absolute pressure of 90 to 200 kilopascals for a time effective to yield a first reaction mixture comprising at least partially 22SHPP0066-WO-PCT (SS290012PCT) depolymerized poly(ethylene terephthalate); wherein the catalyst is selected from the group consisting of acetate salts of copper, aluminum, tin, nickel, iron, lead, manganese, titanium, and antimony; chloride and bromide salts of copper, aluminum, tin, nickel, iron, lead, manganese, zinc, titanium, and antimony; ionic liquids consisting of a cation and an anion, wherein the cation is 1-ethyl-3-methylimidazolium, 1-butyl-3-methylimidazolium, 1-octyl-3 methylimidazolium, 1-decyl-3-methylimidazolium, 1-dodecyl-3-methylimidazolium, 1-butyl- 2,3-dimethylimidazolium, 1,3-di(N,N-dimethylaminoethyl)-2-methylimidazolium, 4-methyl-N- butyl-pyridinium, N-octylpyridinium, tetraethylammonium, or tetrabutylammonium, and the anion is tetrafluoroborate (BF ₄ -), hexafluorophosphate (PF ₆ -), bis(trifluoromethanesulfonyl)amidate ((CF ₃ SO ₂ ) ₂ N-), trifluoromethanesulfonate, dicyanamide, hydrogen sulfate (HSO ₄ -), ethyl sulfate (CH ₃ CH ₂ SO ₄ -), or tetrachloroferrate (FeCl ₄ -); (C ₁ -C ₆ )- alkoxide salts of copper, aluminum, tin, nickel, iron, lead, manganese, zinc, titanium, or antimony; hydrotalcites; zeolites; montmorillonites; lipases; and combinations thereof; adding an alkali metal hydroxide to the first reaction mixture to yield a second reaction mixture, and maintaining the second reaction mixture at a temperature of 35 to 100°C and an absolute pressure of 90 to 200 kilopascals for a time effective to yield a third reaction mixture comprising ethylene glycol and an alkali metal salt of terephthalic acid; optionally, contacting the third reaction mixture with a decolorizing agent that is insoluble in the third reaction mixture to yield a fourth reaction mixture, and filtering the fourth reaction mixture to yield a filtrate; and adding an aqueous solution of an inorganic acid to the filtrate or the third reaction mixture to produce a fifth reaction mixture comprising a precipitate comprising terephthalic acid. [0003] This and other embodiments are described in detail below. DETAILED DESCRIPTION OF THE INVENTION [0004] The present inventors have determined that high yields of high purity terephthalic acid are produced by a method that includes a glycolysis step conducted in the presence of a specific catalyst, followed by a hydrolysis step and an acidification step, each step being conducted at ambient or near-ambient pressure. With the method, it is possible to avoid the use of organic solvents other than ethylene glycol. [0005] Thus, one embodiment is a method of converting poly(ethylene terephthalate) to terephthalic acid, comprising: reacting poly(ethylene terephthalate) with ethylene glycol in the presence of a catalyst at a temperature of 150 to 230 °C and an absolute pressure of 90 to 200 kilopascals for a time effective to yield a first reaction mixture comprising at least partially depolymerized poly(ethylene terephthalate); wherein the catalyst is selected from the group 22SHPP0066-WO-PCT (SS290012PCT) consisting of acetate salts of copper, aluminum, tin, nickel, iron, lead, manganese, titanium, and antimony; chloride and bromide salts of copper, aluminum, tin, nickel, iron, lead, manganese, zinc, titanium, and antimony; ionic liquids consisting of a cation and an anion, wherein the cation is 1-ethyl-3-methylimidazolium, 1-butyl-3-methylimidazolium, 1-octyl-3 methylimidazolium, 1-decyl-3-methylimidazolium, 1-dodecyl-3-methylimidazolium, 1-butyl- 2,3-dimethylimidazolium, 1,3-di(N,N-dimethylaminoethyl)-2-methylimidazolium, 4-methyl-N- butyl-pyridinium, N-octylpyridinium, tetraethylammonium, or tetrabutylammonium, and the anion is tetrafluoroborate (BF4-), hexafluorophosphate (PF6-), bis(trifluoromethanesulfonyl)amidate ((CF ₃ SO ₂ ) ₂ N-), trifluoromethanesulfonate, dicyanamide, hydrogen sulfate (HSO ₄ -), ethyl sulfate (CH ₃ CH ₂ SO ₄ -), or tetrachloroferrate (FeCl ₄ -); (C ₁ -C ₆ )- alkoxide salts of copper, aluminum, tin, nickel, iron, lead, manganese, zinc, titanium, or antimony; hydrotalcites; zeolites; montmorillonites; lipases; and combinations thereof; adding an alkali metal hydroxide to the first reaction mixture to yield a second reaction mixture, and maintaining the second reaction mixture at a temperature of 35 to 100°C and an absolute pressure of 90 to 200 kilopascals for a time effective to yield a third reaction mixture comprising ethylene glycol and an alkali metal salt of terephthalic acid; optionally, contacting the third reaction mixture with a decolorizing agent that is insoluble in the third reaction mixture to yield a fourth reaction mixture, and filtering the fourth reaction mixture to yield a filtrate; and adding an aqueous solution of an inorganic acid to the filtrate or the third reaction mixture to produce a fifth reaction mixture comprising a precipitate comprising terephthalic acid. [0006] The method includes a glycolysis step, in which poly(ethylene terephthalate) is reacted with ethylene glycol in the presence of a catalyst to effect at least partial depolymerization of the poly(ethylene terephthalate). The poly(ethylene terephthalate) starting material is preferably recycled poly(ethylene terephthalate) from household and/or industrial sources. The poly(ethylene terephthalate) can be clear or colored. In some embodiments, the recycled poly(ethylene terephthalate) is rinsed with water, dilute aqueous alkali, or both prior to the glycolysis step. In some embodiments, prior to the glycolysis step the poly(ethylene terephthalate) is chipped to produce irregularly shaped flakes having a major dimension of 0.05 to 5 centimeters, or 0.1 to 2 centimeters, as determined by optical microscopy. In a very specific embodiment of pre-treatment, the poly(ethylene terephthalate) starting material is recycled poly(ethylene terephthalate) bottles from which any separable labels have been removed, and the bottles are then water washed prior to being chipped into flakes having a major dimension of 0.05 to 5 centimeters, or 0.1 to 2 centimeters, as determined by optical microscopy, and the flakes are washed with dilute aqueous alkali then water before being used in the glycolysis step. 22SHPP0066-WO-PCT (SS290012PCT) [0007] In the glycolysis step, poly(ethylene terephthalate) is reacted with ethylene glycol in the presence of a catalyst. In some embodiments, reacting poly(ethylene terephthalate) with ethylene glycol comprises reacting 1 to 3 moles ethylene glycol per mole of ethylene terephthalate units in the poly(ethylene terephthalate). In other words, the molar ratio of ethylene glycol to ethylene terephthalate units in the poly(ethylene terephthalate) can be 1:1 to 3:1. Within this range, the molar ratio of ethylene glycol to ethylene terephthalate units in the poly(ethylene terephthalate) can be 1.5:1 to 3:1, or 1.5:1 to 2.5:1. [0008] The catalyst used in the glycolysis step is selected from the group consisting of acetate salts of copper, aluminum, tin, nickel, iron, lead, manganese, titanium, and antimony; chloride and bromide salts of copper, aluminum, tin, nickel, iron, lead, manganese, zinc, titanium, and antimony; ionic liquids consisting of a cation and an anion, wherein the cation is 1- ethyl-3-methylimidazolium, 1-butyl-3-methylimidazolium, 1-octyl-3 methylimidazolium, 1- decyl-3-methylimidazolium, 1-dodecyl-3-methylimidazolium, 1-butyl-2,3-dimethylimidazolium, 1,3-di(N,N-dimethylaminoethyl)-2-methylimidazolium, 4-methyl-N-butyl-pyridinium, N-octylpyridinium, tetraethylammonium, or tetrabutylammonium, and the anion is tetrafluoroborate (BF ₄ -), hexafluorophosphate (PF ₆ -), bis(trifluoromethanesulfonyl)amidate ((CF ₃ SO ₂ ) ₂ N-), trifluoromethanesulfonate, dicyanamide, hydrogen sulfate (HSO ₄ -), ethyl sulfate (CH3CH2SO4-), or tetrachloroferrate (FeCl4-); (C1-C6)-alkoxide salts of copper, aluminum, tin, nickel, iron, lead, manganese, zinc, titanium, or antimony; hydrotalcites; zeolites; montmorillonites; lipases; and combinations thereof. [0009] In some embodiments, the catalyst is selected from the group consisting of chromium acetate (Cr2(O2CCH3)4; CAS Reg. No.14976-80-8), magnesium chloride (MgCl2, CAS Reg. No.7786-30-3), magnesium bromide (MgBr2, CAS Reg. No.7789-48-2), calcium chloride (CaCl2, CAS Reg. No.10043-52-4), strontium chloride (SrCl2, CAS Reg. No.10025- 70-4), zinc chloride (ZnCl2, CAS Reg. No.7646-85-7), zinc bromide (ZnBr2, CAS Reg. No. 7699-45-8), stannous chloride (SnCl2, CAS Reg. No.7772-99-8), aluminum chloride (AlCl3, CAS Reg. No.7446-70-0), ferric chloride (FeCl3, CAS Reg. No.7705-08-0), cobalt chloride (CoCl ₂ , CAS Reg. No.7646-79-9), 1-butyl-3-methylimidazolium bromide (CAS Reg. No. 85100-77-2), 1-butyl-3-methylimidazolium chloride (CAS Reg. No.79917-90-1), 1-butyl-3- methylimidazolium acetate (CAS Reg. No.284049-75-8), titanium isopropoxide (Ti(OCH(CH ₃ ) ₂ ) ₄ , CAS Reg. No.546-68-9), titanium isobutoxide (Ti(OCH ₂ C(CH ₃ ) ₂ ) ₄ , CAS Reg. No.5593-70-4), aluminum isopropoxide (Al(OCH(CH ₃ ) ₂ ) ₃ , CAS Reg. No.555-31-7), aluminum magnesium isopropoxide (Mg[Al(OCH(CH ₃ ) ₂ ) ₄ ] ₂ , CAS Reg. No.69207-83-6), tin(IV) isopropoxide (Sn(OCH(CH ₃ ) ₂ ) ₄ , CAS Reg. No.546-68-9), antimony(III) isopropoxide 22SHPP0066-WO-PCT (SS290012PCT) (Sb(OCH(CH3)2)3, CAS Reg. No.18770-47-3), magnesium aluminum hydroxycarbonate (Mg6Al2(CO3)(OH)16.4H2O, CAS Reg No.11097-59-9), the zeolite ZSM-5 (NanAlnSi96-nO192.16H2O (0<n<27); CAS Reg. No. 1318-02-1), montmorillonite K10 (CAS Reg. No.1318-93-0), lipase (CAS Reg. No.9001-62-1), and combinations thereof. [0010] In some embodiments, the catalyst is selected from the group consisting of magnesium chloride, titanium isopropoxide, 1-butyl-3-methylimidazolium bromide, magnesium aluminum hydroxycarbonate, ZSM-5, montmorillonite K10, and combinations thereof. [0011] In some embodiments, the catalyst is magnesium chloride (MgCl2, CAS Reg. No. 7786-30-3). [0012] In some embodiments, the catalyst is titanium isopropoxide (Ti(OCH(CH ₃ ) ₂ ) ₄ , CAS Reg. No.546-68-9). [0013] In some embodiments, the catalyst is titanium isobutoxide (Ti(OCH ₂ C(CH ₃ ) ₂ ) ₄ , CAS Reg. No.5593-70-4). [0014] In some embodiments, the catalyst is montmorillonite K10 (CAS Reg. No.1318- 93-0). [0015] In some embodiments, the catalyst is the zeolite ZSM-5 (Na _n Al _n Si _96-n O ₁₉₂ .16H ₂ O (0<n<27); CAS Reg. No.1318-02-1). [0016] In some embodiments, reacting poly(ethylene terephthalate) with ethylene glycol in the presence of a catalyst comprises reacting 100 parts by weight poly(ethylene terephthalate) in the presence of 0.025 to 10 parts by weight catalyst. Within the range of 0.025 to 10 parts by weight, the catalyst amount can be 0.05 to 8 parts by weight, or 0.05 to 0.6 parts by weight, per 100 parts by weight poly(ethylene terephthalate). [0017] In some embodiments, reacting poly(ethylene terephthalate) with ethylene glycol in the presence of a catalyst comprises reacting 100 parts by weight poly(ethylene terephthalate) in the presence of 0.025 to 0.4 parts by weight catalyst. Within the range of 0.025 to 0.4 parts by weight, the catalyst amount can be 0.05 to 0.2 parts by weight, or 0.05 to 0.15 parts by weight, per 100 parts by weight poly(ethylene terephthalate). [0018] The reaction of poly(ethylene terephthalate) with ethylene glycol in the presence of the catalyst is conducted at a temperature of 150 to 230 °C. Within this range, the temperature can be 150 to 210 °C, 160 to 200 °C, or 170 to 200 °C, or 180 to 230 °C, or 180 to 200 °C, or 185 to 200 °C. The reaction is conducted at an absolute pressure of 90 to 200 kilopascals. Within this range, the absolute pressure can be 90 to 150 kilopascals, or 90 to 110 kilopascals. It is an important advantage of the present method that the glycolysis step can be conducted at ambient or near-ambient pressure. The reaction is conducted for a time effective to 22SHPP0066-WO-PCT (SS290012PCT) yield a first reaction mixture comprising at least partially depolymerized poly(ethylene terephthalate). The extent of depolymerization can be determined by analyzing the first reaction mixture by gel permeation chromatography with polystyrene standards to determine the weight average molecular weight of the partially depolymerized poly(ethylene terephthalate). In some embodiments, the at least partially depolymerized poly(ethylene terephthalate) has a weight average molecular weight of 500 to 10,000 grams/mole, determined by gel permeation chromatography using polystyrene standards. Within the range of 500 to 10,000 grams/mole, the weight average molecular weight of the at least partially depolymerized poly(ethylene terephthalate) can be 500 to 5,000 grams/mole, or 500 to 2,000 grams/mole. These values can be compared to the weight average molecular weight of the poly(ethylene terephthalate) starting material, which is typically on the order of 60,000 grams/mole, and the molecular weight of the complete glycolysis product, bis(hydroxyethyl) terephthalate, which is about 254 grams/mole. [0019] In some embodiments, the glycolysis reaction is conducted for 1.5 to 20 hours. Within this range, the glycolysis reaction time can be 1.5 to 15 hours, 1.5 to 12 hours, 1 to 6 hours, or 1.5 to 6 hours, or 2 to 5 hours. [0020] In a very specific embodiment of the glycolysis step, reacting poly(ethylene terephthalate) with ethylene glycol in the presence of catalyst is conducted at a temperature of 180 to 230 °C and an absolute pressure of 90 to 110 kilopascals, for a time of 1.5 to 20 hours. [0021] In another very specific embodiment of the glycolysis step, reacting poly(ethylene terephthalate) with ethylene glycol in the presence of catalyst is conducted at a temperature of 180 to 230 °C and an absolute pressure of 90 to 110 kilopascals, for a time of 1.5 to 6 hours. [0022] In some embodiments, the glycolysis step comprises little or no hydrolysis. Specifically, in these embodiments, reacting poly(ethylene terephthalate) with ethylene glycol in the presence of catalyst is conducted in the presence of 0 to 1 parts by weight water, based on 100 parts by weight of the poly(ethylene terephthalate). Within the range of 0 to 1 parts by weight, the water amount can be 0 to 0.5 parts by weight, or 0 to 0.1 parts by weight, or zero parts by weight per 100 parts by weight of the poly(ethylene terephthalate). [0023] In addition to the glycolysis step, the method includes a hydrolysis step that follows the glycolysis step. The hydrolysis step can immediately follow the glycolysis step, or the hydrolysis step can follow one or more intermediate steps between the glycolysis step and the hydrolysis step. In the hydrolysis step, an alkali metal hydroxide is added to the first reaction mixture to yield a second reaction mixture, and the second reaction mixture is maintained at a temperature of 35 to 100 °C and an absolute pressure of 90 to 200 kilopascals for 22SHPP0066-WO-PCT (SS290012PCT) a time effective to yield a third reaction mixture comprising ethylene glycol and an alkali metal salt of terephthalic acid. Within the range of 35 to 100 °C, the temperature of the hydrolysis step can be 35 to 90 °C, or 35 to 70 °C, or 35 to 60 °C, or 40 to 90 °C, or 40 to 70 °C, or 40 to 60 °C. Within the range of 90 to 200 kilopascals, the absolute pressure of the hydrolysis step can be 90 to 150 kilopascals, or 90 to 110 kilopascals. Suitable alkali metal hydroxides include lithium hydroxide, sodium hydroxide, potassium hydroxide, and combinations thereof. In some embodiments, the alkali metal hydroxide comprises sodium hydroxide. In some embodiments, adding the alkali metal hydroxide to the first reaction mixture comprises adding 2 to 5 moles of the alkali metal hydroxide, based on 1 mole of ethylene terephthalate units in the poly(ethylene terephthalate) starting material. Within this range, the moles of alkali metal hydroxide can be 2 to 4 moles, or 2.5 to 3.5 moles, based on 1 mole of ethylene terephthalate units in the poly(ethylene terephthalate). The hydrolysis step is conducted for a time effective to yield a third reaction mixture comprising ethylene glycol and an alkali metal salt of terephthalic acid. In some embodiments, hydrolysis step reaction time is 0.25 to 4 hours, or 0.5 to 2 hours, or 0.5 to 1.5 hours. In a very specific embodiment of the hydrolysis step, the second reaction mixture is maintained at a temperature of 35 to 60 °C and a pressure of 90 to 110 kilopascals for a time of 0.5 to 2 hours to yield the third reaction mixture. [0024] The method optionally comprises a decolorizing step, which is particularly useful when the poly(ethylene terephthalate) starting material includes colored material (e.g., colored poly(ethylene terephthalate) bottles). The decolorizing step comprises contacting the third reaction mixture with a decolorizing agent that is insoluble in the third reaction mixture to yield a fourth reaction mixture, and filtering the fourth reaction mixture to yield a filtrate. Suitable decolorizing agents include activated carbon, alumina, silica, and combinations thereof. In some embodiments, the decolorizing agent comprises activated carbon. In some embodiments, the decolorizing agent is used in an amount of 1 to 100 parts by weight per 100 parts by weight poly(ethylene terephthalate). Within this range, the decolorizing agent amount can be 2 to 50 parts by weight, or 5 to 20 parts by weight, per 100 parts by weight poly(ethylene terephthalate) starting material. In a very specific embodiment of the decolorizing step, the second reaction mixture is contacted with 5 to 20 parts by weight activated carbon per 100 parts by weight poly(ethylene terephthalate). [0025] In addition to the glycolysis step, the hydrolysis step, and the optional decolorizing step, the method comprises an acidification step. In the acidification step, an aqueous solution of an inorganic acid is added to the filtrate (if the decolorizing step was conducted) or to the third reaction mixture (if the decolorizing step was not conducted) to 22SHPP0066-WO-PCT (SS290012PCT) produce a fifth reaction mixture comprising a precipitate comprising terephthalic acid. Suitable inorganic acids include hydrochloric acid, sulfuric acid, and combinations thereof. In some embodiments, the inorganic acid comprises hydrochloric acid. The amount of inorganic acid used in an amount effective to reduce the pH of the solution to which it is added to a value less than or equal to 2 (the pKa values of terephthalic acid are approximately 3.5 and 4.8). Within this limit, the amount of inorganic acid used can be an amount effective to reduce the pH of the solution to which it is added to a value of 1 to 2, or a value of 1.5 to 2. [0026] The method can, optionally, further comprise isolating the precipitate from the fifth reaction mixture. In some embodiments, the method further comprises filtering the fifth reaction mixture to separate the precipitate, washing the separated precipitate, and drying the washed and separated precipitate. Terephthalic acid yields of greater than 90 mole percent, and in some cases greater than 95 mole percent can be achieved, wherein mole percent values are based on moles of ethylene terephthalate units in the poly(ethylene terephthalate) starting material. In some embodiments, the yield of isolated terephthalic acid is 92 to 98 mole percent, or 93 to 97 mole percent, based on moles of ethylene terephthalate units in the poly(ethylene terephthalate) starting material. The purity of the isolated terephthalic acid can be greater than 99.5 percent, based on 100 percent total peak area in a 254 nanometer absorbance chromatogram derived from high performance liquid chromatography. In some embodiments, the purity of the isolated terephthalic acid is 95 to 99.7 percent, or 98 to 99.7 percent, or 99 to 99.7 percent, based on 100 percent total peak area in a 254 nanometer absorbance chromatogram derived from high performance liquid chromatography. The only significant impurity in the isolated terephthalic acid is isophthalic acid, which is typically present in small amounts as a comonomer with terephthalic acid in the poly(ethylene terephthalate) starting material. The isophthalic acid is typically present in an amount of less than or equal to 0.5 percent, based on 100 percent total peak area in a 254 nanometer absorbance chromatogram derived from high performance liquid chromatography. [0027] In some embodiments of the method, ethylene glycol is separated from the first reaction mixture before an alkali metal hydroxide is added to the first reaction mixture. In some embodiments of the method, ethylene glycol is not separated from the first reaction mixture before an alkali metal hydroxide is added to the first reaction mixture. In still other embodiments, ethylene glycol is separated from the filtrate (if a decolorizing step is conducted) or the fifth reaction mixture (if a decolorizing step is not conducted). [0028] In some embodiments, the method excludes a transesterification reaction between the glycolysis step and the hydrolysis step. In some embodiments, the method does not employ 22SHPP0066-WO-PCT (SS290012PCT) an organic solvent other than ethylene glycol (e.g., it does not employ ethanol). In some embodiments, the method does not employ an aromatic hydrocarbon solvent. [0029] In a very specific embodiment of the method, the reacting poly(ethylene terephthalate) with ethylene glycol comprises reacting 100 parts by weight poly(ethylene terephthalate) with 50 to 80 parts by weight ethylene glycol; the reacting poly(ethylene terephthalate) with ethylene glycol in the presence of a catalyst comprises reacting 100 parts by weight poly(ethylene terephthalate) in the presence of 0.025 to 0.4 parts by weight of a catalyst selected from the group consisting of titanium (IV) isopropoxide, titanium (IV) isobutoxide, and combinations thereof; the reacting poly(ethylene terephthalate) with ethylene glycol in the presence of catalyst is conducted at a temperature of 180 to 230 °C and an absolute pressure of 90 to 110 kilopascals, for a time of 1.5 to 6 hours; the reacting poly(ethylene terephthalate) with ethylene glycol in the presence of catalyst is conducted in the presence of 0 to 0.1 parts by weight water, based on 100 parts by weight of the poly(ethylene terephthalate); the adding an alkali metal hydroxide to the first reaction mixture comprises adding 1.5 to 5 moles of the alkali metal hydroxide, based on 1 mole of ethylene terephthalate units in the poly(ethylene terephthalate); and the second reaction mixture is maintained at a temperature of 35 to 60 °C and a pressure of 90 to 110 kilopascals, for a time of 0.5 to 2 hours to yield the third reaction mixture. [0030] In some embodiments, the method further comprises isolating the precipitate from the fifth reaction mixture, and using the isolated precipitate in a reaction to form a product selected from the group consisting of dimethyl terephthalate, dioctyl terephthalate, bis(hydroxyethyl) terephthalate, poly(ethylene terephthalate), glycol-modified poly(ethylene terephthalate), poly(butylene terephthalate), poly(butylene adipate-co-terephthalate),^ poly(trimethylene terephthalate), poly(cyclohexylenedimethylene terephthalate), glycol- modified poly(cyclohexylenedimethylene terephthalate), poly(cyclohexylenedimethylene terephthalate-co-isophthalate), poly(hexamethylene terephthalamide), poly(ethylene terephthalamide), poly(butylene terephthalamide), poly(2-methylpentamethylene terephthalamide), and poly(para-phenylene terephthalamide). [0031] All ranges disclosed herein are inclusive of the endpoints, and the endpoints are independently combinable with each other. Each range disclosed herein constitutes a disclosure of any point or sub-range lying within the disclosed range. [0032] The invention includes at least the following aspects. [0033] Aspect 1: A method of converting poly(ethylene terephthalate) to terephthalic acid, comprising: reacting poly(ethylene terephthalate) with ethylene glycol in the presence of a 22SHPP0066-WO-PCT (SS290012PCT) catalyst at a temperature of 150 to 230 °C and an absolute pressure of 90 to 200 kilopascals for a time effective to yield a first reaction mixture comprising at least partially depolymerized poly(ethylene terephthalate); wherein the catalyst is selected from the group consisting of acetate salts of copper, aluminum, tin, nickel, iron, lead, manganese, titanium, and antimony; chloride and bromide salts of copper, aluminum, tin, nickel, iron, lead, manganese, zinc, titanium, and antimony; ionic liquids consisting of a cation and an anion, wherein the cation is 1-ethyl-3- methylimidazolium, 1-butyl-3-methylimidazolium, 1-octyl-3 methylimidazolium, 1-decyl-3- methylimidazolium, 1-dodecyl-3-methylimidazolium, 1-butyl-2,3-dimethylimidazolium, 1,3- di(N,N-dimethylaminoethyl)-2-methylimidazolium, 4-methyl-N-butyl-pyridinium, N-octylpyridinium, tetraethylammonium, or tetrabutylammonium, and the anion is tetrafluoroborate, hexafluorophosphate, bis(trifluoromethanesulfonyl)amidate, trifluoromethanesulfonate, dicyanamide, hydrogen sulfate, ethyl sulfate, or tetrachloroferrate; (C ₁ -C ₆ )-alkoxide salts of copper, aluminum, tin, nickel, iron, lead, manganese, zinc, titanium, or antimony; hydrotalcites; zeolites; montmorillonites; lipases; and combinations thereof; adding an alkali metal hydroxide to the first reaction mixture to yield a second reaction mixture, and maintaining the second reaction mixture at a temperature of 35 to 100°C and an absolute pressure of 90 to 200 kilopascals for a time effective to yield a third reaction mixture comprising ethylene glycol and an alkali metal salt of terephthalic acid; optionally, contacting the third reaction mixture with a decolorizing agent that is insoluble in the third reaction mixture to yield a fourth reaction mixture, and filtering the fourth reaction mixture to yield a filtrate; and adding an aqueous solution of an inorganic acid to the filtrate or the third reaction mixture to produce a fifth reaction mixture comprising a precipitate comprising terephthalic acid. [0034] Aspect 2: The method of aspect 1, wherein the catalyst is selected from the group consisting of chromium acetate, magnesium chloride, magnesium bromide, calcium chloride, strontium chloride, zinc chloride, zinc bromide, stannous chloride, aluminum chloride, ferric chloride, cobalt chloride, 1-butyl-3-methylimidazolium bromide, 1-butyl-3-methylimidazolium chloride, 1-butyl-3-methylimidazolium acetate, titanium (IV) isopropoxide, titanium (IV) isobutoxide, aluminum (III) isopropoxide, aluminum magnesium isopropoxide, tin (IV) isopropoxide, antimony (III) isopropoxide, magnesium aluminum hydroxycarbonate, montmorillonite K10, ZSM-5 (a zeolite), lipase, and combinations thereof. [0035] Aspect 3: The method of aspect 1 or 2, wherein the catalyst is selected from the group consisting of magnesium chloride, titanium (IV) isopropoxide, titanium (IV) isobutoxide, Montmorillonite K10, ZSM-5, and combinations thereof. [0036] Aspect 4: The method of aspect 1, wherein the catalyst is magnesium chloride. 22SHPP0066-WO-PCT (SS290012PCT) [0037] Aspect 5: The method of aspect 1, wherein the catalyst is titanium (IV) isopropoxide. [0038] Aspect 6: The method of aspect 1, wherein the catalyst is titanium (IV) isobutoxide. [0039] Aspect 7: The method of aspect 1, wherein the catalyst is Montmorillonite K10. [0040] Aspect 8: The method of aspect 1, wherein the catalyst is the zeolite ZSM-5. [0041] Aspect 9: The method of any one of aspects 1-8, wherein the reacting poly(ethylene terephthalate) with ethylene glycol in the presence of a catalyst comprises reacting 100 parts by weight poly(ethylene terephthalate) in the presence of 0.025 to 0.4 parts by weight of the catalyst. [0042] Aspect 10: The method of any one of aspects 1-9, wherein the reacting poly(ethylene terephthalate) with ethylene glycol in the presence of a catalyst is conducted at a temperature of 180 to 230 °C and an absolute pressure of 90 to 110 kilopascals, for a time of 1.5 to 20 hours. [0043] Aspect 11: The method of any one of aspects 1-9, wherein the reacting poly(ethylene terephthalate) with ethylene glycol in the presence of a catalyst is conducted at a temperature of 180 to 230 °C and an absolute pressure of 90 to 110 kilopascals, for a time of 1.5 to 6 hours. [0044] Aspect 12: The method of any one of aspects 1-11, wherein the at least partially depolymerized poly(ethylene terephthalate) has a weight average molecular weight of 500 to 10,000 grams/mole, determined by gel permeation chromatography using polystyrene standards. [0045] Aspect 13: The method of any one of aspects 1-12, wherein the reacting poly(ethylene terephthalate) with ethylene glycol in the presence of a catalyst is conducted in the presence of 0 to 1 parts by weight water, based on 100 parts by weight of the poly(ethylene terephthalate). [0046] Aspect 14: The method of any one of aspects 1-13, wherein the adding an alkali metal hydroxide to the first reaction mixture comprises adding 2 to 5 moles of the alkali metal hydroxide, based on 1 mole of ethylene terephthalate units in the poly(ethylene terephthalate). [0047] Aspect 15: The method of any one of aspects 1-14, wherein the second reaction mixture is maintained at a temperature of 35 to 60 °C and a pressure of 90 to 110 kilopascals, for a time of 0.5 to 2 hours to yield the third reaction mixture. [0048] Aspect 16: The method of any one of aspects 1-15, comprising the contacting the second reaction mixture with a decolorizing agent. [0049] Aspect 17: The method of aspect 16, wherein the contacting the second reaction 22SHPP0066-WO-PCT (SS290012PCT) mixture with a decolorizing agent comprises contacting the second reaction mixture with 5 to 20 parts by weight activated carbon per 100 parts by weight poly(ethylene terephthalate). [0050] Aspect 18: The method of any one of aspects 1-17, wherein the reacting poly(ethylene terephthalate) with ethylene glycol comprises reacting 100 parts by weight poly(ethylene terephthalate) with 50 to 80 parts by weight ethylene glycol; the reacting poly(ethylene terephthalate) with ethylene glycol in the presence of a catalyst comprises reacting 100 parts by weight poly(ethylene terephthalate) in the presence of 0.025 to 0.4 parts by weight of a catalyst selected from the group consisting of titanium (IV) isopropoxide, titanium (IV) isobutoxide, and combinations thereof; the reacting poly(ethylene terephthalate) with ethylene glycol in the presence of a catalyst is conducted at a temperature of 180 to 230 °C and an absolute pressure of 90 to 110 kilopascals, for a time of 1.5 to 6 hours; the reacting poly(ethylene terephthalate) with ethylene glycol in the presence of a catalyst is conducted in the presence of 0 to 0.1 parts by weight water, based on 100 parts by weight of the poly(ethylene terephthalate); the adding an alkali metal hydroxide to the first reaction mixture comprises adding 1.5 to 5 moles of the alkali metal hydroxide, based on 1 mole of ethylene terephthalate units in the poly(ethylene terephthalate); and the second reaction mixture is maintained at a temperature of 35 to 60 °C and a pressure of 90 to 110 kilopascals, for a time of 0.5 to 2 hours to yield the third reaction mixture. [0051] Aspect 19: The method of any one of aspects 1-18, further comprising isolating the precipitate from the fifth reaction mixture. [0052] Aspect 20: The method of aspect 19, further comprising using the isolated precipitate in a reaction to form a product selected from the group consisting of dimethyl terephthalate, dioctyl terephthalate, bis(hydroxyethyl) terephthalate, poly(ethylene terephthalate), glycol-modified poly(ethylene terephthalate), poly(butylene terephthalate), poly(butylene adipate-co-terephthalate),^poly(trimethylene terephthalate), poly(cyclohexylenedimethylene terephthalate), glycol-modified poly(cyclohexylenedimethylene terephthalate), poly(cyclohexylenedimethylene terephthalate-co-isophthalate), poly(hexamethylene terephthalamide), poly(ethylene terephthalamide), poly(butylene terephthalamide), poly(2-methylpentamethylene terephthalamide), and poly(para-phenylene terephthalamide). [0053] The invention is further illustrated by the following non-limiting examples. EXAMPLES [0054] Materials used in these examples are summarized in Table 1. Poly(ethylene 22SHPP0066-WO-PCT (SS290012PCT) terephthalate) (PET) was provided in the form of flakes derived from a process that started with recycled PET bottles and included removing the necks and printed labels from the bottles, water washing the remaining bottle parts, chipping the bottle parts into irregularly shaped flakes of having a major dimension of about 5 millimeters, washing the flakes with dilute alkali followed by hot water, and drying the flakes. Table 1 [0055] In the following examples, “yield” refers to the yield of terephthalic acid based on the moles of terephthalate units in the poly(ethylene terephthalate) starting material. Specifically, ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ ^^^^^ ^ ^^^ ^ ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ [0056] “Purity” refers to the purity of the isolated terephthalic acid product versus a terephthalic acid standard, determined by high-performance liquid chromatography (HPLC) as follows. The exact weight of an approximately 25 milligram sample of isolated terephthalic acid was determined. The isolated terephthalic acid sample added to a 25 milliliter volumetric flask, and 20 milliliters of dimethyl sulfoxide were added. The resulting suspension was sonicated for 10 minutes to produce a homogeneous solution, and additional dimethyl sulfoxide was added to form 25 milliliters of solution. Two microliters of the solution were injected into the high- performance liquid chromatograph, and all peak areas in the product sample (product and 22SHPP0066-WO-PCT (SS290012PCT) impurity peaks) were integrated and compared to a blank sample (dimethyl sulfoxide). HPLC conditions are summarized below. Purity was calculated as follows. ^^^ !"^#^ ^ where all peak areas are at 254 nanometers. [0057] “APHA” refers to the color of liquids determined by the platinum-cobalt color test according to ASTM D1209-05(2019). A color standard with an APHA value of 500 was prepared according to ASTM D1209-05(2019). Specifically, 124.5 milligrams of potassium chloroplatinate (K2PtCl6) and 100.0 milligrams of cobalt chloride (CoCl2.6H2O) were added to a 100 millimeter volumetric flask, followed by addition of 10 milliliters of 12 N hydrochloric acid. Deionize water was used to dilute the resulting solution to 100 milliliters. Test solutions contained 10 weight percent isolated terephthalic acid in dimethylsulfoxide. A blank solution of dimethylsulfoxide was also analyzed, and its APHA value (typically 4-5 units) was deducted from the test sample APHA values. EXAMPLE 1 [0058] Poly(ethylene terephthalate) flakes (100 grams) was combined with ethylene glycol (65 grams) in a three neck round bottom flask, equipped with overhead stirrer and water cooled condenser. Magnesium chloride catalyst (0.1 gram) was added to the flask, and the resulting mixture was heated to 200 °C and maintained at that temperature for 10 hours. This glycolysis step converted insoluble PET flakes to soluble oligomers that were more easily 22SHPP0066-WO-PCT (SS290012PCT) hydrolyzed in the subsequent hydrolysis step. After 10 hours, the reaction mixture was cooled to 50 °C with stirring, then 54 grams of a 2 weight percent sodium hydroxide solution were added to the flask, and stirring was continued for one hour at 50 °C. This hydrolysis step converted the PET oligomers to ethylene glycol and terephthalic acid disodium salt. Activated carbon (10 grams) was then added to the flask and the resulting mixture was stirred for 1 hour at 50 °C, after which the mixture was filtered to remove the activated carbon. Aqueous hydrochloric acid (20 weight percent) was then added to the filtrate until the pH is less than 2, resulting in the formation of a precipitate. The precipitate was filtered, washed with about 750 grams of water, dried at room temperature while pulling air through the filtrate, then dried in a vacuum oven at 100 °C for ten hours. Yield = 81%, purity = 99.79%, and APHA color value = 38. EXAMPLE 2 [0059] Poly(ethylene terephthalate) flakes (100 grams) were combined with ethylene glycol (65 grams) in a three neck round bottom flask, equipped with overhead stirrer and water cooled condenser. Titanium (IV) isopropoxide catalyst (0.1 gram) was added to the flask, and the resulting mixture was heated to 190 °C and maintained at that temperature for 3 hours. After 3 hours, the reaction mixture was cooled to 50 °C with stirring, then 54 grams of a 2 weight percent sodium hydroxide solution was added to the flask, and stirring was continued for one hour at 50 °C. This hydrolysis step converted the PET oligomers to ethylene glycol and terephthalic acid disodium salt. Activated carbon (10 grams) was then added to the flask and the resulting mixture was stirred for 1 hour at 50 °C, after which the mixture was filtered to remove the activated carbon. Aqueous hydrochloric acid (20 weight percent) was then added to the filtrate until the pH was less than 2, resulting in the formation of a precipitate. The precipitate was filtered, washed with about 750 grams of water, dried at room temperature while pulling air through the filtrate, then dried in a vacuum oven at 100 °C for ten hours. Yield = 81%, purity = 99.83%, and APHA color value = 30. EXAMPLE 3 [0060] Poly(ethylene terephthalate) flakes (100 grams) were combined with ethylene glycol (65 grams) in a three neck round bottom flask, equipped with overhead stirrer and water cooled condenser. Titanium (IV) isobutoxide (0.1 gram) was added to the flask, and the resulting mixture was heated to 190 °C and maintained at that temperature for 3 hours. After 3 hours, the reaction mixture was cooled to 50 °C with stirring, then 54 grams of a 2 weight percent sodium hydroxide solution were added to the flask, and stirring was continued for one hour at 50 °C. This hydrolysis step converted the PET oligomers to ethylene glycol and terephthalic acid disodium salt. Activated carbon (10 grams) was then added to the flask and the 22SHPP0066-WO-PCT (SS290012PCT) resulting mixture was stirred for 1 hour at 50 °C, after which the mixture was filtered to remove the activated carbon. Aqueous hydrochloric acid (20 weight percent) was then added to the filtrate until the pH was less than 2, resulting in the formation of a precipitate. The precipitate was filtered, washed with about 750 grams of water, dried at room temperature while pulling air through the filtrate, then dried in a vacuum oven at 100 °C for ten hours. Yield = 81%, purity = 99.84%, APHA color value = 34. EXAMPLE 4 [0061] Poly(ethylene terephthalate) flakes (100 grams) were combined with ethylene glycol (65 grams) in a three neck round bottom flask, equipped with overhead stirrer and water cooled condenser. Montmorillonite K10 (MMT-K10) catalyst (5.0 grams) was added to the flask, and the resulting mixture was heated to 200 °C and maintained at that temperature for 10 hours. After 10 hours, the reaction mixture was cooled to 50 °C with stirring, then 54 grams of a 2 weight percent sodium hydroxide solution was added to the flask, and stirring was continued for one hour at 50 °C. The obtained solution was filtered to remove MMT-K-10 and activated carbon (10 grams) was then added to the flask and the resulting mixture is stirred for 1 hour at 50 °C, after which the mixture is filtered to remove the activated carbon. Aqueous hydrochloric acid (20 weight percent) was then added to the filtrate until the pH was less than 2, resulting in the formation of a precipitate. The precipitate was filtered, washed with about 750 grams of water, dried at room temperature while pulling air through the filtrate, then dried in a vacuum oven at 100 °C for ten hours. Yield = 81%, purity = 99.84%, APHA color value = 34. EXAMPLE 5 [0062] Poly(ethylene terephthalate) flakes (100 grams) were combined with ethylene glycol (65 grams) in a three neck round bottom flask, equipped with overhead stirrer and water cooled condenser. ZSM-5 catalyst (5.0 gram) was added to the flask, and the resulting mixture was heated to 200 °C and maintained at that temperature for 10 hours. After 10 hours, the reaction mixture was cooled to 50 °C with stirring, then 54 grams of a 2 weight percent sodium hydroxide solution was added to the flask, and stirring was continued for one hour at 50 °C. The obtained solution was filtered to remove ZSM-5 and activated carbon (10 grams) was then added to the flask and the resulting mixture was stirred for 1 hour at 50 °C, after which the mixture was filtered to remove the activated carbon. Aqueous hydrochloric acid (20 weight percent) was then added to the filtrate until the pH was less than 2, resulting in the formation of a precipitate. The precipitate was filtered, washed with about 750 grams of water, dried at room temperature while pulling air through the filtrate, then dried in a vacuum oven at 100 °C for ten hours. Yield = 81%, purity = 99.89%, APHA color value = 34. 22SHPP0066-WO-PCT (SS290012PCT) [0063] All ranges disclosed herein are inclusive of the endpoints, and the endpoints are independently combinable with each other. Each range disclosed herein constitutes a disclosure of any point or sub-range lying within the disclosed range.