Chemical Kinetic Model and Thermodynamic Compensation Effect of

Ind. Eng. Chem. Res. 2006, 45, 7985-7996

7985

Chemical Kinetic Model and Thermodynamic Compensation Effect of Alkaline Hydrolysis of Waste Poly(ethylene terephthalate) in Nonaqueous Ethylene Glycol Solution Adhemar Ruvolo-Filho* and Priscila S. Curti Group of Processing and Properties in Polymer, Department of Chemistry, Center of Exact Sciences and Technology, Federal UniVersity of Sa˜ o Carlos, P.O. Box 676, Sa˜ o Carlos, 13565-905, SP, Brazil

The depolymerization of waste poly(ethylene terephthalate) (PETW) flakes from bottles was investigated using a nonaqueous NaOH in ethylene glycol solution and was carried out at patm from 150 to 185 °C, using a NaOH:PET molar ratio of 4:1. The increasing amount of water taken up by the flakes and after submitting them to thermopressing at 260 °C increased the reactivity of the rectangular specimens thermopressed during the depolymerization. At a stirring rate value of 1360 rpm, the product was removed from the unreacted PET surface and the chemical reaction was rate-determining. Using the kinetic model of shrinking core of heterogeneous chemical reaction control, considering the formation and growth of cracks and pores on the polymer surface, the Ea value was 172.7 kJ‚mol-1, which was relatively high. However, in the thermodynamic analysis it was shown that the compensation effect of the ∆Sq over the ∆Hq is sufficiently high to compensate for the high Ea. Introduction Among the main thermoplastics used in industrial applications, poly(ethylene terephthalate) (PET) occupies first place in Brazilian municipal waste. At present, the production of PET in this country is about 400 000 tons/year, 90% of which is used to produce liquid containers (beverage bottles). However only 40% of the total production is recycled. This is the main driving force responsible for the increased recycling of postconsumer PET in this country. The general aspects of plastic waste recovery were described by Leidner.1 Although the mechanical recycling of some waste polymers has been extensively studied,2-7 chemical recycling, which is applied to postconsumer condensation polymers, such as PET, has received much attention and two important reviews of this subject have been published.8,9 There is considerable interest in the total depolymerization of PET via hydrolysis, from which terephthalic acid (TPA) and ethylene glycol (EG) are recovered. These products can be used as raw materials for virgin PET synthesis or to manufacture new polyester resins. The main disadvantage of chemical recycling is its high cost.10 This aspect constitutes a major industrial challenge. The melting range of PET is around 245-265 °C, and it is clear that chemical recycling via hydrolysis at temperatures below this range is a heterogeneous reaction that proceeds at the solid-liquid interface. Thus, the influence of the varying effective surface area of the PET during depolymerization should be considered. Studies about the hydrolysis of virgin PET or waste PET using different reaction media at temperatures below its melting range have been made by some researchers.11-14 Although the depolymerization occurs in a heterogeneous medium, all authors considered that as a homogeneous medium and applied a homogeneous first-order model for the kinetic study. They also did not make any preliminary study of the stirring rate effect in the solution to evaluate the influence of the mass transfer * To whom correspondence should be addressed. Tel.:+ 00 (21) 55 16 3351 8080. Fax: +00 (21) 55 16 3351 8350. E-mail address: [email protected].

resistance on the reactions, in which maximum conversions were achieved just after long times. Probably this behavior is due to precipitation of sodium terephthalate (Na2-TPA) on the unreacted PET surface, and the mass transfer resistance is ratedetermining. Thus this parameter could influence the kinetics of PET depolymerization, as observed by Kao, Wan, and Cheng.15 Yoshioka, Okayama, and Okuwaki studied the kinetics of hydrolysis of powdered waste PET bottles in two different acid media at high concentrations, under atmospheric pressure, and at temperatures below its melting range.16,17 The kinetic model adopted was a modified shrinking-core model of chemical reaction control, considering a heterogeneous medium. In the original model,18 the effective surface area of the sample that was available to react was proportional to the geometric area. However, Yoshioka et al. demonstrated that the effective surface area of the unreacted PET samples increased proportionally with the fraction of conversion and introduced a correction term in the kinetic equation, related to the increase in the effective surface area, due to formation and growth of pores and cracks on unreacted PET samples. Although they did not evaluate the effect of the stirring rate in the solution, they observed that the time of hydrolysis decreased by removing the TPA from the unreacted PET powder and the value of the effective surface area was affected by the deposition of TPA on the unreacted PET surface. More recently, Kumar and Guria19 studied the depolymerization of waste PET from bottles using an aqueous potassium hydroxide solution. They carried out the reactions at temperatures between 110 and 135 °C. For the kinetics study, they used a shrinking-core model but they did not evaluate the influence of the change in the surface area of the PET particles during the depolymerization to deduce the kinetic equation. Many researchers have also studied the methanolysis of PET waste.20-24 However, they only have achieved a reasonable percentage of PET waste conversion under supercritical conditions. In that case, good reaction times can be achieved, but the reaction conditions are extreme. In all the papers cited, the reaction conditions used generally

10.1021/ie060528y CCC: $33.50 © 2006 American Chemical Society Published on Web 10/24/2006

7986

Ind. Eng. Chem. Res., Vol. 45, No. 24, 2006

were costly and probably unviable from an industrial point of view. In this context, this paper will present a study of the depolymerization of waste PET from bottles using alkaline hydrolysis in nonaqueous ethylene glycol solution, with the following objectives: (i) to obtain the optimal waste PET conversion time, using more convenient and cheaper reaction conditions; (ii) to propose a kinetic model, based on a shrinkingcore model of chemical reaction control, applied to small rectangular plates of waste PET, since this is the most common geometric shape for recycled PET, obtained after the grinding process in the recycling industry; (iii) to apply a thermodynamic analysis, assuming the equilibrium between reagents and activated complex, in order to find and to explain any correlation between the activation enthalpy and the activation entropy. Experimental Section Materials. Commercial flakes of PET waste (PETW) from plastic bottles were obtained from Embrapol (Brazil). The PETW flakes were cleaned with detergent, rinsed in abundant water, and dried in an oven. After cleaning, the flakes were stored in a closed room, at 23 °C and with air humidity around 70%. Pellets of virgin PET S80 (PETV) were obtained from Mossi & Ghisolfi Group (Brazil). Commercial-grade sodium hydroxide (NaOH) and ethylene glycol (EG) were used as received, without further purification. Preparation of the PETW Specimens by Thermal Processing. Three kinds of pretreatment were carried out on PETW flakes in order to evaluate whether any hydrolytic degradation takes place during the thermal processing: (i) PETW flakes were previously dried in a controlled oven at 180 °C for 4 h (PETWD); (ii) PETW flakes were stored at 70% relative humidity at room temperature up to the moment of use, and were not dried (PETWH); (iii) PETW flakes were saturated by immersion in water for a minimum time of 10 days at 23 °C (PETWS). PETV pellets, dried in a controlled oven at 180 °C for 4 h, were used for comparison (PETVD). The amount of water taken up by the flakes in each of these three pretreatments was estimated by thermogravimetric analysis (TG) using a TG 2050 (TA Instruments). The experimental conditions were heating rate of 10 °C‚min-1, N2 flow rate of 10 mL‚min-1 in the thermobalance and 90 mL‚min-1 in the furnace, and 19.16 ( 0.16 mg of distinct samples (PETWD, PETWH, PETWS, or PETVD) placed on a platinum crucible. PETW flakes and PETV pellets, pretreated as described, were introduced into a metal mold and processed identically, by thermopressing at 260 °C until complete polymer fusion. After melting, the polymer was quenched at 0 °C to obtain the plates denominated PETWDT, PETWHT, PETWST, and PETVDT, respectively. After the thermopressing, the plates were cut into smaller rectangular plates, all of 0.8 cm width and 2.3 cm length, to be used as reaction specimens whose thickness varied from 0.4 to 4.0 mm. Values of the intrinsic viscosity (IV) of pellets of PETV, flakes of PETWH, and flakes of PETWST were measured in a 6:4 (w/w) phenol:1,1,2,2-tetrachoroethane solution at 25 °C. Polymer solutions of 0.2 mol‚L-1 were prepared. Also, the melt flow index (MFI) was estimated for some materials using a Davenport Plastometer at 255 °C, under a load of 0.395 g, according to ASTM D1238-95 test method. Depolymerization of Polymer Specimens. Individual PETWT and PETVDT specimens were submitted to the depolymerization reaction in 1.1 mol‚L-1 NaOH nonaqueous ethylene glycol solution. The molar ratio of NaOH:PET monomer was 4:1 in all the experiments (1 mol of the repeating unit of PET is 192

Table 1. Percentage of Conversion of PETWST Samples into Na2-TPA, after 10 min of Reaction at 170 °C, Using Various Concentrations of NaOH in Ethylene Glycol Nonaqueous Solution NaOH concn (mol‚L-1)

conversion (%)

0.53 0.75 1.05 2.64

87.7 ( 4.4 92.3 ( 4.6 100.0 ( 0.0 100.0 ( 0.0

g). These conditions were optimized in an earlier study conducted by this group,25 in which it was shown that the time to achieve the maximum PET conversion did not increase at concentrations of NaOH above 1.05 mol‚L-1, when the reaction was carried out at 170 °C for 10 min. These results are shown in Table 1. PETWT and PETVDT depolymerization reactions were carried out in a 100 mL three-necked stirred reactor bath at atmospheric pressure. It used a mechanical stirrer (a horizontal steel axe, which are fixed two shoulder blades with 1 cm length and 1 cm between the extreme points). A thermometer and a reflux condenser completed the reactor system. The ratio between the volume of NaOH nonaqueous EG solution and the weigh of PETWT or PETVDT specimens was 20:1 (v/w) in all experiments, because the volume of the solution used depends on the thickness of PETWT or PETVDT specimens used during the depolymerization. For example, the weight of the PETWT and PETVDT specimens with 2.7 mm thickness was about 0.75 and 0.85 g; thus the volume of the alkaline solution used was about 15 and 17 mL, respectively. After the solution reached the temperature set, one distinct PETWT or PETVDT specimen was introduced in the reactor, in which it remained suspended in the solvent during the reaction. After a distinct time, the reaction was stopped by quenching the reactor in a water-ice bath and the fraction of conversion of PETWT and PETVDT was determined by gravimetry, defined as follows:

χPET )

WiPET - WrPET WiPET

(1)

where WiPET is the initial weight of the specimen and WrPET is the weight of unreacted PETWT or PETVDT after reaction for a given time. Some reaction parameters considered important were evaluated in order to improve the depolymerization. These were the thickness of the PETWT specimens for which the fractions of conversion obtained at given times were reproducible within the interval of temperature used in this study, the stirring rate in the solution at which the effect of mass transfer resistance ceases to influence the reaction, and the influence of the reactivity of PETWT samples, obtained from PETW flakes with different water contents, on the time to reach the maximum conversion. After the best values of these reaction parameters had been found, the effect of temperature was evaluated. The effective surface area of PETWST specimens was estimated by Brunauer-Emmett-Teller (BET) analysis, with an ASAP 2000 BET instrument (Micromeritics), using nitrogen gas. Before the analysis, the specimens were washed in abundant water and previously maintained in a vacuum oven at 30 °C to ensure that the humidity on the surface of PETWST specimens was eliminated and could not interfere in the measurements. The effective surface area was measured by BET for each PETWST specimen before the depolymerization (So) and after each period of depolymerization (Sef). The normalized effective surface area, Sef/So, was evaluated as a function of the extent of conversion of the PETWST specimens after different reaction times.

Ind. Eng. Chem. Res., Vol. 45, No. 24, 2006 7987

The morphology of the PETWST surfaces, before and after various times of depolymerization, in which the unreacted PETWST specimens were not washed, was evaluated by SEM, using a Zeiss Model DSM 940 A scanning electronic microscope. PETWST specimens were supported and covered with gold by sputtering. The covering time was 3 min. The beam current used was 0.80 µA, and the beam power was 20 keV. The analyses were performed at 22 °C. The BET and SEM analyses were used to develop a kinetics model and a thermodynamic analysis of PETWST depolymerization in alkaline medium, with a nonaqueous ethylene glycol solution. Characterization of Depolymerization Solid Product. The solid product of PETWST specimen depolymerization was characterized by elemental analysis using a Fisons EA 1108 CHNS, in which the chemical elements were identified by gas chromatography. Also, electrospray ionization mass spectrometry (IES-MS) was used for the solid product characterization. Accurate-mass analyses were performed on an UltrOTOF-Q (Brucker, Daltonics Billerica MA). The sample was introduced through a syringe pump at a flow rate of 10 µL‚min-1. After a systematic investigation in negative mode,26 the heated capillary and the voltage were maintained at 250 °C and 3 kV, respectively. Results and Discussion Parameter Optimization in PETWT Specimen Depolymerization. The influence of OH- ion concentration on the efficiency of PETWT depolymerization has been studied previously by this group.25 The optimum concentration of NaOH, presented in the Experimental Section, was 1.05 mol‚L-1, and this was used in all experiments in this study. Also, in the present study, the effect of the initial thickness of PETWST specimens on the time to reach 100% conversion (Na2-TPA yield) at 170 and 150 °C was evaluated, in order to obtain reproducible results for the fraction of depolymerization in the interval of temperature considered. The initial thickness of PETWST samples ranged from 0.4 to 4.0 mm, and the results are presented in Figure 1. It seems that in the reactions carried out at 170 °C (Figure 1A), very short times are needed to reach 100% conversion, when PETWST specimens between 0.65 and 1.8 mm thick are used. This behavior makes it difficult to control the reaction time and to obtain reproducible values with such thin specimens. Using 2.7 mm thick PETWST samples, the time to reach 100% conversion was more reproducible, and for specimens above 2.7 mm thickness, the time to reach 100% PETWST conversion was not significantly altered. At 150 °C (Figure 1B), it is observed that the time to reach 100% PETWST conversion is more reproducible, even using PETWST samples thinner than 2.7 mm. For the reactions carried out at 150 °C, the time to reach 100% PETWST conversion varied from 270 to 4200 s, while in the reactions carried out at 170 °C the time to reach 100% PETWST conversion varied from about 30 to 470 s. This represents a 9-fold increase in the time to reach 100% PETWST conversion when the temperature is diminished from 170 to 150 °C. Thus, for the kinetic study, performed between 150 and 185 °C, PETWST samples of 2.7 mm thickness were chosen. Another parameter analyzed was the stirring rate in the reaction solution during the depolymerization. In heterogeneous systems, the stirring rate influences the kinetics of the reaction, because it affects the rate-controlling step of the reaction.18 At slow stirring rates, a layer of product may form on the unreacted solid surface (PETWT). In this situation, the reaction is

Figure 1. Effect of PETWST specimens thickness on time to reach 100% conversion at (A) 170 and (B) 150 °C. All reactions were carried out at a stirring rate of 1360 rpm.

controlled by diffusion, because the product causes a mass transfer resistance between the unreacted PETWT surface and the solution. On the other hand, at higher stirring rates all product formed at the unreacted PETWT surface is removed from it and in this case the reaction rate is controlled by the chemical reaction. In Figure 2A, results of the degree of PETWST conversion, in the depolymerization performed at 170 °C, are plotted against time for different stirring rates from 110 to 1360 rpm. These data are compared with results of PETWST conversion, in the reaction carried out at 110 rpm and 170 °C, in the presence of DMSO, CHA, and THF solvents, as cited by Goje et al.14 (Figure 2B). There are two interesting observations that can be made. First, it is clear in Figure 2A that the conversion of PETWST samples into Na2-TPA is influenced by the stirring rate parameter. At 1360 rpm, 100% conversion (Na2-TPA yield) is achieved in 6 min, while at 110 rpm, the time to achieve the same degree of conversion is 16 min. Second, from the results presented in Figure 2B, it is seen that the solvents used in the reaction medium, as cited by Goje et al.,14 were not able to completely eliminate the mass transfer resistance. This effect was eliminated only when high stirring rates were used. These observations can be confirmed in Figure 3, which presents photographs of PETWST specimens before the reaction and after submitting them to the reaction at 110 rpm, using DMSO, CHA, and THF in the reaction medium, and without these solvents at 110 rpm and at 1360 rpm, up to

7988


Figure 2. Degree of PETWST conversion as a function of reaction time at 170 °C using (A) different stirring rates in the solution and (B) dimethyl sulfoxide (DMSO), cyclohexylamine (CHA), and tetrahydrofuran (THF) as specific solvents in the reaction medium, as cited by Goje et al.14

three fractions of PETWST conversion. These results highlight that only in conditions of high solution stirring rate can the mass transfer resistance be eliminated in this reaction medium, as reported by Kao et al.15 According to Levenspiel,18 the controlling stage of the reaction can also be determined from the relation between the geometric volume and area, i.e., with a dimension of the specimen, and the time needed to achieve one determined percentage sample conversion, as shown in the equation

t ∝ (V/A)x

(2)

where t is the time needed to reach a given degree of conversion, V and A are the geometric volume and area of the sphere, respectively, and x is related to the kind of controller stage: when x ) 1, the controller stage is the chemical reaction; when x is between 1.5 and 2, the controller stage is the diffusion process. Taking natural logarithms of eq 2 gives

ln(t%) ) x ln(V/A)

(3)

The relation presented in eq 3 is not so simple when rectangular plate specimens are used. Thus, for the rectangular PETWST plates, the ratio between the geometric volume (V ) xoyozo)

Figure 3. Photographs of PETWST specimens (I) without depolymerization and after (II) 30%, (III) 50%, and (IV) 70% conversion at 170 °C: (A) at 110 rpm, using CHA, THF, and DMSO as specific solvents, as cited by Goje et al.;14 (B) at 110 rpm without specific solvents; and (C) at 1360 rpm without specific solvents, as described in our method.

and the initial effective surface area value (So), estimated by BET analysis, was used for each PETWST specimen between 0.65 and 2.7 mm thick. This relation is presented as follows:

ln(t%) ) x ln(xoyozo/So)

(4)

Using this equation, the time required to reach 80% PETWST conversion was analyzed as a function of the ratio V/So (cm3/ cm2‚g-1), in order to evaluate the types of control stage operating during the depolymerization, at stirring rates of 110 and 1360 rpm. The reactions were carried out at 170 °C, and the results are presented in Figure 4. At 110 rpm, the logarithm-scale curve observed is concave, while at 1360 rpm it is a straight line. The slope of the fitted line at 1360 rpm is unity, which confirms, according to Levenspiel,18 that the reaction carried out at 1360 rpm is controlled by the chemical reaction and that the influence of mass transfer resistance was eliminated. The study of the effect of the stirring rate was complemented by BET and SEM analyses of the same PETWST specimens submitted to depolymerization. Figure 5 presents the normalized effective surface area (Sef/So) data for PETWST samples,


Figure 4. Logarithimic plot of the time necessary to achieve 80% PETWST conversion and V/So, determined for depolymerization reactions carried out at 170 °C.

Figure 5. Influence of stirring rate on Sef/So values obtained at different fractions of PETWST conversion. All reactions were carried out at 170 °C.

estimated after various fractions of depolymerization, at 170 °C and three stirring rates. Up to 40% conversion, there is one linear curve. Above this fraction of conversion, a change occurs in Sef/So curves, which depends on the stirring rate used during the reaction. When the depolymerization of PETWST was carried out at 110 rpm, the Sef/So value remained low and linear even above 40% conversion, characteristic of a polymer surface covered by the Na2-TPA formed during the reaction. On the other hand, when the stirring rate in the solution is increased to 930 and 1360 rpm, the Sef/So curve rises exponentially with the extent of reaction, because the product on the PET surface is removed as the reaction proceeds. Figure 6 shows SEM micrographs of PETWST specimens before depolymerization (Figure 6A) and submitted to the reaction, at stirring rates of 110 (Figure 6B) and 1360 rpm (Figure 6C), until 70% conversion. It can be observed that the surface of the unreacted PETWST, obtained by thermopressing, is not totally smooth, exhibiting defects homogeneously distributed. Probably these defects arise from the hydrolytic degradation that the PETWST flakes suffer during thermopressing, due to the excess water content taken up by the polymer. However, this plate was found to be very rigid. The SEM image of plates submitted to the reaction up to 70% conversion, at 110 and 1360 rpm, show different surface morphologies that depend on the stirring rate. In Figure 6B it can be seen that the

Figure 6. Scanning electronic microscopy (SEM) micrographs of PETWST samples submitted to depolymerization reactions at 170 °C after (A) 0 min, (B) 9 min at 110 rpm (70% conversion), and (C) 4 min at 1360 rpm (70% conversion). Magnification 200×.

unreacted surface is completely covered by the Na2-TPA salt when the depolymerization is carried out at 110 rpm. In this case the reaction achieves 70% conversion after 9 min. When the same reaction is carried out at 1360 rpm (Figure 6C), the image of the unreacted PETWST surface is very different from Figure 6B, because the Na2-TPA deposition does not occur and no trace of salt product is observed after 70% conversion, which is now achieved after only 4 min. These observations verify

7990


Figure 7. Effect of water uptake by PETW flakes on reactivity of processed plates, observed by extent of reaction plotted against reaction time for PETWHT, PETWDT, PETWST, and PETVDT specimens. All reactions were carried out at 170 °C and 1360 rpm. Table 2. Water Content, IV, and MFI Data Estimated in PETVD Pellets and PETW Flakes (in the Three Pretreatment Conditions) before and after Thermopressing specimen

water content (%)

IV (g‚dL-1)

MFI (g 10‚min-1)

PETVD PETWH PETWD PETWS PETVDT PETWHT PETWDT PETWST

0.00 0.21 ( 0.02 0.00 0.77 ( 0.10

0.81 ( 0.015 0.70 ( 0.01

3.67 ( 0.61 5.53 ( 0.63

0.44 ( 0.01

5.68 ( 0.7 3.74 ( 0.21 6.23 ( 0.52 6.26 ( 0.14 7.89 ( 0.43

that at a stirring rate of 1360 rpm the depolymerization was controlled by the chemical reaction, which is rate-determining, corroborating the analyses of Figures 3-5. Another reaction condition evaluated was the pretreatment of the PETW flakes, with respect to water uptake before the thermopressing. The amount of water taken up by each kind of pretreated PETW flakes were estimated by TG analysis, and the results are presented in Table 2. It was verified that flakes of PETW immersed in water up to 10 days present more water content in their flakes than those just stored at 70% relative humidity. After the thermopressing of these distinct flakes, the times necessary to achieve 100% conversion for PETWST, PETWHT, PETWDT, and PETVDT specimens were compared. The results are presented in Figure 7. The total conversion of PETWST samples occurred in 6 min, PETWHT required an estimated time of 10 min, while PETWDT and PETVDT specimens achieved total conversion in 22 min. These results corroborate the IV and MFI data presented in Table 2, and it is an indication that the water content in the PETW flakes before thermopressing acts as a hydrolytic agent of PET degradation during the thermopressing process at 260 °C, and probably causes the breakup of PET chains, according to the literature,15,27-30 as can be observed by decreasing the IV and by increasing the MFI values obtained in the experiments. Hydrolytic degradation increases the number of polar groups, such as carboxylic groups15,27,29 and acetaldehyde.28,30 PETWST flakes show the greatest water content, which contributes to forming more polar chemical groups, mainly on the sample surface, during thermopressing. This process increases the reactivity on the surface, making the material more susceptible to depolymerization in alkaline medium. This pretreatment has thus improved the efficiency of the degradation, reducing the time required for total conversion of PETWST samples to Na2-TPA.

Figure 8. Degree of PETWST conversion as a function of reaction time at 150, 170, and 185 °C, at 1360 rpm.

Other researchers12,15-17,19-24,31,32 obtained high degrees of PET conversion only after long periods of reaction. This may be explained by the different reaction medium and conditions used in each paper, as discussed in the Introduction. In contrast, the results reported in the present work show that one simple and cheap stage, with high stirring rates in the solution, could enhance the efficiency of waste PET depolymerization, making this method effective and clean, since it is not necessary to introduce other solvents to improve the product yield, as suggested in published reports.13,14,31,32 The proposed method may thus be industrially viable. In sum, the evaluation of reaction parameters showed that the best conditions for the kinetic study of PETWT depolymerization were to use PETWT samples obtained from PETW flakes previously immersed in water up to saturation and then submitted to the thermopressing to obtain PETWST specimens 2.7 mm thick, and to use a stirring rate of 1360 rpm in the solution during the reaction. Therefore, the analyses of the thermodynamics formalism in the next section were based on the hydrolysis of PETWST under the fixed conditions cited here. Kinetic and Thermodynamic Study of Depolymerization of PETWST Specimens in Alkaline Medium. The effect of temperature on the rate of conversion of PETWST specimens can be seen in Figure 8. At 150 °C, the reaction achieved total conversion only after 46 min, while at 185 °C the time required to complete the conversion was only 1 min. At 170 °C, total conversion was achieved after 6 min. It is clear that PETWST hydrolysis, in the experimental conditions studied, is very sensitive to temperature; this confirms that the chemical reaction is rate-determining. Many papers included a kinetic analysis of PET depolymerization, using temperatures below the PET melting range. Such studies have utilized alkaline medium,11,12,14,19,33 glycolysis using catalysts,13,34 or glycolysis without catalysts.35 In almost all of these papers the authors treated the real heterogeneous medium as a simple homogeneous medium, as cited in the Introduction. Yoshioka et al.16,17 proposed a kinetic model for waste PET hydrolysis that takes the heterogeneous system into account, which was presented in the Introduction. The kinetic equation that they deduced is more consistent and acceptable for the reaction medium used. These authors based their equations on spherical particles, while in this present work the kinetic model proposed is based on small rectangular plates of PETWST. Figure 9 is a sketch of the modified shrinking-core model of chemical reaction control proposed in this work, which takes into account the formation and growth of cracks and pores during the depolymerization of


Figure 9. Sketch of proposed shrinking-core model of chemical reaction control for small rectangular plates of PETWT submitted to depolymerization by NaOH in nonaqueous ethylene glycol solution.

PETWST plates. The x- and y-axes represent the length and width, respectively, and the z-axis represents the thickness. The SEM micrographs in Figure 10 show PETWST surfaces that were submitted to different depolymerization times at 170 °C and 1360 rpm, to achieve 30% (Figure 10A), 50% (Figure 10B), and 70% (Figure 10C) conversion. According to Figure 10A, after the reaction reached 30% PETWST conversion, the unreacted PET surface showed some small cracks and pores. It is necessary to point out that these pores are found sporadically scattered at just some points on the unreacted PETWST surface. In contrast, cracks appear homogeneously distributed all over the surface and make it more fragile. The SEM image presented in Figure 10B shows that the unreacted polymer surface presented more evident pores. Some crystals of sodium terephthalate still adhered to the unreacted PETWST surface. After 70% conversion (Figure 10C), the unreacted PETWST surface no longer showed large pores. However, it can be observed that this surface had many small pores. Probably the large pores were smoothed during the depolymerization process due to the removal of layers from the PETWST surface. Because of this behavior, in BET analysis, the adsorbent gas finds more points at which to adsorb, and thus, the effective surface area of the unreacted PETWST increases. The results observed by SEM are consistent with the kinetic model proposed in Figure 9. Thus, because the hydrolysis of esters is proportional to the ester concentration, based on the considerations above, it will be supposed that the effective surface area of the PET specimens (Sef) can represent the ester concentration, and that changes during the reaction. The equation for the rate of reaction is

V ) kCASef

(5)

where k is the rate constant per unit surface area, Sef is the effective surface area available to react, and CA is the initial NaOH concentration. If PET specimens is regarded as consisting of specimens like rectangular plates, and supposing that the reaction can occurs preferentially in the z-axis, that is, the specimen is reduced in thickness, from the balance of its mass results that

d(xoyoztF) V)dt

xoyoztF xoyozoF

The effective surface area of the PETWST samples varies as a function of the fraction of conversion after different reaction times and is given by Sef ) Sgeom(1 - χ)(correction term). The Sgeom ) 2(xozo + yozo + xoyo) term represents the initial geometric area of the PETWST specimens, which diminishes during the reaction time, and the correction term is introduced due to the formation and growth of cracks and pores on the unreacted PETWST surface. Thus the real value of Sef is greater than that of the simple geometric area measured. In Figures 11 and 12 the values of Sef/So of PETWST specimens (where So is the initial effective surface area of the different samples before the reaction) are plotted as functions of fraction of conversion and of time, respectively. In Figure 11, the Sef/So values rise exponentially as a function of the degree of conversion of PETWST. It is clear that, as the temperature of the reaction is increased, the relation between Sef/So values and fraction of PETWST conversion is not altered. The correction term for rising Sef/So was obtained by regression of the points in Figure 11, based on an exponential expression: a exp(χ/c), where a and c are constants and their values are 0.23 and 0.09, respectively. However, according to Figure 12, at high temperatures, such as 185 °C, the time to reach the maximum Sef/So values is much shorter than at lower temperatures, such as 150 °C, showing that the temperature strongly influences the values of Sef/So and hence the kinetic parameters. This result is very interesting and useful, because the analysis of the effective surface area, at different moments in the reaction, can be carried out at one temperature and then extended to the other temperatures, making this analysis faster and less costly. From the analysis, the real Sef values of the PETWST samples can be estimated by

Sef ) 2a(xozo + yozo + xoyo)(1 - χ) exp(χ/c)

(6)

(8)

Equation 9 can be derived from eqs 5-8:

-

The degree of conversion of the particles is given by

χ)1-

where zt is the PETWST thickness at any reaction time, F is the density of PETWST, and xo, yo, and zo are the initial dimensions of the PETWST rectangular plates.

d(1 - χ) 2akCA ) (x z + yozo +xoyo) × dt xoyozoF o o (1 - χ) exp(χ/c) (9)

Integrating eq 9 gives

(7)

-

1 1-χ - ln(1 - χ) + ) kvt c c

(10)

7992


Figure 11. Sef/So plotted against extent of PETWST conversion estimated at 150, 170, and 185 °C, at 1360 rpm.

Figure 12. Sef/So plotted against reaction time for PETWST specimens submitted to depolymerization at 150, 170, and 185 °C, at 1360 rpm.

Figure 10. SEM micrographs of PETWST surfaces that were submitted to depolymerization reaction at 170 °C and 1360 rpm for (A) 1 min (30% conversion), (B) 2 min (50% conversion), and (C) 4 min (70% conversion). Magnification for (A) and (C) is 500× and for (B) is 100×.

where kv is the apparent rate constant of the reaction, which is

kv )

2akCA exp(1/c) (xozo + yozo + xoyo) xoyozoF

(11)

The effect of the temperature was evaluated in terms of the kinetic data, using eq 10. The results are presented in Figure 13. Fitting of the kinetic data provided the apparent rate

Figure 13. Kinetic data based on eq 10 for PETWST specimens submitted to depolymerization at 150, 170, and 185 °C, at 1360 rpm.

constants at each temperature studied, which are presented in Table 2. Linear correlations were obtained at all three temperatures studied, indicating that eq 10 is consistent with the experimental data. An Arrhenius plot of the apparent rate constants is presented in Figure 14. The apparent activation energy, Ea, of this process was 172.7 kJ‚mol-1.

Ind. Eng. Chem. Res., Vol. 45, No. 24, 2006 7993 Table 3. Estimated Times for the Maximum Degree of PET Conversion at Different Temperatures and kv Values Obtained from the Kinetic Model Used by Each Author and Our Results, for Comparison

source

temp (°C)

max time of conversion (min)

present work present work present work Oku et al.11 Yoshioka et al.17 Wan et al.12 Goje et al.13 Goje et al.14 Kumar et al.19

150 170 185 170 170 160 (4.6 atm) 170 170 130

46 6 1 25 300 60 a a a

kv 10.08 h-1 59.65 h-1 453.46 h-1 32.5 h-1 0.058 h-1 1.3 × 10-4 L‚h-1‚cm-2 0.2 h-1 14.4 h-1 1.3 m h-1

a Authors did not present the value of the time to reach the maximum conversion the these temperatures.

Figure 14. Arrhenius plot for kv values obtained from kinetic data of PETWST depolymerization.

(Figure 11), and it is an indication that the diminution of the specimens occurs, and for specimens with initial thickness e2.3 mm this diminishing can occurs mainly in the thickness. The Ea value determined in this work is higher than the other values found in the literature.11-14,17 However, when the time to reach the maximum conversion and the apparent rate constant values of each paper cited are compared with our results, it is noted that kv values obtained in this present work are higher than the others and the times to reach total conversion are shorter, as can be seen in Table 3. These results can be tentatively explained in thermodynamic terms as follows. Initially, assume that in a reaction medium there are reagent molecules A and B:

A + B h ABq f C

Figure 15. kv values plotted against reciprocal thickness of PETWST specimens submitted to depolymerization at 170 °C and 1360 rpm.

It must be emphasized that the kinetic study was made in the range of PETWST conversion between 0% and 80%. Above 80% PETWST conversion, it may not be realistic to expect reproducible values for Sef/So analysis, because the reaction on the polymer surface proceeds very quickly and it is difficult to have good control over the particle size during the reaction. Probably above 80% PETWST conversion a change in the reaction mechanism occurs, from the shrinking-core model to the progressive conversion model, since the exponential increase in the effective surface area may be related to the rising number of pores and the reaction can also occur inside the specimens. In the latter model, the reaction may be very unstable and the particle can collapse. Also, experiments of depolymerization using PETWST specimens of different initial thicknesses between 1.8 and 4.0 mm were carried out at 170 °C and 1360 rpm, in order to observe if the PETWST diminution is mainly in thickness. It was verified that Sef/So values showed a similar behavior compared to those estimated at other temperatures. Thus, for PETWST specimens of different thicknesses, the same correction term was used. The kinetic data obtained from eq 10 provided linear correlations. In Figure 15 is presented the relation between kv and reciprocal thickness of PETWST specimens, in which it is observed that up to 2.3 mm thick there is a fall in kv. Above this thickness, the kv values diminish linearly in a slower way. This result is similar to the Sef/So results

In the present case, [A] and [B] are concentrations of reagents PETWST and NaOH, respectively, in the reaction medium; [ABq] represents the concentration of the activated complex that is formed by the approach of hydroxyl ions to carbonyl groups on the PETWST. This reaction occurs by nucleophilic substitution, which is similar to the SN2 mechanism. Thus, to form the product, the reagents need to pass through an activated complex state. The term “[C]” refers to the concentration of the product, Na2-TPA, which was the mainly solid product obtained and estimated by elemental analysis (product 97.3% purity) and by IES-MS analysis (experimental m/z ) 165.0199 ( 6 ppm compared to theoretical m/z ) 165.0188 for TPA). After some time, the reagents, A and B, form the activated complex, ABq. At this point, the reaction may be completed, and a product C formed, or the activated complex may return to the reagents. For the first step, there are rate constants for the forward and backward reactions. Since the formation of the activated state is an equilibrium reaction and the forward rate constant determines the rate of the chemical reaction, the thermodynamic analysis, for the equilibrium between reagents and the activated complex, can be performed by considering the Eyring equation:

kv )

( )

-∆Gq kT exp h kT

(12)

where k is the Boltzmann constant, h is the Planck constant, T is the thermodynamic temperature, and ∆Gq is the Gibbs free energy of formation of the activated complex. The Gibbs free energy reflects the total energy increase of the system at the approach of the reagents and the formation of

7994


Figure 16. Compensation effect of activation entropy and activation enthalpy, estimated for activated complex formation in various reaction media, for comparison with literature data.

the activated complex. This energy is influenced by two thermodynamic properties, the enthalpy and entropy of activatedcomplex formation, according to ∆Gq ) ∆Hq - T∆Sq. Thus

kv )

( ) ( )

-∆Hq ∆Sq kT exp exp h kT k

(13)

Dividing by T and taking natural logarithms:

ln

( ) ()

kv ∆Sq ∆Hq k ) ln + T h k kT

(14)

The activation enthalpy shows the energy difference between the reagents and the activated complex. If this difference is small, the formation of the activated complex is favored, because the potential energy barrier is low. The activation entropy reflects how near the system is to its own thermodynamic equilibrium. Low activation entropy means that the material has just passed through some kind of physical or chemical aging process, bringing it to a state near its own thermodynamic equilibrium. In this situation, the material shows little reactivity, increasing the time taken to form the activated complex. On the other hand, when high activation entropy values are observed, the material is far from its own thermodynamic equilibrium. In this case, the reactivity is high and the system can react faster to produce the activated complex, and consequently short reaction times are observed. From eq 14 the activation enthalpy and the activation entropy were calculated. The data obtained in the present work were compared with those calculated by other authors11-14,17,19 and are presented in a thermodynamic compensation plot in Figure 16, which shows that the activation entropy increases with and compensates the activation enthalpy (depends on the type of polymer used in the depolymerization study). Some researchers12,17,19 used PET waste from bottles. It is plausible to suggest that the material had suffered some aging process during its life cycle. These authors did not apply any kind of treatment to the polymer to obtain a more reactive material, before the degradation reaction. In this case they observed that long reaction times were necessary to achieve a high percentage of waste PET conversion, as can be seen in Table 3. Although the activation enthalpy values were small, the activation entropies were very low, with even negative values being observed. It could thus be postulated that these systems were near their thermodynamic equilibrium, leading to a reduced reactivity.

Oku et al.11 used pellets of virgin PET to perform the depolymerization reaction, while Goje et al.13,14 used PET left over after some products were made from raw material. Thus, neither of these polymers had passed through any kind of aging process and should be more reactive. In the cases of Oku et al.11 and Goje et al.,13 the activation enthalpy and the activation entropy values determined using eq 14 are higher than the values determined by Yoshioka et al.17 and Wan et al.12 However, the activation entropy value determined by Goje et al.14 is very low, and it deviates from the linear behavior observed for results obtained in the other papers (Figure 16). In this case, although Goje et al.14 used samples of left-over raw PET, as in the earlier paper,13 probably the depolymerization method used had some influence on the reaction medium and consequently on the kinetics. Oku et al.11 observed two apparent rate constants from the homogeneous first-order model adopted. They attributed the second apparent rate constant to Na2-TPA covering the unreacted PET surface, after some time of reaction, so that mass transfer resistance interfered in the reaction. In the present work, a depolymerization experiment was performed under reaction conditions similar to those cited by Goje et al.14 and carried out at 110 rpm (Figure 2B). It was observed in this experiment that the mass transfer resistance was not eliminated by using specific solvents and, from the initial moments of the reaction, the unreacted PETWST surface was covered by product. Thus, probably this resistance had an influence in determining the kinetic parameters of this reaction. In the present work, it was shown that the step of immersing the PETWST samples in water until saturation, before the thermopressing, made these samples more reactive and also that the influence of mass transfer resistance was eliminated only at 1360 rpm. Under these conditions, the activation entropy determined was relatively higher than the activation enthalpy and also it was higher than the activation entropy determined for other papers cited above. This result suggests that the activation entropy value compensates the high activation enthalpy value because the reaction medium is far from its own thermodynamic equilibrium, increasing its reactivity, and in this case the short reaction times to reach maximum conversion are expected. At the present point in our discussion it has been demonstrated that the step of saturating flakes of postconsumer PET in water and then submitting them to thermopressing at 260 °C (obtaining plates) improved the reaction time needed to reach maximum conversion, since the polar groups formed during the thermopressing act as catalysts in the depolymerization. However, the step of thermopressing may make this method costly and unviable for an industrial application. But is the thermopressing an essential step in order to reach maximum conversion in very short times and make this method attractive from a technological point of view? An experiment was carried out to answer this question: the depolymerization of postconsumer PET flakes, which had previously been immersed in water up to saturation (PETWS), without going through the processing step. These flakes were about 0.8 ( 0.34 mm thick. The reactions were carried out at 1360 rpm and at temperatures of 170 and 150 °C. The results of these analyses are presented in parts A and B, respectively, of Figures 17, and were compared with the results obtained from PETWST specimens (flakes of PETW saturated in water and processed at 260 °C) of different initial thicknesses. It is observed in Figure 17A that the PETWS flakes reached 90% conversion after 5 min. This time is about 30 times and 10 times higher than the time needed to reach the same conversion of PETWST samples of thickness 0.65 and 1.0 mm,


Figure 17. Degree of conversion data for PETWS flakes (previously immersed in water) and for PETWST plates of different thicknesses, as a function of reaction time. Reactions were carried out at 1360 rpm and at (A) 170 and (B) 150 °C.

respectively; however, comparing the reaction time observed for PETWS flakes with those obtained for PETWST plates 1.8 and 2.3 mm thick, the results are similar. The same results are observed in Figure 17B. These results lead us to make two observations. First, the thermopressing step increases the reactivity of PETWST samples due to the uptake of water which acts as a hydrolytic agent more efficiently at high temperatures than at room temperature. Thus the process of thermopressing turned the PETWST more reactive than the PETWS flakes. Second, the reaction time required to reach a high degree of depolymerization of PETWS flakes is still shorter than other results from the literature.11-14,16,17,19 This is an indication that the thermopressing step could be eliminated in an industrial application and still good results of degradation would be observed. Thus, the immersion of PETW flakes in water up to saturation is essential, to improve the efficiency of this cheap and clean depolymerization method, which has a high potential for industrial application. Conclusions The depolymerization of flakes of waste PET (PETW) from bottles in nonaqueous alkaline medium was studied. Some reaction parameters considered important to achieve good rates

of PET conversion were evaluated. It was found that pretreatment of the flakes by saturating them in water for 10 days and then submitting them to thermopressing reduced the time needed to achieve the maximum conversion into Na2-TPA. In this case, the improvement observed is due to the hydrolytic degradation that occurred (mainly on the polymer surface) during the thermopressing. However, it was also observed that the thermopressing is a step that can be eliminated and good times are still obtained. Another point noted was the strong dependence on high stirring rates in the solution, in order to reach the maximum polymer conversion in short reaction times. Specific solvents used, such as DMSO, CHA, and THF, did not appear to eliminate the mass transfer resistance in the solution, and the times to reach maximum conversion were longer than ours, in the same interval of temperature. A stirring rate of 1360 rpm in the solution provided the best time of PETWST conversion into Na2-TPA. In this case, the effect of mass transfer did not interfere and this result was corroborated by BET and SEM analysis. Thus, the chemical reaction was rate-determining. The kinetic analysis based on the shrinking-core model of chemical reaction control and the formation and growth of pores and cracks fitted the experimental data very well. The dependence of kv data on the reciprocal thickness values is an indication that the depolymerization can occur preferentially for specimens below 2.3 mm thick, agreeing with the assumption made in deducing the kinetic equation. The apparent activation energy, obtained from an Arrhenius plot, was 172.7 kJ‚mol-1. This parameter is not sufficiently low to explain the very fast reactions and the kv values observed in this present work. The activation enthalpy and activation entropy of the reaction values showed that the activation entropy is sufficiently high to compensate the activation enthalpy, making the PETWST depolymerization a very fast reaction and indicating that the reaction medium was far from its thermodynamic equilibrium. Therefore, the depolymerization method presented here makes this material very reactive and improves this chemical recycling process for industrial application. Acknowledgment The authors are grateful for financial support provided by CNPq-Brazil. Note Added after ASAP Publication: In the version of this paper that was published on the Web October 24, 2006, Figure 7 was mistakenly duplicated and identified as Figure 8. The corrected version of this paper was published on the Web November 8, 2006. Notation PETW ) waste PET PETV ) virgin PET PETWD ) waste PET dried for 4 h at 180 °C PETWH ) waste PET exposed to relative humidity at room temperature PETWS ) waste PET saturated in water by immersion PETVD ) virgin PET dried for 4 h at 180 °C PETWT ) flakes of waste PET processed by thermopressing PETVDT ) pellets of waste PET processed by thermopressing χPET ) PET conversion WiPET ) initial weight of PET sample WrPET ) weight of unreacted PET So ) initial effective surface area of unreacted PET sample

7996


Sef ) effective surface area of unreacted PET sample at any reaction time Sgeom ) geometric surface area of PET sample V ) geometric volume of PET sample A ) geometric area of PET sample V ) rate of reaction for PET sample k ) rate constant kv ) apparent rate constant CA ) initial NaOH concentration F ) density of PET xo ) initial length of PET sample yo ) initial width of PET sample zo ) initial thickness of PET sample zt ) thickness of PET sample at any reaction time c ) constant value a ) constant value h ) Planck constant k ) Boltzmann constant Ea ) apparent activation energy ∆Gq ) activation free energy ∆Hq ) activation enthalpy ∆Sq ) activation entropy Literature Cited (1) Leidner, J. Plastic Wastes; Marcel Dekker: New York, 1981. (2) La Mantia, F. P. Recycling of PVC and Mixed Plastic Wastes; Chemical Technology Publishing: Toronto, 1996. (3) Valenza, A.; La Mantia, F. P. Photo-Oxidation of Blends of Polypropylene With Recycled Polypropylene. Arab. J. Sci. Eng. 1988, 13, 497. (4) La Mantia, F. P.; Curto, D. Recycling of Degraded Polyethylene: Blends With Nylon 6. Polym. Degrad. Stab. 1992, 36, 131. (5) La Mantia, F. P. Recycling of Heterogeneous Plastics Wastes: Is Blends with Low-Density Polyethylene. Polym. Degrad. Stab. 1992, 37, 145. (6) La Mantia, F. P. Recycling of Heterogeneous Plastics Wastes. IIs The Role of Modifier Agents. Polym. Degrad. Stab. 1993, 42, 213. (7) Morrone, M.; La Mantia, F. P. Re-Stabilization of Recycled Polypropylenes. Polym. Recycl. 1996, 2, 17. (8) Paszun, D.; Spychaj, T. Chemical Recycling of Poly(ethylene terephthalate). Ind. Eng. Chem. Res. 1997, 36, 1373. (9) Awaja F.; Pavel, D. Recycling of PET. Eur. Polym. J. 2005, 41, 1453. (10) Scheirs, J. Polymer Recycling, Science, Technology and Application; John Wiley and Sons: New York, 1998. (11) Oku, A.; Hu, L.-C.; Yamada, E. Alkali Decomposition of Poly(ethylene terephthalate) with Sodium Hydroxide in Nonaqueous Ethylene Glycol: A Study on Recycling of Terephthalic Acid and Ethylene Glycol. J. Appl. Polym. Sci. 1997, 63, 595. (12) Wan, B.-Z.; Kao, C.-Y.; Cheng, W.-H. Kinetics of Depolymerization of Poly(ethylene terephthalate) in a Potassium Hydroxide Solution. Ind. Eng. Chem. Res. 2001, 40, 509. (13) Goje, A. S.; Mishra, S. Chemical Kinetics, Simulation, and Thermodynamics of Glycolytic Depolymerization of Poly(ethylene terephthalte) Waste With Catalyst Optimization for Recycling of Value Added Monomeric Products. Macromol. Mater. Eng. 2003, 288, 326. (14) Goje, A. S.; Thakur, S. A.; Diware, V. R.; Chauhan, Y. P.; Mishra, S. Chemical Recycling, Kinetics, and Thermodymics of Hydrolysis of Poly(ethylene terephthalate) Waste With Nonaqueous Potassium Hydroxide Solution. Polym.-Plast. Technol. Eng. 2004, 43, 369. (15) Kao, C.-Y.; Wan, B.-Z.; Cheng, W.-H. Kinetics of Hydrolytic Depolymerization of Melt Poly(ethylene terephthalate). Ind. Eng. Chem. Res. 1998, 37, 1228.

(16) Yoshioka, T.; Okayama, N.; Okuwaki, A. Kinetics of Hydrolysis of PET Powder in Nitric Acid By a Modified Shrinking-Core Model. Ind. Eng. Chem. Res. 1998, 37, 336. (17) Yoshioka, T.; Motoki, T.; Okuwaki, A. Kinetics of Hydrolysis of Poly(ethylene terephthalate) Powder in Sulfuric Acid By a Modified Shrinking-Core Model. Ind. Eng. Chem. Res. 2001, 40, 75. (18) Levenspiel, O. Engenharia das Reaç o˜ es Quı´micassCa´ lculo de reatores; Edgar Blucher: Rio de Janeiro, 1974; pp 303, 304 and 311. (19) Kumar, H. S.; Guria, C. Alkaline Hydrolysis of Waste Poly(ethylene terephthalate): A Modified Shrinking Core Model. J. Macromol. Sci., Part A: Pure Appl. Chem. 2005, 42, 237. (20) Kint, D. P. R.; Ilarduya de, A. M.; Bou, J. J. Munõz-Guerra, S. Poly(Ethylene Terephthalate) Copolymers Containing Nitroisophthalic Units. III. Methanolytic Degradation. J. Polym. Sci., Part A: Polym. Chem. 2002, 40, 2276. (21) Kim, B.-K.; Hwang, G.-C.; Bae, S.-Y.; Yi, S.-C.; Kumazawa, H. Depolymerization of Polyethyleneterephthalate in Supercritical Methanol. J. Appl. Polym. Sci. 2001, 81, 2102. (22) Goto, M.; Koyamoto, H.; Kodama, A.; Hirose, T.; Nagaoka, S. Depolymerization of Polyethylene Terephthalate in Supercritical Methanol. J. Phys.: Condens. Matter. 2002, 14, 11427. (23) Genta, M.; Iwaya, T.; Sasaki, M.; Goto, M.; Hirose, T. Depolymerization Mechanism of Poly(ethylene terephthalate) in Supercritical Methanol. Ind. Eng. Chem. Res. 2005, 44, 3894. (24) Yong, Y.; Lu, Y.; Xiang, H.; Xu Y.; Li, Y. Study on Methanolytic Depolymerization of PET With Supercritical Methanol for Chemical Recycling. Polym. Degrad. Stab. 2002, 75, 185. (25) Ruvolo-Filho, A. C.; Soares, K. Regeneraç aõ do A Ä cido Terefta´lico (TPA) a partir da reaç aõ de despolimerizaç aõ do Poli(Tereftalato de Etileno) Reciclado via Hidro´lise Alcalina em Meio de Etileno Glicol (EG) Puro. B.R. Patent PI 0400074-9, 2004. (26) Crotti, A. E. M.; Vessecchi, R.; Lopes, J. L. C.; Lopes, N. P. Electrospray ionization mass spectrometry: chemical processes involved in the ion formation from low molecular weight organic compounds. Quı´m. NoVa 2006, 29, 287. (27) Campanelli, J. R.; Kamal, M. R.; Cooper, D. G. A Kinetic Study of the Hydrolytic Degradation of Polyethylene Terephthalate at High Temperatures. J. Appl. Polym. Sci. 1993, 48, 443. (28) Villain, F.; Coudane, J., Vert, M. Thermal Degradation of Poly(ethylene terephthalate) and the Estimation of Volatile Degradation Products. Polym. Degrad. Stab. 1994, 43, 431. (29) Sammon, C.; Yarwood, J.; Everall, N. An FT-IR Study of the Effect of Hydrolytic Degradation on the Structure of Thin PET Films. Polym. Degrad. Stab. 2000, 67, 149. (30) Ruvolo-Filho, A. C.; Carvalho de, G. M. The Mesomorphic Phase Structure in PET Films: A Conformational Analysis. J. Macromol. Sci.: Phys. 1996, 35, 255. (31) Goje, A. S.; Thakur, S. A.; Patil, T. M.; Mishra, S. Glycolytic Aminolysis of Poly(ethylene terephthalate) Waste for Recovery of ValueAdded Comonomer at Atmospheric Pressure. J. Appl. Polym. Sci. 2003, 90, 3437. (32) Mishra S.; Goje, A. S. Chemical Recycling, Kinetics, and Thermodynamics of Alkaline Depolymerization of Waste Poly(ethylene terephthalate) (PET). Polym. React. Eng. 2003, 11, 963. (33) Karayannidis, G. P.; Chatziavgoutis, A. P.; Achilias, D. S. Poly(Ethylene Terephthalate) Recycling and Recovery of Pure Terephthalic Acid by Alkaline Hydrolysis. AdV. Polym. Technol. 2002, 21, 250. (34) Mishra S.; Goje, A. S. Kinetics of Glycolysis of Poly(Ethylene Terephthalate) Waste Powder at Moderate Pressure and Temperature J. Appl. Polym. Sci. 2003, 87, 1569. (35) Gu¨ç lu¨, G.; Kasgo¨z, A.; O ¨ zbudak, S.; O ¨ zgu¨mu¨s, S.; Orbay, M. Glycolysis of Poly(ethylene terephthalate) Wastes in Xylene. J. Appl. Polym. Sci. 1998, 69, 2311.

ReceiVed for reView April 25, 2006 ReVised manuscript receiVed July 25, 2006 Accepted September 16, 2006 IE060528Y

Chemical Kinetic Model and Thermodynamic Compensation Effect of

Recommend Documents