Chemical recycling of PET by catalyzed glycolysis: Kinetics of the heterogeneous reaction

Chemical Engineering Journal 173 (2011) 210–219

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Chemical recycling of PET by catalyzed glycolysis: Kinetics of the heterogeneous reaction Mateus E. Viana, André Riul, Gizilene M. Carvalho ∗ , Adley F. Rubira, Edvani C. Muniz Grupo de Materiais Poliméricos e Compósitos, GMPC, Departamento de Química, Universidade Estadual de Maringá, Av. Colombo 5790, 87020-900, Maringá, Brazil

a r t i c l e

i n f o

Article history: Received 29 March 2011 Received in revised form 5 July 2011 Accepted 20 July 2011 Keywords: Glycolysis PET Granulometry Surface area Mathematical model Glycolysis kinetic

a b s t r a c t Polyethylene terephthalate post-consume (PET-pc) glycolysis was investigated by the use of ethylene glycol (EG) and zinc acetate, as catalyst. It was focused the kinetic aspects through use of mathematical model specially developed for application in this study. The grains-lot was sieved in different size ranges and a relation between surface area and granulometry, surface area and temperature on the conversion and depolymerization rate was proposed. At temperatures ranging 180–190 ◦ C the depolymerization rate is quite elevated and almost 100% of conversion is obtained up to 3 or 4 h reaction time. For lower temperatures (170–180 ◦ C), equilibrium is achieved and it becomes more important as the temperature is decreased. The conversion profile showed an initial activation stage where the mass transfer between the liquid and solid phases is minimal. The proposed mathematic model was based on these findings and on reaction mechanism that differentiates the reaction sites present in the PET surface. By that model the value of rate constant (k) for each temperature, and the dependence of k with 1/T was calculated. Four our best knowledge it is the first time that a mathematical model considers the activation stage in the earlier times of PET depolymerization reaction. The inputs yielding, time and temperature were included in the used mathematical model that fits very well the experimental data obtained at temperatures higher than 180 ◦ C. This model helps to predict the necessary mass of PET for producing a desired amount of products. © 2011 Elsevier B.V. All rights reserved.

1. Introduction Technological advances in the manufacture of PET allowed it to be produced at low cost. Allied to its mechanical properties, this has led to a significant increase in the production of this polymer. According to the Brazilian PET industry association, ABIPET (Associac¸ão Brasileira da Indústria do PET) [1], the quantity and proportion of PET that is recycled have been growing year-by-year and currently 263 k Tons (55.6% of production) are recycled. There are three main types of PET-recycling [2–6]: (a) chemical recycling (or depolymerization); (b) quaternary recycling (energy recovery); and (c) mechanical recycling. Chemical recycling such as depolymerization by hydrolysis [7–9], alcoholysis and glycolysis [10–13] have been recently gained much attention. For instance, terephthalic acid (TPA) and ethylene glycol (EG) can be recovered and used as raw materials in many industrial processes, including polymer synthesis while the bis-hydroxyethyl terephthalate (BHET) can be used in synthesis of new PET or other co-polymers. Lorenzetti et al. [2] focused on the resulting products in their review of PET degradation methods. Their study shows that gly-

∗ Corresponding author. Tel.: +55 44 3261 3664; fax: +55 44 3261 4125. E-mail address: [email protected] (G.M. Carvalho). 1385-8947/$ – see front matter © 2011 Elsevier B.V. All rights reserved. doi:10.1016/j.cej.2011.07.031

colysis has advantages over other degradation methods because of the versatility of the resulting product (BHET). Important studies have been published by Pardal and Tersac [11–13] on glycolysis of post-consume PET (PET-pc). In the first study [11], the reactivities of different glycols used in the depolymerization of PET were compared. In a later study [12], the authors evaluated the kinetics of heterogeneous glycolysis of PET with diethylene glycol (DEG) at 220 ◦ C. The change in total mass in each phase was evaluated and it was observed that initially there is an “induction” period (of about 15 min) with minimum mass transfer between the phases. Subsequently, the reaction accelerates (60–90 min) and then the reaction rate decreases. A gradual decrease in the PET molar mass was demonstrated using size exclusion chromatography (SEC), and the authors concluded that under the used conditions the monomer to oligomer ratio remains nearly the same during the reaction but at end of the reaction the monomers constitutes the larger fraction of final products. Yoshioka et al. [14] studied the kinetics of the hydrolysis of micronized PET catalyzed by nitric acid at temperatures from 70 ◦ C to 100 ◦ C (heterogeneous reaction). The principal finding was that the reaction rate depends on the effective area (proportional to the fraction of unreacted PET). This model correlated well with the experimental data, although, in this case, the operating conditions of the reaction did not give rise to the “induction period” found in

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Nomenclature a ABET A0 Ap Aps Au c d Dp f(%) K k k1 L m(t) m0 ma mBHET MBHET MEG moligomer mprod mtheo mu ¯v M r s s S0 S1 S2 St ti Vu X yi [] ε red

Mark–Houwink–Sakurada parameters surface area from BET method initial contact area between the PET-EG phases surface area of the actual particle area of a perfect sphere with volume equal to that of the a actual particle unitary area of a particle bigger size of PET grains to 3 parameters model proportionality constant mean mesh size of the sieves mass fraction of sample retained in a specific mesh size of the sieves. Mark–Houwink parameters rate constant of the reaction rate constant of the reaction mean thickness of PET grains residual mass of solid PET as function of time mass of PET added to the reactor and m is the mean mass values for each sample BHET mass molar mass of bis(hydroxiethyl)terephthalate molar mass of ethylene glycol mass of oligomers mass of products retained on the filter paper theoretical mass of BHET calculated based on the weight of reacts PET mean mass of a grain average viscosimetric molar weight PET grains radius from geometrical two-parameter model standard deviation of the mass of the samples standard deviation of the thickness of PET grains carbonyl groups that do not generate reaction products when cleaved (the middle of the chain) carbonyl groups that generate reaction products when cleaved (end of the chain) carbonyl group does not change the polymer the total number of sites at the beginning of the reaction (t = 0) induction time mean volume of a grain percentage conversion of solid PET ratio between the number of sites of a determined species on the surface of the polymer intrinsic viscosity reaction yield reduced viscosity sphericity

the glycolysis by Pardal and Tersac [12]. In Yoshioka et al.’s study, the fastest reaction rates occurred at the beginning of the reaction, when the contact surface between the phases remained greatest. Wan et al. [8] proposed a kinetic model for the hydrolysis of PET catalyzed by potassium hydroxide. In such model, the reaction rate is proportional to the contact-area between the phases and to the concentration of KOH (with the first and second order hypotheses tested). The rate of reaction is first order with regard to both of these factors. Higher reaction rate in the first moments was found by this model and was attributed to the greatest contact area and also to the concentration of KOH. Ruvolo and Curti [15] published the first study relating the influence of surface area on the alkaline hydrolysis of PET in ethylene

211

glycol solution. They compared the geometric area and the effective surface area of PET, as measured by BET (Brunauer–Emmett–Teller) analysis, and demonstrated that the effective area increases as the reaction progresses. Based on this, the authors proposed a kinetic model in which the effect provoked by the decrease in geometric area, due to the reaction, on the reaction velocity is considered. The glycolysis of PET has been object of study from different point of view. Although the influence of variables such as time, temperature, EG:PET molar ratio, nature of catalyst, concentration, particle size, stirring rate, reaction time on the glycolysis process have been investigated [15–17], available kinetic models do not cover all aspects of depolymerization process. The method of catalyzed glycolytic depolymerization with optimization technique was described by Goje and Mishra [16]. The authors pointed that procedures and resulting kinetic parameters vary with assumed kinetic model and applied data fitting procedure. The different values of activation energy (Ea ) cited in literature for depolymerization of PET was attributed to the changes in reaction parameters and to different chemicals employed for PET depolymerization. According to Paszun and Spychaj [6], the literature related to the glycolysis of PET covers mainly the application of the resulting products, while only few authors turn their attention to the reaction kinetics. When glycolysis is carried out below the melting temperature of PET, the reaction medium consists, initially, of a solid phase (pure PET) and a liquid phase (EG + catalyst). However, as the reaction proceeds, other phases appear: swollen PET, a solution of polyesters and oligoesters, until at the end of the reaction there is only a liquid phase (solution of glycols and oligoesters) [12]. The depolymerization changes from a heterogeneous reaction to a homogeneous reaction, as the reaction progresses. López-Fonseca et al. [17] developed a theoretical model to predict the time conversion of PET during glycolytic depolymerization. The authors observed that at initial stages the reaction occurred in a heterogeneous phase and only at higher reaction times the reaction became a single homogeneous phase. The kinetic model was developed according to a homogeneous reversible catalytic model and was found to be consistent with experimental data in the range temperature of 150–196 ◦ C. If the depolymerization reaction occurs initially on the surface of the PET particles, what is the influence of contact-area between the phases (that is, the surface area of the PET grains)? The progress of the reaction depends on the EG diffusing onto the surface of the PET and on the removal-rate of the depolymerized material from the surface of the PET (dry and swollen) into the solution. Hence, the diffusion process can be taken to control the reaction rate and, accordingly, the rate at which the solution is stirred also becomes an important parameter in the reaction mechanism. In one of their studies, Pardal and Tersac [12] examined the influence of temperature, the presence of a catalyst and the morphology of the PET. The observation that reactivity is much greater at 220 ◦ C suggests that the diffusion of diethylene glycol in the PET is favored at this temperature, increasing the reaction rate as compared to reactions at lower temperatures. With the objective of contributing to the understanding of the glycolysis reaction mechanism for PET-pc with EG, this study proposes a new kinetic model for this reaction. The proposed reaction mechanism is based on the possibility that the PET chain is cleaved at different sites by the EG and that the amount of cleavages depends on the ratio of the number of sites on the surface of the PET grains. The following steps were performed to achieve this objective (i) determination of the geometric surface area of the PET-pc grains using geometric models with two and three parameters; (ii) experimental determination of conversion (X) as a function of the granulometry of the grains of PET-pc; (iii) study of the influence of time and temperature on the heterogeneous depolymerization reaction; (iv) determination of the PET-pc conversion (X) using the proposed model, for different time and temperature conditions, and

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comparison with the experimental results; (v) characterization of the products obtained in the PET depolymerization reaction by DSC. 2. Experimental method 2.1. Materials EG and zinc acetate (catalyst) were acquired from Synth (Brazil) and used without purification. PET-pc, from soft drinks bottles, supplied by the company Plaspet Reciclagens Ltda (Maringá, Brazil), was washed and dried in an oven at 50 ◦ C to constant mass. Viscosity measurements were made at 25 ◦ C in a 1:1 solution of 1,2-dichlorobenzene/phenol (m/m) to estimate the viscosity-average molecular weight of PET. The equation due Mark–Houwink–Sakurada ¯ va [] = K M

(1)

was used, being the values of K and a equal to 0.469 × 10−3 dL g−1 and 0.68, respectively [18]. The intrinsic viscosity value found was ¯ v ) cal[] = 0.78 dL g−1 . The viscosity-average molecular weight (M culated for the polymer was 54.600 g mol−1 . 2.2. Analyses To study the influence of the size of the PET particles on the kinetics of the reaction, a granulometry test was carried out using a series of Tyler standardized sieves [19]. To do this, samples of PET, washed and dried in an oven at 50 ◦ C to constant weight, were vibrated for 20 min in a sieves set to split them into six size ranges. The weight distribution as a function of mean particle size was evaluated by weighing the fraction retained by each sieve. The mean mass of a grain (mu ) was estimated by weighing 15 random samples containing n = 30 grains each. The value of mu was calculated from the mean mass, as given in equation

30

mu =

n (mu )i i=1 i 30 n i=1 i



30

=

m

i=1 30 n i=1 i



(2)

The mean volume of a grain (Vu ) was estimated based on the nominal density of PET (1.375 g cm−3 ) and its mean mass, mu . The Grubs test was applied to the data to reject anomalous data [20], after which the values of mu and Vu were estimated for each size range. As the mean thickness (L) of particulate PET is limited by the thickness of the bottles, a digital micrometer was used for measuring this axis for each granulometry. Thus, two hypothetical models related to the characteristic geometric-thickness of this material could be proposed and evaluated. The surface area was measured by means of BET adsorption isotherms using a Quantachrome® instrument, model NOVA-1000. The mean grain area values (ABET ) as a function of granulometry were used to evaluate the best geometric model further utilized for calculating the area of a single PET particle. The glycolysis reactions were designed to produce conversion curves as a function of a given variable keeping the others constant. The variables studied were: time, temperature and particle size. The mass of PET-pc used for each run was 15 g (78 mmol repeat units) and the initial amount of the zinc acetate catalyst was 1.76 g (8 mmol), giving a mol ratio of 9.75:1 for PET:zinc acetate. The amount of EG, 60 g, was used thus in great excess to avoid problems of homogenization in the reaction batch. The reactions were carried out at atmospheric pressure using a three-necked flask equipped with magnetic stirring, heating, a thermometer and a reflux condenser. EG and the catalyst were weighed and added to the reactor, and then heated to a requested temperature. Simultaneously, the PET-pc was heated to the same temperature, in an oven, and then quick transferred to the reactor. A stopwatch was triggered at the

moment the PET-pc was added. When a specified reaction time had been elapsed, the heating was removed and boiling water was slowly added to the system. Next, the contents of the reactor were filtered (first filtration) using a Tyler series sieve with a mesh size of 80 to collect the unreacted PET (PET-NR), and more boiling water was used to remove the product eventually adhered to the PET. The total volume of water added was 300 mL for each run. The filtrate was cooled to 4 ◦ C for precipitating the glycolysis products, which were further filtered (second filtration) using quantitative filter paper, and dried in an oven to constant weight. The ratio between the mass resulting of second filtration products (mprod ) and the theoretical mass of BHET obtained (mtheo ), in accordance with the stoichiometry of the reaction, was used to analyze the reaction yielding by the equation ε=

mprod mtheo

(3)

The conversion (X) of solid PET was calculated using X=

m0 − m(t) m0

(4)

where m0 is the mass of PET added to the reactor and m(t) is the remaining solid PET mass as a function of time. The relationship between conversion and the PET-pc geometric area was evaluated for the glycolysis reaction at 180 ◦ C for 90 min. A plot of conversion against time at the different temperatures for A0 = 593.5 cm2 was produced and analyzed. Thermal characterization of the samples was performed using a Shimadzu DSC 50 calorimeter, with a heating rate of 10 ◦ C min−1 in an atmosphere of nitrogen at a flow rate of 20 mL min−1 . The DSC curve obtained for the product from second filtration was compared with the DSC curve for the oligomeric diols derived from terephthalic acid [18]. 3. Mathematical modeling 3.1. The reaction mechanism and definition of variables In this study, a kinetic model with equations based on the different possibilities for polymer chain cleavage by EG is proposed. The following hypotheses were considered for building the model: (a) The reaction between an EG molecule and an ester group located at the surface of the polymer causes a cleavage of polymer chain at the point of the reaction. The reaction occurs at the interface between the solid PET-pc and the diffused EG. (b) If the reaction occurs between an EG molecule and an ester group situated close to the end of PET chain, the each cleavage contributes to the reaction progressing and a leaving group is formed consisting of a monomer (BHET) or an oligomer of low molar mass. (c) If the reaction occurs between an EG molecule and an ester group situated far from the end of the chain, the cleavage does not contribute to the reaction progress. In this case, the polymer molecule splits into two, forming two new chain-ends at the point of cleavage. If this happens, the mass of the polymer is increased by the “accommodation” of a molecule of EG relative to the mass of polymer chain before the cleavage. The sites where reaction may take place, that are the ester groups located at the surface of the polymer, are classified as: S0 , S1 and S2 . The S0 sites indicate carbonyl groups that do not generate reaction products when cleaved (situated at the middle of the chain). The S1 sites indicate carbonyl groups that generate reaction products when cleaved (situated at the end of the chain). The S2 sites are inert, as a reaction involving these carbonyl groups do not

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change the mass of polymer chain. In this case the intermediate resonance structure would contain two identical leaving groups, which are two ethylene glycol molecules. To simplify the model, only BHET is considered to be a leaving group. Hence, there are two S1 -type sites next to each end of the chain. These considerations are illustrated in Fig. 1. Another important definition to be considered in the proposed mathematical model is the ratio between the number of sites of a determined species on the surface at given reaction time, t, and the number of sites at the beginning of the reaction, given by S (t) yi = i St

(5)

where yi is the ratio of sites of type i. Si (t) is the number of sites of type i located on the surface of the polymer, and St is the total number of sites at the beginning of the reaction (t = 0). At t = 0, almost all of the sites on the surface are S0 -typed, such that the first cleavages do not contribute to the conversion of the polymer, but to the creation of “chain ends” at the polymer surface (generating S1 sites). Accordingly, there is an increase in the yS1 ratio and a decrease in the yS0 ratio, as shown in the schema of Fig. 2. As a consequence of the yS1 growing ratio, an increase in the number of effective cleavages occurs, that is, the cleavages that generate leaving groups rise (reaction products). Accordingly, the solid phase mass increases with each cleavage at S0 due to the absorption of EG, and decreases with cleavages at S1 due to the formation of BHET because EG is also absorbed in this situation. 3.1.1. Definition the differential equations The material balance equation (instantaneous mass balance) to a dynamic system gives the following equation [9], being the units of each term in Eq. (6) [mass time−1 ]. dm ˙ in − m ˙ out =m dt

(6)

The terms for the rates of mass entering and leaving will be substituted by differential or algebraic equations, as required for each specific case. Mathematically, the proposed mechanism can be described by the material balance, as given in Eq (6), where the solid PET granule is considered as the dynamic system. According to this equation, the change in the PET granule mass over time (dm/dt) equals the difference between the mass entering in the granule and the mass ˙ in ) rises as EG leaving out the granule. The rate of mass entering (m attacks the S0 sites. Taking this rate as being of first order in relation to yS0 and to mass of solid residual PET, gives the equation ˙ in = kyS0 (t)m(t) m

(7)

where k is a rate constant dependent on temperature and represents the cleavage rate. ˙ out ) as EG attacks the S1 sites, The rate of mass leaving rises (m at which time the EG molecules condense onto the polymer and simultaneously soluble BHET molecules leave out of PET chain. Taking the leaving rate to have a first-order relationship with yS1 and to mass of solid residual PET, gives the equation ˙ out = k1 yS1 (t)m(t) m

(8)

where k1 is the rate constant of the reaction, also temperaturedependent. Taking the cleavage velocity to be independent of the site type, the probability of cleavage is greater for sites existing in greater numbers. A cleavage at S0 site produces an increase on polymer mass equal to the mass of EG molecule, and a cleavage at S1 site produces condensation of one EG molecule into the polymer while,

213

simultaneously, the one BHET molecule leaves. Accordingly, the ratio between the rate constants k and k1 is given by MEG k1 = 0.32299 = d = MBHET − MEG k

(9)

Substituting Eqs. (7)–(9) into (6), gives dm(t) dt

= [kyS0 (t) − dkyS1 (t)]m(t)

(10)

To find a solution for this equation, it is necessary to express the variables as a function of time, in order to generate an analytical solution for the conversion as a function of time. This makes possible to evaluate the effect of temperature on the rate constants. Expressing m(t) as a function of X. The following equation m(t) = m0 (1 − X)

(11)

arises immediately from Eq. (4). Differentiating this equation and substituting into Eq. (10), gives dX(t) = [kyS0 (t) − dkyS1 (t)][1 − X(t)] at X(0) = 0 dt

(12)

Expressing yS0 and yS1 as functions of time. As the term is proportional to the S0 cleavage rate, the following hypothesis can be written: dyS0 (t) = kyS0 (t) at yS0 (0) = 1 dt

(13)

In accordance with the illustration given in Fig. 1, taking into account that each attack on an S0 site will form four S1 sites, the following differential equation is proposed dyS1 (t) = 4kyS0 (t) at yS1 (0) = 0 dt

(14)

Hence, three ordinary differential equations (ODE) with their respective contour conditions have been defined and were used to obtain an analytical solution for the conversion as a function of time. 4. Results and discussion 4.1.1. Granulometry and the surface area of PET-pc grains The granulometric characterization of the PET-pc under investigation gave seven different particle sizes (Table 1). The term Dp is the mean mesh size of the indicated sieves. The sample of the fraction at the bottom of the sieve set (7th sieve) was excluded from the other analyses due to the low volume of this sample. The particles in all size ranges presented very different axis sizes. As the thickness of the grains is limited to the thickness of the PET bottles, so it was not possible to take these as spherical particles with an average diameter equal to Dp , which is a common simplification used for characterizing solid particles [19]. As it is useful to relate the area to the mean size of the particles, two geometric models were tested. The first geometric model (twoparameter model) assumes that the solid can be represented by cylindrical particles, being the area dependent on the mean diameter and thickness of the particles, as shown in left side of Fig. 3. The mean radius is calculated from the values obtained for the thickness and the volume of each particle. The second geometric model (three-parameter model) assumes that the solid can be represented by particles with a rectangular profile, as shown in right side of Fig. 3. The shorter axis, c, is equal to the value estimated for L; the intermediate axis, b, was taken to be equal to the value of Dp for the particles; the longer axis, a, was calculated from the values for Vu , a and b.

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Fig. 1. Schematic representation of sites S0 , S1 and S2 in the PET molecule.

Fig. 2. Illustration of how S0 decreases and S1 increases during the conversion (X) of PET-pc. Table 1 Estimates for mu and Vu and L as a functions of the granulometry from 15 samples of 30 grains each. Dp (mm)

f (%)

ma (g)

s (g)

mu (mg)

Vu (mm3 )

L (mm)

s (mm)

7.18 5.56 3.56 2.03 1.44 0.89

5.43 25.15 60.62 6.16 1.80 0.77

1.1893 0.8212 0.6371 0.2140 0.1575 0.0921

0.1400 0.0243 0.0201 0.0176 0.0152 0.0117

39.64 27.37 12.74 3.567 2.230 1.149

28.83 19.91 9.267 2.594 1.622 0.835

0.5465 0.5014 0.4400 0.4027 0.3735 0.3401

0.0109 0.0093 0.0365 0.0200 0.0548 0.0346

Sample mass of 30 grains = ma ; Standard deviation of mass = s; Standard deviation of thickness (L) = s ; Mean mesh size of the shieves = Dp ; Unitary mass of grains = mu ; Unitary volume of grains = Vu ; Percent of PET mass retained in the Tyler sieves f(%).

Another important characteristic of a given sample is its form factor. The most common form factor for solid particles is the sphericity ( ), a form factor based on the surface and the volume of particles [21,22]. The sphericity is defined as being the ratio between the surface area of a perfect sphere with volume equal to that of the particle and the surface area of the actual particle, given by =

Aps Ap

(15)

where Aps is the area of the equivalent sphere; Ap is the area of the particle. Accordingly, 0 < < 1, and = 1 for an ideal spheric particles. Sphericity ( ) was calculated for the PET-pc grains from the surface area data obtained using two geometric assumptions. The two geometric assumptions take into account a thickness limit for the particles. Table 1 gives the mean mass values for each sample, ma , and the values calculated for mu , Vu and the standard deviation (s). The increase in the PET thickness as a function of Dp

Fig. 3. Hypothetical models surface area. (a) Two-parameter model and (b) threeparameter model.

was attributed to the fact that it is more difficult to grind thicker bottles. The capacity of the two hypothetical geometric models to correlate the geometric area to the PET granulometry was tested using these data. 4.2. Evaluation of the models used to calculate the surface area of the PET grains The estimated parameter values (Table 1) and the two hypothetical models (Table 2) were used to calculate the surface area and the sphericity of the PET grains. For an additional analysis, the surface area was measured using the BET method. However, instrument limitations allowed measurements of only the three smallest size ranges. The instrument measures the specific area (Aesp = area mass−1 ) of the PET. Hence, the values were multiplied by mu to calculate the unitary area (ABET ). The values calculated for Au by applying the two models correspond to a geometric area, without taking surface roughness into account. The values obtained for the sphericity are very low, providing evidence of the great surface irregularity of PET. For the area determined using the BET method (ABET ), which does take surface roughness into consideration, the values are greater than the calculated geometric areas; however, they must be proportional to Au . Aiming do a selection of best model, the Zingg Classification [23] was used. It deals with the morphology of gross particles, separating them into four classes (Fig. 4). The values of p and q were calculated from the values of a, b and c in the three-parameter model. For the lamellar PET grains (p and q ≤ 2/3), the values of Au were estimated using the three-parameter

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215

Table 2 Unitary area and sphericity as a function of granulometry. Dp (mm)

7.18 5.56 3.56 2.03 1.44 0.89

2 parameters model

3 parameters model

r (mm)

Au (mm2 )

4.223 3.555 2.589 1.432 1.176 0.884

125.7 90.62 49.28 16.51 11.44 6.804

0.362 0.392 0.433 0.553 0.583 0.631

c (mm)

Au (mm2 )

7.804 7.142 5.916 3.173 3.015 2.761

127.5 92.26 50.46 17.07 12.01 7.397

ABET (mm2 ) 0.357 0.385 0.423 0.535 0.556 0.580

– – – 52.00 36.57 20.48

Fig. 4. Zingg classification of different geometric particles.

A0 = nAu

(16)

where n is the number of particles present in the reaction medium, estimated for each size range by the ratio between the total mass (ma ) added to the reactor and the unitary mass (mu ). The results are given in Table 3. As expected, Au was greater for the larger size ranges, whereas A0 was smaller for the larger size ranges.

90

Conversion (X, %)

model, while for the discoidal PET grains (p ≤ 2/3 and 2/3 < q ≤ 1.0), the values of Au used were calculated using the two-parameter model. To calculate the initial contact area between the PET-EG phases (A0 ) for each size range, the values of the unit mass and the total mass added to the reactor were used, as given in equation

60

30

4.3. Glycolysis reactions

400 The relationship between the conversion and the geometric area of the PET-pc grains in the glycolysis reaction, (T = 180 ◦ C and t = 90 min) were evaluated as a function of the initial contact area, A0 , and are given in Fig. 5. As the reaction time was fixed at 90 min, it can be seen that the reaction velocity is largely dependent on the contact area. As pointed by some authors [12,15–17,24], stirring rate influence the conversion of PET. In conditions of high solution stirring rate the mass transfer resistance can be eliminated in the reaction medium. In all experiments the magnetic stirring is maintained constant at ca. 200 rpm and the mass transfer mechanism was not eliminated neither considered in the mathematical model. To estimate the PET mass required to produce a specific mass of product (mprod ), the product yield was assessed. In accordance with the stoichiometry of the reaction, 1.323 g of BHET (mtheo ) is formed for every gram of PET reacted. However, due to inherent process losses and to incomplete depolymerization, the mass of products obtained on the filter paper, after drying, was smaller than the theoretical BHET mass, mtheo . The conversion (X) for the reactions was

600

800

1000

Initial contatct surface (Ao, cm2) Fig. 5. Conversion of PET as a function of initial contact surface (reaction 90 min, at 180 ◦ C).

defined in Eq. (4). From this equation and take into account the stoichiometry of PET glycolysis to form BHET, the following equation was obtained: ε=

mprod mtheo

=

mprod 1.323(m0 X)

(17)

The mass of products for each conversion was determined. All of the values were normalized for an initial PET mass of 15 g. Subsequently, to calculate the mean reaction yield (ε), the mass of products formed was compared with the theoretical value (mtheo ). The results are given in Fig. 6.

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Table 3 Values of p and q and the Zingg classification of the particles studied and the surface area for a 15 g sample of PET. Dp (mm)

p

q

Class

Au (mm2 )

mu (mg)

n

A0 (cm2 )

7.18 5.56 3.56 2.03 1.44 0.89

0.072 0.090 0.124 0.198 0.259 0.382

0.920 0.779 0.602 0.640 0.478 0.322

discoidal discoidal lamelar lamelar lamelar lamelar

125.7 90.62 50.46 17.07 12.01 7.397

39.64 27.37 12.74 3.567 2.230 1.149

376 553 1176 4258 6726 13055

473.3 501.6 593.5 727.0 808.0 965.7

25 100

80

75

%)

15

10

40 mprod

5

mtheo

0 0

20

40

60

80

20

X (%)

60

yield (

mass (g)

20

100

o

170 C o 175 C o 180 C o 185 C o 190 C

50

25

0 100

0

Conversion (X, %)

0

Fig. 6. Reaction yield in comparison with maximum theoretical yield (reaction 90 min, at 180 ◦ C).

50

100

150

200

250

Reaction time (min) Fig. 7. Profile of PET-pc conversion with A0 593.5 m2 against time at different temperatures.

The left vertical axis on Fig. 6 gives the values of mprod and mtheo ; the right vertical axis gives values of ε. The Grubbs test suggests that the yield from the smallest conversion reaction should be excluded when calculating the mean yield (as the conversion is small, any loss results in large errors). Excluding the smallest conversion, the mean reaction yield was 91.6%. Therefore, the mass of products collected on the filter paper can be estimated, in terms of mean value, using

area between the phases. Note that, for the used operating conditions, the induction period is greater at lower temperatures. This behavior was not predicted by the proposed model and suggests that diffusion may play an important role in the reaction mechanism allowing the reaction to take place more readily in the solid phase at temperatures above 180 ◦ C.

mprod = 1.212m0 X

4.5. Mathematical modeling

(18)

4.4. Heterogeneous depolymerization kinetics for the glycolysis of PET The influences of the reaction temperature and time on the reaction conversion were evaluated simultaneously for PET samples of initial surface area of 593.5 mm2 , due the high volume of this sample. The graph of conversion as a function of time was plotted for 170, 175, 180, 185 and 190 ◦ C, as shown in Fig. 7. The conversion rate (dX/dt) shows a delay at initial reaction times (“activation” time), manly at 170 and 175 ◦ C. This behavior differs from that described in the literature for mathematical models of PET degradation, but it agrees with the results of Pardal and Tersac [12]. In the present study, this behavior was attributed to the types of polymer surface sites. During the initial period of the reaction, nearly all of the surface sites were of S0 type and the first cleavages did not contribute to the conversion of the polymer. During the induction time, cleavage of mainly this type occurs and produces “chain ends” on the polymer surface (production of S1 ). After a certain number of groups at S1 sites have been generated, the number of effective cleavages (at the S1 sites) increases, increasing the conversion of PET-pc into reaction products (BHET), followed by a subsequent decrease as the reaction progress. The decrease in (dX/dt)T for longer reaction times can be explained by the decrease in the solid phase and, consequently, in the contact

4.5.1. Analytical solution The analytical solutions for the ODEs were obtained using the computational tool Maple11TM . The rate constant was estimated using the PolymathTM software. The differential equations and the experimental data were inserted into the algorithm to obtain the best fit. To achieve correlation between k and T, a graph of ln(k) versus 1/T was constructed for these 5 points, thus the parameters for the Arrhenius equation were extracted from the plots of Fig. 8. Note that a better fit is obtained when two temperature ranges, 170–180 ◦ C; and 180–190 ◦ C, are considered. Considering only the three higher temperatures (180, 185 and 190 ◦ C) the equation k = 572.5 exp(−5013.2/T )

(19)

is obtained. From this equation the calculated value for Ea was 41.7 kJ/mol. For the lower temperatures (170, 175 and 180 ◦ C), the best fit in Fig. 8 gives the equation mprod = 1.212m0 X

(20)

is obtained and from this equation the Ea value calculated was 99.6 kJ/mol. The Ea values reported for PET depolymerization by various researchers are different [15–17]. The different values of Ea were attributed to the change in reaction parameters and different chemicals employed for depolymerization of PET [16]. The value of Ea calculated for lower temperatures, 99.6 kJ/mol, agrees

M.E. Viana et al. / Chemical Engineering Journal 173 (2011) 210–219

-4,4

y=-11977x+21.69 R2=0.990

-4,6

9

k=2.637.10 e-11977/T

-4,7 -4,8

lnk

-4,9 -5,0 -5,1 -5,2

-5,4

y=-5013.2x+6.346 2 R =0.994 -5013.2/T k=572.5e 0,00218

80

40

0 170

-5,5 0,00216

induction time, t i (min)

120

-4,5

-5,3

217

0,00220

0,00222

0,00224

0,00226

1/T (K -1 )

180

190 o

temperature C Fig. 10. Induction times (ti ) at different temperatures. The ti value was obtained, in each case, from an intercept to the straight line in the major decomposition stage.

Fig. 8. Values of k as a function of 1/T. Fitting for lower temperatures (170 175 and 180 ◦ C, dash line) and higher temperatures (at 180, 185 and 190 ◦ C, solid line).

with the values reported in the literature, ranging between 85 and 100 kJ/mol, for the catalytic glycolysis of PET. The value of Ea calculated for higher temperatures, 41.7 kJ/mol, is less than values from other researches. Therefore, this small value can indicate that the glycolysis was rate determining by the kind of sites in the PET surface. In our case these two values of Ea obtained indicated that in the conditions utilized in this work, the mechanism of reaction is, probably changed as the temperature change from 170–180 ◦ C to 180–190 ◦ C. For the reaction to proceed EG must first reach the surface of PET and then access to any site S1 . After the BHET molecule be released from PET grain, new site is formed in the reminiscent chain. Temperature affects the kinetic energy of molecules in solution, so that at low temperatures the low kinetic energy causes the reaction rate depends on the mass transfer process. At higher temperatures the average kinetic energy of molecules in solution is sufficient to overcome this barrier and the reaction rate becomes controlled only by the access of EG molecules to sites S1 . Thus the model gives good results only under conditions where mass transfer has no control over the process. The validity of the model was confirmed by comparing the experimental data with the data calculated for each of the temperatures. The values for k in the analytical solution were substituted for the relationships given above, and the results given by the model are shown together with the experimental data in Fig. 9(a) and (b).

These results point to the consistency of the model presented here for 180 ◦ C and higher temperatures (Fig. 9(a)). This model brings a new perspective on heterogeneous depolymerization, even explaining the “induction period” first reported by Pardal and Tersac [12]. However, the model was unsatisfactory at temperatures below 180 ◦ C (Fig. 9(b)), as already mentioned. As the glycolysis reaction occurs below the PET melting temperature, it is a heterogeneous reaction. In this case, the effect of the EG diffusion mechanism at the surface of the PET-pc grains and the diffusion of the reaction products in the solution must be considered in addition to the sites available for effective cleavage. Above 180 ◦ C, this is not the determinant effect and it is the number of effective cleavages that controls the reaction velocity. The proposed model fits the experimental data perfectly at these temperatures. The proposed model does not fit the experimental data for temperatures below 180 ◦ C. In this temperature range, the greater induction period (Fig. 10) suggests that, apart from the numbers of available sites for effective cleavage, the diffusion process must also be considered and that both determine the reaction rate. Then the Ea value for reaction above 180 ◦ C is smaller than for reaction below 180 ◦ C. The ti values decreased with increasing temperature, and seemed to reach an asymptotic value. Since the system examined in this study is a solid–liquid heterogeneous reaction, the conditions contacting a reaction, solvent to the solid polymer, significantly affect the reaction rate.

Fig. 9. Conversion of PET-pc as given by the experimental data (points) and the proposed model (line) as a function of temperature. (a) Temperatures of 180, 185 and 190 ◦ C and (b) temperatures of 170 and 175 ◦ C.

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Heat flux rate /mW Endotermic

BHET

Oligomers

PET-pc

0

100

200

Temperature /

300 o

C

Fig. 11. DSC thermogram for (a) PET-pc; products obtained in the second filtration: (b) oligomeres retained on quantitative filter paper and (c) BHET obtained after cooling the filtrated at 4 ◦ C.

4.6. Characterization of products 4.6.1. Thermal characterization Depolymerization at intermediate operating conditions (T = 180 ◦ C, t = 90 min, X = 55.9%) was conducted and the resulting products were characterized. The solid mass obtained in the hot filtration corresponded to 6.6% of the total product mass, and the solid obtained in the cold filtration, corresponded to 93.4% of the total product mass. The DSC curves for the hot and cold filtration products are given in Fig. 11, with the PET-pc curve for comparison. The peak at approximately 110 ◦ C in the DSC curve obtained for the products of the first (hot) filtration corresponds to the melting temperature of the BHET monomer. Less intense melting peaks attributed to the presence of dimers and trimers can also be seen at 151 ◦ C and 210 ◦ C. The peak in the region of 253 ◦ C is attributed to the melting of the remaining solid PET, which then percolates through the 180 ␮m mesh into the products phase. The other peaks were attributed to the vaporization of the materials and to impurities contained in the PET-pc that were retained in the first filtration. Although the values are not rigorously equal to those found for the dimers in the literature, endothermic peak shifts were observed when a mixture of products was analyzed because of the intense interactions between the dimers [25]. For the material obtained in the second (cold) filtration, a first peak was observed at approximately 110 ◦ C corresponding to the BHET melting range. The second peak was attributed to the vaporization of the sample above 255 ◦ C. 5. Conclusions PET-pc is a granular solid with peculiar characteristics. The low sphericity of the particles is an obstacle that restricts the particles be treated as spheres. The approach used in characterizing the solid demonstrated that the smaller particles can be treated as lamellar particles and the larger particles as discoid particles. Glycolysis was found to be efficient for PET-pc chemical recycling, as it can be conducted at atmospheric pressure and the operating conditions required are relatively mild compared with other methods. The reaction can achieve conversion percentages close to 100% at temperatures above 180 ◦ C, when 78 mmol PET repeat units is catalyzed by 8 mmol L−1 zinc acetate. At lower temperatures, there is apparent reaction equilibrium between oligomers and unreacted PET, which leads to lower conversion.

An initial delay in the PET conversion can be seen at all temperatures. This induction period was attributed to the low initial probability of the EG attacking the PET chain ends, which leads principally to the formation of BHET. Mathematical modeling and the reaction mechanism presented here estimates the experimental data for temperatures of 180 ◦ C and above. At these temperatures, the induction time observed can be explained in terms of the types of sites (S0 ) on the polymer surface. For temperatures below 180 ◦ C, the diffusion process must also be taken into consideration. The product characterization showed that BHET is the main reaction product, with small quantities of dimers and trimers also being produced. In the reaction yield study, the relationship established to calculate the mass of BHET formed as a function of the conversion, showed that recovery was 91.6% of the theoretical value. This percentage may be increased by implementing more efficient separation methods. However, the development of such methods was not an objective of this study. Using this relationship and the solution from the mathematical model, it is possible to predict the operating conditions and PET mass required to produce any quantity of products, thus providing a production planning tool for the recycling of PET-pc and other polymers from a solid–liquid reaction such as the type studied here.

Acknowledgements M.E.V. thanks to (CNPq, Brazil) for the master fellowship. The authors thank CNPq, Brazil for the financial support (proc. no. 309005/2009-4 and 481424/2010-5). All authors thank to COMCAP/UEM for access to DSC experiments.

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