Chemical Recycling of PET by Catalyzed Glycolysis Kinetics of Th

8/9/2019 Chemical Recycling of PET by Catalyzed Glycolysis Kinetics of Th

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Chemical Engineering Journal 173 (2011) 210219

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Chemical recycling ofPET by catalyzed glycolysis: Kinetics oftheheterogeneous reaction

Mateus E. Viana, Andr Riul, Gizilene M. Carvalho, Adley F. Rubira, Edvani C. MunizGrupo de Materiais Polimricos e Compsitos, GMPC, Departamento de Qumica, UniversidadeEstadual de Maring, Av.Colombo 5790, 87020-900, Maring, Brazil

a r t i c l e i n f o

Article history:

Received29 March 2011

Receivedin revised form 5 July 2011Accepted 20 July 2011

Keywords:

GlycolysisPETGranulometrySurface areaMathematical modelGlycolysis kinetic

a b s t r a c t

Polyethylene terephthalate post-consume (PET-pc) glycolysis was investigated by the use of ethyleneglycol (EG) and zinc acetate, as catalyst. It was focused the kinetic aspects through use ofmathematicalmodel specially developed for application in this study. The grains-lot was sieved in different size rangesand a relation between surface area and granulometry, surface area and temperature on the conversionand depolymerization rate was proposed. At temperatures ranging 180190 C the depolymerizationrate is quite elevated and almost 100% ofconversion is obtained up to 3 or 4 h reaction time. For lowertemperatures (170180 C), equilibrium is achieved and it becomes more important as the temperatureis decreased. The conversion profile showed an initial activation stage where the mass transfer betweenthe liquid and solid phases is minimal. The proposed mathematic model was based on these findings andon reaction mechanism that differentiates the reaction sites present in the PET surface. By thatmodel thevalue ofrate constant (k) for each temperature, and the dependence ofkwith 1/Twas calculated. Four ourbest knowledge it is the first time that a mathematical model considers the activation stage in the earliertimes ofPET depolymerization reaction. The inputs yielding, time and temperature were included in theused mathematical model that fits very well the experimental data obtained at temperatures higher than180 C. This model helps to predict the necessary mass ofPET for producing a desired amount ofproducts.

2011 Elsevier B.V. All rights reserved.

1. Introduction

Technological advances in the manufacture of PET allowed it tobe produced at low cost. Allied to its mechanical properties, thishas led to a significant increase in the production of this poly-mer. According to the Brazilian PET industry association, ABIPET(Associaco Brasileira da Indstria do PET) [1], the quantity andproportion of PET that is recycled have been growing year-by-yearand currently 263k Tons (55.6% of production) are recycled.

There are three main types of PET-recycling [26]: (a) chemicalrecycling (or depolymerization); (b) quaternary recycling (energyrecovery); and (c) mechanical recycling. Chemical recycling suchas depolymerization by hydrolysis [79], alcoholysis and glycoly-sis [1013] havebeen recently gained much attention.For instance,terephthalic acid (TPA) and ethylene glycol (EG) can be recoveredand used as raw materials in many industrial processes, includ-ing 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 theirreview of PET degradation methods. Their study shows that gly-

Corresponding author. Tel.: +55 44 3261 3664; fax: +5544 3261 4125.E-mail address: [email protected] (G.M. Carvalho).

colysis has advantages over other degradation methods because ofthe versatility of the resulting product (BHET). Important studieshave been published by Pardal and Tersac [1113] on glycolysisof post-consume PET (PET-pc). In the first study [11], the reactivi-ties of different glycols used in the depolymerization of PET werecompared. In a later study [12], the authors evaluated the kinet-ics of heterogeneous glycolysis of PET with diethylene glycol (DEG)at 220C. The change in total mass in each phase was evaluatedand it was observed that initially there is an induction period (ofabout 15min) with minimum mass transfer between the phases.Subsequently, the reaction accelerates (6090min) and then thereaction rate decreases. A gradual decrease in the PET molar masswas demonstrated using size exclusion chromatography (SEC), andtheauthors concludedthat under theused conditionsthe monomerto oligomer ratio remains nearly the same during the reaction butat end of the reaction the monomers constitutes the larger fractionof final products.

Yoshioka et al. [14] studied the kinetics of the hydrolysis ofmicronized PET catalyzed by nitric acid at temperatures from 70 Cto 100 C (heterogeneous reaction). The principal finding was thatthe reaction rate depends on the effective area (proportional tothe fraction of unreacted PET). This model correlated well with theexperimental data, although, in this case, the operating conditionsof the reaction did not give rise to the induction period found in

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M.E. Viana et al. / Chemical Engineering Journal 173 (2011) 210219 211

Nomenclature

a MarkHouwinkSakurada parametersABET surface area from BET methodA0 initial contact area between the PET-EG phasesAp surface area of the actual particleAps area of a perfect sphere with volume equal to that

of the a actual particle

Au unitary area ofa particlec bigger size of PET grains to 3 parameters modeld proportionality constantDp mean mesh size of the sievesf(%) mass fraction of sample retained in a specific mesh

size of the sieves.K MarkHouwink parametersk rate constant of the reactionk1 rate constant of the reactionL mean thickness of PET grainsm(t) residual mass of solid PET as function of timem0 mass of PET added to the reactor and m is thema mean mass values for each samplemBHET BHET mass

MBHET molar mass of bis(hydroxiethyl)terephthalateMEG molar mass of ethylene glycolmoligomer mass of oligomersmprod mass of products retained on the filter papermtheo theoretical mass of BHET calculated based on the

weight of reacts PETmu mean mass of a grainMv average viscosimetric molar weightr PET grains radius from geometrical two-parameter

models standard deviation of the mass of the sampless standard deviation of the thickness of PET grainsS0 carbonylgroups that do not generate reaction prod-

ucts when cleaved (the middle of the chain)

S1 carbonyl groups that generate reaction productswhen cleaved (end of the chain)S2 carbonyl group does not change the polymerSt the total number of sites at the beginning of the

reaction (t= 0)ti induction timeVu mean volume of a grainX percentage conversion of solid PETyi ratio between the number of sites of a determined

species on the surface of the polymer[] intrinsic viscosity reaction yieldred 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 PETcatalyzed by potassium hydroxide.In such model, the reaction rateis proportional to the contact-area between the phases and to theconcentration of KOH (with the first and second order hypothesestested). The rate of reaction is first order with regard to both ofthese factors. Higher reaction rate in the first moments was foundby this model and was attributed to the greatest contact area andalso to the concentration of KOH.

Ruvoloand Curti [15] published thefirst study relating the influ-

ence of surface area on the alkaline hydrolysis of PET in ethylene

glycol solution.Theycomparedthe geometric area andthe effectivesurface area of PET, as measured by BET (BrunauerEmmettTeller)analysis, and demonstrated that the effective area increases as thereaction progresses. Based on this, the authors proposed a kineticmodel in which the effect provoked by the decrease in geometricarea, due to the reaction, on the reaction velocity is considered.

The glycolysis of PET has been object of study from differentpoint 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 processhave been investigated [1517], available kinetic models do notcover all aspects of depolymerization process. The method of cat-alyzed glycolytic depolymerization with optimization techniquewas described by Goje and Mishra [16]. The authors pointed thatprocedures and resulting kinetic parameters vary with assumedkinetic model and applied datafitting procedure. The different val-uesofactivationenergy(Ea)citedinliteraturefordepolymerizationof PET was attributed to the changes in reaction parameters and todifferent chemicals employed for PET depolymerization. Accordingto Paszun and Spychaj [6], the literature related to the glycolysis ofPET covers mainly the application of the resulting products, whileonly few authors turn their attention to the reaction kinetics.Whenglycolysis is carried out below the melting temperature of PET, thereaction medium consists, initially, of a solid phase (pure PET) anda liquid phase (EG + catalyst). However, as the reaction proceeds,other phases appear: swollen PET, a solution of polyesters and oli-goesters, until at the end of the reaction there is only a liquid phase(solution of glycols and oligoesters) [12]. The depolymerizationchanges from a heterogeneous reaction to a homogeneous reac-tion, as thereaction progresses. Lpez-Fonseca et al.[17] developeda theoretical model to predict the time conversion of PET duringglycolytic depolymerization. The authors observed that at initialstages the reaction occurred in a heterogeneous phase and only athigher reaction times the reaction became a single homogeneousphase. The kinetic model was developed according to a homoge-neous reversible catalytic model and was found to be consistentwith experimental data in the range temperature of 150196 C.

If the depolymerization reaction occurs initially on the surface ofthe PETparticles, what is the influence of contact-areabetween thephases (that is, the surface area of the PET grains)? The progress ofthe reaction depends on the EG diffusing onto the surface of thePET and on the removal-rate of the depolymerized material fromthe 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 becomesan important parameter in the reaction mechanism.

Inoneoftheirstudies,PardalandTersac[12] examinedtheinflu-ence of temperature, the presence of a catalyst andthe morphologyof thePET. The observation that reactivity is much greater at 220 Csuggests that the diffusion of diethylene glycol in the PETis favoredat 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 pro-poses a new kinetic model for this reaction. The proposed reactionmechanism is based on the possibility that thePET chain is cleavedat different sites by the EG and that the amount of cleavagesdepends onthe ratioof thenumber ofsites onthe surface ofthe PETgrains. The following steps were performed to achieve this objec-tive (i) determination of the geometric surface area of the PET-pcgrains using geometric models with two and three parameters; (ii)experimental determination of conversion (X) as a function of thegranulometry of the grains of PET-pc; (iii) study of the influenceof time and temperature on the heterogeneous depolymerizationreaction; (iv) determination of the PET-pc conversion (X) using the

proposedmodel,fordifferenttimeandtemperatureconditions,and


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212 M.E. Viana et al./ Chemical Engineering Journal 173 (2011) 210219

comparison with the experimental results; (v) characterization oftheproductsobtainedin thePET depolymerization reaction by DSC.

2. Experimentalmethod

2.1. Materials

EG and zinc acetate (catalyst) were acquired from Synth (Brazil)

and usedwithout purification. PET-pc, fromsoft drinksbottles, sup-pliedbythecompany PlaspetReciclagensLtda (Maring, Brazil), waswashed and dried in an oven at 50C to constant mass.

Viscosity measurements were made at 25C in a 1:1 solu-tion of 1,2-dichlorobenzene/phenol (m/m) to estimate theviscosity-average molecular weight of PET. The equation dueMarkHouwinkSakurada

[] = KMav

(1)

was used, being the values ofKand a equal to 0.469103 dL g1

and 0.68, respectively [18]. The intrinsic viscosity value found was[]=0.78dLg1. The viscosity-average molecular weight (Mv) cal-culated for the polymer was 54.600g mol1.

2.2. Analyses

To study the influence of the size of the PET particles on thekinetics of the reaction, a granulometry test was carried out usinga series of Tyler standardized sieves [19]. To do this, samples ofPET,washed and dried in anoven at50 C to constant weight,werevibrated for 20min in a sieves set to split them into six size ranges.Theweight distributionas a function of mean particle size waseval-uated by weighing the fraction retained by each sieve. The meanmass of a grain (mu) was estimated by weighing 15 random sam-ples containing n=30 grains each. The value ofmuwas calculatedfrom the mean mass, as given in equation

mu =

30i=1ni(mu)i

30

i=1ni

=

30i=1m

30

i=1ni

(2)

The mean volume of a grain (Vu) was estimated based on thenominal density of PET (1.375 g cm3) and its mean mass, mu.

TheGrubs test was applied to the data to reject anomalous data[20], after which the values ofmuand Vuwere estimated for eachsize range. As the mean thickness (L) of particulate PET is limitedby the thickness of the bottles, a digital micrometer was used formeasuring this axis for each granulometry. Thus, two hypotheti-cal models related to the characteristic geometric-thickness of thismaterial could be proposed and evaluated.

The surface area was measured by means of BET adsorptionisotherms using a Quantachrome instrument, model NOVA-1000.The mean grain area values (ABET) as a function of granulometrywere 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 con-stant. The variables studied were: time, temperature and particlesize.ThemassofPET-pcusedforeachrunwas15g(78mmolrepeatunits) and the initial amount of the zinc acetate catalyst was 1.76g(8mmol), giving a mol ratio of 9.75:1 for PET:zinc acetate. Theamount ofEG, 60g, was used thusin great excessto avoid problemsof homogenization in thereactionbatch.The reactionswere carriedout at atmospheric pressure using a three-necked flask equippedwith magnetic stirring, heating, a thermometer and a reflux con-denser. EG and the catalyst were weighed and addedto the reactor,and then heated to a requested temperature. Simultaneously, thePET-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 timehad been elapsed, the heating was removed and boiling water wasslowly added to the system. Next, the contents of the reactor werefiltered (first filtration) using a Tylerseries sieve with a mesh size of80 to collect the unreacted PET (PET-NR), and more boiling waterwas used to remove the product eventually adhered to the PET.The total volume of water added was 300 mL for each run. The fil-trate was cooled to 4 C for precipitating the glycolysis products,which were further filtered (second filtration) using quantitativefilter paper, and dried in an oven to constant weight. The ratiobetween the mass resulting of second filtration products (mprod)and the theoretical mass of BHET obtained (mtheo), in accordancewith the stoichiometry of the reaction, was used to analyze thereaction yielding by the equation

=mprodmtheo

(3)

The conversion (X) ofsolid PETwas calculated using

X=m0 m(t)

m0(4)

where m0 is the mass of PET added to the reactor and m(t) is theremaining solid PET mass as a function of time.

The relationship between conversion and the PET-pc geometricarea was evaluated for the glycolysis reaction at 180C for 90min.A plot of conversion against time at the different temperatures forA0 =593.5cm2 was produced and analyzed.

Thermal characterization of the samples was performed using aShimadzu DSC 50 calorimeter, with a heating rate of 10 Cmin1 inan atmosphere of nitrogen at a flow rate of 20mLmin1 . The DSCcurve obtained for the product from second filtration was com-pared with the DSC curve for the oligomeric diols derived fromterephthalic acid [18].

3. Mathematicalmodeling

3.1. The reactionmechanismand definition of variables

In this study, a kinetic model with equations based on the dif-ferent possibilities for polymer chain cleavage by EG is proposed.The following hypotheses were considered for building the model:

(a) Thereactionbetween anEG moleculeand anestergrouplocatedat the surface of the polymer causesa cleavage of polymer chainat the point of the reaction. The reaction occurs at the interfacebetween the solid PET-pc and the diffused EG.

(b) If the reaction occurs between an EG molecule and an estergroup situated close to the end of PET chain, the each cleav-age contributes to the reaction progressing and a leaving groupis formed consistingof a monomer (BHET)or an oligomer of lowmolar mass.

(c) If the reaction occurs between an EG molecule and an estergroup situated far from the end of the chain, the cleavage doesnot contribute to the reaction progress. In this case, the poly-mer molecule splits into two, forming two new chain-ends atthe point of cleavage. If this happens, the mass of thepolymer isincreased by the accommodation of a molecule of EG relativeto the mass of polymer chain before the cleavage.

The sites where reaction may take place, that are the estergroups located at the surface of the polymer, are classified as: S0,S1and S2. The S0sites indicate carbonyl groups that do not gener-ate reaction products when cleaved (situated at the middle of thechain). The S1sites indicate carbonyl groups that generate reactionproducts 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 intermediateresonance structure would contain two identical leaving groups,which are two ethylene glycol molecules.

To simplify the model, only BHET is considered to be a leavinggroup. Hence, there are two S1-type sites next to each end of thechain. These considerations are illustrated in Fig. 1.

Another important definition to be considered in the proposedmathematical model is the ratio between the number of sites of adetermined species on the surface at given reaction time, t, and thenumber of sites at the beginning of the reaction, given by

yi =Si(t)St

(5)

where yi is the ratio of sites of type i. Si(t) is the number of sitesof type i located on the surface of the polymer, and St is the totalnumber of sites at the beginning of the reaction (t=0).

At t= 0, almost all of the sites on the surface are S0-typed, suchthat the first cleavages do not contribute to the conversion of thepolymer, but to the creation of chain ends at the polymersurface(generating S1 sites). Accordingly, there is an increase in the yS1ratio and a decrease in the yS0 ratio, as shown in the schema ofFig. 2.

As a consequence of the yS1 growing ratio, an increase in the

number of effective cleavages occurs, that is, the cleavages thatgenerate leaving groups rise (reaction products).

Accordingly, the solid phase mass increases with each cleavageat S0due to the absorption of EG, and decreases with cleavages atS1due to the formation of BHET because EG is also absorbed in thissituation.

3.1.1. Definition the differential equations

The material balance equation (instantaneous mass balance) toa dynamic system gives the following equation [9], being the unitsof each term in Eq. (6) [masstime1].

dmdt

= min mout (6)

The terms for the rates of mass entering and leaving will be sub-stituted by differential or algebraic equations, as required for eachspecific case.

Mathematically, the proposed mechanism can be described bythe material balance, as given in Eq (6), where the solid PETgranuleis considered as the dynamic system. According to this equation,the change in the PET granule mass over time (dm/dt) equals thedifference between the mass entering in the granule and the massleaving out the granule. The rate of mass entering (min) rises as EGattacks the S0sites.Takingthis rate as being of first order in relationtoyS0 and to mass of solid residual PET, gives the equation

min = kyS0 (t)m(t) (7)

where k is a rate constant dependent on temperature and repre-

sents the cleavage rate.The rate of mass leaving rises (mout) as EG attacks the S1sites,at which time the EG molecules condense onto the polymer andsimultaneously soluble BHET moleculesleaveout of PETchain. Tak-ing the leaving rate to have a first-order relationship withyS1 andto mass of solid residual PET, gives the equation

mout = k1yS1(t)m(t) (8)

where k1 is the rate constant of the reaction, also temperature-dependent.

Taking the cleavage velocity to be independent of the site type,the probability of cleavage is greater for sites existing in greaternumbers. A cleavage at S0 site produces an increase on polymermass equal to the mass of EG molecule, and a cleavage at S1 site

produces condensation of one EG molecule into the polymer while,

simultaneously, the one BHET molecule leaves. Accordingly, theratio between the rate constants k and k1is given by

k1k =

MEGMBHET MEG

= 0.32299 = d (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 expressthe variables as a function of time, in order to generate an ana-lytical solution for the conversion as a function of time. This makespossible to evaluate the effect of temperature on the rate constants.

Expressingm(t)as a function ofX.The following equation

m(t) =m0(1 X) (11)

arises immediately from Eq. (4). Differentiating this equation andsubstituting into Eq. (10), gives

dX(t)dt

= [kyS0 (t) dkyS1 (t)][1 X(t)] atX(0) = 0 (12)

ExpressingyS0

and yS1

as functions of time.As the term is proportional to the S0cleavage rate, the following

hypothesis can be written:

dyS0(t)dt

= kyS0 (t) atyS0 (0) = 1 (13)

In accordance with the illustration given in Fig. 1, taking intoaccount that each attack on an S0 site will form four S1 sites, thefollowing differential equation is proposed

dyS1(t)dt

= 4kyS0 (t) atyS1 (0) = 0 (14)

Hence, three ordinary differential equations (ODE) with theirrespective contour conditions have been defined and were usedto 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 inves-tigation gave seven different particle sizes (Table 1). The term Dpisthe mean mesh size of the indicated sieves. The sample of the frac-tion at the bottom of the sieve set (7th sieve) was excluded fromthe other analyses due to the low volume of this sample. The par-ticles in all size ranges presented very different axis sizes. As thethickness of the grains is limitedto 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 simplificationused for characterizing solid particles [19].

Asit is useful to relate the area to the mean size of the particles,two geometric models were tested.The first geometric model (two-parameter model) assumes that the solid can be represented bycylindrical particles, being the area dependent on the mean diame-terand thickness of the particles, as shown in left side ofFig. 3. Themean radius is calculated from the values obtained for the thick-ness and the volume of each particle. The second geometric model(three-parameter model)assumes that the solidcan be representedby particles with a rectangular profile, as shown in right side ofFig. 3. The shorter axis, c, is equal to the value estimated for L; theintermediate axis, b, was taken to be equal to the value ofDp forthe particles; the longer axis, a, was calculated from the values for

Vu, a and b.


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Fig. 1. Schematic representation of sitesS0, S1and S2in thePET molecule.

Fig. 2. Illustration of how S0decreases and S1 increasesduring theconversion (X)of PET-pc.

Table 1

Estimates formuand Vuand L as a functionsof thegranulometry from 15 samples of 30 grains each.

Dp(mm) f(%) ma(g) s (g) mu(mg) Vu(mm3) L (mm) s (mm)

7.18 5.43 1.1893 0.1400 39.64 28.83 0.5465 0.01095.56 25.15 0.8212 0.0243 27.37 19.91 0.5014 0.00933.56 60.62 0.6371 0.0201 12.74 9.267 0.4400 0.03652.03 6.16 0.2140 0.0176 3.567 2.594 0.4027 0.02001.44 1.80 0.1575 0.0152 2.230 1.622 0.3735 0.05480.89 0.77 0.0921 0.0117 1.149 0.835 0.3401 0.0346

Samplemassof 30grains= ma; Standarddeviation ofmass= s; Standard deviationof thickness(L) = s; Meanmeshsize ofthe shieves =Dp; Unitarymassof grains=mu; Unitaryvolume of grains=Vu; Percent of PETmass retained in theTyler sievesf(%).

Another important characteristic of a given sample is its form

factor. The most common form factor for solid particles is thesphericity (), a form factor based on the surface and the vol-ume of particles [21,22]. The sphericity is defined as being theratiobetween the surface area of a perfect sphere with volume equal tothat of theparticle and the surface area of theactual particle, givenby

=ApsAp

(15)

where Aps is the area of the equivalent sphere; Ap is the area of the particle. Accordingly, 0


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Table 2

Unitary area and sphericity as a function of granulometry.

Dp(mm) 2 parameters model 3 parameters model

r(mm) Au(mm2) c(mm) Au(mm2) ABET(mm2)

7.18 4.223 125.7 0.362 7.804 127.5 0.357 5.56 3.555 90.62 0.392 7.142 92.26 0.385 3.56 2.589 49.28 0.433 5.916 50.46 0.423 2.03 1.432 16.51 0.553 3.173 17.07 0.535 52.001.44 1.176 11.44 0.583 3.015 12.01 0.556 36.570.89 0.884 6.804 0.631 2.761 7.397 0.580 20.48

Fig. 4. Zingg classification of different geometric particles.

model, while for the discoidal PET grains (p2/3 and 2/3 < q1.0),the values ofAu used were calculated using the two-parametermodel. To calculate the initial contact area between the PET-EGphases (A0) for each size range, the values of the unit mass and thetotal mass added to the reactor were used, as given in equation

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 resultsare given in Table 3.

As expected,Auwas greater for the larger size ranges, whereasA0was smaller for the larger size ranges.

4.3. Glycolysis reactions

The relationship between the conversion and the geometricarea of the PET-pc grains in the glycolysis reaction, (T=180 C andt=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 90min,it can be seen that thereaction velocity is largely dependent on thecontact area. As pointed by some authors [12,1517,24], stirringrate influence the conversion of PET. In conditions of high solutionstirring rate the mass transfer resistance can be eliminated in thereaction medium. In all experiments the magnetic stirring is main-tained constant at ca. 200 rpm and the mass transfer mechanismwas not eliminated neither considered in the mathematical model.

To estimate the PET mass required to produce a specific mass ofproduct(mprod), the product yield wasassessed.In accordance withthestoichiometry of the reaction, 1.323g of BHET (mtheo) is formedfor every gram of PET reacted. However, due to inherent processlosses and to incomplete depolymerization, the mass of productsobtained on the filter paper, after drying, was smaller than thethe-

oretical BHET mass,mtheo. The conversion (X) for the reactions was

400 600 800 1000

30

60

90

Conversion(X,

%)

Initial contatct surface (Ao, cm2)

Fig. 5. Conversion of PET as a function of initial contact surface (reaction90 min, at180 C).

defined in Eq. (4). From this equation and take into account the sto-ichiometry of PET glycolysis to form BHET, the following equationwas obtained:

=mprodmtheo

=mprod

1.323(m0X) (17)

The mass of products for each conversion was determined. Allof the values were normalized for an initial PET mass of 15g. Sub-sequently, to calculate the mean reaction yield (), 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 ofp and q andthe Zingg classification of theparticles studied and thesurface area fora 15g sampleof PET.

Dp(mm) p q Class Au(mm2) mu(mg) n A0(cm2)

7.18 0.072 0.920 discoidal 125.7 39.64 376 473.35.56 0.090 0.779 discoidal 90.62 27.37 553 501.63.56 0.124 0.602 lamelar 50.46 12.74 1176 593.52.03 0.198 0.640 lamelar 17.07 3.567 4258 727.01.44 0.259 0.478 lamelar 12.01 2.230 6726 808.00.89 0.382 0.322 lamelar 7.397 1.149 13055 965.7

0

5

10

15

20

25

200 40 60 80 1000

20

40

60

80

100

yield(

%)

mprod

mtheo

mass(g)

Conversion (X, %)

Fig. 6. Reaction yield in comparison with maximum theoretical yield (reaction90 min,at 180 C).

The left vertical axis on Fig.6 givesthevaluesofmprodandmtheo;therightverticalaxisgivesvaluesof.TheGrubbstestsuggeststhatthe yield from the smallest conversion reaction should be excludedwhen calculating the mean yield (as the conversion is small, anyloss results in large errors). Excluding the smallest conversion, themean reaction yield was 91.6%. Therefore, the mass of productscollected on the filter paper can be estimated, in terms of meanvalue, using

mprod = 1.212m0X (18)

4.4. Heterogeneous depolymerization kinetics for the glycolysis of

PET

Theinfluencesof thereaction temperature andtime on thereac-tion conversion were evaluated simultaneously for PET samples ofinitial surface area of 593.5mm2, due the high volume ofthis sam-ple. The graph of conversion as a function of time was plotted for170, 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 behav-ior differs from that described in the literature for mathematicalmodels of PET degradation, but it agrees with the results of Pardaland Tersac [12]. In the present study, this behavior was attributedto the types of polymer surface sites. During the initial period ofthe reaction, nearly all of the surface sites were ofS0type and thefirst cleavages did not contribute to the conversion of the poly-mer. During the induction time, cleavage of mainly this type occursand produces chain ends on the polymer surface (production ofS1). After a certain number of groups at S1 sites have been gener-ated, 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. Thedecrease in (dX/dt)Tfor longer reaction times can be explained by

the decrease in the solid phase and, consequently, in the contact

500 100 150 200 250

0

25

50

75

100

X(%)

Reaction time (min)

170oC

175oC

180oC

185oC

190oC

Fig. 7. Profile of PET-pc conversion withA0593.5m2 against time at differenttem-peratures.

area between the phases. Note that, for the used operating condi-tions, the induction period is greater at lower temperatures. Thisbehavior was not predicted by the proposed model and suggeststhat diffusion may play an important role in the reaction mecha-

nism allowing the reaction to take place more readily in the solidphase at temperatures above 180C.

4.5. Mathematicalmodeling

4.5.1. Analytical solutionThe analytical solutions for the ODEs were obtained using the

computational tool Maple11TM. The rate constant was estimatedusing the PolymathTM software. The differential equations and theexperimental data were inserted into the algorithm to obtain thebest fit. To achieve correlation between k and T, a graph of ln(k)versus 1/Twas constructed for these 5 points, thus the parametersfor the Arrhenius equation were extracted from the plots ofFig. 8.

Note that a better fit is obtained when two temperature ranges,170180 C; and 180190 C, are considered. Considering only thethree higher temperatures (180, 185 and 190C) the equation

k = 572.5exp(5013.2/T) (19)

is obtained. From this equation the calculated value for Ea was41.7kJ/mol. For the lower temperatures (170, 175 and 180C), thebest fit in Fig. 8 gives the equation

mprod = 1.212m0X (20)

is obtained and from this equation the Ea value calculated was99.6kJ/mol. The Ea values reported for PET depolymerization byvarious researchers are different [1517]. The different values ofEa were attributed to the change in reaction parameters and dif-ferent chemicals employed for depolymerization of PET [16]. The

value ofEa calculated for lower temperatures, 99.6 kJ/mol, agrees


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0,00216 0,00218 0,00220 0,00222 0,00224 0,00226

-5,5

-5,4

-5,3

-5,2

-5,1

-5,0

-4,9

-4,8

-4,7

-4,6

-4,5

-4,4

y=-5013.2x+6.346

R2=0.994

k=572.5e-5013.2/T

ln

k

1/T (K -1 )

y=-11977x+21.69

R2=0.990

k=2.637.109e

-11977/T

Fig. 8. Values ofk as a functionof 1/T. Fitting forlowertemperatures (170 175 and180 C, dash line) and highertemperatures (at 180, 185 and 190 C, solid line).

with the values reported in the literature, ranging between 85 and100kJ/mol, for the catalytic glycolysis of PET. The value ofEacalcu-lated for higher temperatures, 41.7 kJ/mol, is less than values fromother researches. Therefore, this small value can indicate that theglycolysis was rate determining by the kind of sites in the PET sur-face. In our case these two values ofEaobtained indicated that inthe conditions utilized in this work, the mechanism of reaction is,probably changed as the temperature change from 170180 C to180190 C. For the reaction to proceed EG must first reach the sur-face of PET and then access to any site S1. After the BHET moleculebe released from PET grain, new site is formed in the reminiscentchain. Temperature affects the kinetic energy of molecules in solu-tion, so that at low temperatures the low kinetic energy causesthe reaction rate depends on the mass transfer process. At higher

temperatures the average kinetic energy of molecules in solutionis sufficient to overcome this barrier and the reaction rate becomescontrolled only by the access of EG molecules to sites S1. Thusthe model gives good results only under conditions where masstransfer has no control over the process. The validity of the modelwas confirmed by comparing the experimental data with the datacalculated for each of the temperatures. The values fork in theana-lytical solution were substituted for the relationships given above,and the results given by the model are shown together with theexperimental data in Fig. 9(a) and (b).

170 180 1900

40

80

120

induction

time,

ti(min)

temperatureo

C

Fig.10. Inductiontimes (ti) at different temperatures. The tivalue wasobtained, ineach case, from an interceptto thestraight line in themajor decomposition stage.

These results point to the consistency of the model presented

here for 180

C and higher temperatures (Fig. 9(a)). This modelbringsa new perspectiveon heterogeneous depolymerization,evenexplaining the induction period first reported by Pardal and Ter-sac [12]. However, the model was unsatisfactory at temperaturesbelow 180C (Fig. 9(b)), as already mentioned.

As the glycolysis reaction occursbelow the PETmelting temper-ature, it is a heterogeneous reaction. In this case, the effect of theEG diffusion mechanism at thesurface of thePET-pc grains and thediffusion of the reaction products in the solution must be consid-ered in addition to the sites available for effective cleavage. Above180 C, this is not the determinant effect and it is the number ofeffectivecleavagesthatcontrolsthereactionvelocity.Theproposedmodel fits the experimental data perfectly at these temperatures.Theproposed model does notfit theexperimental data fortempera-

tures below 180

C. In thistemperaturerange, thegreater inductionperiod (Fig. 10) suggests that, apart from the numbers of availablesites for effective cleavage, the diffusion process must also be con-sidered andthat both determine thereaction rate. Then theEa valuefor reaction above 180C is smaller than for reaction below 180C.

The ti values decreased with increasing temperature, andseemedto reach an asymptotic value.Sincethe system examined inthis study is a solidliquid heterogeneous reaction, the conditionscontacting a reaction, solvent to the solid polymer, significantlyaffect the reaction rate.

Fig. 9. Conversion of PET-pc as given by theexperimental data (points) andthe proposedmodel(line) as a function of temperature. (a)Temperatures of 180, 185 and190C

and (b)temperatures of 170 and 175

C.


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0 100 200 300

Heatfluxrate/mW

Endotermic

Temperature /oC

BHET

PET-pc

Oligomers

Fig.11. DSC thermogram for (a) PET-pc; productsobtainedin the second filtration:(b) oligomeres retained on quantitative filter paper and (c) BHET obtained aftercooling thefiltrated at 4 C.

4.6. Characterization of products

4.6.1. Thermal characterizationDepolymerization at intermediate operating conditions

(T=180 C, t=90min, X=55.9%) was conducted and the resultingproducts were characterized. The solid mass obtained in the hotfiltration corresponded to 6.6% of the total product mass, and thesolid obtained in the cold filtration, corresponded to 93.4% of thetotal product mass. The DSC curves for the hot and cold filtrationproducts are given in Fig. 11, with the PET-pccurve for comparison.

The peak at approximately 110C in the DSC curve obtained forthe products of the first (hot) filtration corresponds to the melt-ing temperature of the BHET monomer. Less intense melting peaksattributed 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 attributedto the melting of the remaining solid PET, which then percolatesthrough the 180m mesh into the products phase. The other peakswere attributed to the vaporization of the materials and to impuri-ties containedin the PET-pcthat were retained in the first filtration.Although the values are not rigorously equal to those found for thedimers in the literature, endothermic peak shifts were observedwhen a mixture of products was analyzed because of the intenseinteractions between the dimers [25].

For the material obtained in the second (cold) filtration, a firstpeak was observed at approximately 110C corresponding to theBHET melting range. The second peak was attributed to the vapor-ization of the sample above 255 C.

5. Conclusions

PET-pc is a granular solid with peculiar characteristics. The lowsphericity of the particles is an obstacle that restricts the particlesbe treated as spheres. The approach used in characterizing the soliddemonstrated that the smaller particles can be treated as lamellarparticles and the larger particles as discoid particles.

Glycolysis was found to be efficient for PET-pc chemical recy-cling, as it can be conducted at atmospheric pressure and theoperating conditions required are relatively mild compared withother methods. The reaction can achieve conversion percentagesclose to 100% at temperatures above 180 C, when 78mmol PETrepeat units is catalyzed by 8mmol L1 zinc acetate. At lowertemperatures, 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 tem-peratures. This induction period was attributed to the low initialprobability of the EG attacking the PET chain ends, which leadsprincipally to the formation of BHET.

Mathematical modeling and the reaction mechanism presentedhere estimates the experimental data for temperatures of 180Cand above. At these temperatures, the induction time observed canbe explained in terms of the types of sites (S0) on the polymer sur-face. For temperatures below 180 C, the diffusion process mustalso be taken into consideration.

The product characterization showed that BHET is the mainreaction product, with small quantities of dimers and trimers alsobeing produced.

In the reaction yield study, the relationship established to cal-culate the mass of BHET formed as a function of the conversion,showed that recovery was 91.6% of the theoretical value. Thispercentage may be increased by implementing more efficient sep-aration methods. However, the development of such methods wasnot an objective of this study. Using this relationship and the solu-tion from the mathematical model, it is possible to predict theoperating conditions and PET mass required to produce any quan-tity of products, thus providing a production planning tool for therecyclingof PET-pcand other polymers from a solidliquid reactionsuch as the type studied here.

Acknowledgements

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

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