Study of Polystyrene Degradation Using Continuous Distribution Kinetics in a Bubbling Reactor

Korean J. Chem. Eng., 19(2), 239-245 (2002)

Wang Seog Cha†, Sang Bum Kim* and Benjamin J. McCoy**

School of Civil and Environmental Engineering, Kunsan National University, Kunsan 573-701, Korea *Department of Chemical Engineering, Korea University, Seoul 136-701, Korea **Department of Chemical Engineering and Material Science, University of California, Davis, CA 95616, USA (Received 3 April 2001 • accepted 10 September 2001)

Abstract−A bubbling reactor for pyrolysis of a polystyrene melt stirred by bubbles of flowing nitrogen gas at atmospheric pressure permits uniform-temperature distribution. Sweep-gas experiments at temperatures 340-370 oC allowed pyrolysis products to be collected separately as reactor residue(solidified polystyrene melt), condensed vapor, and uncondensed gas products. Molecular-weight distributions (MWDs) were determined by gel permeation chromatography that indicated random and chain scission. The mathematical model accounts for the mass transfer of vaporized products from the polymer melt to gas bubbles. The driving force for mass transfer is the interphase differ- ence of MWDs based on equilibrium at the vapor-liquid interface. The activation energy and pre-exponential of chain scission were determined to be 49 kcal/mol and 8.94×1013 s−1, respectively. Key words: Pyrolysis, Molecular-Weight-Distribution, Random Scission, Chain-end Scission, Continuous Distribution Theory

INTRODUCTION Westerout et al. proposed a random-chain dissociation (RCD) model, based on evaporation of depolymerization products less than Fundamental and practical studies of plastics processing, such a certain chain length. In a subsequent paper [Westerout et al., 1997b] as energy recovery (production of fuel) and tertiary recycle (recov- on screen-heater pyrolysis, the RCD model was further described. ery of chemicals) [Carniti et al., 1991] are being promoted. Both of For the screen-heated system, as well as for thermogravimetry, mass these recycling processes are based on chemical decomposition of transfer of vaporized depolymerization products can strongly influ- polymers to low molecular-weight (MW) compounds. For process ence rate. Such interphase mass transfer depends on a driving force design, development, and evaluation, a complete quantitative descrip- that should account for equilibrium at the vapor-liquid (melt) in- tion would entail mathematical modeling of the composition of the terface. Evaluation of a flow reactor with entrained polymer particles reaction mixture during thermolysis by accurate representation of [Westerout et al., 1996] showed that melted particles tended to stick decomposition rates. to the reactor walls, making their residence times unpredictable. The review [Westerout et al., 1997a] of low-temperature pyroly- Seeger and Gritter [1997] studied pyrolysis of 1-mg samples of sis (T<450 oC) states that most chemical-reaction kinetics studies polyethylene and n-alkanes with programmed temperature rise under of pyrolysis were performed by standard thermogravimetric analy- hydrogen sweep gas. Gas chromatographic analysis of the volatil- sis (TGA). Weight-loss data for a small polymer mass (a several ized reaction products yielded a carbon-number distribution. Rec- milligram sample) in a small heated crucible comprise the primary ognition of the key role of the volatilization process was the result information for determining pyrolysis kinetics. The review, in a crit- of that work. Ng et al. [1995] used nitrogen as carrier gas for poly- ical discussion of several models for analyzing TGA data, pointed ethylene pyrolysis and catalytic cracking, noting that volatile prod- out that the observed weight loss in pyrolysis involves evaporation ucts were purged from the reactor and prevented from reacting. of low-MW products. Any low-MW molecules in the polymer will For the most part, empirical reaction-kinetics expressions for initially evaporate. The empirical power-law rate expression em- weight loss due to volatilization of low-MW depolymerization prod- ployed in most studies to fit TGA weight-loss data is considered ucts were applied in polymer pyrolysis studies. The mathematical valid only at large polymer conversions, where random scission of models usually disregarded mass-transfer resistance for volatile de- the remaining low-MW polymer molecules yields volatile prod- polymerization products. Understanding the chain-scission reactions ucts. The widespread use of the simple power-law model is a prob- that produce low-MW volatile products is obviously required for a able reason that reported rate coefficients differ by a factor of 10. fundamental quantitative description of pyrolysis. Many studies have Reported kinetic parameters (pre-exponential factor and activation tried to model random-chain scission, but chain-end scission, which energy) for polymer also cover a wide range. is accompanied with random scission, has been ignored. The present objective is to study pyrolysis and a mathematical †To whom correspondence should be addressed. model combining mass-transfer, interfacial vapor-liquid equilibrium, E-mail: [email protected] and chain-scission processes. We take experiments for a polysty- ‡Presented at the Int’l Symp. on Chem. Eng. (Cheju, Feb. 8-10, 2001), rene melt decomposing at pyrolysis temperatures to form low-MW dedicated to Prof. H. S. Chun on the occasion of his retirement from evaporating compounds. These products are swept away by flow- Korea University. ing inert gas into a cooled flask where condensed vapors are trapped. 239 240 W. S. Cha et al.

The MWDs of reactor residue and liquid condensate are determined less steel frit (Supelco) with 2-µm pores, which disperse the gas but by HPLC gel permeation chromatography (GPC). Nonconden- prevent backflow of the polymer melt. The stainless steel reactor sable gases are analyzed downstream by gas chromatography. Pop- of internal volume 10 cm3 is fitted into a steel protective sleeve lined ulation balance equations, incorporating random and chain-end scis- with a steel shot (3.4 mm diameter) to improve heat transfer. The sion as well as liquid-vapor mass transfer, are applied to polymer volume available to condensable vapor, Vv=64 cm3, includes reac- melt, vapor, condensable vapor, and gas. An MW-moment method tor and condenser vapor spaces and a connecting tube. The vol- applied to the governing integrodifferential equations allows formu- ume available to noncondensable gas, Vg=324 cm3, includes Vv lation of ordinary differential equations for zeroth moments (molar and the tube leading away from the condenser. concentrations), first moments (mass concentrations), and second The reactor holds 2 g of unreacted polystyrene pellets. The stain- moments of melt, vapor, condensate, and gas MWDs. less steel tube leading from the reactor to the condenser vessel was wrapped with heating tape to maintain a temperature 5 oC higher than EXPERIMENTAL the reaction temperature. This prevented condensation in the line. The cooled pyrolysis products at the end of an experiment are Polystyrene pyrolysis experiments were conducted at atmospheric solid polymer remaining in the reactor, liquid condensate in the con- pressure under nitrogen gas at 340, 350, 360 and 370 oC. The di- denser vessel, and gas. Gas product was collected at 20-min inter- agram of the experimental apparatus (Fig. 1) shows a polymer melt vals during the experiment and analyzed by GC. Reactor and con- in the heated reactor (immersed in a molten-salt bath) and vapor denser vessels were separately weighed before and after each ex- carried to the condenser vessel (immersed in an ice bath) by flow periment to determine the final polymer and condensate masses. of nitrogen sweep gas. The gas flows through 1.59 mm stainless Each product was dissolved at 25 oC in 100 ml of HPLC reagent- steel tubing, 3.4 m of which is coiled and immersed in the molten grade THF and analyzed by HPLC-GPC (Waters). Two GPC col- salt so that the gas temperature reaches the bath temperature. Nitro- umns (Waters HR3) packed with cross-linked styrene-divinylben- gen enters at the reactor base through a 12.7 mm-diameter, 316 stain- zene copolymer beads (10-µm diameter) were used in series. Conversion of MW from GPC retention time was computed by a spreadsheet computer program. Knowing the mass of the polymer and the volume of the solvent allows calculation of MWD as mass/MW. Mass MWDs are reported in this work as g/MW normalized for 1.00 g of initial sample (area under mass MWD represents 1.00 g). Molar MWDs can be calculated by dividing each mass MWD by MW. MW moments of these molar MWDs are repre- sented as P(n) (the units are mol for n=0 and mass for n=1). The re- spective molar concentration moments are expressed on a volume basis, p(n) =P(n)/V. The molecular weight distribution (Fig. 2) indicates a number average MW of 50,000 and a weight average MW of 210,000. The many peaks in the lower MW range would interfere with the analysis of the degradation products. To eliminate these low MW peaks, the polymer was fractionated by partially dissolving 50 g of polymer in 500 ml of toluene. The solution was continuously stirred with a magnetic stirrer and 750 ml of

Fig. 1. (A) Schematic drawing of the experimental apparatus: (1) nitrogen cylinder, (2) valve, (3) rotameter, (4) heater, (5) stirrer, (6) reactor, (7) thermocouples, (8) molten-salt bath, (9) ice bath, (10) soap-bubble meter, (11) controllers, (12) digi- tal thermometer readout. (B) Sketch of the apparatus for the mathematical model showing the notation for volumes, Fig. 2. Molecular weight distribution of untreated polystyrene and molar MWDs, and flow rate. pretreated feed polystyrene. March, 2002 Study of Polystyrene Degradation using Continuous Distribution Kinetics in a Bubbling Reactor 241

the precipitating agent, 1-butanol, was slowly added until 70% of the where Q(xs) is a monomer or oligomer of mass xs. The rate expres- polymer was precipitated. The precipitate was dried to a constant sions for reactions A and B have been related to radical mechanisms weight at 110 oC and stored under nitrogen. The molecular weight [Kodera and McCoy, 1997]. The random-scission rate should in- distribution of the treated polymer, with number average MW of crease with the number of bonds that can be cleaved. Hence, kd 95,000 and weight average MW of 190,000, is shown in Fig. 2. should generally increase with x [Madras et al., 1997]. Polymerization rates, according to the equal-reactivity approxi- THEORY mation, are independent of MW. The chain-end scission rate is es- sentially proportional to the number of chain ends and is thus in- The experimental apparatus (Fig. 1) shows a polymer melt in dependent of the chain length and of x, the MW of a macromole- the heated reactor, vapor flow to the condenser vessel, and flow of cule [Wang et al., 1995]. The stoichiometric kernels and 1/x' for ran- δ − − δ − inert nitrogen sweep gas. The subscripts m, v, c, and g denote poly- dom scission and [x (x' xs)] and (x xs) for the two products of mer melt, condensable vapor, condensate, and noncondensable gas chain-end scission. Rate expressions for reactions A and B have products, respectively. Polymer melt volume, Vm, decreases with been applied previously in polymer degradation studies [Madras et reaction time due to evaporation of low-MW components. Con- al., 1996; Song and Hyun, 1999]. densate volume, Vc, increases with reaction time. Volume changes We consider that random-scission and repolymerization reac- of the relatively large vapor volume, Vv, and gas-product volume, tions, as well as chain-end scission, occur in the polymer melt with

Vg, are negligible. The gas flow rate, Q, was constant. rate coefficients kd(x), ka, and ks, respectively. The random-scission MWDs [mol/(vol·MW)] are defined so that at time t, p(x, t) dx is rate coefficient is considered a function of x, whereas the two other the molar concentration (mol/volume) of a compound having val- coefficients are independent of x. The vapor is dilute as it is swept ues of MW x in the range x to x+dx. Moments of MWDs are de- out of the reactor. Hence, no significant reaction occurs in the vapor. fined as integrals over x, If composition is assumed uniform at any time throughout the gas

() ∞ bubbles and the liquid, the mass balances are as follows: n = n p ()t ∫ pxt(), x dx (1) 0 for polymer melt The zeroth moment (n=0) is the time-dependent total molar concentration (mol/volume). The first moment, p(1)(t), is the mass con- ∂() Vmpm = − − + − ------χ()p p ⁄K V [ k ()x p ()x centration (mass/volume). The normalized first moment (average ∂t m v m d m + ∞ () ()()⁄ − ()()0 MW) and second central moment (variance of the MWD) are given 2k∫ d x' pm x' 1x'dx' 2kapm x pm avg (1) (0) var (2) (0) avg 2 x by p =p /p and p =p /p −[p ] , respectively. The polydis- ∞ + () ()− − () ka∫ pm x' pm x x' dx' kspm x persity index is defined as the ratio of mass (or weight) average MW, 0 (2) (1) avg + ∞ ()δ[]−()− ] Mw=p /p , to molar (or number) average MW, Mn=p , thus, ks∫ pm x' x x' xs dx' (3) D(polydispersity)=p(2)p(0)/[p(1)]2. The three moments, p(0), pavg, and x pvar, provide shape characteristics of the MWD and can be used to for vapor construct the MWD mathematically. ∂()∂⁄ =χ()− ⁄ − Population balances for the MWDs are based on mass balances; Vvpv t pm pv K Qpv (4) that is, the accumulation rate is equal to the net generation by reac- for condensate tion minus the net loss by flow or mass transfer. The mass-transfer = rate from the polymer melt to vapor bubbles, described by an over- ∂()∂V p ⁄ t Qp (5) − c c v all mass-trasfer coefficient, k(x)=k0 k1x, is assumed to decrease linearly with MW to account for lower mass-transfer rates of higher- for noncondensable gas products

MW components. The interphase mass-transfer driving force is given ∞ ∂()∂⁄ = ()δ()− − − Vgpg t Vmks∫ pm x' x xs dx' Qpg (6) by pm pv/K, where pm, pv, and K are all functions of x so that the x driving force depends on the particular component that is evaporat- We first consider that k is constant with x and comment later ing. The vapor liquid phase equilibrium constant is assumed to de- d on the effect of a linear dependence on x. Applying the moment crease with MW according to an inverse polynomial operation to each equation yields [McCoy and Madras, 1997] the j following differential equations: () = ⁄ + ∑ Kx K0 1 ajx (2) j = 1 for polymer melt These expressions for k(x) and K(x) permit mathematical solutions ()n () + to the mass balance equations through MW moments. dVmpm ()n ()n ()n j = − χ − + ∑ ⁄ ------0 pm pv ajpv K0 Simultaneous random-scission and repolymerization reactions dt j = 1

+ + + + can be written as +χ ()n 1 −()n 1 + ()n 1 j ⁄ 1 pm pv ∑ajpv K0 j = 1 kd + − ()n ()n ()0 Px'() P() x Px'() x (A) + [− ()− ⁄()+ − Vm kdpm n 1 n 1 2kapm pm ka n − n − + ()()j ()n j − ()n + ()()− j ()n j and irreversible chain-end scission as ka∑ nj pm pm kspm ks∑ nj xs pm (7) j = 0 j = 0 k ()s ()+ ()− Px Q xs Px xs (B) for vapor

Korean J. Chem. Eng.(Vol. 19, No. 2) 242 W. S. Cha et al.

()n () + dVvpv = +χ n −n + n j ⁄ thus recovering the overall mass balance for the equipment. Because ------0 pm pv ∑ajpv K0 dt = (1) j 1 dPg /dt is vanishingly small, from Eq. (18) and the definition of the ()+ ()+ ()+ + () n 1 n 1 n 1 j n polymer melt MW, Mnm, we have − χ − + ∑ ⁄ − 1 pm pv ajpv K0 Qpv (8) j = 1 ⁄ = − ()⁄ ()1 dmtot dt ks xs Mnm Pm (20) for condensate According to this equation, the rate of change of the total polymer ()()n ⁄ = ()n (1) (1) dVcpc dt Qpv (9) mass is first-order in melt mass, Pm =Vmpm . This is a rationale for the first-order rate expression that is frequently applied to calculate for noncondensable gas products rate coefficients for pyrolysis data [Westerout et al., 1997]. The calcu- ()()n ⁄ = n ()0 − ()n (1) dVgpg dt Vmksxs pm Qpg (10) lation, however, is usually based on polymer melt mass, Pm , rather

than total mass, mtot, according to the supposed first-order expression For n=0 the differential equations are molar balances: ()1 ⁄ ≈ − ()1 dPm dt ksapprPm (21) for polymer melt Eq. (21) ignores the vaporization contribution to weight loss and ()()n dVmpm = −χ ()0 −()0 + ()j ⁄ lumps all chain-scission processes into one rate constant. There------0 pm pv ∑ajpv K0 = dt j 1 fore, this expression is an approximation to the realistic rate. + + ()1 −()1 + ()j 1 Initial conditions for polymer melt and condensate MWDs are χ p p ∑a p ⁄K 1 m v j v 0 (0) (0) j = 1 pm(x, 0) and pc(x, 0) and, for moments, pm (0) and pc (0). + []− ()0 ()0 Vm kd kapm pm (11) RESULTS AND DISCUSSION for vapor ()()0 Experimental results demonstrate how MWDs of reactor poly- dVvpv = +χ ()0 −()0 + ()j ⁄ ------0 pm pv ∑ajpv K0 = dt j 1

()1 ()1 ()j + 1 ()0 − χ − + ∑ ⁄ − 1 pm pv ajpv K0 Qpv (12) j = 1 for condensate

()()0 ⁄ = ()0 dVcpc dt Qpv (13) for noncondensable gas products

()()0 ⁄ = ()0 − ()0 dVgpg dt Vmksxspm Qpg (14) For n=1 the differential equations are mass balances: for polymer melt

()1 () + dVmpm = −χ ()1 −()1 + ()j 1 ⁄ ------0 pm pv ∑ajpv K0 = dt j 1 Fig. 3. Molecular weight distribution of pretreated feed polysty-

()2 ()2 ()j + 2 ()0 rene, polymer melt and condensate (pyrolysis temperature: + χ − + ∑ ⁄ − 1 pm pv ajpv K0 Vmksxspm (15) o j = 1 360 C, pyrolysis time: 1 hr). for vapor

()1 () + dVvpv = +χ ()1 −()1 + ()j 1 ⁄ ------0 pm pv ∑ajpv K0 = dt j 1

+ −χ ()2 −()2 + ()j 2 ⁄ − ()1 1 pm pv ∑ajpv K0 Qpv (16) = j 1 for condensate

()()1 ⁄ = ()1 dVcpc dt Qpv (17) for noncondensable gas products

()()1 ⁄ = ()0 − ()1 dVgpg dt Vmksxspm Qpg (18) If these four mass balance equations are added, terms cancel so that (1) (1) (1) (1) the rate of change of the total mass, mtot=Pm +Pv +Pc +Pg , equals the loss of gas products in the outflow, (1) Fig. 4. Change of polymer melt mass, Pm (g), with time at four py- ⁄ = − ()1 dmtot dt QPg (19) rolysis temperatures. March, 2002 Study of Polystyrene Degradation using Continuous Distribution Kinetics in a Bubbling Reactor 243

(1) Fig. 7. Change of cumulative gas product mass, N (g), with time Fig. 5. Change of condensate mass, Pc (g), with time at four py- g rolysis temperatures. at four pyrolysis temperatures.

gas-product masses increase. The time dependences of polymer- mer and vaporized depolymerization products vary with time. melt mass, condensate mass, combined mass, and product-gas mass Fig. 3 represents the molecular weight distribution of pretreated were approximated as second-order polynomials (Figs. 4-7). feed polystyrene and its degradation products. Polymer remaining The condensate accumulation rate increases with the gas flow in the reactor after pyrolysis time is mainly produced by random rate, as indicated by Eqs. (5), (9), (13), and (17). Higher flow rates scission and condensate collected in the condensate vessel is prod- cause the mass of the reactor melt to be smaller and the mass of uced by the chain end scission. the condensate to be larger. The influence of flow rate is greater at Typical pyrolysis experiments measure only loss of polymer mass higher temperatures and longer reaction times. As the reaction tem- due to evaporation of depolymerization products and unreacted low- perature approaches the boiling point of the polymer melt, vapor- MW polymer. The present approach provides two measurements ization increases. (0) of reactor polymer mass (Fig. 4) and of condensate (Fig. 5) at the The moles of reactor polymer, Pm , decrease with time (Fig. 8), end of each experiment. One method of the measurements is by because low-MW products are vaporized. Chain-end scission to prod- weighing and the other is by the first moment of the MWD, which uce gas products and very low-MW liquid products does not change requires that the weight be known. As the measurements are not the polymer molar concentration. (0) independent, reactor polymer mass and condensate mass calculated The moles of condensate, Pc , increase with time (Fig. 9) due to by the two methods coincide. Reactor polymer mass decreases with accumulation of condensed vapor. Calculations by Eq. (13) show increasing the condensate, and their sum decreases with time due the vapor molar concentration is only 2% of the polymer melt molar to gas product loss (Fig. 6). The mass of gaseous products (Fig. 7) concentration, which confirms the negligible contribution of vapor is found by subtracting the sum of polymer melt and condensate degradation. masses from the initial polymer mass. For example, at 370 oC and Following application of the moment operation, mass-transfer 3 h, 10% of the original polymer remains in the reactor while 84% terms cancel when melt and condensate moment equations are added. is condensate and 6% gaseous products. As temperature and time Thus, numerical values of coefficients in the mass-transfer polyno- increase, the reactor polymer mass decrease while condensate and mial values expressions will not directly affect final results or con-

(0) Fig. 6. Change of combined polymer melt and condensate masses, Fig. 8. Change of the zeroth moment, Pm (mol), of the polymer melt (1) (1) Pm +Pc (g), with time at four pyrolysis temperatures. with time at four pyrolysis temperatures. Korean J. Chem. Eng.(Vol. 19, No. 2) 244 W. S. Cha et al.

(0) Fig. 9. Change of the zeroth moment, Pc (mol), of the condensate with time at four pyrolysis temperatures. Fig. 11. Change of condensate volume, Vc(cc), with time at four pyrolysis temperatures. clusions. Relative amounts of reactor residue and condensate, however, do depend on the mass-transfer rate and therefore on the sweep- with 2nd-order polynomials. gas flow rate. An approximate estimate of the chain scission rate coefficient (1) Density of the polystyrene was determined by heating 1.00 g of can be determined from the mass of the polymer melt, Pm . By ap- raw polystyrene in a tube and measuring the volume in the temper- plying Eq. (21), we calculated an approximate rate coefficient, ks ap, ature range 151-295 oC. The weight of the tube and contents did not change, indicating there are no vaporization losses in this temperature range. The density (g/cm3) as a function of temperature (oC) was fitted with a 2nd degree polynomial,

− −6 2 Pm=0.996 0.0015T+2×10 T (22) and extrapolated to 370 oC to calculate polymer-melt volume from melt mass. After an experiment, weights of reactor residue and condensate were determined by weighing reactor and condensate vessels with their contents and subtracting weights of the empty vessels. Poly- mer-melt volume as a function of time, Vm(t), was determined from reactor residue mass (Fig. 4) and density (Eq. (22)). Values of Vm versus time at four reaction temperatures (Fig. 10) are well approximated. The condensate volume, Vc(t), was calculated from condensate mass (Fig. 5) and density, measured as 0.79 g/cm3. Values Fig. 12. Plot of ln[P (1)/P (1) ] versus time at four pyrolysis temper- of Vc versus time at four reaction temperatures (Fig. 11) are fitted m m(0) atures.

Fig. 10. Change of the polymer melt volume, Vm(cc), with time at Fig. 13. Arrhenius plot for a polystyrene chain scission rate coeffi- four pyrolysis temperatures. cient. March, 2002 Study of Polystyrene Degradation using Continuous Distribution Kinetics in a Bubbling Reactor 245

(1) (1) 3 at each reaction temperature from the slope of ln[Pm (t)/Pm (0)] Q : gas flow rate [m /s] versus time (Fig. 12). The Arrhenius plot of these rate coefficients t : time [s] 12 3 gave the activation energy of 49 kcal/mol and prefactor 8.94×10 Vc : volume of polymer melt [m ] −1 3 s (Fig. 13). Compared with other reports, these values are similar Vg : volume of gas product [m ] 3 to recommended values. For example, Westerhout et al. [1997a] Vm : volume of polymer melt [m ] 13 −1 3 for polystyrene suggested 49 kcal/mol and 10 s , and Kim et al. Vv : volume of vapor volume [m ] [1999] also suggested 53 kcal/mol for polystyrene of MW 222,000. REFERENCES CONCLUSIONS Carniti, P., Beltrame, P. L., Massimo, A., Gervasini, A. and Audisio, A., The analysis and results of this investigation are for a two-phase, “Polystyrene Thermodegradation. 2. Kinetics of Formation of plastics-pyrolysis process with polymer degradation occurring in Vloatile Products,” Ind. Eng. Chem. 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