APPLIED CHEMISTRY

Kinetics of Degradation of Polycarbonate in Supercritical andSubcritical Benzene

G. Sivalingam and Giridhar Madras*

Department of Chemical Engineering, Indian Institute of Science, Bangalore 560 012, India

The degradation kinetics of polycarbonate [poly(Bisphenol A carbonate)] in supercritical andsubcritical benzene was studied at various temperatures (523-618 K) at 50 atm. The degradationwas also investigated in other solvents at 573 K and 50 atm. The time evolution of molecularweight distribution was obtained by gel permeation chromatography and modeled withcontinuous distribution kinetics to obtain the degradation rate coefficients. The activation energy,determined from the temperature dependence of the rate coefficient, increased from 16.7 to 20.4kcal/mol from the subcritical region to the supercritical region of the solvent. The degradationrate coefficients at the supercritical conditions were an order higher than the rate coefficientsat subcritical conditions, indicating enhanced degradation at supercritical conditions. TheArrhenius plot showed a break at the supercritical transition point, whereas the semilogarithmicplot of rate coefficients with the density of the reaction mixture showed a continuous linearvariation.

Introduction

Environmental concerns have prompted the scientificcommunity to find ways to recycle plastics. The commontechnique to degrade polymers has been pyrolysis. This,however, has some disadvantages such as nonuniformheat transfer, low yields of desired products, and exces-sive char and gas formation. Degradation in solutionhas been proposed to ameliorate some of these problems.In this method, the polymer is dissolved in a solventand degraded thermally in a single phase. Apart fromplastic recycling,1 degradation studies can be appliedto investigate the stability2 and decomposition charac-teristics3 of polymers. There are a few studies on thedegradation of polymers in solution at ambient pres-sures.4,5

Supercritical fluids are attractive media for chemicalreactions because of their unique properties. Manyphysical and transport properties of supercritical fluidsare intermediate between liquid and gas.6 The reactionrates undergo dramatic changes7 in the supercriticaltransition region. The diffusion-limited reactions areenhanced because of enhanced solubilities and dif-fusivities.8 These interesting properties have led todiversified applications in a variety of reactions includ-ing homogeneous and heterogeneous catalysis,9 enzy-matic reactions,10 and polymerization.11,12 However,there are only a few studies on depolymerization insupercritical fluids. Polymers can be degraded to lowmolecular weight products by thermolysis in supercriti-cal fluids13,14 with high degradation rates. Recently, thesubstantial enhancement in the degradation rate ofpolystyrene in supercritical benzene has been re-ported.15

To the best of our knowledge, this is the first studyon the degradation of polycarbonate in solution. In thisstudy, the degradation of polycarbonate in both super-critical and subcritical conditions was investigated. Therate coefficients were obtained from the time evolutionof the molecular weight distribution (MWD) by usingthe continuous distribution theory. The objective of thepresent investigation was to determine the degradationrate coefficients of random degradation of polycarbonateunder supercritical conditions and quantify the enhance-ment vis-a-vis the rates obtained at subcritical condi-tions. The activation energy was determined from thetemperature dependence of the rate coefficients.

Experimental Section

Polycarbonate (Mn ) 40 000; polydispersity ) 1.2) wasdegraded in benzene, toluene, chlorobenzene, and di-chlorobenzene (all chemicals from Merck, India). Thedegradation reactions were conducted in a benchtopParr reactor (Moline, IL; 250 mL reactor), with an initialpolymer concentration of 2 kg/m3. The reactor pressurewas kept constant at 50 atm for all experiments bysuitably varying the initial amount of the solution. Thetemperature was controlled to within (1 °C with aproportional-integral-derivative controller, and themixture was continuously stirred with a magneticstirrer. Samples were collected at regular intervals andanalyzed by gel permeation chromatography (Waters)at 50 °C with tetrahydrofuran as the eluent. The detailsof this setup are described elsewhere.15

Theoretical Model

Assuming the molecular weight x to be a continuousvariable, the polymer molecule of size x is represented

* To whom correspondence should be addressed. Fax: 91-080-3600683. E-mail: giridhar@chemeng.iisc.ernet.in.

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10.1021/ie020444z CCC: $22.00 © 2002 American Chemical SocietyPublished on Web 10/09/2002

by P(x). The polymer undergoes binary fragmentationat random points along the chain. This can be repre-sented as

The time-dependent molar MWD of P(x) is representedby p(x,t). The rate of disappearance of reactant speciescan be obtained by population balance as

The stoichiometric kernel Ω(x,x′) in eq 1 determines thedistribution of scission products, and kd(x) is the deg-radation rate coefficient. For random scission of poly-mers, the distribution of degraded products,16 Ω(x,x′),is 1/x′, and assuming a linear dependence of kd on xyields kd(x) ) kdx. Thus, eq 1 becomes

Applying the moment operation p(j) ) ∫0∞xjp(x,t) dx to eq

2 yields the jth moment

The first-order ODE for the zeroth and first momentsare obtained from eq 3 by substituting j ) 0 and 1,respectively,

Equation 5 indicates that the total mass concentrationof the polymer is constant, p(1) ) p0

(1) (at t ) 0). Solvingeq 4 with the initial condition

leads to

Under invariant mass concentration, eq 7 simplifies to

i.e.,

Equation 9 shows the relationship for the variation ofthe average molecular weight with time.

Results and Discussion

The effect of supercritical conditions on the degrada-tion rate of polycarbonate has been investigated. Thepressure was held constant at 50 atm for all of the

reactions at various temperatures by suitably manipu-lating the volume of the initial mixture. The ratecoefficients for polymer degradation in benzene (Tc )562.2 K; Pc ) 48.9 atm) were measured in the temper-ature range of 523-618 K. To quantify the extent ofenhancement in the degradation rate at supercriticalconditions, the reactions were carried out at 573 K and50 atm with other solvents, such as toluene (Tc ) 591.8K; Pc ) 41.0 atm), chlorobenzene (Tc ) 632.4 K; Pc )45.2 atm), and dichlorobenzene (Tc ) 729 K; Pc ) 41.0atm) that are below their critical temperatures at 573K.

Figure 1 shows the time variation of the number-average molecular weight for the reactions in super-critical benzene. The lines in the figure for varioustemperatures are nearly linear, indicating the validityof eq 9. The degradation rate coefficients for polycar-bonate in supercritical benzene are determined from theslopes of Figure 1 and are in the range of (113.8-382)× 10-4 s-1. Figure 2 depicts the variation in the number-average molecular weight with time when the reactionswere conducted in subcritical conditions in benzene andother solvents. The degradation rate coefficients forbenzene in the temperature range of 523-553 K are inthe range of (3.78-9.36) × 10-4 s-1. It is clear that therate coefficients for the reactions in supercritical ben-zene are an order higher than the rate coefficients forthe reactions in subcritical benzene. The slopes of Figure

P(x′) f P(x) + P(x′-x) (A)

∂p(x,t)∂t

) -kd(x) p(x,t) + 2∫x

∞kd(x′) p(x′,t) Ω(x,x′) dx′

(1)

∂p(x,t)∂t

) -kdxp(x,t) + 2∫x

∞kdx′p(x′,t) Ω(x,x′) dx′ (2)

dp(j)

dt) - j - 1

j + 1kdp

(j+1)(t) (3)

dp(0)

dt) kdp

(1)(t) (4)

dp(1)

dt) 0 (5)

p(0)(t)0) ) p0(0) (6)

p(0)(t) - p0(0) ) kdp

(1)t (7)

1Mn

- 1Mn0

) kdt (8)

Mn0

Mn- 1 ) kdMn0t ) kt (9)

Figure 1. Variation of the number-average molecular weight withreaction time in supercritical benzene at 50 atm. Legend: (2) 618K; (b) 593 K; (9) 573 K.

Figure 2. Variation of the number-average molecular weight withreaction time in subcritical media at 50 atm. Legend: (9) benzeneat 523 K; (b) benzene at 538 K; (2) benzene at 553 K; (1)dichlorobenzene at 573 K; ([) chlorobenzene at 573 K; (rotated2) toluene at 573 K.

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2 also provide the rate coefficients for degradation intoluene (30.1 × 10-4 s-1), chlorobenzene (10.89 × 10-4

s-1), and dichlorobenzene (8.37 × 10-4 s-1). The ratecoefficient increases as the solvent approaches thevicinity of the supercritical region.

Figure 3 shows the Arrhenius plot for the degradationrate coefficients of polycarbonate in benzene. The acti-vation energies in the subcritical and supercriticalregions are 16.7 and 20.4 kcal/mol with a transitionregion near the supercritical point. These activationenergies are slightly higher than the activation energyof 13.8 kcal/mol for the degradation of polystyrene insupercritical benzene.15

Many factors that influence the rate coefficients insupercritical fluids are the activation volume, solvents,pressure, temperature, dielectric constant, etc.6 Amongthese parameters, the density of the solvent may playa role in determining the kinetics. It is well-known thatthe solubilities of organics near the supercritical regionsshow a direct proportionality to the density of themixture.17 Figure 4 shows the effect of density on therate coefficient on a semilogarithmic scale. This figureclearly indicates that the variation of rate coefficientsnear the critical region can be represented by usingdensity as a parameter, rather than temperature. Thishypothesis is further confirmed by Figure 5, whichshows the variation of the rate coefficients with thedensity of different solvents at various temperatures.The variation of the rate coefficients with temperature

does not follow an Arrhenius behavior, but the variationof the logarithm of the rate coefficient is linear withdensity. This is similar to the variation of the logarithmof the solubility with density. This indicates that densityplays an important role in determining the kinetics ofthe system. The local density enhancement8 can reducereaction rates by providing a dense environment andlowering the activation energy.

Concluding Remarks

The degradation of polycarbonate was carried out insubcritical and supercritical media at 50 atm. The timeevolution of MWDs, determined experimentally, wasmodeled by continuous distribution kinetics. The ratecoefficients for degradation in supercritical benzenewere an order of magnitude higher than the ratecoefficients for degradation in subcritical fluids. The ratecoefficients decreased exponentially with an increase inthe density of the solvent.

Literature Cited

(1) Miller, A. Industry Invests in Reusing Plastics. Environ. Sci.Technol. 1994, 28, 16A.

(2) Hawkins, W. L. In Polymer Degradation and Stabilization;Spring-Verlag: New York, 1984.

(3) Flynn, J. H.; Florin, R. E. Degradation and PyrolysisMechanisms. In Pyrolysis and GC Polymer Analysis; Leibbeman,S. A., Levy, E. S., Eds.; Dekker: New York, 1985.

(4) Murakata, T.; Wagatsuma, S.; Saito, Y.; Suzuki, T.; Sata,S. Solvent Effect on Thermal Degradation of Poly(p-methyl-styrene). Polymer 1993, 34, 1431.

(5) Sterling, W. J.; McCoy, B. J. Distribution Kinetics ofThermolytic Macromolecular Reactions. AIChE J. 2001, 47, 2289

(6) Savage, P. E.; Gopalan, S.; Mizan, T. I.; Martino, C. J.;Brock, E. E. Reactions at Supercritical conditions: Application andFundamentals. AIChE J. 1995, 41, 1723.

(7) Milner, S, T.; Martin, P. C. Critical Slowing of ChemicalReactions. Phys. Rev. A 1986, 56, 1996.

(8) Brennecke, J. F.; Chateaneuf, J. E.; Homogeneous OrganicReactions as Mechnaistic Probes in Supercritcal Fluids. Chem.Rev. 1999, 99, 433-452.

(9) Subramaniam, B.; McHugh, M. A. Reactions in SupercriticalFluids: A Review. Ind. Eng. Chem. Process. Des. Dev. 1986, 25,1.

(10) Kamat, S.; Barrera, J.; Beckman, E. J.; Russel, A. J.Biocatalytic Synthesis of Acrylates in Supercritical Fluids: I.Optimization of Enzyme Environment. Biotechnol. Bioeng. 1992,40, 158.

(11) Ahvenainen, A.; Kanazawa, K.; Arai, K. Rapid and Con-tinuous Hydrothermal Crystallization of Metal Oxide Particles inSupercritical Water. J. Am. Ceram. Soc. 1992, 75, 2615.

Figure 3. Arrhenius plot of the rate coefficient with temperaturein benzene. Legend: (b) supercritical benzene; (9) subcriticalbenzene.

Figure 4. Variation of the rate coefficient with the density ofbenzene throughout the subcritical to supercritical regime at 50atm.

Figure 5. Variation of the rate coefficients with the density ofthe solvents at 300 °C and 50 atm. Legend: (9) dichlorobenzene;(b) chlorobenzene; (2) toluene; (1) benzene.

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(12) Stassin, F.; Halleux, O.; Jerome, R. Ring-Opening Poly-merization of ε-Caprolactone in Supercritical Carbon Dioxode.Macromolecules 2001, 34, 775.

(13) Goto, M.; Koyamoto, H.; Kodama, A.; Hirose, T.; Nagaoka,S.; McCoy, B. J. Degradation Kinetics of Poly(ethylene terephtha-late) in Supercritical Methanol. AIChE J. 2002, 48, 136.

(14) Dhawan, J. C.; Legendre, R. C.; Bencsath, A. F.; Davies,R. M. Reaction products of styrene-Butadiene ABA Block Co-polymer in Supercritical Toluene and Tetralin. J. Supercrit. Fluids1991, 4, 160.

(15) Karmore, V.; Madras, G. Continuous Distribution Kineticsfor the Degradation of Polystyrene in Supercritical Benzene. Ind.Eng. Chem. Res. 2000, 39, 4020.

(16) McCoy, B. J.; Wang, M. Continuous-Mixture Fragmenta-tion Kinetics: Particle Size Reduction and Molecular Cracking.Chem. Eng. Sci. 1994, 49, 3773.

(17) Madras, G.; Erkey, C.; Akgerman, A. A New Techniquefor Measuring Solubilities of Organics in Supercritical Fluids. J.Chem. Eng. Data 1993, 38, 422.

Received for review June 17, 2002Revised manuscript received August 29, 2002

Accepted August 31, 2002

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