Enzymatic and Thermal Degradation of Poly(E-caprolactone),Poly(D,L-lactide), and Their Blends

G. Sivalingam, S. P. Vijayalakshmi, and Giridhar Madras*

Department of Chemical Engineering, Indian Institute of Science, Bangalore 12, India

The enzymatic degradation of poly(d,l-lactide) (PLA), poly(ε-caprolactone) (PCL), and their blendsby Novozym 435 was studied in toluene at 60 °C. Both of the polymers were found to degradeby specific chain end scission. A model based on the continuous distribution kinetics wasdeveloped to determine the rate coefficient. The degradation rate coefficient was determinedfrom the time evolution of the specific product. The pyrolytic degradation of these polymers andtheir blends was also investigated. The presence of PLA did not affect either the thermal orenzymatic degradation of PCL. It was thus concluded that the degradations of the polymerswere independent of each other.

Introduction

Environmental issues have led to an escalated inter-est in biodegradable polymers such as poly(ε-caprolac-tone) (PCL), poly(glycolide), poly(lactide), etc., as alter-natives to traditional commodity plastics. Amongbiodegradable polymers for biomedical applications,poly(lactide) and poly(ε-caprolactone) have attractedconsiderable attention because of their biodegradabilityand miscibility with various polymers.1 Poly(lactide) hasproperties similar to those of conventional packingresins; therefore, it can be used for food packaging andas diapers and is found in contaminated hospital wastesthat are more suitable for disposal rather than recy-cling.2 PCL is biocompatible and permeable to manycompounds and is used as a matrix for controlled drugrelease3 and agriculture.4

Poly(D,L-lactide) (PLA) stereocopolymer or poly(L-lactidex) (where x denotes the fraction of PLA in thecopolymer) degrades more rapidly compared to semi-crystalline poly(L-lactide),1 and hence the former can beused for controlled drug delivery. PCL degrades slowlycompared to poly(glycolide) and poly(lactide).5 Slowerdegradation of the drug carrier is favored for long-termdelivery, and the structural modification of PCL isrequired to avail its usage for a wide range of applica-tions. The degradability of the homopolymers can beenhanced by chemically modifying the polymer to formcopolymers of lactide, glycolide, and other lactones.6Degradation of hydrolytically degradable polyesters canlead to significant morphology changes with partialcrystallization of the degradation products.7,8 Thismakes the study of enzymatic and thermal degradationof PCL and PLA interesting.

The presence of one polymer influences the degrada-tion of the other polymer.9-11 The presence of poly(vinylacetate) decreases the enzymatic degradability of PLA,12

poly(hydroxy butyrate),13 poly(ethylene oxide),14 andPCL.15 However, the copolymers of lactones have beenreported to enhance the biodegradability of the copoly-mers.6 Because the copolymer degrades faster than thehomopolymers, some kind of interaction is expected.

Thus, the objective of the present study is to investigatethe interaction between PCL and PLA during pyrolytic/enzymatic degradation.

In the present investigation, the thermal degradationof PCL, PLA, blends of PCL and PLA, and a copolymerhas been investigated in pyrolysis. The enzymaticdegradation of these polymers has also been studied intoluene catalyzed by lipase, Novozym 435 (from CandidaAntartica). The enzymatic degradation and the interac-tion between these polymers have been modeled usingcontinuous distribution kinetics.

Experimental SectionMaterials. PLA (Mn ) 18 300 g/mol), PCL (Mn )

93 000 g/mol), and poly(D,L-lactide-co-caprolactone) (Mn) 93 000 g/mol) were purchased from Sigma Aldrich.Novozym 435 (commercial grade) was received as a giftfrom Novo-Nordisk. Because the water content plays acrucial role in the activity of the enzyme, Novozym 435was freed from moisture content by drying it in adesiccator prior to usage. Toluene and tetrahydrofuran(THF) (S.D. Fine-Chemicals, Ltd., Boisar, India) weredistilled and filtered prior to use.

Sample Preparation for Pyrolytic Degradation.A solution blending technique16 was employed in thepresent study to prepare the physical blends of PCL andPLA. In this method, preproportioned amounts of thepolymers were dissolved in THF. The mixture wasstirred vigorously to obtain homogeneity. The solventwas removed by evaporation under vacuum, and thepolymer mixture was further dried at 40 °C for 72 h.To check whether oxidative degradation of the polymerstook place during sample preparation, thermogravimet-ric analysis (TGA) studies were carried out for indi-vidual polymers and a polymer prepared by the aboveblending method. The thermogravimetric profiles forboth cases were the same, indicating the absence ofoxidative degradation of samples during sample prepa-ration.

Thermogravimetry Analysis. Thermal decomposi-tion studies were carried out by TGA (Perkin-Elmer,Pyris) under inert flowing nitrogen (at a rate of 150 cm3/min) at a heating rate of 5 K/min. The referencematerial was R-alumina, and samples of 25-30 mg wereplaced in a platinum crucible. All of the runs werecarried out between 50 and 600 °C.

* To whom correspondence should be addressed. Tel.:91-80-22932321. Fax: 91-80-23600683. E-mail: Giridhar@chemeng.iisc.ernet.in.

7702 Ind. Eng. Chem. Res. 2004, 43, 7702-7709

10.1021/ie049589r CCC: $27.50 © 2004 American Chemical SocietyPublished on Web 10/26/2004

Enzymatic Degradation Experiments. Polymersof concentration 2 kg/m3 were dissolved in toluene. Theenzyme concentration used was 1 kg/m3. A total of 15mL of the polymer solution was placed in culture tubeswith screw caps and sealed with Teflon tapes and keptin an incubator shaker. The temperature of the incuba-tor was controlled by a proportional-integral-deriva-tive (PID) controller with a variation of (1 °C. Aliquotsof 200 µL were withdrawn at different time intervalsfor further analysis.

Specific Product Analysis. The specific productsformed were determined through gel permeation chro-matography (GPC). The gel permeation chromatographconsisted of three columns (HR 4, HR 3, and HR 0.5)connected in series and maintained at 50 °C. Anisocratic pump (Waters Manufacturing, Inc., Wayland,MA) was used to pump the eluent THF through thecolumn at a flow rate of 1 mL/min. Samples wereinjected through a Rheodyne valve of 50-µL capacity intothe column, and the response was recorded in a dif-ferential refractrometer (Waters model 401). The chro-matogram thus obtained was converted to molecularweight using polystyrene standards (Polymer Labora-tories, Amherst, MA), and the details are given else-where.17 The samples were centrifuged, and enzymeswere returned to the reactor prior to injection into thegel permeation chromatograph. The chromatographshows two distinct peaks, one for the parent polymerand the other for the specific product. The mass fractionof the specific products formed can be determined fromthe area under the peak.

Theoretical Model

The current model, though similar to the previousmodel,9 is more exhaustive by including the interactionof the polymers and allowing for both of the polymersto degrade at comparable rates. The molecular weightof the polymer, x, is assumed to be a continuousvariable. Lipase cleaves the ester bonds in the mainchain of PCL and PLA, leading to specific products, asreported elsewhere.9 In both cases, the molecular weightof the polymer is not significantly affected and onlythe amount of specific product formed increases withtime.

Mechanism of Polymer Degradation in Mix-tures. Let PA and PB represent the polymer moleculesof species A (PCL) and B (PLA), respectively, and Erepresent the enzyme, Novozym 435. The adsorption ofenzymes over the polymer is reversible and is given by

where PAE(x) and PB

E(x) are the adsorbed polymer sub-strate of individual polymers PCL (A) and PLA (B),respectively. The adsorbed polymer substrate undergoesa reversible reaction to form the transition complex

PAE/ and PB

E/ are the activated (adjunct) complex

formed in the above step of polymers A and B, respec-tively. These activated complexes undergo irreversiblespecific chain scission to form the specific products asfollows:

QsA and QsB represent specific products of A and Bformed with molecular weights xsA and xsB, respectively.Because the enzyme activity reduces with time, therate of degradation will decrease with time and ceaseafter a long time. To account for this behavior, ratecoefficients in the above expressions are multiplied bythe activity of the enzyme (a). The enzyme deactiva-tion is assumed to be first order. The adsorbed en-zyme-polymer B intermediate, PB

E(x), combines withpolymer A to form an intermediate complex that un-dergoes transformation to polymer B and PA

E(x). Theextent of interaction of polymer A with polymer B wouldbe different from the extent of interaction of B with A.Therefore, we have used individual rate coefficientsfor the interaction of polymer with the transitioncomplex. The coefficient kd1 is the interaction coefficientfor polymer A with the transition complex of B, andkD1 is the interaction coefficient for polymer A andtransition complex B. Similarly, kd2 and kD2 representthe rate coefficients for polymer B with the transitioncomplex A.

Population Balances for Polymers and Interme-diates. The concentration of the polymer, P(x), ofmolecular weight x is denoted as p(x,t) by assuming xto be a continuous variable. The population balances foreach of the polymer species, adsorbed species, andtransition complex and intermediates are written9 basedon the reactions (A)-(G).

PAE/(x) 98

ksAQsA(xsA) + PA

E(x-xsA) (E)

PBE/(x) 98

ksBQsB(xsB) + PB

E(x-xsB) (F)

PBE(x) ) PA(x′) {\}

kd1

kD1PE(x+x′) {\}

kD2

kd2PB(x) + PA

E(x′)(G)

∂pA

∂t) -kaApAe + kdApA

E - kd1pApBE,(0) +

kD1∫x

∞pE(x′) (1/x′) dx′ (1)

∂pB

∂t) -kaBpBe + kdBpB

E - kd2pBpAE,(0) +

kD2∫x

∞pE(x′) (1/x′) dx′ (2)

∂qsA

∂t) ksAa∫x

∞pA

E/(x′) δ(x′-xs) dx′ (3)

∂qsB

∂t) ksBa∫x

∞pB

E/(x′) δ(x′-xs) dx′ (4)

∂pAE/

∂t) ktfApA

E - ktbApAE/ - ksAapA

E/ (5)

∂pBE/

∂t) ktfBpB

E - ktbBpBE/ - ksBapB

E/ (6)

PA(x) + E {\}kaA

kdAPA

E(x) (A)

PB(x) + E {\}kaB

kdBPB

E(x) (B)

PAE(x) {\}

ktfA

ktbAPA

E/(x) (C)

PBE(x) {\}

ktfB

ktbBPB

E/(x) (D)

Ind. Eng. Chem. Res., Vol. 43, No. 24, 2004 7703

Moment operation on these integrodifferential equationsconverts them into ordinary differential equations ami-cable for the analytical solution. The moment operationdefined as p(j)(t) ) ∫0

∞xjp(x,t) dx on eqs 1-9 yields

In eqs 10-18, all of the quantities are not measurable,and thus nonmeasurable quantities should be expressedin terms of measurable variables. The zeroth moment

(set at j ) 0) of any species in the above equationsrepresents the molar concentration, and the first mo-ment (j ) 1) represents the mass concentration. Quasi-steady-state assumption (QSSA) is used wherein the netconcentration of the intermediates is assumed to beconstant and thus the net rate of formation is zero.Using QSSA, the molar concentration of the intermedi-ates are obtained from eqs 14-17 and are given asfollows:

The QSSA to the interaction equation (18) yields

Using these expressions for the polymers (eqs 10 and11), the rate of change of molar concentration of thepolymers is given by

Equations 24 and 25 clearly indicate that the molarconcentration of the polymer does not change with time,and this is a characteristic of the specific chain endscission.9

Results and Discussion

Miscibility of PCL and PLA. There are contradict-ing observations on the miscibility of these polymersobserved by several researchers.18-21 Differential scan-ning analysis performed on a PLA and PCL blendshowed a complex phase behavior sensitive to themethod of preparation.18 However, NMR studies indi-cated the presence of phase separation.18 Tsuji andIkada19 studied the same system and found a nonin-teractive behavior between these blends and also ob-served spherulite formation due to PCL. When poly-mers are made by solution blending, as was carried outin the present study, in dichloromethane, followed bylow-temperature evaporation, clear, homogeneous poly-mer blends were formed, as evidenced by spectralanalysis.20 The polymer blends were made in thepresent study by the same method as that described inthe literature.20 The thermogravimetry studies werecarried out by randomly picking out the samples atdifferent regions of the film formed. The mass fractionswere calculated in the temperature domains of degrada-tion of each polymer and found to represent the initialcomposition, the entire time indicating a uniform dis-tribution of these polymers in the blends. A recent study

∂pAE

∂t) kaApAe - kdApA

E - ktfApAE + ktbApA

E/ +

ksAa∫x

∞pA

E/(x′) δ[x-(x′-xs)] dx′ - kd2pB

(0) pAE +

kD2∫x

∞pE(x′) (1/x′) dx′ (7)

∂pBE

∂t) kaBpBe - kdBpB

E - ktfBpBE + ktbBpB

E/+

ksBa∫x

∞pB

E/(x′) δ[x-(x′-xs)] dx′ - kd1pA

(0) pBE +

kD1∫x

∞pE(x′) (1/x′) dx′ (8)

∂p∂t

) kd1∫0

xpA(x′) pB

E(x-x′) dx′ +

kd2∫0

xpB(x′) pA

E(x-x′) dx′ - (kD1 + kD2)pE (9)

dpA(j)

dt) -kaApA

(j)e + kdApAE,(j) - kd1pA

(j) pBE,(0) +

kD1pE,(j)

j + 1(10)

dpB(j)

dt) -kaBpB

(j)e + kdBpBE,(j) - kd2pB

(j) pAE,(0) +

kD2pE,(j)

j + 1(11)

dqsA(j)

dt) ksAaxsA

j pAE/

,(0)(12)

dqsB(j)

dt) ksBaxsB

j pBE/

,(0)(13)

dpAE/

,(j)

dt) ktfApA

E,(j) - ktbApAE/

,(j)- ksAapA

E/

,(j)(14)

dpBE/

,(j)

dt) ktfBpB

E,(j) - ktbBpBE/

,(j)- ksBapB

E/

,(j)(15)

dpAE,(j)

dt) kaApA

(j)e - kdApAE,(j) - ktfApA

E,(j) + ktbApAE/

,(j)+

ksAa∑i)0

jjCi(-xsB)ipA

E/

,(j-i)- kd2pB

(0) pAE,(j) +

kD2pE,(j)

j + 1(16)

dpBE,(j)

dt) kaBpB

(j)e - kdBpBE,(j) - ktfBpB

E,(j) + ktbBpBE/

,(j)+

ksBa∑i)0

jjCi(-xsA)ipB

E/

,(j-i)- kd1pA

(0) pBE,(j) +

kD1pE,(j)

j + 1(17)

dpE,(j)

dt) kd2∑

i)0

jjCipA

E,(i) pB(j-i) + kd1∑

i)0

jjCipB

E,(i)pA(j-i) -

(kD1 + kD2)pE,(j) (18)

pAE/

,(0))

ktfA

ksA + ktbApA

E,(0) (19)

pBE/

,(0))

ktfB

ksB + ktbBpB

E,(0) (20)

pAE,(0) )

kD2pE,(0) + kaApA

(0)e

kd2pB(0) + kdA

(21)

pBE,(0) )

kD1pE,(0) + kaBpB

(0)e

kd1pA(0) + kdB

(22)

pE,(0) ) 1kD1 + kD2

(kd2pAE,(0) pB

(0) + kd1pBE,(0) pA

(0)) (23)

dpA(0)/dt ) 0 (24)

dpB(0)/dt ) 0 (25)

7704 Ind. Eng. Chem. Res., Vol. 43, No. 24, 2004

on this blend observed a low critical solution tempera-ture (LCST); for instance, a 36 wt % PCL blend showed86 °C as the LCST, suggesting the miscibility of thepolymers.21 From these studies, it appears that the mis-cibility behavior of these polymers is not clear. However,the objectives of the present study are to investigate theinteraction between these polymers under pyrolyticconditions and solution degradation. Under pyrolyticconditions, the temperature is higher than the LCSTand should be miscible over the entire range of inves-tigations (>200 °C). Similarly, when polymers aredissolved in solution, homogeneity is present becauseof stirring and the low concentration of the solutes.

Pyrolytic Degradation. The pyrolysis of PCL andPLA was studied under a dynamic heating rate. Figure1a shows the differential thermogravimetry (DTG)profile for all of the polymers. PCL degrades by bothrandom chain scission and specific chain end scissionduring nonisothermal heating. Though both of themechanisms occur during degradation,22 the molecularweight dynamics suggests that random chain scissionpredominates at lower temperature whereas specificchain scission predominates at higher temperatures.23

Activation energies of 55 and 18 kcal/mol were observedfor specific chain scission and random scission of PCL,respectively.22 A similar mechanism is observed for the

degradation of PLA wherein degradation proceeds byester interchange at lower temperatures and by decar-boxylation at higher temperatures.24-26 The activationenergies for random and specific scission are 10.2 and25.2 kcal/mol of PLA, respectively.23

In a polymer mixture, there can be either positive,negative, or no interaction between the polymers.16 Thedegradation of a blend of PCL and poly(vinyl acetate)(PVAC) in solution showed enhanced thermal degrada-tion of PVAC and reduced degradation of PCL. This wasattributed to the hydrogen-accepting nature of PCL andthe hydrogen-donating nature of PVAC.9-11 However,the pyrolytic degradation of the PCL-PVAC blendshowed no interaction although synergistic enhance-ment in mechanical properties was observed.15 However,the degradation of copolymer showed considerable de-viation from ideality. Figure 1b shows the degradationof the copolymer 86:14 PLA-PCL along with theindividual homopolymers. The figure shows that thedegradation of the copolymer is significantly differentfrom the degradation of the individual polymers.

The DTG profiles for the individual polymers and thepolymer blends are given in Figure 1a,b. To check theinteraction in the degradation of the polymers, theentire DTG curve is divided into two sections. Region Icovers the temperature range of 180-329 °C, where allof the PLA components degrade, and region II coversthe temperature range of 329-453 °C, which is pre-dominantly the PCL decomposition region. These re-gions are marked in Figure 1. The fractional massesreleased during the degradation of the physical mixturesin these regions are calculated and are shown in Figure2. The solid lines in the plot are the prediction byassuming no interaction between the polymers using asimple additive rule,15 (DTG)total ) ∑i)1

n xi(DTG)i (wheren ) 2 for the binary mixture). The absence of interactionbetween the two is implied from the linearity of theexperimental data (Figure 2). The deviation from thepredicted behavior is negligible, and thus it can beinferred that the polymers do not interact and thus showideal behavior during pyrolysis. The points marked inthe figure for the copolymer showed good interactionbetween the polymers. Though no interaction was ob-served for the degradation of PCL and PVAC in pyroly-sis conditions,23 the enzymatic degradation of these

Figure 1. (a) DTG profile for PCL, PLA, and various physicalblends. Region I shows the temperature region of 180-330 °C, andregion II shows the temperature region of 330-450 °C. (b) DTGprofile for the copolymer 86:14 PLA-PCL and blend 85:15 PLA-PCL along with the pure polymers.

Figure 2. Weight loss regime plot for regions I and II during thedegradation of various physical blends of PLA, PCL, and thecopolymer.

Ind. Eng. Chem. Res., Vol. 43, No. 24, 2004 7705

polymers under solution showed an order decrease inthe enzymatic degradation of the PCL in solution.9Hence, it would be interesting to see the enzymaticdegradation behavior of the present system in solution.

Enzymatic Degradation in Solution. When kd1 )kd2 ) kD1 ) kD2 ) 0, the two polymers undergo degrada-tion independently. The degradation rates for the binarymixture can decrease or increase or are independentdepending on the other polymer. Thus, the rate coef-ficient for the specific chain scission of PCL is a functionof the concentration of PLA in the blend based on theexperimental conditions or vice versa. The degradationrate of the individual polymer can be obtained by settingthe other intermediates and species to zero. For ex-ample, to get the degradation kinetics of polymer A(PCL), setting pB

(0) ) pBE,(0) ) 0 in the governing equa-

tions yields

where KA ) (ksAkaA/kdA)[ktfA/(ksA + ktbA)]e and the massconcentration of the specific product formed can befollowed by setting j ) 1 in the above equations:

As stated earlier, a first-order deactivation kinetics hasbeen used [a(t) ) a0 exp(-kenzt)], where a0 is the initialactivity of the enzyme and kenz is the enzyme specificdeactivation constant. This transforms eq 27 into

Solving eq 28 with the initial condition of qsA(1)(t)0) ) 0

yields the specific product mass concentration as afunction of time:

Because the enzyme deactivates with time, the enzymewill not be functional at a long time and thus thedegradation rate will be zero and the amount of specificproduct formed will reach a constant value. Such asaturation value is obtained by setting the time toinfinity in eq 29. Under the experimental conditions,this saturation value is measured after 20 days, wherethe concentration of the specific products formed doesnot change with time.

Equation 29 can be transformed into the following formusing eq 29:

Equation 31 suggests that a plot of -ln[1 - qr(t)] withtime will be linear, with the slope being the enzymedeactivation constant.

The enzymatic degradation of PLA and PCL and theirphysical mixtures in solution was studied at 60 °C usingNovozym 435. An earlier study27 indicated that higherdegradation rates of PCL were observed at 60 °C in

toluene and that the degradation of PCL by Novozym435 proceeds by specific chain end scission. The amountof the specific product formed increases with time, butsaturation is attained at long times27 because of enzymedeactivation. The enzymatic degradation of the blendof PCL and PVAC showed that there was a reductionin the degradation of PCL upon the addition of PVAC,whereas PVAC did not degrade significantly in theblend.9 This implies that PCL has a positive interactionwith PVAC, whereas PVAC has almost no interactionwith PCL.

In the present investigation, it is seen that the purepolymers and mixtures degrade by specific chain endscission and the molecular weight of the specific prod-ucts formed is in the range of 290-350 g/mol. Thereaction was continued for 20 days to ensure thatsaturation was attained. The value of qssA used was thevalue that was obtained at the end of 20 days, afterwhich no further degradation was observed. Parts a-cof Figure 3 show the degradation mechanism of thePCL, PLA, and copolymer, respectively. The enzymeattack is specific toward the carbonyl bonds in both PLAand PCL. The point of enzyme attack is also shown inthe figure. Figure 4 shows the plot of -ln[1 - qr(t)] withtime, and it can be seen from the figure that the experi-mental data are linear, indicating the validity of themodel. Figure 5 shows the time dynamics of the specificproducts formed for pure polymers. This figure alsoshows the specific product profile for the physical mix-tures and copolymers. The solid lines in the plot are themodel fits obtained by regressing the experimental data.

The concentration of the complex formed can beobtained by simultaneously solving eqs 21-23

where k1 ) 1 + kdpB(0)/kdA and k2 ) 1 + kdpA

(0)/kdB.Substituting the expressions for p(0) into eq 21 yields

dqsA(0)/dt ) KAapA

(0) (26)

dqsA(1)/dt ) KAaxsApA

(0) (27)

dqsA(1)/dt ) KAa0 exp(-kenzt)xsApA

(0) (28)

qsA(1) )

KAa0xsApA0(1)

kenzMnA0[1 - exp(-kenzt)] (29)

qssA ) qsA(1)(tf∞) )

KAa0xsApA(1)

kenzMnA0(30)

qr(t) )qsA(t)

qssA(tf∞)) 1 - exp(-kenzt) (31)

Figure 3. Point of attack of the polyesters by the lipaseemployed: (a) PLA; (b) PCL; (c) 14:86 PCL-PLA.

pAE,(0) ) 1

kd2pB(0) + kdA

[kaAepA(0) +

kD2pA(0) pB

(0)

kd2/k1 + kD2/k2(kd1kaBe

kdBk2+

kd2kaAekdAk2

)] (32)

pAE,(0) ) 1

kdA + kd2pB(0)

[kaAepA(0) + k3kD2pA

(0) pB(0)e] (33)

7706 Ind. Eng. Chem. Res., Vol. 43, No. 24, 2004

Equation 33 can be further simplified to

where k3 is given by [(kaBkd1/k2kdB) + (kaAkd2/k1kdA)]-[1/(kD1/k2 + kD2/k1)], and substituting eq 34 into eq 19results in

Now, the rate of change of the mass concentration ofthe specific products formed can be written as

Equation 36 can be simplified to the following form by

excluding the scission coefficient of the individualpolymers:

Because the molar concentrations of the pure polymersare constant (eqs 24 and 25), eq 37 reduces to

where kint,B is equal to [1 + (kD2k3/kaA)pB(0)]/[1 +

(kd2pB(0)/kdA)]. k1, k2, and k3 are independent of time and

are used as the overall rate coefficients. It can be seenfrom the kint,B expression that if the other polymer isabsent, i.e., pB

(0) ) 0, kint,B will be unity and thus eq 38will reduce to the homopolymer degradation as givenin eq 27. Similarly, the rate of change of specificproducts formed from the PLA (B) can be written as

In the chromatogram response from GPC, it is notpossible to separate the specific products formed fromeach polymer because they are of similar molecularweights. Only the combined response is possible, andthus the total specific products formed can be obtainedby summing eqs 38 and 39:

It can be seen from eq 40 that all of the variables areknown except kint,B and kint,A and these can be obtainedfrom regressing the experimental data. Using the first-order deactivation for Novozym 435 and integrating theequation lead to

qcombined(1) is the summation of qsA

(1) and qsB(1). At longer

Figure 4. (a) Plot of -ln[1 - q(1)(t)/qs] vs reaction time showingthe validity of the model developed for the pure homopolymers,physical mixtures, and copolymers catalyzed by Novozym 435 intoluene at 60 °C. Legends: 9, PCL; b, PLA; 2, 50:50 PCL-PLA;1, 70:30 PCL-PLA; [, 14:86 PCL-PLA copolymer. (b) Variationof the mass fraction of specific products formed with time intoluene at 60 °C catalyzed by Novozym 435. See part a for thelegend.

pAE,(0) )

kaApA(0)e

kdA + kd2pB(0)[1 +

k3kD2

kaApB

(0)] (34)

pAE/

(0))

kaApA(0)ektfA

ksA + ktbA

1kdA + kd2pB

(0)[1 +k3kD2

kaApB

(0)] (35)

dqsA(1)

dt)

ksAaxsA

ksA + ktbA

kaApA(0)ektfA

kdA + kd2pB(0)[1 +

kD2k3

kaApB

(0)] (36)

Figure 5. Variation of the saturation value with blend composi-tion. The solid line is the prediction by the theory and shows theideal behavior of the blends.

dqsA(1)

dt) KA

kdA

kdA + kd2pB(0)

xsApA(0)[1 +

kD2k3

kaApB

(0)]a (37)

dqsA(1)

dt) KAkint,BxsApA

(0)a (38)

dqsB(1)/dt ) KBkint,AxsBpB

(0)a (39)

d(qsA(1) + qsB

(1))/dt ) [KAkint,BxsApA(0) + KBkint,AxsBpB

(0)]a(40)

qcombined(1) ) [KAkint,BxsApA

(0) + KBkint,AxsBpB(0)

kenz][1 -

exp(-kenzt)] (41)

Ind. Eng. Chem. Res., Vol. 43, No. 24, 2004 7707

times, the enzyme activity will be zero, thus leading tosaturation, and can be obtained by setting the time toinfinity. The saturation value is given as

Equations 41 and 42 can be written like polymerdegradation as written in eq 31. Thus, the plot of -ln[1- qcombined

(1) /qcombined,s(1) ] versus time will be linear, with

the slope being the enzyme deactivation coefficient. Themaximum specific product formed is determined fromthe saturation value of the experiment.

The copolymer degrades at a faster rate comparedwith pure polymers and is consistent with the litera-ture.6 The degradation rate of PCL is also lower thanthat of PLA.5 The validity of the model for the physicalmixtures is also evident from the plot of -ln[1 - (1 -q/qs)] with reaction time (Figure 4a). The values ofenzyme deactivation rate coefficients are 0.0011, 0.0024,0.0035, 0.0024, and 0.0019 for PCL, PLA, copolymer,50:50 PCL-PLA, and 70:30 PCL-PLA mixtures, re-spectively.

The saturation values of qsmax obtained from experi-ment are 0.035, 0.045, 0.05, and 0.085 for PCL, 70:30PCL-PLA, 50:50 PCL-PLA, and PLA, respectively.However, for the copolymer 14:86 PCL-PLA, the valueis considerably higher (0.15). Figure 5 shows the varia-tion of the saturation value for the polymers and theirmixtures. The interaction parameter between the twopolymers in solution can be predicted from theory fromeq 42. It is estimated that for both of the physicalmixtures the values of kint,A and kint,B are unity, indicat-ing that there is no interaction between the polymersin solution, contrary to the observation for the degrada-tion of PCL and PVAC. The solid line in Figure 5 is theprediction obtained from the model (generated by usingkint ) 1 in eq 42). It can be seen that it matches wellwith the experimental values, thus indicating idealityof behavior in the mixtures. This effect is different fromthat observed in PCL-PVAC mixtures, where no inter-action existed during pyrolytic degradation but positiveinteraction for PVAC occurred in solution.9 From theabove results, it can be concluded that there is nointeraction between PLA and PCL during enzymaticand pyrolytic degradation.

Conclusions

The thermal degradation of PCL and PLA has beeninvestigated under pyrolytic conditions. A model basedon continuous distribution kinetics was developed con-sidering the interaction between the polymers duringenzymatic degradation and was able to predict theexperimental data well. The physical blends of thesepolymers did not show any interaction under pyrolyticconditions. The enzymatic degradation of these blendsalso showed no interaction between them, while thecopolymer showed enhanced degradation.

Acknowledgment

G.S. thanks the General Electric Co. for a fellowshipduring this study, and the authors thank the Depart-ment of Science and Technology, India, for financialsupport.

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Received for review May 15, 2004Revised manuscript received September 1, 2004

Accepted September 11, 2004

IE049589R

Ind. Eng. Chem. Res., Vol. 43, No. 24, 2004 7709