Modeling of Lipase Catalyzed Ring-Opening Polymerization ofE-Caprolactone

G. Sivalingam and Giridhar Madras*

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

Received October 30, 2003; Revised Manuscript Received November 18, 2003

Enzymatic ring-opening polymerization ofε-caprolactone by various lipases was investigated in toluene atvarious temperatures. The determination of molecular weight and structural identification was carried outwith gel permeation chromatography and proton NMR, respectively. Among the various lipases employed,an immobilized lipase fromCandida antarticaB (Novozym 435) showed the highest catalytic activity. Thepolymerization ofε-caprolactone by Novozym 435 showed an optimal temperature of 65°C and an optimumtoluene content of 50/50 v/v of toluene andε-caprolactone. As lipases can degrade polyesters, a maximumin the molecular weight with time was obtained due to the competition of ring opening polymerization anddegradation by specific chain end scission. The optimum temperature, toluene content, and the variation ofmolecular weight with time are consistent with earlier observations. A comprehensive model based oncontinuous distribution kinetics was developed to model these phenomena. The model accounts forsimultaneous polymerization, degradation and enzyme deactivation and provides a technique to determinethe rate coefficients for these processes. The dependence of these rate coefficients with temperature andmonomer concentration is also discussed.

Introduction

Recent advances in nonaqueous enzymology have signifi-cantly expanded the range of conditions for carrying outvarieties of polymerization reactions such as self-condensa-tion, AA-BB polytransesterification, ring-opening of lactones,polymerization of carbonates, ring-opening copolymerization,and combined condensation and ring-opening polymeriza-tion.1 Various aspects of in vitro enzyme catalyzed ring-opening polymerization of lactones have been investigated.2-8

The major concern in these reactions in the nonaqueousmedia is the low catalytic activities of high activity enzymesdemanding large amount of lipases to achieve the desiredconversions and high molecular weights.8-10 Attempts havebeen made to enhance the understanding of ring-openingpolymerization by studying various parameters such asenzyme loading, water content, reaction media, and operatingtemperature.9,11,12

The polymerization and degradation rates are stronglydependent on the water content of the reaction media.9,13Thewater molecules surrounding the enzyme play an importantrole in maintaining the enzyme’s conformational flex-ibility. 13,14 The presence of water in both of the cases(polymerization and degradation) showed a maximum in thereaction rate. The increase in enzyme concentration increasesthe rate of monomer conversion, whereas the averagemolecular weight of the polymer decreases with the enzymeloading.9 To achieve high molecular weights, diffusionlimitations are overcome by using lower enzyme concentra-

tions. In all of the cases of polymerization and degradation,9-13

an optimum temperature for reaction was observed.Lipases are also known to be biocatalysts for the degrada-

tion of polyesters and polycarbonates.13-19 Unlike conven-tional thermal degradation, the polymers degrade by specificchain end scission13,17-19 when catalyzed by lipases. Similarto the ring-opening polymerization, the degradation rates arealso dependent on the solvent properties such as viscosity,polarity, water content, and presence of other polymers.13

The interactions between the polymers in the mixtures havealso been investigated and modeled using continuousdistribution kinetics.17 Enzymes deactivate in organicmedia.9,13,17-19 However, most of the studies reported for thering-opening polymerization have been limited to the studieson the mechanism of ring-opening polymerization andparameters affecting the polymerization. These studies didnot include the degradation of the polymer that occurs atthe reaction conditions.

A polymer is a mixture of molecules with varying sizes,and therefore, a molecular weight distribution (MWD) isneeded to describe the polymer. The MWDs are generallydescribed by the moments of the distribution of the moleculeswherein the zeroth and first moment represent the molar andmass concentration of the polymer, respectively. Continuousdistribution models provide a simple, yet an effective,technique to analyze the time evolution of MWDs of reactingpolymers.20 These models have been widely used forsimultaneous polymerization and degradation,21,22 includingdegradation by pyrolysis.23 In this study, the simultaneouspolymerization and degradation of PCL in toluene wasinvestigated. A new model is developed that accounts for

* To whom the correspondence should be addressed. E-mail: Giridhar@chemeng.iisc.ernet.in. Phone: 091-80-2932321. Fax: 091-80-3600683.

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10.1021/bm0344405 CCC: $27.50 © 2004 American Chemical SocietyPublished on Web 12/23/2003

simultaneous polymerization and degradation coupled withenzyme deactivation was developed.

Experimental Section

Materials and Methods. The monomerε-caprolactone,purchased from Sigma Aldrich, was dried over CaH2 andthen vacuum distilled in nitrogen atmosphere prior to use.Enzymes were desiccated in an airtight desiccator prior touse for the polymerization and depolymerization reactions.Novozym 435 and Lipolase (commercial grades) werereceived as gifts from Novo Nordisk, Denmark. Lipases fromCandida Rugosa (specific activity, 724 PLU/g) and HogPancreas (specific activity, 147 PLU/g) were procured fromSigma Aldrich. Among the enzymes employed, Lipolase andNovozym 435 are immobilized while Hog Pancreas andCandida Rugosa are free enzymes. All solvents were distilled,filtered, and dehydrated prior to use.

Enzymatic Polymerization. A 20 mL solution withappropriate amounts ofε-caprolactone and toluene withlipase was taken in a dry test tube and sealed. The reactionmixture was maintained at the desired temperature using anincubator shaker at various temperatures (25-75 °C) con-trolled by a PID temperature controller ((1 °C). The amountof enzymes taken in all of the cases is 0.02 g, correspondingto a concentration of 0.11 mg/mmol ofε-caprolactone, when20 mL of ε-caprolactone is used. When the effect of diluentis investigated, the concentration ofε-caprolactone is reducedup to 10% and thus the enzyme concentration varies from0.11 to 1.1 mg/mmol ofε-caprolactone, though the mass ofenzymes taken is constant. Aliquots of 100µL were takenat the regular intervals for the subsequent analysis. Severalexperiments were conducted in triplicate, and the standarddeviation of the determined rate coefficients are within 5%.

Enzymatic Degradation.Enzymatic degradation of PCLwas conducted to determine the enzyme deactivation throughindependent experiments. PCL (Mn: 80 000, polydispersity,1.3, Sigma Aldrich) was used at a concentration of 2-10g/L to determine the enzymatic degradation under theoperating conditions employed. The concentration of theenzyme used is 0.02 g in 10 mL of the solution. Becauselipases degrade the polymers by specific chain endscission,13,17-19 the degradation was monitored through thedynamics of the specific products formed. The specificproducts obtained during the degradation of the polymer areoligomers of the parent polymer.

NMR Analysis. Proton NMR analysis of the polymerformed was recorded on a Bruker AC-F 250 MHz spec-trometer in CDCl3, and chemical shifts were measured inppm with reference to tetramethylsilane. The proton NMRspectrum of PCL showed resonance signals at 1.3, 1.6, 2.3,and 4.0 ppm, and the signals were assigned to various protonsof the PCL and matches with the spectra reported else-where.10

GPC Analysis. The polymer solution was diluted withtetrahydrofuran (THF), centrifuged to remove the enzyme,and analyzed in an HPLC-GPC system (Waters Inc). TheHPLC system consisted of an isocratic pump, a sample loopwith Rheodyne valve (50µL), three GPC columns, and an

online differential refractive index detector. Styragel columns(300 × 7.5 mm) HR 4, HR 3, and HR 0.5 (Waters Inc.)with pore sizes of 104, 103, 500 Å, respectively, were usedin series. The columns were maintained at 50°C to ensureuniform temperature and good separation of the peaks. THFwas used as eluent at a constant flow rate of 1.0 mL/min.The chromatogram obtained was converted to MWD usinga calibration curve based on polystyrene standards (PolymerLab, U.K.).20 The MW of polystyrene was converted to MWof the individual polymers using the Mark-Houwinkparameters,KPS ) 1.25× 10-5 dL/g, RPS ) 0.717;KPCL )1.09× 10-5 dL/g, RPCL) 0.60.

Theoretical Model

In this section, models are developed for the simultaneousring-opening polymerization and degradation of PCL bylipases. The enzymes lose their catalytic activity in non-aqueous media,9,13,17-19 and the deactivation was determinedby following the rate of formation of specific products. Thedegradation of polyesters by lipases in solution indicates thatthe degradation occurs by specific chain scission withproducts of an average molecular weight of 500. In this study,the molecular weight of the polymer initially increases andthen decreases indicating simultaneous polymerization anddegradation. Typical profiles of chromatographs correspond-ing to the molecular weight distribution (MWD) at variousreaction times are shown in Figure 1. The retention time inthe x axis corresponds to MW, and this indicates that theMW goes through a maximum, wherein the MW increasesinitially but declines at longer times. This is consistent withan earlier study24 on the lipase catalyzed ring-openingpolymerization ofε-caprolactone

Because lipases cleave the bonds of polymers leading todegradation by specific chain end scission,13,17-19 the occur-rence of degradation during polymerization cannot beneglected. The observed phenomenon is due to simultaneouspolymerization and degradation reactions with specificproducts of an average molecular weight of 500 increasing

Figure 1. Typical chromatographs during the lipase catalyzedpolymerization of ε-caprolactone. The numbers on the figure denotereaction time in hours.

604 Biomacromolecules, Vol. 5, No. 2, 2004 Sivalingam and Madras

with time. Thus, the model was developed for simultaneouspolymerization and degradation. The ring-opening polym-erization can be written as

The specific chain end scission of PCL can be representedby the following reaction

Here, P(x) represents the polymer of molecular weightx,Q(xs) is the specific product of molecular weightxs, andp(x,t)andq(t) represent the time dependent concentration of thepolymer and the specific products, respectively. The specificproducts are the oligomeric component of the polymer taken.The models use the assumptions of adsorption of enzymeson the polymer substrate, formation of transition complex,and then specific chain end scission. The activity of theenzyme,a(t), decreases due to deactivation, and the decayis assumed to be first order. Details of the mode of scissionand the structural identification of products during degrada-tions are given elsewhere.13,16

The population balance for the polymerization and deg-radation (reactions A-C) can be written as

the rate of formation of specific products formed is givenby

The rate coefficient of polymerization,ka, is usually assumedto be independent of molecular weight.20-22 The degradationrate coefficients for specific chain end scission,ks, are alsoreported to be independent of molecular weight.13,17,20,22Thus,eq 1 can be written in terms of a dimensionless time,θ,defined asksa(t)t

whereγ is the ratio of polymerization rate coefficient to thedegradation rate coefficient and will vary with the reactiontime as the polymerization is predominant at the start of thereaction and degradation rate dominates at the later stages.The specific product formation is due to the degradation(molar concentration is conserved) and the decrease in molarconcentration is due to polymerization (mass concentrationis conserved).13,17,22 Thus, the relative contribution of po-

lymerization with respect to degradation is proportional tothe ratio of polymer mass in the system to the specificproduct and can be written in terms of the activity of theenzyme. The ratio of the aggregation rate coefficient to thedegradation rate coefficient,γ, is represented asγ0 a/(1 -a). The parameterγ0 is the ratio of ka and ks and isindependent of molecular weight. The variation ofγ withtime is through the activity of the enzyme,a(t). a(t) isrepresented asa in the following discussion. Applyingmoment operation, defined as

the above equation yields

Modeling the Pure Degradation.By pure degradationstudies, we mean studies wherein the degradation of PCL isinvestigated and no polymerization occurs. Models for thedegradation of polymers can be obtained by settingka ) 0.Equation 4 reduces to the following form

Equation 5 can be written in terms of dimensional time forthe pure degradation as

The decline of activity13,17-19 is assumed to be exponential,a ) exp(-kdt), and the molar and mass concentration of thepolymer and specific products are given by

and

and

These equations indicate that the mass concentration of thepolymer decreases due to the generation of specific productswhile the molar concentration of the polymer is constant.

P(x′) + P(x - x′)98ka(x′,x - x′)

P(x) (A)

P(x′) + P(x)98ka(x′,x)

P(x + x′) (B)

P(x) 98ks

P(x - xs) + Q(xs) (C)

∂p(x,t)∂t

) ∫0

xka(x′,x - x′)a(t)p(x′,t)p(x - x′,t) dx′ -

2p(x,t)∫0

∞ka(x,x′)a(t)p(x′,t) dx′ +

ksa(t)∫x

∞p(x′,t)δ(x,x′ - xs) dx′ - ksa(t)p(x,t) (1)

dq(t)dt

) ∫xs

∞ksa(t)p(x′,t)δ(xs,x′) dx′ (2)

∂p(x,θ)∂θ

) γ∫0

xp(x′,θ)p(x - x′,θ) dx′ -

2γp(x,θ)∫0

∞p(x′,θ) dx′ +

∫x

∞p(x′,θ)δ(x,x′ - xs) dx′ - p(x,θ) (3)

p(j)(θ) ) ∫0

∞xjp(x,θ) dx

dp(j)(θ)

dθ) γ0

a

1 - a∑i)0

jjCip

(j-i)(θ)p(i)(θ) -

2γ0

a

1 - ap(n)(θ)p(0)(θ) + ∑

i)0

jjCi(- xs)

ip(j-i)(θ) - p(n)(θ) (4)

dp(j)(t)

dθ) ∑

i)0

jjCi(-xs)

ip(j-i)(θ) - p(n)(θ) (5)

dp(j)(t)

dt) ksa∑

i)0

jjCi(-xs)

ip(j-i)(t) - ksap(n)(t) (6)

dq(j)(t)dt

) ksaxsp(n)(t) (7)

dp(0)

dt) 0

dp(1)

dt) -ksaxsp

(0)

dq(0)

dt) ksap(0) (8)

dq(1)(t)dt

) ksaxsp(0) (9)

Ring-Opening Polymerization of ε-Caprolactone Biomacromolecules, Vol. 5, No. 2, 2004 605

Equations 8 and 9 indicate that the degradation (rate offormation of specific products) can be determined from therate of formation of specific products. Equation 9 is solvedwith the initial condition ofq(1)(t ) 0) ) 0 to yield

It can be rearranged as

A semilogarithmic plot of 1- qr(t) with time will be linearwith slope as deactivation coefficient.

Modeling the Simultaneous Polymerization and Deg-radation. After the determination of enzyme deactivationcoefficient, the dynamics of molecular weight for simulta-neous polymerization and degradation was solved. The molarand mass concentration of the polymer, obtained by settingj ) 0 and 1 in eq 4, respectively, is

The molecular weight is the ratio of the first moment to thezeroth moment, i.e., the mass concentration to the molarconcentration. Equations 12 and 13 show the variation ofthe zeroth and first moment with time, respectively. The unitsof the polymerization and depolymerization rate coefficientsare time-1 indicating the first order processes. By fitting theresults to the experimental data, the population balanceequations provide an unique way to correlate the polymer-ization and degradation rate directly to the measurablequantity, the number-average molecular weight. The timeevolution of the molecular weight can thus be obtained bysolving eqs 12 and 13 simultaneously. Although an analyticalsolution of eqs 12 and 13 in terms of hypergeometricfunctions is possible, it is too complicated for use. Theequations were, therefore, solved numerically by the Runge-Kutta technique with an adaptive step size control. Theaccuracy of the numerical solution was verified for certaincases with the analytical solution.

Results and Discussion

Because the reaction rate of nonaqueous reactions is slow,experiments are usually conducted in organic media. How-ever, the rate of polymerization9,11 and degradation13 isstrongly dependent on the nature of the organic solvents.These studies have shown that the polymerization ratesdepend on the partition coefficient of organic solvents andwater. The solvents with logP values less than 0.5 showedlower rates of polymerization and low molecular weights.Solvents with logP values higher than 2 showed higher rateof polymerization and high molecular weight.9,11 This wasattributed to the deactivation of the enzyme due to hydro-

philicity of solvents.9,13 However, solvent geometry, dipolemoment, solubilization of substrates, and other factors thatinfluence the physicochemical properties of the solvent inaddition to the logP values15 can influence the rate ofdegradation. The study11 with various solvents for thedegradation of polymer showed that the degradation ratesare the highest when the reaction medium is toluene, whichcan keep the polymer in solution and the enzyme as insolublematerial. Hence in the present study, toluene is taken as thereaction medium.

Lipase Effects. The effect of various lipases such asNovozym 435, Candida Rugosa, Hog Pancreas, and Lipolasehas been investigated with 10/90 v/v ofε-caprolactone/toluene at 65°C. The variation of the number averagemolecular weight with time indicates that the molecularweight initially increases and then decreases. The largedifference in the polymerization rates can be attributed tothe widely varying activities of lipases (see Figure 2). TheNovozym 435 showed better catalytic activity compared tothe other lipases used in the present study. Hence, Novozym435 has been adopted as the model enzyme to study thekinetics of simultaneous polymerization and degradation. Thedeactivation coefficients of the lipases,kd, were obtainedbased on the degradation of PCL in toluene. The solid linesin the figure are the model predictions based on numericalsolution of eqs 12 and 13 through regression of theexperimental data.

Temperature Effects. Figure 3 shows the variation ofmolecular weight with reaction time at various temperatures(25-75 °C) with 50/50 v/v ε-caprolactone/toluene. Thepolymerization rates increase with an increase of temperaturefrom 25-65 °C and decreases with further increase intemperature. It can be attributed to the denaturation anddeactivation of the enzymes due to temperature.11,16 Thedeactivation of enzyme is determined from the pure degrada-tion studies, and the plot is given in Figure 4. As the peaksof monomer and the specific products overlap in the GPCchromatograph, the deactivation coefficient cannot be easilydetermined from the simultaneous polymerization and deg-

q(1)(t) )ksxsp0

(1)

kdMn0(1 - exp(-kdt)) (10)

qr(t) )q(1)(t)

q(1)(tf∞)) 1 - exp(-kdt) (11)

dp(0)

dθ) -γ0

a1 - a

[p(0)]2 (12)

dp(1)

dθ) -xsp

(0) (13)

Figure 2. Effect of various lipases on the polymerization anddegradation of ε-caprolactone in toluene (10/90 vol/vol) at 65 °C.Legend: 9, Candida Rugosa; b, Hog Pancreas; 2, Novozym 435;1, Lipolase; s, model fits.

606 Biomacromolecules, Vol. 5, No. 2, 2004 Sivalingam and Madras

radation experiments. Therefore, the deactivation coefficientswere determined from the degradation of PCL. Figure 4 isthe plot of the mass fraction of specific products formed asa function of time. At longer times (∼30 days), the massfraction of specific products reaches saturation (a constantvalue) due to the complete loss of catalytic activity oflipases.13,17-19 The reaction system does not attain a steadystate or equilibrium but the enzyme deactivates.9,13,17,18,19Thiscan be attributed entirely to the deactivation of the enzyme17

because the addition of new enzymes leads to furtherdegradation. This is further confirmed by adding the enzymefrom the saturated solution after filtration and desiccationto a fresh batch of polymer solution and this polymer solutiondid not show any degradation. The saturation values, (qs )q(1)(t f ∞)), are 0.032, 0.048, 0.056, 0.069, and 0.047 h-1

at 25, 45, 55, 65, and 75°C, respectively. The saturationvalue has been used in determination of the deactivationconstant. The deactivation constant is obtained from the slope

of -ln(1 - q(1)/qs) against time and is shown in the inset ofFigure 4. The solid lines in the Figure 3 are the modelpredictions and are satisfactory for the entire range ofpolymerization and degradation.

Dilution Effects. The effect of diffusion limitations onthe catalytic activity of lipases has been studied by varyingthe concentration of the monomer in the solution. Figure 5shows the effect of monomer concentration in toluenesolution on the molecular weight evolution at 65°C.Althoughe experiments with 100% PCL showed higher MW,the degradation rates were also higher resulting in aconsequent rapid decrease of MW. However, in the case ofexperiments with 50/50, a high MW is attained for a longertime compared to other dilutions. At lower concentrations,the polymerization rate is lower because of lower monomerconcentration. At higher concentrations, the polymerizationrates are lower due to diffusion limitations for the sameamount of enzyme loading.

The effect of different dilutions of monomer with tolueneon the degradation rate and the observation of enzymedeactivation at high monomer concentrations are similar toobservations by Panova et al.,25 who investigated the lipasecatalyzed polymerization of caprolactone in toluene withmethoxy-poly(ethylene glycol) and water as initiators. Lowermonomer conversion in concentrated monomer solutions wasattributed to decreased partitioning of PCL between thesolvent and the enzyme. This effect resulted in inhibition ofthe lipase by the reaction product and slow diffusion ofmonomer to the enzyme active site.

The variation of polymerization coefficients and degrada-tion coefficients for temperature effects, lipase effects, anddilution effects are shown in Figure 6a-c, respectively.Figure 6a shows the variation of polymerization and deg-radation rate coefficients with temperatures. The rate in-creases from 25 to 65°C but decreases at higher temperature.This study shows that the degradation rates are nearly samefor all of the lipases and the polymerization rates are differentfor each lipase as can be seen from Figure 6b. Interestingly,

Figure 3. Effect of temperature on the solution polymerization anddegradation of ε-caprolactone in equal volume of toluene andε-caprolactone at 65 °C. Legend: 9, 25 °C; b, 45 °C; 2, 55 °C; 1,65 °C; (, 75 °C; s, model fits.

Figure 4. Variation of specific products formed with time for thedetermination of the enzyme deactivation constant from the puredegradation experiments at various temperatures. See Figure 3 forlegends.

Figure 5. Effect of dilution on the polymerization and degradation ofε-caprolactone in toluene at 65 °C. Legend: 9, 10/90; b, 20/80; 2,40/60; 1, 50/50; O, 70/30; 0, 100/0 ε-caprolactone/toluene; s, modelfits.

Ring-Opening Polymerization of ε-Caprolactone Biomacromolecules, Vol. 5, No. 2, 2004 607

Figure 6c shows the rate coefficients variation under diffusionlimitations. The degradation rate increases with increase inthe caprolactone concentration. As the concentration in-creases, more polymer comes in contact with the lipase andthe degradation rate increases. Figure 7 shows the deactiva-tion coefficients of enzymes at various temperatures andmonomer concentration. The deactivation coefficients forvarious lipases are nearly equal (0.029 h-1). The enzymedeactivates with increase in temperature and increase inmonomer concentration. This can be due to structuralconformation under high monomer concentrations anddenaturation of the proteins at higher temperatures.11,13

Simple regression analysis indicates that the differencebetween the simulated values and the experimental data ofthe number-average molecular weight is roughly 3%. Thisis in addition to the variability of 2-3% in the experimentaldetermination of the number-average molecular weight. Thus,a simple continuous distribution model developed in thisstudy is able to model the experimental data for the ring-opening polymerization successfully. The population balancemodel developed in this paper is general and can be applied

to any system undergoing polymerization with simultaneousdegradation by specific chain scission, as reported in thisstudy and other studies.10,11,24,25,26By choosing the appropriatestoichiometric kernel and rate coefficients, the present modelcan be extended to systems undergoing polymerization only22

or degradation only.13,17 The model provides a simpletechnique to determine the rate coefficients for both polym-erization and degradation taking into account the deactivationof the enzyme.

Conclusions

Lipase catalyzed ring-opening polymerization ofε-capro-lactone was studied with various lipases at various temper-atures and various dilutions of monomer in toluene. All ofthe studies indicated that degradation and polymerizationoccur simultaneously. A model based on continuous distribu-tion kinetics was developed considering the enzyme de-activation and competition polymerization and degradationreactions. The model could satisfactory explain the data overthe entire range of operation in the present study. The enzymedeactivates with increase in enzyme concentration andmonomer concentration. The polymerization and degradationrate coefficients showed a maximum with temperature andcan be attributed to the deactivation of enzymes at highertemperatures. The increase of monomer concentration in-creased the degradation coefficient while the polymerizationrate coefficients remain unaffected.

Acknowledgment. The authors thank the Department ofScience and Technology, India for Financial Support. Thefirst author thanks the General Electric Company, U.S.A.,for a Fellowship.

References and Notes

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Figure 7. Variation of enzyme deactivation constant with temperatureand dilution of ε-caprolactone with toluene.

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