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Equilibrium free-radical polymerization of methyl methacrylate under nanoconfinement
Polymer 66 (2015) 173e178
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Polymer journal homepage: www.elsevier.com/locate/polymer
Equilibrium free-radical polymerization of methyl methacrylate under nanoconfinement H.Y. Zhao, Sindee L. Simon* Department of Chemical Engineering, Texas Tech University, Box 43121, Lubbock, TX 79409-3121, USA
a r t i c l e i n f o
a b s t r a c t
Article history: Received 10 February 2015 Received in revised form 4 April 2015 Accepted 6 April 2015 Available online 12 April 2015
The effect of nanoconfinement on the equilibrium free radical polymerization of methyl methacrylate (MMA) is investigated using differential scanning calorimetry. The ceiling temperature is shifted to lower temperatures in 13 nm diameter pores, with pore surface chemistry showing no significant effect. The results indicate that the change in the entropy of propagation decreases in nanopores due to confinement effects (i.e. DSp,conf is a more negative value than DSp,bulk). The change in the entropy of propagation is independent of temperature for the bulk equilibrium polymerization, whereas the change in the entropy of propagation in nanopores becomes less negative and more bulk-like with increasing polymerization temperature presumably due to the lower molecular weight chains produced at high temperature. The data suggest that our system is one of weak confinement with chain entropy scaling with molecular weight to the 1.1 power (i.e. ~ N1.1). © 2015 Elsevier Ltd. All rights reserved.
Keywords: Nanoconfinement MMA equilibrium polymerization Entropy effect
1. Introduction The properties of polymers synthesized under nanoconfinement can be enhanced relative to bulk polymerization, with observations of increased molecular weight [1e8], increased tacticity [7,9], and increased glass transition temperature [6,10e12]. In previous work, we investigated the reaction kinetics and properties of free radical polymerization of methyl methacrylate (MMA) in the nanopores of controlled pore glass (CPG) [13,14] and found that the onset of autoacceleration shifted to shorter times presumably due to the reduced diffusivity of the nanoconfined chains. In addition, in hydrophilic pores, the initial propagation rate was higher than that in either hydrophobic pores or the bulk system due to the catalysis by silanol groups on the CPG surface [13]. The enhanced reactivity was accompanied by increased molecular weight and increased isotacticity [14]. However, previous experiments were carried out at relatively low temperatures (<95 C); here we examine higher reaction temperatures where monomer/polymer equilibrium plays an important role. Neat polymerization of MMA can be divided into two regimes depending on the temperature. When the reaction temperature is below the glass transition temperature of pure PMMA
* Corresponding author. E-mail address: [email protected] (S.L. Simon). http://dx.doi.org/10.1016/j.polymer.2015.04.017 0032-3861/© 2015 Elsevier Ltd. All rights reserved.
(Tg,p z 111 C), conversion will be limited by vitrification which occurs when the Tg of the system (polymer plus MMA as plasticizer) rises to the reaction temperature. On the other hand, as the reaction temperature increases beyond Tg,p, complete polymerization becomes hard to achieve since depolymerization gradually becomes important [15]. In other words, the competition between propagation and depropagation of MMA leads to a temperaturedependent equilibrium conversion. Our interest here is the influence of nanoconfinement on the equilibrium conversion. Such studies have been performed for sulfur polymerization [16,17]. In that work, conversion at a given temperature decreases as the size of the silica nanopores decreases from bulk to 2.5 nm and the floor temperature (the lowest temperature where polymerization can occur since sulfur has a positive change in enthalpy and entropy upon polymerization) is shifted to higher temperatures indicating that the change in the entropy of propagation in confined nanopores (DSp,conf) decreases compared with the change in the entropy of propagation in bulk (DSp,bulk). Our modeling work [18] well describes the nanoconfinement effect on sulfur polymerization assuming that the change in the entropy of confined polymer chains scales with chain length N and pore diameter D: DSpolymer, conf e NpDm, where p ¼ 2 represents strong confinement [19,20] and m ¼ 3.0 from self-consistent field theory [21] or 3.8 or 3.9 from blob scaling in semidilute solutions [22], both for spherical confinement. Similar to sulfur polymerization, polymerization of MMA is
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expected be affected by nanoconfinement. However, in the case of MMA, the ceiling temperature is expected to decrease because the signs of DSp and DHp for MMA polymerization are negative rather than positive as in the case of sulfur. One motivation of this work is to obtain information concerning the entropy change upon confining a chain to nanoscale dimensions, which is anticipated to depend on chain length [19e22], with greater confinement entropy associated with longer chains. This is hypothesized to lead to a decrease in the change in the entropy of reaction and a concomitant decrease in the equilibrium conversion. Fig. 1 schematically shows our expectations, where the solid and dashed lines represent the entropy for samples in bulk and in nanoconfined pores, respectively. Given that the entropy of polymer chains is reduced due to restricted chain configurations under confinement (Spolymer, bulk > Spolymer, confined), whereas the entropy of small molecules is not significantly influenced under confinement (Smonomer, bulk z Smonomer, confined), it is anticipated that the change in the entropy of nanoconfined MMA polymerization on confinement (DSconfined rxn) will be a more negative value than the change in the entropy for the bulk reaction (DSbulk rxn). To test these ideas, in this work, we polymerize MMA in nanopores and evaluate the effect of nanoconfinement on the polymer/ monomer equilibrium using differential scanning calorimetry (DSC). The experimental data are modeled to investigate the changes in thermodynamic properties in a nanoconfined environment. 2. Thermodynamics of MMA polymerization The thermodynamics of free radical polymerization can be described by the equation:
DGp ¼ DHp T$DSp
(1)
where DGp, DHp, DSp are the changes in the Gibbs free energy, enthalpy, and entropy of the propagation reaction, respectively. For MMA polymerization, DHp is negative since heat is released upon breaking the monomer p-bond and forming the polymer sbond, and DSp is also negative due to the reduced degrees of freedom of the polymer compared to the monomer. Since the
reaction spontaneously occurs when DGp is negative, polymerization is favorable at low temperatures; however, DGp becomes less negative as temperature increases and a polymer/monomer equilibrium exists at high temperatures. Above the ceiling temperature (Tc), DGp will be positive such that monomer will not convert to polymer. The equilibrium between polymer and monomer is described by the following equation: K
$ $ e Mm þ M ⇔ eMmþ1
where Mm$ is the free radical species of length m, M is the monomer, and K is the equilibrium constant defined as the ratio of the activities (ai) of the products to the reactants:
K¼
aMmþ1 1 1 ¼ ¼ aMm $aM 4M 1 xeq
(3)
where ai is the activity of species i. The activities of the free radical species of length m and m þ 1 are proportional to their concentrations and considered to be equivalent, whereas the activity of the monomer can be approximated by the monomer volume fraction 4M, which is in turn equal to 1xeq assuming no volume change on polymerization, where xeq is the equilibrium conversion of monomer. The equilibrium constant K also depends on temperature:
K ¼ exp DGp RT
(4)
Substituting equations (1) and (3) into equation (4) and rearranging, the conventional relationship between conversion and the change in enthalpy or entropy is obtained:
DHp DSp ln 1 xeq ¼ RT R
(5)
At the ceiling temperature, DGp is zero so that Tc is simply defined as the ratio of DHp to DSp:
Tc ¼
Fig. 1. Schematic plot showing entropy changes under nanoconfinement. Solid lines represent the entropy in bulk and the dashed lines represent the entropy in a nanoconfined system.
(2)
DHp DSp
(6)
The thermodynamics of polymer chains in confined environments has been discussed by De Gennes [19] who suggested that the decrease in entropy due to confinement of an ideal chain (DSpolymer, conf) in a tube or in a cylindrical pore is linearly proportional to the square of the ratio of the unperturbed size of the chains (Ro) to the tube or pore diameter (D): DSpolymer, conf e (Ro/ D)2eN/D2, where N is the number of monomer units in the chain. On the other hand, Kong and Muthukumar reported that the free energy of a confined non-ideal chain in a nanopore is proportional to wN2/D3, where w represents the excluded volume interaction [21]. Moreover, the scaling of the change in entropy on confinement has been hypothesized to depend on the strength of the confinement being proportional to N for the weak confinement regime and N2 for the strong confinement regime [20,22]. Based on the propagation reaction (see equation (2)), the change in the entropy of propagation between the confined and bulk reactions will depend on the strength of the confinement regime. For weak confinement, no effect is anticipated: DSp,conf e DSp,bulk e[(Nþ1)N1] e 0. On the other hand, for the strong confinement environment, the difference in the entropy of propagation between confined and bulk reactions should be influenced by the chain length: DSp,conf e DSp,bulk e [(Nþ1)2N21]eN1.
H.Y. Zhao, S.L. Simon / Polymer 66 (2015) 173e178
3. Experimental methodology 3.1. Materials and instrumentation Methyl methacrylate (MMA) monomer and 2,20 -azo-bis-isobutyronitrile (AIBN) initiator were obtained from Aldrich. The concentration of initiator is 0.5 wt %. Controlled pore glasses (CPG, Millipore) with pore diameters (D) of 13 nm ± 7.4% (based on manufacturer's specifications) were used as the confinement system. In this work, the pores with surface silanol groups (eSiOH) are termed hydrophilic pores, whereas the pores with silanol replaced by trimethylsilyl groups (eSi(CH3)3) are termed hydrophobic pores. The purification of reactants and the surface treatment of nanopores follow the same procedures outlined in previous work [13,14]. A Mettler-Toledo differential scanning calorimeter DSC1 was used with an ethylene glycol cooling system and nitrogen purge gas. Samples were prepared in 20 m L hermetic pans under a nitrogen blanket. As in previous work [13,14], the pore fullness ranged from 70 % to 90 % based on the ratio of the monomer volume added to the CPG pore volume (based on manufacturer's specifications). Indium was used to calibrate the enthalpy and the DSC temperature at 10 K/min. For the isothermal condition used to react the samples, an isothermal calibration [23] was performed using indium at 0.1 K/min. 3.2. Polymerization procedure The polymerization of MMA in bulk and in nanoporous confinement was carried out isothermally at temperatures ranging from 60 to 180 C using the DSC as an oven. After a given isothermal reaction, dynamic scans at 10 K/min from room temperature to 200 C were used to measure any residual heat of reaction. One to three replicate samples were used for each reaction condition. For reaction temperatures above 100 C, we were faced with a challenge because the temperature is higher than the boiling point of pure monomer (Tb,MMA ¼ 101 C). We initially tried to use pans with o-rings capable of withstanding 24 bars but were unsuccessful. Hence, in order to decrease the vapor pressure of the reactant mixture, we partially converted the samples at a low temperature (80 C) to a monomer conversion (x z 10e15%) prior to the polymerization at higher temperature. Thus, two DSC programs were used depending on the reaction temperatures, which are described by one step and two step methods, respectively.
175
For the one step method shown in Fig. 2a, a temperature ramp at 100 K/min was applied from room temperature to the specified temperature for polymerization, which ranged from 60 to 140 C for bulk samples and from 60 to 130 C for nanoconfined samples. For the two step method shown in Fig. 2b, the monomer was first reacted at 80 C for a prespecified time prior to the onset of autoacceleration to form a monomer/polymer mixture and then heated at 100 K/min to the specified temperature from 110 to 180 C where the equilibrium polymerization is completed. The conversion of isothermally polymerized MMA is related to the integrated heat flow (Q_ ) by the equation:
x¼
1 DHp
Zt
Q_ dt
(7)
0
where the average total heat of reaction DHp is 560 J/g obtained from literature reports [24] and in agreement with our previous work [13] where we obtained a value of 563 ± 12 J/g, independent of reaction temperature, confinement size, and surface treatment. The integration is performed over the entire isothermal history. Thus, for the one step method, conversion is calculated from the sum of the heat of reaction for the temperature ramp to the isothermal temperature and the heat during the isothermal reaction (DHramp þ DHiso). The conversion associated with the two step method is calculated from the heat of reaction for each of the two isothermal steps (DH1 þ DH2) using equation (7) plus the conversion associated with heat of reaction during the temperature ramp between the two steps (DHramp). Although DHramp is obtained based on the experimental observation for both one and two step methods, we can also integrate the following equation to examine the conversion x associated with DHramp:
dx keff Mo ð1 xÞ ¼ dT b
(8)
where keff is the temperature-dependent effective rate constant from previous work [13], Mo is the bulk MMA initial concentration, and b is heating rate. Based on both the measurements and equation (8), DHramp is negligible (<1% of DHP) for ramps to temperatures below 100 C, and DHramp is less than 20% of DHP for temperatures ranging from 100 C to 140 C. This is important
Fig. 2. a) On left, schematic of one step method to investigate the equilibrium reaction at temperatures from 60 to 140 C for bulk polymerization and from 60 to 130 C for nanoconfined polymerization. b) On right, schematic of two step method to investigate the equilibrium reaction at higher temperatures.
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because it means that the onset of autoacceleration occurs after reaching the specified polymerization temperature. The uncertainties in the data (see later) are based on the weight loss during polymerization at high temperature. Weight loss increases as the reaction temperature increases, and the weight loss for nanoconfined samples is greater than for bulk samples. For the one step method, the weight loss for both bulk and nanoconfined sample is less than 10% and errors in the equilibrium heat of reaction range from 1 J/g to 7 J/g, with the largest error at the highest temperature of 140 C; the associated error in conversion is less than 1.3%. On the other hand, for the two step method, the largest weight loss for bulk samples is around 20% at 180 C, whereas the weight loss of nanoconfined samples is around 50% at 180 C. Based on experimental observation, these weight losses occur in the temperature ramp between the two steps, i.e., during the ramp from 80 C to the temperature of interest; the heat released during the ramp (DHramp) is, thus, determined based on the average weight before and after polymerization. The error bars of equilibrium heat of reaction range from 0.5 J/g to 68 J/g, again, with the largest error at the highest temperature (T ¼ 180 C) for the samples in hydrophilic pores; the resulting error in conversion ranges from less than 1 % to 12 %. 4. Results The dependence of conversion on reaction temperature is shown in Fig. 3 for bulk samples. Data obtained from the one step method are represented by open symbols and those obtained from the two step method are represented by solid symbols. The conversions at relatively low temperatures (<100 C) are less than 100% due to the effect of vitrification. As the reaction temperature approaches the glass transition of neat polymer (Tg,p), the conversion reaches the maximum limit of 1.0 and then it decreases as the reaction temperature increases since depolymerization gradually becomes dominant at higher temperatures. In Fig. 3, the dashed line is the best fit of equation (5) based on a plot of ln (1xeq) vs. T1 to obtain DSp assuming the bulk value of DHp (560 J/g). The prediction by equation (5) deviates from experimental data below Tg,p since the vitrification effect is not accounted for. The value obtained for the entropy of propagation for the bulk reaction, DSp,bulk ¼ 114.6 ± 0.9 J mol1 K1, is consistent with the value in the literature (DSp,bulk ¼ 117 J mol1 K1) [25]. In addition, Tc for
Fig. 3. The heat of reaction and equilibrium conversion (xeq) as a function of isothermal temperature for bulk using one step (open symbols) and two step (solid symbols) methods. The dashed line is based on equation (5) using constant values of DHp (56 kJ/mol) and DSp,bulk (114.6 J mol1 K1).
the bulk polymerization is 216 ± 2 C, which is also consistent with the value reported in the literature of 220 C [24]. Based on the data and modeling predictions for the bulk reaction, both the one and two step methods give good results. The temperature-dependent conversion is compared for bulk and nanoconfined samples in Fig. 4, where the open symbols refer to the one step method and the solid symbols refer to the two step method. Similar to the bulk case, the reaction at relatively low temperatures (<100 C) is incomplete (x < 1.0) due to the influence of vitrification. In the vicinity of the glass transition of pure polymer (Tg,p), the conversion gradually reaches a maximum value of 1.0, and then it decreases with increasing polymerization temperature due to the effect of depolymerization at high temperature. As hypothesized in the introduction, for polymerization temperatures in this regime, the equilibrium conversion of nanoconfined samples is less than that of the bulk samples at a given reaction temperature. Although the equilibrium polymerization is performed in both hydrophobic and hydrophilic nanopores with different pore surface chemistries, we do not observe any difference in equilibrium conversion between samples in hydrophilic and hydrophobic pores within the error of the measurements. Considering that the bulk data were quantitatively described by equation (5) with constant DSp, we first applied this to the nanoconfined case assuming the same DHp as in the bulk case (a reasonable assumption based on our prior work [13]). The model (shown as a dashed line) only qualitatively describes the trend with DSp,conf ¼ 123.7 ± 0.8 J mol1 K1. To further examine the temperature dependence of DSp,conf, we note that the difference between the changes in entropy of propagation between bulk and confined polymerizations is simply related to the difference in the equilibrium conversions for the two cases since the heat of reaction (DHp) is independent of pore size or pore wall chemistry [13]:
DSp;bulk DSp;conf
1 xeq conf ¼ Rln 1 xeq bulk
(9)
Fig. 5 shows the dependence of DSp,bulk e DSp,conf on temperature for both one step and two step methods at and above 110 C. An Arrhenius-type temperature dependence is assumed to describe the decrease in DSp,conf with increasing temperature, as indicated
Fig. 4. The heat of reaction and equilibrium conversion (xeq) as a function of isothermal temperature for both bulk and nanoconfined samples using one step (open symbols) and two step (solid symbols) methods. The dashed lines are based on equation (5) using constant values of DHp and DSp, and the solid line assumes that DSp is a function of temperature; see Table 1 for values.
H.Y. Zhao, S.L. Simon / Polymer 66 (2015) 173e178
177
based on the kinetic chain length [24] and previous modeling [27,28] become similar for both pore surfaces when the reaction temperatures increase. To test the literature scaling of the changes in entropy of confined chain (DSpolymer, conf) on the number of bonds in the chain (N), recall that DSp,bulk e DSp,conf is proportional to Np1:
DSp;bulk DSp;conf N p1
(10)
Taking the natural logarithm of both sides and then taking the derivative with respect to reciprocal temperature, we relate the apparent activation energy for the kinetic chain length (En) to that for the change in the entropy of propagation EDSp:
EDSp ¼ ðp 1ÞEn
Fig. 5. The difference between the change in entropy for the propagation reaction of bulk samples and nanoconfined samples as a function of polymerization temperature. The definitions of symbols are the same as in Fig. 4. The dashed line represents an exponential fit.
by the dashed line. The fact that DSp,conf becomes less negative and more bulk-like at high temperatures presumably arises from the reduction of chain lengths as temperature increases resulting in weaker confinement effects. The temperature dependence for DSp,conf obtained in Fig. 5 can be used in equation (5), resulting in the solid line in Fig. 4, which well describes the decrease in the equilibrium conversion and the ceiling temperature in nanopores. The fitting parameters are shown in Table 1 for both constant DSp and DSp(T), and the decrease in ceiling temperature is quantified being 180 ± 2 C for the constant DSp case and 190 ± 7 C for the case of DSp(T). Both are considerably lower than the ceiling temperature for the bulk polymerization of 216 ± 2 C. 5. Discussion The experimental data show no significant differences in the equilibrium conversion as a function of temperature between samples synthesized in hydrophobic and hydrophilic pores. This was initially unexpected since it has been reported that the PMMA carbonyl group can interact with the silanol group on the hydrophilic pore surface [26] which might be expected to influence the entropy of chain confinement (DSp,conf). In addition, changes in the molecular weight between hydrophobic and hydrophilic pore surface are observed for polymerization at low temperatures [14]. Our explanation for the similar results is that the strength of the specific interaction between the monomer/polymer and the hydrophilic pore wall is reduced at high reaction temperatures relative to kBT (where kB is the Boltzmann constant). Furthermore, although we observed differences in molecular weight for the two pore chemistries at low temperatures [14], molecular weights calculated
(11)
The exponential fit in Fig. 5 yields a value of EDSp ¼ 6.3 ± 5.4 kJ/ mol. On the other hand, in the absence of autoacceleration and depolymerization, En ¼ Ep e Ed/2 e Et/2 ¼ 43 kJ/mol, where Ep, Ed, and Et are the activation energies for the chain propagation, initiator dissociation, and termination, respectively, and their values are based on previous modeling [27,28] (Ep ¼ 22.4 kJ/mol, Ed ¼ 128.2 kJ/ mol Et ¼ 2.9 kJ/mol) and are consistent with literature values [24]. In this case, the value of (p1) equals 0.15 ± 0.12 for xeq z 1.0 at low temperatures. At high temperatures, En becomes a larger more negative value due to the decrease in molecular weight associated with depolymerization. Thus, the p value is anticipated to be less than 1.15 and to decrease towards 1.0 at the ceiling temperature. We plan to verify the results in future work by measuring the molecular weight of polymers synthesized by free radical polymerizations, both MMA polymerization and others, at high temperatures under nanopore confinement. 6. Conclusion The equilibrium polymerization of methyl methacrylate (MMA) synthesized in bulk and nanoscale controlled glass pores (CPG) is investigated by DSC. One and two step methods are developed to cover the reaction temperatures ranging from 60 to 180 C. The equilibrium conversion decreases as the reaction temperature increases due to the effect of depolymerization. Nanoconfined samples have smaller equilibrium conversions relative to bulk samples above 110 C, although, there is no significant difference for the equilibrium conversion of samples synthesized in hydrophobic and hydrophilic pores. The equilibrium conversion of bulk samples as a function of temperature can be quantitatively described using a constant change in entropy of propagation, but this is insufficient to describe the equilibrium conversion of nanoconfined samples; rather, the nanoconfined entropy of propagation becomes more bulk-like as the reaction temperature increases presumably due to the lower molecular weight chains produced at higher temperatures. Based on the difference in the apparent activation energy for the kinetic chain length and that for the change in entropy of propagation, the entropy of confining a chain appears to scale with molecular weight to the 1.1 power suggesting that we are in the weak confinement region (i.e., DSpolymer,conf ~ N1.1). Acknowledgment
Table 1 Values for DSp and Tc assuming DHp ¼ 56 kJ/mol.
DSp (J mol1 K1) Tc ( C)
Bulk
Nanoconfined DSp ¼ constant
Nanoconfined DSp ¼ f (T)
114.6 ± 0.9
123.7 ± 0.8
216 ± 2
180 ± 2
e 114.6e1.36$exp(760 T1) [T in K] 190 ± 7
Funding from ACS PRF 52426-ND7 and NSF CMMI-1235346 are gratefully acknowledged. References [1] Li XC, King TA, Pallikari-Viras F. J Non-Crystalline Solids 1994;170(3):243e9.
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[2] Ng SM, Ogino S, Aida T, Koyano KA, Tatsumi T. Macromol Rapid Commun 1997;18(12):991e6. [3] Kageyama K, Ng SM, Ichikawa H, Aida T. Macromol Symp 2000;157:137e42. [4] Ni XF, Shen ZQ, Yasuda H. Chin Chem Lett 2001;12(9):821e2. [5] Kalogeras IM, Vassilikou-Dova A. J Phys Chem B 2001;105(32):7651e62. [6] Kalogeras IM, Neagu ER. Eur Phys J E 2004;14(2):193e204. [7] Uemura T, Ono Y, Kitagawa K, Kitagawa S. Macromolecules 2008;41(1): 87e94. [8] Ikeda K, Kida M, Endo K. Polym J 2009;41(8):672e8. [9] Uemura T, Ono Y, Hijikata Y, Kitagawa S. J Am Chem Soc 2010;132(13): 4917e24. [10] Zanotto A, Spinella A, Nasillo G, Caponetti E, Luyt AS. eXPRESS Polym Lett 2012;6(5):410e6. [11] Ouaad K, Djadoun S, Ferfera-Harrar H, Sbirrazzuoli N, Vincent L. J Appl Polym Sci 2011;119(6):3227e33. [12] Moller K, Bein T, Fischer RX. Chem Mater 1998;10(7):1841e52. [13] Zhao HY, Simon SL. Polymer 2011;52(18):4093e8. [14] Zhao HY, Yu ZN, Begum F, Hedden RC, Simon SL. Polymer 2014;55(19): 4959e65.
[15] Horie K, Mita I, Kambe H. J Polym Sci Part A-1: Polym Chem 1968;6(9): 2663e76. [16] Kalampounias AG, Andrikopoulos KS, Yannopoulos SN. J Chem Phys 2003;119(14):7543e53. [17] Andrikopoulos KS, Kalampounias AG, Yannopoulos SN. Soft Matter 2011;7: 3404e11. [18] Begum F, Sarker RH, Simon SL. J Phys Chem B 2013;117(14):3911e6. [19] De Gennes PG. Scaling concepts in polymer physics. Ithaca, NY: Cornell University Press; 1979. [20] Sakaue T, Raphael E. Macromolecules 2006;39(7):2621e8. [21] Kong CY, Muthukumar M. J Chem Phys 2004;120(7):3460e6. [22] Cacciuto A, Luijten E. Nano Lett 2006;6(5):901e5. [23] Simon SL, Sobieski JW, Plazek DJ. Polymer 2001;42(6):2555e67. [24] Odian G. Principles of polymerization. 3rd ed. New York: Wiley; 2004. [25] Sawada H. J Macromol Sci Part C: Polym Rev 1969;3(2):313e38. [26] Keddie JL, Jones RAL, Cory RA. Faraday Discuss 1994;98:219e30. [27] Begum F, Zhao HY, Simon SL. Polymer 2012;53(15):3238e44. [28] Begum F, Zhao HY, Simon SL. Polymer 2012;53(15):3261e8.
Contents lists available at ScienceDirect
Polymer journal homepage: www.elsevier.com/locate/polymer
Equilibrium free-radical polymerization of methyl methacrylate under nanoconfinement H.Y. Zhao, Sindee L. Simon* Department of Chemical Engineering, Texas Tech University, Box 43121, Lubbock, TX 79409-3121, USA
a r t i c l e i n f o
a b s t r a c t
Article history: Received 10 February 2015 Received in revised form 4 April 2015 Accepted 6 April 2015 Available online 12 April 2015
The effect of nanoconfinement on the equilibrium free radical polymerization of methyl methacrylate (MMA) is investigated using differential scanning calorimetry. The ceiling temperature is shifted to lower temperatures in 13 nm diameter pores, with pore surface chemistry showing no significant effect. The results indicate that the change in the entropy of propagation decreases in nanopores due to confinement effects (i.e. DSp,conf is a more negative value than DSp,bulk). The change in the entropy of propagation is independent of temperature for the bulk equilibrium polymerization, whereas the change in the entropy of propagation in nanopores becomes less negative and more bulk-like with increasing polymerization temperature presumably due to the lower molecular weight chains produced at high temperature. The data suggest that our system is one of weak confinement with chain entropy scaling with molecular weight to the 1.1 power (i.e. ~ N1.1). © 2015 Elsevier Ltd. All rights reserved.
Keywords: Nanoconfinement MMA equilibrium polymerization Entropy effect
1. Introduction The properties of polymers synthesized under nanoconfinement can be enhanced relative to bulk polymerization, with observations of increased molecular weight [1e8], increased tacticity [7,9], and increased glass transition temperature [6,10e12]. In previous work, we investigated the reaction kinetics and properties of free radical polymerization of methyl methacrylate (MMA) in the nanopores of controlled pore glass (CPG) [13,14] and found that the onset of autoacceleration shifted to shorter times presumably due to the reduced diffusivity of the nanoconfined chains. In addition, in hydrophilic pores, the initial propagation rate was higher than that in either hydrophobic pores or the bulk system due to the catalysis by silanol groups on the CPG surface [13]. The enhanced reactivity was accompanied by increased molecular weight and increased isotacticity [14]. However, previous experiments were carried out at relatively low temperatures (<95 C); here we examine higher reaction temperatures where monomer/polymer equilibrium plays an important role. Neat polymerization of MMA can be divided into two regimes depending on the temperature. When the reaction temperature is below the glass transition temperature of pure PMMA
* Corresponding author. E-mail address: [email protected] (S.L. Simon). http://dx.doi.org/10.1016/j.polymer.2015.04.017 0032-3861/© 2015 Elsevier Ltd. All rights reserved.
(Tg,p z 111 C), conversion will be limited by vitrification which occurs when the Tg of the system (polymer plus MMA as plasticizer) rises to the reaction temperature. On the other hand, as the reaction temperature increases beyond Tg,p, complete polymerization becomes hard to achieve since depolymerization gradually becomes important [15]. In other words, the competition between propagation and depropagation of MMA leads to a temperaturedependent equilibrium conversion. Our interest here is the influence of nanoconfinement on the equilibrium conversion. Such studies have been performed for sulfur polymerization [16,17]. In that work, conversion at a given temperature decreases as the size of the silica nanopores decreases from bulk to 2.5 nm and the floor temperature (the lowest temperature where polymerization can occur since sulfur has a positive change in enthalpy and entropy upon polymerization) is shifted to higher temperatures indicating that the change in the entropy of propagation in confined nanopores (DSp,conf) decreases compared with the change in the entropy of propagation in bulk (DSp,bulk). Our modeling work [18] well describes the nanoconfinement effect on sulfur polymerization assuming that the change in the entropy of confined polymer chains scales with chain length N and pore diameter D: DSpolymer, conf e NpDm, where p ¼ 2 represents strong confinement [19,20] and m ¼ 3.0 from self-consistent field theory [21] or 3.8 or 3.9 from blob scaling in semidilute solutions [22], both for spherical confinement. Similar to sulfur polymerization, polymerization of MMA is
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expected be affected by nanoconfinement. However, in the case of MMA, the ceiling temperature is expected to decrease because the signs of DSp and DHp for MMA polymerization are negative rather than positive as in the case of sulfur. One motivation of this work is to obtain information concerning the entropy change upon confining a chain to nanoscale dimensions, which is anticipated to depend on chain length [19e22], with greater confinement entropy associated with longer chains. This is hypothesized to lead to a decrease in the change in the entropy of reaction and a concomitant decrease in the equilibrium conversion. Fig. 1 schematically shows our expectations, where the solid and dashed lines represent the entropy for samples in bulk and in nanoconfined pores, respectively. Given that the entropy of polymer chains is reduced due to restricted chain configurations under confinement (Spolymer, bulk > Spolymer, confined), whereas the entropy of small molecules is not significantly influenced under confinement (Smonomer, bulk z Smonomer, confined), it is anticipated that the change in the entropy of nanoconfined MMA polymerization on confinement (DSconfined rxn) will be a more negative value than the change in the entropy for the bulk reaction (DSbulk rxn). To test these ideas, in this work, we polymerize MMA in nanopores and evaluate the effect of nanoconfinement on the polymer/ monomer equilibrium using differential scanning calorimetry (DSC). The experimental data are modeled to investigate the changes in thermodynamic properties in a nanoconfined environment. 2. Thermodynamics of MMA polymerization The thermodynamics of free radical polymerization can be described by the equation:
DGp ¼ DHp T$DSp
(1)
where DGp, DHp, DSp are the changes in the Gibbs free energy, enthalpy, and entropy of the propagation reaction, respectively. For MMA polymerization, DHp is negative since heat is released upon breaking the monomer p-bond and forming the polymer sbond, and DSp is also negative due to the reduced degrees of freedom of the polymer compared to the monomer. Since the
reaction spontaneously occurs when DGp is negative, polymerization is favorable at low temperatures; however, DGp becomes less negative as temperature increases and a polymer/monomer equilibrium exists at high temperatures. Above the ceiling temperature (Tc), DGp will be positive such that monomer will not convert to polymer. The equilibrium between polymer and monomer is described by the following equation: K
$ $ e Mm þ M ⇔ eMmþ1
where Mm$ is the free radical species of length m, M is the monomer, and K is the equilibrium constant defined as the ratio of the activities (ai) of the products to the reactants:
K¼
aMmþ1 1 1 ¼ ¼ aMm $aM 4M 1 xeq
(3)
where ai is the activity of species i. The activities of the free radical species of length m and m þ 1 are proportional to their concentrations and considered to be equivalent, whereas the activity of the monomer can be approximated by the monomer volume fraction 4M, which is in turn equal to 1xeq assuming no volume change on polymerization, where xeq is the equilibrium conversion of monomer. The equilibrium constant K also depends on temperature:
K ¼ exp DGp RT
(4)
Substituting equations (1) and (3) into equation (4) and rearranging, the conventional relationship between conversion and the change in enthalpy or entropy is obtained:
DHp DSp ln 1 xeq ¼ RT R
(5)
At the ceiling temperature, DGp is zero so that Tc is simply defined as the ratio of DHp to DSp:
Tc ¼
Fig. 1. Schematic plot showing entropy changes under nanoconfinement. Solid lines represent the entropy in bulk and the dashed lines represent the entropy in a nanoconfined system.
(2)
DHp DSp
(6)
The thermodynamics of polymer chains in confined environments has been discussed by De Gennes [19] who suggested that the decrease in entropy due to confinement of an ideal chain (DSpolymer, conf) in a tube or in a cylindrical pore is linearly proportional to the square of the ratio of the unperturbed size of the chains (Ro) to the tube or pore diameter (D): DSpolymer, conf e (Ro/ D)2eN/D2, where N is the number of monomer units in the chain. On the other hand, Kong and Muthukumar reported that the free energy of a confined non-ideal chain in a nanopore is proportional to wN2/D3, where w represents the excluded volume interaction [21]. Moreover, the scaling of the change in entropy on confinement has been hypothesized to depend on the strength of the confinement being proportional to N for the weak confinement regime and N2 for the strong confinement regime [20,22]. Based on the propagation reaction (see equation (2)), the change in the entropy of propagation between the confined and bulk reactions will depend on the strength of the confinement regime. For weak confinement, no effect is anticipated: DSp,conf e DSp,bulk e[(Nþ1)N1] e 0. On the other hand, for the strong confinement environment, the difference in the entropy of propagation between confined and bulk reactions should be influenced by the chain length: DSp,conf e DSp,bulk e [(Nþ1)2N21]eN1.
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3. Experimental methodology 3.1. Materials and instrumentation Methyl methacrylate (MMA) monomer and 2,20 -azo-bis-isobutyronitrile (AIBN) initiator were obtained from Aldrich. The concentration of initiator is 0.5 wt %. Controlled pore glasses (CPG, Millipore) with pore diameters (D) of 13 nm ± 7.4% (based on manufacturer's specifications) were used as the confinement system. In this work, the pores with surface silanol groups (eSiOH) are termed hydrophilic pores, whereas the pores with silanol replaced by trimethylsilyl groups (eSi(CH3)3) are termed hydrophobic pores. The purification of reactants and the surface treatment of nanopores follow the same procedures outlined in previous work [13,14]. A Mettler-Toledo differential scanning calorimeter DSC1 was used with an ethylene glycol cooling system and nitrogen purge gas. Samples were prepared in 20 m L hermetic pans under a nitrogen blanket. As in previous work [13,14], the pore fullness ranged from 70 % to 90 % based on the ratio of the monomer volume added to the CPG pore volume (based on manufacturer's specifications). Indium was used to calibrate the enthalpy and the DSC temperature at 10 K/min. For the isothermal condition used to react the samples, an isothermal calibration [23] was performed using indium at 0.1 K/min. 3.2. Polymerization procedure The polymerization of MMA in bulk and in nanoporous confinement was carried out isothermally at temperatures ranging from 60 to 180 C using the DSC as an oven. After a given isothermal reaction, dynamic scans at 10 K/min from room temperature to 200 C were used to measure any residual heat of reaction. One to three replicate samples were used for each reaction condition. For reaction temperatures above 100 C, we were faced with a challenge because the temperature is higher than the boiling point of pure monomer (Tb,MMA ¼ 101 C). We initially tried to use pans with o-rings capable of withstanding 24 bars but were unsuccessful. Hence, in order to decrease the vapor pressure of the reactant mixture, we partially converted the samples at a low temperature (80 C) to a monomer conversion (x z 10e15%) prior to the polymerization at higher temperature. Thus, two DSC programs were used depending on the reaction temperatures, which are described by one step and two step methods, respectively.
175
For the one step method shown in Fig. 2a, a temperature ramp at 100 K/min was applied from room temperature to the specified temperature for polymerization, which ranged from 60 to 140 C for bulk samples and from 60 to 130 C for nanoconfined samples. For the two step method shown in Fig. 2b, the monomer was first reacted at 80 C for a prespecified time prior to the onset of autoacceleration to form a monomer/polymer mixture and then heated at 100 K/min to the specified temperature from 110 to 180 C where the equilibrium polymerization is completed. The conversion of isothermally polymerized MMA is related to the integrated heat flow (Q_ ) by the equation:
x¼
1 DHp
Zt
Q_ dt
(7)
0
where the average total heat of reaction DHp is 560 J/g obtained from literature reports [24] and in agreement with our previous work [13] where we obtained a value of 563 ± 12 J/g, independent of reaction temperature, confinement size, and surface treatment. The integration is performed over the entire isothermal history. Thus, for the one step method, conversion is calculated from the sum of the heat of reaction for the temperature ramp to the isothermal temperature and the heat during the isothermal reaction (DHramp þ DHiso). The conversion associated with the two step method is calculated from the heat of reaction for each of the two isothermal steps (DH1 þ DH2) using equation (7) plus the conversion associated with heat of reaction during the temperature ramp between the two steps (DHramp). Although DHramp is obtained based on the experimental observation for both one and two step methods, we can also integrate the following equation to examine the conversion x associated with DHramp:
dx keff Mo ð1 xÞ ¼ dT b
(8)
where keff is the temperature-dependent effective rate constant from previous work [13], Mo is the bulk MMA initial concentration, and b is heating rate. Based on both the measurements and equation (8), DHramp is negligible (<1% of DHP) for ramps to temperatures below 100 C, and DHramp is less than 20% of DHP for temperatures ranging from 100 C to 140 C. This is important
Fig. 2. a) On left, schematic of one step method to investigate the equilibrium reaction at temperatures from 60 to 140 C for bulk polymerization and from 60 to 130 C for nanoconfined polymerization. b) On right, schematic of two step method to investigate the equilibrium reaction at higher temperatures.
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because it means that the onset of autoacceleration occurs after reaching the specified polymerization temperature. The uncertainties in the data (see later) are based on the weight loss during polymerization at high temperature. Weight loss increases as the reaction temperature increases, and the weight loss for nanoconfined samples is greater than for bulk samples. For the one step method, the weight loss for both bulk and nanoconfined sample is less than 10% and errors in the equilibrium heat of reaction range from 1 J/g to 7 J/g, with the largest error at the highest temperature of 140 C; the associated error in conversion is less than 1.3%. On the other hand, for the two step method, the largest weight loss for bulk samples is around 20% at 180 C, whereas the weight loss of nanoconfined samples is around 50% at 180 C. Based on experimental observation, these weight losses occur in the temperature ramp between the two steps, i.e., during the ramp from 80 C to the temperature of interest; the heat released during the ramp (DHramp) is, thus, determined based on the average weight before and after polymerization. The error bars of equilibrium heat of reaction range from 0.5 J/g to 68 J/g, again, with the largest error at the highest temperature (T ¼ 180 C) for the samples in hydrophilic pores; the resulting error in conversion ranges from less than 1 % to 12 %. 4. Results The dependence of conversion on reaction temperature is shown in Fig. 3 for bulk samples. Data obtained from the one step method are represented by open symbols and those obtained from the two step method are represented by solid symbols. The conversions at relatively low temperatures (<100 C) are less than 100% due to the effect of vitrification. As the reaction temperature approaches the glass transition of neat polymer (Tg,p), the conversion reaches the maximum limit of 1.0 and then it decreases as the reaction temperature increases since depolymerization gradually becomes dominant at higher temperatures. In Fig. 3, the dashed line is the best fit of equation (5) based on a plot of ln (1xeq) vs. T1 to obtain DSp assuming the bulk value of DHp (560 J/g). The prediction by equation (5) deviates from experimental data below Tg,p since the vitrification effect is not accounted for. The value obtained for the entropy of propagation for the bulk reaction, DSp,bulk ¼ 114.6 ± 0.9 J mol1 K1, is consistent with the value in the literature (DSp,bulk ¼ 117 J mol1 K1) [25]. In addition, Tc for
Fig. 3. The heat of reaction and equilibrium conversion (xeq) as a function of isothermal temperature for bulk using one step (open symbols) and two step (solid symbols) methods. The dashed line is based on equation (5) using constant values of DHp (56 kJ/mol) and DSp,bulk (114.6 J mol1 K1).
the bulk polymerization is 216 ± 2 C, which is also consistent with the value reported in the literature of 220 C [24]. Based on the data and modeling predictions for the bulk reaction, both the one and two step methods give good results. The temperature-dependent conversion is compared for bulk and nanoconfined samples in Fig. 4, where the open symbols refer to the one step method and the solid symbols refer to the two step method. Similar to the bulk case, the reaction at relatively low temperatures (<100 C) is incomplete (x < 1.0) due to the influence of vitrification. In the vicinity of the glass transition of pure polymer (Tg,p), the conversion gradually reaches a maximum value of 1.0, and then it decreases with increasing polymerization temperature due to the effect of depolymerization at high temperature. As hypothesized in the introduction, for polymerization temperatures in this regime, the equilibrium conversion of nanoconfined samples is less than that of the bulk samples at a given reaction temperature. Although the equilibrium polymerization is performed in both hydrophobic and hydrophilic nanopores with different pore surface chemistries, we do not observe any difference in equilibrium conversion between samples in hydrophilic and hydrophobic pores within the error of the measurements. Considering that the bulk data were quantitatively described by equation (5) with constant DSp, we first applied this to the nanoconfined case assuming the same DHp as in the bulk case (a reasonable assumption based on our prior work [13]). The model (shown as a dashed line) only qualitatively describes the trend with DSp,conf ¼ 123.7 ± 0.8 J mol1 K1. To further examine the temperature dependence of DSp,conf, we note that the difference between the changes in entropy of propagation between bulk and confined polymerizations is simply related to the difference in the equilibrium conversions for the two cases since the heat of reaction (DHp) is independent of pore size or pore wall chemistry [13]:
DSp;bulk DSp;conf
1 xeq conf ¼ Rln 1 xeq bulk
(9)
Fig. 5 shows the dependence of DSp,bulk e DSp,conf on temperature for both one step and two step methods at and above 110 C. An Arrhenius-type temperature dependence is assumed to describe the decrease in DSp,conf with increasing temperature, as indicated
Fig. 4. The heat of reaction and equilibrium conversion (xeq) as a function of isothermal temperature for both bulk and nanoconfined samples using one step (open symbols) and two step (solid symbols) methods. The dashed lines are based on equation (5) using constant values of DHp and DSp, and the solid line assumes that DSp is a function of temperature; see Table 1 for values.
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177
based on the kinetic chain length [24] and previous modeling [27,28] become similar for both pore surfaces when the reaction temperatures increase. To test the literature scaling of the changes in entropy of confined chain (DSpolymer, conf) on the number of bonds in the chain (N), recall that DSp,bulk e DSp,conf is proportional to Np1:
DSp;bulk DSp;conf N p1
(10)
Taking the natural logarithm of both sides and then taking the derivative with respect to reciprocal temperature, we relate the apparent activation energy for the kinetic chain length (En) to that for the change in the entropy of propagation EDSp:
EDSp ¼ ðp 1ÞEn
Fig. 5. The difference between the change in entropy for the propagation reaction of bulk samples and nanoconfined samples as a function of polymerization temperature. The definitions of symbols are the same as in Fig. 4. The dashed line represents an exponential fit.
by the dashed line. The fact that DSp,conf becomes less negative and more bulk-like at high temperatures presumably arises from the reduction of chain lengths as temperature increases resulting in weaker confinement effects. The temperature dependence for DSp,conf obtained in Fig. 5 can be used in equation (5), resulting in the solid line in Fig. 4, which well describes the decrease in the equilibrium conversion and the ceiling temperature in nanopores. The fitting parameters are shown in Table 1 for both constant DSp and DSp(T), and the decrease in ceiling temperature is quantified being 180 ± 2 C for the constant DSp case and 190 ± 7 C for the case of DSp(T). Both are considerably lower than the ceiling temperature for the bulk polymerization of 216 ± 2 C. 5. Discussion The experimental data show no significant differences in the equilibrium conversion as a function of temperature between samples synthesized in hydrophobic and hydrophilic pores. This was initially unexpected since it has been reported that the PMMA carbonyl group can interact with the silanol group on the hydrophilic pore surface [26] which might be expected to influence the entropy of chain confinement (DSp,conf). In addition, changes in the molecular weight between hydrophobic and hydrophilic pore surface are observed for polymerization at low temperatures [14]. Our explanation for the similar results is that the strength of the specific interaction between the monomer/polymer and the hydrophilic pore wall is reduced at high reaction temperatures relative to kBT (where kB is the Boltzmann constant). Furthermore, although we observed differences in molecular weight for the two pore chemistries at low temperatures [14], molecular weights calculated
(11)
The exponential fit in Fig. 5 yields a value of EDSp ¼ 6.3 ± 5.4 kJ/ mol. On the other hand, in the absence of autoacceleration and depolymerization, En ¼ Ep e Ed/2 e Et/2 ¼ 43 kJ/mol, where Ep, Ed, and Et are the activation energies for the chain propagation, initiator dissociation, and termination, respectively, and their values are based on previous modeling [27,28] (Ep ¼ 22.4 kJ/mol, Ed ¼ 128.2 kJ/ mol Et ¼ 2.9 kJ/mol) and are consistent with literature values [24]. In this case, the value of (p1) equals 0.15 ± 0.12 for xeq z 1.0 at low temperatures. At high temperatures, En becomes a larger more negative value due to the decrease in molecular weight associated with depolymerization. Thus, the p value is anticipated to be less than 1.15 and to decrease towards 1.0 at the ceiling temperature. We plan to verify the results in future work by measuring the molecular weight of polymers synthesized by free radical polymerizations, both MMA polymerization and others, at high temperatures under nanopore confinement. 6. Conclusion The equilibrium polymerization of methyl methacrylate (MMA) synthesized in bulk and nanoscale controlled glass pores (CPG) is investigated by DSC. One and two step methods are developed to cover the reaction temperatures ranging from 60 to 180 C. The equilibrium conversion decreases as the reaction temperature increases due to the effect of depolymerization. Nanoconfined samples have smaller equilibrium conversions relative to bulk samples above 110 C, although, there is no significant difference for the equilibrium conversion of samples synthesized in hydrophobic and hydrophilic pores. The equilibrium conversion of bulk samples as a function of temperature can be quantitatively described using a constant change in entropy of propagation, but this is insufficient to describe the equilibrium conversion of nanoconfined samples; rather, the nanoconfined entropy of propagation becomes more bulk-like as the reaction temperature increases presumably due to the lower molecular weight chains produced at higher temperatures. Based on the difference in the apparent activation energy for the kinetic chain length and that for the change in entropy of propagation, the entropy of confining a chain appears to scale with molecular weight to the 1.1 power suggesting that we are in the weak confinement region (i.e., DSpolymer,conf ~ N1.1). Acknowledgment
Table 1 Values for DSp and Tc assuming DHp ¼ 56 kJ/mol.
DSp (J mol1 K1) Tc ( C)
Bulk
Nanoconfined DSp ¼ constant
Nanoconfined DSp ¼ f (T)
114.6 ± 0.9
123.7 ± 0.8
216 ± 2
180 ± 2
e 114.6e1.36$exp(760 T1) [T in K] 190 ± 7
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