ARTICLE pubs.acs.org/JPCB
Kinetic Study of Trimerization of Monocyanate Ester in Nanopores Yung P. Koh and Sindee L. Simon* Department of Chemical Engineering, Texas Tech University, Lubbock, Texas 79409, United States ABSTRACT: A kinetic study of the trimerization of monocyanate ester both in the bulk and in the nanoconfinement of controlled pore glass is performed using differential scanning calorimetry. Both isothermal and dynamic experiments are analyzed. Although the activation energy for the reaction is the same within experimental error for the bulk and nanoconfined samples (approximately 21-23 kcal/mol), the reaction is accelerated under nanoconfinement by approximately 50 times in 13 nm pores compared with bulk.
’ INTRODUCTION The effects of nanoconfinement on the glass transition phenomena of low molecular weight and polymeric materials have been extensively investigated since Jackson and McKenna1 first showed a depression for glass formers confined in nanopores. Although contradictory results have been reported, it is generally found that the glass transition temperature at the nanoscale is depressed relative to the bulk unless strong interactions between the confined material and the confinement medium are present.2-4 The leading explanation for the depressed Tg in cases where the interaction between the confined material and the confinement medium is weak is that the free surface or interface has enhanced mobility.5-11 However, interfacial effects cannot readily explain either the Tg depression or the existence of two Tgs observed for glasses confined in nanopores,1,12-16 indicating a more comprehensive explanation is still required to describe the large range of findings in the literature. In addition to changes in Tg, chemical reactions confined to nanoscale geometries also often change from the bulk. For example, the cycloaddition reaction of quadricyclane and diethyl azodicarboxylate in nanosize micelles in water is completed within 10 min whereas the time scale for the bulk reaction is more than 2 days in toluene solvent.17 A variety of other reactions in micelles have been studied and rate changes are often attributed simply to differences in the reactant concentrations in the surface and micellar pseudophases.18,19 On the other hand, the rate of the photoinduced reaction of phthalic anhydride and pyridine in the hard confinement of sol-gel nanopores decreases by 25% from the bulk, presumably due to reduced diffusivity.20 In prior work from our laboratory,16 the nanoconfined trimerization of monocyanate ester in controlled pore glasses (CPG) was studied. The reaction is an important one since it is the basis for making polycyanurate themosetting materials (when difunctional reactants are used), and these materials are used in microelectronic and composite applications.21 The reaction rate for the nanoconfined monofunctional cyanate ester was found to increase as pore size decreased, being accelerated by 21 times in 8.1 nm pores relative to the bulk.16 The heat of reaction and r 2011 American Chemical Society
reaction kinetic model appeared to be unchanged under nanoconfinement. The difunctional cyanate ester used to make polycyanurate also shows acceleration of the reaction rate upon nanocofinement in CPG, in this case by 20-30 times in 11.5 nm hydrophobic pores relative to the bulk.13-15 In addition, both monofunctional and difunctional cyanate ester reactants and their products show lower Tgs upon nanoconfinement compared to the bulk; the Tg depression increases with conversion and is more pronounced for the fully reacted products, suggesting that molecular stiffness influences the magnitude of nanoconfinement effects. Our previous studies of the reactivity of nanoconfined monocyanate ester were based on comparing the bulk and nanoconfined trimerization reactions at a reaction temperature of 141 C for various sizes of nanopore confinement. Here, we expand the range of reaction temperatures to 220 C for the bulk reaction and to 200 C for the nanoconfined reaction in 13 nm pores, in order to examine the activation energy and to further elucidate the reaction kinetics.
’ METHODOLOGY Materials. The monofunctional cyanate ester (MCE) reactant used in this study is 4-cumylphenol cyanate ester (Oakwood Products), used as received. The chemical structure of monocyanate ester is shown in Figure 1; its molecular weight is 237.3 g/mol, and its density is 1.10 g/cm3 at 25 C. Three cyanate ester (-O;CtN) groups react to form a cyanurate trimer product with molecular weight of 711.9 g/mol, also shown in Figure 1. The nanoconfinement medium used in this study is controlled pore glass (CPG, Millipore) with pore diameter of 13.0 nm (7.4%. The CPG has a mesh size of 120/200, a bulk density of 300 g/L, a specific pore volume of 0.68 cm3/g, and specific surface area of 130.0 m2/g, as provided by the manufacturer. The native CPG is made from borosilicate glass and inherently Received: October 25, 2010 Revised: December 20, 2010 Published: January 19, 2011 925
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of monocyanate ester reactant. The CPG are all underfilled and the fullness ranges from 70% to 90%, as calculated from the ratio of the reactant to CPG weights, the manufacturer-reported CPG pore volume, and the density of the reactant. We reported previously that the Tg and heat of reaction were independent of both the degree of pore fullness and the sample size for the reactant studied here, as well as for a similar but difunctional monocyanate ester.13,14,16 All samples were prepared under a nitrogen blanket to minimize adsorption of adventitious water. In addition to isothermal studies, the results of dynamic temperature scans are also analyzed. These scans, previously shown,16 were performed on initially uncured samples for heating rates of 2, 5, 10, 20, and 30 C/min. The reaction exotherms obtained in these dynamic scans are integrated to yield conversion as a function of temperature, and the activation energy is then calculated using an isoconversion method.27 The DSC temperature was calibrated with n-octane, mercury, indium, and tin at 10 C/min on heating. The isothermal calibration, which is relevant for the isothermal reaction temperature, was performed at 0.1 C/min, which was found in other work28 to be equivalent to performing an isothermal calibration. Temperature at other heating rates, as well as heat flow, was calibrated with indium. Separate calibrations were performed for the two types of cooling systems used.
Figure 1. Trimerization reaction of 4-cumylphenol cyanate ester to produce its cyanurate product.
contains hydroxyl groups on its surface. Cleaning with nitric acid was followed by a silanization using hexamethyldisilazne (SigmaAldrich) to replace the hydroxyl groups with hydrophobic trimethylsilyl groups using the procedure of Jackson and McKenna.22 The silanization treatment has been reported to result in negligible changes in pore diameter and pore size distribution.23 The silanized CPGs were stored in a desiccator before use. DSC Measurement. A Perkin-Elmer Pyris 1 differential scanning calorimeter (DSC) was used with an intracooler and a nitrogen atmosphere for the measurements of samples having Tg values above -30 C. The system was changed to Mettler Toledo DSC1 with a liquid nitrogen cooling system for measurements of samples having Tg values below -30 C. Since Tg can be obtained only on cooling by its definition,24 here we measure the limiting fictive temperature (Tf0 ) on heating using Moynihan’s method.25 We refer to the Tf0 value as the Tg in this study since Tf0 is approximately equal (within ∼1 K) to the Tg value that would be obtained on cooling at the same rate as heating.24,26 The DSC was also used as a reactor for the isothermal reaction studies, since it provides good control of reaction temperature. An initially unreacted sample was scanned to the prespecified isothermal reaction temperature (ranging from 140 to 220 C), partially reacted for a prespecified time, cooled to -60 C, and then scanned on heating back to the reaction temperature. Further reaction was then accomplished, followed by cooling to -60 C, and heating back to the reaction temperature. From the heating scans, all performed at 10 C/min, Tg as a function of isothermal reaction time was obtained. This cycle was continued until complete reaction was reached. A similar procedure but with cooling to -100 C was used for short reaction times with the liquid nitrogen cooling system. Previous work16 showed that data from this methodology is consistent with that obtained using one sample for each isothermal reaction time because insignificant reaction occurs during the periodic scans used to measure the Tg. The advantage of using one sample to obtain Tg versus reaction time data is the reduced errors associated with multiple samples. To make the DSC samples, CPG with weight ranging from 2 to 6 mg was loaded into DSC hermetic pans followed by 2-4 mg
’ RESULTS DSC dynamic heating scans at 10 C/min for the monocyanate ester reactant in both bulk and nanopore confined states are shown in Figure 2a. The corresponding scans for the fully reacted cyanurate trimer product are shown in Figure 2b. For the monocyanate ester, Tg is observed in the vicinity of -40 to -60 C, followed by the reaction exotherm, with two Tgs observed for the material confined in 13 nm CPG, as shown in the inset for Figure 2a. Although the reaction exotherm for the monocyanate ester shifts to lower temperatures upon nanoconfinement, indicating acceleration of the reaction, the heat of the reaction calculated from the area of the exotherm peak is unchanged (104 ( 1.3 kJ/mol),16 indicating that full conversion is obtained in the nanopores. For the bulk cyanurate trimer reaction product, shown in Figure 2b, Tg is followed by a cold crystallization exothermic peak and a subsequent endothermic melting peak. On the other hand, the cyanurate trimer in 13 nm CPG shows two Tgs and a significant Tg depression of approximately 35 C relative to the bulk, presumably due to its high molecular stiffness.16 Interestingly, nanopore confinement suppresses cold crystallization and its melting, as reported in the literature.29-31 As shown in Figure 2a,b, Tg increases from a value near -60 C for the monocyanate ester reactant to a value near 45 C for the trimer reaction product in bulk. Thus, we can use the evolution of Tg as a function of reaction time to follow the reaction; such data is shown in Figure 3 for the bulk state at reaction temperatures ranging from 141 to 220 C. As the reaction proceeds, the glass transition temperature increases from the value of monocyanate ester reactant, leveling off near the completion of reaction, and then it decreases at longer times due to degradation for the highest reaction temperatures. At reaction temperatures of 180 C and below, no significant degradation is observed in the time scale of the experiment. The reaction occurs most rapidly at the highest reaction temperature, 220 C, and the curves shift to longer times with 926
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Figure 3. Evolution of the glass transition temperature as a function of reaction time for the bulk reaction. The solid lines are the best fit to the reaction model for fixed b = 0.303. The dotted lines are the best fit to the reaction model for variable b; at the lowest temperatures, the results for the two models are nearly the same.
The kinetics of the degradation reaction must be added to the model in order to adequately describe the data shown in Figure 3 at the highest temperatures. The degradation is assumed to result from cleavage of the propylidene linkages to produce small molecules,33-35 and we have confirmed by GC-MS analysis that the degradation products in this work are those expected: principally benzene, R-methylstyrene, and propylbenzene. The degradation is assumed to be first order in the concentration of degrading units dy ¼ k2 ð1 - yÞ dt
Figure 2. DSC heating scans at 10 K/min heating rate (a,top) for initially unreacted monocyanate ester (MCE) and (b,bottom) for fully reacted cyanurate trimer. The solid red curves are for the bulk and the dashed blue curves are for sample confined to 13 nm CPG. The inset in the upper panel shows the two Tgs in the nanoconfined sample.
where k2 is the Arrhenius reaction rate constant for the degradation reaction and y is the conversion of degrading units. The Tg of the degrading mixture can be modeled as a ternary mixture of unreacted monocyanate ester, fully reacted trimer, and small molecule degradation products. We assume additivity of configurational entropy to obtain Tg of this ternary mixture
decreasing reaction temperature. The exception to this trend is the data at the lowest reaction temperature of 141 C, which is below the temperature of complete melting, as shown in Figure 2b, suggesting that trimer crystals accelerate the reaction kinetics below 150 C. The evolution of Tg as a function of reaction time for the bulk monocyanate ester was found to follow a first-order plus first-order autocatalytic reaction model in our previous study at 141 C:16 dx ¼ k1 ð1 - xÞðx þ bÞ dt
Tg ¼ Tg12 þ ðTg3 - Tg12 Þ
λð1 - xÞ ðTg¥ - Tg0 Þ þ Tg0 1 - ð1 - λÞx
λξy 1 þ ξyðλ - 1Þ
ð4Þ
where Tg12 is given by eq 2, Tg3 is the Tg of the small molecule degradation products, ξ is the weight fraction of small molecule plasticizer when y = 1.0, and λ* is a fitting parameter related theoretically to ΔCp3/ΔCp12. Taking Tg3 = -142 C (a value reported for benzene36) and ξ = 0.325, two additional fitting parameters, k2 and λ*, are introduced to describe the degradation behavior. The resulting fits of Tg versus logarithm of time reasonably represent the experimental data, as shown by the solid lines in Figure 3. The fitting results without degradation (141, 160, and 180 C) and with degradation (200 and 220 C) are summarized in Table 1 for b taken as a constant (=0.303) for all temperatures. Better fits can be achieved if b is allowed to vary with temperature and these fits are shown as dashed lines in Figure 3; the fitting parameters with variable b are tabulated in Table 2. The activation energy of the degradation reaction is found to be approximately 52-54 kcal/mol from the k2 values at temperatures of 200 and 220 C.
ð1Þ
where k is Arrhenius reaction rate constant of trimerization reaction, x is the conversion of monocyanate ester to trimer product, and b has been related to the fraction of trace impurities which catalyze the reaction initially.32 The conversion x is directly related to the Tg of the mixture of reactant and product (Tg12) through the Debenedetto equation Tg12 ¼
ð3Þ
ð2Þ
where Tg0 is the Tg of the unreacted monocyanate ester and Tg¥ is the Tg of the completely reacted cyanurate trimer, and λ is a structure-dependent parameter value of 0.375.16 927
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Table 1. Fitting Results of the Bulk Reaction and the Reaction in 13 nm Pores for b = 0.303 bulk Tg
k1 (10-5 s-1)
140 C
160 C
180 C
2.30
1.95
3.61
200 C
220 C
10.4
37.3
k2 (10-7 s-1)
5.39
λ*
0.351
55.7 0.351
13 nm Tg1
-5 -1
k1 (10
s )
140 C
160 C
180 C
200 C
15.4
75.2
176
520
13 nm Tg2
-5 -1
k1 (10
s )
140 C
160 C
180 C
200 C
16.5
81.3
185
566
Table 2. Fitting Results of the Bulk Reaction and the Reaction in 13 nm Pores for Variable b bulk Tg 140 C
160 C
180 C
200 C
220 C
b
0.285
0.358
0.380
0.536
k1 (10-5 s-1)
2.28
1.79
3.30
7.60
16.5
k2 (10-7 s-1)
5.16
49.4
λ*
0.365
1.12
0.365
13 nm Tg1
b k1 (10-5 s-1)
140 C
160 C
180 C
200 C
0.770 9.15
1.58 26.5
1.32 71.0
0.314 511
Figure 4. Evolution of the glass transition temperature as a function of reaction time for monocyanate ester in 13 nm pores (a,top) for Tg1 and (b,bottom) for Tg2. The solid lines are the best fit to the reaction model for fixed b = 0.303, and the dotted lines are the best fit to the reaction model for variable b.
13 nm Tg2 140 C b
1.81
k1 (10-5 s-1)
5.32
160 C 2.03 23.0
180 C 1.99 54.8
taking b as a fitting parameter. The fitting results for fixed b = 0.303 for the reaction in 13 nm CPG are summarized in Table 1, and the results for variable b values are summarized in Table 2. The kinetic model fits provide the values of the reaction rate constant k at each reaction temperature. Using the reaction rate constants obtained assuming b = 0.303, Arrhenius plots of ln k versus 1/T are constructed in Figure 5. The resulting activation energies are 20.9 ( 3.7 kcal/mol for the bulk reaction and 22.6 ( 1.2 kcal/mol for the reaction in 13 nm CPG. The values indicate that the activation energy is unchanged at the nanoscale within experimental error and that the enhanced reactivity at the nanoscale is not due, for example, to catalysis by the surface since this would be expected to reduce the activation energy. Catalysis at the surface would also be expected to result in higher rate constants for material near the surface, which is characterized by Tg2; however, k values for Tg1 and Tg2 are similar as indicated by the open and closed triangles in Figure 5. Also shown in Figure 5, the reaction rate constant at the reaction temperature 141 C for the bulk reaction deviates from the Arrhenius slope of other reaction temperatures, presumably due to the presence of trimer crystals. On the other hand, at the same reaction temperature of 141 C for the reaction in 13 nm CPG, the data follow the Arrhenius slope for the higher reaction temperatures
200 C 0.634 381
For the nanoconfined reaction, similar plots of Tg versus reaction time are shown in Figure 4, a and b, for primary Tg1 and secondary Tg2. Although the temperature dependence of the reaction kinetics is similar to that of the bulk reaction, the curves for a given temperature are shifted to shorter times, indicating that the reaction is accelerated under nanopore confinement. The reaction rate at 160 C is faster than that of 141 C, unlike for the bulk reaction, and no evidence of crystallization at 141 C is observed, consistent with the dynamic scan results shown in Figure 2b. The data in Figure 4a,b are fit to the same reaction kinetic model (eqs 1 and 2), albeit without degradation since degradation was not observed for the nanoconfined systems, presumably because the time scales for reaction were considerably shorter than for the bulk reaction. The solid lines are the fitting results using the fixed value of b (0.303) previously obtained from fitting the bulk data, whereas the dotted lines are the fitting results 928
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Figure 5. Arrhenius plot of rate constants obtained assuming constant b = 0.303. For the reaction in 13 nm pores, the filled symbols indicate the results for the primary Tg1 and the open symbols are those for the secondary Tg2.
Figure 7. Arrhenius plot of the shift factors used to obtain superposition in Figure 6. For the reaction in 13 nm pores, the filled symbols indicate the results for the primary Tg1 and the open symbols are those for the secondary Tg2.
The resulting shift factors are plotted as a function of the inverse reaction temperature to calculate the activation energy in Figure 7. The activation energies from this method are found to be 22.8 ( 1.8 and 22.7 ( 1.0 kcal/mol, for the bulk reaction and the reaction in 13 nm CPG, respectively. In addition to the reaction kinetic model and the model-free isoconversion methods used to obtain the activation energy from isothermal data, the activation energy can also be obtained by applying an isoconversion method to dynamic heating scans made at the different heating rates (β).27 Following the methodology of Flynn and Wall27 dx dx Ea ¼ β ¼ f ðxÞA0 exp ð6Þ dt dT RT dx A0 Ea ¼ exp dT f ðxÞ β RT Figure 6. Superposition of Tg versus natural logarithmic time curves using horizontal shifts to Tr = 160 C.
ð7Þ
where A0 is a pre-exponential factor and f(x) is an unknown function of conversion x. Assuming A0, f(x), and Ea are independent of T and also assuming A0 and Ea are independent of x, eq 7 can be solved by separation of variables: Z dx A0 Ea ¼ FðxÞ ¼ p f ðxÞ β R Z ð8Þ R Ea exp dT where p ¼ Ea RT
supporting the observation that crystallization is suppressed for nanoconfined trimer in 13 nm CPG. The activation energy can also be obtained from the isothermal reaction data using a model-free isoconversion method, in which Tg versus ln t curves are shifted to superpose at a given reference temperature. The shift factor (ln aT) is related to the activation energy37 Ea 1 1 ln aT ¼ ln t - ln tr ¼ ð5Þ R Tr T
The logarithm of p is known to be linear with (Ea/R)(1/T) for Ea/RT > 20.38 We found log p = -0.455(Ea/R)(1/T) - 2.326 by the numerical integration for Ea/RT from 20 to 70. Taking the logarithm of eq 8 and then taking the derivative with respect to 1/T at constant conversion, an equation for Ea is obtained: R ∂ log β Ea ¼ ð9Þ 0:455 ∂ð1=TÞ x
where aT is a shift factor, tr is reference reaction time, and Tr is reference temperature. The advantage of this shift factor method is that no detailed kinetic information is required. Figure 6 shows the shifted curves of Tg versus ln t for the bulk reaction, as well as Tg1 and Tg2 versus ln t for the nanoconfined reaction, with superposition at the reference temperature of 160 C. For the bulk reaction data, the degradation at long time is excluded from the shifting process. The shifted curves both for the bulk and the nanopore confined reaction superpose well at all glass temperatures.
Equation 9 is similar to that obtained by Flynn and Wall27 and Zacharia and Simon,39 although those authors obtained values of 0.45727 and 0.45039 rather than 0.455. 929
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Figure 9. Activation energy obtained from dynamic temperature scans shown in Figure 8 as a function of conversion for the bulk reaction and the reaction in 13 nm pores.
mechanism for trimerization of cyanate ester,32 such an interpretation is problematic for our reaction system.
Figure 8. (a,top) Heating rate dependence of the temperature to reach a given conversion from dynamic heating scans for the bulk; (b,bottom) for samples in 13 nm CPG. Conversions x are 0.1, 0.2, 0.3, 0.4, 0.5, 0.6, 0.7, 0.8, and 0.9, from right to left. The insets show the normalized heat flow versus temperature for various heating rates, as published in ref 16.
In order to apply eq 9, we calculate the conversion as a function of temperature from the ratio of the partial heat of reaction to the total heat of reaction from the heat flow versus temperature data shown in the insets of Figure 8, a and b. The resulting plots of log β versus inverse temperature for the bulk reaction and the reaction in 13 nm CPG are shown in Figure 8, a and b, respectively, for various conversions ranging from 0.1 to 0.9. The slopes of Figure 8 appear to be similar for all conversions, and also for the unconfined and confined reaction conditions. Figure 9 shows the calculated activation energies as a function of conversion. The average activation energies from the isoconversion method are 23.9 ( 1.0 kcal/mol for the bulk reaction and 23.7 ( 1.5 kcal/mol for the reaction confined in 13 nm CPG, consistent with the results from the isothermal data using both model and model-free methods. Interestingly, the value of the activation energy for trimerization of monocyanate ester in this study is also similar to that for cure of dicyanate ester without catalyst (22 kcal/mol).32 According to Eyring,40 if two reactions have similar activation energies but different reaction rates, the increase in reaction rate can be attributed to an increase in the entropy of activation. However, given the complex reaction
’ DISCUSSION The magnitude of the accelerated reaction rate upon nanopore confinement can be quantified in terms of an acceleration factor from the ratio of reaction rate constants for the isothermal bulk and nanoconfined studies. It can also be obtained from dynamic studies using the activation energy of the reaction to convert conversion versus temperature curves to conversion versus time at an arbitrary reference temperature. In our previous work15 we reported a large difference in the acceleration factors between isothermal and dynamic data for the monocyanate ester reaction, whereas the two data sets gave similar acceleration factors for a difunctional cyanate ester. However, the isothermal reaction temperature of 141 C was used for the monocyanate ester in that study. Here, we have shown that due to incomplete melting at 141 C, trimer crystals exist in the bulk at this reaction temperature and seem to accelerate the reaction. Due to suppression of crystallization at the nanoscale, this effect is not observed for the nanoconfined reaction. Hence, the acceleration factor based on the bulk reaction at 141 C results in a low value for the isothermal reaction compared to the dynamic reaction. Here we compare the acceleration factors obtained at various isothermal reaction temperatures to those obtained from the dynamic data in our previous study. Figure 10 shows that the acceleration factors for isothermal reaction temperatures above the completion of melting are higher than that for the isothermal temperature of 141 C. However, the new isothermal acceleration factors increase with increasing temperature and are approximately a factor of 2 higher than the acceleration factor calculated from the dynamic data. Presumably, this discrepancy is related to the assumptions underlying the dynamic method as described in our previous study15;namely, that the activation energy and overall reaction mechanism are constant over the wide range of dynamic reaction temperatures (from 180 to 350 C). The lack of validity of these assumptions is backed up by the change in the shapes of the dynamic scans at low temperatures (see the insets in Figure 8). In fact, it was previously reported that the acceleration factors obtained from the dynamic scans at 10% 930
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Figure 10. Reaction acceleration factor versus reciprocal nanopore diameter from isothermal and dynamic studies. For the isothermal studies, the filled symbols indicate the results for the primary Tg1 and the open symbols are those for the secondary Tg2. The acceleration factors for isothermal data at 141 C and for dynamic data were previously reported.15
conversion were 3-5 times higher than those obtained at 50% conversion. Hence, the discrepancy in acceleration factors from the isothermal and dynamic studies is suggested to be attributable to the complexity of the reaction mechanism coupled with different ranges of reaction temperatures.32 In our previous study,16 both for nanoconfined unreacted monocyanate ester and for the nanoconfined cyanurate trimer product, the differences between Tg1 and Tg2 are similar regardless of pore size, backing up the fact that Tg1 and Tg2 represent the more mobile core and less mobile surface layer in a two-layer model.41 Furthermore, the surface layer mobility is dominated by the adjacent core, rather than unconfined bulk or by interactions with the surface. Here we further examine the evolution of Tg2 - Tg1 as a function of conversion, as shown in Figure 11a. All of the values of Tg2 - Tg1 are close, being 28.7 ( 2.2 C, regardless of reaction temperature and regardless of reaction time or conversion, backing up the previous assertion that the surface layer mobility (Tg2) is dominated by the mobility in the adjacent core (Tg1). The difference, Tg2 - Tg1, found here is also similar to the differences found for nanoconfined dicyanate ester, polycyanurate, and polystyrene/o-terphenyl in CPG, which were reported to be 25.4, 23.5, and 38.0 C, respectively.15,12 The thickness of the surface layer associated with Tg2 can be calculated from the two-layer model assuming that the volume of material in a given layer is proportional to the step change of the heat capacity for that layer, that the density of the material does not change along the pore radius, and that the shape of pore is cylindrical12 sffiffiffiffiffiffiffiffiffiffiffi ΔCp1 d ð10Þ ¼ 1r ΔCpT where ΔCp1 is the step change of heat capacity at Tg1, ΔCpT is the total change of heat capacity (ΔCp1 þ ΔCp2), r is the nanopore radius, and d is the surface layer thickness. The square root of the fractional heat capacity change at Tg1 was plotted as a function of conversion in Figure 11b to calculate the thickness of surface layer in nanopores. The resulting surface layer thickness decreases slightly with increasing conversion and gives an average of
Figure 11. (a,top) Difference between Tg1 and Tg2 as a function of conversion (upper figure) for monocyanate ester confined in 13 nm CPG; (b,bottom) square root of the fractional heat capacity change at Tg1 versus conversion (lower figure).
1.1 ( 0.2 nm, in good agreement with previous results16 for various pore sizes for the monocyanate ester reactant and product only.
’ CONCLUSIONS The trimerization reaction kinetics of monocyanate ester are studied using Tg to follow the reaction at various reaction temperatures. Upon nanoconfinement in 13 nm diameter CPG pores, the reaction is significantly accelerated. The activation energies for reaction of the bulk and the nanoconfined monocyanate ester were obtained from both kinetic model and modelfree isoconversion analyses and were found to be the same at 21-23 kcal/mol within experimental error. Previous dynamic data was also analyzed and similar values were obtained. The trimer reaction product crystallizes and then melts in the temperature range from approximately 120 to 150 C for the bulk reaction, whereas crystallization is suppressed in 13 nm CPG. At the reaction temperature of 141 C for the bulk reaction, the crystalline trimer product seems to enhance the reaction rate. As a result, the acceleration factor for the nanoconfined reaction at 141 C shows a lower value than those obtained at higher temperatures 931
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where no trimer crystals exist. Above the trimer melting point, the acceleration factor increases slightly with increasing temperature and is approximately 50 at 200 C. Two glass transition temperatures exist for samples confined in 13 nm CPG consistent with our previous results. The difference Tg2 - Tg1 is found to be independent of reaction temperature and conversion. Assuming that the Tg1 and Tg2 represents a more mobile core and less mobile surface layer, respectively, the mobility in the surface layer appears to be dominated by the mobility of the adjacent core rather than being related to the bulk value or to interfacial interactions. The surface layer thickness decreases slightly with increasing conversion and is an average of 1.1 ( 0.2 nm thick.
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