Enthalpy Recovery of Polystyrene: Does a Long-Term Aging Plateau

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Enthalpy Recovery of Polystyrene: Does a Long-Term Aging Plateau Exist? Yung P. Koh and Sindee L. Simon* Department of Chemical Engineering, Texas Tech University, Lubbock, Texas 79409-3121, United States ABSTRACT: A glass is not in thermodynamic equilibrium below its glass transition temperature (Tg), and consequently, its properties, such as enthalpy, volume, and mechanical properties, evolve toward equilibrium in a process known as structural recovery or physical aging. Several recent studies have suggested that the extrapolated liquid line is not reached even when properties have ceased to evolve. In this work, we present measurements of the enthalpy recovery of polystyrene at an aging temperature 15 °C below the nominal Tg, for aging times up to 1 year. The results indicate that the equilibrium liquid enthalpy line can indeed be reached for aging 15 K below Tg. The results are analyzed in the context of the TNM model of structural recovery.

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INTRODUCTION Upon cooling from the equilibrium liquid state, the mobility of a glass-forming material slows down as volume and enthalpy decrease with decreasing temperature. At the glass transition temperature, Tg, the properties depart from their equilibrium values, and on further cooling, properties follow the glass line.1 Hence, the nonequilibrium thermodynamic properties in the glassy state, such as volume or enthalpy, evolve spontaneously toward their equilibrium values when held isothermally at temperatures below Tg. This process is known as structural recovery or structural relaxation; it can further be classified as volume recovery or enthalpy recovery depending on the thermodynamic property being monitored. The term physical aging is often used to refer to changes in mechanical properties that accompany structural recovery.2 The evolution of structure during structural recovery can be monitored by the fictive temperature (Tf) introduced by Tool.3 For a glass with a given volume or enthalpy at temperature T, Tf is the intersection of the extrapolated glass line and the extrapolated equilibrium liquid line. As shown in Figure 1, Tf decreases with increasing aging time from an initial value of Tfo = Tg. If the extrapolated liquid line is reached at the completion of structural recovery, Tf should cease to evolve when Tf = Ta. However, several enthalpy recovery studies reported that the extrapolated liquid line is not reached even at the completion of enthalpy recovery.4−10 Cowie and co-workers4−7 fit enthalpy loss versus aging time data obtained from differential scanning calorimetry and estimated that the enthalpy loss at equilibrium was significantly less than the expected value based on the extrapolated liquid line. However, Cowie’s results are based on models which have been criticized by us and others.11,12 In addition, their data does not extend to aging times long enough to reach equilibrium, resulting in the inability to corroborate their prediction. © XXXX American Chemical Society

Figure 1. Schematic diagram of the evolution of volume or enthalpy during structural recovery at aging temperature Ta. Tf decreases from an initial value of Tfo (= Tg in this diagram). Boucher et al. suggest that structural recovery ceases at an aging plateau (shown by the green line) before reaching the extrapolated equilibrium line (red dotted line) where Tf = Ta.

Similarly, Andreozzi and co-workers suggested that high molecular weight PMMA did not reach the theoretical equilibrium value9 due to topological constraints, such as chain entanglement, whereas low molecular weight PMMA did.10 Recently, Boucher et al. performed enthalpy recovery experiments for four polymeric samples at aging temperatures up to 43 K below Tg and seemingly achieved equilibrium for Received: May 29, 2013

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aging times shorter than 1 year.13 On the basis of their experimental results, Boucher et al. concluded that enthalpy ceases to evolve at a so-called long-term aging plateau before reaching the extrapolated liquid line (as shown schematically in Figure 1). As a part of their work, elegant up and down jump experiments (asymmetry of approach) were performed to demonstrate that the same equilibrium point was obtained after down and up jumps, thereby confirming the equilibrium enthalpy change. However, these up and down jump experiments appear to have been performed at only one aging temperature, less than 10 K below Tg. At lower aging temperatures, where their aging plateau is observed, both their equilibrium enthalpy loss and their time scales required to reach equilibrium (t∞) are inconsistent with previous works on polystyrene and polycarbonate11,14−16 in which equilibrium was achieved. However, there is no available enthalpy data where equilibrium is reached for aging temperatures more than 10 K below Tg due to the long experimental time scales involved. In this work, we performed measurements of the enthalpy recovery of polystyrene at the aging temperature of 85 °C, 15 °C below the nominal Tg, for aging times up to 1 year in order to check the results of Boucher et al.13 Our results show that the experimental equilibrium enthalpy loss is significantly higher than that of Boucher et al. and indicate that extrapolated liquid enthalpy line can indeed be reached for aging 15 K below Tg. The results are analyzed in the context of the TNM model of structural recovery.

heating scans, respectively. The integration temperature range is Ta < Tg < Tb and is large enough to cover the whole glass transition range including the enthalpy overshoot; Ta = 50 °C and Tb = 125 °C. This method, developed by Petrie,17 has been widely used4−7,9−16,18,19 and minimizes the error introduced by instrument baseline drift. In this work to further minimize error, we superpose the liquid and glass lines of the aged and unaged scans away from the transition by minimizing the sum of χ2. The theoretical enthalpy loss at equilibrium (ΔHa∞) depends on the step change in heat capacity between glass and liquid states as a function of temperature, ΔCp(T), as will be discussed later. To obtain ΔCp(T), the absolute heat capacities in glass and liquid states were measured using the step-scan method, which consists of multiple temperature ramp/isothermal steps. Step sizes were 2 K, holds were 0.8 min at each temperature, and a 10 K/min heating or cooling rate was used between sequential isothermal hold temperatures. The methodology is the same as those used in our previous works to obtain the absolute heat capacities of linear and cyclic alkanes,20 high molecular weight polystyrene,21,22 and germanium selenide alloys23 and is found to be a reliable method in good agreement with data in the literature24,25 for the organic compounds. The DSC temperature was calibrated with indium and a liquid crystal CE-3 ((+)-4-n-hexyloxyphenyl-4′-(2′methylbutyl)biphenyl-4-carboxylate) at 10 K/min on heating. The isothermal calibration, which is relevant for setting the aging temperature Ta, was performed at 0.1 K/min as in other work.14,26 For the step-scan method, the DSC temperature was also calibrated with indium and a liquid crystal CE-3 at 0.1 K/ min, since the relevant data are obtained during the isothermal holds. The heat flow was calibrated with indium, and the heat capacity was calibrated with sapphire. Check runs are made regularly with indium; standard deviations are less than 0.05 K and 0.06 J/g for the melting point and heat of melting, respectively. TNM Model. The TNM (Tool−Narayanaswamy−Moynihan) model successfully describes the kinetic features of structural recovery and the glass transition including nonlinearity and nonexponentiallity.27−29 The TNM model can be written in terms of the fictive temperature (Tf) for a single down jump from equilibrium conditions at To to an aging temperature Ta:

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METHODOLOGY Materials. The polystyrene used in this study is Dylene 8 from Arco Polymers. Dylene 8 has a number-average molecular weight of 92 800 g/mol and a weight-average molecular weight of 221 000 g/mol. This polystyrene is identical to that used in the earlier structural recovery studies by Simon and coworkers.11,14 DSC Measurements. A PerkinElmer Pyris 1 differential scanning calorimeter (DSC) with an ethylene glycol cooling system maintained at 5 °C was used for enthalpy recovery measurements and for measurements of the absolute heat capacity in step-scan mode. All of the measurements were repeated three times using different samples. Prior to all of the experiments, samples were heated to 130 °C and held for 3 min in the DSC to erase the previous thermal history. For aging experiments, samples were then cooled to the aging temperature at 30 K/min, and aging was performed isothermally at 85 °C in the DSC itself for the aging times up to 24 h and in a convection oven, calibrated with a 1560 Black Stack (Hart Scientific),11 for the aging times longer than 24 h. After aging for a specified time ranging from 1 min to 1 year, samples were cooled from the aging temperature to 35 °C at 30 K/min and then heated to 130 °C at 10 K/min to obtain the DSC scan for the aged material. After the aged scan, the sample was cooled from 130 to 35 °C, and then a subsequent heating scan at 10 K/min was performed to obtain the unaged scan. The enthalpy loss (ΔHa) as a function of aging time at a given aging temperature was determined from the difference in the area under aged and unaged scans:17 1 ΔHa = m

∫T

Tb

a

(Q̇ aged−Q̇ unaged) dT

⎡ ⎡ ⎛ Tf = To + ΔT ⎢1 − exp⎢ −⎜ ⎢ ⎢⎣ ⎝ ⎣

∫0

t

β ⎤⎤ d t ⎞ ⎥⎥ ⎟ τo ⎠ ⎥⎦⎥⎦

(2)

where To is the initial temperature, ΔT = Ta − To, τo is the characteristic relaxation time, and β is the nonexponentiality parameter in the Kohlraussch−Williams−Watts (KWW) function.30,31 The characteristic relaxation time τo is assumed to have an Arrhenius-type dependence on both temperature and instantaneous structure (represented by Tf): ⎡ xΔh (1 − x)Δh ⎤ τo = A exp⎢ + ⎥ RTf ⎦ ⎣ RT

(3)

where A is the pre-exponential factor, Δh is the apparent activation energy for structural recovery, R is the gas constant, and x is the nonlinearity parameter which varies from 0 to 1 and partitions the dependence of the relaxation time on temperature and structure. In equilibrium, when Tf = Ta, the relaxation time is expected to follow Williams−Landell−Ferry

(1)

where m is heating rate (10 K/min) and Q̇ aged and Q̇ unaged are the normalized DSC heat flows (W/g) for aged and unaged B

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(WLF)/Vogel−Tammann−Hess−Fulcher (VTHF)32−35 temperature dependence above Tg and then crosses over to an Arrhenius temperature dependence below Tg.11,14,36−38 Such a temperature dependence can be incorporated in the model39 but over a narrow temperature range, as is used in this work, eq 3 is generally found to be a reasonable approximation.14 The fictive temperature, Tf, is related to the enthalpy loss during structural recovery: ΔHa(t ) = −

∫T

Tf

ΔCp dT

fo

(4)

where ΔCp is the difference between liquid heat capacity (Cpl) and glass heat capacity (Cpg) at a given T, and Tfo is the initial fictive temperature, i.e., the fictive temperature of the unaged sample at zero aging time which depends on Ta and the cooling rate. Hence, the TNM model in terms of enthalpy loss (or recovery) can be applied to experimental structural recovery data using eqs 2−4 for the perfect quench condition where no relaxation occurs during cooling. For the case of a finite cooling rate, Boltzmann superposition is used to modify eq 2 by adding the response of a series of small temperature steps.29 The maximum theoretical attainable enthalpy loss at equilibrium, ΔHa∞, is obtained from eq 4 when equilibrium is reached, i.e., when Tf = Ta: ΔHa ∞ = −

∫T

Ta

ΔCp dT

fo

Figure 2. Absolute heat capacity versus temperature for Dylene 8 polystyrene from step-scan runs for three different samples. The extrapolated lines of liquid and glassy heat capacities are obtained by the linear regression with T in K. The literature data complied by Gaur and Wunderlich25 are also shown.

where the temperature is in Kelvin. The theoretical enthalpy loss at equilibrium will be later calculated using this ΔCp. The temperature at which the heat capacity attains a value midway between the extrapolated liquid and glassy values is 100.6 ± 0.2 °C, and the corresponding ΔCp is found to be 0.288 ± 0.005 J/ (g K). Representative DSC heating scans after aging for various times at 85 °C, 15 K below the nominal Tg, are shown in Figure 3. As aging proceeds, the magnitude of the enthalpy overshoot

(5)

The temperature dependence of the equilibrium enthalpy loss is often estimated by integrating eq 5 assuming that ΔCp is a constant value equal to ΔCpg and that Tfo is Tg:4−7,9,10,12,18,19 ΔHa ∞ = ΔCpg(Tg − Ta)

(6)

Equation 6 underestimates the theoretical value of ΔHa∞ at aging temperatures near Tg due to the breadth of glass transition if Tg is taken to be the experimental midpoint value.11 Equation 6 also underestimates ΔHa∞ far below Tg since the temperature dependence of ΔCp is neglected.12 On the other hand, if too high of values for ΔCpg and Tg are used, ΔHa∞ will be overestimated. Hence, eq 5 should be employed with the correct values of ΔCp (= a + bT) and Tfo for the accurate prediction of theoretical value of ΔHa∞, especially at aging temperatures near Tg and more than 10 K below Tg. Inaccurate prediction of the theoretical value of ΔHa∞ can lead to the interpretation that the equilibrium line is not reached at the completion of structural recovery, as discussed by Li and Simon11 and Hutchinson and Kumar,12 in relation to Cowie’s work.4−7 A similar problem seems to be the case in the work of Boucher et al., as will become clear.

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Figure 3. Representative DSC heating scans as a function of aging time for aging up to 1 year at the aging temperature of 85 °C. The aging times are 0, 3, 7, 17, 42, 105, 264, and 664 min, and 3, 7, 13, 30, 180, and 365 days, from the left to right.

RESULTS The absolute heat capacity of Dylene 8 polystyrene is shown in Figure 2 along with the linear regressions of liquid and glass heat capacities for three different samples. The reproducibility (standard deviation) is better than 0.8% for three runs. These step-scan results of Dylene 8 polystyrene are in good agreement with our previous studies of polystyrene,21,22,38 as well as with the compiled data of Gaur and Wunderlich25 as is also shown in Figure 2. The step change in the heat capacity at Tg (ΔCp) was obtained from the linear regression equations of the absolute heat capacity data in liquid and glass states: ΔCp = Cpl − Cpg = 0.781 − 0.00132T

increases and the peak shifts to higher temperatures. At equilibrium, the enthalpy overshoots will cease to evolve, and heating scans will superpose. However, as shown in Figure 3, heating scans after 6 months and 1 year do not superpose indicating the enthalpy is continuing to evolve at 85 °C at these aging times. The time scale is significantly longer than the 36 days that Boucher et al.’s sample13 took to supposedly achieve equilibrium at 85 °C for polystyrene of similar molecular

(7) C

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fixed to 126.6 kK as in our earlier study,11 and the resulting TNM parameters, β, x, and ln(A/s) were found to be 0.69, 0.29, and −334.74, respectively. The values are compared to those obtained in our earlier studies11,14,38 in Table 1 as well as to the range of values reported in the literature compiled by Hodge.40

weight (Mn = 85 000 g/mol); a quantitative comparison of time scales required to reach equilibrium will be shown later. The enthalpy loss (ΔHa) is calculated from the DSC scans using eq 1, as illustrated in Figure 4 for data after 110 days

Table 1. TNM Model Parameters Used To Model the Enthalpy Relaxation Data in This Work, Our Earlier Studies, and Literature parameters

this work

ref 11

ref 14

ref 38

Δh/R (kK) β x ln (A/s)

126.6 0.69 0.29 −334.74

126.6 0.53 0.37 −335.83

100.4 0.74 0.36 −264.25

82.7 0.6 0.43 −217.05

lit. value (ref 40) 53−110 0.55−0.80 0.44−0.52

A direct comparison with the experimental results of Boucher et al.13 is shown in Figure 6 for the aging temperature of 85 °C. Figure 4. Specific heat of representative aged and unaged heating scans. The difference in the areas under the aged and unaged curves represents the enthalpy loss (ΔHa) using the method of Petrie.17

aging. The result as a function of aging time is plotted in Figure 5 with the data at 85 °C from this work shown as red squares.

Figure 6. Comparison of enthalpy loss data of this work with those of Boucher et al.13 for a similar molecular weight polystyrene at the same aging temperature (85 °C). The data of this work are shown as filled red squares (■), and Boucher et al.’s data are shown as blue diamonds (⧫). Lines in the main figure and in the inset are TNM model predictions based on the fit of the data in Figure 5. The inset is the comparison of model predictions with data of Boucher et al. at the aging temperatures of 70, 80, and 93 °C in green, blue, and black, respectively. View in color for best clarity.

Figure 5. Enthalpy loss (ΔHa) as a function of aging time for polystyrene. The data at the aging temperature of 85.0 °C (red squares) are from this work. The other aging temperatures are from our earlier studies: 90.0, 95.6, 99.0, 100.0, and 103.0 °C are from ref 11, and 91.0, 94.0, 95.6, and 97.8 °C are from ref 14. The solid line is the best fit of the TNM model to the experimental data. View in color for best clarity.

The initial evolution shows similar aging behavior, an approximately linear increase in enthalpy recovery with logarithmic aging time for 3 decades. However, at the logarithmic aging times of approximately 5.5, the data of Boucher et al. level off and deviate from the data of this work, the latter of which continue evolving toward the theoretical equilibrium enthalpy loss. The reason for the discrepancy is unclear. At log ta/s = 6.9, the difference between the two data sets is 0.5 J/g, much larger than the error generally incurred in such measurements. The inset in Figure 6 shows a comparison between data of Boucher et al. at three other temperatures and the TNM model predictions based on the fit to our data shown in Figure 5. The data of Boucher et al. agree reasonably well with our TNM model predictions for the initial decades, but the data at 70 and 80 °C deviate from the TNM predictions at ΔHa values near 2.3 J/g.

Data at other aging temperatures between 88 and 103 °C are from our earlier studies on the same polystyrene.11,14 The enthalpy loss increases approximately linearly with the logarithm of the aging time and then levels off at equilibrium. With decreasing aging temperature, the enthalpy loss at equilibrium (ΔHa∞) and the time required to reach equilibrium (t∞) increase. At the lowest temperatures, the slope of the linear region increases slightly and shifts to longer times. The solid lines are the fit of the TNM model using one set of model parameters for all of the data; the activation energy (Δh/R) was D

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The enthalpy loss at equilibrium (ΔHa∞) is plotted as a function of aging temperature in Figure 7 for data from our

Figure 8. Enthalpy versus temperature diagram showing data from this work (■), our earlier studies11,14 (⧫), and work from Rault15 (▼) and Boucher et al.13 (▲). Symbols are the same as in Figure 7. The solid black lines are glassy and liquid enthalpies calculated from absolute heat capacity and TNM model results. The dotted blue line is the long-term aging plateau reported by Boucher et al.13 View in color for best clarity.

Figure 7. Enthalpy loss at equilibrium (ΔHa∞) as a function of temperature for this work (■), our earlier studies11,14 (⧫), and work from Rault15 (▼) and Boucher et al.13 (▲). The black solid line is the theoretical prediction of this work which takes into account the temperature dependence of ΔCp, and the black dotted line is the prediction with fixed value of ΔCp at Tg. The extrapolated enthalpy loss of Boucher et al. is shown as a blue dash-dotted line. The data point from this work is a lower bound. View in color for best clarity.

to perhaps gain insight into the reasons for discrepancies. The time required to reach equilibrium (t∞) is calculated by fitting the enthalpy recovery data near equilibrium to a KWW function and assuming equilibrium is reached when the enthalpy departure from equilibrium δ (= ΔHa∞ − ΔHa) is 0.01 J/g:14

earlier studies11,14 as well as for the results of Rault15 and Boucher et al.13 The one data point from this work is also shown; although it is not yet at equilibrium, it gives a lower bound on the equilibrium enthalpy loss. The theoretical prediction is shown as a solid line and was calculated using eq 5, which includes the temperature dependence of Tfo and ΔCp, obtained from the TNM model and step-scan method, respectively, whereas the dotted line is the TNM prediction obtained using a fixed value of ΔCp at Tg (0.288 J/(g K)). The assumption of constant ΔCp appears to be a reasonable approximation. The theoretical ΔHa∞(T) prediction of Boucher et al., shown as a dash-dotted line, is linear and has a higher slope, due to the use of eq 6 with Tg = 375 K and a higher value of ΔCp (= 0.87 − 0.0015T = 0.308 J/(g K) at T = 375 K). The result is a substantial overestimation of ΔHa∞. In fact, our ΔHa∞ data follow the TNM theoretical prediction for ΔHa∞ within experimental error, and Rault’s results are slightly above the theoretical prediction (perhaps because Rault did not perform an isothermal calibration, which would shift data to slightly higher temperatures). On the other hand, Boucher et al.’s data show a weaker temperature dependence, with values considerably lower than ours below Ta = 90 °C. All of the experimental data in Figure 7 are replotted in an enthalpy vs temperature diagram in Figure 8. It should be emphasized that Figure 8 is not a schematic diagram. Rather, the enthalpy as a function of temperature is based on the absolute heat capacity data. The enthalpy diagram confirms that our enthalpy recovery results do not show the long-term aging plateau of Boucher et al. Instead, our results and Rault’s suggest that the equilibrium liquid enthalpy line is indeed reached for aging below Tg. In addition to the differences in ΔHa∞ between our data, Rault’s, and Boucher et al.’s, it is of interest to compare the time required to reach equilibrium between these data sets in order

⎡ ⎛ δ ⎞⎤1/ β t∞ = τo⎢ln⎜ o ⎟⎥ ⎣ ⎝ 0.01 ⎠⎦

(8)

where the relaxation time τo, initial enthalpy departure δo, and nonexponentiallity parameter β are the KWW fitting parameters fit to each relaxation curve near equilibrium. It is emphasized that the KWW function has no predictive value, but it is able to well describe the data near equilibrium and, hence, to give t∞ values. The dependence of the time required to reach equilibrium on aging temperature is shown in Figure 9 for our earlier data,11,14 along with results based on our fitting of the data of Rault15 and Boucher et al.13 The error bars are based on the standard deviation of KWW fitting parameters. The time required to reach equilibrium for our studies and Rault’s are in good agreement, whereas values from Boucher et al.’s work are over 1 decade smaller at and below 90 °C. As previously emphasized, the data obtained at 85 °C has not yet reached its equilibrium state, and hence, the longest aging time (365 days) is a lower bound. Also shown in Figure 9 are the times required to reach equilibrium as predicted by the Arrhenius TNM and Vogel−Tammann−Hess− Fulcher (VTHF)33−35 equations, as represented by solid and dotted lines, respectively. Our and Rault’s data follow the Arrhenius TNM temperature dependence due to the limited temperature range of the data, and the equilibrium time scales for both of these sets of data also deviate from VTHF as previously discussed.36−38 In addition to reporting an aging plateau for polystyrene, Boucher et al. also reported aging plateaus for polycarbonate and poly(methyl methacrylate). We have shown that their polystyrene data is inconsistent with ours and that in the literature. As a part of this work, we also compare their polycarbonate data to that in the literature. The enthalpy loss at E

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Figure 9. Logarithmic time required to reach equilibrium as a function of aging temperature for our earlier studies11,14 (⧫) and work from Rault15 (▼) and Boucher et al.13 (▲). The solid line is the TNM model with Δh/R = 126.6 kK, and the dotted line is the VTHF equation with parameters from our earlier study.14 The experimental data of this work (■) is a lower bound. View in color for best clarity.

equilibrium (ΔHa∞) and the time required to reach equilibrium (t∞) for polycarbonate are compared in Figure 10 for data from Rault,15 Bauwens-Crowet and Bauwens,16 and Boucher et al.13 Although the times required to reach equilibrium at Ta ≥ 135 °C from the work of Boucher et al. are in reasonable agreement with literature data, their enthalpy losses at equilibrium have a much weaker temperature dependence. Again there is a significant difference between the theoretical equilibrium enthalpy loss estimated11 using the TNM model and eq 5, given by the dotted lines, and the theoretical line published by Boucher et al. using eq 6 and shown by the dash-dotted line. The TNM model prediction used parameters from the literature (Δh/R = 150 kK, x = 0.19, β = 0.46, ln(A/s) = −355.8,15 and ΔCp = 0.23 J/(g K)41), whereas Boucher et al. used Tg = 419 K and ΔCp = 0.52 − 0.0006 T = 0.269 J/(g K) at T = 419 K. It is emphasized that Boucher et al.’s interpretation of an aging plateau for their polycarbonate data arises in part from their incorrect theoretical ΔHa∞ vs temperature line, in addition to questions surrounding whether equilibrium was reached at their lowest aging temperatures.

Figure 10. Aging temperature dependences of enthalpy loss at equilibrium (top figure) and the time required to reach equilibrium (bottom figure) for polycarbonate. Data are shown from the work of Bauwens-Crowet and Bauwens16 (⧫), Rault15 (▼), and Boucher et al.13 (▲). The black dotted lines are the TNM model predictions, and the blue dash-dotted line in the upper figure is the extrapolated enthalpy loss of Boucher et al.13 View in color for best clarity.

from a problem with their measured equilibrium enthalpy losses coupled with an incorrect theoretical prediction. A similar issue appears to be the case for their polycarbonate data based on comparisons with the literature data and the TNM prediction.

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CONCLUSIONS Enthalpy recovery of polystyrene was investigated at the aging temperature of 85 °C (15 K below the nominal Tg) for aging times up to 1 year using DSC in order to test the idea of an aging plateau suggested by Boucher et al. and to examine whether the extrapolated liquid enthalpy line is reached when enthalpy ceases to evolve. We find no indication of an aging plateau, and our data indicate that the extrapolated liquid line can be attained. We then compare our enthalpy loss vs logarithmic aging time data with Boucher et al.’s and find that the two data sets are consistent for the initial few decades, but Boucher et al.’s data deviate from ours at their plateau. We also compared the results of Boucher et al.13 with both our results and those of Rault in terms of the enthalpy loss at equilibrium (ΔHa∞) and the time required to reach equilibrium (t∞); both ΔHa∞ and t∞ from Boucher et al. show significant discrepancies at aging temperatures below 90 °C. Boucher et al.’s interpretation of a long-term aging plateau seems to arise

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AUTHOR INFORMATION

Corresponding Author

*E-mail [email protected] (S.L.S.). Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS The authors gratefully acknowledge funding from NSF DMR1006972. REFERENCES

(1) McKenna, G. B. In Booth, C., Price, C., Eds.; Comprehensive Polymer Science Polymer Properties; Pergamon Press: Oxford, 1989; Vol. 2.

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dx.doi.org/10.1021/ma4011236 | Macromolecules XXXX, XXX, XXX−XXX