Effects of Preexisting Poly(butylene succinate-co-24

Jan 14, 2014 - Regardless of crystallization conditions, PBHS crystallized first, and PBA must crystallize in the presence of preexisting PBHS crystal...
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Effects of Preexisting Poly(butylene succinate-co-24 mol % hexamethylene succinate) Crystals on the Crystallization Behavior and Crystalline Morphology of Poly(butylene adipate) in Their MeltMiscible Polymer Blend Guyu Wang and Zhaobin Qiu* State Key Laboratory of Chemical Resource Engineering, Key Laboratory of Carbon Fiber and Functional Polymers, Ministry of Education, Beijing University of Chemical Technology, Beijing 100029, China S Supporting Information *

ABSTRACT: The effects of preexisting poly(butylene succinate-co-24 mol % hexamethylene succinate) (PBHS) crystals on the crystallization behavior and crystalline morphology of poly(butylene adipate) (PBA) were studied in their fully biodegradable melt-miscible crystalline/crystalline blend. Regardless of crystallization conditions, PBHS crystallized first, and PBA must crystallize in the presence of preexisting PBHS crystals. The preexisting PBHS crystals may not only enhance the nonisothermal melt crystallization behavior but also favor the nucleation and growth of only α-form crystals of PBA, providing an easy method of controlling the polymorphic crystals of PBA through polymer blending; moreover, the preexisting PBHS crystals could accelerate the overall isothermal melt crystallization process of PBA in the blend. PBA must crystallize as tiny crystals at the same orientation as the crystallites of the host PBHS spherulites in the blend, unlike the spherulitic morphology in its neat state. Both components crystallized separately according to their own crystal structures in the blend.

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INTRODUCTION Depending on blend composition and crystallization conditions, melt-miscible polymer blends consisting of two crystalline polymers may provide various possibilities to study the crystallization behavior and crystalline morphology of crystalline polymer blends, because both components are able to crystallize.1−14 The two components of melt-miscible crystalline/crystalline polymer blends crystallize separately or simultaneously, depending on the differences in melting point (Tm) and crystallization rate of each component in their neat state and in the blends. When the crystallization rate of one component (usually high-Tm component) is significantly faster than that of the other (usually low-Tm component) because of the large difference in Tm, both components can only crystallize separately.2−7 Under most crystallization conditions, the highTm component crystallizes first, and the low-Tm component must crystallize in the presence of the preexisting crystals of high-Tm component. Both the crystalline morphology and crystallization kinetics of the low-Tm component must be obviously influenced by the preexisting crystals of high-Tm component in the blends, showing often some different features to those of neat component.2−7 The two components can crystallize simultaneously for a narrow range of blend compositions at the same crystallization temperature, when their crystallization rates are comparable because of small difference in Tm.8−14 The differences in Tm and crystallization rate of both the components determines the final crystallization behavior and crystalline morphology of melt-miscible crystalline/crystalline polymer blends. Until now, only a small number of melt-miscible crystalline/crystalline polymer blends have been reported; 1−14 however, some of them are fully biodegradable polymer blends.6−9 From the both academic © 2014 American Chemical Society

and practical viewpoints, the crystallization behavior and crystalline morphology studies of such systems are of great interest and importance, because they will in turn influence not only the final physical properties but also the biodegradation behaviors of these fully biodegradable polymer blends.6−9 In this research note, the crystallization behavior and crystalline morphology of a 70/30 poly(butylene adipate) (PBA)/poly(butylene succinate-co-24 mol % hexamethylene succinate) (PBHS) blend (in weight ratio) was investigated. Both PBA and PBHS are biodegradable polyesters, with PBA being the low-Tm component and PBHS being the high-Tm component. The difference in Tm of the two neat components is around 50 °C; therefore, they cannot crystallize simultaneously but only separately, providing an ideal model to study the effects of preexisting crystals of high-Tm component on the crystallization behavior and crystalline morphology of low-Tm component. In addition, depending on crystallization conditions, two crystal modifications, that is, α- or β-form may be developed for PBA.15−19 The thermodynamical stability of αform crystals is higher than that of the β-form crystals, and the degradation rate of the former is faster than that of the latter; therefore, the biodegradation behavior of PBA may be tuned via its polymorphic crystals control.15−19 Thus, PBA/PBHS blend may also be an ideal system to study how the preexisiting crystals of PBHS may affect the polymorphic crystals formation of PBA in their crystalline/crystalline polymer blend. The objective of this research is to investigate the effects of Received: Revised: Accepted: Published: 1712

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Figure 1. (a) DSC cooling traces at 1 °C/min and (b) subsequent heating traces at 20 °C/min of neat PBA, neat PBHS, and their 70/30 blend.

order retardation plate and a temperature controller (Linkam THMS 600). Wide-angle X-ray diffraction (WAXD) experiments were performed on a Rigaku D/Max 2500 VB2+/PC X-ray diffractometer at 40 kV and 200 mA from 5° to 45° at 4°/ min. The samples for the WAXD experiments were crystallized at 35 °C for 3 days in an oven, after they were first pressed on a hot stage at 140 °C for 3 min into films with a thickness of ∼1 mm.

preexisting PBHS crystals on the crystallization behavior, crystalline morphology, and polymorphic crystals control of PBA in their crystalline/crystalline blend after the confirmation of the miscibilty of the two components. For this purpose, a 70/30 PBA/PBHS blend was chosen as a model system, because PBA was the focus of this research as the main component after the formation of PBHS crystals as the minor component in their crystalline/crystalline blend.

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EXPERIMENTAL SECTION PBA (Mw = 1.2 × 104 g/mol) was bought from Sigma-Aldrich (Shanghai) Trading Co., Ltd. PBHS (Mw = 5.2 × 104 g/mol) was synthesized via a two-step melt polycondensation method in our laboratory.20 The film samples of neat PBA, neat PBHS, and a 70/30 PBA/PBHS blend were obtained through a solution and casting method. Chloroform was used as a solvent for both neat components and the blend. The solution was cast on a Petri dish at room temperature, and the resulting films were further dried in vacuum at 30 °C for 3 days after chloroform was evaporated for 1 day in a hood. The nonisothermal melt crystallization and subsequent melting behaviors of neat PBA, neat PBHS, and the blend were measured by a TA Instruments differential scanning calorimeter (DSC) Q100. The samples were first annealed at 140 °C for 3 min to erase any thermal history, cooled to 0 °C at 1 °C/min, and then heated to the melt again at 20 °C/min. The overall isothermal melt crystallization kinetics of neat PBA and its blend was also studied with DSC. Neat PBA was crystallized via one-step crystallization. The sample was crystallized at the chosen crystallization temperature (Tc) for a period of time to ensure complete crystallization, after it was annealed at 140 °C for 3 min to erase any previous thermal history. The blend was crystallized via two-step crystallization. The sample was first crystallized for 10 min at the first crystallization temperature (Tc1), that is, 60 °C for the high-Tm component PBHS to crystallize completely after erasing any previous thermal history and then further cooled to the second crystallization temperature (Tc2) at 60 °C/min for the low-Tm component PBA to crystallize. The so-called two-step isothermal crystallization involved both the first-step crystallization and the second-step crystallization. PBHS crystallized at Tc1 during the first-step crystallization from the homogeneous melt, while PBA crystallized at Tc2 during the second-step crystallization from the melt phase after the previous formation of PBHS crystals at Tc1. An optical microscope (Olympus BX51) was used to study the crystalline morphology, which was equipped with a first

RESULTS AND DISCUSSION Figure S1 of the Supporting Information shows that the melt was single-phased when the blend sample was heated to 140 °C, above Tm of PBHS, indicating that PBHS and PBA were miscible in the melt. Figure S2 of the Supporting Information shows that the equilibrium melting point (Tom) of PBHS in the blend was determined to be 105.1 °C from the Hoffman− Weeks plot, which was lower than that of neat PBHS by ∼5 °C.20 The depression of Tom of PBHS in the blend indicated again that PBHS and PBA were miscible.21 When the blend sample was crystallized at a temperature below Tm of PBHS and above that of PBA, PBA was actually in the melt, forming a typical miscible polymer blend consisting of both crystalline and amorphous components. The effects of PBA on the overall isothermal melt crystallization kinetics, spherulitic morphology, and spherulitic growth rate of PBHS were studied extensively. The results are shown in Figures S3− S5 and Table S1 of the Supporting Information. From these results, the blending with PBA reduced both the overall isothermal melt crystallization rate and spherulitic growth rate of PBHS in the blend, compared with those of neat PBHS; however, the crystallization mechanism of PBHS did not change, and both neat PBHS and the blend showed spherulitic morphology. The focus of this research is to study the effects of preexisting PBHS crystals on the crystallization behavior and crystalline morphology of PBA. The nonisothermal melt crystallization and subsequent melting behaviors of neat PBA, neat PBHS, and their blend were first investigated with DSC. Figure 1a shows the nonisothermal melt crystallization behaviors at a cooling rate of 1 °C/min, while Figure 1b displays the subsequent melting behaviors at a heating rate of 20 °C/min. As shown in Figure 1a, neat PBA exhibited a typical two-stage crystallization behavior. Upon cooling from the melt, neat PBA showed two crystallization peak temperature (Tcc) values of 32.6 and 31.8 °C with a total crystallization enthalpy (ΔHcc) of 66.3 J/g, arising from the α- and β-form crystallization at the higher and lower temperature region, respectively.15−19 There was an 1713

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intersection at about 32.1 °C between the two stages, indicating that a mixture of α- and β-form crystals had developed when neat PBA was crystallized nonisothermally at a slow cooling rate of 1 °C/min. For the 70/30 blend, two crystallization exotherms were observed at higher and lower temperature regions, which originated from the crystallization processes of both crystalline components, respectively. In the 70/30 blend, PBHS showed a Tcc of 54.2 °C with a ΔHcc of 17.6 J/g, while neat PBHS had a Tcc of 74.6 °C with a ΔHcc of 67.1 J/g. Relative to neat PBHS, Tcc shifted apparently downward to a low temperature range in the 70/30 blend, indicating that the nonisothermal melt crystallization of PBHS was suppressed in the blend. It is interesting to note that PBA showed a single Tcc of 34 °C with a ΔHcc of 42.5 J/g in the blend. During the nonisothermal melt crystallization process of the blend at 1 °C/ min, PBHS crystallized first at the higher temperature range; therefore, the preexisting PBHS crystals may favor the nucleation and growth of PBA crystals at the lower temperature range. As a result, blending with PBHS enhanced the nonisothermal melt crystallization of PBA; moreover, Tcc was higher than 32.1 °C in the blend, indicating that only the αform crystals were developed.15−19 Figure 1b shows the subsequent melting behaviors of neat PBA, neat PBHS, and their blend at a heating rate of 20 °C/ min, after they finished the nonisothermal melt crystallization processes at a cooling rate of 1 °C/min. Both neat components showed double melting endotherms, and the blend also displayed double melting endotherms for each component at the low and high temperature range, respectively. For neat PBA and the blend, the two melting peaks were attributed to the fusion of α-form crystals; moreover, the lower melting peak (TmL) was attributed to the original α-form crystals formed during the nonisothermal melt crystallization, while the higher one (TmH) arose from the crystals formed through the melting and recrystallization of α-form crystals during the heating process.15−19 Figure 1b shows that the TmL and TmH values were 46.6 and 51.7 °C, respectively, for neat PBA, while they were increased slightly to be 48.4 and 53.0 °C, respectively, for the blend. Because Tcc was higher in the blend than in neat PBA, the blend sample was crystallized at relatively higher temperature region than neat PBA. As a result, the formed crystals were more perfect in the blend than in PBA; therefore, the TmL and TmH values of the blend were higher than those of neat PBA. Similarly, both neat PBHS and the blend also displayed double melting endotherms, which may well be explained by the melting, recrystallization, and remelting model.20 The TmL and TmH values were 91.2 and 103.4 °C, respectively, for neat PBHS, while they were reduced significantly to be 75.9 and 88.0 °C, respectively, for the blend. Such an apparent depression of Tm of PBHS indicated that the blend was miscible. For comparison, Table 1

summarizes the basic thermal properties of neat PBA, neat PBHS, and their blend after they finished the nonisothermal melt crystallization and subsequent melting processes. The apparent reduction of Tcc and Tm values of PBHS indicated that PBHS and PBA were miscible in the blend, and the nonisothermal melt crystallization behavior of PBHS was suppressed in the blend. On the contrary, both the Tc and Tm values of PBA were slightly higher in the blend than in neat PBA. In brief, blending with crystalline PBHS slightly promoted the nonisothermal melt crystallization of PBA, thereby favoring the formation of α-form crystals of the blend. The nonisothermal melt crystallization process of the 70/30 blend was further investigated with polarized optical microscopy (POM). Figure 2 displays the crystalline morphology evolution of a 70/30 blend during the nonisothermal melt crystallization process at a cooling rate of 1 °C/min. Figure 2a shows that some PBHS spherulites appeared and continued to grow to a size of around 100 μm in diameter when the sample was cooled to 58 °C, while Figure 2b displays that PBHS spherulites filled the whole space when the sample was further cooled to 49 °C, indicating that PBA should reside inside the PBHS spherulites. When the sample was further cooled to 36 °C, Figure 2c shows that PBA started to crystallize randomly within the preexisting PBHS crystals, as evidenced by the increase of brightness of PBHS crystals. Unlike the spherulitic morphology of neat PBA, the PBA component could only crystallize as tiny crystals in the interlamellar and interfibrillar regions of the preexisting PBHS spherulites.1 When the sample was further cooled to 32 °C, Figure 2d illustrates that PBA finished its nonisothermal melt crystallization within the preexisting PBHS crystals and filled the whole sample again. In brief, PBHS and PBA crystallized separately in the blend, and PBA crystallized inside the preexisting PBHS crystals, which is consistent with the DSC results shown in Figure 1. The crystallization behavior and crystalline morphology were studied by DSC and POM for the PBA/PBHS blend in the above section, when it was crystallized from the melt at a cooling rate of 1 °C/min. In this section, the crystalline morphology and overall isothermal melt crystallization kinetics of PBA in the blend were further investigated via a two-step crystallization process. The crystalline morphology of PBA in the blend was investigated with POM via a two-step crystallization process. The two-step crystallization process was as follows. The blend sample was first crystallized at a Tc1 of 65 °C for 150 min for PBHS to ensure complete crystallization and then further crystallized at a Tc2 of 40 °C to observe the crystalline morphology evolution of PBA. Figure 3 illustrates the crystalline morphology evolution of PBA in the blend. Figure 3a shows that PBHS spherulites almost filled the whole space, even though some nonbirefringent space was observed at the spherulitic boundaries. When the blend sample was just cooled to 40 °C, PBA was still in the melt. Therefore, for the 70/30 blend sample, most of the PBA melt should reside in the interlamellar and interfibrillar regions of the preexisting PBHS spherulites, while few of the PBA melt was rejected into the interspherulitic region. With prolonging crystallization time, PBA started to crystallize in the confined space of the preexisting PBHS spherulites. Figure 3b illustrates that the crystallization of PBA started to occur in the interspherulitic regions of the preexisting PBHS spherulites. Figure 3c indicates that PBA continued to crystallize and may even develop inside the PBHS spherulites. Because of their strong birefringence in

Table 1. Summary of Basic Thermal Properties of Neat PBA, Neat PBHS, and Their 70/30 Blend 70/30 blend

Tcc (°C) ΔHcc (J/g) TmL/TmH (°C) ΔHm (J/g)

neat PBA

PBA component

PBHS component

neat PBHS

31.8/32.6 66.3 46.6/51.7 70.6

34.0 42.5 48.4/53.0 45.1

54.2 17.6 75.9/88.0 17.9

74.6 67.1 91.2/103.4 72.6 1714

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Figure 2. Crystalline morphology evolution of a 70/30 blend during the nonisothermal melt crystallization process at 1 °C/min when crystallization temperature reached (a) 58 (b) 49, (c) 36, and (d) 32 °C (same scale bar = 100 μm).

Figure 3. Crystalline morphology evolution of a 70/30 blend crystallized at 40 °C for (a) 0 min, (b) 3 min, (c) 7 min, and (d) 20 min after first crystallizing at 65 °C for 150 min (same scale bar = 50 μm).

the 70/30 blend, the PBA crystals were brighter than those PBHS spherulites. Figure 3c clearly shows that the brightness increased in the area where the crystallization of PBA had occurred and kept unchanged in the region where the growth front of PBA crystals did not reach. It is obvious from Figure 3c that PBA must crystallize at the same orientation as the crystallites of the host PBHS spherulites.1 Figure 3d shows that PBA finished its crystallization inside the preexisting PBHS spherulites, with the PBA crystals filling the whole volume again. Unlike the spherulitic morphology of neat PBA, the spherulitic morphology and growth were not observed for the PBA component of the blend through the two-step crystallization process. PBA was only able to crystallize as

tiny crystals at the boundaries of the spherulites or inside the host spherulites of PBHS. The well-known Avrami equation was used to analyze the overall isothermal melt crystallization kinetics of neat PBA and its 70/30 blend. According to the Avrami equation, the relative degree of crystallinity (Xt) develops with crystallization time (t) as 1 − X t = exp( −kt n)

(1)

where n is the Avrami exponent reflecting the feature of nucleation and growth dimension of the crystals, and k is the crystallization rate constant relating to both nucleation and growth processes.22,23 Crystallization half-life time (t0.5) was 1715

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Figure 4. Avrami plots for (a) neat PBA and (b) a 70/30 blend.

Table 2. Avrami Parameters for Neat PBA and a 70/30 Blend at Various Tc Values neat PBA Tc (°C) 34 36 38 40

n 2.3 2.3 2.3 2.4

−n

k (min ) 4.33 8.06 1.82 2.43

× × × ×

70/30 blend n

1.22 2.55 4.85 10.72

2.3 2.5 2.6 2.5

10 10−2 10−2 10−3

⎛ ln 2 ⎞1/ n ⎜ ⎟ ⎝ k ⎠

6.77 1.95 3.38 5.22

× × × ×

10−1 10−1 10−2 10−3

t0.5 (min) 1.01 1.66 3.23 7.04

thereby accelerating the overall crystallization rate of PBA in the blend. The other factor is that being blended with PBHS may lower the growth rate of the PBA crystals due to a dilution effect in a miscible blend, thereby reducing the overall crystallization rate of PBA. Because the enhanced nucleation rate prevailed against the slower crystal growth rate, the overall crystallization rates were enhanced slightly in the blend than in neat PBA. Figure 5 illustrates the WAXD patterns of neat PBA, neat PBHS, and their blend, where it can be seen that the effect of

used for the discussion of crystallization kinetics, which corresponded to the time required to achieve 50% of the final crystallinity of the samples and could be calculated by the following equation

t0.5 =

k (min−n)

t0.5 (min)

−1

(2)

Figure 4a displays the Avrami plots of neat PBA, which was crystallized in a temperature range of 34 to 40 °C via a one-step crystallization process. Figure 4b illustrates the Avrami plots of the PBA/PBHS blend, which was crystallized in the same temperature range via a two-step crystallization process. Regardless of Tc, a series of almost parallel lines were obtained for both samples, indicating that the isothermal melt crystallization processes of neat PBA and its blend may well be described by the Avrami method. From Figure 4, the Avrami parameters n and k were calculated from the slopes and intercepts, respectively, and are listed in Table 2 for comparison. Regardless of Tc, the average n value was around 2.3 for neat PBA, indicating a three-dimensional spherulitic growth with athermal nucleation crystallization mechanism.24 For the PBA/PBHS blend, a similar average n value of around 2.5 was also found; however, it might not show the same crystallization mechanism as neat PBA, because the previous POM study indicated it did not crystallize according to spherulitic growth. From Table 2, the t0.5 values increased with increasing Tc from 34 to 40 °C for both neat PBA and the PBA/PBHS blend, indicating a reduced crystallization rate because of small supercooling. Table 2 also clearly shows that the t0.5 values were slightly smaller in the blend than in neat PBA at the same Tc, suggesting that the preexisting PBHS crystals had accelerated the crystallization of PBA in the blend. It is essential to discuss the influence of preexisting PBHS crystals on the crystallization kinetics of PBA in the blend, which was crystallized via a two-step crystallization process. PBA must crystallize in a confined space within the preexisting PBHS crystals; therefore, the following two factors may account for the overall crystallization rate of PBA. One factor is that the preexisting PBHS crystals may promote the nucleation of PBA,

Figure 5. WAXD patterns of neat PBA, neat PBHS, and their 70/30 blend isothermally crystallized at 35 °C.

blending another crystalline component on the crystal structure of one component may be obtained clearly. Neat PBA showed three main characteristic diffraction peaks at 21.5°, 22.3°, and 24.1°, corresponding to (110), (020), and (021) planes of αform crystals, respectively, because it was crystallized at 35 °C.15−19 Neat PBHS exhibited three main characteristic diffraction peaks at 19.4°, 21.9°, and 22.5°, which were assigned to (020), (021), and (110) planes, respectively.20 The WAXD pattern of the blend involved all the main diffraction peaks of each neat component. In brief, blending with another crystalline component did not modify the crystal structure of one component, and both components crystallized 1716

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CONCLUSIONS The crystallization behavior and crystalline morphology of PBA were studied in a fully biodegradable melt-miscible 70/30 PBA/ PBHS blend under different crystallization conditions. During the nonisothermal melt crystallization process at a cooling rate of 1 °C/min, the nonisothermal melt crystallization peak temperature was slightly higher in the blend than in neat PBA, because the crystallization of high-Tm component PBHS was prior to that of low-Tm component PBA. The crystalline phase of neat PBA was composed of both α- and β-form crystals, while the preexisting PBHS crystals may favor the nucleation and growth of only α-form crystals of the blend, providing an easy method of controlling the polymorphic behavior of PBA. The isothermal melt crystallization kinetics of PBA in the blend was investigated under two-step crystallization conditions and compared with that of neat PBA crystallized under one-step crystallization condition. The crystallization-half time was shorter in the blend than in neat PBA at the same crystallization temperature, indicating that the preexisting PBHS crystals had enhanced the overall isothermal melt crystallization rate of PBA. Although they showed the similar Avrami exponent values, the blend and neat PBA did not exhibit the same crystallization mechanism. The crystalline morphology studies indicated that PBHS crystallized first and PBA must crystallize in the presence of the preexisting PBHS crystals. PBA started to crystallize randomly within the preexisting PBHS spherulites during the nonisothermal melt crystallization, while the crystallization of PBA started to occur in the interspherulitic regions of the preexisting PBHS spherulites and then continued to develop inside the PBHS spherulites during the two-step crystallization process. Regardless of crystallization conditions, the preexisting PBHS crystals may accelerate the crystallization process of PBA; moreover, PBA did not show spherulitic morphology and growth and must crystallize as tiny crystals at the same orientation as the crystallites of the host PBHS spherulites. The crystal structure study revealed that both PBA and PBHS crystallized separately according to their own crystal structures in the crystalline/crystalline blend.

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REFERENCES

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ASSOCIATED CONTENT

S Supporting Information *

A POM image showing the homogeneous melt of a 70/30 PBA/PBHS blend; the Hoffman−Weeks plot for the determination of equilibrium melting point temperatures of the 70/30 PBA/PBHS blend; Avrami plots for neat PBHS and 70/30 PBA/PBHS blend; spherulitic morphology of neat PBHS and 70/30 PBA/PBHS blend; variation of spherulitic growth rate with crystallization temperature for neat PBHS and 70/30 PBA/PBHS blend; and Avrami parameters for neat PBHS and 70/30 PBA/PBHS blend at various Tc values. This material is available free of charge via the Internet at http:// pubs.acs.org.

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ACKNOWLEDGMENTS

Part of this research was financially supported by the National Natural Science Foundation, China (Grant No. 51221002).

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Fax: +86-10-64413161. Notes

The authors declare no competing financial interest. 1717

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(19) Weng, M.; He, Y.; Qiu, Z. Effect of Uracil on the Isothermal Melt Crystallization Kinetics and Polymorphic Crystals Control of Biodegradable Poly(butylene adipate). Ind. Eng. Chem. Res. 2012, 51, 13862−13868. (20) Wang, G.; Qiu, Z. Synthesis, Crystallization kinetics and Morphology of Novel Biodegradable Poly(butylene succinate-cohexamethylene succinate) Copolyesters. Ind. Eng. Chem. Res. 2012, 51, 16369−16376. (21) Nishi, T.; Wang, T. Melting Point Depression and Kinetic Effects of Cooling on Crystallization in Poly(vinylidene fluoride)Poly(methyl methacrylate) Mixtures. Macromolecules 1975, 8, 909− 915. (22) Avrami, M. Kinetics of Phase Change. II TransformationTime Relations for Random Distribution of Nuclei. J. Chem. Phys. 1940, 8, 212−224. (23) Avrami, M. Granulation, Phase Change, and Microstructure Kinetics of Phase Change. III. J. Chem. Phys. 1941, 9, 177−184. (24) Wunderlich, B. Macromolecular Physics; Academic Press: New York, 1976; Vol. 2, p 147.

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