A. Melting enthalpies and crystallinity as a function of crystallization time for different crystalline forms in sPS irradiated with gamma rays in air

sPS is known to crystallize rapidly from the melt and tends to crystallize before the crystallization temperature (T _c) is reached. Further, depending on crystallization conditions, crystalline materials in an sPS material may change from one form to another during crystallization. Therefore, the heat flow curve of sPS crystallization is very complex, comprising of multiple overlapping peaks representing various crystalline forms. This intricate behavior often complicates the analysis of sPS crystallization data. When sPS is irradiated with gamma rays, its chemical and morphological properties are greatly changed, and its melting behaviors are markedly altered.^{Reference Liu, Nguyen, Yang and Lee15} Such a strong radiation effect on the microstructure and phase changes makes the study of crystallization kinetics of gamma-irradiated sPS even more challenging. As indicated in the experimental section, to effectively study the crystallization characteristics of gamma-irradiated sPS, we have used a particular heating/cooling/holding scheme to generate resolvable endothermic peaks in the heat flow curves. Figure 1(a) representatively displays such curves in the 250–285 °C range for sPS irradiated with gamma rays in air (air gamma-irradiated sPS). These are the DSC thermograms at four different crystallization times (t) for an sPS sample irradiated at a 400 kGy dose followed by isothermally crystallizing at T _c = 230 °C. It is noted here that because numerous experimental irradiation and crystallization variables were included in this study, unless specified, only representative graphical results are presented in this paper to show the effects of some key variables. Figure 1(a) shows that the DSC curves of air gamma-irradiated sPS material crystallized at 230 °C composed of three endothermic peaks. Similar three melting peak curves were also observed for other T _c values in the 220 °C ≤ T _c ≤ 242 °C range. However, only two melting peaks were detected for DSC curves at T _c = 250 °C and only one peak for T _c = 260 °C. In general, crystallization time, crystallization temperature, and gamma radiation dose had a strong influence on the endothermic peak areas (proportional to crystalline fractions and heats of melting) and crystallization kinetic parameters but imparted only a small effect on the melting peak temperatures of air gamma-irradiated sPS (see Tables I–V).

FIG. 1.

(a) Typical DSC thermograms in the 245–280 °C range for different crystallization times of sPS irradiated in air with gamma rays at, as an example, 400 kGy and isothermally crystallized at 230 °C, showing overlapping melting endothermic peaks, and (b) typical deconvoluted Gaussian functions for sPS irradiated in air with gamma rays at, as an example 800 kGy, and isothermally crystallized at 240 °C for 15 min.

TABLE I.

Effect of crystallization time t (min) on A _i (J/g, °C), T _i (°C), and γ_i (°C) for sPS irradiated in air at 800 kGy and crystallized at 240 °C; i = 1, 2, and 3.

TABLE II.

Effect of crystallization time t (min) on A _i (J/g, °C), T _i (°C), and γ_i (°C) for sPS irradiated at 800 kGy and crystallized at 250 °C; i = 1 and 2.

TABLE III.

Effect of crystallization time t (min) on A _i (J/g, °C) and γ_i (°C) for sPS irradiated at 800 kGy and crystallized at 260 °C; i = 1.

TABLE IV.

Glass transition temperature of sPS, T _g, as a function of Φ.

TABLE V.

Dependence of exponent n and crystallization rate k on T _c and radiation dose for crystalline α in air-irradiated sPS.

As seen in Fig. 1(a), the multiple endothermic peaks corresponding to the melting behavior of various crystalline forms in air gamma-irradiated sPS overlapped with each other. To provide quantitative data for accurately assessing the effects of crystallization and irradiation conditions on the melting enthalpy and the amount of each crystalline form in the gamma-irradiated sPS material, these endothermic peaks were resolved through the use of Eq. (1). The melting enthalpy change with temperature of the endothermic envelop composing of multiple Gaussian distributions is written as:

(1)$${{\Delta H} \over {\Delta T}} = \mathop\sum\limits_{i = 1}^n {{A_i}\exp \left[ { - {{\left( {{{T - {T_i}} \over {{{\rm{\gamma }}_i}}}} \right)}^2}} \right]} + B\quad ,$$

where ΔH, A _i, T _i, and γ_i denote the melting enthalpy fraction corresponding to temperature change from T to T + ΔT, peak amplitude, melting peak temperature, and the Gaussian radius, respectively; B is a constant. Integer n can be 1, 2, or 3, and subscript i corresponds to the ith peak of the endotherm. When n = 3, the endothermic peaks 1, 2, and 3 are designated as P1, P2, and P3 corresponding to the crystalline forms β, α, and β′, respectively.^{Reference Liu, Nguyen, Yang and Lee15}

Figure 1(b) provides an illustration of using Eq. (1) to fit the experimental data for, as an example, an sPS sample gamma-irradiated at 800 kGy and isothermally crystallized at 240 °C for 15 min. Values of the parameters used to fit the experimental data corresponding to this T _c are given in Table I, which also include values for other crystallization periods. Note that at this T _c, three endothermic peaks corresponding to the three crystalline forms are present. All A _i and γ_i values increased with an increase in t, and each melting peak temperature, T _i, raised about 1 °C when t was increased from 5 to 50 min. Tables II and III provide values of parameters A _i, T _i, and γ_i for sPS samples irradiated at the same dose but crystallized at 250 and 260 °C, respectively. For these two high T _c values, the changes of both A _i and γ_i with t followed the same trend with those for T _c at 240 °C but essentially had no effect on T _i. In summary, sPS samples irradiated with gamma rays in air at doses from 0 to 1000 kGy composed three crystalline forms, β, α, and β′ when they are crystallized in the 220–242 °C range. They contained two crystalline forms, α and β, when T _c = 250 °C and had only the β form when T _c = 260 °C.

Using the Gaussian function deconvolution procedure described above, the effects of gamma radiation dose and crystallization conditions (t and T _c) on melting enthalpy, amount of each crystalline form, and crystallization kinetics of air gamma-irradiated sPS were quantitatively investigated. Figure 2 depicts the total melting enthalpy (H) (i.e., sum of all three peaks and is proportional to crystallinity of the sample) with crystallization time for four T _c values. Note that the 250 °C results are displayed in the inset because the crystallization time scale for this T _c is considerably greater than that for T _c at 220, 230, or 240 °C. If data of all four crystallization temperatures were presented in the same graph, the differences between the H versus t curves for the three lower T _c values cannot be readily seen.

FIG. 2.

Plots of total melting enthalpy versus t for sPS irradiated in air with gamma rays: (a) at 400 kGy and isothermally crystallized at different T _c values and (b) at different doses and isothermally crystallized at 260 °C.

Figure 2(a) shows a general S shape curve, similar to that observed for nonirradiated sPS.^{Reference Cimmino, Di Pace, Martuscelli and Silvestre20} However, the induction time (defining here as the time between 0 and the steep rise of the melting enthalpy), the rate of H change with crystallization time, and the time required to reach a constant H value changed greatly with T _c for air gamma-irradiated sPS. The induction period rose, the rate of H change with t decreased, and the time required to complete the crystallization markedly increased with increasing T _c. As revealed in Fig. 2(a), the crystallization started almost immediately at T _c = 220 °C, but it needed an induction period of more than 10 min for this phase change to begin at 250 °C. Similarly, the crystallization time to attain a saturated amount of crystalline material increased with increasing T _c. For example, it took approximately 5 min to complete the crystallization at T _c = 220 or 230 °C but needed nearly 1 and 11 h for all crystalline materials to form in the air gamma-irradiated sPS crystallized at T _c = 250 and 260 °C, respectively. Obviously, the crystallization was faster, and the enthalpy change rate was higher when the difference between the melting temperature and the crystallization temperature was greater.

The effect of gamma radiation dose on melting properties is demonstrated in Fig. 2(b), where the dependence of H on t at different doses is plotted for the highest T _c used in this study (260 °C). The 0 kGy results represent the nonirradiated sPS material. It is interesting to observe from Fig. 2(b) that although the degree of influence is different, an increase in the gamma radiation dose had a similar effect on the H versus t behaviors as an increase in T _c. That is, the induction period and the time required to attain full crystallinity in the sample increased, whereas the rate of H change with t decreased with an increase of the radiation dose. Further, for a given t, the total melting enthalpy increased with decreasing dose. Similar effects have also been observed for other T _c values used in this study (220 °C ≤ T _c ≤ 260 °C).

Figure 3(a) depicts the dependence of the melting peak temperatures, T _i, on T _c for sPS gamma irradiated in air at, as an example, 800 kGy. The results for nonirradiated sPS are presented in Fig. 3(b) for comparison. For both irradiated and nonirradiated sPS materials, T ₁ and T ₂ increased linearly with T _c, but T ₃ was essentially unaffected by T _c. Further, the rate of increase for T ₁ was greater than that for T ₂. For irradiated sPS [Fig. 3(a)], the T ₁ line intercepted with the T ₂ line at approximately 242 °C. The interception between the two melting peak temperatures suggests that the crystalline forms corresponding to T ₁ and T ₂, i.e., β and α, respectively, coexist in an air gamma-irradiated sPS material when it is crystallized at this temperature. This result is different from that for the nonirradiated sPS material, which showed that the T ₂ line was always above the T ₁ line [Fig. 3(b)], similar to that observed by Woo and Wu.^{Reference Woo and Wu21} Experimental data obtained at other T _c values also revealed that the highest melting peak (P3) of an air gamma-irradiated sPS was vanished when T _c > 242 °C, and this result is indicated in Fig. 3(a). The disappearance of P3 suggests that the crystalline form corresponding to this melting peak, i.e., β′, does not exist in the air gamma-irradiated sPS material when it is crystallized above this temperature.

FIG. 3.

Relationship between melting temperatures, T _i, and T _c for (a) sPS irradiated in air with gamma rays and (b) nonirradiated sPS.

The relative amount of crystalline material, X _it, in %, in each of the three melting peaks (P1, P2, and P3) at a crystallization time t was obtained from the area of the ith Gaussian distribution as:

(2)$${X_{it}}\left( \% \right) = {{\int_{ - \infty }^\infty {{\textstyle{{\Delta {H_i}(t)} \over {\Delta T}}}{\rm{d}}T} } \over {\mathop\sum\limits_{i = 1}^n {\int_{ - \infty }^\infty {{\textstyle{{\Delta {H_i}(t)} \over {\Delta T}}}{\rm{d}}T} } }}\quad. $$

The relationship between X _it and t for sPS irradiated with gamma ray in air is representatively displayed in Fig. 4 for two T _c values and at 200 kGy. For T _c at 220 °C [Fig. 4(a)], X _1t values (i.e., crystalline fraction of P1) were small compared with those for X _2t and X _3t at all crystallization times. At this crystallization temperature, both X _1t and X _3t values decreased, and X _2t increased with t. Further, the rates of these changes were greater at shorter crystallization times (<25 min) than at longer ones. Figure 4(a) also showed that, among the three fractions, the relative decrease for X _1t was greatest: it lost nearly 75% of its value after 50 min of crystallization. Similar X _it versus t plots were obtained for other T _c values between 230 and 242 °C and at other gamma doses. The results showed that for all irradiation doses and T _c between 220 and 242 °C, X _1t and X _3t decreased, and X _2t increased, with increasing t. In summary, the amounts of all three crystalline forms in an air gamma-irradiated sPS sample crystallized between 220 and 242 °C varied greatly with t. Further, in this T _c range and for all crystallization times, the fractions of X _3t and X _1t were highest and lowest, respectively, with X _2t fraction was in between. Recalling that X _1t, X _2t, and X _3t are the crystalline contents of the β, α, and β′ forms, respectively, in an sPS material. Thus, an air gamma-irradiated sPS material crystallized for any duration in the 220–242 °C range contains the largest amount of β′ and the smallest amount of β, with the quantity of α falls in between.

FIG. 4.

Variation of crystalline fractions of P1, P2, and P3 with t for sPS irradiated in air with gamma rays at, as an example, 200 kGy and isothermally crystallized at (a) 220 °C and (b) 250 °C (note that only the P1and P2 fractions are shown in Fig. 4(b) because P3 is vanished at 250 °C).

The variations of X _1t and X _2t with t up to 140 min for an sPS sample irradiated at 200 kGy and crystallized at 250 °C is illustrated in Fig. 4(b). Note that at this T _c, which is closer to the 270 °C melting temperature, the X _3t curve disappears regardless of the radiation dose. At this T _c, X _1t decreased and X _2t increased rapidly between 15 and 40 min but slowed down afterward. At low t values (15 and 20 min), X _1t was the largest fraction in an air-gamma irradiated sPS (∼78% after 15 min) but became a minor component at high t values (∼18% after 140 min). However, the quantity of X _2t changed in the opposite direction with crystallization time, from approximately 22% after 15 min to almost 82% after 140 min. As also seen in Fig. 4(b), the X _1t curve intercepted with the X _2t curve (at the 31 min, 50% point). Because the summation of X _1t and X _2t is unity, the X _2t curve can be estimated from the X _1t curve and vice versa. Further, the intercepted time of the X _2t and X _1t curves increased with increasing dose. Other curves of X _1t and X _2t versus t of sPS samples irradiated at other doses and then crystallized at T _c = 250 °C (not shown) displayed similar trends to those of Fig. 4(b).

The effects of radiation dose on X _it at a fixed T _c or t were not well defined. In general, at a fixed t and in the T _c range between 220 and 240 °C, X _1t values at high doses (600 and 800 kGy) tended to be higher than X _1t values for nonirradiated sPS or sPS irradiated at low dose (200 kGy). The opposite was true for X _2t where its values at low doses were higher than those at high doses. The effect of dose on X _3t followed a similar trend to that of X _1t for T _c = 220 and 230 °C. However, gamma radiation dose had a negligible effect on X _3t at T _c =240 °C. For more detailed results on the effects of gamma radiation dose on X _it at various T _c and t values, see supporting Tables I–III.

The glass transition temperatures, T _g, of air gamma-irradiated sPS was also observed to increase slightly with an increase of radiation dose from 99 °C for nonirradiated sPS to 101.8 °C for 800 kGy (supporting Table IV). Although the effect of radiation dose on T _g was small, but the trend was obvious. A rise in T _g with increasing dose suggests a decrease of chain mobility in the irradiated sPS, which was likely a result of an increase in the crosslinking of the sample as the amount of radiation was increased. This relationship between crosslinking and radiation dose may explain the decrease of H with increasing gamma radiation dose observed in Fig. 2(b). Higher crosslinked polymer chains tend to be more difficult to crystallize than lower crosslinked ones. In our previous work,^{Reference Liu, Nguyen, Yang and Lee15} the T _g of sPS irradiated with gamma rays in both vacuum and oxygen was found to decrease with increasing radiation dose, and this was explained as due to an increase of chain scission at higher doses. The contradiction on T _g between this and our previous study^{Reference Liu, Nguyen, Yang and Lee15} probably arose from the dose rate. The dose rate for the previous work was 9.57 kGy/h and that for this study was 30 kGy/h. Janik and Rosiak^{Reference Janik and Rosiak22} and Adem et al.^{Reference Adem, Richards, Burillo and Avalos-Borja23} also have reported similar observation for sPS and suggested that, at high dose rates, polymer chains set in motion and move about before cleavage. But at low dose rates, they are essentially stationary until broken. Therefore, high dose rates tend to cause entanglement of the polymer chains and low dose rates result in chain scissions.

B. Morphological and chemical changes of crystallized air gamma-irradiated sPS

XRD technique was used to follow relative changes of the α and β forms as function of crystallization time for sPS irradiated under different environments and doses. Figure 5 displays the XRD patterns for two different t values for sPS irradiated in air followed by isothermal crystallization at, as an example, 250 °C. The diffraction angles, diffraction planes, and the assignments of the peaks have been given previously.^{Reference Liu, Nguyen, Yang and Lee15} Clearly, under the crystallization conditions used in this experiment, a mixture of α- and β-crystalline forms existed in the gamma-irradiated sPS, consistent with the DSC enthalpy data shown above. For irradiation in air (Fig. 5), the α diffraction peaks at 2θ = 6.7, 11.6, and 13.2° increased and those of the β diffraction peaks at 2θ = 12.3 and 13.6° decreased with increasing t. These results indicated that the crystallinity fractions of the α form increased and those of the β form decreased with increasing t for sPS irradiated in air. These results were consistent with those obtained by DSC as seen in Fig. 4(a).

FIG. 5.

XRD patterns of sPS irradiated in air at 600 kGy and crystallized at 250 °C for two different times.

We have shown previously that FTIR is useful for studies of crystallization behaviors of gamma-irradiated sPS.^{Reference Liu, Nguyen, Yang and Lee15} It can not only characterize the chemical changes caused by the gamma radiation but also effectively follow the evolution of various materials formed during crystallization of the irradiated samples, such as the amorphous material and the α- and β-crystalline forms. Figure 6 presents the FTIR-ATR spectra in the 800–920 cm⁻¹ region for several t values of sPS irradiated in air at, as an example, 800 kGy and then crystallized at 250 °C. This region was selected for analysis because it is sensitive to polymer chain packing and phase changes in sPS.^{Reference Woo and Wu21,Reference Musto, Tavone, Guerra and De Rosa24} The bands at 840 and 905 cm⁻¹ have been assigned to the amorphous material, those at 857 and 911 cm⁻¹ are associated with the β form, and the 901 cm⁻¹ band is attributed to the α form.^{Reference Ho, Lin, Hseih and Chung13,Reference Woo and Wu21} For irradiation in air, the band at 901 cm⁻¹ was more pronounced when t was increased from 20 to 80 min, but the band at 911 cm⁻¹ had the opposite trend. These results indicated that the crystallinity fraction of the β form decreased and that of the α increased with t for air-irradiated sPS. Qualitatively, FTIR results were consistent with XRD and DSC data.

FIG. 6.

FTIR spectra at different crystallization times of sPS irradiated in air at 800 kGy.

C. Crystallization kinetics of sPS irradiated with gamma rays in air

The isothermal crystallization kinetics of sPS irradiated with gamma rays under different environments and doses have been investigated using the Avrami model [Eq. (3)]^{Reference Avrami25–Reference Avrami27}:

(3)$$1 - {X_{it}} = {\rm{exp}}\left( { - {k_i}{t^{{n_i}}}} \right)\quad ,$$

where X _it is the crystalline fraction at time t, k _i is the crystallization rate, and n _i is the exponent related to the growth mode and nucleation mode. Subscript i denotes the melting peak corresponding to the crystalline form in the polymers as stated previously. Although this model was developed for single-phase transformation from one to another, it has successfully been applied for studying the crystallization kinetics of polymorphic nonirradiated sPS.^{Reference Cimmino, Di Pace, Martuscelli and Silvestre20,Reference Wessen28–Reference Wu, Hsu, Chen and Wu30} Equation (3) is valid only for crystal growth. As shown in Fig. 4(a), the amount of X _2t (i.e., crystalline fraction of the α form) increased, but those of the X _1t and X _3t (β and β′ forms) in the 220 °C < T _c < 242 °C range decreased with t. Therefore, Eq. (3) is applied here to study crystallization kinetics of the α form existed in sPS materials irradiated with gamma rays in air. Table V gives n and k values for the α form, as a function of radiation dose and T _c. The exponent n increased with increasing T _c but decreased with increasing radiation dose. This is different from that for nonirradiated sPS, where n was reported to be constant in the T _c ranges of 122–132 °C and 244–252 °C,^{Reference Wang, Huang, Cheng, Cheng and Shong31} and for n is equal to 3 for all T _c values.^{Reference Wessen28} However, the crystallization rate k decreased with an increase of both T _c and radiation dose. Wang et al.^{Reference Wang, Huang, Cheng, Cheng and Shong31} also reported a decrease of crystallization rate with increasing gamma radiation dose. These results suggest that gamma irradiation in air at high dose tends to retard the crystallization of the α form in sPS.

The crystallization half time τ at each temperature was determined using the relation:

(4)$${\rm{\tau }}(T) = {\left[ {\ln 2/k(T)} \right]^{{1 \over n}}}\quad ,$$

and the activation energy of isothermal crystallization of air gamma-irradiated sPS was determined using a modified Arrhenius equation:

(5)$${1 \over {{\rm{\tau }}(T)}} = {1 \over {{{\rm{\tau }}_0}}}{\rm{exp}}\left( { - {U \over {R\left( {T - {T_\infty }} \right)}}} \right){\rm{exp}}\left( { - {A \over {T\left( {{T_{\rm{m}}} - T} \right)}}} \right)\quad ,$$

where τ(T) is the crystallization half time at crystallization temperature T, τ₀ is the preexponent factor, U is the activation energy, R is gas constant, A is the thermodynamic driving force, T _m is the melting temperature, and T _∞ is the temperature in which polymeric chains stop segmental motion. Note that T _∞ is usually taken as T _g − 30 K,^{Reference St. Lawrence and Shinozaki32,Reference Yoshioka and Tashiro33} where T _g is the glass transition temperature. Equation (5) can be rearranged as

(6)$$Z = - {\rm{ln[\tau (T)]}} + {A \mathord{\left/ {\vphantom {A {T(T_{\rm{m}} - T)}}} \right. \kern-\nulldelimiterspace} {T(T_{\rm{m}} - T)}} = \,- {\rm{ln\tau }}_0 \,- {U \mathord{\left/ {\vphantom {U {R(T - T_\infty )}}} \right. \kern-\nulldelimiterspace} {R(T - T_\infty )}}\quad .$$

Figure 7 displays plots of Z versus ${1 \mathord{\left/ {\vphantom {1 {\left( {T - T_\infty } \right)}}} \right. \kern-\nulldelimiterspace} {\left( {T - T_\infty } \right)}}$ for the α-crystalline form in sPS irradiated in air at different radiation doses. U and τ₀ were obtained from the intercept and slope, respectively, of Fig. 7, and A was determined using the least square method described in Ref. Reference St. Lawrence and Shinozaki32. Values of U, τ₀, and A for the α-crystalline form is presented in Table VI. The preexponent factor k ₀, A, and the activation energy U of crystallized air gamma-irradiated sPS increased with increasing dose. The results of U suggested that a higher energy is required to crystallize an sPS material irradiated at a higher dose than a material irradiated at a lower dose. That is, both the rate of crystallization and the crystalline fraction are lower for sPS irradiated with gamma irradiation at higher dose than those exposed to the same radiation at a lower dose, consistent with the results shown in Fig. 2(b). Furthermore, as seen from Table VI, the thermodynamic driving force increases with increasing dose. This is also implied that thermodynamic driving force is required to crystallize an sPS materials irradiated with a higher dose than with a lower dose. Note that if n is constant, Eq. (5) has an alternative form,

(7)$$k(T) = {k_0}\exp \left[ {{{ - U} \over {R(T - {T_\infty })}} - {A \over {T({T_{\rm{m}}}^0 - T)}}} \right]\quad .$$

FIG. 7.

Plots of Z versus 1/(T–T _∞) for α-crystalline form of sPS irradiated in air with gamma rays at different doses.

TABLE VI.

The values of crystallization half time τ₀ (min⁻¹), thermodynamic driving force A (10⁴ × K ²), and activation energy U (kJ) of α form, samples of which are irradiated in air.

Equation (7) was used by Wesson^{Reference Wessen28} and St. Lawrence and Shinozaki^{Reference St. Lawrence and Shinozaki32} for studying crystallization kinetics of sPS.