Introduction

Determining the higher order structures of glassy polymers in detail is notably important, not for only academic purposes but for solid polymeric material applications in many fields. Microvoids form in dense polymer matrices as interspaces between molecular chains, when the polymer becomes glassy and the segmental mobility of the main chains is frozen. Figure 1 schematically represents both a specific volume–temperature, V – T, and occupied volume curve typical of an amorphous polymer. The total amount of microvoids corresponds to the unrelaxed volume, as defined in Figure 1. The unrelaxed volume in the glassy state increases with decreasing temperature until the temperature, T2, reaches the intersection between the hypothetical equilibrium supercooled liquid- and occupied volume–temperature curves. Temperature T2 is defined in thermodynamics as the configuration where entropy becomes zero (that is, it is the temperature where the smallest number of possible configurations form). Generally, evaluating the gas sorption properties of a glassy polymer provides information about the unrelaxed volume and microvoids.

Figure 1
figure 1

Schematic representation of typical specific volume–temperature (bold line) and occupied volume (dotted line) curves for an amorphous polymer. The free volume is defined as the difference between the specific and occupied volumes, and, in the glassy state, includes the unrelaxed volume, which is defined as the gap between the specific and hypothetical equilibrium supercooled liquid (dashed line) volumes. The temperature T2 is defined as the intersection between the volumes of a hypothetical equilibrium supercooled liquid- and the occupied volume–temperature curves.

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The free volume of polymers determined by their gas sorption properties has also been discussed by many researchers.1, 2, 3, 4, 5 The mechanisms of gas sorption below and above Tg are different, which reflects the difference in the microscopic structure of the respective thermodynamic state, namely, the non-equilibrium nature of the glassy state and the equilibrium liquid-like nature of the rubbery state. The sorption isotherms of gases to glassy polymers are interpreted using the dual-mode sorption model, which is based on the assumption that the gas is sorbed via both Henry and Langmuir sorption mechanisms.6 The former sorption mechanism behaves similarly to gas sorption to rubbery polymers, whereas in the latter mechanism, the gas sorbs in microvoids that exist in the glassy polymer, and saturation only occurs at high pressures. Therefore, it is possible to understand the behavior of the unrelaxed volume by examining the Langmuir sorption mechanism. The presence of unrelaxed volume in glassy polymers has an important role in the gas sorption of microvoids.

129Xe NMR spectroscopy is a powerful technique for measuring the micropore size of a material.7, 8, 9, 10, 11, 12, 13, 14, 15, 16 The 129Xe NMR signal is sensitively influenced by its environment, and the induced 129Xe NMR chemical shifts strongly correlate to the microvoid size because certain interactions with the host system disturb the Xe electron density. It has been reported by our research group that the mean microvoid size in glassy polymers can be determined based on the Xe density dependence of the 129Xe NMR chemical shift.17, 18, 19, 20, 21, 22, 23 Therefore, the behavior of the unrelaxed volume can be studied via the microvoid size by investigating the 129Xe NMR spectra below the Tg.

To elucidate the thermal behavior of the unrelaxed volume in poly(2,6-dimethyl1,4-phenylene oxide), PPO, the Xe sorption isotherms of PPO were measured using a quartz crystal microbalance24, 25 across the temperature range of –55 °C to +80 °C. Furthermore, we investigated the relationship between the 129Xe NMR chemical shift and Xe sorption properties across a similar temperature range and attempted to characterize the PPO microvoids.

Experimental Procedure

PPO (Japan GE plastics Co., Osaka, Japan; Tg=216 °C) was used after a standard purification as the glassy polymer in this study. Xe purchased from Nagoya Kosan Co. (Nagoya, Aichi, Japan) (>99.9% purity) was used for the gas sorption. A thin film was prepared by casting a chloroform solution of PPO onto the quartz crystal oscillator. This oscillator was annealed at 220 °C for 3 h, to remove a portion of the residual tension caused by casting. This annealing condition was nearly identical to that in the investigations of PPO by dilatometry reported elsewhere.26, 27 The PPO-coated quartz oscillator was subsequently installed inside a home-made quartz crystal microbalance cell with a metallic seal. After drying at approximately 10−3 mm Hg, Xe was introduced into the cell at various pressures. The resonant frequency was measured by a frequency counter. The frequency change because of gas sorption was converted into a weight variation. The sorption cell was immersed in methanol as a refrigerant, and the temperature variation inside the system was controlled to at least ±1 °C. 129Xe NMR measurements were performed using the following steps. Approximately, 1 g of a film sample was packed into a 10-mmφ Pyrex NMR tube with thick walls, and the desired pressure of Xe (with the natural abundance of 129Xe) was subsequently introduced into the NMR tube. This tube joined a long stainless tube attached to a home-made apparatus equipped with a gas supplier and pressure gauges. The internal pressure was monitored in real time by this apparatus. After a sufficient time to reach sorption equilibrium, the 129Xe NMR spectra were recorded via a single pulse method at 110 MHz on an INOVA 400 plus NMR spectrometer (Agilent Technologies, Ltd., Santa Clara, CA, USA) equipped with a temperature controller. All of the 129Xe NMR chemical shifts were referenced to an external standard of zero-pressure 129Xe gas at each temperature.28

Results and discussion

Estimation of the unrelaxed volume using an equation of state

From a thermodynamics viewpoint, the temperature dependence of the total amount of microvoids at low temperatures is related to the specific volume of the glassy polymer. The unrelaxed volume is defined as the difference between the specific volume of the glassy state and the volume of the supercooled liquid state. Figure 1 shows a schematic representation of the specific and occupied volumes. The occupied volume was calculated in the present study using Sanchez–Lacombe’s equation of state29, 30 based on the V–T curve observed for PPO in the liquid state from published data.26, 27 The calculated temperature dependence of the occupied PPO volume is shown in Figure 2 with its V–T curves. The characteristic temperature, T2, was predicted to be −75±20 °C from the intersection between the temperature dependence of the occupied and specific volumes at the hypothetical equilibrium supercooled liquid state, as shown in Figure 2. A discontinuous change is expected for the temperature dependence of the unrelaxed volume at approximately T2. The temperature dependence of the unrelaxed volume in PPO will be discussed in the following section.

Figure 2
figure 2

Temperature dependence of the observed specific volumerefs 26, 27 and calculated occupied volume for PPO.

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Temperature dependence of sorption properties

The Xe sorption isotherms of PPO at various temperatures are shown in Figure 3. It was observed that the amount of Xe sorption increased with decreasing temperature, and all of the sorption isotherms obtained were concave toward the pressure axis, which is common in glassy polymers. The solid lines through the experimental data in Figure 3 represent the nonlinear least-square curves fit using the dual-mode sorption model.6 The dual-mode sorption model is given by the following equation:

Figure 3
figure 3

Xe sorption isotherms of PPO at various temperatures. The solid lines represent the nonlinear least-square curve fit using the dual-mode sorption model.

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where C is the concentration of the penetrant into the polymer at pressure p. In all equations, the subscripts D (Dissolved) and H (Hole) correspond to the Henry and the Langmuir sites, respectively. C is composed of the concentrations at Henry site, CD, and Langmuir site, CH. Henry’s law parameter, kD, characterizes sorption to the densified equilibrium matrix of the glassy polymer, whereas the Langmuir saturation parameter, CH′, characterizes sorption into the microvoids related to the non-equilibrium unrelaxed volume of the glassy state and b is the Langmuir affinity parameter.

At low temperatures, the sorption isotherm in the high-pressure region is nearly a straight line because nearly all of the microvoids had already saturated with the penetrant atoms at relatively low pressures. The dual-mode sorption parameters estimated by the fitted nonlinear least-square curve are shown in Table 1. The Arrhenius plot of kD indicates a linear relationship with the measured temperature (Figure 4). The heat of solution for a Henry-type sorption mechanism is obtained from the above plot and tabulated in Table 1. This value is comparable to that of carbon dioxide.31, 32

Table 1 Dual-mode sorption parameters, CH′ and kD, and heat of solution, ΔHs, for Xe in polyphenyleneoxide at various temperatures
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Figure 4
figure 4

The Arrhenius plot of kD for Xe in PPO.

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The CH′ value corresponding to the total amount of microvoids in a glassy polymer at a temperature, T, can also be represented by the following equation:33

where Vg and Vl are the specific volumes of the polymer in the glassy and supercooled liquid states, respectively, Vgas is the molar volume of the sorbed gas in a liquid-like state, and αl and αg are the thermal expansion coefficients above and below the Tg, respectively. Equation 2 indicates that CH′ is proportional to the difference between the Tg and T. The CH′ value was plotted against the temperature as shown in Figure 5. It can be observed that the CH′ value for PPO increased linearly with decreasing temperature above a certain temperature. When the straight line obtained for PPO was extrapolated to CH′=0 (the solid lines in Figure 5), the obtained temperature was notably close to the Tg of PPO. This finding indicates the CH′ value is related to the unrelaxed volume.

Figure 5
figure 5

Temperature dependence of CH′ for Xe in PPO.

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Though few data are available, Figure 5 suggests that CH′ corresponds to the unrelaxed volume, which becomes nearly constant below approximately −30 °C. Although this temperature is markedly different from the value of T2 as shown in Figure 2 (–75 °C), we equate this characteristic temperature for PPO to T2. This suggestion should at least be confirmed by observing Xe sorption at lower temperatures in the near future.

Temperature dependence of the microvoid size, as determined by 129Xe NMR

Figure 6 shows the 129Xe NMR spectra of 129Xe in PPO obtained at various pressures using −25 °C as an example. It is obvious that the peak position of the 129Xe in PPO shifts to a low magnetic field with increasing Xe pressure. The peak width narrows with increasing Xe pressure. Similar results were obtained at the other temperatures used in this study. The two diffusion coefficients of the carbon dioxide in PPO were determined elsewhere26 according to the dual-mode sorption and partial immobilization27 models. The diffusion coefficient for the Henry site, DD is larger than that for the Langmuir site, DH. If a similar phenomenon occurs with Xe, the obtained results shown in Figure 6 are reasonable. Specifically, the narrowing of 129Xe NMR peak should be caused by the increasing mean diffusivity of Xe in PPO at higher pressures because the concentration contribution from Henry’s law is larger than that of the Langmuir sorption site.

Figure 6
figure 6

129Xe NMR spectra of 129Xe in both PPO and the gas phase for various pressures of Xe at −25 °C.

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In this study, the symmetrical line shapes and downfield shifts were used to analyze the glassy state based on the microvoid size. The downfield shift was caused by increasing the interactions between Xe atoms. The symmetrical peaks indicate that the Xe atoms quickly dissolve and diffuse throughout the PPO and subsequently exchange rapidly between the Henry and the Langmuir sites on the time scale of these NMR observations. We plotted the observed downfield shifts against the pressure in Figure 7 at each of the temperatures examined. The chemical shift of the gaseous Xe moves downfield linearly with increasing pressure. A similar linear dependence was observed for the NMR chemical shifts of 129Xe in zeolites with no strong charges.34, 35 Therefore, one would observe a linear dependence, assuming the density of Xe is proportional to C. However, Figure 7 shows a linear dependence in the higher pressure/temperature regions but not the lower pressure/temperature regions. These findings show that the Xe density in glassy polymers is not proportional to C. Because the total sorption amount, C, of a glassy polymer consists of the partial sorptions, CD and CH (see Equation 1), it is necessary to evaluate the dependence of the NMR chemical shifts of 129Xe in glassy polymers on CD and CH.

Figure 7
figure 7

Pressure dependence of the 129Xe NMR chemical shift of 129Xe in PPO at various temperatures.

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The NMR chemical shifts for the Henry and Langmuir sites were calculated using the dual-mode sorption parameters and assuming a rapid exchange of the Xe atoms between each site (Table 1).

where δobs. is the observed NMR chemical shift, φD and φH are the fractional concentrations of Xe at the Henry and Langmuir sites at each pressure, respectively, and δD and δH are the NMR chemical shifts at the Henry and the Langmuir sites, respectively. Thus, the 129Xe NMR chemical shift for each site is explained using the following equations, assuming a linear low-field shift in the Xe sorption amount:

where AD and AH are constants proportional to the Xe concentration at each site, CD and CH are the sorption amounts of Xe at each site, and δ(S)D and δ(S)H are the NMR chemical shifts caused by interactions between Xe atoms and the porous inner walls at each site, respectively. Using these equations, the Xe concentration dependence of the NMR chemical shifts of both the Henry and Langmuir sites were calculated. Figure 8 illustrates the result at 25 °C using pressure (atm) as the unit of the horizontal axis. The fractional Xe concentration for the Langmuir site, φH, is larger than that for the Henry site, φD, in the low-pressure region, whereas the opposite is true in the high-pressure region. These observed nonlinear low-field shifts can thus be explained using the two-site model.

Figure 8
figure 8

129Xe NMR chemical shifts of 129Xe in PPO plotted against the Xe pressure at 25 °C. The symbols □, ●, ▪, and ▴ are the observed δ, calculated δ, δD and δH, respectively.

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The NMR chemical shift extrapolated to CH=0, that is, δ(S)H, reflects the mean hole size of the microvoids in the glassy polymer. According to Fraissard and Ito34 and Demarquay and Fraissard,36 when the NMR chemical shift of the 129Xe in zeolites is determined only by collisions with the walls, and disturbances from paramagnetic species or electric fields are either absent or negligible, the mean free path λ is linked to δ(S). Therefore, the mean hole size in the glassy polymer can be estimated using following relation:

where λ is a function of both the hole’s shape and dimensions. Assuming the shape of the hole in the glassy polymer is spherical, the following relation can be derived:

where ds is diameter of the sphere and dXe is the van der Waals diameter of Xe=4.4 Å. The calculated δ(S)H and ds values at each temperature are shown in Table 2. It appears that the ds value increases with decreasing temperature. The mean volume of individual microvoids, v (cm3), was calculated from ds. Figure 9 shows the plot of v versus temperature. The extrapolated volume at the Tg was close to the van der Waals volume of a Xe atom (44.6 × 10−24 cm3). Notably, the temperature-independent regions in Figures 5 and 9 indicate that the value of v remains constant below approximately −30 °C. These findings support the interpretation of the unrelaxed volume as shown in Figures 1 and 2 above.

Table 2 129Xe NMR chemical shifts due to the interaction between Xe atoms and inner walls of microvoids, δ(S)H and the mean diameter of the spherical microvoids, ds of polyphenyleneoxide at various temperatures
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Figure 9
figure 9

Temperature dependence of the mean volume of individual microvoids, v, in PPO determined by analyzing the 129Xe NMR chemical shifts (details were described in the text).

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In this study, we tried to estimate quantitatively the degree of temperature dependence for the unrelaxed volume, CH′, and v for PPO. The ratio of the unrelaxed volume at −25 °C to that at +25 °C was 1.28 based on the experimental and calculated data shown in Figure 2. The ratios for CH′ and v at the same temperature, that is, CH′at −25 °C/CH′at +25 °C and vat −25 °C/vat +25 °C, were 1.32 and 1.22, respectively. It can be observed that these ratios coincide with each other within the error bounds. As the unrelaxed volume (nearly identical to CH′) is the product of both the individual volume and number of microvoids, we conclude that the thermal changes result primarily from the individual sizes of the microvoids.

Conclusions

Sorption of Xe to PPO as a glassy polymer was measured at various temperatures below its Tg. The observed sorption isotherms at each temperature were analyzed using the dual-mode sorption model characteristic of glassy polymers. The Langmuir saturation parameter, CH′, which corresponds to the unrelaxed volume, increased proportionally with decreasing temperature. And then this parameter became a constant value below approximately −30 °C, whereas the Henry’s law parameter, kD, obeys the Arrhenius relation. After analyzing the 129Xe NMR chemical shifts of 129Xe in PPO at various temperatures, the mean volume of the individual microvoids was determined. The temperature dependence of the microvoid size was notably similar to that of the unrelaxed volume and CH′. These findings show that the gas sorption properties of glassy polymers should be interpreted based on the temperature dependence of their unrelaxed volume and microvoids in addition to the thermodynamics of dissolution. Therefore, the 129Xe NMR spectroscopy is a good tool for characterizing microvoids in glassy polymers.