Introduction

The microvoids in glassy polymers are part of the interchain microspaces in the frozen segmental motions of the main chains.1, 2, 3 The microvoids significantly affect the gas permeation, diffusion and sorption properties of glassy polymers.4, 5, 6 In other words, the gas sorption property of a glassy polymer can provide information about the microvoids. Generally, the gas sorption isotherm of a glassy polymer can be interpreted using the dual-mode sorption model,1, 2, 3, 4, 5, 6, 7 which is represented by the following equation,

where C is the equilibrium sorption amount at pressure p. The subscripts D (Dissolved) and H (Hole) correspond to the Henry and Langmuir sites, respectively. CD and CH are concentrations due to Henry’s law and the Langmuir mode contributions, respectively. kD is Henry’s law solubility coefficient, b is an affinity constant of the Langmuir site and CH′ is the hole saturation constant in the Langmuir sorption mode. The value of CH′ corresponds to the unrelaxed volume (so-called ‘excess free volume’) of a glassy polymer. This volume is defined as a gap between the specific and hypothetical equilibrium super-cooled liquid volumes. The unrelaxed volume increases with the increasing difference between the observation temperature and the glass-transition temperature and is related to the total amount of microvoids. Therefore, one can obtain essential information about the unrelaxed volume and microvoids from the CH and CH′ parameters.

Recently, we demonstrated that 129Xe NMR spectroscopy is a powerful technique for characterizing the higher-ordered structures of polymer solids.8, 9, 10, 11, 12, 13, 14, 15 As the Xe atom has a very large polarizability, the 129Xe NMR signal is sensitive and easily influenced by its environment; specifically, the induced 129Xe NMR chemical shift is strongly altered by the Xe electron density. The NMR chemical shifts for glassy polymers exhibited a nonlinear low-field shift with an increasing amount of Xe sorption because of the fast exchange of Xe between the Henry and Langmuir sites; therefore, we calculated the NMR chemical shifts for each site using the dual-mode sorption parameters. Consequently, we were able to evaluate the mean size of the microvoids in glassy polymers.9 Our reported data for polystyrene (PS), bisphenol A polycarbonate (PC), tetramethyl bisphenol A PC (TMPC) and poly(2,6-dimethyl-1,4-phenylene oxide) (PPO) were similar to data from a related reported technique, positron annihilation lifetime spectroscopy, which suggests that 129Xe NMR spectroscopy is a good method for characterizing microvoids in glassy polymers. Most recently, we have reported the Xe sorption properties and 129Xe NMR spectra of PPO measured at various temperatures.10 By analyzing the 129Xe NMR chemical shift, it was observed that the mean diameter of the microvoids in PPO increases linearly with decreasing temperature, and the extrapolated value at the glass-transition temperature was close to 4.4 Å, which is the diameter of a Xe atom. Furthermore, the characteristic cavity in a crystalline region of poly(4-methyl-1-pentene) (PMP) was investigated using gas permeation and 129Xe NMR measurements of PMP membranes with various degrees of crystallinity.11 The measured size of the cavity in the PMP crystal was consistent with the results from not only crystallographic analysis but also gas permeation and Xe sorption measurements. The size of the molecular cavity in the crystalline syndiotactic PS has also been characterized using 129Xe NMR spectroscopy.12 In addition, the density of the side chain regions in a low-density liquid-crystalline polyester with n-alkyl side chains has been estimated.13 We have also demonstrated that the line width of the 129Xe NMR signal of the 129Xe in this polyester corresponds to its diffusivity.

To establish the microvoid size determination using 129Xe NMR spectroscopy, the accumulation of experimental data is important. Actually, for a miscible polymer blend system, PPO/PS blends, it has been successfully concluded that the contraction of microvoids occurs by blending, based on the Xe sorption properties and the 129Xe NMR chemical shift analysis.14, 15 In this study, a miscible polymer blend system, TMPC/PS blends, was analyzed. The TMPC/PS blend system is a well-known miscible blend, and many studies on this system have been reported elsewhere.16, 17, 18, 19, 20 Using these blends, it becomes easy to control the contents of microvoids, as in the case of PPO/PS blends. However, because the glass-transition temperature of TMPC is lower than that of PPO, the unrelaxed volume and the total amount of microvoids in the TMPC/PS blends are smaller than those of the PPO/PS blends. If the results obtained are similar to those obtained with PPO/PS blends despite the relatively small size of the microvoids in TMPC/PS blends, this study will be a good indicator of the high reliability of microvoid size determination using 129Xe NMR spectroscopy. Therefore, the relationship between variations of microvoids and Xe sorption properties for TMPC/PS blends were investigated using Xe sorption and 129Xe NMR measurements.

Experimental Procedure

Sample films (TMPC/PS ratio=0/100, 20/80, 50/50, 80/20 and 100/0) were prepared using the solution-casting method with chloroform as a co-solvent for TMPC and PS. The film thickness was ∼50–100 μm. Each film was annealed above the glass-transition temperature (Tg) for 3 h and then cooled slowly. The film density was determined using the flotation method with a NaBr aqueous solution at 25 °C.

Xe sorption measurements were performed using a gravimetric sorption apparatus with an electromicrobalance (CAHN 2000, Cahn Instruments, Inc., Cerritos, CA, USA) at 25 °C. After the sorption apparatus containing the film was sufficiently evacuated, the desired pressure of Xe was introduced into the apparatus. The amount of Xe sorbed into the film was determined after correcting for the buoyancy. The Tg of the sample films were measured using a differential scanning calorimeter (DSC-7, Perkin-Elmer Co., Waltham, MA, USA) at a heating rate of 10 °C min−1.

The cut and weighed film samples were packed into a 10-mmф Pyrex NMR sample tube with thick walls (type 513-7 JYH-7, Wilmad-LabGlass, Vineland, NJ, USA) and degassed in vacuo for at least 24 h. A desired amount of Xe (with a natural abundance of 129Xe) was introduced into the NMR tube with the aid of liquid nitrogen, and then the tube was sealed with a Teflon valve. After a sufficient amount of time required to achieve an equilibrium sorption state under isothermal conditions (at 25 °C) had elapsed, the NMR experiment was performed. The internal pressure of this sealed NMR tube was determined by subtracting the amount of Xe sorbed into a sample from the total amount of Xe in the tube. The sorption amount at any pressure can be exactly predicted from the sorption isotherm data, and the total amount of Xe in the tube is easily obtained by weighing. The 129Xe NMR spectrum was recorded on an INOVA400 NMR spectrometer (Agilent Technologies, Ltd., Santa Clara, CA, USA) at 110 MHz and 25 °C using the single pulse method with a 45° pulse. The repetition time was set to be 10 s, and the accumulation times were from 500 to 3000 to obtain a good signal to noise ratio. All of the 129Xe NMR chemical shifts were referenced to an external standard of gaseous 129Xe at zero pressure.

Results and Discussion

The Tg and density values are summarized in Table 1. In the DSC thermograms from all of the blended sample films, only one heat flow jump was observed. Therefore, all of the blended films prepared in this study are miscible, and the observed Tg values were similar compared with those reported in the literature.17 It was also confirmed that all of the sample films were in a glassy state at 25 °C. Figure 1 shows the dependence of the specific volume (Vsp) on the composition of the films, which was determined from the density measurements. The Vsp of the blend is lower than that expected from the simple additive rule of the weight fraction of a pure polymer in a blend and the specific volumes of pure polymers, which is presented as a dotted straight line in Figure 1. Therefore, it can be said that volume contraction results from blending in the TMPC/PS blend system.

Table 1 Glass-transition temperature (Tg) and density of TMPC/PS blend system at 25 °C
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Figure 1
figure 1

Specific volume (Vsp) plotted against the weight fraction of TMPC in the TMPC/PS blend system at 25 °C.

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The Xe sorption isotherms are presented in Figure 2. It is clear that these isotherms are concaved toward the pressure axis. These isotherms could also be explained using the dual-mode sorption model (see equation (1)), and the results of curve fitting are presented in Figure 2 as solid lines. The dual-sorption parameters were determined using the nonlinear least-squares method, and are summarized in Table 2. The composition dependence of b was not confirmed because the b values of pure polymers are similar to each other. However, the kD and CH′ values appeared to show a systematic variation with the polymer ratio. CH′ is a good indicator of microvoids in glassy polymers. Figure 3 shows the plot of CH′ against the volume fraction of TMPC in the blend system. It appears that the obtained CH′ value is smaller than that expected from the simple additive rule for each blend sample, whereas kD generally follows the exponential additive rule. This fact indicates that blending has induced a reduction in the amount of microvoids in the TMPC/PS blend system, whereas the solubility behavior was not remarkably changed by blending. These findings are consistent with the density measurement results.

Figure 2
figure 2

Sorption isotherms of Xe in the TMPC/PS blend system at 25 °C.

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Table 2 Dual-mode sorption parameters of Xe of TMPC/PS blend system at 25 °C
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Figure 3
figure 3

Langmuir saturation constant (CH′) of Xe plotted against the volume fraction of TMPC in the TMPC/PS blend system at 25 °C.

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As an example, Figure 4 shows the 129Xe NMR spectra of 129Xe in a TMPC/PS (=80/20) blend film under various pressures of Xe at 25 °C. It is obvious that the NMR peak shifts to lower magnetic fields with increasing pressures of Xe, and the peak shape is almost symmetric. Similar results were obtained for other samples. These downfield shifts are caused by increasing interactions among the Xe atoms.21, 22 Additionally, these symmetric peaks indicate that Xe atoms, which are dissolved in the samples, diffuse fast and then rapidly exchange between the Henry and Langmuir sorption sites on the NMR time scale.

Figure 4
figure 4

129Xe NMR spectra of the 129Xe in a TMPC/PS (=80/20) blend film under various pressures of Xe at 25 °C.

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Jameson et al.23 reported that the 129Xe NMR chemical shift of gaseous pure Xe linearly shifts to low field with increasing densities in amagat units (1 amagat is the density of a gas under STP conditions) in the low pressure region until ∼100 amagat. Furthermore, Fraissard and collegues21, 22 reported that the chemical shifts of 129Xe in zeolites without strong charges also shift linearly with increasing amounts of Xe sorbed in them. The pressure dependence of the 129Xe NMR chemical shift can be interpreted by the interactions between Xe atoms. The influence of this interaction is basically expressed by the time-averaged distance between them, and this distance can be replaced by frequencies of collisions among them. As a result, the chemical shift shows a linear relationship with the density of Xe, because the probability of three or more body collisions at considerably high densities is ignored. However, the observed 129Xe NMR chemical shifts of all of the sample films prepared in this study exhibit a nonlinear low-field shift with increasing Xe density, that is, the total sorption amount, C. As the total sorption amount (C) for glassy polymers is composed of CD and CH (see equation (1)), it is necessary to individually evaluate the dependencies of CD and CH on the NMR chemical shift of 129Xe. Assuming that there is a fast exchange of Xe atoms between the Henry and Langmuir sites, the observed NMR chemical shift (δobs) appears as a single peak at the resonant position described by

where φD and φH are the fractional concentrations of Xe for the Henry and Langmuir sites and δD and δH are the NMR chemical shifts for the Henry and Langmuir sites, respectively. The definitions of φD and φH are:

These parameters are functions of pressure and can be calculated using the dual-mode sorption parameters (Table 2); therefore, φH is larger than φD in the low pressure region, whereas the opposite relationship is observed in the high pressure region. Under the assumption of a linear low-field shift of Xe sorption amount, δD and δH are individually defined by the following equations,

where δ(Xe)i and δ(S)i are the NMR chemical shifts due to the interactions between the Xe atom and the inner wall of the pore, namely, the polymer sample, and between Xe atoms, Ai is a constant proportional to the concentration of Xe and Ci is the amount of Xe sorbed in site i. Using equations (2), (3), (4), (5)), a set of δobs values at observed pressures were reproduced by substituting suitable values for four unknown parameters, AD, δ(S)D, AH and δ(S)H. These four parameters were determined when the sum of squares of deviation from the experimental data, Σ[(δobscalc−δobsexp)2], reaches a minimum in the variation steps considered by experimental error, which is defined as a digital resolution of ∼0.1 p.p.m. As an example, the results from the pure PS film are plotted against pressure in Figure 5. The relationships between δD–p and δH–p are linear and concave, respectively, which is in agreement with the results of the pressure dependences of CD and CH. However, the calculated values of the observed chemical shift, δobscalc, exhibit good agreement with the corresponding experimental data, δobsexp. From these results, the NMR chemical shift of 129Xe sorbed in a glassy polymer apparently exhibits a nonlinear low-field shift with respect to the total sorption amount, C. Similar results were obtained for the other samples. The parameters in equations (4) and (5) are summarized in Table 3. This result proves that AH is larger than AD. This finding indicates that the dependence of the NMR chemical shift of 129Xe on the Xe density in the Langmuir site is larger than that in the Henry site. In practice, for rubbery polymers that contain ‘only’ Henry sites, the NMR chemical shift of sorbed 129Xe rarely presents a dependency on the Xe density (data not shown), which indicates the relatively large inhibition of the interaction between Xe atoms by the mobile polymer chains. In a similar manner, for a glassy polymer, it can be considered that the local molecular motions of the main chain and/or side chains may provide the Henry-mode sorption site and inhibit the Xe–Xe interaction. As there are no inhibitory factors in the Langmuir-mode sorption site, that is, microvoids, AH becomes larger than AD. In other words, the contribution of the Xe–polymer interaction (which is the frequencies of collision between Xe and polymer) to the 129Xe NMR chemical shift at the Henry site is relatively larger than that at the Langmuir site. Therefore, the δ(S)D values become larger than those of δ(S)H, and the polymer composition dependence of δ(S)D is lower than that of δ(S)H.

Figure 5
figure 5

129Xe NMR chemical shifts of the 129Xe in a PS film plotted against the pressure of Xe at 25 °C.

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Table 3 Parameters of 129Xe NMR chemical shifts and ds of TMPC/PS blend system at 25 °C
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It can be said that the NMR chemical shift extrapolated to CH=0 for the Langmuir site, that is, δ(S)H, reflects the mean size of the hole correlated with the microvoids in the glassy polymer. According to Fraissard and collegues21, 22, when the NMR chemical shift of 129Xe in a micropore of dense materials, such as zeolites, is determined only by the interaction with the walls, the mean free path (λ) is linked to this chemical shift, δ(S). Therefore, δ(S) can be estimated by the mean size of the hole using the following relationship,

where λ is a function of both the shape and dimension of the hole. δ(S) can be experimentally obtained by linear extrapolating to the zero pressure of Xe using the pressure dependence data of chemical shifts. In the case of glassy polymers, the mean size of the microvoids can be estimated by δ(S)H rather than δ(S). The individual shape of the microvoids is not a complete sphere, but the both shapes and directions of the microvoids are random even if the shape is anisotropic, such as an ellipsoidal hole. In addition, Xe atoms experience many microvoids for NMR observation because of their state in diffusion. Therefore, the statistically averaged shape of the considerable number of microvoids from viewpoints of both of space and time can be regarded as a sphere. When the shape of the hole is spherical, λ is derived by

where ds is the diameter of the sphere and dXe is the van der Waals diameter of the Xe atom (4.4 Å). The calculated values of ds are listed in Table 3. The order of the ds value is consistent with those of Tg and CH′ (see Tables 1 and 2). Here, the mean volume of individual microvoids, v (cm3), is calculated from ds. Figure 6 shows the plot of v against the volume fraction of TMPC in the blend system. The v values for the blends are smaller than those predicted by a simple additive rule, which is also the case for the CH′ values (see Figure 3). This finding indicates that there is a decrease in the total amount of microvoids; in other words, CH′ is attributed to contraction of the volume of individual microvoids.

Figure 6
figure 6

The mean volume of individual microvoids (v) plotted against the volume fraction of TMPC in the TMPC/PS blend system at 25 °C.

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Conclusions

In this study, relationships between variations of microvoids and gas sorption properties for a miscible TMPC/PS blend system were investigated using Xe sorption and 129Xe NMR measurements. The CH′ values for the blends were smaller than those expected from a simple additive rule because of the decrease in the total amount of microvoids resulting from blending. The 129Xe NMR spectra of 129Xe in the blends obtained at various pressures exhibited a nonlinear low-field shift because of a fast exchange of Xe between the Henry and Langmuir sites. This behavior is one of the characteristic features of glassy polymers compared to many cases of rubbery polymers and zeolites. From the analysis of δ(S)H, which is the NMR chemical shift that reflects the mean size of the microvoids, it was demonstrated that the mean volume of the individual microvoids varied nonlinearly from 71 Å3 for PS to 124 Å3 for TMPC with respect to the volume fraction of TMPC in the blend, which indicates a blending-induced contraction of the microvoids. For TMPC/PS blends, it is concluded that the contraction of microvoids occurs by blending and affects the gas sorption properties.