Xe NMR Chemical Shift in Glassy Polymers - American Chemical

Chapter 31

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Dependence of the Amount of Xe Sorption on the 129Xe NMR Chemical Shift in Glassy Polymers H. Yoshimizu* Graduate School of Engineering, Nagoya Institute of Technology, Gokiso-cho, Showa-ku, Nagoya 466-8555, Japan *E-mail: [email protected]

Microvoids in glassy polymers are considered to be correlated with unrelaxed volume (so-called “excess free volume”). In this article, the microvoids were investigated by Xe sorption and 129Xe NMR measurements. The Xe sorption isotherms of glassy polymers were successfully interpreted by the dual-mode sorption model composed of Henry and Langmuir sorption sites. 129Xe NMR chemical shifts of 129Xe in glassy polymers showed a non-linear low-field shift with increasing amount of Xe sorption because of fast exchange of Xe atoms between the two sites. From the 129Xe NMR chemical shift, we could determine the mean size of the microvoids. In several polymers, this methodology was examined from three perspectives of free volume, viz., thermal expansion, miscibility with reduced free volume in a polymer blend, and specific crystalline structure. From these findings, 129Xe NMR spectroscopy is shown to be a powerful technique to determine the mean size of microvoids in glassy polymers.

Introduction A complete understanding of a solid amorphous polymer at molecular level is very difficult because of the complex static, dynamic, and steric structures present. Yet, it is important to understand the detailed structures of glassy polymers, such as the amount, the size and the shape of inter-spaces between polymer chains, and connectivity among them. These are not only important from an academic point © 2011 American Chemical Society In NMR Spectroscopy of Polymers: Innovative Strategies for Complex Macromolecules; Cheng, H., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 2011.


of view but also relevant to many applications. For example, the design and the development of gas barriers or polymeric separation membranes both need the information on the qualities and the quantities of the inter-space. It is often thought that computational chemistry (such as MD simulations) (1) and positron annihilation lifetime spectroscopy (2) are good approaches for the detailed characterization of the polymeric inter-space. In this article, another method is described, which should be complementary to the above approaches. Xenon is an inert gas and some of its isotopes are NMR active. Through the use of Xe as a gaseous penetrant and an NMR probe, the micro-interspaces within a polymeric material can be characterized from the observed NMR signals. Thus, it is demonstrated here that 129Xe NMR spectroscopy is a powerful technique for the characterization of glassy polymers.

Background of 129Xe NMR 129Xe

is an isotope of xenon with spin number I = 1/2 and a natural abundance of 26.4 %. The relative sensitivity for NMR observation of 129Xe is larger than that of 13C; thus, 129Xe NMR of Xe gas at relatively low pressures can be easily observed with good sensitivity. The gyromagnetic ratio of 129Xe is about 1.1 times larger than that of 13C, indicating that the resonant frequency for 129Xe is close to that for 13C, i.e., easily tunable using standard multinuclear NMR probes in commercial spectrometers. In addition, Xe atom is slightly larger than methane, so it is a suitable probe for the sorption environment experienced by typical gases in polymer membranes. The most attractive aspect of 129Xe NMR is the sensitivity of the shielding to the sorption environment. The shift range of sorbed xenon relative to the resonance of the free gas is well over 200 ppm. Since the Xe atom has a very large polarizability, it is expected that 129Xe NMR signal is sensitive to its environments. Indeed, the induced 129Xe NMR chemical shifts are strongly correlated with the size and the nature of micro-pores, because the interactions with the host system can disturb the Xe electron density. In the case of microporous materials like zeolites, 129Xe NMR chemical shift (δ ) of adsorbed 129Xe obeys the following equation (3–7);

where δ(S) is due to the interactions between Xe and porous inner walls; δ(Xe) corresponds to the interactions among Xe atoms; δ(E), δ(SAS), and δ(M) are the contribution of electric field created by multivalent cations, the interaction of Xe with the strong adsorption site, and the contribution of the magnetic field created by the paramagnetic compensation cations, respectively. Figure 1 shows schematically the relationships between δ and density of Xe. The δ(E), δ(SAS), and δ(M) terms can be ignored for glassy polymers because most of them have no strong charge groups. Therefore, 129Xe NMR chemical shifts of 129Xe sorbed in glassy polymers can be interpreted by only two terms: δ(S) and δ(Xe). As shown in Figure 1, for common polymers the observed δ increases linearly with Xe density. The value of δ(S) can be experimentally determined through linear extrapolation of the data obtained at various pressures of Xe. For zeolites, there are many 510 In NMR Spectroscopy of Polymers: Innovative Strategies for Complex Macromolecules; Cheng, H., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 2011.


reports that δ(S) values of adsorbed 129Xe are strongly correlated with the sizes of micro-cage (3–10). Similarly it is possible to characterize the mean sizes of micro-interspaces between polymer chains using δ(S) values.

Figure 1. Schematic representation of the relationships between 129Xe NMR chemical shift and density of Xe. According to Fraissard et.al., when the NMR chemical shift of 129Xe in zeolites is only determined by the collisions with the walls, where disturbances due to paramagnetic species or electric fields (δ(E), δ(SAS), or δ(M)) are absent or negligible, the mean free path λ is linked to δ(S) in equation [1]. Hence δ(S) can be related to the mean size of the micro cage by the following equation (3, 5).

λ is a function of both the shape and dimension of micro cage. In the case of a sphere, the following relationship has been derived,

where DS is the diameter of the sphere and DXe is the diameter of Xe = 4.4 Å. When the shape of the cage is cylindrical, the diameter of crosssection, λ is related to DC as follows,

Usually, the average shape of micro inter-spaces in the glassy polymer is assumed to be spherical because of random coil conformations. However, in the crystalline structures of helical rigid rod chains, the shape of inter space in chain bundles should be closer to cylindrical. It is of interest that some researchers have published many articles on polymeric systems, but they have rarely paid any attention to the density dependence of 129Xe NMR chemical shift (11–16). In order to obtain δ(S) which reflects the micropore size in glassy polymer, it is important to evaluate density 511 In NMR Spectroscopy of Polymers: Innovative Strategies for Complex Macromolecules; Cheng, H., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 2011.

dependence of Xe chemical shift together with the sorptive properties of Xe. In view of the considerations mentioned above, we have tried to investigate the relationship between the 129Xe NMR chemical shift and Xe sorptive properties for glassy polymers in this work.

Gas Sorption Properties of Glassy Polymers


In general, gas sorption of glassy polymers can be rationalized by the dualmode sorption model (17–20), which is represented by the following equation,

where C is the equilibrium sorption amount at pressure p; C was defined as the molar concentration of a gas per unit volume in the polymer, usually expressed in unit of cm3 (STP) / cm3polym , which corresponds to the density of the gas in the polymer. CD is the concentration due to Henry’s law contribution, CH is the concentration due to Langmuir mode contribution, kD is the Henry’s law coefficient, b is the affinity constant of the Langmuir site, and CH′ is the hole saturation constant in the Langmuir sorption mode. The value of CH′ generally corresponds to the unrelaxed volume (so-called “excess free volume”) of glassy polymer as mentioned below. Figure 2 shows a schematic representation of specific volume–temperature (V–T) curve of a typical amorphous polymer together with its occupied volume. In the temperature region for the glassy state, the apparent slope of V–T curve is almost similar as the curve of occupied volume. Thus, the volume of non-equilibrium state (i.e., the unrelaxed volume) linearly increases with decreasing temperature. The polymer free volume has also been discussed by other researchers from the viewpoints of gas sorption properties (19–23). The mechanisms of gas sorption below and above the glass transition temperature, Tg, are different, reflecting the differences in physical structures and thermodynamic states, viz., the non-equilibrium nature of the glassy state and the equilibrium liquid–like nature of the rubbery state. In general, the sorption isotherms for gases in glassy polymers are interpreted in terms of a dual–mode sorption model, based on the assumption that the gas is sorbed both by Henry and Langmuir sorption mechanisms. The former sorption behavior is similar to the gas sorption in rubbery polymers (20), whereas in the latter mechanism, the gas sorbs into the microvoids that exist in the glassy polymer and gets saturated at high pressures.

512 In NMR Spectroscopy of Polymers: Innovative Strategies for Complex Macromolecules; Cheng, H., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 2011.


Figure 2. Schematic representation of specific volume–temperature (V–T) curve of typical amorphous polymer together with its occupied volume.

Therefore, it is possible to understand the behavior of unrelaxed volume by examining the Langmuir sorption mechanism. The presence of unrelaxed volume in glassy polymers plays an important role in the gas sorption as microvoids. As shown in Figure 2, the unrelaxed volume depends on the difference between measurement temperature and Tg. The aim of utilization of 129Xe NMR for glassy polymer is to clarify the relationship between the unrelaxed volume and microvoid size. As another technique, positron annihilation lifetime spectroscopy (PALS) is also useful in investigating size and distribution of free volume in polymers (2, 24–27). PALS can estimate the micro-space whose size is larger than that determined by 129Xe NMR, because positron is smaller than Xe atom. However, PALS technique probably cannot estimate the microvoids in glassy polymers independently, due to the fact that PALS data rely on the very short lifetime of o-positronium and are not affected by molecular motions. This means PALS cannot distinguish between rubbery and glassy states. Figure 3 shows Xe sorption isotherms of polystyrene (PS), polycarbonate (PC), tetramethyl polycarbonate (TMPC), and polyphenyleneoxide (PPO) at 25 °C (28, 29). All sorption isotherms obtained here are concave toward the pressure axis, which is commonly observed in glassy polymers. The solid curves show the results of curve fitting by a non-linear least-square method based on equation [5]. These isotherms can be explained successfully on the basis of the dual-mode sorption model. The calculated parameters are summarized in Table I. The value of CH′ is followed by the fact that the orders of CH′ and temperature difference between Tg and observing temperatures show a similar trend with one another (see Table I). CH′ of PS is the minimum of all samples. It indicates that the total amount of microvoid in PS is the smallest.



Figure 3. Xe sorption isotherms of polystyrene (PS), polycarbonate (PC), tetramethyl polycarbonate (TMPC), and polyphenyleneoxide (PPO) at 25 °C.

Table I. Dual-mode sorption parameters of Xe and glass transition temperature of selected glassy polymers Sample

kD × 102

CH′

b × 103

Tg*

PS

1.1

4.8

8.8

98

PC

1.8

13.3

6.0

160

TMPC

1.5

17.4

6.0

196

PPO

1.7

20.6

7.8

216

kD : [cm3 (STP)/cm3polym.

cmHg], Tg was determined by DSC.

CH′:

[cm3 (STP)/cm3polym.],

b : [1/cmHg], Tg : [°C].

*

Determination of Microvoid Size through 129Xe NMR 129Xe

NMR spectrum obtained for the PS film in a NMR sample tube with thick wall at 25 °C and 760 cmHg of Xe (with natural abundance of 129Xe) by single pulse method is shown in Figure 4 as an example. Internal pressure can be determined from the Xe sorption amount and weight change of the NMR sample tube, and/or the chemical shift value of gaseous 129Xe signal. All 129Xe NMR chemical shifts are referenced to an external standard of zero-pressure of Xe gas. The peak width of the 129Xe in PS is broad compared with that of gaseous xenon, showing considerably restricted motion of Xe atom in PS. It may be emphasized that the peak shape of 129Xe in PS is almost Gaussian, completely symmetric, although two sorption sites in PS are clearly confirmed from Xe sorption isotherm measurements as mentioned above. Similar results are obtained for the other samples and pressure conditions. In view of this interpretation, the pressure dependence of 129Xe NMR chemical shift will be described below. 514 In NMR Spectroscopy of Polymers: Innovative Strategies for Complex Macromolecules; Cheng, H., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 2011.


Figure 4. 129Xe NMR spectrum obtained for the PS film in a NMR sample tube with thick wall at 25 °C and 760 cmHg of Xe (with natural abundance of 129Xe) by single pulse method at 110 MHz. Figure 5 shows the plots of 129Xe NMR chemical shift against total Xe sorption amounts of C for four glassy polymers (28, 29). These downfield shifts with increasing C are caused by increasing of interactions among Xe atoms, i.e., the contribution of term δ(Xe) in equation [1]. The symmetric peak at about 230 ppm as shown in Figure 4 indicates that the Xe atoms that dissolve in glassy polymer diffuse quickly, and exchange rapidly between the Henry and Langmuir sites in the time scale of NMR observation. When contributions of δ(E), δ(SAS), and δ(M) in equation [1] can be ignored, the 129Xe NMR chemical shift shows linear lowfield shift with Xe density. Actually, the chemical shift of gaseous 129Xe shifts to low-field linearly with increasing pressure. Thus, it is expected that 129Xe NMR chemical shifts in the glassy polymers shift linearly with total Xe sorption amounts (C) because Xe density can correspond to C. As shown in Figure 5, however, the shift is non-linear. This finding indicates that the density of Xe in glassy polymer is not proportional to C. Since the value of C for glassy polymer is composed of CD and CH (see equation [5]), which is different from the case of gaseous Xe, it is necessary to evaluate the dependence of 129Xe chemical shifts in glassy polymers on CD and CH.

Figure 5. Plots of 129Xe NMR chemical shift against total Xe sorption amounts (C) for four glassy polymers. 515 In NMR Spectroscopy of Polymers: Innovative Strategies for Complex Macromolecules; Cheng, H., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 2011.


Assuming fast exchange of Xe atoms between Henry and Langmuir sites, the pressure-dependence of NMR chemical shifts for each site can be described via CD and CH at each pressure and calculated using the dual-mode sorption parameters. Thus, the observed NMR chemical shift, δobs. is expressed in the following equations,

where φD and φH are fractional concentrations of Xe for the Henry and Langmuir sites at each pressure, and δD and δD are NMR chemical shifts for the Henry and Langmuir sites, respectively. In subsequent equations, subscripts D and H correspond to the Henry and Langmuir sites, respectively. From the equation [1], NMR chemical shift for each site is explained by following equations,

where AD and AH are constants proportional to Xe concentration for each site, and δ(S)D,H and δ(Xe)D,H are NMR chemical shifts due to the interactions among Xe and porous inner walls, respectively. Using these equations, Xe concentration dependence of NMR chemical shifts for the Henry and the Langmuir sites can be calculated. Figure 6 illustrates the result for PS, and it is noted that the unit of the x axis is the pressure (cm Hg).

Figure 6. The plots of 129Xe NMR chemical shift against pressure of Xe for PS at 25 °C. 516 In NMR Spectroscopy of Polymers: Innovative Strategies for Complex Macromolecules; Cheng, H., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 2011.

Table II. 129Xe NMR parameters of glassy polymers Sample

AD

δ(S)D

AH

δ(S)H

PS

0.012

230.8

5.82

205.4

PC

0.18

225.0

1.59

200.7

TMPC

0.18

210.5

1.88

169.7

PPO

0.67

210.1

1.90

166.4


AD,H : [ppm cm3polym./cm3 (STP)], δ(S)D,H : [ppm].

δD is shifted more downfield than δobs., and δH is more upfield. The parameters for each polymer are summarized in Table II. It can be seen from Table II that AH is larger than AD by about one order of magnitude for each polymer. It indicates that Xe density dependence of the 129Xe NMR chemical shift of 129Xe in the Langmuir site is larger than that in the Henry site. In practice, for rubbery polymer that contains “only” the Henry site, 129Xe NMR chemical shift of sorbed 129Xe rarely reveals Xe density dependence. Moreover, the proportion of Xe in the Langmuir site is larger than that in the Henry site at low-pressure region, while this is opposite at high-pressure region. From these facts, 129Xe NMR chemical shift of 129Xe sorbed in glassy polymer apparently shows non-linear low-field shift against total sorption amount of C. Additionally AH corresponds to total amount of microvoids in the glassy polymer; it becomes small with increasing amount of microvoids. For example, the AH value for PS is larger than that for PPO. It may be said that the NMR chemical shift extrapolated to CH = 0, i.e., δ(S)H, reflects the mean size of microvoids in the glassy polymer. The value of δ(S)H can be substituted in equation [2] and then the diameter of spherical space, D S can be calculated. The results are summarized in Table III together with literature data of PALS (25, 26). It appears that the spherical spaces correlated to microvoids in glassy polymers are on the order of angstroms. The order of mean size of microvoid in four glassy polymers, PPO > TMPC > PC > PS, is consistent with that of Tg and CH′ for Xe as shown in Table I. In addition, DS value is close to the corresponding PALS data, suggesting that the 129Xe NMR spectroscopy is a good method for characterizing microvoids in glassy polymers.

Table III. Mean size of microvoid and/or micro-pore in glassy polymers determined by 129Xe NMR (DS, NMR ) and PALS (DS, PALS ) Sample

*

D

S, NMR

/ [Å]

D

S, PALS

/ [Å]*

PS

5.15

5.76

PC

5.27

5.88

TMPC

6.17

6.40

PPO

6.29

6.56

from references (25) and (26).



Reliability of Microvoid Size Determination by 129Xe NMR This section examines the reliability of microvoid size determination by using the 129Xe NMR chemical shift from three perspectives of free volume, viz., thermal expansion (30), miscibility with reduced free volume in polymer blends (31, 32), and specific crystalline structures (33). First, we show the Xe sorption properties and 129Xe NMR spectra of PPO measured at various temperatures. All the sorption isotherms obtained in temperature range of –60 to +80 °C can be analyzed based on the dual–mode sorption model. The Langmuir saturation constant CH′, which corresponds to unrelaxed volume, is then determined. CH′ increases linearly with decreasing temperature. When this straight line is extrapolated to CH′ = 0, the temperature obtained is almost the same as Tg of PPO as shown in Figure 7(a). Yet, the mean diameter of the microvoids (assuming spheres) of PPO which are determined from the analyses of the pressure-dependence 129Xe NMR chemical shift of the 129Xe in PPO, also increases with decreasing temperature. The straight line drawn in Figure 7(b) is a rough estimation because only a few data points are available, but this suggests that the extrapolated value at Tg is close to 4.4 Å, which is the diameter of Xe atom. These findings support the interpretation of unrelaxed volume as shown above in Figure 2.

Figure 7. Langmuir saturation constant of Xe (CH′) (a) and the mean diameter of individual microvoids (b) of PPO plotted against temperature. The next topic is the relationship between the variations of microvoids and gas sorption properties for miscible PPO / PS blend in the glassy state (31, 32). 518 In NMR Spectroscopy of Polymers: Innovative Strategies for Complex Macromolecules; Cheng, H., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 2011.


This has been investigated by Xe sorption and 129Xe NMR measurements. The composition dependence of the specific volume (Vsp) has been determined from the density measurement. It has been shown that Vsp values of the blends are lower than those calculated by the simple additive rule. Thus, a volume contraction has taken place when blending PPO and PS, and this may be attributed to an attractive interaction between the methyl groups of PPO and the phenyl rings of PS (34). Xe sorption isotherms of this blend system can be interpreted successfully on the basis of the dual-mode sorption model, indicating that both polymers are in the glassy state. In Figure 8(a), CH′ is plotted against the volume fraction of PPO in the blend. It appears that CH′ is smaller than that expected from a simple additive rule drawn as dashed line, whereas kD and b follow additive rules. The data indicate that the decrease in the total amount of microvoids in the blends has occurred by blending, which is consistent with the result of the density measurement. 129Xe NMR spectra of 129Xe in the blends show a non-linear low-field shift with increasing sorption amount of Xe because of fast exchange of Xe atoms between Henry and Langmuir sites. From the analysis of 129Xe NMR chemical shifts, it has been found that the mean volume of individual microvoids (v) varies with a negative deviation versus volume fraction of PPO in the blend as well as versus Vsp and CH′ (Figure 8(b)). For PPO / PS blend system, it is confirmed that the contraction of individual microvoids occurs by blending.

Figure 8. Langmuir saturation constant of Xe (CH′) (a) and the mean volume of individual microvoids (v) (b) plotted against volume fraction of PPO in the PPO / PS blend system at 25 °C. Additional data on microvoid size determined by means of 129Xe NMR chemical shift are summarized here. Figure 9 shows the plots of the mean volume of individual microvoids (v) against CH′ (35). A good linear relationship between v and CH′ is obtained. This relationship can be seen as a result of an equation (v = 3.8 x CH′ + 48.8), indicating that the minimum microvoid volume is 48.8 Å3, which is close to that of Xe atom (44.6 Å3). In other words, if the microvoid size is smaller than Xe atom, sorption is impossible. These results make it clear that unrelaxed volume (total amount of microvoids) takes on its value in response to the changing size of individual microvoids, and CH′ is a parameter which 519 In NMR Spectroscopy of Polymers: Innovative Strategies for Complex Macromolecules; Cheng, H., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 2011.


indicates the total amount of microvoids. Also, it is possible that microvoid size can be predicted from CH′.

Figure 9. Plot of the mean volume of individual microvoids (v) against Langmuir saturation constant of Xe (CH′) for many glassy polymers at various temperatures. The final topic in this section is the characteristic cavity in a crystalline part of poly(4-methyl-1-pentene), (PMP) investigated by gas permeation and 129Xe NMR measurements on PMP membranes with various degrees of crystallinity (33). PMP is one of the semi-crystalline polymers and is widely used in industry because of its good transparency, heat stabilty, and solvent-resistance. It is one of the significant properties of PMP that the density of the crystalline region is lower than that of amorphous region at around room temperature. Kusanagi et.al. have investigated the crystalline structure of PMP, which is characterized by molecular chains in 7/2 helical conformation packed in a tetragonal unit cell and concluded that the lower density of crystal region is attributed to a coarse packing of the chains; as a result, the cylindrical cavity with a diameter of about 4 Å is formed in the crystalline phase (36). This fact means that transport of gas and vapor molecules occurs not only in amorphous but also in crystalline regions. Figure 10 presents a schematic model of crystalline PMP as a cross-section of four 7/2 helical chain bundle. It can be expected that small gases can diffuse in the center circle of about 4 Å diameter drawn in the figure. The permeability coefficient extrapolated to 100 % crystallinity, i.e., the permeability coefficient for the cylindrical cavity along the helical PMP chains can be determined from the permeation data of PMP membranes with various degrees of crystallinity. For the cavity, permeability coefficients of He, N2, O2, CH4, and CO2 have shown finite values, whereas those of C3H8 and tert-C4H10 are zero. Xe sorption measurements of PMP membranes lead to the conclusion that Xe with a diameter of 4.4 Å is able to penetrate the cylindrical cavity of crystalline PMP. From the analysis of 129Xe NMR chemical shifts of 129Xe in PMP membranes with various degrees of crystallinity by using equations [2] and [4], it has been able to evaluate the size of the cavity in PMP crystal as about 4.5 Å. This value is consistent with the results of not only crystallographical analysis but also gas permeation and Xe sorption 520 In NMR Spectroscopy of Polymers: Innovative Strategies for Complex Macromolecules; Cheng, H., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 2011.


measurements mentioned above. From the present study, it is concluded that the width of the cylindrical cavity in PMP crystal is about 4.5 Å.

Figure 10. Schematic model of PMP crystal as a cross-section of four 7/2 helical chain bundle: stick (upper) and CPK (lower) models. The circle with a diameter of ~ 4 Å has been drawn in the center of the CPK model.

Concluding Remarks In this article, the potential of 129Xe NMR spectroscopy for the characterization of glassy polymers is demonstrated through the pressure dependence of 129Xe NMR chemical shift. Previously it has been reported that the size of molecular cavity in the crystalline form of syndiotactic polystyrene can be determined by means of 129Xe NMR spectroscopy (37). In our work, 129Xe NMR chemical shift of the 129Xe in rubbery polymers and liquids is shown to depend on Xe concentration, δD, and AD, as mentioned above (Table II and Figure 6). The relationships between 129Xe NMR chemical shift (δ(S) ) of 129Xe in n-alkane liquid (38), and its fractional free volume (Vf ) are very useful in predicting the density of organic and polymeric materials in the liquid and rubbery states. In addition, we successfully reported the estimation of the density of side chain regions in low-density liquid-crystalline polyester with n-alkyl side chain (39, 40). We have also demonstrated that the linewidth of 129Xe NMR signal of the 129Xe in this polyester corresponds to its mobility and (therefore) diffusivity. It is anticipated that 129Xe NMR spectroscopy will be increasingly used in the near future as a sophisticated technique for the characterization of diffusive properties 521 In NMR Spectroscopy of Polymers: Innovative Strategies for Complex Macromolecules; Cheng, H., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 2011.

of polymeric materials and for the determination of microvoid size in glassy polymers.

Acknowledgments


We gratefully acknowledge partial financial support by a Grant-in-Aid for Scientific Research (C), No. 20550186 (2008) from the Japan Society for the Promotion of Science.

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