Free volume hole size

Figure 10.2 Correlation of o-Ps lifetime and free volume hole size for molecular solids and zeolites [16].

Muramatsu, M., Okura, M., Kuboyama, K., Ougizawa, T., Yamamoto, T., Nishihara, Y., Saito, Y., Ito, K., Hirata, K., and Kobayashi, Y, Oxygen permeability and free volume hole size in ethylene-vinyl alcohol copolymer film temperature and humidity dependence, Radiat. Phys. Chem., 68, 561-564 (2003). 

Temperature dependence of the free-volume hole size... 

TEMPERATURE DEPENDENCE OF THE FREE-VOLUME HOLE SIZE 431... 

Jean, Y. C., Comments on the paper Can positron annihilation lifetime spectroscopy measure the free-volume hole size distribution in amorphous polymers Macromolecules, 29,5756-5757 (1996). 

These observations were explained in terms of a free-volume treatment that adopts the Grest-Cohen model, in which a system consists of free-volume cells, each having a total hole volume vh. These free-volume cells can be classified as solidlike (n < v c) or liquidlike (w > Vhc), where Vhc is a critical hole volume. Moreover, it is assumed that the free volume associated with a liquidlike cell of the amorphous phase consists of free-volume holes whose size distribution is given by a normal frequency distribution, H vk). This leads to a cumulative distribution function of free-volume hole sizes, r vh), given by... 

In recent years, positron annihilation lifetime (PAL) spectroscopy has been demonstrated to be a special sub-nanometer probe to determine the free-volume hole size, fraction and distribution in a variety of polymers (4-9). In this technique, measured lifetimes and relative intensities of the positron and positronium, Ps (a bound atom which consists of an electron and a positron), are related to the size and fraction of sub-nanometer holes in polymeric materials. Because of the positive-charge nature, the positron and Ps are repelled by the ion core of polymer molecules and trapped in open spaces, such as holes, free volumes, and voids. The observed... 

G. Dlubek, A. P. Clarke, H. M. FretweU, S. B. Dugdale, M. A. Alam, Positron lifetime studies of free volume hole size distribution in glassy polycarbonate and polystyrene, Phys. Stat. Sol. A, 157, 351 (1996). 

Utiu et al. investigated the PFSA/Si02 composites by Xe NMR spectroscopy and relaxometry. The average free volume hole size, estimated by extrapolation of Xe chemical shift to zero pressure, reaches a maximum at... 

Positron Annihilation Lifetime Spectroscopy The principal experiment utilized in examination of the free-volume hole size has been positron annihilation lifetime spectroscopy (PALS), first developed by Kobayashi and co-workers (90,91). Positrons from a Na source are allowed to penetrate the polymer, and the lifetime of single positrons is registered. The... 

Using PALS, Dammert et al. (92) and Yu et al. (93) examined the hole volume of a series of polystyrenes of different tacticity. They arrived at a free-volume hole size distribution maximum of around 110 at room temperature see Rgure 8.24 (92). This corresponds to an effective spherical hole radius of approximately 3 A. While this radius is somewhat larger than the theoretical value of 1.5 A found above, if the holes are actually irregular in shape the values are seen to agree quite well. 

Figure 8.24 PALS study of free volume hole size distribution in polystyrenes and poly(p-methylstyrenes) calculated from lifetime distributions of o-positronium.

A simplified theory was proposed by Brandt, Berko and Walker [104] in which the positron of Ps wave function in the field of the electron was replaced by the wave function of the Ps atom. The Ps wave function was then calculated for different lattice structures in the Wigner-Seitz approximation. This approximation is generally referred to as the free volume model, since the free volume is used as one of the parameters in the calculation. This model relates o-Ps lifetime to the average free volume hole size of the medium, and results construed that the o-Ps lifetime would measure the lattice-Ps interaction. Later, Tabata et al. [105] and Ogata and Tao [106] each adopted similar - but different - approaches by considering a unit cell and Ps located at the center instead of the center of the molecule, as used by Brandt et al. [104]. 

Figure 27.7 (a) Free volume hole size distributions in PS/TMPC blends (b) Calculated inter-... 

PC was exposed to high pressure CO2. The free-volume hole size was observed to monotonically increase with CO2. Upon depressurization, a large hysteresis was seen. After CO2 exposure, the fractional free volume and average hole size were larger. This behavior results from the strong conditioning effect of CO2 that was described in a previous section. 

The results summarized in Table 9 show that intrinsic porosity of the polymer, i.e. the fraction of its total volume accessible to N2 molecules at 77 K, can exceed 20% for the sample conditioned at high propylene pressure and room temperature, decreasing down to ca. 6% upon annealing in vacuum at 373 K. These results allow assuming that the variations in propylene permeability through a membrane described above apparently stem from the changes in the free volume structure, i.e. accessibility of the intrinsic micropores for the gas molecules. Similar conclusion on the expansion of the free volume hole size and the increase in the number of holes upon sorption of CO2 in polycarbonate has been made in [47] on the basis of positron annihilation lifetime spectroscopy investigations. 

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