Free-volume holes

The rate of solvent diffusion through the film depends not only on the temperature and the T of the film but also on the solvent stmcture and solvent-polymer iuteractions. The solvent molecules move through free-volume holes iu the films and the rate of movement is more rapid for small molecules than for large ones. Additionally, linear molecules may diffuse more rapidly because their cross-sectional area is smaller than that of branched-chain isomers. Eor example, although isobutyl acetate (IBAc) [105-46-4] has a higher relative evaporation rate than -butyl acetate... 

Diffusion Molecules of a fluid already inside a polymer at a high-concentration region compared with surrounding regions will diffuse over a finite time away from the high concentration until an equilibrium situation is achieved. If the high concentration is at the surface, diffusion occurs into the bulk. The diffusant molecules move stepwise into free volume holes as they form according to kinetic theory. 

Positrons emitted for a radioactive source (such as 22Na) into a polymeric matrix become thermalized and may annihilate with electrons or form positronium (Ps) (a bound state of an electron and positron). The detailed mechanism and models for the formation of positronium in molecular media can be found in Chapters 4 and 5 of this book. The para-positronium (p-Ps), where the positron and electron have opposite spin, decays quickly via self-annihilation. The long-lived ortho positronium (o-Ps), where the positron and electron have parallel spin, undergo so called pick-off annihilation during collisions with molecules. The o-Ps formed in the matrix is localized in the free volume holes within the polymer. Evidence for the localization of o-Ps in the free volume holes has been found from temperature, pressure, and crystallinity-dependent properties [12-14]. In a vacuum o-Ps has a lifetime of 142.1 ns. In the polymer matrix this lifetime is reduced to between 2 - 4 ns by the so-called pick-off annihilation with electrons from the surrounding molecule. The observed lifetime of the o-Ps (zj) depends on the reciprocal of the integral of the positron (p+(rj) and electron (p.(r)) densities at the region where the annihilation takes place ... 

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

In practice the lifetime distributions are usually obtained using a computer program such as the MELT [21] or CONTIN [22, 23] programs. The reliablity of these programs for measurring the o-PS lifetime distribution in polymers was shown by Cao et al [24]. A detailed description of these methods of data analysis is presented in Chapter 4. The advantage of the continuous lifetime analysis is that one can obtain free volume hole distributions rather that the average values obtained in the finite analysis. 

Alternative ways of determining the free volume fraction without using I3 have also been proposed by Dlubek et al [28], as well as, Brandzuch et al [29], Dlubek et al used the coefficient of thermal expansion of the amorphous regions and hole volume determined from positron data to determine the number density of the free volume holes. Brandzuch et. al. used the coefficient of thermal expansion just above and just below the Tg to estimate the fractional free volumes. This model is based on the assumption that the expansion of the holes of the free volume, as seen by positrons, reflects the expansion of the total volume of the material. 

The affect of polymer stereoregularity in the chains on the PAL data has also been studied. Hamielec et al [56] found what appears to be an increased lifetime (hole size) with increased randomness of the chain configuration in a series of polyvinlychloride (PVC) polymers, despite the large degree of scatter in the sample (probably due to the fact that a series of commercially available products were used.). They however found little correlation with tacticity in polypropylene. More recently a PAL study on a series of very well characterized polystyrene and poly(p-methlystyrene) samples of differing tacticity [57] was performed. In addition to finding that the polystyrene samples have smaller free volume holes than the poly(p-methylstyrene) samples, they found that the syndiotactic samples had broader hole distributions than the attactic samples. 

The variation of I3 on e+ exposure illustrates that after prolonged exposure the I3 values can no longer be considered to be related to the number of free volume holes and therefore equation 6 cannot be used. These effects have also lead a number of authors to completely discount the reliability of equation 6 as a measure of the free volume fractions [49, 75, 78, 79]. Other authors have suggested that Eq. 6 may still be used provided the samples are rejuvenated at high temperatures between each measurement [67],... 

The decrease/increase in I3 on exposure illustrates that after prolonged exposure the I3 values can no longer be considered to be related to the number of free volume holes. Therefore Eq. 6 is not valid after long exposure times. 

Since both positrons and Ps could, be localized in free-volume holes, the data of positron lifetime (t2) and o-Ps bulk lifetime (t3) provide information about the size and distribution of free-volume size as a function of the depth near the surface. Figure 11.6 shows the variation of positron lifetime and o-Ps bulk lifetime vs the depth. A significant increase of lifetimes near the surface shows a larger size of free volumes near the surface than in the bulk. Similar variations vs the positron energy indicates that both positrons and Ps are localized in free volumes and holes. Figure 11.7 shows the distributions of hole size in the polymer from the data of o-Ps lifetime distribution. Near the surface, not only the size is larger than the bulk, the distribution is significantly wider [10]. 

The larger free volume and distribution also indicates a larger fraction of free volume near the surface than in the bulk. According to the WFL theory [43], a larger free volume leads to a lower Tg. Indeed a significant Tg depression (as much as 70 °C) has been reported in the surface of polystyrene by using PAL method [10]. Other studies of polymer surfaces have shown that the size of the free volume holes near the surface of polyethylene [47] and polypropylene [48] are larger than the bulk. 

Okamoto, K., Tanaka, K., Katsube, M., Kita, H., Ito, Y. (1993) Free volume holes of rubbery polymers probed by positron annihilation . Bull. Chem. Soc. 66, 61. 

Jean, Y.C., Yuan, J.-P., Liu, J., Deng, Q., Yang, H. (1995) Correlations between gas permeation and free volume hole properties probed by positron annihilation spectroscopy . J. Poly. Sci..Part B Poly. Phys.33,1. 

El-Samahy, A.E., Abdel-Rehim, N., El-Sayed, A.M.A. (1996) Temperature dependence of free-volume holes in poly(vinyl alcohol) studied by positron annihilation technique . Polymer 37(19), 4413. 

Cao, H., Zhang, R., Yuan, J.P., Huang, C.M., Jean, Y.C., Suzuki, K., Oh-daira, T. (1998) Free-volume hole model for position formation in polymers surface studies . J. Phys. Cond. Mart. 10. 10429. 

Jean, Y.C., Shi, H. (1994) Positron lifetime in an ellipsoidal free-volume hole of polymers . J. Non-cryst. Solids. 806, 172. 

Wang, Z.F. Wang, B. Yang, Y.R. Hu, C.P. Investigation of gas permeation and free volume hole properties of polyurethane membranes by positrons. In Positron Annihilation, ICPA-13, Proceedings, 2004 Vol. 445, 352. 

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). 

MORPHOLOGY OF FREE-VOLUME HOLES IN AMORPHOUS POLYMERS BY MEANS OF POSITRON ANNIHILATION LIFETIME SPECTROSCOPY... 

It can be observed that an infinite channel with a square cross section is obtained from Eq. (10.9) when m oo. Prisms and layered cavities have been used, for example, in structural studies of clays [Joshi et al., 1998 Consolati et al 2002], A discussion of pore-size distributions in low-dielectric thin films [Gidley et al 2000] was based on cubic structures. Of course, other geometries are possible For example, ellipsoidal holes were also considered [Jean and Shi, 1994], in an interesting attempt to frame free-volume holes in semicrystalline polymers subjected to tensile deformation. 

An alternative approach is to make use of the o-Ps intensity h. This parameter has been proposed [Wang et al., 1990] to be linearly correlated to the number density of free-volume holes, so that the free-volume fraction can be written only in terms of parameters derived from PALS ... 

---