Lattice hole theory

The GC-EOS based on a series expansion of the nonrandom lattice-hole theory is written by[l,6],... 

Figure 2.17. Surface tension of linear alkanes as a function of (a) temperature and (b) redueed temperature. Cp Cg, etc. refer to alkanes with 1, 2,. .. CH2 groups per chain. Lattice hole theory, redrawn after Schlangen et al. (J. Phys. Chem. 100 (1996) 3607.)...

We want to pursue the subject by starting with a brief review for the present purposes of the essentials of lattice-hole theory, then follow with a consideration of free-volume mobility connections, and continue with some comparisons of experiment versus theory. Finally, we propose and sketch modifications of the theory. These may open the way to generalizations and more insightful relations to empirical formulations, such as the KAHR model [Kovacs et al., 1977, 1979] for volume relaxation. 

Utracki, L. A., and Simha, R., Analytical representation of solutions to lattice-hole theory, Macrvmol. Theory Simul., 10, 17-24 (2001). 

Simha, R., and Xie, H., Applying lattice-hole theory to gas solubility in polymers, Polym. Bull., 40, 329-335 (1998). 

Consolati, G., Quasso, R, Simha, R., and Olson, G. B., On the relation betwen positron annihilation lifetime spectroscopy and lattice-hole-theory free volume, J. Polym. Sci. B, 43, 2225-2229 (2005). 

Experimental data from our laboratories will be shown for an extensive series of amorphous polymers with glass transitions between Tg = 200 and 500 K. We discuss the temperature dependence of the hole-size distribution characterized by its mean and width and compare these dependencies with the hole fraction calculated from the equation of state of the Simha-Somcynsky lattice-hole theory from pressure-volume-temperature PVT) experiments [Simha and Somcynsky, 1969 Simha and Wilson, 1973 Robertson, 1992 Utracki and Simha, 2001]. The same is done for the pressure dependence of the hole free-volume. The free-volume recovery in densified, and gas-exposed polymers are discussed briefly. It is shown that the holes detected by the o-Ps probe can be considered as multivacancies of the S-S lattice. This gives us a chance to estimate reasonable values for the o-Ps hole density. Reasons for its... 

Since Chapter 6 presents detailed discussion of Simha-Somcynsky lattice-hole theory, only an outline is provided here. The theory was derived for spherical and chain molecule fluids [Simha and Somcynsky, 1969 Somcynsky and Simha, 1971]. The model lattice contains a volume fraction y of occupied sites and h= —y of nonoc-cupied sites, or holes. From the Helmholtz free energy, F, the S-S equation of state was obtained in the form of coupled equations ... 

Jain, R. K., Simha, R., Lattice-hole theory Bulk properties and surface tension of oligomers and polymers, Journal of Colloid and Interface Science, 216(2), pp. 424 28 (1999). 

Simha, R., Polymer and oligomer melts, thermodynamics, correlations, and lattice-hole theory. Polymer Engineering and Science, 36(12), pp. 1567-1573 (1996). 

To improve on the cell model, two other classes of models were developed, namely, lattice-fluid and lattice-hole theories. In these theories, vacant cells or holes are introduced into the lattice to describe the extra entropy change in the system as a function of volume and temperature. The lattice size, or cell volume, is fixed so that the changes in volume can only occur by the appearance of new holes, or vacant sites, on the lattice. The most popular theories of such kind were developed by Simha and Somcynsky or Sanchez and Lacombe. ... 

Woodward, C.E. Harris, K.R. (2010). A lattice-hole theory for conductivity in ionic liquid mixtures application to ionic liquid + water mixtures. Phys. Chem. Chem. Phys. 12, 5 (February 2010) 1172-1176. 

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