Simha-Somcynsky

The quantity q has the physical interpretation of the free volume. It is the state variable used in the Simha-Somcynski equilibrium theory of polymeric fluids (Simha and Somcynski, 1969). The new variable p that we adopt has the meaning of the velocity (or momentum) associated with q. 

The physical insight involved in the Simha-Somcynski theory and an additional insight that we need to extend it to the time evolution will now be expressed in the building blocks of (55). We shall construct a particular realization of (55). We begin with the state variables. They have already been specified in (58). 

Lhx = Lnx = 0. The kinematics of q and p is chosen to be the same as if q is the position coordinate and p the momentum associated with it. In other words, whatever is the physical interpretation of q (e.g., free volume in the Simha-Somcynski theory), p is the momentum associated with it. 

Returning now to our more general discussion of cquations-of-state, note that a concise review of cquations-of-state for the PVT behavior of polymers was provided by Zollcr [39], who compared the ability of several equations-of-state (some developed empirically and some developed based on fundamental theoretical considerations) to represent PVT data for homopolymers, copolymers and polymer blends. He concluded [39] that, among theoretically-based equations-of-state, the Simha-Somcynsky equation [40,41] represents the available data best over extended ranges of temperature and pressure. 

Flory-Orwoll-Vrij, 1964] (FOV), [Sanchez-Lacombe, 1976-8] (S-L), and [Simha-Somcynsky, 1969] (S-S). Large deviations (< 0.01 mL/g) were observed for S-G, the two following relationships were useful only at low P and over small P-ranges, whereas S-S consistently provided the best representation of data over extended ranges of T and P, with deviations < 0.003 mL/g, comparable to the experimental uncertainties. The FOV model can be expressed as ... 

Thermodynamics PVT - dependence Simha Somcynsky, 1969 Simha Jain, 1984... 

Simha-Somcynsky (S-S) statistical thermodynamics of chain molecules... 

Simha-Somcynsky equation of state for a single component... 

SIMHA-SOMCYNSKY (S-S) STATISTICAL THERMODYNAMICS OF CHAIN MOLECULES 243... 

Simha-Somcynsky Equation of State for a Single Component... 

Nies, E., Stroeks, A., Simha, R., and Jain, R. K., LCST [lower critical solution temperature] phase behavior according to the Simha-Somcynsky theory apphcation to the n-hexane/polyethylene system. Colloid Polym. Sci., 268, 731-743 (1990). 

Wang, M., Takishima, S., Sato, Y, and Masuoka, H., Modification of Simha-Somcynsky equation of state for small and large molecules. Fluid Phase Equilibria, 242. 10-18 (2006). Wang, W, Liu, X., Zhong, C., Twu, C. H., and Coon, J. E., Simplified hole theory equation of state for liquid polymers and solvents and their solutions, Ind. Eng. Chem. Res., 36, 2390-2398 (1997). 

BULK AND SURFACE PROPERTIES OF RANDOM COPOLYMERS IN VIEW OF THE SIMHA-SOMCYNSKY EQUATION OF STATE... 

Equation (8.9) is obtained from the first relation in Eq. (8.8) after separating external variables, P and T, and m int al variable, the cell volume. This equation with appropriate definition of A and B (see below) is identical to the first equation of the coupled Simha-Somcynsky equation of state. Its form allows for comparison of cell and hole theories. In terms of the S-S theory,Jhe reduced van der Waals quantities A and B depend only on reduced cell volume, W = >/ , and are given by... 

Equation (8.11) is fully equivalent to the second equation of the coupled Simha-Somcynsky equation of state discussed by Moulinie and Utracki in Chapter 6. 

Much of the work stems from Simha-Somcynsky (S-S) [1969] hole theory, developed originally to describe polymers in the liquid state. They introduced the free volume by using the formalism of vacant cells or holes in a lattice and developed an equation of state that could be used to calculate the fraction of sites occupied and hence the fractional free volume. As discussed in Chapter 6, the concept has been developed further by Simha and his co-workers. 

Dlubek, G., Pionteck, J., and Kilburn, D., The structure of the free volume in poly (styrene-co-acrylonitrile) from positron lifetime and pressure-volume-temperature PVT) experiments I. Free volume from the Simha-Somcynsky analysis of PVT experiments, Macromol. Chem. Phys.,205, 500-511 (2004). 

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... 

COMPARISON OF PALS RESULTS WITH THOSE FROM THE SIMHA-SOMCYNSKY 441... 

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