Flory-Huggins-Staverman

Equation (9.9), however, only approximately describes the internal dilution of a liquid crystalline copolymer [64]. Here internal means that the diluent is part of the chain and not a second independent component. Nishi and Wang [67] have derived equation (9.10) which describes polymers diluted by polymers. Their extension of the Flory-Huggins-Staverman theory gives the melting point depression ... 

A linearizing plot of the melting point depression vs. (I) theoretically starts at the origin. The Flory-Huggins-Staverman interaction parameter X, which depends principally on the temperature and the composition, can be obtained from the slope of equation (9.10). 

For the disordered state it is just the enthalpic part similar to the Flory-Huggins-Staverman free energy of polymer blends ... 

Definition of terms relating to individual macromolecules, their assemblies, and dilute solution.This document includes the recommended definitions for molecular weight, molecular weight averages, distribution functions, radius of gyration, end-to-end-distance vector, the Flory-Huggins-Staverman theory, solution viscosity, scattering of radiation by polymers and polymer solutions, fractionation, separation techniques, and so on. The document on dispersity is an important extension of this recommendation. 

Fractionation by liquid liquid phase separation relies on the molar mass dependence of the distribution coefficient which, in terms of the Flory-Huggins-Staverman theory [8 13] (FHS), reads... 

Parameters related to differences in size and shape and respectively change in internal energy of mixing Entropy correction terms Parameter related to average interaction energy Internal energy of the system Flory s equation of state Flory-Huggins Staverman theory... 

Figure 5 Phase diagram of diblock copolymers with equal segmental lengths and segmental volumes of both block components. % Flory-Huggins-Staverman interaction parameter, N degree of polymerization, ( ) volume fraction, D disordered phase, CPS close packed spheres, BCC body-centered cubic spheres, H hexagonally packed cylinders, G gyroid, L lamellae. (From Ref. 110, Copyright 1996 American Chemical Society.)...

For more than two decades researchers have attempted to overcome the inadequacies of Flory s treatment in order to establish a model that will provide accurate predictions. Most of these research efforts can be grouped into two categories, i.e., attempts at corrections to the enthalpic or noncombinatorial part, and modifications to the entropic or combinatorial part of the Flory-Huggins theory. The more complex relationships derived by Huggins, Guggenheim, Stavermans, and others [53] required so many additional and poorly determined parameters that these approaches lack practical applications. A review of the more serious deficiencies... 

Statistical thermodynamic mean-field theory of polymer solutions, first formulated independently by Flory, Huggins, and Staverman, in which the thermodynamic quantities of the solution are derived from a simple concept of combinatorial entropy of mixing and a reduced Gibbs-energy parameter, the X interaction parameter. 

To approach AG of quasi-binary polymer solutions in an empirical way it is usual to invoke the Koningsveld-Staverman formalism [5], which chooses the familiar Flory-Huggins (FH) atheimal solution as the reference system and expresses AG as... 

Instead of the Flory-Huggins combinatorial contribution. Equation [4.4.68], the Staverman relation is used. 

Thermodynamic descriptions of polymer systems are usually based on a rigid-lattice model published in 1941 independently by Staverman and Van Santen, Huggins and Flory where the symbol x(T) is used to express the binary interaction function [16]. Once the interaction parameter is known we can calculate the liquid liquid phase behaviour. 

Besides the earliest theories by Flory (95 ), Huggins (128") and Miller (183 ), all improved theories are concerned with the effect of ring closure of chains on the mixing entropy [Staverman (237) Guggenheim and McGlashan (7) Tompa (21) MCnster (15) and Kurata, Tamura and W atari (756)]. The problem of ring closure is essentially the excluded volume problem. 

Equations (4.98) and (4.102) are the backbone of a method describing thermodynamic properties of macromolecular systems akin to the van der Waals approach to low molecular weight systems. The lattice approach outlined here was pioneered independently by Staverman and van Santen (Stavermann and van Santen 1941), Huggins (Huggins 1941,1942) and Flory (Paul John Flory, Nobel prize in chemistry for his work on the physical chemistry of macromolecules, 1974) (Flory 1941,1942 Koningsveld and Kleintjens 1988). 

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