Flory-Huggins formalism

According to the Flory-Huggins formalism (Section 6.8.11), the isotherm corresponding to this equilibrium is given by... 

In systems with specific interactions random mixing cannot be assumed. Hence, the thermodynamic theories traditionally used to interpret ternary system properties, such as the Flory - Huggins formalism or the equation of state theory of FI ory, are expected not to apply to such systems. 

The majority of the work done thus far has dealt with mixing of two random coil polymers. The Flory-Huggins formalism is usually used to describe the expected free energy of mixing. As such, miscibility is normally dominated by the enthalpic part of the free energy. 

Simulations [73] have recently provided some insights into the formal 5c —> 0 limit predicted by mean field lattice model theories of glass formation. While Monte Carlo estimates of x for a Flory-Huggins (FH) lattice model of a semifiexible polymer melt extrapolate to infinity near the ideal glass transition temperature Tq, where 5c extrapolates to zero, the values of 5c computed from GD theory are too low by roughly a constant compared to the simulation estimates, and this constant shift is suggested to be sufficient to prevent 5c from strictly vanishing [73, 74]. Hence, we can reasonably infer that 5 approaches a small, but nonzero asymptotic low temperature limit and that 5c similarly becomes critically small near Tq. The possibility of a constant... 

Here, again, we start from compressible SCFT formalism described in Section 2.2 and consider a model system in which bulk polymer consists of "free" matrix chains (Ny= 300) and "active" one-sticker chains (Na= 100). Flory-Huggins interaction parameters between various species are summarized in Table 1. This corresponds to the scenario in which surfactants, matrix chains, and functionalized chains are all hydrocarbon molecules (e.g., surfactant is a C12 linear chain, matrix is a 100,000 Da molecular weight polyethylene, and functionalized chain is a shorter polyethylene molecule with one grafted maleic group). The nonzero interaction parameter between voids and hydrocarbon monomers reflects the nonzero surface tension of polyethylene. The interaction parameter between the clay surface and the hydrocarbon monomers, Xac= 10 (a = G, F, A), reflects a very strong incompatibility between the nonpolar polymers and... 

This is the Flory-Huggins (FH) equation for athermal solutions [5, 6]. The equation formally appears symmetric to all components of a mixture, but in fact it describes the great asymmetry between the polymer and the small solvent in solution. Consider the solution of a small solvent and a polymer that is r times the volume of the solvent. The solvent may well be the monomer, here designated as component 1, and the polymer may be an r-mer as component 2. Setting V2/V1 in Equation (4.367) gives... 

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... 

One of the key results from application of the equation of state approach to predicting phase behavior is the observation that lest behavior can be predicted based upon a non-combinatorial contribution to entropy inherent with this formalism. The Flory-Huggins lattice model theory is an incompressible model that does not allow for the compressibility effects on the system thermodynamics. For equation of state approaches that allow for compressibility effects, the miscibility condition expressed by Eq. 2.2 [18] becomes ... 

But the concentrated phase is in equilibrium with a diluted phase which is not consistently described by a Flory-Huggins model it is difficult to imagine that a diluted solution of the two types of polyelectrolytes with an opposite global charge and a rather stiff conformation can be treated by the lattice formalism. 

Like the two-parameter formalism, the Flory-Huggins theory contains nothing specific in its structure to account for the temperature dependence of the free energy of mixing that leads to the... 

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