Flory-Huggins parameter temperature dependence

In many applications the phase stmcture as a function of the temperature is of interest. The discussion of this issue requires the knowledge of the temperature dependence of the Flory-Huggins parameter x (T). If the interactions... 

The general agreement between mean-field prediction and experimental results was excellent. Other than PE-PEE, PEP-PEE (sample VI) undergoes an ODT which is observed at 473 K. An analysis by the modified RPA theory due to Fredrickson [265] yields a strong stretching of the radii of gyration around the ODT and a temperature-dependent Flory-Huggins parameter ... 

The advantage of expressing H in terms of the Flory-Huggins parameter Xn is that the latter is often insensitive to temperature, and may better reflect the dependence on concentration than H. Its disadvantage is that it does not apply near and above the critical temperature of the volatile component. 

In addition to these morphologies, perforated layers, bicontinuous layers and other unstable morphologies have been described (Sperling, 2001). It has also been noted that, unlike polymer blends that become less miscible at higher temperatures, block copolymers become more miscible due to the temperature dependence of the Flory-Huggins parameter, x-... 

Phase diagrams of polymer blends under atmospheric pressure are usually presented in terms of the variables 0a and T. Emanating from the discussed universal phase diagram in terms of x and 0a, these can be obtained by introducing into the consideration the temperature dependence of the Flory-Huggins parameter. This function, x( )> fhen solely determines the appearance. For different types of temperature dependencies x(T), different classes of phase diagrams emerge and we discuss them in this section. 

Fig. 3.17. Endothermal symmetrical mixture with a constant heat of mixing. Temperature dependence of the Flory-Huggins parameter (left) and phase diagram showing a lower miscibility gap right)...

The temperature dependencies x T) which lead to these diagrams are shown on the left-hand side of Fig. 3.18. Their main common property is a change of the Flory-Huggins parameter from negative to positive values. The crossing of the zero line takes place at a certain temperature, denoted Tq. Coming from low temperatures, unmixing sets in for T = T with... 

For the solubility of TPA in prepolymer, no data are available and the polymer-solvent interaction parameter X of the Flory-Huggins relationship is not accurately known. No experimental data are available for the vapour pressures of dimer or trimer. The published values for the diffusion coefficient of EG in solid and molten PET vary by orders of magnitude. For the diffusion of water, acetaldehyde and DEG in polymer, no reliable data are available. It is not even agreed upon if the mutual diffusion coefficients depend on the polymer molecular weight or on the melt viscosity, and if they are linear or exponential functions of temperature. Molecular modelling, accompanied by the rapid growth of computer performance, will hopefully help to solve this problem in the near future. The mass-transfer mechanisms for by-products in solid PET are not established, and the dependency of the solid-state polycondensation rate on crystallinity is still a matter of assumptions. 

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