Flory temperature INDEX

Our discussion here explores active connections between the potential distribution theorem (PDT) and the theory of polymer solutions. In Chapter 4 we have already derived the Flory-Huggins model in broad form, and discussed its basis in a van der Waals model of solution thermodynamics. That derivation highlighted the origins of composition, temperature, and pressure effects on the Flory-Huggins interaction parameter. We recall that this theory is based upon a van der Waals treatment of solutions with the additional assumptions of zero volume of mixing and more technical approximations such as Eq. (4.45), p. 81. Considering a system of a polymer (p) of polymerization index M dissolved in a solvent (s), the Rory-Huggins model is... 

The value of the powers, superscripts s and /, in Eqs. (6) and (7) are 1.3 and 1.8, respectively, by replacing p with the polymer concentration. There are many careful measurements reported on the modulus near the gel point. Tokita and Hikichi [187] measured the modulus of dilute agarose aqueous solution as a function of temperature and determined the value of / to be 1.9 and the critical temperature, = 80°C. The concentration dependence of the agarose aqueous solution at 20°C was also measured and obtained as = 0.0137 g/lOOmL, /=1.93. Gauthier-Manuel et al. [188] measured the dynamic viscoelasticity if = 10 Hz) of silica particle suspension as a function of reaction time and obtained / = 2. The experimental value is closer to the index 1.9 of the 3D percolation theory than is / = 3 of the Flory-Stockmayer... 

Some assumptions were made for the derivation of Equation [4.4.54], especially the partial specific volume, the refractive index, and the derivative dn/dw2 must not depend on the molar mass distribution of the polymer. If one further assumes that the Flory-Huggins X-function depends only on temperature and concentration, but not on molar mass, the partial derivative of the chemical potential can be calculated by Equation [4.4.13a] to obtain values of the x-function. Scholte carried out experiments for solutions of polystyrene in cyclohexane or toluene at different temperatures and in a concentration range of 0 to 80 wt%. 

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