Flory-Huggins thermodynamic parameter

Another important application of experimentally determined values of the osmotic second virial coefficient is in the estimation of the corresponding values of the Flory-Huggins interaction parameters x 12, X14 and X24. In practice, these parameters are commonly used within the framework of the Flory-Huggins lattice model approach to the thermodynamic description of solutions of polymer + solvent or polymer] + polymer2 + solvent (Flory, 1942 Huggins, 1942 Tanford, 1961 Zeman and Patterson, 1972 Hsu and Prausnitz, 1974 Johansson et al., 2000) ... 

Flory-Huggins interaction parameter randomness coefficient. (P21/ i) = ( 12/ 2) thermodynamic solution parameter wavefunction... 

The theory of the scattering of radiation by large molecules has been reviewed in several recent publications Thermodynamic data can be obtained using scattering techniques via the Flory-Huggins interaction parameter, Xi2> or the second osmotic... 

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... 

IGC was used to determine the thermodynamic miscibility behavior of several polymer blends polystyrene-poly(n-butyl methacrylate), poly(vinylidene fluoride)-poly(methyl methacrylate), and polystyrene-poly(2,6-dimethyl-1,4-phenylene oxide) blends. Specific retention volumes were measured for a variety of probes in pure and mixed stationary phases of the molten polymers, and Flory-Huggins interaction parameters were calculated. A generally consistent and realistic measure of the polymer-polymer interaction can be obtained with this technique. 

The usefulness of inverse gas chromatography for determining polymer-small molecule interactions is well established (1,2). This method provides a fast and convenient way of obtaining thermodynamic data for concentrated polymer systems. However, this technique can also be used to measure polymer-polymer interaction parameters via a ternary solution approach Q). Measurements of specific retention volumes of two binary (volatile probe-polymer) and one ternary (volatile probe-polymer blend) system are sufficient to calculate xp3 > the Flory-Huggins interaction parameter, which is a measure of the thermodynamic... 

There are some who question the usefulness of the Flory-Huggins solubility parameter for problems related to the solubilization of polymers, although it is agreed that it is useful for study of the thermodynamics of dilute solutions. Barton (1975) has referred to literature that cites its shortcomings as a practical criterion of solubility. Some of these are ... 

There is an upper limit for the Flory-Huggins thermodynamic interaction parameter X if the polymer solution is homogeneous ... 

Quantitative estimation of the compatibility of polymers and oligomers can be made from the concentration dependence of the Flory— Huggins thermodynamic interaction parameter X2,a- The shape of the phase diagram is judged to a certain extent by the type of this dependence in that there is a relation AG ix = RTx2,3 P2 Pa between the... 

Classical polymer solution thermodynamics often did not consider solvent activities or solvent activity coefficients but usually a dimensionless quantity, the so-called Flory-Huggins interaction parameter % is not only a function of temperature (and pressure), as was evident from its foundation, but it is also a function of composition and polymer molecular mass. As pointed out in many papers, it is more precise to call it %-function (what is in principle a residual solvent chemical potential function). Because of its widespread use and its possible sources of mistakes and misinterpretations, the necessary relations must be included here. Starting from Equation [4.4.1b], the difference between the chemical potentials of the solvent in the mixture and in the standard state belongs to the first... 

Figure 4.24. Diffusion coefficients as functions of the composition in the miscible blend polystyrene-poly(xylenyl ether) (PS-PXE) at a temperature 66 °C above the (concentration-dependent) glass transition temperature of the blend, measured by forward recoil spectrometry. Squares represent tracer diffusion coefficients of PXE (VpxE = 292), circles the tracer diffusion coefficients of PS and diamonds the mutual diffusion coefficient. The upper solid line is the prediction of equation (4.4.11) using the smoothed curves through the experimental points for the tracer diffusion coefficients and an experimentally measured value of the Flory-Huggins interaction parameter. The dashed line is the prediction of equation (4.4.11), neglecting the effect of non-ideality of mixing, illustrating the substantial thermodynamic enhancement of the mutual diffusion coefficient in this miscible system. After Composto et al. (1988).

The second contribution influencing polymer adsorption from solution is the Flory-Huggins interaction parameter between poljnner and solvent. Such an enthalpy of mixing term adds a contribution of X (t)2 z) — 4> ) to the interaction energy contribution, where 4) is the bulk solution concentration of the polymer (2) and, when approaches thermodynamically poor values, then the adsorbed amoimt of pol3mier increases significantly. Figure 5.13 shows experi-... 

MO2 Morariu, S., Nichifor, M., Eckelt, J., and Wolf, B.A., Dextran-based polycations Thermodynamic interaction with water as compared with unsubstituted dextran, 2 -Flory/Huggins interaction parameter, Macrowo/. Chem. Phys., 212, 1932, 2011. 

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