Interaction coefficient, Huggins

Several authors have attempted to corrolate the degradation rate with such solvent parameters as osmotic coefficient [35], viscosity [36-38] and the Flory Huggins interaction parameter, % [39,40] - a low % value indicates a good solvent in which the polymer is expected to exhibit an open conformation (as opposed to coiled) and therefore is more susceptible to degradation (Fig. 5.15). 

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) ... 

Since there had not been any measurements of thermal diffusion and Soret coefficients in polymer blends, the first task was the investigation of the Soret effect in the model polymer blend poly(dimethyl siloxane) (PDMS) and poly(ethyl-methyl siloxane) (PEMS). This polymer system has been chosen because of its conveniently located lower miscibility gap with a critical temperature that can easily be adjusted within the experimentally interesting range between room temperature and 100 °C by a suitable choice of the molar masses [81, 82], Furthermore, extensive characterization work has already been done for PDMS/PEMS blends, including the determination of activation energies and Flory-Huggins interaction parameters [7, 8, 83, 84],... 

Once the second virial coefficient has been obtained for a given polymer - solvent system one can calculate the corresponding Flory - Huggins interaction parameter, X, from the equation ... 

Calculate the for solutions in chlorobenzene of polystyrenes with molar weights of 2 x 105,5 x 105 and 106 g/mol the intrinsic viscosity, the critical concentration, the swelling factor, the hydrodynamic swollen volume, the second virial coefficient and the Flory-Huggins interaction parameter. 

This method is to be used to estimate the activity coefficient of a low molecular weight solvent in a solution with a polymer. This procedure, unlike the other procedures in this chapter, is a correlation method because it requires the Flory-Huggins interaction parameter for the polymer-solvent pair which must be obtained from an independent tabulation or regressed from experimental data. In addition, the specific volumes and the molecular weights of the pure solvent and the pure polymer are needed. The number average molecular weight of the polymer is recommended. The method cannot be used to estimate the activity of the polymer in the solution. 

The infinite dilution activity coefficient of the solvent is calculated from the limit as the weight fraction of component 1 goes to zero. The infinite dilution Flory-Huggins interaction parameter,/ 2, can be reduced to the infinite dilution activity coefficient, Q", by the relation ... 

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

It is to be expected that measurements of the osmotic pressures of I he same polymer in different solvent should yield a common intercept. The slopes will differ (Fig. 3-1 a), however, since the second virial coefficient reflects polymer-solvent interactions and can be related, for example, to the Flory-Huggins interaction parameter x (Chapter 12) by... 

Dilute solution viscosities used for determining the intrinsic viscosity of the polymer systems in 2.0 wt % NaCl were obtained in a capillary viscometer (Ubbe-lohde) by using standard methods (iO, 11). Some of the measurements were obtained fi om an automatic capillary viscometer (Schott AVS/G). A conventional Huggins relationship 11) in which reduced viscosity is a linear function of polymer concentration was used to fit the data. A regression analysis was used to yield the intrinsic viscosity (the intercept) and the Huggins interaction coefficient, K, (the slope divided by the square of the intrinsic viscosity). 

Hydrophobic associations can dominate polymer conformation in solution and solution rheological properties. Intrinsic viscosity and Huggins interaction coefficients provided information on the conformation and intramolecular aggregation behavior of these polymers in dilute solution. The presence of hydrophobic associations caused a decrease in the intrinsic viscosity and an increase in the Huggins constant. These effects could be counterbalanced by increasing the ionic charge on the polymer through hydrolysis or by copolymerization with sodium acrylate. 

Flory-Huggins interaction parameter a packing coefficient, medium viscosity initial viscosity, constant... 

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).

D is the interdiffusion coefficient, A a and Ab are the segment mobilities of polymers A and B, respectively, Aa and Ab are the number of repeat units in each polymer, i a and are the molar fractions of each pol5uner and x is the Flory-Huggins interaction parameter. The slow-mode theory predicts that interdiffusion is dominated by the slow-diffusing polymer. Later, de Gennes [69] showed that the mobility was directly related to the diffusion coefficient of each polymer. The limitation of this theory is that it assumes that the fluxes of the two polymers are equal and opposite, which means that the interface remains symmetrical as interdiflfusion proceeds. 

Monomeric friction coefficient I Correlation length K Flory/Huggins interaction parameter UL Dipole moment to Angular frequency (co = 2 7i f)... 

The Flory-Huggins interaction parameter, x. was related to the binary diffusion coefficient. 

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