Solvent-segment interaction parameter

The thermodynamic behavior of the dilute polymer solution depends on three factors (1) the molecular weight, (2) the thermodynamic interaction parameters and ki, or ipi and 0, which characterize the segment-solvent interaction, and (3) the configuration, or size, of the... 

When this procedure is applied to the data shown for polystyrene in Fig. 116 and to those for polyisobutylene shown previously in Fig. 38 of Chapter VII, the values obtained for t/ i(1 — /T) decrease as the molecular weight increases. The data for the latter system, for example, yield values for this quantity changing from 0.087 at AT-38,000 to 0.064 at ilf = 720,000. This is contrary to the initial definition of the thermodynamic parameters, according to which they should characterize the inherent segment-solvent interaction independent of the molecular structure as a whole. 

A comparison between the Eg values listed in tables I and II with theoretical Gg values is not possible at present, since for calculation of Gg one needs to know the polymer-solvent interaction parameter as a function of Na2S04 concentration. Moreover, an assumption must be made about the segment distribution of the adsorbed layer. In the absence of such information, it is not possible to calculate Gg. However, the values of Eg obtained from rheology (tables I and II) are reasonable, considering the approximation made and the crude model used for calculating Es. 

In Fiery s theory of the excluded volume (27), the chains in undiluted polymer systems assume their unperturbed dimensions. The expansion factor in solutions is governed by the parameter (J — x)/v, v being the molar volume of solvent and x the segment-solvent interaction (regular solution) parameter. In undiluted polymers, the solvent for any molecule is simply other polymer molecules. If it is assumed that the excluded volume term in the thermodynamic theory of concentrated systems can be applied directly to the determination of coil dimensions, then x is automatically zero but v is very large, reducing the expansion to zero. 

In the above equations, v stands for the highest layer which can be reached by a chain. For the present case, v=2m. In the supermatrix G, r, represents a backward bond starting from layer, q,- a lateral bond in layer, and p, a forward bond starting from layer. In the elements r, and p, the Heaviside functions vrp and vpr are included to avoid bondfolding, since a bond can not be backward when the previous bond was forward and vice versa. The elements r, q-, and p, depend on three kinds of parameters. The first kind of parameters a, (3, and co arise from the local chain stiffness and bond arrangements, the second p, from the segment-solvent interactions, and the third kind from the correlations between nearest-neighboring parallel bonds. 

The interaction parameter /i and Kj or /i and 0, which characterize the segment-solvent interactions... 

Values of the polymer-solvent interaction parameters, defined by Eq. (El) in terms of volume fractions, have been collected. They are tabulated as a function of polymer eoncentration for various temperatures. Data given on the basis of segment fractions, sj, or weight fractions, W2, were eonverted into volume fractions ifj. 

The degree to which a cross-linked polymer will swell when immersed in a solvent depends upon the polymer-solvent interaction parameter at the test temperature and the average moleeular weight of the chain segments separating crosslinks (effective chains). This relationship is defined by the Floiy-Rehner equation [89,90]. 

We saw in Sec. 1.11 that coil dimensions are affected by interactions between chain segments and solvent. Both the coil expansion factor a defined by Eq. (1.63) and the interaction parameter x are pertinent to describing this situation. 

More fundamental treatments of polymer solubihty go back to the lattice theory developed independentiy and almost simultaneously by Flory (13) and Huggins (14) in 1942. By imagining the solvent molecules and polymer chain segments to be distributed on a lattice, they statistically evaluated the entropy of solution. The enthalpy of solution was characterized by the Flory-Huggins interaction parameter, which is related to solubihty parameters by equation 5. For high molecular weight polymers in monomeric solvents, the Flory-Huggins solubihty criterion is X A 0.5. 

---