Interactions solvent-segment

In a poor solvent, where both ki and Ki/rpi generally are positive, also will be positive. At the temperature T = , the chemical potential due to segment-solvent interactions is zero according to Eq. (430- Hence the temperature is that at which the excess chemical potential is zero and deviations from ideality vanish. The free energy of interaction of the segments within a volume element is therefore zero also. 

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. 

The effect of the solvent is a complex one, but can again be taken care of empirically. It is possible to define a solvent (a theta, 6, solvent) whereby the net effect of an unfavourable segment-solvent interaction is to reduce the dimensions of the chain so as to exactly compensate for the excluded volume effect. 

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 a good solvent, the segment - solvent interaction tends to pull a pair of segments apart, so that the solvent - mediated force F should be repulsive as is F. On the other hand, F should be attractive in poor solvents. Hence, as the solvent is made poorer by changing either solvent species or temperature, the situation should be reached in which the attractive F cancels or suppresses the repulsive F so that the net force F + F becomes zero or even negative. 

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... 

The final factor results from the mutual interaction between segments and solvent molecules. In a poor solvent, the segment-solvent interaction is unfavourable. This forces the polymer out of the solution, thus promoting adsorption. In a good solvent, the segment-solvent interaction is favourable, while the aggregation of segments is unfavourable and as a result the adsorbed amount is less. 

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