Polymer-solvent interaction parameter concentration dependence

X is the polymer solvent interaction parameter, which is a dimensionless quantity characterizing a polymer solvent system, x may generally depend on temperature, pressure, concentration, but only a little on the functionality/ h2>3 is the memory term, already discussed ... 

The Flory-Rehner phenomenological theory [9,10] has beei most widely used to analyze the volume phase transition of gels. This theory, extended [11] to take into account the concentration dependence of the polymer-solvent interaction parameter x, can predict basic features of the phase transition. 

Direct experimental data providing the temperature dependence of are not available in the literature. However, as discussed earlier, the dependence of 0 on the quality of the solvent (change in the values of the polymer-solvent interaction parameter) is expected to suggest the trend with temperature also. The experimental determination of

silica particles having polystyrene as the free polymer, indicated [5] that the amount of polymer required to produce phase separation decreased by a factor of three when the theta solvent cyclohexane (x = 0.5) is replaced by the good solvent toluene (x < 0.5). This implies that increased temperatures (reduced values for x) should lead to lower values of the amounts of polymer required for phase separation. It can be safely concluded that the available experimental and theoretical information thus far, exhibits the trend of smaller values of the limiting polymer concentration at higher temperatures. 

Here, the second virial coefficient (excluded-volume parameter), vb = [1 -2x T)]<0, is negative because water is a poor solvent for the hydrophobic block B. The third virial coefficient, Wb, is positive, and x= T- e /d is the relative deviation from the theta temperature. At small deviations from the theta point, r < 1, the surface tension y and the polymer volume fraction (p are related as y/k T = (p. However, at larger deviations from the theta point, (p becomes comparable to unity and the latter relationship breaks down. Because in a typical experimental situation (p = 1, we treat (p and y as two independent parameters. Note that in a general case, surface tension y and width A of the core-corona interface depend on both the polymer-solvent interaction parameter Xbs T) for the core-forming block and the incompatibility Xab between monomers of blocks A and B. That is, y could depend on the concentration of monomers of the coronal block A near the core surface. We, however, neglect this (weak) dependence and assume that the surface tension y is not affected by conformations of the coronal blocks in a micelle. 

Kamide,K., Sugamiya,K. Role of concentration dependence of polymer/ solvent interaction parameter in the polymer fractionation by successive precipitational method. Makromol. Chem. 139,197 (1970). 

To avoid confusion with the polymer-solvent interaction parameter, the symbol gsp [Eq. (36)] is used instead of/, which is independent of concentration. Equations (37a)-(37c) are examples of expressions used for the temperature and composition dependence of gsp [27-29]. 

The viscosity dependence on polymer molecular weight is demonstrated in Figure 2.21 whereas Figure 2.22 shows the effect of polymer/solvent interaction. In the latter, the viscosity of solutions of a thermoplastic rubber at constant concentration and temperature is given in various hydrocarbon(blend)s. In this example hydrogen bonding or polar effects play no or only a very limited role. It is clear that in this case the solution viscosity is very much influenced by the Hildebrand solubility parameter of the solvent in relation to that of the polymer (8.2-9.1). 

The concentration dependence of many physical properties indicates the quality of the polymer-solvent interactions, through the second virial coefficients. Study of the concentration and temperature dependence of these parameters provides information on the theta temperature, radius of gyration, and the mean square end-to-end distance for a polymer coil. The radius of gyration is defined as the root mean square distance from the center of mass of a polymer chain to a given mass element. The characteristic ratio is a measure of the ratio of the square of the average random-flight end-to-end distance to the product of a number of backbone imits times the interactions along the polymer chain. These parameters provide useful information on the validity of a particular theoretical model and its ability to describe the architecture and conformation of a polymer (104). 

Similar to proton conductivity, the effective membrane parameter nd is determined by the membrane molecular architecture, in particular, by the concentration of acid protons in water-filled channels. The structural effects translate into characteristic dependencies of nd on X. In general, it is observed that nd increases with increasing X. The prevalence of surface proton transport for low X suggests nd nmoi T is reduced in membranes with narrow channels and strong polymer-solvent interactions, for example, in S-PEEK as compared to Nafion. These trends can be explained with the decrease of the hydrodynamic component nhydr, as discussed above. 

From the discussion of swelling equilibrium follows that a volume phase transition of a gel needs further contributions to free energy, resulting, for example, in specific polymer-solvent interactions. The high-temperature collapse of a nonionic single chain and gels in water has been described by using the concentration-dependent interaction parameters x"-... 

Another possible variable for the characterization of the goodness of solvents is the interaction parameter x values, expressing the measure of deviations of actual solutions from ideal ones. This value can be determined by several methods, which are, mostly experimentally demanding and time-consuming, x is dependent on both the polymer concentration and molecular weight and information provided about the specific interactions in the solution is of no particular interest [11,30,31], Solvents, obviously different in quality, yield quite close values and thus the resolving capability is low. Comparison of results obtained by various methods and/or experimenters is thus fairly difficult [30,32-34],... 

In describing the polymer-polymer interaction parameters for pairs which are normally incompatible as those discussed in this work, it therefore appears that the free volume (or the equation-of-state) contribution can usually be neglected except when the pair is on the verge of compatibility. This is in a marked contrast to polymer-solvent systems where the free volume effect is usually very large. From this follows that the dependence of A for polymer-polymer pairs on concentration or on temperature would also be fairly small. Table I shows only a modest variation of A with a change in Wi from 0.1 to 0.9. The relatively more pronounced variation of A for NR/PS as compared with other two pairs still arises mostly from the contact enthalpy term and reflects the larger Sx/s2 ratio for this system. 

Because of these uncertainties, equations 1, 2, 3, 4, and 5 may not be relied upon as a means of quantitative evaluation of A until more data for other polymer-solvent systems become available. The equation-of-state thermodynamics is, however, useful in its ability to give us insight into the physical factors and their relative magnitudes which contribute to the polymer-polymer interaction parameter. The results in this work clearly show that the dependence of A on concentration and temperature is moderate. This gives a justification as a good approximation to the use of a constant polymer-polymer interaction parameter in the polymer interface theories where the polymer concentration encompasses the whole range Wi = 0 to 1 across the phase boundary. 

Using well-known relationships for swollen gels (3), we computed "apparent crosslink densities" from the gel swell ratios and the solvent-polymer interaction parameter determined from the temperature dependence of those ratios (4) With lower ABP concentrations, the gels produced from the blends were fragile, leading to appreciable experimental uncertainties. With the higher ABP concentrations, more meaningful information was obtained. 

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