Free volume dissimilarity

The effect of an applied pressure on the UCFT has been investigated for polymer particles that are sterically stabilized by polyisobutylene and dispersed in 2-methy1-butane. It was observed that the UCFT was shifted to a higher temperature as the hydrostatic pressure applied to the system increased. There was also a qualitative correlation between the UCFT as a function of applied pressure and the 6 conditions of PIB + 2-methylbutane in (P,T) space. These results can be rationalized by considering the effect of pressure on the free volume dissimilarity contribution to the free energy of close approach of interacting particles. Application of corresponding states concepts to the theory of steric stabilization enables a qualitative prediction of the observed stability behaviour as a function of temperature and pressure. 

It was suggested in a previous publication (9) that flocculation at the UCFT can be ascribed to the free volume dissimilarity between the polymer stabilizing the particle and the low molecular weight dispersion medium. Incorporating this idea in a quantitative way into the theory of steric stabilization allowed for a qualitative interpretation of the experimental data. This idea is further extended to include the effect of pressure on the critical flocculation conditions. 

Figure 3 (a) Shows the combinational contribution of AG-j plotted as a function of temperature while, (b) Shows the free volume dissimilarity contribution to AG- plotted as a function of temperature for atmospheric and 180 bars pressure. 

From the family of AG (P, T) curves the projection on the (P, T) plane of the critical lines corresponding to the UCFT for these latexes can be calculated and this is shown plotted in Figure 4. It can be seen that the UCFT curve is linear over the pressure range studied. The slope of the theoretical projection is 0.38 which is smaller than the experimental data line. Agreement between theory and experiment could be improved by relaxing the condition that v = it = 0 in Equation 6 and/or by allowing x to be an adjustable parameter. However, since the main features of the experimental data can be qualitatively predicted by theory, this option is not pursued here. It is apparent from the data presented that the free volume dissimilarity between the steric stabilizer and the dispersion medium plays an important role in the colloidal stabilization of sterically stabilized nonaqueous dispersions. 

More recent polymer soluticm theories (41. 42) recognize the importance of the free volume dissimilarity of the solute and polymer. This effect, first introduced in theories of solution by Prigogine and collaborators (43), has important thermodynamic consequences. Flory and collaborators (42) now suggest that (In A Xioncotnb be composed of two terms, an equation of state and a contact interaction contribution, The newly defined parameter, denoted x, becomes... 

Schreiber, Tewari and Patterson 53) reported interaction parameters of more than 20 hydrocarbons in linear and branched polyethylenes, at temperatures above the melting point. The corresponding x parameters are given in Table 5. Despite the chemical identity of the components, substantial interaction parameters were obtained. This was attributed to the large contribution arising from the free volume dissimilarities of the components. Indeed it proved possible to correlate the magnitude... 

The contribution to the interaction parameter from free volume dissimilarity persists down to room temperature and below. It accounts for the dominant positive values of Xs noted above (see Table 3.1). It further explains the observed increase in % with increasing volume fraction of polymer found with some systems the extent of condensation of the solvent is related to the amount of polymer present. The greater is the amount of polymer present, the more will the solvent molecules condense onto the polymer segments, thus increasing the numerical magnitude of Xs- If X does not increase with the polymer volume fraction, as not infrequently happens (e.g. polystyrene in toluene), then specific interactions must provide compensatory effects. Such specific interactions appear at present to be beyond the grasp of any fundamental theoretical analysis. 

The free volume dissimilarity provides one of the important conceptual features that is missing from the Flory-Huggins theory. It rationalizes (i) the observed phase separation on heating (ii) the strong entropic contribution to X that opposes mixing and (iii) the observed increase in x with volume fraction of polymer in certain systems. Qualitatively, we can write for the mixing of polymer and solvent at room temperature ... 

In summary, for nonaqueous dispersions, the combinatorial free energy of interpenetration favours stabilization. Both of the corresponding free energies associated with contact dissimilarity and free volume dissimilarity favour flocculation. These conclusions are represented schematically in Fig. 7.2. Since the combinatorial free energy is purely entropic in origin, it is scarcely surprising that nonaqueous sterically stabilized systems are usually found to be entropically stabilized at room temperature and pressure for it is this term that imparts stability. Anticipating the results of the next section, we stress that this does not necessarily imply that all nonaqueous dispersions are entropically stabilized at room temperature. 

A dispersion that flocculates on heating, as was mentioned previously, must be enthalpically stabilized just below the UCFT. For nonaqueous dispersions, the origin of the enthalpy contribution that imparts stability in these circumstances is readily pinpointed from Table 7.4. The only enthalpy contribution that is positive is that associated with the free volume dissimilarity. It is therefore this term that imparts stability just below the UCFT. 

It is not possible, as was noted previously, to move from a domain of entropic stabilization to a domain of enthalpic stabilization without passing through a region of combined enthalpic-plus-entropic stabilization. Again the enthalpy term promoting stability in the combined region is that associated with the free volume dissimilarity. The entropy term that contributes to stability is the combinatorial term, just as it is in the purely entropic domain. 

Combinatorial J5C0MB Contact dissimilarity ONT J5CONT Free volume dissimilarity... 

It might be expected that just below the UCFT, the enthalpies associated with the contact and free volume dissimilarities should impart enthalpic stabilization. Conversely, just above the LCFT (if accessible), the combinatorial entropy of mixing should give rise to entropic stabilization. Flocculation on cooling appears to result from the free volume contribution. This may explain why such flocculation is not always readily achieved in aqueous systems of this type. 

The two terms in equation (12.92) are physically interpretable. The first term is the contact dissimilarity contribution arising from the difference in cohesive energy and size of the polymer and solvent segments. The second term is the free volume dissimilarity contribution. 

It is apparent from Fig. 12.11 that the enthalpic contribution from the free volume dissimilarity is relatively small, always positive and increases linearly with the temperature. The entropy terms are relatively large by comparison but of opposite signs the combinatorial term is repulsive whereas the contact dissimilarity term is attractive. Both results are as expected physically. The... 

For many polymer mixtures that are known to be compatible, the extent of their compatibility decreases as the temperature increased. This diminution in miscibility with tempCTature is a forerunner of the occurrence of a lower critical solution temperature. At higher temperatures, the effect of the favourable interactions between the two components is reduced whereas any free volume dissimilarity difference is enhanced. The conjunction of these competing effects eventually leads to phase separation. 

Free-volume dissimilarities become increasingly important as the size of one component increases with respect to the second, as in polymer solutions, and when these differences arc sufficienily large, phase separation can be observed at the LCST. 

Many attempts have been made to improve the UNIFAC-frf model which cannot be listed here. A comprehensive review was given by Fried et al. An innovative method to combine the free-volume contribution within a corrected Flory-Huggins combinatorial entropy and the UNIFAC concept was found by Elbro et al. and improved by Kontogeorgis et al. These authors take into account the free-volume dissimilarity by assuming different van der Waals hard-core volumes (again from Bondi s tables ) for the solvent and the polymer segments... 

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