Cohesive Energies and Solubility Parameters

Once reliable estimates of the molar enthalpies of vaporization of RTILs are available, their cohesive energies, ce = AyH - RT, are readily obtained. Note that no ionic dissociation of the vapor is used in this derivation (otherwise, —IRThad to be employed). Hence, the cohesive energy densities, ced = AyH — RT)/V, shown 

the melting point, T , and the temperature of decomposition, heat capacity at 25 C of RTIL quaternary ammonium and phospho- 

RTILs the predictions are lower than the experimental values (4) 

An indirect method was applied to obtain Hildebrand solubihty parameters of 6 imidazolium RTILs from a linear solvation energy relationship (LSER) correlation of the solvent dependency of a rate constant for a certain reaction by Swiderski et al. [199]. Another indirect method was based by Lee and Lee [198] on the comparison of the viscosity of eight imidazolium RTILs with those of organic solvents. The resulting values of n/MPa were in the range 24—32. These values are less reliable than those obtained from ced = A H — RT)/V. 

Individual ionic values of 5h+ and h- were thus obtained for the key imis, and Lq. (6.11) were then used to obtain values for altogether 210 RTILs involving also 17 other cations of various types and 6 other anions. The values diminish as the chain lengths of the alkyl substituents or the size of the anion increases. 

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Improvements in the ability to predict the cohesive energies and solubility parameters of polymers... 

A.5. Improvements in the Ability to Predict the Cohesive Energies and Solubility Parameters of Polymers... 

Cohesion energy and solubility parameters eould then be estimated for any moleeule ... 

Pressure effects on surfactant systems containing conventional liquid alkanes have not often been studied because of the very low compressibility of liquids. Conflicting results have been reported [38-40]. It is likely that the changes in cohesive energy density (solubility parameter) of the phases over the pressure ranges used were too low to produce definitive trends in phase behavior. The solubility parameter of compressed liquid propane, however, is moderately adjustable with pressure, and therefore a propane-brine-AOT system could be expected to show pressure-driven phase transitions [20,22,41]. 

Although rigorous additivity rules are not applicable in this case, a fair estimation of the cohesive energy and the solubility parameter of polymers can be made by group contribution methods. 

As electrical forces due to polarisability and polar moment determine the cohesive energy, a certain correlation between dielectric constant and solubility parameter may be expected. Darby et al. (1967) suggested such a correlation for organic compounds. It appeared that a surprisingly simple correlation holds for polymers, viz. ... 

Correlations for the cohesive energy and the solubility parameter will be presented in Chapter 5, to allow the calculation of these properties at the same level of accuracy as can be attained by group contributions but for much wider classes of polymers. The pitfalls of using solubility parameters in miscibility calculations will also be highlighted in the context of a discussion of the various types of phase diagrams that are observed for blends and mixtures. 

The solubility parameter will be estimated indirectly, by combining the correlations for the cohesive energy and the molar volume. 

Furthermore, in calculations performed manually instead of using software implementing our method, the calculation of the properties of many homopolymers with large repeat units can be simplified by treating them formally as alternating copolymers of smaller repeat units of polymers whose properties have already been calculated. Simple additivity is then assumed to hold for the extensive properties of the alternating copolymer, such as its connectivity indices, cohesive energy, and molar volume. All extensive properties can thus be calculated. Intensive properties, such as the solubility parameter, are defined in terms of extensive properties. Their prediction therefore does not require any detailed calculations either. 

Table 17.6. Number of vertices N in the hydrogen-suppressed graph, connectivity indices °%, V, and %v> an

For example, the cohesive energy and molar volume (extensive properties) and solubility parameter (an intensive property) of a random copolymer containing two different types of repeat units with mole fractions of irq and m2 can be estimated by using equations 17.7-17.10 ... 

The concept of cohesive energy density and solubility parameter was introduced by Hildebrand ... 

For liquids of low molecular weight the energy necessary to separate molecules from one another is evaluated from the heat of evaporation or from the dependence of vapor pressure on temperature. Since polymers cannot be evaporated, the cohesive energy density is estimated indirectly by dissolution in liquids of known cohesive energy density. To do this, we employ the relation between the cohesive energy density and solubility parameter (Equation 3.11). 

Cohesive Energy Density and Solubility Parameters. As a result of attractive or cohesive forces the molecules in pure solvents have a cohesive energy that has to be expended in molecular separation processes (e.g., dilution, evaporation, or addition of another substance). The cohesive energy can be calculated from the enthalpy of vaporization AHy and the work that is required to expand the vapor against the atmosphere (volume work) [14.20], The cohesive energy per unit volume, i.e., the cohesive energy density, is defined as [14,16], [14.21], [14.22] ... 

The separation of the cohesion energy into contributions of various forces implies fliat it is possible to substitute energy for parameter and sum contributions proportional to the second power of a difference of corresponding components. Hansen s treatment permits evaluation of the dispersion and polar contribution to cohesive energy. The fitting parameter of the approach (the solubility sphere radius) reflects on the supermolecular structure of polymer-solvent system. Its values should be higher for amorphous polymers and lower for glass or crystalline polymers. 

Selected values of the cohesion energy and the solubility parameter 6 are listed below for definitions, see Ge(CH3)4, p. 35 [41]. 

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