Example calculations solubility parameter

Table 7.2 Examples of solubility parameters calculated from those constants in Table 7.1... 

Thus, for example, for C60 fullerene that has 20 hexagons, the calculation of the solubility parameter is ... 

Because the law of mixtures applies to the solubility parameter, it is possible to easily calculate the solubility parameter of blended liquids forming mixtures that can serve as solvents. For example, an equal molar mixture of -pentane (5 = 7.1 H) and -octane (5 = 7.6 H) will have a solubility parameter value of 7.35 H (simply (7.1 + 7.6)/2). 

It is possible to determine C quantitatively using Hildebrand s theory of microsolutes. An example of the accuracy that can be achieved is provided by the calculation of the solubilities of a series of p-aminobenzoate esters in hexane (17,18). Michaels, et al. (19) used this approach to estimate the solubility of steroids in various polymers. The solubilities of seven steroids in six polymers were calculated from the steroid melting points, heats of fusion, and solubility parameters. Equation 8 was derived, where Jjj is the maximum steady state flux, h is the membrane thickness, x is the product of V, the molar volume of the liquid drug, and the square of the difference in the solubility parameters of the drug and polymer, p is the steroid density, T is melting point (°K), T is the temperature of the environment, R is the gas constant, and AH and ASf are the enthalpy and entropy of fusion, respectively. 

Many computational studies of the permeation of small gas molecules through polymers have appeared, which were designed to analyze, on an atomic scale, diffusion mechanisms or to calculate the diffusion coefficient and the solubility parameters. Most of these studies have dealt with flexible polymer chains of relatively simple structure such as polyethylene, polypropylene, and poly-(isobutylene) [49,50,51,52,53], There are, however, a few reports on polymers consisting of stiff chains. For example, Mooney and MacElroy [54] studied the diffusion of small molecules in semicrystalline aromatic polymers and Cuthbert et al. [55] have calculated the Henry s law constant for a number of small molecules in polystyrene and studied the effect of box size on the calculated Henry s law constants. Most of these reports are limited to the calculation of solubility coefficients at a single temperature and in the zero-pressure limit. However, there are few reports on the calculation of solubilities at higher pressures, for example the reports by de Pablo et al. [56] on the calculation of solubilities of alkanes in polyethylene, by Abu-Shargh [53] on the calculation of solubility of propene in polypropylene, and by Lim et al. [47] on the sorption of methane and carbon dioxide in amorphous polyetherimide. In the former two cases, the authors have used Gibbs ensemble Monte Carlo method [41,57] to do the calculations, and in the latter case, the authors have used an equation-of-state method to describe the gas phase. 

In an attempt to separate the various contributions to the small molecule solubility parameters the slopes of the graphs in Figures 2 to 4 were calculated separately using aromatic and aliphatic probes. The latter of these was assumed to account for 6 while the difference between them was ascribed to 6. An overall value of 6 was then calculated from Equation 7. The procedure is illustrated in Figure 5 using NMP as an example. The results for all the liquids are summarized in Table IV. 

The simplest criterion for a theoretical calculation of the miscibility of the hydrophobic portions of small molecules with the hydrophobic microphase of a membrane polymer appears to be a partial solubility parameter that is, calculation of the solubility parameter of only the hydrophobic portions of the molecules. This can be done using a group contribution approach in which each group (for example, a CHg-group) in the molecule contributes a certain attractive force and a certain volume to the molecule. In this way, a solubility parameter may be estimated for either a portion of a molecule or for a whole molecule. 

As already mentioned, in evaluating the dispersive component of the solubility parameter in the literature, reference is usually made to the homomorph concept. The homomorph is typically the hydrocarbon with the structure closest to the studied substance. The homomorph of n-pentanol, for example, is n-hexane and of isopropanol is isobutane. The homomorph concept may be used with the present approach as well. Equation 2.36 indicates how to use it The homomorph and the studied substance should be brought at the same reduced density — a type of corresponding states. Table 2.5 also includes the calculated homomorph component, 8, of the solubility parameter. 

Mn(II), Sr, Ba, Li, and Br, with provision for calculations at temperatures other than 25 C. The need to maintain an internally consistent data base of interaction parameters and equilibrium constants is emphasized through an example of the calculated solubility of nahcolite in Na2C03 solutions. 

While the solubility parameter of a homopolymer can be calculated from the molar attraction constants as illustrated in Example 6, the solubility parameter of random copolymers, 6, may be calculated from... 

The calculation methods of the solubility parameters for polymers have an advantage over experimental methods that they do not have any prior assumptions regarding interactions of polymer with solvents. The numerous examples of good correlation between calculated and experimental parameters of solubility for various solvents support the assumed additivity of intermolecular interaction energy. 

The solvent can aiiect the copolymerization behavior, however, inasmuch as it can change the monomer concentration at the reaction site. Examples of this are association of monomers, adsorption of monomers on precipitated polymers, and solubility differences in different phases. The local concentrations are no longer identical to the total concentration of monomer in all of these cases. Conventionally calculated copolymerization parameters are different according to solvent or phase, even though the reactivities are not necessarily different and only the effective monomer concentrations vary. 

An example of the calculation of the properties of an existing blend using the Nelson-Hemwall-Edwards solubility parameter concept and the results of a consequent cost optimisation exercise with 14 different solvents and with constraints (set limits) as obtained from the starting point blend are given in Tables 3.7 and 3.8. 

---