Solubility parameter, definition

Solubility parameters are generally tabulated, together with the corresponding liquid molar volumes, only at 25°C. Although solubility parameters are themselves temperature-dependent, the combination of quantities in Eq. 70 is not. Differentiating Eq. 70 with respect to temperature gives — the excess entropy, a quantity which has been assumed to be zero in accord with the definition of a regular solution. Thus only data at 25°C are needed. Solubility parameters may be... 

Section 2.3 describes various methods for the characterization and classification of mobile and stationary phases for chromatography. In section 2.3.1 the solubility parameter is introduced as a quantitative definition of the word polarity . Section 2.3.2 describes the characterization of GC stationary phases according to Rohrschneider and section 2.3.3 the classification of LC solvents according to Snyder. The applicability of the different methods is summarized in section 2.3.4. 

In table 2.2 values are given for a variety of materials, including both typical solvents and typical stationary phases. The inclusion of the latter involves some rigorous assumptions, because the simple definition above (eqn.2.1) bears no relevance for solid adsorbents. Nevertheless, by looking at table 2.2 the usefulness of the solubility parameter as a quantity to describe polarity in quantitative terms becomes instantly apparent. The... 

By definition, the relative retention is larger than (or equal to) 1. Thus, for a normal phase system, where 8S > 5m, it follows from eqn.(3.31) that 5- > Sp and hence the more polar solute will elute last. Again, the reverse is true for a reversed phase system. Because the signs of the two factors in eqn.(3.31) which involve solubility parameters will always be thesame, we may state that it is the absolute difference between the polarities of the two phases that should be maximized. Therefore, the selectivity of a phase system (V) may be defined as... 

There are other advantages of the above definition of A, one of them being the fact that the values of x depend on the assumed volume of a polymer segment (usually taken equal to the volume of the solvent molecule V2), while A is defined per unit volume of the mixture. Another advantage is that the values of A can be related approximately to the solubility parameters of the components 81 and 82 by ... 

Since the Flory interaction parameter, x> was derived by considering only interaction energies between the molecules, it should not contain any entropic contributions and Equation (2D-9) should yield the correct value for the Flory-/ parameter. Unfortunately, x contains not only enthalpic contributions from interaction energies, but also entropic contributions. The solubility parameter includes only interaction energies and by the definition of regular solutions does not include any excess entropy contributions. Blanks and Prausnitz (1964) point out that the Flory / parameter is best calculated from... 

The classical method for measuring the solubility parameter of a polymer is to determine the solubility of that polymer in a large number of liquids with known solubility parameters, and then to plot the observed solubility as a function of the solubility parameters of the test liquid. The solubility parameter where the polymer solubility is maximal [40] is by definition the solubility parameter of the polymer, 5pol. 

According to Hildebrand s solubility parameter approach [101], two liquids are miscible if their solubility parameters 8 differ by no more than 3.4 units [101, 102] cf. Eqs. (2-1) and (5-77) for the definition of 8. That is, mutual miscibility decreases as the 8 values of two solvents become farther apart. Higher mutual solubility will follow if the 8 values of the solvents are closer. A comprehensive collection of 8 values has been given by Barton [100]. 

Thermodynamic Properties The variation in solvent strength of a supercritical fluid from gaslike to liquidlike values may be described qualitatively in terms of the density, p, or the solubility parameter, 5 (square root of the cohesive enei density). It is shown for gaseous, liquid, and SCF CO2 as a function of pressure in Fig. 22-17 according to the rigorous thermodynamic definition ... 

Often referred to as the solvent cohesive energy density, the Hildebrand solubility parameter is considered to be a measure of the solvent contribution to the cavity term, and is used as a correction factor in the - solvatochromic equation. It is related to the general definition of London cohesive energy between two interacting species ... 

In using Eqs. (17) and (18), the molar liquid volume of the solvent, can be estimated by resorting to generalized density correlation chart (17). The solubility parameter of the solvent can be determined based on its definition, or. 

Alternatively, the molar volume of liquids may be estimated by generalized correlation methods (17) or group contribution methods (see Table 3). The subscript 2 is omitted in Eq. (20). The solubility parameter can be estimated based on its definition, or. 

Obviously, a large number of compounds would seem to fit these two definitions. (Salicylic acid and galacturonic acid, for example, would fit the solubility parameters for soil humic and fulvic acids, respectively.) However, the added restrictions of elemental analysis (see Table 1)—dark color (e.g., absorption spectra) titration data, and molecular weight—would narrow the possible chemical structures. 

Researchers usually use a diagram of pure component to discuss the definition of an SCF. This is reasonable because supercritical has clear meaning for a pure substance. A pure SCF has some unique features, especially near its critical point. The solvent properties (e g. density, dielectric constant, solubility parameter, difiusivity) are sensitive to pressure. Therefore, pressure is an effective variable factor to optimize the operating conditions in the applications. However, a SCF loses most of these features as it is far from the critical point. 

The Hoftyser-van Krevelen method These researchers proposed group values for the cohesive energy, i.e., for the ratio A W. The total cohesive energy is estimated from the group values via Equation 16.1. Then the solubility parameter is estimated from the definition. Equation 16.8. 

The equation is discussed in Section 4.3.3. Two parameters are required for each component v, is the pure i liquid molar volume at 298°K, and 5 is the solubility parameter of component i. The solubility parameter of the mixture 8 , is given by the volumetric average of the components 8 , = Zpi ,v,8,/2 pi ,v,. Parameters are available for numerous substances. Additional parameters can be readily determined from their definitions, when the need arises, except for light gases. 

In examining the reasons for the fundamental use of the solubility parameter concept, it must be recognized that independent of any assumptions in the derivation of Equation 1 and the definition of 6 in Equation 2 there is a computational and experimental problem. This problem is often overlooked. Consider mixing two components, each having molar volumes of 100 cm /mol and energies of vaporization of 8000 and 9000 cal/mol. From Equations 1 and 2, AE would be computed as 13.6 cal/mol. If AE for the first component is in error by only 5%, so that AE is 7600 cal/mol instead of 8000 cal/mol, the computed value of AEjq will be 19.2 cal/mol, almost 50% higher than the earlier value of 13.6 cal/mol. Yet it is rare indeed that AE is known to within 5%. Table II, compiled by... 

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