Hildebrand-Scott solubility parameter

Distinctly different is the solubility behaviour of poly(a-phenylethyl isocyanide), which can be dispersed truly by thermodynamic mixing. It is soluble is more than 40 solvents, as shown in the mode of representation following Hansen s treatment (27), (Fig. 5). The well known Hildebrand-Scott solubility parameter by this treatment is divided into three indices which separately account for cohesive energy contributions from dispersion, permanent dipole-dipole, and hydrogen bonding forces. Thus, the conventional Hildebrand-Scott parameter equals 9.56 (cal/cm3) for an unfractionated sample of poly(a-phenylethyl iso-... 

The species concentrations are formulated in activities using the Pitzer model (207) for the aqueous phase and the Hildebrand-Scott solubility parameter (208) for the organic phase. 

Charles M. Hansen (4) was working in the area of paint technology. He was aware oT the Hildebrand/Scott solubility parameter, and explored the use of the solubility parameter in polymer-solvent interactions. He began his research with the consideration of the thermodynamic equation for the energy of mixing... 

Other molecular properties have been also proposed to model the hydrophobic interactions. The parachor, which is related to the surface tension of a compound (139, 140) represents mainly the intermolecular interactions in a liquid. The Hildebrand-Scott solubility parameter, 6, (141) is related to intermolecular van der Waals forces and the closely related molar attraction constant, F, is obtained by multiplying 6 by the molar volume (142). The partition coefficient between two solvents can be obtained from the solubility parameters and the molar volumes of the solute and the solvents (193). This relationship is based on regular solution theory (194) and the assumption that the partial molar volumes of the solute is not different from its molar volume. Recently this has been criticized and a new derivation was proposed (195) in which the partial molar volumes are taken into account. The molar refractivity, MR, is related to dispersion forces and can be obtained as a sum of the partial molar refractivi-ties assigned to atoms and bonds (140, 143). These parameters have been compared (144) to establish their relative applicability to correlations with biological activity. The conclusion was that logP and molecular refractivity were the best parameters. Parameters obtained from high pressure liquid chromatography (144,... 

Estimates for Cp were based on Hildebrand s solubility parameters, Sij, (Hildebrand and Scott 1950), which are related to the enthalpy of vaporisation and the... 

When the only effects that have to be taken into account are those of cavity formation in the solvent and the dispersion interactions, i.e., when both the solvent and the solute are non-polar, then Hildebrand s solubility parameter concept (Hildebrand and Scott 1950) provides good estimates of the solubility. The mole fraction of a gaseous solute, x2, in a solution in equilibrium at a partial pressure p2 of this gas, can be estimated from the following expression ... 

The nature of polymer-solvent interactions plays an important role in deciding the influence of chemical and solvent effects on blends. The Hildebrand s solubility parameter, has been extended to systems that have dispersive (subscript d), polar (subscript p) and hydrogen bonding (subscript h) interactions, i.e., 5, 5p, and 5j, respectively [Hildebrand and Scott, 1949 Burrel and Hansen, 1975]. 

According to Hildebrand and Scott [5], the enthalpy of mixing per unit volume A/im is related to the volume fraction

solubility parameter 5 of the two components ... 

The solubility parameter 5 of a pure solvent defined initially by Hildebrand and Scott based on a thermodynamic model of regular solution theory is given by Equation 4.4 [13] ... 

The solubility parameter has been defined by Hildebrand and Scott (1950) as ... 

Hansen (2007) has shown that the solubility parameter proposed by Hildebrand and Scott does not take into account the contribution of polar forces and hydrogen bonding, therefore, a more complex solubility parameter has been proposed ... 

As a possibility to classify the mixing behaviour of solvents, Hildebrand and Scott [26,27] developed the theory of the solubility parameter (S). It is... 

The square root of the cohesive pressure c as defined in eqn. 3.11 has been termed the solubility parameter 5 by Hildebrand and Scott (1962) because of its value in correlating and predicting the solvency of solvents for nonelectrolyte solutes. Solvency is defined as the ability of solvents to dissolve a compound. A selection of 5-values is given in table 3.10. 

One approach that was considered is based upon the solubility parameter theory of Hildebrand and Scott (36, 37). This approach attempts to determine the best solvent for cleaning resins as a function of the known resin contaminants. Hildebrand and Scott (36, 37) developed the solubility parameter (6) to describe the property of solvents ... 

This scale ranges from 7.3 for n-hexane to 23.4 for water. Compounds with higher solubility parameters are generally more polar or hydrophilic than those with lower solubility parameters. The solubility parameter of Hildebrand and Scott (36, 37) has been subdivided into... 

The square roots of the cohesive energy densities are given the designation have been labeled solubility parameters by Hildebrand (Hildebrand, 1949 Hildebrand and Scott, 1962). The... 

Furthermore, Hildebrand and Scott [32] found a relationship between the solubility parameter, 5, and surface tension, as, for polar and non-polar liquids. Their relationship can be written as [66]... 

An empirical relationship between the solubility parameter and the liquid surface tension of a nonpolar liquid was obtained by Hildebrand and Scott (9)... 

Aprotic Solvents, in J. F. Coetzee and C. D. Ritchie (eds.) Solute-Solvent Interactions, Dekker, New York, London, 1969, Vol. 1, p. 219ff. [95] H. Liebig Prdparative Chemie in aprotonischen Ldsungsmitteln, Chemiker-Ztg. 95, 301 (1971). [96] E. S. Amis and J. F. Hinton Solvent Effects on Chemical Phenomena, Academic Press, New York, London, 1973, Vol. 1, p. 271ff. [97] P. K. Kadaba Role of Protic and Dipolar Aprotic Solvents in Heterocyclic Syntheses via 1,3-Dipolar Cycloaddition Reactions, Synthesis 1973, 71. [98] J. H. Hildebrand and R. L. Scott The Solubility of Nonelectrolytes, 3 ed., Reinhold, New York, 1950 Dover, New York, 1964 J. H. Hildebrand and R. L. Scott Regular Solutions, Prentice-Hall, Englewood Cliffs/New Jersey, 1962 J. H. Hildebrand, J. M. Prausnitz, and R. L. Scott Regular and Related Solutions, Van Nostrand-Reinhold, Princeton/New Jersey, 1970. [99] A. E. M. Barton Handbook of Solubility Parameters and other Cohesion Parameters, CRC Press, Boca Raton/Elorida, 1983. [100] M. R. J. Dack, Aust. J. Chem. 28, 1643 (1975). 

Graessley et al, (1994,1995) have proposed an alternative scheme that correlates the x values for polyolefin blends with differences in inferred values of the solubility parameters of the pure components [see Eq. (2-31)]. For the series of polyolefins they studied, values of for the pure components can be assigned in such a way that the x parameters of the mixtures computed from Eq. (2-31) are in reasonable qualitative agreement with measured values. Direct estimates of the (5 s can be obtained from the following formula derived from the van der Waals cohesive energy density (Hildebrand and Scott 1950 Krishnamoorti et al. 1996) ... 

More commonly used descriptors of polymer solubility are the solubility parameters introduced by Hildebrand and Scott for dispersive interaction forces, and extended by Hansen " for dispersive (8 ), polar (8d), and hydrogen bonding contributions (8 ) to interaction energies. An equation sometimes used to estimate the solubility range of Polymer 2 in a solvent (subscript 1) is ... 

For non-polar mixtures with species interacting mainly by dispersion forces, the interaction parameter x can be estimated by the method developed by Hildebrand and Scott. It is based on the solubility parameter... 

Hildebrand and co-workers gave rise to the concept of the one-component solubility parameter (8) more than 50 years ago (see Hildebrand and Scott, 1951 1962 Hildebrand et al., 1970). It is defined as the square root of the cohesive energy density (CED) and may be expressed as... 

Following the introduction of the Hildebrand model, the topic of solubility parameters has been extensively discussed (Hildebrand and Scott, 1962 Hildebrand et al., 1970 Kumar and Prausnitz, 1975 Barton, 1983), and values of S can be found in these reference works. As a general rule, compounds having stronger London forces will be characterized by larger solubility parameters values. 

Hildebrand and Scott (1950) proposed that the solubility parameters of similar molecules could be calculated using the enthalpy of vaporization (AH,) and the molar volume of the liquid component (L)) at the temperature of interest ... 

Hildebrand and Scott used the geometric mean rule to describe the interaction between molecules of two unlike species to arrive at the total solubility parameter. Strictly speaking, this was valid for nonpolar type molecules only. The fact that Equation 10.4 has produced hundreds of satisfactory correlations of solubility, swelling, permeation, surface phenomena, etc., confirms that the geometric mean rule is likewise applicable to molecules engaging in permanent dipole-permanent dipole and hydrogen bonding interactions as well. 

Hildebrand and Scott warned that it is dangerous to employ solubility parameters for esters, ketones, alcohols, and other polar liquids. 

Sixty years ago "The Solubility of Nonelectrolytes" by Hildebrand and Scott was published. Their concepts of regular solutions and of the solubility parameter have been extremely important to the treatment of practical solution problems in the coatings and polymer chemistry field. These concepts have been generalized and broadened over the years to meet the needs of the industrial chemists who must deal with matters associated with solution formation. 

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