Hildebrand and Hansen solubility parameters

Belmares, M., M. Blanco, W. A. Goddard, R. B. Ross, G. Caldwell, S.-H. Chou, J. Pham, P. M. Olofson, and C. Thomas. 2004. Hildebrand and Hansen solubility parameters from molecular dynamics with applications to electronic nose polymer sensd>.r omputat. Chen25 1814-1826. 

It is evident from Table 2 that both Hildebrand and Hansen solubility parameters increase with an increase in DS of polymer. This increase is not the same for all parameters. For example, when DS increases from 0 to 70.5% the dispersive term of Hansen parameter SJ) increases only by 1.7%,... 

In addition, the theoretical equations in the Hildebrand and Hansen approaches can be effectively applied to predicting the solubility of a new compound by employing the experimental solubility data of a structurally related compound. The predicted values for the new compound would be based on the experimental one- or three-dimensional solubility parameter of the structurally related compound, and the group additivity principles would be applied to estimate the respective solubility parameter of the second compound. Solubility parameters associated with the Hildebrand and Hansen approaches have proved useful in the selection of not only solvents, but also of other excipients found in formulations (Belmares et al., 2004). 

Predictions of Woo could be performed using global (Hildebrand) or partial (Hansen) solubility parameters, but these are very difficult (and perhaps impossible) to determine accurately from solvent-sorption experiments, so that this way is not realistic. The best experimental approach is, in our opinion, using the ultrasonic modulus. 

Solvating efficiency of the plasticiser for PVC -predicted using Hansen solubility parameters (350) and the Hildebrand solubility parameter (442)... 

A number of methods based on regular solution theory also are available. Only pure-component parameters are needed to make estimates, so they may be applied when UNIFAC group-interaction parameters are not available. The Hansen solubility parameter model divides the Hildebrand solubility parameter into three parts to obtain parameters 8d, 5p, and 5 accounting for nonpolar (dispersion), polar, and hydrogenbonding effects [Hansen,/. Paint Technot, 39, pp. 104-117 (1967)]) An activity coefficient may be estimated by using an equation of the form... 

The solubility parameter has found previous use in membrane science. Casting solution components and composition have been selected using the Hansen solubility parameters (68-71). The total Hansen solubility parameter, which is equivalent to the Hildebrand parameter (.72), has been used to explain permeation and separation in reverse osmosis (23). Hansen s partial parameters have also been used to explain permeation and separation in pervaporatlon (61). The findings of these studies (61,73) plus those reported elsewhere in this volume (74) do lend credence to the use of 6, 6, and 6, for membrane material selection. 

Hildebrand applied the solubility parameter approach to mixing of two polymers, to estimate the enthalpy of mixing per unit volume [Hildebrand and Scott, 1964]. The concept was extended to incorporate the polar and hydrogen bonding interactions [Hansen, 1967, 1969 Nelson et al., 1970]. Thus, the three-dimensional solubility parameter was expressed as ... 

Several parameters are suitable as measures of polarity the dielectric constant the Hildebrand solubility parameter 8 and its extension, the three-component (or three-dimensional) Hansen solubility parameters, which cannot be discussed here. However, the most practical value and significance has gained Poctanoi because it is the most easily accessible parameter, and many useful correlations for its utilization in a number of relationships have been worked out in the past decades. 

The total solubility parameter, 5, corresponds to the overall Hildebrand solubility parameter, and the Hansen solubility parameters, 5p, and h, are contributions from non-polar interaction, polar interaction, and hydrogen bonding, respectively [15]. The end point of the radius vector represents the solubility parameter. This means that each solvent and each polymer can be located in a three-dimensional space. 

Sulfonation of PPO results in an increase in hydrophilicity of the modified polymer due to introduction of an electrophilic subsistent into the polymer backbone. Quantitatively, polymer hydrophilicity can be expressed by the magnitude of Hildebrand solubility parameter and the components of the Hansen solubility parameter. Table 2 presents the values of the above parameters calculated using a group contribution approach for HSPPO of different degrees of sulfonation [23]. 

Table 2. Hildebrand solubility parameter and components of Hansen solubility parameter for HSPPO of different degree of sulfonation [23],...

Numerous reports of comparable levels of success in correlating adhesion performance with the Scatchard-Hildebrand solubility parameters can be found in the literature [116,120-127], but failures of this approach have also been documented [128-132J. Particularly revealing are cases in which failure was attributed to the inability of the Scatchard-Hildebrand solubility parameter to adequately account for donor-acceptor (acid-base) interactions [130,132]. Useful reviews of the use of solubility parameters for choosing block copolymer compatibilizers have been prepared by Ohm [133] and by Gaylord [134]. General reviews of the use of solubility parameters in polymer science have been given by Barton [135], Van Krevelen [114], and Hansen [136]. 

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 ... 

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-... 

Solubility parameters were developed by Charles Hansen as a way of predicting if one material will dissolve in another and form a solution. They are based on the idea that "like dissolves like" where one molecule is defined as being like another if it bonds to itself in a similar way. The Hildebrand solubility parameter (8) provides a numerical estimate of the degree of interaction between materials, and can be a good indication of solubility, particularly for non-polar materials such as many rubbers. Materials with similar values of solubility parameters are likely to be miscible [7]. 

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... 

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 ... 

Modifications to the Hildebrand solubility parameter model have been advanced in attempts to achieve better degrees of solubility prediction (Taft et al., 1969 Rohrschneider, 1973). Among these, the three-dimensional solubility parameter introduced by Hansen and Beerbower (1971) showed the most practical application. These workers calculated the total solubility parameter (5totai) using three partial parameters, 3d, 3p, and 3h ... 

Fortunately, most organic solvents are nonpolar and therefore their intermolecular forces are weak London or dispersion forces. Hildebrand used the term "regular solutions" to describe solutions of nonelectrolytes and their nonpolar solvents. Additional theories on the solubility of polymers were developed by Flory ( ) and Huggins O). Probably the most important publications leading to the practical use of solubility theories by polymer scientists were those published by Burrell in 1955 ( ) and 1966 ( ). Modifications in the Hildebrand solubility parameter concept for regular solutions to account for larger intermolecular forces were made by Liebermann ( ), Crowley (.7), Hansen and Beerbower ( ) and Nelson et al. (9). 

The above interaction parameters may be related to the Hildebrand solubility parameter [22] 8 (at the oil side of the interface) and the Hansen [23] nonpolar, hydrogen-bonding and polar contributions to 8 at the water side of the interface. The solubility parameter of any component is related to its heat of vapourisation AH by the expression. 

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