Solubility parameter theory

The concept of solubility parameters as it relates to the internal energy of solutions and solutes was first proposed by Hildebrand in 1916 [1]. Internal pressure is the energy required to vaporize one cubic centimeter of a sub- 

The total solubility parameter, 6, of a material is a point in three-dimensional space where the three partial solubility parameter vectors meet. The distance in space between two sets of parameters, solvent and resin (i.e., how closely they are matched) can be represented by the radius of interaction, 

In Equation 4.2 the i terms correspond to the parameters of the resin and the j terms to the parameters of the solvent. The radius of interaction values for a series of solvents and a resin can be quickly calculated with a computer spreadsheet. The solubility parameters of a large number of solvents and polymers are known and listed in standard references [4,5]. While the original solubility parameter values had unit dimensions of (cal/cm ) and were designated as a Hildebrand (H) unit, the current usage favors the SI units where  

In older literature if the dispersion (nonpolar) value for a substance ranges from values of 6.0-9.0, one would know that the units of dimension were caP /cm. To convert these values to the favored SI units, multiply the old units by 2.05. 

Molecular structure determines the polarity and hydrogen-bonding characteristics of a solvent or polymeric resin. Little association or interaction 

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In earlier work on the applicability of the solubility parameter theory to HPLC, attention was focused on quantitation for this work, the model did not prove to be successful. Schoenmakers et al. [87] believe that the potential of the solubility parameter can aid in designing a genuine framework for retention behavior in LC. Based on their work, the following conclusions have been drawn ... 

Specific separation effects can be understood from the multicomponent solubility parameter theory. Specific effects for nonpolar compounds are predictable with perfluorinated and graphitized carbon black stationary phases. Specific selectivity for polar compounds in reversed-phase HPLC can be realized with polar additives to the mobile phase. 

Several studies attempted to relate the partition coefficient P of a solute in a liquid chromatographic or a gas chromatographic system with the composition of the two phases, one of which has a varying composition [19-23]. Tijssen et al. [24] and Schoenmakers [25] derived a relation between the partition coefficient and a binary mobile phase in reversed-phase HPLC from the solubility parameter theory of Hildebrand et al. [26]. Similarly, a relation can be derived for liquid-liquid extraction with extraction liquids composed of three components ... 

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 ... 

These very simple relationships can be verified experimentally as is shown in figure 3.16. The iso-eluotropic compositions of binary mixtures of THF and acetonitrile with water have been plotted against the binary methanol-water composition. The thin straight lines indicate the theoretical relationships from solubility parameter theory (eqns. 3.50 and 3.51). The thick lines correspond to average experimental data over large numbers of solutes [335]. An (average) experimental data point can be found as follows. 

Due to specific effects, the corresponding compositions of methanol and THF will not be exactly the same for all solutes. Conversely, when the iso-eluotropic composition is taken as the average of that observed for many solutes (or from solubility parameter theory), some solutes will be eluted later than with the original methanol/water mixture, and some will be eluted earlier. The relative differences may amount to a factor of two for certain solutes. This should not be seen as an error in establishing iso-eluotropic mixtures. Rather, it enables us to exploit iso-eluotropic mixtures to enhance selectivity, whilst keeping retention roughly constant. This principle is widely used for the optimization of selectivity in LC. 

Figure 3.16 shows that there is good agreement between (solubility parameter) theory... 

Figure 3.16 Iso-eluotropic compositions for binary mixtures of THF and acetonitrile in water, relative to methanol/water mixtures. The solid lines represent the average experimental compositions for a large number of solutes. The thin lines represent calculated compositions from solubility parameter theory (eqns.3.50 and 3.51). Figure taken from ref. [311]. Reprinted with permission.

Burke J, "Solubility Parameters Theory and Application", The Book and Paper Group Annual, Vol 3, American Institute for Conservation, 1984. 

The paper by Glatzhofer describes how a computer can be used to operate a viscometer and the paper by Meusberger describes how computer calculations based on solubility parameter theory can be used to optimize the choice of emulsifiers for pesticide emulsi-fiable concentrates. 

The solubility parameter theory (Eq. 4), first proposed by Hildebrand [21], was combined with the Flory-Huggins theory [43] to produce yet another means for determination of x-... 

Values of 6 for many liquids have been reported, and these have been recorded in extensive Tables [27, 28, 32, 34, 56-59]. The availability of these data provide an easy means of estimating 8. The solubility parameter theory also has serious shortcomings, however, which limits further the reliability of thermodynamic properties computed by the combination of both theories. Nevertheless it does provide useful qualitative, if not quantitative, descriptions of polymer-solvent systems. 

Equations (5) follow from the functional relationship of interaction energies to properties of the two interacting species (/) a is therefore a measure of the interaction strength of the adsorbent surface. It is believed that in most LSC systems the solution terms are effectively zero, as a result of cancellation of solvent-solute interactions in the two phases (/). Arguments in terms of solubility parameter theory lead to a similar conclusion 28) Inserting Eqs. (5) into Eq. (4), with neglect of the solution terms, then gives... 

In spite of widespread applications, the exact mechanism of retention in reversed-phase chromatography is still controversial. Various theoretical models of retention for RPC were suggested, such as the model using the Hildebrand solubility parameter theory [32,51-53], or the model supported by the concept of molecular connectivity [54], models based on the solvophobic theory [55,56) or on the molecular statistical theory [57j. Unfortunately, sophisticated models introduce a number of physicochemical constants, which are often not known or are difficult and time-consuming to determine, so that such models are not very suitable for rapid prediction of retention data. 

The retention times of analytes are controlled by the concentration(s) of the organic solvent(s) in the mobile phase. If a relatively small entropic contribution to the retention is neglected, theoretical considerations based either on the model of interaction indices [58], on the solubility parameter theory [51,52] or on the molecular statistical theory [57], lead to the derivation of a quadratic equation for the dependence of the logarithm of the retention factor of a solute. A, on the concentration of organic solvent. aqueous-organic mobile phase ... 

One possible explanation lies in the nature of the intermol-ecular forces involved. Amongst the most popular extensions to the basic solubility parameter theory is that due to Hansen [38] which considers contributions from three types of intermolecular forces ... 

The solublity parameter theory has been applied extensively using a mixed value of the solubility parameter ... 

When this theory was used to predict the solubility of polymers in a variety of solvents, it was only partially successful. It was apparent that other intermolecular forces were at work which could not be calculated by this simple procedure. Hydrogen bonding, probably the strongest type of intermolecular force in a nonelectrolyte, was the clue for making solubility parameter theory work. 

Ideally, Xi is a measure of the heat of mixing of the sorbed molecules with the polymer the less endothermic this process is, the greater the extent of sorption will be. For nonpolar components, the interaction parameter can be estimated by using solubility parameter theory... 

Crowley, J. D. "Some Applications of Three-Dimensional Solubility Parameter Theories," presented at Kent State University, 1972, short course on "Solubility Parameters—Their Origin and Use."... 

Correlation between the solubility parameter theory SPT and the EoS based on the Flory model, was explored by Biros et al. [1971]. The authors demonstrated that 5 = / V, where P is the... 

Complications such as these extend also to the case of polytetra-fluoroethylene. The large difference in estimated solid-vacuum tensions between this polymer and polyethylene is not imexpected, since a proportionately large difference exists for the liquid surface tensions of hydrocarbons and fluorocarbons having five to eight carbon atoms [58]. The underlying cause of this difference is, however, more obscure. The inter molecular forces for fluorocarbons apparently have features wuich lead to anomalous behavior, at least from the point of view of solubility parameter theory [59]. Thus, theoretical calculations of the surface tension for the bare solid in the case of polytetrafluoroethylene would face a number of difficulties not encountered with paraffin crystals. 

For the description of such interactions as well as of polymer swelling, models based on the Flory-Huggins Theory (Flory, 1953 Mulder, 1991) and UNIQUAC are often applied for mixtures in general and, for binary mixtures, also the Solubility Parameter Theory if the feed components are hydrophobic (Hildebrand and Scott,... 

By definition, any model, however closely it approximates reality, remains only an analogy. Thus, for example, modeling infinite-dilution activity coefficients by assuming that atoms (or segments of molecules) occupy positions of a three-dimensional lattice and that interactions occur only at cross-points, offers at best only a crude incture of the continuum of intermolecular interactions in the liquid state. Lattice models have therefore been roundly criticized on occasioiq even so, the results thereby predicted, at least for systems for which the equations are tractable (i.e., those comprised of n-alkanes cf. refs. 40.65) far exceed those arising, e.g., from solubility-parameter theory. 

Burke, J. (1984). Solubility parameters theory and application. The Book and Paper Group Annual The American Institute for Conservation (3) [online]. Available from http // aic.stanford.edu/sg/bpg/annual/v03/bp03-04.html [Accessed 20 December 2006]. Hansen, C. M. (1971). Solubility in the coatings industry. Sksnd. Tidskr. Eaerg. Lack., 17, 69. 

The Hildebrand-Scatchard Solubility Parameter Theory. —According to this theory the interaction parameter is given by... 

More recently Young has measured the upper critical solution temperatures of mixtures of n-C7Fi6 with a series of n-alkanes (n-Cs to n-Qs) and has shown that, although solubility-parameter theory is unable to predict the experimental critical temperatures with any accuracy, a modification of this theory due to Reed is more successful. Reed s improved theory takes into account the effect of the size and ionization potential diffidences between the two component molecules and is thus similar in many respects to the theory of Hudson and McCoubrey discussed in the next Section. 

Hildebrand and his co-workers have produced accurate gas solubilities for a great variety of systems over a lengthy period, and many of their measurements are tabulated in the comprehensive review of Battino and Clever. They have, however, persisted in the use of solubility parameter theory to correlate and interpret their measurements and in much of this work systems containing fluorocarbons either as the gaseous solute or as the liquid solvent appear to behave anomalously when compared with most other mixtures composed of non-polar molecules. 

Of presently available methods for the prediction of solvent physical properties, the solubility parameter theory by Hildebrand may still supply one of the most accurate and eompre-hensive results. However, the solubility parameter used there has no purely molecular character. Many other methods are more or less of empirical character. 

The dependence of solubility on pressure can be described only by modem theories taking into account the free volume of components. The corresponding states theory predicts a pressure dependence of the parameter through the effect on the free volume of the solution components. This dependence is predicted by the so-called solubility parameters theory as well, where the interaction between solvent and solute is described by solubility parameters with their dependencies temperature and pressure (Fig. 4.2.2). 

When Gjj / e < 1 then 8j < 82 and hence dX, / dP < Oin the solubility parameters theory and in the eorresponding states theory. When ej, / 22 is greater than unity 8j > 82 and the solvent becomes less compressible than the polymer. Then pressure ean inerease the (5j - 82) value, giving / dP > 0. 

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