Hildebrand solubility parameter theory

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. 

If we express the heat of mixing in terms of the Hildebrand solubility parameter theory, the B parameter is (see Eq. 3.17) ... 

Various models of SFE have been published, which aim at understanding the kinetics of the processes. For many dynamic extractions of compounds from solid matrices, e.g. for additives in polymers, the analytes are present in small amounts in the matrix and during extraction their concentration in the SCF is well below the solubility limit. The rate of extraction is then not determined principally by solubility, but by the rate of mass transfer out of the matrix. Supercritical gas extraction usually falls very clearly into the class of purely diffusional operations. Gere et al. [285] have reported the physico-chemical principles that are the foundation of theory and practice of SCF analytical techniques. The authors stress in particular the use of intrinsic solubility parameters (such as the Hildebrand solubility parameter 5), in relation to the solubility of analytes in SCFs and optimisation of SFE conditions. 

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 ... 

The solubility of a gas is an integral part for the prediction of the permeation properties. Various models for the prediction of the solubility of gases in elastomeric polymers have been evaluated (57). Only a few models have been found to be suitable for predictive calculations. For this reason, a new model has been developed. This model is based on the entropic free volume activity coefficient model in combination with Hildebrand solubility parameters, which is commonly used for the theory of regular solutions. It has been demonstrated that mostly good results are obtained. An exception... 

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 ... 

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-... 

The solubility of a solute in a supercritical fluid can be quantitatively estimated using Giddings theory, which relies on differences between the Hildebrand solubility parameters for the SF and solute concerned. Solubility in a supercritical fluid can be understood by examining the Gibbs-Helmholtz equation ... 

A thermodynamic method, more fitting to this chapter, has been proposed by Nauman et al. They claim a process for the separation of a physically mixed solid polymers by selective dissolution. They rely on the different polymer solubility characteristics. Tables of this property have been reported and are based on regular solution theory and Hildebrand solubility parameters. The core of the Nauman invention is to find suitable solvents to dissolve particular polymers under defined temperature and pressure conditions. A mixture of polymers is first added to one solvent, at a given temperature, in order to dissolve a particular polymer. The remaining polymer mixture is then treated at a higher temperature with the same solvent or with a different solvent. For clarity, two examples are taken from the patent."... 

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... 

In the above considerations, the hydrophobic portions of both the membrane polymer and the small molecules that enter the membrane are expected to interact in the hydrophobic microphases in the membrane. It therefore becomes useful to find a numerical measure of the miscibility of these hydrophobic portions of molecules. In the case of complete molecules, both small and polymeric, the solubility parameter concept has been useful in the past. This concept is related to the enthalpy change which occurs on mixing in regular solution theory as developed by Hildebrand and coworkers (10) and as used for polymer solution theory by Flory (11). The Hildebrand solubility parameter is a measure of the attraction between molecules of the same kind, including dispersion forces, polar forces, and hydrogen bonding... 

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). 

Snyder has discussed liquid solvent characterization on several occasions (29,30,38,39). One of the very interesting points is that when several solvents have essentially the same solvent power as described by the Hildebrand solubility parameter (40), those solvents often do not dissolve a particular solute to the same extent. This is attributed to the fact that the Hildebrand solubility parameter does not, and cannot by regular solution theory. 

Compatibility signifies the ability of two or more substances to mix intimately to form a homogeneous composition with useful plastic properties. The anomalies of why one solvent will dissolve a given resin, another will only swell it, and a third will leave the resin unaffected have promoted a considerable amount of empirical work and extensive theoretical explanation. Applying thermodynamic theory to real solutions led to several the Hildebrand solubility parameter 6 based on cohesive energy (12). the Flory-Huggins parameter, X (13). and several newer parameters with sharper precision but which are more difficult to apply. 

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,... 

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

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. 

If the interactions are confined to van der Waals ones and the solution conforms to the restrictions of regular solution theory (Hildebrand and Scott (1950)) then the well known Scatchard-Hildebrand solubility parameter expression can be applied ... 

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. 

Miscibility between the individual polymers is the most important factor to determine the performance characteristics of a polymer blend. Mutual solubility of the phases, the thickness and properties of the interphase formed during blending and the structure of the blend are mainly dependent on the miscibility of individual polymers within a polymer. As a result, a quantitative estimation of interactions is very much important for the prediction of blend properties. Comparison of solubility parameters of individual polymers is an effective method to predict the extent of miscibility within a blend. According to the Hildebrand solubility theory, a large difference in solubility parameters (6p) of individual matrices results in immiscibility between them in the absence of any interfacial compatibil-izer [222]. Jandas et al. have reported that PLA and PHB have Hildebrand solubility parameters (6p) of 23.5 J /cm and 19.8 J Vcm which can turn out to be partially miscibile blends in between them [35]. In case of partially miscible blends, the miscibility can be controlled by compatibili-zation using proper interactables. 

Regular solution theory assumes that specific interactions such as hydrogen bonding are absent, and therefore Hildebrand solubility parameters are generally applicable only to systems containing relatively nonpolar constiments. It is important to remember that neither of these approaches are theoretically justified for mixtures in which specific solvation interactions are important. 

Another useful tool is the Hildebrand solubility theory, which is applicable to apolar and moderately polar systems. For strongly polar systems, it is unable to correctly qualify the compatibility between components. However, the massive amount of interaction parameters data obtained in recent decades, and mainly Small s method, allowing to assess them, make this method quite efficient and readily applicable. The Hildebrand solubility parameter, 5, can be defined as the square root of the cohesive energy density (CED) and it is measured in (MJ m )° . This parameter indicates the polarity level of the component and goes from 12 (MJ m )° for nonpolar components to 23 (MJ m )° for water. The larger the difference... 

The Flory—Huggins theory, which is based upon statistical thermodynamic models, has been used to assess the miscibility of polymer blends and was developed by Flory (1941, 1942) and Huggins (1941,1942) in the 1940s. Unlike the Hildebrand solubility parameter, it provides a fundamental understanding backed with classical thermodynamic theories. 

For PMMA, poly(methyl methacrylate), with a degree of polymerization of 1000, calculate the Hildebrand solubility parameter using the EOS from lattice fluid theory. 

Solubility parameter theory (Hildebrand ) is not separately considered below but is still widely used in industry. It has led to the construction of comprehensive tables that provide an easy means of estimating thermodynamic quantities of rather limited reliability. Harris and Seymour have edited a collection of papers in several of which solubility parameter theory is used and these offer more details. 

An attempt has also been made to relate the solvent effect to the degree of substrate film plasticity induced by the grafting solution. This theory relates grafting yield to the plasticizing efficiency, expressed as the Hildebrand solubility parameter, of the grafting solution. 

Applying the solubility parameter theory first introduced by Hildebrand, X-,- was expressed as ... 

The quality of a solvent-polymer system can be correlated with their Hildebrand solubility parameters (<5) in such a way that, when these parameters are similar ds—dp <2.5 (cal/cm ) the solubility is acceptable (where <5s and 5p are the Hildebrand solubUity parameters for the solvent and the polymer, respectively). The above criterion comes from the approximate Flory-Huggins theory. 

Solubility parameter theory was advanced first by Hildebrand and Scott. Small developed a method for calculating the parameters from the contributions of groups within the molecule. Bunell, Hansen, and Crowley et al. were especially successful in utilizing the concept for the formulation of solvent-based... 

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