Hildebrand approach

Adjei, A., J. Newburger, and A. Martin. 1980. Extended Hildebrand approach Solubility of caffeine in dioxane-water mixturesJ. Pharm. Sci69 659-661. 

Wu, P. L, A. Beerbower, and A. Martin. 1982. Extended Hildebrand approach Calculating partial solubility parameters of solid solutaii.Pharm. Sci71 1285-1287. 

Adjei, A., Newburger, J., and Martin, A. Extended Hildebrand approach solubility of caffeine in dioxin-water mixturesj. Pharm. Sci., 69, 659-661,1980. 

Also, the original Hildebrand approach has been refined to take into account the contribution of polar groups and hydrogen bsolubility parameters. These mndifications of the Flory-Huggins theory and of the solubility parameter concept have made these methods an even more useful tool in the description of solutions, especially of mixtures containing polymer compounds. A comprehensive treatment of these extensions of Flory-Huggins and Hildebrand s theories, as well as the new equation of state approach of Flory (1965), bns re ntly been published (Shinoda, 1978 Olahisi et al 1979). 

Bustamante, P, Escalera, B., Martin, A., Selles, E., 1993. A modification of the extended Hildebrand approach to predict the solubility of structurally related drugs in solvent mixtures. J. Pharm. Pharmacol. 45, 253-257. 

Adamson AW, Cast AP (1997) Physical chemistry of surfaces, 6th edn. Wdey, New York Adjei A, Newburger J, Martin A (1980) Extended Hildebrand approach solubility of caffeine in dioxane-water mixtures. J Pharm Sd 69 659-661 Amidon GL, Lennernas H, Shah VP, Crison JR (1995) A theoretical basis for a biopharmaceutic drug clas sification t he correlation of in vitro dmg product dissolution and in vivo bioavailabUity. Pharm Res 12 413-420... 

A primary goal is to Investigate the combined Influences of conformational asymmetry (characterized by -y = Tb/Ta) and interaction or chemical asymmetry (characterized by A) on blend miscibility as conveniently quantified by the effective chi parameter of Eq. (5.6). Investigating the validity of regular solution, or Hildebrand, approaches is also of interest since it has been recently suggested to work surprisingly well for hydrocarbon polymer alloys based on experimental studies of polyolefin blends. For simplicity, we focus here on equimolar mixtures (< >= ), although the blend composition-dependence of the effective chi parameter is found to be very weak under the conditions of the calculations stated above." ... 

Matthews-Akgerman The free-volume approach of Hildebrand was shown to be valid for binary, dilute liquid paraffin mixtures (as well as self-diffusion), consisting of solutes from Cg to Cig and solvents of Cg and C o- The term they referred to as the diffusion volume was simply correlated with the critical volume, as = 0.308 V. We can infer from Table 5-15 that this is approximately related to the volume at the melting point as = 0.945 V, . Their correlation was vahd for diffusion of linear alkanes at temperatures up to 300°C and pressures up to 3.45 MPa. Matthews et al. and Erkey and Akger-man completea similar studies of diffusion of alkanes, restricted to /1-hexadecane and /i-octane, respectively, as the solvents. 

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]. 

This approach to solution chemistry was largely developed by Hildebrand in his regular solution theory. A regular solution is one whose entropy of mixing is ideal and whose enthalpy of mixing is nonideal. Consider a binary solvent of components 1 and 2. Let i and 2 be numbers of moles of 1 and 2, 4>, and 4>2 their volume fractions in the mixture, and Vi, V2 their molar volumes. This treatment follows Shinoda. ... 

The promising approach taken by Vandenburg et al. [37,489] is to use initially a solvent with a Hildebrand solubility parameter several MPa1/2 different from the polymer (i.e. a poor , nonswelling solvent for the polymer) to determine experimentally the maximum... 

The use of the Hildebrand solubility parameter approach to aid solvent selection with a few simple experiments, starting from the liquid solvents used in traditional extraction methods, limits the efforts needed in method development. As for other extraction... 

A more explicit approach to solvent selection for ASE of polymers, based on Hildebrand solubility... 

There have been numerous approaches to describing the temperature dependence of the properties. For aqueous solubility, the most common expression is the van t Hoff equation of the form (Hildebrand et al. 1970) ... 

In this respect, the solvatochromic approach developed by Kamlet, Taft and coworkers38 which defines four parameters n. a, ji and <5 (with the addition of others when the need arose), to evaluate the different solvent effects, was highly successful in describing the solvent effects on the rates of reactions, as well as in NMR chemical shifts, IR, UV and fluorescence spectra, sol vent-water partition coefficients etc.38. In addition to the polarity/polarizability of the solvent, measured by the solvatochromic parameter ir, the aptitude to donate a hydrogen atom to form a hydrogen bond, measured by a, or its tendency to provide a pair of electrons to such a bond, /, and the cavity effect (or Hildebrand solubility parameter), S, are integrated in a multi-parametric equation to rationalize the solvent effects. 

Hildebrand developed solubility parameters to predict the solubility of nonpolar polymers in nonpolar solvents. The solubility parameter is the square root of the CED. For polar solvents, special solvent-polymer interactions can be incorporated into the solubility parameter approach. 

One of the approaches to calculating the solubility of compounds was developed by Hildebrand. In his approach, a regular solution involves no entropy change when a small amount of one of its components is transferred to it from an ideal solution of the same composition when the total volume remains the same. In other words, a regular solution can have a non-ideal enthalpy of formation but must have an ideal entropy of formation. In this theory, a quantity called the Hildebrand parameter is defined as ... 

Because the entropy of formation in Hildebrand theory is ideal, this approach should be restricted to those systems in which there are no structure effects due to solute-solvent and solvent-solvent interactions. The implication of this is that the solute should be non-ionic and not have functional groups which can interact with the solvent. According to Equation (4.8), the maximum solubility occurs when the Hildebrand parameter of the solvent is equal to the Hildebrand parameter of the solute. That is, when plotting the solubility versus the Hildebrand parameter, the solubility exhibits a maximum when the solubility parameter of the solvent is equal to the solubility parameter of the solute. 

Solvent-polymer compatibility problems are often encountered in industry, such as in the selection of gaskets or hoses for the transportation of solvents. A rough guide exists to aid the selection of solvents for a polymer, or to assess the extent of polymer-liquid interactions. A semi empirical approach has been developed by Hildebrand based on the principle of like dissolves like. The treatment involves relating the enthalpy of mixing to a solubility parameter, S, and its related quantity, 8, called the cohesive energy density. 

Godfrey gave an alternate approach for the prediction of mutual miscibility of solvents (Godfrey, 1972). As a measure of lipophilicity (that is, affinity for oil-like substances) the so-called miscibility numbers (M-numbers, with values between 1 and 31) have been developed. These are serial numbers of 31 classes of organic solvents, ordered empirically by means of simple test tube miscibility experiments and critical solution temperature measurements. There is a close correlation between M-numbers and Hildebrand s 5-values. 

The requirement that AG be negative for spontaneous dissolution is readily met if the first term, AH, is less than the second term, — 7A5. Because the polymer chain units are bound through primary, covalent bonds, the units are not free to move independent of their neighboring units. Thus the — TAS term is lower for polymer solution than for the solution of smaller molecules. Most approaches for correlating structure with polymer solubility have focused on the AH term. Hildebrand has proposed the following relationship,... 

Hildebrand, J. A., Liang, K. K., and Bennett, S. D. (1983). Fourier transform approach to materials characterization with the acoustic microscope. /. Appl. Phys. 54, 7016-19. [108]... 

Since there are so many solvents to choose from, it is natural that the search for guidelines for solvent selection has been intense. Researchers have tried to correlate enzyme activity, stability, and selectivity with different solvent descriptors, such as logP, dielectric constant, dipole moment, Hildebrand solubility parameters, and many others. When this approach is successful, the search for the optimal solvent can be limited to those having suitable values of the selected solvent descriptor(s). A list of solvent descriptors of a range of commonly used solvents is given in Table 1.4. 

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 ... 

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