Hildebrand-Scatchard

High yield, high selectivity (HY/HS) catalysts, 20 536, 537, 544 Hildebrand-Scatchard hypothesis, 23 97 Hill climbing, 7 400... 

Prausnitz (16) discusses this and related equations as well as the contributions of Margules, Hildebrand, Scatchard, Guggenheim, and others to this topic. For the activity of either component, referenced to the pure liquid, one has... 

The extended Van Arkel equation contains the same volume factor as that of Hildebrand-Scatchard. Van Arkel s extended equation is then as follows ... 

The Flory-Huggins interaction parameter x and the Hildebrand-Scatchard solubility parameter 0 for the polymer may also be calculated using previously described procedures (3). 

The Hildebrand-Scatchard equation (see Hildebrand and Scott, 1951), which is derived on semiempirical grounds, is... 

Determination of the Flory-Huggins interaction parameter (x) for solvent-polymer pairs again requires careful fractionation of the humic macromolecules. In the view of this author, much can be learned about the ways in which humic substances are associated through determination of Flory-Huggins and solubility parameters of carefully fractionated humic substances, and through applications of empirical equations such as those of Flory-Huggins [Equation (6)] and Hildebrand-Scatchard [Equation (7)]. 

This is the case for the C6H6 - CC14 system, but not for the C6H6 - CS2 system. Therefore, regular solution theory is not applicable to the C6H6-CS2 system. To test the Hildebrand-Scatchard model we use... 

This equation is known as the Hildebrand—Scatchard equation. Of course (Ec/V) / is the solubility parameter, 5, so we can write this equation as... 

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

The absence of the volume change presumes that AU" is equal to the enthalpy or to heat of mixing which was equated to the right terms of the equation (under the equality of 8 of both components, AU = 0). The Hildebrand-Scatchard approach corresponds to the geometric mean rule. ... 

Based on the pioneering work of van der Waals [16] and van Laar [17], the Hildebrand-Scatchard equation was derived on semitheoretical grounds by Scatchard [18,19] and Hildebrand [20-24] and popularized by Hildebrand, Scott, Prausnitz and others [25-37, 10-12]. For a binary mixture, the Hildebrand-Scatchard equation is expressed as... 

For nonpolar systems the activity coefficient can be estimated using the Hildebrand-Scatchard theory of regular solutions. To calculate the activity coefficient of a dissolved solute using regular solution theory, solubility parameters must be available for the components. For ntany materials these paraiiteters can be calculate and/or are available in standard engineering references. 

Hildebrand and Scott [12] first correlated the enthalpy of mixing with the cohesive properties of the permeant, and for a binary mixture of a polymer and a solvent, the Hildebrand-Scatchard equation is expressed as ... 

Martire [29] utilized van Arkel s modification of the Hildebrand — Scatchard theory [30] to extend eqn (3.40) so that it takes accoimt of dipole interactions the following relation was obtained for the activity coefficient ... 

The Hory treatment can be combined "with the Hildebrand-Scatchard theory to give the follo wing relationship for the interaction parameter [59] ... 

The solubility parameter defined by eqn (5.39) is not identical to that conventionally measured by swelling, solubility or surface tension data, since in the first case the solute is at infinite dilution in the polymer, while in the other cases its concentration is high. Because it is possible that at high dilutions the behaviour as a regular solution, inherent to the development of the Hildebrand-Scatchard theory, is more rigorously obeyed, 8" may be more meaningful than 8j. 

For solubility of solids in liquid, Hildebrand and Scatchard independentiy derived another equation, now called the Hildebrand-Scatchard equation ... 

When X values are determined for a given polymer or other nonvolatile component of a polymer system, and for a series of vapors for which solubility parameter values are known, the IGC method provides a unique approach to determining the solubility parameter, dr, for the polymer phase. The method is based on the principle that the Flory-Hu ins interaction parameter, x> can be related to dr by combining the Hildebrand-Scatchard solution theory with the Flory-Huggins theory [21] ... 

We may also mention at this stage the semi-empirical Hildebrand-Scatchard formula for the excess free energy (cf. Hildebrand and Scott [1950])... 

The first effect tends to be the dominating factor in mixtures of molecules that are not very different in size and the early investigators in the field van Laar, Hildebrand, Scatchard, Wohl, etc., assumed that =... 

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