Hildebrand Scatchard approach

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. ... 

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] ... 

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]. 

Acree and Rytting [54,55] developed the nearly ideal binary solvent (NIBS) approach to predict solubilities. NIBS did show an increased ability to predict solubilities versus the Scatchard-Hildebrand equation. However, it is limited to use in systems only involving nonspeciLc interactions. 

A linear plot of A<5/[HJ0 against AS will have a slope of —Ka with an intercept of ASmax. This particular use of NMR data is derived from the work of Foster and Fyfe [3], which in turn is a variation on the well-known Scatchard plot [4], It differs slightly from the Hanna-Ashbaugh approach [5], itself a method of applying the Benesi-Hildebrand solution to NMR, that is also widely used. For the data to be valid the chemical shifts of the guest protons must relate to the... 

Perhaps the most important term in Eq. (5.2-3) is the liquid-phase activity coefficient, and methods for its prediction have been developed in maiiy forms and by many workers. For binary systems the Van Laar (Eq. (1.4-18)], Wilson [Eq. (1.4-23)], NRTL (Eq. (1.4-27)], and UmQUAC [Eq. (t.4-3ti)] relationships are useful for predicting liqnid-iffiase nonidealities, but they require some experimental data. When no dim are available, and an approximate nonideality correction will suffice, the UNIFAC approach (Eq. (1.4-31)], which utilizes functional group contributions, may be used. For special cases involving regular solutions (no excess entropy of mixing), the Scatchard-Hildebrand method provides liquid-phase activity coefficients based on easily obtained pure-component properties. 

Scatchard Hlldebrand regular-solution activity coefficients. Hildebrand (1929) defined a regular solution as the mixture in which components mix with no excess entropy provided there is no volume change on mixing. Scatchard in an independent work arrived at the same conclusion. The definition of regular solutions (Hildebrand and Scott, 1950) is in line with van Laar s assumption that the excess entropy and the excess volume of mixing are negligible. Scatchard and Hildebrand used an approach different from van Laar s to calculate G. They defined parameter C as... 

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