Hildebrande

Hildebrand, J. H., and R. L. Scott "Regular Solutions," Prentice-Hall, Englewood Cliffs, N.J., 1962. 

Updates some of the material in Hildebrand s 1950 boo)c primarily for chemists. 

Taken together, these solvent-solute interactions make up the solvent polarity, which is represented well by Hildebrand s solubility parameter (1950). 

Hildebrand, J.H. and R.L. Scott (1962), Regular solutions. Prentice Hall, Engelwood Cliffs, NJ. 

Hildebrand B.P., Harrington TP. Mapping of materials stress with ultrasonic tomography //Proc. Symp. Microstmctural Characterization and Reliability Strategies - Pittsburgh, 1980. -P. 349-365. 

Hildebrand T., Ruegsegger P. Quantifieation of bone microarchitecture with the structure model index. CMBBE, v.l, 15-23, 1997. 

Figure III-9u shows some data for fairly ideal solutions [81] where the solid lines 2, 3, and 6 show the attempt to fit the data with Eq. III-53 line 4 by taking ff as a purely empirical constant and line 5, by the use of the Hildebrand-Scott equation [81]. As a further example of solution behavior, Fig. III-9b shows some data on fused-salt mixtures [83] the dotted lines show the fit to Eq. III-SS.

Figure A2.5.18. Body-centred cubic arrangement of (3-brass (CiiZn) at low temperature showing two interpenetrating simple cubic superlattices, one all Cu, the other all Zn, and a single lattice of randomly distributed atoms at high temperature. Reproduced from Hildebrand J H and Scott R L 1950 The Solubility of Nonelectrolytes 3rd edn (New York Reinliold) p 342.

Hildebrand J H, Prausnitz J M and Scott R L 1970 Regular and Related Solutions (New York Van Nostrand)... 

These solubiHty relationships are consistent with the predictions based on the Hildebrand solubiHty parameter (23). For perfluorinated Hquids, the solubiHty parameters are on the order of 10-12 /cm (5-6 caF /cm ) which are the lowest known values for Hquids. 

Solubility Parameter. CompatibiHty between hydrocarbon resins and other components in an appHcation can be estimated by the Hildebrand solubiHty parameter (2). In order for materials to be mutually soluble, the free energy of mixing must be negative (3). The solubiHty of a hydrocarbon resin with other polymers or components in a system can be approximated by the similarities in the solubiHty parameters of the resin and the other materials. Tme solubiHty parameters are only available for simple compounds and solvents. However, parameters for more complex materials can be approximated by relative solubiHty comparisons with substances of known solubiHty parameter. 

Solution Properties. Lignin in wood behaves as an insoluble, three-dimensional network. Isolated lignins (milled wood, kraft, or organosolv lignins) exhibit maximum solubiUty in solvents having a Hildebrand s solubiUty parameter, 5, of 20.5 — 22.5(J/cm ) (10 — ll(cal/cm ) > and A// in excess of 0.14 micrometer where A]1 is the infrared shift in the O—D bond when the solvents are mixed with CH OD. Solvents meeting these requirements include dioxane, acetone, methyl ceUosolve, pyridine, and dimethyl sulfoxide. 

The Hildebrand Solubility Parameter. This parameter, 4 can be estimated (10) based on data for a set of additive constants, E, for the more common groups ia organic molecules to account for the observed magnitude of the solubiHty parameter d = EE/V where Erepresents molar volume. SolubiHty parameters can be used to classify plasticizers of a given family ia terms of their compatibihty with PVC, but they are of limited use for comparing plasticizers of differeat families, eg, phthalates with adipates. 

The Hildebrand solubiUty parameter, 5, is the square root of the CED. It is a measure of all interactions that occur between molecules of the solvent. 

Hildebrand, F. B. Introduction to Numerical Analysis, 2d ed., McGraw-Hill, New York (1974). 

Another advance in the concepts of hquid-phase diffusion was provided by Hildebrand, who adapted a theory of viscosity to self-diffusivity. He postulated that = B(V — where is the... 

Ertl and DuUien [ibid.] found that Hildebrand s equation could not fit their data with B as a constant. They modified it by applying an empirical exponent n (a constant greater than unity) to the volumetric ratio. The new equation is not generally useful, however, since there is no means for predicting /i. The theory does identify the free volume as an important physical variable, since n > for most hquids implies that diffusion is more stronglv dependent on free volume than is viscosity. 

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