Wilson expression

In the above equations denotes the vapor mole fraction of component i, Pf is the vapor pressure of the pure component i, Bu is the second virial coefficient of component i, dn = 2Bn — Bn — B22 and B 2 is the crossed second virial coefficient of the binary mixture. The vapor pressures, the virial coefficients of the pure components and the crossed second virial coefficients of the binary mixtures were taken from [32], The Wilson [38], NRTL [39] and the Van Ness-Abbott [40] equations were used for the activity coefficients in Eq. (17). The expressions for the activity coefficients provided by these three methods were differentiated analytically and the obtained derivatives were used to calculate D = 1 -I- Xj(9 In Yil 2Ci)pj. There is good agreement between the values of D obtained with the three expressions for the systems V,V-dimethylformamide-methanol and methanol-water. For the system V,V-dimethylformamide-water, the D values calculated with the Van Ness-Abbott equation [40] were found in good agreement with those obtained with the NRTL equation, but the agreement with the Wilson expression was less satisfactory. 

Recently, a modification of the Wilson expressions for LCs was proposed by assuming that the interaction energy parameter between molecules of different t5rpes depends on the composition, and the following expressions were obtained ... 

When the activity coefficients are expressed via the Flory-Huggins equation, one adjustable parameter is introduced. When, however, the Wilson expressions are employed, two adjustable parameters are needed. The solubilities of the solute in the individual solvents are also necessary to calculate the composition-independent constants A P,T) and B P, T). Therefore, our method can be considered a three-parameter method, when based on the Flory-Huggins equations, and a four-parameter one, when based on the Wilson equations (see Table 2). 

The Wilson equation is based on local composition theories and accounts for inter-molecular interactions between a molecule and its immediate neighbors. The Wilson expression for the excess Gibbs energy and the resulting equations for the activity coefficients are... 

In this formulation the concentration dependence of the activity coefficient is described by a one-parameter expression (Eq. (3.64)). To extend the analysis to allow for more pronounced deviations from ideal Langmuir behavior it is only necessary to use a two-parameter expression for the activity coefficient. Danner and Suwanayuen used the Wilson expression ... 

The plot of p cosO versus sin0 is a straight line with slope rj and intercept kX/D. This expression is a combination of the Debye-Scherrer formula for size broadening and the Stokes and Wilson expression for strain broadening. The value of t] is the strain in the crystallites, and the value of D represents the size of the crystallites. The constant k is typically close to unity and ranges from 0.8 to 1.39. The Scherrer equation is mainly used for crystallites up to 1000 A (100 nm). 

The Wilson parameters A,, NRTL parameters G,, and UNIQUAC parameters X all inherit a Boltzmann-type T dependence from the origins of the expressions for G, but it is only approximate. Computations of properties sensitive to this dependence (e.g., heats of mixing and liquid/hquid solubihty) are in general only qualitatively correct. 

Outlined below are the steps required for of a X T.E calciilation of vapor-phase composition and pressure, given the liquid-phase composition and temperature. A choice must be made of an equation of state. Only the Soave/Redlich/Kwong and Peng/Robinson equations, as represented by Eqs. (4-230) and (4-231), are considered here. These two equations usually give comparable results. A choice must also be made of a two-parameter correlating expression to represent the liquid-phase composition dependence of for each pq binaiy. The Wilson, NRTL (with a fixed), and UNIQUAC equations are of general applicabihty for binary systems, the Margules and van Laar equations may also be used. The equation selected depends on evidence of its suitability to the particular system treated. Reasonable estimates of the parameters in the equation must also be known at the temperature of interest. These parameters are directly related to infinite-dilution values of the activity coefficients for each pq binaiy. 

M Wilson, J DeRisi, HH Kristensen, P Imboden, S Rane, PO Brown, GK Schoolmk. Exploring drug-induced alterations m gene expression m Mycobacterium tuberculosis by microairay hybridization. Proc Natl Acad Sci USA 96 12833-12838, 1999. 

There are many other specific techniques applicable to particular situations, and these should often be investigated to select the method for developing the vapor-liquid relationships most reliable for the system. These are often expressed in calculation terms as the effective K for the components, i, of a system. Frequently used methods are Chao-Seader, Peng-Robinson, Renon, Redlich-Kwong, Soave Redlich-Kwong, Wilson. 

Clos, J., Westwood, J.T., Becker, P.B., Wilson, S., Lambert, K., Wu, C. (1990). Molecular cloning and expression of a hexameric Drosophila heat shock factor subject to negative regulation. Cell 63, 1085-1097. 

Lovenberg TW, Roland BL, Wilson SJ, Jiang X, Pyati 61 J, Huvar A, Jackson MR> Erlander MG Cloning and functional expression of the human histamine H3 receptor. Mol Pharmacol 1999 55 1101. 

Figure 5.11 The time-dependent variation, in setting and hardening cements, of the concentration of soluble ions Al ", Ca, F and PO (expressed as P Oj). These ions are released from the glass powder into the cement matrix (Crisp Wilson, 1974b).

The composition of the leachates does not correspond to the composition of the cement at all (Wilson Batchelor, 1967a,b). The predominant species eluted are the soluble sodium salts of phosphate and fluorides, although sodium is only a minor constituent of the cement. For one example of cement examined, the leachate contained 0-28 % sodium and 0-20% phosphate (expressed as a percentage of the amount of the species contained in the cement). For the major constituents of the glass the figures were 0 07% fluoride, 0 02% Al Oj, 0 01 % SiOj and 0 003% CaO. 

An analysis of equipment costs and capital investment for chemical plants (Wilson, 1947 Chilton, 1950 Vilbrandt and Dryden, 1959 Guthrie, 1970) showed that the six-tenths factor can be applied for a rough evaluation of the influence of equipment size on its cost. The six-tenths rule can be described as a power law expression ... 

This work and any practicable results derived therefrom have been encouraged and expedited throughout by the American Cyanamid Company. Additionally, the authors wish to express appreciation for aid in various phases of the work to Mrs. M. Elliot Miller, Charlotte McHale, Jacquelyn Sellers, L. D. Anderson, M. M. Barnes, G. E. Carman, J. H. Barkley, J. C. Ortega, C. R. Shafer, and H. U. Meyer of these laboratories, and to W. E. Baier and C. W. Wilson of the California Fruit Growers Exchange, Ontario. 

I prepared a white paper and circulated it among members of the Committee, which included Chaunccy Starr, Bertram Wolfe, Edward Arthur, Richard Kennedy, Anthony Favale, Richard Wilson, Pierre Zaleski, and Glenn Seaboig. Their viewpoints and comments were taken into consideration while revising the white paper. I received a letter from Edward Teller delivered by Federal Express indicating that he would not sign it. At... 

Bird, D.M. and Wilson, M.A. (1994) DNA sequence and expression analysis of root-knot nematode elicited giant cell transcripts. Molecular Plant-Microbe Interactions 7, 419-424. 

Wilson, A.D., Bland, P.W. and Stokes, C.R. (1990) Expression and distribution of la antigen in the murine small intesine influence of environment and cholera toxin. International Archives of Allergy and Applied Immunology 91, 348—353. 

Burd, P.R., Rogers, H.W., Gordon, J.R., Martin, C.A., Jayaraman, S., Wilson, S.D., Dvorak, A.M., Galli, S.J. and Dorf, M.E. (1989) Interleukin 3-dependent and -independent mast cells stimulated with IgE and antigen express multiple cytokines. Journal of Experimental Medicine 170, 245-257. 

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