Kirkwood modified

Shire, SJ Hanania, GIH Gurd, FRN, Electrostatic Effects in Myoglobin. Application of the Modified Tanford-Kirkwood Theory to Myoglobins from Elorse, California Grey Whale, Harbor Seal, and California Sea Lion, Biochemistry 14, 1352, 1975. 

Once the QFH formula for the excess chemical potential is linearized in (11.37), the logarithmic expression can be expanded to first order and all or part of the classical-average term can be integrated by parts to yield the Wigner-Kirkwood correction to the free energy. Then if (11.40) is reorganized, computation of the chemical potential can be viewed as a classical average with a modified interaction potential of the same form as (11.3). 

In deriving (8.3.11) we took into account the fact that despite the reaction rate is still defined through the integral (4.1.19), its magnitude depends greatly on the equation for the correlation function for dissimilar particles. Making use of the definition of the functional (5.1.5), let us write down equation (8.3.8) (in usual dimensional units) modified by the Kirkwood... 

Over an extended pressure range we can represent V by the modified Kirkwood-Tait equation, V Vo/(l + where B and C are positive constants, B in the range of... 

To show the influence of various microscopic and structural factors on linear and non-linear effects in dense dielectrics, it is convenient to apply first a semi-macroscopic treatment of the theory, and then to proceed to its molecular-statistical interpretation, assuming appropriate microscopic models. The semi-macroscopic method was initially applied by Kirkwood and modified by Frohlich in the theory of linear dielectrics, and has beat successfully used in theories of non-linear tUelectrics. "... 

In a previous paper (Ruckenstein and Shulgin, 2003), the Kirkwood-Buff theory of solutions (Kirkwood and Buff, 1951) was employed to obtain an expression for the solubility of a solid (particularly a drug) in binary mixed (mainly aqueous) solvents. A rigorous expression for the composition derivative of the activity coefficient of a solute in a ternary solution (Ruckenstein and Shulgin, 2001) was used to derive an equation for the activity coefficient of the solute at infinite dilution in an ideal binary mixed solvent and further for the solubility of a poorly soluble solid. By considering that the excess volume of the mixed solvent depends on composition, the above equation was modified empirically by including one adjustable parameter. The modified equation was compared with the other three-parameter equations available in the literature to conclude that it provided a better agreement. 

However, recalculating the value of y using the method described in the paper for the field factors, gives the value in brackets. The unbracketed value, for the overall microscopic nonlinearity, converts to 2859 au. In the case of associating liquids the authors argue that equation (7) can be used in modified form with the inclusion of a factor, g, which they deduce from the Kirkwood-Frohlich modification of the Onsager theory,... 

Auguste DT, Kirkwood J, Kohn J, Fuller GG, Prud homme RK (2008) Surface Rheology of Hydrophobically modified PEG polymers associating with a Phospholipid monolayer at the air-water interface. Langmuir 24 4056 1064... 

In the case of pure liquids numerical computations for the transport coefficients in argon, krypton, and xenon have been carried out by Palyvos et al. using a modified Lennard-Jones potential and the radial distribution function of Kirkwood, Lewinson, and Alder. The results, for instance for argon, represent percentages betw een 60 and 90% of the experimental values in a wide range of temperatures and densities. Besides, they agree with experiment better than the results derived from the Kirkwood of Rice-AIInatt types of theories. 

Third, to specify the spatial difference in the degree of preferential exclusion, we define and analyze the preferential exclusion parameters of ectoine for two solutes with the aid of the Kirkwood-Buff (KB) theory [36,37] (Section 8.2.3). To obtain the spatial profiles of the preferential exclusion parameter, we modified the calculation procedure of the KB integral from that in the original KB theory so as to enable systematic discussion of the dependence of the KB integral on the... 

Here C is a constant for converting between the units of e and a, and Nf is the effective number of electrons, which may be taken either as the number of valence electrons or treated as a fitting parameter. The Ro parameter may similarly be taken from atomic quantities. One problem with this procedure is that the atomic polarizability will of course be modified by the bonding situation (i.e. the atom type), which is not taken into account by the Slater-Kirkwood equation. 

The spiro [3,4]octane-2-carboxylic acids (1—4) have been prepared and used in experiments designed to test the applicability of either the field or inductive models for the effects of polar substituents. The experimentally determined ApK, values of these acids have been compared with values calculated using either spherical or ellipsoidal cavities in a modified Kirkwood-Westheimer expression. 

The transmission of substituent effects in the cis- and trans-spiro[3,4]octan-6-one-2-carboxylic acids (31a and b) and related systems has been explored by comparing the observed ApK values with those calculated using spherical and ellipsoidal cavities in the Tanford-modified Kirkwood-Westheimer electrostatic field expression. The solution dipole moments of the trons-a-halogenodecalones (32a, b, and c) have shown that within experimental error the observed data are independent of halogen but dependent on whether it is located in an axial or an equatorial postion. Strong polar interactions between the halogen, carbonyl, and nitrile groups are indicated. 

Still, the radius of gyration does not equal the effective radius of a polymer coil in solution in terms of the flow behavior. For the calculation of a so-called hydro-dynamic radius R that reflects this effective radius of the polymer coil in a flow field, several theoretical approaches have been made. For theta conditions for example, the modified Kirkwood-Riseman theory [47] predicts a ratio of radius of gyration to hydrodynamic radius of... 

If we incorporate backflow effects at the Kirkwood level, the friction is modified Ctot 6 irq, R. If the chain is still an ideal phantom chain R = Ro), we get ... 

Equations (25) - (29) determine the simplest approach to the dynamics of a macromolecule, even so, it appears to be rather complex if the effects of excluded volume, hydrodynamic interaction, and internal viscosity are taken into account. Due to these effects, all the beads in the chain ought to be considered to interact with each other in a non-linear way. To tackle with the problem, this set of coupled non-linear equations is usually simplified. There exist the different simpler approaches originating in works of Kirkwood and Riseman [46], Rouse [2], Zimm [5], Cerf [4], Peterlin [6] to the dynamics of a bead-spring chain in the flow of viscous liquid. The linearization is usually achieved by using preliminary-averaged forms of the matrix of hydrodynamic resistance (hydrodynamic interaction) [5] and the matrix of the internal viscosity [4]. In the last case, to ensure the proper covariance properties when the coil is rotated as a whole, Eq. (29) must be modified and written thus... 

The modified Poisson-Boltzmann (MPB) approximation is the product of many theoretical investigations into improvements of the PB approach of Gouy and Chapman based on classical statistical mechanics [22, 23] for the description of the electric double layer at a charged plane interface. These extensions originated in a work of Kirkwood [24] who used the Giintelberg charging process to examine the fluctuation terms neglected in the DH theory of electrolytes. 

An employment of effective dipoles determined from FIR bands has been proposed to enter the computation of static angular correlation factors, the Kirkwood g" factors. In the modified formula the integrated band intensity enters instead of the usual dipole moment value determined in vacuum (17). There, a dynamical property is being used to understand more closely the static structure, as controled by the angular position of neighbouring molecules with respect to each other. 

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