Parameter Dependence

As is so often pointed out, the so-called protein dielectric , geff, used in most continuum studies has little to do with the actual internal dielectric constant of the protein, ep, but is in fact a scaling factor that represents the contributions not explicitly included. In this respect, it is analogous to the effective protein dielectric used in the PDLD-type methods mentioned earlier. The neglect of 

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The equation of state detemiined by Z N, V, T ) is not known in the sense that it cannot be written down as a simple expression. However, the critical parameters depend on e and a, and a test of the law of corresponding states is to use the reduced variables T, and as the scaled variables in the equation of state. Figure A2.3.5 bl illustrates this for the liquid-gas coexistence curves of several substances. As first shown by Guggenlieim [19], the curvature near the critical pomt is consistent with a critical exponent (3 closer to 1/3 rather than the 1/2 predicted by van der Waals equation. This provides additional evidence that the law of corresponding states obeyed is not the fomi associated with van der Waals equation. Figure A2.3.5 (b) shows tliat PIpkT is approximately the same fiinction of the reduced variables and... 

The Universal Force Field, UFF, is one of the so-called whole periodic table force fields. It was developed by A. Rappe, W Goddard III, and others. It is a set of simple functional forms and parameters used to model the structure, movement, and interaction of molecules containing any combination of elements in the periodic table. The parameters are defined empirically or by combining atomic parameters based on certain rules. Force constants and geometry parameters depend on hybridization considerations rather than individual values for every combination of atoms in a bond, angle, or dihedral. The equilibrium bond lengths were derived from a combination of atomic radii. The parameters [22, 23], including metal ions [24], were published in several papers. 

Each combination of four atoms (A, B. C. and D) is characterized by two parameters, e and e.. As for the CICC, is a parameter that depends on atomic properties and on distances, and is calculated by Eq. (27), with r, again being the sum of bond lengths between atoms on the path with the minimum number of bond counts. However c is now a geometric parameter (dependent on the conformation)... 

Th e off-diagonal elemen ts represen t the domman t effects of bonding and are set to be proportional to the overlap by a parameter dependent on the two atoms involved in the overlap,... 

S.-i is the overlap integral, and are ionisation potentials for the appropriate orbitals and /J. a is a parameter dependent upon both of the two atoms A and B. 

The key term is which is the bond order between the atoms i and j. This parameter depends upon the number of bonds to the atom i the strength of the bond between i and j decreases as the number of bonds fo fhe atom i increases. The original bond-order potential [Abell 1985] is mathematically equivalent to the Finnis-Sinclair model if the bond order by is given by ... 

The significance of G G tan 5, Tj, and Tj is that they can be determined experimentally and used to characterize real materials. These parameters depend on frequency and temperature, and this dependence can be used to define behavior. For example, viscoelastic fluids are often characterized by log—log plots of one or more of these quantities vs the angular frequency CO, as shown in Figure 21, which illustrates the behavior of a polymer melt (149). 

All eight parameters depend on composition moreover, parameters Co, b, and y are for some applications treated as functions of X By Eq. (4-171), the residual Gibbs energy is... 

Theory Cross-flow-elecfrofiltration can theoretically be treated as if it were cross-flow filtration with superimposed electrical effects. These electrical effects include elecfroosmosis in the filter medium and cake and elecfrophoresis of the particles in the shiny. The addition of the applied electric field can, nowever, result in some quahta-tive differences in permeate-flux-parameter dependences. 

These three groups of parameters are arranged in order of their priority, so that the necessity for detailed investigation of succeeding parameters depends on the results from the preceding group. 

F = dimensionless parameter depending on limiting conditions noted below... 

Equations (7.45) and (7.46) show that air velocity along compact, linear, and radial jets is proportional to the value of K. This parameter depends upon... 

The van der Waals distance, Rq, and softness parameters, depend on both atom types. These parameters are in all force fields written in terms of parameters for the individual atom types. There are several ways of combining atomic parameters to diatomic parameters, some of them being quite complicated. A commonly used method is to take the van der Waals minimum distance as the sum of two van der Waals radii, and the interaction parameter as the geometrical mean of atomic softness constants. 

Atoms are assigned types , much as in force field methods, i.e. the parameters depend on the nuclear charge and the bonding situation. The a a and /3ab parameters for atom types A and B are related to the corresponding parameters for sp -hybridized carbon by means of dimensionless constants /ia and /cab-... 

Orders with quotation marks mean that the rate constants given by the authors are complex parameters depending on the add concentration. (In this case see corresponding reference.) The overall reaction order does not indude the order with respect to catalyst. 

When the propellant burning rate is espressed by Eq. (5b), the parameter p /e can be considered as the transient sensitivity of the burning rate to pressure. This parameter depends on the transient combustion characteristics, and its evaluation depends on the particular model of the combustion process. Thus, the acoustic admittance provides the link between experimental observation and theoretical prediction. 

For gas-liquid solutions which are only moderately dilute, the equation of Krichevsky and Ilinskaya provides a significant improvement over the equation of Krichevsky and Kasarnovsky. It has been used for the reduction of high-pressure equilibrium data by various investigators, notably by Orentlicher (03), and in slightly modified form by Conolly (C6). For any binary system, its three parameters depend only on temperature. The parameter H (Henry s constant) is by far the most important, and in data reduction, care must be taken to obtain H as accurately as possible, even at the expense of lower accuracy for the remaining parameters. While H must be positive, A and vf may be positive or negative A is called the self-interaction parameter because it takes into account the deviations from infinite-dilution behavior that are caused by the interaction between solute molecules in the solvent matrix. 

Fig. 2. The pulse sequence for the CP/MAS experiment. The values of the different time parameters depend on the relaxation behaviours and on the mobilities of the nuclei in the compounds investigated. (Reproduced with permission of Ref. I0))...

Here a and b are considered as fitting parameters depending on temperature. De-excitation rate constants (s < 0) are obtained from the detailed balance principle. AH fitting laws differ in the pre-exponential factor in Eq. (5.70). In the PEG model... 

It was possible to formulate a rule describing how the copolymerization parameters depend on the polarity of the solvent used. This rule is a result of contemplation about the connection between the copolymerization parameters and propagation rate constants during the cationic polymerization as well as about the changes of solvation of educts and activated complexes of the crossed propagation steps in solvents with varied polarity 14 U7). The rule is as follows ... 

Significant simplification of the governing equations may be achieved by using a quasi-one-dimensional model for the flow. Assume that (1) the ratio of meniscus depth to its radius is sufficiently small, (2) the velocity, temperature and pressure distributions in the cross-section are close to uniform, and (3) all parameters depend on the longitudinal coordinate. Differentiating Eqs. (8.32-8.35) and (8.37) we reduce the problem to the following dimensionless equations ... 

When examining this kind of data, one reahzes how difficult is to make general statements on the effects of chitosans on the cells another example is the antimicrobial effect of chitosans that varies with molecular size, degree of substitution and other parameters depending on the particular microorganism considered. 

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