Interaction coefficient/parameter

Fugacity is expressed as a function of the molar volume, the temperature, the parameters for pure substances Oj and h, and the binary interaction coefficients )... 

From the changes in the obtained potential profiles, we evaluated the interaction coefficient P and, compared it with the theoretical calculation of p, we also confirmed that the proposed method could evaluate the interaction force without any fitting parameters, which have usually been required in the typical correlation method. 

From Tables 6.3 and 6.4 it seems that the size and charge correlations can be extended to complex ions. This observation is very important because it indicates a possibility to estimate the ion interaction coefficients for complexes by using such correlations. It is, of course, always preferable to use experimental ion interaction coefficient data. However, the efforts needed to obtain these data for complexes will be so great that it is unlikely that they will be available for more than a few complex species. It is even less likely that one will have data for the Pitzer parameters for these species. Hence, the specific ion interaction approach may have a practical advantage over the inherently more precise Pitzer approach. 

Empirical and semi-empiriad approaches. The problem of making dieoretical estimates for the interaction coefficients for the liquid phase has been tackled in different ways by various authors. Kaufman and Bernstein (1970) considered that the liquid state would exhibit the lowest repulsive forces of all the states of condensed matter and that a description of the interaction parameters for the liquid state would be the best basis for die prediction of interaction parameters for various solid phases. 

Effective cluster interactions. The second important parameter in all cluster models is a series of interaction coefficients that define the bond strengths. An... 

Effective pair interaction parameters. In the CVM formalism, effective pair interaction coefficients, defined by the symbol are given in Eq. (7.20)... 

Inserting Eq. (91) into Eq. (93) for the liquidus line of AC(s) gives the liquidus temperature at x =. The experimental value TAc is treated as special and it is required that the resulting equation be satisfied for T=TAC. The equation then becomes a restriction on the interaction coefficients. We use it to provide a relation between cos and vs in terms of the other coefficients and a new model parameter z, the value of z at x = and T = TAC. The relation is... 

In the discussion of the associated model for the A-C binary, the possibility of an infinite heat capacity at 50 at. % was discussed in connection with Eq. (106). This was shown to arise because the temperature derivative of the mole fraction of the molecular ac species becomes infinite for certain values of the interaction coefficients. This behavior is discussed here only for a simplified version of the model in which the interaction coefficients / 14 and of Eq. (68) for AGJ, are equal and opposite. (These parameters then cancel out of k4 at x = ). The discussion below therefore covers the version of the model applied to Ga-In-Sb. 

The kinetic theory of rubber elasticity is so well known and exhaustively discussed (17, 27, 256-257, 267) that the remarks here will be confined to questions which relate only to its application in determining the concentration of elastically effective strands. In principle, both network swelling properties and elasticity measurements can provide information on network characteristics. However, swelling measurements require the evaluation of an additional parameter, the polymer-solvent interaction coefficient. They also involve examining the network in two states, one of which differs from its as-formed state. This raises some theoretical difficulties which will be discussed later. Questions on local non-uniformity in swelling (17) also complicate the interpretation. The results described here will therefore concern elasticity measurements alone. 

To circumvent the above problems with mass action schemes, it is necessary to use a more general thermodynamic formalism based on parameters known as interaction coefficients, also called Donnan coefficients in some contexts (Record et al, 1998). This approach is completely general it requires no assumptions about the types of interactions the ions may make with the RNA or the kinds of environments the ions may occupy. Although interaction parameters are a fundamental concept in thermodynamics and have been widely applied to biophysical problems, the literature on this topic can be difficult to access for anyone not already familiar with the formalism, and the application of interaction coefficients to the mixed monovalent-divalent cation solutions commonly used for RNA studies has received only limited attention (Grilley et al, 2006 Misra and Draper, 1999). For these reasons, the following theory section sets out the main concepts of the preferential interaction formalism in some detail, and outlines derivations of formulas relevant to monovalent ion-RNA interactions. Section 3 presents example analyses of experimental data, and extends the preferential interaction formalism to solutions of mixed salts (i.e., KC1 and MgCl2). The section includes discussions of potential sources of error and practical considerations in data analysis for experiments with both mono- and divalent ions. 

The key concept of the analysis developed here is the interaction coefficient, which we will use to assess the net interactions (favorable or unfavorable) taking place between ions and an RNA. We first introduce interaction coefficients by describing the way they might be measured in an equilibrium dialysis experiment, and give an overview of their significance. These parameters are defined in more formal thermodynamic terms in Section 2.2 and are subsequently used to derive formulas useful in the interpretation of experimental data. 

The effects of the culturing variables, interaction coefficients (95%), correlation matrix for estimated parameters, respective confidence inter-... 

In these equations, c j is the interaction energy parameter between molecule i and j while ojj is the intermolecular interaction distance between the two molecules. Knowing that coefficients a and b of the van der Waals equation of state are proportional to < and a according to the following expressions ... 

An experimental measurable quantity that is of fundamental importance in nucleic acid is the preferential interaction coefficient T. The parameter T is a statistical thermodynamic quantity that probes nonideality effects of nucleic acids in aqueous solution. This quantity also provides information on the characteristics of co-ions and counterions distributions in the vicinity of polyions [65-76]. 

An alternate way to define preferential interaction coefficient is to consider the ionic density , (p) of species i at a radial distance p from the polyion. The parameter T, can then be defined, per polyion charge and per unit length, as an integral over the excess local density [68, 71]... 

Assuming that the average dipole moment remains constant in a layer regardless ofthe tilt angle, one obtains for the interaction coefficients the values listed in Table 1. Additionally, we computed the decay lengths for the parameter values given in section II.4 Ai from the continuous approximation, eq 27 A2 from the continuous approximation which treats the polarization of one layer as an average over its two sublayers, eq 30 and Ag from... 

The knowledge of both thermodynamic constants at zero ionic strength and of the specific interaction coefficients will allow the speciation diagram of the element in the considered medium to be established. At higher electrolyte concentrations, more sophisticated theories (Pitzer, MSA,. .. [29,31]) have been developed. However, they involve a larger number of characteristic parameters, which unfortunately are unknown for the majority of chemical elements. 

Binary interaction coefficient for co-volume parameter in Peng Robinson equation of state ... 

The difference between the extended Debye-Hiickel equation and the Pitzer equations has to do with how much of the nonideahty of electrostatic interactions is incorporated into mass action expressions and how much into the activity coefficient expression. It is important to remember that the expression for activity coefficients is inexorably bound up with equilibrium constants and they must be consistent with each other in a chemical model. Ion-parr interactions can be quantified in two ways, explicitly through stability constants (lA method) or implicitly through empirical fits with activity coefficient parameters (Pitzer method). Both approaches can be successful with enough effort to achieve consistency. At the present, the Pitzer method works much better for brines, and the lA method works better for... 

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