Calculation of osmotic coefficient

Calculations of departures from ideality in ionic solutions using the MSA have been published in the past by a number of authors. Effective ionic radii have been determined for the calculation of osmotic coefficients for concentrated salts [13], in solutions up to 1 mol/L [14] and for the computation of activity coefficients in ionic mixtures [15]. In these studies, for a given salt, a unique hard sphere diameter was determined for the whole concentration range. Also, thermodynamic data were fitted with the use of one linearly density-dependent parameter (a hard core size o C)., or dielectric parameter e C)), up to 2 mol/L, by least-squares refinement [16]-[18], or quite recently with a non-linearly varying cation size [19] in very concentrated electrolytes. 

The potential can be obtained from the (r) profile through a simple integration (Eq. [230]). The difference in (r)/r between the DH and PB values is also shown in Figure 23 (top frame, dotted line) with most of the difference occurring within one Debye length of the surface = 13.6 A). Of particular relevance to biophysical systems is the competition between mono- and divalent counterions at the cylindrical surface,the discussion of which we defer until later, and that between monovalent counterions with different radii. Also, Deserno and Holm have compared molecular dynamics simulations with the prediction of PB cell model theory for the calculation of osmotic coefficients and the quantification of counterion condensation. ... 

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