Surface Equations of State in Adsorption from Solution

Evaluation of a surface equation of state generally involves an evaluation of its ability to represent raw experimental data, or information derived from such data, after the parameters of the equation have been adjusted to optimize this representation, followed by an evaluation of the physical reasonableness of the optimizing parameters in terms of the physical model on which the equation of state is based. This process is analyzed critically for the adsorption of polar organic compounds at the mercury-electrolytic solution interface using high precision electrocapillary data as test data and the Frumkin and Flory—Huggins equations as test equations. In one approach, ir vs ln a data were represented by a set of hyperbolae with coefficients chosen to give best least squares representations of data, and adsorption isotherms obtained by analytical differentiation; parameters for the isotherms were selected to give best least squares fits to these data. Parametrizations depending on high surface pressure limiting tangents to ir vs ln a plots, intercept and slope of low surface pressure ln (ir/a) vs ir plots, were also investigated. Parameter sets obtained by different methods of parametrization agreed only moderately well, reflecting sensitivities to different portions of the experimental data. When all Flory—Huggins parameters were freely adjusted, best fits resulted when the water co-area was taken as larger than the organic compound co-area, a physically unrealistic result.