Simple Expressions for Contact Values of Density Profiles in a Planar Double Layer

Local semi-empirical formulae for the contact values of the singlet distribution functions of a double layer

The electrochemical double layer is an important practical and theoretical problem. Generally speaking, experiment gives valuable information about quantities, such as potential differences, that involve integrals of density and charge profiles but does not provide direct information about the profiles themselves. Computer simulations have given numerical information about these profiles. However, explicit expressions are useful in understanding these data. For some years an exact expression has been known for the contact value of total density profile of the ions in the double layer but, until recently, an expression for the contact value of the more important charge profile has been lacking. A few years ago, a semi-empirical local result for the charge profile, valid at low electrode charge, was proposed and, very recently, extended to higher electrode charge. This expression contains a parameter; the effect of variations in this parameter is explored in this paper and the result is compared with a large set of simulation data for the contact values of various profiles that we have accumulated in the past few years. The agreement of the semi-empirical expression with our simulation results is excellent. The best values for this parameter are fairly close to the value suggested by theory.

A MODIFIED POISSON-BOLTZMANN STUDY OF THE SINGLET ION DISTRIBUTION AT CONTACT WITH THE ELECTRODE FOR A PLANAR ELECTRIC DOUBLE LAYER

The properties of the singlet ion distributions at and around contact in a restricted primitive model double layer are characterized in the modified Poisson-Boltzmann theory. Comparisons are made with the corresponding exact Monte Carlo simulation data, the results from the Gouy-Chapman-Stern theory coupled to an exclusion volume term, and the mean spherical approximation. Particular emphasis is given to the behaviour of the theoretical predictions in relation to the contact value theorem involving the charge profile. The simultaneous behaviour of the coion and counterion contact values is also examined. The performance of the modified Poisson-Boltzmann theory in regard to the contact value theorems is very reasonable with the contact characteristics showing semi-quantitative or better agreement overall with the simulation results. The exclusion-volume-treated Gouy-Chapman-Stern theory reveals a fortuitous cancellation of errors, while the mean spherical approximation is poor.