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Calculating the surface potential of unionized monolayers.

A quantitative model is presented which enables contributions to the surface potential of a monolayer at the air-water interface to be determined from known values of group dipole moments. Based on the Lennard-Jones and Dent approach, the model shows that the head- and tail-group moments in a condensed, long-chain, n-alkanoic acid monolayer may be assumed to be noninteracting so long as the monolayer-forming molecule is more than about 0.5 nm in length, thus confirming one of the main tenets of the model by Demchak and Fort [J. Colloid Interface Sci. 46, 191 (1974)]. By the same token, it is shown that imaging effects in the subphase are only important for the head group and negligible for the tail group of a molecule more than about 0.5 nm long. The present model shows that the local field acting on dipoles in the monolayer can be described in terms of a relative permittivity for the monolayer. An upper bound of between 1.98 and 2.24 is established for the local relative permittivity of the hydrophobic chain region of alkanoic acids. The major contribution to the local field which leads to these values is from the ``layers'' of methylene groups forming the hydrophobic region of the monolayer. For the case of the distal methyl groups of an alkanoic acid, consideration of only the mutual induced depolarization of in-plane methyl dipoles leads to a local relative permittivity as low as 1.18. Thus, it is shown that even though horizontally directed methylene-group moments cannot make a direct contribution to the surface potential of a condensed monolayer, they do make a significant indirect contribution via their local field.