Rigid rod adsorption including long-range dispersion interactions

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Abstract
The Caillé-Ågren analysis of rigid rod adsorption is extended by applying the van Kampen theory of condensation to include long-range dispersion interactions between the adsorbed rods. We discuss in greater detail the characteristics of the phase transition predicted by Caillé and Ågren between states having an isotropic and anisotropic distribution of rods adsorbed parallel to the surface. The maximum density range over which the anisotropic adsorbed phase is stable is determined as a function of the length-to-breadth ratio x of the rigid rods and the strength of the anisotropic dispersion energy. Critical surface adhesion and anisotropic dispersion energies necessary for anisotropic adsorption are also obtained as a function of x. In agreement with Caillé and Ågren the isotropic-anisotropic transition for rigid rod adsorption with attractive forces present is found to be second order. We also discuss the spreading pressure-density or area per molecule isotherms obtained for adsorbed rods having various values of x and surface adhesion and dispersion energies. Whenever feasible we compare our results with the spreading pressure isotherms obtained for monolayers of lyotropic molecules on either aqueous or mercury subphases and obtain qualitative agreement. In particular, the critical density and pressure associated with the two dimensional adsorbed gas-liquid condensation for rigid rods with x = 10 gives reasonable agreement with the critical constants observed by Hawkins and Benedek and Kim and Cannell for the corresponding condensation of pentadecanoic acid monolayers on neutral and acidified aqueous subphases. This agreement suggests that considerable dimerization of the pentadecanoic acid molecules may occur on aqueous surfaces.

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