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We construct a nonsparse transfer matrix (T-matrix) for a lattice gas model of monomers adsorbed on planar and nanotube surfaces of arbitrary geometry. The model can accommodate any number of higher-order pairwise adsorbate-adsorbate interactions. The technique is sufficiently general for application to nonequivalent adsorption sites and coadsorption of two or more monomer species. The T-matrices for monomer adsorption on a finite width terrace and for monomer adsorption on a nanotube, both of the same lattice geometry, share a basic G-matrix. First, the G-matrix is diagrammatically and recursively constructed. Then, its elements are modified to provide the T-matrix elements for either the terrace or the nanotube. The T-matrices for several particular lattice geometries previously studied as special cases are easily recovered with the generalized technique presented here. This generalization also provides a vectorized algorithm for efficient use on multi-parallel processors and supercomputers.

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A model of monomer adsorption on equilateral triangular terraces three atomic sites in width is presented where step sites are considered first neighbors. Adsorbate-substrate interactions at the terrace step are treated differently than at bulk sites. Adsorbate-adsorbate first neighbor interactions are considered to be repulsive while second neighbors are allowed to be either repulsive or attractive. All low temperature phases have been identified under these conditions. The effect of increasing the temperature has also been investigated. Application of the model to chemisorption of CO on Pt(112) suggests experiments that would allow the various interaction energies to be obtained from a knowledge of the relatively low temperature phases and the conditions prevailing at the transitions between phases. Currently available experimental data is very extensive on the manner in which step sites are filled. However, there is insufficient data on the sequence of low temperature phases which appear when the pressure is gradually increased that would show the manner in which bulk sites are filled until full coverage of the terrace is reached.