Monomer Adsorption on Equilateral Triangular Lattices with Attractive First-neighbor Interactions
Abstract Book of the XXIII IUPAP International Conference on Statistical Physics, Genova, Italy, (9-13 July 2007)Аннотация
We present a model of monomer adsorption on infinitely long, finite width M equilateral triangular lattices with non-periodic boundaries. The study includes adsorbate-adsorbate first- and second-neighbor interactions with attractive first-neighbors. This work extends the results obtained for repulsive first-neighbors (A. J. Phares. D. W. Grumbine, Jr., F. J. Wunderlich, Langmuir 23, 1928-1936, 2007). The matrix method and numerical algorithms are new and based on a recently published paper (A. J. Phares. D. W. Grumbine, Jr., F. J. Wunderlich, Langmuir 23, 558-573, 2007). This method allows determination of the occupational characteristics of the adsorption crystallization phases with an accuracy exceeding nine significant figures. The numerical results fit exact analytic expressions in the width M of the lattice. The limit as M approaches infinity provides the complete phase diagram for the infinite two-dimensional surface. We list the occupational characteristics of each phase in the order: coverage, and the numbers of first- and second-neighbor adsorbates per site. There are three phases in addition to empty and full coverage: (1/3, 1/3, 0), (1/2, 1, 1/2) and (2/3, 4/3, 1). The 1/3-coverage consists either of isolated triangular clusters each containing three adsorbates, or of every third row of nearest neighbor sites being occupied. The 1/2-coverage consists of two consecutive rows of occupied sites separated by two consecutive rows of vacant sites, and is its own complementary phase. The 2/3-coverage is the complement of the 1/3-coverage. It consists either of isolated triangular clusters of vacant sites, or of two consecutive rows of occupied sites separated by one row of vacant sites. These phases are different from those identified in the case of adsorbate first-neighbor repulsion, which were (2$\times$1), (2$\times$2), (3$\times$1), ($3 3$)R30°, and the complementary phases of only the (2$\times$2) and ($3 3$)R30°. Therefore, hole-particle symmetry holds in the case of attractive first-neighbors, but not in the repulsive case. The model predicts that the experimental knowledge of the structure of the phases is sufficient to determine whether adsorbate first-neighbors are attractive or repulsive. The model also suggests the manner in which to conduct relatively low temperature experiments to allow determination of most, if not all, of the interaction energies from the knowledge of the sequences of phases and the conditions prevailing at the transitions between phases.
This research is supported by an allocation of advanced computing resources supported by the National Science Foundation. The computations were performed in part on the Cray XT3 of the Pittsburgh Supercomputing Center.