Behavior of dipolar monolayers adsorbed on polar surfaces: A comparison of statistical mechanical approaches for predicting net polarization and a description of phase behavior

Net polarization of dipolar monolayers on one- and two-dimensional polar surfaces is studied with an Ising lattice model. Complete and incomplete monolayers are considered. Exact statistical mechanical methods are used to explain trends in net polarization with lateral interaction energy, dipole-surface interaction energy and surface coverage. Approximate statistical mechanical methods are compared to exact approaches with respect to difficulty of deriving equations for net polarization, difficulty of solving those equations, and accuracy of results. A preferred method is selected for each type of lattice (one-dimensional completely filled lattice, etc.).; For the one-dimensional completely filled lattice (no “holes”) the approximate “semi-empirical” method is preferred, because of its simplicity and accuracy, to both the exact (Monte Carlo, exact combinatorial) and other approximate (Bragg-Williams) methods.; The exact method (Monte Carlo simulation) is required for quantitative accuracy on the two-dimensional, completely filled lattice. The approximate methods (“semi-empirical,” Bethe-Guggenheim, and Bragg-Williams) do not yield quantitatively accurate results.; The Bethe-Guggenheim approach is found to yield results equal to the exact (transfer matrix and Monte Carlo) approaches for the one-dimensional lattice with holes. Either the Bethe-Guggenheim or transfer matrix approach is preferred as they are of comparable difficulty.; The Bethe-Guggenheim approximation does not yield quantitatively accurate results on the two-dimensional lattice with holes. Monte Carlo simulation is required.; The energetics of dipolar systems on the two-dimensional completely filled lattice are compared to those of antiferromagnetic systems to reveal that second-order phase transitions occur in the dipolar systems. The existence of one such phase transition is verified by a maximum in the heat capacity vs. temperature curve, generated by simulation.; Spreading pressure vs. surface coverage isotherms are generated from the Bethe-Guggenheim method to demonstrate the existence of first-order phase transitions on the two-dimensional incompletely filled lattice via the occurrence of van der Waals loops. Surface coverages and molar net polarizations of the equilibrium phases are determined using Maxwell's equal area theorem. Monte Carlo simulation in the Gibbs ensemble provides further evidence that these phase transitions occur.