Correlations of particle orientation in monolayer films

Two-dimensional and three-dimensional models of an extended layer that consists of orientation-ally ordered particles are used to describe the ordering in monolayer films. In both models, when the distance between particles of the layer increases, the correlation function decreases to zero (for the parameter of adhesion to the substrate a = 0) or remains constant (for a ≠ 0, i.e., when the energy of interaction between the particles and the substrate is taken into account). In the latter case, this means that the layers have a long-range orientation order. The proposed models of an extended monolayer can be used to interpret data obtained by the light scattering and molecular dynamics methods for Langmuir-Blodgett films with the adhesion parameter a = 0.05 and the particle-particle interaction parameter b = 0.6 in the three-dimensional model or b = 1 in the two-dimensional model. The smaller value of b in the three-dimensional layer model can be explained by a stronger effect of cooperation of particle-particle interactions as compared to the two-dimensional layer model.