Computer Simulation of Models for Confined Two-Dimensional Colloidal Crystals: Evidence for the Lack of Positional Long Range Order

Point particles interacting with inverse power-law potentials can describe colloidal particles at the air-water interface, a model system for the experimental study of melting in two dimensional (2d). Monte Carlo simulations are used to investigate the effect of confinement on such a system in the crystalline state. It is shown that the state of the system (a strip of width D) depends very sensitively on the precise boundary conditions at the two parallel “walls” providing the confinement. In the y-direction parallel to these walls, orientational order is locally always enhanced but positional long range order is destroyed, if the wall is just a smooth repulsive boundary with no corrugation in the y-direction. Then the mean-square displacement of two particles n lattice parameters apart in y-direction cross over from the logarithmic increase (characteristic for 2d) to a linear increase (characteristic for 1d). However, using a suitable corrugated boundary stabilizes the positional long range order, illustrating the fact systems which may exhibit long range order are sensitive to boundary conditions at their surfaces even if these boundaries are far apart.