Anomalous structural and mechanical properties of solids confined in quasi one dimensional strips

We show using computer simulations and mean field theory that a system of particles in two dimensions, when confined laterally by a pair of parallel hard walls within a quasi one dimensional channel, possesses several anomalous structural and mechanical properties not observed in the bulk. Depending on the density $\rho$ and the distance between the walls $L_y$, the system shows structural characteristics analogous to a weakly modulated liquid, a strongly modulated smectic, a triangular solid or a buckled phase. At fixed $\rho$, a change in $L_y$ leads to many reentrant discontinuous transitions involving changes in the number of layers parallel to the confining walls depending crucially on the commensurability of inter-layer spacing with $L_y$. The solid shows resistance to elongation but not to shear. When strained beyond the elastic limit it fails undergoing plastic deformation but surprisingly, as the strain is reversed, the material recovers completely and returns to its original undeformed state. We obtain the phase diagram from mean field theory and finite size simulations and discuss the effect of fluctuations.