Thermodynamics, structure and dynamics of cylindrically confined hard spheres: The role of excess helical twist

Abstract

Hard spheres confined to narrow quasi-one-dimensional cylindrical channels form perfect helical structures at close packing. Here, we use molecular dynamics simulation to show that the thermodynamics, structure and dynamics of the fluid below close packing are dominated by the presence of topological defects that reverse the local twist direction of the helix. When compressed from a random, low density state, or decompressed from high density ordered states with zero excess helical twist, the system equilibrates to an achiral fluid that exhibits two heat capacity maxima along the equation of state. The low density heat capacity maximum corresponds to the onset of helix formation and the high density maximum occurs when the system rapidly loses defects in a Schottky-like anomaly. The local twist auto-correlation function in the achiral fluid exhibits a stretched exponential decay and the structural relaxation times undergo a fragile-to-strong crossover located at the high density heat capacity maximum. We also study the effect of excess helical twist by using initial starting configurations consisting of two helical domains with opposite twist directions of different lengths. This leads to the formation of topologically protected states that are characterized by the presence of loosely bound defect pairs which become more tightly bound with increasing excess helical twist. The local twist auto-correlation function in the chiral fluid decays as a power law at long times. The possible kinetic or thermodynamic origin of this topological protection is discussed.