Nematic to Smectic: A “Hard” Transition

Abstract

The history of the Nematic-Smectic (N-S) transition in hard rod models is a colourful one. Until the mid 1980’s, it was still widely believed that attractive forces where necessary to stabilize the smectic phase, in spite of preliminary theoretical work by Hosino, Nakano and Kimura [1]. Only after MC simulations by Stroobants, Lekkerkerker and Frenkel [2] was the occurrence of a Smectic phase purely on entropie grounds accepted. Subsequent density functional theories by several groups (Somoza and Tarazona [3], Poniewierski and Holyst [4], Poniewierski and Sluckin [5]) mapped out the phase diagram of the hard rod system, predicting among others the existence of a tricritical point on the N-S transition line as a function of the aspect ratio L/D of the rods. Intuitively one expects the transition to be continuous for large aspect ratios. In that case the nematic order at the N-S transition is nearly saturated and the particles more or less fully aligned. For perfectly aligned rods a rather general Landau-type symmetry argument then predicts that the transition to the smectic phase should be second order. However, Poniewierski’s later work [6] on the hard rod model in the limit L/D → ∞ which included the contribution from the third virial coefficient, quite surprisingly predicted a first order transition even in this limit. In a seemingly independent development van Roij et al.