Hard rods in a cylindrical pore: the nematic-to-smectic phase transition

TL;DR

This study uses Onsager's theory to explore how cylindrical confinement influences the phase transition of parallel hard rods, revealing a shift from bulk nematic-smectic transition to inhomogeneous phases under confinement.

Contribution

It provides a theoretical analysis of phase behavior of hard rods in cylindrical pores, highlighting the transition from bulk to confined phases and the destabilization of smectic order with decreasing pore width.

Findings

Homogeneous one-dimensional Tonks gas in very narrow pores.

Transition from bulk nematic-smectic to inhomogeneous phases in wider pores.

Smectic phase destabilized as pore width decreases below 10 times the rod diameter.

Abstract

The effect of cylindrical confinement on the phase behaviour of a system of parallel hard rods is studied using Onsager's second virial theory. The hard rods are represented as hard cylinders of diameter $D$ and length $L$, while the cylindrical pore is infinite with diameter $W$. The interaction between the wall and the rods is hard repulsive, and it is assumed that molecules are parallel to the surface of the pore (planar anchoring). In very narrow pores ($D<W<2 D$), the structure is homogeneous and the system behaves as a one-dimensional Tonks gas. For wider pores, inhomogeneous fluid structures emerge because of the lowering of the average excluded volume due to the wall-particle interaction. The bulk nematic-smectic A phase transition is replaced by a transition between inhomogeneous nematic and smectic A phases. The smectic is destabilized with respect to the nematic for decreasing pore width; this effect becomes substantial for $W<10 D$. For $W>100 D$, results for bulk and confined fluids agree well due to the short range effect of the wall ($\sim 3-4D$).