Phase behavior of the hard-sphere Maier-Saupe fluid under spatial confinement

The Maier-Saupe hard-sphere fluid is one of the simplest models that accounts for the isotropic-nematic transition characteristic of liquid crystal phases. At low temperatures the model is known to present a gas-liquid-like transition with a large difference between the densities of the coexistence phases, whereas at higher temperature the transition becomes a weak first-order transition resembling the typical order-disorder (nematic-isotropic) phase change of liquid crystals. Spatial dimensionality directly conditions the character of the orientational phase change (i.e., the high temperature transition), that goes from a first-order transition in the purely three-dimensional case, to a Berezinskii-Kosterlitz-Thouless-like continuous transition which occurs when the three dimensional Maier-Saupe spins are constrained to lie on a plane. In the latter instance, the ordered phase is not endowed with true long-range order. In this work we investigate how the continuous transition transforms into a true first-order phase change, by analyzing the phase behavior of a system of three dimensional Maier-Saupe hard spheres confined between two parallel plates, with separations ranging from the quasi-two-dimensional regime to the bulk three-dimensional limit. Our results indicate that spatial confinement in one direction induces the change from first order to a continuous transition with a corresponding decrease of the transition temperatures. As to the gas-liquid transition, the estimated “critical” temperatures and densities also decrease as the fluid is confined, in agreement with previous results for other simple systems.

Figure 1

(Color online) Density profile of a MS hard-sphere fluid confined in a slit pore with varying pore widths.

Figure 2

(Color online) Graphical determination of the vapor-liquid coexistence densities in an $NpT$ simulation (see Eq. (10).

Figure 3

(Color online) Amplitude ratio $G_4\left(L,T\right)$ for different system sizes, at constant pore width $h=1.5\sigma$ from Grand-Canonical Wang-Landau simulations. The dashed horizontal line marks the Universal value for the 2D-Ising model at the same boundary conditions.

Figure 4

(Color online) Size dependence of the density probability for the (possible) phase equilibrium conditions for a confined Maier-Saupe fluid with $h=8\sigma$ (left graph) and for the bulk three dimensional system, both at $T^{\ast }=2.50$. Curves are labeled according to the system size, $L$, and as $L$ increases the well depth of the bimodal distribution increases (dramatically in the bulk case). The bulk phase is simulated in cubic cells of length $L$ and periodic boundary conditions.

Figure 5

(Color online) Size dependence of the order parameter in the vicinity of the order-disorder transition of the confined MS fluid for the three interwall separations under consideration. Symbols denote the simulation result and lines are obtained using a histogram reweighting approach.

Figure 6

(Color online) Size dependence of the order-parameter susceptibility in the vicinity of the order-disorder transition of the confined MS fluid for the three interwall separations under consideration. Symbols denote the simulation result and lines are obtained using a histogram reweighting approach.

Figure 7

(Color online) Size dependence of the excess heat capacity in the vicinity of the order-disorder transition of the confined MS fluid for the three interwall separations under consideration. Symbols denote the simulation result and lines are obtained using a histogram reweighting approach.

Figure 8

(Color online) Phase diagram for the MS fluid confined in a plane (continuous $\mathbb{R}{P}^2$ model), confined between two walls separated a distance $h$ (shown in the labels), and 3D bulk phase behavior. Solid symbols indicate the location of the apparent multicritical points. Lines are drawn as guide to the eyes. The inset shows the results for the confined $\left(h=1.5\sigma \right)$ and the 2D system with the density appropriately rescaled.