Simulation study of the phase behavior of a planar Maier-Saupe nematogenic liquid

Using extensive Monte Carlo simulations and a simple approximation in density functional theory, we study the phase behavior of a fluid of nematogenic molecules with centers of mass constrained to lie in a plane but with axes free to rotate in any direction, both with and without an external disorienting field perpendicular to the plane. We find that simulation predicts the existence of an order-disorder phase transition belonging to the Berezinskii-Kosterlitz-Thouless type, along with a low temperature gas-liquid transition. In contrast to the simulation results, density functional theory predicts a first-order orientational phase transition coupled continuously with a first-order gas-liquid transition. The approximate theoretical approach qualitatively reproduces the field dependence of the order-disorder and gas-liquid transitions but is far from quantitative.

Figure 1

(Color online) Temperature and size dependence of the eigenvalues of the three-dimensional Saupe tensor for a coplanar Maier-Saupe fluid at $\rho {\sigma }^2=0.8$ without external fields. The orientational order parameter is $S={\lambda }_{+}$. Curves are labeled in the legend according to sample size. Symbols denote simulation data and the solid curves are obtained from the histogram reweighting technique.

Figure 2

(Color online) Temperature and size dependence of the eigenvalues of the three-dimensional Saupe tensor for a coplanar Maier-Saupe fluid at $\rho {\sigma }^2=0.8$ in the presence of a perpendicular disorienting field $W_0^{*}=1$. Labels as in Fig. 1.

Figure 3

(Color online) Temperature and size dependence of the eigenvalues of the two-dimensional Saupe tensor for a coplanar Maier-Saupe fluid at $\rho {\sigma }^2=0.8$ in the presence of a perpendicular disorienting field $W_0^{*}=\infty$. This is a fully two-dimensional system of planar rotors. Labels as in Fig. 1.

Figure 4

(Color online) Constant volume specific heat per particle (in units of $k_B$) and susceptibility (normalized fluctuation of the order parameter $S={\lambda }_{+}$) for a coplanar Maier-Saupe fluid at $\rho {\sigma }^2=0.8$. Labels as in Fig. 1.

Figure 5

(Color online) Size and temperature dependence of Binder’s cumulants for a coplanar Maier-Saupe fluid at $\rho {\sigma }^2=0.8$. Labels as in Fig. 1.

Figure 6

(Color online) Finite size scaling of the temperature corresponding to a maximum susceptibility, $T_m^{*}$, for a coplanar Maier-Saupe fluid at $\rho {\sigma }^2=0.8$ with and without disorienting fields.

Figure 7

(Color online) Finite size scaling of the average of the order parameter squared at a temperature corresponding to a maximum susceptibility $\left({⟨S^2⟩}_m\right)$ for a coplanar Maier-Saupe fluid at $\rho {\sigma }^2=0.8$ with and without disorienting fields. Solid lines are drawn as a guide to the eye and dotted lines represent the corresponding least-squares fits.

Figure 8

(Color online) Size dependence of the angular correlation $G_2\left(r\right)$ in the absence of external field for the planar nematogenic liquid at $\rho {\sigma }^2=0.8$ and $T^{*}=0.7$. Notice the ${\log }_{10}$ scale of the abscissa.

Figure 9

(Color online) Liquid-vapor equilibria of the different models. The symbols show the estimates of the critical points; the critical temperatures of the different models satisfy $T_c^{*}(W_0^{*}=-1)<T_c^{*}(W_0^{*}=1)<T_c^{*}(W_0^{*}=0)<T_c^{*}(W_0^{*}=\infty )<T_c^{*}(W_0^{*}=-\infty )$.

Figure 10

(Color online) Simulation results for the phase diagram of the planar nematogenic liquid for various disorienting fields. Filled circles indicate the location of the gas-liquid critical point estimates. Filled triangles denote the location of the BKT order-disorder transition for various densities. These points are connected with straight lines which separate the fully isotropic phase from the BKT ordered phase.

Figure 11

(Color online) Phase diagram of the planar nematogenic liquid for various disorienting fields in the MF and MMF approximations.