Phase behavior of the confined Lebwohl-Lasher model

The phase behavior of confined nematogens is studied using the Lebwohl-Lasher model. For three-dimensional systems the model is known to exhibit a discontinuous nematic-isotropic phase transition, whereas the corresponding two-dimensional systems apparently show a continuous Berezinskii-Kosterlitz-Thouless-like transition. In this paper, we study the phase transitions of the Lebwohl-Lasher model when confined between planar slits of different widths in order to establish the behavior of intermediate situations between the pure planar model and the three-dimensional system, and compare with previous estimates for the critical thickness, i.e., the slit width at which the transition switches from continuous to discontinuous.

Figure 1

(Color online) Order parameter ${\lambda }_{+}$ as a function of the temperature for different system widths, $H=1,4,16$, and different systems sizes, $L$. Symbols denote the result of different simulation runs, and lines represent the results of the reweighting analysis. The legends in the figures indicate the different values of $L$.

Figure 2

(Color online) Order parameter susceptibility, $\chi$ as a function of the temperature for different system widths, $H=1,4,16$, and different systems sizes, $L$. Symbols and lines as in Fig. 1.

Figure 3

(Color online) Absolute value of the derivative of the nematic order parameter with respect to the temperature, $\left|d{\lambda }_{+}/dT\right|$ as a function of the temperature for different system widths, $H=1,4,16$, and different systems sizes, $L$. Symbols and lines as in Fig. 1.

Figure 4

(Color online) Reduced excess heat capacity as a function of the temperature for different system widths, $H=1,4,16$, and different systems sizes, $L$. Symbols and lines as in Fig. 1.

Figure 5

(Color online) Temperature and system size dependence of various properties of the 3D LL model (cubic cells without walls). The length of the cell side, $L$, is shown in the legends. Symbols and lines as in previous figures.

Figure 6

(Color online) Pore width dependence of the transition temperatures estimated using the scaling law Eq. (4). The result of a linear fit to $1/H$ is represented by a solid line. Values taken from Refs. [2, 4, 14] are also included for comparison. Note that the bibliographic values and those of this work fall on top of each other and can hardly be distinguished.

Figure 7

(Color online) Value of the maximum of excess heat capacity per particle as a function of the system size for cubic systems $\left(H=L\right)$ with PBC (bulk LL), systems with $H=16$ and PBC (anisotropic LL), and systems with $H=16$ confined between neutral walls. The line connecting points for the bulk system corresponds to a fit of the results to the equation $c_v\left(L\right)=a_0+a_1{L}^3$.

Figure 8

(Color online) Cumulant ratio $g_4=⟨{\lambda }_{+}^4⟩/{⟨{\lambda }_{+}^2⟩}^2$ as a function of the inverse of the system size for $T^{\ast }=0.50$, 0.54, and 0.50.

Figure 9

(Color online) Detail of the Cumulant ratio $g_4=⟨{\lambda }_{+}^4⟩/{⟨{\lambda }_{+}^2⟩}^2$ as a function of the inverse of the system size for $T=0.50$.

Figure 10

(Color online) Probability of finding cluster percolation in, at least, one direction in the simulation of the three-dimensional Lebwohl-Lasher model as a function of the temperature. Different curves represent results for different system sizes.

Figure 11

(Color online) Probability of finding cluster percolation in, at least, one direction, in the simulation of the planar Lebwohl-Lasher model as a function of the temperature. Different curves represent results for different system sizes.