Structures and phase transition in a two-dimensional system of Gay-Berne molecules

Exceptionally large fluctuations in orientational order: The lessons of large-deviation theory for liquid crystalline systems

How condensed-matter simulations depend on the number of molecules being simulated (N) is sometimes itself a valuable piece of information. Liquid crystals provide a case in point. Light scattering and 2d-IR experiments on isotropic-phase samples display increasingly large orientational fluctuations ("pseudo-nematic domains") as the samples approach their nematic phase. The growing length scale of those locally ordered domains is readily seen in simulation as an ever-slower convergence of the distribution of orientational order parameters with N. But the rare-event character and exceptionally slow time scales of the largest fluctuations make them difficult to sample accurately. We show in this paper how taking a large-deviation-theory perspective enables us to leverage simulation-derived information more effectively. A key insight of the theory is that finding quantities such as orientational order parameters (extensive variables) is completely equivalent to deducing the conjugate (intensive) thermodynamic field required to equilibrate that amount of order-and that knowing the relationship between the two (the "equation of state") can easily be turned into knowing the relative free energy of that degree of order. A variety of well-known thermodynamic integration strategies are already founded on this idea, but instead of applying an artificially imposed external field, we use a priori statistical mechanical insights into the small and large-field limits to construct a simulation-guided, interpolated, equation of state. The free energies that result mostly need information from the most probable configurations, making the simulation process far more efficient than waiting for (or artificially generating) large fluctuations.

On Capacitance and Energy Storage of Supercapacitor with Dielectric Constant Discontinuity

The classical density functional theory (CDFT) is applied to investigate influences of electrode dielectric constant on specific differential capacitance Cd and specific energy storage E of a cylindrical electrode pore electrical double layer. Throughout all calculations the electrode dielectric constant varies from 5, corresponding to a dielectric electrode, to εwr= 10⁸ corresponding to a metal electrode. Main findings are summarized as below. (i): By using a far smaller value of the solution relative dielectric constant εr=10, which matches with the reality of extremely narrow tube, one discloses that a rather high saturation voltage is needed to attain the saturation energy storage in the ultra-small pore. (ii): Use of a realistic low εr=10 value brings two obvious effects. First, influence of bulk electrolyte concentration on the Cd is rather small except when the electrode potential is around the zero charge potential; influence on the E curve is almost unobservable. Second, there remain the Cd and E enhancing effects caused by counter-ion valency rise, but strength of the effects reduces greatly with dropping of the εr value; in contrast, the Cd and E reducing effects coming from the counter-ion size enhancing remain significant enough for the low εr value. (iii) A large value of electrode relative dielectric constant εrw always reduces both the capacitance and energy storage; moreover, the effect of the εrw value gets eventually unobservable for small enough pore when the εrw value is beyond the scope corresponding to dielectric electrode. It is analyzed that the above effects take their rise in the repulsion and attraction on the counter-ions and co-ions caused by the electrode bound charges and a strengthened inter-counter-ion electrostatic repulsion originated in the low εr value.

Demixing and tetratic ordering in some binary mixtures of hard superellipses

We examine the fluid phase behavior of binary mixtures of hard superellipses using the scaled particle theory. The superellipse is a general two-dimensional convex object that can be tuned between the elliptical and rectangular shapes continuously at a given aspect ratio. We find that the shape of the particle affects strongly the stability of isotropic, nematic, and tetratic phases in the mixture even if the side lengths of both species are fixed. While the isotropic-isotropic demixing transition can be ruled out using the scaled particle theory, the first order isotropic-nematic and the nematic-nematic demixing transition can be stabilized with strong fractionation between the components. It is observed that the demixing tendency is strongest in small rectangle-large ellipse mixtures. Interestingly, it is possible to stabilize the tetratic order at lower densities in the mixture of hard squares and rectangles where the long rectangles form a nematic phase, while the squares stay in the tetratic order.