We present the results of a detailed Monte Carlo study of the phase diagram of infinitely thin hard platelets. A weak first order isotropicnematic transition is observed. The equation of state in the isotropic regime is compared with several current theories, none of which is found to be fully satisfactory. The density dependence of the nematic order parameter is found to be compatible with a ‘critical’ exponent β=0·25. A study of the fluctuations of the order parameter in the isotropic phase casts doubt on the applicability of the Landau-de Gennes expression for the free energy. We observe that the relation between the nematic order parameters and is compatible with the predictions of mean-field theory. Practical aspects of the computation are discussed. A novel method to compute the pressure in a constant-volume Monte Carlo run is presented.

Monte Carlo study of the isotropic and nematic phases of infinitely thin hard platelets

The van der Waals picture focuses on the differing roles of the strong short-ranged repulsive intermolecular forces and the longer ranged attractions in determining the structure and dynamics of dense fluids and solids. According to this physical picture, the attractive interactions help fix the volume of the system, but the arrangements and motions of molecules within that volume are determined primarily by the local packing and steric effects produced by the repulsive forces. This very useful approach, its limitations, and its successful application to a wide variety of static and dynamic phenomena in condensed matter systems are reviewed.

https://science.sciencemag.org/content/sci/220/4599/787.full.pdf

Van der waals picture of liquids, solids, and phase transformations.

Colloidal suspensions that form periodic self-assembling structures on sub-micrometre scales are of potential technological interest; for example, three-dimensional arrangements of spheres in colloidal crystals might serve as photonic materials, intended to manipulate light. Colloidal particles with non-spherical shapes (such as rods and plates) are of particular interest because of their ability to form liquid crystals. Nematic liquid crystals possess orientational order; smectic and columnar liquid crystals additionally exhibit positional order (in one or two dimensions respectively). However, such positional ordering may be inhibited in polydisperse colloidal suspensions. Here we describe a suspension of plate-like colloids that shows isotropic, nematic and columnar phases on increasing the particle concentration. We find that the columnar two-dimensional crystal persists for a polydispersity of up to 25%, with a cross-over to smectic-like ordering at very high particle concentrations. Our results imply that liquid crystalline order in synthetic mesoscopic materials may be easier to achieve than previously thought.

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Liquid crystal phase transitions in suspensions of polydisperse plate-like particles

By reviewing experimental and theoretical works, we discuss the phase diagram of Laponite suspensions, with the aim of clarifying several issues that have caused a long-time controversy on the system. We claim that, if aging and sample preparation are correctly taken into account, a unifying picture emerges from different experimental studies. Multiple non-ergodic states are identified, including a low concentration equilibrium gel and a high concentration Wigner glass in the absence of salt. These findings are critically discussed also with respect to recent evidence of phase separation at extremely low densities and to existing theoretical and numerical works.

A fresh look at the Laponite phase diagram

Through the use of the limited materials palette, optimally designed micro- and nanostructures, and tightly regulated processes, nature demonstrates exquisite control of light–matter interactions at various length scales In fact, control of light–matter interactions is an important element in the evolutionary arms race and has led to highly engineered optical materials and systems In this review, we present a detailed summary of various optical effects found in nature with a particular emphasis on the materials and optical design aspects responsible for their optical functionality Using several representative examples, we discuss various optical phenomena, including absorption and transparency, diffraction, interference, reflection and antireflection, scattering, light harvesting, wave guiding and lensing, camouflage, and bioluminescence, that are responsible for the unique optical properties of materials and structures found in nature and biology Great strides in understanding the design principles a

Bio-Optics and Bio-Inspired Optical Materials.

The first numerical determination of the thermodynamic isotropic-nematic transition in a simple three-dimensional model fluid, viz., a system of infinitely thin hard platelets, is reported. Thermodynamic properties were studied with use of the constant-pressure Monte Carlo method; Widom's particle-insertion method was used to measure the chemical potential. The phase diagram is found to differ considerably from predictions of a second-virial ("Onsager") theory. Virial coefficients up to the fifth were computed; b5 is found to be negative.

Rob Eppenga

Papers

Monte Carlo Study of the Isotropic-Nematic Transition in a Fluid of Thin Hard Disks