Thermodynamic properties of fluids with Lennard–Jones–Gauss potential from computer simulation and the coupling parameter series expansion

A bottom-up design strategy for controllable self-assembly based on the isotropic double-well potential

Controllable self-assembly of particles or atoms is still challenging in the synthesis of materials with desirable properties that are highly relevant to the microscopic structures determined by the interparticle interactions. To gain insight into how the interactions affect the self-assembly, we designed various kinds of isotropic double-well potentials and simulated the motion of the particles. By controlling the depth and location of the potential wells and the height of the barriers, we studied their effects on the aggregation structures and the related microscopic kinetic processes. We identified five aggregation patterns at different temperatures and eight kinds of crystals, including Frank-Kasper phases, and observed the expansion or contraction of crystals. We found that the system usually stays in a sparse configuration at very low or very high temperatures. The particles typically assemble into a loosely packed cluster at medium temperatures and then deplete into a tightly packed state with a specific pattern. These phenomena can be explained from the perspective of energy. In contrast, very few structures could be obtained for the system guided by a single-well potential under the same simulation conditions. Thus, the interparticle interactions driven by the double-well potential greatly enrich the possible packing morphology of the system. The information obtained from this work helps us to understand how to achieve a specific self-assembled architecture through a reasonable selection of materials.

Formula of compressibility and using it for air, noble gases, some hydrocarbons gases, some diatomic simple gases and some other fluids

Based on solutions of the Ornstein–Zernike equation (OZE) of Lennard–Jones potential for mean spherical approximation (MSA), we derive analytical formula for the compressibility assuming that the system is of low density, homogeneous, isotropic and composed of one component. Depending on this formula, we find the values of the bulk modulus and the compressibility of air at room temperature and the bulk modulus and the compressibility of Methane, Ethylene, Propylene and Propane at nine per ten of critical temperature of each hydrocarbon. Also, we find the speed of sound in the air at various temperatures, the speed of sound in each of Helium, Neon, Argon, Krypton, Xenon, Methane, Ethylene, Propylene, Propane, Hydrogen, Nitrogen, Fluorine, Chlorine, Oxygen, Nitrous oxide (laughing gas), Carbon dioxide, Nitric oxide, Carbon monoxide, Sulphur dioxide and dichlorodifluoromethane at room temperature. Besides, we find the speed of sound in Methane, Ethylene, Propylene and Propane at nine per ten of critical temperature of each hydrocarbons depending on the formula we find. We show that the simple formula we derive in this work is reliable and agrees with the results obtained from other studies and literatures. We believe it can be used for many systems which are in low densities and described by Lennard–Jones potential.

Numerical simulation of the space dependent fractional Schrödinger equation for London dispersion potential type

In this study, we apply the definition of one of the fractional derivatives definitions of increasing values of the variable, which is the fractional derivative of Riemann-Liouville, and the numerical-integral methods to find numerical solutions of the fractional Schrödinger equation with the time-independent form for Van Der Walls potential type. We use the dimensionless formalism of the fractional Schrödinger equation in the space-dependent form in case of London dispersion potential in the stationary state. The solutions are found for multiple values of the space-dependent fractional Schrödinger equation parameter with a certain value of the energy. We find that the numerical solutions are physically acceptable for some values of the space dependent fractional parameter of the fractional Schrödinger equation but are not physically acceptable for others for a specific case. The numerical solutions can be applied for the systems that obey London dispersion potential type, which is resulted from the polarization of the instantaneous multi-poles of two moieties, such as soft materials systems and fluids of the inert gases.