Location Of Phase Transition Point Research Articles

Self-Assembly of Model Triblock Janus Colloidal Particles in Two Dimensions.

A simplified two-dimensional effective-solvent model of triblock Janus particles, consisting of three interaction sites in a linear configuration, a core particle, and two particles modeling the attractive patches at the poles, is developed to study the mechanism of nucleation and self-assembly in triblock Janus particles. The potential energy parameters are tuned against phase transition temperatures and free energy barriers to the nucleation of crystalline phases, calculated from our previous detailed model of Janus particles. Vapor-liquid equilibria and critical temperatures are calculated by grand-canonical molecular dynamics simulations for particles of different patch widths. With metadynamics, phase equilibria, mechanism of nucleation, and free energy barriers to nucleation are investigated. The minimum free energy path to nucleation indicates two steps. The first step, with a higher free energy increase, consists of the densification of the fluid into a disordered cluster. In the second step, of a lower free energy barrier, the inner particles of the disordered cluster reorient to form a crystalline nucleus. This two-step mechanism of nucleation of a kagome lattice is in complete agreement with the experiment and with our previous simulations using a detailed model of Janus particles. Large systems at a slight supersaturation generate multiple crystalline domains, which are misaligned at the grain boundaries. In complete agreement with the experiment and with previous simulation results, we observe a two-step mechanism for crystal growth: melting of the smaller (less stable) crystallites to a fluid followed by recrystallization at the surface of neighboring bigger (more stable) crystallites. A comparison of the present softer modeling of a Janus particle with harder models in the literature for self-assembly of Janus particles indicates that softer potentials stabilize open lattices (e.g., kagome) more than dense lattices (e.g., hexagonal). Also, experimental locations of phase transition points and barrier heights to nucleation are better reproduced by the present model than by the existing simple models.

Analytical estimates of the locations of phase transition points in the ground state for the bimodal Ising spin glass model in two dimensions

We analytically estimate the locations of phase transition points in the ground state for the $\pm J$ random bond Ising model with asymmetric bond distributions on the square lattice. We propose and study the percolation transitions for two types of bond shared by two non-frustrated plaquettes. The present method indirectly treats the sizes of clusters of correlated spins for the ferromagnetic and spin glass orders. We find two transition points. The first transition point is the phase transition point for the ferromagnetic order, and the location is obtained as $p_c^{(1)} \approx 0.895 \, 399 \, 54$ as the solution of $[p^2 + 3 (1-p)^2 ]^2 \, p^3 - \frac{1}{2} = 0$. The second transition point is the phase transition point for the spin glass order, and the location is obtained as $p_c^{(2)} = \frac{1}{4} [2 + \sqrt{2 (\sqrt{5} - 1)}] \approx 0.893 \, 075 \, 69$. Here, $p$ is the ferromagnetic bond concentration, and $1 - p$ is the antiferromagnetic bond concentration. The obtained locations are reasonably close to the previously estimated locations. This study suggests the presence of the intermediate phase between $p_c^{(1)}$ and $p_c^{(2)}$; however, since the present method produces remarkable values but has no mathematical proof for accuracy yet, no conclusions are drawn in this article about the presence of the intermediate phase.

PHASE TRANSITION, GEOMETROTHERMODYNAMICS AND CRITICAL EXPONENTS OF BARDEEN BLACK HOLE

In this paper, we investigate the phase transition of Bardeen black hole for the first time. First, we calculate thermodynamic quantities and correct the misuse of formula in former literature. Second, we investigate in detail the behavior of specific heat. We not only discuss the influence of parameter on phase transition, but also show the three-dimensional behavior of the specific heat. It is shown that phase transition takes place from a locally unstable large black hole to a locally stable small black hole. It is also shown that the location of phase transition point is proportional to the charge. Meanwhile, we study the behavior of the inverse of the isothermal compressibility and find that it diverges at the phase transition point. Thirdly, we build up geometrothermodynamics to examine the phase transition structure. It is shown that Legendre invariant thermodynamic scalar curvature diverges exactly where the specific heat diverges, which leads to the conclusion that the Legendre invariant metrics can correctly produce the behavior of the phase transition structure. Furthermore, to gain a thorough understanding of critical behavior, we calculate the relevant critical exponents and examine the scaling laws. It is shown that they are in agreement with the scaling laws.