Solid phase stability of a double-minimum interaction potential system

Abstract

We study phase stability of a system with double-minimum interaction potential in a wide range of parameters by a thermodynamic perturbation theory. The present double-minimum potential is the Lennard-Jones-Gauss potential, which has a Gaussian pocket as well as a standard Lennard-Jones minimum. As a function of the depth and position of the Gaussian pocket in the potential, we determine the coexistence pressure of crystals (fcc and bcc). We show that the fcc crystallizes even at zero pressure when the position of the Gaussian pocket is coincident with the first or third nearest neighbor site of the fcc crystal. The bcc crystal is more stable than the fcc crystal when the position of the Gaussian pocket is coincident with the second nearest neighbor sites of the bcc crystal. The stable crystal structure is determined by the position of the Gaussian pocket. These results show that we can control the stability of the solid phase by tuning the potential function.

Free-energy functional method for inverse problem of self assembly

“…(9). The use of a terraced (discretized) interparticle potential is a possible candidate for the way to reduce the computation time.…”

“…Improving the numerical efficiency is necessary for the future work, e.g., the use of the trial potential with many variational parameters; the inverse problem for the 3D structure, which requires time-consuming six-dimensional numerical integration in Eq. (9). The use of a terraced (discretized) interparticle potential is a possible candidate for the way to reduce the computation time.…”

“…Therefore, in this paper, σ is set to 0.15, which is the typical value of the Lindemann ratio at crystallization. Since ρ (2) (x, 0)/ρ(0) remains finite near x = 0, where ϕ fix (x) diverges rapidly, the approximations ( 11) and ( 12) cause the second term at the right-hand side of (9) to diverge. This is caused by neglecting the correlation between the particles in the derivation of (12).…”

“…Density functional theory (DFT), another tool to find the thermodynamically stable phases, has shown that in three dimensions (3D), the LJG fluid forms a body centered cubic (bcc) crystal as a stable phase. 9 When a structure of a condensed phase is known from experiments or is designed artificially, determination of the interparticle interaction is more efficient by using the inverse approach, in which the interparticle interaction is derived from the given structure, than using the forward approach of exhaustive search by the molecular simulations or DFT. The inverse statistical mechanical method, 10 which is the most elaborated inverse approach, has been successfully used to design the interparticle interaction potentials that generate the square, honeycomb, [10][11][12][13] kagome, and rectangular 13,14 lattices in 2D, and the simple cubic, bcc, simple hexagonal, 13,15,16 diamond, 13,16,17 and wurtzite lattices 17 in 3D.…”

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

“…16 It exhibits an fcc structure for large clusters, 17 and the phase transition of LJ systems has been extensively studied. 18,19 On the other hand, the double-well potential, a simplified form of a more complex potential, 12 such as the Lennard-Jones-Gauss (LJG) potential, 8,[20][21][22] has attracted considerable interest for exploring various physical phenomena or mathematical properties since it permits, in many cases, explicit calculation without oversimplification. For example, it was proposed that the potential for water-water could be designed to be a double-well form to present a subsidiary secondneighbor oxygen-oxygen minimum.…”