Cooperative Phenomena below Melting of the One-Component Two-Dimensional Plasma

Abstract

This Letter reports investigations by molecular dynamics of the melting transition of a two-dimensional one-component plasma consisting of 511 particles with logarithmic interactions confined to a disk. Evidence is presented for a weak first-order transition occurring at T^ = ^V^r^ with r^ ^ 142 and with a melting entropy =^0.17 K. This small entropy is attributed to important premelting phenomena which are cooperative, cyclic permutations of six and more particles as revealed by labeling experiments.PACS numbers: 64.70.Dv, 52.25.Kn, 61.20.JaThe first investigation by molecular dynamics of the melting transition of the two-dimensional one-component plasma (2D-OCP) was carried out by de Leeuw and Perram/ Using periodic boundary conditions, they reported strong evidence of a first-order transition occurring at T^ c-135. A value of r^ c-140 has been obtained by Caillol et al,'^ They compared the free energy of the harmonic crystal with the free energy resulting from integrating internal energies from a Monte Carlo simulation of particles confined to the surface of a sphere with respect to T starting from the r=2 result. Using for the fluid phase a careful extrapolation of the free energy calculated for a small number of particles confined to a disk, Johannesen and Merlini^ gave an estimate of r^ c-137. In this Letter, we report extensive molecular dynamics investigations of the coexistence and premelting regions for the 2D-OCP. Following individual particle histories shows the importance of cooperative motions, strikingly reminiscent of phenomena occurring in hard-disk systems as recently reviewed by Alder, Ceperly, and Pollock/ The OCP model consists of an assembly of charged point particles immersed in a neutralizing background. In two dimensions, the Coulomb potential between two particles of charge e and separated by a distance r= |r| is -g^ln(r/l.), where L is a scaling length. For a neutral system of AT particles confined in a disk of radius R, the potential energy is^ V^-e' Sini <J -I N^e^ -R . ^sIn where r^ is the position of particle i and r^j = |r^ --Vj |. Our simulations are performed with free boundary conditions on the disk. The simplicity of the corresponding Hamiltonian makes very fast calculations possible, particularly at low temperature where the kinetic pressure turns out to be vanishingly small. The number of particles is chosen from a sequence such that the neutralizing disk accommodates exactly a perfect triangular lattice of particles centered at the origin of the disk. This sequence has been investigated by Sari, Merlini, and Calinon.^ iV= 511 is the number from this sequence which best fits our computing facilities. While the Madelung energy is -0.3744^^, the energy per particle of this crystal is -0.3652^^ Relaxation of the system toward its configuration of minimum energy yields an energy per particle of -0.3727^^, but this is accompanied by a strong deformation of the outer shells of particles due to the circular boundary conditions. In order to avoid this effect, we have pinned the twelv...

String-like cooperative motion in homogeneous melting

“…Qualitative evidence for such heterogeneity has been apparent since the earliest simulations of melting in hard discs by Alder et al 50,51 where large-scale cooperative particle motion was found to be a conspicuous feature of the melting process. This type of permutational particle motion was also noticed long ago in the simulated melting of one-component plasmas 52 and measurements on granular fluid, 53 colloidal fluid, 54,55 and dusty plasma [56][57][58] melting in near two dimensions. Quite recently there have been molecular dynamics studies of collective atomic motion associated with superheating of three dimensional crystals of Lennard-Jones particles 59,60 where many aspects of dynamics heterogeneity in GF liquids are exhibited such as a strong growth of the non-Gaussian parameter, clusters of mobile particles, cooperative particle motion, etc.…”

“…55 This type of particle permutation motion has also been observed in particle tracking measurements of melting in quasi-two dimensional lattices of colloidal particles, 54,[96][97][98] quasi-two dimensional driven granular fluids 53 and simulations of the melting of quasi-two dimensional plasma crystals. 13,52,56 It is thus not surprising that we see prevalent string-like collective motion in our simulations of melting in Ni crystals. What is somewhat surprising is that the size distribution and geometrical form of the excitations is so similar in geometrical form to GF liquids.…”

Control of the conformations of ion Coulomb crystals in a Penning trap

“…Monte Carlo simulations show that large, three-dimensional (3D) clouds of ions form solid-phase crystals at Γ≈172–178 (see ref. 1 and references therein) and at Γ≈140 for two-dimensional (2D) systems2. In these crystals, the inter-ion distance is typically of the order of 10 μm, set by the strength of the applied trapping fields.…”

Slow Magnetic Relaxation in Iron: A Ferromagnetic Liquid

“…In the Landau-Lifshitz formalism, excitations are coherent over the magnetic exchange length (27), which is -8 nm in Fe at low temperatures. Similar dynamical correlations, characteristic of DCDs, are found in a variety of physical systems (28).…”