One-component plasma

The results of the simple DHH theory outlined here are shown compared with DH results and corresponding Monte Carlo results in Figs. 10-12. Clearly, the major error of the DH theory has been accounted for. The OCP model is greatly idealized but the same hole correction method can be applied to more realistic electrolyte models. In a series of articles the DHH theory has been applied to a one-component plasma composed of charged hard spheres [23], to local correlation correction of the screening of macroions by counterions [24], and to the generation of correlated free energy density functionals for electrolyte solutions [25,26]. The extensive results obtained bear out the hopeful view of the DHH approximation provided by the OCP results shown here. It is noteworthy that in... 

FIG. 10 The calculated internal energy of a one-component plasma as a function of coupling strength is compared with corresponding simulation results (open circles) by Brush, Sahlin, and Teller (J. Chem. Phys. 45 2102 (1966). The Debye-Huckel (DH) and hole-corrected Debye-Huckel (DHH) theories were used with results as shown (indicated lines). 

Hansen, J.P. Statistical mechanics of dense ionized matter. I. Equilibrium properties of the classical one-component plasma. Phys. Rev. A 1973, 8, 3096-109. 

For one-component plasmas (OCP) of ionic charge Ze, one obtains, A2 = -TTni +Z r, where n is the electron density of plasma far from the ionic site. The spherically symmetric solution of Equation (7) yields... 

The IET as well as the simulations indicate that the dielectric constant increases from the macroscopic dielectric value to infinity and then becomes negative at some value of k. Such exotic pole-like behaviour is not unique and has been reported for the one-component plasma and the degenerate electron gas [36]. This overscreening effect leads to... 

It allows for extensive simulations of ionic systems, containing up to few thousand of particles in the main cell, even on PC. New MD simulation software, implementing the above-mentioned approach, was recently developed Yakub and Ronchi, 2005) and tested on simple model systems like one-component plasma and primitive ionic model of electrolyte. 

The latter comments are broadly consistent with experiment. Thus, one observes, in simulations of the one component plasma (a system with r repulsive interactions) a frequent fluctuation in and out of the ordered state,although in a 500-particle system, a supercooling to 0.95 7 has recently been obtained. Conversely, in the opposite extreme of the hard-sphere system, spontaneous ordering is not seen at all [in very small (32-particle) systems, the periodic boundaries seem to induce some artificial... 

N. D. Mermin, Exact lower bounds for some equilibrium properties of a classical one-component plasma, Ihys. Rev. 171, 272-275 (1968). 

Ceperley, D. M. and G. V. Chester. 1977. Perturbation approach to classical one-component plasma. Physical Review A. 15, 756. 

Galam, S. and J. P. Hansen. 1976. Statistical-mechanics of dense ionized matter. 6. Electron screening corrections to thermodynamic properties of one-component plasma. Physical Review A. 14, 816. 

Although an ion ensemble is a classical system (except in the special case of extremely low temperatures, which shall not be considered here), the large number of degrees of freedom, the finite size and the nonlinear ion-ion interaction make analytical treatments very difficult. Fortunately, molecular dynamics (MD) simulations provide an excellent tool for their analysis. They can even be used to analyze novel methods before implementing them experimentally. MD simulations of three-dimensional cold trapped charged particle ensembles have been performed for the one-component plasma in a conservative harmonic potential since the mid-1970s and in radio-frequency traps since the first experimental studies [50,51]. 

Schiffer, J.P., Layered structure in condensed, cold, one-component plasmas confined in external fields, Rfeyf. Rev. Lett, 61,1843, 1988. 

Bussmann, M., Schramm, U., Habs, D., Kolhinen, V.S., and Szerpypo, 1., Stopping highly charged ions in a laser-cooled one component plasma of Mg ions, Int. J. Mass. Spectrom., 251, 179, 2006. 

In his original works, Rosenfeld considered hard spheres, soft spheres, Lennard-Jones system, and one-component plasma [52,53]. Thereafter, the excess entropy scaling was applied to many different systems, including core-softened liquids [17,18,51,54,55], liquid metals [56,57], binary mixtures [58,59], ionic liquids [60,61], network-forming liquids [54,60], water [62], chain fluids [63], and bounded potentials [51,64,65]. 

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