Glass transition of charged particles in two-dimensional confinement

Abstract

The glass transition of mesoscopic charged particles in two-dimensional confinement is studied by modecoupling theory. We consider two types of effective interactions between the particles, corresponding to two different models for the distribution of surrounding ions that are integrated out in coarse-grained descriptions. In the first model, a planar monolayer of charged particles is immersed in an unbounded isotropic bath of ions, giving rise to an isotropically screened Debye-Hückel (Yukawa)-type effective interaction. The second, experimentally more relevant system is a monolayer of negatively charged particles that levitate atop a flat horizontal electrode, as frequently encountered in laboratory experiments with complex (dusty) plasmas. A steady plasma current toward the electrode gives rise to an anisotropic effective interaction potential between the particles, with an algebraically long-ranged in-plane decay. In a comprehensive parameter scan that covers the typical range of experimentally accessible plasma conditions, we calculate and compare the mode-coupling predictions for the glass transition in both kinds of systems.

Structure and thermodynamics of two dimensional Yukawa liquids

“…Some work in this direction was performed in Ref. [18], where some qualitative agreement between Monte Carlo simulations and the T/2-HNC approximation was reported for the 2D YOCP. However, (a) these simulations were performed in the stable fluid regime, thus the extension to the supercooled regime involves an unjustified extrapolation, (b) the documented accuracy of the SHNC approach within the stable fluid region and the strong deviations of the SHNC mapping from the T/2-HNC mapping (see Fig.…”

“…It is generally prescribed by approximations that are constructed on theoretical grounds [38,59] or that are aided by computer simulations [60,61]. Popular approximations include the hypernetted-chain (HNC) approach which assumes that B(r) = 0 and has proven to be successful for systems with soft interaction potentials [18,19,62,63] or the Percus Yevick approach which assumes that B(r) = ln[1+γ(r)]−γ(r) and has proven to be successful for hard-sphere-like systems [64,65]. Here γ(r) = h(r) − c(r) is the indirect correlation function.…”

“…For the YOCP, this approach corresponds to a simplified version of the SHNC approach for which Γ SHNC (Γ, κ) = 2Γ. This empirical approach was recently applied to determine the glass transition line of the 2D-YOCP with the aid of mode coupling theory [18]. This was carried out without any discussion concerning the validity of the T/2-HNC approximation for metastable or even for stable 2D-YOCP liquids.…”

“…In more recent years, a renewed interest in 2D-YOCP systems was sparked by the observation that they can adequately model dust monolayers levitating in the sheath region of low temperature noble gas discharges [9][10][11][12][13] and to investigate combustion phenomena in confined geometries [14]. As a consequence, a considerable amount of effort has been dedicated to investigate the phase behavior [15][16][17][18] as well as the structural [19][20][21], thermodynamic [22][23][24][25][26][27] and dynamic properties [28][29][30][31][32] of the 2D-YOCP.…”

Theoretical Estimate of the Glass Transition Line of Yukawa One-Component Plasmas

“…Within MCT, the static structural properties of the supercooled fluid constitute the only external to the theory input that is required for the calculation of the glass transition line and the critical form factors. In the literature, such properties have been obtained either from computer simulations [ 59 , 60 , 61 ] or from IET calculations combined with elementary closures (when simulation input was unavailable) which include the aforementioned HNC approximation for soft long range interaction potentials [ 29 , 62 ] or the Percus–Yevick (PY) approximation for hard sphere short range interactions [ 16 , 17 , 33 , 63 , 64 , 65 ]. More advanced IET closures which enforce thermodynamic consistency through free parameters or resemble the VMHNC approximation by featuring an optimized correspondence rule have also been considered [ 66 , 67 , 68 ].…”