Nature of the metal–nonmetal transition in metal–ammonia solutions. I. Solvated electrons at low metal concentrations

Abstract

Using a theory of polarizable fluids, we extend a variational treatment of an excess electron to the many-electron case corresponding to finite metal concentrations in metal-ammonia solutions (MAS). We evaluate dielectric, optical, and thermodynamical properties of MAS at low metal concentrations. Our semianalytical calculations based on a mean-spherical approximation correlate well with the experimental data on the concentration and temperature dependencies of the dielectric constant and the optical absorption spectrum. The properties are found to be mainly determined by the induced dipolar interactions between localized solvated electrons, which result in the two main effects: the dispersion attractions between the electrons and a sharp increase in the static dielectric constant of the solution. The first effect creates a classical phase separation for the light alkali metal solutes (Li, Na, K) below a critical temperature. The second effect leads to a dielectric instability, i.e., polarization catastrophe, which is the onset of metallization. The locus of the calculated critical concentrations is in a good agreement with the experimental phase diagram of Na-NH(3) solutions. The proposed mechanism of the metal-nonmetal transition is quite general and may occur in systems involving self-trapped quantum quasiparticles.

Nature of metal–nonmetal transition in metal–ammonia solutions. II. From uniform metallic state to inhomogeneous electronic microstructure

“…58 Above T c , the mixture entropy should outweigh the difference in the energies of the states, resulting in a mixed state. 2 It is worth noting that the mixed state qualitatively, described here, is of a new kind in condensed matter ͑to our knowledge͒ and really results from the competition, driven by strong thermal fluctuations, between the delocalized and the self-trapped quantum states. 41 However, at a qualitative level, we may already say that above the critical temperature, the system should be a microscopic mixture of both states, which is highly thermally fluctuating and roughly described by the relative fractions n m = ͑1+exp͓␤͑f m ͑n͒ − f nm ͑n͔͒͒͒ −1 and 1 − n m of electrons in the metallic and nonmetallic state, respectively, as a function of the metal concentration.…”

“…Earlier on, 2 we have determined the low-density spinodal line n s ͑T͒ above which the solvated electrons become thermodynamically unstable. Now we evaluate the highdensity counterpart of the spinodal line n c2 ͑T͒ corresponding to the zero derivative of the excess chemical potentials or the excess pressure…”

“…2 mass, is the surface tension, and nm = n͑r e + r vdW ͒ 3 / 3 is an effective packing factor, that we take equal to the mean value between the solvated electron and ion diameters. 2 mass, is the surface tension, and nm = n͑r e + r vdW ͒ 3 / 3 is an effective packing factor, that we take equal to the mean value between the solvated electron and ion diameters.…”

A Molecular Perspective on Lithium–Ammonia Solutions

“…Our findings suggest that the cavity may optimally contain 5-8 molecules, in reasonable agreement with other estimates of 7-8 ammonia molecules. [52,121] For all of the cavities considered, the N À N and H À H distances are quite large, owing to the diffuse nature of the 3a 1 orbitals. The large NÀN distances (see Figures 17 and 18) are also in accordance with experimental estimates of the cavity radius (2.5-3.0 ).…”

Lithium‐Ammoniak‐Lösungen: eine molekulare Betrachtung

“…In Tabelle [52,121] Wegen der diffusen Eigenschaften der 3a 1 -Orbitale weisen alle hier betrachteten Käfige relativ große N-N-und H-H-Abstände auf. Die großen N-N-Abstände (siehe Abbildungen 17 und 18) sind auch im Einklang mit experimentellen Abschätzungen des Käfigradius (2.5-3.0 ).…”