Metal-ammonia solutions, concentrated

The alkali metals also release their valence electrons when they dissolve in liquid ammonia, but the outcome is different. Instead of reducing the ammonia, the electrons occupy cavities formed by groups of NH3 molecules and give ink-blue metal-ammonia solutions (Fig. 14.14). These solutions of solvated electrons (and cations of the metal) are often used to reduce organic compounds. As the metal concentration is increased, the blue gives way to a metallic bronze, and the solutions begin to conduct electricity like liquid metals. 

Doped semiconductors, expanded metals, metal-ammonia solutions and rare gas-metal films where the transition occurs because of change of donor concentration or density. 

We turn now to an evaluation of nc, the concentration of centres at which the transition occurs. We remark first of all that an experimental value is difficult to obtain. We do not know of a crystalline system, with one electron per centre in an s-state, that shows a Mott transition. Figure 5.3 in the next chapter shows the well-known plot given by Edwards and Sienko (1978) for nc versus the hydrogen radius aH for a large number of doped semiconductors, giving ncaH=0.26. In all of these the positions of the donors are random, and it is now believed that for many, if not all, the transition is of Anderson type. In fluid caesium and metal-ammonia solutions the two-phase region is expected, but this is complicated by the tendency of one-electron centres to form diamagnetic pairs (as they do in V02). In the Mott transition in transitional-metal oxides the electrons are in d-states. 

Fig. 10.15 Conductance per ion pair of metal-ammonia solutions. The ratio of electrical conductivity to the concentration of metal (equivalent conductance) is shown as a function of concentration. O represent data of Kraus (1921) and data of Dye et al. (I960), both at 240 K and in Na-NH3 solutions. + and x represent the equivalent conductances assigned to positive and negative carriers respectively by Dye on the basis of transference-number measurements. From Cohen and Thompson (1968).

Fig. 10.18 Hall coefficient R for metal-ammonia solutions, plotted as a function of concentration in the form RFE/R0bs- From Cohen and Thompson (1968).

Metal-ammonia solutions show a dramatic increase in the dielectric constant as the concentration approaches that for a metal-insulator transition from below. We think this has to be interpreted as in Chapter 5, Section 8. Investigations of this behaviour through ESR measurements in LixNH3 have been made by Damay et al (1988), with a theoretical interpretation given by Leclercq and Damay (1988). 

There have been many theories of metal-ammonia solutions that differ from that presented here. Cohen and Thomson (1968) and more recently Cohen and Jortner (1973) supposed that large fluctuations in concentration occur over large distances, sufficient to invalidate the pseudogap model and substitute a semiclassical percolation theory. For the reasons given above, we think that this is only likely to be so within a few degrees of the critical point. 

FIGURE 14.17 Sodium dissolves in liquid ammonia to form the deep blue solution in the lower half of the tube. At higher concentrations, the metal ammonia solution becomes bronze in color, as in the top half of the tube. 

What is the nature of the transition to the metallic state in a liquid containing a high density of excess electrons When the concentration of excess electrons in a liquid is gradually increased, a transition from behavior characteristic of a localized state to that characteristic of a delocalized state is observed—e.g., in concentrated metal-ammonia solutions and in metal-molten salt mixtures. 

Solutions containing a high concentration of excess electrons display a transition to the metallic state. Thus, for sodium-ammonia solutions in the concentration region 1-6 M the specific conductance increases by about three orders of magnitude, and the temperature coefficient of the conductance is very small (27). Similar behavior is exhibited by other metal-ammonia solutions (but surprisingly, not by concentrated lithium-methylamine solutions ) (10) and by metal-molten salt solutions (17). 

It is, however, not clear at present whether such a model can be applied to metal solutions. It is worth mentioning again at this point that the specific conductivity of a saturated solution of lithium in methyl-amine (10) (concentration 5.5M) has been found to be 28 ohm l cm."-1, which is two orders of magnitude lower than that for a corresponding saturated metal-ammonia solution. This experimental result seems to indicate that the overlap between electron trapping centers may not be... 

Physical chemical studies of dilute alkali metal-ammonia solutions indicate the principal solution species as the ammoniated metal cation M+, the ammoniated electron e , the "monomer M, the "dimer" M2 and the "metal anion" M. Most data suggest that M, M2, and M are simple electrostatic assemblies of ammoniated cations and ammoniated electrons The reaction, e + NH3 - lf 2 H2 + NH2 is reversible, and the directly measured equilibrium constant agrees fairly well with that estimated from other thermodynamic data. Kinetic data for the reaction of ethanol with sodium and for various metal-ammonia-alcohol reductions of aromatic compounds suggest that steady-state concentrations of ammonium ion are established. Ethanol-sodium reaction data allow estimation of an upper limit for the rate constant of e + NH4+ 7, H2 + NH3. 

The general shape of the equivalent conductance vs. concentration plot for metal-ammonia solutions is shown by the behavior of sodium in NHs at —33° C. in Figure 2. The conductance behavior of metal-ammonia solutions is quite analogous to the behavior of electrolytes in solvents of low dielectric constant. The dilute region equivalent conductance decreases with increasing concentration, eventually goes... 

Conduction Processes in Concentrated Metal-Ammonia Solutions... 

The metallic nature of concentrated metal-ammonia solutions is usually called "well known." However, few detailed studies of this system have been aimed at correlating the properties of the solution with theories of the liquid metallic state. The role of the solvated electron in the metallic conduction processes is not yet established. Recent measurements of optical reflectivity and Hall coefficient provide direct determinations of electron density and mobility. Electronic properties of the solution, including electrical and thermal conductivities, Hall effect, thermoelectric power, and magnetic susceptibility, can be compared with recent models of the metallic state. 

Jhe concentrated (>0.4Af) metal-ammonia solutions were first called metallic" by Kraus in 1921 (7). On several recent occasions the term semiconductor" has implicitly been substituted for metal" in interpreting various data (1, 2). Since Kyser and Thompson (8) have established the truly metallic nature of the solutions by measuring the free carrier concentration, it is worthwhile to re-examine the relative data and interpret it in terms of liquid metal theory. 

The electrical conductivities of several alkali metals dissolved in liquid ammonia are shown in Figure 1 (7, 119 15). The strong variation of the conductivity, a, with concentration has been most difficult to explain. This difficulty can be assessed by referring to a simple model of conductance, the Thomas-Fermi model of a screened Coulomb potential (19). This model has been used in describing semiconductors as well as in theories of metal-ammonia solutions (1). 

The volume expansions of alkali metals in liquid ammonia are discussed in the light of the current available data. Special emphasis is made of the anomalous volume minimum found with sodium-ammonia and potassium-ammonia solutions. Recent studies of potassium in ammonia at —34° C. were found to exhibit a large minimum in the volume expansion, AV, vs. concentration curve. The results of these findings were compared with the previous results of potassium in ammonia at —45° C. The volume minimum was found to be temperature dependent in that the depth of the minimum increased and shifted to higher concentrations with increasing temperature. No temperature effect was observed on either side of the minimum. These findings are discussed in light of the Arnold and Patterson and Symons models for metal-ammonia solutions. 

Solutions of alkali metals in liquid ammonia at all concentrations, with the exception of cesium, are less dense than either of the constituents. This behavior for metal ammonia solutions is unique in that the expansion in volume is much larger than that shown on forming solutions of normal electrolytes or non-electrolytes. 

A large volume expansion for solutions of sodium in ammonia was first reported by Kraus and Lucasse (17). Since this initial report, many investigations have been made of the volume expansion for a number of alkali metal-ammonia solutions. The techniques employed in these investigations have varied from density measurements for concentrated solutions using the Westphal Balance or Pycnometer to dilatometric studies for dilute solutions, which measure the volume expansion directly. 

Ordinarily, high temperature and ultraviolet radiation seem to promote the decomposition of metal-ammonia solutions. However there is evidence that these factors merely accelerate decomposition which was initially begun by catalytic amounts of contaminants on the walls of the containers. A silica tube was rinsed with liquid ammonia, the rinse-ammonia removed by evaporation, and the tube evacuated a concentrated blue metal-ammonia solution ( 1M) was prepared in the tube,... 

Section IV gives an overall view of concentrated solutions and the nonmetal-metal (NM-M) transition. Here again, the majority of data are for metal-ammonia solutions. However, in the past decade a substantial body of experimental data has emerged for the NM-M transition in lithium-methylamine solutions, which allows a direct comparison with the situation existing in metal-ammonia solutions (60). This section also considers recent developments in the study of the "expanded-metal compounds, as typified by LilNHs),, Ca(NH3)8 (82), and Li(CH3NH2)4 66), and formed by slow cooling of the concentrated metal solutions. 

The overall changes in magnetic and transport properties of metal-ammonia solutions from the dilute to concentrated regimes are shown in Fig. 4. 

Fig. 4. The concentration dependence of various electronic properties of metal-ammonia solutions, (a) The ratio of electrical conductivity to the concentration of metal-equivalent conductance, as a function of metal concentration (240 K). [Data from Kraus (111).] (b) The molar spin (O) and static ( ) susceptibilities of sodium-ammonia solutions at 240 K. Data of Hutchison and Pastor (spin, Ref. 98) and Huster (static, Ref. 97), as given in Cohen and Thompson (37). The spin susceptibility is calculated at 240 K for an assembly of noninteracting electrons, including degeneracy when required (37).

Fig. 5. Electron spin pairing in metal-ammonia solutions at 25°C (298 K), 0°C (273 K), and -33°C (240 K). Paramagnetic spin concentrations for sodium-ammonia and potassium-ammonia solutions. [Experimental data from Refs. 47, 76, 98, 114,115, and 159. Adapted from Harris (88). Used with permission.] The solid line indicates the expected spin-pairing behavior for noninteracting electrons (88).

Na-NH3, 1.02 x 108 ohm-1 cm2 mol-1 for Hg, 0°C, 0.16 x 10 ohm-1 cm2 mol-1). In the intermediate composition range 1 to 7 MPM, a NM-M transition occurs, and changes in the electronic, thermodynamic, and mechanical properties of the system are equally impressive (35, 37, 124, 154). A detailed discussion of the concentration dependence of various properties of metal-ammonia solutions is given in the book by Thompson (164). In addition, a recent review (60) at Colloque Weyl V also summarizes the available data for lithium-methylamine solutions (10, 11, 63, 127, 128, 166). 

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