190
Table II: Coefficients of ml in the Line-Width Expression Using the Two-State Model
JAMES L. DYEAND LARRYR. DALTON
then the line widths of the individual hyperfine components will be different, with broader lines resulting for the higher mI values. If a significant portion of the distribution of solvent structures arises from molecules outside of the primary solvation layer, one would expect abrupt changes in hyperfine splitting and line width at the freezing point. Since abrupt changes in hyperfine splitting are not observed, the significant distributions would have to involve solvent molecules close to the monomer. A quantitative treatment of this model would require knowledge of the distribution of hyperfine spljttings and g values, and has not yet been carried out. An approximate treatment indicates that at a given temperature the line width should be quadratic in m1.12
Summary
quantitative treatment for the case of very large splittings exists. Analysis of the variation of hyperfine splitting and g value with temperature in terms of a three-state equilibrium model has proved successful.1 4 , 1 5 This indicates that the atom-monomer equilibrium A & B is important at high temperatures but requires the introduction of a third species C at low temperatures. This species has a low contact density and a g value approximately that of the solvated electron. Attempts to interpret the line width dependence upon mI and temC equilibrium perature using eq 3 and only the B were unsuccessful. If the line-width behavior is to be attributed to chemical relaxation, it appears necessary to include all three species and a modified theoretical treatment. Instead of describing the variation of magnetic parameters with temperature in terms of two or more interconverting species, one can consider stationarystate models in which the wave function for the unpaired electron is strongly dependent upon solvent configuration about the & unit. !I Two models based upon this assumption have been used to explain hyperfine interactions in metal-amine solutions. 19,20 These models require a distribution of electron environments in the solution with a broad range of hyperfine contact densities. Such a distribution is necessary since a change in temperature brings about a change in the observed hyperfine splitting. Presumably this distribution arises from variations in solvent structure about the monomer. If the correlation time associated with fluctuations of the solvent environment is long enough to contribute significantly to line broadening, The Journal of Physical Chemistry
The complexity of the experimental results, which yield large variations of hyperfine splitting, g value, and line width with temperature, as well as dependence of line width upon hyperfine component, prohibits a quantitative treatment of the relaxation phenomena over the entire temperature range at this time. Several simplified models, amenable to quantitative treatment, have been tested but are unable to account for all of these variations. Acknowledgments. We are grateful to H. -If. McConnell of Stanford University and C. Kikuchi and R. H. Sands of the University of Michigan for permitting us to use their apparatus and for helpful discussions about the various mechanisms considered in this paper. We also acknowledge helpful discussions with L. S. Singer and correspondence with D. Kivelson. Particular thanks are due V. A. n'icely and J. D. Rynbrandt for assistance with the measurements and calculations.
Discussion M. C. R. SYMONS (University of Leicester, Leicester). I have one or two comments to make, based on results obtained by Dr. Catterall and Mr. Tipping at Leicester. (1) Fresh solutions of potassium in ethylamine, which show mainly a band at 850 mr, have esr spectra as shown in Figure 9. Dilution causes a relative increase in the intensity of the central line, and this is reversible, the equation ill eill+ e- being satisfied if the central singlet is assigned to the solvated electron. (2) The plateau in the plot of hyperfine splitting against temperature is not observed for the pure amine solvents that we have used. (3) We want to stress that, as the hyperfine splitting tends toward the atom value, so the g value tends away. Hence the limiting, hightemperature species is not the atom. The situation can be compared with that found for silver atoms. When silver atoms are
+
(19) K. Bar-Eli and T. R. Tuttle, Jr., J . Chem. Phys., 40, 2408 (1964). (20) D. E. O'Reilly and T. Tsang, ibid., 42, 3333 (1965).
NUCLEAR SPINDEPENDENT RELAXATION PROCESSES IN METAL-AMINE SOLUTIONS
191
identical with the gaseous atom but view it as a solvated atom in which spin-orbit coupling through both solvent and metal orbitals reduces the g value.
I
Figure 9. The esr spectrum of potassium in ethylamine a t room temperature: (a) -10-6 M K ; (b) -10-7 M K. isolated from the gas phase into polar matrices such as water, the hyperfine and g values are very close to those for atoms in the gas phase. However, when silver cations solvated in rigid media gain an electron, the hyperfine coupling is reduced by about 10% and there is a negative g shift. The trend can be understood in terms of a residual occupancy of the outer s orbital by solvent line-pair electrons such that the outer sp separation is reduced.
J. L. DYE. (1) and (2) The properties of metal-amine solutions are very dependent upon the cleaning procedure used for the glassware as well as upon solvent purity. I n our work with potassium in ethylamine, the central line was observed only in decomposing solutions. Under these conditions, the plateau in the plot of hyperfine splitting against temperature haa also been observed to disappear. Obviously, we need to try various methods of solvent purification to remove these discrepancies. (3) We also conclude that the high-temperature species is not
T. R. TUTTLE, JR. (Brandeis University, Waltham, Mass.). (1) I wish to report on some results on the optical spectra of potassium-ethylamine solutions obtained by Mr. Ian Hurley a t Brandeis. One of the difficulties which has been found in dealing with these solutions is that the experimental results are often nonreproducible. Different results (apparently under the same set of circumstances) have been obtained a t different laboratories, and even at the same laboratory by the same investigator. We have found that a t least part of the difficulty (of nonreproducible results) is that the equilibria between the species in solution are affected by ionic materials. I n particular, we have found that the optical spectrum of a freshly prepared solution of potassium in ethylamine which displays essentially a single band at about 850 mp with some absorbance in the infrared region (in agreement with the findings of Symons and Catterall) is converted completely to a spectrum containing a single band a t 650 mp through the addition of potassium iodide. (2) Where is the electron in species C? (3) Does the variation with temperature of the hyperfine coupling in potassiiim-ethylamine solutions a t low temperature, below the freezing point of ethylamine, make sense in terms of the equilibrium model? (4) I wish to emphasize that the explanations of the temperature variation of the hyperfine coupling in terms of thermally accessible vibrational states, on one hand, or species in equilibrium, on the other, are equivalent, even in t e r m of utility, unless some difference exists in the compositions of the species, for example.
J. L. DYE. (2) We do not wish to speculate on the detailed nature of species C except to note that it has a low splitting (less than lY0 of the free atom) and could be an ion pair between the cation and the solvated electron. (3) Since both B and C are monomeric, a dynamic equilibrium could be maintained below the solvent freezing point if long-range solvent interactions are unimportant. (4) The equilibrium model simply assumes that a small number of stable configurations rather than a continuous distribution of states can be used to describe the results quantitatively.
Volume 71, Number 1
January 1967
