JAMES L. DYEAND LARRYR. DALTON
184
Nuclear Spin Dependent Relaxation Processes in Metal-Amine Solutions
by James L. Dye and Larry R. Dalton Department of Chemistry, Michigan State University, East Lansing, Michigan
(Received September 97, 1966)
An analysis of certain relaxation processes operative in metal-amine solutions has been attempted. Since many factors can affect line widths, particular attention has been paid to those solutions showing paramagnetic relaxation dependent upon the nuclear spin quantum number, mI. It is clear that the results cannot be explained on the basis of a single asymmetric species. An equilibrium between two species accounts for many aspects of the esr behavior but fails to describe quantitatively the temperature dependence of the line widths. A temperature-dependent distribution among states differing in solvent configuration might give rise to the observed behavior. The difficulty in characterizing these distributions has prevented a quantitative test of this model.
Introduction One of the most puzzling features of the esr spectra of metal-amine solutions is the dependence of the line width upon hyperfine component observed for solutions of rubidium and cesium in methylamine' and in ethylamine.2-4 One explanation for such behavior is in terms of a strong anisotropy of the electric field at the splitting nucleus, modulated by rotation of the paramagnetic species. This "McConnell mechanism"6 requires the line widths to be dependent upon both viscosity and frequency and has successfully explained the esr spectra of several first- and second-row transition I n all of these cases, a metal ions and marked asymmetry of the field can logically arise from the geometry of the ion in the presence of its ligands. Several refinements of the original treatment of R4cConnell have been Recently, Wilson and Kivelson" have modified the treatment for the case of large hyperfine interactions by including second-order effects and have given expressions for the dependence of line width upon mIthrough third order. It is difficult to rationalize interactions between rubidium or cesium ions and amine solvent molecules which are strong enough to result in marked asymmetry of the electric field. However, the introduction of such a field anisotropy is required to explain the experimental line widths using the McConnell mechanism. An alternate mechanism which could also result in a dependence of line width upon m x involves rapid interconversion of two monomeric species, A and The Journal of Physical Chemistry
B, having different hyperfine contact densitie~.'~-'~ For exchange slower than the exchange-narrowed limit, this leads to an expression for line widthsI3
in which U A and U B are the time-independent hyperfine splitting frequencies (in radians per second) of the two species undergoing exchange, P A and p~ are the respective fractions of these species, T ~ and A T ~ are B the relaxation times of A and B separately, and T A and T B (1) K. D. Vos and J. L. Dye, J . Chem. Phys., 38, 2033 (1963). (2) T. R. Tuttle, Jr., K. Bar-Eli, Abstracts, 146th National Meeting of the American Chemical Society, Denver, Colo., Jan 1964, p 7D. (3) J. L. Dye, L. R. Dalton, E. & Hansen, I. Abstracts, 149th Na-
tional Meeting of the American Chemical Society, Detroit, Mich., April 1965, p 45s. (4) K. Bar-Eli and T. R. Tuttle, Jr., J. Chem. Phys., 44, 114 (1966). (5) H. M. McConnell, ibid., 25, 709 (1956). (6) R. N. Rogers and G. E. Pake, ibid., 33, 1107 (1960). (7) A. J. Marriage, Australian J . Chem., 18, 463 (1965). (8) L. R. Dalton, L. A. Nehmer, J. L. Dye, and C. H. Brubaker, Jr., to be published. (9) D. Kivelson, J . Chem. Phys., 27, 1087 (1957). (10) D. Kivelson, ibid., 33, 1094 (1960). (11) R. Wilson and D. Kivelson, ibid., 44, 154, 4440, 4445 (1966). (12) J. H. Freed and G. K. Fraenkel, ibid., 39, 326 (1963). (13) N. Hirota and R. Kreilick, J . Am. Chem. SOC.,88, 614 (1966). (14) L. R. Dalton, J. D. Rynbrandt, E. M.Hansen, and J. L. Dye, J . Chem. Phys., 44, 3969 (1966).
NUCLEAR SPIN DEPENDEKT RELAXATION PROCESSES IN METAL-AMINE SOLUTIONS
are the mean lifetimes of the two species. Although eq 1 shows dependence only upon mz2,the high-field approximation was used, and it was assumed that A and B have the same g values. The formal similarity between this model and the McConnell mechanism for an axially symmetric system should be noted. Both treatments involve the timedependent modulation of two magnetically nonequivalent states. Therefore, distinction between these models requires correlation with viscosity and examination of the pattern in frozen solutions. Another possible source of the dependence of line width upon mI requires a species whose hyperfine splitting is strongly dependent upon the solvent environment around the splitting nucleus so that a distribution of hyperfine contact densities exists. If the fluctuations of this environment are not too rapid, esr absorptions will result whose width depends upon the distribution of contact densities, the hyperfine splitting, and the value of m,. Once again, approximate treatments yield dependence only upon m12.12 Previous measurements1p2 demonstrated the dependence of line width on hyperfine component. However, the signals were either too weak or exhibited too much overlap to permit analysis of the results in t e r d of a mechanism of line broadening. This paper reports studies on the line widths of a number of metalamine solutions, both liquid and frozen, and a discussion of the results in terms of the mechanisms considered above. I n a separate paper15 we consider the variation of hyperfine splittings, g values, and spin concentrations with temperature and composition in the light of recent models for these solutions.
Experimental Section The instrumental arrangements used, as well as the method of sample preparation, have been described elsehere.^^,^^ Special care was taken to assure that spurious contributions to line widths resulting from instrumental factors were absent. Since the results are strongly dependent upon the extent of decomposition of the solutions, l 4 , I 5 results reported here were obtained only with fresh, stable solutions. The presence of decomposition could be detected by the building-in of an extra narrow absorption which we do not see in fresh saturated solutions. Attempts were also made to study the spectra at higher frequencies (17.5, 24.3, and 35.5 GHz). Because of dielectric losses and low concentrations of the paramagnetic species even in saturated solutions, we were unable to obtain strong enough signals to permit comparison with X-band results. The viscosities of ethylamine and methylamine were
185
measured as functions of temperature using a modified Ostwald viscometer. Attachment to a vacuum line permitted degassing and solvent transfer by distillation. A mercury-filled leveling bulb was used to manipulate the liquid in the viscometer by changing the pressure of the nitrogen covering gas. The viscometer was calibrated over the temperature range of interest using redistilled spectroscopic grade acetone. l6 The results are given in Table I. Table I : Viscosities of Methylamine and Ethylamine -
7 , CP
Temp, OK
296.4 296.4 289.2 283.2 273.2 263.2 263.2 258.8 253.2 243.2 239.7 238.3 233,2 223.2 223.2 217.5 213.5 203.5 193.2
Methylamine
0.236 0.285 0.291 0.300 0.331 0.372 0.400 0.422 0.480
Ethylamine
0,250 0.259 0.276 0.299 0.328 0.343 0.370 0.415 0.467 0.437 0.588 0.780 0.771 0.800
0.552 0.665 0.829
Extensive use was made of a Control Data 3600 computer to perform the calculations outlined in this paper.
Results The line widths of solutions of potassium in ethylamine and propylamine and of rubidium and cesium in methylamine, ethylamine, and propylamine exhibit a dependence upon the nuclear spin quantum number mz. This may be seen qualitatively from a consideration of Figure 1. This dependence upon mz is sensitive to temperature as can be seen from Figure 2 for a solution of cesium in ethylamine. Similar behavior is observed for rubidium in ethylamine and for rubidium and cesium in other amine solvents. (15) L. R. Dalton, V. A. Nicely, J. D . Rynbrandt, and J. L. Dye, to be published. (16) :‘International Critical Tables,” Vol. 7, The Kynoch Press, Birmingham, England, 1930, p 214.
Volume 71, Number 1 January 1967
186
JAMESL. DYEAND LARRYR. DALTON
METHY LAMlNE
23OC, g = 2.00170
ETHYLAMINE
PROPYL AMINE
5OoC, g = 2.00149, a = 15.006.
23"C, g = 1.99986, a=25.606. 23"C, g = 199982,
Q
=64.066.
2 3 T , g = 2.00150, a = 14.00G.
23*C, g = 1.99979 , a = 83.916.
CS
23"C, g = 1.99481 , a=55.89G.
23°C , g = 1.99484, a = l216G.
Figure 1. The esr spectra of alkali metals in some amines.
Data given are for s°K, 86Rb, and lWs.
Before we consider the dependence of the line widths upon mI, let us review some other aspects of the electron spin resonance spectra of these solutions. As can be seen from Figures 3 and 4, the g value and hyperfine coupling constants display a marked dependence upon temperature. Field corrections through third order have been made t o obtain these values. Although such a strong dependence of the magnetic parameters upon temperature is virtually unknown in other paramagnetic systems, it is a well-defined characteristic of solutions of rubidium and cesium in the various amine~.l*3.1~ Solutions of potassium in ethylamine and in the higher molecular weight amines display an a value which increases with temperature in a rather unusual fashion14 while the g value for these solutions appears to be independent of temperature or a t most changes only slightly with increasing temperaturel4*l5in contrast to the behavior observed for rubidium and cesium solutions. The spectra characteristic of liquid solutions of rubidium and cesium in the amines continue to be observed some 20-50" below the freezing point of the solvent with only a gradual decrease in signal intensity. At still lower temperatures, the signal intensity drops markedly and a different pattern is observed. A representative trace is shown in Figure 2. Although the The Journal of Physical Chemistry
2 3 O C , g = 1.99479, a = 171.5G.
extremely low intensity prevents characterization of these spectra, the pattern appears to result from the superposition of two hyperfine spectra. The same spectra are obtained when the liquid solutions are quickly frozen with liquid nitrogen. Warming the quickly frozen solutions results in a transition to the liquidlike spectra at temperatures well below the melting point of the solvent. Thus the transition from one form to another occurs not a t the melting point but a t temperatures for which the bulk of the solution is frozen. Another interesting aspect of the electron spin resonance spectra of metal-amine solutions is the extra line which appears upon decomposition. If great care is exercised in solvent and solution preparation, only the absorption due to the monomeric species ill is obtained for solutions of potassium, rubidium, and cesium in low molecular weight amines. If these solutions are heated, allowed to stand for long periods of time, or subjected to any other conditions which favor decomposition, an extra line appears at g = 2.0019 0.0002. The position of this absorption is independent of the metal and solvent used. The constant g value and a comparison with the free-electron value (ge = 2.0023), suggest the assignment of the single absorption to the solvated electron. The in-
*
NUCLEAR SPIN DEPENDENT RELAXATION PROCESSES IN METAL-AMINE SOLUTIONS
187
C E S I U M I N ETHYLAMINE 24
20
-
>
1: m
z
16-
Y 0
+ 0 a
-
!-
z
0 0
12
I 0 i-
a LL
0
r
2
-soot
Y
8
0
K Y P
01
-
I
2
O
0
C
Y
b
-80
-40
0
40
t PC)
Figure 3. Variation of hyperfine splitting with temperature for a9K (A), *6Rb (O), and 1 W s (0) in ethylamine.
Figure 2. Temperature dependence of the cesium hyperfine pattern in ethylamine.
tensity of this extra absorption relative to the hyperfine pattern depends upon the method of solvent preparation, the metal used, and the amine employed. I n potassium solutions the extra absorption appears only after the solutions have remained for long periods at high temperatures. For rubidium solutions, this absorption is never predominant but appears upon heating or upon allowing the solutions to stand at room temperature for long periods of time. In the case of cesium solutions it is sometimes the predominant absorption or even the only absorption. Although the extra absorption is usually absent in freshly prepared, stable solutions, it appears under relatively mild conditions. For rubidium and cesium solutions this absorption increases with decreasing temperature while for potassium solutions its intensity is relatively independent of temperature. The appearance of this line also seems to be a function of the solvent used, increasing in the Z < CHaNHz. order: C H ~ C H ~ C H ~ N
