1230
J. Phys. Chem. 1980, 8 4 , 1230-1232
vosjelov, and Y. I. Talahov, Phys. Leff. A , 63, 339 (1977). (86) D. Pines, J. Bardeen, and C. P.Slichter, Phys. Rev., 106, 489 (1957). (87) H. Fritsche in ref 4, p 193. (88) G. E. Jellison, Jr., and S.G. Bishop, Phys. Rev. Lett., 40, 1204 (1978).
(89) P.P. Edwards and R. Catterall, Phil. Mag. 8 , 39, 81, 371 (1979). (90) P. Damay and M. J. Sienko, Phys. Rev. B , 13, 803 (1976). (91) N. S. VanderVen, Phys. Rev., 166, 787 (1968). (92) R. Catterall and P. P. Edwards, Mol. Phys., 32, 555 (1976).
Temperature Dependence of the Electron Spin-Lattice Relaxation in Lithium-Methylamine Solutions James R. Buntaine, M. J. Sienko," Deparfment of Chemistry, Cornell University, Ithaca, New York 14853
and Peter P. Edwards Inorganic Chemistry Laboratory, Oxford UniversW, Oxford OX1 30R, England (Received July 17, 1979) Publication costs assisted by the Nafbnal Science Foundation
The temperature dependence of the electron spin-lattice relaxation time, T1,, is reported for the lithiummethylamine system. Samples of 6.5-21.1 mol % metal (mpm) have relaxation times in the range 0.6 X IO-'-8 X lo-' s. The electronic g factor is 2.00172 f 0.00002 for all concentrations. It is demonstrated for this nonfluctuating system that dTl,/dT is a sensitive means for determining the concentration at which the metal-nonmetal transition occurs. The present study indicates this transition takes place between 13.4 and 15.6 mpm in the temperature range 160-260 K.
Introduction Experimental Section A great deal of interest has been generated by the The preparation, homogenization, and line shape properties of alkali metals dissolved in liquid anhydrous analysis for T1,values of the Li-MeA solutions are deammonia since their discovery more than 100 years ag0.l scribed el~ewhere.~ All spectra were recorded on a Varian In particular, dilute solutions behave much like electrolytic E-12 ESR spectrometer at X-band frequencies and either solutions whereas concentrated solutions are metallic in 100- or 10-kHz modulation frequency; 10 kHz was used for nature. This class of materials thus provides great exline widths of less than 300 mG. Precision g value meaperimental and theoretical interest with particular regard surements were made with a Harvey-Wells Corp. NMR to the metal-nonmetal transition (MNMT).2 precision gaussmeter indicator model G-502 with a Systron The description of the MNMT in a liquid must take into Donner frequency counter model 1255A. Temperature account several factors that affect the electronic behavior. control was facilitated with an Oxford Instruments liquid helium flow system. The temperature stability was f0.1 These include the following: (i) the disorder of the system by virtue of its being liquid, (ii) the role of large-scale K over the entire range of 160-260 K. The Varian E-12 spectrometer employs an AFC device concentration fluctuations, if present, and (iii) thermal motion within the liquid. In this article we address ourwhich stabilizes the klystron frequency to at least 1 ppm for a cavity Q of 6000 at low power levels. Any reduction selves to these factors with particular attention to the in the cavity Q reduces the stability of the frequency and thermal characteristics of spin scattering. therefore the precision of the measured resonance line There is evidence in the lithium-methylamine (Li-MeA) system that concentration fluctuations are a b ~ e n t , ~ ! ~width, Methylamine has a room temperature dielectric constant of ~ 9 . which 4 ~ reduces the Q over the entire whereas in the ammonia solutions (except Cs-NH3) they magnetic field scan range. play a predominant role. Li-MeA solutions therqfore There is another contribution to the cavity Q which is provide an opportunity to investigate the MNMT in a fluid sometimes neglected but must be considered under the without the complications associated with large-scale inpresent circumstances. During the magnetic-resonance homogeneities. phenomenon absorption of microwave power OCCUFS. This In the present study we emphasize the differences in the incorporates into the loaded cavity Q a factor which is electron spin relaxation mechanisms occurring in the inmagnetic field dependent and occurs only at resonance. sulating and metallic regimes. Relaxation in the insulating In the present study the resonance occurs over such a sharp regime proceeds via modulation of the 14N hyperfine interval (-0.1-1 G) and is so strong (due to the large contact i n t e r a c t i ~ n ,whereas ~,~ in the metallic regime renumber of spins involved, -10'~-1020) that the cavity Q laxation is due to modulation of the spin-orbit coupling is significantly reduced during resonance. This causes of the electron to the Li+ The response of the spin-lattice relaxation time, T,,, to temperature variation drastic reduction in the frequency stability. Line widths of 0.1 and 1 G represent 30 and 300 ppm, is demonstrated to be a sensitive means for determining respectively, in a field of 3300 G. To maintain 10% prethe dominant relaxation mechanism. This in turn indicision of the line widths at frequencies of 1O'O Hz, it becates directly the concentration at which the MNMT occomes necessary t~ stabilize the frequency to at least 3 ppm curs. 0022-3654/80/2084- 1230$0 1.OO/O
0 1980 American Chemical Society
The Journal of Physical Chemistry, Vol. 84, No. IO, 1980
Spin-Lattice Rellaxation in Lithium-Methylamine 6.5 M P M
1231
21.1 MPM
r-
A
Li-CH,NH,
i
U
I
(sed
Figure 1. Typical ESR firstderivative spectra for a dilute and concentrated U-Met\ solution at 160 and 260 K. The values in parentheses are the peak-to-peak line widths. Note the change in line width with temperature as well as the asymmetric line shape for the concentrated sample.
i O
" n
t 3 &PM U
.I- f __
0 0
I
0
0
Li-CH,NH,
4
.5MPM
160
210
260
T(K)
as a function of temperature for dilute solutions. d Tl,ld T > 0 is indicative of the localized electronic regime. Flgure 2. The relaxation time, T,
t T(K)
Flgure 3. The relaxation time, TI,, as a function of temperature for
concentrated solutions. d Tl,ld T electrons.
0 is characteristic of delocalized
and negative in the metallic samples (Figure 3). Electronic g factors were measured with a precision an order of magnitude better than was previously reported? It was found that g, = 2.00172 f 0.00002 for all concentrations at 210 K. This implies the electron's spin-orbit coupling is nearly constant throughout the range of compositions studied. Dilute Solutions. In the insulating regime, relaxa,tion proceeds via modulation of the contact hyperfine interaction of the electron with the 14Nnucleus of the methylamine. In the present study we are experimenting in the temperature range 160-260 K. At these temperatures methylamine is a liquid and, as such, the motion of the liquid is the dominant factor in the ESR line widths. 'This is the region of extreme motional narrowing. The spin-lattice relaxation rate for an electron through modulation of the hyperfine contact mechanism is given by
(&lo kHz) and 30 ppm (A100 kHz), respectively. All spectra not falling within these bounds were discarded. In order t o keep the klystron frequency within the bounds mentioned, it was necessary to reduce the sample volume placed into the cavity. Those solutions in the metallic regime did not present much difficulty as the skin depth ( cm at 1O1OHz) allowed only a limited number of spins to interact with the microwave magnetic field. The metallic solutions were prepared in 2 mm i.d. Spectrosil tubing. The solutions in the insulating regime were prepared for 1-nim tubing. Still, all samples were gradually pulled out of ithe cavity until the desired frequency stability was attained.
where g, and gn are electronic and nuclear g factors, respectively, p, and @, are the Bohr and nuclear magneton, respectively, I, is the spin of the nucleus, N is the number of identical nuclei with which the electron has contact, l$(o)12 is the electron spin density at the nucleus, and 7, is the correlation time for a given electron-nucleus interaction. The contact interaction dominant in dilute Li-ILTeA solutions is between the electron and the I4N nuc1eus.l' The following values are then appropriate: g, = 2.00172, gn = 0.4036, and I,, = 1. Equation 1 reduces to
Results and Discussion Figure 1 shows typical ESR spectra for two concentrations at two different temperatures. These spectra highlight the change in line width with temperature for the dilute and concentrated samples, as well as the asymmetric line shape of the concentrated samples. Figures 2 and 3 show the relaxation time, T1,, as a function of temperature for seven Li-MeA solutions. It has been previously reported that a MNMT occurs in this system9J0anid that ESR is a particularly sensitive technique for determining the properties of the electron in both the insulating and conducting regimesS4In particular, the temperature (dependenceof the relaxation time, dTle/dT, is seen to be positive in the insulating samples (Figure 2)
At present 14NKnight-shift data are unavailable for the Li-MeA system; thus (NI$(0)I~4~2) is unknown. T1;-I is a sensitive function of (Al$(o)l~~Nz) (as well as any temperatwe dependence of ( A l $ ( 0 ) l ~ 4 N 2 ) as is the case in the Na-NH, and K-NH3 systems12) and thus this value is crucial for a quantitative fit of the experimental values to eq 2. T~ is usually taken to be the Debye rotational relaxation time which is proportional to q/pT. Assuming constant {W$(,$I*N~), and the values for p and q reported by Shimoji et al., 3~14our data show a weaker temperature dependence than is given by T1, cc pT/q. The origin of the weak temperature dependence lies with the following: (i) The cavity model supposes the electron
N
1232
J. Phys. Chem. 1980, 84. 1232-1240
is localized with MeA molecules oriented about it. The electron is then expected to have a stabilizing effect on its solvation sheath. This would reduce the temperature dependence of TI,. (ii) In the discussion of the dilute solutions, no mention has been made about the contribution of the spin-orbit coupling mechanism. This mechanism is relatively inefficient until higher concentrations (as will be discussed below) and high temperatures. It is noteworthy that T,,vs. T (Figure 2) does start to level off at the highest temperatures. Concentrated Solutions. Those solutions in the metallic regime show a negative T1, dependence on temperature (Figure 3). This is due to the increased efficiency of the spin-orbit coupling relaxation mechanism over that of the hyperfine contact mechanism. As the electron centers approach each other, through an increase in lithium concentration, the binding energy of an electron to a particular site is reduced. The adiabatic response of the electron to molecular motion in the liquid (as is the case in dilute solutions) is thus reduced; the spin-orbit coupling of the electron to the Li+ core is increasingly modulated. This mechanism then becomes more efficient. The temperature dependence of T,, arises from the fact that the rate of modulation is proportional to the temperature of the system. Thus it is when the electron wave function begins to be extended that (i) the conductivity increases rapidly and (ii) the spin-orbit coupling mechanism becomes dominant. It is this point which allows the identification of the MNMT with the change of the sign of dT,,/dT. It should be realized that the conductivity of Li-MeA
-
at its solubility limit (-22 mpm) is 400 0-’ cm-l ( 1/40 that of saturated Li-NH,). This is very close to Mott’s minimum conductivity value of 200 Q-’ cm-’. Therefore this system is in the strong-scattering regime of metallic behavior. A conventional analysis of the relaxation times in conjunction with conductivity data is not possible (Q’Reilly6treated the K-NHB solutions in this manner). However, the fact that dT,,/dT changes sign at the concentration where the MNMT has been placed by transport measurements highlights the sensitivity of the ESR experiment.
Acknowledgment. This research was sponsored by the NSF under Grant No. CHE 78-12238. References and Notes W. Weyl, Poggendorffs Annln., 121, 601 (1864). For an extensive review of the properties of metals dissolved in ammonla and other solvents, see J. C. Thompson “Electrons in LiquM Ammonia”, Ciarendon, Oxford, 1976. Y. Nakamura, Y. Horie, and M. Shimoji, J. Chem. SOC., Faraday Trans. 1 , 70, 1376 (1974). P. P. Edwards, J. R. Buntaine, and M. J. Sienko, Phys. Rev. 6,W, 5835 (1979). V. L. Pollak, J . Chem. Phys., 34, 864 (1961). D. E. O’Reiily, J . Chem. Phys., 35, 1856 (1961). R. J. Elliot, Phys. Rev., 96, 266 (1954). Reference 1, p 269. T. Toma, Y. Nakamura, and M. Shimoji, Phil. Mag., 33, 181 (1976). Y. Nakamwa, T. Toma, and M. Shimoji, phys. Left., 60A, 373 (1977). P. P. Edwards, A. Lusis, and M. J. Sienko, J. Chem. Phys., in press. D. E. O’Reilly, J. Chem. Phys., 41, 3729 (1964). M. Yamamoto, Y. Nakamura, and M. Shimoji, Trans. Faraday SOC., 67, 2292 (1971). M. Yamamoto, Y. Nakamura, and M. Shimoji, J. Chem. Soc., Faraday Trans 7, 68, 135 (1972).
Current Problems in the Localization and Solvation of Excess Electrons in Glasses Larry Kevan Department of Chemistw Wayne State Universiw, Detroit, Michigan 48202 (Received July 17, 1979)
Recent advances and limitations on our knowledge of electron localization and solvation are highlighted. The kinetics and mechanism of electron localization remain unknown. The physical interpretation of localization time is clarified. The minimum potential well depth for electron localization appears to be -0.4 eV. A possible explanation of why electron solvation appears to ignore hydrogen bonding in liquids is advanced in terms of preferential selection of lower energy molecular reorientation pathways by analogy to recent results in glasses. New experiments on the molecular details of electron solvation in mixed MTHF-methanol matrices are reported which argue against a tunneling mechanism from an MTHF environment to a methanol cluster and which support solvation shell conversion by a stepwise mechanism. Results on the electronic structure of presolvated electrons in various polar matrices imply that bound-continuum transitions generally predominate. The implications of this for the trapping potential are discussed. A rationale is given for the different energy level structure that obtains when two OH dipoles occur in one solvent molecule. Current information on the geometricalstructure of solvated electrons is surveyed and new models of the solvated electron geometry in methanol, methyltetrahydrofuran, and 3-methylpentane glasses are presented.
Introduction In recent years an overall, self-consistent picture of the gross details of electron localization and solvation in condensed media has been developed.’ However, many details, some of which are fundamental, remain to be elucidated. Here we highlight some of the areas of our lack of understanding together with several recent results which help to clarify the nature of electron solvation in glassy 0022-3654/80/2084-1232$01 .OO/O
matrices. The focus will be on experimental problems and results since related theoretical problems are discussed ehwhere in this volume and in a current review.’ We may define electron localization in condensed media as the creation of an electron state characterized by an exponentially decreasing wave function from the electron 0 1980 American Chemical Society
