J. Phys. Chem. 1993,97, 4284-4287
4284
Excess Electrons in the Lithium-Methylamine System Studied by Electron Spin Resonance at 200 MHz Hisato Matsui,? Eiji Yamada,* Shigezo Shimokawa,*and Yoshio Nakamura'J Department of Chemistry, Faculty of Science, and NMR Laboratory, Faculty of Engineering, Hokkaido University, Sapporo 060, Japan Received: July 14, 1992; In Final Form: November 3, 1992
The electron spin resonance of lithium-methylamine solutions has been measured at 200 MHz over a wide concentration range of the dissolved metal. The transverse relaxation times of the excess electrons deduced from the observed spectral widths show two different regions: the lower metal concentration region where the relaxation times increase with metal concentration and temperature and the higher metal concentration region where the trend is opposite. It is concluded that in the former region the hyperfine interaction of the excess electron spins with 14Nnuclei is dominant, while in the latter region the spin-orbit interaction to the metal ions is dominant. The crossover occurs at a metal concentration lower than the bulk metal-nonmetal transition located at ca. 15 mol% metal.
Introduction Solutions of alkali metals in liquid ammonia or methylamine show a metal-nonmetal (MNM) transition at a certain metal concentration. The behaviors of excess electrons from the localized to itinerant states in such solutions have been studied by using various experimental methods.' Among them the electron spin resonance (ESR) method is very useful, because it can provide direct informationon the state of the excess electrons in solutions.* In experiments by ESR, however, the skin effect is important in the penetration of the electromagneticwave into highly conducting metallic samples such as concentrated metalammonia solutions. A measure of this effect is given by'the relative magnitude of the sample thickness and the skin depth d, which is written as
where v is the frequency of the electromagnetic wave used and u and p are the electrical conductivity and the magnetic permeability of samples. The skin effect decreases with increasing the depth which can be attained by decreasing the frequency Y of measurements. Although this skin effect is taken account in theories for ESR spectra,'^^ it is still desirable to reduce it as low as possible. ESR measurements for lithium-methylamine solutions have so far been made at the X-band or at about 9300 M H Z ~and -~ partly at radio frequencie~.~,~O For alkali metal-ammonia solutions, several ESR measurements have been carried out at radio frequencies,but they are limited to the nonmetallic region or below 2 mol %metal (MPM).9-13 It is known that the MNM transition in alkali metal-ammonia solutions takes place around 4 MPM.'In the present study, we attempted to make continuous wave ESR measurements for lithium-methylamine solutions at a radio frequency (193.3 MHz) up to a metal concentration of about 15 MPM, where the MNM transitions occur.16J7 The results are compared with those obtained at the X-band.j
Experimental Section Sample solutions were prepared from lithium metal (99%, Wako Pure Chemical Co., Ltd.) and methylamine which had been purified beforehand by the reaction with lithium metal. Methylamine was prepared from its hydrochloride salt.18 Lithium +
f
Department of Chemistry, Faculty of Science. NMR Laboratory, Faculty of Engineering.
metal was cut and put into a sample tube of 4 mm i.d. with a stopcock in a glovebox filled with argon gas. Then purified methylamine was distilled under vacuum into the sample tube, which was then sealed off. The sample solutions were homogenized by shaking in an ethanol bath at about 210 K and stocked at liquid nitrogen temperature. ESR measurements were made with a home-made apparatus, whose block diagram is shown in Figure 1. The resonance frequency was 193.3 MHz and the modulation frequency was 4 kHz. The magnetic field was varied from 6.3 to 7.4 mT using twocurrent sources, a constant and a sweepingone. The resolution of the apparatus was 1.1 pT. DPPH (g = 2.0036) was used as a reference of the magnetic field. The frozen sample solutions were melted and homogenized thoroughly at about 210 K just before each measuring run. The temperature of the samples during the measurements was kept constant using a flow of cold nitrogen gas controlled within f l K. The composition of each sample solution was determined as follows. The amount of methylamine transferredinto each sample tube was determined from the difference in weight of the stock vessel. After each experimental run, methylamine was evaporated from the sample solution and the residual metal was dissolved slowly in water. The resulting alkaline solution was titrated with a standard hydrochloric acid solution to determine the content of lithium metal.
Results ESR signals of the first derivativeform were recorded for each run. The S/N ratio in the present experiment was from 200 to 2.5. Signals were accumulated in the latter case up to 25 times. The observed g-factors were 2.005 f 0.005 and their variation with composition and temperature was not determined because of relatively large experimental errors. The reported value of g measured at the X-bands for lithium-methylamine solutions is 2.00172 f 0.00002 for all concentrations at 210 K. Almost all the observed signals were Lorentzianand integrationof the signals was made numerically. The integral intensity of absorption spectra was normalized by the amount of the dissolved lithium metal. The relative integral intensities thus obtained,S,are shown in Figure 2 as a functionof temperature. The typical uncertainty in S is about &lo%. Values of S increase with increasing temperature at low metal concentrations and decrease with increasing metal concentration. The temperature variation of the half width at the half maximum, AB, of the absorption curve is given in Figure 3. For
0022-3654193/2097-4284~04.00f0 0 1993 American Chemical Societv
The Journal of Physical Chemistry, Vol. 97, No. 17, 1993 4285
Excess Electrons in the Lithium-Methylamine System Synthesizer 193.3MHz
15
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Figure 1. Block diagram of the radio frequency ESR apparatus used in the present study. I
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Temp. ( K ) Figure 2. Temperature dependence of the relative integral intensity S per unit amount of the dissolved lithium metal. I
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Figure 4. Skin depth d for some representative solutions in the present study.
solutions,while the trend is oppositeat lower metal concentrations. At the intermediate concentration, i.e. 7.7 and 9.0 MPM (not included in Figure 3), the curve for ABshows a shallow minimum.
Discussion
12.2 15.8
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Temp. (K)
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In Figure 4 we plot calculated values of the skin depth d from eq 1 for some of the solutions studied. Here, the electrical conductivity values were taken from ref 16 and the magnetic permeability of vacuum p~ was used for p. It should be noted that the skin effect may be still important at the higher metal concentration range in the present system. Since the integrated intensity of the ESR spectra, S, is strongly affected by the skin effect, our discussion on the composition and temperature dependence of S is limited to the lower metal concentration range. From the data for the lowest metal concentration in the present study, Le., 1.6 MPM (Figure 2), it is seen that the values of S increase with increasing temperature, while they show a trend to decrease with increasing metal concentration. These results reflect the dissociationof spin-paired species with increasing temperature and also that the spin-pairing reaction proceeds with increasing metal concentration. As the skin effect would affect the observed integral intensities with increasing metal content,our discussion on S is left only qualitative. For quantitative analyses of the data of S, further investigation of the skin effect will be needed for the present experimental conditions. As to the apparent transverse relaxation time, Tz*,however, the skin effect is much less serious than in the case of the signal intensity up to high metallic concentrations. The arrows in Figure 5 show the concentration where the skin depth is comparable to the sample diameter at each temperature. When absorption spectra are Lorentzian, T2* is given by the relation
1/T2* = g B , M / h
200
250
Temp. (K) Figure 3. Temperature dependence of the half width of the half maximum, AL3, of the absorption curve.
the 15.8 MPM solution, whose spectrum is asymmetric above 210 K, the value of AB was determined from the half width of the maximum slope of the absorption spectrum by multiplying it by d3.I9The typical uncertainty in AB was &5%. Values of AB increase with increasing temperature at concentrated metal
(2)
where g is the g-factor of the excess electron, Be is the Bohr magneton, AB is the half width of the half maximum of the absorption curve, and h is the Planck constant divided by 2 ~ . The observed relaxation rate, 1/T2*, includes the additional contribution from the surface r e l a ~ a t i o n ,(1~/. ~T2)srand that from the inhomogeneity of the field, ( l / T ~ ) i and , thus we have
It is argued that the transverse relaxation time, T2, in metal ammonia or amine solutions is attributed mainly to the two contributions, the hyperfine interaction with the 14Nnuclei and the spin-orbit interaction to themetal i0n.1~Then, the relaxation
Matsui et al.
4286 The Journal of Physical Chemistry, Vol. 97, No. 17, 199'3 0.6 I 0.5
0.4
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7
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10 15 C (MPM) Figure 5. Composition dependence of the apparent transverse relaxation time T2*. The solid curves are from the present experiments and the broken curve from the X-band measurement (ref 5).
rate can be written by the sum of these two contributions
(4) where the first term denotes the hyperfine interaction and the second the spin-orbit interaction. In the concentrated solution range where the skin effect is appreciable, we must consider the contribution of (1/T& The contribution from the hyperfine interaction in eq 4 for the region of extreme motional narrowing usually valid for liquids can be written as13J4+20 ( l / T2)h = A7h
-i -5
I
5
0
(5)
in which A is given by5
where g, and g, are the g-factors for electron and nuclei and 8, and 8, are the Bohr and nuclear magneton, respectively. Inis the nuclear spin, N is the number of interacting nuclei with the electron, I@(0)ln* is the electron spin density at the nuclear site, and Th is the correlation time for the hyperfine interaction. On the other hand, the contribution from the spin-orbit interaction is given by14120.21 (l/T2)so = B / T s o
(7) where B is a coefficient representing the strength of the spinorbit interaction and 7s0is the correlation time for the spin-orbit interaction. Figure 5 shows the apparent transverse relaxation time T2* as a function of metal concentration. The results obtained by the X-band ESR5 are partly included. The values of the skin depth d at the respective maxima of T2*-metal concentration curves are about 9 mm at 190 K (9.0 MPM), 7 mm at 220 K (7.7 MPM), and 10mm at 250 K (4.5 MPM). Assuming that the contributions from the surface relaxation and the field inhomogeneity, (1 / T z )and ~ (1 / T&, are negligible,the observed relaxation rate is written approximately as (8) 1/T2* = (1/T2)h + (1/T2)s0 which may be applicable to the region of low metal concentrations up to the maxima in T2* shown in Figure 5. We assume further that the composition dependence of the coefficients A and B is small in comparison with that of the correlation times, 7s0and Th, as is found in the K-NH3 system.14 Then we have
(9) 1/T2*(T90 = A ( T ) T h ( T , C ? + B ( T ) / T s o ( T , C ) where Tis the temperature and Cis the concentration expressed in MPM. The correlation times T,, and T h are decreasing with
15
0
10
5
C
(MPM)
Figure 6. Relaxation rates due to the hyperfine interaction, extracted by use of eq 11.
increasing metal concentration and increasingtemperature.14Thus the first term due to the hyperfine interaction in eq 9 decreases with increasing metal concentration, and the trend is opposite for the second term due to the spin-orbit interaction. From the experimental results given in Figure 5 it is suggested that the first term is dominant in the low metal concentration region, while the second term is dominant in the higher metal concentrations. Both contributions are comparable at the composition where the maximum is found in the T2*-composition curves in Figure 5. This maximum is located well below the concentration where the MNM transition occurs in the present system, Le., around 15 MPM.I6J7 We suppose that the change of the electronic states seen by ESR in the solutions occurs before the bulk metalnonmetal transition takes place, probably due to local concentration fluctuation. As shown in Figure 5, the maximum in Tz* in the X-band ESRSis located at a little higher metal concentration than that in the present experiments. It is also reported5 that the location of maxima observed by the X-band ESR is not affected much by change of temperature. The origin of these different behaviors is not yet clear, and further experimentson the frequency dependence of T2* are planned. Now we try to analyze the present results for T2* more quantitatively, using the following procedure. For high metal concentrations and high temperatures, i.e., C > 12 MPM and T > 210 K, experimental results of T2*are well fitted to a purely empirical equation
where a,8, y, and 6 are constants independent of concentration and temperature, which are given by a = 84.0, 8 = 1750, y = 19.2, and 6 = 0.0437. Here we suppose that the contributions other than the hyperfine interaction, i.e., those given by the second and third terms in eq 3 and by the second term in eq 4, can be expressed by eq 10 and that this relation can be extrapolated to low metal concentrations below 12 MPM and to temperatures below 210 K. Then we can extract the hyperfine contribution from the relation 1/T2* -(1/Tz*),xt = (1/T2)h A7h (1 1) The results are shown in Figure 6 for three temperatures. The points for 15.8 MPM deviate from the common curve. This is probably related to the bulk metal-nonmetal transition observed in the present system.'6J7 Using eq 11, we can calculate values of Th. From a I4N NMR study by Holton et a1.22we have Ala(0)1,2 = 2.35 X 1024 ~ m at- 218 ~ K for the solution of 17 MPM. Then, taking N = 4 for the coordination number of an excess electron in solutionsz2and appropriate values for other constants
Excess Electrons in the Lithium-Methylamine System
TABLE I: Correlation Time for Hypefiine Interaction at 220 K 1.6 2.9 4.5 5.7
4.0 2.8 2.1 1.8
2.4 X lo-" 1.7 X 1.3 X lo-" 1.1 x lo-"
ineq6,wehaveA = 1.66 X 1017s-2. Ifthecompositiondependence of the coefficient A in eq 11 is negligible, we can evaluate values of 7 h for relatively low metal concentration where the contribution of the hyperfine interaction has been determined from the present experiment. The calculated values of 7 h for 220 K are given in Table I. As expected, the values of 7 h are decreasing with increasingmetal concentration, reflecting the increasing mobility of localized electrons in these solutions. These values are about 10times larger than that reported for lithium-ammonia solutions14 in the dilute solution range, ~ 1 0 - I s, ~reflecting also lower electrical conductivity in lithium-methylamine solutions compared with that in ammonia solutions.
Conclusions From ESR measurements at 200 MHz, two different regions in the behavior of thespin relaxation have been found for lithiummethylamine solutions. The hyperfine interaction with the neighboring nuclear spins of nitrogen is predominant in the lower metal concentrations, while the spin-orbit interaction becomes dominant in the higher metal concentrations. The cross-over takes place prior to the bulk metal-nonmetal transition at 15 MPM. Since the skin effect is found still appreciable in highly conducting samples, further quantitative estimation of this effect will be needed,*3~~~ as well as measurements at much lower radio frequencies than the present one. Acknowledgment. We thank Mr. T. Haraguchi for the help in the early stage of the experiments and Dr.J. Kawamura for
The Journal of Physical Chemistry, Vol. 97, No. 17, 1993 4281 the aid in computer programming involved in the present apparatus. This work was partly supported by the Grant-in-Aid for Scientific Research Fund from the Ministry of Education, Science and Culture of Japan (B 01470003).
References and Notes (1) Thompson, J. C. Electrons in Liquid Ammonia: Clarendon: Oxford, 1976. (2) Edwards, P. P. J . Phys. Chem. 1980, 84, 1215. (3) Feher, G.; Kip, A. F. Phys. Rev. 1955, 98, 337. (4) Dyson, F. J. Phys. Rev. 1955, 98, 349. (5) Buntaine, J. R.; Sienko, M. J.; Edwards, P. P. J . Phys. Chem. 1980, 84, 1230. (6) Page, C. J.; Millhauser, G.L.; Edwards, P. P.; Freed, J. H.; Sienko, M. J. J. Phys. Chem. 1984, 88, 3785. (7) Edwards, P. P.; Buntaine, J. R.; Sienko, M. J. Phys. Rev. B 1979, 19, 5835. (8) Edwards, P. P.; Lusis, A. R.; Sienko, M. J. J . Chem. Phys. 1980,72, 3103. (9) Levinthal, E. C.; Rogers, E. H.; Ogg, R.A., Jr. Phys. Rev. 1951,83, 182. (10) Levy, R. A. Phys. Rev. 1956, 102, 31. (1 1) Hutchison, C. A,, Jr. J. Phys. Chem. 1953, 57, 546. (12) Hutchison, C. A., Jr.; Pastor, R. C. J . Chem. Phys. 1953,21,1959. (13) Hutchison, C. A., Jr.; O'Reilly, D. E. J . Chem. Phys. 1961,34, 1279. (14) O'Reilly, D. E. J . Chem. Phys. 1969, 50,4743. (15) Blume, R. J. Phys. Reu. 1958, 109, 1867. (16) Toma, T.; Nakamura, Y.; Shimoji, M. Philos. Mag.1976,33, 181. (17) Nakamura, Y.; Niibe, M.; Shimoji, M. J . Phys. Chem. 1984, 88, 3755. (18) Yamamoto, M.; Nakamura, Y.;Shimoji, M. Trans. Faraday SOC. 1971,67, 2292. (19) Poole, C. P., Jr. Electron Spin Resonance; Wiley-Interscience: New York, 1983. (20) OReilly, D. E. J . Chem. Phys. 1961, 35, 1856. (21) Lloyd, J. P.; Pake, G. E. Phys. Rev. 1954, 94, 579. (22) Holton, D. M.; Edwards, P. P.; McFarlane, W.; Wood, B. J . Am. Chem. SOC.1983, 105, 2104. (23) Leclercq, F.: Damay, P. Philos. Mug. B 1988, 57, 61. (24) Damay, P.; Leclercq, F.; Lelieur, J. P. Philos. Mag.B 1988, 57, 75.
