Free Solvated Electron in HMPA
Tiepel and Gubbins.9 The main difference is that the pressure term in their eq 11, which in Pierotti's and this paper yield the term LVa3c3/6 in the equation for VZ, yields a more complex term. The fit between calculated and experimental dVz/brn is much better but the fit for L z / m is much worse when Tiepel and Gubbins equations are used, so that we cannot decide between the two sets of equations. However, the main conclusion of this paper is that scaled-particle theory makes it possible to ascribe the variation of the solute partial molal properties to the anomalous behavior of a(3"ldP and @"/d?' for pure water rather than the solute structural effects. Supplementary Material Available. The derivation of eq 4 will appear following these pages in the microfilm edition of this volume of the journal. Photocopies of the supplementary material from this paper only or microfiche (105 X 148 mm, 20x reduction, negatives) containing all of the supplementary material for the papers in this issue may be obtained from the Journals Department, American Chemical Society, 1155 16th St., N.W., Washington, D. C., 20036. Remit check or money order for $3.00 for
2483
photocopy or $2.00 for microfiche, referring to code number JPC-73-2479.
References and Notes (1) J. E. Desnoyers, M. Arel, G. Perron, and C. Jolicoeur, J. Phys. Chem., 73,3346 (1969). (2) J. J. Kozak. W. S. Knight, and W. Kauzmann. J , Chem. Phys., 48, 675 (1968). (3) W. S.Knight, doctoral dissertation, Princeton University, 1962. (4) J . Kenttamaa, E. Tommila, and M. Martti, Ann. Acad. Sci. fennicae A I/93. 1 11959). M. M.'Marciacq-Rousselot and M. Lucas, J , Phys. Chem.. 77, 1056 (1973). R. A. Pierotti, J. Phys. Chem., 67 1840 (1963) R. A. Pierotti, J. Phys. Chem., 69, 281 (1965). J. L. Lebovitzand J . S. Rowlinson, J. Chem. Phys.. 41, 133 (1964). E. W. Tiepel and K. E. Gubbins, J. Phys. Chem., 76, 3044 (1972) See paragraph at end of paper regarding supplementary material. F. Franks, Ed., "Water, a comprehensive Treatise," Plenum Press, New York, N. Y., 1972, Vol. 1. Chapter IO. G . S. Kell and E. Whalley, Phii. Trans. Roy. Soc., Ser. A , 258, 565 (1965). F. H.Stillinger, J. Chem. Phys., 35, 1581 (1961). H . D. Nelson, Ph.D. Dissertation, Utrecht, 1967. M. LucasJ. Phys. Chem., 76,4030 (1972). F.Franks and H. T. Smith, Trans. Faraday Soc., 64, 2962 (1968). F. Franks, J. R . Ravenhill, and D. S. Reid, J. Sol. Chem., 1, 1 (1972) J . E. Desnoyers and P. R. Phiiip. Can. J. Chem.. 50, 1094 (1972)
The Free Solvated Electron in Hexamethylphosphoric Triamidel G. Dodin and J. E. Dubois" Laboratoire de Chirnie Organique Physique de I'Universitb Paris VI/, associe au C. N.R.S., Paris, France (Received April 16, 1973) Publication costs assisted by the Laboratoire de Chimie Organique Physique de i'Universite Paris V i /
The width of the esr narrow line from the solvated electron in hexamethylphosphoric triamide (HMPA)sodium solutions arises from exchange narrowing and the activation energy for the hyperfine coupling modulation as well as the volume of the solvated electron increase with increasing solvent viscosity. When the viscosity is extrapolated to zero, the line width has a nonzero value resulting presumably from electron-nuclear spin dipolar coupling. The resonance line in the ideal nonviscous state might he attributed to a species we shall refer to as a "free" solvated electron which would consist of an electron trapped in a cavity formed by a layer of solvent molecules. The contributions to the experimental line width variation from both viscosity effects and technological artifacts arising from cavity shifts and 100kHz modulation are easily differentiated provided certain experimental conditions are satisfied.
Introduction Esr spectroscopy has been widely used to study the paramagnetic species formed in the solutions of alkali metals in organic solvents.2 For solvents with low dielectric constants (ethers and amines), a hyperfine resonance signal arising from the interaction of the electron spin with the nuclear spin of the metal is observed: the spectrum is assigned to the monomer M.2-* In solvents with higher dielectric constants such as liquid ammonia and hexamethylphosphoric triamide (HMPA) the resonance spectrum consists of a single line and is attributed to the solvated electron. In metal-ammonia solutions, the width of the resonance line is due to exchange narr0wing;s.G the process of hyperfine coupling
modulation is, however, controversial. According to the Kaplan and Kittel theory,7 this modulation is due to the rotation of the solvent layer around the electron involving an interaction whose correlation time is the Deb ye dipolar relaxation time. On the other hand, Dewald and Lepoutre,8 and more recently Lambert.9 have suggested that the modulation of the hyperfine coupling could be achieved by the passage of the electron from one cavity to another uia a tunneling mechanism resulting in a correlation time for the interaction corresponding t o the lifetime of the electron in a given cavity. Whatever the modulation process, the exchange rate should follow the Arrhenius law; when log AN (where A H is the line width) is plotted against 1/T a straight line is indeed observed.9 The Journal of Physicai Chemistry, Vol. 77, No. 20, 1973
G . Dodin and J. E. Dubois
2484
The properties of alkali metal-HMPA solutions are quite similar to those of metal-ammonia solutions. However, esr studies appear somewhat ambiguous in the assignment of the observed single line spectrum. According to the various authors, the lines have widths as different as 351° and 200 mGll and are, nevertheless, attributed t o the same species, the solvated electron. One may wonder if ( a ) several kinds of solvated electrons are present in HMPA or ( b ) the observed resonance signal results from the contribution of two relaxation mechanisms, one specific to a unique solvated electron and the other arising from the interaction of the solvated species with the surrounding medium. Current theories of the structure of alkali metal-HMPA solutions make it possible to rule out the existence of several solvated electrons,l2 and we can therefore reasonably assume b as a working hypothesis. The present work has been developed along these lines.
Experimental Section
Recording of the Esr Spectra. The spectra were recorded with a Varian E-3 esr spectrometer. Temperatures were controlled by means of the Varian variable temperature accessory. Since calculation of relaxation times TI and TZ is derived directly from line width measurements, one has to be sure that the observed width is the actual one and does not arise from some instrumental artifact. As we have shown in a previous paper,l3 esr spectra should be recorded with samples of low filling factors. In the range of concentration of the Ka-HMPA solutions we used, proper esr spectra are observed with 0.8-mm sample tubes; when 2-mm sample tubes are used, the filling factor is too high and the cavity frequency shifts. The automatic frequency control (AFC) locks the frequency of the klystron on that of the cavity and consequently gives to the high-frequency magnetic field a frequency beyond the resonance frequency of the spin system leading to the narrowing of the observed resonance line. This phenomenon is accounted for by the theory proposed by Dumais and Merle d'AubignF4 in the case of AFC narrowing of resonance lines from F centers. If the AFC is disconnected in the experiment with the 2-mm sample tube, the recorded resonance line is identical with that recorded hith AFC and 0.8 mm tubes. Another technological perturbation of the observed line width may arise from the 100-kHz modulation detection which is not quite suitable for recording narrow resonance lines since the minimum detectable width is 6 = 2 w m ( y ) - l where y is the magnetogyric ratio of the electron, and wm = BIIv,; for v m = 100 kHz, 6 = 70 mG. Hyde and Brown15 have shown, however, that line widths less than 70 mG can be measured with a 100-kHz modulation spectrometer if the phase of the lock-in detector is set away from its proper value; in this case, the resonance line is thereby distorted, and information from the line shape can no longer be obtained. Measurement of HI. HI is measured from the saturation data of DPPH and BDPA resonance signals for which the relaxation times 2'1 and 2'2 are known:I6 2'1 = 8 X lo-* sec and T z = 3.86 x 10-8 sec for l,l-diphenyl-2-hydrazyl sec for sec and Tz = 6.75 X (DPPH); TI= 7 X a ,y-bisdiphenylene-8-phenylallyl(BDPA). The abscissa of the maximum of d(Hl x")/d(w - w g ) = f(&) are respec= 1.45 G (the corresponding microwave tively Hmax,DPPH ~ G (microwave power of 130 mW) and H m a x i B ~=p 1.15 The Journal o f Physical Chemistry, Voi. 77, No. 20. 7973
Figure 1. Apparatus for the preparation of Na-HMPA salutions: A, from the distillation unit: B, solution compartment: C , esr
sample tube; D , conductivity bridge.
1
1
power of 84 mW); consequently, H12 = 16P if H1 is expressed in gauss and P i n watts. Sample Preparation. Commercial HMPA (Prolabo) is distilled twice under reduced pressure; water concentration, as determined by the Karl Fischer method, is less than 300 mg/kg. The solvent is allowed t o react with a known quantity of sodium (see Figure I). The metal does not dissolve immediately. Electrical conductivity (measured with a Wayne-Kerr bridge) reaches a maximum some minutes after the beginning of dissolution. The value of the maximum (-3.7 X O/cm) is apparently not significantly affected by the variations of CNa/Csolvent ratio from 0.01 to 0.18 (where CNa and Csolventare the number of moles initially introduced in the apparatus), nor by temperature variation. A typical curve is presented on Figure 2.
2485
Free Solvated Electron in HMPA
The metal concentration in the solutions is estimated by the method described in ref 17. This method is, however, not accurate in evaluating the concentration of the dissolved metallic species since it is based on the titration of the ouerall basicit), of the solution while the only basicity to be considered is t h a t arising from the reaction
M
+
CH30H
-
+
MOCH,
%H,
The viscosity of the solutions was measured with a n Ostwald viscosimeter a t the standard temperature of 20".
Results Line width measurements were effected a t different sodium concentrations (with CNa/CHMp4 ratios between 0.01 and 0.18, and effective metal concentrations, as measured by the above-mentioned method, between 0.3 and 0.6 M ) . Under these conditions we observed no correlation between line width variations and the metal concentrations, while line widths appeared to increase with increasing viscosities of the medium (see Tables I and 11). The viscosity a t 20" of the various samples is likely to be dependent on the state of decomposition of the solutions, the freshly prepared solutions being the least viscous. The independence of line width variations with the initial metal concentration is linked to the fact t h a t the effectiue metal concentration is small, even for high CNa/CH.?.1pA ratios. Similarly, Pollak5 has shown, for Na-NH3 solutions. that relaxation times are independent of C N for ~ CNa/CNH3 ratios Up to lo-' Saturation Experiments Resonance line saturation was studied for samples characterized by different viscosities, between -10 and 30". When H1 increases, the phase of the lock-in detector, initially set to go", shifts; the amplitude of the absorption line derivative decreases rapidly because of both saturation and phase shift effects. For a given power level, depending on sample, temperature, and initial phase setting, the recorded adsorption line is distorted (Figure 3). T o measure the true values of the derivative width and amplitude, the phase of the detector has to be adjusted for each H I value by means of the phase shifter so that the maximum amplitude for the adsorption derivative is reached. No g shift is observed when HI increases. We must mention that the minimum klystron power output corresponds to H I = 56 mG which is already greatcannot er than H m a x (as defined previously). Since H,,, be determined, relaxation time measurements will be carried out by studying the line width variation as a function of H I . The plot of A H us HI deriving from the Bloch equations shows for low H I values t h a t the width of the line which begins to saturate is not significantly different from AH when HI approaches zero (while the amplitude of the derivative decreases sharply with (Hl)-2 from HI > Hrnax).
The development of the Bloch equations leads to the classical result18
[!mHL-O;Hpp]~
-
1
1
+
1 qH12y2T1Tz
where AHpp is the peak t o peak distance for the absorption derivative. Tz is given by the relation
T 2 = 1.313 x 10--/gAHP,
1/ I
2
3
\\\
Figure 3. Saturated esr lines f r o m Na-HMPA solutions (upper spectra) (o = go", T = 269"K, the distortion of the line is observable at a power level of 8 m W (spectrum 2 ) , (lower spectra) (o = go", T = 293"K, the distortion of the line is observable at a power level 2 of 6 3 m W (spectrum 3)
TABLE I: Experimental Values of the Relaxation Times T I and TP in Na-HMPA Solutions at 277'K
AH,,' Sample CNaBM
1
0.38
2 3 4
0.58 0.52 0.45
mGa
T1, sec
61 56 47 39
1.075 X 1 0 - 6 1.17 X 1.395 X 10-6 1.65 X
Tt,
sec
1.21 X 1.33 X 1.46X 1.60 X
a Modulation broadening is avoided by proper phase setting of the phase sensitive detector.
-
when H1 0 (see Table I). Because of the instrument limitations mentioned previously, great significance should not be placed on the absolute value of line widths. Line Width Variation with Temperature. The microwave power is taken at its lowest level which corresponds to H I = 56 mG. The phase of the phase sensitive detector was successively set to 110. 95, and 80" in different experiments. The lowest line width values for a given sample were observed with (o = 110",and the largest with cp = 80" (see Table 11). The initial phase setting does not affect the slope from plot log AH = f(l/T).
Discussion We shall assume first t h a t the resonance lines are homogeneously saturated and that the behavior of the spin system is accounted for by the Bloch equations. Phase Shifts. The distortion of the absorption line a t various power levels depending on the initial phase setting is a consequence of a phase difference between the modulated signal and the modulation of the static magnetic field (100 kHz). This results from the modulation frequency (urn = 2IIXm = 211105) being equal to ( T z ) - l . Halbachlg observed this phenomenon for spin systems obeying the Bloch equations. He derives a convenient method The Journal of Physicai Chemistry, Voi. 77, N o . 20, 1973
2486
G.Dodin and J. E. Dubois TABLE II: Activation Energies for Line Width Variation with Temperature in Na-HMPA Solutions
Samplea
kcal mol -
7 (20O). cst
:
3.3 2.87 2.33
We I
2 3 4
&‘/!I‘
(ZOO)*
6.6
14.7 8.1
2.45 2
5.4 4.1
4.1 1
1.6 1
8.3
1.4
ri/ri
1
(20
aSamples and sample numbering are as in Table I. 6 r is the cavity radius.
+
LO
5
3
10
Figure 4. Esr of Na-HMPA solutions. Lock-in with l / H 1 .
1/H, (G-’) phase variations
log AH = log (Ce”’eifi7)
of evaluating relaxation time Tz independently of the nonhomogeneity of the static magnetic field. In the case of our experiments with Na-HMPA solutions, the equivalence of wrn is obviously fortuitous since the frequency of the modulatior. is not adjustable on our spectrometer, but it has allowed us to evaluate T2. According to Halbach’s equations, the ordinate at the origin cpo of cp = f(l/HI) is related to urn and Tz tgpo = 0 J “ z A typical plot, the variation of cp us. 1/H1, is shown in Figure 4. The calculated relaxation times TZ are in good agreement with those from saturation data. Actiuation Energj. As in Na-NH3 solutions, we shall assume that the line width arises from exchange narrowing. The fact that activation energy, WE, for the electron spin exchange, measured from the plot log AH = W,/kT, depends on the solutions viscosity is an argument for a modulation mechanism which associates the correlation time for the interaction with the Debye dipolar relaxation time.20 Let us assume that the relaxation of the spin system is described by the following equations21
IIT, =
r
1
1/T1= DC 3- 2A2/3J(07 + 111
1
.+
(wu
-
w,)272
where DC is a residual line width, 1H0, arising from the dipolar coupling (DC) of the nuclear and electronic spins. J is the spin of the nucleus responsible for the relaxation; 7 is the correlation time of the contact interaction; A is the hyperfine interaction between the nuclear spin J and the electron spin; WN and we are the Larmor frequencies of the nucleus and the electron, respectively. When ( u N- ~ , ) ~ +
