Ron Catterall and Peter P. Edwards
3010
Scripta Technica, Inc., Prentice Hall, New York. N.Y., 1962;(b) V. V. Rachinskii, "General Theory of Surface Dynamics and Chromatography", translated from Russian by Consultants Bureau, New York, N.Y., 1965.
Silbernagel and F. J. Gamble, Phys. Rev. Lett., 37, (1974). (a)E. 0.Stejskal,J. Chem. Phys., 43,3597 (1965);(b) J. E. Tanner and E. 0. Stejskal, ibid., 49,1768 (1968). F. Daniels, J. W. Williams, P. Bender. R . A. Alberty, C. D. Cornwell, and J. F. Harriman. "Experimental Physical Chemistry", 7th ed, McGraw-HIII, New York, N.Y., 1970,p 451. G. Hooley, Can. J. Chem., 35, 374 (1957);Carbon, 2, 131 (1964). J. V. Acrivos. J. Phys. Chem., 78, 2399 (1974).. (a)J. A. Wilson, F. J. DiSalvo,and S. Mahajan, Bull. Am. Phys. Soc., 18, 386 (1973);Phys. Rev. Lett., 32, 16,882 (1974);(b) C. B. Scruby,P. M. Wllllarns, and G. S.Parry, Phil. Mag., 31, 255 (1975). S. F. Meyer, J. V. Acrivos, and T. H. Geballe, Proc. Natl. Acad. Sci. B.
U.S.,72, 464 (1975).
Discussion M. J. SIENKO.(a) Where does the NzH4 go? Does it go between each pair of layers or leave some unchanged? (b) Does TaSz stay in 2H polytype? (c) NH3 on side in TaS2. Similar for NzH4. Lone pair avoids layer.
J. V. ACRIVOS. The complete x-ray diffraction spectra taken 0.50 and 76 hr after the start of reaction were analyzed by EI weighted least-squares program [S. F. Meyer, R. E. Howard, G. R. Stewart, J. V. Acrivos, and T. H. Geballe, J.Chem. Phys., 62, 4411. (197511.These show that there is only one ordered phase present at all times and that the sequence of the Ta and S layers is as indicated in the figure shown. We have not determined the structure of the hydrazine layer. However the most important observation it3 that although the magnitude of the a axis in the hcp 2H phase does not change appreciably, the magnitude of the c axis changer, from 18.5 8, at 0.5 hr after the start of reaction to 18.0 A 76 hr after the start of reaction. This is dramatically shown by coniparing the 0010 reflection with the Be reference given by the window of the cell in Figure 3. The changes in base line suggest also the presence of other disordered phases. (c) We cannot answer the last question without doing a neutron diffraction study of NzD4 intercalated compounds. Please give ref erence of NH3 intercalated compound. Our work with NH3 + TaS.2 indicates that the final product depends strongly on the pressure of the gas during the reaction.
Electron Spin Resonance Studies of Localized Excess Electron States in Frozen Solutions of Alkali Metals in Hexamethylphosphoramide Ron Catterall' and Peter P. Edwards Depatfment of Chemistry and Applied Chemistry, University of Salford, Salford M5 4WT, England (Received July 25, 1975)
Electron spin resonance spectra of frozen solutions of sodium, potassium, rubidium, and cesium metals in HMPA are reported. Spectra a t low microwave power levels (51mW) showed the existence of several, discrete, localized excess electron states with unpaired electron spin density lying between -36 and -80% of the free atom value. In potassium, rubidium, and cesium solutions, a localized state with spin density 51% of the free atom value was also identified. Magnetic parameters (hyperfine coupling constant, electronic 4; factor) for both the high and low atomic character states in frozen metal-HMPA solutions showed similarities with results for fluid metal-amine solutions. The relevance of our observations to current models for metal-amine solutions is discussed. The experimental distribution function for localized excess electron states provides strong support for a multistate model for fluid metal-amine solutions. The high atomic character states are described in terms of intermediate impurity states in the host (HMPA) matrix, while the low atomic character state approximates closely to a true Wannier-Mott impurity ground state.
Introduction Fluid solutions of alkali metals in ammonia,1,2HMPA,3 amines,4-8 and ethersg>l0 have electron spin resonance (ESR) spectra which can be classified into two groups: those for which only a single, time-averaged signal is observed, and those for which two signals are observed, a hyperfine multiplet from electron-cation aggregates, and a central singlet from isolated solvated electrons. A quantitative explanation for these differences in spectra is possiblell in terms of simple ion-pairing theory
In solvents of high dielectric constant (ammonia, HMPA) the rate constants for (1) are such that the average The Journal of Physical Chemistry, Vol. 79, No. 26, 1975
lifetime, ( T M ) , of Msolv is short compared to the inverse of the metal hyperfine coupling constant (AiS0-l), and ( 7 ~ ) A> ~1 ~ and ~ signals from both paramagnetic centers ~ ~a ~wide are observed. Calculated values1' of ( T M ) Afor range of metal-solvent systems are illustrated in Figure 1. Perhaps the most intriguing aspect of fluid amine and ether solutions lying above the critical region, ( 7 ~ ) A i ~ ~ 1, is the marked temperature dependence of the metal hyperfine coupling c o n ~ t a n t s . ~ In - l ~some cases Aiso varies by almost two orders of magnitude over a relatively small temperature interval, and two conceptually different models have been proposed to explain this behavior.
3011
ESR Study of Alkali Metal-HMPA Solutions In a “continuum” model, a single species is proposed whose structure is markedly temperature dependent,43l2 while a “multistate” model pictures a dynamic and temperature-dependent equilibrium between two (or more) species of the same stoichiometry whose structures are relatively insensitive to temperature.6arsb Both models are equally capable of explaining both the temperature dependence of A,,, and the strong dependence of line widths upon nuclear spin configuration. Again both models contain too many parameters for adequate testing to be carried out. An unambiguous distinction between the models should be possible by examination of ESR spectra of frozen s o h tions,13 but unfortunately several factors have contributed to an almost complete failure to obtain frozen metal solutions which preserve the structure of the liquid state: (i) solutions in more polar solvents show a strong tendency to separate out on freezing into crystalline phases of pure metal and pure solvent;14-16 (ii) although crystallization is more readily avoided in the less polar amines and ethers, solubilities are much 1ower;’O (iii) the spin-pairing equilibrium in less polar solvents is generally shifted strongly away from states involving unpaired electron spin.9b This problem is further enhanced a t lower temperature^.^*^^^ Although the high static dielectric constantls of fluid HMPA (Figure 1)ensures that only a single, time-averaged ESR absorption is found a room t e m p e r a t ~ r e ,the ~ presence of metal-dependent bands in the visible region3J9 establishes a strong link with amine and ether solutions. In addition, the high solubilities3 of alkali metals in HMPA, the high fraction of unpaired electron spins (-10%),339b and the high freezing point (-7OC) and viscosity20of HMPA all suggest strongly that homogeneous frozen solutions might be obtained with sufficient concentrations of unpaired electron spins for practical study. In accord with these suggestions we have found that rapid freezing of solutions of alkali metals in HMPA does give rise to homogeneous blue glasses, and in this paper we report some preliminary results of ESR investigations of frozen solutions of sodium, potassium, rubidium, and cesium metals in HMPA.
Experimental Section Samples were prepared using conventional high vacuum techniques modified for use with a high boiling solvent. Spectra were recorded on a Varian V4502 spectrometer using standard accessories and operating at -9.1 GHz. Microwave power levels incident upon the cavity were -1.0 mW. Results Spectra (77 K) of frozen solutions of sodium, potassium, rubidium, and cesium are shown in Figure 2. The main characteristics of the spectra are summarized as follows. (i) Strong central singlets had line widths and g factors which varied from one metal to another. (ii) Isotropic multiplet signals consisted of 21 1 lines, where I is the nuclear spin of the alkali metal. (iii) Line width of multiplet spectra were dependent upon the nuclear magnetic quantum number, mI, of the alkali metal. Line width variations were particularly marked for rubidium and cesium solutions. (iv) Spectra at high machine amplification revealed a multitude of weaker signals (Figures 3, 6, and 7). (v) Both singlet and multiplet resonances had line shapes approximating closely to Gaussian. (vi) Microwave power saturation behavior of both singlet and multiplet resonances was characteristic of
+
ha-HMPA
Time-aueraged Spectra
C5-AM
13
1
Na-AM
Strong resonance broadenlnQ
Critical
...- . -.
4
reglon 10
i
K - DG K -EA
2
10
c
Cs-EA
3
10
4 10
Resolved metal h.f.5
K -THF
Flgure 1. Classification of ESR spectra (-296 K) of fluid metal solutions on the basis of the product (7,)Aiso: THF = tetrahydrofuran, EA = ethylamine, DG = diglyme, MEA = methylamine (-220 K), 1,PPDA = 1,2-propanediamine,EDA = ethylenediamine, AM = ammonia ( ~ 2 4 K). 0
-
inhomogeneously broadened lines.Z1 Saturation curves for the narrowest hyperfine components (AHms 4.4 G) of POtassium, rubidium, and cesium spectra are compared in Figure 4. For potassium through cesium, the onset of saturation moves to higher microwave power in accord with enhanced spin-orbit coupling for the heavier atoms. (vii) All line positions, widths and shapes, and all relative and absolute intensities were independent of temperature over the accessible range (77-180 K). Analysis of Spectra. Singlet Resonances. Line widths showed a marked dependence upon the nature of the metal in solution (Table I) and spectra were simulated to first order to obtain metal hyperfine coupling constants. Assuming coupling to a single metal nucleus and an intrinsic width of 4.3 G, comparable to the narrowest of the hyperfine components of multiplet spectra, the hyperfine coupling constant was adjusted to fit the observed line shapes. Results are given in Table I. Multiplet Resonances. Experimental line positions for the dominant multiplets were fitted to the Breit-Rabi equationz2
where W ( F , ~is~the ) energy of a state with magnetic quantum numbers F and mF, and
[ (-)
Q = 1 + 4mFx 21 + 1
+x2y2
(3)
The zero field splitting, AW, is given by (4) and x = (ge - gI )PBHO/A
w
(5)
where gr is the nuclear g factor and WBthe Bohr magneton. A comparison of observed and calculated line positions, together with the derived magnetic parameters ( g e and Ais,,), is given in Table 11. The Journal of Physical Chemistry, Vol. 79, No. 26, 1975
Ron Catterall and Peter P. Edwards
3012
a
a
I
I
23
Na
b
b
I i ,I
'I
i
9
t 9-2 1
I
23M
I
I
39K I
2 3 M 3 N3 Flgure 3. Electron spin resonance spectra at higher amplification of frozen solutions of (a)potassium and (b) sodium in HMPA.
C
L
85
I
d
l
l
23
87
s-2
I
c
I
I
I
Rb
I 9 9
15-2
,i4
I
ii
,I
JFnlcrowave power',(mW)M
-
Figure 4. Microwave power saturation of the narrowest hyperfine 4.4 G) of the species MG in potassium, rubidicomponents (AH,, um, and cesium solutions in HMPA (77 K). TABLE I: Magnetic Parameters for the Central Singlet Resonance in Frozen Solutions of Potassium, Rubidium, and Cesium Metals in HMPA? ge I
1
1
I
1
1
133
I
I
CS
Figure 2. Electron spin resonance spectra (77 K) of frozen solutions of (a)sodium, (b) potassium, (c) rubidium, and (d) cesium in HMPA. Analysis of spectra obtained at high machine amplification was more complicated; spectra of rubidium and cesium solutions in particular gave resonance patterns which at first sight appeared unrelated. In these cases, analysis in the first instance relied heavily upon calculated plots such as that given in Figure 5 which show the variation of resonant field position of a given line as a function of the metal hyperfine coupling constant. Our identification of lines in The Journal of Physical Chemlstry, Vol. 79, No. 26, 7975
Isotope
AH,,, G
(+0.0004) Aiso, G
% atomic character
39K
4.9 ?: 0 . 3 b 2.0018 0.80 i 0.1 0.97 i 0.10 85Rb 9.4 + 0 . 5 C 0.41 * 0.03 2.0009 1.48 i O . l I 3 T s 14.9 r 0.8d 1.9994 1.85 t 0.1 0.23 i 0.02 a The intense colloidal metal resonance from sodium solutions (Figure l a ) effectively obscures all other resonances in the ge 2 region (ca. 3200 G). b Average of five samples examined. C Average of two samples examined. d Average of four samples examined.
-
rubidium and cesium spectra are given in Figures 6 and 7. Lines correlated in this manner were then subjected to a full least-squares analysis to yield final values of Ais{, and &!e.
3013
ESR Study of Alkali Metal-HMPA Solutions
TABLE 11: Magnetic Parameters Derived from the Dominant Multiplet Resonance in the ESR Spectra (77 K)of Frozen M-HMPA Solutionfl
Line positions
+7/2
+5/2
+3/2
+1/2
-112
-312
-512
-712
Magnetic parametersb Isotope, (frequency), sample GHz
23Na 198.36 3329.3 3543.1 2946.2 3132.3 2.00135 (1.0) (2.0) (2.0) (1.0) Na-3 (9.1138) 3541.0 3330.4 3131.9 2945.6 Calcd 9K 54.75 3348.7 3292.8 3238.3 3184.3 Obsd 2.00090 (0.3) (0.3) (0.3) (0.3) K-5 (9.1504) 3348.6 3238.2 3184.4 3238.2 Calcd 85Rb 251.34 3594.0 3885.9 3322.8 Obsd 2626.8 2838.6 3072.2 1.99806 (0.2) (1.0) (0.1) (0.5 1 (1.0) (2.0) Rb-1 (9.1735) 3594.2 3885.0 3322.7 3071.1 Calcd 2626.6 2839.1 Obsd 1815.8 2430 d 4406 87Rb 849.0 1.99802 (1.5) (1.0) (1.5) Rb-1 (9.1735) Calcd 1816.7 2430.4 3293.4 4405.9 Obsd 924.6 1153.8 1473.3 1936 2534 d 4200.5 5198.5 133Cs 604.0 1.99213 (1.0) (1.5) (5.0) (3.0) (3.0) (10) (3.0) Calcd 934.6 1156.2 1472.3 1920.5 2529.6 3299.8 4201.9 5198.5 Cs-3 (9.1019) QCalculatedline positions are given by the Breit-Rabi equation (eq 2). b To conserve space we have adopted the following convention for tabulating parameters: e.g., 198.4, value of Aiso (G); 2.0014, g, derived from Breit Rabi analysis; (9.1134), experimental frequency, GHz. C Values in parentheses denote estimated error (G) in line positions. d Line obscured by strong central singlet. Obsd"
TABLE 111: Magnetic Parameter@ for the Localized States (MB-MH) in Frozen Solutions of the Alkali Metals in HMPA (77 K ) Isotope
IJ,(0)I d x
Ais0 9 G
% atomicb
character
10-24
Designation
age
x 104c
ge
198.36 3.173 62.75 2.00135 9.6 23M~d 150.95 2.415 47.75 2.00119 11.0 23M~ 9K 54.75 4.964 66.45 2.00090 15.1 39M~d 2.0009 15 'Mc 3.51 -47 38 2.00082 14.9 39M~ 2.734 36.60 30.16 1.99824 41.7 "MI 85Rb 277.3 12.153 76.8 1.9982 42 85M~ 2 68 11.74 74.2 251.34 11.015 69.61 1.99806 43.5 ''MG~ 233.2 64.6 1.9992 32 *'ME 10.223 210 9.210 58.2 1.9985 39 "MD 179.1 7.851 49.6 1.9988 36.1 'Mc 8'Rb 849.0 10.978 69.63 1.99802 43.9 87M~d 8'M~ 706.3 9.134 57.93 1.9986 38 I33M 133cs 655 21.16 80 1.992 H 135M d 104.5 604.0 19.440 73.5 1.99 2 13 I 3 3MG' 595 19.18 72.5 1.992 133MF 555 17.91 67.7 -1.992 E 133M 49 3 15.92 60.2 -1.992 D a Taken from experimental data at 77 K which gave the smallest rms deviation in the Breit-Rabi analysis. b Calculated from free atom hyperfine coupling constants (A), given in P. Kusch and V. W. Hughes, "Handbuch der Physik", Vol. XXXVII/l, Springer-Verlag, Berlin, 1959, pp 100 and 117. C he= (g,(free atom) -ge). Free atom values: 23Na
-
-
-
A, G ge d Dominant states.
23Na 316.109 2.00231
"K 82.38 2.00231
A full listing of magnetic parameters for states identified so far is given in Table I11 where we have provisionally classified states on the basis of their percentage occupation of the outer metal n s orbital. We use a system24which labels, for example, the lowest atomic character state ('MA), where I: denotes the mass number of the particular isotope. We stress that there are still some unidentified lines in the spectra; more complete analysis will be attempted elsewhere on the basis of further experimental studies. Line W i d t h Variations. The mI dependence of line widths in the solid state spectra (Figure 2) was superficially
"Rb 361.07 2.00241
"Rb 1219.25 2.00241
133cs 819.84 2.00258
similar to that observed for fluid solutions of alkali metals in amine^.^-^ However, we stress that the interpretation of this behavior for fluid solutions (i.e., rapidly fluctuating structural changes) cannot be applied to our spectra obtained from rigid solutions. Likewise, the explanation we propose below cannot be applied to fluid solutions. We first express the observed line width as sums of mIdependent (AH,,,,) and mp independent (AHreB)contributions
The Journal of Physical Chemistry, Vol. 79, No. 26, 1975
Ron Catterall and Peter P. Edwards
3014
- a \ \
\
\
\
I
/
I1
1 1 , I I
5001
U
2
1
4
3
5
6
I
External t i e l d ( H o ) , kG
ll
Ill I II Ill
111 I 11 II I
1
I 11'1
Theory
Figure 7. Analysis of the ESR spectrum of a solution of cesium in HMPA (77 K). (A) is the observed spectrum and (B) the calculated stick spectrum for the five Cs states with Ai,, values given in Table 111. Resonant field positions as funttions of AI,, were obtained from eq 2 with ge = 1.9921 at a microwave frequency of 0.1018GHz.
c
-
L?
$
40-
I
!
-
20-
E z
-
"Rb
85
____
m -250
0
1 1
I
2
3
4
5
Figure 5. Variation in the resonant field positions with metal hyperfine coupling constant for (a) 13%s ( / = 712)and (b) ssRb ( / = 5/2) and 87Rb ( I = 3/2).Calculated using eq 2.
Flgure 8. Computer simulation of the ESR spectra of the 39MG state (potassium)for residual line widths (AHre,) (a) 3.18,(b) 4.00, and (c) 4.18 G.
about the metal atom. To first order, the mpdependent contribution is given by Mrn, =
Figure 8. Analysis of the ESR spectrum of a solution of rubidium in HMPA (77 K). Full lines show the variation of resonant field position with AI,, (eq 2) for ge = 1.99800 and a microwave frequency of 9.1735 GHz. The lines are anchored at the crossovers of the MG s ecies (AI,, = 251.3 G). Insert A shows the low-field (m, = +3/2) PRb line; insert B gives a rerun of the high-field section. and postulate the existence of normal (Gaussian) distributions of hyperfine coupling constants to metal nuclei centered on each of the derived Aiso values. The width of the distributions must be small to account for the narrow line widths and could, for example, arise from centers differing slightly in the orientation and density of HMPA molecules The Journal of Physical Chemistry, Voi. 79, No. 26, 1975
26A(aH/aAiSdrn,
(7)
where 6A is the half-width at half-height of the Gaussian distribution. Numerical convolution of the distribution function with a Gaussian line shape using gradients (aH/aAi,,) obtained from the Breit-Rabi equation, yielded a two-parameter model (6A and AHres)capable of a precise simulation of ESR spectra. To illustrate the process, potassium spectra are given in Figure 8. simulated for various values of anres A least-squares fit yielded optimum values of AH,,,and 6A, and experimental and simulated spectra for potassium and rubidium solutions are compared in Figure 9. It should be stressed that the equations defining the fit are particularly well defined, and the minimum in the least-squares surface is both sharp and deep permitting considerable confidence to be placed on the derived parameters given in Table IV. Variations in g, factors, while undoubtedly present, cannot account for the mpdependence in the line widths since
3015
ESR Study of Alkali Metal-HMPA Solutions
a (i) 39
K
a
-5O 0I
o
-160
m
-80
'
80 '
0'
b
loot
133
4
cs
Flgure 9. Comparison of observeql (i) and simulated (ii) ESR spectra ~ of (a)the 39Ma quartet in potassium solutions and (b) the 8 5 Msextet
in rubidium solutions in HMPA.
TABLE IV: Analysis of Multiplet Line Widths in the ESR Spectra of Frozen M-HMPA Solutions0
3
P0 23
6 Ab Isotope
Species
A.H,e,, G
Std dev, 6A, G
(% atomic
character)
0.7 4.2 2.1 39K 4.12 0.92 1.1 2.34 0.648 4.320 (+'%) "5Rb 4.285 (-%) 2.66 0,737 85Rb "MD 4.3 55 51.5 133Cs 133ME 4.3 4.1 0.5 a Final estimates of the residual widths (&Ires)and the standard deviations (6A) for the species XMG,D,E.b 6 A = (6A(G)/A(free atom)) X 100%.
23Na
23M~ 39M~ "MG
gradients aHIag, are approximately independent of mI. Any line width contributions from g, factor variations appear in AHres.
Discussion The significance of our solid state results lies first in their relevance to current models for solutions of alkali metals in amines, and secondly in the nature of the wide variety of solvated atoms detected. Magnetic Parameters from Solid and Liquid Phase Spectra. In Figure 10 we compare available metal hyperfine coupling constants, expressed in terms of percent atomic character, for fluid solutions of potassium and cesium in various amines and ethers together with our results
-200
-12
T
("C)
Figure I O . Temperature dependence of the metal hyperfine coupling constant in (a)fluid solutions of potassium in amines and ethers, and frozen potassium solutions in HMPA, and (b) solutions of cesium in amines (fluid) and HMPA (solid):(0) ethylamine (EA), ref Ed; ( 0 )methylamine (MEA); (El) butylamine (BUA), ref Ea; (Q) n-propylamine (nPA) ref 6b and Ea; ( 0 )isopropylamine (iPA) ref 6b and Ea; (om) 1,2- and 1,3-propylenedamine (1,2- and 1,3-PDA),ref 6b; (0)tetrahydrofuran (THF), ref 9 and 10;).( HMPA, this work. Cesium solutions: MEA, ref 5b and 6b; EA, ref 4b and 6b; nPA, iPA, and 1,2- and
1,3-PDA,ref 6b.
for frozen solutions of these metals in HMPA. Coupling constants in the fluid amine and ether solutions always lie intermediate between the values for the two dominant states in HMPA (MA and MG), but tend toward these values at low and high temperature, respectively. In Figure 11 we show Age = g,(free atom) - g, as a function of percent atomic character for the species MA to MH together with values for fluid solutions. For all systems a common trend emerges; as the Aiso factor moves toward the free atom value, so the g, factor moves away from the corresponding atomic g, factor. This substantiates earlier predictions8b,cthat the limiting high atomic character state in fluid solutions is not the free alkali atom. However, for The Journal of Physical chemistry, Vol. 79, No. 26, 1975
Ron Catterall and Peter P. Edwards
3016 23
Na 39K
ys
85,87
133
Rb
7 /
u
20
40
60
EO
N(ac) (arbitrary)
150
100
i
A ’l
% Atomic character
100
Figure 11. Correlation of percentage atomic character with Ago for frozen solutions of sodium, potassium, rubidium, and cesium in HMPA and for fluid solutions in amines and ethers. Solvent identification as In Figure 10: (A)ammonia-ethylamine mixtures (ca. 40 mol % ammonia, ref 8b). Metal identification: (A)Na; (U)K; (6)%b; (e) 87Rb; (0)Cs. Continuum model
Figure 13. Observed density of states for solutions of rubidium in HMPA.
perature 77-180 K. The latter clearly provides strong support for the multistate mode16a18band is a t variance with the postulates of the continuum m ~ d e l . ~We J ~ conclude that the spectra of fluid metal-amine and ether solutions arise from a dynamic equilibrium between several (three or more are r e q ~ i r e d l ~species , ~ ~ ) whose structures are approximately independent of temperature. The High Percent Atomic Character States, MB-MH. Strong matrix perturbations on gas-phase alkali atom eigenstates bring about large deviations in both Ais0 and g , factors from their free atom values (Table 111).The parameter AA defined by AA = 100(Ai,,
Mukistate model (sirnpie 2-state model)
% At.character
High (--)and low(-)
temperature situations
Figure 12. Schematic representation of multistate and continuum models.
each metal there is a maximum Age which increases from sodium through cesium, in line with greater spin-orbit coupling in the higher alkali atoms (Table 111). The points made in Figures 10 and 11 are adequate confirmation of the underlying similarity between fluid amine solutions and our frozen HMPA solutions and justify our use of results from rigid solutions to distinguish models for fluid solutions. Relevance to Current Models for Fluid Amine Solutions. The two conceptually different models currently in vogue to explain the temperature dependence of Aiso and the mI dependence of AHrns for fluid solutions have been outlined in the Introduction. A schematic representation of the fundamental difference between the two models is given in Figure 12 where the distribution functions for the Aiso factor are shown a t different temperatures. In Figure 13 we present a typical distribution function obtained from a frozen rubidium-HMPA solution, independent of temThe Journal of Physical Chemistry, Vol. 79, No. 26, 1975
- A(free atom))/A(free atom)
(8)
represents a quantitative measure of the perturbation of the alkali atom gas phase ns wave function by the surrounding matrix. Alkali atoms trapped in rare gas matrices have been reported,26 but in general deviations from free atom coupling constants are small IAAl < lo%, and negative, i.e., Ais0 < A(free atom), and arise from second-order dispersion-type interactions between the trapped alkali atom and the surrounding matrix. In marked contrast, our values of AA range from -30 to -99%. A descriptionz6”in terms of an atomic interaction potential between the trapped atom and a rare gas atom accounts semiquantitativelyZ7for the observed shifts (AA), while similar calculat i o n ~ for~ the ~ interaction between an alkali atom and an HMPA “atom” predict maximum shifts of -3%
-AAcalcd,
%
‘jNa
39K
”Rb
‘33Cs
2.35
2.70
2.50
2.60
We may therefore rule out this mechanism for species MB-MH and conclude that our species cannot be described as trapped atoms, but must involve more specific bonding interactions with the solvent. A general molecular orbital scheme, originally proposedz8 to explain results for trapped silver gives a qualitative picture of the observed deviations in both Aisoand g, from free atom values.23 Alternatively we might describe the centers MB-MH as “intermediate impurity states” in the host (HMPA) matrix, that is, as states which retain a unique parentage in the states of the gas-phase alkali atoms, but are subject to large perturbations from the host. A theoretical description31 of such states must be either in terms of a strongly perturbed Heitler-London scheme, or by a modified Wan-
3017
ESR Study of Alkali Metal-HMPA Solutions
(3)(a) R. Catterall, L. P. Stoduiski, and M. C. R. Symons, J. Chem. Soc. A, 437 (1966);(b) Pure Appl. Chem. (Metal Ammonia Solutions Suppl.), 151 (1970);(c) L. P. Stodulski, Ph.D. Thesis, Leicester University, 1969. (4)(a) K. Bar-Eli and T. R. Tuttie, Jr., J. Chem. Phys., 40, 2508 (1964);(b) /bid., 44, 114 (1966). (5) (a) K. D. Vos and J. L. Dye, J. Chem. Phys., 38,2033 (1963);(b) K. D. Vos, Ph.D. Thesis, Michigan State University, 1962. (6)(a) J. L. Dye and L. R. Dalton, J. Phys. Chem.,this issue; (b) L. R. Dalton, M.Sc. Thesis, Michigan State University, 1966. (7)R. Catterail and M. C. R. Symons, J. Chem. Soc., 6656 (1965). (6)(a) R. Catterall, M. C. R. Symons, and J. W. Tipping, J. Chem. Soc., 1529 (1966);(b) /bid., 1234 (1967);(c) J. L. Dye and L. R. Dalton, J. Phys. Chem., 71, 184 (1967),see Discussion on p 190;(d) R. Catterall,
TABLE V: Unpaired Electron Spin Densities, i q ( 0 ) l D at the Donor Nucleus in Shallow Impurity States Donor
Host
P As
Sia
0.43 1.73
Sb
P
Geb
As
K
HMPAC
Rb
cs a
1.18 0.17 0.69 0.073 i. 0.007 0.065 0.005 0.060 * 0.006
unpublished results.
*
(9)(a) R. Catterall, J. Slater, and M. C. R. Symons, J. Chem. Phys., 52, 1003 (1970);(b) Pure Appl. Chem. (Metal Ammonia Solutions Suppl.), 329 (19701. ~, (IO) J.Slater, Ph.D. Thesis, Leicester University, 1970.
.
See ref 32. b See ref 34. C T h i s work.
nier-Mott formalism (see below). In any description of intermediate impurity states dielectric screening reduces the electron-parent ion (M+) coulomb interaction and the unpaired donor electron moves in an expanded centrosymmetric Bohr orbit about the parent ion. The Low Atomic Character State, MA. The extremely low unpaired electron spin density on the metal nucleus in this state (Table V) suggests considerable dielectric screening and a correspondingly large Bohr radius. However, the Gaussian line shape requires that the unpaired electron remain associated with a particular metal nucleus for 21OW6 sec. The effective mass formalism for Wannier-Mott impurity states gives the ground state wave function for the donor electron33 N
# ~ ( r=) C a,F,(r)$j(r) J=1
(9)
where FJ ( r ) is the hydrogenic envelope function a t the j t h conduction band minimum, of which there are N . $ , ( r ) is the Bloch function at the same minimum and a, the relative contribution from the j t h valley. A wave function of the form (9) requires that I#(O)JD~, the unpaired electron spin density a t the donor nucleus, be independent of the nature of the donor atom. Our observed values for the states labeled MAare consistent with this (Table V). To a first approximation, shallow impurity states in group 4 semiconductors are also described by (9), but in these systems I + ( O ) ~ D ~ is dependent upon the donor atom,32,34 and the effective mass formalism obviously 0 and requires a significant admixture breaks down as r of donor atom wave functions in the ground state. So far as we know, therefore, the states MA characterized in this investigation represent the closest approximation to true Wannier-Mott impurity ground states. Wannier-Mott excited states (excitons) have been characterized in doped liquid and solid rare
-
Acknowledgments. We thank the Science Research Council for financial assistance.
References and Notes (1) C. A. Hutchison, Jr., and R. C. Pastor, J. Chem. Phys., 21, 1959 (1953). (2) R. Catterall and M. C. R. Symons, J. Chem. SOC.,4342 (1964).
~
(11) R. Catterall, P. P. Edwards, M. C. R. Symons, and J. Slater. Chem. Phys. Lett., Submitted for publication. (12)D. E. O'Reilly and T. Tsang, J. Chern. Phys., 42,3333 (1965). (13)R. Catterall and P. P. Edwards, J. Chem. Soc., Chem. Commun., 96
(1975). (14)R. A. Levy, Phys. Rev., 102,31 (1956). (15)R. Catterail, W. T. Cronenwett, R. J. Egland, and M. C. R. Symons, J. Chern. SOC. A, 2396 (1971). (16) . . R. Catterail and P. P. Edwards, Adv. Mol. Relaxation Processes, submitted for publication.
(17)R. Catterail, I. Hurley, and M. C. R. Symons, J. Chem. Soc., Dalton Trans., 139 (1972). (18)J. E. Dubois and H. Viellard, J. Chim. Phys., 62,699 (1965). (19)J. M. Brooks and R. Dewald, J. Phys. Chern., 72,2655 (1968). (20)H. Normant, Angew. Chem., lnt. Edit. Engl., 6, 1046 (1967). (21)T. 0. Castner, Phys. Rev., 115,1506 (1959). (22)G. Breit and I. I. Rabi, Phys. Rev., 38,2062 (1931). (23)R. Catterail and P. P. Edwards, J. Chem. Soc., submitted for publication. (24)R. Catterall and P. P. Edwards, Chem. Phys. Lett., submltted for publication.
(25)(a) V. A. Nicely and J. L. Dye, J, Chem. Phys., 52, 119 (1970);(b) V. A. Nicely, Ph.D. Thesis, Michigan State University, 1969. (26)(a) C. K. Jen, V. A. Bowers, E. L. Cochran, and S.N. Foner, Phys. Rev., 128, 1749 (1962);(b) S. L. Kupferman and F. M. Pipkin, ibld., 166, 207 (1968). (27) P. P. Edwards, Ph.D. Thesis, Salford University, 1974. (28)M.C. R. Symons, J. Chem. SOC.,1482 (1964). (29)C. J. Delbecq, W. Hayes, M. C. M. O'Brien, and P. H. Yuster, Proc. R. SOC.(London), 271,243 (1963). (30)(a) R. A. Zhitnikov, N. V. Koiesnikov, and V. I. Kosyakov, Soviet Phys. J€TP (Engl. Trans/.), 17, 815 (1963);(b) A. Zhitnikov and A. L. Orbeli, Soviet Phys. Solid State (Engl. Trans/.), 7, 1559 (1966). (31)(a) S. Webber, S. A. Rice, and J. Jortner. J. Chem. Phys., 42, 1907 (1965);(b) B. Raz and J. Jortner, Chem. Phys. Lett., 4, 511 (1970);(c) B. Raz and J. Jortner, Proc. R. SOC.(London),Ser. A, 317, 113 (1970). (32)G. Feher, Phys. Rev., 114, 1219 (1959). (33)W. Kohn In "Solid State Physics", Vol. 5, F. Seitz and D. Turnbull, Ed., Academic Press, New York, N.Y., 1957. (34)D. K. Wilson, Phys. Rev., 134,A265 (1964).
Discussion W. GLAUNSINGER. Y o u r ESR analysis is very impressive, but is it n o t possible t h a t these frozen solutions m a y contain a greater n u m b e r o f d i s t i n c t localized centers t h a n the solutions? In other words, d o y o u believe t h a t t h e spectra o f quick-frozen solids really represent t h e state o f affairs in t h e liquid state?
R. CATTERALL. F i r s t our spectra are reproducible f r o m one preparation t o another w h i c h argues against any accidental changes o n freezing. Secondly a r o u g h spin count f r o m t h e area under t h e ESR lines shows, by comparison w i t h t h e static susceptibility measurements o n fluid solutions (reported a t Colloque W e y l 111, t h a t there is n o great change in t h e concentration o f u n p a i r e d spins o n freezing. W e believe t h a t these t w o points, coupled w i t h t h e observation o f very precise states in t h e frozen solutions, p r o vide very strong evidence for t h e t r a p p i n g o u t o f fluid solution structure.
The Journal of Physlcal Chemlstry, Vol. 79, No. 26, 1975
