J. Phys. Chem. 1984, 88, 5608-5614
5608
where g = (1/3)(2gl + g2). One observes the transition in solution, 13/2,'/2) which is independent of J 1 and J2 with
AE = g @ B / h
f,
+ ( a / 3 ) ( m $ I )+ mt2))
13/2,-1/2), (-43)
On the other hand, if we use the spin functions in the S = manifold, we expect the following results:
It/z,'/z)
El = ( 1 / 2 ) g p B / h + ( l / 3 ) a ( m 1 ( '+ ) mI(*))+ (1/12)J1 - ( 1 / 3 ) J 2 E2 = ( - 1 / 2 ) g @ B / h- ( ~ / ~ ) u ( w z + $ ' m~")) ) + ( 1 / 1 2 ) J 1- ( 1 / 3 ) J 2 ('44) and AE = g p B / h
=
(~6~/~)[~ . ( (12)4)3 ) - 2 ~ 4 )
~ ( 3 +) ~ ( 1 4) 2 ) 4 3 1 1
= ( 1 / 6 1 / ~ ( ~1 )( 2~) ( 3-) 2 m ~ ( 24 )3 )
lY29-'/2)
+~
m ~(311
( 1 )
The eigenvalues to first order are
+ ( 2 / 3 ) a ( m I ( '+) mI(Z))
('45)
where g = (4/3)gl - (1/3)g2. Thus, we expect a spacing of ( 2 / 3 ) afor the hyperfine coupling if the system is in the S = 1/2 state. Registry No. VO(0EP) radical cation, 62535-02-8;VO(PROT0) radical cation, 92144-53-1; VO(MES0) radical cation, 92144-54-2.
Nuclear Magnetic Resonance Studies of 14N and 'H in Metal-Ammonia Solutions Masahito Niibe and Yoshio Nakamura* Department of Chemistry, Faculty of Science, Hokkaido University, 060 Sapporo, Japan (Received: April 2, 1984)
The Knight shifts and spin-lattice relaxation times of 14N and 'H in sodium- and potassium-ammonia solutions have been measured as a function of temperature and composition up to the saturation region. The hyperfine interaction between these nuclei and paramagnetic unpaired electrons from the dissolved metals is responsible for the shifts which increase with increasing metal concentration. The observed maximum arouund 2 MPM in the relaxation rates for 14Nand 'H can also be explained by the contribution from the paramagnetic electrons.
Introduction Although metal-ammonia solutions have been extensively studied, the microscopic picture is still incompletely understood, especially in the transition region from the nonmetallic to metallic states.' Nuclear magnetic resonance (NMR) investigation on these solutions provides much useful information on the microscopic behaviors of the valence electrons from the dissolved metals, via the resonance shifts (Knight shifts) and relaxation times of various nuclei in solutions. In previous paper^,"^ we have reported the composition and temperature dependence of the Knight shifts and spin-lattice relaxation times of 'Li and 23Nain the respective metal-ammonia solutions. In this paper, we report the results of the N M R investigation on I4N and 'H of ammonia molecules in sodium- and potassium-ammonia solutions. The electron spin density on the nitrogen nuclei has been studied from N M R measurements by many authors,b-ll but the exact nature of the concentration dependence was not well established for a wide range of composition. No measurements have so far been made for the spin-lattice relaxation time of nitrogen nuclei in metal-ammonia solutions, although some works have been reported for proton^.'^^'^ The present results will be discussed on the basis of the models (1) Thompson, J. C. "Electrons in Liquid Ammonia"; Clarendon Press: Oxford, 1976.
(2) Nakamura, Y.; Hirasawa, M.; Niibe, M.; Kitazawa, Y.; Shimoji, M. Phys. Lett. A 1980,79A, 131; J . Phys. (Orsay, Fr.)1980,41,C8-32. (3) N!ibe, M. Doctor Thesis, Hokkaido University, 1983 (in Japanese). (4) Niibe, M.; Nakamura, Y.; Shimoji, M. J . Phys. Chem. 1984,88,3555. ( 5 ) Nakamura, Y.;Niibe, M.; Shimoji, M. J . Phys. Chem. 1984,88,3755. (6) McConnell, H. M.; Holm, C . H. J. Chem. Phys. 1957, 26, 1517. (7) Acrivos, J. V.;Pitzer, K. S.J . Phys. Chem. 1962,66, 1693. (8) O'Reilly, D. E. J . Chem. Phys. 1964,41, 3729. (9) Catterall, R. In "Metal-Ammonia Solutions",Colloque Weyl 11; Lagowski, J., Sienko, M. J., Eds.; Butterworth: London, 1970; p 105. (10) Duval, E.; Rigny, P.;Lepoutre, B. Chem. Phys. Lett. 1968,2,237. (11) Lelieur, J. P.; Rigny, P. J. Chem. Phys. 1973,59, 1148. (12) Newmark, R. A.; Stephenson, J. C.; Waugh, J. S. J . Chem. Phys. 1967,46,3514. (13) Mehner, A.-W.; Mueller-Warmuth,W. Z . Nuturforsch. 1972,27A, 833.
0022-3654/84/2088-5608$01.50/0
and their dynamics, which have been put forward in the previous works .495
Experimental Section The procedures for sample preparation and N M R measurements were essentially the same as those described e l ~ e w h e r e . ~ The pure ammonia, which was the reference for the Knight shifts for 'H and I4N, was prepared following the method reported by Ogg and Ray,14 in a Faraday tube to ensure complete dehydration. The content of metal in sample solutions were analyzed by titration with standard hydrochloric acid after each run. Flame photometry was also used for dilute alkaline solutions. N M R measurements were made with a Bruker SXP 4-100 spectrometer operating at 90.00 MHz for 'H and 6.50 MHz for I4N. The spin-lattice relaxation times were measured by the usual 18O0-r9Oo pulse sequence method. For highly conducting samples, the direction of the 90° pulse was inverted relative to the 180" pulse, in order to reduce the space dependence of the rotation angle of the magnetization due to the skin effect. The temperature range of measurements was from 0" to -40 "C for sodium-ammonia solutions and from -35" to -75 "C for potassium-ammonia solutions. the temDerature being controlled within *1 "C.
-
Results Figure 1 shows the resonance spectrum for I4N in pure ammonia and that in a sodium-ammonia solution at -40 "C. The quartet due to the I4N-IH spin-spin coupling was observed for all samples of metal solutions studied. These quartets have so far been reported only for pure liquid ammonia,I4 but not for metal-ammonia HughesI5 has pointed out that the disappearance of triplet lines of 'H in concentrated metal-ammonia solutions might be due to the exchange of 'H with that of the amide formed by the decomposition of the solutions. In the present experiment, (14) Ogg, Jr., R. A.; Ray, J. . D. J . Chem. Phys. 1957,26, 1515. (15) Hughes, Jr., T. R. J . Chem. Phys. 1963,38, 202.
0 1984 American Chemical Society
N M R of Metal-Ammonia Solutions
The Journal of Physical Chemistry, Vol. 88, No. 23, 1984 5609 I
Na- NH3
I
--Figure 1. I4N NMR spectra for pure ammonia and sodium-ammonia solution (0.4MPM) at -40 OC and 6.50 MHz.
h
E Q Q
v
-6 h
r
v
Y
C N ~ (MPM)
-4
Figure 3. Knight shifts for I4N,K(N), in sodium-ammonia solutions at -40 (0),-20 (A),and 0 "C (0). 1000
-2
100
0
5
10
CM
15
(MPM)
Figure 2. Knight shifts for IH, K(H), for sodium-ammonia solutions at -40 OC (0) and for potassium-ammonia solutions at -35 OC (0). ---,
corrected values of K(H) for the magnetic susceptibility. a quartet of lines for 14N has been observed up to the most concentrated solution near the saturation region and up to 0 OC. The separation between the adjacent lines of the quartet is 46 f 1 Hz for pure ammonia and 46 f 2 Hz for the metal solutions, being constant over the composition and temperature ranges studied. This indicates that the excess electrons in metalammonia solutions do not affect significantly the coupling constant J of the N-H coupling in each ammonia molecule. The present value of J is in good agreement with that obtained from the triplet of lines for 'Hin pure ammonia.14 Figure 2 shows the observed Knight shifts for 'Hof ammonia in potassium-ammonia solutions at -35 OC and those in sodiumammonia solutions at -40 OC. The sign of the shifts was negative (diamagnetic shifts) and the absolute values of the shift, IK(H)l, increase with increasing metal concentration. The concentration of solutions is expressed by mole percent metal, MPM. The values of K(H) in the both systems are nearly equal a t the same composition. The observed Knight shifts were corrected for the difference in the magnetic susceptibilities of the reference (pure ammonia) and sample solutions.16 The susceptibility data of Lelieur and Rigny" were used for sodium-ammonia solutions. These data were also used for potassium-ammonia solutions, for which no susceptibility data are available over the whole concentration range studies. The values of the corrected shifts are shown in Figure 2 by a dashed line. The correction does not exceed 25% of the observed values. The results for the Knight shifts of I4N, K(N), in sodiumammonia solutions are shown in Figure 3 for three different temperatures, -40, -20, and 0 OC. The values of K(N) increase (16)Zimmerman, J. R.;Foster, M. R. J . Phys. Chem. 1957, 61, 282. (17) Lelieur, J. P.; Rigny, P. J . Chem. Phys. 1973, 59, 1142.
h
En
v
10 h
X Y
Y
. . .. d
l t
,
,
-35.C
1
Flgure 4. Knight shifts for I4N,K(N), and 13Na,K(Na), in sodiumammonia solutions at -40 O C , for 'Li, K(Li), in lithium-ammonia solutions at -55 O C , and for IH, K(H), in sodium-ammonia (A) and potassium-ammonia (A)solutions at -35 OC. ---, K(H)for sodium-ammonia solutions at -33.2 O C due to Hughes.I5
with metal concentration and also with temperature. Since the Knight shifts of 14Nare as large as 102-103 ppm, the susceptibility correction was not necessary. The present results for K(N) and K(H)are compared with those for K(Li) and K(Na) reported earlier,4,5as shown in Figure 4 as a function of the mole ratio of ammonia to metal, R. The curves for K(N) and K(H) decrease monotonically with dilution or increase of R,while the curves for the metallic nuclei become constant in dilute solutions. Our results for K(H)are in good agreement with those of Hughesls for dilute sodium-ammonia solutions. Figure 5 shows the temperature coefficients of the shifts, d In K(N)/dT, as a function of composition. The present values are in fair agreement with those reported by Lelieur and Rigny" but differ significantly from those by O'Reilly.1-8
5610 The Journal of Physical Chemistry, Vol. 88, No. 23, 1984
' I
I I 3
- 3
i
1
I
r
Niibe and Nakamura
Y N
0 v c
+2 U
\
> C d
U
1
0.01 1000 ~
Figure 5. Temperature coefficients of quantity Y,d In Y/dT, in sodiumand potassium-ammonia solutions: 0, Y = K (N); 0 , (l/Tl)efor 'H;A,
xL(ESR);*'---, static);'^
-.-., K(Na)!
5
function of the mole ratio of metal to ammonia, R.
10
CM
10
R
Figure 7. Contribution from the hyperfine interaction with paramagnetic electrons, (l/T,)e, to the relaxation rates for 'H, 23Na,and 'Li as a
0
0
100
15
(MPM)
Figure 6. Spin-lattice relaxation rates for 'H, l/Tl(H), in sodium-ammonia solutions at -55 (a) and -35 OC (A),and in potassium-ammonia solutions at -78 (0),-55 (0),and -35 OC (A).
Figure 6 shows the spin-lattice relaxation rate of 'H,l/Tl(H), in sodium- and potassium-ammonia solutions. The values of 1/ T,(H) are positive and have a maximum around 2 MPM. The values of l/Tl(H) (s-l) for pure ammonia are in good agreement with those in 1iteraturels and given by a function of v/T as l / T l ( H ) = 64.6(v/T) 0.013 (1)
+
where 7 is the viscosity coefficient (cP) and T the absolute temperature. We used this equation to estimate the contribution from inter- and intramolecular proton-proton dipolar coupling, (1/ T1)H-H, to the observed relaxation rate in metal-ammonia solutions, taking account of the difference in viscosities of pure amm ~ n i a ' and ~ ~ *the ~ solutions.21 The resulting values of the con(18) Smith, D. W. G.; Powles, J. G. Mol. Phys. 1966, 10, 451. (19) Kikuchi, S. J . SOC.Chem. Ind., Jpn. 1944, 47, 488. (20) Nozaki, T.; Shimoji, M. Trans. Faraday SOC.1969, 65, 1489.
5
15
10
C N ~
(MPM)
Figure 8. Spin-lattice relaxation rates for 14N, l/Tl(N), in sodiumammonia solutions at -40 (0),-20 (A), and 0 OC (0).
tribution to the relaxation rate due to the presence of the paramagnetic electrons, (l/Tl)e, are shown in Figure 7. The values are multiplied by R , where R is the mole ratio of metal to ammonia. These values are decreasing with metal concentration in the nonmetallic region, similar to those for ( l / T l ) e for metal n ~ c l e isuch ~ , ~ as 23Naand 'Li. The temperature coefficients of (1/ Tl)e for protons in potassium-ammonia solutions are shown in Figure 5. These values are in agreement with those for the metal nuclei except for the concentration range between 3 and 5 MPM, where the values for the proton become negative. The observed results of the spin-lattice relaxation rates for I4N, l/Tl(N), in sodium-ammonia solutions are shown in Figure 8. The values of l/Tl(N) tend to increase with metal concentration, but have a maximum around 2 MPM. This maximum just corresponds to the maximum found for the curve of l/Tl(H), shown in Figure 6 . The temperature coefficient of l / T l ( N ) is negative over the whole concentration range studied, which is in contrast to the positive temperature coefficients of l/Tl(H). These results indicate the the quadrupolar contribution is dominant in (21) Demortier, A.; DeBacker, M.; Lepoutre, G. J . Chim. Phys. Phys.Chim. Biol. 1972, 69, 1123.
The Journal of Physical Chemistry, Vol. 88, No. 23, 1984 5611
N M R of Metal-Ammonia Solutions
-- 5 0 0 -
r----
‘V
a,
ln v
--
0
Ndl-NH,
A
NaN0,-NH,
,
A
d
400 -
fa
5.84 m o l %
s o l ~ t i o n s . ~ This , ~ ~ indicates *~~ that these nuclei undergo an isotropic hyperfine interaction with paramagnetic unpaired electrons in the solutions. Therefore, we call these observed shifts of N M R frequencies of these nuclei “Knight shifts” for the whole range of solutions, including the nonmetallic region. We introduce then an expression for the Knight shift which can be used for both the metallic and nonmetallic regions. For the nonmetallic region, the usual expression for the shift has the form6
h
-5
300-
where X denotes the nucleus under study, ’H or I4N. xt and Ne arc respectively the electron paramagnetic susceptibility and number of unpaired electrons per unit volume, I+(0)lxzthe undenotes the paired electron spin density at the nucleus X. ( time average for a specific nucleus during the time of N M R observation, typically of the order of lo-* s. On the other hand, the expression for the metallic region is given byz6 87 K(X) = -j-X,PQ(IJ.(O)lX2)F (3)
5.1 1
I=
7
200 ure
100I
I
I
0
1
2
I
3
‘IIT
I
4 (ldacp/K )
Figure 9. Spin-lattice relaxation rates for 14N, l/T,(N),,,,, in some salt-ammonia solutions as a function of viscosity divided by absolute temperature, 7/T.
where ( )F denotes the ensemble average for electrons near the Fermi level. It is noted that the electron wave function +(I) is normalized in the atomic volume Q, each of which contains a nucleus X under study. In order to unify these two expressions, eq 2 and 3, we first introduce a quantity P ( X ) following the definition of McConnell and Holm6
N A X ) = N x ( l + ( O ) l ~=~N) ~M~( N x / N M ) ( I ~ ( O ) I X (4)’ ) ~ ~ the relaxation rate of I4N. Figure 9 shows the relation of the observed relaxation rates l / T l ( N ) and q / T for pure ammonia and some sodium salt solutions in ammonia. Viscosity data for the salt solutions were taken from the literature.22 Linear relations between 1/T,(N) and q/T are found for each solution, but the slopes of these lines increase with salt concentration. This suggests that the electric field gradient at a 14N nucleus increases with the addition of ions to the solvent. Thus, it appears extremely difficult to separate the quadrupolar contribution from the observed relaxation rate of I4N, to obtain the contribution from the paramagnetic electrons, ( 1 /
Discussion It is well established that electrons liberated from the dissolved metals are localized as solvated electrons in dilute metalammonia solutions.’ These solutions behave like electrolytic solutions containing solvated electrons and solvated metal ions. In concentrated solutions, on the other hand, valence electrons from the dissolved metals are delocalized and the resulting solutions show liquid metallike properties.’ The transition of the excess electrons from the localized state to the nonlocalized state is regarded to take place around a comosition of 4-5 MPM.5,23 In previous N M R s t u d i e ~of~ 23Na * ~ and 7Li, we have reported that in dilute solutions below 2 MPM the monomeric species are responsible for the N M R shifts and relaxations of the metallic nuclei through the hyperfine contact interaction with the localized unpaired electrons. In the metallic region between 5 and 8 MPM, the electrons are delocalized but show a significant deviation from nearly free electron behaviors, for which the strong scattering model may be a p p r ~ p r i a t e .In ~ the nonmetallic region between 2 and 4-5 MPM, partial delocalization of the excess electrons or clustering of the metallic monomers has been suggested4 from the bulk conductivity dependence of the Korringa enhancement factors in sodium- and lithium-ammonia solutions. The present results of the N M R shifts and relaxation times for 14Nand ‘H will be discussed in terms of the models employed in these previous works. Knight Shift. Positive Overhauser enhancements have been observed for ‘H and I4N of ammonia molecules in metal-ammonia (22) Kikuchi, S. J . SOC.Chem. Ind., Jpn. 1944, 47, 305. (23) Niibe, M.; Nakamura, Y.; Shimoji, M. J . Phys. Chem. 1982, 86, 4513.
P ( X ) is of direct physical interest, which denotes the density of the nuclei X a t an unpaired electron. Here N x and NM are the number of the nuclei X and that of the dissolved alkali metal nuclei M per unit volume. With eq 4, eq 2 reduces to (5)
In alkali metal-ammonia solutions, the atomic volume Q for H and N is given by Q = l / N x = (l/NM)(MM/Nx). In the metallic region, we have P ( X ) = (I+(0)lx2)F, since an unpaired electron is always contained in an atomic volume Q. From these relations, the expression for the metallic region, eq 3, can also be reduced to eq 5 . Using the mole ratio of ammonia to metal, R, we have Nx/NM = R for N and Nx/NM = 3R for H. Thus, we have following expressions for the Knight shifts of I4N and ‘H for the whole range of composition 8a X! RK(N) = - -P(N)
8a X k = - -P(N)
NM
NA
(6)
8a Xk 3RK(H) = - -P(H) (7) 3 NA where xk is the molar electron paramagnetic susceptibility and NA is the Avogadro number. Then, we can determine values of P ( X ) from the observed Knight shifts, together with the magnetic susceptibility Figure 10 shows the plot of K(H) vs. K(N), which is almost linear for the whole concentration range studied. The slope of the line, which corresponds to P(H)/3P(N), is -1/130. We discuss first the origin of the negative shift for protons. Such negative shifts for protons have also been observed for aromatic radical^,^^,^^ in which the a-orbital spin density for a carbon nucleus is found to be proportional to the hyperfine coupling constant of ‘H directly bound to the carbon for various radicals. If such an indirect hyperfine coupling is occurring between the ~
~~~~
(24) Carver, T. R.; Slichter, C. P. Phys. Rev. 1956, 102, 975. (25) Lambert, C. J. Chem. Phys. 1968, 48, 2389. (26) Abragam, A. “The Principles of Nuclear Magnetism”; Clarendon Press: London, 1961; p 59. (27) Hutchison, Jr., C. A.; Pastor, R. C. J . Chem. Phys. 1953, 21, 1959. (28) McConnell, H. M. J . Chem. Phys. 1956, 24, 764. (29) McConnell, H. M.; Chesnut, D. B. J . Chem. Phys. 1958, 28, 107.
5612 The Journal of Physical Chemistry, Vol. 88, No. 23, 1984
Niibe and Nakamura
I
I"'
' ' I
n
Q
t
-4 -2
I /
0
200
400
600
800
K(N) (ppm) Figure 10. Relation between the Knight shifts for 'H, K(H), and those for 14N,K ( N ) , in sodium-ammonia (A) and potassium-ammonia (0) solutions.
excess electron on a nitrogen nucleus and a proton bound to it via N-H bonding, we can expect a similar linear relation between the electron spin density a t the I4N nuclei and the hyperfine coupling constant of IH, which may be reduced to the relation
m-9 = P m )
(8)
The proportionality constant, 0, is found to be -1/43.3 from the present data for sodium-ammonia solutions. Our recent determination30 of this constant for 14N and 'H of methylamine (CH,NH,) in lithium solutions gives /3 = -1/42.5. A similar value was calculated from the data of Holton et al." This common value of p for the N-H bonds in ammonia and methylamine strongly suggests the presence of an indirect hyperfine coupling between the excess electrons on 14Nand IH, in analogy to the McConnell relation found for aromatic radical^.^^^^^ Next we estimate values of P(N) from the Knight shift data, using the xP, data of Hutchison and Pastor27for dilute solutions and of Lelieur and Rigny" for metal-rich solutions. Values of xP, for solutions around 2 MPM are interpolated4 from these two sets of data. The resulting values of P(N) are plotted against R in Figure 11. A similar curve was obtained for P(H) but is not given here because of much larger experimental scatters due to the smallness of the 'Hshifts. The values of P(Na) in sodiumammonia solutions are also shown in Figure 11. In previous we have shown that the electron spin density on metallic nuclei, 23Naand 7Li, can be explained by the assumption that only unpaired electrons associated strongly with metal ions (monomers) are responsible for the hyperfine coupling in the nonmetallic region. For 'Hand 14N,however, the hyperfine interaction arises from both types of unpaired electrons: solvated electrons and monomer electrons, Using the ratio,f, of the monomer electrons to the total unpaired electrons, P(N) can be expressed as P(N) = P O W )
+ (1 - f)Ps(N)
(9)
where Po(N) and P,(N) are respectively the density of I4N nuclei seen by a monomer electron or a solvated electron. In the analysis for the metal nuclei,"*5the values off have been determined as a function of composition below 2 MPM (or R > 50). Then, using eq 9,we obtained Po(N) = 11 X 10" cmm3and P,(N) = 4 X ~ m - ~The . relation Po(N) > P,(N) may reflect the fact that nitrogen atoms of solvated ammonia molecules are oriented toward the central metal atom in the monomers, while hydrogen atoms are oriented to the center in the solvated electrons. In the dilute solution region, the observed values of P(N) become constant, as shown in Figure 11, while the values of P(Na) decrease mono-
1000
100
10
R Figure 11. Nuclear spin density at an unpaired electron for I4N, P(N), and for 23Na,P(Na).4
tonically with dilution. These behaviors clearly support the existence of two types of the unpaired electrons. At infinite dilution, the free solvated electrons predominate due to the dissociation of the monomers, which causes a constant spin density at the nitrogens and a very small value for the metal nuclei separated from the solvated electrons. Above 2 MPM (R> 50), where f is assumed to be unity," the values of P(N) decrease with metal concentration. In this region, the values of P(Na) are rather constant, as shown in Figure 11. These results indicate a relative decrease of the electron spin density at the nitrogen nuclei, which is not explicable by a simple picture of a delocalized electron in each atomic volume. Spin-Lattice Relaxation Time, As described in the analysis of the Knight shifts, 14N and 'H nuclei are interacting with both types of unpaired electrons, solvated electrons and monomer electrons. A detailed description of the relaxation rates for the proton and nitrogen has been given by LarnberP on the basis of the model given above. According to experiments on the Overhauser e f f e ~ t , ~the , ~hyperfine ~ , ~ ~ interaction is expected to be dominant in the composition range of the present study, from 0.3 MPM to the saturation region. The relaxation rate due to the hyperfine interaction with unpaired electrons for nitrogen nuclei is given by
where A is the hyperfine coupling constant, a is the ratio of the unpaired electrons to the total valence electrons in solutions, T , is the correlation time of the electron-nuclear interaction, and n is the number of solvated ammonia molecules. The subscripts o and s denote respectively the monomer and solvated electron states. Values of A are calculated from the observed values of P ( N ) , using the relation
where yeand yn are the gyromagnetic ratios for the electron and nucleus, respectively. The values of a are determined from the observed electron paramagnetic susceptibility xP,(obsd) and the Curie susceptibility for independent electron spins, xP,(free) a = X&(obsd)/XP,(free)
= xk(obsd) /(A. 2y>NA/4kT)
(12)
As eq 10 contains a number of parameters, we employ here for (30)Niibe, M.; Nakamura, Y.,to be published.
(31) Holton, D. M.; Edwards, P. P.;McFarlane, W.; Wood, B. J . Am.
Chem. SOC.1983, 205, 2104.
(32) Lambert, C. In "Electron in Fluids"; Jortner, J., Kestner, N. R., Us.; Springer-Verlag: West Berlin, 1973; p 57.
N M R of Metal-Ammonia Solutions
0 ' ' 10000 1 '
' '
'an''';
1000
' '
' ' a l l
100
The Journal of Physical Chemistry, Vol. 88, No. 23, I984
8
8
I
.., , 10
,
,
I
R Figure 12. Spin-lattice relaxation rates for 14N in sodium-ammonia solutions at -40 "C. ---, contribution from the hyperfine interaction with paramagnetic electrons, calculated from eq 13.
the sake of simplicity the average values, A, ri, and be for the two types of unpaired electrons. Then, the simplified expression for a nitrogen nuclei is
For protons, the corresponding equation is obtained32if we divide the right-hand side of eq 13 by 9. The observed relaxation rate for nitrogen, l/Tl(N), consists of three contributions, the quadrupolar, nuclear dipolar, and paramagnetic electron contributions: 1/Tl(N) = (l/TI)q + (l/Tl)d -k (l/Tl)e (I4) As mentioned in the Result section, an empirical evaluation of the first two terms in eq 14 is not possible for a wide range of composition. We assumed therefore that, in the very dilute solutions of the present study (0.3-0.6 MPM) values for these two terms are very close to those for pure ammonia. It may be noted that the effect of an increase of the field gradient at 14N would cancel the effect of an increase of viscosity, when metals are added to ammonia. The electronic contribution (1 /Tl)e thus obtained was used for the estimation of the value of ri, using eq 13 together for of the values of T , determined from an analysis of (1 / 23Na.4 We obtained ri = 7 for the average solvation number for the monomer and the solvated electron. On the other hand, for the relaxation rate of 'H we could separate the term (1/Tl), for a wider concentration range. By use of the values of P(H) determined from the Knight shift data and the values of T , deduced from (1 / TI), for 23Na,we obtain ri N 5 for 0.4 to 2 MPM. In view of crude assumptions involved in eq 13, we regard that the average solvation numbers determined from the 14N and 'H relaxations are in reasonable agreement. Pinkowitz and Swift33have reported a much larger value of the solvation number, n = 16-48, for the solvated electron in dilute sodium-ammonia solutions from the line shape analysis of the 'H triplet of ammonia molecules. We think that their analysis is less reliable than the present one because of the many more assumptions involved in their analysis. In fact, Acrivos et al. have reported a value of n = 5.2-5.7 for the number of solvated ammonia molecules around a rubidium metal determined from EXAFS structural analysis of rubidium-ammonia solutions.34 These values are close to those obtained in the present analysis. Using a value of ri = 6 for the concentration range up to 4 MPM, we have calculated the values of (1/ T I ) ,for I4N from eq 13 with the values of T, deduced from the relaxation rates for 23Na. The results are shown in Figure 12 by a dashed line. The curve has a maximum around R = 70, which corresponds well to the (33) Pinkowitz, R. A,; Swift, T. J. J . Chem. Phys. 1971, 54, 2864. (34) Acrivos, J. V.; Hathaway, K.; Robertson, A,; Thompson, A,; Klein, M. P. J . Phys. Chem. 1980, 84, 1206.
5613
maximuxq found for the 1 / T,(N) curve. Thus we can conclude that the maximum of the l/Tl(N) curve is attributed to the cotnribution from the hyperfine interaction with the paramagnetic superimposed on the dominant quadrupolar electrons, (1 / contribution. The magnitude of the peak height is also well reproduced by the calculated value of ( l/Tl)e, as shown in Figure 12. These results may indicate that the analysis based on eq 13, as well as the adopted values of the correlation time, T,, and solvatiqn number, ri, is reasonable. As there is no quadrupolar contribution, the paramagnetic electron contribution ( l/Tl)e is dominant in the 'H relaxation. Thus, the observed large peak around 2 MPM on the l/T,(H) curve (Figure 6) is well explained by the maximum of (1 / Tl)e at this composition. The observed values of l/Tl(H) increase again above 7 MPM. It is noted that the Korringa relation gives only 1/10 of the observed relaxation rates in the concentration range from 7 to 15.5 MPM. We can attribute this increase rather to the skin depth effect, as shown by the following arguement. In highly conducting samples, the diffusion of nuclear spins under investigation from the skin depth region causes an apparent increase in the relaxation rate.35 The skin depth effect becomes important when the diffusion length 1 during the time of the order of the relaxation time, T I ,is comparable with the skin depth 6. The diffusion length 1 = ( D T l ) 1 /was 2 calculated to be 170 pm, if we put TI = 4 s and the diffusion coefficient D = 7 X 1 0-5 cmz s-I for 1H.36 This value is close to the skin depth 6 = 170 pm at 8 MPM and for 90 MHz. Thus, we conclude that the increase of I/Tl(H) in the metal-rich region above 7 MPM is mostly due to this skin depth effect. For 14N, on the other hand, a much shorter relaxation time (Tl = 7 ms) gives a much smaller diffusion length (I N 7 pm) than the skin depth (6 = 280 pm) at 15 MPM and 6.5 MHz. The skin depth effect is, therefore, negligible for I4N over the whole concentration range studied. Temperature Coefficient. We denote the temperature coefficient of a physical quantity Y as y[Yl 2 (a In Y/dT),. For the Knight shift we have
As seen in Figure 5, in the nonmetallic region below 4 MPM, values of y[K(N)] are very close to those of y[K(Na)] and decrease rapidly with increasing metal cqncentration. These values of y[K(N)] are also in good agreement with the temperature coefficient of the paramagnetic susceptibility, y [&(ESR)], determined by the ESR method below 2 MPM.27 From these facts, it is concluded that y[P(X)] is negligibly small in this region. On the other hand, the temperature coefficient of the electron paramagnetic susceptibility determined by the static method", y[xP,(static)], differs significantly from y[xP,(ESR)] or y [K(N)]. We think that the nominal values of y[&(static)] due to Lelieur and Rigny" in the nonmetallic region are not correct, because the diamagnetic contribution due to the formation of spin-paired species may not be well separated from them. In the metallic region, however, values of y[K(N)] are in good agreement with those of y[&(static)]. These values also become closer to the theoretical relation y[x&] = (2/3)a, calculated from the change of the density of states a i the Fermi level due to thermal expansion, where apis the thermal expansion coefficient. The values of y[x&(static)] in the metallic region can be regarded as much more reliable than those in the nonmetallic region, because the diamagnetic species are absent in the metallic region. In this region, values of y[K(Na)] are larger than those of y[&] or y[K(N)]. They are also larger by a factor of 10 to loz than those for typical liquid metals.37 This large temperature coefficient for K(Na) may be attributed to a large temperature dependence of the electron spin density at the metal nuclei. As shown in Figure 5, the temperature coefficient of ( l / T l ) e for 'H in the nonmetallic region is also very close to y[x;(ESR)]. (35) Bloembergen, N. J . Appl. Phys. 1952, 23, 1383. (36) Garroway, A. N.; Cotts, R. M. In "Electrons in Fluids"; Jortner, J., Kestner, N. R., Eds.; Springer-Verlag: West Berlin, 1973; p 213. (37) Shimoji, M. "Liquid Metals"; Academic Press: London, 1977.
J. Phys. Chem. 1984, 88, 5614-5620
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From eq 12 we have y [ a ] = y[&] + 1/T, and thus TI-'),] N y [ a ]at -55 "C. This indicates that the temperature variation of (l/Tl)e for 'H is mainly due to that of a in eq 13 or, in other words, the relaxation rate increases with an increase in the number of paramagnetic electrons due to the dissociation of the spin-paired diamagnetic species with increasing temperature.
Conclusion From the observed linear relation between the Knight shifts of I4N and 'H, the origin of the negative shifts of 'H of ammonia molecules in metal-ammonia solutions can be attributed to the indirect hyperfine interaction between the excess electrons on I4N
nuclei and 'H through the N-H bond. The observed maximum in the curves for the relaxation rates of 14Nand 'H is explained by the contribution from the hyperfine interaction with the excess electrons. The average solvation numbers of the solvated electrons and monomers is determined to be rf = 5-7 from the present N M R data. The temperature dependence of the Knight shifts of I4N is mainly due to the temperature variation of the paramagnetic electron susceptibility over the whole concentration range studied.
Acknowledgment. The authors thank Mr. S. Shimokawa of N M R Laboratory for useful suggestions. Registry No. NH3, 7664-41-7; Na, 7440-23-5; K, 7440-09-7.
Vibrational Study of the Dynamics of n -Decylammonium Chains in the Perovsklte-Type Layer Compound (C10H2,NH,)2CdCI, L. Ricard, M. Rey-Lafon,* Laboratoire de Spectroscopie Infrarouge, LA 124, UniversitZ de Bordeaux I , 351, Cours de la Libdration, 33405 Talence Cddex, France
and C. Biran Laboratoire des Composb Organiques du Silicium et de I'Etain, LA 35, Universitd de Bordeaux I, 351, Cours de la Libzration, 33405 Talence CZdex, France (Received: April 3, 1984; In Final Form: June 19, 1984)
The perovskite-typecompound (CloH21NH3)2CdC14 (CloCd) exhibits two phase transitions, at 35 and 39 "C, connected with reorientations of the whole decylammonium chains and melting of the hydrocarbon parts. A temperature-dependencestudy of the infrared and Raman spectra of CloCdand three selectively deuterated derivatives, CloCd-l, I d 2 , CloCd-2,2-d2,and CloCd-4,4-d2,provides evidence for coupling between the two types of chain dynamics and allows for a more precise description of the conformational disorder of decylammonium cations in the high-temperature phases.
Introduction The perovskite-type layer compounds of general formula (CnH2n+lNH3)2MC14 (short notation, C,M) have drawn the attention of numerous scientists during the past 10 They crystallize in nearly isolated inorganic sheets constituted of corner-sharing MC16 octahedra with a divalent metal ion in their center (M = Cd2+,MnZ+,Cuz+,...) which form a two-dimensional solid matrix. The cavities between octahedra are occupied by the NH3 polar heads of the n-alkylammonium groups which are involved in NH-..Cl hydrogen bonds. Thus, the metallic sheets are sandwiched between hydrocarbon layers. Both van der Waals interactions between the alkyl ends and Coulomb forces between the positively charged organic ions and the negatively charged octahedra account for the interlayer bonding.I0 These compounds show a large variety of structural phase transitions'-I0 governed by the dynamics of the alkylammonium (1) Peterson, E. R.; Willett, R. D. J . Chem. Phys. 1972, 56, 1879. (2) Chapuis, G.; Arend, H.; Kind, R. Phys. Status Solidi A 1975,31,449. (3) Heger, G.; Mullen, D.; Knorr, K. Phys. Status Solidi A 1975,31,455. (4) Chapuis, G. Phys. Status Solidi A 1977, 43, 203. (5) Depmeier, W. Acta Crystallogr.,Sect. B 1977, 6'33, 3713. (6) Kind, R. Phys. Status Solidi A 1977, 44, 661. (7) Blinc, R.; peks, B.; Kind, R. Phys. Rev. E Solid Srare 1978,17, 3409. (8) Chapuis, G. Acta Crystallogr., Sect. B 1978, 834, 1506. (9) Kind, R.; Plbko, S.; Arend, H.; Blinc, R.; geks, B.; Seliger, J.; Loiar, B.; Slale, J.; Levstik, A.; FilipiE, C.; 2agar, V.; Lahajnar, G.; Milia, F.; Chapuis, G.J . Chem. Phys. 1979, 71, 2118. (10) Geick, R.; Strobel, K. J . Phys. C.1979, 12, 27.
0022-3654/84/2088-5614$01 .50/0
groups and by the "rotations" of the MC16 octahedra about the three crystallographic axes. Up to now, these structural phase transitions have been divided into two classes: (a) order-disorder transitions of the rigid alkylammonium chains and (b) conformational transitions leading to a partial "melting" of the hydrocarbon part of the chains. This second type exists only if the number of carbon atoms is large enough ( n 1 4). Of the compounds which undergo these two kinds of phase transitions, (CloH21NH3)2CdC14 (Cl0Cd) has been the most extensively ~ t u d i e d . The ~ results of different techniques (X-ray diffraction, calorimetric, and dielectric measurements, 'H N M R spin-lattice relaxation and second-moment investigations, 35Cl and I4N quadrupole resonance spectroscopy: and I3C N M R measurements") have shown that CloCdundergoes two first-order phase transitions at T,, = 35 OC and T,, = 39 "C. The structure of the low-temperafure phase (LT) is ordered. Its projections on the (b$) and (ci,b) planes are reproduced in Figure 1. Alkylammonium chain axes are tilted by f40° with respect to the normal to the layers ( E axis) and form a zigzag arrangement along it. There are two types of inequivalent chains (A and B) which are packed together. They correspond to almost extended conformations with only a single gauche configuration about the bond between the first and the second carbon atoms for A chains and between the second and the third ones for B chains. 'H N M R spin-lattice relaxation investigations show the existence of a slow process in the intermediate-temperature phase (11) Blinc, R.; Burgar, M. I.; Rutar, V.; 2ek3, B.; Kind, R.; Arend, H.; Chapuis, G . Phys. Rev.Lett. 1979, 43, 1679.
0 1984 American Chemical Society
