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A Study of Solvation-Shell Symmetry in Electrolyte Solutions Using Quadrupolar NMR Relaxation of the Nuclei of Monoatomic Ions
JOURNAL OF MAGNETIC RESONANCE, ARTICLE NO.
Series A 123, 1–6 (1996)
0207
A Study of Solvation-Shell Symmetry in Electrolyte Solutions Using Quadrupolar NMR Relaxation of the Nuclei of Monoatomic Ions V. I. CHIZHIK, I. S. PODKORYTOV, A. P. KAIKKONEN,
AND
V. I. MIKHAILOV
St. Petersburg State University, 198904 St. Petersburg, Russia Received June 5, 1995; revised July 15, 1996
The spin–lattice relaxation rates of 7Li, 23Na, 27Al, 71Ga, and La nuclei in electrolyte solutions have been investigated as functions of the isotopic composition of the solvent. The results show that quadrupolar relaxation of the nuclei of monoatomic ions is extremely sensitive to the symmetry of the solvation shells. The data are compared to the results for the 2H and 17O nuclei of the solvent molecules and the 14N nucleus of the nitrate anion. A semiquantitative description of the observed effects is given. q 1996 Academic Press, Inc.
EXPERIMENTAL
139
Spin–lattice relaxation rates, T 01 1 , were measured using a homebuilt relaxometer with operating frequencies of 8, 16, 20, and 60 MHz for the 2H, 7Li, 23Na, and 27Al resonances, and the Bruker AM-500 spectrometer for the 14N, 17O, 27Al, 71 Ga, and 139La resonances. The pulse sequence used was 1807 — t —907. Single-exponential relaxation functions were observed in all experiments. The precision of the measurements depended on the salt concentration and resonance frequency, but it was not worse than {10%. Signals were accumulated, as needed, to obtain proper signal-to-noise ratios. The error limits of the sample temperature were within {17. The samples were prepared gravimetrically using salts of the highest chemical purity. All salt and acid concentrations are given in units of aquamolality, m, i.e., moles of solute per 55.5 moles of solvent. Samples of different isotopic composition were obtained by mixing two solutions of equal salt concentration in ordinary and deuterated solvents. The degree of deuteration was 99.8% for water, 99.8% for acetone, 99.7% for methanol-d4 , and 99.5% for the hydroxyl group of methanol-d1 . The water content of the organic solvents was checked by high-resolution NMR and did not exceed 2 and 0.5% for methanol and acetone, respectively. Additional measurements were carried out with twofold amounts of water in organic solvents. In these limits no marked influence of water on the effects discussed in this work was observed.
INTRODUCTION
The investigation of ion solvation-shell regularity is very complicated, because of the lack of suitable research methods. Even X-ray and neutron scattering data are difficult to interpret for liquid media. Solving the problem becomes especially hard in the case of labile complexes characterized by fast exchange of ligands. Investigations of the magnetic relaxation processes of the nuclei of ions in electrolyte solutions give information about the microstructure in the immediate vicinity of the ions. A large number of the nuclei of monoatomic ions relax via the quadrupolar interaction (nuclear spin I ú 12 ). An initial consideration of the problem by Hertz (1) and Valiev (2) was made on the basis of an electrostatic model, in which the fluctuating gradients of the electric field were created by the dipoles of the solvent molecules and the point charges of the counterions. As there were considerable discrepancies between theory and experiment, it was necessary to improve the description of the relaxation process. One of the authors suggested (3, 4) that the existence of solvation-shell symmetry and its distortion due to thermal motion of the ligands should be taken into account. Somewhat later, similar concepts were developed by Marshall (5), Hertz (6), and Takahashi (7). Using this idea, it was possible to explain the strong influence of hydrolysis on the 27Al 3/ and 71Ga 3/ quadrupolar relaxation in aqueous solutions (8–10). The extreme sensitivity of quadrupolar relaxation to the symmetry of hydration shells was demonstrated in previous investigations (9, 10) of 27Al 3/ and 71Ga 3/ relaxation in H2O/D2O solutions. This paper presents some new data on this subject.
QUADRUPOLAR RELAXATION OF NUCLEI OF MONOATOMIC IONS
The spin–lattice relaxation rate, T 01 1 , is given by (11, 12) 1 1 Å∑ Å ∑ Akn Jkn ( vn ), T1 k T 1k k ,n
where the values Akn are proportional to the mean square of the interaction energy for the ‘‘k’’ mechanism of relaxation. 1
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where t is the correlation time for the random fluctuations and characterizes the reorientation time of the solvent molecules located near the ion. If the thermal motion is fast, i.e., v 2t 2 ! 1, then J( v ) É 2t and 1 Å At. T1
FIG. 1. The time-dependent electric-field gradient q according to the (a) Hertz–Valiev and (b) ‘‘pulse’’ gradient models.
The exponential correlation function presupposes an entirely random movement of the particles in the solution, but this assumption is inconsistent with the concept of symmetrical hydration (or solvation) shells. In completely symmetrical complexes, the electric-field gradient vanishes, but it arises during the time intervals when the solvation-shell symmetry is distorted by the thermal motion of the ligands (see Fig. 1b). The spectral density of the ‘‘pulse’’ gradient is reduced (3, 4) by the factor ( D / t ) 2 , and the relaxation rate T 01 1sym of the ion nuclei is 1
In the case of quadrupolar relaxation Akn are proportional to (eqQ) 2 , where eqQ is the quadrupole coupling constant, which is a product of the quadrupolar moment eQ of a nucleus and the gradient q of the electric field. Jkn ( vn ) is the spectral density of the internal inhomogeneous electric field, which fluctuates due to the thermal motion of the molecules and ions in the solution, and vn is the frequency of transitions permitted for the relaxation processes. The spectral densities, Jkn , depend on the velocity and on the type of thermal motion. To a first approximation the total relaxation rate of the nuclei of ions can be expressed as 1 1 1 Å / , T 1 T 1solv T 1ion
[2]
where the times T 1solv and T 1ion describe the relaxation of the nuclei due to the interaction with the solvent molecules and the other ions, respectively. The dependence of the relaxation rate on the electrolyte concentration is mainly determined by the second term in Eq. [2], and it is possible to consider only the first term for low (or in many cases moderate) concentrations. In the following, only the first term in Eq. [2] is discussed, and the subscript ‘‘solv’’ is omitted. A typical time-dependent electric-field gradient according to the Hertz–Valiev model (1, 2) is shown pictorially in Fig. 1a. A simple exponential correlation function was used for the calculation of the spectral density of the fluctuating inhomogeneous electric field. In this case the spectral density is given by J( v ) Å
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T 1sym
Å At
SD D t
2
,
[5]
where t is the average time interval between the successive symmetry distortions, and D is the average duration of the distortion. In contrast to the Hertz–Valiev model, the solvent molecules should be approximated by a system of charges, but not by point dipoles, because of the strong dependence of the electric-field gradient on the distance. In this case the relaxation rate of nuclei with an arbitrary spin I is given by the expression (4, 15)
F GS D
9 bzeQ 2I / 3 1 Å n1 2 T 1 20 I (2I 0 1) \r 3
2
D t1
2
t1 .
[6]
In this equation n1 is the number of neighboring molecules, i.e., the coordination number of the ion, z is the effective charge situated in the solvent molecule at a distance r from the nucleus, b is the antishielding and polarization factor (1), eQ is the quadrupole moment of the nucleus, and t1 is the time interval between the successive symmetry distortions due to tumbling of a single molecule in the solvation shell. In Fig. 1b, t is equal to t1 /n1 . Equation [6] may be used to describe the quadrupolar relaxation of the nuclei of monoatomic ions in dilute aqueous electrolyte solutions. A comparison of experimental data for unicharged ions with the relaxation rates calculated from Eq. [6] gives the D / t1 values; see Table 1. The results for multicharged ions will be published later, when the complete set of parameters in Eq. [6] is analyzed. The experimental values of the spin– lattice relaxation rates of the 35Cl, 81Br, 87Rb, and 127I nuclei were taken from Refs. (13, 14). The parameters n1 and t1
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TABLE 1 Values of D/t, Calculated According to Eq. [6] at 227C Nucleus
1/T1exp , (s01)
n1
t1/t0
r (nm)
z/e
D/t1
D/ t
Li/ Na/ 87 Rb/ 35 Cl0 81 Br0 127 0 I
0.03 17 420 40 1050 5300
4 6 8 4 4 4
2.3 1.6 0.9 1.4 0.9 0.8
0.19 0.23 0.28 0.20 0.21 0.23
02.0 02.0 02.0 /0.5 /0.5 /0.5
0.10 0.12 0.11 0.16 0.20 0.25
0.40 0.72 0.88 0.64 0.80 1.00
7
23
Note. t0 is the reorientation time of the molecules in pure water, and e is the unit charge.
were taken from Refs. (4, 15); the charges z and distances r were obtained using the new system of ionic radii (16, 17) and the model for the water molecule discussed in (18). The ratio D / t1 increases with the ionic radius and decreases with the charge. It should be noted that the D / t1 values are close to those obtained by neutron scattering in water (18). The fact that D / t1 ! 1 provides additional evidence for the concept of the quasicrystalline structure of water and aqueous electrolyte solutions.
states, which is realized in the systems investigated, one can write (22, 23) pi 1 Å∑ , T1 i T 1i
[8]
where T 1i is the relaxation time of the nucleus in the substructure marked by index i, and pi is the relative concentra-
INFLUENCE OF THE ISOTOPIC COMPOSITION OF SOLVENTS ON THE QUADRUPOLAR RELAXATION OF NUCLEI OF IONIC SPECIES
As already mentioned, quadrupolar relaxation of nuclei of strongly hydrated monoatomic ions is very sensitive to the isotopic composition of the water (9, 10). Figures 2 and 3 present the results of measurements of the 27Al 3/ and 71 Ga 3/ relaxation rates in H2O/D2O mixtures over a wide temperature range. The data reflect the dependences of the relative relaxation rates, T 10 /T 1 , on the relative molal concentration, x, of deuterons in solution, where T 10 is the relaxation time in pure H2O, and x is the mole fraction of deuterated solvent: xÅ
[D2O] . [H2O] / [D2O]
[7]
All curves in Figs. 2 and 3 have distinguishable maxima. To explain the shape of the curves it is necessary to take into account several effects. The data of previous works (3– 10, 19–21) show that the monoatomic ions possess symmetrical hydration shells in aqueous solutions. It is well known that the first layers of the hydration shells of the Al 3/ and Ga 3/ ions consist of six water molecules arranged octahedrally. In pure H2O or D2O a single type of solvent molecule is present, but the mixtures contain three types of molecules (H2O, D2O, and HDO). In solutions the ions can be involved in a variety of surroundings. In the case of fast exchange of the ions among all possible
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FIG. 2. The dependence of the 27Al relaxation rates, 1/T 1 , on the isotopic composition of water in 0.02 m Al(NO3 )3 solution with 0.07 m HNO3 added to suppress hydrolysis. The resonance frequency is 130 MHz. The straight line passes through the data for the relaxation rate, 1/ T s1 , of 17O in the water molecules (open triangles) and 14N in the anions (closed triangles) at 657C (natural abundance of both nuclei). T 10 and T s10 are the relaxation times of the nuclei of the ions and the solvent molecules, respectively, in pure H2O; x is the mole fraction of deuterated component in the solvent (see Eq. [7]).
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to viscosity variations can be predicted from the relaxation times, T s1 , of the solvent molecule nuclei, 2H and 17O. These nuclei also relax via quadrupolar interactions, but in this case the electric-field gradient, q, is determined mainly by the electronic structure of the solvent molecule, and the symmetry of the solvation shell has no influence on the relaxation process. Therefore, the relaxation times can be described by expressions similar to Eq. [4] and Eq. [8]. This means that the relaxation rates of the solvent nuclei reflect an average molecular mobility in solution, and 1/T s1 is proportional to the viscosity. It is well known that in the H2O/D2O mixtures the density, viscosity, and dielectric constant, as well as the relaxation rates of 2H and 17O nuclei, depend linearly on the mole fraction x of D2O, and therefore, T s10 Å 1 / bx, T s1 FIG. 3. The dependence of the 71Ga relaxation rate, 1/T 1 , on the isotopic composition of water in 0.05 m Ga(NO3 )3 solution with 0.5 m HNO3 added to suppress hydrolysis. The resonance frequency is 152.5 MHz. The straight line passes through the data for the resonances of 17O in the water molecules (open triangles) and 14N in the anions (closed triangles) at 707C (natural abundance of both nuclei). Other symbols are as in Fig. 2.
tion of this substructure in the solution. If the exchange is fast, i.e., the lifetime of the nuclei in each substructure is less than the corresponding nuclear-magnetic relaxation time, Eq. [8] is valid for any exchange mechanism (23). Various symmetrical and asymmetrical ionic environments are expected to exist in H2O/D2O mixtures, but to a first approximation, Eq. [8] can be rewritten as psym pnon 1 Å / , T 1 T 1sym T 1non
[9]
or, taking into account the relation psym / pnon Å 1, as
S
1 1 1 1 Å / pnon 0 T 1 T 1sym T 1non T 1sym
D
,
[10]
where the subscripts ‘‘sym’’ and ‘‘non’’ stand for the appropriate complex types. It is known from previous works (5– 10, 19, 20) that T 1non is markedly smaller than T 1sym . The concentration dependence of the probability pnon can be expressed as pnon Å ax(1 0 x),
[11]
where a is a constant. The concentration dependence of the relaxation rates due
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[12]
where T s10 is the relaxation time of nuclei in pure H2O, and b is a constant. Indeed, the relaxation rates of the 2H and 17 O nuclei demonstrate a linear dependence on x for all systems investigated, and Eq. [10] can be rewritten as T 10 Å T1
F
S
1 / pnon
T 10 01 T 1non
DG
(1 / bx).
[13]
Summarizing the above, we conclude that the concentration dependence of the relaxation rate of the ion nuclei can be described by T 10 Å [1 / cx(1 0 x)](1 / bx), T1
[14]
where c is a constant depending parametrically on temperature via T 10 and T 1non . The experimental data are fitted well by Eq. [14]. It is obvious that the maxima on the plots in Figs. 2 and 3 are determined by the second term in Eq. [10]. The magnitude of the maximum depends on the difference between T 1sym and T 1non . The difference is expected to be smaller at high temperatures, due to the decrease of hydration shell symmetry in the cases when x is equal to 0 or 1, and this effect is observed in experiments. The appearance of a maximum cannot be attributed to hydrolysis effects, because (i) the samples contain the proper amount of acid (8, 10, 20), and (ii) the influence of hydrolysis should be more pronounced at high temperature. The isotope effect discussed here can be observed over a wide range of salt concentrations, and was first observed for 1 m aqueous AlCl3 (9). As can be seen from Eqs. [13] and [14], the relative relaxation rate, T 10 /T 1 , is determined by the structure of the
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QUADRUPOLAR RELAXATION AND SOLVATION OF MONOATOMIC IONS
FIG. 4. The dependence of the 139La relaxation rate, 1/T 1 , on the isotopic composition of water in 0.05 m La(NO3 )3 solution at 37C. The resonance frequency is 70.6 MHz. Triangles represent data for 17O resonance in the water molecules at natural abundance of the isotope. Other symbols are as in Fig. 2.
ionic solvation shells, but does not depend on the quadrupole moment eQ of the nuclei investigated. In contrast to the data for the 27Al 3/ and 71Ga 3/ resonances, the plot of 139La 3/ relaxation rate versus concentration (Fig. 4) does not show an extremum. This fact requires some additional consideration, because two possible explanations of the experimental data can be proposed. The first, for the absence of a maximum, could be weak hydration of the La 3/ ion, but this is scarcely probable, considering the high charge and small radius of the ion. Another and more attractive explanation for the linear dependence of the 139La 3/ relaxation rate on the D2O content is a low initial symmetry of the La 3/ hydration shell. It is very plausible that the coordination numbers of the lanthanide ions are equal to nine, and this does not allow the formation of a highly symmetrical arrangement, such as an octahedron or tetrahedron (24). Another result of this type was observed for the 23Na / resonance. The hydration shell of the sodium cation contains six water molecules, but it was impossible to obtain the extremum effects in H2O/D2O solutions of sodium salt. Probably the ratio D / t for the sodium ion is close to unity (see Table 1), and the symmetry effects cannot be observed in aqueous solutions even at low temperatures (down to the freezing point). However, a greater decrease of temperature is possible for nonaqueous solutions. Data for NaClO4 in the acetone/acetone-d6 system at 030 and 0607C are shown in Fig. 5. The deuteron resonance data demonstrate the absence of marked concentration dependence for the average mobility of the solvent molecules, but the isotope effect considered here arises again and can easily be observed. Figure 6 presents the data for the 7Li / resonance in CH3OD/CD3OD. The solvation shell of the lithium cation in methanol usually consists of four solvent molecules in a regular tetrahedron and is characterized by high symmetry.
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FIG. 5. The dependence of the relaxation rates, 1/T 1 , of 23Na (circles) and 2H (triangles) on the isotopic composition of acetone in 1 m NaClO4 solution. The resonance frequency is 8 MHz for both nuclei. Other symbols are as in Fig. 2.
on the Therefore, a maximum for the dependence of T 01 1 CD3OD content was expected. The effect was indeed observed for methanol solutions, but only at very low temperatures. It is probable that the overall change in T 10 /T 1 of the plot in Fig. 6 is due to the contribution from the dipole– dipole relaxation mechanism, which decreases with the magnetic dilution as the content of deuterated component increases. The d4 and d1 methanols were used to reduce the influence of dipole–dipole interaction between the 7Li / nuclei and the protons in the solution. Formally, the dipole– dipole contribution can be described in the same way as the viscosity influence in Eq. [13], i.e., by a (1 / bx) term, but with a negative value for the coefficient b.
FIG. 6. The dependence of the 7Li relaxation rate, 1/T 1 , on isotopic composition for 1 m solutions of LiClO4 in CH3OD/CD3OD. The resonance frequency is 8 MHz (closed circles) and 20 MHz (open circles). Other symbols are as in Fig. 2.
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CONCLUSION
Quadrupolar relaxation of the nuclei of monoatomic ions is quite sensitive to solvation-shell symmetry. The results obtained in this study provide clear evidence that in some cases the solvation shells of monoatomic ions have high symmetry. Distortions of symmetry have been detected, when some of the solvent molecules are replaced by their deuterated analogues. The maxima in the concentration dependences of the quadrupolar relaxation rates were not observed for nuclei in polyatomic ions, for example, the 14N resonance data for the NO 30 anion shown in Figs. 2 and 3. In this case the electric-field gradient is determined by the electronic structure of the ions, and the symmetry of the solvation shells has no influence on the relaxation process. The observed isotope effects can be used to investigate the degree of symmetry in the solvation shells of monoatomic ions. This investigation has presented results on the behavior of cation solvation shells. The study of this effect for monoatomic anions is in progress.
4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16. 17. 18.
ACKNOWLEDGMENTS 19.
The authors are grateful to Professor J. H. Strange for his critical reading of the manuscript and stimulating discussions. Financial support of the Russian Foundation for Basic Research (Grant 94-03-09554) is gratefully acknowledged.
20.
REFERENCES
21. 22. 23.
1. H. G. Hertz, Z. Electrochem. 65, 20 (1961). 2. K. A. Valiev, Zh. Strukt. Khim. 3, 653 (1963). [In Russian] 3. V. I. Chizhik, Zh. Strukt. Khim. 8, 350 (1967). [In Russian]
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24.
V. I. Chizhik, Proc. 16th Congr. AMPERE, Buchurest, 711 (1971). A. G. Marshall, J. Chem. Phys. 52, 2527 (1970). H. G. Hertz, Ber. Bunsen-Ges. Phys. Chem. 77, 531 (1973). A. Takahashi, J. Phys. Soc. Jpn. 43, 968 (1977). A. W. Akitt and J. M. Elders, J. Chem. Soc. Faraday Trans. 1 81, 1923 (1985). V. I. Chizhik and V. I. Mikhailov, Vestn. Leningr. Univ. Fiz.-Khim. 16, 81 (1982). [In Russian] I. S. Podkorytov and V. I. Chizhik, Vestn. St. Petersburg Fiz.-Khim. 11, 73 (1993). [In Russian] A. Abragam, ‘‘The Principles of Nuclear Magnetism,’’ Oxford Univ. Press, London/New York, 1961. C. P. Slichter, ‘‘Principles of Magnetic Resonance,’’ Springer-Verlag, Berlin/New York, 1980. H. G. Hertz, M. Holz, G. Keller, H. Versmold, and C. Yoon, Ber. Bunsen-Ges. Phys. Chem. 78, 493 (1974). H. G. Hertz, M. Holz, R. Klute, G. Stalidis, and H. Versmold, Ber. Bunsen-Ges. Phys. Chem. 78, 24 (1974). V. I. Chizhik, ‘‘Nuclear Magnetic Relaxation,’’ St. Petersburg Univ. Press, St. Petersburg, 1991. [In Russian] B. S. Gourary and F. J. Adrian, Solid State Phys. 10, 144 (1960). R. D. Shannon, Acta Crystallogr. A 32, 751 (1976). D. Eisenberg and W. Kauzmann, ‘‘The Structure and Properties of Water,’’ Oxford Univ. Press, New York, 1969. L. Helm and H. G. Hertz, Z. Phys. Chem. (Wiesbaden) 127, 23 (1981). J. Kodweiß, D. Ko¨hnlein, G. Ko¨ssler, O. Lutz, W. Messner, K. R. Mohn, A. Nolle, G. Nothaft, P. Ruppert, N. Steinhauser, D. Zepf, E. Haid, and W. Schich, Z. Naturforsch. A 41, 471 (1986). M. Holz, Prog. NMR Spectrosc. 18, 327 (1986). J. R. Zimmerman and W. E. Brittin, J. Phys. Chem. 61, 1328 (1957). D. D. Skirda, V. A. Sevryugin, and A. I. Maklakov, Khim. Fiz. 2, 1499 (1983). [In Russian] V. I. Chizhik, C. Cabal, M. N. Rodnikova, and A. Guzman, Koord. Khim. 14, 349 (1988). [In Russian]
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Series A 123, 1–6 (1996)
0207
A Study of Solvation-Shell Symmetry in Electrolyte Solutions Using Quadrupolar NMR Relaxation of the Nuclei of Monoatomic Ions V. I. CHIZHIK, I. S. PODKORYTOV, A. P. KAIKKONEN,
AND
V. I. MIKHAILOV
St. Petersburg State University, 198904 St. Petersburg, Russia Received June 5, 1995; revised July 15, 1996
The spin–lattice relaxation rates of 7Li, 23Na, 27Al, 71Ga, and La nuclei in electrolyte solutions have been investigated as functions of the isotopic composition of the solvent. The results show that quadrupolar relaxation of the nuclei of monoatomic ions is extremely sensitive to the symmetry of the solvation shells. The data are compared to the results for the 2H and 17O nuclei of the solvent molecules and the 14N nucleus of the nitrate anion. A semiquantitative description of the observed effects is given. q 1996 Academic Press, Inc.
EXPERIMENTAL
139
Spin–lattice relaxation rates, T 01 1 , were measured using a homebuilt relaxometer with operating frequencies of 8, 16, 20, and 60 MHz for the 2H, 7Li, 23Na, and 27Al resonances, and the Bruker AM-500 spectrometer for the 14N, 17O, 27Al, 71 Ga, and 139La resonances. The pulse sequence used was 1807 — t —907. Single-exponential relaxation functions were observed in all experiments. The precision of the measurements depended on the salt concentration and resonance frequency, but it was not worse than {10%. Signals were accumulated, as needed, to obtain proper signal-to-noise ratios. The error limits of the sample temperature were within {17. The samples were prepared gravimetrically using salts of the highest chemical purity. All salt and acid concentrations are given in units of aquamolality, m, i.e., moles of solute per 55.5 moles of solvent. Samples of different isotopic composition were obtained by mixing two solutions of equal salt concentration in ordinary and deuterated solvents. The degree of deuteration was 99.8% for water, 99.8% for acetone, 99.7% for methanol-d4 , and 99.5% for the hydroxyl group of methanol-d1 . The water content of the organic solvents was checked by high-resolution NMR and did not exceed 2 and 0.5% for methanol and acetone, respectively. Additional measurements were carried out with twofold amounts of water in organic solvents. In these limits no marked influence of water on the effects discussed in this work was observed.
INTRODUCTION
The investigation of ion solvation-shell regularity is very complicated, because of the lack of suitable research methods. Even X-ray and neutron scattering data are difficult to interpret for liquid media. Solving the problem becomes especially hard in the case of labile complexes characterized by fast exchange of ligands. Investigations of the magnetic relaxation processes of the nuclei of ions in electrolyte solutions give information about the microstructure in the immediate vicinity of the ions. A large number of the nuclei of monoatomic ions relax via the quadrupolar interaction (nuclear spin I ú 12 ). An initial consideration of the problem by Hertz (1) and Valiev (2) was made on the basis of an electrostatic model, in which the fluctuating gradients of the electric field were created by the dipoles of the solvent molecules and the point charges of the counterions. As there were considerable discrepancies between theory and experiment, it was necessary to improve the description of the relaxation process. One of the authors suggested (3, 4) that the existence of solvation-shell symmetry and its distortion due to thermal motion of the ligands should be taken into account. Somewhat later, similar concepts were developed by Marshall (5), Hertz (6), and Takahashi (7). Using this idea, it was possible to explain the strong influence of hydrolysis on the 27Al 3/ and 71Ga 3/ quadrupolar relaxation in aqueous solutions (8–10). The extreme sensitivity of quadrupolar relaxation to the symmetry of hydration shells was demonstrated in previous investigations (9, 10) of 27Al 3/ and 71Ga 3/ relaxation in H2O/D2O solutions. This paper presents some new data on this subject.
QUADRUPOLAR RELAXATION OF NUCLEI OF MONOATOMIC IONS
The spin–lattice relaxation rate, T 01 1 , is given by (11, 12) 1 1 Å∑ Å ∑ Akn Jkn ( vn ), T1 k T 1k k ,n
where the values Akn are proportional to the mean square of the interaction energy for the ‘‘k’’ mechanism of relaxation. 1
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where t is the correlation time for the random fluctuations and characterizes the reorientation time of the solvent molecules located near the ion. If the thermal motion is fast, i.e., v 2t 2 ! 1, then J( v ) É 2t and 1 Å At. T1
FIG. 1. The time-dependent electric-field gradient q according to the (a) Hertz–Valiev and (b) ‘‘pulse’’ gradient models.
The exponential correlation function presupposes an entirely random movement of the particles in the solution, but this assumption is inconsistent with the concept of symmetrical hydration (or solvation) shells. In completely symmetrical complexes, the electric-field gradient vanishes, but it arises during the time intervals when the solvation-shell symmetry is distorted by the thermal motion of the ligands (see Fig. 1b). The spectral density of the ‘‘pulse’’ gradient is reduced (3, 4) by the factor ( D / t ) 2 , and the relaxation rate T 01 1sym of the ion nuclei is 1
In the case of quadrupolar relaxation Akn are proportional to (eqQ) 2 , where eqQ is the quadrupole coupling constant, which is a product of the quadrupolar moment eQ of a nucleus and the gradient q of the electric field. Jkn ( vn ) is the spectral density of the internal inhomogeneous electric field, which fluctuates due to the thermal motion of the molecules and ions in the solution, and vn is the frequency of transitions permitted for the relaxation processes. The spectral densities, Jkn , depend on the velocity and on the type of thermal motion. To a first approximation the total relaxation rate of the nuclei of ions can be expressed as 1 1 1 Å / , T 1 T 1solv T 1ion
[2]
where the times T 1solv and T 1ion describe the relaxation of the nuclei due to the interaction with the solvent molecules and the other ions, respectively. The dependence of the relaxation rate on the electrolyte concentration is mainly determined by the second term in Eq. [2], and it is possible to consider only the first term for low (or in many cases moderate) concentrations. In the following, only the first term in Eq. [2] is discussed, and the subscript ‘‘solv’’ is omitted. A typical time-dependent electric-field gradient according to the Hertz–Valiev model (1, 2) is shown pictorially in Fig. 1a. A simple exponential correlation function was used for the calculation of the spectral density of the fluctuating inhomogeneous electric field. In this case the spectral density is given by J( v ) Å
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[4]
T 1sym
Å At
SD D t
2
,
[5]
where t is the average time interval between the successive symmetry distortions, and D is the average duration of the distortion. In contrast to the Hertz–Valiev model, the solvent molecules should be approximated by a system of charges, but not by point dipoles, because of the strong dependence of the electric-field gradient on the distance. In this case the relaxation rate of nuclei with an arbitrary spin I is given by the expression (4, 15)
F GS D
9 bzeQ 2I / 3 1 Å n1 2 T 1 20 I (2I 0 1) \r 3
2
D t1
2
t1 .
[6]
In this equation n1 is the number of neighboring molecules, i.e., the coordination number of the ion, z is the effective charge situated in the solvent molecule at a distance r from the nucleus, b is the antishielding and polarization factor (1), eQ is the quadrupole moment of the nucleus, and t1 is the time interval between the successive symmetry distortions due to tumbling of a single molecule in the solvation shell. In Fig. 1b, t is equal to t1 /n1 . Equation [6] may be used to describe the quadrupolar relaxation of the nuclei of monoatomic ions in dilute aqueous electrolyte solutions. A comparison of experimental data for unicharged ions with the relaxation rates calculated from Eq. [6] gives the D / t1 values; see Table 1. The results for multicharged ions will be published later, when the complete set of parameters in Eq. [6] is analyzed. The experimental values of the spin– lattice relaxation rates of the 35Cl, 81Br, 87Rb, and 127I nuclei were taken from Refs. (13, 14). The parameters n1 and t1
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TABLE 1 Values of D/t, Calculated According to Eq. [6] at 227C Nucleus
1/T1exp , (s01)
n1
t1/t0
r (nm)
z/e
D/t1
D/ t
Li/ Na/ 87 Rb/ 35 Cl0 81 Br0 127 0 I
0.03 17 420 40 1050 5300
4 6 8 4 4 4
2.3 1.6 0.9 1.4 0.9 0.8
0.19 0.23 0.28 0.20 0.21 0.23
02.0 02.0 02.0 /0.5 /0.5 /0.5
0.10 0.12 0.11 0.16 0.20 0.25
0.40 0.72 0.88 0.64 0.80 1.00
7
23
Note. t0 is the reorientation time of the molecules in pure water, and e is the unit charge.
were taken from Refs. (4, 15); the charges z and distances r were obtained using the new system of ionic radii (16, 17) and the model for the water molecule discussed in (18). The ratio D / t1 increases with the ionic radius and decreases with the charge. It should be noted that the D / t1 values are close to those obtained by neutron scattering in water (18). The fact that D / t1 ! 1 provides additional evidence for the concept of the quasicrystalline structure of water and aqueous electrolyte solutions.
states, which is realized in the systems investigated, one can write (22, 23) pi 1 Å∑ , T1 i T 1i
[8]
where T 1i is the relaxation time of the nucleus in the substructure marked by index i, and pi is the relative concentra-
INFLUENCE OF THE ISOTOPIC COMPOSITION OF SOLVENTS ON THE QUADRUPOLAR RELAXATION OF NUCLEI OF IONIC SPECIES
As already mentioned, quadrupolar relaxation of nuclei of strongly hydrated monoatomic ions is very sensitive to the isotopic composition of the water (9, 10). Figures 2 and 3 present the results of measurements of the 27Al 3/ and 71 Ga 3/ relaxation rates in H2O/D2O mixtures over a wide temperature range. The data reflect the dependences of the relative relaxation rates, T 10 /T 1 , on the relative molal concentration, x, of deuterons in solution, where T 10 is the relaxation time in pure H2O, and x is the mole fraction of deuterated solvent: xÅ
[D2O] . [H2O] / [D2O]
[7]
All curves in Figs. 2 and 3 have distinguishable maxima. To explain the shape of the curves it is necessary to take into account several effects. The data of previous works (3– 10, 19–21) show that the monoatomic ions possess symmetrical hydration shells in aqueous solutions. It is well known that the first layers of the hydration shells of the Al 3/ and Ga 3/ ions consist of six water molecules arranged octahedrally. In pure H2O or D2O a single type of solvent molecule is present, but the mixtures contain three types of molecules (H2O, D2O, and HDO). In solutions the ions can be involved in a variety of surroundings. In the case of fast exchange of the ions among all possible
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FIG. 2. The dependence of the 27Al relaxation rates, 1/T 1 , on the isotopic composition of water in 0.02 m Al(NO3 )3 solution with 0.07 m HNO3 added to suppress hydrolysis. The resonance frequency is 130 MHz. The straight line passes through the data for the relaxation rate, 1/ T s1 , of 17O in the water molecules (open triangles) and 14N in the anions (closed triangles) at 657C (natural abundance of both nuclei). T 10 and T s10 are the relaxation times of the nuclei of the ions and the solvent molecules, respectively, in pure H2O; x is the mole fraction of deuterated component in the solvent (see Eq. [7]).
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to viscosity variations can be predicted from the relaxation times, T s1 , of the solvent molecule nuclei, 2H and 17O. These nuclei also relax via quadrupolar interactions, but in this case the electric-field gradient, q, is determined mainly by the electronic structure of the solvent molecule, and the symmetry of the solvation shell has no influence on the relaxation process. Therefore, the relaxation times can be described by expressions similar to Eq. [4] and Eq. [8]. This means that the relaxation rates of the solvent nuclei reflect an average molecular mobility in solution, and 1/T s1 is proportional to the viscosity. It is well known that in the H2O/D2O mixtures the density, viscosity, and dielectric constant, as well as the relaxation rates of 2H and 17O nuclei, depend linearly on the mole fraction x of D2O, and therefore, T s10 Å 1 / bx, T s1 FIG. 3. The dependence of the 71Ga relaxation rate, 1/T 1 , on the isotopic composition of water in 0.05 m Ga(NO3 )3 solution with 0.5 m HNO3 added to suppress hydrolysis. The resonance frequency is 152.5 MHz. The straight line passes through the data for the resonances of 17O in the water molecules (open triangles) and 14N in the anions (closed triangles) at 707C (natural abundance of both nuclei). Other symbols are as in Fig. 2.
tion of this substructure in the solution. If the exchange is fast, i.e., the lifetime of the nuclei in each substructure is less than the corresponding nuclear-magnetic relaxation time, Eq. [8] is valid for any exchange mechanism (23). Various symmetrical and asymmetrical ionic environments are expected to exist in H2O/D2O mixtures, but to a first approximation, Eq. [8] can be rewritten as psym pnon 1 Å / , T 1 T 1sym T 1non
[9]
or, taking into account the relation psym / pnon Å 1, as
S
1 1 1 1 Å / pnon 0 T 1 T 1sym T 1non T 1sym
D
,
[10]
where the subscripts ‘‘sym’’ and ‘‘non’’ stand for the appropriate complex types. It is known from previous works (5– 10, 19, 20) that T 1non is markedly smaller than T 1sym . The concentration dependence of the probability pnon can be expressed as pnon Å ax(1 0 x),
[11]
where a is a constant. The concentration dependence of the relaxation rates due
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[12]
where T s10 is the relaxation time of nuclei in pure H2O, and b is a constant. Indeed, the relaxation rates of the 2H and 17 O nuclei demonstrate a linear dependence on x for all systems investigated, and Eq. [10] can be rewritten as T 10 Å T1
F
S
1 / pnon
T 10 01 T 1non
DG
(1 / bx).
[13]
Summarizing the above, we conclude that the concentration dependence of the relaxation rate of the ion nuclei can be described by T 10 Å [1 / cx(1 0 x)](1 / bx), T1
[14]
where c is a constant depending parametrically on temperature via T 10 and T 1non . The experimental data are fitted well by Eq. [14]. It is obvious that the maxima on the plots in Figs. 2 and 3 are determined by the second term in Eq. [10]. The magnitude of the maximum depends on the difference between T 1sym and T 1non . The difference is expected to be smaller at high temperatures, due to the decrease of hydration shell symmetry in the cases when x is equal to 0 or 1, and this effect is observed in experiments. The appearance of a maximum cannot be attributed to hydrolysis effects, because (i) the samples contain the proper amount of acid (8, 10, 20), and (ii) the influence of hydrolysis should be more pronounced at high temperature. The isotope effect discussed here can be observed over a wide range of salt concentrations, and was first observed for 1 m aqueous AlCl3 (9). As can be seen from Eqs. [13] and [14], the relative relaxation rate, T 10 /T 1 , is determined by the structure of the
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FIG. 4. The dependence of the 139La relaxation rate, 1/T 1 , on the isotopic composition of water in 0.05 m La(NO3 )3 solution at 37C. The resonance frequency is 70.6 MHz. Triangles represent data for 17O resonance in the water molecules at natural abundance of the isotope. Other symbols are as in Fig. 2.
ionic solvation shells, but does not depend on the quadrupole moment eQ of the nuclei investigated. In contrast to the data for the 27Al 3/ and 71Ga 3/ resonances, the plot of 139La 3/ relaxation rate versus concentration (Fig. 4) does not show an extremum. This fact requires some additional consideration, because two possible explanations of the experimental data can be proposed. The first, for the absence of a maximum, could be weak hydration of the La 3/ ion, but this is scarcely probable, considering the high charge and small radius of the ion. Another and more attractive explanation for the linear dependence of the 139La 3/ relaxation rate on the D2O content is a low initial symmetry of the La 3/ hydration shell. It is very plausible that the coordination numbers of the lanthanide ions are equal to nine, and this does not allow the formation of a highly symmetrical arrangement, such as an octahedron or tetrahedron (24). Another result of this type was observed for the 23Na / resonance. The hydration shell of the sodium cation contains six water molecules, but it was impossible to obtain the extremum effects in H2O/D2O solutions of sodium salt. Probably the ratio D / t for the sodium ion is close to unity (see Table 1), and the symmetry effects cannot be observed in aqueous solutions even at low temperatures (down to the freezing point). However, a greater decrease of temperature is possible for nonaqueous solutions. Data for NaClO4 in the acetone/acetone-d6 system at 030 and 0607C are shown in Fig. 5. The deuteron resonance data demonstrate the absence of marked concentration dependence for the average mobility of the solvent molecules, but the isotope effect considered here arises again and can easily be observed. Figure 6 presents the data for the 7Li / resonance in CH3OD/CD3OD. The solvation shell of the lithium cation in methanol usually consists of four solvent molecules in a regular tetrahedron and is characterized by high symmetry.
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FIG. 5. The dependence of the relaxation rates, 1/T 1 , of 23Na (circles) and 2H (triangles) on the isotopic composition of acetone in 1 m NaClO4 solution. The resonance frequency is 8 MHz for both nuclei. Other symbols are as in Fig. 2.
on the Therefore, a maximum for the dependence of T 01 1 CD3OD content was expected. The effect was indeed observed for methanol solutions, but only at very low temperatures. It is probable that the overall change in T 10 /T 1 of the plot in Fig. 6 is due to the contribution from the dipole– dipole relaxation mechanism, which decreases with the magnetic dilution as the content of deuterated component increases. The d4 and d1 methanols were used to reduce the influence of dipole–dipole interaction between the 7Li / nuclei and the protons in the solution. Formally, the dipole– dipole contribution can be described in the same way as the viscosity influence in Eq. [13], i.e., by a (1 / bx) term, but with a negative value for the coefficient b.
FIG. 6. The dependence of the 7Li relaxation rate, 1/T 1 , on isotopic composition for 1 m solutions of LiClO4 in CH3OD/CD3OD. The resonance frequency is 8 MHz (closed circles) and 20 MHz (open circles). Other symbols are as in Fig. 2.
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CONCLUSION
Quadrupolar relaxation of the nuclei of monoatomic ions is quite sensitive to solvation-shell symmetry. The results obtained in this study provide clear evidence that in some cases the solvation shells of monoatomic ions have high symmetry. Distortions of symmetry have been detected, when some of the solvent molecules are replaced by their deuterated analogues. The maxima in the concentration dependences of the quadrupolar relaxation rates were not observed for nuclei in polyatomic ions, for example, the 14N resonance data for the NO 30 anion shown in Figs. 2 and 3. In this case the electric-field gradient is determined by the electronic structure of the ions, and the symmetry of the solvation shells has no influence on the relaxation process. The observed isotope effects can be used to investigate the degree of symmetry in the solvation shells of monoatomic ions. This investigation has presented results on the behavior of cation solvation shells. The study of this effect for monoatomic anions is in progress.
4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16. 17. 18.
ACKNOWLEDGMENTS 19.
The authors are grateful to Professor J. H. Strange for his critical reading of the manuscript and stimulating discussions. Financial support of the Russian Foundation for Basic Research (Grant 94-03-09554) is gratefully acknowledged.
20.
REFERENCES
21. 22. 23.
1. H. G. Hertz, Z. Electrochem. 65, 20 (1961). 2. K. A. Valiev, Zh. Strukt. Khim. 3, 653 (1963). [In Russian] 3. V. I. Chizhik, Zh. Strukt. Khim. 8, 350 (1967). [In Russian]
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24.
V. I. Chizhik, Proc. 16th Congr. AMPERE, Buchurest, 711 (1971). A. G. Marshall, J. Chem. Phys. 52, 2527 (1970). H. G. Hertz, Ber. Bunsen-Ges. Phys. Chem. 77, 531 (1973). A. Takahashi, J. Phys. Soc. Jpn. 43, 968 (1977). A. W. Akitt and J. M. Elders, J. Chem. Soc. Faraday Trans. 1 81, 1923 (1985). V. I. Chizhik and V. I. Mikhailov, Vestn. Leningr. Univ. Fiz.-Khim. 16, 81 (1982). [In Russian] I. S. Podkorytov and V. I. Chizhik, Vestn. St. Petersburg Fiz.-Khim. 11, 73 (1993). [In Russian] A. Abragam, ‘‘The Principles of Nuclear Magnetism,’’ Oxford Univ. Press, London/New York, 1961. C. P. Slichter, ‘‘Principles of Magnetic Resonance,’’ Springer-Verlag, Berlin/New York, 1980. H. G. Hertz, M. Holz, G. Keller, H. Versmold, and C. Yoon, Ber. Bunsen-Ges. Phys. Chem. 78, 493 (1974). H. G. Hertz, M. Holz, R. Klute, G. Stalidis, and H. Versmold, Ber. Bunsen-Ges. Phys. Chem. 78, 24 (1974). V. I. Chizhik, ‘‘Nuclear Magnetic Relaxation,’’ St. Petersburg Univ. Press, St. Petersburg, 1991. [In Russian] B. S. Gourary and F. J. Adrian, Solid State Phys. 10, 144 (1960). R. D. Shannon, Acta Crystallogr. A 32, 751 (1976). D. Eisenberg and W. Kauzmann, ‘‘The Structure and Properties of Water,’’ Oxford Univ. Press, New York, 1969. L. Helm and H. G. Hertz, Z. Phys. Chem. (Wiesbaden) 127, 23 (1981). J. Kodweiß, D. Ko¨hnlein, G. Ko¨ssler, O. Lutz, W. Messner, K. R. Mohn, A. Nolle, G. Nothaft, P. Ruppert, N. Steinhauser, D. Zepf, E. Haid, and W. Schich, Z. Naturforsch. A 41, 471 (1986). M. Holz, Prog. NMR Spectrosc. 18, 327 (1986). J. R. Zimmerman and W. E. Brittin, J. Phys. Chem. 61, 1328 (1957). D. D. Skirda, V. A. Sevryugin, and A. I. Maklakov, Khim. Fiz. 2, 1499 (1983). [In Russian] V. I. Chizhik, C. Cabal, M. N. Rodnikova, and A. Guzman, Koord. Khim. 14, 349 (1988). [In Russian]
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