J. Phys. Chem. 1987, 91, 6309-6315
6309
An NMR Contribution to the Interpretation of the Dynamical Behavior of Water Molecules as a Function of the MgClp Concentration at 25 OC R. P. W. J. Struis, J. de Bleijser, and J. C. Leyte* Gorlaeus Laboratories, Department of Physical and Macromolecular Chemistry, University of Leiden, 2300 RA Leiden, The Netherlands (Received: January 27, 1987)
The relaxation rates of 2H and I7O in various concentrated MgC12solutions (T= 25 "C) ranging from 0.246 to 6.44 m were determined and interpreted in terms of a two-phase model corresponding to the water molecules in fast exchange between the Mg(HzO)62+units and the remaining bulk water. The self-diffusion data of water and Mg2+ions in MgCI, solutions were used to estimate the concentration dependences of the reorientational correlation time of bulk water and the overall correlation time of the hydrated magnesium ions. With this two-phase model, relaxation rates determined previously have been reinterpreted to obtain the 2H and 170interaction constants in the magnesium hydration phase. From the hydrodynamic analysis of the concentration-dependentviscosity and the self-diffusion coefficientof the bulk water the radius of the.magnesium hydration units is obtained, rMg= 3.4 f 0.1 A. The overall correlation time in infinitely diluted MgC12solutions is estimated to be 36 f 4 ps (25 "C). It is concluded that the hydration water reorients anisotropically. The anisotropic motion of the hydration water is interpreted in terms of the overall correlation time of the hydration units, the correlation time of the internal diffusion of the water molecule about the internal axis, and the orientation of this axis with respect to the molecular frame and the cation-oxygen axis.
Introduction The study of the magnetic relaxation rates of water nuclei in electrolyte solutions provides information about the dynamical and related molecular properties of water molecules in these solutions.' The relaxational behaviors of the quadrupolar nuclei 2H and "0are dominated by interactions which are determined within the water molecular frame. The quadrupole moments of the deuteron and oxygen nuclei interact with the electric field gradient tensor present at the respective nuclei. The electric field gradient tensors are almost completely intramolecularly determined. If the extreme narrowing limit applies for the relaxation process then the relaxation rate is the product of an interaction constant and a correlation time. The correlation time is characteristic for the loss of orientational correlation of the interaction tensor of the water nucleus under study. The intramolecularly determined interactions are most effectively modulated by the reorientation of the water molecule. Recently it has been shown that in pure water at room temperature the water molecules reorient isotropically on a picosecond time scale and that the values of the interaction constants are intermediate between the gas- and solutions however, icephase values of pure ~ a t e r . ~In, electrolyte ~ especially those solutions containing, e.g., cations with a high charge density, the d y n a m i ~ a l ~and v ~ ,intramolecular ~ properties of water molecules neighboring the cations are significantly alteredS2It was concluded that for the water molecules hydrating the magnesium ions the values of the interaction constants of the water nuclei are shifted to values one obtains in iceous water. The reorientational correlation times of the water nuclei are significantly larger than in pure water and because the values of the deuteron and oxygen correlation times differ it was concluded that the water molecules in the cationic hydration shell reorient anisotropically. It was shown2 that the anisotropical reorientation could be interpreted in terms of an axially symmetric diffusion tensor resulting from two (assumed) random rotational diffusion processes, that is, the overall (isotropic) diffusion of the hydrated cation (Do")together with an internal diffusion within the hy( 1 ) Abragam, A. Principles of Nuclear Magnetism; Clarendon: Oxford,
U.K.,1961.
(2) Struis, R. P. W. J.; de Bleijser, J.; Leyte, J. C. J . Phys. Chem. 1987, 91, 1639. ( 3 ) van der Maarel, J. R. C.; Lankhorst, D.; de Bleijser, J.; Leyte, J. C. Chem. Phys. Lett. 1985, 122, 541. (4) Hertz, H. G. r a t e r , a Comprehensiue Treatise; Franks, Ed.; Plenum: New York, 1973; Vol. 3. (5) van der Maarel, J. R. C.; Lankhorst, D.; de Bleijser, J.; Leyte, J. C. J . Phys. Chem. 1986, 90, 1470.
dration shell (Di). Furthermore, it was demonstrated that the symmetry axis of the molecular diffusion tensor may consistently be taken to lie in the bisectrix plane of the water molecule, albeit that only a restricted range of values apply for the angle p between this axis and the symmetry axis of the water molecule. However, one must bear in mind that in the evaluation of the above-discussed parameters D,, Di, p, and the 2H and I7O interaction constants in the hydration phase several assumptions have been made: (1) The observed relaxation rates of the water nuclei in the electrolyte solution are assumed to result from of the relaxational behavior of water molecules in fast exchange between two distinguishable phases, corresponding to the hydrated cations and the bulk water. (2) For the cationic hydration site only the first hydration layer with six water molecules per cation is considered. (3) The influence of C1- ions on the dynamical and intramolecular properties of neighboring water molecules is assumed to be negligibly small in respect to Mg2+ ions and is confined to the bulk water phase. (4) The properties of the bulk water phase are identified with those of pure water. For the assumptions 1, 2, and 3, experimental support can be given and one may expect that these assumptions apply for a reasonable range of electrolyte concentrations. With the assumptions 1-4, together with the expectation that the correlation time T~~ (=1/6D,v)of the overall diffusion of the hydrated cations lies in the range of 25-38 ps, one obtains acceptable values for p and T~ (=ll6D1),respectively. However, assumption 4 and the value for T~~ only apply to infinitely diluted MgClz solutions. In the present study the dynamical behavior of magnesium hydration water in the concentration range of 0.246-6.44 m MgC12 ( T = 25 "C) is investigated. It will be clear that for the higher concentrated solutions assumption 4 and the value of T~~ are no longer maintainable. Estimation of the deuteron and oxygen relaxation rates in the bulk water phase of a MgC12solution using, e.g., the values of the shear viscosity of pure water and of the electrolyte solution fails to account for the experimentally observed relaxation rates in the MgC12 solution. Therefore additional information will be used from the translational diffusion of the water molecules and the cations to estimate the rotational behavior of water molecules in the bulk water phase and the overall correlation time T~ of the hydrated magnesium ions as a function of the MgCl, concentration. Previously determined 2H, 170,and IH-l7O relaxation ratesZ in 1 and 4 m MgCl, have been reinterpreted to obtain the interaction constants of the respective relaxation rates in the hydration phase, now taking into account the concentration dependence of the reorientational correlation time of water molecules in the bulk phase. Also the viscosity data and the self-diffusion coefficients of the bulk water will be analyzed
0022-3654/87/2091-6309$01.50/00 1987 American Chemical Society
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Struis et al.
The Journal of Physical Chemistry, Vol. 91, No. 24, 1987
by a hydrodynamic approach to estimate the radius of the hydrated magnesium ions. With the estimated radius the overall correlation time T~~ = 1/6Dovin (infinitely) diluted MgCI2 solution can be estimated.
Experimental Methods For the determination of the deuteron and oxygen relaxation rates in MgClz solutions, several different isotopically enriched stock solutions were prepared on the basis of weight, with distilled and deionized water, D 2 0 , H2170,and MgC12.6H20. Distilled water was deionized and filtered with a Milli-Q water purification system (Millipore Corp.). D 2 0 was obtained from Merck (purity 2 99.9%) and H2170from Monsanto Research Corp. containing 3.13 wt 9% 0-16, 28.15 wt % 0-17, and 68.72 wt % 0-18. The analytical reagent MgC12.6H20 was obtained from Baker. All manipulations were done in a cold room (4 "C) to minimize exchange with atmospheric humidity. The concentration of magnesium ions in the stock solutions were checked (in triplo) by complexometric titrations with EDTA. The EDTA solution was standardized by titration of a solution containing a weighed amount of Pb(N03)2.6 The electrolyte solutions up to 5.49 m were prepared by mixing weighted amounts of different stock solutions mutually or by dilution with 2H- and I7O-enriched distilled and deionized water. Concentrations above 5.49 m were obtained by evaporation of the 5.49 m stock solution. The N M R tubes (Wilmad 10 mm) were heated in an EDTA solution, heated in a NaHCO, solution, and stored for several days filled with distilled and deionized water. The longitudinal relaxation rates R , were measured by the alternating phase inversion recovery methode7 For several electrolyte solutions the transversal relaxation rates R2 were also measured by using a spin-echo or a Carr F'urcell Gill Meiboom sequence.' In all cases it was observed that the extreme narrowing limit ( R , = R 2 ) applies and that the free induction decay falls off exponentially with the time. The measurements have been performed on a modified SXP spectrometer (Bruker), equipped with a 6.3-T superconducting magnet (Oxford Instruments). The temperature was maintained at 25 f 0.3 O C by fluid thermostating using Fluorinert FC-43 (3M Co.). The temperature was observed during the N M R experiments with a calibrated copper-constantin thermocouple. The external reference voltage was supplied by a cold junction compensator (Therm0 Electric). For all relaxation measurements of R1 100 data points were collected and fitted to a single exponential by a nonlinear least-squares procedure based on the Marquardt-Levenberg algorithm.8 The experimental reproducibility of the 2Hand the 170longitudinal relaxation rates is of the order of less than 2%. For all electrolyte solutions the mole fractions of 2H and 170were less than 0.1%. The isotopic enrichments were held low on purpose in order to avoid isotope effects on the reorientational correlation time. Lankhorst et ale9 estimated these effects as a function of the 2H and I7O mole fractions in water, using the isotope effects on the viscosity. With this estimation the values of the observed and the isotope effect corrected relaxation rates differed less than 0.2% and hence the correction was neglected. The 2H and I7O relaxation rates as a function of the molal MgCI2 concentration are presented in Table I. Table I also includes the molar MgC12 concentration c, the viscosity q , the self-diffusion coefficient of water D,, and the self-diffusion coefficient of the magnesium ions DMg.D, is obtained from proton spin-echo experiments and DMg from tracer diffusion experiments of 28Mg in MgC12 solutions. The values of c, q, Dw,and DMg are derived from data cited in the literature by means of polynomial interpolation. The polynomial coefficients, references to the literature, etc., are listed in Table 11.
TABLE I: Relaxation Rates R D and Ro,Shear Viscosity 8, Self-Diffusion Coefticient of Water and of Mg2' Ions, Relative to the Pure Water Results' as a Function of the MgC12Concentration at 25 OC m.
c.
0.246 0.488 0.985 1.49 2.19 2.78 3.47 3.98 4.49 4.99 5.39 5.49 5.97 6.44
0.244 0.482 0.964 1.44 2.08 2.60 3.18 3.60 4.00 4.39 4.69 4.76 5.11 5.43
b
1.10 1.20 1.41 1.63 1.98 2.33 2.76 3.15 3.55 4.08 4.48 4.63 5.26 5.94'
1.08 1.16 1.33 1.51 1.81 2.13 2.56 2.98 3.41 4.01 4.51 4.68 5.52 6.42'
1.10 1.21 1.47 1.78 2.36 3.07 4.23 5.42 6.97 8.89 10.8 11.4 14.3 17.7
b
1.07 1.15 1.37 1.62 2.05 2.54 3.43 4.43 5.83 7.68 9.58 10.1 13.1 16.6
b
1.09 1.16 1.32 1.50 1.85 2.28 2.99 3.70 4.60 5.67 6.70 6.99 8.49 10.2
b
OAt 25 OC the values of RD,Ro, 7, D,, and D M gin pure water are respectively RD(0) = 1.96 s-', Ro(0) = 141 s-', q(0) = 0.891 cP, D,(O) cm2/s. bThe values of c, = 2.30 cm2/s, and DMg(0)= 0.706 7,Dw, and DMgare derived from data cited in the literature by means of polynomial interpolation. For details see Table 11. C A t T = 25 OC the 6.44 m MgClz solution shows crystallization fragments. The 'H and " 0 relaxation rates in this solution equal the results obtained in the (clear) 5.97 m solution. The relaxation rates denoted in Table I were obtained for the overconcentrated 6.44 m solution. Here the solution was first heated up to 37 OC and then slowly cooled down to 25 OC. This procedure delayed the visible crystallization process for at least one-half hour.
Theoretical Section I . Relaxation Rates of 2H and I7O in Water. In the case of the extreme narrowing limit the relaxation rates of 2H (=D) and 170(=O) may be expressed according to eq 1 and 2, where x RD
= (3/8)(2axD)2(1 -k 7D2/3)TD
Ro = ( 3 / 1 2 5 ) ( 2 9 ~ 0 ) ~ (-k1 1102/3)70
(1)
(2)
(=e2qQ/h)is the quadrupolar coupling constant, Q the nuclear quadrupole moment, eq the main component of the electric field gradient in its principal axis system, h Planck's constant, and e the proton charge. The asymmetry parameter 7 expresses the symmetry of the principal components of the electric field gradient tensor. The correlation times 7 are effective correlation times because the nature of the reorientational motion has not yet been specified. Due to experimental conditions RD, and therefore T ~ refer to HDO molecules. To allow direct comparison of the oxygen and deuteron correlation times T~ must be corrected for a small isotope effect to obtain T ~ which * refers to H 2 0dynamics with' TD(HDO)/TD*(H~O)= 1.05 f 0.02 (3)
In the remaining text all the deuteron correlation times mentioned refer to H 2 0 dynamics. 2. Relaxational Behavior of 2H and 170in MgCl, Solutions. 2A. The Two-Phase Model. Following procedures often used in the interpretation of relaxation measurements of water nuclei in strong electrolyte solutions the water molecules are considered to be in fast exchange between distinguishable phases corresponding to the hydrated ions and the remaining (bulk) water. The implication of the hydrate concept, that is, that a definite
(6) Vogel, A. I. Quantitative Inorganic Analyses, 3rd ed.; Longmans, Green and Co.: London, 1961; Ch apter IV. (7) Demco, D. E.; van Hecke, P.; Waiugh, J. S. J . Magn. Reson. 1974, 16,
(10) Miller, D. G.; Rard, J. A.; Eppstein, L. B.; Albright, J. G . J . Phys. Chem. 1984, 88,5739. ( 1 1) Handbook of Chemistry and Physics; Weast, R. C., Ed.; CRC: Boca Raton, FL, 1984-1985. (12) Harris, K. R.; Mills, R.; Back, P. J.; Webster, D. S. J. Mogn. Reson.
Ah7 ._ .
1978. 29. 473. -, -.
(8) Nash, J. C . Compact Numericol Methods; Adam Hilger: Bristol, 1979. (9) Lankhorst,D.; Schriever, J.; Leyte, J. C. Ber. Bumen-Ges. Phys. Chem. 1982, 86, 2 15.
__
(13) McCall, D. W.; Douglas, D. C . J . Phys. Chem. 1965, 69, 2001. (14) Jones, J. R.; Rowlands, D. L. G.; Monk, C. B. Trans. Faraday SOC.
1965, 61, 1384.
(15) Harris, K. R.; Hertz, H. G.; Mills, R. J . Phys. 1978, 75, 391.
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The Journal of Physical Chemistry, Vol. 91, No. 24, 1987 6311
Dynamical Behavior of Water Molecules TABLE 11: Polynomial Coefficients b, in P = x,b,m' polynomial coeff ?(m)/?(O) bo 0.992 f 0.010 b, 0.431 f 0.030 lob, 0.32f 0.24 100b3 1.54 f 0.68 1000b4 4.93 f 0.62 ref 11" reproducibility of lit data, % 10.9
C
~w(O)/Dw(m)
-0.00277 f 0.00046 1.00675 f 0.00069 -0.2604 f 0.0026 0.0124 f 0.0028
1.015 f 0.011 0.150 f 0.049 3.48 f 0.60 -15.9 f 2.5 34.3 f 3.2 12: 13, 14
