1938
The Journal of Physical Chemisfty, Vol. 82, No. 17, 1978
(9) (10) (11) (12) (13)
W. 8. Veldkamp and J. R. Votano, J. Phys. Chem., 80, 2794 (1976). S. S. Alpert and G. Banks, Biophys. Chem., 4, 287 (1976). R. Nossal and J. Gethner, personal communication. A. R. Gordon, Ann. N . Y . Acad. Sci., 46, 285 (1945). P. D.Ross, R. W. Briehl, and A. P. Minton, Biopolymers, 27, in press (1978). (14) C. Tanford, "Physical Chemistry of Macromolecules", Wiley, New York, N.Y., 1961, Chapter 6.
J. F. Harmon and E. J. Sutter (15) S. S. Alpert, J . Chem. Phys., 65, 4333 (1976). (16) J. L. Anderson, F. Rauh, and A. Morales, J. Phys. Chem., 82, 608 (1978). (17) J. M. Burgers, Proc. Acad. Sei. Amst., 45, 126 (1942). (18) C. W. Pyun and M. Fixman, J . Chem. Phys., 41, 937 (1964). (19) G. K. Batchelor, J . Fluid Mech., 52, 243 (1972). (20) J. L. Anderson, Ind. Eng. Chem. Fundam., 12, 488 (1973). (21) A. D.Maude and R. L. Whffmore, Brit. J. Appl. Phys., 9, 477 (1958).
Molecular Motion in Supercooled Liquids. 2. Nuclear Magnetic Resonance Relaxation of Deuterons and Protons in 11 M Aqueous Lithium Chloride J. F. Harmont and E. J. Sutter" Physics and Chemistry Departments, Idaho State University, Pocatello, Idaho 83209 {Received April 5, 1978) Publication costs assisted by Idaho State University Faculty Research Committee
Proton, deuteron, and 7Li relaxation times as a function of temperature through their respective T I minima are presented. The frequency dependence of 1'2 indicates that molecular reorientation is the dominant relaxation mechanism. A model based upon anisotropic reorientation of water in the hydration sphere of the lithium ion gives an adequate description of the relaxation data. In addition a small contribution to proton relaxation from translation is found. Correlation times and self-diffusionconstants are presented as functions of temperature.
Introduction The study of liquids in the supercooled state yields much useful structural and dynamical inf~rmationl-~ despite theoretical and experimental difficulties inherent in this region. Theoretically, it is not yet certain that this metastable region is a legitimate extension of the liquid in its normal state (i.e., above its thermodynamic liquidus temperature), yet the possibility that it is makes data collection in this region extremely important. Experimentally, metastability presents problems, not the least of which is the imminence of spontaneous crystallization, yet the benefit of maintaining liquid structure while slowing down motional time scales is worth these difficulties. One such benefit is the possibility of unravelling complicated motions which occur in the stable liquid region into the sum of simpler motions by studying them with NMR relaxation experiments in the supercooled region. It is this particular benefit which we focus on in this paper. We have chosen aqueous and D20 18 mol % ' (11 M) lithium chloride BS a model system for studying relaxation rates through the use of pulsed NMR for three reasons. One is that this particular concentration of lithium chloride in water supercools easily and is not subject to crystallization even at the lowest temperatures, and can thus be studied where random thermal fluctuations are relatively small. The second is that the system possesses three abundant nuclei for NMR study 7Li, lH, and 'H (in D20 solutions). The third is that the ratio of water molecules to lithium ions is very low (4.9:l) allowing the simplifying assumption that all water exists in the first hydration sphere of the lithium ion. In an earlier paper,6 hereafter referred to as I, the temperature dependence of the spin-lattice relaxation time (TI)behavior of the Li ion in 18 mol % LiCl was reported through the minimum. This paper is an extension of that study and includes the presentation of the temperature *Author t o whom correspondence should be addressed at t h e Chemistry Department, Idaho State University. 'Physics Department.
0022-3654/78/2082-1938$01 .OO/O
dependent relaxation behavior of the proton and deuteron. From these data and the data in I we argue that the relaxation behavior of the proton and deuteron is due to restricted rotation of the water molecule about its dipolar axis. In addition, the relaxation behavior of the protons has a component due to translation of the water molecule. The 7Linucleus is found to be relaxed by motions related to the reorientation of the water. A more coherent relaxation model emerges than the one presented in I and we amend the conclusions presented there to fit this model. The temperature dependences of the correlation time for the reorientation and the self-diffusion constant of the water are displayed.
Experimental Section The proton, deuteron, and lithium TI values were determined by measuring the magnetization following the last pulse in 180°-t-900 or 90°-t-900 sequences at a Larmor frequency of 7 MHz. In addition, proton data were taken at 14 MHz and deuteron data were taken at 4 MHz. Due to the poor recovery time of the 4-MHz spectrometer, Tl could not be followed through the minimum at this frequency. Signal-to-noise considerations yield reproducibilities in the data to 10% or less for the Li and deuterons and 5 % or less for the protons. The magnetization vs. t data fitted a simple exponential decay with a single time constant within experimental error. The decay of the magnetization was followed over at least one decade of the exponential. The spectrometer used was of conventional design, with a field regulated magnet and phase detector. Data were accumulated with a boxcar integrator and chart recorder. Integration times sufficient to improve the signal-to-noise ratio by a factor of 3 or 4 were used. Temperatures in the cryostat, a blowing gas type, were electronically controlled and measured by a copper-constantan thermocouple. The temperatures were controlled to within 1 K and measured to within 2 K. Baker Analyzed reagent grade lithium chloride was dried at 130 "C for several days and was used without further purification (99.2% pure). Distilled water and 99.7% D20 0 1978 American Chemlcal Society
Molecular Motion in Supercooled Liquids
Figure 1. A sketch to scale of the static structure of the LiCl solutions with indications of the types of motions important for spin-lattice relaxation (intramolecular proton-proton distance is 1.56 A).
(BDH Chemicals, Ltd.) were used for the solvents. Approximately 100 g of solution was prepared by weighing the reagents. Aliquots (2 mL) of these solutions were placed in 10-mm 0.d. Pyrex tubing with a thermocouple well fused into one side. Dissolved gases were removed by repeated freeze-thaw-pump cycles, and the tubes were sealed off under vacuum.
The Model We begin by assuming that all water is present in the first hydration sphere of the lithium ions; an assumption supported by calculations of ion activity functions by Hogfeldt and Leifer6 which indicated that chloride and bromide ions are unhydrated in the region 18 mol % to saturation in LiCl and LiBr solutions. The average minimum number of water molecules in each hydration sphere is 4.9, deduced by breaks in the proton relaxation rate curves vs. concentration for aqueous LiCl and LiBr solution^,^ and from dielectric relaxation work at low ion concentrations by Giese et ale8Further, this value fits well within the range of lithium ion hydration numbers (2-10) calculated by a variety of methods and presented by McCall and Dougla~s.~ Thus, in this ion rich system, only 4.9 water molecules per cation, the water sheaths each cation. This hydration sheath effectively insulates the ions one from another and thus facilitates the relative ionic motions responsible for the fluid properties. Viewed statically, each lithium ion is surrounded by four to five waters of hydration with the dipolar water axis perpendicular to the cation surface, while the chloride ions occupy the interstitial sites among the hydrated lithium ions (see Figure 1). From X-ray diffraction studies on dilute lithium chloride solutionslO and from our notion that the hydration number of each lithium ion is about 5 , we construct to scale a two-dimensionalrepresentation of the lithium ion-water system (Figure 1). Each proton will have eight intermolecular nearest neighbor protons at distances ranging from 2.91° to 4.6 A with an average nearest neighbor distance of about 3 A. Viewed dynamically the bulk fluid properties as reflected in transport phenomena such as viscosityll are due to cooperative motions between the chloride and hydrated lithium ions. These motions are facilitated by the reorientation and translation of the individual water molecules. It is the motion of the water molecules that is primarily responsible for the spin-lattice relaxation times
The Journal of Physical Chemistry, Vol. 82, No. 17, 1978 1939
we observe. It is clear that if cooperative motion is extant then the translating water molecule will be sensitive to the same potential barriers as are reflected in bulk transport properties. This has been noted by McCall and Douglass in their classic studies of self-diffusion and viscosity in this and similar system^.^ The reorientation of the water molecules occurs anisotropically about the dipolar axis in a thermally activated random walk among several preferred equilibrium sites. The translation takes place by random flights from one hydration sphere to another. It is plausible to suggest that the chloride ion reorientation is involved in this motion in the following manner. A water molecule leaves the lithium ion hydration sphere, attaches itself by means of anion-dipole and hydrogen bonding to the nearest chloride ion, and the chloride ion rotation delivers the water molecule to a vacancy in a neighboring hydration sphere with the negative end of the water dipole presented toward the lithium ion. The mean time between these translational motions is assumed to be long compared to the reorientation of the water on the hydration sphere. The reorientation of the chloride ion is assumed to be very rapid so that the attachment and subsequent translation and concomitant rotation of the water molecule occurs instantaneously compared to the mean time between translational motions. These conditions assure that the rotation of the water, as it is translated by the chloride ion, will not be a significant relaxation mechanism.
Relaxation Times In general a nucleus with nonzero spin can couple with other nonzero spin nuclei magnetically and/or electrically. In the case of magnetic dipolar coupling it is the summation of all external magnetic fields sensed by a particular nucleus which determines the strength of the dipolar interaction. Thus all motions (both translation and rotation) can modulate the strength of the coupling. In the case of electrical coupling it is the quadrupole moment of the nucleus which interacts with the electric field gradient at the nuclear site. In molecules these field gradients are produced by chemical bonds, and to the extent that chemical bonds are localized, so are the gradients and hence quadrupole coupling is largely intramolecular and localized in nature. Because of its short range nature this coupling is modulated by molecular rotations alone.I2 If these couplings can be modulated at the appropriate rate, energy can be exchanged between the nucleus and the lattice (spin-lattice relaxation). The relaxation rate of the protons is entirely determined by translational and rotational modulation of the magnetic dipolar coupling between intramolecular and intermolecular protons. The 7Li nucleus possesses a relatively large magnetic dipole moment and a significant electric quadrupole moment so that both dipolar and quadrupolar couplings can be important in 7Li relaxation; but we observed in I that, at least near the minimum, the dipolar contribution is negligible because the behavior of 7Li relaxation near the minimum was the same in both D20 and H20. The deuteron has a very small magnetic moment (only about 5% the value for the proton), and its dipolar couplings are therefore very small. By contrast, the quadrupole interactions which the deuteron experiences are large and give rise to a relaxation rate which is the result of rotation only of the D20 molecule. The total relaxation rate (l/Tl) for a particular nucleus can be written as R = RA + RB (1) where RA is due to couplings modulated by reorientations
1940
The Journal of Physical Chemistry, Vol. 82, No. 17, 1978
and R B to couplings modulated by translation. In writing eq 1it is assumed that the relaxation mechanisms are not correlated. The expression for R A must take into account the anisotropy of the reorientation of the H20 (and D20) molecules. A treatment due to Woessner is used13in which the relaxation rate is derived for two spins a fixed distance r apart, performing a random walk between equilibrium positions. The correlation time for this process is TR. The molecular skeleton supporting this pair of spins undergoes a random isotropic reorientation with correlation time rc. Applied to our system the spin pair becomes the protons (or deuterons) of a water molecule reorienting about the molecular symmetry axis with correlation time r R X (x = D for deuterons, H for protons) (see Figure 1). The entire complex, lithium plus hydrate water, would have a correlation time rc if it were not for translation of the water molecules which limits the lifetime of the complex. Under the above conditions and (rR
