J. C. HISDMAN, A. SVIRMICKAS, AND M. WOOD
4188
for solids and gaseous samples, but they point up the unreliability of coupling constants of liquids, determined by considering bulk properties to calculate the correlation times.
Table V : Quadrupole Couplings for AlRa’s eqQ,
AIRS
Slope
MHz
TEA TIBA TNBA
1.5 2.2 4.4
13.0 15.6 16.8
Table VI: Comparison of ea& Calculated from Microviscosity and Debye Models -----eqQ,
MHz-----
Solute
Solvent
rDebye
‘microvim
TEA TIBA
Isopentane Isopentane
13.0 15.6
27.0 34.3
VI. Conclusions The dominant relaxation mechanism for the aluminum nuclei of aluminum alkyls, neat and in solution in
hydrocarbons, is through the coupling of the electric quadrupole moment with the electric field gradient. It is shown that the use of the Debye relation to obtain correlation times must be made with considerable caution. There is a linear dependence of line width on macroscopic viscosity, and for similar molecules of not too variable viscosity the A H / q Vm is fairly constantindicating that the Debye relation may be used for determination of relative correlation times and for comparisons. The constraints of the applicability of the Debye equation, however, are severe. At zero viscosity there is a residual line width, and the temperature dependence of the line width results in non-Arrhenius behavior. The use of a microviscosity model yields some improved agreement with experimental correlation times. The observed line widths correspond to quadrupole coupling constants which are apparently solvent independent and are reasonable in absolute magnitude for these systems. This detailed experimental examination points to the need for possible theoretical reevaluation of the crude models that are being used for determining correlation times.
Acknowledgment. The author acknowledges the diligent technical assistance provided by Mr. A. V. Fareri.
Deuteron Spin-Lattice Relaxation of D,O in Organic Solvents1 by J. C. Hindman, A. Svirmickas, and M. Wood Chemistry Division, Argonne National Laboratory, Argonne, Illinois
60.439
(Receiued M a y 83, 1968)
Radiofrequency pulse techniques have been used to measure the deuteron spin lattice-relaxation time for DgO in certain organic solvents. I n particular, we have examined solutions where infrared observations indicate that the properties of the dissolved water molecules are only slightly altered from the gas state and where there is little evidence for strong intermolecular complex formation. Concentration dependence studies were used to derive the relaxation times for infinite dilution of DzO in the organic solvent. The T Ivalues were combined with deuteron quadrupole coupling constants calculated from infrared data to give values for the molecular reorientational correlation times, f Q , As expected, these correlation times are much shorter than reorientational correlation times calculated from the Debye-Bloembergen-Purcell-Pound equations. We have briefly considered the implications of these observations with respect to models of water structure where the existence of freely rotating monomers is assumed.
Introduction Demonstrably, many of the properties of liquid water can be explained by assuming that it is a mixture of two species, a hydrogen-bonded species and a nonhydrogenbonded species, Further, as Frank has pointed OUt,z the persistence of the tetrahedral structure in the liquid The Journal of Physical Chemistry
can be readily accounted for in terms of a number of hydrogen-bonded structures, including various forms of? (1) Based on work performed under the auspices of the U. 8. Atomic Energy Commission and presented in part before the Physical Chemistry Division, 155th National Meeting of the American Chemical Society, Sari Francisco, Calif., Apr 1-5, 1968.
4189
DEUTERON SPIN-LATTICE RELAXATION OF D 2 0 ice as well as the clathrates. On the other hand, the nature of the monomer species is less readily defined. Depending on the data that are to be explained, a diversity of properties has been assumed varying from the view that such monomers may be in gas-like free rotational states to considering that they may be almost indistinguishable from lattice water. The experiments described in the present paper were designed to yield information about the properties of water molecules under conditions where we can reasonably expect that they exist as monomers. I n particular, we have examined solutions where the infrared data3t4 indicate that the properties of the water molecules are somewhat altered from the gas state but where there is little evidence for strong intermolecular complex formation. The aim is to obtain data for the rotational correlation times under conditions where the relaxing unit should be the monomeric water molecule. Two aspects of the results were of particular interest to us. First, we were interested in whether the abnormalities of water as a solvent were reflected to an appreciable degree in the behavior of water as a solute. Second, we were concerned with the question of what might be inferred about the properties of monomeric water molecules in liquid water from observations on such monomers in organic solvents.
Experimental Section The deuteron relaxation time measurements were made using an N X R Specialities pulse spectrometer operating at 9.2 MHe. The T1 values were obtained using the null method (180-90° pulse sequence with variable 7 ) . Temperature control was maintained to within h 0 . 2 ” by means of a liquid cryostat system. The fluorochemical, (C4F9)3n’,obtained from the 11MM company was used for the circulating liquid. Conductivity grade DzO (99.8% D) was used. Fluka purissimuin grade p-dioxane was purified by refluxing over sodium in a N2 atmosphere for 6 hr to remove peroxides, then distilled and stored under nitrogen. Samples were prepared immediately, degassed, and sealed on a vacuum line. The CH3S02 and CH3CN were spectro grade. All other solvents were reagent grade. All solvents, except p-dioxane, were dried with a molecular sieve. CHC13 was freshly distilled under nitrogen and samples prepared immediately. All solutions were prepared volumetrically, transferred to the appropriate sample tube, frozen, pumped, and sealed on the vacuum line.
Treatment of the Data The quadrupole coupling constants for DzO in the various solvent systems have been calculated using Chiba’s relationship5 between the 0-H stretching frequency, V O H (taken as the mean of the symmetric
stretch, VI, and the asymmetric stretch, va), and the quadrupole coupling constant, i.e. (e2qQ/h) = 2.26 X
(VOH)~
(1)
The quadrupole coupling constant is in Hertz if V O H is in wave numbers. The results are given in Table I.6-14 Also given in the table are the experimental values for D20 in the gas and solid (ice). Note in this table the fact that the species designated by Walrafren13 as water “monomer” has a quadrupole coupling constant much closer to that for monomeric water in organic solvents than for water in ice. That the species designated as “lattice” water has a calculated coupling constant greater than in ice could indicate that the hydrogen bonds are stretched in this fraction. This interpretation would be in accord with the observation that the near neighbor separation of water molecules in liquid water is appreciably greater than in ice. For D20 the spin-rotational, inter- and intramolecular dipole-dipole contributions to the spin-lattice relaxation time, TI,can be neglected.16 The quadrupole correlation time, T Q , is then calculated from the equationI6
using the appropriate quadrupole coupling constants from Table I. As indicated in this table, the asymmetry parameter, 7, is small and the correction due to this quantity is neglected in the calculations. To eliminate as far as possible the effects of molecular association, the T1 values used in the calculations were infinite dilution values. Except for the dioxane solutions, these were obtained by linear extrapolation of plots of T l us. mole per cent DzO. The data for CH,NO, and CH3CN solutions are illustrated in Figure 1. For the dioxane-water mixtures it was (2) H. S. Frank, Fed. Proc., 24, No. 2, Part 111, Suppl. No. 15, 9-1 (1965). (3) E. Greinacher, W. Luttke, and R. Mecke, 2. Elektrochem., 59, 23 (1955). (4) P. Saumagne and M. L. Josien, Bull. Soc. Chim. Fr., 813 (1958). (5) T. Chiba, J . Chem. Phys., 41, 1352 (1964). (6) G. H. Herrberg, “Infrared and Raman Spectra,” D. Van Nostrand Co., Inc., New York, N. y., 1945, p 280. (7) E. B. Treacy and Y . Beers, J . Chem. Phys., 36, 1473 (1962). (8) P. Thaddeus, L. C. Krisher, and J. H . N. Loubser, ibid., 40, 1637 (1964). (9) M. J. Taylor and E. TVhalley, ibid., 40, 1660 (1964). (10) G. A. Gabrichidre, O p t . Spectrosc., 19, 317 (1965). (11) P. Waldstein, S. W. Rabideau, and J. A. Jackson, J . Chem. Phys., 41, 3407 (1964). (12) E. Fishman and P. Saumagne, J . Phys. Chem., 69, 3671 (1965). (13) G. E. Walrafen, J . Chem. Phys., 47, 114 (1967). (14) G. S. Landsberg, Compt. Rend. (Dokl.) URSS, 18, 549 (1938). (15) J. G. Powles, -34.Rhodes, and J. H. Strange, Mol. Phys., 11, 515 (1966). (16) A. Abragam, “The Principles of Nuclear Magnetism,” Clarendon Press, Oxford, 1961, p 314.
Volume 73, Number I8 h’ovember 1968
4190 -~~
J. C. HINDMAN, A. SVIRMICKAS, AND M. WOOD ~
~
~~~
Table I : Deuteron Quadrupole Coupling Constants Calculated from Infrared and Raman Data
Species
Ref
HzO (gas)
3756
3655
310
HzO (ice)
3210
3085
224
HzO (374’) HzO (A)“ HzO (B)“ HzO (cc14) HzO (CHCls) HzO (Benzene) HzO (CHsNOz) HzO (CHaCN) HzO (Dioxane)
3650 3247 3622 3708 3676 3678 3667 3628 3596
3545 3435 3535 3613 3598 3591 3580 3540 3512
293 252 289 303 299 299 297 291 285
314.2 f 1 . 5 310.3 & 3 318.6 f 2 . 4
Ir 6, 7 7 8 Ir 9, 10 11 12 13 13 4 4 3 3, 4 4 14, 3, 4
a Component A, “lattice water,” not present a t critical temperature.1a Component B, “monomer water.”’$ asymmetry parameter, 7 = 0.100 ie 0.002.
1.5
1
Hexagonal axis
I
1.0 0.9 0.B
0.7 v)
0.6
D
‘0 0.5 0.4 c:
0.3
+ 0.2 0.5 Mol % D 2 0 in CH3N02
1
3
5
7
9
Mol % D 2 0 in CH3CN
0.1
Figure 1. Concentration-temperature dependence of relaxation of DzOin CHaN02 and CHsCN. Estimated uncertainties are indicated by vertical lines for 60.1’ data. These are based on percentage uncertainties in TI f l % for 8.5 mol 76 Dt0, &3% for 5.7 mol % DzO, f 5 % for 3 mol % DzO, and & l l ~for i 1.4 mol % DtO, applicable for both solvents at all temperatures.
clearly established that a linear relationship did not exist, and a semilogarithmic plot was used for extrapolation (Figure 2). It is of interest to note the difference in behavior indicated by our data (Figures 1 and 2) from that observed for mixtures of noninteracting polar components by Kilp, Garg, and Smyth.17 From their results we would have expected little or no variation in the relaxation time over these small concentration regions. The large changes observed suggest that we may, in fact, have association in the solutions, either between water molecules or between water molecules and the solvent. Unless the effect of this association is removed by the extrapolation procedure, the T Q values will represent The Journal of Physical Che’mistry
u 0.1
0.2
3
Mole Fraction D 2 0 in Diaxone
Figure 2. Concentration-temperature dependence of relaxation of DtO in p-dioxane.
upper limits to the true values for the monomeric molecules.
Discussion One of the unique aspects of the behavior of water is that essentially a single dielectric relaxation time is observed and that the correlation time for molecular reorientation calculated from the experimental observations is in reasonable agreement with that predicted from the Debye equation.18 This implies that the molecules relax by a spherically symmetric rotational diffusion process. As a consequence, the quadrupole (17) H. Kilp, S. K. Garg, and C. P. Smyth, J . Chem. Phys., 45, 2799 (1966); E. Forest and C. P. Smyth, J . Phys. Chem., 69, 1302 (1965); S. K. Garg and P. K. Kadaba, ibid., 69, 674 (1965). (18) P. Debye, “Polar Molecules,” Dover Publications, New York, N. Y., 1945, pp 84, 85.
4191
DEUTERON SPIN-LATTICE RELAXATION OF D20
correlation time can be equated with the correlation time for the intramolecular dipole-dipole relaxation16 or derived from the correlation time for dielectric relaxation. 19-21 If correlation times derived from such data are used, together with the experimental spin-lattice relaxation times for liquid D20, to calculate the quadrupole coupling constant for the relaxing species, it is found that the quadrupole coupling constant is much closer to the value for D20 in ice than for the monomeric molecule in the gaseous state. I n fact, the data have been interpreted to indicate that the molecules in liquid water are essentially completely hydrogen bonded even at temperatures as high as ' ' ' ' 0.5 ' ' ' ' ' I.o 300".l5 Mole Fraction DpO in p-Dioxane This is in direct contrast to what we would have exFigure 3. Concentration-temperature dependence pected on the basis of Walrafen's analysis of Raman and of relaxation of D20 in p-dioxane. infrared data for water. According to him, approximately 60% of the molecules in liquid water at 25" are nonhydrogen-bonded monomers. Furthermore, as we have already indicated in Table I, a calculation of the quadrupole coupling constant for this monomer species yields a value close to that for gaseous water molecules. With this discrepancy in mind, we can consider more closely the experimental results. Since a t least qualitatively our experimental results (Figure 3) for mixtures of DzO and p-dioxane parallel those that would have been predicted from S m y t h ' ~ ~ ~ , ~ ~ observations on the dielectric behavior of HzO and DzO mixtures with dioxane, we will first consider his interpretation of the latter data. He suggests that the single dielectric relaxation time for pure water can be interpreted in terms of the relaxation of a polarization process associated with the formation or breaking of ~ r ~ 5of hydrohydrogen bonds He adopts F r a n k ' ~ ~ view 3.0 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 gen bond formation and breaking as a cooperative Mole Fraction of De0 in p-Dioxane process. He suggests that the intrusion of dioxane Figure 4. Concentration dependence of apparent activation molecules into the water structure has two effects which energy of relaxation of DzO in p-dioxane. result in the separate dielectric relaxation processes that are observed. The first is to lengthen the relaxation time for the process associated with the breaking of the associated with the formation of a water-dioxane hydrogen bonds. The second is to screen Some of the plex. According to Fratiello and Douglass,26 a 1 : 1 water molecules from their neighbors. These molecules complex is formed with an association constant of can then relax by rotation with a relaxation time charapproximatelyo.15. From this, approximately 60% acteristic of a monomeric water molecule. He also of the water should be in the form of at the suggests that if some of the water molecules are attached lowest concentration investigated by us. One could by single hydrog:en bonds to the dioxane molecules, they also infer from the experimental data and the infrared should be able .to orient bv rotation around the bond. The correlation time associated with this relaxation D* E* Woessner7J. Phys*i 40*2341 (1964)* might be sufficilently close to that for the reorientation (20) E. N. Ivanov, Soviet Phys. JETP,8, 1041 (1964). of the monomers so as to be experimentally indistin(21) K. A. Valiev and A. Sh. Agishev, Opt. Spectrosc., 16,477 (1964). guishable. (22) C. J. Clemett, E. Forest, and c. P. Smyth, J. Chenz. Phys., 40, By way of illustrating the possibilities, we have 2123 (1964). (23) S. K. Garg and C . P. Smyth, ibid., 43, 2959 (1965). plotted the apparent activation energy for the deuteron relaxation time against the mole fraction of D 2 0 (24) H. S. Frank and W. Y . Wen, Discussions Faraday SOC.,24, 133 (1957). (Figure 4). The maximum a t mole fraction ca. 0.8 (25) H. S. Frank, Proc. Roy. SOC.,A247, 481 (1958). clusters' The be associated with (26) A. Fratiello and D. C . Douglass, J . Mol. Spectrocrc., 11, 476 variation at lower water concentrations might be (1963).
4
'
Volume 7.9, Number 1.9 November 1968
4192
J. C . HINDMAN, A. SVIRMICKAS, AND M. WOOD
observations that the correlation time for the complex would be longer than for the monomer. Table I1 summarizes the data for the quadrupole correlation times derived from the data for water a t infinite dilution in the various solvents a t 25". A number of comments can be made with respect to these data. First, the longest correlation time and the largest activation energy is found for the dioxane solution where we would infer from the infrared and from chemical shift data that the water-solvent interaction is the greatest. The shortest correlation times are noted for the benzene, carbon tetrachloride, chloroform, and nitromethane solutions where the infrared data indicate the least water-solvent interacti~n.~'If we adopt Bondi's view that the correlation time is a funcTable I1 : Quadrupole Correlation Times for Water at Infinite Dilution in Various Solvents at 25'
Solventa
TQ(exPt1) X 1012 see
E,, kcall
9.
mol
CP
see
0'42
2.4
0.601
2.9
0.44 0.55
2.2
0.904
3.7
0.541
2.2
0.345 0.627 1.204
1.4 2.6 4.9
Benzene (I) Benzene (11) CCh (1) CCla (11) CHCla (I) CHC13 (11) CHaCN CHsNOz Dioxane
0.40
rd(calcd)*
0.51 0.81 0.74
2.7 2.3 3.2
0.48 1.23
a 1 = CHaNOz; I I o = CHICN. equation); a = 1.59 A.
'
Td
=
x
7Debye
10'2
(Debye-BPP
tion of the intermolecular energyz8and use the infrared data as an index of the strength of the intermolecular interactions, then we might expect Walrafen's monomer water to have a correlation time somewhere between that for water in dioxane and water in acetonitrile. We also note the experimental correlation times are not simply related to the solvent viscosities and are appreciably shorter than reorientational correlation times calculated on the basis of the Debye-BPP equationZ9 TQ
=
Td
=
4nya3/3kT
(3)
where 7 is the solvent viscosity and a is the molecular radius. These correlation times are, however, considerably longer than would be calculated on the assumptiOn that the mOleCUleS are free or only slightly restricted rotors, i.e.30 TQ
)%(A2
=
I/%
3kT
=
0'5
'0-13
at 250
(4)
where I is the mean moment of inertia of the DzO mOleCUle. The activation energy for the reorientation The Journal of Physical Chemistry
process is also much greater than the approximately 0.5RT expected on the assumption of the molecules as classically rotating spheres with zero or small friction coefficients. These data indicate that water as a solute behaves much as do other substances, either in solution31or as pure I n accord with this, there is better order of magnitude agreement between the experimental and calculated T'S if the appropriate viscosities to be used in eq 3 are calculated using the microviscosity theory. 31-34 Although the differences in TQ for the different solvents are not related to the viscosity differences, it is found that in a given solvent the temperature coefficient is within experimental error that is predicted by the Debye-BPP equation (eq 3 ) . This is illustrated by the data for the nitromethane-carbon tetrachloride solutions (Table 111). Comparison of the quadrupole and dielectric correlation times for the two systems, waterdioxane22 and water-benzene, 2 3 where data are available, indicates that the motion of the water molecules is probably that of isotropic rotational (Brownian) d i f f u ~ i o n ~as ~ - assumed ~~ in the derivation of the Debye-BPP equation (Table IV). Because of experimental difficulties, we have not been able to determine whether or not there is an isotope effect as mould be expected on the basis of the Hill t h e ~ r y . ~The ~ , dielec~~ tric data for the water-dioxane do indicate that an inertial factor may be important. This point must be settled before any final decision can be made as to the best theoretical approach for the calculation of the correlation time. Table 111: Comparison of CCL (CHaN02)Solution;
TQ
r)
and
=
x
Td
for D20 in
TJCCI~ TQ
Temp,
11CCl4,
O C
OP
sec
20.1 27.1 30.1 39.9 50.0
0.966 0.874 0.843 0.739 0.651
0.48 0.40 0.39 0.35 0.31
10'2
x
rd
10'2 see
4.0 3.5 3.4 2.9 2.4
TQ/rd
0.12 0.11 0.11 0.12 0.13
(27) Other data also indicate that water exists primarily as a monomer in benzene, carbon tetrachloride, and chloroform: (a) J. R. Johnson, S. D. Christian, and H. E. Affsprung, J . Chem. SOC.,77 (1966); (b) W.L. Masterson and M. C. Gendrano, J . Phys. Chem.,
70, 2895 (1966). (28) A. Bondi, J . Am. Chem. SOC.,88, 2131 (1960). (29) N. Bloembergen, E. M. Purcell, and R. V. Pound, Phys. Rev., 73, 679 (1948). (30) W.B. Moniz, W.A. Steele, and J . A. Dixon, J . Chem. Phys., 38, 2418 (1963). (31) . , R. W. Mitchell and M. Eisner, ibid., 33, 86 (1960). (32) W.B. Monis and H. S. Gutowslry, ibid., 38, 1155 (1963). (33) A. Spernol and K. Wirts, 2. Naturforsch., Sa, 522 (1953). (34) A. Gierer and K. Wirtz, ibid.,8a, 532 (1953). (35) N. Hill, prOc.r h u s . sot., 6 7 ~ 149 , (1954). (36) R. TV. Mitchell and MI.Eisner, J . Chem. Phys., 33, 86 (1960).
DEUTERON SPIN-LATTICE RELAXATION OF DzO
4193
Table IV : Comparative Correlation Times
x
+Q
10’2
Tdiel
x
101s
Solution
Be0
#eo
rdiel/rQb
DzO (dioxane) DzO (benzene 1
1.23 0.42
5.6
4.6 2.4
1.0“
‘
a HzO. Isotropic rotational (Brownian) diffusion 3; sudden large angle motion, 7 d i e 1 / 7 & = 1.
7die1/7Q
=
Finally, we can conclude by considering briefly the problems involved in reconciling our experimental observations with, on one hand, the infrared data indicating the presence in liquid water of a large concentration of monomer13 with a “gaslike” quadrupole coupling constant, and on the other, the dielectric and proton spin-lattice relaxation data which can be interpreted to indicate that the relaxing species in liquid first the compariwater is “ i ~ e - l i l r e . ” ~We ~ , ~consider ~ son of the dielectric data3’ with the result that is obtained on the assumption that the liquid has monomer and lattice water in the 0.6 to 0.4 ratio indicated by Walrafen. l 3 The experimental spin-lattice relaxation time, T1, can be written
(5)
tion times should be readily detected if the monomer and lattice concentrations and relaxation times are as indicated in the prior discussion.22 Based on the error limits for the dielectric data for water, it appears improbable that we could have as much as 10% of the monomer present. We find a similar discrepancy if we make a calculation based on the assumption that the quadrupole correlation time and the intramolecular dipole-dipole correlation time are equal. l6 The intramolecular contribution to the spin-lattice relaxation time for HzO can be writtenI5
where y is the gyromagnetic ratio, r is the H-H distance in the molecule (1.519 8 for gaslike water molecules), and 7 d is the intramolecular dipole correlation 1 X 10-l2 sec and an experitime. With 7 d = 7Q mental value of TI = 3.39 sec for H20at 25”, the fractional contribution, f, to 1/T1 from the intramolecular relaxation process is 0.24. This compares with an f value of 0.59 calculated on the basis of Krynicki’sa8 evaluation of the intermolecular contribution to T1 and the relation 1/T1
=
1/T1 i n t r a
+
TI inter
(8)
and anfvalue of 0.5 f 0.1 obtained by Powles, Rhodes, and Strangels from an analysis of the variation with temperature of the experimental T1 for HzO and T,Q for DzO. I n summary, our results are in better agreement with the evidence that the concentration of nonhydrogenbonded monomers is low in liquid water4a than with interpretations of various data in terms of appreciable concentrations of such monomers. 13,44-46 On this basis the experimental relaxation times would be primarily controlled by the relaxation of the lattice.
where f m and fl are the mole fractions of monomer and lattice water and T1, and 7’11 the corresponding relaxation times. Wjth the quadrupole coupling constant for the monomer from Table I and a T Q of 1.0 X 10-l2 sec, T1m is calculated from eq 2. With this T1m value, an experimental TI of 0.420 sec for DSO a t 25”, and the quadrupole coupling constant for the lattice from Table I, eq 5 and 2 are used to calculate T Q for the lattice. The result is q(1attice) = 4.4 X 10-l2 sec. A correlation time for comparison is calculated from the dielectric relaxation data37on the assumption that1g~29~38 (37) C.H. Collie, J. B. Hasted, and D. M. Ritson, Proc. Phys. Soe., 60, 145 (1948).
rQ =
(Tdiel,
rnacrosoopic/3)~
(6)
where p is an internal field c o r r e c t i ~ n . Using ~ ~ ~ ~the ~ P o ~ l e svalue ~ ~ for the internal field correction, q = 0.69 at 25”, we calculate TQ = 2.45 X 10-l2. That the correlation time obtained from the dielectric data is intermediate in value is in accord with the idea that it represents a mean of the lattice and monomer contributions. The difficulty is, of course, that within a very small experimental uncertainty, water has a single dielectric relaxation time.41#42Two dielectric relaxa-
(38) K. Krynicki, Physica, 32, 167 (1966). (39) J. G. Powles, J . Chem. Phys., 21, 633 (1953). (40) S. H. Glarum, ibid., 33, 1371 (1960). (41) E. H. Grant, T. J. Buchanan, and H. F. Cook, ibid., 26, 156 (1957). (42) R. Pottel and 0. Lossen, Ber. Bunsenges. Phys. Chem., 71, 135 (1967). (43) D. P. Stevenson, J . Phys. Chem., 69, 2145 (1965). (44) G. Nemethy and H. A. Scheraga, J . Chem. Phys., 36, 3382 (1962). (45) R. P. Marchi and H. Eyring, J . Phys. Chem., 68, 221 (1964). (46) K. Buijs and G. R. Choppin, J . Chem. Phys., 39, 2035 (1963)
Volume 71, Number 11 November 1968
