L. S. FRANKEL, C. H. LANGFORD, AND T. R. STENGLE
1376 have discovered the low-intensity intercombination bands in a number of substituted chromium(II1) octahedral complexes. These bands, along with the spin-allowed quartets in the complexes studied, have been assigned on the basis of quadrate fields and the electron correlation parameters have been evaluated. Although these parameters are subject to minor variation because of the uncertainty in the ligand field parameters, the general trend in the variation of these parameters with varying complexes seems to follow a pattern similar to that noted in cubic complexes. I n order to refine further the evaluation of the parameters and confirm the noted trends, studies have to be made on an extended number of complexes. Such studies
should include uncovering the low-intensity doublets, better resolution of the spin-allowed quartets, and, finally, confirmation of the band assignments by polarized spectral measurements on single crystals. Investigations along these lines are currently in progress. Acknowledgments. We wish to thank Mr. Bruce Alper of the Florida Atlantic University Computer Center for programming and Professor S. F. Clark for making many helpful suggestions in the writing of the manuscript. Acknowledgment is made to the donors of the Petroleum Research Fund, administered by the American Chemical Society, for partial support of this research.
Nuclear Magnetic Resonance Techniques for the Study of Preferential Solvation and the Thermodynamics of Preferential Solvation by Lawrence S. Frankel,' Cooper H. Langford,2and Thomas R. Stenglea Departments of Chemistry, Amherst College,and the University of Massachusetts, Amherst, Massachusetts 01002 (Received September 4, 1060)
Two methods for investigating the degree of preferential solvation in mixed solvents have been developed. One depends on the effect of solvent on the nmr chemical shift of sensitive nuclei in the solute. The other utilizes the effect of paramagnetic solutes on the transverse relaxation times of solvent nuclei. The solvation of tris-acetylacetone complexes of Co(II1) and Cr(II1) in several solvent mixtures has been studied. A thermodynamic model of preferential solvation has been devised to interpret these results.
Introduction When a solute is dissolved in a mixed solvent, the solvation shell of the solute need not have the same composition as the bulk solvent, but it may preferentially contain one component of the solvent mixture. Such a case is shown in Figure 1 which illustrates preferential solvation by chloroform in a CCLH-CCId mixture. This phenomenon has long been considered important, and it has been tentatively explored by thermodynamic methods which unfortunately often focus on the properties of the bulk solvent rather than on the solvation shell itself. Recently nmr spectroscopy has been applied to this problem with encouraging results.' Two techniques capable of observing preferential solvation were developed. One depends on the effect of the solvent on the nmr chemical shift of the solute, while the other utilizes the effect of a paramagnetic solute on the transverse relaxatiotl time (Tz) of the solvent nuclei. The interactions responsible for both of these effects are The Journal of Physical Chemistry
short ranged,6,6 and they should isolate contact solvation.
Experimental Section Materials. The solutes, tris(acety1acetone)cobalt(111) and tris(acety1acetone)chromium(111)' were prepared by previously described methods.s The solvents (1) Research Laboratory, Rohm and Haas Co., Philadelphia, Pa. (2) Department of Chemistry, Carleton University, Ottawa 1,
Canada. (3) University of Massachusetts; author to whom correspondence should be addressed. (4) L. 8. Frankel, T. R. Stengle, and C. H. Langford, Chem. Commun., 393 (1965). (5) J. 8. Griffith and L. E. Orgel, Trans. Faraday Soc., 53, 601 (1957);J. S.Griffith and L. E. Orgel, ibid., 60, 1803 (1964). (6) N. Bloembergen and L. 0.Morgan, J . Chem. Phya., 34, 842 (1961). (7) Hereafter referred to as Co(acac), and Cr(acac)s. (8) W. C. Fernelius and J. E. Blanch, Inorg. Syn., 5, 130 (1957); B. E.Bryant and W. C. Fernelius, &id.,5, 188 (1957).
1377
NMRSTUDYOF SOLVATION THERMODYNAMICS
I
1
I
.8
I
I
Mole Fractlon CCl3H
.c
1
Figure 2. Solvation of Co(acac)a in chloroform-carbon tetrachloride mixtures; WOchemical shift method. The equisolvation point is indicated by the arrow. Figure 1. Preferential solvation by chloroform from a chloroform-carbon tetrachloride mixture.
either were of reagent grade quality or were purified by distillationat reduced pressure. N m r Measurements. Proton relaxation times were measured from absorption mode spectra taken on a Varian A-60 or a DP-56.4 spectrometer. Values of TZ were determined from the line width at half-height. The maximum error was 5%, although a lower value was achieved in favorable cases. Chemical shifts for 6 g Cwere ~ measured on the Varian DP instrument operating at 8.1 MHz. The spectra were recorded as derivative curves of the absorption mode. A set of coaxial sample tubes was used to measure the chemical shift of the solute in a mixed solvent relative to the solution in a pure solvent as an external standard. An error of 2 ppm, or 1%, was usually observed in this procedure.
1
I
I
I
E
I 2
Male Fraction CC13H
Figure 3. Solvation of Cr(acac)a in chloroform-carbon tetrachloride mixtures; solvent relaxation time method. The equisolvation point is indicated by the arrow.
In the absence of strong chemical bonds, the residence time of solvent molecules in the solvation shell is quite short, and the fast exchange condition is fulfilled. When no preferential solvation occurs, a plot of 5 g C chemical ~ shift vs. bulk solvent composition will Results yield a straight line. The results of such an experiment Two methods for the nmr study of preferential solfor the CClaH-CCI4 solvent system are given in Table vation were developed. In the first method one obI, and shown in Figure 2. The pronounced deviation serves the effect of solvent composition on the chemical from a straight line indicates strong preferential solshift of a nucleus in the solute. For this experiment vation, with CC13H predominating in the solvation we have chosen a diamagnetic, neutral solute which shell. A convenient measure of the degree of prefercontains a nucleus which is especially sensitive to its ence is the bulk solvent composition at which both solenvironment. The complex Co(a~ac)~,which convents participate equally in the contact solvation shell. tains the sensitive 69C0 nucleus, served as the paradigm This is the composition at which the chemical shift for this work. The second method depends on the lies midway between the values for the pure solvents. effect of a paramagnetic solute on the transverse relaxWe have called this the equisolvation point; it is indiation time ( T2)of nuclei in the solvent molecules. We cated by an arrow in Figures 2 and 3. have chosen Cr(acac)a as the paramagnetic solute beThe chemical shift method can be used only when cause one expects the solvation properties of Co(acac)s the solute contains a nucleus which is particularly soland Cr(acac)a to be quite similar. Thus the two methr vent sensitive. In this sense, the 69C0nucleus is a good ods can be used to check one another. probe since the low-lying excited electronic states cause Chemical Shift Method. The chemical shift of the the chemical shift to be exceedingly sensitive to the 6 9 Cnucleus ~ in Co(acac)s is very sensitive to s o l ~ e n t . ~ surroundings.6 In a mixed solvent the composition of the solvation Relaxation Time Method. In the Vicinity of a parashell will fluctuate about some average value. If the magnetic solute there are strong fluctuating magnetic fluctuatjons are fast compared with the reciprocals of the chemical shifts (in cycles per second), the observed (9) R. Freeman, G . R. Murray, and R. E. Richards, Proc. Rot/. shift will reflect the average solvation shell composition. Soc., A242, 465 (1957). Volume Yh, Number 6 March 19, IDYO
1378 fields which cause nearby nuclei to have very short relaxation times. If solvent molecules exchange rapidly between a diamagnetic (bulk solvent) environment and a paramagnetic (solvation shell) environment, the observed relaxation time will be the average of the values in the two environments weighted for the fraction of solvent present in the two environments. That is, the experimental relaxation time (determined from the width of the absorption line a t half-height by Tz-' = n A Y) is given by lo
where P A is the probability of finding a solvent molecule in the diamagnetic environment, T ~isAthe relaxation B the cortime in that environment, and p~ and T ~ are responding quantities for the paramagnetic environment. I n solutions relatively dilute in paramagnetic solute, PA is near unity, and TU can be estimated from relaxation times in the absence of paramagnetic solute. Thus for a solution the experimental line width minus a B. small correction for T ~ isAproportional to ~ B / T ~One cannot readily determine T 2 ~but , under the assumption that it is a constant, information concerning values of p~ for different solvent compositions can be obtained. For a given component of a mixed solvent (e.g., CClsH in a CC13H-CClt mixture) the product of P B / T ~with B the bulk concentration of that component is proportion81 to the number of moles of that component in environment B. In the absence of preferential solvation the fraction of CC13H in the solvation shell will be directly proportional t o the bulk concentration of CCl3H. The effect of preferential solvation is to cause a deviation from linearity in a plot of the solvation shell composition us. bulk solvent composition. The appropriate plot is shown in Figure 3 using data from Table I. Here the product of the line width (corrected for T 2 ~of)CClsH and the volume fraction of CClsH in the solvent mixture is plotted VS. the mole fraction of CC&Hin the bulk solvent. The shape of the curve shows preferential solvation by CCl3H; it is almost identical with Figure 2. The equisolvation point occurs a t a chloroform mole fraction of 0.075. This compares well with the value of 0.090 obtained by the chemical shift method for Co(acac)3. The line width experiment was performed on two sets of solutions one of which contained twice the Cr(acac)a concentration of the other. The line widths of the concentrated solutions were double those of the dilute solutions, and the same solvation shell compositions resulted. The data reported here are the averages of both runs with the line width normalized to the lower concentration of Cr(acac)a. There is an important assumption inherent in this approach. This is, the magnetic coupling between the central metal atom and a given molecule in the solvation The Journal of Phyedcal Chemistry
L, S. FRANREL, C. H. LANOFORD, AND T. R. STENGLE Table I: Preferential Solvation of Cobalt(II1) and Chromium(II1) Acetylacetones in CClaH-CCla Mixtures Mole fraction CClaH
Volume fraction CClsH
1.000 0.916 0.829 0.738 0.645 0.548 0.447 0,342 0.232 0.119 0.060 0.000
1.000 0,900 0,800 0.700 0.600 0.500 0.400 0.300 0.200 0.100 0.050 0.000
SQCO
Line width CClaH
38.4 42.9 46.1 51.6 61.3 73.5 86.4 115 149 256
ohemical shift,a Ha
647 640 652 656 649 652 635 607 550 434 303 000
a Reported as the shift between the given solution and the pure CCh solution.
sphere is independent of the overall composition of the solvation sphere. For example, we assume that the replacement of some CCLH molecules by CC14 will not affect the coupling between the metal atom and each of the remaining CCLH molecules. Although this assumption seems quite valid for the systems studied here, it will not necessarily hold for every system. It should be carefully checked when applying these techniques t o other systems, particularly for systems involving strong or unusual types of solvent-solute interaction. The assumptions involved were tested by determining solvation curves for a number of solvent systems. The consistency of the results obtained by the chemical shift method, used for C o ( a c a ~ )and ~ , the relaxation time method, used for C r ( a ~ a c )is ~ ,shown by the equisolvation data in Table 11. The nature of the magnetic coupling leading to paramagnetic relaxation is quite different from that which produces the 6 9 Cchemical ~ shifts. Since the two methods give similar results, the assumption of a lack of dependence of the magnetic coupling on the solvation sphere composition is amply confirmed. Furthermore, the expectation that solvation will be similar for such similar solutes is fulfilled. The most preferred solvents in the list are CClaH and CHaOH, the only ones capable of forming hydrogen bonds. Recent work has shown that these two solvents do indeed form weak hydrogen bonds with acetylacetone complexes.11
Discussion I n many respects preferential solvation resembles preferential adsorption from a liquid mixture onto a surface-active solid. Indeed, the thermodynamics of both processes can be described in similar terms. I n (10) H. M . McConnell, J . Chen. Phgs., 28,430 (1958). (11) T. S. Davis and J. P. Fackler, Jr., Inorg. Chem., 5 , 242 (1966).
1379
NMRSTUDY OF SOLUTION THERMODYNAMICS Table I1 : Equisolvation Points for Various Solvent Systems Equiaolvation point mole fraction chloroform W o chemical Line width methoda shift method
Solvent system
The configuration entropy can be calculated on the assumption that both the bulk solvent and the solvation shell obey the laws of regular solutions. Then we can use the relationship
-R
S(configuration)
0.075 0.135 0.265 0.235*
CClaH-CCld (25') CClaH-CClr (48') CClrH-acetone CClsH-p-dioxsne CClsH-CsHa (5') CClsH-CaHe (22') CClaH-C& (36") CClaH-CHaOH CClaH-dimethylformamide
c c E
0 . 55d 0
0.090
0.435
a The line width of the chloroform was used to determine the solvation. b The width of the dioxane line gives the equisolvation point as 0.32. The line width method could not be applied because the two solvent signals overlap. d The hydroxyl line width of the CHaOH gives the equisolvation point as 0.72. 0
preferential solvation we consider the solvent to be distributed between two phases, the bulk solvent and the solvation shell of the solute. We assume that the solvation shell is made up of independent sites which are always occupied. For simplicity we will take the solvation number t o be the same for both solvents and assume that there is a one-to-one replacement of solvent molecules. Thus if J is the solvation number, and we take a quantity of solution containing 1/J moles of solute, the solvation shell phase will contain exactly 1mol of solvent regardless of its composition. If one starts with N moles of a mixed solvent containing X A mole fraction of A and X B of B and adds to it 1/J moles of pure solid solute, the solution process which takes place causes n A moles of solvent A and n~ moles of B to be removed from the bulk and transferred to the solvation shell phase. The size of the system is such that n A n~ = 1. After the solution has been formed, the bulk phase consists of x A N - n A moles of A and X B N - n B moles of B. The change in free energy for the process can be represented as
+
- TAb'(configuration) nBAHB -
AG'
1ZAAHA
nATASA(therrna1)
- nBTASB(therrna1)
(2)
TASA(therrna1)
(3)
(4)
and make a similar definition for solvent B, we have AG =
nAAG'A
f nBAG'B
- TAS(configuration)
(6)
21
SUI t
=
+ Sa + SZ- SI
(7) The additional term, SA,is the entropy of mixing the 1/J moles of solute into the N - 1 moles of bulk solvent. It is a constant in reasonably dilute solutions; that is, it depends only on solute concentration, and not on n A and ?LB. Rewriting eq 7 in more detail, we have AS(oonfiguration)
AS(configuration)
-R{
=
S 4
[nA In
+
(n~)
nB
In
(nB)]
(XAN- n ~In) [(%AN - ~A)/(N 1)l
(XBN- n ~In) [(xBN- n B ) / ( N N[xA
In
(28)
+
XB
In
+
+
- l)](zB)I)
+ S4
(8)
The condition for equilibrium is that the AG of eq 2 be a minimum with respect to composition of the solvation shell. Differentiating with respect to %A while holding the total quantities of all phases constant (e.g., use n~ n B = l),as well as temperature and pressure, and then equating the result to zero gives
+
bAG -BnA
- (AG'A - AG'B)
+
RT In [ ~ A ( z B-N~ B ) / ~ B ( x-A~NA
)I
(9)
and
-AGo/RT = In [ ~ A ( x B-Nn B ) / n B ( Z A N
- n ~ ) ] (10)
where
Where AHA is the molar enthalpy change associated with the transfer of solvent A from the bulk phase to the solvation shell, and AXA(therma1) includes all entropy changes for A molecules other than those due to the composition of the two phases. Similar definitions hold for solvent B. If we define AG'A = AHA -
zt In
to calculate S(configuration) for the three phases of interest: (1) the bulk solvent before the solution process, ie., N moles of liquid composed of XANmoles of A and x B N moles of B, (2) the bulk solvent in the final state, i.e., N - 1 moles of liquid composed of XAN- n A moles of A and ZBN- n~ moles of B, and (3) the solvation shell in the final state, 1 mol of mixture composed of n A moles of A and n B moles of B. We obtain the re-
0.245 0.220 0.135 0.160 0.190 0.70
AG = AG'
i
(5)
AGO = AG'A
- AG'B
(11)
The expression for AGO can be cast into a familiar form if we note that the argument of the logarithm is simply a ratio of mole fractions. That is AGO = -RT In K
(12)
K
(13)
with the definition =
YAYB/YBYA
where Z/A and Z/B refer to the mole fractions of A and B in the solvation shell, and Y Aand Y Brefer to the bulk SOL vent. Volume 74,Number 6 March 19,l B r O
L. S. FRANKEL, C . H. LANGFORD, AND T. R. STENGLE
1380 This treatment of preferential solvation predicts a simple relationship between the composition of the bulk solvent and the solvation shell along an isotherm, Le., YA/YB = K ( Y A / Y B ) . A plot of the proper ratios should give a straight line of slope K. For this purpose it is awkward to use systems that have a very large (or very small) value of K . Here the solvation shell is made up almost entirely of one component, and a small experimental error in the mole fraction in the predominant component will lead to a large error in the mole fraction of the minor component. This will be particularly true when the relaxation time method cannot be used to study the minor component directly. For this reason the CClaH-CCld system will not be discussed in this context. A value of K can be estimated from the data taken in solutions quite rich in CCL; the result is K = 14.
I
1
i
'CC13H/Y
benzene
Figure 6. Temperature dependence of the solvation isotherm of Co(acac)a in chloroform-benzene mixtures; 6 9 C chemical ~ shift method.
-
.8
x
Y
(3
0
I
.5
Yc ci3H/
1
2.5
Yo c e ton e
Figure 4. Solvation isotherm of Co(acac)a in chloroform-acetone mixtures; W o chemical shift method,
I
I.
.6
3.2 3.4 1 0 ~PK-~) 1 ~ Figure 7. van? Hoff plot for the solvation of Co(acac)a in chloroform-benzene mixtures.
4.O
.3 'CC13H
Y ~x A N i E~ Figure 5. Solvation isotherm of Co(acac)a in chloroform-p-dioxane mixtures; 59Co chemical shift method. The Journal of Physical Chemistry
The appropriate plots for solvent mixtures containing chloroform with acetone, with p-dioxane, and with benzene are presented in Figures 4, 5, and 6 . Both the acetone and p-dioxane systems show some curvature just outside the limit of experimental error. This is most probably due to a weak interaction with the chloroform causing the bulk phase to be a nonregular solution. However it could also be due to a breakdown of the assumption of equal solvation numbers. Since the CC13H-C6H6 system seemed to be especially well behaved, it was studied a t several temperatures. Due to overlap of the proton signals, the relaxation time method could not be used, and all the data are derived from WOchemical shift measurements. As one would expect, the solvation becomes less preferential a t higher temperatures. Figure 6 shows the equilibrium plot for three different temperatures and the resulting values of K . Applying the van't Hoff equation to these data gives the plot shown in Figure 7.
NMRSTUDY OF SOLVATION THERMODYNAMICS
1381
'CC13H
Y C H -~O H
Figure 8. Solvation isotherm of Co(acac)a in chloroform-methanol mixtures; 6gCo chemical shift method.
From this we obtain the values AHo = -2.3 kcal and A S 0 = -4.7 eu. I n this treatment the AHo obtained ~ ~ is the quantity AHA - AHBand ASo is A S ~ ( t h ~ A S ~ ( t h e r m ~ i evaluated ), at 298'K. Not all solvent mixtures show the isotherm predicted by eq 12 and 13. A deviant system is illustrated by Figure 8 which is the isotherm plot for chloroformmethanol solvation. The results for this system are somewhat less precise than usual because the solvent shift of the W Oresonance is small, and when using the line width technique, difficulty is encountered because the signals from the two solvents often overlap. The b9C0data give the equisolvation point as 0.70 mol fraction CCLH, while the line width of the hydroxyl group yielded 0.70 and of the CC13H gave 0.55. I n Figure 8 the dashed line is the isotherm that would be followed in the case of random solvation, Le., for K = 1. The
~
experimental curve divides itself into two distinct regions. At low CCI3H concentration, CClaH is preferred in the solvation shell; a t high CCLH concentration, CHBOH is the solvent of preference. This result can be understood in terms of the structure of liquid methanol and the effect produced by diluting it with a second solvent. I n the pure liquid state, methanol exists as a mixture of various polymeric hydrogenbonded s ~ e c i e s . ~ The ~ J ~addition of a small amount of CC13H will not affect this structure significantly. I n mixtures which are dilute in CClaH it is seen that CClaH is the preferred solvent, and that the preference for methanol is to remain in the polymeric bulk solvent state rather than enter the solvation shell. At high CCllH concentration, however, the polymeric methanol structure is broken up, and in t,he main, the methanol exists as free CHaOH molecules. I n these circumstances, is the preferred solvent. I n short, the devialmethanol ) tion shown by the CCLH-CHsOH system is simply due to tlie fact that the bulk solvent phase is not a regular solution. This is consistent with the results of MoelwynHughes and Missen,14 who observed that this system exhibited large excess entropies of mixing and is thus far from regular. Acknowledgment. This investigation was supported by the Directorate of Chemical Science, Air Force Office of Scientific Research under Grants AFOSR 21265 and 68-1384. (12) M. Falk and E. Whalley, J. Chem. Phys., 34, 1654 (1961). (13) E.D.Becker, ibid., 31,269 (1959). (14) E.A. Moelwyn-Hughes and R. W. Missen, J . Phys. Chem., 61, 618 (1967).
Volume 74, Number 6 March 19, 1970
