Volume of mixing effect on solvent shifts in fluorine magnetic resonance spectra

JOURNAL

OF MAGNETIC

RESONANCE

22, 479-485 (1976)

Volume of Mixing Effect on SolventShifts in Fluorine Magnetic ResonanceSpectra NORBERTMULLER Department of Chemistry, Purdue University, West Lafayette, Indiana 47907 Received November 7, 1975 Fluorine chemical shifts have been determined for dilute solutions of 1,1,1,10,10,10-hexafluorodecane in twenty saturated hydrocarbon solvents. The van der Waals contribution to the solvents shifts was found to depend on the cohesive energy density of the solvent in an unexpected way. After correcting for bulk magnetic susceptibility effects, the shifts are fairly well correlated by an equation of the form S, = A + B(1 - 243 (n’ - I)@’ + 2), where A and B are empirical constants, n is the solvent refractive index, and c is a function of the cohesive energy density closely related to that used to predict volume changes on mixing for dilute solutions of fluorocarbons in hydrocarbon solvents. INTRODUCTION

The pronounced solvent sensitivity of chemical shifts in fluorine magnetic resonance spectra has been the basis of a number of investigations in physical and biophysical chemistry dealing with such diverse phenomena as surfactant aggregation (I) and protein conformational changes (2,3), Although much useful information is obtainable in this way, the precise magnitudes of these solvent effects remain rather poorly understood. Four additive contributions to the total solvent shift, c,, are generally recognized (4), i.e., cs = CJb+ (Tw+ oa + qE,

PI

where c,, is the effect of the bulk magnetic susceptibility of the solvent, (T, the contribution of van der Waals interactions between solvent and solute, c’athe effect of magnetic anisotropy of the solvent, and cE a reaction field effect. A further term, (r,, arising from specific complex formation is sometimes included (5), but then Go, bE, and 0, are not mutually independent. Despite its usefulness in rationalizing certain trends in solvent shifts, Eq. [l] has not provided a means of predicting fluorine shifts with a satisfying degree of accuracy, or of understanding many of the observed variations of (T,. Even when attention is restricted to nonpolar solvents with essentially zero magnetic anisotropy, so that the last two term,s in Eq. [I] can be neglected, the solvent shifts often behave anomalously. For example, the fluorine shift of 1, 1,l, lO,lO, lo-hexafluorodecane (HFD), after correcting for c,,, is nearly the same in n-heptane as in cyclohexane, even though 6, should change rapidly with changes in the index of refraction of the solvent (6, 7), which is 1.3876 for n-heptane and 1.4262 for cyclohexane. Copyright 0 1976 by Academic Press, Inc. All rights of reproduction in any form reserved. Printed in Great Britain

479

480

NORBERT

MULLER

In this work, the chemical shift of HFD was measured in twenty saturated hydrocarbon solvents. The major objective was to discover whether or not it is possible to account for solvent effects, at least within this limited range of solvents, in terms of bulk properties of the solvent; a negative answer would imply that one can understand the effects only with the help of detailed information about the time-averaged conformation of the solvent molecules and their preferred manner of packing around the solute. An initial attempt to correlate the shifts using empirical parameters representing additive contributions from methyl groups, methylene groups, methine groups, and quadruply substituted carbon atoms quickly proved to be unprofitable. It then became apparent that the shifts for sets of isomeric solvent molecules depend on the heat of vaporization in an unexpected way. It was eventually inferred that gW can vary by a mechanism related to that which gives rise to the positive volume changes on mixing often found for nonideal solutions of nonpolar compounds. EXPERIMENTAL

PROCEDURE

The solvents were the best commercially available materials, in most cases stated to be of 99 % purity or better, and were used without further purification. The HFD was prepared several years ago in this laboratory, as described previously (8). Solutions consisted of 6 ,~l of solute in 600 ~1 of solvent, and the reference signal was that of 1,1,2-trichlorotrifluoro-1-propene, enclosed in a capillary in each NMR sample. The reference compound contained perhaps 4 mole ‘A of 1,2-difluorotetrachloroethane, giving rise to a small fluorine signal having a shift that could be used to establish that the temperature was 35°C f I” for all measurements (9). The spectrometer was a PerkinElmer R-32 operated at 84.67 MHz. Shifts were reproducible to f0.003 ppm or better; the positive sign is used to indicate that shifts are in the high-field direction. RESULTS

AND

DISCUSSION

As a first step in analyzing solvent shifts, it is customary to correct for the bulk susceptibility contribution using the standard equation (10) 6corr= &x + 2.094(x, - XA

PI

in which xr and xs are the volume susceptibilities of the reference and of the sample. Since the diamagnetic susceptibility of 1,1,2-trichlorotrifluoro-I-propene is not readily available, and the origin of the chemical shift scale is arbitrarily chosen anyway, it was decided simply to characterize each solvent by the adjusted chemical shift 6, = &bs - 2.094x,,

[31

using for xs the volume susceptibility of the pure solvent, taken from the tabulation in Ref. (20). For 3-methylhexane, not included in the table, it was assumed that the molar susceptibility was equal to that of the most closely similar isomer, 2-methylhexane, and the volume susceptibility was obtained from this value and the known molar volume at 20°C. The values of 6, are given in Table 1. Semiempirical formulas for estimating rr, have been derived in several ways (11). A typical result is 6, = -4zBct, Il/ro3 V,,

141

FLUORINE

NMR TABLE

ADJUSTED

Cyclopentane Cyclohexane n-Hexane 2-Methylpentane 3-Methylpentane 2,2-Dimethylbutane 2,3-Dimethylbutane Methylcyclohexane n-Heptane 2-Methylhexane 3-Methylhexane 3-Ethylpentane 2,2-Dimethylpentane 2,3-Dimethylpentane 2,CDimethylpentane 2,2,3-Trimethylbutane n-Decane n-Hexadecane cis Decalin trans Decalin

4 (mm) -___-7.557 7.348 7.539 7.384 7.450 7.215 7.333 7.006 7.361 7.198 7.251 7.326 6.994 7.189 7.039 6.953 7.020 6.701 6.796 6.552

481

SHIFTS

1

SOLVENT SHIFTS FOR 1,1,1,10,10,10-HEXAFLUORODECANE AND SELECTED MOLECULAR CONSTAN-BOFTHE

Compound 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16. 17. 18. 19. 20.

SOLVENT

IN HYDROCARBON SOLVENTSATWC

2 - 1 d- + 2

A&IV (cal/cm3)

SOLVENTS,

5 -

0.24436 0.25481 0.22742 0.22549 0.22830 0.22397 0.22745 0.25337 0.23441 0.23287 0.23494 0.23750 0.23139 0.23675 0.23100 0.23530 0.24758 0.25963 0.28347 0.27757

65.73 67.16 52.47 48.96 50.54 44.78 48.25 61.24 55.22 52.00 53.12 54.21 47.84 52.35 48.48 48.36 59.64 63.89 75.94 68.24

0.06199 0.06582 0.02704 0.01863 0.02233 0.00981 0.01702 0.04993 0.03402 0.02588 0.02867 0.03143 0.01611 0.02674 0.01754 0.01727 0.04565 0.05704 0.08900 0.06870

where B is a bond parameter, ~1~and V, are the solvent polarizability and molar volume, r, is an effective solvent-solute distance, and Z, is a mean excitation energy, generally taken to be the solvent ionization potential. For the majority of the solvents used here, ionization potential values are not available. Moreover, this use of the ionization pot’ential has no rigorous theoretical justification and, as a matter of empirical fact, the few available ionization potentials are not helpful in correlating the data in Table 1. For saturated hydrocarbons it seems more profitable a posteriori to replace Z, by a single empirical constant and to treat the data using as a first approximation ow = const(n2 - 1)&r’ + 2),

[51 where the function (n’ - 1) (n’ + 2) is taken as a measure of cc,/VI. This approach is very similar to that originally proposed by Evans (6). F’igure 1 is a plot of S, against (n” - I)/@” + 2). The points for the four n-alkanes fall on .a straight line as required by Eq. [5], but the rest of the data deviate markedly. At first sight it appears that for isomers of about equal refractive index, increasing chain branching produces an enhanced downfield shift, suggesting a possibility of correlating the data by assigning separate empirical constants to methyl groups, methylene groups, and so forth, but such a procedure cannot reproduce the observed differences between isomeric pairs like 2,3- and 2,4-dimethylpentane or cis and tram decalin. For both pairs, the compound with the smaller refractive index actually produces the larger downfield shift.

482

NORBERT

MULLER

(n2-lV(n’

+2)

FIG. 1. Adjusted chemical shifts, 6, = Sobs- 2.094xS, as a function of (n2 - l)/(n” + 2). Numerals are used to identify the solvents as shown in Table 1. The solid line is drawn through the points for the four n-alkanes.

Another suggestion in the literature (4) is that cW may be expected to increase in magnitude as the heat of vaporization of the solvent increases. Figure 2 is a plot of the chemical shifts as a function of the cohesive energy density (22) of the solvent, that is, the energy of vaporization per unit volume at 25°C AE,/ V. Values of AE,/ V calculated from data in standard compilations (13,14) appear in column 4 of Table 1. The series of n-alkanes shows the expected trend of increasing downfield shifts with increasing AE,/ V. However, the really striking and unexpected feature of Fig. 2 is that within each family of isomers 6, is strongly correlated with the cohesive energy density, but with the solvent of highest AEJ V giving the greatest upfield shift.

I 50

Cohesive

70

60

Energy

Density(Ca

l/cm31

FIG. 2. Adjusted chemical shifts as a function of the cohesive energy density of the solvent. The solid line is drawn through the points for the n-alkanes. The points near the upper dashed line represent the isomers of hexane, those near the lower dashed line the isomers of heptane.

A clue as to the possible origin of this peculiar behavior is provided by the discussion by Hildebrand et al. (12, pp. 184-185) of the volume changes on mixing for

FLUORINE

NMR

SOLVENT

SHIFTS

483

solutions of nonelectrolytes. The following equation is given, relating the partial molal volume of the solute, VZ,,and its molar volume, VZo: ( P2 - V,“)/V,O = (dl - dJ’/(~E/iW’),.

WI

Here d1 and dZ are the solubility parameters of solvent and solute, respectively, defined as the square root of the cohesive energy density. The symbol 6 is used for this quantity in Ref. (12) but is replaced here by d to avoid confusion with the symbol for chemical shifi:s. For dilute solutions in saturated hydrocarbons, the derivative (iYE/aV), is approximately (12, pp. 60-61) equal to l.O9d,*. The solvents used in this study have solubility parameters ranging from 6.6 to 8.7. The solubility parameter for HFD is not known, but values given in Ref. (12) for typical fluorocarbon liquids lie close to 6.0. Since the present discussion is centered not on the overall solvent-solute interaction but instead on the interactions between solvent molecules and solute trifluoromethyl groups, it seemed reasonable to attempt to correlate the unexpected solvent shifts with the help of a parameter 5 related to the volume change in Eq. [6] and defined as 5 = (dl - 6.00)2/l.09d,z.

[71

Numerical values of 5 appear in column 5 of Table 1. The physical picture suggested here is that, when the solubility parameter of the solvent is larger than that of the solute, the net effect of the intermolecular forces is to mak.e the solvent molecules pull away slightly from the solute so that the average solvent-solute distance is somewhat increased. To see how such an effect might modify (TV,one may recall that the derivation of Eq. [4] starts with the contribution to 6, from a single perturbing molecule, given (15) by (gppair)w= -3Ba1 Zl/r6,

i?l

where r is the intermolecular distance. The preceding discussion suggests replacing r3 by X3( 1 + 0, where R is some reference value, so that (Cpair)w= -3B~l Il/P(l

+ 9)2.

[91

Since 5 is small, this in turn suggests replacing Eq. [5] with cw = const (1 - 25) (n’ - l)/(n’ + 2).

WI

Figure 3 is a plot of 6, against (1 - 25) (n” - l)/(n’ + 2), with the solid line representing the equation 6, = 17.320 - 45.57(1 - 25) (n’ - I)/@’ + 2). 1111 The root mean square deviation between the measured values of 6, and those calculated with Eq. [l l] is 0.086 ppm. The accuracy of this heuristic equation as a predictive tool still leaves much to be desired. It may be significant that a further improvement can be realized by replacing the term 25 in Eq. [ll J by one which changes with the molar volume of the solvent. With the equation 18.55 a,= 16.181-40.54 l3.6 + Vl1’3I ’

484

NORBERT

MULLER

the root mean square deviation between the observed and calculated shifts is reduced to 0.067 ppm. Here the factor (3.6 + VIli3) is approximately the sum of the cube roots of the molar volumes of liquid carbon tetrafluoride and of the solvent and hence is roughly proportional to the distance of closest approach between a trifluoromethyl group and a solvent molecule. Unpublished data obtained here with benzotrifluoride and 1,3-di(trifluoromethyl)benzene as solutes indicate that solvent shifts for other trifluoromethyl compounds run roughly parallel to those reported above. The same would not be expected for solutes

-. E B co”

FIG. 3. Adjusted chemical shifts as a function of the quantity (1 - 25) (n2 - l)/(n2 + 2), defined in the text. The solid line represents Eq. [ll].

of greatly different structure (6, II), where appropriate “site factors” would have to be included. Extension of the present treatment to other nonpolar isotropic solvents such as carbon tetrachloride seems attractive, but requires an adequate procedure for dealing with the mean excitation energy of Eq. [4]. The use of one constant value both for hydrocarbons and for halogenated compounds is probably not appropriate, but it is not at all certain that uncritical use of the ionization potentials, even when they are available, represents a much better approach. The extent of agreement between the experimental values of 6, and those calculated from Eqs. [l l] or [12] supports two major conclusions. First, many of the apparently erratic shifts can be rationalized without appealing to arguments which involve the details of molecular geometry and packing properties. Second, rr, appears to be strongly affected by a factor which has not previously been recognized and which reflects the same underlying causes as the volume of mixing effects found in hydrocarbonfluorocarbon solutions. Future efforts to account for fluorine resonance solvent shifts on a rigorous theoretical basis must then make allowance for such a factor. REFERENCES I. 2. 3. 4. 5.

N. MULLER, J. H. PELLERIN, AND W. W. CHEN,J. P/zys. Cheer. 76,3012 (1972), and workcited W. H. HUE~TIS AND M. A. RAFTERY, Biochemistry lo,1181 (1971). R. A. PASELK AND D. LEVY. Biochemistry 13,334O (1971). A. D. BUCKINGHAM, T. SCHAEFER, AND W. G. SCHNEIDER, J. Chem. Phys. 32,1227 (1960). J. W. EMSLEY AND L. PHILLIPS, Mol. Phys. 11,437 (1966).

there.

FLUORINE

6. 7. 8. 9. IO. 11. 12. 13.

14. 15.

D. B. N. N. 1.

NMR

SOLVENT

SHIFTS

485

F. EVANS, J. Chem. Sue., 877 (1960). B. HOWARD, B. LINDER, AND M. T. EMERSON, J. Chem. Phys. 36,485 (1962). MULLER AND R. H. BIRKHAM, J. Phys. Chem. 71,957 (1967). MULLER AND T. W. JOHNSON, J. Phys. Chem. 73,246O (1969). W. EMSLEY, J. FEENEY, AND L. H. SUTCLIFFE, “High Resolution Nuclear Magnetic Resonance Spectroscopy, ” p. 260, Van Nostrand Reinhold, Oxford, 1965. F. H. A. RUMMENS, W. T. RAYNES, AND H. J. BERNSTEIN, J. Phys. Chem. 72,211l (1968). J. H. HILDEBRAND, J. M. PRAUSNITZ, AND R. L. SCOTT, “Regular and Related Solutions,” p. 85, Van Nostrand Reinhold, New York, 1970. F. D. ROSSINI, K. S. PITZER, R. L. ARNETT, R. M. BRAUN, AND G. C. PIMENTEL, “Selected Values of Physical and Thermodynamic Properties of Hydrocarbons and Related Compounds,” Carnegie Press, Pittsburgh, 1953. R. R. DREISBACH, “Physical Properties of Chemical Compounds,” American Chemical Society, Washington, D.C., 1955. W. T. RAYNES, A. D. BUCKINGHAM, AND H. J. BERNSTEIN, J. Chem. Phys. 36,348l (1962).