JOHNC.SCHUG
1816
Solvent Effects in Proton Magnetic Resonance
by John C. Schug Department of Chemistry, Virginia Polytechnic Institute, Blacksburg, Virginia
(Receiued November 6 , 1966)
A method is presented for calculating the proton chemical shifts produced in liquid solutions by magnetically anisotropic molecules of cylindrical symmetry. The method is based on the assumption of complete randomness in the liquid state, and makes use of earlier results based on the cylindrical symmetry. Accounting for all anisotropic molecules in the solution, rather than nearest neighbors only, provides theoretical anisotropy chemical shifts which are comparable to those observed. The calculated results are compared to experimental data on benzene in solutions of n-hexane, carbon tetrachloride, and carbon disulfide, and an empirical set of van der Waals contributions to the chemical shift are derived. These are shown to be comparable to theoretically estimated values. The temperature dependence exhibited by the data is interpreted on the basis of thermal expansion, and is also consistent with the theory. When the theory is applied to proton chemical shifts of toluene, the comparisons are much worse, as is expected from the fact that toluene does not approach cylindrical symmetry.
I. Introduction In recent years a great deal of study has been devoted to solvent effects in high-resolution nuclear magnetic resonance spectroscopy. -6 The understanding gained from this study is apparent in the relation that is commonly used to express the chemical shift, 6, observed for a particular species in solution 6=
6G
+ + 6B
6A
-k
6W
f 63 f 6C
(1)
The several contributions to the experimental chemical shift which are recognized here are 6 ~ the , chemical , shift due shift of an isolated gaseous molecule; 6 ~ the to the bulk diamagnetic susceptibility of the medium; 6 ~ that , due to the anisotropic diamagnetic susceptibili, from van der ties of surrounding molecules; 6 ~ arising Waals interactions with neighboring molecules; 6 ~ , due to the reaction field of the medium, induced if the molecule of interest is polar; and 6c, the shift due to specific intermolecular interactions (complex formation) .6 The usual investigation results from an interest in a single one of these effects, and there then arises the obvious problem of subtracting all other contributions from the experimental chemical shifts. In particular, the three terms 6 ~ ,6w, and 8~ are often troublesome. Buckingham has provided2 the theory for the electricThe Journal of Physicd C h m b t r y
field effect and this, with later refinements which take better account of the molecular shapelg gives a good basis for estimating 63. As the present study is concerned only with nonpolar molecules, this effect is not considered further in this paper. Howard, Linder, and Emerson have tried to develop a similar theory for the van der Waals contribution^,^ and have achieved qualitative success. Similarly, in regard to 8 ~ quali, tative understanding of the effect has been gained, but a general result which accounts for the effect of all molecules in the solution has not been given. Consequently, one generally tries to eliminate 6~ and 6~ experimentally by judicious choices of systems. It is generally possible to convince oneself that the pro(1) Early studies are summarized by J. A. Pople, w. G. Schneider, and H. J. Berydtein, “High-Resolution ,Nuclear Magnetic Resonance,’’ McCiaw-Hill Book Co. Inc., New York, N. T.,1959. (2) A. D. Buckingham, Can. J . Chem., 38, 300 (1960). (3) A. D. Buckingham, T. Schaeffer, and W. G. Schneider, J . Chem. Phys., 32, 1227 (1960). (4) A. A. Bothner-By, J. ,WOE. Spectry., 5 , 52 (1960). (5) B. B. Howard, B. Linder, and M. T. Emerson, J . Chem. Phys., 36, 485 (1962). (6) R. J. Abraham, Mol. Phys., 4, 369 (1961). (7) W.G. Schneider, J. Phys. Chem., 6 6 , 2653 (1962). ( 8 ) J. V. Hatton and W. G. Schneider, Can. J. Chem., 40, 1285 (1962). (9) P. Diehl and R. Freeman, Mol. Phys., 4, 39 (1961).
SOLVENT EFFECTS IN PROTON MAGNETIC RESONANCE
1817
cedures employed are satisfactory, but a firmer basis anisotropic species on the molecule of interest when the for calculating these quantities is highly desirable. two are separated by the vector r, and gt(r) gives the The purpose of the present paper is to describe a probability of finding molecule i in this location. The simple method for calculating the anisotropy shift, brackets indicate that (8At(T)) must represent an average 8A, produced by cylindrically symmetrical molecules. over all possible relative orientations of the two moleThe method makes use of the idea introduced by Bothcules. In addition, the protons of interest are usually ner-By and Glick,’O and further developed by Abralocated on the periphery of the molecule, rather than ham,6 of a proton moving over a cylindrical surface at its center, and this fact must also be taken in account, encasing the anisotropic molecule. It is assumed that at least at small intermolecular separations. Although liquid solutions are completely random in nature,“ these calculations can be done, at least in principle, and the anisotropy shift is therefore found to be directly they are likely to be quite complicated. Therefore, proportional to the volume fractions of the anisotropic this approach is droppcd in favor of a different and much species. Previous attempts to estimate 8~ have only simpler one. approximated the effects of nearest-neighbor moleFocus attention for the moment on a single, say the cules. The present method accounts for the effects jth, molecule of the ith species. The molecule is conof all anisotropic molecules in the solution, and, considered to be a cylinder of radius rl and height h,. sequently, the calculated results are of a considerably Concentric with this molecule we consider a cylindrical larger magnitude. For the first time, it is possible to shell whose height and radius are given, respectively, by calculate dilution shifts (for anisotropic solvents) which h = h, 22 (44 are comparable to those observed. The results are applied in a study of the benzener=ri+x (4b) proton chemical shift in n-hexane, carbon tetrachloride, The shell is of uniform thickness, dz. By allowing x and carbon disulfide solutions. Both the concentrato take on values between zero and infinity, it is postion dependence and the temperature dependence are sible to fill up the entire space which surrounds this investigated. Comparison of the calculated anisoparticular central molecule. The geometry is iltropy shifts with the experimental data makes possible lustrated in Figure 1. The volume of the cylindrical the empirical determination of a sel€;consistent set of shell is easily found to be van der Waals contributions, 8w, for all molecular species concerned. The values obtained for these dV(z) = 2 ~ ( 3 z ri hi)(z ri)dx (5) contributions are shown to be of the same order of In this volume, dV, let there be dN(x) molecules of the magnitude as those predicted by various theories. species whose chemical shift concerns us. If it is asThe high degree of self-consistency attained in the sumed that these molecules are randomly distributed interpretation of the data leads to the conclusion t~hat throughout dV, then the average effect of this jth any contributions, k,from specific molecular interactype i molecule is obtained by integrating over all tions are too sniall to be observed in the present studies. values of z, and dividing by N , the total number of the 11. Effect of Anisotropic Molecules molecules of interest that are present We wish here to obtain a general estimate for 8 ~ and , must therefore calculate the average effect of all anisowhere S,(x) is the average chemical shift effected by the tropic species in the solution on the particular molecule central molecule over the surface of the cylinder at x. of interest. If there is more than a single anisotropic I f p is the distance from the center of the central molespecies present, then cule, and 0 is the angle between p and the molecular 8A = C 8 A I (2) axis, as shown in Figure 1, then, using the equivalent i dipole approximation, l 2 we have where each term on the right refers to the effect of an individual species. Clearly, if the molecule of interest &(x) = ( A x i / 3 ) ( ( 3 cos2 0 - l ) / ~ ~ ) ~(7) is itself anisotropic, its effect must also be included Here, Ax, = xL is the magnetic anisotropy of in the sum. Each term in the summation (2) corresponds to an (10) A. A. Bothner-By and R. E. Glick, J . Chem. Phys., 26, 751 integral over a distribution function
+
+ +
+
(1957).
where
(6At(r))
= f(8~i(r>)gt(r)d~r
(3) is the effect of a molecule of the ith 8Ai
L. Scott, “Regular Solutions,” Prentice-Hall, Inc., Englewood Cliffs, N. J., 1962. (12) H. M. hTcConne11, J . Chem. Phys., 27, 226 (1957). (11) J. H. Hildebrapd and R.
Volume 70,Number 6 June 1966
JOHNC. SCHUG
1818
the result is
where 2h,]/(4ri2
Figure 1. Illustration of a cylindrical shell encasing a cylindrically symmetrical molecule a t a distance, 2.
species i, and the brackets indicate that we require the average value of the enclosed quantity over the surface of the cylinder a t z. This average has been carried out by Abraham,6 and is &(z) = (8Axi/3)(2r - h ) / ( r
+ h)(h2 + 4r2)*’* (8)
In this expression, r and h are given by eq 4, and all quantities are in cgs units. In order to account for the effects of all type i molecules, it is necessary to evaluate t’hesum
=
(l/N)$,fdN(z)& (z) j=l
(9)
where N , is the total number of type i molecules present. This sum can be evaluated by multiplying its average term by the total number, N , , of terms = (Ni,”)Jdfl(x)
6,(x>
(10) where dR(x) is the average number of the molecules of interest inside the cylindrical shell at a distance z from a type i molecule. This is 8Ai
dn’(z) = (p/u)dV(z) (11) where cp represents the volume fraction and u is the molecular volume of the species of interest. The calculation is now a matter of inserting expressions (4) into (8), (5) into ( l l ) , and (8) and (11) into (lo), and integrating over all positive values of z. When this is done, and use is made of the relationship
N t / N = (Pi/4/(cp/4 The Journal of Physical Chemistry
+ hi2)’”
(14)
It should be particularly noted that the result (13) and, therefore, the total anisotropy shift (2) are completely independent of the nature, size, and shape of the molecule under study. This is a direct result of the assumption that every molecule (and each of its protons) visits every possible magnetic environment in a completely random fashion. The magnetic environment, however, is completely determined by the concentrations and characteristics of the anisotropic species. It follows, then, that the anisotropy shift should be identical for every proton in the solution. This explains, among other things, why the solutes, methane and cyclohexane, experience the same highfield shift in benzene as compared with cyclohexane as solvent (one of the questions recentIy raised by Abraham6). One might wish to relate the molecular volume, vi, to the molecular dimensions r f and hi which occur in the result (14). However, it is preferable to interpret r f and hf as the smallest distances at which a proton can approach the molecular center, and we therefore include in ri and hi the van der Waals radius of a hydrogen atom as well as the actual dimensions of the ith molecular species. The anisotropic molecules which primarily concern us here are benzene and carbon disulfide, and assuming for these the same parameters that Abraham used,6 we obtain the results listed in Table I. The usual method for estimating anisotropy effects has been to apply eq 8 directly with x = 0. For example, Abraham has estimated6in this way that a solute in benzene would experience a high-field shift of 0.08 ppm, while one in carbon disulfide would experience a shift of -0.046 Table I : Parameters Employed and Predicted Anisotropy Coefficients Species (4 1029
A hi, A vi, A’ Qii PPm Ti,
Carbon Benzene
8.16 4.3 4.8 147.7 0.507
disulfide
5.0 2.5
8.12 100.1 -0.302
SOLVENT EFFECTS IN PROTON MAGNETIC RESONANCE
ppm. The corresponding numbers obtained from the present calculation are 0.507 and -0.302 ppm, respectively. These are in much better agreement with the values generally associated with 6~ in these
111. Data on Benzene Solutions To determine whether the calculated results agree quantitatively, as well as qualitatively, with experimental data, we now examine the proton chemical shift of benzene dissolved in n-hexane, carbon tetrachloride, and carbon disulfide. The measurements were made on a Varian Model A-60 nmr spectrometer equipped with a variable temperature probe. All measurements were made relative to an external reference of acetic anhydride sealed in a capillary, and all measurements were corrected for bulk susceptibility differences. In connection with the bulk susceptibility differences, the following is noted. The volume susceptibility of each binary system concerned was measured as a function of concentration by means of the concentric tube method developed by Zimmerman and Foster. l 3 In all cases, the volume susceptibilities determined for the mixtures agreed very closely with those calculated on the basis of volume additivity. The experimental data are given in parts per million relative to benzene vapor, corrected for bulk susceptibility differences. The resonance held for benzene vapor was obtained from the work of Schneider, Bernstein, and Pop1e.l' The data obtained at 30' are shown in Figure 2. To within the experimental uncertainty, the benzene chemical shifts depend linearly on the volume fractions, as is required by the results of the previous section. The straight lines shown in the figure were obtained by least-squares analyses, and have the slopes and intercepts listed in Table 11. In all cases, the volume fraction of benzene is taken as the independent variable, so that the slopes and intercepts correspond to the parameters in the empirical relation 6 =
mqBz
+b
(15) ~~~
Table 11: Empirical Constants m and b (in ppm) for the Benzene Proton Chemical Shift in Solutions (See Eq 15) Solvent
n-CeH14 CCla CW
m
b m b m b
30°
00
-209
0.497 -0.083 0.656 -0.248 0.766 -0.351
0.519 -0.101 0.690 -0.283 0.805 -0.389
0.534 -0.113 0.715 -0.313 0.830 -0.413
1819
a Y
%ln
Oa6
i -
0.4
-I
4
0.2
5I u z
0
2 8 a -0.2 W
z
W N
5
-0.4
m
0
0.2
0.4
0.6
0.0
1.0
BENZENE VOLUME FRACTION
Figure 2. Benzene proton chemical shifts as a function of benzene volume fraction in (a) n-hexane, (b) carbon tetrachloride, and (c) carbon disulfide. Chemical shifts are in parts per million relative to gaseous benzene, corrected for bulk susceptibility differences. The lines drawn are the results of least-squares analyses.
In Table I1 also are given the results for these same systems at temperatures of 0 and -20'. Discussion of the temperature dependence will be deferred unt'il a later section, however. Because the data are referred to gaseous benzene and have been corrected for bulk susceptibility differences, it is necessary to interpret these relations in terms of anisotropy (6~), van der Waals (6w), and specific interaction (6,) contributions. To do this, let us consider the 30' data with the aid of the following two assumptions. First, if 2 sizeable van der Waals contribution is felt, it can be consistent with the linear empirical relation (15) only if it can be expressed as
where the summation is extended over all species in solution. The coefficients, wt,will be evaluated empirically. Second, considerable simplification is effected by the tentative assumption that 6, is zero. If this assumption is valid, it should be possible to obtain a selfconsistent interpretation of all the data. If it is not valid, it is expected that some inconsistencies will appear. (13)J. R. Zimmerman and M. R. Foster, J . Phys. Chem., 61, 282 (1957). (14) See ref 1, p 90; W.G. Schneider, H. J. Bernstein, and J. A. Pople, J . Chem. Phys., 28, 601 (1958).
Volume 70, Number 6 June 1966
1820
JOHN C. SCHUG
Our present concern is with binary mixtures only, so that (Osolvent
= 1
- (Obenzene
(17)
and the parameters of eq 15 become m =
- a s o l v + W B ~- wsolv
U B ~
b =
Golv
t
IV. Discussion of van der Waals Coefficients (18a) (18b)
Wsolv
On changing the solvent mixture from pure CCI, to pure CS2, we expect the solute chemical shift to change by -0.103 ppm, which can be compared with Abraham's empirical estimate8 of -0.13 ppm.
Now, taking a, = 0 for i either n-hexane or carbon betrachloride, and employing the U-values calculated for benzene and carbon disulfide (Table I), it is possible to determine W B ~and w'solv for each solution from the empirical constants given in Table 11. The results so obtained are shown in Table 111. The degree of selfconsistency sought is evident in the close agreement of the three independent values obtained for W B ~ . Since there is a possibility that the van der Waals shift depends upon the chemical environment of the proton, it is noted again that the present results were obtained for the aromatic protons of benzene.
In this section, we investigate the possibilities of interpreting the van der Waals coefficients, w,,whose empirical values are given in Table 111. First let us apply the theory found appropriate by Raynes, Buckingham, and Bernstein15 for proton chemical shifts in the gas phase. When a molecule of species i is at a distance r from the proton of interest, this theory gives the chemical shift as aWt(r)=
-10-1s(3aJt)/~6
where at and I , represent the polarizability and ionization potential of molecule i, and electrostatic cgs units are to be used for a, I , and r . In a spherical shell of radius r and thickness dr centered on the proton, the number of molecules of the ith species is dNl(r) = ((0JvJ4m~dr
cc14 csz
-0.083 -0.248 -0.049
-0.093 -0.099 -0.092
=
- 1 2 ~ ( 1 0 - ' ~ ( 0 ~ a ~J I , / vdr/r4 ~) ro
= -4a(10-1s~,I*/viro3)~t
While these results are fresh a t hand, it is interesting to consider two experimental facts which have hitherto been difficult to explain. A. For a nonpolar solute at infinite dilution in a mixture of benzene and cyclohexane, the assumption that w tis identical for cyclo- and n-hexane leads to the conclusion that the proton chemical shift of the solute should depend upon the solvent composition as 6 = 0 . 4 9 7 9 ~-~ 0.083 ppm
(19)
It is thus predicted that upon proceeding from pure cyclohexane OB^ = 0) to pure benzene OB^ = 1) as solvent, a chemical shift of 0.497 ppm should be observed. Abraham6 has estimated this quantity experimentally as 0.43 ppm for both cyclohexane and methane as solvents. B. Considering a solute infinitely dilute in a mixture of carbon disulfide and carbon tetrachloride leads to the result IS = - 0 . 1 0 3 ~-~ 0.248 ~ ppm
The Journd of Physical Chemistry
(22)
The total effect produced by species i is then obtained approximately as
Table 111: Empirical van der Waals Coefficients, WI (ppm), a t 30"
n-C&
(21)
(20)
(23)
where ro is some approximate distance of closest approach. The coefficient of the volume fraction pi is of course w,,by definition. When ro is taken to be 5 A, the values displayed in Table IV are obtained. Obviously, in comparison with the empirical coefficients, these quantities are much too similar for all four species. It is possible t,o change the magnitudes of these theoretical quantities by varying ro, but in order to produce agreement with experiment it would clearly be necessary to use a different ro for each solvent. There are two probable causes for the discrepancies. First, as pointed out by Raynes, et a1.,15 the basic formula (21) is probably not valid at small intermolecular distances. Second, just as in the calculation of the anisotropy effect, an accurate cakulation must account for the actual position of the proton in the molecule, at least for relatively small separations. This latter factor might be used to justify the use of different ro (15) W. T. Raynes, A. D. Buckingham, and H. J. Bernstein, J. Chem. Phys., 36, 3481 (1962).
SOLVENT EFFECTSIN PROTON MAGNETIC RESONANCE
values for various molecules, but this will not be done at the present time.
Table IV : Theoretical Estimates for the van der Waals Coefficients,
Wi
Species
(0
Benzene
n-CsHlr
cc14
CSa
102.4 87.4 103.2 118.5 18.4 16.7 15.3 16.3 1.60 1.00 1.48 2.17 -0.626 -0.567 -0.684 -0.681
10%,, cm3 10121,,ergs 1022vi, cm3 1oB (volume susceptibility) Index of refraction
1.50112 1.37226 1.45759 1.62950
w,, PPm”
-0.108
-0.090
-0.108
-0.147
-0.26
-0.08
-0.27
-0.34
-0,106 -0.076 -0,078
-0.096 -0.060
-0.115 -0.070 -0.071
-0.115 -0.095 -0,098
(TO
=
5 A)
W,‘, PPmb
Wi”, ppmC
-0,058
‘Calculated from eq 23 of this paper. a Calculated according to the methods and correlations presented in ref 5. ’ The three values are based, respectively, upon the approximate eq 22, 23, and 24 of ref 5.
Another attempt to rationalize the empirical constants can be based upon the continuum theory developed by Howard, Linder, and E m e r ~ o n . ~ Actually, their theory yielded poor quantitative agreement with experimental data, but a number of correlations predicted by the theory were exhibited. The two solutes discussed by Howard, et aL15cyclopentane and methane, produced separate and somewhat different correlations; since we are concerned here with benzene as solute, it was natural to employ the correlation obtained for cyclopentane. This correlation was determined by drawing a straight line through the cyclopentane data in Figure 1 in the paper of Howard, et aL5 The square of the effective dispersion field was then calculated in the manner given in that paper; the dispersion chemical shift could then be read directly off the correlation line. As the theory of Howard, et al., was developed for infinitely dilute solutions, these dispersion shifts can be associated directly without van der Waals coefficients. The resulting values are listed in Table IV under the symbol wi’,to differentiate them from the quantities derived earlier. These values are seen to be somewhat larger than those evaluated above. It is encouraging to note, in particular, that a wider range of these quantities now appears reasonable. The relatively large empirical value found (Table 111) for carbon tetra-
1821
chloride might have been thought to be anomalous, but we must now recognize the possibility that this is correct. The values of wt’ calculated for n-hexane and carbon tetrachloride are seen to be in reasonable agreement with the empirical values, but those for the other two solvents appear to be rather poor. Before closing this section, it should also be pointed out that Howard and co-workers also derived5 three more approximate relations for the van der Waals shift. These depend, respectively, upon the solvent properties: (a) volume susceptibility, (b) polarizability and molecular volume, and (c) refractive index. Calculations have also been made on the basis of these approximations, and the resulting values (called wf”) are also listed in Table IV. These values are seen to be comparable to the w 1evaluated above on the basis of the rb dependence, and also remain fairly constant for all four solvents considered. On the basis of this discussion it is impossible to draw any firm conclusions regarding either the validity of the empirical van der Waals coefficients or the possibility of theoretically calculating these a t the present time. We have seen that various approximate theories give values similar to the empirical ones, but fail to reproduce the variation observed between different solvents. Much more work is obviously needed in this vein.
V. Discussion of Temperature Dependence The most obvious possible source of temperature dependence in these chemical shift data are due to the phenomenon of thermal expansion. It is recalled that the expressions (14) and (23) for the anisotropy and van der Waals coefficients, respectively, contain the molecular volume, v,, in the denominators. To determine the importance of this effect, it is convenient to evaluate empirical thermal expansion coefficients from the experimental data (Table 11), and then to compare these with the known values. Two simplifying assumptions are made. 1. Each of the four liquids in question has the same coefficient of thermal expansion ff
=
(dV/bT),/V
(24)
This ensures that once a solution is prepared at any temperature, the volume fractions of all substituents remain fixed at all temperatures. 2. The expansion coefficient, CY, is assumed to be independent of temperature. This simplifies the integration of eq 24, and the result may now be expressed as
V ~ V T=,exp[a(Tz - TI)]
(25)
Volume 70,Number 6 June 1966
1822
JOHNC. SCHUG
This relation is now inserted for the molecular volume in each of the coefficients a, and wi. The exponential temperature dependence (25) is, then, a factor common to every term making up the slopes, m, and intercepts, b (cf. eq 18). Because thermal expansion coefficients are small for liquids, and because a relatively small temperature range is presently of interest, it is permissible to expand the exponential factor and retain only the first two terms. This leads to the approximate temperature dependences mT2/mT1 =
1 - a(TZ
- T1)
The data of Table I1 may now be inserted into these expressions and empirical expansion coefficients evaluated. When the experimental slopes are used in eq 26a, there are obtained the approximate expansion coefficients, CY, = 1.4 X 1.7 X and 1.6 X deg-l, for benzene solutions in n-hexane, carbon tetrachloride, and carbon disulfide, respectively. Treatment of the experimental intercepts with eq 26b leads 4.4 X to the approximate values a b = 5.6 X and 2.7 X low3deg-l, for the three solutions in the same order. The values quoted here are average values, only, as even these empirical expansion coefficienh are found to vary with temperature. These empirical thermal expansion coefficients must be compared with the accepted values16which are about 1.2 X deg-’. The values, a,, derived from the slopes of the chemical shift data, are in fair agreement with this value; the discrepancies could conceivably result from the inadequacy of the two assumptions used in the analysis. The values, ab,derived from the intercepts of the chemical shift data, indicate more serious discrepancies. However, it must be remembered that any temperature dependence which occurs in the reference samples employed will appear directly as a temperature dependence of the intercepts, b. This is probably responsible for these discrepancies, though it is not clear why the values obtained from the three different solvents should differ so greatly. The possibility of specific intermolecular interactions, i.e., complex formation between solutesolvent pairs, must also be entertained as a possible cause of temperature dependence. Of the three solvents employed in this work, there is, as far as we are aware, evidence indicating the formation of a benzene complex only in the case of carbon tetrachloride.11~’~*~~ There is some temptation to relate the relatively large magnitude of the carbon tetrachloride van der Waals coefficient to this phenomenon, and it also appears that the excessive temperature dependeqce of the empirical intercepts, The J O U Tof ~Physical Chemistry
b, noted above, could be so interpreted. These possibilities, though, must be considered in the light of the following facts. 1. The intercepts, b, exhibit excessive temperature dependence for all three solvents, and in fact the dependence is greatest in the case of n-hexane. Carbon disulfide is expected to behave similarly to carbon tetrachloride, and might, therefore, also form a benzene complex. On the other hand, one would expect no corresponding phenomenon in the case of n-hexane. 2. It was shown in the preceding section that the continuum theory of Howard, et U E . , ~ predicts a dispersion chemical shift in dilute carbon tetrachloride which is in good agreement with the empirical van der Waals coefficient. 3. The interpretations presented in earlier parts of this paper are highly self-consistent, and it must be said that they explain the data well. The postulate of solute-solvent complex formation would make it necessary to reinterpret the concentration dependence of the chemical shift data for each solution, as well as the temperature dependence. While the good agreement achieved above is probably somewhat fortuitous, the possibility of disrupting the harmony is not welcomed at the present time. The recent study of Anderson and Prausnitz18 indicates that the equilibrium constant for benzenecarbon tetrachloride complex formation is indeed small. It furthermore appears that if a complex forms, then its chemical shift relative to uncomplexed benzene must be relatively small ( i e . , appreciably less than 1 ppm), else its effect would be observed in the present studies. In view of the formulations developed and employed in this paper, it is clear that if internal references are employed, their chemical shifts will suffer anisotropy and van der Waals effects identical with those experienced by the species under study. It thus appears that any small effects due to complexing might in fact be observable under such conditions.
VI. Data on Toluene Solutions At the single temperature of 30°, we have also obtained chemical shift data for both the aromatic and the methyl protons of toluene in the solvents n-hexane, carbon tetrachloride, and carbon disulfide. Methods of obtaining and treating these data were identical with those described earlier for the benzene solutions. (16) See, for example, J. 6 . Rowlinson, “Liquids and Liquid Mixtures,” Academic Press, New York, N.Y.,1959. (17) J. R. Goatee, R. J. Sullivan, and J. B. Ott, J. Phys. Chem., 63, 589 (1959). (18) R. Anderson and J. M. Prausnita, J . Chem. Phys., 39, 1225 (1963).
SOLVENT EFFECTSIN PROTON MAGNETIC RESONANCE
Again, the chemical shifts were linear functions of the toluene volume fraction, and least-squares analyses produced the slopes and intercepts listed in Table V. These correspond to the empirical constants in the equation 6=
"PTol
+b
(27)
As before, these chemical shifts are hopefully referred to the respective toluene resonances in the gas phase, corrected for bulk susceptibility differences. It must be noted, however, that toluene, to our knowledge, has not been studied in the gas phase, so the origins of the chemical shifts were simply guessed. This could cause sizeable errors in the intercepts, b, but cannot affect the slopes, m. Table V : Slopes and Intercepts Describing the Proton Chemical Shifts in Toluene as a Function of the Toluene Volume Fraction (See Eq 28) Bromatic protons
Solvent
n-CaH14
ccl4
csz
m,PPm b,ppm m,PPm b,ppm m, PPm b, ppm
0.434 -0.100
0.577 -0.248 0.636 -0.342
Methyl protons
Estimated values
0.548 -0.116 0.724 -0.296 0.820 -0.420
0.393 -0.083 0,592 -0.248 0.695 -0.253
1823
In the last column of Table V are given some estimated values for comparison. These were derived from relations (18) by replacing the benzene van der Waals and anisotropy coefficients by the corresponding ones for toluene. The latter were estimated by scaling the benzene coefficients inversely with respect to molecular volume, to obtain aTol = 0.424 ppm, W T =~ ~ -0.080 ppm. This procedure is not expected to yield good results, as toluene does not approach cylindrical symmetry as closely as does benzene. I n fact, the estimated and observed slopes and intercepts are fairly close for the aromatic protons, but are quite different for the methyl protons. The reasons for this are not clear, and this requires additional study. It might be noted that similar studies on the more highly methylated benzenes should also prove interesting, as these again approach more closely the assumed cylindrical symmetry.
Acknowledgments. The author is extremely grateful to Mr. E. G. Cook of the University of Virginia for his very able assistance in obtaining the data employed in this paper. As an undergraduate National Science Foundation participant, I s h . Cook spent the summer of 1965 in the author's laboratory. Thanks are also extended to Ish. D. A. Giardino of Gulf Research and Development Co. for his cooperation in the early stages of experimentation.
Volume 70,Wumber 6 June 1966
