Solvent Effect on 'F Chemical Shifts
An average value of --x= 3.90 f 0.04 is found from 11other related chelates that are not adducts. The uncertainty quoted in the average is the standard deviation from the mean. Thus we have more evidence to support the hyDothesis that small differences in the immediate environment of the copper(I1) ion may be reflected in the x value. Hydrogen bonding to the ligand oxygen may not be the only parameter affecting the value of x for there is evidence that x is also affected by the amount of tetrahedral distortion about the Cu(II), an effect that is still under investigation,,15The increase in frequency of the d-d transition would seem to rule out any significant tetrahedral distortion since the shift is in the wrong direction. Acknowledgment. The authors thank Dr. M, 1,Scullane for in the synthesis and crysta1 growth phases Of this work, and Professor R. s. Andersen for the use of his
The Journal of Physical Chemistry, Vol. 83,
No. 11, 1979 1393
K-band equipment. A grant from the Research Coporation is gratefully acknowledged.
References and Notes H. C. Allen, Jr., and M. I. Scullane, J . Coord. Chem., 8, 93 (1978). M. I . Scullane and H. C. Allen, Jr., J . Coord. Chem., 8, 87 (1978). M. I. Scullane and H. C. Allen, Jr., J . Coord. Chem., 4, 255 (1975). E. N. Baker, D. Hall, and T. N. Waters, J. Chem. SOC.A , 406 (1970). (5) E. N. Baker, D. Hall, and T. N. Waters, J. Chem. SOC.A , 406 (1970). (6) M. I. Scullane, Ph.D. Thesis, Clark University, 1976. (7) D. Close, Ph.D. Thesis, Clark University 1973. (8) B.J. Hathaway and D. E. Billing, Coord. Chem. Rev., 5, 143 (1970). (9) J. E. Geusic and L. C. Brown, Phys. Rev., 112, 64 (1958). (10) A. H. Maki and B. R. McGarvey, J . Chem. Phys., 29, 35 (1958). (11) D. E. Billing and B. J. Hathaway, J . Chem. Phys., 50, 2258 (1969). (12) D. Hall and T. N. Waters, J. Chem. Soc., 2664 (1960). (13) L. M. Shkol'nikova, E. M. Yumal, E. A. Shugam, and A. Voblikova, Z. Strukt. Khim., 11, 886 (1970). (14) M. I. Scullane and H. C. Allen, Jr., J . Coord. Chem., in press. (15) H. C. Ailen, Jr., and D. J. Hodgson, unpublished. (1) (2) (3) (4)
Use of Fluorine-19 Chemical Shifts to Measure Deviations from Random Mixing in Binary Solutions Near the Consolute Temperature. The System Hexane/Perfluorohexane Norbert Mullert Department of Chemistry, Purdue University, West Lafayette, Indiana 47907 (Received March 6, 1978)
The 19Fchemical shifts of the trifluoromethyl groups have been measured as a function of composition in hexane/perfluorohexane mixtures at 25,35,45, and 55 "C. The lowest temperature is just above the reported upper consolute temperature of 22.65 "C. Differences between the observed shifts and values anticipated for hypothetical ideal solutions are ascribed to the known volume increase on mixing and to the persistence of short-range order, with 1-1 and 2-2 contacts preferred over 1-2 contacts. Interpreted in this way, the data at each temperature provide a means of evaluating the quantity w/z appearing in Guggenheim's quasi-chemical treatment and equal to half the energy cost of converting a 1-1 pair and a 2-2 pair into two 1-2 pairs. The effects of imperfectly random mixing found at 55 "C are roughly 60% as large as those at 25 "C.
Introduction Although there is as yet no theoretical treatment which yields accurate predictions of solvent effects on fluorine NMR chemical shifts, significant information about interactions between components can sometimes be obtained by studying the shift of a probe molecule as a function of composition in a mixed solvent system. When an inert probe is used and the solvent molecules are magnetically isotropic, the solvent shift is dominated by the bulk susceptibility and van der Waals contributions,l and if the cosolvents mix ideally with one another the observed shift is a linear function of the volume fraction, i.e. where J1, ti2,and 6, are the shifts when neat 1, neat 2, or a mixture is used as the solvent. Since the probe concentration typically is kept very low, the volume fraction 420may be evaluated by using where n, is the number of moles of cosolvent i, having molar volume V,O. Behavior consistent with eq 1was first reported by Filipovich and Tiers2 and has been found for a number of other systems in this laboratory. Thus, though no rigorous (derivation of (1)exists, it now seems appropriate to look for special effects whenever observed 0022-365417912083-1393$01 .OO/O
values of 6, deviate appreciably from those given by (1). Several examples of such deviant behavior have recently been reported and explanations proposed. When one of the cosolvents is an electron donor and the probe is an acceptor, charge transfer interactions3 produce a strong curvature in the dependence of 6, on $2. When the probe is inert, but there is a substantial volume change on mixing the cosolvents, as for waterldioxane, a less pronounced but readily measurable curvature is found.' In the solvent systems water / tetrahydrofuran and water/ tert-butyl alcohol, 6, depends on the composition in a much more complex way, suggesting that water tends to enclathrate cosolvent molecules in the highly aqueous region while a t higher cosolvent concentrations the solutions become microheterogenous, with the trifluorohexanol probes located preferentially in cosolvent-rich d0mains.l Such microheterogeneity is also anticipated for strongly nonideal mixtures of nonaqueous solvents, especially in the neighborhood of the critical solution point. For example, it is well known that two-component systems having an upper consolute temperature show strong opalesence just above the consolute point, which is attributed to large concentration fluctuation^.^ This opalescence dies off rapidly when the temperature is raised, as is to be expected since increasing the molecular kinetic energies should tend to erase any residual order. Very few simple experimental approaches exist that permit one to determine to what (E 1979 American Chemical Society
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The Journal of Physical Chemistry, Vol. 83, No. 11, 1979
extent nonrandom mixing persists at temperatures when opalescence is no longer observable. This sort of information is needed to test relevant theoretical treatments, and this work was undertaken in the hope that I9F chemical shift measurements would provide it. In an earlier proton NMR study of a binary liquid system near its critical solution point, data were obtained at only one temperature and no quantitative conclusions about the deviations from random mixing were drawna5 The system n-hexane (component 1)lperfluoro-n-hexane (component 2) is ideally suited for such an investigation. Since neither component is self-associated and both are inert and nonpolar, the only terms expected to contribute to the medium effect are those due to bulk susceptibility and van der Waals interactions. Since perfluorohexane is itself a source of I9F signals, it is not necessary to risk perturbing the system by adding a third component as a probe. The upper consolute point, at 22.65 "C, is easily accessible,6 while the boiling points are high enough to allow measurements to be made at atmospheric pressure up to 55 "C. The volume change on mixing is large and temperature dependent, but an unusually complete set of data is available6 allowing density corrections to be made without need for additional experiments. The results given below show that deviations from random mixing can be inferred from the concentration dependence of the 19F shifts and that they remain appreciable even at 55 "C.
Experimental Section Research grade (99.96%) hexane from Phillips Petroleum Co. was used without further purification. Perfluoro-rz-hexanepurchased from PCR Research Chemicals, Inc., was initially about 85% pure. One group of impurities, which could be removed by careful fractional distillation, apparently consisted mainly of isomers of perfluoro(dimethylcyclobutane), identified by their NMR ~ p e c t r aand , ~ perhaps traces of material containing CFzH groups. The remaining impurities could not be entirely removed by distillation even with a spinning band column and probably consisted of branched isomers of perfluorohexane having boiling points within 1 or 2O of that of the rz isomer.8 One major component, perfluoro(2methylpentane), could be definitely identified by its characteristic multiplet in the CF, region of the ~ p e c t r u m . ~ Two fractions were eventually obtained that were free of the first group of contaminants, one containing about 8% branched isomers, the other 15%. The principal CF, peaks of these fractions gave identical chemical shifts both as neat liquids and on dilution with equal volumes of hexane. Noting further that even the crude perfluorohexane gave CF, shifts differing from those for the purified samples by only 0.02 ppm or less, depending on the concentration, it was concluded that meaningful data could be obtained without a need for complete removal of the branched isomers. The perfluorohexane finally used to prepare the solutions was distilled material containing about 10% branched isomers. Samples were made by injecting known amounts of the liquid components from volumetric syringes into NMR tubes and inserting sealed capillaries filled with neat trifluoroacetic acid to provide the reference signals. Spectra were taken with a Perkin-Elmer R-32 spectrometer operated at 84.669 MHz. The reported shifts are for the CF, peak, which lies upfield from the reference line, making it convenient to assign positive values to shifts to higher fields. The temperature was adjusted as required using the temperature controller provided with the spectrometer. Past experience with this instrument shows that in the range of interest the true temperature differs
Norbert Muller
TABLE I: T r i f l u o r o m e t h y l Group Chemical S h i f t s in Hexane/Perfluorohexane M i x t u r e s as a F u n c t i o n of ComDosition a n d TemDerature
"F chemical shiftsa @2O
0 0.01 0.02 0.04 0.07 0.10 0.20 0.30 0.40 0.50 0.60 0.70 0.80 0.90 1.0
25°C
35°C
45 " C
55 "C
3.62gb 3.665 3.698 3.785 3.879 3.980 4.286 4.534 4.714 4.851 4.967 5.082 5.176 5.286 5.387
3.652b 3.682 3.715 3.793 3.888 3.985 4.267 4.515 4.712 4.837 4.957 5.078 5.175 5.284 5.387
3.676b
3.700b
3.738 3.803 3.899 3.996 4.273 4.500 4.699 4.831 4.958 5.017 5.190 5.294 5.381
3.760 3.821 3.915 3.999 4.273 4.498 4.679 4.832 4.960 5.085 5.193 5.301 5.387
In ppm u p f i e l d from e x t e r n a l t r i f l u o r o a c e t i c acid. E x t r a p o l a t e d values.
a
_----
" I
X
w .x,
____ ---,IO
.20
---_
.30
.40
.SO
.60
,70
.80
.90
1.0
PERFLUOROHEXANE CONCENTRATION,
Figure 1. Excess chemical shifts as a function of the volume fraction of perfluorohexane in mixtures with hexane. The dashed curves were calculated assuming random mixing but allowing for the reported volume changes attending mixing. The solid curves represent results of model calculations including also the effects of nonrandom mixing.
by less than 1" from the nominal value. It is difficult to set rigid limits on the accuracy of the shifts, but each one represents an average of several determinations, and it seems likely that the errors do not exceed f0.005 ppm in most cases. The shifts obtained at four temperatures are presented in Table I as a function of the ideal volume fraction of perfluorohexane.
Discussion Inspection of the data immediately reveals that the points cannot be adequately represented by eq 1. By analogy with the definitions of excess thermodynamic quantities for binary mixtures, it is convenient to focus attention on the excess chemical shifts, 6E, defined as 6E =
bobsd -
41'61 - 42'62
(3)
The excess shifts are readily evaluated from the values in Table I, and they are graphically presented in Figure 1 together with curves representing results of model calculations described below. Effect of the Excess Volume of Mixing. As already noted, large volume changes attending mixing have been
The Journal of Physical Chemistry, Vol. 83,
Solvent Effect on 'F Chemical Shifts
found for hexane/perfluorohexane solutions. The effect of such a change on the chemical shift can be predicted fairly accurately on the assumption that the total medium effect should be multiplied by the ratio DIDO, the actual density of the solution divided by the value that would be expected if the components mixed idea1ly.l This is expressed in the formula 6, =: 6, - (I)/Do){(6,- 6,)
+ 42(61 - 62))
(4)
where 6, is the shift in the absence of any solvent, Le., in the gaseous phase. It has been reported that the shift of the CF3 peak of perfluorohexane in the gaseous phase is 3.867 ppm upfield from that in the liquid,'O and accordingly 6, was taken to be 9.224 ppm a t each temperature. Neglecting the possible temperature dependence of 6, probably introduces some inaccuracy, but as previously notedl an error of Ad, in this quantity gives rise to an error A6, given by As, = A6,(Do - D ) / D o
(5)
Since the magnitude of (Do- D ) / D onever exceeds 0.037, even an error as large as 0.25 ppm in 6 could be tolerated. Bedford and Dunllap6 give empiricaf equations for the excess volume as a function of composition at 2 5 , 3 5 , 4 5 , and 55 "C, and these were used to evaluate DIDo for each sample at each temperature. Equation 4 was then used to calculate values of 6,, and the corresponding excess shifts are represented by the dashed curves in Figure 1. The excess shifts computed in this way agree in sign with the experimental ones, but they are too small by a factor of 2-3. Each dashed curve is nearly symmetrical about its midpoint, 42 = 0.5, while the experimental points define very noticeably skewed curves with maxima near 42 = 0.4, becoming more nearly symmetrical as the temperature rises. The excess shifts calculated from the density data are largest at, the highest temperature, where the expansion on mixing is maximal, but the largest observed excess shifts are found at 25 " C , nearest the critical point. It is then natural to suppose that the deviations between the experimental points and the dashed curves measure the persistence of short-range order, which should be largest near the consolute temperature and progressively smaller as the system is heated. Effect of Nonrandom Mixing. Since medium effects on chemical shifts depend predominantly on short-range interactions, the key variables to consider in accounting for the excess shifts are Nll, N12,and NZ2,that is the numbers of nearest neighbor pairs involving 1-1, 1-2, or 2-2 contacts. The quasi-chemical treatment of Guggenheim'l provides useful relations which should be obeyed by these variables. It is strictly valid only for systems made with molecules of equal size and shape and showing no volume change on mixing. For the present system, the excess volume effect can be included by retaining the factor DIDo in an appropriate way. The ratio of the molar volumes is Vlo/VZo= 0.65, close enough to unity to suggest that the treatment should be useful at least as a first approximation. If the effective coordination number of each molecule is z , and N , is the number of molecules of component i, it is readily seen that zN1 = 2Nll .t. N12 and zN, = 2NZ2+ N12 (6) The fundamental postulate of the quasi-chemical treatment is expressed in the equation N1Z2 = (zNl - N l z ) ( z N z- N1Z)e-2W/LkT (7)
where 2w/z is esseintially the energy needed to transform
No. 11, 1979 1395
TABLE 11: Parameters Derived from the Excess Shifts with the Quasi-Chemical Treatment T, "C
ya
w/zkT
25 35
0.9292 0.7245 0.5923 0.4876
0.329 0.272 0.233 0.199
45 55 a
Nowlz,
J/mol 815 697 616 543
See eq 10.
a 1-1 pair and a 2-2 pair into two 1-2 pairs. This quantity should be positive for hydrocarbon/ fluorocarbon mixtures, where the incomplete miscibility reflects strong positive deviations from Raoult's law. When w = 0, the mixture is ideal and ( 7 ) implies Nl2 = ZNlN,/(N,+ N,) (8) as required on statistical grounds for perfectly random mixing. When w is finite, it is convenient to write (9) Nl2 = 2zN,N2/(N, + N,)(fl + 1) and find the value of fl required to satisfy (7). With the abbreviation = e2w/zkT - 1 (10)
,,
the result is',
p = (1 + 4x1x2y)1/2
(11)
the x's being the mole fractions. The average concentration of component 2 in the immediate neighborhood of a molecule of 2 is then given not by the bulk mole fraction xz but by the quantity (12) x 2 , 2 = 2N,2/(2N22 + N12) which becomes identical with x 2 in the limit as w approaches zero. Using eq 6 and 9-11 this becomes x2,2 = 1 - 2x,/(/3 + 1) (13) When both nonrandom mixing and excess volume effects are present it is proposed that the chemical shifts should obey an equation similar to (4) but with 420replaced by a local volume fraction given in the first approximation by the product 420x2,2/x2, that is 6, = 6, -
To evaluate y independently requires a knowledge of the quantities w and z. The former is related to the excess free energy of mixing, but the system under investigation shows a large excess entropy of mixing,,, and for such solutions the relation between w and the excess free energy is not known with satisfactory accuracy. Since it is also difficult to determine the value of z a priori, it seems best to treat y as a disposable parameter which may be fixed by forcing agreement between the observed and calculated shifts at some selected composition at each temperature. Values of y obtained from the data a t 4,O = 0.50 appear in Table I1 together with corresponding values of the quantity w l z k T and of Now/z, where No is the Avogadro number. Once y is determined, eq 14 allows 6, and hence 6E to be calculated over the whole composition range. The solid curves in Figure 1 represent excess shifts evaluated in this way. The agreement between the data points and the solid curves is very encouraging, though there are possibly
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No. 11, 1979
systematic deviations slightly larger than the experimental error at the lower temperatures, particularly in the region d20 = 0.3-0.4. The proposed interpretation of the excess shifts gains credibility when it is noted that the calculated curves depart from symmetry about the midpoint of the concentration scale just as the data require, with maxima near 42 = 0.4 or x2 = 0.3 and with the most pronounced asymmetry occurring nearest the consolute temperature, where y is largest. The available facts are consistent with the conclusion that the short-range order in these solutions may be quantitatively described by eq 9-11 with the parameters given in Table 11. The question of whether or not the values of y produced by this treatment should be considered acceptable can be further discussed but not conclusively answered by appealing to thermodynamic data. For a strictly regular solution at the critical temperature, T,, the quasi-chemical treatment requires
w / z k T , = In z / ( z
-
2)
(15)
Extrapolating the values of y in Table I1 to the critical temperature of 22.65 "C yields the unexpected result yc = 1.0. Then 2 w / z k T , = In 2, and with (15) this implies that z is about 7. In considering data for the related system cyclohexane/ perfluorocyclohexane, Guggenheim13deduces that the best value of z is about 8, and the present value is at least similar. The cause of the difference may be that the molecules of hexane and perfluorohexane are much less nearly spherical than those of the cyclic compounds. Alternatively, it could be argued that because these solutions are not in fact strictly regular one cannot place too much reliance on (15). The temperature dependence of the quantity Now/z presents some additional difficulties. The numbers in the last column of Table I1 show that d(Now/z)dTis large and negative. As pointed out by Guggenheim,13such behavior is not unexpected because of the expansion of the lattice which attends heating. A rapid drop of w / z with rising temperature also implies that the free energy cost of creating a given concentration fluctuation should increase fairly rapidly above the consolute temperature, and this would be in harmony with the statement: "All of the pertinent evidence supports the conclusion that, except in the neighborhood of the critical point, clustering is negligible and thermal agitation causes practically random mixing."14 On the other hand, when x1 = x2 = 0.5, the excess free energies of mixing deduced from vapor pressure measurements12 are AGmE = 1.371 kJ/mol at 25 " C , 1.330 kJ/mol a t 35 "C, and 1.304 kJ/mol a t 45 "C. Guggenheimll derived an equation for the mixing free energy in terms of p and x2 which on simplification when x 2 = 0.5 becomes
AGmE = (zRT/2) In [2/(1
+ e-LU/Zk?]
(16)
With the data in Table 11, this allows Now and z to be evaluated separately at each of the three temperatures, giving, at 25 "C, Now = 5.97 kJ/mol, z = 7.3; at 35 "C, Now = 5.70 kJ/mol, z = 8.2; at 45 "C, Now = 5.54 kJ/mol, z = 9.0. Each set of values, taken alone, appears quite plausible. However, it is surprising to find that a 20"
Norbert Muller
temperature rise seems to cause a 20% increase in z and only a 7.5% drop in w. This may indicate that the use of (161, based on the assumptions of equal molecular volumes and a vanishing volume change on mixing, is not entirely satisfactory. It was inferred earlier from results of small-angle X-ray scattering determinations with perfluoroheptane/isooctane solutions that the nonideality of these mixtures causes formation of cylindrical clusters consisting of as many as 140 fluorocarbon molecule^.^^ Because the chemical shifts are not sensitive to long-range interactions the present data provide no information about the size, shape, or indeed the existence of such clusters, though they do allow an upper bound to be set on the total number of molecules that could be involved in clusters. Considering that the components remain partially miscible even below the consolute temperature, it is highly unlikely that a region large enough to contain 140 molecules would be found to be populated exclusively by molecules of one component in a 50-50 mixture. Instead, the NLivalues implied by the chemical shifts probably reflect less extreme local concentration fluctuations not easily described in terms of well-defined clusters. The cluster concept is perhaps more useful in very dilute solutions, where most molecules of component 2 have only molecules of 1as nearest neighbors; then a value of NZ2exceeding that predicted for a random mixture would require a heightened concentration of short-lived dimeric, trimeric, or oligomeric aggregates. In the range T L T , the values of y are represented to within 1 or 2% by the empirical equation y = [ l + 0.032(T - T J - '
(17)
which again brings up the finding that y = 1 when T = T,. There appears to be no theoretical reason to expect this. Further studies, including also 13C shift measurements, are planned both in order to discover whether y = 1 for other binary systems a t the consolute point and, perhaps more importantly, to obtain additional data to test the validity of this approach.
Acknowledgment. The author is indebted to Mr. J. C. Deaton for help with the experimental work and to Dr. H. Morrison for the use of a spinning band column. References and Notes (1) N. Muller, J . Magn. Reson., 28, 203 (1977). (2) G. Filipovich and G. V. D. Tiers, J . Phys. Chem., 63, 761 (1959). (3) N. Muller, J . Magn. Reson., 25, 111 (1977). (4) J. H. Hildebrand, J. M. Prausnitz, and R. L. Scott, "Regular and Related Solutions", Van Nostrand-Reinhold, New York, 1970, p 70. (5) J. E. Anderson and W. H. Gerritz, J. Chem. Phys., 53, 2584 (1970). (6) R. G. Bedford and R. D. Dunlap, J. Am. Chem. Soc., 80, 282 (1958). (7) B. Atkinson and P. B. Stockwell, J . Chem. Soc. B.,740 (1966). (8) G. A. Crowder, 2. L. Taylor, T. M. Reed, 111, and J. A. Young, J. Cbem. Eng. Data, 12, 481 (1967). (9) S. K. Alley, Jr., and R. L. Scott, J. Chem. Eng. Data, 8, 117 (1963). (10) R. J. Abraham, D. F. Wileman, and G. R. Bedford, J . Chem. SOC., Perkin Trans. 2 , 1027 (1973). (1 1) E. A. Guggenheim, "Mixtures", Oxford University Press, London, 1952, p 38. (12) R. D. Dunlap, R. G. Bedford, J. C Woodbrey, and S. D. Furrow, J . Am. Chem. Soc., 81, 2927 (1959). (13) E. A. Guggenheim, "Applications of Statistical Mechanics", Oxford University Press, London, 1966, p 97. (14) Reference 4, p 73. (15) G. W. Brady, J . Chem. Phys., 32, 45 (1960).
