10197
J. Phys. Chem. 1991, 95, 10197-10203
is shown in Figure 9. Considering the fact that all results were obtained during a series of time-consuming measurements and, that the surface of the electrode could be controlled only once before closing the cell, they are very self-consistent and clearly reflect the pressure dependence, which is mainly due to the change of viscosity of the solution (Figure 9B). The proposed procedure of making cylindrical microelectrode results in relatively durable electrodes of good quality. Such electrodes enable us to perform voltammetric experiments under high pressure, and these kinds
of studies are now being continued. Acknowledgment. We are grateful to the National Science Foundation for supporting this work under Grant CHE-86-07984 and the Materials Science Division of the Department of Energy under Contract DEFG02-91ER45439. We also thank Ann Zielinski for helpful editing of the manuscript. Registry No. Pt, 7440-06-4; K,Fe(CN),. 13746-66-2; 0, 7782-44-7; KCI, 7447-40-7.
Solvatochromic Study of the Effect of Chain Length, Chain Branching, and Polymethylation of Alkylbenzenes on Solvent Poiarizabllity Edward T. Ulrich and Peter W. Cam* Department of Chemistry, Kolthoff and Smith Halls, University of Minnesota, 207 Pleasant Street Southeast, Minneapolis, Minnesota 55455 (Received: January 29, 1991; In Final Form: June 24, 1991)
The contribution of solvent polarizability to solvatochromic measures of solvent strength, such as the Kamlet-Taft scale of solvent dipolarity-polarizability, is well recognized. In this work, we measured the A* values of 23 nonpolar aromatic solvents, including 10 n-alkylbenzenes (benzene to pentadecylbenzene), 5 branched-chain alkylbenzenes, and 8 di-, tri-, and tetramethylated benzenes. The A* values of n-alkane solvents increase monotonically with chain length. In contrast, the A* values of the aromatic liquids systematically decrease with homologue number. The direction of these changes is consistent with the increase in the polarizability of the n-alkanes and the decrease in the polarizability of the n-alkylbenzenes as homologue number increases. For both series of liquids, A* increases linearly with solvent polarizability; however, the slopes and intercepts of the relationships are quite different. We hypothesize that this difference in behavior is due to concentration of the phenyl groups of the long-chain alkylbenzenes in the cybotactic region of the very polar solvatochromic probes. Chain branching decreases A* of the alkylbenzenes,as it does for the alkanes. Ring methylation increases K* relative to that of the n-alkylbenzene of the same carbon number. However, when compared on the basis of polarizability, ring-methylated aromatics have a lower A* than the hypothetical n-alkylbenzeneof the same refractive index. The extent of this decrease is not related to the dipole moment of the polymethylated aromatic but does follow the extent of crowding of the methyl groups about the ring.
Introduction The Kamlet-Taft A* parameter is a well-established scale of solvent dipolarity-polarizability and has been used as the basis for a large number of correlations involving the effect of solvent dip01arity.l~ The A* scale of solvent strength was experimentally derived from the effect of solvent on the A to T * transition of a large number of judiciously chosen test solutes. The basic tenet of the Kamlet-Taft approach to the determination of A* is that some observed property of a solvent (j),such as its effect on the transition energy (vmJ of a suitable solute, will vary with solvent in accord with the linear solvation energy relationship
+
= v0.j (1) Equation 1 has proven to be generally quite useful, but only if the type of solvent tested is limited to the so-called ‘select” solvents. These are defined as aliphatic, monodipolar, aprotic liquids. The parameters vo,, and si are established by least-squares fitting of the observed transition energies to eq 1 in a large number of select solvents. A numerical value is obtained by defining the A * ~scale to be zero for cyclohexane and unity for DMSO. The solute susceptibility parameter, si, varies with the nature of the process under study and with the specific probe solute. In general, the A * ~parameter of a very wide variety of liquids can be correlated with simple functions of solvent dielectric constant and refractive index. As shown in previous work, contributions from distortional polarization (solute dipole-solvent-induced dipole effects) to the A* scale are suppressed when one considers the select solvents as a single group. However, in the alkanes where distortional polarization is the only solute-solvent interaction that can lead to vi4
Author to whom correspondence should be addressed.
a solvent-induced change in the transition energy, we have shown that the measured A * ~values are well represented by the simple regression A*
= -1.11 (f0.03)
+ 5.75 (f0.12)
,
(2)
n = 12 r = 0.995 S D = 0.01 The term O(n2)represents the Onsager reaction field function of the refractive index
O(n2) = (nZ- l)/(2n2
+ 1)
(3)
and is used to measure the ability of nonpolar alkanes to interact with a solute dipole. Equation 2 predicts the A* of the gas phase (1) Kamlet, M. J.; Abboud, J. L.; Taft, R. W. Prog. Phys. Org. Chem. 1980, 13, 485-630.
(2) Kamlet, M. J.; Abboud, J. L.; Taft, R. W. J . Am. Chem. Soc. 1977, 99, 6027-38. (3) Fong, C. W.; Kamlet, M. J.; Taft, R. W. J . Org. Chem. 1983, 48, 822-5. (4) Kamlet, M.J.; Doherty, R. M.; Taft, R. W.; Abraham, M. H. J . Am. Chem. SOC.1983, 105, 6741-3. (5) Abraham, M. H.; Kamlet, M. J.; Taft, R. W.; Weathersby, P. K. J . Am. Chem. SOC.1983, 105, 6797-801. (6) Kamlet, M. J.; Abraham, M. H.;Doherty, R. M.; Taft, R. W. J . Am. Chem. SOC.1984, 106,464-6. ( 7 ) Kamlet, M.J.; Doherty, R. M.; Taft, R. W.;Abraham, M. H.; Koros. W. J. J. Am. Chem. SOC.1984, 106, 1205-12. (8) Taft, R. W.; Abboud, J. L.; Kamlet, M. J. J . Urg. Chem. 1984, 49, 2001-5. (9) Brady, J. E.; Carr, P. W . Anal. Chem. 1982, 54, 1751-7. (IO) Brady, J. E.; Carr, P. W . J . Phys. Chem. 1982, 86, 3053-7. (1 1) Brady, J. E.; Bjorkman, D.; Herter, C. D.; Carr, P. W. Anal. Chem. 1984, 56, 278-83. (12) Brady, J. E.; Carr, P. W . J . Phys. Chem. 1984, 88, 5796-9. (13) Brady, J. E.; Carr, P. W . J. Phys. Chem. 1985, 89, 1813-22.
0022-3654191 12095-10197%02.50/0 , 0 1991 American Chemical Society I
O(n2)
10198 The Journal of Physical Chemistry, Vol. 95, No. 24, 1991
to be -1.1 1, in excellent agreement with the measured value of -1.06.‘’
Even though the generalized relationships between A* and solvent proper tie^'^.^' can fit the A* values for the perfluorinated alkanes9 (ca. -0.3 to -0.49,they cannot accommodate themselves to aromatic hydrocarbons. This behavior is very commonly observed in many solvatochromically based linear solvation energy relationships where it is necessary, when one is dealing with aromatic and polychlorinated solvents, to introduce a “polarizability correction” factor denoted which is only loosely related to the concept of distortional polarization. This term was defined to be 0.00 for alkanes, 0.50 for polyhalogenated alkanes, and 1-00for aromatic solvents. Although ad hoc and approximate, this approach has successfully brought these nonselect liquids into line in many diverse correlations.I6 Prior to the present study, experimental values of A* were only available for a few nonpolar aromatic liquids” and solutes.I8 The largest range in polarizability thus far studied within one group of closely related substances is found in our previous study of a series of nonpolar polymers.” In that work, a set of seven silicone oils whose substituents were varied from 100% methyl to 75% phenyl was found to be well correlated with O(n2). This class of liquids is more complex than the alkanes or alkylbenzenes due to the presence of the polar and hydrogen bond basic siloxane backbone of the polymer, and the results are not readily compared to those for a homologous series of low molecular weight liquids. The present study of the A* of alkylbenzenes and related liquids was undertaken to extend the range of polarizabilities scanned in a simple homologous series of liquids. In addition, we wanted to compare the relative dependence of A* on polarizability between the alkanes and alkylbenzenes. Such a comparison might lead to a better understanding of the differences in distortional polarizabilities of the aliphatic and aromatic liquids. The recent work of ReichardtIg and his co-workers in which the solvatochromism of a single indicator (Dimroth-Reichardt betaine20*21) was measured in a very large number of nonpolar and polar aromatic solvents is very pertinent to the present study. The work of B ~ n c e l is~ also ~ ~ very * ~ relevant in that it underscores some of the difficulties in establishing a single parameter scale that can successfully represent both the orientational and distortional stabilization processes that enter into any solvatochromic scale of solvent strength. Buncel’s work shows very clearly that the Kamlet-Taft A* scale, although very useful, is not a uniquely fundamental scale of solvent polarity.
Experimental Section The indicators used in this work were N,N-dimethyl-4aminobenzophenone (7), 2-nitro-p-toluidine (23), 4-nitro-4’(dimethy1amino)stilbene (27), N-methyl-2-nitroaniline (32), and 2-nitro-p-anisidine (35). The numbers in parentheses designate the Kamlet solute numbers as indicated in ref 1. Indicators 7 and 32 were obtained from Aldrich, 23 and 35 were from MCB, and 27 was from Eastman. The indicators were purified by column chromatography on silica and recrystallized before use. Of the more than 40 Kamlet-Taft indicators, these 5 were chosen because their wavelengths of maximum absorption are quite long, thereby allowing minimal overlap with the intrinsic absorption of the (14) Brady, J. E.; Carr, P. W. J . Phys. Chem. 1985.89, 5759-66. (IS) Essfar. M.; Guiheneuf, J. L.; Abboud, J. L. J . Am. Chem. Soc. 1982, 104, 6786-7. (16) Kamlet. M . J.; Taft, R. W. Acru Chem. S c u d . 1985, E39,611-28. (17) Kamlet, M. J.; Abboud, J. L.; Abraham, M. H.; Taft, R. W. J . Org. Chem. 1983,48, 2877-87. (18) Kamlet, M. J.; Doherty, R. M.; Carr, P. W.; Mackay, D.; Abraham, M. H.; Taft, R. W. Environ. Sci. Technol. 1988, 22, 503-9. (19) Laurence, C.: Nicolet, P.; Lucon, M.; Reichardt, C. Bull. Soc. Chim. 1987, 1001-5. (20) Reichardt, C. Solvents u d Solvenr Effects in Organic Chemistry;2nd ed.; VCH Publishers: Weinheim, Federal Republic of Germany, 1988. (21) Dimroth, K.;Reichardt, C.; Siepman, T.; Bohlmann, F. Jusrus Lie6igs Ann. Chem. 1963,661, 1-37. (22) Buncel. E.; Rajagopal, S.J . Org. Chem. 1989, 54, 798-809. (23) Buncel, E.; Rajagopal, S.Acc. Chem. Res. 1990, 23, 226-31.
Ulrich and Carr TABLE I: Solvrtocbromic Propertiu of the Indicators solute no.
VO”
7 23 27 32 35
30.41 25.72 24.3 1 24.33 24.33
-8
& 0.066 -0.05 1 0.053 0.029 -0.098
2.013 1.621 2.131 1.593 1.596
Least-squares fit estimated frequency of maximum absorption in cyclohexane from ref 1. Least-squares fit sensitivity to solvent changes in T* from ref I . C S ~ l u tsusceptibility e to the polarizability correction factor. 1.2 X S e,
_o
,
I
S B O
1 0 -
x a
0 8 -
1 e, C N e,
6
E Yx
0 6 -
0
. 0
aromatic solvents. Except where noted, the background absorbances at the wavelength of maximum absorption of the indicators were entirely negligible. Ideally, due to the slight but measurable hydrogen bond basicity of a phenyl ring (@= 0.1-0.13 for methyl-substituted aromatic species”), only non hydrogen bond donor solutes should be used. Of the probe solutes used in this work, only indicators 23 and 35 are sensitive to solvent basicity. The solute parameters used in this work are summarized in Table I and were taken from ref 1. The solvents used in this work were the highest purity commercial materials available. Benzene was obtained from Fisher, and 99% pure HPLC grade was from Aldrich; toluene was from Mallinkrodt and n-decylbenzene from Kodak. n-Pentadecylbenzene and tert-pentylbenzene were from TCI. All others (including 98% pure hexadecane) were from Aldrich. All solvents, except tridecylbenzene, which is very expensive, were passed over activated silica gel before analysis or use. The solvents were not further purified before use. They were all analyzed by temperature-programmed gas chromatography either on a DB5 (1 5 m by 0.53 mm id.) capillary column from J & W Scientific or on a DC 410 packed column with Chromosorb W-HP support. All solvents except those given below were at least 98% pure. As expected, the polymethylated benzenes were impure: 1,2,3-trimethylbenzene and 1,2,3,4-tetramethylbenzenewere 94% pure, and 1,2,4-trimethyIbenzene was 95% pure. The 1,2,3,5-tetramethylbenzene was about 80% pure. Since the impurities were nonpolar and were expected to be substituted methylbenzenes of similar solvatochromic strength, these solvents were not further purified before use. The spectrum of rrpentadecylbenzene showed a distinct long-wavelength shoulder which interfered with the measurement of the spectrum of indicator 7. Subsequently, it was purified by passing it over a small column of activated alumina; however, this did not eliminate the problem. All reported A* values were obtained from measurements on a Varian spectrophotometer (Model DMSZOO) at a scan rate of 20 nm/min with slits set to 0.2 nm. The instrument was calibrated before use with a holmium oxide filter. The wavelength of maximum absorption was based on the midpoint of the 90% maximum absorbance method as described by Kamlet et al.,2 so that the data could be directly compared to their results. All spectra were obtained at 25 O C by use of a thermostated cell compartment and an external circulator [Haake Type F (f0.3
+
The Journal of Physical Chemistry, Vol. 95, No. 24, 1991 10199
Solvatochromic Study of Alkylbenzenes 0.720
0.620
ar
Y
2
0.520
*
K 0.420
I;ii, 1
0.320 0 .37
9
1
0.57 u
0.53
-
6
0.49
-
'
0.45 -
L 0)
0.41
@ ,
\
@-• normal
@ A n
0 branched A
nolvmethvlated
-
0.62
~~
0.42
0.61
0.52
0.47
0.57
IT* average
Figure 2. Correlation of raw solute-dependent T * values with average values: (W) solute 1; (0)solute 23;(0) solute 27; ( 0 )solute 32;(A) solute 35. T*
J
037' -1
3
1
5
7
9 Carbon Number
11
13
15
Figure 3. Dependence of average T* on alkyl carbon number: ( 0 ) n-alkylbenzenes; ( 0 )branched alkylbenzenes; (A)polymethylated rings. and the slight susceptibility of two of the solutes to respond to
"C)]. Typically, A* varies by less than 0.002 ~ n i t / " C . ~ ~ - ~ ~ the solvent basicity, in addition to the general solvent dipolari-
Refractive indices were measured using an Abbe-3L refractometer from Bausch and Lomb. It was thermostated to 25 O C . Densities were measured using a simple pycnometer (Ace Glass) to 0.0002 g/cm3 at 25 OC.
Results and Discussion The spectroscopic results, along with some physical properties of the solvents for the solvents studied in this work, are given in Table 11. One of the prerequisites for the development of the A* scale was that the frequencies of maximum absorption for all indicators had to be highly mutually correlated in all select solvents. The aromatic liquids are not select, but clearly it is a necessary condition for the development of a single parameter scale that all of the solutes be highly correlated. The raw data were analyzed via the plots shown in Figure 1. The average value of vmax was computed by summing over all five indicators in each solvent, and the individual solute values were plotted vs the average vmax. It is evident that the data are strongly correlated (see Table 111). The first clear-cut result evident in Table I1 is that the average transition energy increases monotonically and significantly from benzene to tridecylbenzene. The slight decrease from tridecyl to pentadecylbenzene is probably due to experimental error. We note that the individual solute transition energies are not quite so monotonic, but this is due to the difficulty in maintaining the very high precision needed to discern sucii small changes in spectra over a quite lengthy experiment. Raw T * values for each solute in each solvent (see Figure 2) were computed from the measured transition energies, eq 1, and the literature data for uo,maxand s given in Table I. With a single indicator, the A* values are reproducible from day-to-day to within f0.005 unit if the solvent is thermostated. The overall standard deviation between indicators shown here is 0.075. The data in Figure 2 make it very clear that there are systematic solute-dependent differences in the raw A* values. We observed a similar but not so large effect in our previous studies of both n-alkanes and n-alkyl nitrile^.'^ In that work we used 10-12 probes and showed that the deviations correlated with the solute s value. In the present study, the solute-twolute variance is now so large that we felt that the difference in behavior had to be rationalized before considering the average A* for each solvent. We point out that differences between our reported A* values and those which exist in the literature are generally small and, in most instances, were within 0.03 unit, despite the fact that indicator 7 was the only common probe solute. Thus, we believe that on the whole the systematic differential solute-to-solute behavior tends to cancel if enough solutes are used to establish A * . Part of the systematic differences between solutes might be attributable to the hydrogen bond basicity of the aromatic solvents ~~
(24) Laurence, C.; Nicolet, P.; Helbert, M. J . Chem. SOC.,Perkin Trans. 2 1986. 1081-90. ( 2 5 ) Nicolet, P.; Laurence, C. J . Chem. Soc., Perkin Trans. 2 1986, 1071-9.
ty-polarizability. However, approximate calculations indicate that this effect is small. The above solute-to-solute variations in A* can be rationalized as follows. The aromatic fluids are not select, and thus one should use a correlation equation that contains the solvent-dependent polarizability correction factor (SI). This suggests that instead of eq 1 we should base our computation of A * ~on
+
+
= u: si*(**ij diaj) (4) The 6 values for all aromatic solvents are defined as 1 .OO. Since each solute has its own susceptibility (di) to Sj, we can use this factor to bring differences into line. This was not done and should not have been done in our earlier studies of aliphatic solvent^'^ since their 6 values are defined to be zero. We can easily estimate the best value of di to use for each solute by computing the average deviation for each solute over all of the solvents tested. These values are shown in Table I. Note that this approach does not influence the average value of T* for any solvent. When this approach was used, the average standard deviation in A* over all of the solutes decreased from 0.075 to about 0.013. Given that the experimental precision in A* with one solute on one day is about iO.005,we feel that a standard deviation of f0.013 among all solutes over the whole time course of data collection is acceptable. Given that only five adjustable parameters brought about this improvement in 115 data points, we believe that it is at least statistically justifiable. We also point out that the hydrogen bond basicities of all of the nonpolar aromatic solvents are just about equal (0.1-0.13). Thus, the above procedure also approximately corrects for any slight effect due to differences between solutes in their solvent sensitivity to hydrogen bond acceptor strength by subsuming solute-to-solute differences in hydrogen bond donor strength into d,. We also assessed another approach founded on the recent study of Reichardt and his co-~orkers.'~ They observed, in a very wide variety of nonpolar and polar aromatic liquids, that a constant value of 6 for all aromatic liquids did not improve the correlation between the transition energies of the Dimroth-Reichardt betaine and pnitroanisole. Rather, a double correlation in which a simple function of the refractive index was used to represent the variation in solvent polarizability proved to be much more successful. When such was done here, no significant improvement in the mutual correlations was observed. However, given the spectroscopic similarity in the indicators used in this work and the narrow range in polarizabilities explored, we did not expect any significant improvement. After the di term was introduced into the regression used as the basis for computation of A * ~ we ~ , then visually inspected plots of the individual vs the average A * ~ .In 16 of 1 15 cases we observed significant outliers. These were somewhat systematically distributed throughout the data set (see Table 11). In such instances, the suspect value was replaced with a least-squares estimated value and the average over all solutes recomputed to generate the final A * ~value given in Table 11. Our raw A* values are given for comparison. Clearly, our smoothing procedure did u,j
10200 The Journal of Physical Chemistry, Vol. 95. No. 24, 1991
Ulrich and Carr
TABLE II: Solute Transition Energies" of Alkylbenzenes
solute no.
benzene
7
29.300 24.643 23 23.I86 27 23.590 32 23.196 35 cm 24.783 0.616 A*prec 0.616 A*d 1.49792' nr d 0.8736' Onsager field1 0.22665 molar volumeh 89.42 dipole moment/ 0.00'
toluene
n-ethyl
n-propyl
n-butyl
29.369 24.716 23.245 23.685 23.267 24.856 0.574 0.574 1.4941'3 0.86219' 0.22552 106.87 0.31
29.481 24.746 23.337 23.781 23.343 24.938 0.529 0.529 1 ,4932' 0.86253' 0.22524 123.09 0.37'
29.516 24.814 23.332 23.804 23.354 24.964 0.513 0.513 1.48951' 0.8578' 0.224I3 140.12 0.36'
29.551 24.845 23.364 23.838 23.375 24.995 0.496 0.496 1.48742' 0.85607' 0.22349 156.79 0.36"'
'
solvents n-pentyl n-heptyl
29.551 24.869 23.326' 23.872 23.441' 25.012 0.484 0.484 1,48647 0.85372'" 0.22276 173.65 0.36"'
n-decyl
29.665 24.931 23.419 23.941 23.458 25.083 0.446 0.446 1.482985 0.85067'" 0.22214 207.25 0.36"'
n-tridecyl n-pentadecyl
i-propyl
29.656' 25.069' 23.513 24.062 23.602' 25.180 0.388 0.391 1.47952 0.85262 0.22108 305.49 0.36"'
29.595 24.826 23.397 23.832 23.364 25.003 0.493 0.493 1.4889' 0.85743' 0.22394 140.18 0.39'
29.709 24.956' 23.574 24.131' 23.477' 25.169 0.397 0.409 1.481055 0.85189' 0.22I55 256.26 0.36"'
29.471' 25.063' 23.485' 24.056 23.585' 25.132 0.412 0.395 1.47939"' 0.85312 0.22104 338.19 0.36"'
"All data are frequencies in k K . bAverage overall solutes in kK. C~;,, denotes average K* after introduction of d factor but before individual results were smoothed. dBest estimate of average A* based on all solutes. CRefractiveindex at 25 "C. fDensity in g/cm3 at 25 O C . 1 0 ( n 2 ) = (n2 - l)/(2n2+ 1). *Molar volume at 25 O C (cm'/mol). 'Denotes data point which was adjusted to get the final A * . jEstimated from data in ref 28. li From ref 26. 'From ref 27. "'Estimated from lower homologues or based on bond dipoles. TABLE 111: Mutual Correlation of Frequencies of Maximum Absorption solute no. into SDb slopeC SDd f 7 23 27 32 35
6.86 0.043 -2.716 -5.310 1.121
0.06 0.03 0.04 0.03 0.03
0.907 0.992 1.044 1.167 0.891
0.109 0.059 0.078 0.059 0.058
0.876 0.965 0.946 0.974 0.958
1.52 1.51
d
A
1
0-0
A A
0
normal branched
23 23 23 23 23
"Intercept ( k K ) of a least-squares line for vmx of the indicated solute vs the average umal for all solutes as the solvent is varied. bStandard deviation of the intercept. 'Slope of a least-squares line for vmal of the indicated solute vs the average umax for all solutes as the solvent is varied. dStandard deviation of the slope. eCorrelation coefficient. (Number of solvents in the correlation.
not significantly alter the final reported A*, value. The dependence of our best estimate of the A* values on the number of aliphatic carbon atoms in the solvent is shown in Figure 3. It is evident that, in contrast to the alkanes, where A* increases with homologue number, the A* for the alkylbenzenes decreases as the number of alkyl carbons increases. To a first approximation, the difference in trends between the n-alkanes and the n-alkyl aromatics is easily rationalized on the basis of the concept that the high A* value of an aromatic ring is essentially "diluted" out by the alkane chain (see below). We observed a similar decrease in A* for the n-alkylnitriles, wherein acetonitrile has a quite high A* (0.75)but that of pentadecylnitrile is much lower (0.56). Comparison of Normal, Branched, and Polymethylated Solvents. Note that in Figure 3 the n-alkylated solvents are shown as solid symbols and are connected by straight-line segments. All of the branched chain alkanes (0)lie below the curve defined by the n-alkylated aromatics, and six of the eight polymethylated ring compounds (A)lie above the n-alkylated aromatics. Clearly, monomethylation decreases the A* of benzene, but the addition of methyl groups increases the A* of the aromatic ring. Branching decreases the A* of solvents that have the same number of alkyl carbons, as it does in alkane solvents.13 In Figure 4, we show the variation in refractive index with the number of carbon atoms attached to the ring. In contrast to the normal alkanes, the refractive index decreases with carbon number. The refractive index, which can be measured with much greater precision than A * , appears to be approaching a limit at the larger carbon numbers. Branching has only a small effect, but ring methylation considerably enhances refraction. In previous work, we showed that the variation in A* among the n-alkanes, but not the branched and cyclic alkanes, could be linearly correlated with simple functions of the refractive index. On the basis of various theoretical considerations, we chose the Onsager reaction field function; however, in a group of solvents in which the refractive index does not vary very much, the Lorentz-Lorenz function and others serve quite as well. The Onsager function is a measure of the extent of interaction of a nonpo-
I
1.47'
-1
1
3
5
7 9 Carbon Number
11
13
15
Figure 4. Dependence of refractive index on alkyl carbon number: ( 0 ) n-alkylbenzenes; (0) branched alkylbenzenes; (A)polymethylated rings. 0.61 0.57
1
0
-
0
a,
0.53
a,
&
*
'
-
0.37 L 0.220
A A
A
b A
0.49 0.45
A A
0
0 normal 0 branched
0
I 0.223
0.226
0.229
0.232
Onsager Function
Figure 5. Relationship between r* and polarizability: ( 0 ) n-alkylbenzenes; (0)branched alkylbenzenes; (A)polymethylated rings.
larizable dipole with a nonpolar solvent continuum. It represents the distortional polarization contribution to sol~atochromism.'~ We felt it likely that the nonpolar aromatic solvents would depend similarly on this function. The results of this analysis are shown in Figure 5 . Clearly, the n-alkylbenzenes (a) correlate quite strongly with the refractive index, but the branched and polymethylated aromatics are highly scattered. For the 10 linear n-alkyl aromatics T* = -7.99 37.95 ( f 2 . 2 9 ) O(d) (5) n = 10 r = 0.986 SD = 0.014 All of the data are shown in Figure 5. Obviously, the branched, and particularly the polymethylated, solvents do not fall on the line defined by the n-alkyl aromatics. Their A* values are systematically overestimated by eq 5. We infer that reaction field formalisms, which treat the solvent as a continuum and thus do not incorporate molecular shape, really fail to account for all of the important factors. The n-alkylbenzenes fall on a line, not because they are intrinsically better understood but because the
+
The Journal of Physical Chemistry, Vol. 95, No. 24, 1991 10201
Solvatochromic Study of Alkylbenzenes
TABLE 11 (Continued) solvents 1,2,3-tri i-butyl 29.621 24.888 23.419' 23.941 23.425 25.059 0.460 0.460 I .484' 0.84907' 0.22245 158.08 0.44'
s-butyl 29.625 24.857 23.447 23.878 23.403 25.042 0.471 0.471 I .48779' 0.85797' 156.44 0.37'
r-butyl 29.638 24.876 23.557 23.889' 23.416 25.075 0.454 0.459 1.49024' 0.8624' 0.22435 155.64 0.36'
r-pentyl 29.682 24.925 23.491 23.929 23.466 25.099 0.438 0.439 1.49201 0.87017 0.22488 170.25 0.36'"
o-xylene
m-xylene p-xylene
29.412 24.691 23.186 23.702 23.267 24.852 0.576 0.576 1 .50295' 0.87594.' 0.22815 121.20 0.45'
29.499 24.765 23.299 23.753 23.315 24.926 0.536 0.536 1.49464' 0.86009' 0.22567 123.44 0.30'
other factors that contribute to establishment of the solvent shift are constant in this series of liquids. Examination of Figures 3-5 shows that methylation of the ring has a relatively greater effect on the solvent polarizability than on A*; thus, these compounds fall below the n-alkyl line in Figure 5. Within all three series (di-, tri-, and tetramethylated aromatics), one observes a consistent pattern in both refractive index and A*. For example, both polarizability and A* decrease in the sequence ortho, meta, para. Furthermore, displacement of the polymethylated compounds from the line increases with "crowding" of the methyl groups about the ring. For example, o-xylene is more displaced than m-xylene, and 1,2,3,4-tetramethyIbenzene is more displaced than 1,2,3,5-tetramethylbenzene.At this point, we do not believe that the small differences in the dipole moments between the various polymethylated compounds are responsible for the scatter. As shown in Altshuller's work,** from which the estimates of the dipole moment given in Table I1 were obtained, benzene and the symmetrically substituted compounds (p-xylene and 1,3,5-trimethylbenzene) have zero dipole moments. 1,3,5Trimethylbenzene is evidently quite displaced from the line. When we attempted a double regression against O(n2) and dipole moment, the regression was no better than that against just O(n2) and the coefficient of the dipole moment was negative, which is physically m e a n i n g l ~ . 'In ~ general, our results can be rationalized by the concept that the measured A* value reflects ease of access to the phenyl ring. Bulky groups or more crowded rings show lower A* values than one would estimate for less sterically hindered structures of the same net polarizability. We believe that solvent polarizability as determined from refraction is less sensitive to the details of the shape of the solvent than is the solvent polarizability observed via the solvatochromic shift of a given indicator. This result is consistent with the use of a solute-dependent di in eq 6 to explain the solute dependence of the individual A * , ~values shown in Figure 2. We also believe that the very anisotropic polarizability of the aromatic liquids is partially responsible for the very large scatter of the branched and polymethylated solvents about the n-alkane line shown in Figure 5 . Comparison of n-Alkanes and n-Alkylbenzenes. The total change in ** from benzene to n-pentadecylbenzene is about 0.23 unit. This is quite large when one considers that the change in A* from cyclohexane to DMSO is defined to be 1.00 unit. Furthermore, the A* value of benzene is, for a nondipolar liquid, very large. These observations further underscore the important role of distortional polarization in determining the A* of all solvents (26)Riddick. J. A,; Bunger, W. B.;Sakano, S.K. OrganicSoluents, 4th 4.; Techniques of Organic Chemistry; Wiley and Sons: New York, 1986; Vol. 2.
(27)Timmermans, J. Physico-Chemical Comranrs of Pure Organic Compounds; Elsevier: New York, 1950. (28)Altshuller, A. P.J . Phys. Chem. 1954. 58, 392-5.
methyl
29.507 29.386 24.783 24.704 23.337 23.159' 23.764 23.708 23.332 23.261 24.945 24.843 0.525 0.580 0.526 0.573 1 .49325' 1.5115' 0.85661I. 0.89044' 0.22525 0.23066 123.94 134.98 0.02k
I ,2,4-tri 1.3.5-tri methyl methyl 29.343' 24.728 23.277 23.736 23.283 24.873 0.564 0.554 1 .50237' 0.8718' 0.22798 137.87 0.31"'
29.560 24.814 23.375 23.815 23.354 24.984 0.504 0.503 1.49684' 0.861I 1 0.22633 139.58 0.om
1.2.3.4-tetra methyl
1.2.3.5-tetra methyl
29.464 24.716 23.191 23.730 23.272 24.875 0.563 0.558 1 SI 81 1' 0.9015/ 0.23259 148.89 0.45'"
29.516 24.752 23.256 23.776 23.305 24.921 0.538 1.5112' 0.891 0.23058 150.64 0.30"
0.70
o,50
1
0 n-alkylbenzenes
0
0
n-alkanes
Onsager Function
Figure 6. Relationship between ?r* and polarizability for n-alkanes and
n-alkylbenzenes: (+) n-alkanes; ( 0 )n-alkylbenzenes. but especially of the aromatic and polyhalogenated liquids. In the n-alkanes we observed an increase of 0.19 unit in x* from n-pentane to n-hexadecane. Clearly, the 0.23-unit decrease upon addition of a long-chain alkyl group to a benzene ring is both experimentally and chemically very significant. To compare the n-alkanes and n-alkylbenzenes, the A* values were plotted against the Onsager reaction field (see Figure 6). Both series individually correlate quite well; however, taken together they do not. All of the alkylbenzenes have much greater polarizabilities than predicted as reflected in their A* values based on extrapolation of the n-alkane line to the refractive indices of the aromatic liquids. As mentioned above, the n-alkanes fit eq 2. We have a great deal of confidence in the physical interpretation of this result because the intercept corresponds quite well with the measured K* value of the gas phase. We note here that since the refractive indices of the n-alkanes increase with carbon number, extrapolation to refractive index unity corresponds to extrapolation to a smaller n-alkane, and therefore it makes some chemical sense to consider that the extrapolation corresponds to the gas-phase value. Clearly, eqs 2 and 5 do not agree despite the fact that both were obtained for nonpolar liquids. The intercept of the aromatic line [that is, unit refractive index point (-7.99)] does not agree at all with the gas-phase value. However, since the refractive indices of the n-alkylbenzenes actually decrease with an increase in carbon number, the intercept of this plot corresponds to a very long chain alkylbenzene. Thus, it is not reasonable, as it is in the case of n-alkanes, to compare the intercept for the alkylbenzene line to the gas-phase value. Finally, the slopes of the two classes of liquids are not the same. As will evolve below, we feel that in the case of the n-alkanes this line is physically meaningful because the solvent polarizability, as reflected in its Onsager function, is, if not the only process, at least the dominant process controlling the solutesolvent interactions that show up in A*. That is, the change in the Onsager field causes the change in K* and thus causes the
10202 The Journal of Physical Chemistry, Vol. 95, No. 24, 1991
correlation. In contrast, in the aromatic liquids while there is a correlation between T* and the Onsager field, it is only indirect, and other factors related to the length of the alkyl chain attached to the phenyl ring cause the decrease in A * . There is no reason 10 think that these additional factors should disappear at unit refractive index or that they should produce the same slope as 3bserved with the n-alkanes. On the basis of these observations, we believe that the T * values of aromatic liquids do not follow a reaction field formalism, and indeed, such continuum formalisms may not be applicable to nonpolar aromatic solvents. There are a number of possible explanations for the lack of consistency in the two slopes and intercepts in Figure 6. The simplest explanation is the idea that T * is only a local linear approximation to the strength of solutesolvent interactions. This has been extensively d i s p ~ t e d . ’ ~ , *When ~ * ~ ~we attempted to describe the data in Figure 6 with a quadratic function of O(n2), the residuals were highly patterned, the intercept corresponding to the gas phase made no sense at all, and the coefficient of the linear term was negative. Thus, we believe that the aromatic and aliphatic liquids must be treated as two distinct classes of liquids despite the fact that both are nonpolar, rather than invoking some nonlinear function of polarizability. This is consistent with Kamlet and Taft’s use of the 6 correlation factor. However, the great difference in both the slopes and intercepts of eqs 2 and 5 indicates that the two classes cannot be unified by use of a fixed value of S for all solvents within a class. This is consistent with the recent studies of R e i ~ h a r d t . ’ ~ A second explanation of the effect of an increase in the length of the alkyl chain on T* can be based on the phenomenon of solvent sorting in the cybotactic region. In solvent mixtures, this is a very well recognized process both in solvatochromic s t u d i e ~ ~and I-~~ in models of the thermodynamics of mixture^.^' Suppan has presented a detailed analysis of solvent sorting, which he calls dielectric enrichment, of systems that do not involve formation of any specific association or acid-base interaction^.^^ In his view, the polarity of a mixture is not an intrinsic property of the media but is a composite property which also depends on the probe solute. The gist of solvent sorting is that the Bragg-Williams random mixing approximation is not valid for strongly interacting systems. Some solutes (e.g., highly dipolar solvatochromic indicators) microscopically concentrate into their solvation shell that component of a mixture with which the solute most strongly interacts. This entropically disfavored process is driven by the enthalpy derived from the strong interaction. More recently, Abboud and his co-workers3*have investigated the effect of dilute cosolvents on the rate of Menschutkin reactions in cyclohexane. They found that the rate enhancement effect by aromatic cosolvents vastly exceeded that which can be predicted by reaction field theories of mixtures. The excess enhancement was attributed to specific chemical effects in which the aromatic cosolvent was concentrated into the solvation shell of the highly dipolar transition-state complex. Indeed, they state that the principal driving force for solvent sorting in dilute solutions of aromatic liquids in nonpolar solvents is the high quadrupole moment of the phenyl ring. We hypothesize that the alkylbenzene series constitutes a class of highly amphiphilic solvents. The aromatic end of the molecule, as shown by the very high A* value of benzene (0.6) relative to (29) Kamlet, M. J.; Doherty, R. M.; Famini, G. R.; Taft, R. W. Acta Chem. Stand. 1987, 841, 589-98. (30) Sjostrom, M.; Wold, S.Arm Chem. Scand. 1981, 835, 537. (31) Cheong, W. J.; Carr, P. W. Anal. Chem. 1988.60, 820-6. (32) Kamlet, M. J.; Kayser, E. G.;Jones, M. E.; Abboud, J. L.; Eastes, J. W.; Taft, R. W. J . Phys. Chem. 1978.82, 2477-83. (33) Johnson, B. P.; Khaledi, M. G.;Dorsey, J. G . J . Chromatogr. 1987, 384, 221-30. (34) Langhals, H. Angew. Chem., Inr. Ed. Engl. 1982, 21, 724-33. (35) Kolling, 0. Anal. Chem. 1985. 57, 1721-5. (36) Nitsche, K. S.; Suppan, P. Chimia 1982, 36, 346-8. (37) Prausnitz, J. M.; Lichtenthaler, R. N.; Azevedo, E. G . Molecular Thermodynamics of Fluid Phase Equilibrium, 2nd ed.; Prentice Hall: Englewood Cliffs, NJ, 1986; p 299. (38) Abboud, J. L.; Douhal, A.; Arin, M. J.; Diez, M.T.; Homan, H.; Guiheneuf, G. J . Phys. Chem. 1989, 93, 214-20.
Ulrich and Carr TABLE IV: Random Mixing Estimate of the r * of the n- Alkylbenzenes solvent r:,” diffb re1 Diffr
n-pentylbenzene n-heptylbenzene n-decylbenzene n-tridecylbenzene n-pentadecylbenzene
0.278 0.254 0.234 0.222 0.214
0.206 0.192 0.175 0.169
0.425 0.430 0.427 0.432 0.456
0.18 1
“Based on eq 6 . bobserved - estimated. ‘(Observed - estimated)/observed.
*
...
K I
0.30
-
1 .
0 -
0
-0
2 2
0.20
L
-
1
0.10 0.00
0.20
0.40
0.60
0.80
1.00
Volume Fraction of Phenyl Group
Figure 7. Dependence of excess A* of aromatics on volume fraction of phenyl rings computed from eq 2 and the measured refractive index of the n-alkylbenzenes.
that of any alkane (-0.1 to O.l), interacts much more strongly with the extremely dipolar solvatochromic indicator. Thus, in the cybotactic region we imagine that a solute observes a very “aromatic like” environment in which the phenyl rings are on average closer to the solute than are the aliphatic groups in the alkyl tail. Assuming that the cybotactic region comprises a random mixture of the different groups in the solvent molecule, then the ?r* of an alkylbenzene should be given by the following equation in which the T * of benzene and an alkane are volume fraction averaged: “*n-alkylbenzenc “*alkane
-t (vbcnzcne/
Vn-alkylknzcnc)*(A*benzene
- “*n-alkanc)
(6)
v k n z e n e and Vn-alkylknZne are the molar volumes of benzene and an n-alkylbenzene, respectively. The results of these computations are shown in Table IV. For all solvents that could be tested, the estimated ir* based on a volume fraction weighted averaged random mixing model is much lower than the observed value. The relative difference is quite constant at about 0.42-0.45. This is consistent with our hypothesis that the solute seeks out phenyl rings and concentrates them into its microenvironment. In fact, the effect is quite large in view of the fact that the volume fraction of phenyl groups in n-pentadecylbenzene is only 0.26, but the phenyl group causes an increase of nearly 50% in ?r* over the estimated value. In the limit of an infinitely long chain, the random mixing model must be correct; yet, even with pentadecylbenzene, no attenuation in nonrandomness is apparent. This same effect can be demonstrated in a more graphical fashion for a wider range of solvents as follows. This approach is closely related to the excess value of A* seen in the aromatic liquids relative to their refractive index. We now consider the A* predicted for the aromatic liquids based on the aliphatic regression line (eq 2). That is, we will use the measured refractive indices of the n-alkylbenzenes to estimate their ?y* via eq 2. Equation 2 is a physically reasonable model of the contributions to A* from the solvent polarizability. The results are shown in Figure 7. As the volume fraction of the phenyl group decreases, the aromatic and aliphatic solvents behave more similarly; however, the effect of a phenyl group is still very significant, even for pentadecylbenzene, as reflected in the large extrapolated intercept at zero volume fraction of phenyl groups. The assumption of group
The Journal of Physical Chemistry, Vol. 95, No. 24, 1991 10203
Solvatochromic Study of Alkylbenzenes 0 70 0 60
The slope of this plot greatly exceeds that which is observed for the pure aromatic solvents (eq 5 ) and supports our contention that in a mixed solvent benzene will concentrate into the cybotactic region of the solute. The maximum deviation from the ideal line is only about 0.1 A* unit, which is considerably less than what we observe in the pure n-alkylbenzenes. When the data are examined from the opposite extreme, the highest three concentrations fit the equation
-
ni
M 050@ 040-
4
3
030v,
*
020A*
0 00
40 60 80 20 Volume Fraction of Benzene
0
100
Figure 8. r* values for indicator 32 in mixtures of benzene and hexadecane. 0.60
-
c\i 0.50
-
*a,
-
M
0.40
4-
2
0.30 -
*
0.20 -
0 v,
t= 0.10
-
000 I 0.205
0.210
0.215
0.220
0.225
I
0.230
Onsager Function
Figure 9. Plot of T* and an2) for mixtures of benzene and n-hexadecane. Solute 32 was used to determine T * .
sorting cannot explain the very large value of A* of benzene relative to its polarizability, but it does rationalize the decrease in A* as the carbon chain lengthens. On the basis of the above random mixing approximations, we believe that the extent of localization of the phenyl groups in the cybotactic region of the probe solutes is really very large relative to what is observed with true solvent mixtures. This is evident in the data of Figure 8, which show the measured A* values of mixtures of benzene with n-hexadecane. The solid line indicates the result that should be observed if the mixture were to behave as a random mixture. As expected, the measured A* values are always above the ideal line; however, the maximum deviation, about 0.07 A* unit, is much less than the deviations observed with the pure solvents (see Table IV and Figure 7). This enhanced cybotactic effect in the long-chain benzenes relative to that in the solvent mixture is easily rationalized. For a specific component of a mixture to become localized in the cybotactic region, it must give up some translational entropy. In contrast, for a particular group in a molecule to localize, only some rotational and orientational freedom is lost since the molecule as a whole is already in the immediate vicinity of the central solute. Consequently, localization of a group is far less costly, in terms of entropy, than is localization of an entire molecule in a mixture. The same tendency for solvent sorting is displayed in the data of Figure 9. Here the measured ?r* value in the benzene-hexadecane mixtures is plotted against the Onsager reaction field function derived from measurements of the refractive index of the mixture. The ideal mixture result is shown as the solid line. Clearly, addition of a small amount of benzene results in a much greater relative change in A* than it does in the polarizability of the mixture. On the basis of the four lowest concentrations of benzene, we observe the following relationship: A*
= -14.8 (fO.001)+ 74.0 (f2.0) O(n2)
(7)
= -2.97 (fO.OO1)
+ 15.9 (f0.4)
O(nZ)
(8)
This section of the data set encompasses volume fractions of benzene that are within the range explored in the alkylbenzenes, and the fitting coefficients are seen to be smaller that those in eq 5 . This shows, as expected, that the effect of nonrandomness is smaller in a mixed solvent than is the effect of group sorting in a pure solvent. Polarizability Correction Factor and Group Sorting. Kamlet et al. intuitively introduced the polarizability correction factor.' The very significant variations in A* seen in this work naturally raise the question of whether long-chain alkylbenzenes should be treated as aliphatic (6 = 0) or aromatic (6 = 1) solvents. This clearly underscores Reichardt's proposal that the polarizability correction factor should be put on a more substantive f00ting.l~ However, if one accepts our hypothesis that highly polar solutes arrange the solvent so as to localize the phenyl rings in their immediate vicinity, there is no clear-cut way to derive and substantiate a 6 parameter which varies continuously from a "pure" aromatic-like solvent to a "pure" aliphatic-like solvent. Given the strength of the group sorting effect, we believe that a value of 1.OO for 6 for all alkylbenzenes is a reasonable compromise. Our suggestion that "group sorting" takes place in long-chain solvents and does so more readily that does "solvent sorting" in a solvent mixture has considerable consequences. First, it greatly complicates the fundamental interpretation of the meaning of a polarity scale. In any liquid, a more dipolar or more polarizable group will be better able to overcome the thermal randomization of group orientation. This may act either in concert with or in opposition to the other factors responsible for probe-to-probe differences in measurements of solvent propertie~.'~,l~ Second, it provides another rationalization as to why continuum models of solvatochromism must fail. Finally, if we broaden the idea of group sorting to encompass other processes such as specific acid-base interactions between groups, it helps explain the very small changes in measurements of solvent acidity and basicity observed within a homologue ~ e r i e s . ~ J ~ Conclusions. The A* values of both alkyl aromatic and n-alkanes can be correlated with a linear function of the Onsager reaction field; however, extremely different intercepts and slopes are observed despite the fact that both series of liquids are nonpolar. The differences cannot be rationalized by a fixed value of the Kamlet-Taft polarizability correction factor for the two classes of liquids. The differential behavior of long-chain nonpolar aromatic hydrocarbons with respect to the n-alkanes has been rationalized by hypothesizing the existence of group sorting in the cybotactic region of the probe solute. Acknowledgment. This work was supported in part by grants from the Petroleum Research Foundation, the National Science Foundation, and the Undergraduate Research Opportunity Program of the University of Minnesota. E.T.U. was supported in part by a fellowship from the Parenterals Research Division of Baxter Health Care Products. We thank Dr. James E. Brady for his many helpful discussions. This paper is dedicated to the memory of Mort Kamlet, who by his work, advice, and unstinting friendship has done so much to advance the science of solvatochromism and linear solvation energy relationships.
