J. Phys. Chem. 1984,88, 4410-4414
4410
where X, is, as before, the intrinsic mole fraction of ions in the saturated liquid. For steam at the boiling point, this gives k (defined by eq 5 ) = 21.4, somewhat greater than that of the liquid. This is also consistent with our earlier onjecture that dkldp is negative in the liquid phase. What is remarkable is that k has changed so little, despite a nearly 2000-fold change in density. It is not surprising that, over the restricted range of liquid densities accessible to experiment, k should appear to be constant. On the other hand, both the thermodynamic clustering approach and the liquid-drop model show clearly that dkldp is positive at low densities in the vapor?’ Thus, at temperatures above the critical point, where a broad range of densities is accessible to experiment, one can anticipate that k will be a quadratic function of the (21) C. E. Klots, unpublished results.
density. This will be discussed further, elsewhere. In addition to the explicit results obtained, the derivation of the “liquid-drop” model given above clarifies its underpinnings. As its name implies it constitutes essentially a significant structure model of the gas phase. It is in just this spirit that we have introduced an additional element of structure-the spherical cavity within which each cluster is embedded. By doing so, interactions among the clusters seem to have been treated adequately, thus permitting the extension to higher densities than has been customary. Acknowledgment. I am grateful to Rufus H. Ritchie and William Marshall for their help and stimulation. Research is sponsored by the Office of Health and Environmental Research, US.Department of Energy under Contract W-7405-eng-26 with the Union Carbide Corporation.
The Composition of Mixed Micelles of Fluorocarbon and Hydrocarbon Surfactants As Derived from Nuclear Magnetic Resonance Self-Diffusion Measurements Johan Carlfors* and Peter Stilbs Institute of Physical Chemistry, University of Uppsala. S-751 21 Uppsala, Sweden (Received: February 3, 1984; In Final Form: March 27, 1984)
The molal compositions of micelles formed in mixed alkanoate and perfluoroalkanoate surfactant solutions have been determined from NMR self-diffusion measurements. The results are consistent with the coexistence of two kinds of micelles, one rich in hydrocarbon surfactant and the other mainly formed by fluorocarbon surfactant. Constituent segregation was found to increase upon lowering the temperature and on increasing the chain length of the fluorocarbon surfactant. Partitioning of fluorocarbon surfactant between the hydrocarbon-rich micellar phase and the aqueous phase was found to be greater than the partitioning of hydrocarbon surfactant between the fluorocarbon-rich micellar phase and the aqueous phase. The effects constitute a basis for investigations on the nonideality of the mixing process between hydrocarbons and fluorocarbons.
Introduction
The mixing between hydrocarbons (HC) and fluorocarbons (FC) is known to be highly nonideal. Critical effects occur already in relatively simple systems. Heptane and perfluoroheptane mixtures, for example, phase separate around 50 OC.’ The mixing process, as such, provides a means for investigating the underlying nonideality effects, and indeed studies based on effects of this kind have been presented also for surfactants. For mixed HC and FC surfactants in aqueous solutions, one finds that the critical micelle concentrations (cmc’s) of such solutions are much higher than expected from ideal mixing b e h a ~ i o r . ~Results ,~ have been analyzed by the regular solution theory2s4and, in one case, a mixture of ammonium dodecyl sulfate (ADS) and ammonium perfluorononanoate (APFN), the interchange energy per molecule was calculated to be 2.2kT which exceeds 2kT, the condition for critical mixing, entering in this theory. It was concluded that most probably two kinds of micelles, one rich in H C surfactant and the other rich in FC surfactant were present at intermediate mole fractions. Other work indicating the coexistence of two kinds of micelles is based on is the observation of two cmc’s in the system sodium dodecyl sulfate (SDS)/sodium perfluorooctanoate (SPFO).3 Apart from one report (based on surface tension measurem e n t ~ on ) ~ the micellar composition of mixed micelles in a mixture (1) J. H. Hildebrand, B. B. Fisher, and H. A. Benesi, J . Am. Chem. SOC., 72, 4348 (1950). (2) K. Shinoda and T. Nomura, J . Phys. Chem., 84, 365 (1980). (3) P. Mukerjee and A. Yang, J . Phys. Chem., 80, 1388 (1976). (4) R. Fowler and E. Guggenheim, “Statistical Thermodynamics”, Cambridge University Press, London, 1956.
0022-3654/84/2088-4410$01 SO10
of a H C surfactant with a partially fluorinated surfactant (it was concluded that most likely two coexisting types were present), very little is known about the exact compositions of these mixtures. In the present paper, a new method for the quantitative investigation of the mixing of H C and FC surfactants in solution is presented, which is based on self-diffusionmeasurements through the Fourier transform (FT) N M R pulsed-gradient spin-echo (PGSE) technique. A brief study of aqueous solutions of mixtures between sodium decanoate (SD) and sodium perfluorooctanoate (SPFO) or sodium perfluorononanoate (SPFN) is presented, as based on proton and fluorine N M R FT-PGSE experiments. Since the formation of mixed micelles is phenomenologically similar to the process of solubilization of molecules in micelles, a technique originally designed for investigations of the latter process6-8could be adapted for the present purposes. Experimental Section
Materials. Commercial perfluorooctanoic acid was obtained from Fluka AG, Switzerland and perfluorononaoate from Riedel-de-Haen, West Germany. Sodium decanoate of high purity was a generous gift from 0. Kvammen, Bergen University, Norway. Sodium salts of the alkanoic acids were prepared by neutralization with sodium hydroxide, followed by freeze drying and vacuum drying. Solutions have been prepared by weighing. Concentrations are expressed in millimoles per kilogram of solvent ( 5 ) N. Funasaki and S. Hada, J . Phys. Chem., 84, 736 (1980) (6) P. Stilbs and M. E. Moseley, Chem. Scr., 15, 176 (1980). (7) P. Stilbs and M. E. Moseley, Chem. Scr., 15, 215 (1980). (8) P. Stilbs, J . Colloid Interface Sci., 87, 385 (1982).
0 1984 American Chemical Society
The Journal of Physical Chemistry, Vol. 88, No. 19, 1984 4411
Mixed Micelle Compositions from N M R so
,
,
,
,
,
,
1
SD
HOC
.
,
.
SD
TMS
,
,
.-
,
6/PPm
10
factant fluorines are relatively short. This has an adverse effect on of spin-echo amplitudes. For this reason shorter pulse intervals between R F pulses were required, as compared to conditions for protons. Calculations. The partition coefficient, K , may be defined as
K = XA/XB I
LO
50
60 70 80 ~
ol ,--
Figure 1. The upper trace is a normal proton NMR spectrum and the lower a typical sequence of spectra collected in a diffusion experiment. Ar represents the duration of the magnetic field gradient pulses. Signal amplitudes decrease with increasing At as a result of translational diffusion. The SD concentration was 597 mrn and the SPFO concentration 15.0 mrn in the present experiment. Evaluated diffusion coefficients were 0.076 and 0.058 for SD and Me4Sirespectively (expressed in units of mz s-'), For experimental details, see ref 8.
(mm). The solvent, deuterium oxide, was obtained from Norsk Hydro, Rjukan, Norway. Methods. Measurements were performed on a standard JEOL FX-100 Fourier transform N M R spectrometer, equipped with a multinuclear measuring system and a 10-mm tuneable probe. The particular experiments were programmed into the PG-200 pulse programmer system and the moving-head disk system files. Self-diffusion coefficients of the individual components of the solutions have been obtained by a Fourier transform N M R technique, which has been outlined An example of a typical self-diffusion measurement is shown in Figure 1 . The monitoring of aggregation processes in solution is based on the relatively large differences in intrisinic self-diffusion coefficients for substrates (here surfactant monomers) and macromolecules or supramolecular aggregates (here micelles). Partial binding of the substrate to the slowly diffusing species will therefore be quantitively reflected in a rather sensitive fashion in the time-averaged self-diffusion coefficient of the substrate. This general measurement approach has become conveniently feasible through the techniques described in ref 6-8. As outlined, the technique has previously been successfully applied to various types of association phenomena, e.g., solubilization in micelles,8 ion binding to polyelectrolyte^,^ inclusion complexes with cyclodextrins,1° and substrate binding to vesicles." Since there is a fast exchange between surfactants in the aqueous and in the micellar phases on the NMR time scale, the following two-site model applies: ~ P =P p i c + ( 1 - ps)Df=e (1) where D a P P represents the observed (time-averaged (in the present measurement series over ca. 200 ms)) diffusion coefficient of a substrate, p s the fraction of micellized substrate, Nc the diffusion coefficient of the micelle and Dfr"the diffusion coefficient of the substrate in the aqueous phase. At concentrations far above cmc Dmicis identical with the time-averaged diffusion coefficient of the (micellar) surfactant. At lower concentrations, however, the surfctant diffusion coefficient will increase due to contributions from monomeric surfactant. The actual monitoring of micelle self-diffusion was therefore made on signals from added trace amounts of tetramethylsilane (Me4Si) which can be assumed to be completely solubilized in the micellar phase. Dfiee was measured separately in a dilute solution of the constituent in question. Proton N M R was utilized for the study of H C constituents while FC constituents were monitored by I9F N M R on the CF3 group of FC surfactant. (For a fluorine signal assignment, see ref 12.) Fluorine diffusion experiments are analogous to those of protons, although T2 (the spin-spin relaxation time) for sur-
(9) P. Stilbs and B. Lindman, J . Magn. Reson., 48, 132 (1982). (10) R. RymdCn, J. Carifors, and P. Stilbs, J. Inclusion Phenomena, 1, 159 (1983). (1 1) P. Stilbs, G. Arvidson, and G. Lindblom, Chem. Phys. Lipids,in press. (12) N. Muller and H. Simsohn, J . Phys. Chem., 75, 942 (1971).
(2)
where X A is the mole fraction of the substrate in the micellar phase and X Bis the mole fraction of the substrate in the aqueous phase. X, and X B are accessible from diffusion measurements and the known compositions of the solutions through XA = PMbscs + (Csurf XB
= ( l -Ps)Cs/[(l
-
~
S
)
~
- Cmon,surf)l
+ S Cmon,surf + cD,Ol
(3) (4)
which is well approximated by
XB = ( 1 - P s ) C s ~ D , O / 1 o 6
(5)
and where C,represents the concentration of substrate, Csurf the the concentration of moconcentration of surfactant, Cmon,surf nomeric surfactant, CDz0the concentration of D20, and MD,Othe molar weight of D20. Cmon,surf is calculated from the p value obtained by input of diffusion data for the surfactant in eq 1 . HC and FC surfactants enter as substrates in the above expressions when studying their association with micelles consisting of the opposite type of surfactant. In accomplishing this, one must keep the substrate at a concentration low enough to prevent it from forming micelles while the micelle-forming surfactant concentration is well above the cmc. Through this procedure, it becomes possible to determine the partition coefficients of H C surfactant in FC micellar solution and of FC surfactant in H C micellar solutions separately. From these partition coefficients it is then possible to evaluate the actual micellar compositions in a mixed micellar system. The following set of equations, where the FC-rich micelle is labeled ( 1 ) and the HC-rich one ( 2 ) , were utilized in the calculations:
K(1) = X A ( ~ ) H C / ~ B H C
(6)
K ( 2 ) = X A ( ~ ) F CFC/ ~ B
(7)
PHC = p(1)HC + P(2)HC
(8)
PFC
= p(l)FC + p(2)FC
(9)
XA(1)HC = P(l)HCcHC/b(l)HCcHC + P(1)FCCFCl (10) xA(2)FC = P(2)FCcFC/b(2)FCcFC + P(2)HCcHCI ( l 1 ) In practice, experimental difficulties may limit the possible range of applicability. In the present investigation the major problem faced is related to the low cmc of SPFO. It was found that extremely low concentrations (i.e., 5 mm) were needed for ensuring complete dissociation of SPFO micelles in the presence of SD micelles when determining K ( 2 ) . The resulting accuracy of K(2) is low, due to the weak N M R signal obtained in this case. One should not that, in principle, the present measurement approach is applicable to systems of more than two surfactants in solution. The generalized formulations of eq 6-9 then become K ( i ) = xA(i)j/xB, Pj
= CAi)j
(12) (13)
I
i = 1 , 2, ...,N where N is the number of surfactant constituents and j labels individual components. Results SD Association with SPFO Micelles. In Figure 2, the diffusion coefficients of SD, SPFO, and Me4Si are plotted vs. concentation of SPFO at 60 OC. The concentration of SD is kept constant at 42 mm, well below the cmc (100 mm), ensuring complete dissociation of SD micelles. The overall features observed (as manifest the decreasing SD diffusion with addition of SPFO) are similar to those of ordinary solubilization processes.8 The timeaveraged self-diffusion coefficient for SPFO has contributions from
4412
The Journal of Physical Chemistry, Vol. 88, No. 19, 1984 T
TABLE I: Self-Diffusion Coefficients of Monomeric Surfactants below cmc surfactant C/mm temo/"C P SD 40 25 0.49 f 0.01 SD 40 60 1.22 f 0.05 SPFO 16 25 0.57 f 0.02 SPFO 16 60 1.40 h 0.08 SPFN 4 60 1.25 f 0.10
I
I
Carlfors and Stilbs
uAllreported error limits for the diffusion coefficients are calculated by a Monte Carlo simulated error analysis described in ref 18. They are 80%
2 00
100
[S P F 01 mmolal Figure 2. Diffusion coefficients as a function of SPFO concentration at [SD] = 40 mm at 60 OC. Open circles, filled circles, and squares rep resent SD, SPFO, and Me4Si respectively. Dashed curves indicate the expected diffusion behavior at the cmc of SPFO (=21 mm). I
I
1 200
LO 0
[SDI
mmolal Figure 4. Diffusion coefficients as a function of SD concentration at [SPFO]= 15 mm at 25 O C . Notations as in Figure 3.
0.01
I
2c-1
I
I
100
200
I
rs P F o j ' molal Figure 3. Results from TI 19Frelaxation measurements. Relaxation rates, TC1,of SPFO in the presence of 42 mm SD plotted vs. the inverse concentration of SPFO at 25 OC. The intersection of the straight lines occurs at the cmc of SPFO. (Solutions were not degassed.) monomer diffusion and is therefore higher than the micellar value (taken to be equal to that for solubilized Me,Si). The cmc for SPFO in the presence of 42 mrn SD is 21 mm as determined from the fluorine NMR TI relaxation measurements, presented in Figure 3. (The underlying method, which is quite accurate, is described in ref 13.) It should be pointed out that potential obstruction effects14will be very small in these dilute solutions. (In fact, the diffusion coefficient of HDO was found to decrease by only 4% at the highest concentration in this experiment.) One can actually question whether obstruction effects are at all operative in these systems, since the substrates in question are surfactants, which should not experience the micelles as solid obstacles. The overall diffusion coefficient changes for S D can therefore essentially altogether be ascribed to partial SD association with SPFO micelles. Observed self-diffusion coefficients for surfactant monomers below the cmc are summarized in Table I. Table I1 summarizes evaluated data for the association of SD in FC micelles. Here the concentration of SD was kept constant (40 f 2 mm), while the concentration of FC surfactant was varied. Three systems were investigated: SD in SPFO micelles at 25 "C, (13) J. Ulrnius and B. Lindrnan, J. Phys. Chem., 85, 4131 (1981). (14) J. Wang, J . Am. Chem. Soc., 76, 4755 (1954).
SD in SPFO micelles at 60 OC, and S D in SPFN micelles at 60 OC. The latter temperature was chosen to ensure complete homogeneity of the SPFN solutions (the Krafft point in this system is about 50 OCi5). Diffusion coefficients for SPFN were found to be lower than for those for Me4Si. It was therefore concluded on this basis (and on the low cmc for this surfactant) that the concentration of monomeric SPFN could be neglected in the calculations. For the determination of K, in this case, the errors from the measurements of the diffusion coefficients dominate over the possible errors introduced by neglecting diffusion contributions from monomeric SPFN. SPFO Association with SD Micelles. Data for the association of SPFO with SD micelles at 25 OC are reported in Table 111. The concentration of SPFO was similarly held constant (5.0 mm) and low while the SD concentration was varied. The accuracy of these measurements is not very good due to the weak NMR signals from the nuclei of interest. Coexisting SD and SPFO Micelles. In this system the SPFO concentration was kept constant but at a higher level than in the previous case. As seen in Figure 4,the diffusion behavior of the components is very different from that shown in Figure 2. Both the SD and SPFO surfactants exhibit diffusion behavior indicative of micelle formation and SPFO diffusion starts decreasing at a lower concentration than S D does. As described below, this behavior is consistent with the coexistence of two kinds of micelles, one rich in SD and the other rich in SPFO surfactant. Experimental results for this system are presented in Table IV. The composition of the micelles and the micellar fractions of each constituent has been calculated from eq 6-1 1 and are summarized in Table V. The fractions of SPFO in SPFO micelles, p(l)SPFO, and of SPFO in SD micelles, p(2)spF0,from Table V are plotted in Figure 5 as a function of SD concentration. One may note that, at low concentrations of SD, SPFO-rich micelles, (type 1) are the major aggregated species. When the concentration of SD is increased, (IS) K. Fontell and B. Lindrnan, J . Phys. Chem., 87, 3289 (1983).
Mixed Micelle Compositions from N M R
The Journal of Physical Chemistry, Vol. 88, No. 19, 1984 4413
TABLE 11: Results from Diffusion Measurements on the Association of S D with FC Micelles ~~
temp/OC
CsD/mm
CFclmm
XSD‘
25 25 25
42.0 42.0 42.0
97 150 214
0.30 0.22 0.16
60 60 60
40.0 40.0 40.0
104 148 200
0.28 0.21 0.17
Cmon,FC>
xB SD/
DSD DFC DMlerSi SD Association with SPFO Micelles 0.373 f 0.005 0.329 f 0.006 0.285 f 0.002 0.83 f 0.03 0.73 f 0.02 0.61 f 0.03
0.154 0.127 0.093 0.48 0.36 0.34
0.127 0.101 0.07
6 8 10
0.35 0.298 0.248
0.125 0.108 0.090
0.580 0.496 0.437
0.165 0.132 0.121
13 8 16
Kb
lo-’
xASD
K,
215 f 9 220 f 20 205 f 8 = 213
K,,,,
380 f 40 350 f 30 410 f 50 = 380
K,
290 f 30 260 f 30 280 f 30 = 280
0.441 0.377 0.296
SD Association with SPFN Micelles 60 60 60
40.2 40.2 40.2
110 157 209
0.27 0.20 0.16
*
0.80 0.03 0.72 f 0.03 0.62 0.02
*
0.21 0.174 0.156
0 0 0
0.25 0.22 0.19
0.133 0.109 0.097
0.467 0.419 0.354
“XsDis the surfactant mole fraction of SD. bError limits calculated from the 80% confidence intervals of the diffusion coefficients. TABLE III: Results from Diffusion Measurements on the Association of SPFO witb S D Micelles cSPFO/mm cSD/mm xSD DSPFO 4 D DM04Si Cmon.SD/mm xA 5.1 5.0 5.0
196 396 592
0.975 0.988 0.992
0.29 f 0.05 0.14 f 0.01 0.14 f 0.04
0.229 0.113 0.081
0.099 0.064 0.069
63 40 18
SPFO
K 600 f 300 800 f 100 800 f 500 K = 800 f 100“
xB SPFO/ lo-’
0.0216 0.01 18 0.0074
0.04 1 0.015 0.014
Within these limits the three 80% confidence intervals of K overlap. TABLE I V Results from Diffusion Measurements on Solutions at Concentrationsabove the cmc’s of both S D and SPFO cSPFO/ mm cSDlmm xSD DSPFO DSD DMc4S~ Cmon,SPFO/mm 14.9 14.9 14.9
106 209 399
0.88 0.93 0.96
0.29 f 0.01 0.164 f 0.008 0.121 f 0.009
0.43 f 0.02 0.235 f 0.007 0.1 11 f 0.001
TABLE V Calculated Compositions of Coexisting Micelles in SD/SPFO Systems CSD/mm xA(1)SPFO xA(2)SPFO xBSPFO/10-3 XBSD/lO-’ 106 209 399
0.650 0.715 0.830
0.067 0.03 1 0.026
0.084 0.039 0.032
SPFO monomers start associating with SD-rich micelles, leading to a decreasing fraction of type 1 micelles. The uncertainity of the determination of the partitioning of the constituents becomes somewhat greater at higher SD concentrations. This is related to the increasing uncertainty in X , spFo as the concentration of monomeric SPFO becomes very small.
Discussion From Tables I1 and I11 it is seen that apparent partition coefficients (as based on eq 2-5) are essentially composition independent. This would suport an assumption of only one micelle type. This contrasts to the data presented in Table IV; a similar assumption (Le., using eq 2-5) leads to composition-dependent K values in that case. The results are consistent with the assumption of the coexistence of two kinds of micelles, the aggregation of which can be characterized by two composition-independent partition coefficients KsD and KSPFO, as summarized in Table V. The K value for SD inclusion in SPFO micelles at 25 OC is of the order of 21 3. This should be compared with the K value for the solubilization of 1-butanol in SDS of 300 reported from vapor pressure measurements.16 The relatively low value (for a carbon chain of that length) reflects the unfavorable interactions between H C and FC surfactants. When the temperature is raised from 25 to 60 O C , K increases from 213 to 380. This is in agreement with previous findings on liquid H C and FC surfactants,2 demonstrating that increasing temperature enhances the mixing process. (16) K. Hayase and S. Hayano, Bull. Chem. SOC.Jpn., 50, 83 (1977).
0.18 0.105 0.067
d1)SPFO 0.63 0.57 0.25
1.64 1.34 0.80
I
4.2 1.9 1.6
d2)SPF0 0.09 0.30 0.64
Cmon,SD/mm 82 67
40
P(l)SD 0.047 0.016 0.002
d2)SD
I
1
I
0.18 0.66 0.90
0 LL
a
&
200
LOO
cso3 mmolol Figure 5. The total fraction of SPFO associated with micelles, PspFo (circles), the amount of SPFO associated with SPFO-rich micelles, p(1)SpFO (squares), and the amount of SPFO associated with SD-rich micelles,p(2)sPm (triangles), as a function of SD concentration at [SPFO] = 15 mm at 25 O C .
As a result of the extra CF2 group in SPFN the K value decreases from 380 to 280, further reflecting the unfavorable mixing process. Related findings were reported in earlier s t u d i e ~ ,as ~.~ based on measurements of the cmc of HC/FC surfactant mixtures. The results in Table I11 indicate a partition coefficient for SPFO binding to SD micelles of 800, which is higher than the value of KSD = 213. The difference can be understood from the differences in hydrophobicity between the HC and FC molecules in aqueous solutions. The hydrophobicity for FC surfactants is higher than that for the corresponding HC surfactants as judged from the
4414
J . Phys. Chem. 1984,88, 4414-4420
relatively lower cmc’s of FC surfactants. It can be noted in this context that the incremental free energy per CH2 group for transfer from an aqueous to a FC environment is -690 cal/mol, while it is -1210 cal/mol for the transfer of a CF2group to a H C en~ironment.’~These trends in free energy differences are in line with the findings in the present paper. For experimental reasons, all measurements have been made in D20instead of normal water. It could be argued that solubilization and aggregation behavior in micellar systems might differ significantly between these two solvents and that our results might not be comparable to those found in other studies made in normal water. We have investigated this problem in a rather complete study, which clearly indicates that such effects are in~ignificant.’~Also, it is well established that cmc’s, which are (17) P. Mukerjee and T. Handa, J . Phys. Chem., 85, 2299 (1981). (18) P. Stilbs and M. E. Moseley, J . Magn. Reson., 31, 55 (1978). (19) J. Carlfors and P. Stilbs, submitted for publication to J. Colloid Interface Sci.
directly aggregation-related quantities, differ insignificantly between normal and heavy ~ a t e r . ’ ~ , ~ ~ Conclusions
It is demonstrated that NMR self-diffusion measurements provide a tool for the elucidation of the actual compositions of micelles in mixed micellar solutions. In principle, the measurement approach could be extended to system of more than two surfactants. Results from measurements in aqueous solutions in HC and FC surfactants are consistent with an assumption of two coexisting micelle types, one rich in HC surfactant and the other rich in FC surfactant. The origin of the effects leading to separate micelle types is the nonideal mixing process between hydrocarbons and fluorocarbons. Registry No. SD,1002-62-6; SPFO, 335-95-5; SPFN, 21049-39-8. (20) P. Mukerjee, P. Kapauan, and H. Meyer, J . Chem. Phys., 70, 783 (1966).
Llnear Solvation Energy Relationships. 21. Gas-Phase Data as Tools for the Study of Medium Effects Jose-Luis M. Abboud,**Ceorges Guiheneuf,’ M’hammed Essfar,‘ R. W. Taft,2 and Mortimer J. Kamlet3 Dlpartment de Chimie, Universitl Cadi Ayyad, Marrakech, Morocco; Department of Chemistry, University of California, Irvine, California 9271 7; and Naval Surface Weapons Center, White Oak Laboratory, Silver Spring, Maryland 20910 (Received: February 6, 1984; In Final Form: March 26, 1984)
We have examined functions relating the a* scale of solvent dipolarity/polarizability to refractive indexes and dielectric constants for the gas phase and a wide range of solvents. It has been found that the Ooshika-Bayliss-McRae formalism provides an excellent fitting of the data for nonprotonic nonpolychlorinated aliphatic solvents (“select solvents”) and for the gas phase, as well as a reasonable fitting for the perfluoroalkanes. This simple equation also correlates medium effects on other properties. Polychlorinated aliphatic and, particularly, aromatic solvents are not adequately described by this method. We believe that the latter behavior is not a consequence of the inexactitudes of the model but rather reflects more complex solvent/solute interactions at the molecular level. Finally, a clear link has been established between the d6 term in the solvatochromic equations and “cross terms” in equations by Carr and Brady and Taft, Abboud, and Kamlet.
I. The Present Status of the Relationship between the a* Scale and Structural Properties of the Solvents In recent years the use of empirical solvent property scales4has become increasingly generalized and their scope and usefulness seem now to be reasonably well establi~hed.~In this respect, we have been particularly involved in the application of the a* scale of dipolarity/polarizability6 to solvent effects on physical and chemical properties of dipolar reactants and indicators. We have (1) Universite Cadi Ayyad. (2) University of California, Irvine. (3) Naval Surface Weapons Center (4) See, e.g.: (a) Kosower, E. M. “An Introduction to Physical Organic Chemistry”, Wiley: New York, 1968. (b) Schwetlik, K. “Kinetische Methoden zur Untersuchungen von Reaktionsmechanismen”; VEB Deutscher Verlag der Wissenschaften: Berlin, 1971; Chapter 4. (c) Reichardt, C. “Solvent Effects in Organic Chemistry”; Verlag Chemie: Weinheim, 1979. (d) Jones, R. A. Y. “Physical and Mechanistic Organic Chemistry”; Cambridge Press: Cambridge, 1980 Chapter 5 . ( 5 ) (a) Kamlet, M. J.; Abboud, J.-L. M.; Abraham, M. H.; Taft, R. W. J . Org. Chem. 1983,48, 2877; (b) Kamlet, M. J.; Abboud, J.-L. M.; Taft, R. W. Prog. Phys. Org. Chem. 1981, 13, 485, and references cited therein. (c) We emphasize that a good correlation coefficient is a necessary condition for any model to be accepted a priori. It is not a sufficient condition. (6) (a) Kamlet, M. J.; Abboud, J.-L. M.; Taft, R. W. J . Am. Chem. SOC. 1977, 99 6027. An updated compilation of the presently available values is given in ref Sa. (b) Abraham, M. H.; Kamlet, M. J.; Taft, R. W. J . Chem. SOC.,Perkin Trans. 2 1982, 923. (c) Kamlet, M. J.; Taft, R. W.; Carr, P. W.; Abraham, M. H. J . Chem. Sor., Faraday Trans. 1 1982, 78, 1689.
0022-3654/84/2088-4414$01 .50/0
shown5v6that, in cases wherein hydrogen bonding effects are excluded, medium effects of a series of solvents of varying dipolarity on a property, X Y Z , of a dipolar solute follow eq 1.
XYZ = XYZO
+ S(T* + d6)
(1)
XYZ, is the regression value of the property in cyclohexane (the reference solvent), a* is the solvent dipolarity/polarizability parameter, and 6 is a “polarizability correction factor” equal to 0.0 for a select solvent set (SSS) of nonprotic nonhalogenated aliphatic solvents with a single dominant bond dipole, 0.5 for polyhalogenated aliphatic solvents, and 1.O for aromatic solvents. The XYZ’s that have been successfully correlated by eq 1 include positions of maximal absorption in UV/visible a b ~ o r p t i o n ~and ”~~~ fluorescence ~ p e c t r a , ~NMR ~ . ’ ~ shifts and coupling constant^,^^*^^ IR ~pectra,’~ logarithms of rate c o n ~ t a n t s and , ~ ~free ~ ~ energies ~ of transfer of polar solutes between solvents.6b,cFor the SSS, eq 1 takes the extremely simple form of eq 2. X Y Z = XYZO + sa* (2) (7) (a) Taft, R. W.; Abboud, J.-L. M.; Kamlet, M. J. J. Am. Chem. SOC. 1981,103, 1080. (b) Kamlet, M. J.; Taft, R. W. Pol. J. Chem. 1981,55, 1337; Kamlet, M. J.; Dickinson, C.; Taft, R. W. Chem. Phys. Lett. 1981, 77, 69. (c) Kamlet, M. J.; Taft, R. W. J . Chem. Soc., Perkin Trans. 2 1979, 337. (d) Chawla, B. Pollack, S.K.; Lebrilla, C. B.; Kamlet, M. J.; Taft, R. W. J . Am. Chem. SOC.1981, 103, 6924, and references therein. (e) Kamlet, M. J.; Boykin, J.; Hall, T. N.; Taft, R. W. J . Org. Chem. 1979, 44, 2599.
0 1984 American Chemical Society
