1442

pounds where rotation about sp3-sp2 bonds is involved.16 In propionaldehyde and n-alkyl homologues for example, the rotamer with the methyl or methylene group eclipsing the carbonyl is more stable than the rotamer with a hy- drogen eclipsing it.” Our measured barriers are higher hydridization.

J. Phys. Chem. 1981, 85, 1442-1445

than the -3 kcal/mol typically found for rotation about sp3-sp3 bonds and closer to the 1-2 kcal/mol for sp2-sp2 bonds.2J6 Thus we conclude that the radical has an ec- lipsed conformation with some distortion at CB toward sp2

Acknowledgment. This work was supported by a grant (16) Karabataos, G. J.; Fenoglio, D. J. Top. Stereochem. 1970,5,167. (17) Karabatsos, G. J.; Hsi, N. J. Am. Chem. SOC. 1966, 87, 2864. from the MSU Summer Faculty Research Fund.

Mlcellar Properties and Crltical Fluctuatlons in Aqueous Solutions of Nonionic Amphiphiles

Mario Cortl” and Vittorio Degiorgio CISE S.p.A., P.O.B. 12081, Miiano 20100, Itah, and Istkuto di Fislca Appiicata, UniversP dl Pavia, Pavia, Italy (Received: November 21, 1980)

n-Dodecyl hexaoxyethylene glycol monoether (C1&) aqueous solutions are investigated by static and dynamic light scattering in a temperature range from 25 to 50 “C, the latter point being very close to the lower consolution point of the micellar solution. The osmotic isothermal compressibility (apparent molecular weight of the micelle) is found to increase with the temperature following a power-law dependence on the temperature distance from the critical point. These data, together with the intensity-asymmetry and the mass-diffusion-coefficient data, strongly suggest that, in the range 30-50 “C, the observed phenomena are due to the critical concentration fluctuations and not to a temperature dependence of the micelle size.

Introduction Light-scattering experiments on dilute aqueous solutions

of nonionic amphiphiles show in most cases a strong en- hancement of the turbidity as the temperature is in-

Such a phenomenon was at first interpreted as due to an increase of the micelle size with temperature, with a negligible role played by nonideality effects. It is, however, difficult to justify on the basis of the existing theories of micelle formation the large sensitivity of the aggregation number on the tempera t~re .~ Another ex- planation which relates the observed phenomena to the existence of consolute phase boundaries was discussed later on2l4 but went unnoticed by many researchers, as shown by the fact that even recent papers6J treat apparent mo- lecular weights of nonionic micelles as true molecular weights without any discussion of possible nonideality effects. The clarification of this issue is important not only from a physicochemical point of view but also because nonionic amphiphiles are widely used in biochemistry to form mixed micelles of lipid and detergents and to isolate membrane protein^.^^^

Aqueous solutions of nonionic amphiphiles possess in many cases a lower consolution point (called the “cloud

point” in the micelle literature) characterized by a critical temperature T,. The behavior of binary liquid mixtures in the critical region has been extensively investigated in the last 15 yr.lo By approaching the critical point, one finds static parameters, like the osmotic compressibility and the correlation range of concentration fluctuations, and dynamic parameters, like the decay time of concen- tration fluctuations, to diverge, following asymptotically a universal power-law dependence on the reduced tem- perature difference E = IT - TcI/Tc. Since the critical region of nonionic amphiphile solutions covers some tens of degree~,~Jl it is reasonable to expect that critical con- centration fluctuations may play an important role in many light-scattering investigations of nonionic micelles.

In this paper we present a light-scattering study on dilute aqueous solutions of a nonionic amphiphile, n-do- decyl hexaoxyethylene glycol monoether (C1&&), in the temperature range 25-50 OC. The CI2E6 solutions show a critical consolution point slightly above 50 OC. The measured temperature dependence of static and dynamic properties indicates that information about individual micelle properties cannot be simply obtained from light- scattering data unless one works at very low temperature. Experimental Section

High-purity C12E6 was obtained from Nikko Chemicals, Tokyo, in crystalline form and was dissolved without further purification in doubly distilled and degassed water at -40 “C. It is absolutely important to avoid contact with

(1) R. R. Balmbra, J. S. Clunie, J. M. Corkill, and J. F. Goodman,

(2) K. W. Herrmann, J. G. Brushmiller, and W. L. Courchene, J. P ~ Y s .

(3) R. H . Ottewill, C. C. Storer, and T . Walker, Trans. Faraday SOC.,

Trans. Faraday Soc., 58, 1661 (1962); 60, 979 (1964).

Chem., 70, 2909 (1966).

fix 974R (19637) --,-.I- \_--.,.

(4) M Corti and V. Degiorgio, Opt. Commun., 14, 358 (1975). oxygen because Cl2E6 may undergo an oxidation process

0.5 cm) is made of fused silica and is temperature con-

(10) H. L. Swinney in “Photon Correlation and Light-Beating Spectroscopy”, H. Z. C u m i n s and E. R. Pike, Eds., Plenum, New York, 1974, p 331. (11) M. Corti and V. Degiorgio, Phys. Rev. Lett., 46, 1045 (1980).

(5) C. Tanford, “The Hydrophobic Effect. Formation of Micelles and Biological Membranes”, Wiley, New York, 1980, p 81.

(6) R. J. Robson and E. A. Dennis, J. Phys. Chem. 81, 1075 (1977). (7) H. H. Paradies, J. Phys. Chem., 84, 599 (1980). (8) E. A. Dennis, J. Lipid Res., 14,152 (1973); V. G. Cooper, S. Yedgar,

and Y. Barenholz, Biochim. Biophys. Acta, 363, 86 (1974); M. Corti, V. Degiorgio, S. Sonnino, R. Ghidoni, M. Masserini, and G. Tettamanti, Chem. Phys. Lipids, in press.

(9) A. Helenius and K. Simons, Biochim. Biophys. Acta, 415, 29 (1975); C. Bordier, J. Biol. Chem., in press.

which changes its physicochemical properties. The ret- tandm scattering (length, cm; width, cm; height,

0022-3654/81/2085-1442$01.25/0 0 1981 American Chemical Society

Micellar Properties and Critical Fluctuations

trolled within 0.001 "C over 24 h. The cell is filled with the micellar solution through a microporous filter (pore size, 0.2 Hm) having a teflon holder. We have found that prolonged contact of the C12Es solution with metals (Al, Fe) should be avoided because the critical temperature may change by several degrees. The critical temperature was determined by visual observation of the meniscus in sealed cells in a temperature-controlled waterbath and found to be 50.35 "C, with an absolute accuracy of 0.01 "C.

The average scattered intensity I , and the intensity correlation function of the scattered light are measured at two distinct scattering angles, 9 = 22.6" and 90°, by two ITT FW 130 photomultiplier tubes. The apparatus is equipped with an argon-ion laser operating on the 514.5- nm green line and with a 108-channel digital correlator. We have also monitored with separate photodetectors the power of the incident laser beam before and after the scattering cell in order to obtain a rough evaluation of the turbidity. This evaluation is useful for several reasons: (i) it indicates the range of e in which multiple scattering is not negligible; (ii) it allows one to correct the measured I , for the attenuation of the laser beam when the attenu- ation is not negligible and multiple scattering is not yet relevant; (iii) it allows one to give an absolute calibration to the osmotic compressibility, as discussed below.

The extrapolated scattered intensity a t zero scattering angle Id is related to the derivative of the osmotic pressure with respect to the concentration, (d n / d ~ ) T , ~ , according to eq 1, where A is an instrumental constant, dn/dc the

refractive index increment, kB the Boltzmann constant, and T the absolute temperature. We have assumed that the angular dependence of I , is described by the Orn- stein-Zernike relationlo

(2) where k = (47rn/X) sin 9/2 is the modulus of the scattering vector, X being the wavelength of the laser light, and 5 is the correlation length of the concentration fluctuations. The turbidity 7 is obtained by integrating over all angles the light-scattering intensity. The result is eq 3,12 where

7 = (7r3/X4)(2n dn/dc)2ckBT(d II/~C),,~-'F([/X) (3)

F is a known function of the ratio [/A. For f << A, F = 8/312 The mass-diffusion coefficient D is derived from the

decay time 7, of the intensity-correlation function as D = (21t27,)-l. When T is sufficiently close to T,, D is found to depend on the scattering angle. The hydrodynamic mass-diffusion coefficient Do is derived as the limit of D as It goes to zero.

Results and Interpretation The average scattered intensity I , shows an appreciable

asymmetry already at a distance of 5 "C from the critical temperature. By using eq 2 we have derived from the measurement of I , at two scattering angles the two quan- tities Iso and f . The quantity (d n /d~)~ ,~ - l is calculated from Ia0 by using eq 1. The refractive-index increment dnldc depends weakly on T. We used for our data analysis the dn/dc measurements of Balmbra et al.' which can be described by the following approximate linear law: dn/dc = 0.140 - 0.000367(T - 15 "C). We have reported in Figure 1 the behavior of (d I I / ~ C ) ~ , ~ - ' measured as a function of e a t the critical concentration, c, = 12.5 mg/cm3. The

I , = IaO/(l + k2f2)

(12) V. G. Puglielli and N. C. Ford, Phys. Reu. Lett., 25, 143 (1970).

The Journal of Physical Chemlstty, Vol. 85, No. 10, 1981 1443

50 45 40 3020 10 TPC) \ ' I I I / I 1

'\ z

-j

I I '. 1 0 - ~ 10-2 10-1

Flgure 1. The quantity ( d ~ / d l I ) , , ~ as a function of reduced tem- perature c = ( Tc - T)/ Tc at the concentration C = 12.5 mg/cm3. The left-hand vertical scale gives the apparent molecular weight MW The upper horizontal scale gives Tin "C.

. 10-81 I I I

10-3 10'' L 10-1

Flgure 2. The same as for Figure 1 with c = 10 mg/cm3.

absolute calibration of (d II/dc),, is obtained from a turbidity measurement performed at the closest point to T, (e = 9.5 X lo4), where the attenuation suffered by the laser beam over the 1-cm path in the scattering cell is N 13%. We have found that this calibration agrees within 15% with the calibration used in our previous works4J3 which was obtained by making a comparison with known scatterers, like benzene or water. The right-hand vertical scales in Figure 1 report the apparent molecular weight, defined as Mapp = kBT(d II/dc), -l. For an ideal micellar solution, Map would represent t i e true molecular weight of the indivicfual micelle. The results of Figure 1 are well described in the range 30-50 "C by a power law of the type

( d n / d ~ ) T , ~ - ' a e-Y (4)

with an exponent y = 0.97 f 0.05. A similar behavior is found for the concentration c = 10

mg/cm3, with the only difference that the apparent critical temperature at which the osmotic compressibility diverges is now T,' = 50.66 "C. The data shown in Figure 2 follow a simple power-law behavior in the range 30-50 "C with y = 0.98 f 0.05.

Figures 3 and 4 show the measured behavior of the correlation range f which follows asymptotically the power law

f = fo'oe-" (5) with to = 20 f 5 A and v = 0.53 f 0.05.

(13) M. Corti and V. Degiorgio, Ann. Phys. (Paris), 3, 303 (1978).

1444 The Journal of Physical Chemistry, Vol. 85, No. 10, 1981

45 40 3020 10 T( 'C ) 103

50 I I I I 1 I

Corti and Degiorgio

Figure 3. The correlation length 4 and the massdiffusion coefficient Do as function of t at c = 12.5 mg/cm3.

50 45 40 30 20 T ( ' C )

- B I

w

- 102

10" 10-2 0 lo-'

Figure 4. The same as for Figure 3 with c = 10 mg/cm3.

Since the coexistence curve is strongly asymmetric,' it is interesting to check whether the line of maximum (&/a n), coincides with the constant-concentration line at the critical value c, = 12.5 mg/cm3. We have measured Ino along two isotherms at T = 37.715 and 49.615 "C, and we have found that Ino /c peaks at c, for the higher tem- perature whereas for the lower temperature the depen- dence on c is very weak in the range 8-14 mg/cm3.

The time-dependent part of the measured correlation function G(7) was approximately exponential. We have observed a small systematic deviation from exponentiality, but this deviation does not seem to be appreciably de- pendent on T and c. We have derived D from the limiting slope of In G(7) as 7 goes to 2er0.l~ We have found that D depends appreciably on the scattering angle when e < lom2 (T > 47 "C). The hydrodynamic mass-diffusion coefficient Do is calculated from the measurements per- formed at two scattering angles by assuming a linear de- pendence of D on k2. Such a procedure may introduce some error very near to T, where the relaxation rate of concentration fluctuations may have a nonlinear depen- dence on k2.l0 Figures 3 and 4 show the temperature de- pendence of Do for the two investigated concentrations. The solid lines close to the Do data points are calculated from eq 6, where h rrr 1 and q is the macroscopic shear

Do = h k B T ( 6 ~ ~ 6 ) (6) viscosity of the solution which was measured by an Ub- belhode flow viscometer. The viscosity data are reported in Table I. Discussion

The data presented in Figures 1-4 show that the static parameters (dc/aII),, (or Mapp) and 6 diverge as T, is

TABLE I: Viscosity ( q ) of a 12.5 mg/cm3 Aqueous Solution of C,,E, and Viscosity Relative t o Pure Water as a Function of Temperature (2')

24.8 30.0 34.8 39.7 44.6 48.3 49.5 49.9

0.930 1.04 0.895 1.12 0.895 1.23 0.915 1.39 0.940 1.56 0.949 1.67 0.9 53 1.71 0.957 1.73

approached, following a simple power-law behavior as a function of the reduced temperature e in the range 30-50 "C. Furthermore the hydrodynamic mass-diffusion coef- ficient Do is found to obey the Einstein-Stokes relation (eq 6) where, however, q is the viscosity of the solution and not that of the solvent. Therefore, the measurements give unequivocal evidence of the fact that the micellar solution behaves in the range 30-50 "C as a critical binary mixture. It should be noted, however, that the values obtained for the critical exponents y and Y are close to those predicted by the mean-field theory (y = 1, v = 0.5), whereas the critical behavior of binary mixtures is usually described by the so-called renormalization group theory.'O It is possible that the mean-field critical behavior and the considerable extension of the critical region are due to the large difference in size between the micelle and the water molecule, and, as such, they could represent rather general features of macromolecular and micellar s o l ~ t i o n s . ~ ~ J ~

Light-scattering measurements performed by us a few years ago on a commercial nonionic amphiphile (Triton X-100)4 have already suggested that the temperature de- pendence of Mapp and of D can be totally attributed to critical effects without involving a change of the micelle size with T , so that the micellar solution could be con- sidered, from the point of view of critical properties, as a macromolecular solution. Recent measurements of NMR spectra of C12E6 solutions seem indeed to indicate that there is no appreciable change of micelle size in the region 30-50 "C.15

It is very interesting to observe that a strong correlation between the growth of Mapp with T and the position of the cloud point is shown by several sets of data in the litera- ture, like those on the homologous compounds C,Ee (With n = 8,10,12,14, and 16) reported by Balmbra et al.' and on the homologous series of dimethylalkylphosphe oxides obtained by Herrmann et a1.2 In both cases the homo- logues having the lower critical temperature (lower cloud point) show the largest effects on the temperature de- pendence of Mapv This can be easily explained by noting that, at fixed T , the reduced temperature e changes from one homologue to the other because T, is different.

The change of Mapp upon the addition of salts or other compounds to a nonionic amphiphile solution may be in many cases explained by considering that additives gen- erally produce a shift in the critical temperature, and therefore the addition of a compound is equivalent to a change in the reduced temperature E of the solution under study. As an example, we can take the light-scattering data on Triton X-100 solutions at 30 "C with added NaCl re- ported by Kuriyama.16 The observed increase of Mapp from 105 OOO with no NaCl to 150 OOO with 0.5 M NaCl may be correlated with the observed cloud-point depreesion of

(14) C. Ishimoto and T. Tanaka, Phya. Rev. Lett., 39, 474 (1977). (15) E. J. Staples and G. J. Tiddy, J. Chem. SOC., Faraday Trans. 1,

(16) K Kurtyama, Kolloid-Z., 181, 144 (1962). 74, 2530 (1978).

J. Phys. Chem. 1981, 85, 1445-1457 1445

7 "C (from 64 to 57 "C) upon addition of 0.5 M NaC1" by using the temperature dependence of Mapp lor Triton X-100 in water with no salt reported in ref 4. Going from 30 to 37 "C, the increase of M observed in ref 4 is -45%, a value close to that reporteriy Kuriyama for the 0.5 M NaCl addition at constant temperature.

Our results for Ma are in very good agreement with those obtained by Balmbra et al.l in the range 25-45 "C. The authors of ref 1 propose an exponential law for the growth of Mapp with T. Several other workers have suc- cessively proposed the same law,18 but the validity of this law was never checked close to T,. Indeed the deviation of our data from the exponential law becomes very large in the range 45-50 "C.

The plot of Figure 2 shows that the data do not follow the power-law behavior when e is larger than 7 X (temperature below 30 "C). The overall picture provided by all of the available experimental data1m3 on C12Ee dilute aqueous solutions is that there are three temperature re- gions, each characterized by a distinct behavior. In the first region, 5 < T 15 "C, Mapp is nearly constant3 and is probably coincident with the true molecular weight of the individual micelle. In the second region, 15 < T < 30 "C, Mapp increases exponentially.'8 It is possible that this behavior is entirely due to nonideality effects, but no quantitative theory is yet available. In fact the predictions of theories of critical phenomena apply only to the as- ymptotic region where static and dynamic parameters obey

(17) T. Nakagawa in "Nonionic surfactants", M. J. Schick, Ed., Dek-

(18) A. Goto, R. Sakura, and F. Endo, J. Colloid Interface Sci., 67,491 ker, New York, 1967, p 558.

(1978).

a simple power-law dependence on the reduced tempera- ture. In the third region, 30 "C < T < T, the solution behaves as a critical binary mixture, and therefore the light-scattering experiment sees only the effects associated with the large increase of the correlation range of con- centration fluctuations. the situation may be pictorially described by saying that, in proximity to the critical point, the motion of the micelles is correlated over a distance E which is much larger than the micelle size, so that the lightmattering measurement does not probe the individual micelle, but the growth and decay of large statistical clusters which include micelles and water. This picture bears some resemblance to the secondary aggregation picture discussed by Ottewill et aL3 and by Tanford: but the description of critical effects cannot be reduced to a simple secondary aggregation process.

A last point to be mentioned is that the linearity of the plots I, vs. c, as reported in ref 1,2, and 4, was probably considered by many authors an indication that the micellar solution is ideal over a large temperature and concentration range and, therefore, that the experimental data reflect directly individual micelle properties. Such an argument is, however, deceiving, as shown by the observation of Balmbra et al.l that the I, vs. c plots, when extrapolated to low concentrations, give an apparent critical micelle concentration (cmc) which is 10 times larger than the true cmc. Accurate measurements18 performed at low concen- traion show indeed that I, is not a linear function of c and that Mapp considerably increases with c in a very narrow concentration range above the cmc.

This work was supported by CNR/CISE Contract no. 80.00016.02.

Acknowledgment.

Phase Boundary Curves in Toluene, 1-Butanol, and Aqueous Sodium Aikylbenzenesuifonate Systems

Patience C. Ho

Chemistry Divlslon, Oak RMge National Laboratmy, Oak Ridge, Tennessee 37830 (Received; November 4, 1080)

Miscibility relationships in systems containing toluene, 1-butanol, water, and sodium alkylbenzenesulfonates are reported. The sulfonates studied included benzene, p-toluene, p-ethylbenzene, 2,4,6-trimethylbenzene, p-cymene, and 2,5-&isopropylbenzene. In a triangular representation with a constant ratio of 1 mol of sulfonate/kg of water as one component, the phase boundary curves are fairly symmetrical with respect to the alcohol apex for SAC (number of alkyl carbons on benzene ring of benzene sulfonate) less than 3, but highly asymmetrical for SAC greater than 3. The amount of 1-butanol required to produce miscibility decreases with the increasing SAC in the aqueous-rich region (>40% aqueous solution) but increases in the toluene-rich region (>W% toluene) when SAc = 4 and 6. One system, containing sodium 2,5-diisopropylbenzenesulfonate, was studied at eight aqueous solution concentrations at 25 "C from 0.25 to 3.0 mol of sulfonate/kg of water. Phase relationships for limiting three-component systems were also determined. Under the boundary curves of the system containing 0.50,1.0, and 1.5 m aqueous solutions, regions with three liquid phases in equilibrium were observed at 25 "C. The regions of the three coexisting liquid phases varied with changing temperature and composition. Opalescence can be seen at several compositions, especially near the S-shape sector of the phase boundary curves, an observation which, along with low interfacial tension between phases, suggests proximity of critical end points.

Introduction The ability of polar organic compounds to promote

miscibility between hydrocarbons and aqueous solutions is well-known. Surfactants and alcohols can effect clear

0022-3654/81/2085-1445~01.2~l~

microemulsions.' The long hydrocarbon chains typical of surfactants are not required, however. Compounds such

(1) Hoar, T. P.; Schulman, J. H. Nature (London) 1943, 152, 102.

0 1981 American Chemical Society