J. Phys. Chem. 1984, 88, 309-311
Figure 9. Shematic representations for possible structures of a bound monomer (a), a bound racemic aggregate (b), and a bound enantiomeric aggregate (c). The ligands in Cop2+are represented by two ovals around a small open circle. The shaded and unshaded parts denote the portion of a ligand directed downward and upward from the paper, respectively.
below the possible structures of the bound states on the basis of the calculations. For a bound monomer state, the experimental values of pI and pIr (+1.10 and -0.40 in Table I, respectively) were reproduced from the curves in Figure 8, if a and @(E)were chosen as 0' and 0.4, respectively. Under this conformation, it was possible for each of the naphthalene rings in Cop2+ to penetrate between the two neighboring styrenesulfonate residues. Accordingly the bound chelate would be stabilized due to the van der Waals interactions between the naphthalene of COP,+ and the benzene rings of PSS-. The hydrophobicity of PSS- as seen here was already noted by other investigator^.'^ For a racemic aggregate state, the experimental pI and. pII (+0.43 and +O. 10,respectively) corresponded to the theoretical values at a = 35O and @ ( E ) = 0.4. If (+)-Cop2+ and (-)-Cop,+ (13)Tondre, C.;Kale, K. M.; Zana, R. Eur. Polymn. J. 1978,14, 139.
309
were placed alternatively along the Y axis under this conformation as shown in Figure 9b, the two facing ligands belonging to the neighboring chelates stacked preferably with each other. As a result, the racemic aggregate established a rigid rodlike structure. This explains why the racemic mixture attained a stereoregular racemic aggregate as the most thermodynamically stable state. For an enantiomeric aggregate state, the experimental pI and prI(+0.21 and +0.25, respectively) were reproduced by choosing a = 45' and @(E)= 0.4. When (+)-Cop,+ ions were placed along the Y axis with a = 45' in a sequence, no notable stacking appeared between the neighboring ligands. If, however, one chelate was placed at a = 45' and the other at a = -45' instead, the two ligands in the neighboring chelates stacked to a certain degree (Figure 9c).I4 The relative orientations of the stacking ligands were not so favored that the enantiomeric aggregate was much looser than the racemic aggregate. The stopped-flow experiments revealed the presence of an intermediate state during the course of formation of a racemic aggregate. The intermediate aggregate was formed about 4 ms after mixing when the initial rapid increase of absorbance was completed. It is suspected that, in such an intermediate state, the (+) and (-) isomers take a random distribution on the PSSchain. Accordingly, the sequence could not attain a close stacking as a whole. If this was the case, the succeeding slow step in the time range of 1-lo2 s might represent the process that the bound chelates rearranged on each polymer chain until the alternative sequence of (-)-Cop2+ and (+)-Cop2+ was realized. At that stage, the loosely bound aggregate changed into a rigid stereoregular racemic aggregate. This mechanism was consistent with the kinetic results that the half-life of the second step was independent of the reactant concentration, or the process occurred on each polymer chain.
Acknowledgment. Thanks are due to Prof. E. Tsuchida (Waseda University) for his helpful discussions. Registry No. Cop2+,61664-19-5; (+)-Cop2+,87900-42-3; K+PSS-, 901 1-99-8. (14)This conformation also gives almost the same pr and pIIvalues according to eq 8.1 and 8.11.
Cloud Point Transition In Nonionic Micellar Solutions Mario Corti,* Claudio Minero, CISE, Segrate (Milano), Italy
and Vittorio Degiorgio Dipartimento di Elettronica, Sezione di Fisica Applicata, Universith di Pavia, Pavia, Italy (Received: June 17, 1983: In Final Form: October 4, 1983)
Aqueous micellar solutions of the polyoxyethylenenonionic amphiphiles CsEs, C&4, C12ES,and CL4E7have been investigated as a function of temperature and concentration by static and dynamic light scattering, turbidimetry, and viscosimetry. Light-scattering measurements at the critical concentration for phase separation show that the osmotic compressibility and the correlation range of concentration fluctuations diverge as the critical point is approached in all the investigated systems. The results concerning short-chain amphiphiles (C6E3, CsE,) strongly suggest that the observed behavior is due to critical concentration fluctuations and that the phase transition is due to interactions among small globular micelles. The results concerning long-chain amphiphiles (CIZE8,CI4E7)indicate that, besides critical effects, there may be some micellar growth with temperature. It is suggested that this second effect, if existing, is connected to the presence of anisotropic-phaseboundaries not too far from the critical concentration line.
Introduction Dilute aqueous solutions of nonionic amphiphiles usually exhibit a phase separation when the temperature is raised above a value *Address correspondence to this author at the following address: CISE, P.O. Box 12081, 20134 Milano, Italy.
0022-3654/84/2088-0309$01.50/0
which depends on the amphiphile concentration c. In the c-T Plane, the singlephase micellar region is separated from the region in which two immiscible isotropic solutions are present by a lower consolution curve (cloud curve in the micellar literature). The minimum of the curve is a critical point; the temperature and concentration at which the minimum occurs are called the critical 0 1984 American Chemical Society
310 The Journal of Physical Chemistry, Vol. 88, No. 2, 1984 temperature T, and the critical concentration c,, respectively. Earlier light-scattering measurements performed with dilute aqueous solutions of alkylpolyoxyethylenes CH,(CH,),-,(OCH,-CH,),OH (called hereafter C,EJ have shown a considerable increase of the scattered-light intensity Z, as a function of the temperature T.1-4 Similar results have been obtained with other nonionic amphiphiles, such as the n-octylsulfinylalkanols5 and the dimethylalkylphosphine oxidesa6 The common interpretation of those results was that the micellar aggregation number increases with the temperature. However, since it is well-known that the approach to the critical point in binary mixtures is accompanied by long-range concentration fluctuations, and hence by a large light-scattering cross section, the observed phenomena are, at least partially, explainable by the existence of consolute phase b o ~ n d a r i e s . ~Our ~ ~ laser-lightscattering experiment^^.^ have clearly shown that the main parameter determining solution properties is not the temperature itself but the temperature distance from the critical point. The results obtained with CI2E6solutions8 indicate that the apparent micellar molecular weight, Mapp, measured as a function of T along the critical concentration line, diverges as the critical point is approached following a power-law behavior of the type Mapp (T, - T)Y, with a critical exponent y 1. A power-law divergence is also found for the correlation range of concentration fluctuations ( measured through the angular dependence of the scattered intensity or by the quasielastic light-scattering technique. Subsequent measurements on CsE4 and C& solutions have shown a similar behavior, but with distinct critical exponent^.^ Apart from the obtained values of critical exponents, several features of nonionic micellar solutions, observed in a temperature region which extends typically 20 OC away from T,, are identical with those found in a large variety of critical systems studied in the last 20 years. The list of investigated critical binary systems includes liquid mixtures made of two low molecular weight components,1° like aniline and cyclohexane or isobutyric acid and water, and macromolecular solutions, like polymer" and protein12 solutions. In particular, polymer solutions present some similarity with micellar solutions because the coexistence curve may be strongly asymmetric and may have the minimum at a very low polymer concentration. By analogy with critical polymer solutions, the strong temperature dependence of the scattered intensity in nonionic solutions could indeed be totally attributed to critical concentration fluctuations, that is, to a strongly nonideal behavior. Micelles are, of course, different from polymers because their aggregation number may change with temperature and concentration. Several groups have recently performed experiments aimed at a measurement of the temperature dependence of micelle size, using either neutron ~ c a t t e r i n g ' ~ -or' ~ nuclear magnetic
-
(1) R. R. Balmbra, J. S. Clunie, J. M. Corkill, and J. F. Goodman, Trans. Faraday Soc., 58, 1661 (1962). (2) R. R. Balmbra, J. S. Clunie, J. M. Corkill, and J. F. Goodman, Trans. Faraday SOC.,60,979 (1964). (3) R. H. Ottewill, C. C. Storer, and T. Walker, Trans. Faraday Soc., 63, 2796 - -(1967). , -- , (4) D. Attwood, J . Phys. Chem., 72, 339 (1968). (5) J. M. Corkill, J. F. Goodman, and T. Walker, Trans. Faraday SOC., 63, 759 (1967). (6) K. W. Herrmann, J. G. Brushmiller, and W. L. Courchene, J . Phys. Chem., 70, 2909 (1966). (7) M. Corti, and V. Degiorgio, Opt. Commun., 14, 358 (1975). (8) M. Corti and V. Degiorgio, Phys. Reu. Lett., 45, 1045 (1980); J. Phys. Chem., 85, 1442 (1981). (9) M. Corti, V. Degiorgio, and M. Zulauf, Phys. Rev. Lett., 48, 1617 (1982). (10) D. Beysens, A. Bourgou, and P. Calmettes, Phys. Rev. A , 25, 3589 (1982). (1 1) N. Kuwahara, D. V. Fenby, M. Tamsky, and B. Chu, J. Chem. Phys., 55, 1140 (1971); S.P. Lee, W. Tscharnuter, B. Chu, and N. Kuwahara, ibid., 57, 4240 (1972). (12) C. Ishimoto and T. Tanaka, Phys. Reu. Lett., 39, 474 (1977). (13) M. Zulauf and J. P. Rosenbusch, J . Phys. Chem., 87, 856 (1983). (14) R. Triolo, L. J. Magid, J. S. Johnson,-and H. R. Child, J . Phys. Chem., 86, 3689 (1982). (15) J. B. Hayter and M. Zulauf, Colloid Polym. Sci., 260, 1023 (1982) (16) J.-C. Ravey, J . Colloid Interface Sci., 94, 289 (1983).
Corti et al. r e ~ o n a n c e . ' ~ , 'Some ~ author^'^-^^,^^ have concluded that the micelle size at the critical concentration does not change with temperature, whereas others16J8infer from their data a substantial micellar growth with T. As we discuss in this paper, the power-law divergence of the osmotic compressibility is certainly a universal phenomenon to be found with all critical micellar solutions, whereas it is possible that micellar growth may exist or not depending on the nature of the amphiphile. It could be guessed, for instance, that the presence in the phase diagram of anisotropic lamellar or hexagonal phase boundaries not too far from the critical concentration line may favor micellar growth. Such an effect could not give, however, a divergence of the micelle size as the critical point is approached. For sake of completeness it is useful to remember that critical phenomena have been found to play an important role in microemulsions a l s ~ . 'Similarly ~ ~ ~ to the case of micellar solutions, a considerable debate exists about the nature of the transition and about the possibility that the droplet picture may still be adopted as the critical point is approached. In this paper we present new results, obtained by static and dynamic light scattering and by other techniques, on aqueous solutions of the amphiphiles C6E3, C8E4,C&, and C14E7. The system C8E4-H20 is interesting because it has a very high critical micelle concentration co and a high concentration at the critical point c,.~ These features enable one to investigate the possible role of monomers in the phase transition and permit also a study of the solution in the two-phase region above T,. Furthermore, static and dynamic neutron-scattering data are also available on this system.13 The amphiphile ClzE8was chosen because of its high critical temperature ( T, N 76 "C) which makes it easier to study the whole evolution of the system, as T i s raised, from the regime of noninteracting micelles to the critical region. ClzE8 solutions have been studied in great detail by performing lightscattering measurements in a wide range of concentrations. Finally, C6E3and CI4E7have been selected after the discovery that the critical exponents y and Y depend on the choice of the amphiphile, in order to investigate which is the range of possible values for the critical exponents. Light Scattering from Critical Binary MixturesZ5 The total intensity of light scattered from a binary mixture is Z, Zo, where Z, is the contribution of concentration fluctuations and Io the contribution of density fluctuations. In our case, Zo practically coincides with the contribution of the solvent. Near a critical consolution point the intensity Z,depends on the scattering angle 0 according to the Ornstein-Zernike relation:
+
Z, = Z@/( 1 + P ( 2 )
(1) where k = ( 4 4 X ) sin 0/2 is the modulus of the scattering vector, X being the wavelength of incident light and n the index of refraction of the medium, and ( is the correlation length of concentration fluctuations. The extrapolated scattered intensity at zero scattering angle Zs0is related to the derivative of the osmotic pressure with respect to the concentration, ( d n / d ~ ) ~as @follows: , Zs0 = Ac( dn /dc) T(d I I / dc) T,;l (2)
where A is an instrumental constant, dn/dc is the refractive index (17) E. J. Staples and G. J. T. Tiddy, J . Chem. SOC.,Faraday Trans. 1, 74, 2530 (1978). (18) P.-G. Nilsson, H. Wennerstrom, B. Lindman, J . Phys. Chem., 87, 1377 ._ 11983). (19) A. M. Cazabat, D. Langevin, J. Meunier, and A. Pouchelon, J . Phys., Lett. (Orsay, Fr.), 43, L-89 (1982). (20) R. Dorshow, R. de Buzzaccarini, C. A. Bunton, and D. F. Nicoli, Phys. Reu. Lett., 47, 1336 (1981); J. Tabony, M. Drifford, A. De Geyer, Chkm. Phys. Lett., 96, 119 (1983). (21) J. S . Huang and M. W. Kim, Phys. Reu. Lett., 47, 1462 (1981). (22) G. Fourche, A.-M. Bellow, and S.Brunetti, J. Colloid Interface Sci., 88, 302 (1982). (23) M. Kotlarchyk, S.-H. Chen, and J. S . Huang, Reu. A , 28,508 - Phys. . (1983). (24) M. Kahlweit, J . Colloid Interface Sci., 90, 197 (1982). (25) H. L. Swinney in "Photon Correlation and Light Beating Spectroscopy", H. Z. Cummins and E. R. Pike, Ed., Plenum Press, New York, 1974, p 331. \ - - - - I -
The Journal of Physical Chemistry, Vol. 88, No. 2, 1984 311
Cloud Point Transition in Nonionic Micellar Solutions increment, R is the universal gas constant, and T i s the absolute temperature. The quantity (dII/dc), is, in general, a function of T and c which takes very simple expressions in two important limit cases. When the system is far from the critical point, and the solution is sufficiently dilute RT(~II/~C)= ~ ~M/(1 -I
+ 2BMc)
(3)
where B is the second virial coefficient and M is the molecular weight of the solute particles. When the system is close to the critical point both (dII/d~),,~-land t are found to diverge as T T,, and the following relation holds:
-+
(dII/dC)*,p-l
0:
(4)
t2-7
where q is a number much smaller than 1 . When the system approaches the critical point in the single-phase region at the critical concentration c,, the two quantities diverge according to a simple power-law behavior:
4 = to€-"
(drI/dC)T,p-p-l = Bt-Y
+ 3/sk2t2)
The diffusion coefficient D is connected to Einstein formula: D = hkBT/(6T?lst)
I
0
I 10
I 5
I
I
15
20
I
25
Concentration % b y weight
Figure 1. Phase diagram of C6E3in H20.The region above the consolution curve is a two-phase region.
(5)
where e = (T, - i")/ T, and the two critical exponents y and v are related through eq 4, that is, y = 4 2 - q ) . Turning now to dynamic light scattering, we recall that the time-dependent part of the intensity-correlation function measured at a scattering angle 0, corresponding to a scattering vector k, is simply the square of the correlation function of the concentration-fluctuations component with wave vector k. Therefore, the mass-diffusion coefficient D, is derived from the decay time 7, of the intensity-correlation function as D, = (2k27,)-'. When T is sufficiently close to T,, D, is found to depend on k. The hydrodynamic mass-diffusion coefficient D is derived as the limit of D, as k goes to zero. For small values of the product kt, the first correction is, according to the mode-mode coupling theory D, = D(l
";
(6)
4 by
a Stokes(7)
where h N 1 and qs is the macroscopic shear viscosity of the solution. When the system is far from the critical point and the solution is sufficiently dilute D = Do(1 kDC) (8)
+
where Do is the translational diffusion coefficient of the solute particles and kD reflects the effect of two-particle interactions. Experimental Section High-purity CI2E8 and CI4E7 were obtained from Nikko Chemicals, Tokyo; C6E3 and CsE4 were prepared by Bachem, Basel. All components were used without further purification. The sample preparation procedure is the same as described in ref 8. The light-scattering apparatus is equipped with an argon-ion laser operating on the 514.5-nm green line, a scattering cell temperature-controlled within 0.001 "C over 24 h, and a digital correlator. A very detailed description of the apparatus can be found in ref 26. The average scattered intensity I, and the intensity correlation function of the scattered light are measured at two distinct scattering angles 0 = 22O and 90°. We have also monitored the power of the incident laser beam before and after passing through the scattering cell in order to obtain the turbidity of the amphiphile solution. Measurements of viscosity and of refractive index increments are performed with standard apparatus (Ubbelohde viscometer and differential refractometer). The consolution curves were obtained by putting several sealed cells, each filled at a different concentration, into a temperature-controlled water bath whose temperature was increased a t a constant rate (typically 0.1 OC/min). The phase transition (26) V. Degiorgio, M. Corti, and C. Minero, Nuouo Cimento D , in press.
57 0
2
4
Concentration
6 % by
weight
Figure 2. Phase diagram of CI4E7in HzO.
temperature was determined by monitoring with a laser beam the sudden variation of the cell turbidity on approaching the consolution curve. This technique is fast and allows one to get very reproducible results (the transition temperature is determined within 0.01 "C). At the investigated rates of temperature variation we did not see any metastability effect. Since it is known from several experiments on critical binary mixtures that the value of T, is not very sensitive to pressure variations, the use of sealed tubes to measure the consolution curve does not require any correction of the effective temperature for the pressure variation, within the quoted experimental uncertainties. The phase diagram of the C6E3-H20 system is shown in Figure 1. The consolution curve shows a minimum (lower consolution point) at T, = 44.66 OC and around c, = 13% by weight. We have approximately determined the critical micelle concentration co at a few temperatures by filling the light-scattering cell with a solution at a known concentration and observing the behavior of the scattered intensity as the temperature is gradually lowered. We have obtained the following values for co: 1% at 63 OC, 1.75% a t 36 "C, 2.5%at 30 OC, and 3% at 25 OC. The phase diagram of the system C8E4-H20 can be found in ref 9. We recall that the consolution curve presents a rather flat minimum at T, = 40.3 f 0.1 OC and c, = 7%. In the same paperg we have also reported that the critical point of C12E8-H20 solution is at Tc = 76.1 f 0.1 O C and c, = 1.5%. The new measurements, performed with Cl2E8from a new batch, give the minimum of the consolution curve at T, = 75.6 f 0.1 OC and around c, = 3.2%. It is possible that the observed shift of the critical point with respect to the previous results may depend on the fact that the type and amount of impurities change from batch to batch. Figure 2 presents the consolution curve of CI4E7-H20solutions, showing the critical point at T, = 57.5 OC and c, = 1.5%. The measured temperature dependence of the refractive index increment dn/dc of the amphiphile solutions is well described by the linear law dn/dc = A I - A2(T - 298) (9)
312 The Journal of Physical Chemistry, Vol. 88, No. 2, 1984
Corti et al.
TABLE 1: Refractive Index Increments of Amphiphile
Solutions Expressed as dn/dc = A , - A , ( T - 25)' A,,
amphiphile C6E3
C8E4
C,,E8 CME,
104~,,
\
temp
cm3/g
cm3/(g"C)
range, "C
0.1 20 0.124 0.134 0.137
3.1 2.9 2.4
20-45
3.5
15-40 15-75 10-5 5
'The last column reports the investigated temperature range.
TT -;
(Oc)
Figure 4. Viscosity, relative to water, of ClzEsin HzO at various concentrations as a function of temperature. Tc-T
Figure 3. Viscosity, relative to water, of C6E3in HzOat the concentration of 13% by weight, and of CI4& in HzO at the concentration of 1.5% by weight as a function of temperature.
where T i s the temperature in Kelvin and dn/dc is expressed in cm3/g. The results are summarized in Table I. The kinematic viscosity, relative to water, qr, of C6E3solutions at the critical concentration c, = 13% is shown in Figure 3 as a function of the temperature distance from the critical point T, - T. The quantity qr increases smoothly from a value 1.9 far from T, to a value 2.1 at 3 "C from T,. In the region T, - T < 3 O C the increase of qr is more marked. The relative viscosity of C14E7 solutions is 1.06 at low T but starts increasing considerably already at 30 O C far from T, and becomes slightly larger than 4 at 1 O C from T,. The relative viscosity of C&8 solutions at four distinct C& concentrations is reported in Figure 4 as a function of the temperature. The temperature scale is logarithmically expanded around T,* to show in detail the behavior of qr in the critical region. The temperature T,* is defined below in connection with the description of Figure 8. It is convenient to express the experimental data for macromolecular solutions in terms of the intrinsic viscosity, defined as27 [ q ] = lim P O
lo4
(OC)
71- 1
c
The limit to zero concentration is taken to eliminate the effect of interparticle interactions. The parameter [ q ] depends on the shape and the hydration of the particle; it is in the range 2.5-4 cm3/g for globular particles and may become very large for elongated particle^.^' If we calculate [ q ] from our data, without taking the limit for c 0, we obtain [ q ] increasing from 7 to 9 cm3/g for 13% C6E3solutions as T increases from 20 to 40 OC, from 2 to 30 cm3/g for 2.5% C& solutions, and from 6 to 40 cm3/g for 5% C&8 solutions. Furthermore, [ q ] goes from 2.5
-
(27) C. Tanford, "Physical Chemistry of Macromolecules", Wiley, New York, 1961, p 391.
I
u)
9
!A
I?
e
x- lo2
10
I
a
I
Figure 5. Osmotic isothermal compressibility of various nonionic amphiphile solutions as a function of the reduced temperature e = ( T , T ) / T , along the critical isoconcentration line.
to 220 cm3/g for 1.5% CI4E7solutions in the temperature range 10-55 OC. The osmotic compressibility of the solutions is proportional, at fixed concentration, to I,o/T(dn/dc)2, as shown by eq 2. By measuring I, at two distinct scattering angles and using eq 1, we
The Journal of Physical Chemistry, Vol, 88, No. 2, 1984 313
Cloud Point Transition in Nonionic Micellar Solutions
TABLE 11: Critical Temperature Tc and Critical Concentration cc, Molecular Weight M and Hydrodynamic Radius R H of the Micelle Far from Tc, Values of the Parameters of the Power-LawFit to the Osmotic Compressibility and Correlation Range Data, and Apparent Molecular Weight Ma,, at Tc - T = 0.31 "C for Nonionic Micellar Solutions material
1 0 ~6M,pp(Tc-T=0.3 1°C)
C6E3
44.7 13
i
0.1
1.25 0.2 0.63 0.34 2
i
0.03
t
0.03 0.03
?
C,E, 40.3 f 0.1 7 2.5 2.5 1.15 f 0.03 0.8 0.57 f 0.03 0.54 i 0.05
C I A 50.4 * 0.1 1.25 5.0
I
30
C,&, 58.6 i 0.1 1.5
C I A 75.5 i 0.1 3.2 6.5 3.4 0.92 5 0.03 5.8 0.44 i 0.04 1.75 0.5 10
0.97 i 0.05 13 0.53 i 0.05 2.0 i 0.5
0.87-1.0
*
Temperature ("C)
z
Y
hn
100
1 **e* ***e
10
1
e
100
10
T,-T
('C)
Figure 7. Osmotic compressibility and the correlation range of CI2E8-H20at the critical concentration plotted as a function of the reduced temperature E.
1 t
Figure 6. Osmotic compressibility and the correlation range of C6E,-H20 at the critical concentration plotted as a function of the reduced temperature z. derive the extrapolated scattered intensity ZB0. The behavior of the osmotic compressibility as a function of the normalized temperature distance from the critical point, E = ( T , - T)/T,, is reported in Figure 5 for C6E3,C8E4, CI2E6,and C&8 solutions at the critical concentration c,. The (ac/aI'I), plots have been arbitrarily shifted along the vertical axis for clarity of presentation. However, we have also obtained an absolute calibration for the osmotic compressibility by measuring the turbidity near the critical p ~ i n t . The ~ , ~log-log ~ plots in Figure 5 are very well fitted by straight lines in a wide range of values of e. Therefore, the results can be described by the power law (811/d&L1 = B c ~ The . values obtained for B, y, and T, are reported in Table 11. We have derived from the dynamic light-scattering and viscosity data, by using eq 6 and 7, the correlation range E' = E/h. The results relative to CsE3 and C12E8solutions at the critical concentration are shown in Figures 6 and 7. In a wide range of e values E' follows a simple power-law behavior, E' = EO't-", with critical exponent u = 0.63 & 0.03 for C6E3solutions and v = 0.45 f 0.03 for C&8 solutions. The constant h has been obtained by comparing static and dynamic data.8s9 The result is h = 1.1 & 0.04; that is, E' is 10%smaller than the correlation range 5 that one measures from the angular dependence of the scattered intensity. In order to study the behavior of C8E4solutions at low concentration and in the two-phase region we have performed static and dynamic light-scattering measurements along the isotherm
T = 44.84 "C in the concentration range 0.5-4 mg/cm3, and along the isoconcentration line c = 4 mg/cm3 in the temperature range 15-46.2 "C. Since the two paths cross on the coexistence curve (at c = 4 m g / ~ r n ~the ) , ~data taken above 44.84 "C refer to the two-phase region. Because of the geometry of the experimental arrangement, only the low-concentration phase was accessible to light-scattering measurements (the high-concentration phase constitutes a thin layer floating upon the low-concentration phase). The interpretation of light-scattering data obtained along the two paths is hampered by the presence of a small peak in the scattered-light intensity near the cmc which could be due to the effect of a small amount of water-insoluble impurities. We have reported similar effects in Triton X-100 solutions7 (see also ref 28 for a quantitative study of this effect in SDS solutions). We summarize the main results obtained with the low-concentration C8E4solutions: (i) the C8E4micelle has a molecular weight M = 25000 (which corresponds to an aggregation number around 80) and a hydrodynamic radius 2.5 nm; (ii) the lowconcentration phase above T = 44.84 "C is still micellar and shows an apparent molecular weight which decreases by increasing the temperature. The few available points are not accurate enough to try a power-law fit. However, we can say that the data are consistent with a behavior, (ac/aII), = B'eY, along the coexistence curve where y has the same value measured along the critical concentration line and B' = B/3.8. The temperature dependence of the osmotic compressibility and of the correlation range for C&8 solutions, as shown in Figure 7, is qualitatively similar to that observed with ClzE6solutions.8 There is a critical region, 62 < T < T, "C, in which a power-law (28) M. Corti and V. Degiorgio, Chem. Phys. Leu., 49, 141 (1977).
314
The Journal of Physical Chemistry, Vol. 88, No. 2, 1984
Corti et al. exponent y obtainable in the asymptotic region characterized by a power-law behavior is in the range 0.87-1.00, and v is around 0.5. We could not assign accurately the values of y and v because of lack of reproducibility of the data from one run to the other. It seems that the equilibration times of the C14E7 solutions following a temperature change are exceedingly long, much longer than one would expect from a critical binary mixture. This may probably explain the limited reproducibility of the results. The values of M and RH for C8E4and C & micelles and of Mapp(at T, - T = 0.31 "C) for C6E3, C8E4, C12E6, and Cl2Es micelles, obtained with the calibration procedure described in ref 26, are reported in Table 11, together with the value of M for c&6 micelles available from ref 3.
5%
Discussion Coexistence Curves. As explained in the previous section the
1
10
T;-T
(OC)
Figure 8. Osmotic compressibility of C12Esin H 2 0 as a function of the temperature at various concentrations.
behavior is followed, and there is a low-temperature region, T < 40 "C in which both ( d I I / d ~ ) ~ , and ~ - l f' are nearly constant. In the intermediate region, 40 < T < 62 OC, the solution properties are strongly dependent on T . The system C12E8-H20was studied by static and dynamic light scattering at several concentrations in order to verify whether the shape and the asymptotic behavior (as T T,) of the curves shown in Figure 7 is concentration dependent. The osmotic compressibility data are reported in Figure 8. The temperature T,* is concerftration dependent and represents the intersection of the isoconcentration line with the spincdal curve. Of course, whefi c c,, T,* T,. The values obtained for T,* by forcing the data to follow a power-law behavior are T,* = 78.47 OC at 0.5%, 77.13 "C at 1%, 75.87 OC at 2%, 75.64 OC at 2.5%, and 75.70 OC at 5%. The exponent y that we obtain is 0.92 0.03 for all concentratiohs. In the temperature region characterized by a very sharp increase of ( ~ C / ~ I Ithat ) ~ ,is,~ 40 , < T < 62 OC, the 5% concentration sample shows an anomalous behavior. Indeed the intensity correlation measurements yield a nonexponential correlation function. By performing a cumulant fit we obtained the average diffusion coefficient D and the relative variance u. W e recall that u represents an index of polydispersity of the micellar solution. Although the system is so far from the critical temperature, that D is not expected to be k dependent, we find that D is slightly larger at 0 = 22' than at 90'. Note that this dependence cannot be due to critical concentration fluctuations because it goes in the opposite direction (in a critical system b should increase with 0). The polydispersity index u is quite large (v N 0.2) and also k dependent. Several runs have been performed with the system H20-Cl4E7 at the critical concentration. The qualitative behavior of this system is similar to that found with H2O-c&& that is, for small both the osmotic compressibility and the correlation range 5' seem to diverge following a power-law behavior, whereas, far from T,, both ( d ~ l d I I ) ~and $ f' grow very rapidly. We have observed, in this region of rapid growth, the same anomalous behavior of the dynamic data described above for H2&C12E8solution at the 5% concentration. The anomalous effects are however much larger with the C&7 solution as compared to the high-concentration C&8 solution. Furthermore, we have found that the critical
-
- -
*
critical temperature and concentration may change from batch to batch because of the effect of impurities. It is also known that impurities may be generated by oxidation processes which can take place in aqueous solutions of polyoxyethylene amphiphiles. Such impurities have the effect of lowering T,. Furthermore, it may be difficult to precisely evaluate c, because of the flatness of the coexistence curve near T,. For all these reasons one should not expect a complete agreement among the results obtained in different experiments unless a careful control of all the operating conditions is possible. It is nevertheless interesting to compare our data with those reported in two systematic studies29 of the phase behavior of C,E, in water. C h a k h o v ~ k o yfinds ~ ~ T, = 39.6 OC and c, = 10% for C&-H20, and T, = 35.5 OC and c, = 5% for C8E4-H20. Mitchell et find T, = 43 OC for C&-H20, T, = 48 OC for C12E6-H2O, and T, = 77 OC for C12E8-HzO. Lang and Morgan30 have recently discussed a very accurate purification procedure and check of impurities level for nonionic amphiphile solutions. They quote a reproducibility of 0.05 "C of the transition temperature in their Study of the phase diagram of the system CloE4-H20,and they present a power-law fit of the coexistence curve. We believe it is premature to do the same with our data because we still have to understand more thoroughly all the effects which may modify the coexistence curve. Viscosity and Light-Scattering Measurements. The reduced viscosity [v] is found to increase as the temperature of the micelle solution approaches T,. The increase is very weak for C6E3 solutions, more pronounced for C8E4and C&S, and very pronounced for CI4E7solutions. One possible explanation for the increase of [ 7 ] is that the micelles become more and more elongated as T is increased. However, it should be recalled that [v] should show a weak anomaly (logarithmic divergence) in the critical region of any binary liquid mixture.31 Therefore, the interpretation of viscosity data presents problems similar to those encountered with lightscattering data. Let us first consider C6E3solutions. The measured Mappat 0.31 OC from T, is very large, as shown in the last row of Table 11. If MBpp is a true molecular weight, the micelle must be very elongated and its [v] must have a value not smaller than 50 if we compare our situation with the data relative to protein and polymer solutions (see ref 27, Chapter 6). We conclude, therefore, that our data are not compatible with the hypothesis of considerable micellar growth. Similar considerations can be applied to the CsE4data.I3 On the contrary, the large increase of [v]in C & and C l 4 Q solutions is probably not explainable with the only effect of critical concentration fluctuations. The light-scattering data shown in Figure 7 suggest that, below 40 OC, the C& solution behaves as a solution of weakly interacting micelles of nearly constant size. The evaluation of the micellar molecular weight and hydrodynamic radius requires concentration-dependent results as discussed in a previous paper.32 (29) N., Chakhovskoy, Bull. SOC.Chim. Belg., 65, 474 (1956); D. J. Mitchell, G . J. T. Tiddy, L. Waring, T. Bostock, and M. P. McDonald, J . Chem. SOC.,Faraday Trans. I , 79, 975 (1983). (30) J. C. Lang and R. D. Morgan, J . Chem. Phys., 73, 5849 (1980). (31) Y.Izumi and Y . Miyake, Phys. Reu. A , 16, 2120 (1977).
Cloud Point Transition in Nonionic Micellar Solutions With regard to the values obtained for B and to(see Table 11), one would expect that in a critical system B is proportional to 52. Our data are not in contrast with this prediction, taking into account the experimental uncertainties in B and The absolute values of tofor micellar solutions are larger than those found in usual binary mixtures where Eo is between 0.1 and 0.3 nm, as shown by Table I1 in ref 10. The values of B are also larger than those found in usual binary mixtures which are typically cm-2
The Journal of Physical Chemistry, Vol. 88, No. 2, 1984 315
Apparent Micellar Growth and Critical Concentration Fluctuations. The experimental data reported in this paper and in our previous w0rks~9~ show several features which are typical of the behavior of critical binary mixtures: (a) the osmotic compressibility (or Mapp) diverges as T T, following a power-law behavior for all the investigated solutions; (b) the correlation range (or apparent radius of giration, or apparent hydrodynamic radius) also diverges as T T, with a power-law behavior; (c) the ratio of the critical exponents r / v is close to 2; (d) the osmotic compressibility is a decreasing function of T above T, (see the results obtained with C8E4in the two-phase region); (e) the quantity F' obtained from dynamic light-scattering and viscosity measurements coincides, apart from a factor h 1.1, with the correlation range obtained from static light scattering (see the results on C&6 and CsE4 shown in ref 8 and 9, respectively). We suggest therefore that the properties of nonionic amphiphile solutions at concentrations near c, and in the power-law region can be explained by critical concentration fluctuations without invoking a large growth of the micellar aggregation number with T. The behavior at temperatures T much smaller than T, was studied in detail on C& solutions which present a high value of T,. The temperature dependence of the C&8 data is qualitatively similar to that observed with C&6 solutions.8 There is a low-temperature region, in which the micelle size is constant, and a critical region, in which the solution behaves as a critical binary mixture and the micelle size is probably constant (but it may not coincide with the low-temperature value). In the intermediate region, micelle interactions are certainly present, but it is not possible to state with certainty whether the change of Mapp(and of 5') is totally due to nonideality effects. Some information about the micelle size dependence on T has been obtained by using techniques which are less sensitive than light scattering to the collective effects, such as neutron scattering and nuclear magnetic resonance. The neutron-scattering meas u r e m e n t ~ ' ~performed -'~ on C8E4,C8E5,and c& solutions show that the single-micelle scattering function P(k) is independent of T for large k. It is difficult, however, to exclude elongated micelles on the basis of these data alone because at high k values only the smallest dimension influences P(k) (the cylindrical micelle should retain the same radius of the spherical mi~elle).'~ An independent estimate of the micelle geometry was obtained for c8E4and C8ES solutions by dynamic neutron spin-echo measurement^,'^ thus confirming the hypothesis that C8E4and C& micelles maintain constant size and globular shape as the temperature is raised. Triolo et al.14 have analyzed their static neutron-scattering data on CI2E6solutions by using two models: the first model assumes a temperature-dependent growth of spherical micelles into larger and larger cylindrical micelles and neglects critical fluctuations; the second considers critical fluctuations and postulates spherical micelles of constant size. The second model gives a more plausible explanation of the re~u1ts.l~ However, Ravey16 interprets his static neutron-scattering data on C&6 solutions by assuming a growth of micelles into flexible rods and by taking as an adjustable parameter the persistence length of the flexible rod. Staples and Tiddy" have reported N M R spin-lattice relaxation data on C&6 solutions which give indirect evidence against a large micellar growth with temperature. Nilsson et al.18 have performed N M R self-diffusion measurements on C12E5 and C&8 solutions. They conclude that there is good evidence for micellar growth
with temperature for C12E5, whereas the C& micelles are much less affected by temperature. It is interesting to note that the systems presenting the most convincing evidence against micellar growth with T are those which do not show anisotropic phases in the phase diagram (see the C8E4-H20 phase diagram in ref 29). The existence of a hexagonal phase at high amphiphile concentration may imply the formation of rodlike micelles having a length gradually increasing with concentration in the isotropic region. Such an increase would be temperature-dependent33 because the hexagonal-phase boundary is temperature dependent (see the phase diagrams in ref 29). Therefore, it could be guessed that the relative importance of critical fluctuations and micellar growth at a given point in the phase diagram depends on the relative distance of that point from the consolution curve and from the anisotropic-phase boundary. This point of view would imply that along the critical concentration line one can find micellar growth in some temperature region (provided an anisotropic-phase boundary is present at not too high concentration), but it does not suggest that one should expect a micellar size monotonically increasing with temperature and becoming infinite at the critical point. The usual argument which justifies micellar growth with temperature at low amphiphile concentrations is based on the assumption that the interaction between two ethylene oxide segments within the micelle is repulsive at low temperatures when the two segments are hydrated and becomes attractive with increasing temperature because of dehydration. This effect should lead to a decrease of the effective area per polar group, hence to a tendency for micellar growth into larger and larger rod. As we will discuss later on in this article, it is, however, difficult to explain the existing data (in particular, why different homologues behave so differently at the same temperature) by assuming that the relevant interactions are only those among the ethylene oxide chains and water. Two-Phase Region. Many authors believe that in the region above the consolution curve (cloud curve) there are no micelles because surfactant molecules are segregated from the aqueous phase. According to this view, which does not seem to have been tested by any experiment, one phase contains singly dispersed surfactant monomers and the other is a surfactant phase containing dissolved water. C6E3and C8E4solutions are well suited for a study of the two-phase region because T, is low and both c, and the cmc are relatively large. By simple inspection of the phase diagrams it is clear that the isotropic micellar solution separates above the consolution curve into two isotropic micellar solutions. Of course, for temperatures much larger than T,, the low-concentration phase becomes more and more dilute and, presumably, merges into the cmc curve, whereas the high-concentration phase may become anisotropic, depending on the nature of the nonionic amphiphile. The light-scattering measurements on the C8E4-H20 system described in the previous section confirm, at least for the low-concentration branch of the consolution curve, that the solution is still micellar. The observation that Mappdecreases by increasing T above T, represents a further confirmation of the correctness of the description in terms of critical binary mixtures. It would be difficult to explain, within the frame of a theory based only on changes of micelle structure, why the micelle size grows to an infinite aggregation number at T, and decreases progressively, as T become larger than T,, in the two-phase region. Analogy with Polymer Solutions. It may be interesting to see whether some understanding of the behavior of nonionic micellar solutions can be gained by making an analogy with polymer solutions. The problem is, up to now, completely open. We report in the following some qualitative considerations which could give some hint for a quantitative approach. In order to discuss the behavior of the polymer solution it is useful to introduce an interaction parameter x. If we call w l l , w22,w12,respectively, the interaction energy between two solvent
(32) M. Corti and V. Degiorgio, in "Surfactants in Solution", K. L. Mittal and B. Lindman, Ed., Plenum Press, New York, 1983, Vol. I, p 471.
(33) P. G.Neeson, B. R. Jennings, and G. J. T. Tiddy, Chem. Phys. Lett., 95,533 (1983).
S2.10
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The Journal of Physical Chemistry, Vol. 88, No. 2, 1984
molecules, between two polymer units, and between a solvent molecule and a polymer unit, we define the interaction parameter as x = -w/k,T, where w = w l l wZ2- 2w12. A good solvent has x < 0. If x > 0, the solvent is said to be a poor solvent. When x is positive and large enough (x 3 x,), the solution will split into two phases with different composition^.^^ A typical polymer solution (for instance, polystyrene in cyclohexanell) may show the following behavior: at high temperatures the solvent behaves as a good solvent and the system is in a single phase. By reduction of the temperature the solvent becomes less “good”, and below the so-called 0 temperature polymer-solvent interactions are less favored than polymerpolymer and solvent-solvent interactions. The solution shows an upper consolution point, below which it separates into two phases. Several features of the separation process are qualitatively explained by the Flory-Huggins (FH) theory which consists of a lattice model solved by a mean-field appro xi ma ti or^.^^ The FH theory predicts that the critical volume fraction 4, is given by (1 + ml/z)-l, where m is the number of monomers in the polymer molecule. When m = 1, the coexistence curve is symmetric around its maximum at a polymer fraction of 50%. When m is increased, 4, is shifted toward lower concentrations and the coexistence curve becomes less and less symmetric. The critical interaction parameter is x, = (1 m1/2)2/(2m),which is little dependent on m for large m. The two-phase region is characterized by x 3 x,. If w does not depend on T, x increases by decreasing T . This explains the existence of an upper consolution temperature (coexistence curve with downward curvature). Since the F H theory provides the full equation of state of the system, the osmotic compressibility can be analytically computed at any point in the phase plane. In particular, along the critical concentration line in the single-phase region, (dII/d~)~,;l is proportional to m1/2e-1, that is, y = 1, as expected from a mean-field theory. It should be remarked that the line of maximum compressibility does not coincide with the line of critical concentration. Indeed, it is easily shown from the F H theory that c, - c, = IT, - 71, where c, is the concentration corresponding to the maximum compressibility at temperature T . More relevant for the analogy with the nonionic amphiphile solutions are the polymer solutions presenting a lower consolution point, that is, showing phase separation when the temperature is increased (x must increase with T). This is, for instance, the behavior of polyoxyethylene polymers in water.35 The fact that such solutions show a lower consolution point may be physically explained by the observation that the solubility of polyoxyethylene chains in water is due to hydrogen-bond formation between the ether oxygens of polyoxyethylene and water.36 When T i s increased, the hydrogen bonds may break, and water becomes a less “good” solvent for the polymer. Formally, it is possible to describe lower consolution points by using decorated king models, as shown by Wheeler and co-workers3’ (see also ref 30). The consolution curves obtained with the CiE,-H20 system are qualitatively similar to those of high molecular weight polyoxyethylene polymers in water because they have an upward curvature and they are strongly asymmetric. Starting from this observation, there have been some attempts to apply the FH theory to nonionic amphiphile solutions,38 but without trying to describe critical properties. The simplest possible model could assume that the relevant interactions for the phase transition in the micellar solution are those involving the hydrophilic chains and water. This could suggest treating the micelle as a polymer having a molecular weight coincident with the weight of the hydrophilic part of the
+
+
(34) T. L. Hill, “An Introduction to Statistical Thermodynamics”, Addison-Wesley, Reading, MA, 1960, p 401. (35) S. Saeki, N. Kuwahara, M. Nakata, and M. Kaneko, Polymer, 17, 685 (1976). (36) R. Kjellander and E. Florin, J . Chem. SOC.,Faraday Trans. 1, 77, 2053 (1981). (37) G. R. Andersen and J. C . Wheeler, J . Chem. Phys., 69,3403 (1978). (38) J. Goldfarb and L. Sepulveda, J . Colloid Interface Sci., 31, 454 (1969).
Corti et al. TABLE 111: Critical Temperature (in “C) , of the System CiE;-H,Oa
i i
3
4
5
6
7
8
6
45 5-8 0 0 20 20
60 40 21 4
75 60 45 31
80 71-76 59-63 50 40 38
76 65 58 53
96 85 77 12 67
8 10 12 14 16
20
The values are taken from ref 8, 13, and 28, from Nikko’s data sheet, and from B. A. Mulley in “Nonionic Surfactants”, M. J. Schick, Ed, Marcel Dekker, New York, 1967, p 421.
micelle.32 For instance, a C12EB micelle with an aggregation number 120 would be equivalent to a polyoxyethylene polymer composed of (8)(120) = 960 ethylene oxide monomers. The larger asymmetry and the smaller critical concentration of the C12E8-H20 system with respect to C8E4-H20 would reflect, therefore, the fact that the C & micelle is larger than the C8E4 micelle. However, the trend of critical temperatures is in contrast with that expected from the F H theory because T, is higher for Ci2Es. Note that the ratio between the c, of C&4 and that of CizE8should be, according to the same theory, the reciprocal of the square root of the ratio between numbers of ethylene oxide monomers in the micelle. If we take the micelle aggregation numbers measured far from T, the latter ratio is about 3, implying a ratio 1.7 between critical concentrations, not too far from the observed value 7/3.2 = 2.2. It should be noted that T, for poly(ethy1ene oxide)-water solutions is in the range 100-200 “C, the lowest value being relative to high molecular weight polymers, whereas CiE,-water solutions present T, typically in the range 0-100 OC with values of T, increasing with the number j of ethylene oxide units, and decreasing with the length i of the hydrocarbon chain (see Table 111). As noted by Hayter and Zulauf,l5 this behavior suggests a strong contribution of the hydrophobic micellar cores to the van der Waals attraction. Taking a value of the Hamaker constant of A = 5.5 X J, Hayter and Zulaufl* find values of the attraction energy which are comparable with those obtained from fits to neutron data. It is interesting to recall that we have derived, from a light-scattering experiment on sodium dodecyl sulfate J, which is of the same order micelles,3ga value, A = 4.5 X of magnitude as that found in ref 15. An interesting point to discuss is the behavior of the line of maximum (dII/dc)T,p-l in the single-phase region. As we have seen before, the location of this maximum, according to FH theory, does not coincide with the critical concentration line, but the concentration c, at which the maximum appears should be an increasing function of the temperature. This is what is observed experimentally in C8E4solutions (see Figure 4 in ref 13). However, and C14E6 follow the data on long-chain surfactants such as an opposite trend (c, is a decreasing function of Tj as shown in ref 2. In a recent interesting paper$O Kjellander discusses a modified F H theory in which the aggregation number m is taken as temperature dependent. He argues that the reasons for micellar growth and for the cloud curve transition are most likely the same, and therefore the approach to the critical point should be accompanied by substantial micellar growth (even if the micelle size is not diverging at T,). The treatment of Kjellander40 shows that (i) the experimentally observed divergence of Mappdoes not contradict the existence of micellar growth and (ii) the behavior of c, as a function of T observed in long-chain amphiphiles can be explained by assuming a temperature-dependent micellar size. Critical Behauior. The modern theory of critical phenomena predicts that the approach to T, follows a universal pattern. The expected values of the critical exponents are y = 1.24 and v = 0.63. The results shown in Figure 5 do not follow a universal (39) M. Corti and V. Degiorgio, J. Phys. Chem., 85, 711 (1981). (40) R. Kjellander, J . Chem. SOC.,Faraday Trans. 2, 78, 2025 (1982).
Cloud Point Transition in Nonionic Micellar Solutions behavior. Indeed, the values of y go from 0.9 in CI2EBsolutions to 1.25 in C6E3solutions, and a similar trend is shown by v. It should be noted that the measured exponents depend very little on the chosen concentration (see Figure 5 and also the results of ref 8), so that the observed behavior cannot be attributed to errors in the determination of c, or to the choice of a constant concentration path instead of a maximum compressibility path. There are two possible explanations for our results: (i) the investigated temperature range is not sufficiently close to T,, and therefore the measured exponents are not true asymptotic exponents; (ii) a new theoretical model is needed to describe the critical behavior of micellar (and macromolecular?) solutions. In order to discuss explanation i, it is useful to recall that many recent theoretical papers have dealt with the evaluation of the first-order correction-to-scaling contributions. If we callf(e) the quantity which is experimentally determined (compressibility, correlation range, order parameter), the behavior vs. the reduced temperature e can be described near T, as41 where X is the critical exponent, fois the corresponding leading amplitude, and af is the amplitude of the first-order correctionto-scaling contribution with critical exponent A = 0.50.42 As we will show in a separate our data are consistent with eq 11. Presently we do not know whether this agreement is physically significant or not. In case it is, micellar solutions would indeed represent a very good testing ground for the renormalization-group calculations of correction-to-scaling contributions. It is interesting to note that nonnegligible correction-to-scaling contributions have been introduced to interpret coexistence-curve data in a critical polymer solution44and that a similar approach can be presumably applied to the results obtained with a critical protein solution,'* so that one could tentatively guess that corrections to scaling are more likely to be large in macromolecular solutions rather than in binary mixtures of small-molecule liquids. In principle, another complication could arise from the existence of additive nonsingular terms (background terms) on the righthand side of eq 11. In binary mixtures the presence of background terms in the compressibility and the correlation range has never been detected.1° With regard to explanation ii, we note that micellar solutions differ from usual binary mixtures not only because the micelle is much larger than the water molecule but also because the micelles are polydisperse and may change size and shape in going from one point to the other in the temperature-concentration plane. Futhermore, the interactions between micelle and water (41) J. C. Le Guillou and J. Zinn-Justin, Phys. Rev. E , 21, 3976 (1980). (42) J. Adler, M. Moshe, and V. Privman, Phys. Reu. B, 26, 3958 (1982). (43) V. Degiorgio, R. Piazza, M. Corti, and C. Minero, manuscript in preparation. (44) M. Nakata, T. Dobashi, N. Kuwahara, M. Keneko, and B. Chu, Phys. Reu. A , 18, 2683 (1978).
The Journal of Physical Chemistry, Vol. 88, No. 2, 1984 317 involve hydrogen-bond formation between the ether oxygens of polyoxyethylene and and the presence of directional interactions could give rise to new effect^.^ However, in order to distinguish between i and ii, it may be necessary to perform measurements very close to T, which may prove extremely difficult due to the high turbidity of the system.
Conclusions We have presented new experimental results on the phase diagram, the viscosity, the refractive index increment, the osmotic compressibility, and the diffusion coefficient of dilute aqueous solutions of some polyoxyethylene nonionic amphiphiles, namely, C6E3, C&, C I A and C14E7. We have discussed our data and compared them with previous data on the same family of amphiphiles obtained by many researchers with a large variety of techniques. The main conclusions are the following: (a) the cloud point transition is due to intermicellar interactions, and the properties of the micellar solution near the cloud point are those of a critical binary mixture; (b) consistently with the previous point, above T, the micellar solution separates into two isotropic micellar solutions; (c) the results on long-chain surfactants show some indications of changes in the micellar structure of the solution. These changes are probably an additional effect which is not responsible for, but which can modify, the cloud point transition. Whereas the data relative to short-chain amphiphiles (C6E3,C,E4, CsES) seem to be adequately described by a model of small globular micelles with a shortranged, temperature-dependent, attractive pair potential,15 the data available on long-chain amphiphiles can be probably explained by using a more complicated model. The general picture may be tentatively the following: the properties of the micellar solution at a given state (T,c) are strongly influenced by the position of the phase boundaries. The presence of an upper consolution curve will produce an enhancement of concentration fluctuzrtions as the critical point is approached (the solution becomes more and more nonideal), so that measurements will mainly reflect collective properties instead of individual-micelle properties. This effect is mainly temperature dependent, and it is the only effect present in aqueous solutions of short-chain amphiphiles. In the case of long-chain amphiphiles the presence of a hexagonal phase at high concentrations could imply micellar growth from a globular shape to an elongated rodlike shape at the hexagonal phase boundary. This effect would be concentration dependent and also temperature dependent because the hexagonal phase boundary is temperature dependent. Acknowledgment. We thank L. Reatto, M. Zulauf, B. Lindman, R. Piazza, and V. Privman for useful exchange of information. This work was supported by CNR-CISE Contract No. 82.00437.02 and by Progetto Finalizzato Chimica Fine e Secondaria del C N R Contract No. 82.00566.95. Registry No. C6E3,25961-89-1; C8E4,19327-39-0; CIIE8,3055-98-9; C14E7, 40036-79- 1 .
