J . Phys. Chem. 1990, 94, 7588-1596
7588
The present findings provide a quantitative support for earlier
or close to biological membranes.
contention^^*^' that the water-probe interaction is a determinant factor in the probe photoionization process. Similarly, it may be suggested that the interfacial dielectric constant may affect electron or proton transfer occurring across
Acknowledgment. We are grateful to Dr. S. Hautecloque for many fruitful discussions and to Drs. M. Hodges and H. Huppe for having carefully read the manuscript.
Phase Behavlor and Metastabllity In a Nonionic Surfactant-Water-Electrolyte System J. P.Wilcoxon Organization 1152, Sandia National Laboratories, Albuquerque, New Mexico 87108 (Received: December 28, 1989; In Final Form: May I, 1990)
We use static and dynamic light scattering to investigate the concentration fluctuations occurring in the single to binary phase transition of the two analogous systems CI2ES/HZOand CI2E6/H20/NaCI(10 wt %). The effect of surfactant concentration and temperature on the osmotic compressibility,static correlation length, and diffusion coefficient is investigated. Both systems fall into the same universality class as simple binary fluids. For concentrations differing from the critical concentration, the suppression of critical fluctuations results in finite correlation lengths and compressibilities. Measurements at the critical concentration reveal a true divergence of these quantities with correlation lengths exceeding the instrumental resolution (i.e. >5000 A). Measurements of the diffusion coefficient vs momentum transfer follow the predictions of simple mode-mode coupling theory for concentrations less than or equal to the critical concentration but Kawasaki mode-mode fluctuations are suppressed significantly above the critical concentration. The formation of large nonmicellar entities in the two-phase region leads to an asymmetry in the width of the critical region about the critical point.
Introduction In surfactant systems consisting of oil, water, and electrolyte, the phase behavior has traditionally been described by considering the water and electrolyte as a single component of a pseudotwo-component system. Recently, Kahlweit and co-worker~l-~ have convincingly demonstrated that it is more appropriate to group salt and surfactant as a single pseudocomponent to understand the macroscopic phase behavior. This grouping successfully explains why a wide range of phase behavior is not dependent on the underlying microstructure of the solution (e&, whether the surfactant is of sufficient length to form micelles or mesophases). In the case of the simplest two-component (water/surfactant) systems they were able to demonstrate that addition of a hydroscopic salt (10 wt % NaCI) to n-dodecylhexaoxyethylene glycol monoether (C12E6)altered the macroscopic phase boundaries to locations nearly identical with that of its next lowest homologue, C12E5. In this paper we investigate the nature of the concentration fluctuations which cause these simplest surfactant systems to undergo a single to two phase separation as the temperature is increased. In particular, we show that the critical behavior, critical compositions, and static and dynamic scaling of the two systems are identical, even though the C,,E6/NaCI system is strictly speaking a three-component system. In both systems we demonstrate that the osmotic compressibility, static correlation length, and diffusion coefficient obey power laws which depend only on the reduced temperature c = ( T - Tw)/Tw,where Tw is the cloud point temperature. The latter corresponds to the critical temperature for data obtained on the critical isochore. The amplitudes and exponents in the power laws describing the rate of divergence (1) Kahlweit, M.; Strey, R.; Haase, D. J . Phys. Chem. 1985,89, 163-171.
(2) Kahlweit, M.; Lessner, E.; Strey, R. J . Phys. Chem. 1984, 88, 1937- 1944. (3) Kahlweit, M.;Strey, R.; Schomacker, R. and Haase, D. Lnngmuir 1989, 5, 305-315. (4) Degiorgio, V. Physics of Amphiphiles: Micelles, Vesicles and Micro-
emulsions. In Proceedings of the International School of Physics; North Holland: Amsterdam, 1985; pp 303-333.
of the compressibility, correlation length, and diffusion coefficient, however, depend quite sensitively on the surfactant concentration relative to the critical concentration, C,. Critical slowing down is observed over a surprisingly wide range of concentrations. Different kinds of information are provided by the angular dependence of the static scattering intensity and diffusion constant, respectively. In both systems Ornstein-Zernike scattering is observed for all concentrations and temperatures investigated. The main effect of concentration is to reduce the measured values of the correlation length and osmotic compressibility from that found a t the critical concentration. The degree of reduction depends sensitively on the concentration difference, C - C,. By contrast, dynamic light scattering show$ that, for concentrations C >> C,, the diffusion constant is independent of length scale while for C I C,dynamic scaling following the theory of Kawasaki is observed. Critical slowing down occurs at all investigated concentrations 0.5 < C < 3.0 wt % despite the apparent suppression of critical concentration fluctuations as indicated from the lack of angular dependence of the diffusion constant. Except for the critical concentration, the diffusion coefficient saturates to a constant value very close to the cloud point.
Experimental Section Sample Preparation and Characterization. Surfactant systems in the nonionic C,Ej family appear to be sensitive to dissolved oxygen. The chemical explanation for this sensitivity is not obvious since the structure of these amphiphiles contains neither double bonds nor chemically sensitive side groups. Nevertheless, as shown in Figure 1, failure to remove dissolved oxygen and seal the samples in an inert atmosphere results in major changes in the low-angle scattering behavior with time. These changes appear to be consistent with the formation of enormous physical aggregates. The diffusion coefficient behavior in these samples is also anomalous, having a strong angular dependence for length scales greater than Q1 1000 8,. The unexpected angular dependence of the light scattering observed in the unsealed samples is evidence for large correlations or structure absent in the sealed sample. Analysis of the curve for the sealed sample reveals that the static correlation length for this sample is only -200 8, at this temperature. Its
-
0022-3654/90/2094-7588%02.50/0 0 1990 American Chemical Society
Metastability in a Surfactant-Water-Electrolyte System
1
1
o - ~
T=22.0 *UNSEALEDCELL
1
o - ~
I
10-2
-1 Q(
A
1
Figure 1. Intensity (I)in arbitrary units vs momentum transfer Q (A-') for a 1.0 wt % sample of Cl2E5in H20.Samples were prepared at identical times in a unsealed, screw-capped cell and flame-sealed (under Ar) cell, respectively, and studied at the temperature indicated. Failure to remove oxygen results in development of intense low-angle scattering on length scales corresponding to solution structures of 1000-5000 A. Such an angular variation is unexpected since the critical point is many degrees away and thus the spatial correlation length due to critical concentration fluctuations is small (100-200 A).
angular dependence is typical of critical concentration fluctuations while the angular dependence of the unsealed sample is inconsistent with such fluctuations, but could be due to nonspherical aggregate structures. In addition to the effects shown in Figure 1 we observe a systematic lowering of the phase separation temperature with time (not shown). In view of the demonstrated sensitivity of nonionic surfactants to dissolved oxygen, special sample preparation must be employed to obtain reproducible scattering results. Our samples are prepared are as follows. HPLC grade, dust-free water is bubbled with Ar gas for -15 min, the surfactant is introduced into the water at the desired concentration, and the sample is resealed with a torch while under an Ar atmosphere. It is not advisable to attempt to refilter the entire sample for two reasons. Surfactant of unknown nature is present on cellulose-based Millipore filters which may affect the critical behavior, and filtering reintroduces large amounts of dissolved oxygen. The latter observation was established by direct measurements on the amount of dissolved oxygen before and after filtration. Measurements of dissolved oxygen after Ar bubbling for 15 min indicate that this technique removes oxygen to the level of sensitivity (0.1 mg/mL) of the meter after 15 min, and levels do not begin to increase appreciably for 1-2 min, more than enough time to flame seal the ampules under Ar. The most important indication of the efficacy of these sample preparation procedures is no detectable change at the sensitivity level of 0.01 "C in the cloud point temperatures over periods extending to several weeks, as compared to changes of as much as 1 OC over 2 weeks for unsealed samples. We note that establishing a vacuum above the sample and then resealing under vacuum is much less effective at removing oxygen from the system unless very long ( - 12-24 h) equilibration periods are allowed. The time scale for the first observable changes in phase transition temperature in unsealed samples is approximately 3 days. The parent, water-free surfactant systems (Nikko, Japan), on the other hand, are much more stable. To avoid possible problems, however, we also seal the stock (water free) surfactant under Ar and find that for samples prepared from a given lot number the absolute critical point temperature is stable to 0.01 OC over periods up to 1 year. Since many reported critical temperatures appear to be substantially below our measurements for the same systems based upon surfactants also obtained from Nikko, it is possible that those phase measurements may have been made on systems suffering from the "aging effects" shown in Figure 1. We note that the resulting anomalous low-angle scattering has major effects on quantities such as the static correlation length and isothermal
--
The Journal of Physical Chemistry, Vol. 94, No. 19, 1990 7589
compressibility and could give bizarre exponents describing the divergence of these quantities. As we have reported previ~usly,~ chemical analysis of Nikko surfactants reveals impurities (longer and shorter C,Ej molecules) at the 0.3%level. We now discuss the determination of the phase boundaries in these systems. The accurate determination of the coexistence temperature of a given binary fluid system is dependent on the kinetics of phase separation. As the two-phase region is approached, the rate of temperature change must sometimes be reduced to extremely slow rates (e.g., 0.01 "C/day near the critical isochore) to avoid overshooting the two-phase boundary. Thus, direct measurements of the coexistence curve are extremely difficult. This is due to the greatly magnified effect of critical slowing down in micellar systems whose fundamental units are aggregates instead of individual molecules. The cloud point curves are much easier to obtain, fortunately. Also, because of the weak temperature dependence of the cloud point near the critical concentration for micellar systems, these curves are likely to closely follow the coexistence curves. For each surfactant concentration we need to know the temperature at which phase separation first occurs. We require that the criteria for such a determination be reproducible and relatively insensitive to the rate of temperature change. To automate and simplify observations of this phase behavior we have constructed an insulated glass bath in which the sample in a sealed glass ampule is immersed in water. The bath temperature is controlled by a Yellow Springs Instrument Model 72 controller (settability = 0.01 OC,stability = f0.001 OC over days). The temperature of the bath can be automatically read from a Fluke Pt RTD previously calibrated at the water ice-point to an accuracy of f0.005 OC. Also immersed in the bath is a Hewlett-Packard quartz thermometer with a sensitivity of 0.001 OC (1-s measurement) to 0.0001 OC (10-s measurement). We use this thermometer to determine the bath temperature fluctuations and average temperature. The sample is supported on a rod which projects above the bath to a motorized translation stage controlled by a Newport Research Corp. (Model 855C) controller. This allows the sample to be positioned at various heights in the vat relative to a fixed height H e N e laser beam which is focused onto the sample with a 50-cm lens. Outside the bath is located a quadrant cell detector with a 105:1dynamic range and the ability to measure laser beam shifts to -2 pm in either vertical or horizontal directions. We use both transmission measurements and beam shifts to confirm the initiation of phase separation. It turns out that small inhomogeneities in concentration which occur just inside the two-phase region result in a deflection of the laser beam which can easily be sensed by the quad cell. All aspects of the phase boundary determination can be controlled automatically by our PDP 11/73 computer. Also supported on the rod is an immersible magnetic stirrer located just below the cell. In mast experiments a small Teflon stir bar is included in the sealed ampule a t the time of sample preparation. This allows remixing of the sample under computer control since the magnetic stirrer is connected to the computer via a relay. To determine the cloud point, the transmission of an immersed sample is measured while the temperature of the bath is increased at a selected rate. Between temperature changes, the sample is moved to a reference position allowing the laser beam to pass unimpeded through the bath to the quad cell detector. Optionally, the sample may be stirred and then allowed to equilibrate between temperature changes. The sample is then moved to allow the laser beam to traverse the sample at one or more heights to measure the transmittance and beam location. Ampule diameters were 10-16 mm while typical solution heights were 15-20 mm. The transmission remains nearly constant until the cloud point (point of maximum turbidity) is reached, a t which juncture a major change in transmission (and beam deflection) is observed as shown in Figure 2. The temperature interval corresponding to the change from maximum to minimum transmission depends slightly on the rate of temperature change. The width of this interval may be shrunk to less than 0.005 O C , however, by successively reducing this rate. Either the midpoint or end point of this transition is
7590
The Journal of Physical Chemistry, Vol. 94, No. 19, 19'90
Wilcoxon
1 -
1.o
z
33.0
TWO PHASES
0.8
2
8E
5I-
0.6
z a K
z
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v)
32.5
2
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I-
0
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1 I
C12E6 SYSTEM
0
0.0 31.0 31.5
31 .O 32.0
32.5
33.0
TEMPERATURE( OC) Figure 2. Cell transmittance vs temperature ("C) for the C12E6/H20/ NaCl (10 wt 7%) system. These measurements define the location of the cloud point for this system. The point of maximum turbidity is taken as the cloud point and corresponds to the temperature at which spinodal ring formation can first be observed (see text). Note the variation of this point with composition as indicated;the lowest temperature value corresponds to a 50:50 volume ratio of the coexisting phases. E
z 0 v) 2
E v)
z a ee
I-
31.0 31.5
32.0
32.5
33.0
TEMPERATURE( 'C) Figure 3. Cell transmittance vs temperature ("C) for the CI2E5/H20 system on the critical isochore (c = 1.5 wt 5%) determined with (squares,
heating sample, circles cooling cycle) and without stirring (triangles, cooling sample) between absorbance measurements. Optical path length is 16 mm. Hysteresis is observed in the transition if the effect of gravity is not removed by mixing. Heating/cooling rate is 0.03 OC/min, and stability is 10.005 OC. Note the much greater increase in final transmission with no stirring during the cooling cycle.
a very good estimate of the cloud point temperature. The uncertainty was -2k0.02 OC for the four concentrations of C12E6 in H20containing 10 wt % NaCl shown in Figure 2. This uncertainty is the difference between the temperatures of maximum turbidity and that corresponding to the midpoint of the total transmission change. The perspicacious reader will note that the transmission is the smallest for the sample prepared at the critical concentration (c = 1.5 wt %). This is expected if the total light scattered out of the main beam is greatest at this concentration. This observation is consistent with direct measurements of the angular distribution of scattered light for each of these samples which show the light scattering to be greatest for 1.5 wt % sample. These transmission measurements are also useful to ascertain at what distance from the cloud point the specter of multiple scattering may rear its ugly head. Are the changes in transmission observed in Figure 2 reversible, and if so, under what conditions? We found that they are reversible provided that not enough time elapses to allow macroscopic phase separation (formation of a meniscus) to occur. As a practical matter, this means overshooting the coexistence temperature by more than 0.1 OC must be avoided. Deeper quenches
0
1
2
3
4
5
6
C(wT %) Figure 4. Cloud point temperature ("C) vs concentration (wt 7%) for the two systems CI2E5/H20(triangles) and C12E,/H20/NaCI(10 wt W ) (squares). Data was obtained from measurements as shown in Figure 3. An arrow is drawn to show the approach from single to two phases taken along the critical concentration at constant weight fraction surfactant.
result in the hysteresis shown in Figure 3, which can be eliminated upon remixing the sample between transmission measurements as shown in the same figure. When remixing of the surfactant solution between temperature changes is eliminated during the cooling of a sample, a sharp change in light transmission is still observed but occurs at a higher temperature than during the heating of the same sample. In these measurements the laser beam was positioned in the lower, surfactant-depleted phase. The transmission in the unmixed lower phase rises to nearly loo%, presumably due to the reduced amount of surfactant in this phase. The higher transition temperature observed in the unmixed solution during cooling is also reasonable since the cloud point temperature increases at either higher or lower concentration values on each side of the critical point. Spontaneous sample homogenization will not occur even upon allowing the sample to sit at room temperature for several days. Figure 4 shows the cloud point curves for the two systems presented in this paper, CI2E5/H20and CI2E6/H20/NaCI (10 wt %). Note how closely the two curves agree, though the corresponding salt-free C12E6/H20system has a critical temperature nearly 21 OC higher. The effect of addition of a hydrotrophic salt such as NaCl to a nonionic surfactant C,E, is to alter the location of all phase boundaries to positions corresponding to their next lower homologue, C,Ej_,, as first pointed out by Kahlweit et al.' In our scattering measurements we approach the phase boundaries at a constant surfactant concentration along a vertical path, as shown in this figure. We have also studied these surfactant systems in D20, with no qualitative changes in the scattering behavior in either singleor two-phase region. However, the cloud point temperatures are lower by -2.0 OC just as in our earlier workS on C,2E6/D20. Also, the critical concentration appears smaller at C, = 1.0 wt 5%. The CI2E6/H20/NaCl(10 wt %) system's critical behavior has not been studied in detail before, but Hamano and co-workers6 studied the CI2E5/H20system in great detail. They reported a coexistence curve which follows very closely that shown in our Figure 4 with a critical composition of 1.25 wt % and critical temperature of 3 1.89 OC. We find a value of C, = 1.5 wt %, and T, = 32.13 f 0.02 OC. Their source of CI2E5was also Nikko (Japan). In the case of the C12E6/H20/NaC1(10 wt %) system, which has not been studied in detail previously, we find C, = 1.5 wt %, and T, = 31.91 0.02 OC. Changes due to isotopic substitution are related to differences in the strength of interaction
*
(5) Wilcoxon, J. P.; Schaefer, D. W.; Kaler, E. W. J . Chem. Phys. 1989. 90,1909. ( 6 ) Hamano, K.;Kuwahara, N.: Koyama, T. Phys. Rev. A 1985,32,3168.
The Journal of Physical Chemistry, Vol. 94, No. 19, 1990 7591
Metastability in a Surfactant-Water-Electrolyte System
-
TABLE I: Summarv of Single-Phase Critical Behavior system c, wt % 0.5 1 .o 1.5 2.0 3.0 0.5 1 .o 1.5 2.0 2.5 5 .O 1 .o
Y
€09
0.73 0.97 1.13 0.80 0.65 0.77 1 .o 1.22 0.94 0.80 0.38 1.1
A
60 29 20 21 40 49 32 17 22 33 200 14
Ad, cm2/s 3.4 x 10-7 4.9 x 10-7 7.9 x 10-7 8.9 x 10-7 1.5 X IO" 2.9 x 10-7 9.3 x 10-7 1 . 1 x IO" 1.0 x 104 7.1 x 10-7 5.0 x 10-7
Y
0.38 0.53 0.55 0.50 0.32 0.43 0.52 0.62 0.52 0.42 0.0
"d
0.65
"Critical concentration determined by 5050 phase volume criteria. *Correlation length at a reduced temperature of point.
between the surfactant head groups and the solvent. Stronger interactions lead to higher cloud point temperatures and critical compositions. The drastic changes in transmission observed at the cloud point are obviously related to changes in the solution microstructure. Removing the detector allows the changes in low-angle scattering responsible for the transmission variations shown in Figures 2 and 3 to be observed on a screen placed on the wall. Suppose we observe the changes that occur just above (-0.01 "C), the point of maximum turbidity. We find that the initially collimated laser beam is now strongly scattered to form a ring at a scattering angle of -2-3", which grows in intensity while collapsing into a nearly stationary diffuse speckle pattern. The latter is the signal of the formation of a second phase. Its nearly stationary nature implies extremely slow relaxation of concentration fluctuations in the quenched samples (i.e., loss of ergodicity). Quantitative details of this behavior are being obtained as a function of quench depth by using a video camera and frame grabber and will be presented in a subsequent paper. The time scale for the ring growth and collapse is -25 min for shallow quenches ( IO-$) are shown, and the data can be seen to be indistinguishable. As usual, the momentum transfer is defined as Q = 4?m sin (0/2)/A, where n is the solvent refractive index, h the incident wavelength, and 0 the scattering angle. Q has the units of inverse distance and Q I is a measure of the length scale of the concentration fluctuations observed in a scattering measurement. We plot the data on a double log plot because of the large Q and intensity range for these experiments. If critical fluctuations dominate the scattering, then we expect the scattering intensity to depend only on the static correlation length, [ and the intensity I will follow: I-' = I(O)-I( 1
+ Q2t2)
(1)
Thus, a simple fit of values of the inverse scattering intensity I-, vs Q2will give both I(O), which is proportional to the osmotic compressibility, and the correlation length of the concentration fluctuations. Such fits are shown as solid lines in Figure 6 and demonstrate that details of the solution microstructure (for example whether micelles are present or not) need not be invoked to describe the scattering. Finally, by using (1) to analyze our data we obtain both I ( 0 ) and $. as a function of both the temperature distance from the cloud point, and surfactant concentration. Dynamic Light Scuttering. Dynamic light scattering measures the rate of decay of the concentration fluctuations observed by static measurements. According to the well-known fluctuationdissipation theorem, spontaneous fluctuations from equilibrium will dissipate with a time constant which depends on the restoring forces (e.g., the osmotic compressibility) in the system. Near a critical point, for example, the compressibility becomes zero and so a spontaneous fluctuation will take a long time to relax to
Metastability in a Surfactant-Water-Electrolyte System equilibrium. This is the well-known phenomena of critical slowing down. In our experiments the signal from an amplifier discriminator which is connected to our PMT is sent to a Langley-Ford 256 channel real time correlator which computes the autocorrelation function of the scattered light. The correlator is controlled by the PDP 1 1-73 computer over a serial line. As in static scattering experiments, a menu containing the desired cell temperatures, wavelengths, minimum and maximum scattering angles, and equilibration time between temperature changes is written to control the experiment. Data is transferred under computer control and fit by either a single exponential or a cumulants algorithm. For critical systems (including this one), this distinction is irrelevant since the decay of the autocorrelation function is completely exponential. The observation of exponential relaxation in these systems in the single-phase region also implies negligible micellar polydispersity. For homodyne detection, the decay time T for the relaxation is related to the diffusion coefficient D by
The Journal of Physical Chemistry, Vol. 94, No. 19, 1990 7593
A 10'
10
I:
z z
IO
W
c
z
I
IO lo3
10- 1
10'5 10'4 10-3
E
In the long-wavelength limit D is a constant, but in general D depends on the value of Q. Previous experience with the dynamics of nonionic surfactant systemsSsuggests we analyze our relaxation data in terms of the simple Kawasaki mode-mode coupling theory which predicts D(Q) = 0 ( 0 ) ( 3 / 4 x 2 ) [ 1 x2 + (x3 - x-I) tan-' x ] ( 3 ) where x = Qfd, Ed being the dynamic correlation length. At a fixed distance t from the cloud point, this analysis yields both D(0) and &+
B IO
+
Results and Discussion An issue which has attracted much experimental and theoretical attention in recent years4v5is the question of the universality of critical behavior in surfactant phase separation. In other words, to what extent are we justified in thinking about the statics and dynamics of amphiphile systems as if they were simply mixtures of two components of very different sizes, the solvent (small), and the micelle (large). Suppose that neither the average micelle size nor polydispersity varied appreciably as the cloud point is approached at constant surfactant concentration. In that case we might find that fluctuations in micelle number density (the order parameter) would dominate the scattering as the cloud point is approached. Then we might expect that, except for an increase in length scale, the system should exhibit the same type of behavior found in two-component fluids undergoing phase separation. For such systems, it has been established that the correlation length and osmotic compressibility diverge as power laws that depend only on the distance from the critical point Z(0) €7, = foe-" (4) The exponents y and v describe the rate of divergence, while the critical amplitude tomeasures the length scale of the units that are interacting. Many binary fluids and micellar systems fall into the same universality class as the king model and have y 1.24, Y 0.63. If local correlations are unimportant, then mean-field behavior with y 1 .O,v = 0.50 is observed. For small molecules to 2-3 A, but since micelles are roughly an order of magnitude larger we might expect Q 20-30 A. Quite generally, it is known that y = 2v - 7,but 7 is so small in known models that, within experimental uncertainty, y = 2v. Consider the following two issues of interest in the present work. Do critical concentration fluctuations dominate the scattering (i.e., does (1) hold), and how does changing the concentration from the critical value affect behavior such as (4)? We first consider the static data. The variation of intensity with Q as shown in Figure 6 was analyzed by using (1) and the values of Z(0) and [ were obtained for a range of sample concentrations 0.5 < C < 3.0 wt % for the CI2E5/H20system and 0.5 < C < 5.0 wt % for the Cl,E6/H,0/NaCl (IO wt %) system. For all concentrations in both systems the angular variation of the scattered intensity is consistent with the Ornstein-Zernike form (1). The fact that the correlation lengths measured in solution are many times the
-
-
-
-
-
h
Q
3*p
lo3
10 10-5 10-4 10-3 1
o-*
10"
E Figure 7. (A) log-log plot of the extrapolated (Q = 0) scattering intensity (I,arbitrary units) vs reduced temperature c = ((T-T,.+)/T,.+), where Tcpis the cloud point temperature. Several concentrations of surfactant in the C12E6/H20/NaCI(10 wt 7%) system are shown. Note the reduced slope (smaller exponent y) for concentrations other than the critical value ( c = 1.5 wt 8).The solid lines are the best power law fits to the data. The exponents y for these curves are listed in Table I. There is rounding or saturation of the compressibility off the critical isochore and these values are not included in the power-law fit. (B) log-log plot of the correlation length (t, A) vs reduced temperature c = ((7' Tw)/Tw), where Ts is the cloud point temperature. Several concentrations of surfactant in the C,2E6/H20/NaCI(10 wt 7%) system are shown. As in Figure 7A a reduced slope (smaller exponent y) for concentrations other than the critical value (c = 1.5 wt %) is observed. The solid lines are the best power law fits to the data. Note that 5 becomes saturated at a fixed value for small values of c if the concentration differs from the critical value and such values are not included in the fits. On the critical isochore the correlation length diverges beyond the resolution of the instrument (Le., >5000 A; see Figure 8). The solid lines are the best logarithmic fits to the data. The exponents v for these curves are listed in Table I.
micellar size establishes the dominant role of critical fluctuations for both these systems. Using small-angle neutron scattering we have established that the micellar radius of gyration is roughly constant at -20-30 A for both these systems in the single-phase region for the concentration and temperature range that is the subject of this paper. For both surfactant systems we find that the osmotic compressibility and correlation length are largest a t the critical surfactant concentration. Figure 7A,B demonstrates that, to a good approximation, both quantities follow power laws of the form (4) for a considerable range of reduced temperature E . The effect of changing the surfactant concentration on the exponents y and v , and the amplitude to,is shown in Table I. As can be discerned
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The Journal of Physical Chemistry, Vol. 94, No. 19, 1990
from either the figure or the table, both y and u are largest at the critical concentration, falling off quite significantly for greater or lesser concentrations. In fact, the data off the critical isochore do not really diverge but attain a saturated value as a function oft. This maximum correlation length t,, depends on distance from the critical concentration. Due to this saturation effect, we have not included points with reduced temperatures smaller than the saturation value in the power law fits shown in these figures. Within experimental uncertainty, y = 2u for all concentrations. The maximum values of the correlation length t,,, at equivalent distances t = 3 X lo4 from the cloud points are shown in Table I, to illustrate the saturation effect. Previous work’ on the Cl2E5/H20system indicated that both I(0) and 6 saturated at t 6 X 10-4 on the critical isochore, which was reported as 1.2 wt %, and gave mean-field exponents. We found similar results for the 1.0 wt % sample as shown in Table 1, so the differences in the two studies may be due to the different critical concentration studied in the previous work. They reported a value toof 32 A which is very close to the value 29 A shown at 1.0 wt % in Table I. Since plots of I(0) and ( vs t were not presented, it is not known whether the values of ( were smaller than those found by ourselves at equivalent distances t . In our studies of CI2E5/H20at the critical concentration, the correlation length actually becomes larger than the instrumental resolution (SO00 A) and we see no evidence for saturation. A detailed study of the dependence of the exponents y and v on concentration has only been obtained for one other nonionic surfactant/H20 system, CI2Es. There it was reported4 that mean-field behavior was found for both y and v over the concentration range 0.5 < C < 5.0 wt %, which disagrees with these results. However, a later study9 on the C12E8system done only at the critical concentration showed Ising values for y and u, and no satisfactory explanation of these differences has been proposed. The present study indicates that one must be very careful in determining both the critical concentration and the critical temperature if errors in y and v are to be minimized. It may be that some of the nonuniversal values of the critical exponents previously reported for nonionic systems in water result from measurements on systems off the critical isochore.I0 Examination of the data in Table I indicates that the critical amplitude tois smallest at the critical concentration. This is true for both surfactant systems and implies that the interaction between surfactant and water is weakest on the critical isochore. This is consistent with the critical concentration having the lowest phase separation temperature. Also shown in Table I is the effect of isotopic substitution of D20 for H 2 0 in the ClzESsystem. Within the experimental error there is no change of critical exponents. Just as we found previously’ for the C12E6/H20(D20) system, the critical amplitude is smaller corresponding to the reduced hydrogen-bonding interaction between surfactant head groups and D20. Summarizing our results based upon static light scattering, we find that the fits to the Omstein-Zernike expression (1) are very good for a wide range of concentrations. The major effect of variation from the critical concentration is a saturation of the correlation length prior to phase separation. Only samples of the critical concentration exhibit correlation lengths which are beyond the resolution (-5000 A) of our apparatus. An example of such behavior is shown in Figure 8 where the complete absence of any characteristic length scale is demonstrated by the power-law behavior of the data over the range of length scale 20 nm < < 500 nm for t It is interesting to note that the best power-law fit to this data over the full range of Q gives an exponent of 1.8 which differs from the value of 2.0 predicted for pure Ornstein-Zernike behavior. Previous deviation from Ornstein-
t v) 2
w
-
-
(7) Hamano, K.; Sato, T.; Koyama, T.; Kuwahara, N . Phys. Rev. Lerr. 1985, 55, 1472. (8) Wilcoxon, J. P.; Kaler, E. W. J . Chem. Phys. 1987, 86, 4684. (9) Dietler, G.; Cannell, D. S.Phys. Reu. Lerr. 1988, 60, 1852. (10) Corti, M.; Degiorgio, V. Phys. Reo. Lerr. 1985, 55, 2005. (1 I ) Wilcoxon, J. P.; Schaefer, D. W.; Kaler, E. W. Phys. Reu. Lett. 1988, 60,333.
lo3 1
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lo-*
)
Figure 8. log-log plot of the scattering intensity ( I , arbitrary units) vs momentum transfer Q for the C12E6/H20/NaCI(IO wt %) at c = 1.5 wt %, 6 = The correlation length is now larger than the instrumental resolution (5000 A) and pure power-law scaling of I with Q is observed. The best fit exponent is 1.8, not 2.0 as predicted by the Ornstein-Zernike function. This deviation is not likely due to multiple scattering since both visible (633 nm, squares) and UV (334 nm, circles) regions superimpose. It is very similar to the deviation noted previously for the pure C12E,/H20system” just slightly into the two-phase region.
Zernike scattering behavior has been observed by us using SANS measurements on the C12E6/D20system? but only on intermediate length scales between 50 and 500 A. A crossover to OrnsteinZernike behavior was observed in light-scattering data from 500 to 5000 A. It is our belief that the data of Figure 8 also will cross over to ideal Ornstein-Zernike behavior at length scales beyond the resolution of our instrument. In fact, close examination of Figure 8 shows that the slope appears to be slightly steeper at low values of Q. When this is combined with SANS data obtained on this system in DzO, we find a single power law with an exponent of 1.8 on length scales from 50 to at least 5000 A. Such scaling behavior is interesting since Ornstein-Zernike correlations are observed to move to larger length scales as the critical point is approached! It appears that very close to phase separation another characteristic length scale may be required to describe micellar systems. Small molecule systems show only a single correlation length. Data further away from the critical point (e.g., Figure 6 ) have the expected Omstein-Zernike form. Dynamics. Finally, we examine measurements of the variation of the diffusion coefficient with Q. Samples with concentrations well above the critical isochore have D(Q) constant even for very small reduced temperatures (i.e., Kawasaki dynamics is not observed), while those with concentrations at or below the critical follow Kawasaki dynamics very closely for a wide range of temperatures. This is shown in Figure 9A,B where the C12ES/H20 system at 1.5 wt % (critical isochore) and 3.0 wt 3’6 are compared. The lack of Q dependence off the critical isochore (Figure 7A) contrasts with the increasingly strong Q dependence near T, on the isochore (Figure 7B). Very close to the cloud point we find D Q (Kawasaki dynamics) as shown in Figure 10. By fitting of the measurements like that shown in Figure 9A to the Kawasaki expression (3) we obtain the exponent vd describing the rate of critical slowing down for several concentrations. Even in the absence of a Q dependence, (e.g., Figure 7B), D(0) exhibits an apparent divergence near T, which may be written
-
-
D(0) = Ad€-’* (5) We find that the dynamic exponent vd describing the divergence of D(0) shown in Table I is less sensitive to concentration compared to the static measurements for both surfactant systems. The amplitude Ad is also shown in Table I and appears to be largest near the critical concentration. This is consistent with the smallest static correlation length occurring at this location since it is expected that D(0) is proportional to l/&. These observations are in accord with our previous work on the salt-free Cj2E6 system.’
Metastability in a Surfactant-Water-Electrolyte System
The Journal of Physical Chemistry, Vol. 94, No. 19, 1990 7595
A
1.5 wt% Y
.0001
,
-
10 - E 0 Q=.00143 0 Q=.000841 A Q=.000461
0 UI -
? N
10Y
d
1
o - ~
1
o'2
.001
.01
.1
E Figure 10. Semilog plot of the ratio of static to dynamic correlation lengths (5) vs reduced temperature c = ((T-Tq)/Tcp),where T is the cloud point temperature. Surfactant concentration is as indicad. The system is C12E6/Hz0/NaCI(10 wt %), whose critical concentration is 1.5 wt %. The ratio is 1.2 f 0.1 for small t. The dynamic correlation length is obtained from the angular variation of the diffusion constant. Solid lines are guides for the eye.
B
n
2.5wt%
10"
E Figure 9. (A) log-log plot of the measured diffusion constant (D,cm2/s) vs reduced temperature c = (T- Tcp)/Tq,where Tcpis the cloud point temperature. Data is obtained by dynamic light scattering for the CIzE1/H20system on the critical isochore (C = 1.5 wt %) with the momentum transfer (Q, A-l) as a parameter. The angular (Q) dependence can be accurately described by the Kawasaki equation. (B) log-log plot of the measured diffusion constant (D,cm2/s) vs reduced temperature c = (T-Tq)/T9, where Tq is the cloud point temperature. Data is obtained by dynamic light scattering for the C12E1/H20system offthe critical isochore (C = 3.0 wt 36) with the momentum transfer (Q, A-') as a parameter. D is observed to be independent of Q in contrast to Figure 7A. Oddly, the Q dependence of D due to mode-mode coupling is nor suppressed as effectively for C < C,, but resembles that of Figure 9A. The best fit power law to the data is indicated. D saturates to a constant value at all Q for c
