13760
J. Phys. Chem. 1996, 100, 13760-13764
Slowing Down of the Mutual Diffusion Process Approaching the Liquid/Liquid Coexistence Curve of a Nonionic Surfactant/Deuterium Oxide System: Study of the System C12E5/D2O Ana Martı´n, Markus Lesemann, Lhoussaine Belkoura, and Dietrich Woermann* Institut fu¨ r Physikalische Chemie, UniVersita¨ t Ko¨ ln, Luxemburger Strasse 116, D-50939 Ko¨ ln, Germany ReceiVed: February 27, 1996; In Final Form: May 20, 1996X
In the “large aggregates” region of the phase diagram of the system C12E5/D2O the mutual diffusion coefficient of mixtures with critical and noncritical composition is determined by dynamic light scattering (compositions: 0.23 × 10-2 e y e 10.01 × 10-2; yc ) 1.08 × 10-2; y, mass fraction of C12E5). In all experiments the diffusion coefficient decreases with increasing temperatures, approaching the liquid/liquid coexistence curve at fixed values of y. This is a system independent property observed in “simple” as well as in “complex” binary mixtures with a miscibility gap. The change of size and shape of C12E5 micelles with composition and temperature in aqueous solutions reported for the “large aggregates” region appears to be the result of concentration fluctuations existing in a wide temperature and composition region below the binodal curve. Approaching Tp (Tc) the diffusive property of the mixtures is dominated by the dynamics of concentration fluctuations.
I. Introduction In an isobaric phase diagram of a “simple” binary liquid mixture with a miscibility gap (e.g. 2-butoxyethanol/water, nitrobenzene/isooctane) the mutual diffusion process slows down along three paths: (a) in a mixture of critical composition approaching the critical temperature from the homogeneous region of the phase diagram; (b) in a mixture of noncritical composition approaching the temperature of phase separation along the same path; (c) approaching the critical point along the two branches of the liquid/liquid coexistence curve. The slowing down of the diffusion process also shows up in the kinetics of the liquid/liquid phase separation studied along the binodal curve after crossing the coexistence curve by fast temperature or pressure jumps. These are system independent properties.1-7 In this communication experimental results are reported that demonstrate that the same is true for the pathways a and b approaching the liquid/liquid coexistence curve of “complex” binary liquid mixtures of critical and noncritical composition of the nonionic surfactant C12E5 (i.e. CH3‚(CH2)11‚(OCH2‚CH2)5OH) and D2O. The term “complex” draws attention to the fact that approaching the critical temperature Tc and the temperature of phase separation Tp, respectively, concentration fluctuations occur in solutions containing micelles formed by C12E5 molecules. It is known from the literature that in C12E5/water and C12E6/water systems the shape and size of the micelles change with temperature and composition.8 The same is true for other CiEj/water systems with long hydrophobic sections (i ≈ 10) and hydrophilic sections with values of j around 5. The experimental results of this study suggest that in C12E5/water mixtures approaching the limit of their thermodynamic stability local concentration fluctuations cause these structural changes. The diffusive properties of the system C12E5/D2O are studied by dynamic light scattering. D2O is chosen as the solvent to be able to supplement the dynamic light scattering experiments by small angle neutron scattering (SANS) and pulsed field gradient nuclear magnetic resonance (PFG-NMR) experiments. The lower critical point of the system C12E5/D2O is characterized by the value of the critical composition yc ) 1.08 × 10-2 (y, mass fraction of C12E5) and the critical temperature Tc ) X
Abstract published in AdVance ACS Abstracts, July 15, 1996.
S0022-3654(96)00585-0 CCC: $12.00
20.9 °C. Using the mole fraction x as the composition variable, the values of the critical composition xc of the systems C12E5/ H2O and C12E5/D2O are the same.9,10 The critical temperature of the system C12E5/D2O is lower by about ∆Tc ) 2 K than that of the system C12E5/H2O. It is a general experience that the substitution of H2O by D2O leads to a widening of the miscibility gap.11,12 This reflects the fact that the deuterium bond OD-O in deuterium oxide is energetically stronger than the corresponding hydrogen bond OH-O.13 Temperature differences ∆Tc (tTc(H2O) - Tc(D2O); Tc, lower critical temperature) in the range 2.0 K < ∆Tc < 4.0 K are typical for CiEj/water systems.14 The critical micelle concentration was determined by a fluorescence probe (pyrene) technique.15 It has a value of ymicelle(26.0 °C) ≈ 5.3 × 10-5. The value of ymicelle is of the same order of magnitude than that of the system C12E5/H2O.16 It is a characteristic feature of long carbon chain homologues of the series CiEj that their liquid/liquid coexistence curve is flat in the vicinity of the lower critical point and extends to very low concentrations. This is shown in Figure 1 for the system C12E5/D2O (see also refs 17, 18). In binary liquid mixtures with a closed loop miscibility gap formed by low molar mass components and water (e.g. 2-C4E1/H2O, iso-C4E1/H2O, 2,6-dimethylpyridine/H2O) the value of the critical composition is also located in the water rich region of the phase diagram. It is larger by a factor of about 10 compared with systems of the type CiEj/water (i ≈ 10, j ≈ 5). Consequently, the composition range in which both components are completely miscible at all temperatures in the dilute range is larger. The compositions of the C12E5/D2O mixtures used for the dynamic light scattering experiments of this study are marked on the composition axis in Figure 1. II. Experimental Section C12E5 was purchased from NIKKO Chemical Co. (Japan) in a sealed glass vial. The material was divided into small portions (about 1.5 g), filled into small vial, and stored in the dark at T ) -20 °C. D2O was obtained from Merck (D-64271 Darmstadt, Germany). Details of the sample preparation are described in ref 19. The prepared samples were stored in the dark at T ) -20 °C untill the beginning of the experiments. The data characterizing the samples are compiled in the first two columns of Table 1. © 1996 American Chemical Society
Study of the System C12E5/D2O
J. Phys. Chem., Vol. 100, No. 32, 1996 13761
Figure 1. Liquid/liquid coexistence curve of the the system C12E5/ D2O in the vicinity of its lower critical point. The compositions of the samples used for the dynamic light scattering experiments are marked on the composition axis.
TABLE 1: Characterization of the C12E5/D2O Samples Used in This Studya y × 102
Tvis p (°C)
0.230 0.499 0.850 0.989 1.080 ) yc 1.169 2.000 3.460 5.898 10.010
30.71 29.96 29.99 29.96 29.95 30.05 29.77 30.76 31.70 33.35
(Tvis ˜ °0 × 107 p - T)max D (K) (cm2 s-1) 10.8 10.1 4.0 5.0 4.1 4.1 2.9 2.8 3.2 4.4
3.1 3.5 6.7 8.6 9.5 9.9 15 17 20 15
ν˜ *
Tps (°C)
Tps - Tvis p (K)
0.38 0.46 0.62 0.68 0.68 0.68 0.70 0.66 0.63 0.50
31.7 30.16 30.04 30.08 30.01 30.05 29.86 31.15 32.4 34.1
1.0 0.20 0.05 0.14 0.06 0 0.09 0.39 0.7 0.8
a y is the mass fraction of C E . Tvis 12 5 p is the visually determined temperature of phase separation. The critical composition has a value of yc ) 1.08 × 10-2. In columns 4-7, the table contains values of parameters describing the temperature dependence of the mutual diffusion coefficient of C12E5/D2O mixtures of critical and noncritical composition (for details see text). Tps is the pseudospinodal temperature; ν˜ *, exponent (y ) yc: ν*); D ˜ °0, amplitude of the mutual diffusion coefficient (y ) yc: D°0; and (Tvis p - T)max, temperature range in which the D°(T) are represented by power laws (eqs 3 and 4) using the parameter values given in columns 4-6. The sample with the composition y ) 2.0 × 10-2 was prepared from a C12E5 stock different from that from which the other samples were prepared.
It cannot be avoided that the critical temperature and the temperature of phase separation of the system C12E5/D2O vary with time probably because of trace amounts of unknown impurities or chemical reactions (typical value dTp/dt < 1 mK day-1). Therefore Tp (and Tc) was checked before and after each experimental run. During an experimental run that lasted up to 14 days Tp (and Tc) changed by less than 10 mK. A commercial light-scattering photometer (ALV, D-63225 Langen) in combination with an ALV-5000 muliple-τ digital correlator (number of channels: 288; fixed logarithmically distributed delay times τ (“lag times”) in the range 0.2 µs to several hours) was used for the dynamic light scattering experiments. The light source was a helium-neon laser (NEC, Model GLG 5740; 50 mW at λ0 ) 632.8 nm). The scattered light intensities were measured in a range of scattering angles 30° e θ e 140°. This corresponds to values of the scattering vector 6.9 × 104 cm-1 e q e 2.5 × 105 cm-1 (q ) (4πn/λ0) sin(θ/2); n, index of refraction, e.g. n(yc, 25 °C) ≈ 1.337). During the experiments the temperature of the samples was controlled within δT ) (10 mK. The samples put in the light-scattering photometer were contained in flame-sealed Duran-glass cells (internal diameter, 8 mm; external diameter, 10 mm; height, 70 mm). Before the
Figure 2. Results of the analysis of g(1)(t) data obtained with a C12E5/ D2O mixture of critical composition using the program CONTIN: Plot of the relative width of the ΓA(Γ) as a function of temperature difference (Tc - T). Scattering angle θ ) 30°. The line is a guide for the eye.
start of an experiment they were centrifuged in a temperaturecontrolled centrifuge for 2 h at an acceleration of approximately 2800g. From the autocorrelation function G(2)(τ) of scattered light intensity measured by the correlator at the scattering vector q, the normalized second-order correlation function g(2)(t) was calculated. Several runs were made to improve the statistics of the photon counts. g(2)(t) was converted into the normalized first-order electric field time correlation function g(1)(t) using the relation (g(1)(t))2 ) g(2)(t) - 1. It is expected that a spectrum of relaxation rates Γi with different amplitudes A(Γi) contribute to g(1)(t). The g(1)(t) and A(Γi) are related by a Laplace transform given by eq 1.
g(1)(t) ) ∫0 A(Γ) exp(-Γt) dΓ ∞
(1)
Provencher’s program CONTIN was used (version 2DP; number of Γ values, 70; “standard integral method” switched off because a logarithmically spaced grid of Γ values was used).20,21 III. Results and Discussion Plots of the product of the amplitude A(Γ) and the relaxation rate Γ (i.e. (A(Γ)Γ)) (linear scale) versus Γ (logarithmic scale) obtained from data measured at fixed scattering angles show one major peak at Γmax for all mixtures of critical and noncritical composition. The peak position Γmax is identified with the center of mass of a peak. This measure is nearly independent of the resolution on the logarithmically spaced grid of the Γ axis. Γmax is temperature and composition dependent. For scattering angles θ g 90° and temperatures T > 20 °C a second peak in the A(Γ) distribution with a higher relaxation rate is detected. It has a small amplitude compared to the major peak ((A(Γ)Γ)sec/ (A(Γ)Γ)max< 0.1). It is a general experience that the analysis of g(1)(t) using the program CONTIN depends strongly on the quality of the experimental data. The program often produces for no obvious reasons artificial secondary maxima without physical meaning. It is assumed that this is true in the present case. Assuming that the A(Γ) profile can be approximated by a Gauss function, Provencher’s program CONTIN is used to characterize the width of the profile by the ratio of the standard deviation and the peak position.22 The analysis of the data obtained with a mixture of critical composition reveals that the width decreases approaching Tc (see Figure 2). The same is true also for the data obtained with mixtures of noncritical composition (y > yc; y < yc) approaching Tp. The width of the
13762 J. Phys. Chem., Vol. 100, No. 32, 1996
Martı´n et al.
a
b
c
Figure 3. Plots of Γmax/q2 versus q2 for the determination of the mutual diffusion coefficient D° (D° ≡ limqf0(Γmax/q2)). Parameter: ∆T ) Tp - T for y * yc; ∆T ) Tc - T for y ) yc. Tp (Tc) is the visually determined temperature of phase separation of a mixture of noncritical (critical) composition. y is the mass fraction of C12E5. (a) Composition y ) 0.499 × 10-2 < yc; (b) composition yc ) 1.08 ×10-2; (c) composition y ) 0.1001 > yc.
A(Γ) profiles obtained with these mixtures does not narrow down as much. In “simple” systems (e.g. 2-butoxyethanol(C4E1)/ water) the electric field time correlation function g(1)(t) of scattered light is a single exponential. These facts are interpreted as evidence that approaching the binodal curve g(1)(t) is dominated by contributions of concentration fluctuations. The value of the mutual diffusion coefficient D° as function of temperature and composition is obtained from the Γmax(q,T,y) data using plots of Γmax/q2 versus q2 at constant values of T and y. D° is calculated from the intercept of the Γmax/q2 versus q2 curve (D° ) limqf0(Γmax/q2)).23 Typical plots of Γmax/q2
Figure 4. Temperature and composition dependence of the mutual diffusion coefficient D°. The shaded area represents roughly the location of the liquid/liquid coexistence curve. Parameter: y, mass fraction of C12E5.
versus q2 are shown in Figure 3 for four mixtures of different compositions (y < yc; y ) yc; y > yc). The temperature and composition dependence of the mutual diffusion coefficient D° calculated from such data are given in Figure 4 (plot of D° versus T; parameter, composition). The same data are shown in a double logarithmic D° versus y plot (parameter: temperature) in the form of isotherms in the upper part of Figure 5. The following conclusions are drawn from the data. (1) In dilute solutions (y e 5 × 10-3; yc - y ) 5.8 × 10-3) the slope of the Γmax/q2 versus q2 plots is positive. It increases approaching the temperature of phase separation (see Figure 3a). This behavior is commonly observed in “simple” binary liquid mixtures with a miscibility gap of near critical and critical composition approaching Tp and Tc, respectively. It is interpreted to be caused by the dynamics of Fourier components of the composition fluctuations monitored by changing the scattering vector (scattering angle). (2) With increasing concentrations of C12E5 (y > 5 × 10-3) the temperature dependence of the Γmax/q2 versus q2 curves becomes more complicated. For a mixture of critical composition (yc ) 1.08 × 10-2) and decreasing values of Tc - T the slope of the curves decreases starting from positive values. It becomes negative and again positive approaching Tc. The Γmax/q2 versus q2 plots are slightly curved close to Tc (Tc - T e 1 K) (see Figure 3b). The changes of slope and the occurring curvature are assumed to indicate that close to Tc the diffusive behavior is dominated by the dynamics of critical concentration fluctuations (see also Figure 2 in ref 23). A change of the sign of the slope of the Γmax/q2 versus q2 curves
Study of the System C12E5/D2O
J. Phys. Chem., Vol. 100, No. 32, 1996 13763
Figure 6. Plot of the reduced mutual diffusion coefficient D ˜ *(q) (t(6πη/kBT)(D(q)/q)) of a C12E5/D2O mixture of critical composition as a function of the scaling variable (qξ). Figure 5. Mutual diffusion coefficient D° of the system C12E5/D2O as a function of the composition. Parameter: temperature difference ∆T ) Tp - T (y * yc; ∆T ) Tc - T ( y ) yc). Tp (Tc) is the visually determined temperature of phase separation of a mixture of noncritical (critical) composition.
away from Tc is also observed in C12E5/D2O mixtures with compositions larger than the critical (y > yc; see Figure 3c) approaching Tp, but the contribution of concentration fluctuations is not sufficiently large to produce positive slopes near Tp. The change of sign of the slope of the Γmax/q2 versus q2 curves is interpreted qualitatively in terms of a generalized form of the expression of Γmax/q2, i.e. Γmax/q2 ) (kBT/f)(H(q)/S(q)).24 f is the friction factor of the scatterers. H(q) accounts for the indirect hydrodynamic interactions, and S(q) is the solution structure factor. S(q) takes into account the direct interparticle interactions. The q-dependence of H(q) and S(q) describes the spatial distribution of the scattering entities, which are determined by the interparticle interactions. There is evidence that in the system C12E5/water the size and shape of the micelles as well as the interactions between the micelles change as function of temperature and composition.25,26,27 Therefore, changes of the q-dependence of H(q) and S(q) with temperature and composition will cause the observed change of slope of the Γmax/q2 versus q2 curves. A separation of the influence of H(q) from that of S(q) on Γmax/q2 is not possible for the system C12E5/D2O. (3) For C12E5/D2O mixtures with compositions y < yc the mutual diffusion coefficient D° decreases with increasing temperatures in the entire temperature range 0.05 K < (Tp T) < 20 K. In concentrated C12E5/D2O mixtures (y g 4 × 10-2) D° increases with increasing temperatures away from the temperature of phase separation and decreases approaching Tp. This behavior is very similar to that found in “simple” binary mixtures (e.g. C4E1/H2O), polymer solutions (e.g. polystyrene/ cyclohexane), and polymer melts (polystyrene-h/polystyrened).1-5 Assuming that close to Tc (Tc - T < 1.4 K) the measured diffusion coefficient D(q) of a mixture of critical composition can be identified with its critical contribution Dc(q), the scaling properties of the data are checked. In a range of temperature differences 0.04 K < (Tc(vis) - T) < 1.37 K in which the Γmax/ q2 versus q2 curves have a positive slope the dimensionless diffusion coefficient defined by eq 2 is calculated from the experimental data and plotted as a function of the scaling variable (qξ).
D ˜ *(q) ≡
6πη D(q) kBT q
(2)
where ξ is the temperature dependent correlation length; η, shear viscosity; and kB, Boltzmann’s constant. The superscript (∼) indicates that D ˜ *(q) is defined differently from D*(qξ) (t(6πηξ/kBT)D(q)), which is commonly used in this context. The shear viscosity η is measured independently. In the narrow temperature range used for the calculation of D ˜ *(q) the viscosity η changes by less than 2% (mean value η j) 3.13 cP). The correlation length ξ is obtained from static light scattering experiments (ξ ) (1.78 nm)-0.630; ) (Tc(fit) T)/Tc(fit); Tc(fit) ) 30.025 °C). In a double logarithmic plot the D ˜ *(q) data follow a single curve (see Figure 6). This result corresponds to that of Hamano et al., who have studied the system C12E5/H2O.28 The dynamic light scattering data obtained with a critical mixture of the system C8E4/H20 also scale.14 That system has a phase diagram that is more simple than that of C12E5/water.29 It is well established that in a mixture of critical composition the convergence of the mutual diffusion coefficient approaching the critical temperature is represented by a power law of the form given by eq 3
| |
D°(T) ) D°0
Tc - T Tc
ν*
(3)
where ν* is a system independent critical exponent (ν* ) 0.67); D°0, a system dependent critical amplitude. For mixtures of noncritical composition the temperature dependence of D° at constant composition can be discussed in terms of the pseudospinodal concept: D° approaches the value zero within the liquid/liquid coexistence curve at the pseudospinodal temperature Tps (Tps(y) * Tp(y)). Tps is treated as one of the fitting parameters in a fit of the power law given by eq 4 to experimental D°(T) data (fit with three free parameters: D ˜ °0, Tps, νj*).
|
D°(T) ) D ˜ °0
|
Tps - T Tps
ν˜ *
(4)
The results of fits of eqs 3 and 4 to the experimental data are compiled in the fourth to seventh columns of Table 1. For the mixture of critical composition the value of the critical exponent ν* is close to that theoretically expected (ν* ) 0.67). The value of the spinodal temperature is close to the visually determined critical temperature. With increasing values of the difference |y - yc| the difference Tps - Tp(vis) increases (see Figure 5). For a system with a lower critical point Tps is expected to be larger than Tp. These observations are taken again as evidence of the dominating influence of concentration fluctuations on the dynamics of C12E5/D2O mixtures close to the binodal curve.
13764 J. Phys. Chem., Vol. 100, No. 32, 1996 From a thermodynamic point of view the decrease of D° with increasing temperatures approaching the liquid/liquid coexistence curve can be understood qualitatively by assuming that the temperature and composition dependence of the mutual diffusion coefficient is determined by the temperature and composition dependence of the thermodynamic factor (∂µi/∂xi)P,T (µi, chemical potential of component i; xi mole fraction of component i; P, pressure). The thermodynamic factor connects the mutual diffusion coefficient D in Fick’s frame of reference with the phenomenological (Onsager) transport coefficient L (i.e. D ∝ L(∂µi/∂xi)P,T). For “simple” systems the regular solution model (upper critical point) has been used to calculate the temperature and composition dependence of (∂µi/∂xi)P,T. The calculated temperature and composition dependence of the diffusion coefficient is in qualitative agreement with experimental data.1,2,4,5 The observed slowing down of the diffusion process in a wide temperature-composition region along the coexistence curve indicates that from a physical point of view the system is “close” to its binodal curve. Microscopically, the slowing down of the diffusion coefficient in the system C12E5/D2O approaching the liquid/liquid coexistence curve is mainly caused by the temperature and composition dependence of the correlation length of concentration fluctuations (i.e. Stokes-Einstein relation D ∝ 1/ξhyd; ξhyd, hydrodynamic radius of the scattering entities) in combination with structural changes of the micelles formed by C12E5 molecules. The presence of concentration fluctuations seems to be the primary cause. It is well established that the slowing down of the mutual diffusion process approaching the liquid/liquid coexistence curve of systems with a miscibility gap is a system independent phenomenon.1-5 The data shown in Figure 4 are replotted in the form of isotherms in the upper part of Figure 5 to bring out similarities to results reported by Kato et al. for the same system30 and that given by Wilcoxon et al. for the system C12E6/D2O (lower critical point, critical composition yc ) 1.8 × 10-2; critical temperature Tc ) 48.17 °C.31 The minimum of the curves is at the critical composition. Kato et al. interpret their data mainly in terms of scaling concepts developed to describe the properties of entangled solutions of flexible polymers in solutions. Kole et al. have carried out static and dynamic light scattering experiment with the system C12E6/H2O and report that the minimum of D(y) isotherms is a function of y.32 According to Kole et al., it marks the threshold crossover concentration from dilute to semidilute behavior. The critical temperature of the system C12E5/water is about 20 K lower than that of the system C12E6/water. In the system C12E6/water Strey et al. have carried out temperature jump experiments to study the dynamics of the system. These authors construct from their data a linear transition temperature/ composition curve (Ttrans(y)) marking the transition from “globular micelles” to “large aggregates”.18 This curve runs well below the liquid/liquid coexistence curve (y ) 1 × 10-4, Tp - Ttrans ≈ 20 K; y ) 1 × 10-2, Tp - Ttrans ≈ 45 K). Assuming that a Ttrans(y) curve also exists for the system C12E5/D2O, it is expected that it is located below the temperature range in which the experiments are carried out in this study. If this is true, all experiments in this study are carried out in the “large aggregates” regime. IV. Conclusions The mutual diffusion coefficient data obtained with C12E5/ D2O mixtures of critical and noncritical composition in a wide temperature and composition range indicate that under the stated conditions the dynamic properties of the mixtures reflect the
Martı´n et al. fact that they are “close” to the limit of their stability at the binodal curve. All the data support the assumption that in the vicinity of the binodal curve the presence of concentration and temperature dependent composition fluctuations is the cause for the change of size and shape of C12E5 micelles (and their dynamics) with temperature and composition in aqueous solutions. The same appears to be true for other nonionic surfactant/ water systems of the type CiEj with i ) 12, 14, 16 and j ) 5, 6, 7, 8.25,26,31,33 Acknowledgment. One of the authors (A.M.) thanks the Deutscher Akademischer Austauschdienst (DAAD) for its financial support, which made her contributions to this work possible. References and Notes (1) Schmitz, J.; Belkoura, L.; Woermann, D. J. Chem. Phys. 1994, 101, 476. (2) Schmitz, J.; Belkoura, L.; Woermann, D. Ber. Bunsen-Ges. Phys. Chem. 1995, 99, 848. (3) Losch, A.; Woermann, D.; Klein, J. Macromolecules 1994, 27, 5713. (4) Ikier, Ch.; Klein, H.; Woermann, D. Macromolecules 1995, 28, 1003. (5) Heger, R.; Ikier, Ch.; Belkoura, L.; Woermann, D. J. Chem. Soc., Faraday Trans. 1995, 91, 3385. (6) Steinhoff, B.; Woermann, D. J. Chem. Phys. 1995, 103, 8985. (7) Beckmann, V.; Woermann, D. Z. Phys. Chem. 1995, 192, 141. (8) (a) Chevalier, Y.; Zemb, T. Rep. Prog. Phys. 1990, 53, 279. (b) Magid, L. In Dynamic Light Scattering; Brown, W., Ed.; Clarendon Press: Oxford, 1993. (9) Kuwahara, N.; Hamano, K.; Koyama, T. Phys. ReV. A 1985, 32, 1279. (10) Hamano, K.; Kuwahara, N.; Koyama, T.; Harada, S. Phys. ReV. A 1985, 32, 3168. (11) Scho¨n, W.; Wiechers, R.; Woermann, D. J. Chem. Phys. 1986, 85, 2922. (12) Hu¨rth, M.; Woermann, D. Ber. Bunsen-Ges. Phys. Chem. 1987, 91, 614. (13) Rabinovich, I. B. Influence of Isotopy on the Physicochemical Properties of Liquids; Consultants Bureau: New York, London, 1970. (14) Lesemann, M.; Belkoura, L.; Woermann, D. Ber. Bunsen-Ges. Phys. Chem. 1995, 99, 695. (15) Zana R.; Eljebari, M. J. J. Phys. Chem. 1993, 97, 11134. (16) Schubert, K. V.; Strey, R.; Kahlweit, M. J. Colloid Interface Sci. 1991, 141, 21. (17) Strey, R.; Schoma¨cker, R.; Roux, D.; Nallet, F.; Olsson, U. J. Chem. Soc., Faraday Trans. 1990, 86, 2253. (18) Strey, R.; Pakusch, A. In Surfactants in Solutions; Mittal, K. L., Bothorel, P., Eds.; Plenum Press: New York, 1986; Vol. 4, p 465. (19) Sinn, C.; Woermann, D. Ber. Bunsen-Ges. Phys. Chem. 1992, 96, 913. (20) Provencher, S. W. Comput. Phys. Commun. 1982, 27, 213; 1992, 27, 229. (21) Provencher, S. W.; Hendrix, J.; De Maeyer, L.; Paulussen, N. J. Chem. Phys. 1978, 69, 4273. (22) Provencher, S. W. CONTIN users manual (3.6.5). EMBL Technical Report DA07; European Molecular Laboratory, 1984. (23) Lesemann, M.; Zielesny, A.; Belkoura, L.; Woermann, D. J. Chem. Phys. 1995, 102, 414. (24) Schmitz, K. S. Macroions in Solution and Colloidal Suspensions; VCH Publishers: New York, 1993; p 76. (25) Nilsson, P. G.; Wennerstro¨m, H.; Lindman, B. J. Phys. Chem. 1983, 87, 1377. (26) Kato, T.; Anzai, S.; Takano, S.; Seimiya, T. J. Chem. Soc., Faraday Trans. 1989, 85, 2499. (27) Kato, T.; Anzai, S.; Seimiya, T. J. Phys. Chem. 1990, 94, 7255. (28) Hamano, K.; Sato, S.; Koyama, T.; Kuwahara, N. Phys. ReV. Lett. 1985, 55, 1472. (29) Mitchell, D. J.; Tiddy, G. J. T.; Waring, L.; Bostock, T.; Mc Donald, M. P. J. Chem. Soc., Faraday. Trans. 1983, 79, 975. (30) Kato, T.; Anzai, S.; Seimiya, T. J. Phys. Chem. 1987, 91, 4655. (31) Wilcoxon, J. P.; Schaefer, D. W.; Kaler, E. W. J. Chem. Phys. 1989, 90, 1909. (32) Kole, T. M.; Richards, C. J.; Fisch, M. R. J. Phys. Chem. 1994, 98, 4949. (33) Kato, T.; Terao, T.; Seimiya, T. Langmuir 1994, 10, 4468.
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