Deuterium Oxide Mixtures

In the temperature range (TP − Tη,max) the viscosity decreases with increasing ... S. Tanaka , Y. Kubo , Y. Yokoyama , A. Toda , K. Taguchi , H. Ka...
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Langmuir 1997, 13, 5289-5293

5289

Study of the Viscosity of Nonionic Surfactant/Deuterium Oxide Mixtures and of the Self-Diffusion Coefficient of the Surfactant Approaching the Liquid/Liquid Coexistence Curve M. Lesemann,† A. Martin,† L. Belkoura,† G. Fleischer,‡ and D. Woermann*,† Institut fu¨ r Physikalische Chemie, Universita¨ t Ko¨ ln, Luxemburger Strasse 116, D-50939 Ko¨ ln, Germany, and Fakulta¨ t fu¨ r Physik und Geowissenschaften, Abteilung Polymerphysik, Universita¨ t Leipzig, Linne´ strasse 5, D-04103 Leipzig, Germany Received April 3, 1997. In Final Form: June 25, 1997X Plots of the temperature dependence of the shear viscosity η of C12E5/D2O mixtures with compositions in the range 0.60 × 10-2 < y < 10.08 × 10-2 (critical composition yc ) 1.08 × 10-2; y, mass fraction of C12E5) are S-formed (a shallow minimum at a lower temperature Tη,min and a maximum at a higher temperature Tη,max). The measurements are carried out in the temperature range 5 °C < T < TP; TP ≈ 30 °C approaching the lower part of the binodal curve (TP, temperature of phase separation of the mixture). In the temperature range (TP - Tη,max) the viscosity decreases with increasing temperatures. At compositions y < 0.60 × 10-2 the viscosity decreases with increasing temperature monotonically. The self-diffusion coefficient of C12E5 in C12E5/D2O mixtures is measured in the same temperature and composition range. The findings of both types of experiments are rationalized in terms of a model developed by Nilsson et al. (J. Phys. Chem. 1983, 87, 1377). The results give support to the hypothesis that the characteristic features of the temperature and composition dependence of both transport coefficients in the large aggregate region of the phase diagram have a common cause: The structural dynamics of the large micellar aggregates increases approaching the liquid/liquid coexistence curve at compositions y > yc. Concentration fluctuations with long range correlations appear to be involved in this process.

1. Introduction In a wide range of temperatures and compositions adjacent to the lower part of the binodal curve of the “complex” system C12E5 [CH3(CH2)11(OCH2CH2)5OH)]/D2O phenomena have been observed which are typical for the universal properties of binary mixtures with a miscibility gap. The lower critical point of that system has been characterized by a critical composition, yc ) 1.08 × 10-2 (y, mass fraction of C12E5) and a critical temperature Tc ) 30.00 °C. Concentration fluctuations with long range correlations have been found in mixtures of critical and noncritical composition. The mutual diffusion coefficient decreased with increasing temperatures approaching the binodal curve. This information was obtained from static and dynamic light scattering experiments as well as from small angle neutron scattering experiments.1-3 The term “complex” draws attention to the fact that the system has a more complicated phase diagram than “simple” binary mixtures with a miscibility gap (e.g., methanol/cyclohexane).4 The critical micelle concentration (cmc) of C12E5 in water is considerably smaller than the critical concentration (ycmc ≈ 10-5). Therefore, concentration fluctuations with long range correlations occur in the region close to the liquid/liquid coexistence curve in the presence of micellar structures. This region is of interest in the present study. * To whom the correspondence should be addressed. † Universita ¨ t Ko¨ln. ‡ Universita ¨ t Leipzig. X Abstract published in Advance ACS Abstracts, September 15, 1997. (1) Martin, A.; Lesemann, M.; Belkoura, L.; Woermann, D. J. Phys. Chem. 1996, 100, 13760. (2) Lesemann, M.; Martin, A.; Belkoura, L; Woermann, D. Ber. Bunsenges. Phys. Chem. 1997, 101, 228. (3) Lesemann, M.; Belkoura, L.; Woermann, D. Ber. Bunsenges. Phys. Chem. 1995, 99, 695. (4) Mitchell, D. J.; Tiddy, G. T. D.; Wwaring, L.; Bostock, T.; McDonald, M. P. J. Chem. Soc., Faraday Trans. 1 1983, 79, 975.

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The critical properties of the system C12E5/D2O studied by static and dynamic light scattering techniques just mentioned are in quantitative agreement with the prediction of the Landau-Ginzburg-Wilson model.5 The material specific critical amplitude ξo of the correlation length is large (ξo ) 1.08 nm) compared with that of nonaggregating binary liquid mixtures. This finding and the observation that the viscosity-temperature curve of a C12E5/water mixture of critical composition has a minimum and a maximum (see Figure 1) prompted us to study in more detail the composition and temperature dependence of the shear viscosity of the system C12E5/ D2O and the self-diffusion coefficient of C12E5 in C12E5/ D2O mixtures around the lower critical point. The selfdiffusion coefficient is determined using the pulsed field gradient nuclear magnetic resonance technique. It is known from experiments with “simple” binary systems with a miscibility gap that the self-diffusion coefficient is not effected by critical fluctuations.7-11 In Figure 1 the temperature dependence of the viscosity is shown for three different CiEj/H2O mixtures of critical composition. The data were obtained using a capillary viscometer at a shear rate S of about 102 s-1. The weak divergence of the shear viscosity with increasing temperature in the vicinity of Tc showed up clearly only in the systems 2-C4E1/water12 (not shown in Figure 1), C6E3/ water, and C8E4/water.13 The temperature range close to (5) Sengers, J. V.; Levelt-Sengers, J. M. H. In Progress in Liquid Physics; Croxton, C. A., Ed.; John Wiley & Sons: Chichester, New York, Brisbane, Toronto, 1978; p 103. (6) Schmitz, PhD Thesis, Ko¨ln, 1994. (7) Hoheisel, C.; Richterring, H. Z. Phys. Chem. (Munich) 1967, 55, 323. (8) Hamann, H.; Hoheisel, C.; Richtering, H. Ber. Bunsenges. Phys. Chem. 1972, 76, 249. (9) Allegra, J. C.; Stein, A.; Allen, G. F. J. Chem. Phys. 1971, 55, 1716. (10) Anderson, J. E.; Gerritz, W. H. J. Chem. Phys. 1970, 53, 2584. (11) Lang, J. C.; Freed, J. H. J. Chem. Phys. 1972, 56, 4103. (12) Zielesny, A.; Schmitz, J.; Limberg, S.; Aizpiri, A. G.; Fusenig, S.; Woermann, D. Int. J. Thermophys. 1994, 15, 67.

© 1997 American Chemical Society

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Figure 1. Temperature dependence of the shear viscosity of three CiEj/water mixtures of critical composition. The data of the system C6E3/water and C8E4/water are taken from ref 13 and that of the system C12E5/water from ref 6.

Tc in which the viscosity is dominated by critical fluctuations was largest in the system 2-C4E1/water and smallest in the system C8E4/water. It was absent in the system C12E5/water. The critical exponent of the divergent contribution to the measured viscosity had the expected universal value for the systems 2-C4E1/water and C6E3/ water.12,13 For the system C8E4/water the critical exponent could not be determined.13 There is evidence in the literature indicating that in the system C12E5/water as well as in other CiEj/water mixtures of nonionic surfactants with long hydrophobic hydrocarbon chains the micellar structures change with composition and temperature. The structural changes were studied by scattering and other techniques. Among them were measurements of the composition and temperature dependence of the viscosity14-16 and of the selfdiffusion coefficient.17-25 The present study with the system C12E5/D2O differs from that just cited in a major aspect: The experiments are concentrated in a range of compositions near the critical composition and are carried out approaching closely the liquid/liquid coexistence curve. The aim is to probe the possible influence of concentration fluctuations with long range fluctuations on the structural changes of the micelles. 2. Experimental Section 2.1. Materials. C12E5 was purchased from Nikko Chemical Co. (Japan). It was the same material as used recently.1,2 Details of the preparation of the C12E5/D2O mixtures and the handling of the mixtures are given in ref 1. 2.2. Viscosity. The viscosity of the mixtures was measured with a capillary viscometer of the Ostwald type (Schott Gera¨te, (13) Zielesny, A.; Limberg, S.; Woermann, D. Ber. Bunsenges. Phys. Chem. 1994, 48, 195. (14) Strey, R. Ber. Bunsenges. Phys. Chem. 1996, 100, 182. (15) Matsumato, T.; Zenkoh, H. Colloid Polym. Sci. 1990, 268, 536. (16) Richtering, W. H.; Burchard, W.; Jahns, E.; Finkelmann, H. J. Phys. Chem. 1988, 92, 6032. (17) Nilsson, P.; Wennerstro¨m, H.; Lindman, B. J. Phys. Chem. 1983, 87, 1377. (18) Nilsson, P.; Wennerstro¨m, H.; Lindman, B. Chem. Scr. 1985, 25, 67. (19) Brown, W.; Johnsen, R.; Stilbs, P.; Lindman, B. J. Phys. Chem. 1983, 87, 4548. (20) Kato, T.; Seimiya, T. J. Phys. Chem. 1986, 90, 3159. (21) Kato, T.; Anzai, S.; Seimiya, T. J. Phys. Chem. 1987, 91, 4655. (22) Brown, W.; Pu, Z.; Rymden, R. J. Phys. Chem. 1988, 92, 6086. (23) Kato, T.; Anzai, S.; Takano, S.; Seimiya, T. J. Chem. Soc., Faraday Trans. 1 1989, 85, 2499. (24) Kato, T.; Terao, T.; Tsukada, M.; Seimiya, T. J. Phys. Chem. 1993, 97, 3910. (25) Kato, T.; Terao, T.; Seimiya, T. Langmuir 1994, 10, 4468.

Lesemann et al. D-55127 Mainz, Germany, type 517-10, 517-13, 517-20) in an N2-gas atmosphere. With viscometers of the Ostwald type a formation of foam in the viscometer during the measurements could be avoided. The capillaries of the viscometers had different radii (r ) 0.43 mm, 0.60 mm, 0.77 mm). They had a length of L ≈ 150 mm. The mean hydrostatic pressure difference acting during a viscosity measurement (expressed by the difference in height of the two menisci of the fluid in the viscometer) had a value of about 〈h〉 ≈170 mm. The effective shear rate Seff of the viscometers was estimated using the relation Seff ) (4/15) (r F g〈h〉)/(L) (F, density of the mixture, g standard acceleration of free fall). Seff had a value of the order of Seff ≈ 102 s-1. The density data to convert the kinematic viscosity into the dynamic viscosity were determined using a vibrating tube densitometer (Paar, Graz, Austria, type DMA 602). The viscometers were calibrated with water (temperature range, 23 °C < T < 43 °C) and ethylene glycol (temperature range 2 °C < T < 55 °C). The viscometer was immersed into a constant temperature bath (long time temperature stability δT ) (3 mK). The temperature dependence of the viscosity of each C12E5/D2O mixture (except the mixture with the composition y ) 10.01 × 10-2) was determined using two viscometers with different values of the radius of the capillary. An influence of the shear rate on the viscosity could not be detected. The η(T) data sets of the C12E5/ D2O mixtures of different compositions are given elsewhere.26 It cannot be excluded that the viscosity of the solutions with the high viscosity depends on the shear rate at rates much smaller than 102 s-1. 2.3. Self-Diffusion Coefficient. The self-diffusion coefficient of C12E5 in C12E5/D2O mixtures was determined by the pulsed field gradient nuclear magnetic resonance (PFG-NMR) method using a stimulated echo-pulse sequence. The experiments were carried out with the home built FEGRIS 400 spectrometer of the Department of Physics of the University of Leipzig operating at 400 MHz.27 The spin-echo attenuation ψ of the protons of the C12E5 molecules was measured as function of the magnitude of the pulsed field gradient g (0 e g e 24 T m-1) at a constant pulse width δ (0.5 ms e δ e 1.5 ms) and a constant time interval ∆ between the application of the two pulses of the magnetic field gradient. δ was small compared with the time interval ∆ which had values in the range of 13 ms e ∆ < 103 ms. The self-diffusion coefficient was obtained using the relation ψ ) exp{-γδ2 g2 Ds ∆}. γ is the gyromagnetic ratio of the protons. The C12E5/D2O mixtures were contained in sealed NMR tubes. The temperature of the samples was controlled (δT ) (1 K) using a stream of N2 gas of constant temperature. The known temperature of phase separation of the mixtures was used as an internal standard.

3. Experimental Results and Discussion 3.1. Viscosity. Figure 2 shows plots of the shear viscosity of C12E5/D2O mixtures as function of temperature T in the temperature range 5 °C < T < TP (TP, temperature of phase separation). The composition of the mixtures is the parameter of the experiments (0.23 × 10-2 e y e 10.08 × 10-2; y, mass fraction of C12E5). The curves exhibit two characteristic features: (1) For the most dilute mixtures (y ) 0.23 × 10-2; y ) 0.50 × 10-2), the shear viscosity decreases monotonically with increasing temperature. (2) For mixtures with compositions y g 0.60 × 10-2, the η(T) curves are S-formed exhibiting a minimum at Tη,min and a maximum at Tη,max. The values of Tη,min and Tη,max do not change significantly when they are determined from [η/ηo),T] data sets (ηo, viscosity of D2O at the given temperature. With increasing values of y the S-form becomes more pronounced. The extrema are interpreted to reflect structural changes within the mixtures. The observed temperature and composition dependence of the viscosity of C12E5/D2O mixtures are typical for CiEj/water mixtures with long hydrocarbon chains (C12E6/water,14 Tc (26) Lesemann, M. PhD-Thesis, Ko¨ln, 1996. (27) (a) Fleischer, G.; Fujava, F. NMR 1994, 30, 159. (b) Ka¨rger, J.; Pfeifer, H.; Heink, W. Adv. Magn. Reson. 1988, 12, 1. (c) Stejskal, E. O.; Tanner, J. J. Chem. Phys. 1965, 42, 288.

Viscosity of C12E5/D2O

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Figure 2. Temperature dependence of the shear viscosity of C12E5/D2O mixtures of different compositions (y, mass fraction of C12E5). The drawn out line in Figure 2a (curve 0) represents the temperature dependence of the viscosity of D2O. Curves: (1), y ) 0.23 × 10-2, TPvis ) 30.71 °C; (2), y ) 0.50 × 10-2, TPvis ) 29.96 °C; (3), y ) 0.60 × 10-2, TPvis ) 30.12 °C; (4), y ) 0.70 × 10-2, TPvis ) 30.04 °C; (5) y ) 0.85 × 10-2, TPvis ) 29.99 °C; (6) y ) 0.99 × 10-2, TPvis ) 29.96 °C; (7) y ) 1.08 × 10-2, TPvis ) 29.95°C; (8) y ) 1.17 × 10-2, TPvis ) 30.05 °C; (9) y ) 2.00 × 10-2, TPvis ) 29.77 °C; (10) y ) 3.46 × 10-2, TPvis ) 30.76 °C; (11) y ) 5.99 × 10-2, TPvis ) 31.70 °C; (12) y ) 10.01 × 10-2, TPvis ) 33.35 °C. TPvis, visually determined temperature of phase separation.

≈ 51 °C, yc ) 2.6 × 10-2; C12E8/water,15 Tc ≈ 71 °C, yc ) 3.3 × 10-2; C14E8/water,16 Tc ≈ 75 °C; yc ) 2.5 × 10-2 ). It is well established that the weak divergence of the shear viscosity of “simple” (nonaggregating) binary mixtures of critical composition measured with a capillary viscometer (shear gradient 102 s-1 < S < 103 s-1) depends only weakly of the shear gradient approaching Tc closely (shear thinning). The critical amplitude ξo of the correlation length of local concentration fluctuations of these systems has a value of the order of 0.2 nm. If the same experiments are carried out with a CiEj/water mixture of critical composition with long hydrocarbon chains (C10E4/ water;28 C12E5/water29 ), a weak divergence close to Tc [(Tc - T) < 0.1 K] cannot be detected unequivocally. But it shows up when the experiments are carried out with a rotation viscometer designed to generate shear gradients in the range 0.1 s-1 < S < 1 s-1.30-32 This indicates that the critical enhancement in these systems with comparatively large values of the critical amplitudes ξo (of the order of 1 nm) is distorted under shear flow. Measurements of the shear viscosity of the system C12E8/ water at compositions well above the critical composition (y ) 0.2; y ) 0.3)) at temperatures of 22, 30, and 60 °C and at shear rates in the range 0.1 s-1 < S < 103 s-1 indicate that the mixtures are Newtonian fluids.15 From these findings it is concluded that the decrease of the η(T) curves of the system C12E5/D2O after crossing the maximum of the curve and approaching TP is not caused by shear thinning. Minimum of the η(T) Curve. At concentrations of C12E5 larger than y > 0.60 × 10-2, the minimum of the (28) Hamano, K.; Kawazura, T.; Koyama, T.; Kuwahara, N. J. Chem. Phys. 1985, 82, 2718. (29) Hamano, K.; Kuwahara, N.; Mitsushima, I.; Kubota, K.; Ito, J. Phys. Lett. A 1990, 150, 405. (30) Zimm B. H.; Crothers, D. M. Proc. Natl. Acad. Sci U.S.A. 1962, 48, 905. (31) Hamano, K.; Kaneko, T.; Fukuhara K.; Kuwahara, N. Int. J. Thermophys. 1989, 10, 389. (32) Hamano, K.; Sato, T.; Koyama, T.; Kuwahara, N. Phys. Rev. Lett. 1985, 55, 1472.

Figure 3. Lower part of the liquid/liquid coexistence curve of the system C12E5/D2O (data marked by hollow circles; filled circle is critical point) and the composition dependence of the temperatures Tη,min and Tη,max at which the curves representing the temperature dependence of the viscosity of C12E5/D2O mixtures of different compositions have a minimum and maximum, respectively (see Figure 2). y is mass fraction of C12E5. The lines are constructed from η(T,y) data listed in ref 26.

η(T) curves is shifted to lower temperature values (y ) 0.60 × 10-2, Tη,min ≈ 22 °C; y ) 1.17 × 10-2, Tη,min ≈ 5 °C). For experimental reasons no viscosity data were measured at temperatures lower than 5 °C. Using the Tη,min values a Tη,min (y) line can be drawn (see Figure 3). This curve is assumed to separate a region of the phase diagram of the system C12E5/D2O with globular C12E5 micelles in the solution (below this curve) from a region (above this curve) with large micellar aggregates in the solution. Such a line was also constructed for the system C14E8/water by Richtering et al. on the basis of viscosity data (see Figure 1 in ref 16) and for the system C12E6/water by Strey (see Figure 2 in ref 14) using results of temperature jump

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experiments with time-resolved detection of the scattered light intensity. Maximum of the η(T) Curve. In the large aggregate region of the phase diagram, the viscosity increases with increasing temperature and reaches a maximum at Tη,max. For y > yc, the location of the ηmax on the temperature axis is shifted to lower temperature values when the concentration of C12E5 in the mixture is increased. Consequently, the temperature difference (TP - Tη,max) increases with increasing values of y. A plot of Tη,max as function of y for 0.6 × 10-2 < y < 10.01 × 10-2 is shown in Figure 3 (see also Figure 1 in ref 16 and Figure 2 in ref 14). The Tη,max(y) curve touches the liquid/ liquid coexistence curve at the critical point. Interpretation. The interpretation of these findings is based on a model first described by Nilsson et al.17,18 and developed into a quantitavive model by Kato et al.25 It was originally proposed to discuss the temperature and composition dependence of the self-diffusion coefficient of nonionic surfactants with long hydrophobic sections in CiEj/D2O mixtures. At low concentrations (y ) 0.23 × 10-2; y ) 0.50 × 10-2) the temperature dependence of the shear viscosity is that of a solution of small noninteracting micelles (monotonic decrease of η with increasing T, globular micelle region). For composition y g 0.60 × 10-2 the η(T) curves have a shallow minimum followed by a continuous increase of the viscosity with increasing temperature. This is assumed to reflect the onset of micelle-micelle interactions or micellar growth or a combination of both. The η(T) curve reaches a maximum followed by a decrease of η with increasing temperatures approaching the liquid/ liquid phase boundary. This is assumed to be caused by an increase of the structural dynamics (e.g., exchange of monomers and/or clusters of C12E5 molecules between the aggregates). At liquid/liquid coexistence, the majority phase is more rich in water and the minority phase more rich in C12E5 for compositions y < yc. For compositions y > yc, the majority phase at coexistence is more rich in C12E5 and the minority phase more rich in water. These conditions could be favorable to changes of the size and shape of the micellar structures with increasing concentrations approaching the liquid/liquid coexistence curve. It is well established that the mutual diffusion coefficient D at constant composition of binary liquid mixtures with a miscibility gap shows that D decreases approaching the liquid-liquid coexistence curve. This is a material independent property.33-37 For a system with a lower critical point the mutual diffusion coefficient decreases with increasing temperature in the vicinity of the binodal curve. Dynamic light scattering experiments with C12E5/ D2O mixtures in the vicinity of the lower critical point have shown that this occurs in the “large aggregate” region of the phase diagram in a region close to the Tη,max(y) curve shown in Figure 3.1 The assumed increase of the structural dynamics of the large micellar aggregates in the temperature range (TP - Tη,max) is associated with the occurrence of local concentration fluctuations. From a thermodynamic point of view, the characteristic temperature dependence of the mutual diffusion coefficient (33) Schmitz, J.; Belkoura, L.; Woermann, D. Ber. Bunsenges. Phys. Chem. 1994, 100, 476. (34) Losch, A.; Woermann, D.; Klein, J. Macromolecules 1995, 27, 5713. (35) Schmitz, J.; Belkoura, L.; Woermann, D. Ber. Bunsenges. Phys. Chem. 1995, 99, 848. (36) Heger, R.; Ikier, C.; Belkoura, L.; Woermann, D.; Klein. H. J. Chem. Soc., Faraday Trans. 1995, 91, 3385. (37) Ikier, C.; Klein, H.; Woermann, D. Macromolecules 1995, 28, 1003.

Lesemann et al.

D is caused by the temperature dependence of the thermodynamic factor (∂µi/xi)T,P (µi, chemical potential of component i; xi, mole fraction of component i).33-35,37 (µi/ xi)T,P relates D to the Onsager transport coefficient L (D ≈ L(∂µi/xi)T,P). From a microscopic point of view it is caused by an increase of the correlation length in the mixtures approaching the temperature of phase separation.35 3.2. Self-Diffusion Coefficient. With the pulsed field gradient nuclear magnetic resonance method applied to C12E5/D2O mixtures the translational motion of C12E5 monomers as well as C12E5 aggregates will contribute to the measured effective self-diffusion coefficient Ds,eff. This is described by eq 1.38

Ds,eff ) pmonoDs,mono + paggregateDs,aggregate

(1)

pmono is the fraction of the surfactant in monomeric form and paggregate the fraction present in different aggregated forms. Ds,mono and Ds,aggregate are the corresponding selfdiffusion coefficients. It is argued that Ds,eff can be identified to a good approximation with Ds,aggregate. The fraction of the surfactant in the monomeric form is small compared with the fraction present in the form of aggregates. The critical micelle concentration of C12E5 in water is small (ycmc ≈ 10-5). Due to the H/D exchange between the hydroxyl groups of C12E5 and D2O the solvent is slightly contaminated with H2O and HDO. Two independent isotope exchange reactions take place which lead to the formation of H2O and HDO (C12E5(H) + D2O ) C12E5(D) + HDO; 2HDO ) H2O + D2O). In principle the protons of the water interfere with the measurement of Ds,eff. At the values of the magnetic field gradients used in the experiments, no contribution of water to the measured signal could be detected. The concentration of the protons of H2O and HDO is small and the self-diffusion coefficients of H2O and HDO are comparatively large. In this study only a few experiments probing the concentration and temperature dependence of the selfdiffusion coefficient of C12E5 in C12E5/D2O mixtures are carried out because this information is already available in the literature.17-25 To relate the viscosity data discussed in section 3.1 to corresponding self-diffusion coefficient data, the experiments are carried out at compositions and temperatures similar to that used in the viscosity measurements. The results of these measurements are summarized as follows: (a) The temperature dependence of the effective selfdiffusion coefficients of C12E5 in a C12E5/D2O mixture of critical composition is not influenced by critical concentration fluctuations. Whereas the mutual diffusion coefficient of this mixture decreases strongly approaching Tc, the effective self-diffusion coefficient of the solute shows only a small temperature dependence (see Figure 4). This is theoretically expected.7-11 Similar results have been reported in the literature for the system C12E6/D2O.22 (b) The curve representing the effective self-diffusion coefficient as function of composition at fixed temperatures (see Figure 5a) exhibits a shallow minimum at the temperatures 20 and 25 °C at compositions in the range of about y ≈ 1 × 10-2. At compositions y > 1 × 10-2 the self-diffusion coefficient increases slightly with increasing concentrations of C12E5. At T ) 25 °C the location of the minimum on the composition axis is at a lower concentration than at T ) 20 °C. This shift of the minium of the Ds,eff(y) curve with temperature is in agreement with results of extensive measurements of Ds,eff(y) isotherms (38) Fleischer, G. J. Phys. Chem. 1993, 97, 517.

Viscosity of C12E5/D2O

Figure 4. Plot of the effective self-diffusion coefficient Ds,eff of C12E5 in a C12E5/D2O mixture of critical composition and the corresponding mutual diffusion coefficient D as function of the temperature difference ∆T ()Tc - T). Tc is the critical temperature. The D(∆T) values are taken from refs 1 and 26.

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5a taking into account the Tη,max(y) curve shown in Figure 3. The decrease of η with increasing temperatures in the range (Tp - Tη,max) is interpreted as evidence of an increase of the structural dynamics of the micellar C12E5 aggregates (see section 3.2). A qualitative comparison of the Tη,max(y) curve (for y > yc) shown in Figure 3 and the Ds,eff(y) curves in Figure 5a reveals that for a mixture with a given composition the corresponding temperature Tη,max lies the region of y in which the self-diffusion coefficient of C12E5 in the mixture starts to increase with increasing concentration. The location of the onset of the increase of Ds,eff on the temperature axis does not coincide quantitatively with Tη,max. Kato et al. assume that the increase of Ds,eff is caused by a diffusion of the surfactant molecules along the contour line of the large micellar aggregates accompanied by an exchange of surfactant molecules between adjacent micellar aggregates.24 This mechanism generates an increased structural dynamics of the micellar aggregates. It shows up also in the decrease of the viscosity with increasing temperature in the temperature range (Tη,max < T < TP). This picture suggests that both phenomena are correlated: the onset of a decrease of the viscosity above the composition dependent temperature Tη,max and the temperature dependent composition at which the self-diffusion coefficient starts to increase. Measurements of the composition and temperature dependence of the viscosity of C16E7/D2O and C14E6/D2O mixtures for which results of the composition and temperature dependence of the self-diffusion coefficient are available in the literature could broaden the experimental basis for the interpretation just suggested.24,25 4. Conclusions

Figure 5. Composition and temperature dependence of the effective self-diffusion coefficient Ds,eff of C12E5 in a C12E5/D2O mixture. The data shown in Figure 5a are extracted from the larger set of Ds,eff(T) data obtained with mixtures of constant compositions shown in Figure 5b.

reported in the literature for the system C12E5/D2O (ref 17 and Figure 3 in ref 20) and other CiEj/D2O systems (Figure 6 in ref 24 and Figures 1-3 in ref 25). In view of eq 1, changes of Ds,eff with temperature and composition could reflect changes of the size of the aggregates and their size distribution. Plots of self-diffusion coefficients determined in this study as function of temperature at constant composition are shown in Figure 5b. They reveal that the self-diffusion coefficient increases approaching the temperature of phase separation. Interpretation. An interpretation of these findings is given on the basis of Ds,eff(y) isotherms shown in Figure

A model developed by Nilsson et al.17 to discuss the temperature and composition dependence of the selfdiffusion coefficient of CiEj surfactant molecules with long hydrophobic hydrocarbon chains in CiEj/D2O mixtures is used successfully to rationalize two characteristic features of the temperature and composition dependence of the viscosity of C12E5/D2O mixtures and the self-diffusion coefficient of C12E5 in these mixtures: (1) Viscosity measurements with C12E5/D2O mixtures reveal the existence of a Tη,max(y) curve in the large aggregate region of the phase diagram above which the viscosity decreases with increasing temperature approaching the temperature of phase separation of the mixture (Tη,max, temperature at which the viscosity of a C12E5/D2O mixture of a given composition has its maximum value). (2) In the vicinity of the Tη,max(y) curve the self-diffusion coefficient of C12E5 measured at constant temperatures as function of composition starts to increase with increasing concentrations of C12E5. It is assumed that the common cause of both phenomena is an increased structural dynamics of the large micellar aggregates. The Tη,max(y) line is located in a region in which the mutual diffusion coefficient decreases with increasing temperature approaching the liquid/liquid coexistence curve. This suggests that concentration fluctuations with long range correlation contribute to an increase of the dynamics of the micellar structures. Acknowledgment. We thank Professor J. Kro¨ger (Fakulta¨t fu¨r Physik und Geowissenschaften, Universita¨t Leipzig) for the possibility to measure the self-diffusion coefficients. The help of Dr. Appel (now at Exxon Research and Engineering Co., Annandale, NJ) is gratefully acknowledged. LA970344B