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Articles Structural, Kinetics, and Rheological Properties of Low Ionic Strength Dilute Solutions of a Dimeric (Gemini) Surfactant Cl. Oelschlaeger,† G. Waton,† S. J. Candau,*,† and M. E. Cates‡ Laboratoire de Dynamique des Fluides Complexes, UMR No. 7506, Universite´ Louis Pasteur, CNRS, 4 rue Blaise Pascal, 67070 Strasbourg Cedex, France, and Department of Physics and Astronomy, The University of Edinburgh, James Clerk Maxwell Building, The King’s Building, Mayfield Road, Edinburgh EH9 3JZ, United Kingdom Received February 21, 2002. In Final Form: June 6, 2002 The structural and dynamical properties of low ionic strength micellar solutions of a cationic gemini surfactant have been investigated by means of light scattering, T-jump, and rheological experiments. In the dilute regime, below the entanglement concentration, the surfactant molecules self-assemble into polydisperse micellar aggregates with size distribution extending up to ∼100 nm. Rheology and T-jump experiments show that the dynamical processes are speeded-up by the addition of salt. In particular the critical shear rate above which a shear thickening occurs increases with the salt content. Also the characteristic time for chain distribution equilibration after a thermal perturbation increases upon removal of salt to reach very large values in the salt-free case. This result supports the speculation given previously that the reversible scission could explain the strong dependence of the shear thickening behavior on thermal cycling.
I. Introduction Under appropriate conditions, ionic surfactants in solutions self-assemble to form long cylindrical micelles.1,2 At low ionic strength and in the dilute regime, that is at concentrations below the overlap concentration C*, the solutions often exhibit a shear thickening above a critical shear rate γ˘ c.3-18 Recent studies have shown that the † ‡
Universite´ Louis Pasteur. The University of Edinburgh.
(1) Cates, M. E.; Candau, S. J. J. Phys.: Condens. Mater. 1990, 2, 6869. (2) Rehage, H.; Hoffmann, H. Mol. Phys. 1991, 74, 933. (3) Hoffmann, H.; Platz, G.; Rehage, H.; Schorr, W.; Ulbricht, W. Ber. Bunsen-Ges. Phys. Chem. 1981, 85, 255-266. (4) Rehage, H.; Hoffmann, H. Rheol. Acta 1982, 21, 561-563. (5) Hoffmann, H.; Lo¨bl, M.; Rehage, H.; Wunderlich, I. Tenside Deterg. 1985, 22, 290. (6) Ohlendorf, D.; Interthal, W.; Hoffmann, H. Rheol. Acta 1986, 25, 468. (7) Wunderlich, I.; Hoffmann, H.; Rehage, H. Rheol. Acta 1987, 26, 532. (8) Hofmann, S.; Rauscher, A.; Hoffmann, H. Ber. Bunsen-Ges. Phys. Chem. 1991, 95, 2. (9) Berwersdorff, H.-W.; Frings, B.; Lindner, P.; Oberthu¨r, R. C. Rheol. Acta 1986, 25. (10) Lindner, P.; Bewersdorff, H.-W.; Heen, R.; Sittart, P.; Thiel, H.; Langowski, J.; Oberthu¨r, R. C. Prog. Colloid Polym. Sci. 1990, 81, 107112. (11) Oda, R.; Panizza, P.; Schmutz, M.; Lequeux, F. Langmuir 1997, 13, 6407-6412. (12) Liu, C. H.; Pine, D. J. J. Phys. Rev. Lett. 1996, 77, 2121-2124. (13) Boltenhagen, P.; Hu, Y.; Matthys, E. F.; Pine, D. J. Phys. Rev. Lett. 1997, 79, 2359-2362. (14) Berret, J.-F.; Gamez-Corrales, R.; Oberdisse, J.; Walker, L. M.; Lindner, P. Europhys. Lett. 1998, 41, 677-682. (15) Keller, S. L.; Boltenhagen, P.; Pine, D. J.; Zasadzinski, J. A. Phys. Rev. Lett. 1998, 80, 2725-2728. (16) Gamez-Corrales, R.; Berret, J.-F.; Walker, L. M.; Oberdisse, J. Langmuir 1999, 15, 6755. (17) Berret, J.-F.; Gamez-Corrales, R.; Lerouge, S.; Decruppe, J.-P. Eur. Phys. J. E 2000, 2, 343.
structural recovery following a mechanical or thermal perturbations was very slow (hours).17,19-21 The experimental features commonly observed could not be accounted for by the early theoretical models based on shear induced alignment causing end-to-end fusion of small rodlike micelles.8,22,23 More recent models involve as a prerequisite for the shear thickening that large aggregates (micellar rings24 or metastable bundles of linear micelles25) are present in the quiescent state of the solutions. Recent experiments on low ionic strength solutions of a fluorocarbon surfactant revealed the presence in the concentration range cmc e C e C* of micellar aggregates with size of the order of 100 nm.21 In the same concentration range, the solutions exhibit a very large shear thickening (up to factor 50) and a very slow recovery (hours) after the cessation of the shear or in a thermal cycling. The schematic model of ref 24 based on the existence of interlinked rings in the quiescent state assumes that the critical shear rate γ˘ c is of the order of the local delinking time τlink. The steady state at γ > γ˘ c would then comprise a mixture of rings and chains. The structural memory persisting for very long time after a perturbation was explained by assuming that the slow relaxation results (18) Hu, Y. T.; Matthys, E. F. J. Rheol. 1997, 41, 151. (19) Oda, R.; Weber, V.; Lindner, P.; Pine, D. J.; Mendes, E.; Schosseler, F. Langmuir 2000, 16, 4859. (20) Bellour, M.; Knaebel, A.; Munch, J. P.; Candau, S. J. Eur. Phys. J. E 2000, 3, 343. (21) Oelschlaeger, C.; Waton, G.; Candau, S. J.; Cates, M. E. Langmuir 2002, 18, 3076-3085. (22) Cates, M. E.; Turner, M. S. Europhys. Lett. 1990, 7, 681. (23) Wang, S. Q.; Gelbart, W.; Ben-Shaul, A. J. Phys. Chem. 1990, 94, 2219. (24) Cates, M. E.; Candau, S. J. Europhys. Lett. 2001, 55, 887-893. (25) Barentin, C.; Liu, A. J. Europhys. Lett., in press.
10.1021/la025645m CCC: $22.00 © 2002 American Chemical Society Published on Web 09/04/2002
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from a change in the ring/chain balance and is controlled by the reversible scission kinetics. Experimental studies of the shear thickening and related effects in solutions containing salt are rather scarce.7,21 It is commonly admitted that the addition of salt tends to suppress the shear thickening. In fact, early flow birefringence results7 and recent rheological data8 show that upon increasing the salt content, γ˘ c increases and the amplitude of the shear thickening decreases. In the picture of ref 24 the gradual suppression of the shearthickening transition is proposed to occur though the micellar kinetics and more specifically to arise from a decrease of the reversible scission characteristic time upon the addition of salt. Information on the micellar kinetics are provided by T-jump experiments.26 Within simple kinetic models, the latter technique only detects changes in the chain length distribution brought about by reversible scission reactions (in which a chain splits in two at an internal point or two chains join end to end).1,26 Other reaction schemes such as bond-interchange and endinterchange, preserve the number of chains in the system and, to a good approximation, are invisible in smallamplitude T-jump.1,26 This remains true when rings are present as well as chains, and in the model of ref 24 a slow scission process (with a faster interchange) was proposed as the origin of a slow relaxation mode in which both the latency time and the amplitude of the shear thickening effect could evolve very slowly after pretreatment (shear or thermal). Attempts to study the micellar kinetics of the previously studied fluorocarbon surfactant21 failed, presumably because the relaxation times were much larger than the experimental window (300 µs-30 s). We have then investigated another surfactant, namely the gemini ethanediyl-1,2-bis(dodecyldimethylammonium bromide) hereafter called 12-2-12. This surfactant is known to form in salt-free solutions wormlike micelles and to give quite large shear thickening effects.2 It has also, like the fluorocarbon surfactant previously studied, a rather large end-cap energy Ec, due to its dimeric structure. In the second part of the paper we report on a dynamic light scattering (DLS) and static light scattering (SLS) experiments that allow us to investigate the structural properties in solutions containing 20 mM NaF. The observed behavior is found qualitatively the same as that obtained for the fluorocarbon surfactant. In the dilute range the autocorrelation function is bimodal. From the slow mode, the existence of very long aggregates (>100 nm) is inferred. We have then investigated, by means of T-jump experiments, the kinetics properties of the micellar solutions with salt concentration CS ranging from 2 to 30 mM NaF and in a temperature range 25 °C e T e 50 °C. The results that show a slowing of the micellar kinetics upon decreasing salt content are presented in the third part of the paper. In the fourth part of the paper we present the results of a rheological study. We present in particular a comparison of the variations with salt content of the kinetics and rheological characteristic times. II. Structural Properties II.1. Experimental Techniques. a. Static Light Scattering. For light scattering experiments, all solutions are filtered through a 0.22 µm Millipore filter into the cylindrical scattering cells. Static light scattering (SLS) and dynamic light scattering (DLS) experiments are performed on a standard (26) Turner, M. S.; Cates, M. E. J. Phys. Fr. 1990, 51, 307.
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setup27 by means of a spectrometer equipped with an argon ion laser (Spectra Physics model 2020) operating at λ ) 488 nm, an ALV-5000 correlator (ALV, Langen-Germany Instruments), a computer-controlled and stepping-motordriven variable-angle detection system, and a temperature-controlled sample cell. The temperature was 25 ( 0.1 °C unless otherwise noted. The scattering spectrum was measured through a band-pass filter (488 nm) and a pinhole (200 µm for the static experiments and 100 µm for the dynamic experiments) with a photomultiplier tube (ALV). In the SLS experiments, the excess of scattered intensity I(q) was measured with respect to the solvent, where the magnitude of the scattered wave vector q is given by
q)
θ 4πn sin λ 2
(1)
In eq 1, n is the refractive index of the solvent (1.34 for water at 25 °C), λ is the wavelength of light in the vacuum, and θ is the scattering angle. In our experiments, the scattering angle θ was varied between 20 and 120°, which corresponds to scattering wave vectors q in the range from to 6 × 10-3 to 2.97 × 10-2 nm-1. The absolute scattering intensities I(q) (i.e., the excess Rayleigh ratios) were deduced by using a toluene sample reference for which the excess Rayleigh ratio is known. b. Dynamic Light Scattering. In the dynamic light scattering experiments (DLS), the normalized time autocorrelation function g(2)(q,t) of the scattered intensity is measured.
g(2)(q,t) )
〈I(q,0)I(q,t)〉 〈I(q,0)〉2
(2)
The latter can be expressed in terms of the field autocorrelation function or equivalently in terms of the autocorrelation function of the concentration fluctuations g(1)(q,t) through
g(2)(q,t) ) A + β|g(1)(q,t)|2
(3)
where A is the baseline and β is the coherence factor which in our experiments is equal to 0.7-0.9. The normalized dynamical correlation function g(1)(q,t) of polymer concentration fluctuations is defined as
g(1)(q,t) )
〈δc(q,0)δc(q,t)〉 〈δc(q,0)2〉
(4)
where δc(q,t) and δc(q,0) represents fluctuations of polymer concentration at time t and zero, repectively. In the case of a diffusive process, g(1)(q,t) is given by
g(1)(q,t) ) exp(-Dq2t)
(5)
where D is the diffusion coefficient. The apparent hydrodynamic radius RH of the diffusive particles is given by
kBT RH ) limqf0 6πη0RH
(6)
where η0 is the viscosity of the solvent. II.2. Results. The shape of the normalized intensity correlation function g(2)(q,t) depends on the surfactant concentration. At high dilution, for C e 0.4 × 10-2 g cm-3 the correlation function is bimodal as illustrated by Figure 1a. The amplitude and the fast diffusion coefficient Dfast
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Figure 2. Variation of the inverse scattered intensity versus q2. The linear fits provide estimates of ξ (12 nm for C ) 10-2 g cm-3 and 10 nm for C ) 2 × 10-2 g cm-3 ; CS ) 20 mM NaF; T ) 25 °C).
predominant contribution. Figure 3 shows the concentration dependences of RH fast, ξ, and I(q ) 0). The two latter quantities were determined in the regime where the autocorrelation function is unimodal. It can be seen that the three quantities exhibit a maximum at a concentration of the order of 10-2 g cm-3. This concentration can be considered at the overlap concentrations C* of the system. The obtained value of C* agrees with that obtained from viscosity experiments. III. Kinetic Properties
Figure 1. Dynamical structure factors at various angles (given in the figures) for solutions with Cs ) 20 mM NaF, T ) 25 °C, C ) 4 × 10-3 g cm-3 (dilute regime), and C ) 10-2 g cm-3 (in the vicinity of C*). In the inserts are given the results of the Contin fits at θ ) 60°.
) (τfastq2)-1 (τfast: short relaxation time) associated with the fast mode are independent of q within the experimental accuracy. The slow mode is characterized by a slow diffusion coefficient Dslow that increases with q whereas the amplitude strongly decreases. A similar behavior was observed in dilute salt-free solutions of 12-2-12 in D2O.28 At concentrations C g 0.6 × 10-2 g cm-3 the autocorrelation function of the scattered intensity is nearly a single exponential as shown in Figure 1b. The corresponding diffusion coefficient is independent of q and is of the same order of magnitude as Dfast obtained at lower concentrations. In that range of concentrations, the scattered intensity I(q) can be fitted with an Ornstein-Zernicke function I(q) ) I(o)/(1 + q2ξ2). From the representation given in Figure 2 I(q-1) ) f(q) one obtains a linear part from which one extracts a correlation length ξ (ξ ) 12.5 nm at C ) 10-2 g cm-3 and ξ ) 10 nm at C ) 2 × 10-2 g cm-3). The deviations observed at very low q might indicate the presence of few large particles but are more likely due to experimental imperfections. Also the values of ξ are at the very lower limit of the experimental detection. At low concentration where the autocorrelation function is bimodal the analysis of the intensity data is rendered difficult by the fact that neither of the two modes has a (27) Esquenet, C.; Buhler, E. Macromolecules 2001, 34, 5287-5294. (28) Weber, V. Thesis University Louis Pasteur, Strasbourg, France, 2001.
III.1. T-Jump Device. The T-jump device has been described elsewhere.29 For T-jump measurements the surfactant solutions were filtered through a 0.22 µm Millipore filter. The T-jump is produced by Joule heating by means of discharge of a capacitor. The rise time of the T-jump is 1 µs, and its amplitude, calculated from the values of the stored electrical energy and the heat capacity of the sample, can be varied between 0.1 and 2 °C. The scattering cell is illuminated by an intense light beam obtained from a powerful (150 W) mercury xenon lamp in conjunction with large aperture condenser (Oriel Aspherab). Several interference filters allow for the selection of the following wavelengths: 313, 365, 405, 436, 546, and 577 nm. A fraction of the incident light beam is sent to photodiode, which thus delivers a reference signal. An electronic device uses this signal to compensate lamp power or arc position stabilities. Two photomultipliers (PM) are used for the detection of the light scattered at 90 and 20° angles. A photodiode, placed on the optical axis, measures the transmitted light. The variation of scattered intensity I under T-jump is related to the variation of the excess Rayleigh ratio ∆R through
1 δ∆R 1 δI ) I δT ∆R δT
(7)
The PM signal is digitalized and acquired using a pseudologarithmic time-base in which the sampling time is periodically increased. For each measurement, several relaxation functions are summed up to get an averaged curve. This results in a further improvement of the signal/ noise ratio. After the T-jump, the temperature in the cell (29) Faetibold, E.; Waton, G. Langmuir 1995, 11, 1972.
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Figure 4. T-jump response for a solution with C ) 8 × 10-3 g cm-3 (CS ) 30 mM; T ) 20 °C). The dashed area at times e300 µs corresponds to the heating period. The signal between 300 µs and 30 s is the useful part of the signal. The dashed area at t g 10 s corresponds to the return to the thermal equilibrium. The experimental trace is indistinguishable from the singleexponential fit. The dotted line represents the time dependence of the excess of temperature.
Figure 3. Concentration dependence of (a) RH and ξ and (b) Iqf0 (in arbitrary units) (CS ) 20 mM; T ) 25 °C).
decreases slowly, and it may be considered as constant during 5s. The temperature in the cell is controlled to 0.1 °C. A typical T-jump response is given in Figure 4. Three time domains can be distinguished in the signal. At very short times (t < 300 µs), during the heating period, one observes an overshoot of the scattered intensity due to the presence of a very high current variation (peak ∼ 200 A) which produces a high magnetic field on the detection setup. In the second time domain the temperature is constant; this is the useful part of the signal. The relaxation curve shows an exponential-like decay of the scattered light intensity with time. The decrease is well described by a monoexponentiel function with a characteristic relaxation time τT-j. At long time (t >10 s) the variation of scattered intensity corresponds to the return to the initial temperature. III.2. Results. In the range of surfactant concentration, salt concentration, and temperature investigated, the T-jump signal could be fitted with a single-exponential decay. The concentration dependence of τT-j, reported in Figure 5, shows a shallow minimum in the vicinity of C*. The temperature dependencies of the relaxation time τT-j for a solution with concentration 8 × 10-3 g cm-3 at various salt contents are plotted in Figure 6. As in the previously investigated systems,29,30 one observes a large decrease of τT-j upon increasing temperature. At low salt content and low temperature, the relaxation is too slow to be measured experimentally. To get an estimate of τT-j in this region, we performed a quench experiment. Solutions with concentration C ) 8 × 10-3 g cm-3, one salt-free and the (30) Candau, S. J.; Merikhi, F.; Waton, G.; Lemare´chal, P. J. Phys. Fr. 1990, 51, 977.
Figure 5. Concentration dependence of τT-j (CS ) 20 mM NaF; T ) 20 °C).
Figure 6. Variation of τT-j with 103/T for solutions with CS ) 8 × 10-3 g cm-3. The salt concentrations are indicated in the figure.
other with CS ) 30 mM NaF, were stored for 2 days at 50 °C and then quenched at 20 °C. The intensity scattered at 90° was then recorded as a function of time. For the system containing salt, it takes about 0.5 h for the intensity to reach a plateau (Figure 7). This corresponds roughly to the time necessary for the sample to recover its new temperature. This was checked by separate experiments on other micellar systems in the presence of an excess of
Dilute Solutions of a Dimeric (Gemini) Surfactant
Figure 7. Variations of the intensity of scattered light normalized by its value at equilibrium as a function of time for two solutions after variation of temperature from 50 to 20 °C (θ ) 90°; C ) 8 × 10-3 g cm-3): (O) in the presence of 30 mM NaF’ (0) salt-free solution. The solid lines are guides for the eye.
Figure 8. Variations of τT-j and γ˘ c with salt content for solutions with C ) 8 × 10-3 g cm-3 and T ) 20 °C. The data with a horizontal arrow correspond to salt-free solutions. The bar is the result obtained in a quench experiment.
salt, which did not exhibit any structural memory effects. This recovery time is quite long because there is not stirring in the T-jump 1 cm side square cell, in contact with air. Classical T-jump experiments performed during this recovery period show that the (nonequilibrium) relaxation time evolves continuously from its value at 50 °C to its value at 20 °C. For the salt-free system, the relaxation is much slower than the thermal equilibration process, since the plateau value is reached only after ∼3 h. This value agrees with the extrapolation of τT-j at 20 °C at low ionic strength as could be seen in Figure 6. The variations of τT-j with salt concentration at T ) 20 °C are reported in Figure 8. The result of this quench measurement (which could be viewed as a very large amplitude T-jump) is broadly consistent with that extrapolated from conventional (small amplitude) T-jump at higher salt levels. IV. Rheological Properties IV.1. Experimental Techniques. The rheological measurements were performed with two different devices: (1) A HAAKE RS 100 fluid spectrometer using coneplate geometry was employed. The cell has a gap of 0.052 mm, an angle of 1°, and a diameter of 60 mm. (Experiments were carried out with imposed stress.) (2) A low-shear 30 viscometer using Couette geometry was also employed. The Couette cell has a gap of 0.5 mm
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Figure 9. Variation of the apparent viscosity with time for a salt-free solution with C ) 8 × 10-3 g cm-3, T ) 20 °C, and γ˘ ) 80 s-1: (9) solutions at equilibrium; (4) sample stored few days at 50 °C and then 30 min in the cell at T ) 20 °C; (O) sample presheared at γ˘ ) 80 s-1 and started after a 5 min lapse of time.
Figure 10. Variations of the apparent viscosity with the shear rate for solutions with C ) 8 × 10-3 g cm-3. The salt concentrations are indicated in the figure. Inset: Variation of the apparent viscosity with time at γ˘ ) 2γ˘ c.
and a height of 20 mm. (Experiments were carried out with imposed strain.) For both experiments special care was taken to avoid water evaporation. IV.2. Results. Typical rheological responses of a saltfree solution at C ) 8 × 10-3 g cm-3 to a strain, γ˘ > γ˘ c are shown in Figure 9. The behavior is the same as that previously reported.21 One observes an abrupt jump of the viscosity following a latency time TR. The latter is found to be much larger if the sample has been held at higher temperature for a long period beforehand. In the example of Figure 9 the sample has been stored for few days at 50 °C and then quenched at 20 °C. The shear is restarted after 30 min, thus allowing the sample to recover uniformly to its new temperature. However, the latency time is reduced if the sample has been presheared (inset Figure 10). In the present case, the recovery period between the end of preshearing and the start of the main test is 5 min. This shows that a very long time scale controls the disappearance of structural memory after the cessation of the shear or following a temperature change. For systems containing moderate amounts of salt (CS g 15 mM NaF) no detectable structural memory effects can be detected within the experimental accuracy. Also the addition of salt increases drastically the critical shear rate as shown in Figure 10 where the variation of viscosity with γ˘ is shown for systems at C ) 8 × 10-3 g cm-3 and various salt contents. In this experiment, performed with
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a stress imposed rheometer (cone-plate geometry), the stress was varied using a ramp with steps lasting ∼100 s. This was possible because no structural memory was present in these systems containing 20 mM NaF. The variation of γ˘ c with temperature has been reported in Figure 8. The inset of Figure 10 shows the time responses of the solutions at a shear rate γ˘ ) 2γ˘ c. It can be seen that the addition of salt also increases the latency time. V. Discussion V.1. Structure of the Micellar Aggregates. The light scattering experiments show the presence of very large aggregates with sizes g100 nm in the dilute regime of micellar solutions in the quiescent state thus confirming the observation previously reported for a fluorocarbon surfactant. However, in the latter case, the signal scattered from the large aggregates was predominant in both saltfree solutions and in the presence of moderate amount of salt. In the experiments reported here, the amplitudes of the two components of the scattered field autocorrelation function are about the same. The different possible micellar structures that can account for the scattering results have been discussed in detail in ref 21. Among these structures, microgel particles made of interconnected micelles with an internal correlation length of ∼20 nm were envisioned. In the present case, the existence of such microgels can be ruled out because the slow mode of dilute solution of such microgels should be dominant. Therefore, the most likely structure consists of semiflexible linear and/or toroidal micelles with a very large (possibly bimodal) size polydispersity. CryoTEM experiments on salt-free solutions of 12-212 have been recently reported.31 At very low concentrations (C/C* e 1/7), many spheroidal micelles and a few cylindrical micelles are seen in the electron micrographs. At concentrations larger, but still in the semidilute regime (C/C* ∼ 1/2), the density of spheroı¨dal micelles decreases, whereas the length of the elongated micelles significantly increases. In the vicinity of C*, one observes a mixture of linear, branched, and toroidal micelles. These observations are compatible with the light scattering results. The presence of a gap in the micelle size distribution function which is quite surprising for systems with a large end-cap energy was explained on the basis of a spherocylindrical micelle model with swollen end-caps.32 It must however be kept in mind that the experimental protocol in a cryoTEM experiment implies a blotting in which the sample is submitted to a high shear that might perturb somewhat the structure of the system. Still, the presence of small spheroidal micelles in the dilute regime seems to be quite established for the 122-12 surfactant. V.2. Dynamical Properties. The main result of the rheological and T-jump experiments is that the addition of salt speeds-up all the dynamical processes. Figures 8 and 10 show that the T-jump relaxation time τT-j, the inverse critical shear rate γ˘ c-1, and the latency time TR all decrease upon increasing salt content. This is an important observation for the understanding of the shear thickening mechanism. For instance the earlier models based on flow-induced aggregation of small rods or their alignment-induced end-to-end fusion8,22,23 could not easily take into account this effect. On the contrary, the screening of the electrostatic interactions is expected to increase (31) Bernheim-Groswasser A.; Zana, R.; Talmon, Y. J. Phys. Chem. B 2000, 104, 4005. (32) Eriksson, J. C.; Ljunggren, S. Langmuir 1990, 6, 895.
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the micellar length and therefore to slow their rotational diffusion. It seems therefore more likely that γ˘ c, which is a micellar characteristic, independent of the gap of the shear cell,21 is directly connected with the micellar kinetics. In ref 24 it was suggested that γ˘ c was controlled by the local delinking time of interlinked rings existing in the quiescent state. Micellar rings are expected theoretically, and evidence for rings near the crossover concentrations C* has been found for some systems including the ones studied here.31,33 The T-jump data also provide useful information. By monitoring the scattered intensity after a thermal perturbation, one monitors the relaxation of the chain size distribution. Three different model schemes for the kinetics of micellar fusion and breakdown have been analyzed;1,26 these are reversible scission, end-interchange, and bondinterchange. For each scheme, there is a characteristic time τbreak for changes in micellar size. For open chains, the case of a T-jump experiment, which preserves the form of the length distribution but changes the average length, turns out to be unexpectedly simple. For reversible scission, the scattering signal is predicted to decay monoexponentially with relaxation time τT-j ) τbreak/226 whereas there is no decay at all when end-interchange or bond-interchange reactions are present.26 In a system of rings and chains, bond-interchange can create two rings out of one (or vice versa) and endinterchange can create one ring and one chain out of a chain only. However, only the reversible scission process which allows for a change in the size distribution of chains will allow complete relaxation to equilibrium after T-jump. Results of Figure 8 are consistent with the idea that the reversible scission process is considerably slowed by removal of salt and that its characteristic time can be as long as hours in the salt-free case. This gives a strong support to the speculation given in ref 24 that the reversible scission could explain the strong dependence of shear-thickening behavior on thermal cycling or preshearing. For example, a thermal pretreatment at much higher temperature will favor the formation of open chains to the expense of rings. If the system is brought back to the ambient temperature, the distribution of chains and rings will evolve slowly to equilibrium with the reversible scission characteristic time τslow. If the shearing is started after a time less than the reversible scission time, then the system remembers something from its earlier treatment which is revealed by an increased latency time (cf. Figure 9). Preshearing a sample creates, in contrast, a population where the ring/chain balance is closer to the final state attained under steady-state shear. When shear at the same rate is restarted after complete relaxation of stress, but long before the time scale τslow, for equilibration of the chain number, the latency time is reduced (cf. Figure 9). VI. Conclusion This paper outlines two important experimental observations. The first one refers to the structural properties. The light scattering results confirm that surfactant molecules with a large end-cap energy due to an enhanced hydrophobicity of the lipophilic tail self-assemble in the dilute regime into polydisperse micellar aggregates, with size distribution extending up to ∼100 nm. Beyond C* the behavior of the system is that of entangled chains. (33) In, M.; Aguerre-Chariol, O.; Zana, R. J. Phys. Chem. 1999, 103, 7747.
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The second observation concerns the dynamical properties. This is the first report to our knowledge of a speeding up of all the dynamical processes probed by rheology or T-jump experiments under addition of salt. This seems to be a consequence of the effect of salt on the micellar kinetic processes, possibly through moderation of the Coulombic barrier and through relative stabilization of the inverted curvature required for the transition state. In particular, the T-jump data show that in salt-free condition the characteristic time for chain distribution equilibration is very long (hours) which could explain as suggested in ref 24 the slow relaxation observed in response to rheological
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disturbances and temperature concentration changes. The fading away of the shear-thickening when moderate amounts of salt are added might also be linked to the speeding up of a micellar kinetic process like for instance the linking-delinking process of micellar rings.24 Acknowledgment. The authors thank M. Bellour for his help in the light scattering experiments. They are indebted to O. Gavat, who synthesized the gemini surfactant used in this study. LA025645M
