Ultrasound velocimetry in a shear-thickening wormlike micellar solution: Evidence for the coexistence of radial and vorticity shear bands

We carried out pointwise local velocity measurements on 40 mM cetylpyridinium chloride-sodium salicylate (CPyCl-NaSal) wormlike micellar solution using high-frequency ultrasound velocimetry in a Couette shear cell. The studied wormlike solution exhibits Newtonian, shear-thinning and shear-thickening rheological behavior in a stress-controlled environment. Previous rheology, flow visualization and small-angle light/neutron scattering experiments in the shear-thickening regime of this system showed the presence of stress-driven alternating transparent and turbid rings or vorticity bands along the axis of the Couette geometry. Through local velocity measurements we observe a homogeneous flow inside the 1mm gap of the Couette cell in the shear-thinning (stress-plateau) region. Only when the solution is sheared beyond the critical shear stress (shear-thickening regime) in a stress-controlled experiment, we observe inhomogeneous flow characterized by radial or velocity gradient shear bands with a highly sheared band near the rotor and a weakly sheared band near the stator of the Couette geometry. Furthermore, fast measurements performed in the shear-thickening regime to capture the temporal evolution of local velocities indicate coexistence of both radial and vorticity shear bands. However the same measurements carried out in shear rate controlled mode of the rheometer do not show such rheological complexity.     

The effect of stiffness in wormlike micelles

The effect of stiffness in a 2D living polymer system is investigated by Monte-Carlo simulation in a canonical ensemble. As the flexibility decreases, the mean chain contour length decreases and goes through a local maximum. The mean end to end square distance shows a non-monotonic behaviour due to the coil-to-rod transition and the decrease in chain contour length. Near the maximum of chain ordering in the bulk, the chain length distribution adapts itself to increase the configurational entropy. With the parameters used in this simulation, it seems that the effect of the stiffness for high stiffness is to decrease as in the isotropic case, since the ordering decreases again. Received: 16 September 1997 / Revised: 27 June 1998 / Accepted: 29 June 1998     

Velocity profiles in shear-banding wormlike micelles

Using dynamic light scattering in heterodyne mode, we measure velocity profiles in a much studied system of wormlike micelles (CPCl/NaSal) known to exhibit both shear-banding and stress plateau behavior. Our data provide evidence for the simplest shear-banding scenario, according to which the effective viscosity drop in the system is due to the nucleation and growth of a highly sheared band in the gap, whose thickness linearly increases with the imposed shear rate. We discuss various details of the velocity profiles in all the regions of the flow curve and emphasize the complex, non-Newtonian nature of the flow in the highly sheared band.     

Spatiotemporal dynamics of wormlike micelles under shear

Velocity profiles in a wormlike micelle solution (cetyl trimethyl ammonium bromide in D2O) are recorded using ultrasound every 2 s during a startup experiment into the shear-banding regime. The stress relaxation occurs over more than 6 h and corresponds to the very slow nucleation and growth of the high-shear band. Moreover, oscillations of the interface position with a period of about 50 s are observed during the growth process. Strong wall slip, metastable states, and transient nucleation of three-band flows are also reported and discussed in light of previous experiments and theoretical models.     

Linear and nonlinear rheology of wormlike micelles

Several surfactant molecules self-assemble in solution to form long, cylindrical, flexible wormlike micelles. These micelles can be entangled with each other leading to viscoelastic phases. The rheological properties of such phases are very interesting and have been the subject of a large number of experimental and theoretical studies in recent years. We shall report our recent work on the macrorheology, microrheology and nonlinear flow behaviour of dilute aqueous solutions of a surfactant CTAT (Cetyltrimethylammonium Tosilate). This system forms elongated micelles and exhibits strong viscoelasticity at low concentrations (∼0.9 wt%) without the addition of electrolytes. Microrheology measurements of G(θ) have been done using diffusing wave spectroscopy which will be compared with the conventional frequency sweep measurements done using a cone and plate rheometer. The second part of the paper deals with the nonlinear rheology where the measured shear stress σ is a nonmonotonic function of the shear rate . In stress-controlled experiments, the shear stress shows a plateau for larger than some critical strain rate, similar to the earlier reports on CPyCl/NaSal system. Cates et al have proposed that the plateau is a signature of mechanical instability in the form of shear bands. We have carried out extensive experiments under controlled strain rate conditions, to study the time-dependence of shear stress. The measured time series of shear stress has been analysed in terms of correlation integral and Lyapunov exponent to show unambiguously that the behaviour is typical of low dimensional dynamical systems.     

Shear thinning and orientational ordering of wormlike micelles

Shear thinning and orientation of cylindrical surfactant and block copolymer micelles was investigated by rheo-SANS (small-angle neutron scattering) experiments. Shear thinning and orientation occur for shear rates (.)gamma tau(dis)>1, where tau(dis) is the disentanglement time of the micelles. Micelles align in the flow direction with an orientational distribution that can be well described by an Onsager-type distribution function. Over nearly the whole range of concentrations and for all cylindrical micelles investigated, the shear viscosity eta follows a simple eta approximately e(-aS) behavior as a function of the orientational order parameter S with the same prefactor a.     

Intermittency route to rheochaos in wormlike micelles with flow-concentration coupling

We show experimentally that the route to chaos is via intermittency in a shear-thinning wormlike micellar system of cetyltrimethylammonium tosylate, where the strength of flow-concentration coupling is tuned by the addition of salt sodium chloride. A Poincaré first return map of the time series and the probability distribution of laminar lengths between burst events shows that our data is consistent with type-II intermittency. The coupling of flow to concentration fluctuations is evidenced by the "butterfly" intensity pattern in small angle light scattering (SALS) measurements performed simultaneously with the rheological measurements. The scattered depolarized intensity in SALS, sensitive to orientational order fluctuations, shows the same time dependence (like intermittency) as that of shear stress.     

Influence of system size and solvent flow on the distribution of wormlike micelles in a contraction-expansion geometry

Viscoelastic wormlike micelles are formed by surfactants assembling into elongated cylindrical structures. These structures respond to flow by aligning, breaking and reforming. Their response to the complex flow fields encountered in porous media is particularly rich. Here we use a realistic mesoscopic Brownian Dynamics model to investigate the flow of a viscoelastic surfactant (VES) fluid through individual pores idealized as a step expansion-contraction of size around one micron. In a previous study, we assumed the flow field to be Newtonian. Here we extend the work to include the non-Newtonian flow field previously obtained by experiment. The size of the simulations is also increased so that the pore is much larger than the radius of gyration of the micelles. For the non-Newtonian flow field at the higher flow rates in relatively large pores, the density of the micelles becomes markedly non-uniform. In this case, we find that the density in the large, slowly moving entry corner regions is substantially increased.     

Synergistic effects in mixed wormlike micelles of dimeric and single-chain cationic surfactants at high ionic strength

The mixed micellization between the cationic gemini surfactant [ C₁₂H₂₅( CH₃)₂N⁺( C₂H₄) N⁺( CH₃)₂ C₁₂H₂₅•2Br^-] and the cationic cetyltrimethylammonium bromide (CTAB) in 150 mM KBr solutions has been investigated. The variation of the cmc of the mixtures, measured by surface tension experiments, with composition revealed synergism in micelle formation. T-Jump and light scattering experiments performed in the vicinity of the crossover volume fraction showed the existence of two micellar populations, possibly linear and toroidal micelles. Rheological and dynamic light scattering experiments allowed to fully characterize the linear viscoelasticity of the mixtures. These measurements revealed synergistic gains in viscoelastic properties with a maximum of the stress-relaxation time around the equimolar composition. These effects are ascribed to a progressive intermicellar crosslinking resulting from a continuous increase of the end-cap energy with the 12-2-12 content in the mixture. Received: 18 November 2002 / Accepted: 8 April 2003 / Published online: 27 May 2003 RID="a" ID="a"e-mail: candau@fresnel.u-strasbg.fr     

Spontaneous formation of complex micelles from a homogeneous solution

We present an extensive computer simulation study of structure formation in amphiphilic block copolymer solutions after a quench from a homogeneous state. By using a mesoscopic field-based simulation method, we are able to access time scales in the range of a second. A "phase diagram" of final structures is mapped out as a function of the concentration and solvent philicity of the copolymers. A rich spectrum of structures is observed, ranging from spherical and rodlike micelles and vesicles to toroidal and net-cage micelles. The dynamical pathways leading to these structures are analyzed in detail, and possible ways to control the structures are discussed briefly.     

Brownian motion of particles embedded in a solution of giant micelles

We have measured the mean-square displacement of colloidal particles embedded in a semi-dilute solution of worm-like micelles, using diffusing wave spectroscopy. This allowed us to describe their rheological properties over a very wide time range. At very short times, the particles diffuse freely in the solvent, and then, they experience the characteristic relaxation times of the living chains. We deduced directly, from the mean-square displacement of the particles, the mechanical properties of the micellar solution, not only in the high-frequency regime, but also in the low-frequency range, in which we compared our results with direct mechanical measurements, and found good agreement. Received 22 March 2002 and Received in final form 5 June 2002     

Structure and rheology of concentrated wormlike micelles [4]at the shear-induced isotropic-to-nematic transition

We have investigated the simple shear flow behavior of wormlike micelles using small-angle neutron scattering and mechanical measurements. Ternary surfactant solutions made of cetylpyridinium chloride, hexanol and brine (0.2 M NaCl) and hereafter abbreviated as CPCl-Hex were studied in the concentrated regime, . In a preliminary report (Berret et al. [#!ref16!#]), the discontinuity of slope observed in the shear stress versus shear rate curve was interpreted in terms of first-order phase transition between an isotropic state and a shear-induced nematic state ( transition). At the transition rate, , the solution exhibits a macroscopic phase separation into viscous and fluid layers (inhomogeneous shear flow). Above a second characteristic shear rate, the flow becomes homogeneous again, the sheared solution being nematic only. The neutron patterns obtained in the two-state inhomogeneous region have been re-examined. Based on a consistent analysis of both orientational and translational degrees of freedom related to the wormlike micelles, we emphasize new features for the transition. In the present paper, the shear rate variations of the relative proportions of each phase in the two-state region, as well as the viscosity ratio between isotropic and nematic phases are derived. We demonstrate in addition that slightly above the transition rate, the shear induced nematic phase is already strongly oriented, with an order parameter P ₂ = 0.65. The orientational state is that of a nematic flow-oriented monodomain. Finally, from the locations of the neutron scattering maxima for each isotropic and nematic contributions, we evaluate the concentrations for each phase and and derived a dynamical phase diagram of CPCl-Hex, in terms of the stress versus and . According to the classification by Schmitt et al. [#!ref22!#], the transition observed in CPCl-Hex micellar solutions could result from a positive flow-concentration coupling, in agreement with the observed monotonically increasing shear stress in the two-phase region. Received: 16 February 1998 / Revised: 18 February 1998 / Accepted: 24 May 1998     

Adsorption of a semiflexible wormlike chain

Adsorption of ideal polymers with stiff backbone onto a flat surface is considered theoretically. Both scaling approach and quantitative theory are developed. We predict a self-similar monomer concentration profile c(x) ∼ x ^-4/3 near the surface (when the distance to the surface x is much smaller than the chain persistence length l /2). The typical conformation of a weakly adsorbed chain can be viewed as a sequence of alternating flat (2-dimensional) trains of wormlike short loops (flat blobs) and coil-like (3-dimensional) loops forming a triple-layer structure: contact layer (x < Δ) of adsorbed fragments virtually laid on the surface, proximal layer (Δ < x < l) of flat blobs, and more dilute distal corona layer (x > l). Here Δ defines the range of monomer/surface attraction, Δ ≪ l. The adsorption transition is continuous. However, its relative width is small (T ^* is the adsorption temperature, ΔT is the relevant temperature interval): ∼ , i.e. a discontinuous transition in the limit Δ/l↦ 0. Received 10 October 2002 and Received in final form 22 November 2002 RID="a" ID="a"Permanent address: Physics Department, Moscow State University, Moscow 119992, Russia. e-mail: semenov@polly.phys.msu.ru     

Metastable tight knots in a wormlike polymer

Based on an estimate of the knot entropy of a wormlike chain we predict that the interplay of bending energy and confinement entropy will result in a compact metastable configuration of the knot that will diffuse, without spreading, along the contour of the semiflexible polymer until it reaches one of the chain ends. Our estimate of the size of the knot as a function of its topological invariant (ideal aspect ratio) agrees with recent experimental results of knotted dsDNA. Further experimental tests of our ideas are proposed.     

Instabilities in wormlike micelle systems

Shear-banding is ubiquitous in complex fluids. It is related to the organization of the flow into macroscopic bands bearing different viscosities and local shear rates and stacked along the velocity gradient direction. This flow-induced transition towards a heterogeneous flow state has been reported in a variety of systems, including wormlike micellar solutions, telechelic polymers, emulsions, clay suspensions, colloidal gels, star polymers, granular materials, or foams. In the past twenty years, shear-banding flows have been probed by various techniques, such as rheometry, velocimetry and flow birefringence. In wormlike micelle solutions, many of the data collected exhibit unexplained spatio-temporal fluctuations. Different candidates have been identified, the main ones being wall slip, interfacial instability between bands or bulk instability of one of the bands. In this review, we present experimental evidence for a purely elastic instability of the high shear rate band as the main origin for fluctuating shear-banding flows.      

Coherent quadrupole states of three interacting bands and the solution of a Bohr-Mottelson Hamiltonian

The projected functions of the coherent state model (CSM) describing the ground, gamma and beta bands are studied in the intrinsic frame of reference. Several symmetry relations for the intrinsic functions are obtained. Analytical expressions for the matrix elements of the collective operatorβ ^m+n cos ^m γsin ⁿ γ are derived. Important selection rules are established for them. The probability distribution for the deformationsβ andγ are studied and compared to those corresponding to the solution of a microscopically determined Bohr-Mottelson Hamiltonian.     

Aromatic micelles: toward a third-generation of micelles

Micelles are useful and widely applied molecular assemblies, formed from amphiphilic molecules, in water. The majority of amphiphiles possess an alkyl chain as the hydrophobic part. Amphiphiles bearing hydrophilic and hydrophobic polymer chains generate so-called polymeric micelles in water. This review focuses on the recent progress of “aromatic micelles”, formed from bent polyaromatic/aromatic amphiphiles, for the development of third-generation micelles. Thanks to multiple host-guest interactions, e.g., the hydrophobic effect and π-π/CH-π interactions, the present micelles display wide-ranging uptake abilities toward various hydrophobic compounds in water. In addition to such host functions, new stimuli-responsive aromatic micelles with pH, light, and redox switches, aromatic oligomer micelles, saccharide-coated aromatic micelles, and related cycloalkane-based micelles were recently developed by our group.