Shear-induced ordering of lamellar and gyroid structures observed in a nonionic surfactant/water system

The shear-induced ordering of lamellar and gyroid structures of a nonionic surfactant C₁₆E₇/D₂O system in a Couette shear cell ( 0.001 < < 10 s^-1, : shear rate) has been investigated by using a small angle neutron scattering technique. In the lamellar phase, the steady shear flow having > 0.01 s^-1 suppresses undulation fluctuations of lamellae (Maxwell effect). This suppression of fluctuations brings two effects; 1) shear-induced lamellae ordering toward a parallel orientation and 2) obstruction of a lamellar↦gyroid transition. It is quite interesting to note that there is a characteristic shear rate range ( 0.01 < < 0.3 s^-1), where both effects take place. We have also investigated the shear effects on the gyroid phase. Below the characteristic shear rate range, the gyroid structure keeps three-dimensional network lattice, while above the characteristic shear rate range, the gyroid structure transforms to the parallel orientation lamellae (shear-induced gyroid-lamellar transition). Thus the shear flow having the characteristic shear rate plays very important roles in shear ordering phenomena. Received 26 June 2000 and Received in final form 12 January 2001     

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     

Swelling kinetics of the onion phase

A theory is presented for the behavior of an array of multi-lamellar vesicles (the onion phase) upon addition of solvent. A unique feature of this system is the possibility to sustain pressure gradients by tension in the lamellae. Tension enables the onions to remain stable beyond the unbinding point of a flat lamellar stack. The model accounts for various concentration profiles and interfaces developing in the onion as it swells. In particular, densely packed “onion cores” are shown to appear, as observed in experiments. The formation of interfaces and onion cores may represent an unusual example of stabilization of curved interfaces in confined geometry. Received 6 September 2000     

Softening of the interactions between surfactant bilayers in a lamellar phase due to the presence of a polymer

The compressibility modulus of a lamellar phase containing a neutral polymer guest molecule was measured directly using a surface force apparatus. The system studied consisted of sodium dodecyl sulphate (SDS), pentanol, water and polyethylene glycol (PEG) . The lamellar phase was induced from a micellar phase in situ via a confinement induced isotropic to lamellar phase transition. This avoided problems resulting from the viscosity and turbidity normally characteristic of these lamellar phase samples. Increasing the amount of PEG resulted in a marked decrease in the layer compressibility modulus indicating a decrease in the repulsive forces between the lamellae. The origin of such a phenomenon is discussed in terms of different mechanisms including depletion interactions, bridging interactions and modification of the electrostatic interaction between the lamellae by the polymer. Received 2 February 1998     

Undulation instability of lamellar phases under shear: A mechanism for onion formation?

We consider a lamellar phase of bilayer membranes held between two parallel plates and subject to a steady shear. Accounting for the coupling with the shear flow of the short wavelength undulation modes that are responsible for the membrane excess area, we argue that the flow generates an effective force which acts to reduce the excess area. From the viewpoint of the macroscopic lamellar whose geometric dimensions are fixed, this force translates into an effective lateral pressure. At low shear rates this pressure is balanced by the elastic restoring forces of the lamellar. Above a critical shear rate , where d is the interlayer distance and D is the gap spacing, the lamellar buckles into a harmonic shape modulation, and we predict its wavelength and amplitude . We show that our model is isomorphic to a dilative strain, which is known to induce a similar buckling (undulation) instability. Indeed, at threshold the wavelength is and is identical in both cases. Using a non-linear analysis, we discuss how the wavelength and amplitude vary with shear rate away from the threshold. For we find and . We then focus on the coupling of the buckling modulation itself with the flow, and obtain a criterion for the limit of its stability. Motivated by experiments of D. Roux and coworkers, we assume that at this limit of stability the lamellar breakups into “onion"-like, multilamellar, vesicles. The critical shear rate for the formation of onions is predicted to scale as . The scaling with d is consistent with available experimental data. Received 15 April 1998 and Received in final form 4 March 1999     

A dynamic study of onion phases under shear flow: size changes

It has been shown that lyotropic lamellar phases under shear flow form structures corresponding to a close packed assembly of monodisperse multilamellar vesicles (onions). The size, which is fixed by the shear rate, can vary from a few microns to a tenth of a micron. In this study, we investigate for the first time the transient behaviour of size changes of onions under shear flow by means of small angle light scattering, direct microscopic observations, and conductivity measurements. We evidence two regimes: continuous and discontinuous. The nature of which (continuous or discontinuous) depends on the initial and final shear rate, and can be described by a dynamic phase diagram. Received: 14 November 1997 / Received in final form: 2 March 1998 / Accepted: 9 March 1998     

The lamellar-disorder interface: one-dimensional modulated profiles

We study interfacial behavior of a lamellar (stripe) phase coexisting with a disordered phase. Systematic analytical expansions are obtained for the interfacial profile in the vicinity of a tricritical point. They are characterized by a wide interfacial region involving a large number of lamellae. Our analytical results apply to systems with one dimensional symmetry in true thermodynamical equilibrium and are of relevance to metastable interfaces between lamellar and disordered phases in two and three dimensions. In addition, good agreement is found with numerical minimization schemes of the full free energy functional having the same one dimensional symmetry. The interfacial energy for the lamellar to disordered transition is obtained in accord with mean field scaling laws of tricritical points. Received: 28 March 1997 / Revised: 6 February 1998 / Accepted: 16 February 1998     

Non-linear rheology of lamellar liquid crystals

We measure the non-linear relation between the shear stress and shear rate in the lyotropic lamellar phase of C₁₂E₅ /water system. The measured shear thinning exponent changes with the surfactant concentration. A simple rheology theory of a lamellar or smectic phase is proposed with a prediction ∼ σ^3/2 , where is the shear rate and σ is the shear stress. We consider that the shear flow passed through the defect structure causes the main dissipation. As the defect line density varies with the shear rate, the shear thinning arises. The defect density is estimated by the dynamic balance between the production and annihilation processes. The defect production is caused by the shear-induced layer undulation instability. The annihilation occurs through the shear-induced defect collision process. Further flow visualization experiment shows that the defect texture correlates strongly with the shear thinning exponent.     

Coupling between flow and structure for a lamellar surfactant phase

The flow-structure relation of lamellar phases is studied using rheometry and cross-polarized microscopy under flow. The equilibrium phases show different defects. Low salinities lead to very viscous, "onion" phases, whereas at high salinity, a low viscosity plane lamellar phase is found. Under shear, the latter shows a sudden transition to a viscoelastic gel, with a texture and viscosity very similar to that of the onions. Gelation occurs after a certain delay time, increasing rapidly with salinity, by the nucleation of onions. This allows one to relate the delay time to the defect energy.     

Role of dislocation loops on the elastic constants of lyotropic lamellar phases

We study the role of dislocation loops defects on the elasticity of lamellar phases by investigating the variation of the lamellar elastic constants, ˉ and K, induced by the proliferation of these defects. We focus our interest on one particular lamellar phase made up of a mixture of C₁₂E₅ and DMPC in water, which is already well-characterised. This lamellar phase undergoes a second-order (or weakly first-order) lamellar-to-nematic phase transition at about 19^°C and dislocation loops are seen to proliferate within the lamellar structure when temperature is decreased below 30^°C. The values of both elastic constants of this given lamellar phase are measured as a function of temperature, approaching the lamellar-to-nematic transition, with the help of Quasi-Elastic Light Scattering (QELS) on oriented lamellar phases. Very surprisingly we observe a strong and rapid increase in both ˉ and K as the lamellar-to-nematic transition temperature is approached. These increases are seen to start as soon as dislocation loops can be observed in the lamellar phase. We interpret our results as being the consequence of the appearance and proliferation of dislocation loops within the lamellar structure. According to a simple model we developped we show that ˉ and K are proportional to the density of dislocation loops in the lamellar phase.     

Rheological behaviour of polyoxometalate-doped lyotropic lamellar phases

We study the influence of nanoparticle doping on the lyotropic liquid crystalline phase of the industrial surfactant Brij30 ( C₁₂E₄ and water, doped with spherical polyoxometalate nanoparticles smaller than the characteristic dimensions of the host lamellar phase. We present viscometry and in situ rheology coupled with small-angle X-ray scattering data that show that, with increasing doping concentration, the nanoparticles act to decrease the shear viscosity of the lamellar phase, and that a shear-induced transition to a multilamellar vesicle “onion” phase is pushed to higher shear rates, and in some cases completely suppressed. X-ray data reveal that the nanoparticles remain encapsulated within the membranes of the vesicles, thus indicating a viable method for the fabrication of nanoparticle incorporating organic vesicles.     

Anomalous elasticity of an ordered lamellar liquid foam

We investigate experimentally the linear viscoelastic properties of a lamellar liquid foam as a function of the cell size and spatial organisation. The system consists of multilamellar vesicles generated by a simple shear flow on a lyotropic lamellar phase. The vesicles can be prepared either in an amorphous or a spatially ordered state. Their size is easily tunable in the range R = 0.5-15 μm. Whereas the shear modulus of the amorphous lamellar foam is alike that of usual liquid foams or concentrated emulsions and scales linearly with 1/R, the elastic modulus of the ordered foam is almost independent of the cell size. This result --probably the first describing the elasticity of an ordered foam-like system-- remains unexplained. Received 7 August 2000     

d = 3 anisotropic and d = 2 tJ models: phase diagrams, thermodynamic properties, and chemical potential shift

The anisotropic d=3 tJ model is studied by renormalization-group theory, yielding the evolution of the system as interplane coupling is varied from the isotropic three-dimensional to quasi-two-dimensional regimes. Finite-temperature phase diagrams, chemical potential shifts, and in-plane and interplane kinetic energies and antiferromagnetic correlations are calculated for the entire range of electron densities. We find that the novel τ phase, seen in earlier studies of the isotropic d=3 tJ model, persists even for strong anisotropy. While the τ phase appears at low temperatures at 30–35% hole doping away from 〈 n_i〉=1, at smaller hole dopings we see a complex lamellar structure of antiferromagnetic and disordered regions, with a suppressed chemical potential shift, a possible marker of incommensurate ordering in the form of microscopic stripes. An investigation of the renormalization-group flows for the isotropic two-dimensional tJ model also shows a clear pre-signature of the τ phase, which in fact appears with finite transition temperatures upon addition of the smallest interplane coupling.     

A thermodynamic multiphase scheme treating polymer crystallization and melting

A comparison of transition and melting temperatures of n-alkanes with experimentally determined ticknesses and melting points of polyethylene lamellae shows that the variation of the thickness with the crystallization temperature virtually agrees with the chain length dependence of the crystalline-mesomorphic phase transition in n-alkanes. Mesomorphic polyethylene layers are stable objects up to the thickness set by this phase transition. The findings lend further support to the view that polymer crystallization generally uses a route which includes a passage via a mesomorphic phase. We construct a thermodynamic scheme dealing with the transitions between melt, mesomorphic layers and lamellar crystallites, assuming for the latter ones that they exist both in an initial “native” and a final “stabilized” form. Application of the scheme in a reconsideration and quantitative evaluation of SAXS and DSC results previously obtained for PE, sPP, iPS and P(epsilonCL) yields the equilibrium transition temperatures between the various phases, latent heats of transition and surface free energies. According to the results the mesomorphic phases are not liquid-like, but have thermodynamic properties which place them truly intermediate between melt and crystals.     

Oscillating viscosity in a lyotropic lamellar phase under shear flow

We report some time-dependent behavior of lyotropic lamellar phase under shear flow. At fixed stress, near a layering instability, the system presents an oscillating shear rate. We build up a new stress versus shear rate diagram that includes temporal behavior. This diagram is made of two distinct branches of stationary states which correspond, respectively, to disordered and ordered multilamellar vesicle phases. When increasing the shear stress, prior to the transition to the ordered structural state, sustained oscillations of the viscosity are recorded. They correspond to periodic structural change of the entire sample between a disordered and a ordered state of multilamellar vesicles.     

Modeling of a two-regime crystallization in a multicomponent lipid system under shear flow

The kinetics of phase transitions of milk fat triacylglycerols, as model multicomponent lipid systems, were studied under shear in a Couette cell at 17 °C, 17.5 °C and 20 °C under shear rates ranging from 0 to 2880s^-1 using synchrotron X-ray diffraction. Two-dimensional diffraction patterns were captured during the crystallization process. No effect of shear on onset time for phase α from the liquid was observed. Afterwards a two-regime crystallization process was observed. During the first regime, as observed in other systems, shear reduced the onset time of the phase transition from phase α to 2880s⁻. The model previously developed for palm oil (ODE model) worked well to describe this regime, confirming the general value of the proposed ODE model. However, the ODE model did not satisfactorily describe the second regime. We found that, as the system gets closer to equilibrium, the growth regime becomes controlled by diffusion, manifested by the kinetics following a dependence. This regime was found to be consistent with a mechanism combining step growth at a kink with progressive selection of the crystallizing moieties. This mechanism is in agreement with the displacement of the diffraction peak positions, which revealed how increased shear rate promotes the crystallization of the higher melting fraction affecting the composition of the crystallites.     

Optical transmittance spectroscopy of concentric-shell fullerenes layers produced by carbon ion implantation

Concentric-shell fullerenes, also called carbon onions, produced by carbon ion implantation into silver thin films, and subsequently deposited on a silica substrate, were studied by optical transmission spectroscopy in the wavelength range 0.2 - 1.2 μm. In this interval, the strongest absorption is due to the π-plasmon of sp²-like carbon. The position of the plasmon absorption band clearly evolved from 265 nm at low fluence to 230 nm at high implantation fluences. A simulation of the optical spectra based on dielectric models of the concentric-shell fullerenes layer allowed us to identify the first peak as due to disordered graphite and the latter to the carbon onions. The concentration of residual graphite and the filling fraction of the carbon onions produced at high fluences could be estimated by fitting the optical spectra with computed transmittance curves. Received 13 July 2000     

Molar-mass dependence of the lamellar thickness in symmetric diblock copolymers

Summary A homologous series of nine symmetric poly(styrene)-block-poly(butadieme) diblock copolymers was synthesized and characterized. The scaling of the lamellar thickness,D, with the chain lengthN(DαN ^δ ) was investigated with small-angle X-ray scattering. Different sample preparation methods were used: annealing, solvent-casting and shear alignment. We find that the lamellar thickness and thus the value of the exponent δ depends on the preparation method used,i.e. care must be taken to ensure that the samples investigated are in thermodynamic equilibrium. Paper presented at the I International Conference on Scaling Concepts and Complex Fluids, Copanello, Italy, July 4–8, 1994.     

Commensurate-incommensurate transition in two-coupled chains of nearly half-filled electrons

We investigate the physical properties of two coupled chains of electrons, with a nearly half-filled band, as a function of the interchain hopping t _⊥ and the doping. We show that upon doping, the system undergoes a metal-insulator transition well described by a commensurate-incommensurate transition. By using bosonization and renormalization we determine the full phase diagram of the system, and the physical quantities such as the charge gap. In the commensurate phase two different regions, for which the interchain hopping is relevant and irrelevant exist, leading to a confinement-deconfinement crossover in this phase. A minimum of the charge gap is observed for values of t _⊥ close to this crossover. At large t _⊥ the region of the commensurate phase is enhanced, compared to a single chain. At the metal-insulator transition the Luttinger parameter takes the universal value K _ρ ^* = 1, in agreement with previous results on special limits of this model. Received 31 July 2000     

A Monte-Carlo study of equilibrium polymers in a shear flow

We use an off-lattice microscopic model for solutions of equilibrium polymers (EP) in a lamellar shear flow generated by means of a self-consistent external field between parallel hard walls. The individual conformations of the chains are found to elongate in flow direction and shrink perpendicular to it while the average polymer length decreases with increasing shear rate. The Molecular Weight Distribution of the chain lengths retains largely its exponential form in dense solutions whereas in dilute solutions it changes from a power-exponential Schwartz distribution to a purely exponential one upon an increase of the shear rate. With growing shear rate the system becomes increasingly inhomogeneous so that a characteristic variation of the total monomer density, the diffusion coefficient, and the center-of-mass distribution of polymer chains of different contour length with the velocity of flow is observed. At higher temperature, as the average chain length decreases significantly, the system is shown to undergo an order-disorder transition into a state of nematic liquid crystalline order with an easy direction parallel to the hard walls. The influence of shear flow on this state is briefly examined. Received 22 October 1998 and Received in final form 12 April 1999