Vorticity banding during the lamellar-to-onion transition in a lyotropic surfactant solution in shear flow

We report on the rheology of a lyotropic lamellar surfactant solution (SDS/dodecane/pentanol/ water), and identify a discontinuous transition between two shear thinning regimes which correspond to the low-stress lamellar phase and the more viscous shear-induced multilamellar vesicle, or “onion” phase. We study in detail the flow curve, stress as a function of shear rate, during the transition region, and present evidence that the region consists of a shear-banded phase where the material has macroscopically separated into bands of lamellae and onions stacked in the vorticity direction. We infer very slow and irregular transformations from lamellae to onions as the stress is increased through the two-phase region, and identify distinct events consistent with the nucleation of small fractions of onions that coexist with sheared lamellae.     

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     

Observations of the collapse of dilute lyotropic lamellar phases under shear flow

Experimental evidence of the collapse of dilute lamellar phases due to shear flow is presented. Two systems are used: one composed of brine and an ionic surfactant, and another composed of water, a nonionic surfactant, and cosurfactant. We observe this transition for a range of lamellar spacings and brine salinity. The results are in reasonable agreement with recent theory in which the suppression of fluctuations by shear plays an important role.     

Weakly charged lamellar bilayer system: Interplay between thermal undulations and electrostatic repulsion

We study the interplay between thermal undulations and electrostatic interactions for weakly charged surfactant bilayers by measuring the backscattering of light from very dilute lamellar phases of the non-ionic surfactant triethylene glycol monodecyl ether (C₁₀E₃) doped with small amounts of the anionic surfactant sodium dodecyl sulphate (SDS), both with and without added electrolyte. Upon charging, the lamellar phases show a transition from undulation to electrostatic stabilization. Non-lamellar structures develop if the molar mixing ratio exceeds . Deviations from ideal swelling, , where is the lamellar repeating distance and the membrane volume fraction, were detected for all lamellar phases. Salt-free lamellar phases with charge densities below , as well as more highly charged lamellar phases at high ionic strength show a universal logarithmic deviation from ideal swelling that was analyzed using theories for undulation stabilized lamellar phases. Deviations from ideal swelling for electrostatically stabilized lamellar phases were analyzed using theories recently developed for undulations in charged lamellar phases. The fits to the various theories yield a value of for the bending modulus of the C₁₀E₃ bilayers. Received 21 June 1999 and Received in final form 25 August 1999     

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     

Freeze-fracture studies on lipids and membranes

Freeze-fracture electron microscopy is especially useful for investigation of lipid structures by the advantageous fracture course within hydrophobic zones. Freezing is, on the other hand, a restriction because the structures of lamellar and non-lamellar phase states with disordered acyl chains (L(alpha), H(II,) cubic) are difficult to preserve. An important aspect of this method is therefore the lipid structure of phase states with ordered acyl chains (crystal, gel), and with a different degree of hydration. Freeze-fracture of pure lipid systems creates a valid representation of the structure of non-lamellar phases and of the general structure of the "lamellar" lipid bilayer, and lamellar phases with characteristic deformations (ripples, curvatures, plane sectors) can be identified. Fracture through the hydrophobic bilayer centre of biological membranes reveals characteristic protein components, the intramembraneous particles (IMPs). The lateral distribution of the IMPs is a helpful marker for fluid and rigid phase states, also without deformation of the lamella. The overall history and the present state of knowledge concerning the different structures revealed by the freeze-fracture and freeze-etch techniques in lipid systems, and to a limited extent in biological membranes, is reviewed, taking into account studies from our own laboratory.     

Microstructural evolution during containerless rapid solidification of Co-Si alloys

The Co-12%Si hypoeutectic, Co-12.52%Si eutectic and Co-13%Si hypereutectic alloys are rapidly solidified in a containerless environment in a drop tube. Undercoolings up to 207K (0.14T_E) are obtained, which play a dominant role in dendritic and eutectic growth. The coupled zone around Co-12.52%Si eutectic alloy has been calculated, which covers a composition range from 11.6 to 12.7%Si. A microstructural transition from lamellar eutectic to divorced eutectic occurs to Co-12.52%Si eutectic droplets with increasing undercooling. The lamellar eutectic structure of the Co-12.52%Si alloy consists of εCo and Co_3Si phases at small undercooling. The Co_3Si phase cannot decompose completely into εCo and αCo_2Si phases. As undercooling becomes larger, the Co_3Si phase grows very rapidly from the highly undercooled alloy melt to form a divorced eutectic. The structural morphology of the Co-12%Si alloy droplets transforms from εCo primary phase plus lamellar eutectic to anomalous eutectic, whereas the microstructure of Co-13%Si alloy droplets experiences a `dendritic to equiaxed' structural transition. No matter how large the undercooling is, the εCo solid solution is the primary nucleation phase. In the highly undercooled alloy melts, the growth of εCo and Co_3Si phases is controlled by solutal diffusion.     

二元层片共晶凝固过程的特征尺度选择

基于Jackson和Hunt二元规则共晶稳态生长理论,在共晶两相的界面溶质守恒条件中引入密度修正项,改进了共晶两相的界面溶质守恒条件.在此基础上,根据二元层片共晶常规凝固过程中层片组织稳态生长时Gibbs自由能的变化,运用极值形态选择原理确定二元层片共晶凝固过程中层片间距特征尺度选择准则.理论分析表明,对于给定二元共晶合金,在常规凝固条件下的层片间距选择通常为一有限区间.此外,理论分析还表明,二元层片共晶稳态生长时其特征尺度的选择可以呈现超稳定性,而且在给定的凝固条件下超稳定性只和给定合金系的物性参数有关.将该形态选择准则分别运用于物性参数精确已知的Al-Al2Cu,Sn-Pb和CBr4-C2Cl6合金系,表明计算结果与实验结果相符合.     

Melting of lamellar phases in temperature sensitive colloid-polymer suspensions

We prepare a novel suspension composed of rodlike fd virus and thermosensitive polymer poly(N-isopropylacrylamide) whose phase diagram is temperature and concentration dependent. The system exhibits a rich variety of stable and metastable phases, and provides a unique opportunity to directly observe melting of lamellar phases and single lamellae. Typically, lamellar phases swell with increasing temperature before melting into the nematic phase. The highly swollen lamellae can be superheated as a result of topological nucleation barriers that slow the formation of the nematic phase.     

Rheology and Structure of Quenched Binary Mixtures Under Oscillatory Shear

We applied the D2Q9 BGK lattice Boltzmann method to study the rheology and structure of the phaseseparating binary fluids under oscillatory shear in the diffusive regime. The method is suitable for simulating systemswhose dynamicsis described by the Navier-Stokes equation and convection-diffusion equation. The shear oscillationinduces different rheological patterns from those under steady shear. With the increasing of the frequency of the shearthe system shows more isotropic behavior, while with the decreasing of the frequency we find more configurations similarto those under steady shear. By decreasing the frequency of the shear, the period of the applied flow becomes thesame order of the relaxation time of the shear velocity profile, which is inversely proportional to the viscosity, and moreanisotropic effects become observable. The structure factor and the velocity profile contribute to the understanding ofthe configurations and the kinetic process. Oscillatory shear induces nonlinear pattern of the horizontal velocity profile.Therefore, configurations are found where lamellar order close to the wall coexists with isotropic domains in the middleof the system. For very slow frequencies, the morphology of the domains is characterized by lamellar order everywherethat resembles what happens in the case of steady shear.     

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.     

Measurement of multilamellar onion dimensions under shear using frequency domain pulsed gradient NMR

We present a simple method by which the dimensions of shear-induced multilamellar vesicles (MLVs), also known as onions, can be measured during the shearing process itself. This approach is based on the use of a closely spaced train of magnetic field gradient pulses applied during a CPMG echo sequence. The CPMG train compensates flow effects while the frequency-dependence of apparent diffusion can reveal the onion size. We present here a simple phenomenological model for restricted diffusion in multilamellar vesicles, which may be used to interpret the resulting diffusion spectrum. We demonstrate this approach with MLVs formed from the lamellar phase of sodium dodecyl sulfate (SDS) in water and octanol.     

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.     

Dynamic behavior of nickel atoms in graphitic networks

The dynamic behavior of nickel atoms in graphitic carbon onions, observed by in situ atomic-resolution electron microscopy, shows the formation of stable new C-Ni phases. Nickel is observed to take substitutional in-plane positions in graphene layers, forming a planar graphitelike C-Ni lattice. Evidence is furthermore seen for the formation of a cubic C-Ni phase, suggesting a possible phase transformation in C-Ni from a graphitelike to a diamondlike structure. The stability of the planar phases is shown by first-principles calculations which also indicate that the C-Ni planes are metallic.     

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     

Small-Angle and Wide-Angle X-Ray Scattering Study of Slow Relaxation Following Phase Transitions of New Bolaamphiphiles Based on N-(12-Betainylamino-Dodecane)-octyl β-D-Glucofuranosiduronamide Chloride

In the present study, we investigated the polymorphism and its time-dependence of a new series of bolaamphiphile molecules based on N-(12-Betainylamino-dodecane)-octyl β-D-Glucofuranosiduronamide Chloride. To obtain six members of this series, the length of the main bridging chain and the lateral chain were varied in order to modify the hydrophilic–lipophilic balance. Another chemical modification was to introduce a diacetylenic unit in the middle of the bridging chain to study the influence of the π–π stacking on the supramolecular organization of these molecules. Dry bolaamphiphiles self-organize in supramolecular structures such as lamellar crystalline structure, L_c; lamellar gel structure, L_β′; lamellar fluid structure, L_α; and lamellar isotropic structure, L. Thermal hysteresis of these structures, following phase transitions, are investigated by small-angle and wide-angle X-ray scattering. Once the thermal cycle is accomplished, the system remains in the kinetically stabilized undercooled high-temperature phase at the temperature of 20°C. Subsequently, the time-dependence of the relaxation to the thermodynamically stable phase is followed, and very slow relaxation for a period on the order of hours or days is observed. The study of the polymorphism and the stability of various phases of this new series of bolaamphiphiles—which are issued from natural primary resources (sugar beet and wheat) and thus interesting for potential application in pharmaceutical, cosmetics, or food industry—was undertaken in this work.     

Formation of Ring-Banded Spherulites of Poly (L-lactide) in its Miscible Mixture with an Ionic Liquid

Incorporation of an ionic liquid, nonvolatile and thermally stable, promoted formation of ring-banded spherulites in poly (l-lactide) (PLLA) during its sol–gel transition. Their formation is correlated with low viscosity and insignificant chain entanglements in the mixtures induced by the ionic liquid. In addition to a driving force for lamellar twisting that depended on the crystallization temperatures, it is believed that reduced lamellar twisting resistance caused by the ionic liquid plays a vital role in the formation of the ring-banded spherulites of PLLA from the mixtures. This study gives further insights into the structural formation of PLLA during a sol–gel transition, which could open new opportunities to tailor the properties of ion gels based on PLLA.     

Shear-induced first-order sponge-to-lamellar transition in a lyotropic surfactant system

We report a shear-induced sponge (L3) to lamellar (L(alpha)) transition in a surfactant system. Under a constant shear rate, after a delay time t(n) we observe random nucleation and subsequent growth of the L(alpha) phase, demonstrating that the shear-induced transition is first order. A simple argument for the energy of a two-dimensional nucleus accounts for the observed delay and its shear-rate dependence.     

Optical studies of delayed relaxation in Pb<Subscript>0.94</Subscript>Ba<Subscript>0.06</Subscript>Sc<Subscript>0.5</Subscript>Nb<Subscript>0.5</Subscript>O<Subscript>3</Subscript> (PBSN-6) solid solutions

The temperature dependences of the permittivity, birefringence, optical transmittance, and small-angle light scattering and their variations with time are studied for single crystals of the Pb_0.94Ba_0.06Sc_0.5Nb_0.5O₃ relaxor (PBSN-6) in the heterophase region of coexistence of different phases. It is shown that an electric field induces a phase transition to the ferroelectric state, which manifests itself within some time (delay time τ) after application of the electric field to the crystal. The observed dependence of the temperature of this transition on the heating rate of the sample and the changes in the birefringence and small-angle light scattering intensity with time confirm the kinetic character of the induced transition. Temperature dependences of the delay time τ for different electric fields are constructed. It is revealed that, at low temperatures, the delay time τ decreases with increasing temperature. This agrees with the behavior of τ in classical relaxors. At the Vogel-Fulcher temperature, however, one observes that dτ/dT reverses sign and τ increasing as the temperature continues to increase. This anomalous behavior of τ in the heterophase region is accounted for by the coexistence of the cubic relaxor and rhombohedral macrodomain phases.     

Time Delay in Black Hole Gravitational Lensing as a Distance Estimator

We calculate the time delay between different relativistic images formed by black hole gravitational lensing in the strong field limit. For spherically symmetric black holes, it turns out that the time delay between the first two images is proportional to the minimum impact angle. Their ratio gives a very interesting and precise measure of the distance of the black hole. Moreover, using also the separation between the images and their luminosity ratio, it is possible to extract the mass of the black hole. The time delay for the black hole at the center of our Galaxy is just few minutes, but for supermassive black holes with M=10⁸ ÷10⁹ in the neighbourhood of the Local Group the time delay amounts to few days, thus being measurable with a good accuracy.