Nonhomogeneous textures and banded flow in a soft cubic phase under shear

Electrically conductive and antimicrobial Pluronic-based hydrogels

Electrically conductive hydrogels (ECHs) combine the electrical properties of conductive materials with the unique features of hydrogels. They are attractive for various biomedical applications due to their smart response to electrical fields. Owing to their distinctive properties, such as biocompatibility, thermosensitivity and self-assembling behaviour, Pluronics can be adopted for the generation of hydrogels for biomedical applications. Here, innovative self-assembling ECHs holding antimicrobial properties for biomedical applications are developed, providing a full characterization of their macroscopic and microscopic properties. The rheological, morphological, and structural properties of Pluronic F68 (PF68) in the presence of conductive poly(3,4-ethylenedioxythiophene):poly-(styrenesulfonate) (PEDOT:PSS) are studied to optimize the synthesis of novel biocompatible and electrically conductive hydrogels. The addition of silver (Ag) flakes to the aqueous samples of PF68/PEDOT:PSS is used to further enhance the systems electrical conductivity and antimicrobial potency. Aqueous optimal samples with 45 wt% PF68 and different PEDOT:PSS/silver contents are investigated by means of experimental rheology and small-angle X-ray scattering (SAXS), to unveil the influence of both PEDOT:PSS and silver on the phase diagram, macroscopic flow properties, and morphology of the Pluronic-based systems. The presence of PEDOT:PSS and silver flakes endows Pluronic systems with high conductive properties, while preserving the same self-assembly features of PF68 in water. Moreover, the functionalisation with silver flakes confers antimicrobial properties to the ECHs, as demonstrated by growth inhibition of the multi-drug resistant bacterium Staphylococcus aureus. The use of PF68 in this work provides a novel route for the synthesis of innovative ECHs, whose functionalities such as self-assembling behaviour, biocompatibility, conductivity, and bioactivity may inspire future avenues in the biomedical field.

Dynamic Light Scattering Based Microrheology of End-Functionalised Triblock Copolymer Solutions

Nano-sized particles functionalised with short single-stranded (ss)DNAs can act as detectors of complementary DNA strands. Here we consider tri-block-copolymer-based, self-assembling DNA-coated nanoparticles. The copolymers are chemically linked to the DNA strands via azide (N3) groups. The micelles aggregate when they are linked with complementary ssDNA. The advantage of such block-copolymer-based systems is that they are easy to make. Here we show that DNA functionalisation results in inter-micellar attraction, but that N3-groups that have not reacted with the DNA detector strands also change the phase behaviour of the tri-block polymer solution. We studied the triblock copolymer, Pluronic^® F108, which forms spherical micelles in aqueous solutions upon heating. We find that the triblock chains ending with either an N3 or N3-DNA complex show a dramatic change in phase behaviour. In particular, the N3-functionalisation causes the chain ends to cluster below the critical micelle temperature (CMT) of pure F108, forming flower-micelles with the N3-groups at the core, while the PPO groups are exposed to the solvent. Above the CMT, we see an inversion with the PPO chains forming the micellar core, while the N3-groups are now aggregating on the periphery, inducing an attraction between the micelles. Our results demonstrate that, due to the two competing self-assembling mechanisms, the system can form transient hydrogels.

Macroscopic Alignment of Micellar Crystals with Magnetic Microshearing

The effect of small quantities of a magnetic polymer nanocomposite (formed by surfactant Pluronic F127 @ Fe₃O₄ nanoparticles of 10 and 30 nm diameters) on the crystallization behavior of Pluronic F127 micelles solvated by 20% in water was investigated in the vicinity of hydrophilic and hydrophobic interfaces. Introducing magnetic nanoparticle at the core imparts magnetic properties to the polymeric micelle and increases its hydrodynamic diameter. These magnetic polymer nanocomposites act as defects in the pluronic crystal and hinder crystallization in comparison to pure Pluronic F127 micelles' behavior. The magnetic field results in a motion of the magnetic micelles and a microshearing effect. This microshearing assists in self-organization of the crystal. Addition of magnetic micelles formed using 30 nm magnetite particles shows similar crystallization behavior, however, with an overall reduced crystallinity due to their significantly larger size compared to the lattice parameter and the dimension of the interstitial cavity for an fcc structure.

Non-local stresses in highly non-uniformly flowing suspensions: The shear-curvature viscosity

For highly non-uniformly flowing fluids, there are contributions to the stress related to spatial variations of the shear rate, which are commonly referred to as non-local stresses. The standard expression for the shear stress, which states that the shear stress is proportional to the shear rate, is based on a formal expansion of the stress tensor with respect to spatial gradients in the flow velocity up to leading order. Such a leading order expansion is not able to describe fluids with very rapid spatial variations of the shear rate, like in micro-fluidics devices and in shear-banding suspensions. Spatial derivatives of the shear rate then significantly contribute to the stress. Such non-local stresses have so far been introduced on a phenomenological level. In particular, a formal gradient expansion of the stress tensor beyond the above mentioned leading order contribution leads to a phenomenological formulation of non-local stresses in terms of the so-called "shear-curvature viscosity". We derive an expression for the shear-curvature viscosity for dilute suspensions of spherical colloids and propose an effective-medium approach to extend this result to concentrated suspensions. The validity of the effective-medium prediction is confirmed by Brownian dynamics simulations on highly non-uniformly flowing fluids.

Superflexibility of graphene oxide

Graphene oxide (GO), the main precursor of graphene-based materials made by solution processing, is known to be very stiff. Indeed, it has a Young's modulus comparable to steel, on the order of 300 GPa. Despite its very high stiffness, we show here that GO is superflexible. We quantitatively measure the GO bending rigidity by characterizing the flattening of thermal undulations in response to shear forces in solution. Characterizations are performed by the combination of synchrotron X-ray diffraction at small angles and in situ rheology (rheo-SAXS) experiments using the high X-ray flux of a synchrotron source. The bending modulus is found to be 1 kT, which is about two orders of magnitude lower than the bending rigidity of neat graphene. This superflexibility compares with the fluidity of self-assembled liquid bilayers. This behavior is discussed by considering the mechanisms at play in bending and stretching deformations of atomic monolayers. The superflexibility of GO is a unique feature to develop bendable electronics after reduction, films, coatings, and fibers. This unique combination of properties of GO allows for flexibility in processing and fabrication coupled with a robustness in the fabricated structure.

Combined neutron reflectometry and rheology

Neutron reflectometry has been combined with rheology in order to investigate the solid boundary of liquids and polymers under shear deformation. This approach allows one to apply a controlled stress to a material while resolving the structural arrangements on the sub-nanometre length scale with neutron reflectivity, off-specular scattering and small-angle scattering at the same time. The specularly reflected neutron intensity of a 20% by weight solution of Pluronic F127 in deuterated water in contact with an octadecyl trichlorosilane-covered and a piranha-treated silicon wafer is evaluated. A pronounced difference is found in the structure formed by the polymer micelles at the two surfaces, which is explained by the difference in the affinity of the micellar shell to the solid interfaces. Under deformation, the near interface structure changes at deformations of about 2, 30 and 900%. The structural changes are correlated with changes in the storage and loss modulus of the polymer solution, revealing a transition from more solid to more liquid like properties.

Non-linear oscillatory rheological properties of a generic continuum foam model: comparison with experiments and shear-banding predictions

The occurrence of shear bands in a complex fluid is generally understood as resulting from a structural evolution of the material under shear, which leads (from a theoretical perspective) to a non-monotonic stationary flow curve related to the coexistence of different states of the material under shear. In this paper we present a scenario for shear-banding in a particular class of complex fluids, namely foams and concentrated emulsions, which differs from other scenarios in two important ways. First, the appearance of shear bands is shown to be possible both without any intrinsic physical evolution of the material (e.g. via a parameter coupled to the flow such as concentration or entanglements) and without any finite critical shear rate below which the flow does not remain stationary and homogeneous. Secondly, the appearance of shear bands depends on the initial conditions, i.e. the preparation of the material. In other words, it is history dependent. This behaviour relies on the tensorial character of the underlying model (2D or 3D) and is triggered by an initially inhomogeneous strain distribution in the material. The shear rate displays a discontinuity at the band boundary whose amplitude is history dependent and thus depends on the sample preparation.

Nanoscale discontinuities at the boundary of flowing liquids: a look into structure

When downsizing technology, confinement and interface effects become enormously important. Shear imposes additional anisotropy on a liquid. This may induce inhomogeneities, which may have their origin close to the solid interface. For advancing the understanding of flow, information on structures on all length scales and in particular close to the solid interface is indispensable. Neutron scattering offers an excellent tool to contribute in this context. In this work, surface sensitive scattering techniques were used to resolve the structure of liquids under flow in the vicinity of a solid interface. Our results are summarized as follows. First, for a Newtonian liquid we report a depletion distance on the order of nanometers which is far too small to explain the amount of surface slip, on the order of micrometers, found by complementary techniques. Second, for a grafted polymer brush we find no entanglement-disentanglement transition under shear but the grafted film gets ripped off the surface. Third, by evaluating the local structure factor of a micellar solution close to the solid interface it turns out that the degree of order and local relaxation depends critically on the surface energy of the solid surface.

Soft Dynamics simulation. 2. Elastic spheres undergoing a T(1) process in a viscous fluid

Robust empirical constitutive laws for granular materials in air or in a viscous fluid have been expressed in terms of timescales based on the dynamics of a single particle. However, some behaviours such as viscosity bifurcation or shear localization, observed also in foams, emulsions, and block copolymer cubic phases, seem to involve other micro-timescales which may be related to the dynamics of local particle reorganizations. In the present work, we consider a T(1) process as an example of a rearrangement. Using the Soft Dynamics simulation method introduced in the first paper of this series, we describe theoretically and numerically the motion of four elastic spheres in a viscous fluid. Hydrodynamic interactions are described at the level of lubrication (Poiseuille squeezing and Couette shear flow) and the elastic deflection of the particle surface is modeled as Hertzian. The duration of the simulated T(1) process can vary substantially as a consequence of minute changes in the initial separations, consistently with predictions. For the first time, a collective behaviour is thus found to depend on a parameter other than the typical volume fraction of particles.

Rheological response and dynamics of the amphiphilic diamond phase from kinetic lattice–Boltzmann simulations

The purpose of the present paper is to report on the first computational study of the dynamical and rheological response of a self-assembled diamond mesophase under Couette flow in a ternary mixture composed of oil, water and an amphiphilic species. The amphiphilic diamond mesophase arises in a wide range of chemical and biological systems, and a knowledge of its rheological response has important implications in materials science and biotechnological applications. The simulations reported here are performed using a kinetic lattice–Boltzmann method. Lyotropic liquid crystals exhibit characteristic rheological responses in experiments that include shear-banding and a non-Newtonian flow curve as well as viscoelasticity under oscillatory shear. Their behaviour under steady and oscillatory shear is correctly reproduced in our simulations. On cessation of shear, as the morphology returns to the diamond phase, the relaxation of the stress response follows a stretched-exponential form for low initial strain rates.

Effects of shear and charge on the microphase formation of P123 polymer in the SBA-15 synthesis investigated by mesoscale simulations

Mesoscale simulation was performed to investigate the dynamical structural behavior of the pluronic P123 block copolymer in the synthesis of mesoporous SBA-15. Shear is introduced to represent stirring in the actual experiment, and a weak charge is included to simulate the acidic conditions in the synthesis. Under shear, with the increase in weak charge in the PEO [poly(ethylene oxide)] block, the template forms more ordered hexagonal phases, and the pore sizes of the cylindrical hydrophobic PPO [poly(propylene oxide)] blocks decrease. The structural factor shows three types of water molecules in the mesoscale aggregates, including bulk water in the solution, bound water around the hydrophilic PEO corona, and trapped water in the hydrophobic PPO core. When 1,3,5-trimethyl-benzene (TMB) is added to the system as a swelling agent, expanded hexagonal phases are formed, and the density mapping of TMB shows that the TMB molecules are mainly located in the hydrophobic PPO cores. In configurations with spherical micelles, although bimodally dispersed spheres are observed, the face-centered cubic (fcc) packing of the micelles hardly changes with the addition of TMB. In agreement with experimental results, the simulations show that the shear and the weak charge are essential to the formation of hexagonal templates in the copolymer. Mesoscopic simulations complement experimental investigations on the morphology changes of amphiphilic polymer in template syntheses and can provide important guidance for further experiments.

Shear induced relaxation of polymer micelles at the solid-liquid interface

A 20% aqueous solution of (ethylene oxide) 99-(propylene oxide) 65-(ethylene oxide) 99, F127, was investigated by combining rheology in a cone/plate-geometry and surface-sensitive grazing incident neutron scattering. The crystalline structure formed by the polymer micelles becomes less pronounced for low shear rates, but correlations increase for higher shear rates. After stopping shear a slow relaxation of the micelles is found in the vicinity (50 mum thick layer) of a hydrophilic silicon wall (strong micelle-wall interaction), while a fast relaxation is observed in the boundary layer against the hydrophobic silicon wall (weak micelle-wall interaction). The results show that in the vicinity of the interface wall-particle interactions compete heavily with the shear force acting on the liquid.

Regular and chaotic states in a local map description of sheared nematic liquid crystals

We propose and study a local map capable of describing the full variety of dynamical states, ranging from regular to chaotic, obtained when a nematic liquid crystal is subjected to a steady shear flow. The map is formulated in terms of a quaternion parametrization of rotations of the local frame described by the axes of the nematic director, subdirector, and the joint normal to these, with two additional scalars describing the strength of ordering. Our model yields kayaking, wagging, tumbling, aligned, and coexistence states, accommodated in a phase diagram which closely resembles phase diagrams obtained using representations of the dynamics which are based on ordinary differential equations. We also study the behavior of the map under periodic perturbations of the shear rate. Such a map can serve as a building block for the construction of lattice models of the complex spatiotemporal states predicted for sheared nematics.

An elasto-visco-plastic model for immortal foams or emulsions

A variety of complex fluids consists in soft, round objects (foams, emulsions, assemblies of copolymer micelles or of multilamellar vesicles--also known as onions). Their dense packing induces a slight deviation from their preferred circular or spherical shape. As a frustrated assembly of interacting bodies, such a material evolves from one conformation to another through a succession of discrete, topological events driven by finite external forces. As a result, the material exhibits a finite yield threshold. The individual objects usually evolve spontaneously (colloidal diffusion, object coalescence, molecular diffusion), and the material properties under low or vanishing stress may alter with time, a phenomenon known as aging. We neglect such effects to address the simpler behaviour of (uncommon) immortal fluids: we construct a minimal, fully tensorial, rheological model, equivalent to the (scalar) Bingham model. Importantly, the model consistently describes the ability of such soft materials to deform substantially in the elastic regime (be it compressible or not) before they undergo (incompressible) plastic creep--or viscous flow under even higher stresses.

A new parallel plate shear cell for in situ real-space measurements of complex fluids under shear flow

We developed and tested a parallel plate shear cell that can be mounted on top of an inverted microscope to perform confocal real-space measurements on complex fluids under shear. To follow structural changes in time, a plane of zero velocity is created by letting the plates move in opposite directions. The location of this plane is varied by changing the relative velocities of the plates. The gap width is variable between 20 and 200 microm with parallelism better than 1 microm. Such a small gap width enables us to examine the total sample thickness using high numerical aperture objective lenses. The achieved shear rates cover the range of 0.02-10(3) s(-1). This shear cell can apply an oscillatory shear with adjustable amplitude and frequency. The maximum travel of each plate equals 1 cm, so that strains up to 500 can be applied. For most complex fluids, an oscillatory shear with such a large amplitude can be regarded as a continuous shear. We measured the flow profile of a suspension of silica colloids in this shear cell. It was linear except for a small deviation caused by sedimentation. To demonstrate the excellent performance and capabilities of this new setup we examined shear induced crystallization and melting of concentrated suspensions of 1 microm diameter silica colloids.

Shear alignment of sphere-morphology block copolymer thin films with viscous fluid flow

The effect of shear on crystalline order is interesting fundamentally, as well as technologically, for producing long-range alignment of micron- and nanoscale structures. We study the influence of shear on a sphere-forming diblock copolymer thin film consisting of a stack of two to six hexagonal layers, using a stress-controlled rheometer to transmit the stress through a viscous fluid layer. Above a threshold stress, the hexagonal layers align macroscopically in the "easy shear" direction. A simple phenomenological model with an orientation-dependent order-disorder temperature, T*(ODT)(deltatheta)=T(ODT)[1-(sigma/sigma(c))sin2(3 deltatheta)] and recrystallization describes the influence of stress level, temperature, and shearing time remarkably well.

Nanostructure in block copolymer solutions: rheology and small-angle neutron scattering

Triblock copolymers composed of poly(ethylene oxide) (PEO) and poly(propylene oxide) (PPO) present an amphiphilic character in aqueous solutions. Since PPO is less hydrophilic than PEO and since their solubilities decrease when the temperature increases, the copolymers self-assemble spontaneously, forming micelles at moderate temperatures. For higher temperatures or concentrations, the copolymers or the micelles are ordered because of repulsive interactions and form lyotropic liquid crystalline phases. These are phases of very great viscosity with the aspect of gels, and transitions between different crystalline phases can occur at fixed concentration during an increase of temperature. We studied solutions of three different copolymers. The first two have a star structure. They are both composed of four branches (EO)x (PO)y fixed on an ethylene diamine, but differ by the values of x and y . Their commercial name is Tetronic 908 (x=114, y=21) and Tetronic 704 (x=16, y=18) . The third copolymer (EO)37(PO)56(EO)37 is linear and is known under the name of Pluronic P105 . The measurements of the shear complex elastic modulus according to the temperature is used to determine the temperatures of the different transitions. Then, small-angle neutron scattering on samples under flow and true crystallographic arguments make it possible to identify the nature of the crystalline phases. For the systems studied, we show that the branched copolymers form only one type of liquid crystalline phase, which is bcc for the T908 and lamellar for the T704 . For the linear copolymer, it is possible to identify three transitions: micellar solution to hexagonal phase, hexagonal phase to body-centered cubic phase, and finally body-centered cubic phase to lamellar phase.

Crystallization of micelles at chemically terminated interfaces

In aqueous solutions and for high concentrations triblock copolymers are known to aggregate. As a critical volume fraction of micelles is reached they crystallize. We report on grazing incident small angle neutron scattering as an experimental tool to investigate the crystallization of spherical polymer micelles in the immediate vicinity of a flat solid interface. We find for an attractive surface potential a face centered close packed structure with a random orientation perpendicular to the normal of the interface. For a repulsive potential crystallization is suppressed.

Spatiotemporal oscillations and rheochaos in a simple model of shear banding

We study a simple model of shear banding in which the flow-induced phase is destabilized by coupling between flow and microstructure (wormlike micellar length). By varying the strength of instability and the applied shear rate, we find a rich variety of oscillatory and chaotic shear banded flows. At low shear and weak instability, the induced phase pulsates next to one wall of the flow cell. For stronger instability, high shear pulses ricochet across the cell. At high shear we see oscillating bands on either side of central defects. We discuss our results in the context of recent experiments.

A spatio-temporal study of rheo-oscillations in a sheared lamellar phase using ultrasound

We present an experimental study of the flow dynamics of a lamellar phase sheared in the Couette geometry. High-frequency ultrasonic pulses at 36 MHz are used to measure time-resolved velocity profiles. Oscillations of the viscosity occur in the vicinity of a shear-induced transition between a high-viscosity disordered fluid and a low-viscosity ordered fluid. The phase coexistence shows up as shear bands on the velocity profiles. We show that the dynamics of the rheological data result from two different processes: (i) fluctuations of slip velocities at the two walls and (ii) flow dynamics in the bulk of the lamellar phase. The bulk dynamics are shown to be related to the displacement of the interface between the two differently sheared regions in the gap of the Couette cell. Two different dynamical regimes are investigated under applied shear stress: one of small amplitude oscillations of the viscosity delta eta/eta approximately equal to 3%) and one of large oscillations (delta eta/eta approximately equal to 25%). A phenomenological model is proposed that may account for the observed spatio-temporal dynamics.

Shear banding in a lyotropic lamellar phase. II. Temporal fluctuations

We analyze the temporal fluctuations of the flow field associated with a shear-induced transition in a lyotropic lamellar phase: the layering transition of the onion texture. In the first part of this work [Salmon et al., Phys. Rev. E 68, 051503 (2003)], we have evidenced banded flows at the onset of this shear-induced transition which are well accounted for by the classical picture of shear banding. In the present paper, we focus on the temporal fluctuations of the flow field recorded in the coexistence domain. These striking dynamics are very slow (100-1000 s) and cannot be due to external mechanical noise. Using velocimetry coupled to structural measurements, we show that these fluctuations are due to a motion of the interface separating the two differently sheared bands. Such a motion seems to be governed by the fluctuations of sigma(*), the local stress at the interface between the two bands. Our results thus provide more evidence for the relevance of the classical mechanical approach of shear banding even if the mechanism leading to the fluctuations of sigma(*) remains unclear.

Shear banding in a lyotropic lamellar phase. I. Time-averaged velocity profiles

Using velocity profile measurements based on dynamic light scattering and coupled to structural and rheological measurements in a Couette cell, we present evidences for a shear banding scenario in the shear flow of the onion texture of a lyotropic lamellar phase. Time-averaged measurements clearly show the presence of structural shear banding in the vicinity of a shear-induced transition, associated with the nucleation and growth of a highly sheared band in the flow. Our experiments also reveal the presence of slip at the walls of the Couette cell. Using a simple mechanical approach, we demonstrate that our data confirm the classical assumption of the shear banding picture, in which the interface between bands lies at a given stress sigma(*). We also outline the presence of large temporal fluctuations of the flow field, which are the subject of the second part of this paper [Salmon et al., Phys. Rev. E 68, 051504 (2003)].

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.

Determination of the structure of the organized phase of the block copolymer PEO-PPO-PEO in aqueous solutions under flow by small-angle neutron scattering

The organization of Tetronic 908 (T908), a star copolymer of poly(ethylene oxide) (PEO) and poly(propylene oxide) (PPO) blocks, has been examined. Above critical conditions of temperature and concentration, the micelles formed by the aggregation of PPO units self-organize into particular structures. While small-angle neutron scattering (SANS) characterizations performed with static conditions demonstrate the organization of the medium, the experimental results do not allow us to make a distinction between simple cubic and body-centered-cubic structures. However, SANS measurements realized under shear produce characteristic diffraction diagrams. In this paper, an accurate methodology is proposed to identify, without ambiguity, the exact nature of the organized phase. Applied to our system, indexing of the diffraction pattern spots reveals that the organization of T908 is of bcc type oriented with the [111] direction parallel to the direction of flow, but the crystals can present any orientation about this direction. The lattice size has been estimated and compared to previous published results.

Factors determining crystal--liquid coexistence under shear

The interaction between an imposed shear flow and an order--disorder transition underlies a broad range of phenomena. Under the influence of shear flow, a variety of soft matter is observed to spontaneously form bands characterized by different local order---for example, thermotropic liquid crystals subjected to shear flow exhibit rich phase behaviour. The stability of order under the influence of shear flow is also fundamental to understanding frictional wear and lubrication. Although there exists a well developed theoretical approach to the influence of shear flow on continuous transitions in fluid mixtures, little is known about the underlying principles governing non-equilibrium coexistence between phases of different symmetry. Here we show, using non-equilibrium molecular dynamics simulations of a system of spherical particles, that a stationary coexistence exists between a strained crystal and the shearing liquid, and that this coexistence cannot be accounted for by invoking a non-equilibrium analogue of the chemical potential. Instead of such thermodynamic arguments, we argue that a balancing of the crystal growth rate with the rate of surface erosion by the shearing melt can account for the observed coexistence.