Table of contents

Soft matter is a rapidly growing interdisciplinary research field covering a range of subject areas including physics, chemistry, biology, mathematics and engineering. Some of the important universal features of these materials are their mesoscopic structures and their dynamics. Due to the existence of such large-scale structures, which nevertheless exhibit interactions of the order of the thermal energy, soft matter can readily be taken out of equilibrium by imposing a weak external field such as an electric field, a mechanical stress or a shear flow. The importance of the coexistence of microscopic molecular dynamics and the mesoscopic/macroscopic structures and flows requires us to develop hierarchical approaches to understand the nonlinear and nonequilibrium phenomena, which is one of the central issues of current soft matter research.

This special section presents selected contributions from the 'International Symposium on Non-Equilibrium Soft Matter 2010' held from 17–20 August 2010 in Nara, Japan, which aimed to describe recent advances in soft matter research focusing especially on its nonequilibrium aspects. The topics discussed cover statics and dynamics of a wide variety of materials ranging from traditional soft matter like polymers, gels, emulsions, liquid crystals and colloids to biomaterials such as biopolymers and biomembranes. Among these studies, we highlighted the physics of biomembranes and vesicles, which has attracted great attention during the last decade; we organized a special session for this active field. The work presented in this issue deals with (1) structure formation in biomembranes and vesicles, (2) rheology of polymers and gels, (3) mesophases in block copolymers, (4) mesoscopic structures in liquid crystals and ionic liquids, and (5) nonequilibrium dynamics.

This symposium was organized as part of a research project supported by the Grant-in-Aid for the priority area 'Soft Matter Physics' (2006–2010) from the Ministry of Education, Culture, Sports, Science and Technology (MEXT) of Japan. We thank those who contributed to this symposium as well as members of the 'Soft Matter Physics' project for their valuable discussions and collaborations.

Non-equilibrium soft matter contents

Insights on raft behavior from minimal phenomenological modelsG Garbès Putzel and M Schick

Dynamical membrane curvature instability controlled by intermonolayer friction Anne-Florence Bitbol, Jean-Baptiste Fournier, Miglena I Angelova and Nicolas Puff

Numerical investigations of the dynamics of two-component vesicles Takashi Taniguchi, Miho Yanagisawa and Masayuki Imai

Asymmetric distribution of cone-shaped lipids in a highly curved bilayer revealed by a small angle neutron scattering technique Y Sakuma, N Urakami, T Taniguchi and M Imai

Hydration, phase separation and nonlinear rheology of temperature-sensitive water-soluble polymers Fumihiko Tanaka, Tsuyoshi Koga, Isamu Kaneda and Françoise M Winnik

Morphology and rheology of an immiscible polymer blend subjected to a step electric field under shear flow H Orihara, Y Nishimoto, K Aida, Y H Na, T Nagaya and S Ujiie

Surfactant-induced friction reduction for hydrogels in the boundary lubrication regime Kosuke Kamada, Hidemitsu Furukawa, Takayuki Kurokawa, Tomohiro Tada, Taiki Tominaga, Yukihiro Nakano and Jian Ping Gong

Fabrication and structural analysis of polyrotaxane fibers and films Yasuhiro Sakai, Kentaro Ueda, Naoya Katsuyama, Koji Shimizu, Shunya Sato, Jun Kuroiwa, Jun Araki, Akira Teramoto, Koji Abe, Hideaki Yokoyama and Kohzo Ito

Micellization kinetics of diblock copolymers in a homopolymer matrix: a self-consistent field study Raghuram Thiagarajan and David C Morse

Hierarchical self-assembly of two-length-scale multiblock copolymers Gerrit ten Brinke, Katja Loos, Ivana Vukovic and Gerrit Gobius du Sart

Kaleidoscopic morphologies from ABC star-shaped terpolymers Yushu Matsushita, Kenichi Hayashida, Tomonari Dotera and Atsushi Takano

Direct and inverted nematic dispersions for soft matter photonics I Muševič, M Škarabot and M Humar

Solvation effects in phase transitions in soft matter Akira Onuki, Takeaki Araki and Ryuichi Okamoto

Non-equilibrium dynamics of 2D liquid crystals driven by transmembrane gas flow Kazuyoshi Seki, Ken Ueda, Yu-ichi Okumura and Yuka Tabe

Roles of bond orientational ordering in glass transition and crystallization Hajime Tanaka

Shear banding in thixotropic and normal emulsions José Paredes, Noushine Shahidzadeh-Bonn and Daniel Bonn

Effects of hydrodynamic interactions in binary colloidal mixtures driven oppositely by oscillatory external fields Adam Wysocki and Hartmut Löwen

Onsager's variational principle in soft matter Masao Doi

We construct a simple phenomenological theory of phase separation in ternary mixtures of cholesterol and saturated and unsaturated lipids. Such separation is relevant to the formation of 'rafts' in the plasma membrane. We also show how simple cross-linking of proteins which prefer one form of lipid to the other can trigger raft-formation, the first step in a signaling pathway.

We study a dynamical curvature instability caused by a local chemical modification of a phospholipid membrane. In our experiments, a basic solution is microinjected close to a giant unilamellar vesicle, which induces a local chemical modification of some lipids in the external monolayer of the membrane. This modification causes a local deformation of the vesicle, which then relaxes. We present a theoretical description of this instability, taking into account both the change of the equilibrium lipid density and the change of the spontaneous membrane curvature induced by the chemical modification. We show that these two types of changes of the membrane properties yield different dynamics. In contrast, it is impossible to distinguish them when studying the equilibrium shape of a vesicle subjected to a global modification. In our model, the longest relaxation timescale is related to the intermonolayer friction, which plays an important part when there is a change in the equilibrium density in one monolayer. We compare our experimental results to the predictions of our model by fitting the measured time evolution of the deformation height to the solution of our dynamical equations. We obtain good agreement between theory and experiments. Our fits enable us to estimate the intermonolayer friction coefficient, yielding values that are consistent with previous measurements.

We examined the dynamics of the deformation and phase separation of two-component vesicles. First, we numerically investigated the effects of (i) thermal noise, (ii) hydrodynamic flow induced by the line tension of the domain boundary and (iii) composition-dependent bending rigidity on the coarsening dynamics of a phase-separated pattern on the surfaces of vesicles with fixed shapes. The dynamical exponent z (N_DB ∼ t ^{− z}, the total length of the domain boundaries) of the coarsening of the phase-separated pattern was found to decrease from z = 1/3 under no thermal noise to 1/5 < z < 1/4 when including the effects of thermal noise. We also found that the hydrodynamic effect enhances the coarsening in a bicontinuous phase separation for a spherical vesicle. In phase separations of a shape-fixed tubular vesicle, a band-like phase separation with periodicity along the longer axis of the tube occurs because of the composition-dependent bending rigidity and the higher curvatures at the tube end-caps. Second, we also explored the dynamics of shape deformation coupled with phase separation through the bending rigidity of the membrane which depends on the local composition in lipids and found that the composition-dependent bending rigidity crucially influences the phase separation and deformation of the vesicle. The results of simulations are in good agreement with experimentally observed behavior known as 'shape convergence' (Yanagisawa et al 2008 Phys. Rev. Lett. 100 148102).

We have investigated the lipid sorting in a binary small unilamellar vesicle (SUV) composed of cone-shaped (1,2-dihexanoyl-sn-glycero-3-phosphocholine: DHPC) and cylinder-shaped (1,2-dipalmitoyl-sn-glycero-3-phosphocholine: DPPC) lipids. In order to reveal the lipid sorting we adopted a contrast matching technique of small angle neutron scattering (SANS), which extracts the distribution of deuterated lipids in the bilayer quantitatively without steric modification of lipids as in fluorescence probe techniques. First the SANS profile of protonated SUVs at a film contrast condition showed that SUVs have a spherical shape with an inner radius of 190 Å and a bilayer thickness of 40 Å. The SANS profile of deuterated SUVs at a contrast matching condition showed a characteristic scattering profile, indicating an asymmetric distribution of cone-shaped lipids in the bilayer. The characteristic profile was described well by a spherical bilayer model. The fitting revealed that most DHPC molecules are localized in the outer leaflet. Thus the shape of the lipid is strongly coupled with the membrane curvature. We compared the obtained asymmetric distribution of the cone-shaped lipids in the bilayer with the theoretical prediction based on the curvature energy model.

The collapse of a poly(N-isopropylacrylamide) (PNIPAM) chain upon heating and the phase diagrams of aqueous PNIPAM solutions with a very flat lower critical solution temperature (LCST) phase separation line are theoretically studied on the basis of cooperative dehydration (simultaneous dissociation of bound water molecules in a group of correlated sequence), and compared with the experimental observation of temperature-induced coil–globule transition by light scattering methods. The transition becomes sharper with the cooperativity parameter σ of hydration. The reentrant coil–globule–coil transition and cononsolvency in a mixed solvent of water and methanol are also studied from the viewpoint of competitive hydrogen bonds between polymer–water and polymer–methanol. The downward shift of the cloud-point curves (LCST cononsolvency) with the mol fraction of methanol due to the competition is calculated and compared with the experimental data. Aqueous solutions of hydrophobically modified PNIPAM carrying short alkyl chains at both chain ends (telechelic PNIPAM) are theoretically and experimentally studied. The LCST of these solutions is found to shift downward along the sol–gel transition curve as a result of end-chain association (association-induced phase separation), and separate from the coil–globule transition line. Associated structures in the solution, such as flower micelles, mesoglobules, and higher fractal assembly, are studied by ultra small-angle neutron scattering with theoretical modeling of the scattering function. Dynamic-mechanical modulus, nonlinear stationary viscosity, and stress build-up in start-up shear flows of the associated networks are studied on the basis of the affine and non-affine transient network theory. The molecular conditions for thickening, strain hardening, and stress overshoot are found in terms of the nonlinear amplitude A of the chain tension and the tension–dissociation coupling constant g.

We have investigated the structural change of an immiscible polymer blend in shear flow when subjected to a step electric field. During the process three-dimensional images were successfully constructed with a confocal scanning laser microscope and at the same time the transient shear stress was also measured. The interface tensor was calculated from the images. Several factors are incorporated into the shear stress, such as the bulk viscosity, the interfacial tension and the Maxwell stress. We performed an experiment to separate the Maxwell stress from the total shear stress. The results are discussed in terms of the interface tensor.

We studied the ability of surfactants to reduce friction by boundary lubrication for a bulk hydrogel sliding on a solid surface in an aqueous solution. A piece of negatively charged polyelectrolyte hydrogel was slid across solid surfaces with various levels of hydrophobicity, using a strain-controlled parallel-plate rheometer in water. A dramatic reduction in the sliding friction, especially in the low velocity region, was detected by the addition of a surfactant to the water medium. This friction reduction was only observed in gel–solid friction but not in solid–solid friction, indicating that the soft and wet nature of the gel surface was crucial for this surfactant-induced friction reduction. This phenomenon reveals that surfactants can remain at the gel-mated interface, thus preventing direct interfacial interaction between the sliding surfaces, and significantly decreasing the frictional stress. The reported dramatic reduction in friction highlights the frictional characteristics of soft and wet hydrogel materials.

Polyrotaxane (PR), a typical example of topological supramolecular architecture, consists of multiple cyclic molecules threaded onto a linear polymer backbone and capped with bulky end-groups. The PR system of polyethylene glycol and α-cyclodextrin (α-CD) has been extensively studied for its facile synthesis, unique molecular structure, and possible applications for various smart materials. We have previously demonstrated the fabrication of PR-based fibers without chemical cross-links by wet spinning of PR solution. In this paper, we investigate the crystal structure of α-CDs in PR fibers and the effect of drawing on it. The α-CDs in PR fiber are found to form hexagonal channel-type structure. The drawing process promotes formation of the packing arrangement of α-CDs in the c-axis because of the sliding of α-CD molecules along the polymer backbone. In addition, we demonstrate the preparation of an elastomeric PR film having similar network structure to the fibers and ethylene glycol oligomer as plasticizer.

Self-consistent field theory is used to calculate free energy barriers and reaction rates for the spontaneous association and dissociation of micelles formed of block copolymers in a homopolymer matrix. The barriers are prohibitively large for copolymers of typical molecular weights when the unimer (free surfactant) concentration is near the equilibrium critical micelle concentration (CMC). As a result, polymeric micelles normally cannot reach true thermodynamic equilibrium. The rates of association and dissociation are, however, sensitive to unimer concentration, making it possible to form or destroy micelles at observable rates in sufficiently highly supersaturated or subsaturated solutions, respectively, even when both reactions are suppressed near the equilibrium CMC. The barrier to dissociation is particularly sensitive to unimer concentration, and vanishes when the unimer concentration is only slightly (for example, a percentage of a few tens) below the equilibrium CMC.

The self-assembly in diblock copolymer-based supramolecules, obtained by hydrogen bonding short side chains to one of the blocks, as well as in two-length-scale linear terpolymers results in hierarchical structure formation. The orientation of the different domains, e.g. layers in the case of a lamellar-in-lamellar structure, is determined by the molecular architecture, graft-like versus linear, and the relative magnitude of the interactions involved. In both cases parallel and perpendicular arrangements have been observed. The comb-shaped supramolecules approach is ideally suited for the preparation of nanoporous structures. A bicontinuous morphology with the supramolecular comb block forming the channels was finally achieved by extending the original approach to suitable triblock copolymer-based supramolecules.

Star-shaped terpolymers of the ABC type composed of incompatible polymer components give a variety of ordered structures with mesoscopic length scales depending on their composition ratio. Their peculiar features are summarized in this report. Polymer components adopted are polyisoprene (I), polystyrene (S) and poly(2-vinylpyridine) (P), and many monodisperse samples of the I_XS_YP_Z type were anionically prepared. Firstly our focus is on molecules of the I_1.0S_1.0P_x1 type, where x₁ is only a variable. The complex but systematic morphology change was displayed within the range 0.2 ≤ x₁ ≤ 10, that is, their structures change from spherical plus lamellae structure for I_1.0S_1.0P_0.2 to periodic tilings (0.4 ≤ x₁ ≤ 1.9), then to lamellae-in-lamella (3.0 ≤ x₁ ≤ 4.9) and lamellae-in-cylinder (7.9 ≤ x₁ ≤ 10) structures with increasing x₁. Here if we pay attention to the structural variation of the P domain inclusively, it transforms from sphere to cylinder, lamella and then to matrix, which is the same as that for linear polymers. Among them, several periodic Archimedean tiling patterns can be naturally formed when the relative lengths of the three chains are close to one another. Moreover, it has been found that the tiling zone is spread out widely. For example, the series I_1.0S_1.8P_x2 (with 0.8 ≤ x₂ ≤ 2.9) and the other series I_1.0S_yP_2.0 (with 1.1 ≤ y ≤ 2.7) show mostly Archimedean tilings. Additionally, block copolymer/homopolymer blends with a composition of I_1.0S_2.7P_2.5 reveal a quasicrystalline tiling with dodecagonal symmetry. Furthermore, a zinc-blende-type four-branched network structure was created just a little outside of the tiling region for a block copolymer/homopolymer blend of I_1.0S_2.3P_0.8. When some more asymmetry in chain length is introduced, hyperbolic tiling on a gyroid membrane has successfully been constructed for the sample I_1.0S_1.8P_3.2 and it transforms into a hierarchical cylinders-in-lamella structure with further increase in P content to I_1.0S_1.8P_6.4. Thus, kaleidoscopic morphologies have been generated from ABC star-shaped terpolymers and their structural change has turned out to be very sensitive to relative compositions.

General properties and recent developments in the field of nematic colloids and emulsions are discussed. The origin and nature of pair colloidal interactions in the nematic colloids are explained and an overview of the stable colloidal 2D crystalline structures and superstructures discovered so far is given. The nature and role of topological defects in the nematic colloids is discussed, with an emphasis on recently discovered entangled colloidal structures. Applications of inverted nematic emulsions and binding force mechanisms in nematic colloids for soft matter photonic devices are discussed.

Phase transitions in polar binary mixtures can be drastically altered by even a small amount of salt. This is because the preferential solvation strongly depends on the ambient composition. Together with a summary of our research on this problem, we present some detailed results on the role of antagonistic salt composed of hydrophilic and hydrophobic ions. These ions tend to segregate at liquid–liquid interfaces and selectively couple to water-rich and oil-rich composition fluctuations, leading to mesophase formation. In our two-dimensional simulation, the coarsening of the domain structures can be stopped or slowed down, depending on the interaction parameter (or the temperature) and the salt density. We realize stripe patterns at the critical composition and droplet patterns at off-critical compositions. In the latter case, charged droplets emerge with considerable size dispersity in a percolated region. We also give the structure factors among the ions, accounting for the Coulomb interaction and the solvation interaction mediated by the composition fluctuations.

Free-standing films composed of several layers of chiral smectic liquid crystals (SmC*) exhibited unidirectional director precession under various vapor transfers across the films. When the transferred vapors were general organic solvents, the precession speed linearly depended on the momentum of the transmembrane vapors, where the proportional constant was independent of the kind of vapor. In contrast, the same SmC* films under water transfer exhibited precession in the opposite direction. As a possible reason for the rotational inversion, we suggest the competition of two origins for the torques, one of which is microscopic and the other macroscopic. Next, we tried to move an external object by making use of the liquid crystal (LC) motion. When a solid or a liquid particle was set on a film under vapor transfer, the particle was rotated in the same direction as the LC molecules. Using home-made laser tweezers, we measured the force transmitted from the film to the particle, which we found to be several pN.

It is widely believed that crystallization in three dimensions is primarily controlled by positional ordering, and not by bond orientational ordering. In other words, bond orientational ordering is usually considered to be merely a consequence of positional ordering and thus has often been ignored. This one-order-parameter (density) description may be reasonable when we consider an equilibrium liquid–solid transition, but may not be enough to describe a metastable state and the kinetics of the transition. Here we propose that bond orientational ordering can play a key role in (i) crystallization, (ii) the ordering to quasi-crystal and (iii) vitrification, which occurs under rather weak frustration against crystallization. In a metastable supercooled state before crystallization, a system generally tends to have bond orientational order at least locally as a result of a constraint of dense packing. For a system interacting with hard-core repulsions, the constraint is intrinsically of geometrical origin and thus the basic physics is the same as nematic ordering of rod-like particles upon densification. Furthermore, positional ordering is easily destroyed even by weak frustration such as polydispersity and anisotropic interactions which favour a symmetry not consistent with that of the equilibrium crystal. Thus we may say that vitrification can be achieved by disturbing and prohibiting long-range positional ordering. Even in such a situation, bond orientational ordering still survives, accompanying its critical-like fluctuations, which are the origin of dynamic heterogeneity for this case. This scenario naturally explains both the absence of positional order and the development of bond orientational order upon cooling in a supercooled state. Although our argument is speculative in nature, we emphasize that this physical picture can coherently explain crystallization, vitrification, quasi-crystallization and their relationship in a natural manner. For a strongly frustrated system, even bond orientational order can be destroyed. Even in such a case there may still appear a structural signature of dense packing, which is linked to slow dynamics.

When made to flow, yield stress materials rarely flow homogeneously. This is mostly attributed to the fact that such materials show a transition from a solid- to a liquid-like state when the stress exceeds some critical value: the yield stress. Thus, if the stress is heterogeneous, so is the flow. Here we consider emulsion flows in a cone–plate geometry that, for Newtonian fluids, correspond to a homogeneous stress situation and show that shear banding can also be observed either due to wall slip or to the existence of a critical shear rate. By means of velocity profiles obtained using a confocal laser scanning microscope combined with a rheometer we conclude that the last type of shear banding occurs only in thixotropic yield stress materials.

The collective dynamics in a binary mixture of colloidal particles which are driven in opposite directions by an external oscillatory field is examined by computer simulations in two spatial dimensions. Both Brownian dynamics (BD) computer simulations, which ignore solvent-mediated hydrodynamic interactions between the colloidal particles, and multi-particle collision dynamics (MPCD) simulations, which include hydrodynamic interactions, are employed. We first review recent results obtained by BD. Depending on the driving frequency and amplitude, lane formation parallel to the drive and band formation perpendicular to the drive occur. Band formation is stable only in a finite window of oscillation frequencies and driving strengths and is taken over by lane formation if the driving force is increased or the oscillation frequency is decreased. MPCD simulations, on the other hand, reveal that band formation is blurred by hydrodynamic interactions. During the front collisions of oppositely driven particles there is a strong vortical movement of the solvent which tends to mix particles and broaden the interface of the bands. This can either lead to a novel intermittent dynamical behaviour or to band rupture into local clusters. These effects, which are absent for BD, are characterized by the strengths of the enstrophy and its spectrum. We finally discuss possible experimental realizations of the models employed.

In the celebrated paper on the reciprocal relation for the kinetic coefficients in irreversible processes, Onsager (1931 Phys. Rev. 37 405) extended Rayleigh's principle of the least energy dissipation to general irreversible processes. In this paper, I shall show that this variational principle gives us a very convenient framework for deriving many established equations which describe the nonlinear and non-equilibrium phenomena in soft matter, such as phase separation kinetics in solutions, gel dynamics, molecular modeling for viscoelasticity nemato-hydrodynamics, etc. Onsager's variational principle can therefore be regarded as a solid general basis for soft matter physics.

We perform molecular dynamics simulations of 'floating bond' (FB) models of network-forming liquids and compare the structure and dynamics against the BKS model of silica (van Beest et al 1990 Phys. Rev. Lett.64 1955), with the aim of gaining a better understanding of glassy silica in terms of the variety of non-ergodic states seen in colloids. At low densities, all the models form tetrahedral networks. At higher densities, tailoring the FB model to allow a higher number of bonds does not capture the structure seen in BKS. Upon rescaling the time and length in order to compare mean squared displacements between models, we find that there are significant differences in the temperature dependence of the diffusion coefficient at high density. Additionally, the FB models show a greater range in variability in the behavior of the non-ergodicity parameter and caging length, quantities used to distinguish colloidal gels and glasses. Hence, we find that the glassy behavior of BKS silica can be interpreted as a 'gel' at low densities, with only a marginal gel-to-glass crossover at higher densities.

The Asakura–Oosawa–Vrij (AOV) model of colloid–polymer mixtures idealises nonadsorbing polymers as effective spheres that are fixed in size and impenetrable to hard particles. Real polymer coils, however, are intrinsically polydisperse in size (radius of gyration) and may be penetrated by smaller particles. Crowding by nanoparticles can affect the size distribution of polymer coils, thereby modifying effective depletion interactions and thermodynamic stability. To analyse the influence of crowding on polymer conformations and demixing phase behaviour, we adapt the AOV model to mixtures of nanoparticles and ideal, penetrable polymer coils that can vary in size. We perform Gibbs ensemble Monte Carlo simulations, including trial nanoparticle–polymer overlaps and variations in the radius of gyration. Results are compared with predictions of free-volume theory. Simulation and theory consistently predict that ideal polymers are compressed by nanoparticles, and that compressibility and penetrability stabilise nanoparticle–polymer mixtures.

We investigate double-walled vesicles as a simple model system for multi-vesicular structures, where the inner membrane is confined within the outer membrane. Various shapes of double-walled vesicles in two dimensions are obtained by means of our recently-developed discrete space variation method, and the shapes of each layer are found to be interdependent. Confined within the outer membrane, an inner membrane with a larger surface area always shows a cristae shape. As previous simulations and theoretical analyses of a single-walled vesicle have been done before, the geometric properties of double-walled vesicles, including the mean square radius of gyration and volume within the vesicle membrane, are studied in detail as functions of the pressure and surface area. It is found that due to the inter-space restriction of each layer, double-walled vesicles exhibit different behaviors compared with the previously-observed scaling laws of single-walled vesicles. It is straightforward to extend this study to more complicated and realistic biological systems, such as those including electrostatic interactions between membranes and solvent, phase separation, and cooperative interactions between multicomponent membranes.