Friction of a driven chain: role of momentum conservation, Goldstone and radiation modes.

We analytically study friction and dissipation of a driven bead in a 1D harmonic chain, and analyze the role of internal damping mechanism as well as chain length. Specifically, we investigate Dissipative Particle Dynamics and Langevin Dynamics, as paradigmatic examples that do and do not display translational symmetry, with distinct results: For identical parameters, the friction forces can differ by many orders of magnitude. For slow driving, a Goldstone mode traverses the entire system, resulting in friction of the driven bead that grows arbitrarily large (Langevin) or gets arbitrarily small (Dissipative Particle Dynamics) with system size. For a long chain, the friction for DPD is shown to be bound, while it shows a singularity (i.e. can be arbitrarily large) for Langevin damping. For long underdamped chains, a radiation mode is recovered in either case, with friction independent of damping mechanism. For medium length chains, the chain shows the expected resonant behavior. At the resonance, friction is non-analytic in damping parameterγ, depending on it asγ-1. Generally, no zero frequency bulk friction coefficient can be determined, as the limits of small frequency and infinite chain length do not commute, and we discuss the regimes where 'simple' macroscopic friction occurs.

Insights into Hydrogen Gas Environment-Promoted Nanostructural Changes in Stressed and Relaxed Palladium by Environmental Transmission Electron Microscopy and Variable-Energy Positron Annihilation Spectroscopy.

Environmental transmission electron microscopy (ETEM) and variable-energy positron annihilation spectroscopy (VEPAS) are used to observe hydrogen-induced microstructural changes in stress-free palladium (Pd) foils and stressed Pd thin films grown on rutile TiO2 substrates. The microstructural changes in Pd strongly depend on the hydrogen pressure and on the stress state. At room temperature, enhanced Pd surface atom mobility and surface reconstruction is seen by ETEM already at low hydrogen pressures ( pH < 10 Pa). The observations are consistent with molecular dynamics simulations. A strong increase of the vacancy density was found, and so-called superabundant vacancies were identified by VEPAS. At higher pressures, migration and vanishing of intrinsic defects is observed in Pd free-standing foils. The Pd thin films demonstrate an increased density of dislocations with increase of the H2 pressure. The comparison of the two studied systems demonstrates the influence of the mechanical stress on structural evolution of Pd catalysts.

Membrane sorting via the extracellular matrix.

We consider the coupling between a membrane and the extracellular matrix. Computer simulations demonstrate that the latter coupling is able to sort lipids. It is assumed that membranes are elastic manifolds, and that this manifold is disrupted by the extracellular matrix. For a solid-supported membrane with an actin network on top, regions of positive curvature are induced below the actin fibers. A similar mechanism is conceivable by assuming that the proteins which connect the cytoskeleton to the membrane induce local membrane curvature. The regions of non-zero curvature exist irrespective of any phase transition the lipids themselves may undergo. For lipids that prefer certain curvature, the extracellular matrix thus provides a spatial template for the resulting lateral domain structure of the membrane.

Raft formation in lipid bilayers coupled to curvature.

We present computer simulations of a membrane in which the local composition is coupled to the local membrane curvature. At high temperatures (i.e., above the temperature of macroscopic phase separation), finite-sized transient domains are observed, reminiscent of lipid rafts. The domain size is in the range of hundred nanometers, and set by the membrane elastic properties. These findings are in line with the notion of the membrane as a curvature-induced microemulsion. At low temperature, the membrane phase separates. The transition to the phase-separated regime is continuous and belongs to the two-dimensional Ising universality class when the coupling to curvature is weak, but becomes first-order for strong curvature-composition coupling.

A lipid bound actin meshwork organizes liquid phase separation in model membranes.

The eukaryotic cell membrane is connected to a dense actin rich cortex. We present FCS and STED experiments showing that dense membrane bound actin networks have severe influence on lipid phase separation. A minimal actin cortex was bound to a supported lipid bilayer via biotinylated lipid streptavidin complexes (pinning sites). In general, actin binding to ternary membranes prevented macroscopic liquid-ordered and liquid-disordered domain formation, even at low temperature. Instead, depending on the type of pinning lipid, an actin correlated multi-domain pattern was observed. FCS measurements revealed hindered diffusion of lipids in the presence of an actin network. To explain our experimental findings, a new simulation model is proposed, in which the membrane composition, the membrane curvature, and the actin pinning sites are all coupled. Our results reveal a mechanism how cells may prevent macroscopic demixing of their membrane components, while at the same time regulate the local membrane composition. DOI: http://dx.doi.org/10.7554/eLife.01671.001.

A finite-temperature Monte Carlo algorithm for network forming materials.

Computer simulations of structure formation in network forming materials (such as amorphous semiconductors, glasses, or fluids containing hydrogen bonds) are challenging. The problem is that large structural changes in the network topology are rare events, making it very difficult to equilibrate these systems. To overcome this problem, Wooten, Winer, and Weaire [Phys. Rev. Lett. 54, 1392 (1985)] proposed a Monte Carlo bond-switch move, constructed to alter the network topology at every step. The resulting algorithm is well suited to study networks at zero temperature. However, since thermal fluctuations are ignored, it cannot be used to probe the phase behavior at finite temperature. In this paper, a modification of the original bond-switch move is proposed, in which detailed balance and ergodicity are both obeyed, thereby facilitating a correct sampling of the Boltzmann distribution for these systems at any finite temperature. The merits of the modified algorithm are demonstrated in a detailed investigation of the melting transition in a two-dimensional 3-fold coordinated network.

Crossover from a Kosterlitz-Thouless phase transition to a discontinuous phase transition in two-dimensional liquid crystals.

Liquid crystals in two dimensions do not support long-range nematic order, but a quasinematic phase where the orientational correlations decay algebraically is possible. The transition from the isotropic to the quasinematic phase can be continuous and of the Kosterlitz-Thouless type, or it can be first order. We report here on a liquid-crystal model where the nature of the isotropic to quasinematic transition can be tuned via a single parameter p in the pair potential. For pp(t), it is first order. Precisely at p=p(t), there is a tricritical point where, in addition to the orientational correlations, also the positional correlations decay algebraically. The tricritical behavior is analyzed in detail, including an accurate estimate of p(t). The results follow from extensive Monte Carlo simulations combined with a finite-size scaling analysis. Paramount in the analysis is a scheme to facilitate the extrapolation of simulation data in parameters that are not necessarily field variables (in this case, the parameter p), the details of which are also provided. This scheme provides a simple and powerful alternative for situations where standard histogram reweighting cannot be applied.

Fluids in porous media: the case of neutral walls.

The bulk phase behavior of a fluid is typically altered when the fluid is brought into confinement by the walls of a random porous medium. Inside the porous medium, phase-transition points are shifted, or may disappear altogether. A crucial determinant is how the walls interact with the fluid particles. In this work, we consider the situation whereby the walls are neutral with respect to the liquid and vapor phases. In order to realize the condition of strict neutrality, we use a symmetric binary mixture inside a porous medium that interacts identically with mixture species. Monte Carlo simulations are then used to obtain the phase behavior. Our main finding is that, in the presence of the porous medium, a liquid-vapor critical point still exists. At the critical point, the distribution of the order parameter remains scale invariant, but self-averaging is violated. These findings provide further evidence that random confinement by neutral walls induces critical behavior of the random Ising model (i.e., Ising models with dilution type disorder, where the disorder couples to the energy).

Monolayer curvature stabilizes nanoscale raft domains in mixed lipid bilayers.

According to the lipid raft hypothesis, biological lipid membranes are laterally heterogeneous and filled with nanoscale ordered "raft" domains, which are believed to play an important role for the organization of proteins in membranes. However, the mechanisms stabilizing such small rafts are not clear, and even their existence is sometimes questioned. Here, we report the observation of raft-like structures in a coarse-grained molecular model for multicomponent lipid bilayers. On small scales, our membranes demix into a liquid ordered (lo) phase and a liquid disordered (ld) phase. On large scales, phase separation is suppressed and gives way to a microemulsion-type state that contains nanometer-sized lo domains in an ld environment. Furthermore, we introduce a mechanism that generates rafts of finite size by a coupling between monolayer curvature and local composition. We show that mismatch between the spontaneous curvatures of monolayers in the lo and ld phases induces elastic interactions, which reduce the line tension between the lo and ld phases and can stabilize raft domains with a characteristic size of the order of a few nanometers. Our findings suggest that rafts in multicomponent bilayers might be closely related to the modulated ripple phase in one-component bilayers.

Random pinning limits the size of membrane adhesion domains.

Theoretical models describing specific adhesion of membranes predict (for certain parameters) a macroscopic phase separation of bonds into adhesion domains. We show that this behavior is fundamentally altered if the membrane is pinned randomly due to, e.g., proteins that anchor the membrane to the cytoskeleton. Perturbations which locally restrict membrane height fluctuations induce quenched disorder of the random-field type. This rigorously prevents the formation of macroscopic adhesion domains following the Imry-Ma argument [Imry and Ma, Phys. Rev. Lett. 35, 1399 (1975)]. Our prediction of random-field disorder follows from analytical calculations and is strikingly confirmed in large-scale Monte Carlo simulations. These simulations are based on an efficient composite Monte Carlo move, whereby membrane height and bond degrees of freedom are updated simultaneously in a single move. The application of this move should prove rewarding for other systems also.

Membrane lateral structure: the influence of immobilized particles on domain size.

In experiments on model membranes, formation of large domains of different lipid composition is readily observed. However, no such phase separation is observed in the membranes of intact cells. Instead, small transient inhomogeneities called lipid rafts are expected in these systems. One of the numerous attempts to explain small domains refers to the coupling of the membrane to its surroundings, which leads to the immobilization of some of the membrane molecules. These immobilized molecules then act as static obstacles for the remaining mobile ones. We present detailed Molecular Dynamics simulations demonstrating that this can indeed account for small domains. This confirms previous Monte Carlo studies based on simplified models. Furthermore, by directly comparing domain structures obtained using Molecular Dynamics to Monte Carlo simulations of the Ising model, we demonstrate that domain formation in the presence of obstacles is remarkably insensitive to the details of the molecular interactions.

Cross-linked biopolymer bundles: cross-link reversibility leads to cooperative binding/unbinding phenomena.

We consider a biopolymer bundle consisting of filaments that are cross-linked together. The cross-links are reversible: they can dynamically bind and unbind adjacent filament pairs as controlled by a binding enthalpy. The bundle is subjected to a bending deformation and the corresponding distribution of cross-links is measured. For a bundle consisting of two filaments, upon increasing the bending amplitude, a first-order transition is observed. The transition is from a state where the filaments are tightly coupled by many bound cross-links, to a state of nearly independent filaments with only a few bound cross-links. For a bundle consisting of more than two filaments, a series of first-order transitions is observed. The transitions are connected with the formation of an interface between regions of low and high cross-link densities. Combining umbrella sampling Monte Carlo simulations with analytical calculations, we present a detailed picture of how the competition between cross-link shearing and filament stretching drives the transitions. We also find that, when the cross-links become soft, collective behavior is not observed: the cross-links then unbind one after the other leading to a smooth decrease of the average cross-link density.

Fluid phase separation inside a static periodic field: an effectively two-dimensional critical phenomenon.

When a fluid with a bulk liquid-vapor critical point is placed inside a static external field with spatial periodic oscillations in one direction, a new phase arises. This new phase-the so-called "zebra" phase-is characterized by an average density roughly between that of the liquid and vapor phases. The presence of the zebra phase gives rise to two new phase transitions: one from the vapor to the zebra phase, and one from the zebra to the liquid phase. At appropriate values of the temperature and chemical potential, the latter two transitions become critical. This phenomenon is called laser-induced condensation [I. O. Götze, J. M. Brader, M. Schmidt, and H. Löwen, Mol. Phys. 101, 1651 (2003)]. The purpose of this paper is to elucidate the nature of the critical points, using density functional theory and computer simulation of a colloid-polymer mixture. The main finding is that critical correlations develop in two-dimensional sheets perpendicular to the field direction, but not in the direction along the field: the critical correlations are thus effectively two-dimensional. Hence, static periodic fields provide a means to confine a fluid to effectively two dimensions. Away from criticality, the vapor-zebra and liquid-zebra transitions become first-order, but the associated surface tensions are extremely small. The consequences of the extremely small surface tensions on the nature of the two-phase coexistence regions are analyzed in detail.

Statics and dynamics of colloid-polymer mixtures near their critical point of phase separation: A computer simulation study of a continuous Asakura-Oosawa model.

We propose a new coarse-grained model for the description of liquid-vapor phase separation of colloid-polymer mixtures. The hard-sphere repulsion between colloids, and between colloids and polymers, which is used in the well-known Asakura-Oosawa (AO) model, is replaced with Weeks-Chandler-Andersen potentials. Similarly, a soft potential of height comparable to thermal energy is used for the polymer-polymer interaction, rather than treating polymers as ideal gas particles. It is shown by grand-canonical Monte Carlo simulations that this model leads to a coexistence curve that almost coincides with that of the AO model and that the Ising critical behavior of static quantities is reproduced. Then the main advantage of the model is exploited-its suitability for Molecular Dynamics simulations-to study the dynamics of mean square displacements of the particles, transport coefficients such as the self-diffusion and interdiffusion coefficients, and dynamic structure factors. While the self-diffusion of polymers increases slightly when the critical point is approached, the self-diffusion of colloids decreases and at criticality the colloid self-diffusion coefficient is about a factor of 10 smaller than that of the polymers. Critical slowing down of interdiffusion is observed, which is qualitatively similar to symmetric binary Lennard-Jones mixtures, for which no dynamic asymmetry of self-diffusion coefficients occurs.

From capillary condensation to interface localization transitions in colloid-polymer mixtures confined in thin-film geometry.

Monte Carlo simulations of the Asakura-Oosawa model for colloid-polymer mixtures confined between two parallel repulsive structureless walls are presented and analyzed in the light of current theories on capillary condensation and interface localization transitions. Choosing a polymer-to-colloid size ratio of q=0.8 and studying ultrathin films in the range of D=3 to D=10 colloid diameters thickness, grand canonical Monte Carlo methods are used; phase transitions are analyzed via finite size scaling, as in previous work on bulk systems and under confinement between identical types of walls. Unlike the latter work, inequivalent walls are used here: While the left wall has a hard-core repulsion for both polymers and colloids, at the right-hand wall an additional square-well repulsion of variable strength acting only on the colloids is present. We study how the phase separation into colloid-rich and colloid-poor phases occurring already in the bulk is modified by such a confinement. When the asymmetry of the wall-colloid interaction increases, the character of the transition smoothly changes from capillary condensation type to interface localization type. For very thin films (i.e., for D=3 ) and a suitable choice of the wall-colloid interactions, evidence is found that the critical behavior falls in the universality class of the two-dimensional Ising model. Otherwise, we observe crossover scaling between different universality classes (namely, the crossover from the three-dimensional to the two-dimensional Ising model universality class). The colloid and polymer density profiles across the film in the various phases are discussed, as well as the correlation of interfacial fluctuations in the direction parallel to the confining walls. The broadening of the interface between the coexisting colloid-rich and polymer-rich phases (located parallel to the confining walls) is understood in terms of capillary wave fluctuations. The experimental observability of all these phenomena is briefly discussed.

Description of the fluctuating colloid-polymer interface.

To describe the full spectrum of surface fluctuations of the interface between phase-separated colloid-polymer mixtures from low scattering vector q (classical capillary wave theory) to high q (bulklike fluctuations), one must take account of the interface's bending rigidity. We find that the bending rigidity is negative and that on approach to the critical point it vanishes proportionally to the interfacial tension. Both features are in agreement with Monte Carlo simulations.

Colloid-polymer mixtures in the presence of quenched disorder: a theoretical and computer simulation study.

We use theory and computer simulation to study the structure and phase behavior of colloid-polymer mixtures in the presence of quenched disorder. The Asakura-Oosawa model (AO) (Asakura and Oosawa 1954 J. Chem. Phys. 22 1255) is used to describe the colloid-colloid, colloid-polymer, and polymer-polymer pair interactions. We then investigate the behavior of this model in the presence of frozen-in (quenched) obstacles. The obstacles will be placed according to two different scenarios, both of which are experimentally feasible. In the first scenario, polymers are distributed at positions drawn from an ideal gas configuration. In the second scenario, colloidal particles are distributed at positions drawn from an equilibrium hard sphere configuration. We investigate how the unmixing transition of the AO model is affected by the type of quenched disorder. The theoretical formalism is based on the replica method of Given and Stell (1994 Physica A 209 495). Our foremost aim is to test the accuracy of three common closures to the replica Ornstein-Zernike equations, namely the hypernetted chain, the Percus-Yevick, and the Martinov-Sarkisov equations. The accuracy is determined by comparison with grand canonical Monte Carlo simulations. We find that, for quenched polymer disorder, all three closures perform remarkably well. However, when quenched colloid disorder is considered, i.e. the second mentioned scenario, the predictions of all three closures worsen dramatically.

Confinement effects on phase behavior of soft matter systems.

When systems that can undergo phase separation between two coexisting phases in the bulk are confined in thin film geometry between parallel walls, the phase behavior can be profoundly modified. These phenomena shall be described and exemplified by computer simulations of the Asakura-Oosawa model for colloid-polymer mixtures, but applications to other soft matter systems (e.g. confined polymer blends) will also be mentioned. Typically a wall will prefer one of the phases, and hence the composition of the system in the direction perpendicular to the walls will not be homogeneous. If both walls are of the same kind, this effect leads to a distortion of the phase diagram of the system in thin film geometry, in comparison with the bulk, analogous to the phenomenon of "capillary condensation" of simple fluids in thin capillaries. In the case of "competing walls", where both walls prefer different phases of the two phases coexisting in the bulk, a state with an interface parallel to the walls gets stabilized. The transition from the disordered phase to this "soft mode phase" is rounded by the finite thickness of the film and is not a sharp phase transition. However, a sharp transition can occur where this interface gets localized at (one of) the walls. The relation of this interface localization transition to wetting phenomena is discussed. Finally, an outlook to related phenomena is given, such as the effects of confinement in cylindrical pores on the phase behavior, and more complicated ordering phenomena (lamellar mesophases of block copolymers or nematic phases of liquid crystals under confinement).