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A generalized self-consistent field approach for polymer networks with a fixed topology is developed. It is shown that the theory reproduces the localization of cross-links, which is characteristic for gels. The theory is then used to study the order-disorder transition in regular networks of end-linked diblock copolymers. Compared to diblock copolymer melts, the transition is shifted towards lower values of the incompatibility parameter χ (the Flory- Huggins parameter). Moreover, the transition becomes strongly first order already at the mean-field level. If stress is applied, the transition is further shifted and finally vanishes in a critical point. [ABSTRACT FROM AUTHOR]

We develop a dynamic mean-field theory for polar active particles that interact through a self-generated field, in particular one generated through emitting a chemical signal. While being a form of chemotactic response, it is different from conventional chemotaxis in that particles discontinuously change their motility when the local concentration surpasses a threshold. The resulting coupled equations for density and polarization are linear and can be solved analytically for simple geometries, yielding inhomogeneous density profiles. Specifically, here we consider a planar and circular interface. Our theory thus explains the observed coexistence of dense aggregates with an active gas. There are, however, differences from the more conventional picture of liquid-gas coexistence based on a free energy, most notably the absence of a critical point. We corroborate our analytical predictions by numerical simulations of active particles under confinement and interacting through volume exclusion. Excellent quantitative agreement is reached through an effective translational diffusion coefficient. We finally show that an additional response to the chemical gradient direction is sufficient to induce vortex clusters. Our results pave the way to engineer motility responses in order to achieve aggregation and collective behavior even at unfavorable conditions. [ABSTRACT FROM AUTHOR]

We discuss the flow past a flat heterogeneous solid surface decorated by slipping stripes. The spatially varying slip length, b(y), is assumed to be small compared to the scale of the heterogeneities, L, but finite. For such weakly slipping surfaces, earlier analyses have predicted that the effective slip length is simply given by the surface-averaged slip length, which implies that the effective slip-length tensor becomes isotropic. Here we show that a different scenario is expected if the local slip length has steplike jumps at the edges of slipping heterogeneities. In this case, the next-to-leading term in an expansion of the effective slip-length tensor in powers of max [b{y)/L] becomes comparable to the leading-order term, but anisotropic, even at very small b(y)/L. This leads to an anisotropy of the effective slip and to its significant reduction compared to the surface-averaged value. The asymptotic formulas are tested by numerical solutions and are in agreement with results of dissipative particle dynamics simulations. [ABSTRACT FROM AUTHOR]

The "wrapping" of polymer chains on the surface of carbon nanotubes allows one to obtain multifunctional hybrid materials with unique properties for a wide range of applications in biomedicine, electronics, nanocomposites, biosensors, and solar cell technologies. We study by means of molecular dynamics simulations the force-assisted desorption kinetics of a polymer from the surface of a carbon nanotube. We find that, due to the geometric coupling between the adsorbing surface and the conformation of the macromolecule, the process of desorption slows down dramatically upon increasing the windings around the nanotube. This behavior can be rationalized in terms of an overdamped dynamics with a frictional force that increases exponentially with the number of windings of the macromolecule, resembling the Euler-Eytelwein mechanism that describes the interplay between applied tension and frictional forces on a rope wrapped around a curved surface. The results highlight the fundamental role played by the geometry to control the dynamics and mechanical stability of hybrid materials in order to tailor properties and maximize performance. [ABSTRACT FROM AUTHOR]

We study active Brownian particles as a paradigm for a genuine nonequilibrium phase transition requiring steady driving. Access to the critical point in computer simulations is obstructed by the fact that the density is conserved. We propose a method based on arguments from finite-size scaling to determine critical points and successfully test it for the two-dimensional (2D) Ising model. Using this method allows us to accurately determine the critical point of two-dimensional active Brownian particles at Pecr=40(2), ϕcr=0.597(3). Based on this estimate, we study the corresponding critical exponents β, γ/ν, and ν. Our results are incompatible with the 2D-Ising exponents, thus raising the question whether there exists a corresponding nonequilibrium universality class. [ABSTRACT FROM AUTHOR]

We study a generic model for quorum-sensing bacteria in circular confinement. Every bacterium produces signaling molecules, the local concentration of which triggers a response when a certain threshold is reached. If this response lowers the motility, then an aggregation of bacteria occurs which differs fundamentally from standard motility-induced phase separation due to the long-ranged nature of the concentration of signal molecules. We analyze this phenomenon analytically and by numerical simulations employing two different protocols leading to stationary cluster and ring morphologies, respectively. [ABSTRACT FROM AUTHOR]

Aligned superhydrophobic surfaces with the same texture orientation reduce drag in the channel and generate secondary flows transverse to the direction of the applied pressure gradient. Here we show that a transverse shear can be easily generated by using superhydrophobic channels with misaligned textured surfaces. We propose a general theoretical approach to quantify this transverse flow by introducing the concept of an effective shear tensor. To illustrate its use, we present approximate theoretical solutions and Dissipative Particle Dynamics simulations for striped superhydrophobic channels. Our results demonstrate that the transverse shear leads to complex flow patterns, which provide a new mechanism of a passive vertical mixing at the scale of a texture period. Depending on the value of Reynolds number two different scenarios occur. At relatively low Reynolds number the flow represents a transverse shear superimposed with two corotating vortices. For larger Reynolds number these vortices become isolated, by suppressing fluid transport in the transverse direction. [ABSTRACT FROM AUTHOR]

Rafts, or functional domains, are transient nano-or mesoscopic structures in the plasma membrane and are thought to be essential for many cellular processes such as signal transduction, adhesion, trafficking, and lipid or protein sorting. Observations of these membrane heterogeneities have proven challenging, as they are thought to be both small and short lived. With a combination of coarse-grained molecular dynamics simulations and neutron diffraction using deuterium labeled cholesterol molecules, we observe raftlike structures and determine the ordering of the cholesterol molecules in binary cholesterol-containing lipid membranes. From coarse-grained computer simulations, heterogenous membranes structures were observed and characterized as small, ordered domains. Neutron diffraction was used to study the lateral structure of the cholesterol molecules. We find pairs of strongly bound cholesterol molecules in the liquid-disordered phase, in accordance with the umbrella model. Bragg peaks corresponding to ordering of the cholesterol molecules in the raftlike structures were observed and indexed by two different structures: a monoclinic structure of ordered cholesterol pairs of alternating direction in equilibrium with cholesterol plaques, i.e., triclinic cholesterol bilayers. [ABSTRACT FROM AUTHOR]

We propose a design for polymer-based sensors and switches with sharp switching transition and fast response time. The switching mechanism involves a radical change in the conformations of adsorption-active minority chains in a brush. Such transitions can be induced by a temperature change of only about ten degrees, and the characteristic time of the conformational change is less than a second. We present an analytical theory for these switches and support it by self-consistent field calculations and Brownian dynamics simulations. [ABSTRACT FROM AUTHOR]

The elastic properties of a self-assembled bilayer membrane are studied using the self-consistent field theory, applied to a model system composed of flexible amphiphilic chains dissolved in hydrophilic polymeric solvents. Examining the free energy of bilayer membranes with different geometries allows us to calculate their bending modulus, Gaussian modulus, two fourth-order membrane moduli, and the line tension. The dependence of these parameters on the microscopic characteristics of the amphiphilic chain, characterized by the volume fraction of the hydrophilic component, is systematically studied. The theoretical predictions are compared with the results from a simple monolayer model, which approximates a bilayer membrane by two monolayers. The region of validity of the linear elasticity theory is analyzed by examining the higher-order contributions. [ABSTRACT FROM AUTHOR]

We propose a method to separate enantiomers in microfluidic or nanofluidic channels. It requires flow profiles that break chiral symmetry and have regions with high local shear. Such profiles can be generated in channels confined by walls with different hydrodynamic boundary conditions (e.g., slip lengths). Because of a nonlinear hydrodynamic effect, particles with different chirality migrate at different speeds and can be separated. The mechanism is demonstrated by computer simulations. We investigate the influence of thermal fluctuations (i.e., the Péclet number) and show that the effect disappears in the linear response regime. The details of the microscopic flow are important and determine which volume forces are necessary to achieve separation. [ABSTRACT FROM AUTHOR]

Experimental data on thin films of cylinder-forming block copolymers (BC)--free-standing BC membranes as well as supported BC films--strongly suggest that the local orientation of the BC patterns is coupled to the geometry in which the patterns are embedded. We analyze this phenomenon using general symmetry considerations and numerical self-consistent field studies of curved BC films in cylindrical geometry. The stability of the films against curvature-induced dewetting is also analyzed. In good agreement with experiments, we find that the BC cylinders tend to align along the direction of curvature at high curvatures. At low curvatures, we identify a transition from perpendicular to parallel alignment in supported films, which is absent in free-standing membranes. Hence both experiments and theory show that curvature can be used to manipulate and align BC patterns. [ABSTRACT FROM AUTHOR]

We study the energetics and stability of branched tubular membrane structures by computer simulations of a triangulated network model. We find that triple (Y) junctions can be created and stabilized by applying mechanical forces, if the angle between branches is 120°. The same holds for tetrahedral junctions with tetraeder angles. If the wrong angles are enforced, the branches coalesce to a linear structure, a pure tube. After releasing the mechanical force, Y-branched structures remain metastable if one constrains the enclosed volume and the average curvature (the area difference) to a fixed value; tetrahedral junctions however split up into two Y junctions. Somewhat counterintuitively, the energy cost of adding a Y branch is negative in structures with fixed surface area and tube diameter, even if one accounts for the positive contribution of the additional branch end. For fixed average curvature, however, adding a branch also enforces a thinning of tubes, therefore the overall curvature energy cost is positive. Possible implications for the stability of branched networks structures in cells are discussed.

Experimental data on thin films of cylinder-forming block copolymers (BC)-free-standing BC membranes as well as supported BC films-strongly suggest that the local orientation of the BC patterns is coupled to the geometry in which the patterns are embedded. We analyze this phenomenon using general symmetry considerations and numerical self-consistent field studies of curved BC films in cylindrical geometry. The stability of the films against curvature-induced dewetting is also analyzed. In good agreement with experiments, we find that the BC cylinders tend to align along the direction of curvature at high curvatures. At low curvatures, we identify a transition from perpendicular to parallel alignment in supported films, which is absent in free-standing membranes. Hence both experiments and theory show that curvature can be used to manipulate and align BC patterns.

The elastic properties of a self-assembled bilayer membrane are studied using the self-consistent field theory, applied to a model system composed of flexible amphiphilic chains dissolved in hydrophilic polymeric solvents. Examining the free energy of bilayer membranes with different geometries allows us to calculate their bending modulus, Gaussian modulus, two fourth-order membrane moduli, and the line tension. The dependence of these parameters on the microscopic characteristics of the amphiphilic chain, characterized by the volume fraction of the hydrophilic component, is systematically studied. The theoretical predictions are compared with the results from a simple monolayer model, which approximates a bilayer membrane by two monolayers. The region of validity of the linear elasticity theory is analyzed by examining the higher-order contributions.

The influence of the patchiness and correlations in the distribution of hydrophobic and polar residues at the interface between two rigid biomolecules on their recognition ability is investigated in idealized coarse-grained lattice models. A general two-stage approach is utilized where an ensemble of probe molecules is designed first and the recognition ability of the probe ensemble is related to the free energy of association with both the target molecule and a different rival molecule in a second step. The influence of correlation effects are investigated using numerical Monte Carlo techniques and mean field methods. Correlations lead to different optimum characteristic lengths of the hydrophobic and polar patches for the mutual design of the two biomolecules on the one hand and their recognition ability in the presence of other molecules on the other hand.

We present an extensive computer simulation study of structure formation in amphiphilic block copolymer solutions after a quench from a homogeneous state. By using a mesoscopic field-based simulation method, we are able to access time scales in the range of a second. A "phase diagram" of final structures is mapped out as a function of the concentration and solvent philicity of the copolymers. A rich spectrum of structures is observed, ranging from spherical and rodlike micelles and vesicles to toroidal and net-cage micelles. The dynamical pathways leading to these structures are analyzed in detail, and possible ways to control the structures are discussed briefly.

Using Langevin simulations, we find that simple "generic" bead-and-spring homopolymer chains in a sufficiently bad solvent spontaneously develop helical order during the process of collapsing from an initially stretched conformation. The helix formation is initiated by the unstable modes of the straight chain, which drive the system towards a long-lived metastable transient state. The effect is most pronounced if hydrodynamic interactions are screened.

Equilibrium aspects of the molecular recognition of rigid biomolecules are investigated using coarse-grained lattice models. The analysis is carried out in two stages. First, an ensemble of probe molecules is designed with respect to the target biomolecule. The recognition ability of the probe ensemble is then investigated by calculating the free energy of association. The influence of cooperative and anticooperative effects accompanying the association of the target and probe molecules is studied. Numerical findings are presented and compared to analytical results which can be obtained in the limit of dominating cooperativity and in the mean-field formulation of the models.

We reproduce the symmetric and asymmetric "rippled" P(beta') states of lipid membranes by Monte Carlo simulations of a coarse-grained molecular model for lipid-solvent mixtures. The structure and properties compare favorably with experiments. The asymmetric ripple state is characterized by a periodic array of fully interdigitated "defect" lines. The symmetric ripple state maintains a bilayer structure, but is otherwise structurally similar. The main force driving the formation of both ripple states is the propensity of lipid molecules with large head groups to exhibit splay.

We present a simple model which allows us to investigate the equilibrium aspects of molecular recognition between rigid biomolecules on a generic level. Using a two-stage approach, which consists of a design and a testing step, the role of cooperativity and of varying bond strength in molecular recognition is investigated. Cooperativity is found to enhance selectivity. In complexes which require a high binding flexibility, a small number of strong bonds seems to be favored compared to a situation with many but weak bonds.

DNA migration in topologically structured microchannels with periodic cavities is investigated experimentally and with Brownian dynamics simulations of a simple bead-spring model. The results are in very good agreement with one another. In particular, the experimentally observed migration order of lambda - and T2-DNA molecules is reproduced by the simulations. The simulation data indicate that the mobility may depend on the chain length in a nonmonotonic way at high electric fields. This is found to be the signature of a nonequilibrium bistability between two different migration states, a slow one and a fast one. The latter can also be observed experimentally under appropriate conditions.

We investigate the mechanisms underlying selective molecular recognition of single heteropolymers at chemically structured planar surfaces. To this end, we study systems with two-letter (HP) lattice heteropolymers by exact enumeration techniques. Selectivity for a particular surface is defined by an adsorption energy criterion. We analyze the distributions of selective sequences and the role of mutations. A particularly important factor for molecular recognition is the small-scale structure on the polymers.