Friederike Schmid

Self-consistent-field theories for complex fluids

Recent developments in off-lattice self-consistent-field theories for inhomogeneous complex fluids are reviewed. Particular emphasis is given to the treatment of intermolecular interactions and compressibility, to the role of fluctuations, and to the discussion of the coarse-graining length which is inherent to the theory. Valuable insight can be gained from the comparison of self-consistent-field calculations with Monte Carlo simulations. Finally, some applications of the theory to orientational properties of polymers and copolymers at interfaces, and to the phase behaviour of amphiphiles at surfaces, are presented.

Membrane-Protein Interactions in a Generic Coarse-Grained Model for Lipid Bilayers

We study membrane-protein interactions and membrane-mediated protein-protein interactions by Monte Carlo simulations of a generic coarse-grained model for lipid bilayers with cylindrical hydrophobic inclusions. The strength of the hydrophobic force and the hydrophobic thickness of the proteins are systematically varied. The results are compared with analytical predictions of two popular analytical theories: The Landau-de Gennes theory and the elastic theory. The elastic theory provides an excellent description of the fluctuation spectra of pure membranes and successfully reproduces the deformation profiles of membranes around single proteins. However, its prediction for the potential of mean force between proteins is not compatible with the simulation data for large distances. The simulations show that the lipid-mediated interactions are governed by five competing factors: direct interactions; lipid-induced depletion interactions; lipid bridging; lipid packing; and a smooth long-range contribution. The mechanisms leading to hydrophobic mismatch interactions are critically analyzed.

ANOMALOUS SIZE-DEPENDENCE OF INTERFACIAL PROFILES BETWEEN COEXISTING PHASES OF POLYMER MIXTURES IN THIN-FILM GEOMETRY: A MONTE CARLO SIMULATION

The interfacial profile between coexisting phases of a binary mixture (A,B) in a thin film of thickness D and lateral linear dimensions L depends sensitively on both the linear dimensions and on the nature of the boundary conditions and statistical ensembles applied. These phenomena, generic for systems in confined geometry, are demonstrated by Monte Carlo simulations of the bond fluctuation model of symmetric polymer mixtures, using chains containing NA=NB=N=32 effective monomers connected by effective bonds with an attractive interaction between monomers of the same type and a repulsive interaction between different types. We use short-range potentials at the walls, the right wall favoring A monomers and the left wall B monomers. Periodic boundary conditions are applied in the directions parallel to the walls. Both the canonical and semi-grand-canonical ensemble are studied. We argue that the latter case is appropriate for experiments with a lateral resolution L much less than the actual lateral sample ...

Elastic constants from direct correlation functions in nematic liquid crystals: A computer simulation study

Density functional theories such as the Poniewierski–Stecki theory relate the elastic properties of nematic liquid crystals with their local liquid structure, i.e., with the direct correlation function (DCF) of the particles. We propose a way to determine the DCF in the nematic state from simulations without any approximations, taking into account the dependence of pair correlations on the orientation of the director explicitly. Using this scheme, we evaluate the Frank elastic constants K11, K22, and K33 in a system of soft ellipsoids. The values are in good agreement with those obtained directly from an analysis of order fluctuations. Our method thus establishes a reliable way to calculate elastic constants from pair distributions in computer simulations.

Mesoscopic simulations of the counterion-induced electro-osmotic flow: A comparative study

We present mesoscopic simulations of the counterion-induced electro-osmotic flow in different electrostatic coupling regimes. Two simulation methods are compared, dissipative particle dynamics (DPD) and coupled lattice-Boltzmann/molecular dynamics (LB/MD). A general mapping scheme to match DPD to LB/MD is developed. For the weak coupling regime, analytic expressions for the flow profiles in the presence of partial-slip as well as no-slip boundary conditions are derived from the Poisson-Boltzmann and Stokes equations, which are in good agreement with the numerical results. The influence of electrofriction and partial slip on the flow profiles is discussed.

Structure of Cholesterol in Lipid Rafts.

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.

Thermal fluctuations in a lamellar phase of a binary amphiphile-solvent mixture: A molecular-dynamics study

We investigate thermal fluctuations in a smectic A phase of an amphiphile–solvent mixture with molecular-dynamics simulations. We use an idealized model system, where solvent particles are represented by simple beads, and amphiphiles by bead-and-spring tetramers. At a solvent bead fraction of 20% and sufficiently low temperature, the amphiphiles self-assemble into a highly oriented lamellar phase. Our study aims at comparing the structure of this phase with the predictions of the elastic theory of thermally fluctuating fluid membrane stacks [Lei et al., J. Phys. II 5, 1155 (1995)]. We suggest a method which permits to calculate the bending rigidity and compressibility modulus of the lamellar stack from the simulation data. The simulation results are in reasonable agreement with the theory.

Pores in bilayer membranes of amphiphilic molecules: Coarse-grained molecular dynamics simulations compared with simple mesoscopic models

We investigate pores in fluid membranes by molecular dynamics simulations of an amphiphile-solvent mixture, using a molecular coarse-grained model. The amphiphilic membranes self-assemble into a lamellar stack of amphiphilic bilayers separated by solvent layers. We focus on the particular case of tensionless membranes, in which pores spontaneously appear because of thermal fluctuations. Their spatial distribution is similar to that of a random set of repulsive hard disks. The size and shape distribution of individual pores can be described satisfactorily by a simple mesoscopic model, which accounts only for a pore independent core energy and a line tension penalty at the pore edges. In particular, the pores are not circular: their shapes are fractal and have the same characteristics as those of two-dimensional ring polymers. Finally, we study the size-fluctuation dynamics of the pores, and compare the time evolution of their contour length to a random walk in a linear potential.

Surface Tension of the Isotropic-Nematic Interface

We present the first calculations of the pressure tensor profile in the vicinity of the planar interface between isotropic liquid and nematic liquid crystal, using Onsagers density functional theory and computer simulation. When the liquid crystal director is aligned parallel to the interface, the situation of lowest free energy, there is a large tension on the nematic side of the interface and a small compressive region on the isotropic side. By contrast, for perpendicular alignment, the tension is on the isotropic side. There is excellent agreement between theory and simulation both in the forms of the pressure tensor profiles, and the values of the surface tension.

Mesoscopic Simulations of Electroosmotic Flow and Electrophoresis in Nanochannels

Abstract We review recent dissipative particle dynamics (DPD) simulations of electrolyte flow in nanochannels. A method is presented by which the slip length δ B at the channel boundaries can be tuned systematically from negative to infinity by introducing suitably adjusted wall-fluid friction forces. Using this method, we study electroosmotic flow (EOF) in nanochannels for varying surface slip conditions and fluids of different ionic strength. Analytic expressions for the flow profiles are derived from the Stokes equation, which are in good agreement with the numerical results. Finally, we investigate the influence of EOF on the effective mobility of polyelectrolytes in nanochannels. The relevant quantity characterizing the effect of slippage is found to be the dimensionless quantity κ δ B , where 1 / κ is an effective electrostatic screening length at the channel boundaries.