arXiv subjects

Friederike Schmid

Publications and source records attributed to Friederike Schmid.

At least 127 records · Page 7Linked to original sources

arXiv2005

Isotropic-nematic transition in liquid crystals confined between rough walls

The effect of rough walls on the phase behaviour of a confined liquid crystal (LC) fluid is studied using constant pressure Monte Carlo simulations. The LC is modelled as a fluid of soft ellipsoidal molecules and the rough walls are represented as a hard wall with a number of molecules randomly embedded in them. It is found that the isotropic-nematic (IN) transition is shifted to higher pressures for rougher walls.

cond-mat.soft↗

arXiv2005

Nematic-Isotropic Interfaces Under Shear: A Molecular Dynamics Simulation

We present a large-scale molecular dynamics study of nematic-paranematic interfaces under shear. We use a model of soft repulsive ellipsoidal particles with well-known equilibrium properties, and consider interfaces which are oriented normal to the direction of the shear gradient (common stress case). The director at the interface is oriented parallel to the interface (planar). A fixed average shear rate is imposed with Lees-Edwards boundary conditions, and the heat is dissipated with a profile-unbiased thermostat. First we study the properties of the interface at one particular shear rate in detail. The local interfacial profiles and the capillary wave fluctuations of the interfaces are calculated and compared with those of the corresponding equilibrium interface. Under shear, the interfacial width broadens and the capillary wave amplitudes at large wavelengths increase. The strain is distributed inhomogeneously in the system (shear banding), the local shear rate in the nematic region being distinctly higher than in the paranematic region. Surprisingly, we also observe (symmetry breaking) flow in the {\em vorticity} direction, with opposite direction in the nematic and the paranematic state. Finally, we investigate the stability of the interface for other shear rates and construct a nonequilibrium phase diagram.

cond-mat.soft↗

arXiv2005

Nematic liquid crystals at rough and fluctuating interfaces

Nematic liquid crystals at rough and fluctuating interfaces are analyzed within the Frank elastic theory and the Landau-de Gennes theory. We study specifically interfaces that locally favor planar anchoring. In the first part we reconsider the phenomenon of Berreman anchoring on fixed rough surfaces, and derive new simple expressions for the corresponding azimuthal anchoring energy. Surprisingly, we find that for strongly aligning surfaces, it depends only on the geometrical surface anisotropy and the bulk elastic constants, and not on the precise values of the chemical surface parameters. In the second part, we calculate the capillary waves at nematic-isotropic interfaces. If one neglects elastic interactions, the capillary wave spectrum is characterized by an anisotropic interfacial tension. With elastic interactions, the interfacial tension, i.e. the coefficient of the leading $q^2$ term of the capillary wave spectrum, becomes isotropic. However, the elastic interactions introduce a strongly anisotropic {\em cubic} $q^3$ term. The amplitudes of capillary waves are largest in the direction perpendicular to the director. These results are in agreement with previous molecular dynamics simul

cond-mat.soft↗

arXiv2005

A Simple Computer Model for Liquid Lipid Bilayers

We present a simple coarse-grained bead-and-spring model for lipid bilayers. The system has been developed to reproduce the main (gel-liquid) transition of biological membranes on intermediate length scales of a couple of nanometres and is very efficient from a computational point of view. For the solvent environment, two different models are proposed. The first model forces the lipids to form bilayers by confining their heads in two parallel planes. In the second model, the bilayer is stabilised by a surrounding gas of "phantom" solvent beads, which do not interact with each other. This model takes only slightly more computing time than the first one, while retaining the full membrane flexibility. We calculate the liquid-gel phase boundaries for both models and find that they are very similar.

cond-mat.soft↗

arXiv2005

Molecular recognition in a lattice model: An enumeration study

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 criterium. 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.

physics.bio-ph↗

arXiv2005

Incorporating fluctuations and dynamics in self-consistent field theories for polymer blends

We review various methods to investigate the statics and the dynamics of collective composition fluctuations in dense polymer mixtures within fluctuating-field approaches. The central idea of fluctuating-field theories is to rewrite the partition function of the interacting multi-chain systems in terms of integrals over auxiliary, often complex, fields, which are introduced by means of appropriate Hubbard-Stratonovich transformations. Thermodynamic averages like the average composition and the structure factor can be expressed exactly as averages of these fields. We discuss different analytical and numerical approaches to studying such a theory: The self-consistent field approach solves the integrals over the fluctuating fields in saddle-point approximation. Generalized random phase approximations allow to incorporate Gaussian fluctuations around the saddle point. Field theoretical polymer simulations are used to study the statistical mechanics of the full system with Complex Langevin or Monte Carlo methods. Unfortunately, they are hampered by the presence of a sign problem. In dense system, the latter can be avoided without losing essential physics by invoking a saddle point approximation for the complex field that couples to the total density. This leads to the external potential theory. We investigate the conditions under which this approximation is accurate. Finally, we discuss recent approaches to formulate realistic dynamical time evolution equations for such models. The methods are illustrated by two examples: A study of the fluctuation-induced formation of a polymeric microemulsion in a polymer-copolymer mixture, and a study of early-stage spinodal decomposition in a binary blend.

cond-mat.soft↗

arXiv2005

Fluctuations and Defects in Lamellar Stacks of Amphiphilic Bilayers

We review recent molecular dynamics simulations of thermally activated undulations and defects in the lamellar $L_α$ phase of a binary amphiphile-solvent mixture, using an idealized molecular coarse-grained model: Solvent particles are represented by beads, and amphiphiles by bead-and-spring tetramers. We find that our results are in excellent agreement with the predictions of simple mesoscopic theories: An effective interface model for the undulations, and a line tension model for the (pore) defects. We calculate the binding rigidity and the compressibility modulus of the lamellar stack as well as the line tension of the pore rim. Finally, we discuss implications for polymer-membrane systems.

cond-mat.soft↗

arXiv2005

Influence of sequence correlations on the adsorption of random copolymers onto homogeneous planar surfaces

Using a reference system approach, we develop an analytical theory for the adsorption of random heteropolymers with exponentially decaying and/or oscillating sequence correlations on planar homogeneous surfaces. We obtain a simple equation for the adsorption-desorption transition line. This result as well as the validity of the reference system approach is tested by a comparison with numerical lattice calculations.

cond-mat.soft↗

arXiv2005

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 tension less membranes, in which pores spontaneously appear because of thermal fluctuations. Their spatial distribution is similar to that of a random set of repulsive hard discs. 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.

cond-mat.soft↗

arXiv2005

Polymer adsorption onto random planar surfaces: Interplay of polymer and surface correlation

We study the adsorption of homogeneous or heterogeneous polymers onto heterogeneous planar surfaces with exponentially decaying site-site correlations, using a variational reference system approach. As a main result, we derive simple equations for the adsorption-desorption transition line. We show that the adsorption threshold is the same for systems with quenched and annealed disorder. The results are discussed with respect to their implications for the physics of molecular recognition.

cond-mat.soft↗

arXiv2005

Monte Carlo simulations of liquid crystals near rough walls

The effect of surface roughness on the structure of liquid crystalline fluids near solid substrates is studied by Monte Carlo simulations. The liquid crystal is modelled as a fluid of soft ellipsoidal molecules and the substrate is modelled as a hard wall that excludes the centres of mass of the fluid molecules. Surface roughness is introduced by embedding a number of molecules with random positions and orientations within the wall. It is found that the density and order near the wall are reduced as the wall becomes rougher (i.e. the number of embedded molecules is increased). Anchoring coefficients are determined from fluctuations in the reciprocal space order tensor. It is found that the anchoring strength decreases with increasing surface roughness.

cond-mat.soft↗

arXiv2004

Two-State Migration of DNA in a structured Microchannel

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 phase transition between two different migration states, a slow one and a fast one, which can also be observed experimentally under appropriate conditions.

physics.bio-ph↗

arXiv2004

Amphiphiles at Interfaces: Simulation of Structure and Phase Behavior

Computer simulations of coarse-grained molecular models for amphiphilic systems can provide insight into the the structure of amphiphiles at interfaces. They can help to identify the factors that determine the phase behavior, and they can bridge between atomic descriptions and phenomenological field theories. Here we focus on model systems for amphiphilic membranes. After a brief general introduction, we present selected simulation results on monolayers, bilayers, and bilayer stacks. First, we discuss internal phase transitions in membranes and show that idealized models reproduce the generic phase behavior. Then we consider membrane fluctuations and membrane defects. The simulation data is compared with mesoscopic theories, and effective phenomenological parameters can be extracted.

cond-mat.soft↗

arXiv2004

Mechanisms of DNA separation in entropic trap arrays: A Brownian dynamics simulation

Using Brownian dynamics simulations, we study the migration of long charged chains in an electrophoretic microchannel device consisting of an array of microscopic entropic traps with alternating deep regions and narrow constrictions. Such a device has been designed and fabricated recently by Han et al. for the separation of DNA molecules (Science, 2000). Our simulation reproduces the experimental observation that the mobility increases with the length of the DNA. A detailed data analysis allows to identify the reasons for this behavior. Two distinct mechanisms contribute to slowing down shorter chains. One has been described earlier by Han et al.: the chains are delayed at the entrance of the constriction and escape with a rate that increases with chain length. The other, actually dominating mechanism is here reported for the first time: Some chains diffuse out of their main path into the corners of the box, where they remain trapped for a long time. The probability that this happens increases with the diffusion constant, i.e., the inverse chain length.

physics.bio-ph↗

arXiv2004

A density functional theory study of the confined soft ellipsoid fluid

A system of soft ellipsoid molecules confined between two planar walls is studied using classical Density Functional Theory (DFT). Both the isotropic and nematic phases are considered. The excess free energy is evaluated using two different Ansaetze and the intermolecular interaction is incorporated using two different direct correlation functions (DCF). The first is a numerical DCF obtained from simulations of bulk soft ellipsoid fluids and the second is taken from Parsons-Lee theory. In both the isotropic and nematic phases the numerical DCF gives density and order parameter profiles in reasonable agreement with simulation. The Parsons-Lee DCF also gives reasonable agreement in the isotropic phase but poor agreement in the nematic phase.

cond-mat.mtrl-sci↗

arXiv2004

Fluctuation effects in ternary AB+A+B polymeric emulsions

We present a Monte Carlo approach to incorporating the effect of thermal fluctuations in field theories of polymeric fluids. This method is applied to a field-theoretic model of a ternary blend of AB diblock copolymers with A and B homopolymers. We find a shift in the line of order-disorder transitions from their mean-field values, as well as strong signatures of the existence of a bicontinuous microemulsion phase in the vicinity of the mean-field Lifshitz critical point. This is in qualitative agreement with a recent series of experiments conducted with various three-dimensional realizations of this model system. Further, we also compare our results and the performance of the presently proposed simulation method to that of an alternative method involving the integration of complex Langevin dynamical equations.

cond-mat.mtrl-sci↗

arXiv2004

Formation and structure of the microemulsion phase in two-dimensional ternary AB+A+B polymeric emulsions

We present an analysis of the structure of the fluctuation-induced microemulsion phase in a ternary blend of balanced AB diblock copolymers with equal amounts of A and B homopolymers. To this end, graphical analysis methods are employed to characterize two-dimensional configuration snapshots obtained with the recently introduced Field-Theoretic Monte Carlo (FTMC) method. We find that a microemulsion forms when the mean curvature diameter of the lamellar phase coincides roughly with the periodicity of the lamellar phase. Further, we provide evidence to the effect of a subclassification of the microemulsion into a genuine and a defect-driven region.

cond-mat.soft↗

arXiv2004

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.

cond-mat.soft↗