Relaxation of self-entangled many-arm star polymers

We present a description of the relaxation of star polymers based on the conformational scaling properties predicted by Daoud and Cotton and confirmed in our recent simulations. We identify three typical relaxation mechanisms. The first describes elastic deformation of the overall shape. Its relaxation time is nearly independent off. A second type of relaxation occurs via rotational diffusion. We predict that the relaxation time should scale with Nwlfz-v where Y is the correlation length exponent. A third relaxation process is the disentanglement of two or more arms. Here the longest relaxation time should increase exponentially with f llz. We measure various relaxation processes by molecul…

Engineering von Proteinen an Oberflächen: Von komplementärer Charakterisierung zu Materialoberflächen mit maßgeschneiderten Funktionen

Crossover scaling in semidilute polymer solutions: a Monte Carlo test

Evidence for the time-temperature superposition principle from Monte-Carlo simulations of the glass transition in two-dimensional polymer melts

The bond fluctuation model on a square lattice with a bond-length dependent potential exhibits in simulations of slow cooling a kinetic glass transition where the system falls out of equilibrium. Extending previous work, the relaxation functions of gyration radius and end-to-end distance, and the bond autocorrelation function of the polymers are presented and related to the time-dependent displacements of inner monomeric units and center of gravity of the whole chains, respectively. Over a wide temperature range the data can be collapsed on master curves satisfying the time-temperature superposition principle for Rouse dynamics.

Derivation of coarse-grained simulation models of chlorophyll molecules in lipid bilayers for applications in light harvesting systems

The correct interplay of interactions between protein, pigment and lipid molecules is highly relevant for our understanding of the association behavior of the light harvesting complex (LHCII) of green plants. To cover the relevant time and length scales in this multicomponent system, a multi-scale simulation ansatz is employed that subsequently uses a classical all atomistic (AA) model to derive a suitable coarse grained (CG) model which can be backmapped into the AA resolution, aiming for a seamless conversion between two scales. Such an approach requires a faithful description of not only the protein and lipid components, but also the interaction functions for the indispensable pigment mo…

Dynamics of Dense Polymers: A Molecular Dynamics Approach

The physics of polymeric materials[1, 2] is one of the most challenging problems in condensed matter physics today. It is a problem of great interest both from a fundamental viewpoint and for their various technical applications. In addition to theortical and experimental approaches, computer simulations[3–11] have played an important role in our present understanding of polymers. For static properties Monte Carlo methods have been widely used and give excellent results for static critical exponents. To investigate dynamic properties three different methods — Monte Carlo (MC)[3–7], molecular dynamics (MD)[8, 9] and Brownian dynamics methods[10] — have been used. Detailed microscopic dynamic…

Engineering Proteins at Interfaces: From Complementary Characterization to Material Surfaces with Designed Functions

Abstract Once materials come into contact with a biological fluid containing proteins, proteins are generally—whether desired or not—attracted by the material's surface and adsorb onto it. The aim of this Review is to give an overview of the most commonly used characterization methods employed to gain a better understanding of the adsorption processes on either planar or curved surfaces. We continue to illustrate the benefit of combining different methods to different surface geometries of the material. The thus obtained insight ideally paves the way for engineering functional materials that interact with proteins in a predetermined manner.

Indefinitely growing self-avoiding walk.

We introduce a new random walk with the property that it is strictly self-avoiding and grows forever. It belongs to a different universality class from the usual self-avoiding walk. By definition the critical exponent $\ensuremath{\gamma}$ is equal to 1. To calculate the exponent $\ensuremath{\nu}$ of the mean square end-to-end distance we have performed exact enumerations on the square lattice up to 22 steps. This gives the value $\ensuremath{\nu}=0.57\ifmmode\pm\else\textpm\fi{}0.01$.

Precision Anisotropic Brush Polymers by Sequence Controlled Chemistry

The programming of nanomaterials at molecular length-scales to control architecture and function represents a pinnacle in soft materials synthesis. Although elusive in synthetic materials, Nature has evolutionarily refined macromolecular synthesis with perfect atomic resolution across three-dimensional space that serves specific functions. We show that biomolecules, specifically proteins, provide an intrinsic macromolecular backbone for the construction of anisotropic brush polymers with monodisperse lengths via grafting-from strategy. Using human serum albumin as a model, its sequence was exploited to chemically transform a single cysteine, such that the expression of said functionality is…

Comparing equilibration schemes of high-molecular-weight polymer melts with topological indicators.

Abstract Recent theoretical studies have demonstrated that the behaviour of molecular knots is a sensitive indicator of polymer structure. Here, we use knots to verify the ability of two state-of-the-art algorithms—configuration assembly and hierarchical backmapping—to equilibrate high-molecular-weight (MW) polymer melts. Specifically, we consider melts with MWs equivalent to several tens of entanglement lengths and various chain flexibilities, generated with both strategies. We compare their unknotting probability, unknotting length, knot spectra, and knot length distributions. The excellent agreement between the two independent methods with respect to knotting properties provides an addit…

Modelling of Orientational Ordering in Lipid Monolayers

Lipid monolayers at high densities are modelled as rigid rods grafted to an interface at the sites of a regular lattice. The transition between the state where the rods are uniformly tilted to a disordered state with no (average) tilt is studied by computer simulation methods. For the one-dimensional model, the molecular dynamics approach is found much less suitable to equilibrate the system rather than Monte Carlo methods. Both in d=2 discretized versions of Monte Carlo codes are much more efficient than continuum Monte Carlo methods, in spite of huge storage requirements. While in d=l the transition occurs at temperature T=0 via the spontaneous creation of solitons, at d=2 a finite temper…

Monte Carlo simulation of DNA electrophoresis

This paper describes an attempt to study the electrophoresis mobility of a DNA molecule in a gel by means of a Monte Carlo simulation. We find that the electrophoresis mobility mu can be well described by the empirical equation mu v kappa 1/N + kappa 2E2 with N being the number of monomers of the model chain and E being the applied field. For small E the data can merge into the linear response result mu = kappa 1/N. The paper also discusses necessary extensions of the present approach.

Computational Studies of Biomembrane Systems : Theoretical Considerations, Simulation Models, and Applications

This chapter summarizes several approaches combining theory, simulation, and experiment that aim for a better understanding of phenomena in lipid bilayers and membrane protein systems, covering topics such as lipid rafts, membrane-mediated interactions, attraction between transmembrane proteins, and aggregation in biomembranes leading to large superstructures such as the light-harvesting complex of green plants. After a general overview of theoretical considerations and continuum theory of lipid membranes we introduce different options for simulations of biomembrane systems, addressing questions such as: What can be learned from generic models? When is it expedient to go beyond them? And, w…

Structure and dynamics of yukawa systems

Abstract Results of molecular dynamics simulations modelling two component charge stabilized colloidal particles interacting via a Yukawa potential are presented. After cooling, the systems freeze into either substitutionally disordered imperfect crystals or into glasslike states. This freezing is characterized by the divergence of a suitable correlation time due to loss of ergodicity. Describing the structure by bond correlation functions, local orientational ordering is observed in the glassy states which is not present in the liquid. In the liquid the diffusion constant obeys an Arrhenius law. As can be deduced from the van Hove functions, in the crystal the particles only oscillate arou…

Microscopic verification of dynamic scaling in dilute polymer solutions: A molecular-dynamics simulation

The dynamics of a single polymer chain immersed in a large number of solvent particles is studied by molecular dynamics. This is the first simulation where chain length (30, 40, and 60 monomers) and statistical accuracy are sufficient to test the predictions of the Zimm model as a result of the particle-particle interactions: The short-time diffusion constant is in good agreement with the Kirkwood prediction, and the monomer motions exhibit the expected dynamic scaling. The long-range hydrodynamic interaction requires a data analysis that explicitly includes the periodic images via Ewald sums.

Crossover from Rouse to Reptation Dynamics: A Molecular-Dynamics Simulation

We present the results of an extensive molecular-dynamics simulation of a dense polymer system. We show for the first time that simulations are able to cover the whole regime from pure Rouse dynamics to reptation dynamics and give strong evidence of the latter. The mean square displacements clearly exhibit a ${t}^{\frac{1}{4}}$ power law. A mode analysis shows that the high-frequency modes follow the Rouse relaxation while those at lower frequency display reptation relaxation. Both quantities give the same entanglement length.

Computer Simulations for Polymer Dynamics

In this paper we review recent work on the dynamics of polymeric systems using computer simulation methods. For a two-dimensional polymer melt, we show that the chains segregate and the dynamics can be described very well by the Rouse model. This simulation was carried out using the bond fluctuation Monte Carlo method. For three-dimensional (3d) melts and for the study of hydrodynamic effects, we use a molecular dynamics simulation. For 3d melts our results strongly support the concept of reptation. A detailed comparison to experiment shows that we can predict the time and length scales for the onset of reptation for a variety of polymeric liquids. For a single chain, we find the expected h…

Self-diffusion in polymer solutions using the bond-fluctuation MC-algorithm

Abstract A lattice Monte Carlo study of the self-diffusion of polymer chains in an athermal solution of equal chains is presented. The examined chain lengths, N (= 20–200), and volume fractions, φ (= 0.025-0.5), cover the range from dilute solution to concentrated solution, respectively. The dynamics show a gradual crossover from Rouse to reptation-like behaviour. Analysing the data according to a scaling theory and taking into account the density dependence of the microscopic length and time-scales, an almost perfect scaling of the self-diffusion coefficient is achieved. The high statistical accuracy of the data (103–104 chains per parameter combination) was obtainable by using a transpute…

Bridging the Gap Between Atomistic and Coarse-Grained Models of Polymers: Status and Perspectives

Recent developments that increase the time and distance scales accessible in the simulations of specific polymers are reviewed. Several different techniques are similar in that they replace a model expressed in fully atomistic detail with a coarse-grained model of the same polymer, atomistic → coarse-grained (and beyond!), thereby increasing the time and distance scales accessible within the expenditure of reasonable computational resources. The bridge represented by the right-pointing arrow can be constructed via different procedures, which are reviewed here. The review also considers the status of methods which reverse this arrow, atomistic ← coarse-grained. This “reverse-mapping” recover…

Defects and defect engineering in Soft Matter.

Soft matter covers a wide range of materials based on linear or branched polymers, gels and rubbers, amphiphilic (macro)molecules, colloids, and self-assembled structures. These materials have applications in various industries, all highly important for our daily life, and they control all biological functions; therefore, controlling and tailoring their properties is crucial. One way to approach this target is defect engineering, which aims to control defects in the material's structure, and/or to purposely add defects into it to trigger specific functions. While this approach has been a striking success story in crystalline inorganic hard matter, both for mechanical and electronic properti…

Simulations of Polymers in Confined Geometries

The properties of flexible polymers moving inside porous structures are believed to be relevant to practical problems such as filtration, gel permeation chromatography, heterogeneous catalysis, oil recuperation, etc.1. Similarly the adsorption of macromolecules on interfaces plays an important role for problems such as adhesion, flocculation and stabilisation of colloid particles, biological membrane function, artificial organs in medicine, etc. 2. Aside from this eventual practical application, the configurational statistics of polymers in such confined geometries is a challenging problem of theoretical physics. The present brief review will be concerned with the study of a single long fle…

Computer simulation of the glass transition of polymer melts

Bond fluctuation models on square and simple cubic lattices at melt densities are simulated, using potentials depending on the length of the (effective) bond (and also on the bond angle, in d=3 dimensions). Various relaxation functions have the Kohlrausch-Williams-Watts (KWW) form; the associated relaxation time diverges as exp (const/T 2) in d=2 and as exp [const/T−T 0)] in d=3. For d=3 the self-diffusion constant also follows the Vogel-Fulcher law, with T 0=250 K for chain lengths N=20 and potentials adapted to bisphenol-A-polycarbonate [BPA-PC].