Kurt Kremer

Dynamics of entangled linear polymer melts: A molecular‐dynamics simulation

We present an extensive molecular‐dynamics simulation for a bead spring model of a melt of linear polymers. The number of monomers N covers the range from N=5 to N=400. Since the entanglement length Ne is found to be approximately 35, our chains cover the crossover from the nonentangled to the entangled regime. The Rouse model provides an excellent description for short chains N<Ne, while the dynamics of the long chains can be described by the reptation model. By mapping the model chains onto chemical species we give estimates of the times and distances of onset of the slowing down in motion due to reptation. Comparison to neutron spin‐echo data confirm our mapping procedure, resolving a discrepancy between various experiments. By considering the primitive chain we are able to directly visualize the confinement to a tube. Analyzing the Rouse mode relaxation allows us to exclude the generalized Rouse models, while the original reptation prediction gives a good description of the data.

Aggregation and vesiculation of membrane proteins by curvature-mediated interactions

Membrane remodelling plays an important role in cellular tasks such as endocytosis, vesiculation and protein sorting, and in the biogenesis of organelles such as the endoplasmic reticulum or the Golgi apparatus. It is well established that the remodelling process is aided by specialized proteins that can sense as well as create membrane curvature, and trigger tubulation when added to synthetic liposomes. Because the energy needed for such large-scale changes in membrane geometry significantly exceeds the binding energy between individual proteins and between protein and membrane, cooperative action is essential. It has recently been suggested that curvature-mediated attractive interactions could aid cooperation and complement the effects of specific binding events on membrane remodelling. But it is difficult to experimentally isolate curvature-mediated interactions from direct attractions between proteins. Moreover, approximate theories predict repulsion between isotropically curving proteins. Here we use coarse-grained membrane simulations to show that curvature-inducing model proteins adsorbed on lipid bilayer membranes can experience attractive interactions that arise purely as a result of membrane curvature. We find that once a minimal local bending is realized, the effect robustly drives protein cluster formation and subsequent transformation into vesicles with radii that correlate with the local curvature imprint. Owing to its universal nature, curvature-mediated attraction can operate even between proteins lacking any specific interactions, such as newly synthesized and still immature membrane proteins in the endoplasmic reticulum.

Towards high charge-carrier mobilities by rational design of the shape and periphery of discotics

Discotic liquid crystals are a promising class of materials for molecular electronics thanks to their self-organization and charge transporting properties. The best discotics so far are built around the coronene unit and possess six-fold symmetry. In the discotic phase six-fold-symmetric molecules stack with an average twist of 30 degrees, whereas the angle that would lead to the greatest electronic coupling is 60 degrees. Here, a molecule with three-fold symmetry and alternating hydrophilic/hydrophobic side chains is synthesized and X-ray scattering is used to prove the formation of the desired helical microstructure. Time-resolved microwave-conductivity measurements show that the material has indeed a very high mobility, 0.2 cm(2) V(-1) s(-1). The assemblies of molecules are simulated using molecular dynamics, confirming the model deduced from X-ray scattering. The simulated structures, together with quantum-chemical techniques, prove that mobility is still limited by structural defects and that a defect-free assembly could lead to mobilities in excess of 10 cm(2) V(-1) s(-1).

Adsorption of polymer chains at surfaces: Scaling and Monte Carlo analyses

The influence of a hard wall on the configurations of long flexible polymer chains near the wall is studied, in the presence of a short‐range attractive force between monomers and the wall. Particular attention is paid to the region around the temperature Ta below which the polymer becomes adsorbed to the wall, i.e., where the typical polymer linear dimensions perpendicular to the wall become independent of chain length. Both ideal noninteracting chains and chains with excluded volume interactions are treated. Polymer linear dimensions parallel and perpendicular to the wall and their probability distributions are studied, as well as the behavior of the monomer fraction at the surface and a distance z in the interior. The relation of polymer statistics to the problem of correlation functions in the n‐vector model of magnetism in the limit n→0 is exploited to express both the exponents describing the various power laws and the crossover scaling functions near Ta in terms of results for the analogous problem...

Simulation of Polymer Melts. I. Coarse-Graining Procedure for Polycarbonates

The paper introduces a systematic procedure to coarse grain atomistic polymer models into a mesoscopic model, which then allows an effective and fast simulation of melts. The method, which provides information on both static and dynamic properties, is tested for three different modifications of polycarbonate. The models successfully describe the variation in the Vogel -Fulcher temperature as well as the total chain extension. The effective speedup compared to the corresponding atomistic simulation is significantly above 10 3 .

The nature of flexible linear polyelectrolytes in salt free solution: A molecular dynamics study

We present results of molecular dynamics simulations of linear polyelectrolytes in solution. The fundamental model for polyelectrolytes in solution is studied. Specifically, simulations are performed for multichain systems of a flexible chain model of charged polymers. The full Coulomb interactions of the monomers and counterions are treated explicitly. Experimental measurements of the osmotic pressure and the structure factor are reproduced. The simulations reveal a new picture of the chain structure based on calculations of the structure factor, persistence length, end‐to‐end distance, etc. We present a detailed discussion of the chain structure and a comparison with present theories. In contrast to the predicted dilute limit of rodlike chains, we find that the chains have significant bending at very low densities. Furthermore, the chains contract significantly before they overlap. We also show that counterion condensation dramatically alters the chain structure.

Molecular dynamics simulation of a polymer chain in solution

Results of a molecular dynamics simulation of a single polymer chain in a good solvent are presented. The latter is modeled explicitly as a bath of particles. This system provides a first‐principles microscopic test of the hydrodynamic Kirkwood–Zimm theory of the chain’s Brownian motion. A 30 monomer chain is studied in 4066 solvent particles as well as 40/4056 and 60/7940 systems. The density was chosen rather high, in order to come close to the ideal situation of incompressible flow, and to ensure that diffusive momentum transport is much faster than particle motions. In order to cope with the numerical instability of microcanonical algorithms, we generate starting states by a Langevin simulation that includes a coupling to a heat bath, which is switched off for the analysis of the dynamics. The long range of the hydrodynamic interaction induces a large effect of finite box size on the diffusive properties, which is observable for the diffusion constants of both the chain and the solvent particles. The ...

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” recovers a model expressed in fully atomistic detail from an arbitrarily chosen replica generated during the simulation of the coarse-grained system. Taken in conjunction with the efficiency of the simulation when the system is in its coarse-grained representation, the overall process Open image in new window permits a much more complete equilibration of the system (larger effective size of Δt) when that equilibration is performed with the coarse-grained replicas (II → III) than if it were attempted with the fully atomistic replicas (I → IV).

Adaptive resolution molecular-dynamics simulation: Changing the degrees of freedom on the fly

We present a new adaptive resolution technique for efficient particle-based multiscale molecular-dynamics simulations. The presented approach is tailor-made for molecular systems where atomistic resolution is required only in spatially localized domains whereas a lower mesoscopic level of detail is sufficient for the rest of the system. Our method allows an on-the-fly interchange between a given molecules atomic and coarse-grained levels of description, enabling us to reach large length and time scales while spatially retaining atomistic details of the system. The new approach is tested on a model system of a liquid of tetrahedral molecules. The simulation box is divided into two regions: one containing only atomistically resolved tetrahedral molecules, and the other containing only one-particle coarse-grained spherical molecules. The molecules can freely move between the two regions while changing their level of resolution accordingly. The hybrid and the atomistically resolved systems have the same statistical properties at the same physical conditions.

Equilibration of long chain polymer melts in computer simulations

Several methods for preparing well equilibrated melts of long chains polymers are studied. We show that the standard method in which one starts with an ensemble of chains with the correct end-to-end distance arranged randomly in the simulation cell and introduces the excluded volume rapidly, leads to deformation on short length scales. This deformation is strongest for long chains and relaxes only after the chains have moved their own size. Two methods are shown to overcome this local deformation of the chains. One method is to first pre-pack the Gaussian chains, which reduces the density fluctuations in the system, followed by a gradual introduction of the excluded volume. The second method is a double-bridging algorithm in which new bonds are formed across a pair of chains, creating two new chains each substantially different from the original. We demonstrate the effectiveness of these methods for a linear bead spring polymer model with both zero and nonzero bending stiffness, however the methods are applicable to more complex architectures such as branched and star polymer.