Burkhard Dünweg

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 ...

Simulation of a single polymer chain in solution by combining lattice Boltzmann and molecular dynamics

In this paper we establish a new efficient method for simulating polymer–solvent systems which combines a lattice Boltzmann approach for the fluid with a continuum molecular-dynamics (MD) model for the polymer chain. The two parts are coupled by a simple dissipative force while the system is driven by stochastic forces added to both the fluid and the polymer. Extensive tests of the new method for the case of a single polymer chain in a solvent are performed. The dynamic and static scaling properties predicted by analytical theory are validated. In this context, the influence of the finite size of the simulation box is discussed. While usually the finite size corrections scale as L−1 (L denoting the linear dimension of the box), the decay rate of the Rouse modes is only subject to an L−3 finite size effect. Furthermore, the mapping to an existing MD simulation of the same system is done so that all physical input values for the new method can be derived from pure MD simulation. Both methods can thus be com...

Lattice Boltzmann Simulations of Soft Matter Systems

This article concerns numerical simulations of the dynamics of particles immersed in a continuum solvent. As prototypical systems, we consider colloidal dispersions of spherical particles and solutions of uncharged polymers. After a brief explanation of the concept of hydrodynamic interactions, we give a general overview of the various simulation methods that have been developed to cope with the resulting computational problems. We then focus on the approach we have devel- oped, which couples a system of particles to a lattice-Boltzmann model representing the solvent degrees of freedom. The standard D3Q19 lattice-Boltzmann model is de- rived and explained in depth, followed by a detailed discussion of complementary methods for the coupling of solvent and solute. Colloidal dispersions are best de- scribed in terms of extended particles with appropriate boundary conditions at the surfaces, while particles with internal degrees of freedom are easier to simulate as an arrangement of mass points with frictional coupling to the solvent. In both cases, particular care has been taken to simulate thermal fluctuations in a consistent way. The usefulness of this methodology is illustrated by studies from our own research, where the dynamics of colloidal and polymeric systems has been investigated in both equilibrium and nonequilibrium situations.

Molecular-Dynamics Simulations of the Thermal Glass Transition in Polymer Melts: a-Relaxation Behavior

We present molecular-dynamics simulations of the thermal glass transition in a dense model polymer liquid. We performed a comparative study of both constant volume and constant pressure cooling of the polymer melt. Great emphasis was laid on a careful equilibration of the dense polymer melt at all studied temperatures. Our model introduces competing length scales in the interaction to prevent any crystallization tendency. In this first manuscript we analyze the structural properties as a function of temperature and the long time or \ensuremath{\alpha}-relaxation behavior as observed in the dynamic structure factor and the self-diffusion of the polymer chains. The \ensuremath{\alpha} relaxation can be consistently analyzed in terms of the mode coupling theory of the glass transition. The mode coupling critical temperature

Vectorized link cell Fortran code for molecular dynamics simulations for a large number of particles

{T}_{c},

Statistical mechanics of the fluctuating lattice Boltzmann equation

and the exponent \ensuremath{\gamma} defining the power law divergence of the \ensuremath{\alpha}-relaxation time scale, both depend on the thermodynamic ensemble employed in the simulation.

Electrophoresis of colloidal dispersions in the low-salt regime

A highly efficient procedure for calculating forces in a molecular dynamics simulation on a vector computer is described. The algorithm is feasible for several thousand particles on currently available machines. The efficiency comes about by a combination of a Verlet table with a link cell algorithm. By a double list data structure, that treats the pairs of interacting particles in a symmetrical manner, the vectorization can be improved significantly. Moreover, the “layering algorithm” recently described by Rapaport can be incorporated. A standard Fortran formulation of the basic procedure is given. We test the algorithm on a Cray XMP/416 for two different Lennard-Jones fluids with interactions truncated at 216 α and 2.5 α. The CPU time is shown to increase linearly with system size. Our link cell method proves to be more efficient than a straightforward search over all pairs as soon as the particle number exceeds about 500.

LATTICE-BOLTZMANN SIMULATION OF POLYMER-SOLVENT SYSTEMS

We propose a derivation of the fluctuating lattice Boltzmann equation that is consistent with both equilibrium statistical mechanics and fluctuating hydrodynamics. The formalism is based on a generalized lattice-gas model, with each velocity direction occupied by many particles. We show that the most probable state of this model corresponds to the usual equilibrium distribution of the lattice Boltzmann equation. Thermal fluctuations about this equilibrium are controlled by the mean number of particles at a lattice site. Stochastic collision rules are described by a Monte Carlo process satisfying detailed balance. This allows for a straightforward derivation of discrete Langevin equations for the fluctuating modes. It is shown that all nonconserved modes should be thermalized, as first pointed out by Adhikari et al. [Europhys. Lett. 71, 473 (2005)]; any other choice violates the condition of detailed balance. A Chapman-Enskog analysis is used to derive the equations of fluctuating hydrodynamics on large length and time scales; the level of fluctuations is shown to be thermodynamically consistent with the equation of state of an isothermal, ideal gas. We believe this formalism will be useful in developing new algorithms for thermal and multiphase flows.

Brownian Dynamics Simulations Without Gaussian Random Numbers

We study the electrophoretic mobility of spherical charged colloids in a low-salt suspension as a function of the colloidal concentration. Using an effective particle charge and a reduced screening parameter, we map the data for systems with different particle charges and sizes, including numerical simulation data with full electrostatics and hydrodynamics and experimental data for latex dispersions, on a single master curve. We observe two different volume fraction-dependent regimes for the electrophoretic mobility that can be explained in terms of the static properties of the ionic double layer.

A new model for simulating colloidal dynamics

We investigate a new method for simulating polymer-solvent systems which combines a lattice-Boltzmann approach for the fluid with a continuum molecular dynamics (MD) model for the polymer chain. The two parts are coupled by a friction force which is proportional to the difference of the monomer velocity and the fluid velocity at the monomers position. The strength of the coupling can be tuned by a friction coefficient. Using this approach we examine the dynamics of one monomer immersed in the fluid, and by adding fluctuations to the fluid and the monomer, also the velocity autocorrelation function of one monomer. This results in the definition of an effective friction coefficient for the dynamics of the monomer. Furthermore we analyze the mapping of the model to an MD simulation, allowing us to compare results obtained using the new method with MD.