Jt Johan Padding

Hydrodynamic interactions and Brownian forces in colloidal suspensions: Coarse-graining over time and length scales

We describe in detail how to implement a coarse-grained hybrid molecular dynamics and stochastic rotation dynamics simulation technique that captures the combined effects of Brownian and hydrodynamic forces in colloidal suspensions. The importance of carefully tuning the simulation parameters to correctly resolve the multiple time and length scales of this problem is emphasized. We systematically analyze how our coarse-graining scheme resolves dimensionless hydrodynamic numbers such as the Reynolds number Re, which indicates the importance of inertial effects, the Schmidt number Sc, which indicates whether momentum transport is liquidlike or gaslike, the Mach number, which measures compressibility effects, the Knudsen number, which describes the importance of noncontinuum molecular effects, and the Peclet number, which describes the relative effects of convective and diffusive transport. With these dimensionless numbers in the correct regime the many Brownian and hydrodynamic time scales can be telescoped together to maximize computational efficiency while still correctly resolving the physically relevant processes. We also show how to control a number of numerical artifacts, such as finite-size effects and solvent-induced attractive depletion interactions. When all these considerations are properly taken into account, the measured colloidal velocity autocorrelation functions and related self-diffusion and friction coefficients compare quantitatively with theoretical calculations. By contrast, these calculations demonstrate that, notwithstanding its seductive simplicity, the basic Langevin equation does a remarkably poor job of capturing the decay rate of the velocity autocorrelation function in the colloidal regime, strongly underestimating it at short times and strongly overestimating it at long times. Finally, we discuss in detail how to map the parameters of our method onto physical systems and from this extract more general lessons-keeping in mind that there is no such thing as a free lunch-that may be relevant for other coarse-graining schemes such as lattice Boltzmann or dissipative particle dynamics.

Time and length scales of polymer melts studied by coarse-grained molecular dynamics simulations

We present coarse-grained molecular dynamics simulations of linear polyethylene (PE) melts, ranging in chain length from C80 to C1000. The employed effective potentials, frictions, and random forces are all derived from detailed molecular dynamics simulations, leaving no adjustable parameters. Uncrossability constraints are introduced in the coarse-grained model to prevent unphysical bond crossings. The dynamic and zero-shear rate rheological properties are investigated and compared with experiment and other simulation work. In the analysis of the internal relaxations we identify a new length scale, called the slowing down length Ns, which is smaller than the entanglement length Ne. The effective segmental friction rapidly increases around Ns leading, at constant density, to a transition in the scaling of the diffusion coefficient from D~N–1 to D~N–2, a transition in the scaling of the viscosity from ~N to ~N1.8, and conspicuous nonexponential relaxation behavior. These effects are attributed to strong local kinetic constraints caused by both chain stiffness and interchain interactions. The onset of nonlocal (entanglement) effects occurs at a chain length of C120. Full entanglement effects are observed only above C400, where the shear relaxation modulus displays a plateau and the single chain coherent dynamic structure factor agrees with the reptation model.

Uncrossability constraints in mesoscopic polymer melt simulations: Non-Rouse behavior of C120H242

An important feature of a melt of long polymers is that the bonds of the chains cannot cross each other. This seemingly simple fact has a great impact on the long time dynamics and rheology of the material. In this paper an algorithm is described that explicitly detects and prevents bond crossings in mesoscopic simulations of polymers. The central idea is to view the bonds as slippery elastic bands which can become entangled. The method is applied to a simulation of a coarse-grained melt of C120H242, in which each chain is represented by six blobs. The long time dynamics and zero-shear rate rheology are investigated and the relative importance of uncrossability and chain stiffness is established. As a result of the uncrossability of the chains, we observe a subdiffusive exponent in the mean square displacement of the chains, a stretching of the exponential decay of the Rouse mode relaxations, an increase of relaxation times associated with large scales, and a slowing down of the relaxation of the dynamic structure factor. These results are in agreement with results from previous microscopic molecular dynamics simulations. Finally, an increased viscosity as compared to the Rouse model is observed, which is attributed to slowly decaying interchain stress components.

Hydrodynamic and Brownian Fluctuations in Sedimenting Suspensions

We use a mesoscopic computer simulation method to study the interplay between hydrodynamic and Brownian fluctuations during steady-state sedimentation of hard sphere particles for Peclet numbers (Pe) ranging from 0.1-15. Even when the hydrodynamic interactions are an order of magnitude weaker than Brownian forces, they still induce backflow effects that dominate the reduction of the average sedimentation velocity with increasing particle packing fraction. Velocity fluctuations, on the other hand, begin to show nonequilibrium hydrodynamic character for Pe>1.

Systematic coarse-graining of the dynamics of entangled polymer melts: the road from chemistry to rheology

For optimal processing and design of entangled polymeric materials it is important to establish a rigorous link between the detailed molecular composition of the polymer and the viscoelastic properties of the macroscopic melt. We review current and past computer simulation techniques and critically assess their ability to provide such a link between chemistry and rheology. We distinguish between two classes of coarse-graining levels, which we term coarse-grained molecular dynamics (CGMD) and coarse-grained stochastic dynamics (CGSD). In CGMD the coarse-grained beads are still relatively hard, thus automatically preventing bond crossing. This also implies an upper limit on the number of atoms that can be lumped together (up to five backbone carbon atoms) and therefore on the longest chain lengths that can be studied. To reach a higher degree of coarse-graining, in CGSD many more atoms are lumped together (more than ten backbone carbon atoms), leading to relatively soft beads. In that case friction and stochastic forces dominate the interactions, and action must be undertaken to prevent bond crossing. We also review alternative methods that make use of the tube model of polymer dynamics, by obtaining the entanglement characteristics through a primitive path analysis and by simulation of a primitive chain network. We finally review super-coarse-grained methods in which an entire polymer is represented by a single particle, and comment on ways to include memory effects and transient forces.

Interplay between hydrodynamic and Brownian fluctuations in sedimenting colloidal suspensions

We apply a hybrid molecular dynamics and mesoscopic simulation technique to study the steady-state sedimentation of hard sphere particles for Peclet number (Pe) ranging from 0.08 to 12. Hydrodynamic backflow causes a reduction of the average sedimentation velocity relative to the Stokes velocity. We find that this effect is independent of Pe number. Velocity fluctuations show the expected effects of thermal fluctuations at short correlation times. At longer times, nonequilibrium hydrodynamic fluctuations are visible, and their character appears to be independent of the thermal fluctuations. The hydrodynamic fluctuations dominate the diffusive behavior even for modest Pe number, while conversely the short-time fluctuations are dominated by thermal effects for surprisingly large Pe numbers. Inspired by recent experiments, we also study finite sedimentation in a horizontal planar slit. In our simulations distinct lateral patterns emerge, in agreement with observations in the experiments.

Zero-shear stress relaxation and long time dynamics of a linear polyethylene melt: A test of Rouse theory

Results of united atom molecular dynamics simulations of a n-C120H242 melt at 450 K are presented. It is shown that the results of mean square displacement, dynamic structure factor, end-to-end vector autocorrelation, and shear relaxation modulus can consistently be described by the Rouse model with a single set of fit parameters, provided the length scales involved are larger than the statistical segment length b = 1.2 nm. On smaller length scales the stiffness of the chain becomes prominent, and the results deviate increasingly from the Rouse predictions. The shear relaxation modulus G(t) is determined from the stress autocorrelation function from both atomic and molecular points of view. The integrals G(t)dt are found to be identical after 1 ps and a Rouse description is shown to coincide for time scales larger than 0.4 ns. Compared to experimental values, the measured diffusion coefficient is overestimated by 63% and the viscosity is underestimated by 38%, consistent with molecular dynamics simulations of small molecules.

Brownian dynamics simulations of the self- and collective rotational diffusion coefficients of rigid long thin rods

Recently a microscopic theory for the dynamics of suspensions of long thin rigid rods was presented, confirming and expanding the well-known theory by Doi and Edwards [The Theory of Polymer Dynamics (Clarendon, Oxford, 1986)] and Kuzuu [J. Phys. Soc. Jpn. 52, 3486 (1983)]. Here this theory is put to the test by comparing it against computer simulations. A Brownian dynamics simulation program was developed to follow the dynamics of the rods, with a length over a diameter ratio of 60, on the Smoluchowski time scale. The model accounts for excluded volume interactions between rods, but neglects hydrodynamic interactions. The self-rotational diffusion coefficients D(r)(phi) of the rods were calculated by standard methods and by a new, more efficient method based on calculating average restoring torques. Collective decay of orientational order was calculated by means of equilibrium and nonequilibrium simulations. Our results show that, for the currently accessible volume fractions, the decay times in both cases are virtually identical. Moreover, the observed decay of diffusion coefficients with volume fraction is much quicker than predicted by the theory, which is attributed to an oversimplification of dynamic correlations in the theory.

Effects of interparticle attractions on colloidal sedimentation

We use a mesoscopic simulation technique to study the effect of short-ranged interparticle attractions on the steady-state sedimentation of colloidal suspensions. Attractions increase the average sedimentation velocity v(s) compared to the pure hard-sphere case, and for strong enough attractions, a nonmonotonic dependence on the packing fraction phi with a maximum velocity at intermediate phi is observed. Attractions also strongly enhance hydrodynamic velocity fluctuations, which show a pronounced maximum size as a function of phi. These phenomena arise from a complex interplay between nonequilibrium hydrodynamic effects and the thermodynamics of transient cluster formation.

Alignment of particles in sheared viscoelastic fluids

We investigate the shear-induced structure formation of colloidal particles dissolved in non-Newtonian fluids by means of computer simulations. The two investigated visco-elastic fluids are a semi-dilute polymer solution and a worm-like micellar solution. Both shear-thinning fluids contain long flexible chains whose entanglements appear and disappear continually as a result of Brownian motion and the applied shear flow. To reach sufficiently large time and length scales in three-dimensional simulations with up to 96 spherical colloids, we employ the responsive particle dynamics simulation method of modeling each chain as a single soft Brownian particle with slowly evolving inter-particle degrees of freedom accounting for the entanglements. Parameters in the model are chosen such that the simulated rheological properties of the fluids, i.e., the storage and loss moduli and the shear viscosities, are in reasonable agreement with experimental values. Spherical colloids dispersed in both quiescent fluids mix homogeneously. Under shear flow, however, the colloids in the micellar solution align to form strings in the flow direction, whereas the colloids in the polymer solution remain randomly distributed. These observations agree with recent experimental studies of colloids in the bulk of these two liquids.