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We present a hybrid method for the simulation of colloidal systems that combines molecular dynamics (MD) with the Lattice Boltzmann (LB) scheme. The LB method is used as a model for the solvent in order to take into account the hydrodynamic mass and momentum transport through the solvent. The colloidal particles are propagated via MD and they are coupled to the LB fluid by viscous forces. With respect to the LB fluid, the colloids are represented by uniformly distributed points on a sphere. Each such point [with a velocity V(r) at any off-lattice position r] is interacting with the neighboring eight LB nodes by a frictional force F = xi0(V(r)-u(r)), with xi0 being a friction coefficient and u(r) being the velocity of the fluid at the position r. Thermal fluctuations are introduced in the framework of fluctuating hydrodynamics. This coupling scheme has been proposed recently for polymer systems by Ahlrichs and Dunweg [J. Chem. Phys. 111, 8225 (1999)]. We investigate several properties of a single colloidal particle in a LB fluid, namely, the effective Stokes friction and long-time tails in the autocorrelation functions for the translational and rotational velocity. Moreover, a charged colloidal system is considered consisting of a macroion, counterions, and coions that are coupled to a LB fluid. We study the behavior of the ions in a constant electric field. In particular, an estimate of the effective charge of the macroion is yielded from the number of counterions that move with the macroion in the direction of the electric field.

We study semidilute star-polymer solutions under shear flow by hybrid mesoscale simulations. Hydrodynamic interactions are modeled by two particle-based simulation techniques, multiparticle collision dynamics (MPC) and dissipative particle dynamics (DPD). Star polymers are considered as a paradigmatic model for ultra-soft colloids with variable softness. The influence of concentration and shear rate on their structural and rheological properties is investigated. Under flow, a star polymer elongates and displays a well-defined alignment angle with respect to the flow direction. Moreover, the structural and rheological properties exhibit a universal behavior as a function of a concentrationdependent Weissenberg number for various concentrations at a given arm length. The rheological properties are characterized by the shear viscosity and the normal-stress coefficients. In dilute solution, the zero-shear viscosity follows the Einstein relation with an effective radius given by the hydrodynamic radius of a star polymer. At high shear rates, the solutions exhibit shear-thinning behavior, where the viscosity decreases faster with increasing shear rate at higher concentrations. We demonstrate that the results obtained from MPC and DPD agree in all scaling properties, with minor quantitative deviations in the numerical values.

The dynamical and rheological properties of ultrasoft colloids and star polymers are investigated in dilute and semidilute solutions under linear shear flow. We apply a hybrid mesoscale hydrodynamics simulation approach, which combines molecular dynamics simulations for the solute with the multiparticle collision dynamics approach for the solvent. We investigate the effect of concentration on relaxation, diffusion, and the rheological properties of the star polymers. We find that the relaxation time of a star-polymer arm is a universal function of a concentration-dependent Weissenberg number. The center-of-mass mean square displacements of the star polymers are anisotropic under shear flow. At high shear rate, we find shear-induced enhanced center-of-mass displacements along the vorticity and gradient directions. Moreover, we determine the shear viscosity and normal stress coefficients as a function of concentration. The shear viscosity exhibits shear thinning with a weak functionality dependence.

Using computer simulations, the electrophoretic motion of a positively charged colloid (macroion) in an electrolyte solution is studied in the framework of the primitive model. In this model, the electrolyte is considered as a system of negatively and positively charged microions (counterions and coions, respectively) that are immersed into a structureless medium. Hydrodynamic interactions are fully taken into account by applying a hybrid simulation scheme, where the charged ions (i.e., macroion and electrolyte), propagated via molecular dynamics, are coupled to a lattice Boltzmann (LB) fluid. In a recent electrophoretic experiment by Martin-Molina et al. [J. Phys. Chem. B 106, 6881 (2002)], it was shown that, for multivalent salt ions, the mobility mu initially increases with charge density sigma, reaches a maximum, and then decreases with further increase of sigma. The aim of the present work is to elucidate the behavior of mu at high values of sigma. Even for the case of monovalent microions, a decrease of mu with sigma is found. A dynamic Stern layer is defined that includes all the counterions that move with the macroion while subjected to an external electrical field. The number of counterions in the Stern layer, q(0), is a crucial parameter for the behavior of mu at high values of sigma. In this case, the mobility mu depends primarily on the ratio q(0)/Q (with Q the valency of the macroion). The previous contention that the increase in the distortion of the electric double layer (EDL) with increasing sigma leads to the lowering of mu does not hold for high sigma. In fact, it is shown that the deformation of the EDL decreases with the increase of sigma. The role of hydrodynamic interactions is inferred from direct comparisons to Langevin simulations where the coupling to the LB fluid is switched off. Moreover, systems with divalent counterions are considered. In this case, at high values of sigma the phenomenon of charge inversion is found.

We investigate structural and dynamical properties of ultra-soft colloids in dilute and semi-dilute solutions by hybrid mesoscale simulations under linear shear flow. In particular, the influence of functionality on these properties is addressed. Our study combines molecular dynamics simulations for the solute with the multiparticle collision dynamics approach for the coarse-grained solvent. The star polymers exhibit large conformational and orientational changes in shear flow, which we characterize by the radius of gyration tensor and the alignment angle. These quantities show a universal dependence on a concentration- and functionality-dependent Weissenberg number with slight deviations at high shear rates. Moreover, the star polymers display a rotational dynamics with a shear-rate- and concentration-dependent rotation frequency. We attribute the concentration dependence to the screening of hydrodynamic interactions in semi-dilute star-polymer solutions.

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Using data from contact maps of the DNA-polymer of E. Coli (at kilobase pair resolution) as an input to our model, we introduce cross-links between monomers in a bead-spring model of a ring polymer at very specific points along the chain. By suitable Monte Carlo Simulations, we show that the presence of these cross-links leads to a particular architecture and organization of the chain at large (micron) length scales of the DNA. We also investigate the structure of a ring polymer with an equal number of cross-links at random positions along the chain. We find that though the polymer does get organized at the large length scales, the nature of the organization is quite different from the organization observed with cross-links at specific biologically determined positions. We used the contact map of E. Coli bacteria which has around 4.6 million base pairs in a single circular chromosome. In our coarse-grained flexible ring polymer model, we used 4642 monomer beads and observed that around 80 cross-links are enough to induce the large-scale organization of the molecule accounting for statistical fluctuations caused by thermal energy. The length of a DNA chain of an even simple bacterial cell such as E. Coli is much longer than typical proteins, hence we avoided methods used to tackle protein folding problems. We define new suitable quantities to identify large scale structure of a polymer chain with a few cross-links.