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 coarsegraining 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.

Effects of alignment layer thickness on the pretilt angle of liquid crystals APL: Org. Electron. Photonics 3, 270 (2010) Effects of alignment layer thickness on the pretilt angle of liquid crystals Appl. Phys. Lett. 97, 243306 (2010) Field-theoretic model of inhomogeneous supramolecular polymer networks and gels J. Chem. Phys. 133, 174903 (2010) Origin of translocation barriers for polyelectrolyte chains JCP: BioChem. Phys. 3, 11B610 (2009) Origin of translocation barriers for polyelectrolyte chains J. Chem. Phys. 131, 194903 (2009) Additional information on J. Chem. Phys. We present coarse-grained molecular dynamics simulations of linear polyethylene ͑PE͒ melts, ranging in chain length from C 80 to C 1000 . 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 N s , which is smaller than the entanglement length N e . The effective segmental friction rapidly increases around N s leading, at constant density, to a transition in the scaling of the diffusion coefficient from DϳN Ϫ1 to D ϳN Ϫ2 , a transition in the scaling of the viscosity from ϳN to ϳN 1.8 , 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 ͑entanglement͒ effects occurs at a chain length of C 120 . Full entanglement effects are observed only above C 400 , where the shear relaxation modulus displays a plateau and the single chain coherent dynamic structure factor agrees with the reptation model. In this region the viscosity scales as ϳN 3.6 , the tube diameter is dϷ5.4 nm, the entanglement molecular weight is M e Ϸ1700 g/mol, and the plateau modulus is G N 0 Ϸ2.4 MPa, all in good agreement with experimental data.

Effects of alignment layer thickness on the pretilt angle of liquid crystals APL: Org. Electron. Photonics 3, 270 (2010) Effects of alignment layer thickness on the pretilt angle of liquid crystals Appl. Phys. Lett. 97, 243306 (2010) Field-theoretic model of inhomogeneous supramolecular polymer networks and gels J. Chem. Phys. 133, 174903 (2010) Origin of translocation barriers for polyelectrolyte chains JCP: BioChem. Phys. 3, 11B610 (2009) Origin of translocation barriers for polyelectrolyte chains J. Chem. Phys. 131, 194903 (2009) Additional information on J. Chem. Phys. 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 C 120 H 242 , 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.