Assessing numerical methods for molecular and particle simulation

Polymer brushes for friction control: Contributions of molecular simulations

When polymer chains are grafted to solid surfaces at sufficiently high density, they form brushes that can modify the surface properties. In particular, polymer brushes are increasingly being used to reduce friction in water-lubricated systems close to the very low levels found in natural systems, such as synovial joints. New types of polymer brush are continually being developed to improve with lower friction and adhesion, as well as higher load-bearing capacities. To complement experimental studies, molecular simulations are increasingly being used to help to understand how polymer brushes reduce friction. In this paper, we review how molecular simulations of polymer brush friction have progressed from very simple coarse-grained models toward more detailed models that can capture the effects of brush topology and chemistry as well as electrostatic interactions for polyelectrolyte brushes. We pay particular attention to studies that have attempted to match experimental friction data of polymer brush bilayers to results obtained using molecular simulations. We also critically look at the remaining challenges and key limitations to overcome and propose future modifications that could potentially improve agreement with experimental studies, thus enabling molecular simulations to be used predictively to modify the brush structure for optimal friction reduction.

Effects of Slip-Spring Parameters and Rouse Bead Density on Polymer Dynamics in Multichain Slip-Spring Simulations

The multichain slip-spring (MCSS) model is one of the coarse-grained models of polymers developed in the niche between bead-spring models and tube type descriptions. In this model, polymers are represented by Rouse chains connected by virtual springs that temporally connect the chains, hop along the chain, and are constructed and annihilated at the chain ends. Earlier studies have shown that MCSS simulations can nicely reproduce entangled and unentangled polymer dynamics. However, the model parameters have been chosen arbitrarily, and their effects have not been reported. In this study, for the first time, we systematically investigated the effects of model parameters: fugacity of virtual springs, its intensity, and the Rouse bead density. We validated the employed simulation code by confirming that the statistics of the system follow the theoretical setup. Namely, the virtual spring density is correctly controlled, and polymer chains exhibit ideal chain statistics irrespective of the chosen parameter values. For diffusion and linear viscoelasticity, simulation results obtained for different parameters can be superposed with each other by conversion factors for the bead number per chain and units of length, time, and modulus. These conversion factors follow scaling laws concerning the number of Rouse segments between two consecutive anchoring points of virtual springs along the polymer chain. Besides, diffusion and viscoelasticity excellently agree with literature data for the standard bead-spring simulation. These results imply that the coarse-graining level for the MCSS model can be arbitrarily chosen and controlled by model parameters.

Composition Methods for Dynamical Systems Separable into Three Parts

New families of fourth-order composition methods for the numerical integration of initial value problems defined by ordinary differential equations are proposed. They are designed when the problem can be separated into three parts in such a way that each part is explicitly solvable. The methods are obtained by applying different optimization criteria and preserve geometric properties of the continuous problem by construction. Different numerical examples exhibit their improved performance with respect to previous splitting methods in the literature.

Structure-preserving integrators for dissipative systems based on reversible- irreversible splitting

We study the optimal design of numerical integrators for dissipative systems, for which there exists an underlying thermodynamic structure known as GENERIC (general equation for the nonequilibrium reversible-irreversible coupling). We present a frame-work to construct structure-preserving integrators by splitting the system into reversible and irreversible dynamics. The reversible part, which is often degenerate and reduces to a Hamiltonian form on its symplectic leaves, is solved by using a symplectic method (e.g. Verlet) with degenerate variables being left unchanged, for which an associated modified Hamiltonian (and subsequently a modified energy) in the form of a series expansion can be obtained by using backward error analysis. The modified energy is then used to construct a modified friction matrix associated with the irreversible part in such a way that a modified degeneracy condition is satisfied. The modified irreversible dynamics can be further solved by an explicit midpoint method if not exactly solvable. Our findings are verified by various numerical experiments, demonstrating the superiority of structure-preserving integrators over alternative schemes in terms of not only the accuracy control of both energy conservation and entropy production but also the preservation of the conformal symplectic structure in the case of linearly damped systems.

Entropic Effects in Polymer Nanocomposites

Polymer nanocomposite materials, consisting of a polymer matrix embedded with nanoscale fillers or additives that reinforce the inherent properties of the matrix polymer, play a key role in many industrial applications. Understanding of the relation between thermodynamic interactions and macroscopic morphologies of the composites allow for the optimization of design and mechanical processing. This review article summarizes the recent advancement in various aspects of entropic effects in polymer nanocomposites, and highlights molecular methods used to perform numerical simulations, morphologies and phase behaviors of polymer matrices and fillers, and characteristic parameters that significantly correlate with entropic interactions in polymer nanocomposites. Experimental findings and insight obtained from theories and simulations are combined to understand how the entropic effects are turned into effective interparticle interactions that can be harnessed for tailoring nanostructures of polymer nanocomposites.

On the effect of the thermostat in non-equilibrium molecular dynamics simulations

The numerical investigation of the statics and dynamics of systems in non-equilibrium in general, and under shear flow in particular, has become more and more common. However, not all the numerical methods developed to simulate equilibrium systems can be successfully adapted to out-of-equilibrium cases. This is especially true for thermostats. Indeed, even though thermostats developed to work under equilibrium conditions sometimes display good agreement with rheology experiments, their performance rapidly degrades beyond weak dissipation and small shear rates. Here we focus on gauging the relative performances of three thermostats, Langevin, dissipative particle dynamics, and Bussi-Donadio-Parrinello under varying parameters and external conditions. We compare their effectiveness by looking at different observables and clearly demonstrate that choosing the right thermostat (and its parameters) requires a careful evaluation of, at least, temperature, density and velocity profiles. We also show that small modifications of the Langevin and DPD thermostats greatly enhance their performance in a wide range of parameters.