The ability of a highly coarse-grained polymer model is explored to simulate the impact of carbon black (CB) filler concentration on the rheological properties of unvulcanized styrene–butadiene melts—an intermediate stage in the production of styrene–butadiene rubber (SBR) commonly used in tyres. Responsive particle dynamics (RaPiD), previously used to study dilute polymeric systems, models entire polymers as single particles interacting through a combination of conservative interactions and transient entanglement-mimicking forces. The simulation parameters are tuned to the linear rheology of the unfilled melt, as measured using a rubber process analyzer (RPA). For the filled compounds, only the interaction between the polymers and fillers is varied. On top of excluded volume interactions, a slight attraction (≈0.1 kBT) between polymers and fillers is required to attain agreement with RPA measurements. The physical origins of the small strength of this interaction are discussed. This method offers potential for future numerical investigations of filled melts.@en

An updated mesoscopic model for transient forces between two star polymers is presented. Calculation of the transient forces is based on the response of a vectorial structure parameter between two star polymers and differs from previous models that used a scalar structure parameter. The update of the model is motivated by the occurrence of two distinct processes in previous small-scale simulations of two star polymers moving past each other. A simple model that takes these processes into account turns out to fit into an obvious generalization of the RaPiD model introduced by us some time ago. The model reproduces forces from the simulation quite well, and at the same time removes an unphysical feature of the RaPiD model used so far.@en

We present a Galilean invariant, momentum conserving first order Brownian dynamics scheme for coarse-grained simulations of highly frictional soft matter systems. Friction forces are taken to be with respect to moving background material. The motion of the background material is described by locally averaged velocities in the neighborhood of the dissolved coarse coordinates. The velocity variables are updated by a momentum conserving scheme. The properties of the stochastic updates are derived through the Chapman-Kolmogorov and Fokker-Planck equations for the evolution of the probability distribution of coarse-grained position and velocity variables, by requiring the equilibrium distribution to be a stationary solution. We test our new scheme on concentrated star polymer solutions and find that the transverse current and velocity time auto-correlation functions behave as expected from hydrodynamics. In particular, the velocity auto-correlation functions display a long time tail in complete agreement with hydrodynamics.@en

In this paper, a previous coarse-grain model [J. T. Padding and W. J. Briels, J. Chem. Phys. 117, 925 (2002)]10.1063/1.1481859 to simulate melts of linear polymers has been adapted to simulate polymers with more complex hierarchies. Bond crossings between highly coarse-grained soft particles are prevented by applying an entanglement algorithm. We first test our method on a virtual branch point inside a linear chain to make sure it works effectively when linking two linear arms. Next, we apply our method to study the diffusive and rheological behaviors of a melt of three-armed stars. We find that the diffusive behavior of the three-armed star is very close to that of a linear polymer with the same molecular weight, while its rheological properties are close to those of a linear chain with molecular mass equal to that of the longest linear sub-chain in the star.@en

The development of novel pressure sensitive adhesives, formed by the drying of a polymer latex emulsion, is hampered by a lack of understanding of the relation between microscopic details and the large-scale rheology. In a previous paper [Soft Matter, 2011, 7, 5036] we introduced a coarse-grained computer simulation model that aims to provide such a link. To reach sufficiently large time and length scales each latex particle is represented by just six degrees of freedom, and transient forces are introduced to capture the effect of slow changes in the degree of chain intermixing and in the number of sticker groups shared between pairs of latex particles. In this paper we show that this model can nearly quantitatively predict the shear and extensional nonlinear rheology by careful tuning of only a few parameters to the linear rheology. We find a complex transient viscosity with multiple inflection points and maxima under shear flow, as well as a strong strain hardening under extensional flow, all in agreement with experimental observations. We investigate the influence of each of the model's parameters on the linear and nonlinear rheology.@en

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.

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Colloidal solutions posses a wide range of time and length scales so that it is unfeasible to keep track of all of them within a single simulation. As a consequence, some form of coarse graining must be applied. In this work we use the multiparticle collision dynamics scheme. We describe a particular implementation of no-slip boundary conditions upon a solid surface, capable of providing correct forces on the solid bypassing the calculation of the velocity profile or the stress tensor in the fluid near the surface. As an application we measure the friction on a spherical particle when it is placed in a bulk fluid and when it is confined in a slit. We show that the implementation of the no-slip boundary conditions leads to an enhanced Enskog friction, which can be understood analytically. Because of the long-range nature of hydrodynamic interactions, the Stokes friction obtained from the simulations is sensitive of the simulation box size. We address this topic for the slit geometry, showing that the dependence on the system size differs very much from what is expected in a three-dimensional system where periodic boundary conditions are used in all directions.@en

The diffusive motion of a colloidal particle trapped inside a small cavity filled with fluid is reduced by hydrodynamic interactions with the confining walls. In this work, we study these wall effects on a spherical particle entrapped in a closed cylinder. We calculate the diffusion coefficient along the radial, azimuthal, and axial direction for different particle positions. At all locations the diffusion is smaller than in a bulk fluid and it becomes anisotropic near the containers walls. We present a simple model which reasonably well describes the simulation results for the given dimensions of the cylinder, which are taken from the recent experimental work.@en

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.@en

For optimal application, pressure-sensitive adhesives must have rheological properties in between those of a viscoplastic solid and those of a viscoelastic liquid. Such adhesives can be produced by emulsion polymerisation, resulting in latex particles which are dispersed in water and contain long-chain acrylic polymers. When the emulsion is dried, the latex particles coalesce and an adhesive film is formed. The rheological properties of the dried samples are believed to be dominated by the interface regions between the original latex particles, but the relationship between rheology and latex particle properties is poorly understood. In this paper we show that it is possible to describe the bulk rheology of a pressure-sensitive adhesive by means of a mesoscale simulation model. To reach experimental time and length scales, each latex particle is represented by just one simulated particle. The model is subjected to oscillatory shear flow and extensional flow. Simple order of magnitude estimates of the model parameters already lead to semi-quantitative agreement with experimental results. We show that inclusion of transient forces in the model, i.e. forces with memory of previous configurations, is essential to correctly predict the linear and nonlinear properties.@en

The response of many soft materials to external fields is dominated by transient forces, which arise from memory of the configurations the system has undergone in the past. Using large-scale particle-based simulations we show that these transient forces lead to a rich non-equilibrium behavior in networks of soft polymeric particles or polymer-engrafted colloids. We compute the diagram of states for an experimental system of network-forming associative polymers and show viscoelastic instabilities such as shear banding, melt fracture and a shear-induced disorder-order transition.@en

We use particle-based computer simulations to study the rheology of suspensions of high-functionality star polymers with long entangled arms. Such particles have properties which are intermediate between those of soft colloidal particles and entangled polymer chains. In the simulations, each star polymer is coarse-grained to a single particle. In order to faithfully reproduce dynamical properties, it is very important to not only include time-averaged interactions (potentials of mean force) but to also account for transient interactions induced by entanglements between the arms of different star polymers. Using a model which has all these features, it is found that, for sufficiently high shear rates, the start-up shear stress displays an overshoot. With increasing concentration, the core interactions increasingly dominate the initial stress response, leading to a maximum in the stress overshoot at relatively low strain values (0. 1 to 0. 5). Transient forces start to dominate after this initial stage. In a simulated experiment in which the shear rate is suddenly stepped-down from a high to a lower value, the stress shows a clear undershoot, with the minimum stress again at a relatively low strain value (based on the new shear rate). Finally, it is shown that a stress plateau develops in the flow curve. This plateau is absent when the transient forces between the polymer stars are not taken into account.@en

An anisotropic macromolecule confined between two surfaces displays Brownian motion predominantly in the plane parallel to these surfaces. It can be expected that both the rotational and translational diffusion coefficients are strongly affected by hydrodynamic interactions with the walls. This work studies the more extreme case in which a rodlike particle comes into contact with a wall or in very close proximity (order of 100 nm). Experimental data have been gathered and analyzed demonstrating the rod tethering on a surface. This is compared with numerical simulations to allow estimates of proximity to the surface. The experimental data show that particle tethered motion is subject to varied degrees of constraining which imply subtle deviations in the Brownian dynamical behavior. The key finding is that a rotational-translational coupling occurs which is markedly different from the translational and rotational movements normally predicted for anisotropic macromolecules.@en

We present coarse-grained molecular dynamics simulations of poly(ethylene-alt-propylene) (PEP) melts, ranging in chain length from about Ne(the entanglement length) to N=6 Ne. The coarse-grained parameters, potential of mean force and bare friction, were determined from fully atomistic molecular dynamics simulations carried out on a PEP cell containing 12 chains of 80 monomers each and subjected to periodic boundary conditions. These atomistic simulations were previously validated by means of extensive neutron scattering measurements. Uncrossability constrains were also introduced in the coarse-grained model to prevent unphysical bond crossing. The coarse-grained simulations were carried out at 492 K and focus on chain dynamics. The results obtained were analyzed in terms of Rouse coordinates and Rouse correlators. We observe deviations from Rouse behavior for all chain lengths investigated, even when the chain stiffness is incorporated in the Rouse model. These deviations become more important as the chain length increases. The general scenario emerging from the results obtained is that the deviations from Rouse-like behavior are due to correlations among the forces acting upon a chain bead, which seem to be related with the constraint of uncrossability among the chains. As consequence, nonexponentiality of the Rouse correlators and mode- and time-dependent friction are observed. It seems that, in the molecular weight explored, these effects still give not raise to reptation behavior but to a crossover regime between Rouse and reptation. On the other hand, the results obtained are in qualitative agreement with those expected from the so-called generalized Rouse models, based on memory function formalisms.@en

We present particulate simulation results for translational and rotational friction components of a shish-kebab model of a colloidal rod with aspect ratio (length over diameter) L/D=10 in the presence of a planar hard wall. Hydrodynamic interactions between rod and wall cause an overall enhancement of the friction tensor components. We find that the friction enhancements to reasonable approximation scale inversely linear with the closest distance d between the rod surface and the wall, for d in the range between D/8 and L. The dependence of the wall-induced friction on the angle θ between the long axis of the rod and the normal to the wall is studied and fitted with simple polynomials in cos θ.@en

Transient polymer networks are known to undergo a wide variety of viscoelastic flow instabilities. In this paper we investigate two of these flow failure modes: shear banding and melt fracture. Using particle-based simulations we reveal a transition from gradient banding to fracture in transient polymer networks with reversible associative nodes. We discuss the failure-mode transition on the basis of an energetic and a kinetic approach to fracturing in soft materials.@en

We provide a review of our recent work on the development of a multi-scale simulation methodology to calculate the rheology and flow of wormlike micelles. There is a great need for understanding the link between the detailed chemistry of surfactants, forming wormlike micelles, and their macroscopic rheological properties. We show how this link may be explored through particle simulations. First, we calculate the mechanical properties of small units of wormlike micelles from atomistic molecular dynamics simulations. These mechanical properties are subsequently used in a coarse-grained Brownian dynamics model, where the persistence length is the smallest length scale. We show that the non-Newtonian rheology of wormlike micellar systems can be accurately determined from our simple mesoscopic simulation model. Finally, we show that this mesoscopic model can be used to study the flow of wormlike micelles in contraction-expansion geometries.

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We study the relaxation dynamics of capillary waves in the interface between two confined liquid layers by means of molecular dynamics simulations. We measure the autocorrelations of the interfacial Fourier modes and find that the finite thickness of the liquid layers leads to a marked increase of the relaxation times as compared to the case of fluid layers of infinite depth. The simulation results are in good agreement with a theoretical first-order perturbation derivation, which starts from the overdamped Stokes' equation. The theory also takes into account an interfacial friction, but the difference with no-slip interfacial conditions is small. When the walls are sheared, it is found that the relaxation times of modes perpendicular to the flow are unaffected. Modes along the flow direction are relatively unaffected as long as the equilibrium relaxation time is sufficiently short compared to the rate of deformation. We discuss the consequences for experiments on thin layers and on ultralow surface tension fluids, as well as computer simulations.@en

We perform coarse-grained computer simulations of solutions of semidilute wormlike micelles and study their dynamic and rheological properties, both in equilibrium and under shear flow. The simulation model is tailored to the study of relatively large time and length scales (micrometers and several milliseconds), while it still retains the specific mechanical properties of the individual wormlike micelles. The majority of the mechanical properties (persistence length, diameter, and elastic modulus of a single worm) is determined from more detailed atomistic molecular dynamics simulations, providing the link with the chemistry of the surfactants. The method is applied to the case of a solution containing 8% (by weight) erucyl bis(hydroxymethyl) methylammonium chloride (EHAC). Different scission energies ranging from 15.5 kbT to 19.1 kBT are studied, leading to both unentangled and entangled wormlike micelles. We find a decrease in the average contour length and an increase in the average breaking rate with increasing shear rate. In equilibrium, the decay of the shear relaxation modulus of the unentangled samples agrees with predictions based on a theory of breakable Rouse chains. Under shear flow, transient over- and undershoots are measured in the stress tensor components. At high shear rates we observe a steady-state shear stress proportional to γ̇1/3, where γ̇ is the shear rate. This is confirmed by our high shear rate experiments of real EHAC in a parallel-plate geometry.@en

The spinodal decomposition of quenched polymer/solvent and liquid-crystal/solvent mixtures in a miniature Taylor-Couette cell has been simulated by molecular dynamics. Three stacking motifs, each reflecting the geometry and symmetry of the cell, are most abundant among the fully phase separated stationary states. At zero or low angular velocity of the inner cylindrical drum, the two segregated domains have a clear preference for the stacking with the lowest free energy and hence the smallest total interfacial tension. For high shear rates, the steady state appears to be determined by a minimum dissipation mechanism, i.e., the mixtures are likely to evolve into the stacking demanding the least mechanical power by the rotating wall. The partial slip at the polymer-solvent interfaces then gives rise to a new pattern: A stack of three concentric cylindrical shells with the viscous polymer layer sandwiched between two solvent layers. Neither of these mechanisms can explain all simulation results, as the separating mixture easily becomes kinetically trapped in a long-lived suboptimal configuration. The phase separation process is observed to proceed faster under shear than in a quiescent mixture.@en