Steady state sedimentation of ultrasoft colloids

Polymer Thermophoresis by Mesoscale Simulations

We employ mesoscopic simulations to study the thermophoretic motion of polymers in a solvent via multiparticle collision dynamics (MPCD). As the usual solvent-monomer collision rules employed in MPCD involving polymers fail to cause thermophoresis, we extend the technique by introducing explicit solvent-monomer interactions, while the solvent molecules remain ideal with respect to one another. We find that with purely repulsive polymer-solvent interaction, the polymer exhibits thermophilic behavior, whereas to display thermophobic behavior, the polymer-solvent potential requires the presence of attractions between solvent particles and monomers, in accordance with previous experimental findings. In addition, we observe that the thermophoretic mobility is independent of polymer length in the observed regime, again in agreement with experiments. Finally, we investigate the thermophoretic behavior of block copolymers, demonstrating that the thermophoretic mobility can be obtained by linear interpolation, weighted by the relative lengths of the two blocks.

Multi-particle collision dynamics for a coarse-grained model of soft colloids applied to ring polymers

The simulation of polymer solutions often requires the development of methods that accurately include hydrodynamic interactions. Resolution on the atomistic scale is too computationally expensive to cover mesoscopic time and length scales on which the interesting polymer phenomena are observed. Therefore, coarse-graining methods have to be applied. In this work, the solvent is simulated using the well-established multi-particle collision dynamics scheme, and for the polymer, different coarse-graining methods are employed and compared against the monomer resolved Kremer-Grest model by their resulting diffusion coefficients. This research builds on previous work [Ruiz-Franco et al., J. Chem. Phys. 151, 074902 (2019)], in which star polymers and linear chains in a solvent were simulated and two different coarse-graining methods were developed, in order to increase computational efficiency. The present work extends this approach to ring polymers and seeks to refine one of the authors' proposed model: the penetrable soft colloid model. It was found that both proposed models are not well suited to ring polymers; however, the introduction of a factor to the PSC model delivers satisfying results for the diffusion behavior by regulating the interaction intensity with the solvent.

Compression of a confined semiflexible polymer under direct and oscillating fields

The folding transition of biopolymers from the coil to compact structures has attracted wide research interest in the past and is well studied in polymer physics. Recent seminal works on DNA in confined devices have shown that these long biopolymers tend to collapse under an external field, which is contrary to the previously reported stretching of the chain. In this work, we capture the compression of a confined semiflexible polymer under direct and oscillating fields using a coarse-grained computer simulation model in the presence of long-range hydrodynamics. In the case of a semiflexible polymer chain, the inhomogeneous hydrodynamic drag from the center to the periphery of the coil couples with the chain bending to cause a swirling movement of the chain segments, leading to structural intertwining and compaction. Contrarily, a flexible chain of the same length lacks such structural deformation and forms a well-established tadpole structure. While bending rigidity profoundly influences the chain's folding favorability, we also found that subject to the direct field, chains in stronger confinements exhibit substantial compaction, contrary to the one in moderate confinements or bulk where such compaction is absent. However, an alternating field within an optimum frequency can effectuate this compression even in moderate or no confinement. This field-induced collapse is a quintessential hydrodynamic phenomenon, resulting in intertwined knotted structures even for shorter chains, unlike other spontaneous knotting experiments where it happens exclusively for longer chains.

Dynamical and Structural Properties of Comb Long-Chain Branched Polymer in Shear Flow

Using hybrid multi-particle collision dynamics (MPCD) and a molecular dynamics (MD) method, we investigate the effect of arms and shear flow on dynamical and structural properties of the comb long-chain branched (LCB) polymer with dense arms. Firstly, we analyze dynamical properties of the LCB polymer by tracking the temporal changes on the end-to-end distance of both backbones and arms as well as the orientations of the backbone in the flow-gradient plane. Simultaneously, the rotation and tumbling behaviors with stable frequencies are observed. In other words, the LCB polymer undergoes a process of periodic stretched–folded–stretched state transition and rotation, whose period is obtained by fitting temporal changes on the orientation to a periodic function. In addition, the impact induced by random and fast motions of arms and the backbone will descend as the shear rate increases. By analyzing the period of rotation behavior of LCB polymers, we find that arms have a function in keeping the LCB polymer’s motion stable. Meanwhile, we find that the rotation period of the LCB polymer is mainly determined by the conformational distribution and the non-shrinkable state of the structure along the velocity-gradient direction. Secondly, structural properties are numerically characterized by the average gyration tensor of the LCB polymer. The changes in gyration are in accordance with the LCB polymer rolling when varying the shear rate. By analyzing the alignment of the LCB polymer and comparing with its linear and star counterparts, we find that the LCB polymer with very long arms, like the corresponding linear chain, has a high speed to reach its configuration expansion limit in the flow direction. However, the comb polymer with shorter arms has stronger resistance on configuration expansion against the imposed flow field. Moreover, with increasing arm length, the comb polymer in shear flow follows change from linear-polymer-like to capsule-like behavior.

A Trefoil Knot Polymer Chain Translocates through a Funnel-like Channel: A Multi-Particle Collision Dynamics Study

With combining multi-particle collision dynamics (MPCD) for the solvent and molecular dynamics (MD) for the polymer chains, we have studied the conformation and untying behaviors of a trefoil knot polymer chain translocated through a confined funnel-like channel. For the trefoil knot chain, we found that the untying knot behavior mostly happens during the translocation process, and the translocation behavior of linear chains is also simulated as a comparison. Some characteristics of the trefoil knot chain during translocation process, such as average gyration radius and the average end-to-end distances are discussed, and we statistic the scale relations of the translocation time versus the chain length, and that of the chain rigidity. This study may help to understand translocation behaviors of the knotted linear polymer chain in the capillary flow field.

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Simulating wet active polymers by multiparticle collision dynamics

The conformational and dynamical properties of active Brownian polymers embedded in a fluid depend on the nature of the driving mechanism, e.g., self-propulsion or external actuation of the monomers. Implementations of self-propelled and actuated active Brownian polymers in a multiparticle collision (MPC) dynamics fluid are presented, which capture the distinct differences between the two driving mechanisms. The active force-free nature of self-propelled monomers requires adaptations of the MPC simulation scheme, with its streaming and collision steps, where the monomer self-propulsion velocity has to be omitted in the collision step. Comparison of MPC simulation results for active polymers in dilute solution with results of Brownian dynamics simulations accounting for hydrodynamics via the Rotne-Prager-Yamakawa tensor confirm the suitability of the implementation. The polymer conformational and dynamical properties are analyzed by the static and dynamic structure factor, and the scaling behavior of the latter with respect to the wave number and time dependence are discussed. The dynamic structure factor displays various activity-induced temporal regimes, depending on the considered wave number, which reflect the persistent diffusive motion of the whole polymer at small wave numbers, and the activity-enhanced internal dynamics at large wave numbers. The obtained simulation results are compared with theoretical predictions.

Hydrodynamics of immiscible binary fluids with viscosity contrast: a multiparticle collision dynamics approach

We present a multiparticle collision dynamics (MPC) implementation of layered immiscible fluids A and B of different shear viscosities separated by planar interfaces. The simulated flow profile for imposed steady shear motion and the time-dependent shear stress functions are in excellent agreement with our continuum hydrodynamics results for the composite fluid. The wave-vector dependent transverse velocity auto-correlation functions (TVAF) in the bulk-fluid regions of the layers decay exponentially, and agree with those of single-phase isotropic MPC fluids. In addition, we determine the hydrodynamic mobilities of an embedded colloidal sphere moving steadily parallel or transverse to a fluid-fluid interface, as functions of the distance from the interface. The obtained mobilities are in good agreement with hydrodynamic force multipoles calculations, for a no-slip sphere moving under creeping flow conditions near a clean, ideally flat interface. The proposed MPC fluid-layer model can be straightforwardly implemented, and it is computationally very efficient. Yet, owing to the spatial discretization inherent to the MPC method, the model can not reproduce all hydrodynamic features of an ideally flat interface between immiscible fluids.

Hydrodynamics of polymers in an active bath

The conformational and dynamical properties of active polymers in solution are determined by the nature of the activity. Here, the behavior of polymers with self-propelled, active Brownian particle-type monomers differs qualitatively from that of polymers with monomers driven externally by colored-noise forces. We present simulation and theoretical results for polymers in solution in the presence of external active noise. In simulations, a semiflexible bead-spring chain is considered, in analytical calculations, a continuous linear wormlike chain. Activity is taken into account by independent monomer or site velocities, with orientations changing in a diffusive manner. In simulations, hydrodynamic interactions (HIs) are taken into account by the Rotne-Prager-Yamakawa tensor or by an implementation of the active polymer in the multiparticle-collision-dynamics approach for fluids. To arrive at an analytical solution, the preaveraged Oseen tensor is employed. The active process implies a dependence of the stationary-state properties on HIs via the polymer relaxation times. With increasing activity, HIs lead to an enhanced swelling of flexible polymers, and the conformational properties differ substantially from those of polymers with self-propelled monomers in the presence of HIs, or free-draining polymers. The polymer mean-square displacement is enhanced by HIs. Over a wide range of timescales, hydrodynamics leads to a subdiffusive regime of the site mean-square displacement for flexible active polymers, with an exponent of 5/7, larger than that of the Rouse (1/2) and Zimm (2/3) models of passive polymers.

Force driven transition of a globular polyelectrolyte

We have systematically studied behavior of a flexible polyelectrolyte (PE) chain with explicit counterions, subjected to a constant force at the terminal ends. Our simulations reveal that in the hydrophobic regime, a PE globule abruptly opens to a coil state beyond a critical force F_c. At the transition point, the polymer shape shows large scale fluctuations that are quantified in terms of end-to-end distance R_e. These fluctuations suggest that the system coexists in globule and coil states at the transition, which is also confirmed from the bimodal distribution of R_e. Moreover, the critical force associated with the globule coil transition exhibits a nonmonotonic behavior, where surprisingly, F_c decreases with Bjerrum length l_B in the limit of small l_B, followed by an increase in the larger l_B limit. Furthermore, this behavior is also validated from a theory adopted for the PE. From the free energy analysis, we have demonstrated that predominantly, the competition between the intrachain repulsive energy, counterion's translational entropy, and adsorption energy leads to the novel feature of nonmonotonic behavior of force.

Multi-particle collision dynamics for a coarse-grained model of soft colloids

The growing interest in the dynamical properties of colloidal suspensions, both in equilibrium and under an external drive such as shear or pressure flow, requires the development of accurate methods to correctly include hydrodynamic effects due to the suspension in a solvent. In the present work, we generalize Multiparticle Collision Dynamics (MPCD) to be able to deal with soft, polymeric colloids. Our methods build on the knowledge of the monomer density profile that can be obtained from monomer-resolved simulations without hydrodynamics or from theoretical arguments. We hereby propose two different approaches. The first one simply extends the MPCD method by including in the simulations effective monomers with a given density profile, thus neglecting monomer-monomer interactions. The second one considers the macromolecule as a single penetrable soft colloid (PSC), which is permeated by an inhomogeneous distribution of solvent particles. By defining an appropriate set of rules to control the collision events between the solvent and the soft colloid, both linear and angular momenta are exchanged. We apply these methods to the case of linear chains and star polymers for varying monomer lengths and arm number, respectively, and compare the results for the dynamical properties with those obtained within monomer-resolved simulations. We find that the effective monomer method works well for linear chains, while the PSC method provides very good results for stars. These methods pave the way to extend MPCD treatments to complex macromolecular objects such as microgels or dendrimers and to work with soft colloids at finite concentrations.

Sedimentation of a suspension of rods: Monte Carlo simulation of a continuous two-dimensional problem

The sedimentation of a two-dimensional suspension containing rods was studied by means of Monte Carlo (MC) simulations. An off-lattice model with continuous positional and orientational degrees of freedom was considered. The initial state before sedimentation was produced using a model of random sequential adsorption. During such sedimentation, the rods undergo translational and rotational Brownian motions. The MC simulations were run at different initial number densities (the numbers of rods per unit area), ρ_{i}, and sedimentation rates, u. For sediment films, the spatial distributions of the rods, the order parameters, and the electrical conductivities were examined. Different types of sedimentation-driven self-assembly and anisotropy of the electrical conductivity were revealed inside the sediment films. This anisotropy can be finely regulated by changes in the values of ρ_{i} and u.

Single molecule electrophoresis of star polymers through nanopores: Simulations

We study the translocation of charged star polymers through a solid-state nanopore using coarse-grained Langevin dynamics simulations, in the context of using nanopores as high-throughput devices to characterize polymers based on their architecture. The translocation is driven by an externally applied electric field. Our key observation is that translocation kinetics is highly sensitive to the functionality (number of arms) of the star polymer. The mean translocation time is found to vary non-monotonically with polymer functionality, exhibiting a critical value for which translocation is the fastest. The origin of this effect lies in the competition between the higher driving force inside the nanopore and inter-arm electrostatic repulsion in entering the pore, as the functionality is increased. Our simulations also show that the value of the critical functionality can be tuned by varying nanopore dimensions. Moreover, for narrow nanopores, star polymers above a threshold functionality do not translocate at all. These observations suggest the use of nanopores as a high-throughput low-cost analytical tool to characterize and separate star polymers.

Flow Behavior of Chain and Star Polymers and Their Mixtures

Star-shaped polymers show a continuous change of properties from flexible linear chains to soft colloids, as the number of arms is increased. To investigate the effect of macromolecular architecture on the flow properties, we employ computer simulations of single chain and star polymers as well as of their mixtures under Poiseuille flow. Hydrodynamic interactions are incorporated through the multi-particle collision dynamics (MPCD) technique, while a bead-spring model is used to describe the polymers. For the ultradilute systems at rest, the polymers are distributed uniformly in the slit channel, with a weak dependence on their number of arms. Once flow is applied, however, we find that the stars migrate much more strongly towards the channel center as the number of arms is increased. In the star-chain mixtures, we find a flow-induced separation between stars and chains, with the stars located in the channel center and the chains closer to the walls. In order to identify the origin of this flow-induced partitioning, we conduct additional simulations without hydrodynamic interactions, and find that the observed cross-stream migration originates from a combination of wall-induced hydrodynamic lift forces and viscoelastic effects. The results from our study give valuable insights for designing microfluidic devices for separating polymers based on their architecture.