Search

A very stiff finitely extensible nonlinear elastic (FENE)-Fraenkel spring is proposed to replace the rigid rod in the bead-rod model. This allows the adoption of a fast predictor-corrector method so that large time steps can be taken in Brownian dynamics (BD) simulations without over- or understretching the stiff springs. In contrast to the simple bead-rod model, BD simulations with beads and FENE-Fraenkel (FF) springs yield a random-walk configuration at equilibrium. We compare the simulation results of the free-draining bead-FF-spring model with those for the bead-rod model in relaxation, start-up of uniaxial extensional, and simple shear flows, and find that both methods generate nearly identical results. The computational cost per time step for a free-draining BD simulation with the proposed bead-FF-spring model is about twice as high as the traditional bead-rod model with the midpoint algorithm of Liu [J. Chem. Phys. 90, 5826 (1989)]. Nevertheless, computations with the bead-FF-spring model are as efficient as those with the bead-rod model in extensional flow because the former allows larger time steps. Moreover, the Brownian contribution to the stress for the bead-FF-spring model is isotropic and therefore simplifies the calculation of the polymer stresses. In addition, hydrodynamic interaction can more easily be incorporated into the bead-FF-spring model than into the bead-rod model since the metric force arising from the non-Cartesian coordinates used in bead-rod simulations is absent from bead-spring simulations. Finally, with our newly developed bead-FF-spring model, existing computer codes for the bead-spring models can trivially be converted to ones for effective bead-rod simulations merely by replacing the usual FENE or Cohen spring law with a FENE-Fraenkel law, and this convertibility provides a very convenient way to perform multiscale BD simulations. [ABSTRACT FROM AUTHOR]

We compare the predictions of the Vasquez–Cook–McKinley (VCM) [P. a. Vasquez et al., J. Non-Newton. Fluid. Mech. 144, 122–139 (2007)] model, which treats wormlike micelles as Hookean dumbbells that break at half-length to form two shorter dumbbells, to an analogous Brownian dynamics (BD) simulation of the same physical model. We find a discrepancy between VCM model predictions and trace it to the absence in the VCM model of the spatial position of the nascent breakage point in the long micelle, which is needed to satisfy microscopic reversibility of breakage and fusion. We incorporate microscopic reversibility in the VCM model by extending an ensemble-averaged bead-spring phase space model of Wiest et al. [J. Chem. Phys. 90, 587 (1989)] to include reversible scission of two-spring chains. The revision tracks the conformations of the two halves of the long micelle and transmits this information to the short micelles upon breakage and thereby recovers complete agreement with the BD results. A general method is offered for retaining this information in populations of micelles of many different lengths, represented by an ensemble of many-spring chains. The new model also offers the prospect of including additional physics, such as flow-enhanced micelle growth or breakage, and the ability to check the accuracy of closure approximations using parallel BD simulations. [ABSTRACT FROM AUTHOR]

We build a Brownian dynamics simulation model to study the linear rheology of latex particles interacting with telechelic polymers (for example, so-called “HEUR” polymers), with the latter modeled as Finitely Extensible Nonlinear Elastic (FENE) dumbbells with ends that stick to Brownian colloidal spheres. We identify from this model four relaxation modes, including (1) a single chain relaxation time, τ′FENE, which is closely related to τFENE, the relaxation time of a free chain predicted using the FENE model, but is around 1.4 times longer because of surface constraints on polymer configuration; (2) a loop translational-rotational relaxation time, τloop, produced by migration of the chain over the particle surface, allowing it to further relax its orientational conformation while still trapped on the particle surface; (3) a bridge formation/breakage relaxation time, τbridge; and (4) one or more colloidal particle cluster relaxation times. We show that τloop scales as the square of particle radius. τbridge is the same as the lifetime of a bridge and increases exponentially with the adsorption energy of a telechelic hydrophobic sticker to the latex particle surface. The one or more long particle cluster relaxation modes are influenced by the diffusion coefficient of the latex particles, the polymer concentration, and the volume fraction of latex particles. These multiple relaxation times help explain the observed rheological behavior of water-borne coatings and differ from the rheology of reversible networks composed of only telechelic HEUR chains, which frequently show single-relaxation-time behavior. [ABSTRACT FROM AUTHOR]

We study polymer migration in a periodic pressure-driven sudden contraction-expansion flow with contraction dimension comparable to the polymer radius of gyration, for which several polymer migration mechanisms can be important: (1) sieving by the thin channel of polymers too large to easily enter them; (2) deformation-hydrodynamic coupling, including wall-hydrodynamic interaction, which causes polymers to drift away from the walls towards the center of the channel; (3) streamline-curvature-induced migration, in which polymers traveling along curved streamlines migrate towards the center of curvature; and (4) depletion-convection coupling, in which depletion layers in thin channels are convected across wide side chambers, creating a one-sided diffusion barrier that leads to depletion from the side chamber. We use both Stochastic Rotation Dynamics (SRD), which includes hydrodynamic interaction (HI), and simple Brownian dynamics (BD), with HI omitted and flow field given by finite element analysis. The similarity in results from SRD and BD at Weissenberg number Wi less than 10 (where Wi is based on the shear rate in the narrow region of the contraction channel) shows that HI (Mechanism 2) has only a weak effect on polymer migration in our tight geometry. At Wi > 1, the polymer migrates towards the centerline in the wide region, due mainly to streamline-curvature-induced (SCI) migration (Mechanism 3), but also to depletion-convection-induced migration (Mechanism 4). And we demonstrate these two mechanisms more explicitly in a pressure-driven flow in a grooved channel that is significantly wider than the polymer. SCI migration dominates in the contraction geometry, and produces a migration velocity proportional to Wi². Using the central limit theorem, we accurately predict the position and width of a band of polymer passing through N periodic contractions, thereby demonstrating the potential for SCI migration as a mechanism of size separation in a multi-step planar contraction channel. We find that the best separation is achieved at Wi around 2, where SCI migration has the greatest resolving power between polymers of different size. We also find that sieving (Mechanism 1) is dominant at low Wi less than unity, where the chains with large radius of gyration are delayed in their entry to the thin channel, relative to shorter polymers. This sieving separation mechanism differs from that of size-exclusion chromatography which yields faster migration by the shorter chains. Our strategy of combining simulation methods with the central limit theorem could also be used to predict separation efficiencies of a wide variety of polymers and colloids in microfluidic geometries. [ABSTRACT FROM AUTHOR]

Using Brownian dynamics simulations, without excluded volume and hydrodynamic interactions, on single polymer molecules represented by bead-spring models with stiff Fraenkel springs mimicking a single Kuhn step, we find multiple nonlinear regimes of deformation in shear flows that are controlled by the Peclet number (Pe), which is the shear rate times the relaxation time of a Kuhn step. We observe that, for all chain lengths investigated, the average stretch in the flow direction initially increases with increasing Pe, followed by saturation in chain stretch, as observed in previous studies. At even higher Pe, the stretch begins to decrease with increasing shear rate, in accordance with similar simulations of Sendner and Netz, Eur. Phys. J. E 30, 75-81 (2009). At these rates, the trajectories reveal 'premature' recoiling of the chain before attaining a fully extended state during the phase of the 'tumbling orbit' in which the chain is stretching. An increasing stretch at even higher Pe is characterized by peculiar orientation 'locking' effects that may be sensitive to modeling details. We also show that the stretch predictions of coarse-grained springs agree well with those of the fine-grained chains until high shear rates are reached, where the flow perturbs the individual springs from equilibrium. [ABSTRACT FROM AUTHOR]

We develop a Brownian dynamics simulation method with full hydrodynamic interactions (HI) to study the recognition kinetics between two patterned colloidal spheres. We use a general resistance matrix (12*12) to describe both the far and near-field hydrodynamics of translation, rotation, and translation-rotation coupling between the two spheres, adopted from Jeffrey and Onishi [J. Fluid Mech. 139, 261 (1984)]. We apply the method to the specific binding of 'patchy' spheres, including effects of depletion attraction and orientation-specific binding, as are present in 'Janus' spheres whose surfaces contain hydrophobic and hydrophilic faces [Q. Chen, S. C. Bae, and S. Granick, Nature (London) 469, 381 (2011)]. The binding times obtained between two non-patterned spheres (of equal or unequal diameter) with or without HI extrapolated to infinite dilution are shown to be in good agreement with theoretical predictions of the Smoluchowski equation. In addition, the binding times for pairs of spheres for three cases of surface patterning of the two spheres (uniform-uniform, uniform-Janus, and Janus-Janus) are compared with or without rotational motion. [ABSTRACT FROM AUTHOR]

DNA stretching in entangling media with oscillating electric fields is useful in DNA sequencing. We propose that stretching occurs around hairpin loops at the chain ends, caused by interactions with the medium. Brownian dynamics simulations show that this mechanism explains several experimental observations, including a resonance with varying field frequency. [ABSTRACT FROM AUTHOR]

We develop a method which incorporates spring-spring repulsions into Brownian dynamics simulations of flexible polymers. The distance of closest approach between two springs is computed, and a repulsive force is then applied based on this distance. Repulsive potentials of the exponential and power-law forms are considered. We demonstrate that our method is capable of accounting for excluded-volume effects in start-up of extensional flow. Equilibrium simulations indicate that spring-spring repulsions can be used to prevent the passage of two springs through each other, and thus maintain the topological integrity of polymer molecules. The method developed here is expected to be useful for simulating entanglement phenomena in both single and multichain systems. © 2001 American Institute of Physics. [ABSTRACT FROM AUTHOR]

Control over the alignment of colloidal structures plays a crucial role in advanced reconfigurable materials. In this work, we study the alignment of Janus particle lamellar structures under shear flow via Brownian dynamics simulations. Lamellar alignment (orientation relative to flow direction) is measured as a function of the Péclet number (Pe)--the ratio of the viscous shear to the Brownian forces--the particle volume fraction, and the strength of the anisotropic interaction potential made dimensionless with thermal energy. Under conditions where lamellar structures are formed, three orientation regimes are observed: (1) random orientation for very small Pe, (2) parallel orientation--lamellae with their normals parallel to the direction of the velocity gradient--for intermediate values of Pe, and (3) perpendicular orientation--lamellae with their normals parallel to the vorticity direction--for large Pe. To understand the alignment mechanism, we carry out a scaling analysis of competing torques between a pair of particles in the lamellar structure. Our results suggest that the change of parallel to perpendicular orientation is independent of the particle volume fraction and is caused by the hydrodynamic and Brownian torques on the particles overcoming the torques resulting from the interparticle interactions. This initial study of shear-induced alignment on lamellar structures formed by Janus colloidal particles also opens the door for future applications where a reversible actuator for structure orientation is required. [ABSTRACT FROM AUTHOR]

Using Brownian dynamics simulations of polymer chainsover a widerange of resolution, we find universal scaling laws for polymer coildimensions and tumbling time. At high shear rates γ̇,the coil thickness in the gradient direction becomes independent ofchain length, scaling as NK0γ̇–1/4,where NKdenotes the numbers of Kuhn steps,and the tumbling time scales as NKγ̇–3/4, correcting scaling laws presented in prior studies.We find this to be a consequence of the formation of loops whose lengthis limited by the time required to stretch them and derive scalinglaws from a balance of convection and diffusion of monomers. We findthat, in the absence of hydrodynamic interaction (HI) and excludedvolume (EV), for wormlike chains, the shrinkage in chain stretch observedat ultrahigh shear rates is pushed out to arbitrarily high shear ratesif the chain is resolved increasingly finely below the persistencelength. Finally, scaling laws in the presence of excluded volume andhydrodynamic interactions are derived that are expected to be validfor long chains at high shear rates. [ABSTRACT FROM AUTHOR]