Stochastic kinetic theory applied to coarse-grained polymer model.

A stochastic field theory approach is applied to a coarse-grained polymer model that will enable studies of polymer behavior under non-equilibrium conditions. This article is focused on the validation of the new model in comparison with explicit Langevin equation simulations under conditions with analytical solutions. The polymers are modeled as Hookean dumbbells in one dimension, without including hydrodynamic interactions and polymer-polymer interactions. Stochastic moment equations are derived from full field theory. The accuracy of the field theory and moment equations is quantified using autocorrelation functions. The full field theory is only accurate for a large number of polymers due to keeping track of rare occurrences of polymers with a large stretch. The moment equations do not have this error because they do not explicitly track these configurations. The accuracy of both methods depends on the spatial degree of discretization. The timescale of decorrelation over length scales bigger than the spatial discretization is accurate, while there is an error over the scale of single mesh points.

Continuous transition of colloidal crystals through stable random orders.

Randomly stacked 2D hexagonal close-packed (RHCP) layer structures are frequently observed in colloids and other material systems but are considered metastable. We report a stable RHCP phase domain of poly(butadiene-b-ethylene oxide) (PB-PEO) diblock copolymer micellar colloids in water. The stable RHCP colloidal crystals emerge in the middle of a continuously transiting phase domain of close-packed PB-PEO colloids from a face-centered cubic (FCC) polytype to a HCP polytype. We attribute the stability of RHCP structures to two competing contributions, entropic preference for FCC lattices and long PEO corona chains stabilizing HCP lattices. When these two contributions become comparable in the phase space, thermal fluctuation randomizes the stacking order of the 2D-HCP layers, and RHCP orders are stabilized. The continuously transiting close-packed structures of PB-PEO colloids with stable RHCP states suggest that similar structural transitions and equivalent RHCP states may occur in other polytypic crystal systems because polytypic crystals have the common crystal construction rule, i.e., stacking 2D-HCP lattice layer groups in different orders.

Application of a Simple Short-Range Attraction and Long-Range Repulsion Colloidal Model toward Predicting the Viscosity of Protein Solutions.

Some hard-sphere colloidal models have been criticized for inaccurately predicting the solution viscosity of complex biological molecules like proteins. Competing short-range attractions and long-range repulsions, also known as short-range attraction and long-range repulsion (SALR) interactions, have been thought to affect the microstructure of a protein solution at low to moderate ionic strength. However, such interactions have been implicated primarily in causing phase transition, protein gelation, or reversible cluster formation, and their effect on protein solution viscosity change is not fully understood. In this work, we show the application of a hard-sphere colloidal model with SALR interactions toward predicting the viscosity of dilute to semi-dilute protein solutions. The comparison is performed for a globular-shaped albumin and Y-shaped therapeutic monoclonal antibody that are not explained by previous colloidal models. The model predictions show that it is the coupling between attractions and repulsions that gives rise to the observed experimental trends in solution viscosity as a function of pH, concentration, and ionic strength. The parameters of the model are obtained from measurements of the second virial coefficient and net surface charge/zeta-potential, without additional fitting of the viscosity.

Mesoscale simulation approach for assembly of small deformable objects.

We adapt Vertex models to understand the physical origin of the formation of long-range ordered structures in repulsive soft particles. The model incorporates contributions from the volume and surface area of each particle. Sampling using Monte Carlo simulations allows the system to naturally select preferred structures. We observe transitions between a body-centered cubic ordered state and a disordered state. Constraints to the simulation domain can suppress or allow the system to follow a path similar to Martensitic transformations from one ordered state to another ordered state. Finally, we show that rapid quenches from a disordered state into the ordered region lead to metastable local particle arrangements instead of a large-scale single crystal.

Predicting Steady Shear Rheology of Condensed-Phase Monomolecular Films at the Air-Water Interface.

Predicting the non-Newtonian shear response of soft interfaces in biophysical systems and engineered products has been compromised by the use of linear (Newtonian) constitutive equations. We present a generalized constitutive equation, with tractable material properties, governing the response of Newtonian and non-Newtonian interfaces subjected to a wide range of steady shear. With experiments spanning six decades of shear rate, we capture and unify divergent reports of shear-thinning behavior of monomolecular films of the lipid dipalmitoylphosphatidylcholine, the primary constituent of mammalian cell walls and lung surfactant, at near-physiological packing densities.

Examination of the Statistical Effects Associated with Tracking Propulsive Particles.

Particle tracking of active colloidal particles can be used to compute mean-squared displacements that are fit to extract properties of the particles including the propulsive speed. Statistical errors in the mean-squared displacement leads to errors in the extracted properties especially for more weakly propelling particles. Brownian dynamics simulations in which the particle parameters are prescribed were used to examine the statistics of tracking self-propelling objects. It was found that the manner in which tracking data is analyzed has a profound impact on the precision and accuracy of measurements. To properly extract particle parameters, it was necessary to apply a nonlinear fit of the mean-squared displacement over a time region that includes transition behavior from ballistic to diffusive. The dependence of the statistics on the number of particles tracked and the length of movies was examined, showing how and why weakly propelling particles are difficult to analyze.

Passive trapping of rigid rods due to conformation-dependent electrophoretic mobility.

We present computer simulations of a rigid rod in a combination of an extensional fluid flow and extensional electric field. The electrophoretic mobility of the rod is different parallel or perpendicular to the rod. The dependence of the mobility on the conformation (orientation) leads to a new phenomenon where the rods can be passively trapped in all directions at the stagnation point. This contrasts with the behavior in either fluid flow or electric field alone, in which an object can be pushed towards the stagnation point along some directions but is pushed away in others. We have determined the state space where trapping occurs and have developed a model that describes the strength of trapping when it does occur. This new phenomenon could be used in the future to separate objects based on a coupling between their mobility and ability to be oriented.

Influence of shear on globule formation in dilute solutions of flexible polymers.

Polyelectrolytes, polymers in poor solvents, polymers mixed with particles, and other systems with attractions and repulsions show formation of globules/structures in equilibrium or in flow. To study the flow behavior of such systems, we developed a simple coarse-grained model with short ranged attractions and repulsions. Polymers are represented as charged bead-spring chains and they interact with oppositely charged colloids. Neglecting hydrodynamic interactions, we study the formation of compact polymer structures called globules. Under certain conditions, increase in shear rate decreases the mean first passage time to form a globule. At other conditions, shear flow causes the globules to breakup, similar to the globule-stretch transition of polymers in poor solvents.

A Gram-Charlier Analysis of Scattering to Describe Nonideal Polymer Conformations.

Theories of interpreting polymer physics and rheology at the molecular level from experiments, including small-angle scattering, typically rely on the assumption that polymer chains possess a Gaussian configuration distribution. This assumption frequently fails to describe features of real polymer molecules both at equilibrium (when polymers have nonlinear topology or heterogeneous chemistry) and out of equilibrium (when they are subjected to nonlinear deformations). To better describe non-Gaussian polymer conformation distributions, we propose a moments analysis based on the Gram-Charlier expansion as a natural framework for describing structure and scattering from non-Gaussian polymers. The expansion describes the conformation distribution in terms of cumulants (equivalent to moments of the distribution) of the underlying segment density distribution function, providing low-dimensional descriptors that can be inferred directly from measured scattering in a way that is agnostic to a polymer's topology, chemistry, or state of deformation. We use this framework to show that cumulants can be used to "fingerprint" non-Gaussian conformation distributions of polymers either at equilibrium (applied to sequence-defined heteropolymers) or out of equilibrium (applied to polymers experiencing nonlinear deformation due to flow). We anticipate that this new analysis method will provide a general framework for examining nonideal polymer configurations and the properties that arise from them.

Dynamics of confined suspensions of swimming particles.

Low Reynolds number direct simulations of large populations of hydrodynamically interacting swimming particles confined between planar walls are performed. The results of simulations are compared with a theory that describes dilute suspensions of swimmers. The theory yields scalings with concentration for diffusivities and velocity fluctuations as well as a prediction of the fluid velocity spatial autocorrelation function. Even for uncorrelated swimmers, the theory predicts anticorrelations between nearby fluid elements that correspond to vortex-like swirling motions in the fluid with length scale set by the size of a swimmer and the slit height. Very similar results arise from the full simulations indicating either that correlated motion of the swimmers is not significant at the concentrations considered or that the fluid phase autocorrelation is not a sensitive measure of the correlated motion. This result is in stark contrast with results from unconfined systems, for which the fluid autocorrelation captures large-scale collective fluid structures. The additional length scale (screening length) introduced by the confinement seems to prevent these large-scale structures from forming.

Dumbbell kinetic theory for polymers in a combination of flow and external electric field.

Combining Poiseuille flow with an external electric field is a demonstrated method to drive transverse migration in capillary electrophoresis. Despite both computational and experimental studies, a number of questions about how to best model polymers under these conditions remains. Attempts have been made to develop a kinetic theory for a bead-spring dumbbell model, but these have only been accurate at low electric field strength and have not captured the nonmonotonic relationship between migration and electric field strength. In this paper, we revisit the development of a kinetic theory for a bead-spring dumbbell in a combination of parabolic flow and an external electric field. The resultant theory yields a compact formula that predicts polymer concentration profiles that agree excellently with our Brownian dynamics simulations including the aforementioned nonmonotonic relationship. Furthermore, we compare our theoretical results to experimental data and find that our model nearly quantitatively predicts the position of the maximum in migration.

DNA stretch during electrophoresis due to a step change in mobility.

We investigate DNA stretching during electrophoresis when the mobility abruptly changes. This is a simplified geometry that produces a nonhomogeneous strain rate over the scale of a single molecule. An effective Weissenberg number (Wi) and Deborah number were identified, and the degree of stretching was examined as a function of these two parameters. The system does not undergo a coil-stretch transition. The finite extensibility of the chains only affects the response if the chain is stretched to a significant fraction of the contour length. The wormlike chain shows a characteristic approach to full extension of Wi(-1/2).

Coarse-grained model of conformation-dependent electrophoretic mobility and its influence on DNA dynamics.

The electrophoretic mobility of molecules such as λ-DNA depends on the conformation of the molecule. It has been shown that electrohydrodynamic interactions between parts of the molecule lead to a mobility that depends on conformation and can explain some experimental observations. We have developed a new coarse-grained model that incorporates these changes of mobility into a bead-spring chain model. Brownian dynamics simulations have been performed using this model. The model reproduces the cross-stream migration that occurs in capillary electrophoresis when pressure-driven flow is applied parallel or antiparallel to the electric field. The model also reproduces the change of mobility when the molecule is stretched significantly in an extensional field. We find that the conformation-dependent mobility can lead to a new type of unraveling of the molecule in strong fields. This occurs when different parts of the molecule have different mobilities and the electric field is large.

Impact of external flow on the dynamics of swimming microorganisms near surfaces.

Swimming microorganisms have been previously observed to accumulate along walls in confined systems both experimentally and in computer simulations. Here, we use computer simulations of dilute populations for a simplified model of an organism to calculate the dynamics of swimmers between two walls with an external fluid flow. Simulations with and without hydrodynamic interactions (HIs) are used to quantify their influence on surface accumulation. We found that the accumulation of organisms at the wall is larger when HIs are included. An external fluid flow orients the organisms parallel to the fluid flow, which reduces the accumulation at the walls. The effect of the flow on the orientations is quantified and compared to previous work on upstream swimming of organisms and alignment of passive rods in flow. In pressure-driven flow, the zero shear rate at the channel center leads to a dip in the concentration of organisms in the center. The curvature of this dip is quantified as a function of the flow rate. The fluid flow also affects the transport of organisms across the channel from one wall to the other.

Fluctuations in the coil-stretch transition of flexible polymers in good solvents: a peak due to nonlinear force relation.

Long flexible polymers undergo a coil to stretch transition (CST) in an elongational flow. Near the CST, a peak can be observed in the fluctuations of the size of a molecule (|R|). Solvent effects on the fluctuations are studied using Brownian dynamics simulations of a nonlinear spring force relation that can represent real molecules. Ignoring the influence of hydrodynamic interactions, a linear region in the spring force relation is known to cause the peak in |R| fluctuations. In contrast, we find that a peak in the fluctuations can be obtained even for the nonlinear spring force relation. We analyze the influence of hydrodynamic interactions on the fluctuations using a dumbbell model with a conformation-dependent drag coefficient.

Effect of viscoelasticity on the collective behavior of swimming microorganisms.

Hydrodynamic interactions of swimming microorganisms can lead to coordinated behaviors of large groups. Using a mean-field theory and the Oldroyd-B constitutive equation, we show how linear viscoelasticity of the suspending fluid alters the hydrodynamic interactions and therefore the ability of the group to coordinate. We quantify the ability to coordinate by the initial growth rate of a small disturbance from the uniform isotropic state. For small wave numbers the response is qualitatively similar to a Newtonian fluid but the Deborah number affects an effective viscosity of the suspension. At higher wave number, the response of the fluid to small amplitude oscillatory shear flow, leads to a maximal growth rate at a particular wavelength unlike the Newtonian result.

Diffusion and spatial correlations in suspensions of swimming particles.

Populations of swimming micro-organisms produce fluid motions that lead to dramatically enhanced diffusion of tracer particles. Using simulations of suspensions of swimming particles in a periodic domain, we capture this effect and show that it depends qualitatively on the mode of swimming: swimmers "pushed" from behind by their flagella show greater enhancement than swimmers that are "pulled" from the front. The difference is manifested by an increase, that only occurs for pushers, of the diffusivity of passive tracers and the velocity correlation length with the size of the periodic domain. A physical argument supported by a mean field theory sheds light on the origin of these effects.