Response of a polymer network to the motion of a rigid sphere

Structured viscoelastic substrates as linear foundations

The linear (Winkler) foundation is a simple model widely used for decades to account for the surface response of elastic bodies. It models the response as purely local, linear, and perpendicular to the surface. We extend this model to the case in which the foundation is made of a structured material such as a polymer network, which has characteristic scales of length and time. We use the two-fluid model of viscoelastic structured materials to treat a film of finite thickness, supported on a rigid solid and subjected to a concentrated normal force at its free surface. We obtain the foundation modulus (Winkler constant) as a function of the film's thickness, intrinsic correlation length, and viscoelastic moduli, for three choices of boundary conditions. The results can be used to readily extend earlier applications of the Winkler model to more complex, microstructured substrates. They also provide a way to extract the intrinsic properties of such complex materials from mechanical surface measurements.

Measurements and characterization of the dynamics of tracer particles in an actin network

The underlying physics governing the diffusion of a tracer particle in a viscoelastic material is a topic of some dispute. The long-term memory in the mechanical response of such materials should induce diffusive motion with a memory kernel, such as fractional Brownian motion (fBM). This is the reason that microrheology is able to provide the shear modulus of polymer networks. Surprisingly, the diffusion of a tracer particle in a network of a purified protein, actin, was found to conform to the continuous time random walk type (CTRW). We set out to resolve this discrepancy by studying the tracer particle diffusion using two different tracer particle sizes, in actin networks of different mesh sizes. We find that the ratio of tracer particle size to the characteristic length scale of a bio-polymer network plays a crucial role in determining the type of diffusion it performs. We find that the diffusion of the tracer particles has features of fBm when the particle is large compared to the mesh size, of normal diffusion when the particle is much smaller than the mesh size, and of the CTRW in between these two limits. Based on our findings, we propose and verify numerically a new model for the motion of the tracer in all regimes. Our model suggests that diffusion in actin networks consists of fBm of the tracer particle coupled with caging events with power-law distributed escape times.

Surface Response of a Polymer Network: Semi-infinite Network

We study theoretically the surface response of a semi-infinite viscoelastic polymer network using the two-fluid model. We focus on the overdamped limit and on the effect of the network's intrinsic length scales. We calculate the decay rate of slow surface fluctuations, and the surface displacement in response to a localized force. Deviations from the large-scale continuum response are found at length scales much larger than the network's mesh size. We discuss implications for surface scattering and microrheology. We provide closed-form expressions that can be used for surface microrheology: the extraction of viscoelastic moduli and intrinsic length scales from the motions of tracer particles lying on the surface without doping the bulk material.

Structural changes in nanoparticle-hydrogel composites at very low filler concentrations

We study the enhancement of the stiffness of two families of hydrogels (polyacrylamide, PAAm, and polydimethylacrylamide, PDMA) due to the additions of very small amounts of silica nanofillers. It is well established that high concentrations of silica nanoparticles enhance the toughness of both hydrogel types, but significantly more for the PDMA based gels that adsorb readily to silica surfaces. In order to decouple the structural changes in the gels that stem either from polymerization kinetics or from the interactions between nanofillers and polymers, we use a photoinitiator for the polymerization of the composite gels that promotes the structural homogeneity of the hydrogels. We characterize both the mechanical and structural properties of the composite hydrogels as a function of nanofiller concentration, by calculating the single particle diffusion of inert polystyrene tracer particles of three different sizes. In agreement with previous experiments, we find that silica nanoparticles increase the stiffness of PAAm gels more than expected for passive fillers. Surprisingly, we find that a small addition of silica nanoparticles during gel polymerization to PDMA based hydrogels softens them. We attribute this effect to an increase of the average mesh size of the gel, allowing particles of 0.49 μm in diameter to diffuse normally through the gel, but restricting the motion of larger particles. A further increase in silica nanoparticle concentration results in the expected stiffening of the gel. PDMA based composites with a large mean pore size, as reported here, may find applications in particle separation and gentle fixation of microorganisms and cells.

On the calculation of the potential of mean force between atomistic nanoparticles

We study the potential of mean force (PMF) between atomistic silica and gold nanoparticles in the vacuum by using molecular dynamics simulations. Such an investigation is devised in order to fully characterize the effective interactions between atomistic nanoparticles, a crucial step to describe the PMF in high-density coarse-grained polymer nanocomposites. In our study, we first investigate the behavior of silica nanoparticles, considering cases corresponding to different particle sizes and assessing results against an analytic theory developed by Hamaker for a system of Lennard-Jones interacting particles (H.C. Hamaker, Physica A 4, 1058 (1937)). Once validated the procedure, we calculate effective interactions between gold nanoparticles, which are considered both bare and coated with polyethylene chains, in order to investigate the effects of the grafting density [Formula: see text] on the PMF. Upon performing atomistic molecular dynamics simulations, it turns out that silica nanoparticles experience similar interactions regardless of the particle size, the most remarkable difference being a peak in the PMF due to surface interactions, clearly apparent for the larger size. As for bare gold nanoparticles, they are slightly interacting, the strength of the effective force increasing for the coated cases. The profile of the resulting PMF resembles a Lennard-Jones potential for intermediate [Formula: see text], becoming progressively more repulsive for high [Formula: see text] and low interparticle separations.

Scale dependence of the mechanics of active gels with increasing motor concentration

Actin is a protein that plays an essential role in maintaining the mechanical integrity of cells. In response to strong external stresses, it can assemble into large bundles, but it grows into a fine branched network to induce cell motion. In some cases, the self-organization of actin fibers and networks involves the action of bipolar filaments of the molecular motor myosin. Such self-organization processes mediated by large myosin bipolar filaments have been studied extensively in vitro. Here we create active gels, composed of single actin filaments and small myosin bipolar filaments. The active steady state in these gels persists long enough to enable the characterization of their mechanical properties using one and two point microrheology. We study the effect of myosin concentration on the mechanical properties of this model system for active matter, for two different motor assembly sizes. In contrast to previous studies of networks with large motor assemblies, we find that the fluctuations of tracer particles embedded in the network decrease in amplitude as motor concentration increases. Nonetheless, we show that myosin motors stiffen the actin networks, in accordance with bulk rheology measurements of networks containing larger motor assemblies. This implies that such stiffening is of universal nature and may be relevant to a wider range of cytoskeleton-based structures.

Correlations in suspensions confined between viscoelastic surfaces: Noncontact microrheology

We study theoretically the velocity cross-correlations of a viscous fluid confined in a slit between two viscoelastic media. We analyze the effect of these correlations on the motions of particles suspended in the fluid. The compliance of the confining boundaries gives rise to a long-ranged pair correlation, decaying only as 1/r with the interparticle distance r. We show how this long-ranged effect may be used to extract the viscoelastic properties of the confining media without embedding tracer particles in them. We discuss the remarkable robustness of such a potential technique with respect to details of the confinement, and its expected statistical advantages over standard two-point microrheology.

Dynamics in steady state in vitro acto-myosin networks

It is well known that many biochemical processes in the cell such as gene regulation, growth signals and activation of ion channels, rely on mechanical stimuli. However, the mechanism by which mechanical signals propagate through cells is not as well understood. In this review we focus on stress propagation in a minimal model for cell elasticity, actomyosin networks, which are comprised of a sub-family of cytoskeleton proteins. After giving an overview of th actomyosin network components, structure and evolution we review stress propagation in these materials as measured through the correlated motion of tracer beads. We also discuss the possibility to extract structural features of these networks from the same experiments. We show that stress transmission through these networks has two pathways, a quickly dissipative one through the bulk, and a long ranged weakly dissipative one through the pre-stressed actin network.

Anomalous diffusion in viscoelastic media with active force dipoles

With the use of the "two-fluid model," we discuss anomalous diffusion induced by active force dipoles in viscoelastic media. Active force dipoles, such as proteins and bacteria, generate nonthermal fluctuating flows that lead to a substantial increment of the diffusion. Using the partial Green's function of the two-fluid model, we first obtain passive (thermal) two-point correlation functions such as the displacement cross-correlation function between the two-point particles separated by a finite distance. We then calculate active (nonthermal) one-point and two-point correlation functions due to active force dipoles. The time correlation of a force dipole is assumed to decay exponentially with a characteristic time scale. We show that the active component of the displacement cross-correlation function exhibits various crossovers from super-diffusive to subdiffusive behaviors depending on the characteristic time scales and the particle separation. Our theoretical results are intimately related to the microrheology technique to detect fluctuations in nonequilibrium environment.