Abstract:We image semi-flexible polymer networks under shear at the micrometer scale. By tracking embedded probe particles, we determine the local strain field, and directly measure its uniformity, or degree of affineness, on scales of 2-100 μm. The degree of nonaffine strain depends on polymer length and crosslink density, consistent with theoretical predictions. We also find a direct correspondence between the uniformity of the microscale strain and the nonlinear elasticity of the networks in the bulk.

According to the Stokes-Einstein-Debye (SED) relation, the rotational diffusion coefficient of a colloidal tracer sphere scales with the inverse of the solvent viscosity. Here we investigate the generalization of the SED relation to tracer diffusion in suspensions of neutral and charged colloidal host spheres. Rotational diffusion coefficients are measured with dynamic light scattering and phosphorescence spectroscopy, and calculated including two-and three-particle hydrodynamic interactions. We find that rotational tracer diffusion is always faster than predicted by the SED relation, except for large tracer/host size ratios l. In the case of neutral particles this observation is rationalized by introducing an apparent l-dependent slip boundary coefficient. For charged spheres at low ionic strength, large deviations from SED scaling are found due to the strongly hindered host sphere dynamics. Finally, we present some first experiments on tracer sphere diffusion in suspensions of host rods, showing that hydrodynamic hindrance by rods is much stronger than by spheres. We conclude by pointing to some interesting unresolved issues for future research. I IntroductionThe rotational diffusion coefficient of a single colloidal sphere with radius a T suspended in a solvent with shear viscosity Z 0 is given by the familiar Stokes-Einstein-Debye (SED) relationwith k B T the thermal energy and f r 0 the Stokesian friction factor. Eqn. (1) assumes that the particle is large enough for the solvent to behave as a structureless continuum with vanishing response time. Moreover, stick boundary conditions are assumed, i.e. the velocity of the fluid on the tracer surface equals that of the tracer. Eqn. (1) holds quantitatively not only for colloidal particles but,

We report an experimental study of rotational and translational diffusion and sedimentation of colloidal tracer spheres in semidilute solutions of the nonadsorbing semiflexible polymer xanthan. The tracers are optically anisotropic, permitting depolarized dynamic light scattering measurements without interference from the polymer background. The xanthan solutions behave rheologically like model semidilute polymeric solutions with long-lived entanglements. On the time scale of tracer motion the xanthan solutions are predominantly elastic. The generalized Stokes-Einstein relation describing the polymer solution as a continuous viscous fluid therefore severely overestimates the tracer hindrance. Instead, effective medium theory, describing the polymer solution as a homogeneous Brinkman fluid with a hydrodynamic screening length equal to the concentration-dependent static correlation length, is in excellent agreement with the tracer sedimentation and rotational diffusion coefficients. Rotational diffusion, however, is at the same time in good agreement with a simple model of a rotating sphere in a concentric spherical depletion cavity. Translational diffusion is faster than predicted for a Brinkman fluid, likely due to polymer depletion.

Bundles of polymer filaments are responsible for the rich and unique mechanical behaviors of many biomaterials, including cells and extracellular matrices. In fibrin biopolymers, whose nonlinear elastic properties are crucial for normal blood clotting, protofibrils self-assemble and bundle to form networks of semiflexible fibers. Here we show that the extraordinary strain-stiffening response of fibrin networks is a direct reflection of the hierarchical architecture of the fibrin fibers. We measure the rheology of networks of unbundled protofibrils and find excellent agreement with an affine model of extensible wormlike polymers. By direct comparison with these data, we show that physiological fibrin networks composed of thick fibers can be modeled as networks of tight protofibril bundles. We demonstrate that the tightness of coupling between protofibrils in the fibers can be tuned by the degree of enzymatic intermolecular crosslinking by the coagulation factor XIII. Furthermore, at high stress, the protofibrils contribute independently to the network elasticity, which may reflect a decoupling of the tight bundle structure. The hierarchical architecture of fibrin fibers can thus account for the nonlinearity and enormous elastic resilience characteristic of blood clots.

The Brownian motions of microscopic particles in viscous or viscoelastic fluids can be used to measure rheological properties. This is the basis of recently developed one- and two-particle microrheology techniques. For increased temporal and spatial resolution, some microrheology techniques employ optical traps, which introduce additional forces on the particles. We have systematically studied the effect that confinement of particles by optical traps has on their auto- and cross-correlated fluctuations. We show that trapping causes anticorrelations in the motion of two particles at low frequencies. We demonstrate how these anticorrelations depend on trap strength and the shear modulus of viscoelastic media. We present a method to account for the effects of optical traps, which permits the quantitative measurement of viscoelastic properties in one- and two-particle microrheology over an extended frequency range in a variety of viscous and viscoelastic media.

We develop a percolation model motivated by recent experimental studies of gels with active network remodeling by molecular motors. This remodeling was found to lead to a critical state reminiscent of random percolation (RP), but with a cluster distribution inconsistent with RP. Our model not only can account for these experiments, but also exhibits an unusual type of mixed phase transition: We find that the transition is characterized by signatures of criticality, but with a discontinuity in the order parameter. DOI: 10.1103/PhysRevLett.114.098104 PACS numbers: 87.16.Ka, 64.60.ah, 64.60.Bd, 64.60.De Percolation theory has become pervasive in a number of fields ranging from physics to mathematics and even computer science [1]. In particular, it successfully describes connectivity and elastic properties of polymer networks [2,3]. The simplest percolation model is the random percolation (RP) model, consisting of a collection of nodes with controlled connectivity, p, representing the fraction of occupied bonds between the nodes. As a function of p, the order parameter-the mass fraction of the largest clusterbecomes finite above the percolation threshold p c . The nature of the transition is of special interest because the system properties are highly tunable at this point, especially if the transition is discontinuous; in that case, just a few bonds can have a significant impact, even for very large systems [4]. Usually, however, percolation transitions are second order, with a continuous variation of the order parameter and various critical signatures. More specialized percolation models can exhibit different phase behavior, including discontinuous transitions between the two phases (see discussion below).Here, we present a simple model based on random percolation that develops a discontinuous jump in the order parameter in the thermodynamic limit, while exhibiting other features of criticality in such quantities as the correlation length and susceptibility. Interestingly, the transition we observe occurs for the same p c < 1 as for random percolation. Moreover, our model can account for recent experimental results on active biopolymer gels that have been shown to self-organize towards a critical connectivity point [5]. The experimentally observed cluster properties at this point were found to be inconsistent with the ordinary random percolation model.In these experiments, we studied a model cytoskeletal system, composed of actin filaments, fascin cross-links and myosin motors in a quasi-2D chamber of dimensions 3 mm × 2 mm × 80 μm [5] (see Supplemental Material [6]). We observed a motor-driven collapse of the network into disjointed clusters (see Fig. 1(a) and movie of the collapse in the Supplemental Material [6]). The configuration of the clusters prior to the collapse is obtained by analyzing the timereversed movie [see Fig. 1(b)] and their masses were estimated from their initial areas. We found that, over a wide range of the experimental parameters, the number n s of clusters of mass s exhibits a power-l...

We report the formation of strongly inflated sedimentation-diffusion concentration profiles for charged monodisperse colloidal spheres in absolute ethanol. Various additional experiments, such as light scattering, confirm that the very dilute supernatants, left behind by the majority of settling colloids, contain spheres that repel each other at distances of micrometers. We attribute these unusual profiles to a significant counter-ion contribution to the osmotic pressure and to the Debye screening length. An approximate osmotic equation-of-state at the level of the second virial coefficient for dispersions at very low ionic strength indeed implies an algebraic long-distance decay of sedimentation-diffusion profiles, together with significant lowering of the effective colloid mass by an entropic lift due to counter-ions. We have also observed that sedimenting dispersions sometimes demix into two layers, which are both disordered fluids. Since the colloids are clearly repulsive on the DLVO pair level, this layering possibly manifests a phase transition driven by many-body attractions. ᮊ

We present a study on the morphology and kinetics of depletion-induced phase separation in aqueous xanthan-colloid mixtures with light microscopy and small angle light scattering (SALS), using fluorinated colloids with a refractive index close to that of water to prevent complications of multiple scattering. Microscopy with the direction of observation perpendicular to gravity enabled us to observe the development of the microstructure during the entire phase separation process including the formation of a macroscopic interface. Bicontinuous structures typical of a spinodal decomposition mechanism were observed at early times. These structures coarsened in time until hydrodynamic flow resulted in lane formation. Close to the binodal, a nucleation-and-growth mechanism was observed with formation of droplets. The coarsening kinetics were studied in more detail with SALS and turbidity measurements. Above polysaccharide concentrations at which entanglements become dominant, a slower coarsening and macroscopic phase separation were found because of the high continuous phase viscosity.