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.