Soft particles such as polymeric microgels can form ultra-dense phases, where the average center-to-center distance a_s can be smaller than the initial unperturbed particle diameter σ₀, due to their ability to interpenetrate and compress. However, despite of the effort devoted to microgels at ultrahigh densities, we know surprisingly little about their response to their environment at effective volume fractions ϕ _eff above close packing (ϕ _cp ), and the existing information is often contradictory. Here we report direct measurements of the size and shape of poly(N-isopropylacrylamide) microgels at concentrations below and above ϕ _cp using the zero average contrast method in small-angle neutron scattering. We complement these experiments with measurements of the average interparticle distances using small-angle x-ray scattering, and a determination of the glass transition using dynamic light scattering. This allows us to unambiguously decouple interaction effects from density-dependent variations of the particle size and shape at all values of ϕ _eff . We demonstrate that the microgels used in this study significantly interpenetrate and thus change their size and shape only marginally even for ϕ _eff ≫ ϕ _cp , a finding that may require changes in the interpretation of a number of previously published studies on the structural and dynamic properties of dense soft particle systems.

We investigate the microscopic structure and density fluctuations of complex coacervates of flexible polyelectrolytes using scattering of neutrons, X-rays, and light. Poly(acrylic acid) and poly(N,N-dimethylaminoethyl methacrylate) offer a well-defined model system that allows for selective labeling and systematic variation of the strength of the attractive electrostatic interactions. Two neutron scattering experiments have been carried out: (i) we use deuterated polymeric tracers in a complex coacervate with an overall neutron scattering length density that is matched to that of the solvent, to probe the conformation of single polymer chains in the complex coacervates, and (ii) we measure complex coacervates in which all polymer chains of one type are deuterated, to probe their overall structure. The single chain static structure factors reveal that both polycations and polyanions have an ideal Gaussian chain conformation in the complex coacervates. At the same time, the overall structure is similar to that of a semidilute polymer solution, with polycations and polyanions strongly overlapping to form a network with a mesh size that is much smaller than the radius of gyration of the polymers. The mesh size decreases with decreasing salt concentration, following a scaling that is in good agreement with predictions from the corresponding salt–polymer phase diagram. These findings are confirmed by complementary X-ray scattering experiments. Finally, in all scattering experiments with light, X-rays, and neutrons, and for all polymer chain lengths and salt concentrations, we find a remarkable low-q excess scattering, following a power law with a slope close to −2. This points to the presence of equilibrium, large-scale density fluctuations in the complex coacervates. Dynamic light scattering experiments reveal two complementary diffusive modes in the complex coacervates, corresponding to fluctuations of the polymer mesh and diffusion of domains of varying density, respectively.

We report on a joint experimental–theoretical study of collective diffusion in, and static shear viscosity of solutions of bovine serum albumin (BSA) proteins, focusing on the dependence on protein and salt concentration. Data obtained from dynamic light scattering and rheometric measurements are compared to theoretical calculations based on an analytically treatable spheroid model of BSA with isotropic screened Coulomb plus hard-sphere interactions. The only input to the dynamics calculations is the static structure factor obtained from a consistent theoretical fit to a concentration series of small-angle X-ray scattering (SAXS) data. This fit is based on an integral equation scheme that combines high accuracy with low computational cost. All experimentally probed dynamic and static properties are reproduced theoretically with an at least semi-quantitative accuracy. For lower protein concentration and low salinity, both theory and experiment show a maximum in the reduced viscosity, caused by the electrostatic repulsion of proteins. On employing our theoretical and experimental results, the applicability range of a generalized Stokes–Einstein (GSE) relation connecting viscosity, collective diffusion coefficient, and osmotic compressibility, proposed by Kholodenko and Douglas [Phys. Rev. E, 1995, 51, 1081] is examined. Significant violation of the GSE relation is found, both in experimental data and in theoretical models, in concentrated systems at physiological salinity, and under low-salt conditions for arbitrary protein concentrations.