Soft colloids are increasingly used as model systems to address fundamental issues such as crystallization and the glass and jamming transitions. Among the available classes of soft colloids, microgels are emerging as the gold standard. Since their great internal complexity makes their theoretical characterization very hard, microgels are commonly modeled, at least in the small-deformation regime, within the simple framework of linear elasticity theory. Here we show that there exist conditions where its range of validity can be greatly extended, providing strong numerical evidence that microgels adsorbed at an interface follow the two-dimensional Hertzian theory, and hence behave like 2D elastic particles, up to very large deformations, in stark contrast to what found in bulk conditions. We are also able to estimate Young's modulus of the individual particles and, by comparing it with its counterpart in bulk conditions, we demonstrate a significant stiffening of the polymer network at the interface. Finally, by analyzing dynamical properties, we predict multiple reentrant phenomena: By a continuous increase of particle density, microgels first arrest and then refluidify due to the high penetrability of their extended coronas. We observe this anomalous behavior in a range of experimentally accessible conditions for small and loosely cross-linked microgels. The present work thus establishes microgels at interfaces as a new model system for fundamental investigations, paving the way for the experimental synthesis and research on unique highdensity liquidlike states. In addition, these results can guide the development of novel assembly and patterning strategies on surfaces and the design of novel materials with desired interfacial behavior.

In this review, we discuss recent advances in the investigation of colloidal systems interacting via a combination of short-range attraction and long-range repulsion. The prototypical examples of this phenomenology are charged colloids with depletion interactions, but the results apply, to a large extent, also to suspensions of globular proteins, clays, and, in general, to systems with competing attractive (hydrophobic) and repulsive (polar) contributions. After a brief introduction to the problem, we focus on the three disordered states that characterize these systems: equilibrium cluster phase, equilibrium gel, and Wigner glass of clusters. We provide a comparison of their static and dynamic observables, mainly by means of numerical simulations. Next, we discuss the few available studies on their viscoelastic properties and on their response to an external shear. Finally, we provide a summary of the current findings and also raise the main open questions and challenges for the future in this topic. Expected final online publication date for the Annual Review of Condensed Matter Physics, Volume 12 is March 10, 2021. Please see http://www.annualreviews.org/page/journal/pubdates for revised estimates.

Due to their unique structural and mechanical properties, randomly cross-linked polymer networks play an important role in many different fields, ranging from cellular biology to industrial processes. In order to elucidate how these properties are controlled by the physical details of the network (e.g., chain-length and end-to-end distributions), we generate disordered phantom networks with different cross-linker concentrations C and initial densities ρ init and evaluate their elastic properties. We find that the shear modulus computed at the same strand concentration for networks with the same C , which determines the number of chains and the chain-length distribution, depends strongly on the preparation protocol of the network, here controlled by ρ init . We rationalize this dependence by employing a generic stress–strain relation for polymer networks that does not rely on the specific form of the polymer end-to-end distance distribution. We find that the shear modulus of the networks is a nonmonotonic function of the density of elastically active strands, and that this behavior has a purely entropic origin. Our results show that if short chains are abundant, as it is always the case for randomly cross-linked polymer networks, the knowledge of the exact chain conformation distribution is essential for correctly predicting the elastic properties. Finally, we apply our theoretical approach to literature experimental data, qualitatively confirming our interpretations.