Casimir-like forces at the percolation transition

Percolation and critical phenomena show common features such as scaling and universality. Colloidal particles, immersed in a solvent close to criticality, experience long-range effective forces, named critical Casimir forces. %These originate from the confinement of the solvent critical fluctuations between the colloids. Building on the analogy between critical phenomena and percolation, we explore the possibility of observing long-range forces near a percolation threshold. To this aim we numerically evaluate the effective potential between two colloidal particles dispersed in a chemical sol and we show that it becomes attractive and long-ranged on approaching the sol percolation transition. We develop a theoretical description based on a polydisperse Asakura-Oosawa model which captures the divergence of the interaction range, allowing us to interpret such effect in terms of depletion interactions in a structured solvent. Our results provide the geometric analogue of the critical Casimir force, suggesting a novel way for tuning colloidal interactions by controlling the clustering properties of the solvent.Comment: final version of the manuscrip

Internal structure and swelling behaviour of in silico microgel particles

Microgels are soft colloids that, in virtue of their polymeric nature, can react to external stimuli such as temperature or pH by changing their size. The resulting swelling/deswelling transition can be exploited in fundamental research as well as for many diverse practical applications, ranging from art restoration to medicine. Such an extraordinary versatility stems from the complex internal structure of the individual microgels, each of which is a crosslinked polymer network. Here we employ a recently-introduced computational method to generate realistic microgel configurations and look at their structural properties, both in real and Fourier space, for several temperatures across the volume phase transition as a function of the crosslinker concentration and of the confining radius employed during the `in-silico' synthesis. We find that the chain-length distribution of the resulting networks can be analytically predicted by a simple theoretical argument. In addition, we find that our results are well-fitted to the fuzzy-sphere model, which correctly reproduces the density profile of the microgels under study

Generalized Fluctuation-Dissipation Relation and Effective Temperature upon Heating a Deeply Supercooled Liquid

We show that a generalized fluctuation-dissipation relation applies upon instantaneously increasing the temperature of a deeply supercooled liquid. This has the same two-step shape of the relation found upon cooling the liquid, but with opposite violation, indicating an effective temperature that is lower than bath temperature. We show that the effective temperature exhibits some sensible time-dependence and that it retains its connection with the partitioned phase space visited in ageing. We underline the potential relevance of our numerical results for experimental studies of the fluctuation-dissipation relation in glassy systems.Comment: 5 pages, 4 figure

How soft repulsion enhances the depletion mechanism

We investigate binary mixtures of large colloids interacting through soft potentials with small, ideal depletants. We show that softness has a dramatic effect on the resulting colloid-colloid effective potential when the depletant-to-colloid size ratio $q$ is small, with significant consequences on the colloidal phase behaviour. We also provide an exact relation that allows us to obtain the effective pair potential for {\it any} type of colloid-depletant interactions in the case of ideal depletants, without having to rely on complicated and expensive full-mixture simulations. We also show that soft repulsion among depletants further enhances the tendency of colloids to aggregate. Our theoretical and numerical results demonstrate that --- in the limit of small $q$ --- soft mixtures cannot be mapped onto hard systems and hence soft depletion is not a mere extension of the widely used Asakura-Oosawa potential.Comment: Accepted for publication in Soft Matte

Multidimensional Stationary Probability Distribution for Interacting Active Particles

We derive the stationary probability distribution for a non-equilibrium system composed by an arbitrary number of degrees of freedom that are subject to Gaussian colored noise and a conservative potential. This is based on a multidimensional version of the Unified Colored Noise Approximation. By comparing theory with numerical simulations we demonstrate that the theoretical probability density quantitatively describes the accumulation of active particles around repulsive obstacles. In particular, for two particles with repulsive interactions, the probability of close contact decreases when one of the two particle is pinned. Moreover, in the case of isotropic confining potentials, the radial density profile shows a non trivial scaling with radius. Finally we show that the theory well approximates the "pressure" generated by the active particles allowing to derive an equation of state for a system of non-interacting colored noise-driven particles.Comment: 5 pages, 2 figure

Tuning effective interactions close to the critical point in colloidal suspensions

We report a numerical investigation of two colloids immersed in a critical solvent, with the aim of quantifying the effective colloid-colloid interaction potential. By turning on an attraction between the colloid and the solvent particles we follow the evolution from the case in which the solvent density close to the colloids changes from values smaller than the bulk to values larger than the bulk. We thus effectively implement the so-called $(+,+)$ and $(-,-)$ boundary conditions defined in field theoretical approaches focused on the description of critical Casimir forces. We find that the effective potential at large distances decays exponentially, with a characteristic decay length compatible with the bulk critical correlation length, in full agreement with theoretical predictions. We also investigate the case of $(+,-)$ boundary condition, where the effective potential becomes repulsive. Our study provides a guidance for a design of the interaction potential which can be exploited to control the stability of colloidal systems