Giuseppe Foffi

Resonances arising from hydrodynamic memory in Brownian motion

Observation of the Brownian motion of a small probe interacting with its environment provides one of the main strategies for characterizing soft matter. Essentially, two counteracting forces govern the motion of the Brownian particle. First, the particle is driven by rapid collisions with the surrounding solvent molecules, referred to as thermal noise. Second, the friction between the particle and the viscous solvent damps its motion. Conventionally, the thermal force is assumed to be random and characterized by a Gaussian white noise spectrum. The friction is assumed to be given by the Stokes drag, suggesting that motion is overdamped at long times in particle tracking experiments, when inertia becomes negligible. However, as the particle receives momentum from the fluctuating fluid molecules, it also displaces the fluid in its immediate vicinity. The entrained fluid acts back on the particle and gives rise to long-range correlations. This hydrodynamic ‘memory’ translates to thermal forces, which have a coloured, that is, non-white, noise spectrum. One hundred years after Perrin’s pioneering experiments on Brownian motion, direct experimental observation of this colour is still elusive. Here we measure the spectrum of thermal noise by confining the Brownian fluctuations of a microsphere in a strong optical trap. We show that hydrodynamic correlations result in a resonant peak in the power spectral density of the sphere’s positional fluctuations, in strong contrast to overdamped systems. Furthermore, we demonstrate different strategies to achieve peak amplification. By analogy with microcantilever-based sensors, our results reveal that the particle–fluid–trap system can be considered a nanomechanical resonator in which the intrinsic hydrodynamic backflow enhances resonance. Therefore, instead of being treated as a disturbance, details in thermal noise could be exploited for the development of new types of sensor and particle-based assay in lab-on-a-chip applications.

Scaling of dynamics with the range of interaction in short-range attractive colloids

We numerically study the dependence of the dynamics on the range of interaction Delta for the short-range square well potential. We find that, for small Delta, dynamics scale exactly in the same way as thermodynamics, both for Newtonian and Brownian microscopic dynamics. For interaction ranges from a few percent down to the Baxter limit, the relative location of the attractive-glass line and the liquid-gas line does not depend on Delta. This proves that, in this class of potentials, disordered arrested states (gels) can be generated only as a result of a kinetically arrested phase separation.

On the possibility of extending the Noro-Frenkel generalized law of correspondent states to nonisotropic patchy interactions.

Colloidal systems (and protein solutions) are often characterized by attractive interactions whose ranges are much smaller than the particle size. When this is the case and the interaction is spherical, systems obey a generalized law of correspondent states (GLCS), first proposed by Noro and Frenkel (Noro, M. G.; Frenkel, D. J. Chem. Phys. 2000, 113, 2941). The thermodynamic properties become insensitive to the details of the potential, depending only on the value of the second virial coefficient B2 and the density rho. The GLCS does not generically hold for the case of nonspherical potentials. In this Letter, we suggest that when particles interact via short-ranged small-angular amplitude patchy interactions (so that the condition of only one bond per patch is fulfilled), it is still possible to generalize the GLCS close to the liquid-gas critical point.

Multistep kinetic self-assembly of DNA-coated colloids

Equilibrium self-assembly relies on the relaxation of disordered mixtures of building blocks towards an ordered ground state. The main drawback of this traditional approach lies in the kinetic traps that often interrupt the progression of the system towards equilibrium and lead to the formation of arrested phases. The latest techniques to control colloidal interactions open up the possibility of exploiting the tendency to dynamically arrest in order to construct amorphous materials with a specific morphology and local separation between multiple components. Here we propose strategies to direct the gelation of two-component colloidal mixtures by sequentially activating selective interactions. We investigate morphological changes in the structure of the arrested phases both by means of molecular dynamics simulations and experimentally by using DNA-coated colloids. Our approach can be exploited to assemble multicomponent mesoporous materials with possible applications in hybrid photovoltaics, photonics and drug delivery.

Arrested demixing opens route to bigels

Understanding and, ultimately, controlling the properties of amorphous materials is one of the key goals of material science. Among the different amorphous structures, a very important role is played by colloidal gels. It has been only recently understood that colloidal gels are the result of the interplay between phase separation and arrest. When short-ranged attractive colloids are quenched into the phase-separating region, density fluctuations are arrested and this results in ramified amorphous space-spanning structures that are capable of sustaining mechanical stress. We present a mechanism of aggregation through arrested demixing in binary colloidal mixtures, which leads to the formation of a yet unexplored class of materials––bigels. This material is obtained by tuning interspecies interactions. Using a computer model, we investigate the phase behavior and the structural properties of these bigels. We show the topological similarities and the geometrical differences between these binary, interpenetrating, arrested structures and their well-known monodisperse counterparts, colloidal gels. Our findings are supported by confocal microscopy experiments performed on mixtures of DNA-coated colloids. The mechanism of bigel formation is a generalization of arrested phase separation and is therefore universal.

New insight into cataract formation : Enhanced stability through mutual attraction

Small-angle neutron scattering experiments and molecular dynamics simulations combined with an application of concepts from soft matter physics to complex protein mixtures provide new insight into the stability of eye lens protein mixtures. Exploring this colloid-protein analogy we demonstrate that weak attractions between unlike proteins help to maintain lens transparency in an extremely sensitive and nonmonotonic manner. These results not only represent an important step towards a better understanding of protein condensation diseases such as cataract formation, but provide general guidelines for tuning the stability of colloid mixtures, a topic relevant for soft matter physics and industrial applications.

Configurational entropy of hard spheres

We numerically calculate the configurational entropy Sconf of a binary mixture of hard spheres, by using a perturbed Hamiltonian method trapping the system inside a given state, which requires fewer assumptions than the previous methods (Speedy 1998 Mol.Phys. 95 169). We find that Sconf is a decreasing function of the packing fraction φ and extrapolates to zero at the Kauzmann packing fraction , suggesting the possibility of an ideal glass transition for the hard-sphere system. Finally, the Adam-Gibbs relation is found to hold.

Oscillatory athermal quasistatic deformation of a model glass

We report computer simulations of oscillatory athermal quasistatic shear deformation of dense amorphous samples of a three-dimensional model glass former. A dynamical transition is observed as the amplitude of the deformation is varied: For large values of the amplitude the system exhibits diffusive behavior and loss of memory of the initial conditions, whereas localization is observed for small amplitudes. Our results suggest that the same kind of transition found in driven colloidal systems is present in the case of amorphous solids (e.g., metallic glasses). The onset of the transition is shown to be related to the onset of energy dissipation. Shear banding is observed for large system sizes, without, however, affecting qualitative aspects of the transition.

Diffusion-Limited Reactions in Crowded Environments

Diffusion-limited reactions are usually described within the Smoluchowski theory, which neglects interparticle interactions. We propose a simple way to incorporate excluded-volume effects building on simulations of hard sphere in the presence of a sink. For large values of the sink-to-particle size ratio R(s), the measured encounter rate is in good agreement with a simple generalization of the Smoluchowski equation at high densities. Reducing R(s), the encounter rate is substantially depressed and becomes even nonmonotonic for R(s)<<1. Concurrently with the saturation of the rate, stationary density waves set in close to the sink. A mean-field analysis helps to shed light on the subtle link between such ordering and the slowing down of the encounter dynamics. Finally, we show how an infinitesimal amount of nonreacting impurities can equally slow down dramatically the reaction.

Colloidal characterization and thermodynamic stability of binary eye lens protein mixtures.

We present a study of binary mixtures of eye lens crystallin proteins. A coarse-grained model of aqueous alpha- and gamma-crystallin mixtures based on molecular dynamics simulations and SANS experiments is proposed. Thermodynamic perturbation theory is implemented to obtain the stability boundaries, or spinodal surface, of the binary mixture in the full parameter space. The stability of these high-concentration crystallin mixtures was found to depend on the alpha-gamma attraction in a manner that is both extremely sensitive and nonmonotonic; stronger or weaker attraction resulted in a spectacularly enhanced instability. The relevance of these mechanisms as possible sources of the alteration of the spatial distribution of the lens proteins encountered in cataract disease is discussed.