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Brownian motion is a universal characteristic of colloidal particles embedded in a host medium, and it is the fingerprint of molecular transport or diffusion, a generic feature of relevance not only in Physics but also in several branches of Science and Engineering. Since its discovery, Brownian motion or colloid dynamics has been important in elucidating the connection between the molecular details of the diffusing macromolecule and the macroscopic information of the host medium. However, colloid dynamics is far from being completely understood. For example, the diffusion of non-spherical colloids and the effects of geometry on the dynamics of either passive or active colloids are a few representative cases that are part of the current challenges in Soft Matter Physics. In this contribution, we take a step forward to introduce a covariant description of the colloid dynamics in curved spaces. This formalism will allow us to understand several phenomena, for instance, the effects of curvature on the kinetics during spinodal decomposition and the thermodynamic properties of the colloidal dispersion, just to mention a few examples. This theoretical framework will also serve as the starting point to highlight the role of geometry on colloid dynamics, an aspect that is of paramount importance to understanding more complex phenomena, such as the diffusive mechanisms of proteins embedded in cell membranes., Comment: 15 pages, 2 figures

The interplay of phase separation and dynamical arrest can lead to the formation of gels and glasses, which is relevant for such diverse fields as hard and soft condensed matter physics, materials science, food engineering and pharmaceutical industry. Here, the non-equilibrium states as well as the interactions of globular proteins are analyzed. Lysozyme in brine is chosen as a model system with short-range attractions. The metastable gas-liquid binodal and the dynamical arrest line as well as the second virial coefficient $B_2$ have been determined for various solution conditions by cloud-point measurements, optical microscopy, centrifugation experiments and light scattering. If temperature is expressed in terms of $B_2$, the binodals obtained under various conditions fall onto a master curve, as suggested by the extended law of corresponding states. Arrest lines for different salt concentrations overlap within experimental errors, whereas they do not overlap if the temperature axis is replaced by $B_2$. This indicates that the binodals are not sensitive to the details of the potential, but can be described by one integral parameter, i.e. $B_2$, whereas the arrest line appears governed by its attractive part. The experimental findings are supported by numerical results of the non-equilibrium self-consistent generalized Langevin equation theory.

The term single file (SF) dynamics refers to the motion of an assembly of particles through a channel with cross-section comparable to the particles' diameter. Single file diffusion (SFD) is then the diffusion of a tagged particle in a \emph{single file}, i.e., under the condition that particle passing is not allowed. SFD accounts for a large variety of processes in nature, including diffusion of colloids in synthetic and natural-shaped channels, biological motors along molecular chains, electrons in proteins and liquid helium, ions through membrane, just to mention a few examples. Albeit introduced in '65, over the last decade the classical notion of SF dynamics has been generalized to account through a more realistic modeling of, among others, particles properties, file geometry, particle-particle and channel-particles interactions, thus paving the way to remarkable applications in, for example, the technology of bio-integrated nanodevices. We then provide a comprehensive review of the recent advances in the theory of SF dynamics and the ensuing experimental realisations.

The Ornstein-Zernike equation is solved for the hard-sphere and square-well fluids using a diverse selection of closure relations; the attraction range of the square-well is chosen to be $\lambda=1.5.$ In particular, for both fluids we mainly focus on the solution based on a three-parameter version of the Verlet closure relation [Mol. Phys. 42, 1291-1302 (1981)]. To find the free parameters of the latter, an unconstrained optimization problem is defined as a condition of thermodynamic consistency based on the compressibility and solved using Evolutionary Algorithms. For the hard-sphere fluid, the results show good agreement when compared with mean-field equations of state and accurate computer simulation results; at high densities, i.e., close to the freezing transition, expected (small) deviations are seen. In the case of the square-well fluid, a good agreement is observed at low and high densities when compared with event-driven molecular dynamics computer simulations. For intermediate densities, the explored closure relations vary in terms of accuracy. Our findings suggest that a modification of the optimization problem to include, for example, additional thermodynamic consistency criteria could improve the results for the type of fluids here explored., Comment: 12 pages, 6 figures

In colloidal systems, Brownian motion emerges from the massive separation of time and length scales associated to characteristic dynamics of the solute and solvent constituents. This separation of scales produces several temporal regimes in the colloidal dynamics when combined with the effects of the interaction between the particles, confinement conditions, and state variables, such as density and temperature. Some examples are the short- and long-time regimes in two- and three-dimensional open systems and the diffusive and sub-diffusive regimes observed in the single-file dynamics along a straight line. This work studies the way in which a confining geometry induces new time scales. We report on the dynamics of interacting colloidal particles moving along a circle by combining a heuristic theoretical analysis of the involved scales, Brownian Dynamics computer simulations, and video-microscopy experiments with paramagnetic colloids confined to lithographic circular channels subjected to an external magnetic field. The systems display four temporal regimes in this order: one-dimensional free diffusion, single-file sub-diffusion, free-cluster rotational diffusion, and the expected saturation due to the confinement. We also report analytical expressions for the mean-square angular displacement and crossover times obtained from scaling arguments, which accurately reproduce both experiments and simulations. Our generic approach can be used to predict the long-time dynamics of many other confined physical systems., Comment: 11 pages, 7 figures

We introduce a general physical formulation that allows one to obtain uniquely the effectiveinteractions by contracting the bare forces, even in highly concentrated systems. We tested it bystudying depletion forces in two-dimensional binary and ternary colloidal mixtures with a totalpacking fraction up to 70%. Our result opens up the possibility of finding an efficient route todetermine effective interactions at finite concentration and even at thermodynamic conditions nearto meta-stable or out of equilibrium states., Comment: 5 pages, 3 figures

Condensed Matter Physics (CMP) seeks to understand the microscopic interactions of matter at the quantum and atomistic levels, and describes how these interactions result in both mesoscopic and macroscopic properties. CMP overlaps with many other important branches of science, such as Chemistry, Materials Science, Statistical Physics, and High-Performance Computing. With the advancements in modern Machine Learning (ML) technology, a keen interest in applying these algorithms to further CMP research has created a compelling new area of research at the intersection of both fields. In this review, we aim to explore the main areas within CMP, which have successfully applied ML techniques to further research, such as the description and use of ML schemes for potential energy surfaces, the characterization of topological phases of matter in lattice systems, the prediction of phase transitions in off-lattice and atomistic simulations, the interpretation of ML theories with physics-inspired frameworks and the enhancement of simulation methods with ML algorithms. We also discuss in detail the main challenges and drawbacks of using ML methods on CMP problems, as well as some perspectives for future developments., Comment: 48 pages, 2 figures, 300 references. Review paper. Major Revision

We report the combined results of molecular dynamics simulations and theoretical calculations concerning various dynamical arrest transitions in a model system representing a dipolar fluid, namely, N (softcore) rigid spheres interacting through a truncated dipole-dipole potential. By exploring different regimes of concentration and temperature, we find three distinct scenarios for the slowing down of the dynamics of the translational and orientational degrees of freedom: At low ({$\eta$} = 0.2) and intermediate (${\eta}$ = 0.4) volume fractions, both dynamics are strongly coupled and become simultaneously arrested upon cooling. At high concentrations ({$\eta$} $\lt$ 0.6), the translational dynamics shows the features of an ordinary glass transition, either by compressing or cooling down the system, but with the orientations remaining ergodic, thus indicating the existence of partially arrested states. In this density regime, but at lower temperatures, the relaxation of the orientational dynamics also freezes. The physical scenario provided by the simulations is discussed and compared against results obtained with the self-consistent generalized Langevin equation theory, and both provide a consistent description of the dynamical arrest transitions in the system. Our results are summarized in an arrested states diagram which qualitatively organizes the simulation data and provides a generic picture of the glass transitions of a dipolar fluid.

The binary hard-sphere mixture is one of the simplest representations of a many-body system with competing time and length scales. This model is relevant to fundamentally understand both the structural and dynamical properties of materials, such as metallic melts, colloids, polymers and bio-based composites. It also allows us to study how different scales influence the physical behavior of a multicomponent glass-forming liquid; a question that still awaits a unified description. In this contribution, we report on distinct dynamical arrest transitions in highly asymmetric binary colloidal mixtures, namely, a single glass of big particles, in which the small species remains ergodic, and a double glass with the simultaneous arrest of both components. When the mixture approaches any glass transition, the relaxation of the collective dynamics of both species becomes coupled. In the single glass domain, spatial modulations occur due to the structure of the large spheres, a feature not observed in the two-glass domain. The relaxation of the \emph{self} dynamics of small and large particles, in contrast, become decoupled at the boundaries of both transitions; the large species always displays dynamical arrest, whereas the small ones appear arrested only in the double glass. Thus, in order to obtain a complete picture of the distinct glassy states, one needs to take into account the dynamics of both species.

A fundamental challenge of the theory of liquids is to understand the similarities and differences in the macroscopic dynamics of both colloidal and atomic liquids, which originate in the (Newtonian or Brownian) nature of the microscopic motion of their constituents. Starting from the recently-discovered long-time dynamic equivalence between a colloidal and an atomic liquid that share the same interparticle pair potential, in this work we develop a self-consistent generalized Langevin equation (SCGLE) theory for the dynamics of equilibrium multicomponent atomic liquids, applicable as an approximate but quantitative theory describing the long-time diffusive dynamical properties of simple equilibrium atomic liquids. When complemented with a Gaussian-like approximation, this theory is also able to provide a reasonable representation of the passage from ballistic to diffusive behavior. We illustrate the applicability of the resulting theory with three particular examples, namely, a monodisperse and a polydisperse monocomponent hard-sphere liquid, and a highly size-asymmetric binary hard-sphere mixture. To assess the quantitative accuracy of our results, we perform event-driven molecular dynamics simulations, which corroborate the general features of the theoretical predictions., Comment: 11 pages, 12 Figures

We report on the short-time dynamics in colloidal mixtures made up of monomers and dimers highly confined between two glass-plates. At low concentrations, the experimental measurements of colloidal motion agree well with the solution of the Navier-Stokes equation at low Reynolds numbers, which takes into account the increase of the drag force on each particle due to wall-particle hydrodynamic forces. We find that the ratio of the short-time diffusion coefficients of the monomer and that of the center of mass of the dimer remains independent of both the total packing fraction and the dimer molar fraction up to concentrations near to the crystallization transition. The same physical scenario is observed for the ratio between the parallel and perpendicular components of the short-time diffusion coefficients of the dimer. This dynamical behavior is corroborated by means of Molecular Dynamics computer simulations that explicitly include the particle-particle hydrodynamic forces induced by the solvent. Thus, our results point out toward that the effects of the particle-particle hydrodynamic interactions on the diffusion coefficients are identical and, thus, factorable in both species.

The so-called extended law of corresponding states, as proposed by Noro and Frenkel [J. Chem. Phys. 113, 2941 (2000)], involves a mapping of the phase behaviors of systems with short-range attractive interactions. While it has already extensively been applied to various model potentials, here we test its applicability to protein solutions with their complex interactions. We successfully map their experimentally determined metastable gas--liquid binodals, as available in the literature, to the binodals of short-range square-well fluids, as determined by previous as well as new Monte Carlo simulations. This is achieved by representing the binodals as a function of the temperature scaled with the critical temperature (or as a function of the reduced second virial coefficient) and the concentration scaled by the cube of an effective particle diameter, where the scalings take into account the attractive and repulsive contributions to the interaction potential, respectively. The scaled binodals of the protein solutions coincide with simulation data of the adhesive hard-sphere fluid. Furthermore, once the repulsive contributions are taken into account by the effective particle diameter, the temperature dependence of the reduced second virial coefficients follows a master curve that corresponds to a linear temperature dependence of the depth of the square-well potential. We moreover demonstrate that, based on this approach and cloud-point measurements only, second virial coefficients can be estimated, which we show to agree with values determined by light scattering or by DLVO-based calculations.

One major goal in condensed matter physics is identifying the physical mechanisms that lead to arrested states of matter, especially gels and glasses. The complex nature and microscopic details of each particular system are relevant. However, from both scientific and technological viewpoints, a general, consistent and unified definition is of paramount importance. Through Monte Carlo computer simulations of states identified in experiments, we demonstrate that adhesive hard-sphere dispersions are the result of rigidity percolation with average number of bonds, $$, equals to 2.4. This corresponds to an established mechanism leading to phase transitions in network-forming materials. Our findings connect the concept of critical gel formation in colloidal suspensions with short-range attractive interactions to the universal concept of rigidity percolation. Furthermore, the bond, angular and local distributions along the gelation line are explicitly studied in order to determine the topology of the structure of the critical gel state., Comment: 5 pages, 4 figures

Brownian motion of free particles on curved surfaces is studied by means of the Langevin equation written in Riemann normal coordinates. In the diffusive regime we find the same physical behavior as the one described by the diffusion equation on curved manifolds [J. Stat. Mech. (2010) P08006]. Therefore, we use the latter in order to analytically investigate the whole diffusive dynamics in compact geometries, namely, the circle and the sphere. Our findings are corroborated by means of Brownian dynamics computer simulations based on a heuristic adaptation of the Ermak-McCammon algorithm to the Langevin equation along the curves, as well as on the standard algorithm, but for particles subjected to an external harmonic potential, deep and narrow, that possesses a "Mexican hat" shape, whose minima define the desired surface. The short-time diffusive dynamics is found to occur on the tangential plane. Besides, at long times and compact geometries, the mean-square displacement moves towards a saturation value given only by the geometrical properties of the surface., Comment: 16 pages, 4 figures

We determine the structure of charge-stabilized colloidal suspensions at low ionic strength over an extended range of particle volume fractions using a combination of light and small angle neutron scattering experiments. The variation of the structure factor with concentration is analyzed within a one-component model of a colloidal suspension. We show that the observed structural behavior corresponds to a non-monotonic density dependence of the colloid effective charge and the mean interparticle interaction energy. Our findings are corroborated by similar observations from primitive model computer simulations of salt-free colloidal suspensions., Comment: Revised version, accepted to Phys. Rev. Lett

We study macroion correlation effects on the thermodynamics of highly charged colloidal suspensions using a mean-field theory and primitive model computer simulations. We suggest a simple way to include the macroion correlations into the mean-field theory as an extension of the renormalized jellium model of Trizac and Levin [Phys. Rev. E {\bf 69}, 031403 (2004)]. The effective screening parameters extracted from our mean-field approach are then used in a one-component model with macroions interacting via Yukawa-like potential to predict macroion distributions. We find that inclusion of macroion correlations leads to a weaker screening and hence smaller effective macroion charge and lower osmotic pressure of the colloidal dispersion as compared to other mean-field models. This result is supported by a comparison to primitive model simulations and experiments for charged macroions in the low-salt regime, where the macroion correlations are expected to be significant.