Brownian motion of a nano-colloidal particle: the role of the solvent

Machine Learning Memory Kernels as Closure for Non-Markovian Stochastic Processes

Finding the dynamical law of observable quantities lies at the core of physics. Within the particular field of statistical mechanics, the generalized Langevin equation (GLE) comprises a general model for the evolution of observables covering a great deal of physical systems with many degrees of freedom and an inherently stochastic nature. Although formally exact, GLE brings its own great challenges. It depends on the complete history of the observables under scrutiny, as well as the microscopic degrees of freedom, all of which are often inaccessible. We show that these drawbacks can be overcome by adopting elements of machine learning from empirical data, in particular coupling a multilayer perceptron (MLP) with the formal structure of GLE and calibrating the MLP with the data. This yields a powerful computational tool capable of describing noisy complex systems beyond the realms of statistical mechanics. It is exemplified with a number of representative examples from different fields: from a single colloidal particle and particle chains in a thermal bath to climatology and finance, showing in all cases excellent agreement with the actual observable dynamics. The new framework offers an alternative perspective for the study of nonequilibrium processes opening also a new route for stochastic modeling.

Single entity collision for inorganic water pollutants measurements: Insights and prospects

In the context of aquatic environmental issues, dynamic analysis of nano-sized inorganic water pollutants has been one of the key topics concerning their seriously amplified threat to natural ecosystems and life health. Its ultimate challenge is to reach a single-entity level of identification especially towards substantial amount of inorganic pollutants formed as natural or manufactured nanoparticles (NPs), which enter the water environments along with the potential release of constituents or other contaminating species that may have coprecipitated or adsorbed on the particles' surface. Here, we introduced a 'nano-impacts' approach-single entity collision electrochemistry (SECE) promising for in-situ characterization and quantification of nano-sized inorganic pollutants at single-entity level based on confinement-controlled electrochemistry. In comparison with ensemble analytical tools, advantages and features of SECE point at understanding 'individual' specific fate and effect under its free-motion condition, contributing to obtain more precise information for 'ensemble' nano-sized pollutants on assessing their mixture exposure and toxicity in the environment. This review gives a unique insight about the single-entity collision measurements of various inorganic water pollutants based on recent trends and directions of state-of-the-art single entity electrochemistry, the prospects for exploring nano-impacts in the field of inorganic water pollutants measurements were also put forward.

Conditions for the propulsion of a colloid surrounded by a mesoscale phase separation

We study a two-dimensional model of an active isotropic colloid whose propulsion is linked to the interactions between solute particles of the bath. The colloid catalyzes a chemical reaction in its vicinity, that yields a local phase separation of solute particles. The density fluctuations of solute particles result in the enhanced diffusion of the colloid. Using numerical simulations, we thoroughly investigate the conditions under which activity occurs, and we establish a state diagram for the activity of the colloid as a function of the parameters of the model. We use the generated data to unravel a key observable that controls the existence and the intensity of activity: The filling fraction of the reaction area. Remarkably, we finally show that propulsion also occurs in three-dimensional geometries, which confirms the interest of this mechanism for experimental applications.

The Photocatalytic Degradation of Vehicle Exhausts by an Fe/N/Co-TiO2 Waterborne Coating under Visible Light

Based on the three-dimensional network structure of a polymer and the principle of photocatalysts, a visible-light-responsive and durable photocatalytic coating for the degradation of vehicle exhaust (VE) has been constructed using a waterborne acrylic acid emulsion as the coating substrate; Fe/N/Co-TiO2 nanoparticles (NPs) as photocatalytic components; and water, pigments, and fillers as additives. The visible-light-responsive Fe/N/Co-TiO2 NPs with an average size of 100 nm were prepared by sol-gel method firstly. The co-doping of three elements extended the absorption range of the modified TiO2 nanoparticles to the visible light region, and showed the highest light absorption intensity, which was confirmed by the ultraviolet-visible absorption spectra (UV-Vis). X-ray diffraction (XRD) measurements showed that element doping prevents the transition from anatase to rutile and increases the transition temperature. TiO2 was successfully doped due to the reduction of the chemical binding energy of Ti, as revealed by X-ray photoelectron spectroscopy (XPS). The degradation rates of NOX, CO, and CO2 in VE by Fe/N/Co-TiO2 NPs under visible light were 71.43%, 23.79%, and 21.09%, respectively. In contrast, under the same conditions, the degradation efficiencies of coating for VE decreased slightly. Moreover, the elementary properties of the coating, including pencil hardness, adhesive strength, water resistance, salt, and alkali resistance met the code requirement. The photocatalytic coating exhibited favorable reusability and durability, as shown by the reusability and exposure test.

Interfacially driven transport theory: a way to unify Marangoni and osmotic flows

We show that the solvent behaviour in both diffusio-osmosis and Marangoni flow can be derived from a simple model of colloid-interface interactions. We demonstrate that the direction of the flow is regulated by a single value of the attractive parameter covering the purely repulsive and attractive-repulsive interaction cases. The proposed universality between diffusio-osmosis and Marangoni flow is extended further to include diffusio-phoresis. In particular, an object immersed to a colloidal solution moves towards the low concentration of the colloidal particles in the case of colloid-interface repulsion and towards the high concentration of the colloidal particles in the case of colloid-interface attraction. The approach combines the methods of fluid dynamics, molecular physics and transport phenomena and provides a tractable explanation of how the colloid-interface interactions affect the momentum balance and the transport phenomena (interfacially driven transport).

Friction and diffusion of a nano-colloidal disk in a two-dimensional solvent with a liquid-liquid transition

We report on the friction and diffusion of a single mobile nano-colloidal disk, whose size and mass are one and two orders of magnitude, respectively, greater than the molecules of the host solvent; all particles are restricted to move in a two-dimensional space. Using molecular dynamics simulations, the variation of the transport coefficients as a function of the thermodynamic state of the supporting fluid, in particular, around those states in the neighbourhood of the liquid-liquid phase coexistence, is investigated. The diffusion coefficient is determined through the fit of the mean-square displacement at long times and with the Green-Kubo relationship for the velocity autocorrelation function, whereas the friction coefficient is computed from the correlation of the fluctuating force. From the determination of the transport properties, the applicability of the Stokes-Einstein relation in two dimensions around the second critical point is discussed.

Brownian diffusion of a particle at an air/liquid interface: the elastic (not viscous) response of the surface

Here, the effect of the elastic response of the surface on the translational diffusion coefficient of a partly submerged-in-water spherical Brownian particle is considered.

Short-time dynamics of monomers and dimers in quasi-two-dimensional colloidal mixtures

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; the latter takes into account the increase in the drag force on a colloidal particle due to wall-particle hydrodynamic forces. More importantly, we find that the ratio of the short-time diffusion coefficient of the monomer and that of the center of mass of the dimmer is almost independent of both the dimer molar fraction, x_{d}, and the total packing fraction, ϕ, up to ϕ≈0.5. At higher concentrations, this ratio displays a small but systematic increase. A similar physical scenario is observed for the ratio between the parallel and the perpendicular components of the short-time diffusion coefficients of the dimer. This dynamical behavior is corroborated by means of molecular dynamics computer simulations that include explicitly the particle-particle hydrodynamic forces induced by the solvent. Our results suggest that the effects of colloid-colloid hydrodynamic interactions on the short-time diffusion coefficients are almost identical and factorable in both species.

Characterisation of the thermodynamics, structure and dynamics of a water-like model in 2- and 3-dimensions

The physical properties of colloidal particles suspended in an aqueous environment are well-understood when the latter is considered to be a continuum and a structureless medium. However, this approach fails to explain complex phenomena, for example, the critical Casimir forces among colloids and the colloidal self-assembly near critical solvents, and the inertial contribution of the solvent molecules on the diffusion of non-spherical Brownian particles. Therefore, the role played by the solvent on the physical properties of colloidal dispersions is of paramount relevance. Recently, there has been an interest in the (non-trivial) diffusion mechanisms of a nano-colloidal particle in a solvent that undergoes a vapour-liquid transition. Nonetheless, the models typically used to incorporate the solvent details do not capture quantitatively the thermodynamic properties of real substances. It is then important to study the Brownian motion of colloids in more realistic models. To reach such goal, one first has to characterise the thermodynamic states and the microscopic features of the solvent. Hence, in this contribution, we have investigated the coexistence densities of a core-softened potential in two- and three-dimensions, whose potential parameters are able to capture some anomalies of water. We show that in the two-dimensional case, the potential model exhibits, besides the normal vapour-liquid coexistence region, additional liquid-liquid coexistence densities. We particularly focus our attention to the structural properties and the dynamical behaviour of the solvent around the liquid-liquid critical point and assess the differences with the three-dimensional case.