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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. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

Brownian motion is a feature of colloidal particles immersed in a liquid-like environment. Usually, it can be described by means of the generalised Langevin equation (GLE) within the framework of the Mori theory. In principle, all quantities that appear in the GLE can be calculated from the molecular information of the whole system, i.e., colloids and solvent molecules. In this work, by means of extensive Molecular Dynamics simulations, we study the effects of the microscopic details and the thermodynamic state of the solvent on the movement of a single nano-colloid. In particular, we consider a two-dimensional model system in which the mass and size of the colloid are two and one orders of magnitude, respectively, larger than the ones associated with the solvent molecules. The latter ones interact via a Lennard-Jones-type potential to tune the nature of the solvent, i.e., it can be either repulsive or attractive. We choose the linear momentum of the Brownian particle as the observable of interest in order to fully describe the Brownian motion within the Mori framework. We particularly focus on the colloid diffusion at different solvent densities and two temperature regimes: high and low (near the critical point) temperatures. To reach our goal, we have rewritten the GLE as a second kind Volterra integral in order to compute the memory kernel in real space. With this kernel, we evaluate the momentum-fluctuating force correlation function, which is of particular relevance since it allows us to establish when the stationarity condition has been reached. Our findings show that even at high temperatures, the details of the attractive interaction potential among solvent molecules induce important changes in the colloid dynamics. Additionally, near the critical point, the dynamical scenario becomes more complex; all the correlation functions decay slowly in an extended time window, however, the memory kernel seems to be only a function of the solvent density. Thus, the explicit inclusion of the solvent in the description of Brownian motion allows us to better understand the behaviour of the memory kernel at those thermodynamic states near the critical region without any further approximation. This information is useful to elaborate more realistic descriptions of Brownian motion that take into account the particular details of the host medium. [ABSTRACT FROM AUTHOR]