The Stokes−Einstein Relationship and the Levitation Effect: Size-Dependent Diffusion Maximum in Dense Fluids and Close-Packed Disordered Solids

Abstract

We report a molecular dynamics study of a binary mixture consisting of a large (host) particle and a smaller (guest) particle whose radius is varied over a range. These simulations investigate the possible existence of a diffusion anomaly or levitation effect in dense fluids, previously seen for guest molecules diffusing within porous solids. The voids in the larger component have been characterized in terms of void and neck distributions by means of Voronoi polyhedral analysis. Four different mixtures with differing ratios of guest to host diffusivities (D) have been studied. The results suggest that the diffusion anomaly is seen in both close-packed solids with disorder and dense fluids. In the latter, the void network is constantly and dynamically changing and possesses a considerable degree of disorder. The two regimes, viz., the linear regime (LR) and the anomalous regime (AR), found for porous solids are shown to exist for a dense medium as well. The linear regime is characterized by D(g) proportional to 1/sigma(gg)(2), where sigma(gg) is the diameter of the guest. The anomalous regime exhibits a maximum in D up to rather high temperatures (T = 1.663), even though in porous solids the maximum disappears at higher temperatures. In agreement with previous studies on porous solids, a particle in the AR is associated with lower activation energy, lower friction, and less backscattering in the velocity autocorrelation function when compared to a particle in the LR. Wavevector dependent self-diffusivity, Delta, and decay of the intermediate scattering function, F(s)(k, t), exhibit contrasting behaviors for the LR and AR. For LR, Delta exhibits a minimum at values of k at which there are spatial correlations in S(k) while a smooth decrease with k is seen for AR. For LR, F(s)(k, t) shows a biexponential decay corresponding to two different time scales of motion. Probably, the fast decay is associated with motion within the first shell of solvent neighbors and the slow decay with motion past these shells. For AR, a single-exponential decay is seen. The results indicate a breakdown of the Stokes-Einstein (SE) relationship. The relevant quantity that determines the validity of the SE relationship is the levitation parameter which is indirectly related to the solute/solvent radius ratio and not either the size of the solute or the solvent alone.

Non-monotonic size dependence of diffusion and levitation effect: A mode-coupling theory analysis

“…The theory and simulation studies both predict that as the solute size is decreased the diffusion value first increases and then decreases. This diffusivity maximum as discussed earlier has been attributed to levitation effect [9]. Thus it is found that MCT can predict levitation effect and diffusivity maximum as found in simulations [9] and experimental [17] studies.…”

“…As mentioned in the Introduction, this anomalous size dependence of diffusion has been attributed to levitation effect [9] where the solute particles with intermediate sizes are expected to levitate through the neck of the solvent cage whereas the smaller particles are expected to be strongly attracted to one solvent particle. Fig.1.…”

“…Note that for system 1, 2 and 3, the interaction between the solute and the solvent has a soft core which allows inter-penetration between solute solvent pair. However in system 4 the solute-solvent diameter is given by Lorentz-Berthelot (LB) rule [21] [9].…”

“…The motion of tagged particles in various mediums have been extensively studied using, microscopic theories, simulations and experiments [1][2][3][4][5][6][7][8][9][10][11][12]. These studies have predicted many interesting results.…”

“…In general they noticed that in zeolites when the solute size is about 80% of the size of the neck of the zeolite the diffusion is maximum. In their study of solute diffusion in LJ solvent they found that when the solute size is about 0.24 times that of the solvent the diffusion shows a maximum [9]. From Voronoi Polyhedra analysis they have obtained a void and neck size distribution of the solvent transient cages and have shown that, when the solute-solvent diameter is smaller but similar to the size of the neck, the solute can diffuse faster.…”