Diverging Time Scale in the Dimensional Crossover for Liquids in Strong Confinement

Abstract

We study a strongly interacting dense hard-sphere system confined between two parallel plates by event-driven molecular dynamics simulations to address the fundamental question of the nature of the 3D to 2D crossover. As the fluid becomes more and more confined the dynamics of the transverse and lateral degrees of freedom decouple, which is accompanied by a diverging time scale separating 2D from 3D behavior. Relying on the time-correlation function of the transversal kinetic energy the scaling behavior and its density-dependence is explored. Surprisingly, our simulations reveal that its time-dependence becomes purely exponential such that memory effects can be ignored. We rationalize our findings quantitatively in terms of an analytic theory which becomes exact in the limit of strong confinement.Introduction.-Transport of particles in nanoconfinement is of great scientific and industrial importance with applications in heterogeneous catalysis [1], oil recovery [2], or lubrication [3][4][5][6]. In recent years artificial nanoporous materials such as metal organic frameworks [7,8], zeolites [9,10], and biocompatible scaffolds [11] have also triggered many novel applications, including gas storage [12], repairing or regenerating tissues [11], size-selective molecular sieving [13], lab-on-a chip technology and nanofluidics [14,15]. The efficiency of such nanodevices often crucially depends on higher surface to volume ratio, such that the distance between the confining walls may even reach atomic scale [16], or the system effectively becomes quasi-2D. Nevertheless, despite its long history, a deep understanding of the transport mechanisms in nanoconfinement and how the dimensional crossover occurs dynamically is still far from satisfactory.Early theoretical studies on transport in nanoconfinement starting from Knudsen and Smoluchowski [17,18] focused on dilute hard-sphere gases where exact results could be obtained analytically in the low-density limit [17][18][19][20][21][22] by assuming particle-wall collisions as diffusive. In contrast, confinement effects on dense strongly interacting systems have only recently come into focus [23]. There, the simplest geometry to investigate the effects of strong confinement is a slit where fluid particles are restricted to a narrow space between two smooth parallel plates, but also tubes or spherical confinements have been realized experimentally [24][25][26]. Computer simulations and experiments for the planar confinement have revealed an exotic equilibrium phase behavior due to commensurable stacking [27][28][29][30][31][32][33][34] as well as the hexatic phases in the limit of quasi-2D confinement [35,36]. Confinement induced order-disorder phase transitions for certain nonpolar liquids have also been reported in several experiments [37], but the interpretation has been challenged in favor of a glass transition [38][39][40]. The structural properties of strongly confined liquids have been measured directly only recently by x-ray scattering [41,42].The structural changes by ...

Nonergodicity parameters of confined hard-sphere glasses

“…The theory displays unique solutions which reflect all properties of correlation functions [70] and reproduces the limits of a bulk system as well as of a two-dimensional liquid as the wall separations becomes large or small [71]. Surprisingly, for small wall separation the lateral and transverse degrees of freedom decouple [72,73] and a slow divergent time scale emerges controlling the crossover from 2D to 3D systems [74]. The tagged-particle dynamics for slit geometry has also been elaborated within MCT [75].…”

Dense gas flow simulations in ultra-tight confinement

“…These techniques model the Newtonian dynamics of individual atoms and their collisions through potential energy functions, such as Lennard Jones for smooth interactions 33,34 or hardsphere interactions for EDMD 35 . These particle-based approaches have been the dominant modelling route of high-confined fluids [36][37][38][39][40][41][42] , although have mainly focussed on equilibrium properties and flow profiles of the tight confinement, rather than on the overall gasflow response, which we cover in this paper.…”

Long-wavelength fluctuations and dimensionality crossover in confined liquids

“…Indeed the hexatic phase, which is a phase with short-ranged translational order and longranged bond-orientational order only occurring in twodimensional systems, has been only reported for H ≃ a 0 in Lennard-Jones systems [15]. In this extremely confined limit, the occurrence of a two-dimensional behaviour is in line with the observed decoupling of the lateral and transverse degrees of freedom [16,17].…”