Strongly confined fluids: Diverging time scales and slowing down of equilibration

Abstract

The Newtonian dynamics of strongly confined fluids exhibits a rich behavior. Its confined and unconfined degrees of freedom decouple for confinement length L→0. In that case and for a slit geometry the intermediate scattering functions S_{μν}(q,t) simplify, resulting for (μ,ν)≠(0,0) in a Knudsen-gas-like behavior of the confined degrees of freedom, and otherwise in S_{∥}(q,t), describing the structural relaxation of the unconfined ones. Taking the coupling into account we prove that the energy fluctuations relax exponentially. For smooth potentials the relaxation times diverge as L^{-3} and L^{-4}, respectively, for the confined and unconfined degrees of freedom. The strength of the L^{-3} divergence can be calculated analytically. It depends on the pair potential and the two-dimensional pair distribution function. Experimental setups are suggested to test these predictions.

Structural properties of liquids in extreme confinement

“…This result is also particularly important with respect to the understanding of dynamical properties in this regime since we know that the impact of confinement on diffusion and glass-transition is strongly connected to the structural quantities [4,12,[54][55][56]. In future work it would therefore be interesting to extend the present analysis to dynamical properties such as diffusion coefficients and decorrelation time scales [4,27,34,57], the critical packing fraction for the glass transition [12] or the nonergodicity parameters [7] and investigate whether they similarly smoothly approach the properties of their twodimensional counterparts.…”

“…Observing these phenomena in strong confinement immediately suggests the question how the structure of a three-dimensional liquid behaves upon even more extreme confinement and how it finally converges towards the structure of its 2D counterpart. Such questions are particularly interesting to understand the dimensional crossover behavior, for example for the emergence of the hexatic phase [25,26], or the decoupling of lateral and transverse currents [27,34]. Important results have already been obtained from theory and simulations for the inhomogeneous density profiles of hard-sphere liquids, highlighting the emergence of parabolic profiles in the regime of extreme confinement, which become increasingly flat and finally converge towards the area density of the hard-disk fluid [15,19].…”

Complex dynamics induced by strong confinement – From tracer diffusion in strongly heterogeneous media to glassy relaxation of dense fluids in narrow slits

“…Then the use of a collision operator is inappropriate, however the collision events can be averaged over the fast transverse oscillations. Analytic progress in this direction has been achieved [135] and it turns out that the predicted relaxation time diverges as ∼ L −3 . Here we test this prediction by tuning the softness of the interaction potential.…”

Mode-coupling theory of the glass transition for colloidal liquids in slit geometry

“…The confinement, in the simplest case a slit geometry of two parallel smooth walls, introduces a new control parameter into the problem giving rise to plethora of new structural and dynamic phenomena [1][2][3], including the layering of the average density [4], complex intermediate phases due to stacking [5,6], and a shift in the glass transition [4,[7][8][9]. The slit geometry then permits to study the dimensional crossover as the plate separation becomes small and only recently the decoupling of the in-plane degrees of freedom from the transverse ones has been unravelled to make systematic expansion for the structural properties [10,11] as well as for the dynamics [12][13][14].…”