Nonergodicity parameters of confined hard-sphere glasses

Abstract

Within a recently developed mode-coupling theory for fluids confined to a slit we elaborate numerical results for the long-time limits of suitably generalized intermediate scattering functions. The theory requires as input the density profile perpendicular to the plates, which we obtain from density functional theory within the fundamental-measure framework, as well as symmetry-adapted static structure factors, which can be calculated relying on the inhomogeneous Percus-Yevick closure. Our calculations for the nonergodicity parameters for both the collective as well as for the self motion are in qualitative agreement with our extensive event-driven molecular dynamics simulations for the intermediate scattering functions for slightly polydisperse hard-sphere systems at high packing fraction. We show that the variation of the nonergodicity parameters as a function of the wavenumber correlates with the in-plane static structure factors, while subtle effects become apparent in the structure factors and relaxation times of higher mode indices. A criterion to predict the multiple reentrant from the variation of the in-plane static structure is presented.

Confinement-induced demixing and crystallization

“…Furthermore, there is a pronounced nonmonotonic dependence of the free energy on the wall separation H. In Refs. [4,6], a similar nonmonotonic behavior in the structure factor was explained with commensurate and incommensurate packings. Commensurate packing describes the favorable packing of spheres in k layers for wall separations H/σ ≈ k, k ∈ N, whereas incommensurate packing relates to wall separations close to half-integer values.…”

“…However, the onset of ordering can already be seen in standard EDMD simulations of hard spheres in confinement (see the long-wavelength peak in the structure factor for H = 2.30σ shown in Ref. [4]).…”

“…II A. Without the use of this algorithm, nucleation would be too slow to observe crystallization within a reasonable computing time [4,6]. However, the onset of ordering can already be seen in standard EDMD simulations of hard spheres in confinement (see the long-wavelength peak in the structure factor for H = 2.30σ shown in Ref.…”

“…Confinement occurs naturally in many physical, chemical, and biological systems, such as nanotubes, porous rocks, or crowded living cells. Even for the simplest case of monodisperse hard spheres confined between parallel hard walls one observes spatially inhomogeneous density profiles and diffusivities [1,2], anisotropic structure factors [3,4], multiplereentrant glass transitions [5,6] and solid-to-solid transitions between different crystalline phases [7][8][9][10]. Confinement has also been reported to have a strong impact on the structural relaxation of supercooled liquids [6,11,12] since it restricts the range of accessible length scales, which becomes increasingly important as the glass transition is approached [11].…”

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

“…The nonequilibrium state diagram within MCT has been obtained [44,115] by scanning the parameter space (ϕ, H = L + σ) taking the structural input obtained from the inhomogeneous Percus-Yevick closure [67,[127][128][129], see Figure 11. The result demonstrates a striking multiple reentrant behavior.…”