Shape-controlled percolation transition in 2D random packing of asymmetric dimers

Abstract

In this paper, we report on an experimental investigation of a shape-controlled percolation transition in two-dimensional (2D) amorphous packing of dimers without long-range order. In the maximally random jammed (MRJ) packing of asymmetric dimers consisting of head and body, a dramatic increase in the connectivity of heads upon increasing the head-to-body size ratio γ leads to a percolation transition of the heads at the well-defined percolation threshold. In comparison with binary disks, the existence of a bond in dimers causes the heads to be homogeneously distributed over a system by inhibiting the local segregation. Interestingly, we found, however, that the cluster structure at the percolation threshold is insensitive to the bond, even though the existence of the bonds affects the percolation threshold as well as the head distribution. The fractal dimensions at the percolation threshold obey the universal law of the 2D percolation theory independently of the existence of bonds. Our finding can provide us with a new perspective of interesting applications of randomly assembled binary composites by using the homogeneous particle distribution and the sensitively tunable connectivity under particle shape control.

Elongation and percolation of defect motifs in anisotropic packing problems

“…3. The fraction becomes nonzero at around p c = 0.5 on flat surface and p c = 0.55 on spherical or toroidal surface, which is in good agreement with previous literature [24,44,45]. We also compute the fraction of sites in the largest connected component, displayed as gray lines in the middle column of Fig.…”

“…where d ij is the distance between pairs of sites (i, j) and n is the number of sites, scales with the number of sites like n ∝ R D where D is the fractal dimension. In two dimensions this has a value at p c of 91/48 = 1.896 independent of the structure of the system [26,[43][44][45][46][47]. Many disordered systems, both discrete [44,45,48] and continuous [43,[49][50][51][52][53] lie in this class, including forest fires, distribution of oil inside porous rock, the diffusion of atoms and conductivity of electrical networks [25,26].…”

“…In two dimensions this has a value at p c of 91/48 = 1.896 independent of the structure of the system [26,[43][44][45][46][47]. Many disordered systems, both discrete [44,45,48] and continuous [43,[49][50][51][52][53] lie in this class, including forest fires, distribution of oil inside porous rock, the diffusion of atoms and conductivity of electrical networks [25,26]. An important feature of the packing problems considered is that they involve a finite number of particles, either for reasons of tractability or because they occur in compact geometries.…”

“…At finite N , u(p) become sigmoidal in shape and converges toward θ(p − p c ) as the number of particles is increased. The value of p c may therefore be extrapolated from a sequence of simulations of different size [44,45,52,54]. An alternative approach is to study the cluster size R as a function of p, which saturates at p R (N ) as R approaches the system size [24].…”

Vibrational properties of two-dimensional dimer packings near the jamming transition

“…Namely, the dimer particles possess asphericity, but they are not hypostatic in the jammed phase. In recent experimental and numerical works [33][34][35], structures of two-dimensional asymmetric dimer packings were studied. For vibrational properties, it has been reported that the dimer particles exhibit rotational vibrations in the low-frequency region below the translational band [14].…”