Definition
Random close pack (often referred to as random close packing, RCP) is a disordered arrangement of equal-sized particles—typically spheres—such that the packing density is maximized without introducing long‑range crystalline order. It represents an empirically observed limit to how densely particles can be packed in a random configuration.
Overview
In three dimensions, random close packing of ideal spheres yields a volume fraction of approximately 0.64 (or 64 % of the space occupied by the spheres). This value is distinct from the densest possible ordered arrangement, the face‑centered cubic (FCC) or hexagonal close‑packed (HCP) lattices, which achieve a volume fraction of about 0.74. Random close packings are generated experimentally by pouring or shaking granular materials, or computationally using algorithms that simulate compression, sedimentation, or energy minimization while suppressing crystallization. The concept is central to the study of granular matter, colloidal suspensions, amorphous solids, and the statistical mechanics of jammed systems.
Etymology/Origin
The phrase combines “random,” indicating the absence of long‑range order, with “close pack,” denoting a configuration that approaches the maximal possible density for a disordered state. The term emerged in the mid‑20th century within the context of granular physics and the study of dense suspensions. Early quantitative measurements were reported by G. D. Scott and D. M. Kilgour (1969) and later refined by J. D. Bernal (1960s) in the analysis of random packings of spheres.
Characteristics
| Property | Description |
|---|---|
| Packing fraction | Approximately 0.64 ± 0.01 for monodisperse spheres in three dimensions; varies with particle size distribution, friction, and preparation protocol. |
| Structure | No translational or rotational symmetry; local order limited to short‑range correlations (e.g., first‑neighbor coordination number ≈ 6). |
| Isostaticity | Near the jamming transition, the average number of contacts per particle approaches the isostatic value (2 d, where d = 3 for spheres). |
| Mechanical stability | The packing is mechanically stable (jammed) under small perturbations; stress transmission occurs through force chains. |
| Generation methods | Physical shaking, tapping, vibration, compression under gravity, Monte‑Carlo or molecular dynamics simulations with “soft” overlap potentials, Lubachevsky–Stillinger algorithm, collective rearrangement protocols. |
| Dependence on friction | Higher inter‑particle friction generally reduces the achievable random close packing density, leading to values as low as ~0.55. |
| Dimensionality | In two dimensions, the analogous random close packing of disks yields a packing fraction near 0.82; in higher dimensions the fraction decreases further. |
Related Topics
- Random loose pack – the lowest mechanically stable packing density for a given particle system, typically around 0.55 for frictional spheres.
- Jamming transition – the point at which a disordered particle assembly becomes mechanically rigid.
- Granular matter – collections of macroscopic particles where random close packing provides a baseline for bulk behavior.
- Amorphous solids – non‑crystalline solids whose atomic or molecular arrangements often resemble random close packings.
- Lubachevsky–Stillinger algorithm – a computational method for generating dense random packings by expanding particle radii during molecular dynamics.
- Kissing number problem – the maximum number of non‑overlapping equal spheres that can simultaneously touch a central sphere; related to local coordination in packings.
Random close pack remains a fundamental reference state for theoretical and experimental investigations of disordered dense assemblies across physics, materials science, and engineering.