percolation (rus. перколяция otherwise протекание) — In materials science, an abrupt emergence of new properties in a material (electric conductivity in an insulating material, gas permeability in gas barrier materials, etc.) filled with a "filler" that has such properties. In some cases, the filler may be represented by pores and voids.


Examples of percolation processes include the penetration of liquids through a stationary porous phase, infiltration of the liquid phase along the grain boundaries of a polycrystal, the formation of polymer gels, as well as ferromagnetism and electric conductivity of impurity semiconductors.

Percolation occurs when the concentration of a filler or pores reaches a certain critical level (percolation threshold) following the build-up of a continuous network (connections) of filler particles (clusters) from one side of a material specimen to another.

Percolation is easy to demonstrate on the example of electric current passing through a two-dimensional square lattice consisting of conducting and non-conducting elements. Two opposite sides of the lattice have metal terminals soldered to them that are connected to a power source. At a certain critical concentration of conducting elements arranged randomly the circuit closes (see fig.).

Stanislav Smirnov from St. Petersburg was awarded the Fields Medal (a mathematics equivalent of the Nobel Prize) in 2010 “for the proof of conformal invariance of percolation and the planar Ising model in statistical physics”.


Percolation model image.
Percolation model image.


  • Streletskiy Alexey V.


  1. Efros A. L. Physics and Geometry of Disorder: Percolation Theory. — Imported Pubn, 1987. — 135 pp.

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