TY - JOUR
T1 - Tunnelling and percolation in lattices and the continuum
AU - Balberg, I.
PY - 2009
Y1 - 2009
N2 - In a system of conducting particles embedded in a continuous insulating matrix each particle is electrically connected to all others by tunnelling. This scenario is not compatible with percolation connectivity where two particles are either locally connected or disconnected and the global connectivity can be made only via a tortuous path through other particles that are locally connected along this path. It is therefore quite a surprise that a well-defined critical percolation behaviour is observed experimentally in composites where the above scenario prevails. In this paper we explain this paradox by considering the exponential decay of the tunnelling probability, on the one hand, and the very special features of the corresponding distribution function of the interparticle separations, on the other hand. It is concluded that the experimentally observed behaviour is associated with the network of particles that have neighbours within a separation of the order of the tunnelling decay constant. The percolation threshold is determined then by the particle concentration necessary for that network to form while the percolation non-universal critical exponent of the conductivity is associated with the resistor value distribution in that particular network.
AB - In a system of conducting particles embedded in a continuous insulating matrix each particle is electrically connected to all others by tunnelling. This scenario is not compatible with percolation connectivity where two particles are either locally connected or disconnected and the global connectivity can be made only via a tortuous path through other particles that are locally connected along this path. It is therefore quite a surprise that a well-defined critical percolation behaviour is observed experimentally in composites where the above scenario prevails. In this paper we explain this paradox by considering the exponential decay of the tunnelling probability, on the one hand, and the very special features of the corresponding distribution function of the interparticle separations, on the other hand. It is concluded that the experimentally observed behaviour is associated with the network of particles that have neighbours within a separation of the order of the tunnelling decay constant. The percolation threshold is determined then by the particle concentration necessary for that network to form while the percolation non-universal critical exponent of the conductivity is associated with the resistor value distribution in that particular network.
UR - http://www.scopus.com/inward/record.url?scp=63649122261&partnerID=8YFLogxK
U2 - 10.1088/0022-3727/42/6/064003
DO - 10.1088/0022-3727/42/6/064003
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AN - SCOPUS:63649122261
SN - 0022-3727
VL - 42
JO - Journal of Physics D: Applied Physics
JF - Journal of Physics D: Applied Physics
IS - 6
M1 - 064003
ER -