Electrical resistivity and conductivity ions. In biological membranes, currents are carried by ionic salts. Small holes in cell membranes, called ion channels, are selective to specific ions and determine the membrane resistance. The electrical resistivity of a metallic conductor decreases gradually as temperature is lowered. In ordinary conductors, such as copper or silver, this decrease is limited by impurities and other defects. Even near absolute zero, a real sample of a normal conductor shows some resistance. In a superconductor, the resistance drops abruptly to zero when the material is cooled below its critical temperature. An electric current flowing in a loop of superconducting wire
Conductivity near the percolation threshold of the perfect insulator and just finite metallic clusters. The exponent t is one of the two critical exponents for electrical percolation. In the other well-known case of a superconductor-conductor mixture we have formula_18. This case is useful for the description below the percolation threshold: formula_19 for formula_20 Now, above the percolation threshold the conductivity becomes infinite, because of the infinite superconducting clusters. And also we get the second critical exponent s for the electrical percolation. In the region around the percolation threshold, the conductivity assumes a scaling form: formula_21 with formula_22 and formula_23 At the percolation threshold, the conductivity