What is conductivity?
Conductivity can be defined simply by Ohms Law.
Where R is the resistance, I the current and V the voltage present in the material. Thus from this relationship conductivity is found The conductivity depends on the number of charge carriers (number of electrons) in the material and their mobility. For example in a metal it is assumed that all the outer electrons are free to carry charge and the impedance to flow of charge is mainly due to the electrons "bumping" in to each other. Thus for metals as temperature is increased the resistance in the material increases as the electrons bump in to each other more as they are moving faster.
Insulators however have tightly bound electrons so that nearly no electron flow occurs so they offer high resistance to charge flow. So for conductance free electrons are needed.
The diagram below shows how the conductivity of conjugated polymers like polyactelyene can vary from being a insulator to a conductor.