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I understand what causes elements to be conductive or nonconductive. But what causes a substance say rubber to be nonconductive at a molecular level?

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Conductivity requires mobile electrons. Metals tend to have loosely held valence electrons so metals are generally conductive. Metals have loosely held valence electrons for two reasons: metals tend not to be very electronegative (able to stabilize electron density) and metals tend to be somewhat big atoms by nature of many metals having a d-group of electrons. D electrons are further from the nucleus on a time average basis than s electrons or p electrons.

However, conductors do not have to be metals. Consider graphite. Graphite is $\ce{sp^2}$ hybridized. Graphite is made solely of carbon atoms - and carbon isn't a metal! The mobile pi electrons in graphite due to resonance allows graphite to be a good conductor.

I should also note that conductivity does not always imply mobile electrons; solutions can be conductive too and this is due to mobile electrolytes (ions). For example, you will find that deionized water is completely unconductive. However, regular tap water is generally conductive due to the presence of ions (e.g. chloride ions from chlorination). Gatorade is also very conductive because it is especially formulated to contain a lot of electrolytes.

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    $\begingroup$ Another factor that defines a metal is the availability of unoccupied orbitals that are very close in energy to the filled orbitals. Because the filled and empty orbitals are so close in energy, the loosely bound electrons are able to "hop" from atom to atom with a very low activation energy. This low activation energy for the hopping process means that electrons can travel through such materials very rapidly. $\endgroup$ – ron May 20 '14 at 2:54
  • $\begingroup$ Yes! I think I heard of it called "ionization" energy somewhere before. $\endgroup$ – Dissenter May 20 '14 at 2:58
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    $\begingroup$ Metals have a high density of states and many delocalised orbitals. The energy difference between occupied and unoccupied orbitals (band gap) may be measured and can be used to determine conductors, semi-conductors and isolators. In a conductor it is not necessary that there are mobile electrons. There have to be mobile charge transporters, e.g. ions. (Graphite is a 2D conductor.) $\endgroup$ – Martin - マーチン May 20 '14 at 6:59
  • $\begingroup$ True, mobile ions or electrolytes if we're talking about solution does the trick. Pure, deionized water has 0 conductivity but tap water is conductive usually due to the presence of chloride ion and the like. $\endgroup$ – Dissenter May 20 '14 at 7:22

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