particle modle of conductor

I think you refer to the particle model of conductor. Also, you have not specify if you refer to heat conduction or electrical conduction.
Nevertheless, both forms of conduction are attributed to free eelctrons in the substance. As metals generally possess abundance of free eelctrons, metals are therefore good conductors (both heat and electrical) than non-metals.
In heat conduction, free electrons at the hot end acquire larger kinetic energy from the hot source. Such increase of kinetic energy is transmitted by these free electrons through constant collisions to the other end of the conductor.
In electrical conduction, an electric field is set up by an external source, like a battery, free electrons are driven by the established electric field to flow in one direction, thus causing a flow of electric current.
The lacking of free electrons in non-metals makes them to be poor conductors to both heat and electricity.