The transport properties of a set of four copolymers based on poly(vinyl chloride) (PVC) have been studied. The nucleophilic substitution of chlorine atoms with 4-mercaptophenol sodium salt, 2-thionaphthalene, 4-(1-adamantyl) thiophenol, and thiophenolate sodium salt as the nucleophiles has been performed, from low conversion levels (3%) to high levels (40%), and the permeability, solubility, and diffusivity of oxygen, nitrogen, carbon dioxide, and methane have been measured. The introduction of bulky groups to the PVC chain leads to chain separation and results in large increases in the free volume at conversions up to 10%. This brings about a 5-fold increase in the diffusion coefficients that is almost independent of the bulkiness of the substituent. Solubility is little affected and instead tends to decrease as substitution progresses. The substitution of more than 10% of the chlorine atoms does not result in an improvement in the transport properties.