You would never believe the science and engineering that goes into this stuff!
PVC is synthesized in a chemical reaction called "radical chain polymerization from its monomer (basic building block), vinyl Chloride.
Plasticizer is added to PVC to make it soft ( you can not have soft polymer clay without it.)
There are two main kinds of Plasticizer, Phthalates and adipates. The reason why plasticizers make polymer clay soft is simple, and has to do with how plasticizer molecules attractive and repulsive forces exists. The attractive forces bring the molecules closer together, while the repulsive forces them apart. The forces between these molecules is called intermolecular forces. The reason plasticizers make PVC soft is because the plasticizer molecules fit in between the PVC molecules , preventing them from having string attractions to one another. (these attractions are based on the charges.)
Polymer clay needs heat to harden (cure). The reason for this is explained above and by the properties of PVC and Plasticizers. The Plasticizer is Permanently removed by the exposure to high heat.