Scaled Particle Theory for the Coil―Globule Transition of an Isolated Polymer Chain

We have developed a scaled particle theory for the coil―globule transition (CGT) of a chain of attractive hard spheres in an attractive hard sphere solvent. The model predicts a lower critical solution temperature (LCST) related CGT that merges with a high temperature upper critical solution temperature (UCST) related CGT at a high pressure hypercritical point. The predicted hypercritical point is in good agreement with simulations of a bead―spring polymer chain in a symmetric solvent, without the use of any adjustable parameters. The model predicts that increasing bulkiness of monomers relative to solvent molecules, decreasing polymer cohesive energy relative to solvent cohesive energy, and reduced chain length stabilize the expanded coil state, in qualitative agreement with simulations. These trends in the UCST-CGT and LCST-CGT are found to emerge from incompressible-solvent effects and equation-of-state effects, respectively, consistent with the enthalpic origin of the UCST and the entropic origin of the LCST.