1.1 Excluded Volume and Solvency
Excluded volume scales as v ≈ b2d where b is the Kuhn monomer size (length) and d is the diameter (Kuhn
segments are rod-like).
- Athermal Solvents Here, v is independent of temperature. The system only features hard
core repulsion and v ≈ b2d. Monomer-monomer contact is energetically indistinguishable from
monomer-solvent contact, for example.
- Good solvents Excluded volume is reduced due to monomer-monomer attraction. The effect of this
attraction is greater at lower temperatures, causing a reduction in the excluded volume. 0 < v < b2d
- Theta solvent The (positive) contribution to excluded volume from hard core repulsion is exactly
balanced by that (negative) due to attractions and so v = 0. The chains thus have nearly ideal
conformations. This occurs at a temperature called the theta temperature, Θ, which is analogous to
the Boyle temperature in thermodynamics.
- Poor solvents Excluded volume is negative due to large attractive interactions between the monomers,
which prefer monomer-monomer contact strongly over monomer-solvent contact. Chain dimensions are
reduced relative to ideal. -b2d < v < 0.
- Non-solvents Here, v ≈-b2d and the polymer collapses into a very compact structure that excludes
all solvent.