Excluded Volume and Solvent Effects

There are two competing effects that predominantly modify the volume taken up by an N segment polymer in solution. The first of these is self-avoidance. The polymer chain can only occupy a certain point in space once as it coils around on itself therefore, the total space available for the polymer to move is decreased. This means that there is an excluded 

For a particular solvent at the theta temperature 0, the excluded volume effect can be neglected, and the polymer will behave like an ideal chain with a scaling exponent of v = 0.5. This temperature can be considered analogous to the Boyle temperature in a gas. At the Boyle temperature, a nonideal gas will obey the ideal gas law, and the effects of molecular volume can be neglected. 

A theta solvent is a solvent in which the polymer will behave like an ideal chain. If a polymer is dissolved in a particular solvent at temperature and the temperature of the solution is decreased so T 0, then the polymer coil will shrink. If the temperature is increased to T 0, the polymer coil will expand to fill a larger volume. The competing effects of self-avoidance and the van Der Waals attraction have an impact on the density with which the polymer fills space, resulting in changes in the v exponent. The v exponent will only be equal to 0.5 in a theta solvent, but at high temperatures, we can use the Flory approximation to estimate the value of v for a self-avoiding chain. 

---

The subscript 0 on 1 implies 0 conditions, a state of affairs characterized in Chap. 1 by the compensation of chain-excluded volume and solvent effects on coil dimensions. In the present context we are applying this result to bulk polymer with no solvent present. We shall see in Chap. 9, however, that coil dimensions in bulk polymers and in solutions under 0 conditions are the same. 

---