Excluded Volume

alpha² = <r²> / <r² >₀

• The chain will expand in a good solvent, in order to increase its favorable interaction with that medium. alpha² > 1. The size of the effect increases with M; alpha² is proportional to M^0.2.

• The chain will contract in a poor solvent, in order to reduce the unfavorable interaction. alpha² < 1. These systems are not easily studied in experiments, because the polymer molecules tends to aggregate or precipitate in such poor solvents.

• Flory's Theta solvent marks the boundary between the good and bad solvents. In the Theta solvent, the medium provides an exact compensation for the excluded volume effect. The mean square dimensions are controlled entirely by the short-range intramolecular interactions, and they are unaffected by the solvent. alpha² = 1. The Theta state is achieved in carefully selected solvents, at specified temperature, where the excluded volume vanishes. It is also obtained (Flory hypothesis) in the amorphous bulk state of the pure polymer. This hypothesis tells us that the conformations of a polymer in the bulk can be inferred from the study of the polymer in dilute solution, so long as the dilute solution is at the Theta condition.

The exponent nu

In the high molecular weight limit, the mean square unperturbed dimensions can be written as

<r²> proportional to n^{2 nu}

• nu = 3/5 in a good solvent
• nu = 1/2 in a Theta solvent
• nu = 1/3 in a poor solvent

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