AN EQUILIBRIUM THEORY FOR EXCLUSION CHROMATOGRAPHY OF BRANCHED AND LINEAR POLYMER CHAINS

The equilibrium partitioning of random-flight polymer chains between a dilute macroscopic solution phase and liquid within cavities of macromolecular size is obtained from the mathematical formalism for Brownian motion of particles within a bounded region. The derivation applies to linear chains and branched “star” molecules in a ⊖ solvent and to cavities of three shapes–a sphere, an infinite cylinder, and the space between two parallel infinite planes. Chromatographic theory suggests that conditions under which the equilibrium distribution coefficient for a polymer solute determines its elution volume should be easily attained in permeation columns packed with material containing rigid pores. It is found that elution volumes calculated solely from equilibrium thermodynamics agree closely with predictions based on the assumption that the elution volume for any flexible chain species, linear or branched, depends on the effective hydrodynamic volume of the polymer molecule. © 1969, American Chemical Society. All rights reserved.