Theory of chromatography of complex cyclic polymers: eight-shaped and daisy-like macromolecules

Abstract

A theory of chromatography of eight-shaped, trefoil-shaped and daisy-like polymers is developed. For a model of an ideal chain in a slit-like pore exact equations and a number of approximate formulae for the distribution coefficient K of these polymers are derived. All modes of chromatography of complex macrocycles of arbitrary molar mass in both narrow and wide pores are covered by the theory. It is shown that complex macrocycles always elute after linear polymers and rings of the same contour length. The effective chromatographic radius of eight-shaped and daisy-like macromolecules, which determines retention in size-exclusion chromatography are calculated. The increase in the retention with molar mass is predicted for all types of macrocycles at the critical interaction condition. Non-monotonous molar mass dependences of K are found at pre-critical interaction. We simulate separation of complex cyclic polymers from linear and ring precursors, discuss possibilities to separate symmetric and asymmetric eights, and speculates on the use of chromatography for separating knotted and unknotted polymer rings. According to the theory, the chromatography under the critical and pre-critical interaction conditions is expected to be especially efficient in these and similar problems. Boundary conditions for the theory and its applicability to real systems are discussed.