Complexation thermodynamics of free and graft oligomers with complementary polymers

The dilute solution complexation equilibrium between linear macromolecules and smaller complementary oligomers is considered when: (1) the oligomers are free in solution; and (2) the oligomers are covalently attached at one end to the polymer. A general statistical mechanical framework is developed and is illustrated using a simple random walk model for polymer conformation. The statistical mechanical partition functions are formulated using a generating function technique, allowing thermodynamic averages in the complexed state to be calculated. Loops, trains, and tails of all possible length are allowed in the conformation of a complexed oligomer. Simulation results for the free oligomer case are compared with those obtained for oligomers covalently attached to the polymeric molecular. The model provides a theoretical explanation for the experimentally observed enhancement of complexation of oligomers grafted to the complementary polymers.