Approximation, Free energy, Mathematical methods, Polymers, Quantum confinement


De Gennes’ blob theory has been remarkably successful at describing weakly confined polymers in both slits and channels, and comparable results surround Odijk’s theory of deflection segments for strongly confined wormlike polymers in nanochannels. However, given the success of Odijk’s theory in channels, it is remarkable that there is no comprehensive theory for the simple case of a wormlike polymer strongly confined between two parallel plates. We propose such a theory by drawing inspiration from the existing literature on ideal wormlike chains in slits and Daoud and de Gennes’ idea of mapping a slit-confined chain to a two-dimensional chain. We postulate that the chain can be quantitatively described as a two-dimensional wormlike chain with a weak perturbation in the confining dimension due to deflection segments. By incorporating the effects of real chains, where the variable slit depth adds subtlety due to concomitant changes in the strength of excluded volume interactions, our theory predicts the existence of three distinct subregimes. We investigate the validity of our claims by performing Monte Carlo simulations of a slit-confined wormlike chain using an off-lattice implementation of the pruned–enriched Rosenbluth method. From these simulations, we find strong numerical evidence supporting our predictions, including the existence of subregimes within the Odijk regime.

Original Publication Citation

Macromolecules 2014, 47, 11, 3672–3684

Document Type

Peer-Reviewed Article

Publication Date



American Chemical Society




Ira A. Fulton College of Engineering


Chemical Engineering

University Standing at Time of Publication

Assistant Professor