In-plane force–extension response of a polymer confined to a surface

The force–extension response of synthetic polymers and biomolecules governs properties such as bulk elasticity of rubbery materials and the behavior of DNA and several filamentous proteins. In several cases, such as DNA adsorbed on a plasma membrane, or polymers adsorbed onto a hard material, the molecule is confined to two dimensions as it extends under external forces (e.g., due to applied electric field). However, the force response in two dimensions is relatively poorly-studied. In this paper, we present closed-form analytical expressions for the two-dimensional force–extension response of a freely-jointed chain under force control. Our principal results relate end-to-end distance to total force under two modes of stretching: (i) when force is applied only to the free end of the chain, and (ii) when the applied force is distributed uniformly throughout the chain. In both cases, we further propose explicit approximate expressions for force in terms of extension. Analytical results have been verified by Brownian dynamics simulation. We also show that the distributed force model agrees well with experimental measurements of stretching surface-adsorbed DNA by an electric field.