Comparison between Persistence Lengths in Two and Three Dimensions for Flexible and Semi-Flexible Polyelectrolytes within the Debye-Hückel Approximation

When reporting persistence lengths measured on a surface, for example, with AFM, it is often assumed that the two-dimensional result is related to the persistence length in three dimensions by a factor of two: lp,2D = 2 lp,3D. This is the result for the wormlike-chain model, which is established by local interactions that only act through the chain. However, a polyelectrolyte has electrostatic interactions, which are long-ranged and act through space. This poses the question how persistence lengths measured in 2D and 3D are related for a polyelectrolyte.         

To find an answer, Monte Carlo simulations have been performed with chains having various stiffness to approximate (semi-flexible) wormlike chains as well as freely jointed chains in both two and three dimensions with electrostatic interactions treated within the Debye-Hückel approximation, i.e., represented by a screened Coulomb potential, which includes the effect of added salt implicitly. Persistence length is measured as the value for a wormlike chain with the same end-to-end distance.

The conclusion is that lp,2D = 2 lp,3D is applicable at moderate salt concentrations, but at high salt concentrations, chains in two dimensions display stronger electrostatic excluded volume effects, which break the wormlike-chain-like connection between the two dimensions (unless the chain is stiff enough to not bend back on itself). At low salt concentrations, the relation is a reasonable approximation for freely jointed chains, but not for fairly stiff semi-flexible chains, because the balance between the intrinsic stiffness and electrostatic interactions is different in two dimensions, where the intrinsic stiffness extends the chain more compared to three dimensions and this becomes important at low salt concentrations where the chain is unscreened and all electrostatic interactions are significant.