Shape asymmetry of polyelectrolytes in dilute solution

The asymmetric shape of polyelectrolytes is important to predict their thermodynamic and dynamic properties. Although it is well established that electrostatic repulsion stretches polyelectrolytes to a size larger than that of a neutral chain with the same number of monomers, whether this stretching occurs solely in one direction is not well understood. Previous theoretical models assume stretching occurs solely along a longitudinal (or principal) axis and that the size of the chain perpendicular to this axis (i.e., the minor axis) remains unperturbed. However, simulations have reported polyelectrolytes are stretched along the perpendicular direction, an observation that cannot be explained by current theories. Here, we conduct simulations of isolated polyelectrolytes and quantify their size and shape. Results from polyelectrolyte simulations are compared to simulations of neutral force-stretched chains with an equal number of monomers as a control. We find that electrostatic repulsion in polyelectrolytes results in stretching along the perpendicular direction, while force-stretched chains remain unperturbed in the direction perpendicular to the force. To quantify stretching on different length scales, we compute the mean-square amplitude of the chain normal modes. Furthermore, we develop a scaling model that predicts the perpendicular size of polyelectrolytes and agrees with simulations.