Electrostatic bending response of a charged helix

TL;DR

This paper investigates how a chain of charged particles on a helix responds to bending, revealing regimes with different behaviors and oscillations due to charge distribution and long-range interactions.

Contribution

It introduces a novel analysis of electrostatic bending response using energy differences, identifying distinct regimes and oscillatory phenomena not captured by traditional bending rigidity.

Findings

Identifies two regimes with different bending behaviors based on radius-to-pitch ratio.

Discovers oscillations in bending energy related to charge distribution and system parameters.

Shows complex, discontinuous changes in ground state structure affecting bending response.

Abstract

We explore the electrostatic bending response of a chain of charged particles confined on a finite helical filament. We analyze how the energy difference $\Delta E$ between the bent and the unbent helical chain scales with the length of the helical segment and the radius of curvature and identify features that are not captured by the standard notion of the bending rigidity, normally used as a measure of bending tendency in the linear response regime. Using instead $\Delta E$ to characterize the bending response of the helical chain we identify two regimes with qualitatively different bending behaviors for the ground state configuration: the regime of small and the regime of large radius-to-pitch ratio, respectively. Within the former regime, $\Delta E$ changes smoothly with the variation of the system parameters. Of particular interest are its oscillations with the number of charged particles encountered for commensurate fillings which yield length-dependent oscillations in the preferred bending direction of the helical chain. We show that the origin of these oscillations is the non-uniformity of the charge distribution caused by the long-range character of the Coulomb interactions and the finite length of the helix. In the second regime of large values of the radius-to-pitch ratio, sudden changes in the ground state structure of the charges occur as the system parameters vary, leading to complex and discontinuous variations in the ground state bending response $\Delta E$.