Theory of interacting dislocations on cylinders

TL;DR

This paper analytically studies the interactions and unbinding of dislocations on cylindrical surfaces, revealing complex behaviors influenced by external stresses and thermal effects, with implications for biological and colloidal systems.

Contribution

It provides the first analytical solutions for dislocation interactions on cylinders and explores their unbinding dynamics under external stresses and thermal fluctuations.

Findings

Analytical expressions for dislocation interaction energy and forces.

Dislocations on cylinders behave like grain boundaries.

Thermal nucleation rates for dislocation unbinding are derived.

Abstract

We study the mechanics and statistical physics of dislocations interacting on cylinders, motivated by the elongation of rod-shaped bacterial cell walls and cylindrical assemblies of colloidal particles subject to external stresses. The interaction energy and forces between dislocations are solved analytically, and analyzed asymptotically. The results of continuum elastic theory agree well with numerical simulations on finite lattices even for relatively small systems. Isolated dislocations on a cylinder act like grain boundaries. With colloidal crystals in mind, we show that saddle points are created by a Peach-Koehler force on the dislocations in the circumferential direction, causing dislocation pairs to unbind. The thermal nucleation rate of dislocation unbinding is calculated, for an arbitrary mobility tensor and external stress, including the case of a twist-induced Peach-Koehler force along the cylinder axis. Surprisingly rich phenomena arise for dislocations on cylinders, despite their vanishing Gaussian curvature.