Equilibrium and dynamic pleating of a crystalline bonded network

TL;DR

This study uncovers a phase transition in a 2D particle network leading to pleated structures, with external fields stabilizing these phases and revealing complex stress localization and slow dynamics.

Contribution

It introduces a new phase transition mechanism in crystalline networks driven by non-affineness and demonstrates the stabilization of pleated phases via an external field.

Findings

Identification of heterogeneous pleated phases

Stress localization in ordered pleats

Slow kinetics and aging dynamics near phase coexistence

Abstract

We describe a phase transition that gives rise to structurally non-trivial states in a two-dimensional ordered network of particles connected by harmonic bonds. Monte Carlo simulations reveal that the network supports, apart from the homogeneous phase, a number of heterogeneous "pleated" phases, which can be stabilised by an external field. This field is conjugate to a global collective variable quantifying "non-affineness", i.e.~the deviation of local particle displacements from local affine deformation. In the pleated phase, stress is localised in ordered rows of pleats and eliminated from the rest of the lattice. The {\em kinetics} of the phase transition is unobservably slow in molecular dynamics simulation near coexistence, due to very large free energy barriers. When the external field is increased further to lower these barriers, the network exhibits rich dynamic behaviour: it transforms into a {\em metastable} phase with the stress now localised in a {\em disordered} arrangement of pleats. The pattern of pleats shows ageing dynamics and slow relaxation to equilibrium. Our predictions may be checked by experiments on tethered colloidal solids in dynamic laser traps.