Pinning and Tribology of Tethered Monolayers on Disordered Substrates

TL;DR

This paper investigates the phase transition and mechanical properties of tethered crystalline monolayers on disordered substrates, revealing a glassy phase with anomalous fluctuations and the importance of fixed connectivity in maintaining this state.

Contribution

It demonstrates the existence of a glassy phase in tethered monolayers on disordered substrates and highlights the critical role of fixed internal connectivity in this transition.

Findings

Sharp transition to a glassy phase with anomalous phonon fluctuations

Nonlinear force-displacement law with a variable exponent

Transition is destroyed when dislocations are allowed

Abstract

We study the statistical mechanics and dynamics of crystalline films with a fixed internal connectivity on a random substrate. Defect free triangular lattices exhibit a sharp transition to a low temperature glassy phase with anomalous phonon fluctuations and a nonlinear force-displacement law with a continuously variable exponent, similar to the vortex glass phase of directed lines in 1+1 dimensions. The periodicity of the tethered monolayer acts like a filter which amplifies particular Fourier components of the disorder. However, the absence of annealed topological defects like dislocations is crucial: the transition is destroyed when the constraint of fixed connectivity is relaxed and dislocations are allowed to proliferate.