Mechanical instability at finite temperature

Abstract

Many physical systems including lattices near structural phase transitions, glasses, jammed solids and biopolymer gels have coordination numbers placing them at the edge of mechanical instability. Their properties are determined by an interplay between soft mechanical modes and thermal fluctuations. Here we report our investigation of the mechanical instability in a lattice model at finite temperature T. The model we used is a square lattice with a f 4 potential between next-nearest-neighbour sites, whose quadratic coefficient k can be tuned from positive to negative. Using analytical techniques and simulations, we obtain a phase diagram characterizing a first-order transition between the square and the rhombic phase and different regimes of elasticity, as well as an 'order-bydisorder' effect that favours the rhombic over other zigzagging configurations. We expect our study to provide a framework for the investigation of finite-T mechanical and phase behaviour of other systems with a large number of floppy modes.

Two-Dimensional Disorder in Black Phosphorus and Monochalcogenide Monolayers

“…38 If the structural ground state of black phosphorene (BP), black arsenene, and monochalco- Figure 1: (a) The elastic energy landscape E(a 1 , a 2 ) as a function of lattice parameters a 1 and a 2 is generic to all monolayers with a Pnma structure, and it is exemplified on a GeS monolayer at zero temperature. A dashed white curve joins points A and B at two degenerate minima (E A = E B = 0).…”

Stability and anomalous entropic elasticity of subisostatic random-bond networks

“…This indicates that, while sublinear scaling is not confined to lattice models, the exponent does depend on the topology of the network. Indeed, in a recent paper [30] it was found that a square-lattice network with nextnearest-neighbor interactions, which is at the isostatic point when the next-nearest-neighbor interactions are zero, showed a critical regime where G ∝ T α with α ∼ 0.66, different from the α ∼ 0.5 observed both in Ref. [29] for a diluted-triangularlattice network at the isostatic point and in the random-bond networks presented here (see Fig.…”

“…Indeed, in Ref. [30] a square lattice (which is at the isostatic point) with next-nearestneighbor interactions was found to stiffen with a different critical exponent than a randomly diluted triangular lattice also at the isostatic point [29].…”

“…In addition to these athermal models, recent work has shown how temperature can stabilize a mechanically floppy network [25][26][27][28][29][30]. In Ref.…”

Topological Edge Floppy Modes in Disordered Fiber Networks

“…In the topologically nontrivial phase all floppy modes localize on the top edge leaving the bottom edge rigid. This physics of the Maxwell lattices make them both an interesting topic for theoretical study [21][22][23][24][25][26][27] and good candidates for the design of novel mechanical metamaterials where the edges can change stiffness by orders of magnitude reversibly [17].…”