The role of inter-particle cohesive stiffness in determining the size and nature of self-limiting, geometrically-frustrated assemblies*

Geometrically frustrated assemblies are an emerging class of systems where local inter-subunit misfits propagate to large-scale strain gradients in an assembly, giving rise to anomalous self-limiting thermodynamics under certain conditions.  Recently, the “curvamer” model was introduced to study self-limitation in 1D stacks of deformable, shell-like particles, where an elastic energy emerges from bending costs in stacks of uniformly spaced particles.  In general, elastic strains will also be borne by the stretching of cohesive bonds between particles.  Here, we generalize the curvamer model to consider the effect of inter-particle bond stiffness, or alternatively the effect of finite attraction range between particles.  We find that the ratio of intra-particle (bending elasticity) to inter-particle stiffness not only controls the regimes of self-limitation but also the nature of frustration propagation.  We develop and study a continuum elastic description as well as a numerical coarse-grained model of curvamers from which we deduce critical parameter regimes separating uniformly spaced stacks from quasi-uniform (gap-opened) stacks.  We conclude that the self-limiting stack size is unbounded for an infinitely short-range of attraction while a finite range of attraction yields a maximum self-limiting size.  These predictions provide critical guidance for experimental realizations of frustrated particle systems designed to exhibit self-limitation at especially large multi-particle scales.