Self-limitation in geometrically frustrated, deformable particle assemblies with finite attraction range*

Geometrically frustrated assemblies are an emerging class of systems where inter-subunit misfits propagate to large-scale strain gradients, 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, cylindrical shell-like particles, where an elastic energy emerges from curvature changes in stacks of uniformly spaced particles.  In general, elastic strains will also be borne out of stretching cohesive bonds between particles.   Here, we generalize the curvamer model to consider the effect of inter-particle bond stiffness, or alternatively finite attraction ranges between particles.  From a continuum elastic theory and coarse-grained numerical model, we find stack size is controlled by not only the ratio of inter-particle adhesion to intra-particle stiffness but also the ratio of intra-particle stiffness to inter-particle stiffness, which controls the nature of frustration propagation through the stack and the regimes of self-limiting behavior.  We also introduce a numerical model to explore effects of particle geometry, where we expect to see bond-stretched stacking dominate for hyperbolic and spherical curvamers as large elastic costs suppress curvature changes for these shapes. These predictions provide critical guidance for experimental realizations of frustrated particle systems designed to exhibit self-limitation at especially large multi-particle scales.