Collective dynamics in two-dimensional aggregations with competing interactions

A generic aggregate forming system in two dimensions (2D) is studied using canonical ensemble constant temperature molecular dynamics simulation. The aggregates form due to the competition between short range attraction and long range repulsion of pair-wise interactions. Choosing the appropriate set of interaction parameters, we focus on characterising the collective dynamics in two specific morphologies, {\it viz.} compact and string-like aggregates. We focus on the temporal evolution of the mobility of an individual particle and the dynamic change in its nearest neighbourhood, measured in terms of the Debye-Waller factor ($\bar{u}_i^2$) and the non-affine parameter ($\chi$), respectively (defined in the text), and their interrelation over several lengths of observation time $\tau_w$. The distribution for both measures are found to follow the relation: $P(x;\tau_w) \sim \tau_w^{-\gamma}x$ for the measured quantity $x$. The exponent $\gamma$ is equal to $2$ and $1$ respectively, for the compact and string-like morphologies following the ideal fractal dimension of these aggregates. A functional dependence between these two observables is determined from a detailed statistical analysis of their joint and conditional distributions. The results obtained can readily be used and verified by experiments on aggregate forming systems such as globular proteins, nanoparticle self-assembly etc. Further, the insights gained from this study might be useful to understand the evolution of collective dynamics in diverse glass-forming systems.