Evolution of self-organized two-dimensional patterns of nanoclusters through demixing

A mixture of dodecanethiol-capped Au nanoparticles (AuNPs) and the amphiphilic fatty acid, stearic acid, spread as a monomolecular layer on water surface, is observed with Brewster angle microscopy (BAM) to form a two-dimensional network of AuNP clusters through demixing, at concentration of AuNPs by weight (ρ[over ¯])>10% and the surface pressure (π)≥10mNm^{-1}. For π=15mNm^{-1}, the number of nodes (n) remains unchanged till ∼2 hours and then changes over to a lower n state, where the pattern consists of almost perfect circles with greater in-plane thickness of the AuNP lamellae. For the higher n state the mean-square fluctuation of BAM intensity remains flat and then decays as f(ξ)=ξ^{2α} with α∼0.6 (correlated fluctuations) over the length scales of 400μm-6μm and below 6μm, respectively. For the lower n state the fluctuation decays almost over the entire length scale with α=0.3, indicating emergence of aperiodicity from quasiperiodicity and a changeover to anticorrelated fluctuations. These patterns can be looked at as two distinct chaotic trajectories in the I-I^{'} phase space of the system (I being the scattered light intensity at any position of the pattern and I^{'} its gradient) with characteristic Lyapunov exponents.