Evolution of self-organized two-dimensional patterns of nanoclusters through demixing
Physical Review E
A mixture of dodecanethiol-capped Au nanoparticles (AuNPs) and the amphiphilic fatty-acid Stearic Acid (StA), 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 de-mixing, at concentration of AuNPs by weight, (ρ) > 10% and the surface pressure, (π) ≥ 10 mN m −1 . For π = 15 mN m −1 , the number of nodes (n) remains unchanged till ∼ 2 hours and then changes over to a lower n state, where
... r 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 400 µm-6 µm 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 quasi-periodicity and a changeover to anti-correlated 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.