Precise fabrication of nanomaterials: a nonlinear dynamics approach

Modeling of the precise fabrication in the self-assembling of particles is studied using the nonlinear Langevin equation system. The numerical simulation showed a marked ordering of the particles as a function of time after some induction period. The abnormally enlarged fluctuation was found around the start of the evident ordering. After the fluctuation, a sudden increase of the cluster size was observed. The results corresponded well to the dynamics due to the formation of the critical cluster. The shape of the critical cluster around the enlarged fluctuation was not compact and showed fractal-like structures. The fluctuation of the cluster size around the formation of the critical cluster was explained by the anomalous fluctuation theorem for the generalized Langevin equation. The characterization of the stochastic dynamics of the critical clusters rationalized the concept of dynamic templating for the fabrication technique of the self-assembling of nanoparticles, that is, the structural constraint on the particle assembly by externally adding the resonance frequencies that match with the localized nonlinear vibrational modes of the target structures originating from thermal (Brownian) activation.