Increased robustness for fluidic self-assembly

Abstract

Self-assembly methods have been developed at the micro- and nanoscale to create functional structures from subelements stochastically dispersed in a fluid. Self-assembly paradigms have limitations in terms of achievable complexity of the final structure, ability to perform error correction, and scalability. Fluidic self-assembly attempts to overcome these limitations by incorporating a controlled flow structure and/or complex geometric interactions to improve the assembly rate and the specificity of the final positioning. Since the initial position and orientation of a subelement in a stochastic system are indeterminate, the most robust of these schemes are those for which the dependence on the initial condition will be the weakest. In this paper we develop an analytical/numerical model for the fluid forces and torques on a two-dimensional subelement involved in a fluidic self-assembly process and describe the translational and rotational motions of the element due to these forces. We use this model to determine optimal subelement shapes and flow conditions that lead to successful assembly over the broadest range of initial conditions. We quantify the degree to which assembly has been successful by introducing two docking parameters that are descriptive of how close the final subelement position is to the ideal case. Robust self-assembly schemes were developed for the assembly of different tile shapes. This approach to evaluate a self-assembly process based on the final subelement position can be applied to other fluidic self-assembly techniques.