A model for self-assembling circuits with voltage-controlled growth

Abstract

The circuit tile assembly model (cTAM) consists of a voltage source and resistive circuit tiles, configured as a voltage divider, that attach to form resistive ladders or grids if the voltage on the boundary is greater than or equal to a threshold. The model produces a family of circuits whose composition and properties change with time. As growth proceeds, the voltage decreases until it no longer exceeds a threshold, which causes growth to cease. This is referred to as self-controlled growth, because the properties of the assembly itself are the primary determinant in controlling the extent of the assembly. The model augments tile assembly models, which are programmable through specific chemical interactions, with an alternative electrical mechanism. The ladder and grid assemblies have bounded size and unique shape that are determined by parameters from the electrical network. Using the harmonicity of the electric potential, the shape of the grid assembly is shown to be symmetric around the main diagonal. Finally, two models of growth, differentiated by whether the voltage is measured before or after attachment, are equivalent. The model and analysis have potential application to self-assembly of nanostructures, as well as to networks whose structure changes over time.

Publication Title

International Journal of Circuit Theory and Applications

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