Application of the Spatial Distribution Function to Colloidal Ordering

2D colloidal assembly is a vital process in the fabrication of nanostructured devices and receives widespread attention in fundamental research. Characterizing the ordering is crucial to develop an understanding of the driving forces behind the assembly and to optimize processing conditions. Image analysis offers a direct evaluation pathway, typically via the radial distribution function or the 2D fast Fourier transform. Both methods have inherent limitations; the former provides no angular dependence, while the latter is challenged when confronted with imperfection on the mean size, spacing, and coverage of the building blocks. Here, we introduce the 2D spatial distribution function (SDF) as an alternative pathway to evaluate colloidal ordering. We benchmark the method in case studies of prominent examples and provide a tool kit for implementation, including an ImageJ plugin and the standalone software CORDERLY. Application and interpretation are straightforward and particularly powerful to analyze and compare colloidal assemblies with limited order.