Characterisation of heterogeneity and spatial autocorrelation in phase separating mixtures using Moran’s I

In complex colloidal systems, particle-poor regions can develop within particle-rich phases during sedimentation or creaming. These particle-poor regions are overlooked by 1D profiles, which are typically used to assess particle distributions in a sample. Alternative methods to visualise and quantify these regions are required to better understand phase separation, which is the focus of this paper. Magnetic resonance imaging has been used to monitor the development of compositional heterogeneity in a vesicle-polymer mixture undergoing creaming. T₂ relaxation time maps were used to identify the distribution of vesicles, with vesicle-poor regions exhibiting higher T₂ relaxation times than regions richer in vesicles. Phase separated structures displayed a range of different morphologies and a variety of image analysis methods, including first-order statistics, Fourier transformation, grey level co-occurrence matrices and Moran’s I spatial autocorrelation, were used to characterise these structures, and quantify their heterogeneity. Of the image analysis techniques used, Moran’s I was found to be the most effective at quantifying the degree and morphology of phase separation, providing a robust, quantitative measure by which comparisons can be made between a diverse range of systems undergoing phase separation. The sensitivity of Moran’s I can be enhanced by the choice of weight matrices used.