“…Given these challenges of unambiguously determining the morphology, theoretical approaches have been resorted to providing insight into the quantification of morphology for ion-containing membranes. Coarse grained MD and DPD simulations are widely utilized in modeling phase separations within membranes that typically requires long-time relaxation and a large length scale of 10-200 nm (Dorenbos, 2017a;Dorenbos, 2017b;Sepehr et al, 2017;Liu et al, 2018a;Dong et al, 2018b;Liu et al, 2018b;Wang R. et al, 2019;Clark et al, 2019;Dorenbos, 2019;Lee, 2019;Luo and Paddison, 2019;Zhu et al, 2019;Chen C. et al, 2020;Luo et al, 2020a;Dorenbos, 2020;Lee, 2020;Sevinis Ozbulut et al, 2020;Zhu et al, 2022). To further quantify the morphology including the size, shape, and connectivity of the ionic domains, which cannot be extracted from the peaks obtained by scattering methods, cluster analysis including distance-based and density-based algorithms is a powerful tool to provide a plethora of information on water domain size, shape, and connectivity from the trajectory of a MD or DPD simulation, which will be described in this section.…”