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Charge transport in molecular solids, such as semiconducting polymers, is strongly affected by packing and structural order over several length scales. Conventional approaches to modeling these phenomena range from analytical models to numerical models using quantum mechanical calculations. While analytical approaches cannot account for detailed structural effects, numerical models are expensive for exhaustive (and statistically significant) analysis. Here, we report a computationally scalable methodology using graph theory to explore the influence of molecular ordering on charge mobility. This model accurately reproduces the analytical results for transport in nematic and isotropic systems, as well as experimental results of the dependence of the charge carrier mobility on orientation correlation length for polymers. We further model how defect distribution (correlated and uncorrelated) in semiconducting polymers can modify the mobility, predicting a critical defect density above which the mobility plummets. This work enables rapid (and computationally extensible) evaluation of charge mobility semiconducting polymer devices.

Biological membranes can achieve remarkably high permeabilities, while maintaining ideal selectivities, by relying on well-defined internal nanoscale structures in the form of membrane proteins. Here, we apply such design strategies to desalination membranes. A series of polyamide desalination membranes—which were synthesized in an industrial-scale manufacturing line and varied in processing conditions but retained similar chemical compositions—show increasing water permeability and active layer thickness with constant sodium chloride selectivity. Transmission electron microscopy measurements enabled us to determine nanoscale three-dimensional polyamide density maps and predict water permeability with zero adjustable parameters. Density fluctuations are detrimental to water transport, which makes systematic control over nanoscale polyamide inhomogeneity a key route to maximizing water permeability without sacrificing salt selectivity in desalination membranes.