The bulk transport properties of disordered heterogeneous materials that arise
in electrochemical systems are determined by their complex microstructures.
I will discuss the zoology of correlation functions that quantitatively
characterize the microstructures. Of particular interest is the identification of microstructural
descriptors that sensitively detect the degree of order/disorder across length scales,
including the nascent concept of hyperuniformity, which describes microstructures
at the largest lengths scales. I will describe these developments and how these descriptors
can be used to accurately predict transport properties as well as how to employ this
theoretical framework for inverse design of materials with tunable properties.
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