Lithium-ion batteries (LIBs) are critical to decarbonisation, yet the future supply of of lithium-ion (Li-ion) critical minerals such as lithium, nickel, and copper face significant uncertainty and risk. Potassium-ion batteries (KIBs) are emerging as a promising alternative to LIBs due to their reduced dependency on critical minerals, and ability of K+ to intercalate into graphite unlike sodium ions. KIBs may also present an opportunity for superior fast-charging due to the larger K+ size and lower charge density, being speculated to result in faster electrolyte ionic transport. Since there is no current viable potassium-ion (K-ion) electrolyte, a full-cell KIB rate model in commercial cell format is required to determine the fast-charging potential for KIBs and facilitate K-ion electrolyte and materials development. However, accurate characterisation of the fundamental electrolyte and material properties that determine rate performance has not yet been conducted. In this thesis the fundamental rate-determining properties of a K-ion electrolyte and leading K-ion electrode materials are characterised, and the first KIB Doyle-Fuller-Newman model is developed. First, the ionic transport and thermodynamic properties of a K-ion electrolyte is fully characterised for the first time using state-of-the-art methods, characterising potassium bis(fluorosulfonyl)imide (KFSI) in 1,2-dimethoxyethane (DME) and comparing to the Li-ion equivalent. A K metal preparation protocol was developed enabling sufficient K metal stability for electrolyte characterisation. The results show the K-ion electrolyte displays significantly higher salt diffusivities and transference numbers than the Li-ion equivalent. Second, the effective solid-state diffusivities and exchange current densities of the leading K-ion electrode materials—the graphite anode and potassium manganese hexacyanoferrate K2Mn[Fe(CN)6] (KMF) cathode—are characterised, through a combination of optimised material design and state-of-the-art analysis. The results show both the ionic transport and particularly the charge-transfer kinetics are slower for the KMF compared to the graphite. Finally, the first Doyle-Fuller-Newman model of a KIB full cell is presented in a hypothetical commercial cylindrical cell format, demonstrating ionic transport in the current leading K-ion electrolyte is too slow for even moderate rate performance using realistic electrode loading. Should a viable electrolyte be developed, the modelling shows K-ion could be competitive with the lithium iron phosphate (LFP) LIB in fast-charging capability.