A k Descriptor to Design of Current Collectors for Anode-Free Sodium Batteries

The anode-free strategy enables exceptionally high energy density in rechargeable metal batteries, but the lack of theoretical frameworks impedes current collector design. Here, this study mathematically derives three critical parameters: dielectric coefficient (ɛ), ion mobility (µ_C), and the change of concentration (δC_C), and introduces a quantitative descriptor, k, which serves as a benchmark for evaluating current collector efficiency. Experimentally, a carbon nanotube (CNT)-based current collector is fabricated with minimized ɛ, enhanced δC_C (nano/micro-Sb particles), and µ_C (sodium carboxymethylcellulose, CMC-Na). The optimized design achieves remarkable cycling stability-over 24 months at 0.25 mAh cm^-2 and 0.5 mA cm^-2, and 12 months even at a high areal capacity of 20 mAh cm^-2. The lowest k value aligns with half-cell tests, validating this theory. This work establishes a quantitative framework for designing high-efficiency anode-free sodium battery current collectors.