Meaning
Thermodynamic equations define the link between tracer mobility and macroscopic mass transport in solid solutions. The darken-dehlinger relationship provides a mathematical framework to calculate the chemical diffusion coefficient from the self-diffusion coefficient using a thermodynamic factor. This calculation accounts for the non-ideal behavior of concentrated solutions.
Chemical Potential
Driving forces for diffusion arise from gradients in chemical potential rather than simple concentration gradients. The darken-dehlinger relationship incorporates the activity coefficient of the diffusing species to adjust for interactions between atoms in a lattice. It bridges the gap between atomic scale movement and bulk transport.
Transport Coefficient
Measurement of ion movement in battery electrodes requires accounting for the site availability and electrostatic effects. By applying the darken-dehlinger relationship, researchers can predict how fast lithium ions will move through an intercalation material as the state of charge changes. This prediction helps in designing faster charging electrodes.
Large gradients in the thermodynamic factor often occur near phase transitions.
Kinetic Effect
High rate performance in lithium batteries is often limited by the diffusion speed within the solid phase. The darken-dehlinger relationship shows that the diffusion rate can increase near specific state of charge points. This effect explains the high power capability of certain materials.
