Electrode structure

1. A method of designing an electrode for an electric battery cell, the electrode comprising a compound mixture of an electrochemically active material, an electrically conductive material and a binding material, the method comprising:

applying a model for an electrochemical response of the electric battery cell, the model including overpotential dynamics for the electrode; and

optimising parameters of the model to maximise one or more of an energy density, power density, battery health or thermal response of the electric battery cell;

wherein the electrode is a graded electrode and has a thickness L between first and second opposing faces, the method comprising:

i) selecting upper and lower bounds for a weight fraction w(x) of the electrochemically active material at a fractional distance x from the first to second opposing faces;

ii) selecting an initial weight fraction for the electrode for x=0 and x=L;

iii) applying the model of overpotential dynamics for the electrode;

iv) adjusting a variation in the weight fraction w(x) of the electrochemically active material to determine a distribution of the weight fraction w(x) of the electrochemically active material that minimises overpotential across the electrode; and

v) manufacturing the electrode by depositing the electrochemically active material based on the determined distribution of w(x).

2. The method of claim 1 , wherein the model describes the evolution of state-of-charge, overpotential, heat generation, electrolyte displacement and degradation effects including Li-plating, particle cracking and SEI layer growth.

3. The method of claim 1 , wherein the parameters include one or more of a length of an electrode separator, a length of the electrode, porosity, tortuosity, particle radii, electronic or ionic conductivities or dimensions of the electrode.

4. The method of claim 1 wherein the model is configured to minimise a variation in overpotential of the electrode to maximise the energy density, power density, battery health and/or thermal response of the electric battery cell.

5. The method of claim 1 , wherein the electrode is a graded electrode and the method comprises defining an average overall weight fraction m of electrochemically active material for the electrode, step iv) comprising adjusting the variation in w(x) to provide a distribution that minimises overpotential across the electrode for defined average overall weight fraction of electrochemically active material in the electrode.

6. The method of claim 1 , wherein step iv) comprises determining an average overall weight fraction m of electrochemically active material for the electrode.

7. The method of claim 1 , wherein step iv) comprises:

applying a convex relaxation to the model to provide a convex semi-definite program; and

solving the convex semi-definite program to determine the distribution of w(x).

8. The method of claim 1 , wherein step i) further comprises selecting an upper bound for a gradient in w(x) across the electrode.

9. The method of claim 1 comprising a further step of manufacturing the electrode by depositing successive layers of the compound mixture on a substrate.

10. The method of claim 9 wherein the substrate is a current collector layer for the electric battery cell.

11. The method of claim 1 , wherein the electric battery cell is a Li-ion battery cell.