Bias-dependent surface stress by density functional theory combined with the effective screening medium method

We investigated the surface stress at an Al(111) electrode surface under a finite bias voltage using first-principles density functional theory combined with the effective screening medium (ESM) method. The surface stress depends quadratically on the bias voltage, whose profile has a maximum value at a finite voltage and a curvature corresponding to the capacitance obtained from the relationship between the excess charge and the electrode voltage. These features are consistent with the results of the thermodynamics at the electrode surface and previous experiments. The results of the layer-resolved local stress show that the bias dependence of the local stress correlates with the excess charge distribution from the outermost layer to the inner layer; the local stresses at the outermost and inner layers show parabolic and linear voltage dependences, respectively. Thus, the capacitance term of the macroscopic stress mainly originates from the outermost layer, and the contribution of the inner-layer stress is understood by the strain derivative of the excess charge. The stress analysis method with ESM is significant for modeling and understanding the surface stress at the electrode surface under a bias voltage.