Torque between multilayered charged plates using the Green's function in various regions

This study investigates the electrostatic interactions and torque generation in multilayered dielectric-electrolyte systems using Green's function methods. We analyze configurations comprising alternating dielectric half-spaces ϵsub and electrolyte layers ϵelwith charged rods (e.g., DNA-like Z-ions) attached to bounding plates. By rotating the lower plate by an angle θ relative to the fixed upper plate, we derive a θ-dependent torque τ(θ) = τmax sin(2θ). Numerical calculations demonstrate that increasing the number of layers dramatically amplifies the transmitted torque: the maximum torque in a seven-layer system reaches three orders of magnitude stronger than in a three-layer configuration. The Green's function approach enables exact calculation of the free energy for arbitrary layer counts.