Charge-induced deformation of scanning electrolyte before contact

The recent developments in scanning electrochemical probe techniques focus on the strategy of scanning the electrolyte. For example, scanning electrochemical cell microscopy (SECCM) is based on holding the electrolyte in a glass capillary, while scanning gel electrochemical microscopy (SGECM) immobilizes the gel electrolyte on micro-disk electrodes or etched metal wires. In both SECCM and SGECM, the first and essential step is to bring the electrolyte probe into contact with the sample, which is very often achieved by current feedback with a constant applied potential between the probe and the sample. This work attempts to theoretically analyse the deformation of the electrolyte during this approaching process. For a liquid electrolyte in SECCM, surface tension is considered to counterbalance the gravity and electrostatic force in 2D cylindrical coordinates with axial symmetry. The deformation at equilibrium is solved under certain conditions. For a gel electrolyte, a viscoelastic gel is analysed with a simplified 1D geometry. Both equilibrium and dynamic approaching are considered. The results suggest that for both liquid and gel electrolytes, critical conditions exist for breaking the equilibrium. When the applied potential is higher or the distance is lower than the threshold, the force will not equilibrate and the electrolyte will deform until contact. The critical condition depends on the properties (surface tension for a liquid, elastic and viscous moduli for a gel) and geometry (radius of the capillary for a liquid, thickness for a gel) of the electrolyte. Prospects of further extending the work closer to real experimental scenarios, especially SGECM, are also discussed.