Magnetic Field Assisted Electrodeposition of Metal on Conically Structured Electrodes
Authors: Huang Mengyuan , Eckert Kerstin , Mutschke Gerd 
Published: December 2020

Conical structures towards nanometer length scales are attractive for numerous applications including super-hydrophobic and electrocatalytic materials. Among the various methods of synthesizing arrays of micro- and nano-cones, electrochemical deposition techniques have been widely applied. We aim at enhancing the conical growth during deposition by applying an external magnetic field. Most of the magnetic field effects can be attributed to the Lorentz force and the magnetic gradient force [1]. If the magnetic field imposed on the electrochemical cell is well designed, the magnetic forces can generate an electrolyte flow which brings fresh electrolyte towards the tip of a cone, so that the local mass transfer would be enhanced and the conical growth would be supported.
We first performed analytical and numerical studies of electrodeposition on diamagnetic (Cu) and ferromagnetic (Fe) cones of mm size under the influence of a homogeneous vertical magnetic field. The beneficial structuring effects of the Lorentz force has already been shown for the Cu cone case [2]. The magnetization of the Fe cones causes additionally a strong magnetic gradient force near the cone tips and gives rise to a flow that can bring enriched electrolyte to the conical cathode. As the cathodes are placed at the bottom of the electrochemical cell, solutal buoyancy tends to bring upwards lighter electrolyte from the conical cathode and thus counteract the downward flow caused by the magnetic forces. Our results show that for the Cu cones, the Lorentz force becomes smaller than the buoyancy force after the first few seconds of the deposition, while the magnetic gradient force in case of the Fe cones keeps surpassing the buoyancy during the deposition.
Next, scaling studies on cones of sizes ranging from millimeter to micrometer allow to deliver insights into the magnetic field assisted electrodeposition towards micro- and nano-cones. As the cone size shrinks, the geometrical inhomogeneity decreases, and the current density gets more uniformly distributed on the cone, which is making the conical growth more difficult. Furthermore, the beneficial flow forced by the magnetic field near smaller cones suffers from higher wall friction. But this can be partially compensated by the larger magnetic gradients existing at smaller Fe cones, and the flow caused by the magnetic gradient force was found to decrease more slowly than the flow caused by other forces with the decreasing cone size. Such scaling behavior of the flow velocity corresponds well with a theoretical analysis of the Navier-Stokes equation. For a Fe cone with a radius of 10 micron under study here, the magnetic gradient force generates a beneficial downward flow with a velocity of about 5 micron per second. But in general the structuring effects during the deposition is much weaker than at larger length scales.
This work shows the potential of using the magnetic gradient force for growing ferromagnetic conical structures during electrodeposition. Optimization possibilities for conical growth at smaller scales by e.g. enhancing the cell current, applying stronger magnetic fields and pulsed electrodeposition will also be discussed.
References
[1] Mutschke, G.; Tschulik, K.; Weier, T.; Uhlemann, M.; Bund, A.; Fröhlich, J. Electrochim. Acta
2010
, 55, 9060-9066.
[2] Huang, M.; Marinaro, G.; Yang, X.; Fritzsche, B.; Lei, Z.; Uhlemann, M.; Eckert, K.; Mutschke G. J. Electroanal. Chem.
2019
, 842, 203-213.

Figure 1