Interferometric characterization of growth dynamics during dendritic electrodeposition of zinc

Chemotaxis migration and morphogenesis of living colonies

Development of forms in living organisms is complex and fascinating. Morphogenetic theories that investigate these shapes range from discrete to continuous models, from the variational elasticity to time-dependent fluid approach. Here a mixture model is chosen to describe the mass transport in a morphogenetic gradient: it gives a mathematical description of a mixture involving several constituents in mechanical interactions. This model, which is highly flexible can incorporate many biological processes but also complex interactions between cells as well as between cells and their environment. We use this model to derive a free-boundary problem easier to handle analytically. We solve it in the simplest geometry: an infinite linear front advancing with a constant velocity. In all the cases investigated here as the 3 D diffusion, the increase of mitotic activity at the border, nonlinear laws for the uptake of morphogens or for the mobility coefficient, a planar front exists above a critical threshold for the mobility coefficient but it becomes unstable just above the threshold at long wavelengths due to the existence of a Goldstone mode. This explains why sparsely bacteria exhibit dendritic patterns experimentally in opposition to other colonies such as biofilms and epithelia which are more compact. In the most unstable situation, where all the laws: diffusion, chemotaxis driving and chemoattractant uptake are linear, we show also that the system can recover a dynamic stability. A second threshold for the mobility exists which has a lower value as the ratio between diffusion coefficients decreases. Within the framework of this model where the biomass is treated mainly as a viscous and diffusive fluid, we show that the multiplicity of independent parameters in real biologic experimental set-up may explain varieties of observed patterns.

Electrochemical synthesis of dendritic zinc films composed of systematically varying motif crystals

Polycrystalline zinc films with new dendritic frameworks were electrodeposited from nonaqueous formamide media containing 0.01-0.3 M Zn(ClO4)2.6H2O as the Zn2+ source and 0.1 M LiClO4.3H2O as the supporting electrolyte. Formamide media offer a wider range of deposition temperatures and deposition potentials than aqueous solutions, which provides a higher degree of freedom in creating new polycrystalline architectures. The growth patterns of zinc crystals could be precisely controlled (e.g., faceted growth and dendritic growth) by changing the interplay between the growth rate and the mass transport rate. The effect of deposition potential, temperature, and Zn2+ concentration on the onset potential of dendritic growth and the detailed dendritic features were studied systematically. The zinc dendrites obtained in this study were composed of submicron-sized crystals of a uniform shape (motif crystals) that grow repetitively fused together to form three-dimensionally dispersed dendritic backbones. This unique organization achieves a remarkable physical and electrical continuity between crystals while generating high surface areas, which is difficult to accomplish simultaneously in polycrystalline films. The shape of motif crystals can be finely tuned from hexagons to fern-shaped leaves by the deposition potential applied, which in turn alters the overall degree of branching of dendritic backbones. Cyclic voltammetry of the resulting zinc electrodes with various growth patterns was carried out and discussed in conjunction with the films' morphological variation.

Influence of ohmic heating on the flow field in thin-layer electrodeposition

In thin-layer electrodeposition the dissipated electrical energy leads to a substantial heating of the ion solution. We measured the resulting temperature field by means of an infrared camera. The properties of the temperature field correspond closely with the development of the concentration field. In particular, we find that the thermal gradients at the electrodes act similar to a weak additional driving force to the convection rolls driven by concentration gradients.

Transition from gravito- to electroconvective regimes in thin-layer electrodeposition

The transition from gravitoconvective to electroconvective prevailing regimes in thin-layer electrochemical deposition is analyzed through variations of electrolyte viscosity at constant cell thickness. The distribution of velocity directions at the deposit front is a measure of the relative weight of electroconvection versus gravitoconvection, and a signature of that transition. The experiments are carried out under galvanostatic conditions in convection prevailing regimes. Particle image velocimetry reveals that at low viscosities, buoyancy driven convection dominates; as viscosity increases, electrically driven convection becomes more important, eventually prevailing. The transition is observed at 1.5 times the viscosity of water. The theoretical model presented reveals that an increase of the Poisson and Reynolds numbers and a decrease of the Peclet and electric Grashof numbers, when viscosity increases, makes the electroconvective motion relatively more important. The model predicts a transition at approximately two times the viscosity of water. We may conclude that, in a physicochemical hydrodynamic flow involving ions, under galvanostatic conditions, increasing viscosity damps gravitoconvection and enhances electroconvection.

Experimental investigation of the initial regime in fingering electrodeposition: dispersion relation and velocity measurements

Recently a fingering morphology, resembling the hydrodynamic Saffman-Taylor instability, was identified in the quasi-two-dimensional electrodeposition of copper. We present here measurements of the dispersion relation of the growing front. The instability is accompanied by gravity-driven convection rolls at the electrodes, which are examined using particle image velocimetry. While at the anode the theory presented by Chazalviel et al. [J. Electroanal. Chem. 407, 61 (1996)] describes the convection roll, the flow field at the cathode is more complicated because of the growing deposit. In particular, the analysis of the orientation of the velocity vectors reveals some lag of the development of the convection roll compared to the finger envelope.

Internal structure of dense electrodeposits

We report experimental investigations of the structure of dense patterns obtained during electrochemical deposition of copper in thin cells. The deposit correlation function reveals the periodic structuration of the patterns but shows that the primary spacing is not steady during the growth and that moreover it is not simply related to the diffusion length. Another measurable quantity is the occupancy ratio of the fingers in the cell. Its variation as a function of the experimental parameters is interpreted from specific properties of electrochemical growth. The results are discussed with respect to the well-known behavior of cellular solidification fronts.