Amplification of Surface Roughness

Amplification of existing surface irregularities is a general phenomenon observed in metal deposition from pure metal salt solutions it is the more pronounced the higher is the rate of deposition, and the lower is the concentration of metal ions in solution. 

Kritchmar was the first to point out that this is to be expected in prolonged cathodic reduction for conditions close to those of complete diffusion control of the deposition process. 

The reasons for the faster deposition at elevations are that a shorter diffusional path exists between the surface where the deposition takes place and the outer plane of the diffusion layer, than in the case of the recess, and also in the fact that, at tips of elevations, conditions of diffusion are approaching those of spherical diffusion which is always faster than the linear one, because of the wider diffusional field. 

At the flat part of the surface, the diffusion-limiting current density, in the case of steady state linear diffusion, is 

At the side of an irregularity any point at a distance x from the flat part of the surface is closer to the diffusion layer boundary by y (jc) than any point at the flat part of the surface. Hence, the diffusion-limiting current is correspondingly larger, i.e.. 

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An important consequence of the amplification of surface roughness at a constant overpotential is the change of the apparent current density (per unit geometric surface area of the electrode) with time. This was first observed and explained in a qualitative manner by Ibl and Schadegg. ... 

The exponential character of the time dependence indicates that the latter can be divided into two periods for some time after switching on the cathodic overpotential, no change should be observed either in surface roughness or in current. Then a sudden change should appear in both. The first period in phenomena of similar character is termed the induction time. In this case, and based on the above model, the induction time of the amplification of surface roughness could be derived as... 

The basic cause for the appearance of dendrites is the same as that for the amplification of surface roughness, i.e., the formation of a diffusional field of depositing ions, favoring protrusions developing in the direction of increasing concentration. There are, however, three basic differences which make for the specific appearance of dendritic deposits ... 

Hence, there is little doubt that the reasons behind powder formation are the same as those for the amplification of surface roughness or the formation of dendritic deposits, i.e., propagation of metal particles depositing under transport control, up the concentration gradient toward solutions ever richer in depositing species. 

In some electrolytes (e.g., phosphoric acid) an effect opposite to amplification of surface roughness is found upon anodic dissolution, i.e., the surface becomes increasingly smooth, until a mirrorlike finish is achieved. This phenomenon has been widely used for practical purposes of electropolishing, since the work of Jacquet in 1936. ... 

A quantitative treatment, essentially similar to that of amplification of surface roughness, results in an exponential decrease in the amplitude of the surface profile, viz.. 

An effect opposite of amplification of surface roughness, yet under similar conditions of plating, has been known to occur when specific substances are added to the electrolyte surface irregularities are increasingly buried within the deposit in prolonged cathodic deposition and smooth surfaces result. Early work of Meyer,Schmellenmeier, and Gardam showed that this effect of leveling is due to more rapid metal deposition at recesses than at elevated points of the surface. 

Figure 1 Contact angles on structured surfaces in the classic Wenzel (W) and Cassie-Baxter (C-B) states, respectively, where r is the physical amplification of surface area due to roughness and fs is the fractional area in contact with a L Adapted from Shirtdiffe etal.(2010).

The origin of the initial microroughness and the events leading up to its final amplification by mass-transfer limited deposition, have not been clarified definitively (P4a). It has been shown (I9a) that preliminary electropolishing, to assure a smooth surface, does not prevent surface roughness at... 

The collective excitation of the electron cloud of a conductor is known as a plasmon, if the excitation is confined to the surface of the conductor it is known as a surface plasmon. For the excitation of surface plasmons by light, surface roughness or curvature is required. The electromagnetic field of the light at the surface can be greatly increased when the surface plasmon is excited. This results in the amplification of both the incident and scattered and this is the basis of the electromagnetic SERS mechanism [15]. 

The physical reason why a slow-moving liquid jet breaks up into drops at some distance below the nozzle lies in the interaction between small-amplitude disturbances on the jet and surface tension, with subsequent high-gain amplification of the capillary perturbation. The initial disturbances may be a result of random excitations, such as jet friction or nozzle roughness, or they may be impressed on the jet. 

Hence, the maximum overpotential at which the slope of the apparent current density-time dependence remains constant and equal to that in non-dendritic amplification of the surface roughness corresponds to //j. The minimum overpotential at which this slope cannot be recorded corresponds to tjc-... 

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