Mass transport current densities

The analysis of mass transfer in electrochemical cells requires the use of equations that describe the condition of electroneutrality (which applies for the entire elecnolyte outside the double layer at an electrode), species fluxes, mass conservation, current density, and fluid hydrodynamics. Often, mass transport events are rate limiting, as compared to kinetics processes at the electrode surface, in which case the overall electrode reaction rate is solely dependent on species mass transfer (e.g., during high-rate electroplating of some metals and for those elecnochemical reactions where the concentration of reactant in solution is low). 

Mass-Limiting Current Density We previously examined ohmic limiting current density. Now we consider the case of mass transfer hmiting current density U. At the mass transport limiting current density, the rate of mass transport to the reactant surface is insufficient to promote the rate of consumption required for reaction. In this case, the local concentration of reactant will be reduced to zero, which, from Eq. (4.84), must also reduce the cell voltage to zero. Assuming the surface concentration Cr) is zero at the limiting state (//)... 

The expression for the mass-transport-limiting current density may be employed together with the Nemst equation to deduce the complete current-potential response in a solution containing only oxidized or reduced species... 

The effects of ultrasound-enlianced mass transport have been investigated by several authors [73, 74, 75 and 76]. Empirically, it was found that, in the presence of ultrasound, the limiting current for a simple reversible electrode reaction exhibits quasi-steady-state characteristics with intensities considerably higher in magnitude compared to the peak current of the response obtained under silent conditions. The current density can be... 

Mass Transport. Probably the most iavestigated physical phenomenon ia an electrode process is mass transfer ia the form of a limiting current. A limiting current density is that which is controlled by reactant supply to the electrode surface and not the appHed electrode potential (42). For a simple analysis usiag the limiting current characteristics of various correlations for flow conditions ia a parallel plate cell, see Reference 43. 

Inside a pit in electrolytic solution, anodic dissolution (the critical dissolution current density, and diffusion of dissolved metal hydrates to the bulk solution outside the pit take place simultaneously, so that the mass transfer is kept in a steady state. According to the theory of mass transport at an electrode surface for anodic dissolution of a metal electrode,32 the total increase of the hydrates inside a pit, AC(0) = AZC,<0),is given by the following equation33,34 ... 

The net reaction is the transfer of C02 at a rate close to 1 mole per 2 Faradays, and the production of water. The process is quite complex the detailed analysis showed that cathode-side, gas-phase mass transfer of C02 was totally controlling only at the lowest C02 levels and high current densities. At other conditions chemical reaction rates and transport through the membrane became important representative results... 

Therefore, criteria in the selection of an electrode reaction for mass-transfer studies are (1) sufficient difference between the standard electrode potential of the reaction that serves as a source or sink for mass transport and that of the succeeding reaction (e.g., hydrogen evolution following copper deposition in acidified solution), and (2) a sufficiently low surface overpotential and rate of increase of surface overpotential with current density, so that, as the current is increased, the potential will not reach the level required by the succeeding electrode process (e.g., H2 evolution) before the development of the limiting-current plateau is complete. 

A complete dissolution of the oxide at the rate corresponding to extreme current densities in the pits seems very unlikely since it would have to involve too much mass transport inside the pinholes. 

On the submicron scale, the current distribution is determined by the diffusive transport of metal ion and additives under the influence of local conditions at the interface. Transport of additives in solution may be non-locally controlled if they are consumed at a mass-transfer limited rate at the deposit surface. The diffusion of additives in solution must then be solved simultaneously with the flux of reactive ion. Diffusive transport of inhibitors forms the basis for leveling [144-147] where a diffusion-limited inhibitor reduces the current density on protrusions. West has treated the theory of filling based on leveling alone [148], In his model, the controlling dimensionless groups are equivalent to and D divided by the trench aspect ratio. They determine the ranges of concentration within which filling can be achieved. 

In the current-voltage curve in Fig. 14.15, three different regions can be discerned. At low current densities, the performance is kinetically limited. In the linear part, ohmic losses are significant. At high current densities, mass transport losses dominate. 

Little is known about the mechanisms that cause the three other current extrema ]2 to J4. The kinetic and diffusional contributions of the characteristic currents Ji to J4 show a different concentration dependence. While the diffusion current is found to be roughly proportional to Cp, the kinetic current shows an exponent of 2 < <2.5 [Ha3]. No dependence of the characteristic currents to ]4 on doping kind and density is observed. This indicates again that to ]4 depend on mass transport and reaction kinetics rather than on charge supply. For n-type electrodes, of course, strong illumination is necessary in order to generate a sufficient number of minority carriers to support the currents. 

It should be emphasized that n.. and JPS, and therefore c and T, refer to the condition at the pore tip. The dissolution valence and the temperature can be assumed to be independent of pore depth. This is not the case for the HF concentration c. Because convection is negligible in macropores, the mass transport in the pore occurs only by diffusion. A linear decrease in HF concentration with depth and a parabolic growth law for the pores according to Pick s first law is therefore expected, as shown in Fig. 9.18 a. The concentration at the pore tip can be calculated from the concentration in the bulk of the electrolyte c, the pore length l, the diffusion coefficient DHf (Section 1.4) and the flow of HF molecules FHf. which is proportional to the current density at the pore tip ... 

The experimental optimization of Nafion ionomer loading within a catalyst layer has attracted widespread attention in the fuel cell community, mainly due to its critical role in dictating the reaction sites and mass transport of reactants and products [15,128-134]. Nafion ionomer is a key component in the CL, helping to increase the three-phase reaction sites and platinum utilization to retain moisture, as well as to prevent membrane dehydration, especially at low current densities. Optimal Nafion content in the electrode is necessary to achieve high performance. 

The EOD coefficient, is the ratio of the water flux through the membrane to the proton flux in the absence of a water concentration gradient. As r/d,3g increases with increasing current density during PEMFC operation, the level of dehydration increases at the anode and normally exceeds the ability of the PEM to use back diffusion to the anode to achieve balanced water content in the membrane. In addition, accumulation of water at the cathode leads to flooding and concomitant mass transport losses in the PEMFC due to the reduced diffusion rate of O2 reaching the cathode. 

In PEMFCs, Ralph et al. [86] tested a Ballard Mark V single cell with two different DLs a carbon cloth (Zoltek PWB-3) and a carbon fiber paper (Toray TGP-090) all the other operating conditions stayed the same for bofh cases. It was observed that the carbon cloth demonstrated a distinct advantage over the CFP at high current densities (>600 mA/cm ), while at low current densities both DLs performed similarly. If was claimed fhaf this was because the CC material enhanced mass transport properties and improved the water management within the cell due to its porosity and hydrophobicity. 

In order to improve the performance of fuel cells, Wilkinson and St-Pierre [92] and Johnson et al. [93] compared typical CFP cathode DLs with modified DLs (from CFP or CC) that improved the mass transport at high current densities. Figure 4.14 shows the different DLs that were used to improve the cell s performance. Similar strategies can be implemented in other types of DLs, such as metallic or engineered. 

Prasarma et al. [185] were also able to observe an optimum thickness of DLs for fuel cells experimentally. They demonstrated that the thicker DLs experience severe flooding at intermediate current densities (i.e., ohmic region) due to low gas permeation and to possible condensation of water in the pores as the thickness of the DL increases. On the other hand, as the thickness of the DL decreases, the mass transport losses, contact resistance, and mechanical weakness increase significantly [113,185]. Through the use of mathematical modeling, different research groups have reported similar conclusions regarding the effect of DL thickness on fuel cell performance [186-189]. 

Issues with mass transport resistance, especially at higher current densities, represent an important hurdle that fuel cells need to overcome to achieve the required efficiencies and power densifies that different applications require. Diffusion layers represenf one of fhe major fuel cell components that have a direct impact on these mass transport issues thus, optimization of the DLs is required through the use of differenf experimental and characterization techniques. 

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