Mass Transfer Overpotential

One of the cases of the mass transfer overpotential is the diffusion overpotential. This overpotential is purely due to the Fickian diffusion. The current density, j, due to the Pick s first law of diffusion (one-dimensional case) is given as 

D is the diffusion coefficient of the aqueous electrochemically active species [e.g., Cu2+(aq)] 

Making a common approximation for (dc/dx) o Ac/ n, the current density can be connected to the difference between the bulk and surface concentrations, Ac, and the Nernst diffusion layer, 6,  

FIGU RE 6.9 Schematic of the concentration gradient of Cu- (aq) in the cathodic deposition of Cu(s) in unstirred solutions is the bulk concentration and f is the surface concentration. The numbers show the concentration gradients over time. Number 1 shows the initial time without any concentration gradient. Number 3 shows the limiting case when the surface concentration of Cu +(aq) is zero. Number 2 is an intermediate case between Number 1 and Number 3. 

Let us consider the steady state. In such a state for an unstirred solution, 8n can be on the order of 0.1 mm, and in the well-stirred solution, it can be as small as 10 mm. 

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Except for the need to take concentration overpotential into account in electroanalytical studies, it is an important factor for energy losses in electrochemical power sources (e.g., in -> batteries, fuel cells, etc.) and -> electrolysis (e.g., in electrochemical materials production, -> electroplating, etc.). Concentration overpotential is called also concentration polarization and mass transfer overpotential. 

Mass-transfer overpotential results from a finite mass-transfer rate from bulk electrolyte to electrode or vice versa. If the system is mass-transfer controlled, a limiting current density exists. The limiting current density is the maximum reaction rate under mass-transfer control. It increases as the concentration of the reacting species, their diffusion rate, temperature, or flow rate increase. In a system with limiting current density, the overpotential follows Eq. (12). The overpotential increases very rapidly when approaching the limiting current density. 

While the combination of the apphed current and current efficiency in an electrochemical reactor is a measure of the overall rate of product output, it is the product of the current and cell voltage that will determine the reactor s electrical power consumption, as indicated by Equation (26.103). The overall voltage in an electrochemical reactor is composed of the following components (1) thermodynamic cell potential, (2) anode kinetic and mass transfer overpotentials, (3) anolyte IR drop, (4) diaphragm/membrane IR drop, (5) catholyte IR drop, and (6) cathode kinetic and mass transfer overpotentials. For more information on each of these terms, the reader should refer to Section 26.1. 

Each value of current density, j, is driven by a certain overpotential, 17. This overpotential can be considered as a sum of terms associated with the different reaction steps r/mt (the mass-transfer overpotential), (the charge-transfer overpotential), (the overpotential associated with a preceding reaction), etc. The electrode reaction can then be represented by a resistance, R, composed of a series of resistances (or more exactly, impedances) representing the various steps R i, R, etc. (Figure 1.3.7). A fast reaction step is characterized by a small resistance (or impedance), while a slow step is represented by a high resistance. However, except for very small current or potential perturbations, these impedances are functions of E (or /), unlike the analogous actual electrical elements. 

Mass-transfer overpotential results from a finite mass-transfer rate from bulk... 

When a load is applied to the fuel cell and the current flows through the circuit, the active overpotential from the kinetics of charge transfer reactions, the ohmic overpotential from component resistances, and the mass transfer overpotential from the limited rate of mass transfer will rise. The Butler-Volmer Equation (Equation 23.8) describes a relation between the overpotential and the eurrent density on an... 

Charge transfer Mass transfer Others Cell/electrode geometry Charge Electrode and transfer over- electrolyte potentials conductivity Mass transfer overpotential Others ... 

Substituting Equation 5.140 into Equation 5.131 and identifying the limiting current density for cathode as ji, we have the mass transfer overpotential for cathode as... 

Similarly for anode, the mass transfer overpotential is written as... 

For fuel cell, the limiting current density for anode is 20 A/cm and that for the cathode is 2 A/cm. Assuming single electron transfer reaction steps both at anode and cathode, determine the mass transfer overpotential for anode and cathode if the fuel cell is operating at 80°C with a fuel cell current density of 1.5 A/cm. ... 

Two main contributions to the overpotential will be discussed in this book in some details. The first one is the charge (electron) transfer overpotential, which is due to a particular rate of the electrochemical reaction and takes place just at the electrodesolution interface. The second one is the mass transfer overpotential, which is due to delivering reactants to the electrochemical reaction interface or due to transporting products to the bulk solution. Other physicochemical processes taking place in the Nernst diffusion layer (e.g., chemical reactions and adsorption/desorption) can also contribute to the electrode overpotential, but they will not be discussed in this book. Note that chemical reactions occurring in the bulk solution should be taken into account to correctly estimate the concentration of the reduced, / buik nd oxidized, Obuik. species. 

The mass transfer overpotential can be calculated using experimental data in the case of the Fickian diffusion of the electrochemically active species. If the concentrations of the electrochemically active species at the electrode surface and in the solution bulk are different, a concentration overpotential is developed. 

Multiple select For a polarized electrode only under the influence of a mass transfer overpotential, which parameters will change in value with changes in the Nernst diffusion layer ... 

The (th contribution to total overpotential on an electrode [V] Mass transfer overpotential on an electrode [V]... 

The position of the electrodes in the reactor can be optimized as a function of hydrodynamic parameters and current density (j). Complementary rules should include the influences of electrode gap (e) and operating conditions on voltage U (and consequently on energy consumption). The measured potential is the sum of three contributions, namely the kinetic overpotential, the mass transfer overpotential and the overpotential caused by solution ohmic resistance. Kinetic and mass transfer overpotentials increase with current density, but mass transfer is mainly related to mixing conditions if mixing is rapid enough, mass transfer overpotential should be negligible. In this case, the model described by Chen et al., (2004) is often recommended for non-passivated electrodes ... 

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