Electrochemistry Lecture 3 Flashcards
What action must occur in order for an electrochemical cell to run?
For an electrochemical cell to run, the reactant/products of the reaction need to be transported to/away from the electrode.
What are the different modes of transfer in an electrochemical cell
They are depicted in the reader
- Diffusion: Diffusion occurs whenever there is a concentration difference between the electrode interface and the bulk solution. It arises from the natural movement (random thermal motion) of the dissolved species without the effects of an electric field.
- convection: Mass transport by convection arises from the Movement of the fluid in which the species exist. Here
we can distinguish between forced and natural convection, where with forced convection the fluid is set in motion by an external source, while with natural convection the fluid is put in motion due to density differences (arising from temperature gradients). - Migration: Migration is the mode
of transport that only applies to charged species, as this mode of transport results from the charged species moving due to the electric field caused by the (applied) potential of the system.
why is understanding different modes of transport important
Understanding mass transport in an electrochemical cell is of importance as a shift in potential will cause a change in electroactive species near the electrode (as they are consumed or produced by the reaction)
What is diffusion described by (which laws)?
The rate of diffusion is described by Fick’s first and second law.
What is Fick’s first and second law?
Fick’s law describes the relationship
between the flux of a species and its concentration gradient. It tells us that the rate at which a substance moves through a medium is proportional to how steep the concentration gradient is.
Fick’s first law states the diffusive flux (Ji, the amount of species moving through a unit area per unit time) is proportional to the negative of the concentration gradient (species move area of high concentration to areas of low concentration):
Shown in written notes (on notebook paper)
Fick’s second law describes the change in the concentration of species with respect to
time:
Shown in written notes (on notebook paper)
What is the derivation of Fick’s first and second law?
In the reader!
A quick note about Fick’s First and second laws?
The equations have been written for a
Cartesian coordinate system in which only
the x-axis is considered (1-D). Depending on your coordinate system the concentration profile can vary quite significantly. The equations can be generalized for all coordinate systems using the Laplacian operator :
As shown in written notes
A table in the reader shows how the Laplacian operator can be interrupted in different coordinate systems
How is current related to the flux?
The flux can also be directly related to the current density. Consider the scenario where the electroactive species Ox is transported solely by diffusion to an electrode, where it partakes in the following reaction:
Red –> Ox + vₑ + e-
If no other electrode reactions occur, then the current is related to the flux of Red at the electrode surface (x = 0) by the following equation:
Shown in written notes
What is limiting current?
When investigating the effects of mass transport on the electrochemical behavior of a cell it is important to define the limiting current density (or limiting current). The limiting current density is the maximum current density that can be achieved in the cell. At the limiting current density, the rate of electrochemical reaction at the electrode surface is entirely controlled by the transport of reactant species to the electrode. This means that the exact amount of species consumed at the electrode is equal to the amount that can be transported to the electrode via diffusion, migration, and convection. At the
limiting current density the concentration of the reacting species at the electrode is 0.
What is the equation for the diffusion limiting current (Cottrell equation)
The diffusion limiting current density for a planar electrode can be derived under the
assumption that a potential step is applied at time t = 0. Prior to t=0, no reaction is
occurring. The potential applied is of a value where all electroactive species that reach the electrode react immediately.
In the system considered all transport occurs via diffusion. As such, the application of a potential gives rise to a diffusion-limiting current, whose value
varies with time. This diffusion-limiting current density (J(l,d) ) is described by the Cottrell equation shown in written notes
What are the two extreme cases of the Cottrell equation for spherical electrodes?
- When is small, the second term in the cylindrical Cottrell equation can be
neglected. Diffusion at a sphere can be treated as linear diffusion. - When is large, the spherical term dominates, which presents a steady state current. However due to natural convection, this steady state is never reached in conventional electrodes. The smaller the electrode radius the faster the steady state is reached
What does the Cottrell equation tell us
The equation shows that the current decreases with time (as shown in the reader). As such we cannot be confident in
the experimentally measured current after a certain time, owing to contributions arising from natural convection, etc. which perturb the concentration gradients. The time threshold for this can vary from mere seconds to several minutes depending on the system’s arrangement.
What is the diffusion layer?
The diffusion layer is an approximation that simplifies the complex interactions occurring at the electrode-electrolyte interface. it is often a large simplification to make as in real systems, factors such as
convection, migration and the intrinsic nature of the electrochemical reaction can all affect the concentration gradients. However, it is reasonable to assume the diffusion layer to hold when working under steady-state conditions in systems in which diffusion is the dominant mode of transport.
often a linear concentration profile is
assumed within the diffusion layer (shown in the reader), with the concentration at the boundary of the diffusion layer being the bulk concentration. Outside the diffusion layer, the concentration is always the bulk concentration. The equation form is shown in written notes
What simplification can we make to the limiting current density using the diffusion layer?
Shown in written notes
What is the equation that relates the Current Density and Concentration at the Electrode
In written notes and derivation in digital notes!
What is the equation for the convective and migrative flux?
Shown in written notes
How do you prevent convection from occurring?
Convection can occur due to temperature and pressure gradients, and due to movement of a setup. To prevent convection from occurring in an electrochemical cell during experiments,
electrochemists need to control the temperature in the setup (in particular prevent thermal gradients from appearing) and the setup needs to be kept as still as possible.
How do you prevent migration from occurring?
To neglect migration electrochemists ensure to use supporting electrolyte in their system. The use of the supporting electrolyte does not negate migration on the entire system, but it decreases the effects it has on the species of interest. The supporting electrolyte increase the ionic strength of the solution, which reduces the contribution of any single ions to the total ion concentration much smaller, which then reduces the effect of the electric field on the target species
Break moment
Now we will go into overpotentials where the story they are trying to get to is that the overpotential we learned in the last lecture from the Butler-Volmer equation is not the only overpotential we have there is more that defines our system. That is the main story we are telling. I’m saying it now so we don’t get confused
How does a plot of potential versus the current based on the Butler- Volmer equation look like?
Shown in the reader:
When plotting the potential versus the current based on the Butler-Volmer equation, we observe that the potential levels off at a certain point. This means that, beyond a certain point, one could significantly increase the current density with only minor increases in potential—up until the asymptote, where one would theoretically reach infinite current densities. However, this is not physically possible, as it would require an infinite supply of reactant species delivered at an infinitely fast rate.
Note that real potential curves do not look like that, Why?? Next FC
What do real potential curves look like?
Real potential-current density curves have a different shape from the one in FC 20. This is because activation overpotential is only one of the three main overpotentials that typically occur in an electrochemical cell. The other two are the Ohmic overpotential and the mass transfer overpotential. This is depicted in the reader!
When is activation overpotential dominant?
The activation overpotential arises from the kinetics at the electrode. The activation
overpotential is dominant at lower current densities. This overpotential can be described for the anode and cathode separately using the equations derived in the last chapter
When is ohmic overpotential dominant and how do we calculate it?
At intermediate current densities the ohmic overpotential becomes more dominant. The ohmic overpotential arises from Ohmic resistances in each of the cell components that make up the electrical circuit. This can be electronic resistances (resistance to the flow of electrons through the conductive materials in the cell such as the electrodes and wiring), ionic resistance (arising from the flow of ions through the electrolyte) and contact resistances. The ohmic overpotential can then be determined as shown in written notes.
When is mass transfer overpotential dominant and how do we calculate it?
At high current densities, the mass transfer overpotential (also often referred to as the
concentration overpotential) becomes dominant. The mass transfer overpotential arises from limitations in the mass transport of the reactants towards the electrode and the product away from the electrode. If the electrochemical reaction occurs at a faster rate than diffusion (or any other modes of mass transport) can replenish or remove species at the electrode, a concentration gradient forms, leading to a non-ideal, slower reaction rate and an associated overpotential. This mass transfer overpotential can be determined using the equation shown in written notes and derivation in the reader
