Chapter 4 - Kinetics and thermodynamics Flashcards
What are the possible kinetic limitations (of electron transport) to the current in a battery?
1) Electrons in metal contact (Ohmic resistance)
2) Electrons in a network of conductive additive (percolation and tunneling)
3) Electrons in active material (semiconductor/insulator/metal)
4) Electrons through binder / SEI (thermionic activation, tunneling, hopping transport)
5) Electrons over interfaces (Schottky barriers, defect assisted tunneling)
6) Electrons through separator (shouldn’t be any)
7) Electrons in electrolyte (shouldn’t be any)
What are the possible kinetic limitations (of ion transport) to a current in a battery?
1) Ions in electrolyte (diffusion, drift, tortuosity)
2) Ions in active material (diffusion, nearest neighbour interactions, trapping, 2-phase reaction)
3) Ions over interfaces (thermionic activation, three-state reaction of electron/ion(atom)
4) Ions through SEI (hopping, multiple ionization levels)
What is the equilibrium/open circuit voltage of a cell?
It is the difference in chemical potential between the electrodes.
What is the overpotential of the cell?
The overpotential is the voltage change needed to go from equilibrium to actually seeing a current.
What is the source of overpotential?
When we charge a battery, we add electrochemical energy inside the battery. Some of our effort is lost as heat.
Similarly, when the battery does work on the outer circuit, some of the electrochemical energy is lost as heat.
What is hysteresis?
The hysteresis is the ‘history’ of the cell. When cycling a battery, we charge and discharge with constant current. The exact measured voltage is thus dependent on the history (are we charging or discharging?)
What would hysteresis purists count as hysteresis?
Some would only count the systems where the reaction pathway is different in both directions. E.g. a 2-phase reaction in the active material.
Others limit the term to only describe systems where kinetic limitations in the material leads to different phases of the material being involved in the two reaction directions.
What are the four different contributions to the overall overpotential?
1) Thermodynamic overpotential. Due to the activiation barrier. Will be slightly dependent on temperature, not on current.
2) Charge transfer overpotential. Exponential increase with current until it is no longer the limiting mechanism.
3) Ohmic overpoential. Gives a linear current-voltage curve until the current density is so high that…
4) Concentration overpoential. …. the ionic diffusion can no longer maintain the ion concentrations near the interface.
What is the C-rate?
The C-rate is a materials specific current density. It is the current density where the entire capacity of the battery is spent in one hour.
Describe the GITT / PITT technique.
GITT - Galvanostatic Intermittent Titration Technique.
We run the current at constant current for a short while (ie. a given charge), then relax the system and measure the equilibrium voltage.
PITT - Potentiostatic Intermittent Titration Technique
We increase the voltage stepwise. We then first get a rapid current increase, then it slows.
How can we measure the loss associated with charge and discharge from GITT / PITT measurements?
The area under the curve vs. the equilibrium voltage profile would represent energy being lost for us.
Explain dQ/dV
dQ/dV is the “density of states” from a galvanostatic plot. We plot the number of electrons extracted at the different voltage levels.
Explain cyclic voltammetry
Gives the same visual representation of voltages where electrochemical activity occur, but is done with a constant voltage sweep rate (instead of constant current, as in dQ/dV).
In a CV-plot there might be shifts of the peaks in the top and bottom lines. Why is this?
The different lines depend on the way we are cycling (lithiation / delithiation). The same peaks should be in both lines (for reversible reactions), but due to overpotential these peaks can be shifted relative to each other.
Explain impedance spectroscopy
In impedance spectroscopy, we probe the response of the battery to AC-signals of different frequencies.
At different frequencies, different phenomena is measured. At very high frequencies, electron transport is measured (change is too fast for ions).
At very low frequency, electron transport is in a steady state, while ion transport limits the system.
We can model the battery as an equivalent circuit to fit the data to get information about resistance, capacitance and inductance in different sections of the battery. However, we can always overfit, so these results can be dubious.
What can we say that temperature is a measure of, in terms of probabilities of occupying high energy states?
It is a measure of how unlikely it is that many low-energy states combine to give one high energy state.
What is entropy?
Entropy is a way of counting the number of available system configurations. It is defined as the natural logarithm of the multiplicity.
What is the multiplicity of the system?
The number of configurations of a given system.
What is thermal equilibrium?
The situation when the flow of energy from electrons to phonons and from phonons to electrons is equally likely.
This is when the total number of states allowed by the energy distribution is at a maximum.
Why is the entropy, defined as the logarithm of the multiplicity, a good definition for a quantity that determines the equilibrium?
Because it works out nicely mathematically. The equilibrium between two system occurs when the multiplicity is maximised, and the total derivative is 0:
g_tot = g_1*g_2
=> dg_1/dE * g_2 - dg_2/dE * g_1 = 0
=> 1/g_1 * dg_1/dE = 1/g_2 * dg_2/dE
Since the derivative of a logarithm, d ln(g)/dg = 1/g and then d ln(g(E))/dE = 1/g* dg/dE, we see we can rewrite it
d ln g_1 / dE = d ln g_2 / dE
How is temperature defined from the entropy?
d ln g1 / dE = d S / dE = 1 / kT.
It can be interpreted as a typiucal unit of thermal energy. A phonon mode in a lattice or a kinetic or vibrational energy of a gas molecule.
How much energy does kT correspond to at room temperature?
About 1/40 eV.
How can we reach Boltzmann statistics from the definition of entropy and probabilities of finding an electron in a certain state?
If we have two states, a and b, the relative probability Pa/Pb of finding the electron in the two states is determined by how many different ways the phonons can rearrange in the two cases.
Pa/Pb = ga/gb = e^Sa / e^Sb = e^(Sa-Sb) = e^dS
If the energy difference between these are dE, then the entrop difference is:
dS = -dS/dE * dE = - dE/kT
So this gives us:
P(E + dE)/p(E) = e^-(dE/kT)
