Chapter 2 - Basic physics and chemistry

Question 1

What is the main distinction between the physicist’s and chemist’s treatment of the same phenomena?

Answer 1

The perspective of one particle vs. the aggregate (mole),

Question 2

How much is one mole?

Answer 2

6.022 * 10^23 particles.

Question 3

What is the charge of one mole electrons?

Answer 3

Equal to the Faraday constant:

9.64 * 10^4 C per mol

Question 4

What is the charge of one electron?

Answer 4

1.60 * 10^-19 C

Question 5

How many joules is one electronvolt?

Answer 5

1 eV = 1.60*10^-19 J. Defined as the work done on an electron being accelerated through a potential difference of 1 V.

Question 6

What is the Boltzmann constant?

Answer 6

kb = 1.38*10^-23 J / K

Question 7

What is the gas constant?

Answer 7

R = kb*Na = 8.314 J / K mol

Question 8

What is the picture given of p- and d-electrons behaviour in batteries?

Answer 8

p-orbitals are mainly concerned with bonding due to larger spatial extent. This means that the d-orbitals are more free to be removed or added without ruining the bonding. Thus, when a Li-ion is removed, a d-electron from the transition metal can be given to the oxygen. If lithium is present, the d-electron can be given back to the metal.

Question 9

How does the energy required for adding an electron to the system vary?

Answer 9

It varies according to the interaction between the electron and the core of the particle (with some variations due to interactions with other electrons).

Inner shell is close to core, so they have a large interaction (and is thus very low in energy and very stable)

The more protons there are in the nucleus, the higher the attraction to it is. Thus the energy levels are lowered going towards the right.

The magnetic interaction with other electrons means that symmetric states with equal amounts of spin up and spin down are more stable. Full shell most stable.

Question 10

How can the electronegativity trends be explained?

Answer 10

Trend: smaller atom, higher electronegativity. Further to the right in the periodic table, higher electronegativity.

For smaller atoms, the distance to the core is lower. Thus higher interaction with core.

For atoms to the right in the periodic table, the core consists of more protons. Thus higher interaction with the core.

Question 11

What is the electropositivity of an element?

Answer 11

The tendency of an element to give away electrons. Conceptually equivalent with the ionziation energy of the element.

Question 12

Who introduced the terms cation and cathode?

Answer 12

Michael Faraday

Question 13

What happens to sodium metal in water?

Answer 13

The sodium takes the place of hydrogen in water. Hydrogen gas is thus evolved, along with heat, and the hydrogen is after some time ignited.

Question 14

Why can’t we use water as the solvent in electrolytes in Li-ion batteries?

Answer 14

Because the potential difference is so high that lithium will take the place of hydrogen in water and hydrogen gas is evolved.

Question 15

How does the transport of lithium ions in the electrolyte happen?

Answer 15

Negative ends of the electrolyte solvent molecule, typically EC (ethylene carbonate)n surrounds the Li-ion. The ends pointing away are more or less neutral, which gives them a fairly unhindered movement through the liquid. Problems occur when we reach the freezing point.

Question 16

What is the Ethiopian road analogy to band gaps?

Answer 16

Bumpy roads in Ethiopia - you would either have to drive so slow to not shake to pieces while driving from dump to dump, or drive so fast so that the car does not have time to fall into the valleys. Intermediate speeds will destroy the car and comfort.

Question 17

What does the energy of an electron in a band represent?

Answer 17

A mixture of the energy of the electron-nucleus interaction and the energy associated with the momentum of the electron.

Question 18

What is the Fermi level?

Answer 18

The energy level in the middle of the highest occupied and lowest occupied state at zero K.

If there is no external potential, this is equal to the work function.

Question 19

What happens to our view of bandstructure at the interfaces?

Answer 19

At the interfaces there are no longer any translational symmetry, and concepts such as wave number and momentum loses their meaning.

Also, the chemical composition is often different than the bulk material (having been terminated by oxygen or hydrogen for example). There can be dangling bonds or double bonds.

The region near the surface can see effects like band bending - this must be understood with solid state theory.

Question 20

What happens when two metals, one with high Fermi level and one with a lower Fermi level comes into contact?

Answer 20

There is a charge transfer from the high Fermi level material to the low Fermi level material, giving an excess positive charge in the high Fermi level material.

This gives rise to an electric field that counteracts movement of further electrons.

In the region of the space charge region we get band bending (in insulating materials and semiconductors). This does not necessarily happen if the width of the barrier is small enough for electrons to tunnel through. This band bending can be a problem as for Schottky barriers that lead to contacting problems.

Question 21

What is the solid-electrolyte interface?

Answer 21

It is the layer forming between the solid electrode (SEI is typically used to describe what happens at the anode) and the electrolyte.

Question 22

How is the solid-electrolyte interface formed?

Answer 22

Dangling bonds and chemical impurities give plenty of electron states that hold excess charge. Some ions will adsorb to the interface and accept an electron from the solid, leaving a charge.

Then the polar solvent molecules will adsorb to the surface to fit the net charge in the solid. This makes out the inner Helmholtz plane.

Outside this plane, a layer of solvated ions wrapped in solvent are attracted to the charge of the innermost layer. This is the outer Helmholtz plane.

Outside this there can be a diffuse layer with ions not having reached the surface yet.

Question 23

What is the electrochemical potential defined to be?

Answer 23

Electrochemical potential = Chemical potential + zF*electricstatic potential

z is the valency of the ion
F is Faraday’s constant

Question 24

What is the electrochemical potential a useful quantity for?

Answer 24

To estimate where the ions like to spend their time.

Question 25

Describe what happens to the electrochemical potential between a metal and an ion in solvent before and after equilibrium.

Answer 25

At first, the chemical potential will be different between the two. There is no net charge in either and there is no difference in the electrical potential. The electrochemical potential is higher the e.g. the metal just due to the difference in chemical potential.

After equilibrium, there has developed a space charge region. Ions from the metal will have moved to the solvent where the chemical potential is lower. There is then a charge build-up here. There is an excess negative charge that stayed behind in the metal. There will be field set up between the two that will eventually counteract the difference in chemical potential. This evens out the electrochemical potential.

Question 26

What are typical choice for inert electrodes?

Answer 26

Platinum, graphite and gold.

Question 27

How can we describe ions moving to and from reactive metal electrodes in a battery?

Answer 27

The ions will be positively charged - we can imagine that it will be repelled by a too low potential compared to to the electrolyte at the anode and attracted to a high potential compared to the electrolyte at the cathode.

Question 28

What determines the surface of a metal when it attracts a postively charged ion?

Answer 28

The surface tension and the mobility of the ion. The ion can either remaing in place where it first stuck, or it can move around to find an optimal spot. For the latter situation, this means that we can get a uniform plating (such as in electroplating).

It depends on the relative rates of ion transfer to the surface and mobility along the surface.

Question 29

What happens at the surface of lithium when ions are added?

Answer 29

Due to defects and different surface energies of crystal facets, some local bonding sites are more likely to be occupied. This leads to protrusion of the surface, and further increases the likelyhood of this surface relative to the root of the protrusion.

This leads to formation of dendrites.

Question 30

How can we describe ions moving to and from alloying electrodes (e.g. a silicon electrode) in a battery?

Answer 30

In alloying electrodes, the lithium will prefer to insert itself between the host atoms (such as Si). Li-Si bonds are stronger than Li-Li or Si-Si. Each Si atom can bond to four Li.

At the fully lithiated form, it is more closely Si dissolved in Li. It goes through a transformation from a semiconductor (pure Si) to a metal (Si dissolved in Li)

As more and more Li is inserted, the probability of Li finding Si to bond with decreases. It becomes more and more like Li inserting itself into pure Li (it makes it harder for us to force it in).

Question 31

How can we describe ions moving into graphite intercalation electrodes?

Answer 31

Li does not break interlayer C-C bonds in graphite, but inserts itself between the loosely bound layers (held together by vdW-forces).

One Li can insert itself per 6 C (each ring of C). This happens in stages. One Li going into a layer increases its width, and the next Li is likely to go into the same layer. The presence of Li in one layer means that when the layer is filled, the next Li is not likely to go into the adjacent layer. It will instead go into every fourth layer initially.

Question 32

How can we describe lithium ions moving into oxide electrodes?

Answer 32

A positive electrode should hold Li very hard (thus having a large potential compared to Li-metal). In metal oxides there are certain crystalline sites (holes) forming a percolating network where the Li can enter and diffuse through.

Question 33

Why do we not use LiF as a cathode?

Answer 33

Actually ideal due to the bond strength of Li-F-bonds. The potential required would be too high and decompose most other components.

Question 34

What is the difference in transport between olivine, layered materials and spinel structures?

Answer 34

Olivine has 1D-channels of ion transport.

Layered has 2D-sheets where ions can move.

Spinel has a 3D-network of ion sites.

Question 35

How does the cathode voltage profiles differ between olivine, layered materials and spinel structures?

Answer 35

Olivine - 1D transport, flat. There is little interaction between lithium atoms in the structure. One Li-state is not significantly modified by presence of other lithium.

Layered - 2D transport, sloped. More interaction between Li. As the layers get filled, the lithium ions move closer and the energy of the lithium states also rises. It becomes less attractive for lithium to enter the material, and the voltage decreases (during lithiation / discharge).

Spinel - 3D transport, stepped. In the start, it can fill out only the states where there is no neighbouring lithium. As these states are all filled, it has to insert itself into sites between occupied sites. This gives two plateaus.