Direct Energy, 2018a

9 BATTERIES AND FUEL CELLS 205
9.1, it is the vertical distance from the valence band or highest occupied
state to the ground state at the top of the gure. Sometimes chemists
call this amount of energy the work function instead [60, ch. 6] [108]. In
Fig. 9.1, the electron anity is represented by the vertical distance from
the conduction band or lowest unoccupied state to the ground state at the
top of the gure. The magnitude of the Mulliken electronegativity is the
average of these two energies, so it is the magnitude of the Fermi energy
at T =0K. By convention, it has the opposite sign.
χ Mulliken = −E f | T =0 K (9.2)
Fundamentally, electrical engineering is the study of ow of charges.
Chemistry is the study of the strength of chemical bonds. The electrical
conductivity of a material is high when the chemical bonds holding that
material together are easily brokenso that many free charges canow.
The electrical conductivity of a material is low when chemical bonds holding
atoms together require lots of energy to break. Electronegativity is a
measure of the energy required to break chemical bonds, so fundamentally,
it tells us similar information to electrical conductivity.
9.2.3 Chemical Potential and Electronegativity
Another way of dening electronegativity follows the denition introduced
by Pritchard in1956 [132]. This denitionis one of the more commonones,
and it is used by both chemists [131] [133] and by other scientists [2, p.
124.]. The electronegativity of anatom is dened as
( )∣ ∂U ∣∣∣V,S,
χ = −
(9.3)
∂N
where U is the internal energy relative to a neutral atom and N represents
the number of electrons around the atom. An atom is composed of a
charged nucleus and charged electrons moving around the nucleus, so there
is an electric eld, and hence an electrical potential V involts, around
an atom. This potential signicantly depends on the number of electrons
around the atom. Also, when the atom is at a temperature above absolute
zero, the electrons and nuclei are in motion, so the atom has some
entropy S. Electronegativity involves ∂U at constant electrical potential
∂N
and entropy. It applies whether the atoms are part of a solid, liquid, or
gas.
The chemical potential μ chem is dened as the negative of this electronegativity.
μ chem = −χ (9.4)