Direct Energy, 2018a

9 BATTERIES AND FUEL CELLS 207
Both electronegativity dened by Eq. 9.3 and Mulliken electronegativity
dened by Eq. 9.1 have the same units. However, multiple other
denitions of electronegativity can be found in the literature. One of the
oldest denitions is due to Pauling in 1932 [134], and that denition is
measured instead in the units of square root of joules on a relative scale.
Reference [135] expanded on Pauling's denition to show variation with
ionization state and atom radius. Reference [133] also contains a dierent
denition of electronegativity also with its own units.
9.2.4 Chemical Hardness
Chemists sometimes use the term hardness when semiconductor physicists
would use the term half the energy gap. Chemical hardness has nothing to
do with mechanical hardness. As with electronegativity, there are multiple
related denitions of hardness. The Mulliken hardness is dened as [131]
Mulliken hardness = I ioniz − A aff
2
. (9.5)
A more careful denition of chemical hardness is [131] [136, p. 93]
(
∂μchem
)∣
∣∣∣V,S,
. (9.6)
hardness = 1 2
∂N
It is half the change in chemical potential for the next electron, and qualitatively
it is represented by half the energy gap. As with electronegativity,
it is specied for a given potential in volts around the atom and a given
entropy. Liquids may be classied as hard or soft. Hard acids and hard
bases have large energy gaps, so they are electrical insulators. Soft acids
and soft bases have small energy gaps, so they are electrical conductors. No
additional variable will be introduced for hardness because this quantity
can be represented by half the energy gap, E g
2 .
9.2.5 Redox Potential
Redox (from REDuction-OXidation) potential V rp is yet another measure
used by chemists to describe the ability of electrons to be ripped o their
atoms and ow in the presence of an applied voltage, nearby chemical, optical
eld, or other energy source. As dened above, the process of ripping
o electrons is called oxidation. The process of gaining electrons is called
reduction. Together, they form redox reactions. Instead of being measured
in joules like electronegativity, it is measured in volts where a volt is a joule
per coulomb. Redox potential represents the energy stored in a chemical