Voltage of a Single-Phase Battery Electrode

Using the expressions for the chemical potentials in the negative (equation 4.24) and positive (equation 4.22) electrodes, we substitute them into equation (4.6) for the voltage:

V=1F(μLiμ“Li”)=1F[μLi metal0μ“Li”0RTlnX1X](4.25)V = \frac{1}{\mathscr{F}} (\mu_{\text{Li}} - \mu_{\text{“Li”}}) = \frac{1}{\mathscr{F}} \Bigl[ \mu^0_{\text{Li metal}} - \mu^0_{\text{“Li”}} - RT \ln \frac{X}{1-X} \Bigr] \qquad (4.25)

An example voltage plot is shown in Figure 4.10. Note that because of the logarithmic term (due to configurational entropy), the voltage diverges (tends to infinity) as X0X \to 0. In practical terms, it is impossible to completely remove all Li from the positive electrode (i.e. to charge a battery to 100%) because doing so would require an infinite amount of energy.

Colin Ophus Lab | StanfordColin Ophus Lab | Stanford
Understanding materials, atom by atom — Colin Ophus Lab
Lab Group Website by Curvenote