# Battery application analysis and relative permittivity

1. Application analysis of Al/LiCoO2/electrolyte/MCMB/Cu battery:

Figure 1 is a LiCoO2 electrode (LiCoO2: conductive agent (high purity carbon black): PVDF = 94: 4: 4 mass percent), MCMB electrode (MCMB-20-28: PVDF = 92: 8 mass percent) and electrolyte Nyquist plot of the composed full cell. The graphs show different results using liquid and polymer electrolytes.

The mid-frequency region shows an incomplete semicircle and features a combination of electrodes with different resistance and capacitance values. Polymer electrolytes show higher resistance than liquid electrolytes.

1. Relative permittivity

The relative permittivity (εr) is an important characteristic parameter of the solvent, and the vacuum permittivity (ε0) is specified as 8.854 x10-12 F/m. As shown in Equation 1, ε0 is a constant that determines the force between charges q1 and q2 at distance r.

In a liquid dielectric, the force between the two particles is lower than in a vacuum state due to the interaction with the surrounding solute and solvent molecules. The value of the relative permittivity defined by Equation 2 is greater than one.

Based on the above definition, εr = 1 in vacuum state and εr >1 in liquid. εr is generally greater than 15-20 in polar solvents, but smaller in non-polar solvents.

To determine the dielectric constant, a cell as shown in Figure 4.42 can be built. The battery consists of two electrodes (A: contact area with the dielectric substance) with the dielectric substance placed between them (with an interval of L).

The equivalent circuit is shown in Figure 4.43, and the total impedance is represented by Equation (4.44). Figure 4.44 shows the corresponding Nyquist diagram, where Z” is the largest when Z’ is Rb/2. At this point, according to

Rb and Cb are available.

In the formula, ω is 2πf; Rb is the bulk resistance; Cb is the bulk capacitance; Ce is the interface capacitance.

The relative permittivity is the ratio of the capacitance test value under dielectric conditions to the capacitance test value under vacuum conditions [Equation (4.45)]. Defining Cb with Equation (4.46), εr can be obtained through AC impedance analysis.