The electrolyte conducts the ionic component of the chemical reaction between the anode and the cathode, but it forces the electronic component to traverse an external circuit where it does work.
Ionic mobility in the electrolyte is smaller than the electronic conductivity in a metal, so a cell has large-area electrodes separated by a thin electrolyte;
metallic current collectors deliver electronic current from/to the redox centers of the electrodes to/from posts that connect to the external circuit.
During discharge and charge, an internal battery resistance \(R_b\) to the ionic current \(Ii = I\) **reduces the output voltage \(V{dis}\)** from the open-circuit voltage \(V_{oc}\) by a polarization \(η = I_{dis}Rb\) and increases the voltage \(V{ch}\) required to reverse the chemical reaction on charge by an overvoltage \(η = I_{ch}R_b\):
\[ V_{dis}=V_{oc}-η(q, I_{dis}) \quad V_{dis}=V_{oc}+η(q,I_{ch}) 100 \times \frac{\int^{Q_{ids}}_0V_{dis}(q)dq}{\int^{Q_{ch}}_0V_{ch}(q)dq}\quad Q=\int^{\triangle t}_0 Idt=\int^Q_0dq\]
where q represents the state of charge, Q is the total charge per unit weight (Ah\(kg^{-1}\)) or per volume (Ah\(L^{-1}\)) \(I=dq/dt\) and Q(I) is the cell capacity for given I
Q depends on I because the rate of transfer of ions across electrode/electrolyte interfaces becomes diffusion-limited at high currents. A diffusion-limited loss of the Li inserted into an electrode particle at a high rate of charge or discharge represents a reversible loss of capacity.
However, changes in electrode volume, electrode−electrolyte chemical reactions, and/or electrode decomposition can cause an irreversible loss of capacity
Electrode−electrolyte chemical reactions that result in the irreversible formation of a passivating solid−electrolyte interphase (SEI) layer on an electrode during an initial charge of a cell fabricated in a discharged state are distinguished from the irreversible capacity fade that may occur with cycling.
The cycle life of a battery is the number of cycles until the capacity fades to 80% of its initial reversible value. Aside from cost and safety, are its density (specific and volumetric) of stored energy, its output power \(P(q) = V(q)I_{dis}\) for a given discharge current, and its calendar (shelf) life.
The available energy stored in a fully charged cell depends on the discharge current\(I_{dis}=dq/dt\). The stored energy is the product of the average voltage and the capacity.
\[ energy = \int^{\triangle}_0 IV(t)dt = \int^Q_0 V(q)dq \]
This voltage is limited by either the “window” of the electrolyte or the top of the anion-p bands of the cathode. The window of the electrolyte is the energy gap between its lowest unoccupied and highest occupied molecular orbitals (LUMO and HOMO) of a liquid electrolyte or the bottom of the conduction band and top of the valence band of a solid electrolyte.
\(μ_A \) above the electrolyte LUMO reduces the electrolyte unless the anode−electrolyte reaction becomes blocked by the formation of a passivating SEI layer; similarly, a \(μ_C\) located below the HOMO oxidizes the electrolyte unless the reaction is blocked by an SEI layer.
\(μ_C\) cannot be lowered below the top of the cathode anion-p bands, which may have an energy above the electrolyte HOMO.
Since the practical HOMO of the organic liquid carbonate electrolytes used in LIBs is at 4.3 eV below \(μ_A\)(Li), the voltage of the simple \(LiMO2\) layered oxides is also self-limited by the energy of the top of the O-2p bands, Figure 2c. As a result, the original \(Li{1-x}CoO_2\) cathode evolves oxygen or inserts protons on removing Li+ beyond x = 0.55
In the interval 0.5
investigation of these high-voltage cathodes has been limited because the organic liquid carbonate electrolytes used in the LIBs decompose at a voltage V > 5 V. Moreover, the counter cation used to lower the top of the O-2p bands reduces the capacity unless the active redox center can accommodate two electrons without a voltage step between them.
Reversible chemical reactions at solid electrodes are of two types: displacement and insertion reactions. Solid cathodes undergo insertion reactions, and solid anodes commonly undergo displacement reactions, but insertion reactions are also used
insertion reactions consist of an electronically conducting host structure into/from which the working cation, e.g., H+ or Li+, can be inserted/extracted reversibly over a finite solid−solution range; e.g., the cathode reaction:
\[ xH^+ xe^-+NiOOH = NiO_{1-x}(OH)_{1+x} \]
\[ Cd+2xH_2O-2xe^- = Cd(OH)_2 + 2xH^+\]
The window of an aqueous electrolyte restricts the voltage of a battery with a stable shelf life to V ≤ 1.5V
The Li-ion battery was motivated by the need for a rechargeable battery with a larger energy density, i.e., a larger voltage, which requires a nonaqueous electrolyte. Since H+ is only mobile in an aqueous medium, Li+ was chosen as the working ion in a nonaqueous electrolyte.
Li with liquid carbonate offer a lower practical HOMO at ~ 4.3cV below Li., and primary
(unrechargeable) Li batteries with these electrolytes were known to support the anode displacement reaction, provided the the electrolyte included an ethylene carbonate (EC) additive to passivate the Li anode
\[ Li = Li_{1-x}+xLi^+xe^-\]
permeable to Li+, it prevents uniform plating of Li during charge in a rechargeable cell. Consequently, dendrites form and, on repeated charging, can grow across the separator to give an internal short-circuit with incendiary, even explosive, consequences.
However, the concept of a LIB was not abandoned. Goodenough recognized that increasing the voltage of the anode would require a cathode providing a larger voltage vs Li.
Rachid Yazami was exploring Li intercalation into graphite and noted that reversible Li insertion into carbon avoids the problem of dendrite formation,
The first Li-ion battery was assembled by Yoshino with a dischared carbon anode and a discharged LiCoO2
\[ C+xe^-+xLi^+=Li_xC(anode) \\ LiCoO_2 -xe^- -xLi^+ = Li_{1-x}CoO_2(cathode)\]
Insertion of a guest Li+ into a layered host like TiS2, CoO2, or graphite was originally referred to as intercalation.
Nevertheless, O2 evolution inside a cell creates safety problems unless the cell voltage is carefully managed. The addition of ∼10% Al3+ stabilizes the layered oxides against electrode/electrolyte interface reactions on Li extraction, but at the expense of capacity
Another safety issue is internal short-circuits by Li penetration across the separator or by direct cathode and anode contact through a pinhole or thermal shrinkage. To eliminate this problem, a slurry of Al2O3 and a polymeric binder is coated on the separator to block Li-dendrite penetration.
If the Fermi energy μA of the charged anode is above the LUMO of the electrolyte, which is the case with a carbon anode at 0.2 V vs Li, a fraction of the Li from the cathode is consumed irreversibly on the initial charge in the passivating Li+-permeable SEI layer that forms on the anode surfaces.
Moreover, the SEI layer increases the impedance of Li+ transfer across the anode/electrolyte interface, and the SEI layer changes with successive cycling to contribute to a capacity fade.
Since carbon has a limited capacity and Li is plated onto its surface in a fast charge, the carbon anode is being replaced by insertion into Si or alloys of Sn or Sb.
However, a huge lattice expansion (∼300% for Si) on Li insertion requires that the active anode be assembled as small particles or a sponge-like array within a Li+ and electron conductive medium that is sufficiently elastic to absorb the volume changes.
a μA ≤ 0.2 V vs Li does not allow safe fast charge that is desired for an electric vehicle battery. The buffering medium may be carbon or a conductive polymer. However, a μA(Li) − μA(alloy) <1.1 eV still requires formation of an SEI layer with the organic liquid-carbonate electrolyte
In an attempt to improve the stability and lower the impedance of the SEI layer, replacement of EC by other additives to the electrolyte, e.g. fluoroethylene carbonate,22 is being explored.
Kummer & Weber discovered fast 2D Na+ transport in Na2O·11Al2O3, which offered the possibility of a rechargeable battery with molten electrodes and a solid electrolyte, attempt to develop Na+ and Li+ electrolytes.
The larger Na+ ion requires a relatively large 3D interstitial space. The Li+ ion, on the other hand, is small enough to be mobile at room temperature in a close-packed oxide-ion array, However, these 2D Li+ conductors have a degree of freedom along the c axis
cooperative Jahn-Teller distortion : The e-orbital degeneracy on a localized Mn(III):t3e1 high-spin configuration in sufficient concentration gives rise to a cooperative orbital ordering to lower the Mn(III) site symmetry above room temperature.
The Ni couples remain close enough to the top of the O-2p bands that the holes introduced into the σ-bonding 3d orbitals of Ni(II) occupy itinerant states of d-orbital symmetry
Not only high Li+ mobility in the close-packed oxide-ion array of the spinel framework, but also that elimination of the anode SEI layer improves greatly the cycle life of the electrode.
The FePO4 framework is inexpensive and environmentally friendly, but the cost of quality control of the LiFePO4 electrodes is presently too expensive.
→ exposing the surface to S or N anions has been shown to lower the surface charge-transfer impedance, thereby increasing the capacity at higher rates of charge/discharge
two-phase reaction between LiFePO4 and FePO4 gives a flat output voltage, but it prevents sufficient mixed valence on the iron in either phase to give an adequate polaronic conductivity.
Therefore, it has proved necessary to either coat small particles of shorter charge-carrier path length with an electronically conductive surface layer and/or reduce the particle size to the nanoscale where a larger range of single-phase reaction occurs.
\[ 2Na + FeCl_2 = 2NaCl + Fe \]
Sodium is much less expensive than lithium and widely available, but operation at higher temperatures of corrosive materials presents a challenge.
On the other hand, solid electrolytes allow consideration of liquid and gaseous reactants.
An all solid-state Li battery would, in principle, use an inorganic solid or a polymer Li+ electrolyte. An inorganic solid Li+ electrolyte has been used with thin solid electrodes in an all solid-state Li cell, but the volume changes in the electrodes on charge/discharge have not allowed retention of good electrode/electrolyte contact in a rechargeable storage battery
Polymer Li+ electrolytes with a sufficiently large window and a Li+ conductivity \(σ_{Li}\) > 10−4 S cm−1 that retains a good contact with solid electrodes have yet to be demonstrated.
a solid Li+ electrolyte membrane separating different liquid electrolytes contacting the anode and cathode would offer the possibility, if it blocked Li+ dendrites, of a lithium anode and a liquid or gaseous cathode reactant.
However, a solid Li+ electrolyte separator that blocks dendrites from a Li anode would need to have a major ceramic component, but a sufficiently thin ceramic membrane would be too fragile.
A practical solid-electrolyte separator membrane would need:
(a) a \(σ_{Li}\) > 10−4 S cm−1;
(b) the capability to block Li dendrites without being reduced;
(c) to be chemically stable in the liquid electrolytes;
(d) to be easily fabricated into a mechanically robust, flexible thin membrane.
These requirements would appear to require a ceramic-polymer composite
Moreover, coating the surface of the electrolyte particles with a hydrophobic skin, e.g., polydopamine, allows Li+ transport while stabilizing the electrolyte particles in an aqueous electrolyte.
The air cathode offers a high capacity, but the reversible reaction: requires inexpensive catalysts for the oxygen-reduction reaction (ORR) and the oxygen-evolution reaction (OER) at a high rate with a voltage difference Vch − Vdis ≤ 0.3 for storage efficiency
\[ 4Li^+ + 4e^- + O_2 = 2Li_2O \]
\[ 4Li^+ + 4e^- +O_2=2Li_2O\]
With a solid Li+ electrolyte separator of a nonaqueous electrolyte at a Li anode and an aqueous electrolyte at the air cathode, the voltage can be increased to ∼3.5 V.
The lithium−sulfur battery also provides a multielectron redox couple at the sulfur cathode and, therefore, a large increase in capacity
A composite polymer gel containing a large volume fraction of an inorganic oxide and an organic liquid electrolyte immobilized in a polymer can give a flexible, thin membrane, but it needs yet to be tests for block dendrite from Li anode