The classical transport theory considers electrical conduction as a flow of free electrons. Under the application of an external electric field and the internal frictional force, the flow of free electrons attains equilibrium, and a constant current density is observed. By implementing the time relaxation approximation, the electrical conductivity can be expressed as follows [17]:

where σ is the electrical conductivity, τ is the relaxation time, N_f is the number of free electrons, m is the mass of an electron, and e is the charge of an electron. A classical approximation is generally used to describe the typical electrical conduction in metals [18].

The quantum mechanical approach states that only the electrons that are located near the Fermi level contribute to σ of the materials. Such electrons near the Fermi level can be accelerated via an external electrical field. Thus, electron movement only occurs along the direction of the applied field. The displaced free electrons possess equal or slightly higher velocities than the Fermi velocity (γF) [12]. These free electrons could participate in the electron conduction; hence, σ for a quantum mechanical system can be expressed as

Equation (2) describes the dependence of σ on the γF of free electrons, τ, and density of states. The abovementioned equation explains that σ is directly dependent on τ and the average time between successive collisions of free electrons [18].

σ can also be explained in terms of the absolute value of e and the number of conducting electrons, as expressed in equation (3) [17]. Electron mobility is a useful entity for describing the transport or conduction of electrons.

Quantum mechanics provides a range of concepts for a clear understanding of the influence of dopants and impurities in materials on altering carrier concentrations. The quantum mechanical expression for conductivity considers the electrons and density of states near the Fermi level; hence, it is more advantageous as compared to the classical model.

Generally, ionic transport occurs under the influence of different gradients such as the electrical field, chemical potential, and concentration. On a macroscopic scale, diffusion can be better explained by Fick’s first law, as expressed by equation 5 [22]:

where J is the flux of particles, C is the particle concentration, and D is the chemical diffusion coefficient. The negative sign specifies the gradient of the diffusion process, typically from higher to lower concentrations. At the microscopic scale, the self-diffusion coefficient is more useful because it provides additional information regarding the intrinsic nature of Li⁺ migration.

In equation (6), E_a is the activation energy barrier for Li⁺ migration, ν is the vibration frequency of migrating Li⁺ in the lattice, k_B is Boltzmann’s constant, T is the absolute temperature, and a is the hopping distance [17].

In electrochemical devices such as LIBs, ionic conductivity (σ) refers to the movement of Li⁺ under the influence of an external potential. The Nernst–Einstein equation describes the relationship between σ and D:

where,

D_i can be related to ionic mobility through the Nernst–Planck equation. Equation (8) further illustrates this relationship:

where u_i refers to the mobility for species I [17].

Generally, microscopic diffusion is caused by the thermal energy of the material. Below the melting point, the amplitude of phonons at equilibrium is low, and the thermal energy plays a critical role in deviating the atoms from their mean positions by increasing the temperature. In an excited state, atoms tend to overcome the energy barrier, leading to atomic migration. However, some conditions must be satisfied before this atomic migration can occur. An adjacent empty site must be available, and the atom must possess certain energy to break neighboring bonds and cause lattice distortions, thereby leading to atomic migration.

A solid is never perfect, and there exist certain defects in the crystal lattice of solids. These defects exist in various forms within the solids, such as simple missing atoms (vacancies) and interstitial or substitutional impurities within the crystal lattice. The existence of defects not only governs the purity of the solid structure but also affects the material performance. Furthermore, the diffusion inside solids can be categorized into two types: vacancy assisted diffusion and non-vacancy assisted diffusion [22].

The ionic transport in the electrolyte impregnated in the porous electrode is a predominant factor for determining the rate capability of LIBs. Ogihara et al. [26,27] combined electrochemical impedance spectroscopy with a transmission line model theory for cylindrical pores, to understand the internal resistance inside electrolyte-infused porous electrodes.

As shown in Fig. 8, there are different types of internal resistance at the electrode–electrolyte interface. Moreover, the charge transfer resistance to Li⁺ and electron transport is dependent on the thickness of the electrode.

In the electrodes, ionic resistance in the pores (R_ion) is affected by the pore length, whereas R_ct is inversely proportional to the active surface area. R_ion is mainly responsible for the Li⁺ conduction in pores filled with the electrolyte. Hence, the power capability of LIBs is strongly affected by the ionic conduction pathways in electrodes [27].

Fukutsuka et al. [8] conducted a model study involving anodic nanoporous alumina featuring a porous framework with honeycomb-shaped pores ranging from 20 to 68 nm. It was observed that the specific σ of the electrolyte infused in the honeycomb pores was smaller than that of the bulk electrolyte solution (i.e., 7.6 mS/cm), regardless of the pore size. The Nyquist plots exhibited depressed semi-circles, referring to the presence of ionic transport resistance in the honeycomb pores. The plots also indicated the existence of the capacitive element associated with the ionic transport inside the active material. Hence, the specific σ of the electrolyte solution impregnated in the porous electrode influences the ionic transport resistance of the electrodes [8].

The electrochemical kinetics at the electrodes of LIBs are affected by multiple factors. One of these factors is the charge transfer process involved at the electrode–electrolyte interface. Thus, it is also necessary to understand the reaction kinetics of the active materials. Abe et al. [28] evaluated the activation energy required for desolvation at the electrode–electrolyte interface. The semi-circles in the Nyquist plots were influenced by the salt concentration of the electrolyte and the electrode potential. The resistance is inversely proportional to the salt concentration of the electrolyte. The activation energy values were calculated for the de-solvated and solvated Li⁺ transfer based on the charge-transfer resistance vs temperature plots. The activation energy values for Li⁺ solvation were observed to be half of those required for the desolvation process [29].

On the contrary, solid electrolyte interphase (SEI) is a passive layer formed on the surface of the electrodes through the decomposition of electrolytes. The interphases assist in the reversible Li⁺ de/intercalation during the operation of LIBs, while restricting parasitic reactions.

Xu et al. [11] explained the interphasial reactions for solvation and desolvation. The solvation sheath of Li⁺ is composed of the solvent molecules that bind together with the Li⁺ core. These molecules are stabilized and remain undisplaced owing to the strong coulombic forces exerted by Li⁺ on its surrounding molecules.

This sheath tends to stabilize Li⁺ in the electrolyte by compensating the increase of Gibbs free energy. When Li⁺ intercalates into the graphite anode, this solvation sheath must be stripped out because the SEI on the graphite surface only allows the intercalation of naked Li⁺. This corresponds to the existence of a high energy transition state, as shown in Fig. 9. The desolvation process induces an additional resistance to Li⁺ transport and is a rate-determining step at the electrode–electrolyte interface [11].

Ionic diffusion inside the active materials plays a vital role in determining the performance of LIBs. Ionic diffusion is generally favorable inside the battery; however, leakage current should be avoided. Since the rate capability of LIBs depends on the ionic charge transfer kinetics, it is important to understand the critical factors governing charge transfer, to evaluate the power characteristics of LIBs [30]. In LIBs, the Li⁺ de/intercalation process begins with the dissociation of Li⁺-electron pairs and ends with the concomitant entry of Li⁺-electron pairs into active materials via solid-state diffusion [31]. Ionic diffusivity (D_ionic), as expressed in equation (9), is a parameter to characterize the ease of Li⁺ movement in active materials:

A decrease in the energy barrier can increase Li⁺ diffusivity (D_Li). Although an increase in operating temperature (T) enhances diffusivity, it can pose a threat to safety.

D_ionic at the surface must be enhanced to shorten the diffusion time (τd) expressed by equation (10), and the electron/ion diffusion length (λ) should be reduced [31]. The following schematic describes the diffusion pathways of Li⁺ within the active material.

As depicted in Fig. 10, during Li⁺ diffusion in the electrode, the ions sequentially move through different parts of the electrode, namely the crystal structures, primary particles, secondary particles, porous electrodes, and bulk electrolyte [32]. Although the energy density of an LIB can be improved by increasing the thickness of the electrode, the Li⁺ kinetics is significantly reduced.

As shown in Fig. 11(a–b), the thicker electrodes exhibited a significant capacity loss coupled with a low coulombic efficiency. τd is a function of electrode thickness; therefore, the time required for Li⁺ diffusion increased with an increase in electrode thickness. D_Li also depends on electrode thickness and directly affects the specific capacity and rate capability of LIBs (Fig. 11(c)). During the operation of LIBs, a rapid decrease in D_Li was observed for thicker electrodes due to the localized oversaturation or over-depletion of Li⁺ induced by the slower Li⁺ transport [32].

Thin separators are more suitable for enhancing the performance of LIBs, because thick separators are not feasible owing to their poor ionic conductivity. A thin separator typically possesses high porosity, which enables enhanced mass transport through the pores with reduced resistance from the electrolyte. Thus, the porosity of separators is a crucial factor in determining the internal resistance of LIBs. A uniform porosity of separators is desirable for maintaining a uniform current density with a smooth ionic current flow inside the LIBs. A non-uniform current density can cause a significant reduction in performance [33].

As the resistance is also affected by the pore structure of the separators, the total pore volume and pore size of separators could be tailored to enhance σ by decreasing the thickness of the separators (Fig. 12). A thinner separator enables an increase in the mass transportation of ions, thereby effectively lowering the resistance even at high current densities. For improving cycling performance and rate capability, the separator should be as thin as possible to minimize the cell resistance but still be able to maintain high ionic conductivity.

Pan et al. [34] demonstrated that small over-potential and high specific capacity of LiFePO₄ could be attained by employing a thin separator even at high current densities.

As shown in Table 1 and Figs. 12 and 13(a–c), the lowest cell resistance was observed for Cladophora cellulose (CC)-25 separator with the highest porosity and lowest thickness. This supports the hypothesis that a reduction in the ionic transport path is beneficial for lowering cell resistance. As shown in Fig. 13(d–e), the cycling performance of CC-25 is superior to other samples due to the lower cell resistance.

Li-rich cathode materials, commonly known as over-lithiated oxides (OLOs), have received significant attention as promising cathode materials for LIBs. In particular, lithium manganese oxide (Li₂MnO₃), which has a monoclinic structure of the C2/m space group, can offer a high capacity of 300 mAh/g on an initial charge to 4.8 V vs Li/Li⁺. However, the practical use of Li₂MnO₃ is limited due to the low coulombic efficiency and irreversible capacity loss during the first cycle. Kim et al. [35] reported a positive effect of the TiO₂ surface coating on Li₂MnO_3, where TiO₂ acts as a suitable alternative for improving the structural stability of Li₂MnO₃. TiO₂-coated Li₂MnO₃ exhibited a relatively lower interfacial resistance, as compared with that of uncoated Li₂MnO₃. TiO₂ acted as a stabilizer and prevented the decomposition of the active material in the electrolyte at high potentials, thereby improving the rate performance of TiO₂-coated Li₂MnO₃. LiCoO₂ has an α-NaFeO₂ layered structure, which assists in efficient reversible Li⁺ intercalation chemistry. Despite its high theoretical capacity, the working capacity of LiCoO₂ is limited to just 140 mAh/g. This limited capacity of LiCoO₂ originates from a factual phase transition (at >4.2 V) from a hexagonal to a monoclinic structure, causing a decrease in the coulombic efficiency. This leads to a decrease in Li⁺ diffusion, resulting in high internal strain and degradation of mechanical properties.

A large number of LiCoO₂ surface coatings have been explored to overcome these problems. In particular, surface coatings containing metallic compounds were found to be effective because they act as a barrier between the electrolyte and the LiCoO₂ particles. Kaluri et al. [36] reported a hybrid surface coating consisting of magnesium (Mg) and phosphorous (P) on the surface of LiCoO₂.

A surface coating consisting of Mg and P can be effective for improving the electrochemical performance and thermal stability of LiCoO₂ (Fig. 14(a)). After surface coating, Mg and P (MP)-coated LiCoO₂ exhibited a high-capacity retention of 86.5%, even after 100 cycles. As shown in Fig. 14(b–c), the rate capability of MP-coated LiCoO₂ was nearly 25 times higher than the rate capability of bare LiCoO₂, even at a high current density of 10 C [37].

The decrease in the capacity of bare LiCoO₂ cathode could be attributed to the structural degradation at high operating temperatures [36]. As a result, a significant dissolution of Co in the electrolyte was observed based on FIB post mortem analyses (Fig. 14(a)).

In addition, post-processes (i.e., heat-treatment and washing) can improve the rate performance of nickel (Ni)-rich layered materials. The surface of a treated, Ni-rich layered material is considerably cleaner than that of an untreated material, as shown in Fig. 15. As a result, treated cathodes exhibit a significantly higher rate performance than untreated materials due to the reduction in surface contamination [38].

As a commercial binder, PVDF is commonly used for electrode fabrication owing to its excellent electrochemical stability and binding property. However, the insulator PVDF induces an increase in the internal resistance of the electrodes. Ling et al. [42] incorporated naturally occurring conductive binder sodium alginate (SA) along with poly(3,4-propylene-dioxythiopene) (PProDOT) in electrodes, as shown in Fig. 16 (a).

As shown in Fig. 16(b), the electrochemical performance of LiFePO₄ could be improved by employing the conductive SA-PProDOT binder. The cycling performance and capacity retention of LiFePO₄ are depicted in Fig. 16 (c–d). The capacity retention of LiFePO₄ with the SA-PProDOT binder was estimated to be 86.6%, without a significant capacity loss even at a high current density of 1 C. Moreover, excellent Coulombic efficiency was noticeable even after 400 cycles. This clearly indicated that the conductive SA-PProDOT binder would be beneficial for improving electrochemical performance owing to its conductive nature [42].

Nano-structuring is useful for tailoring active materials so as to obtain desirable morphologies and microstructures such as particles, wires, sheets, and hollow porous structures. A short diffusion length and large surface area of nanostructured active materials could enhance the rate of ionic and electronic transport at the electrode–electrolyte interface. At the nanoscale, materials tend to have a large surface area, which is responsible for facilitating electrochemical reactions at the interfaces inside electrodes. Nanostructured materials lead to a decrease in the thermodynamic activation energy barrier at the electrode–electrolyte interface [31,43]. For example, LTO is a commonly used active material featuring a high capacity and a suitable potential window. However, due to its low conductivity, the insertion of Li⁺ in bulk LTO is limited. However, this could be further enhanced by decreasing the crystallite or particle size via nano-structuring. Feckl et al. [44] reported that Li⁺ insertion is greater in nano-LTO than in porous LTO.

As shown in Fig. 17, nano-LTO-400 with a particle size of 3 nm exhibited a better cycling performance, as compared to nano-LTO-500 with a particle size of 6 nm. Such an improvement in the performance can be explained by the enhanced insertion of Li⁺ induced by the smaller crystallite size [44].

Simultaneously achieving high energy and high power at robust charging and discharging rates is a crucial requirement for the development of LIBs. Currently, LIBs still suffer from low power densities due to the use of bulk materials as active materials. Although bulk metal oxides or graphite anodes can offer high energy densities, the power density achieved is limited by the slow kinetics in bulk materials. The power characteristics of LIBs are dependent on efficient charge storage capability and also on the kinetics of charge transport during electrochemical reactions in the bulk electrode and electrolyte. Doping or substitution in bulk materials is an effective approach to introduce ions, heteroatoms, or vacancies in the crystal structure; this in turn enhances conductivity due to the excess or deficiency of charged species, leading to an improvement in the overall performance of the battery. Wu et al. [45] reported the substitution of nitrogen (N) and boron (B) atoms in place of carbon (C) atoms on the edges of graphite. B and N doping in graphene facilitates Li⁺ intercalation into the host structure of graphite and enhances electrical conductivity, thereby leading to high power and energy densities.

Graphene exhibited an enhanced coulombic efficiency during the cycles, after N and B doping, as shown in Fig. 18. The reversible capacity retentions for N-doped and B-doped graphene were measured to be 83.6% and 79.2%, respectively. The improvements in the parameters indicated the effective suppression of side reactions and electrolyte decomposition as well as the enhancement in Li⁺ absorption and the diffusion inside electrodes [45].

In addition, the Li⁺ diffusion path length in the 2D layered system can be controlled through the dopant ratio. For instance, the inter-slab size of LiO₆ in the Nirich layered material can be increased by reducing the amount of Mn ions (Fig. 19). Consequently, this leads to a favorable environment for Ni²⁺ to diffuse in the Li layer (i.e., lowering the activation energy). Therefore, NCM721 exhibits a significantly higher D_Li than NCM523 [46].

A hybrid composite approach involves the synthesis of various composite materials by integrating conducting additives into active materials. The conducting additives induce the formation of sufficient conduction pathways in the electrodes. In addition to increasing the electrical conductivity, these conducting additives tend to decrease the length of Li⁺ diffusion, enabling faster Li⁺ de/intercalation.

Magasinski et al. reported a porous silicon (Si)-C composite containing irregular open channels that facilitate the adsorption and diffusion of Li⁺ within the composite material. Si typically undergoes a large volume expansion; however, in this case, the volume expansion of Si could be compensated by integrating free spaces in the composite. The Si-C composite exhibited better capacity retentions at high current densities, compared with those of simply annealed carbon black [47]. Thus, hybrid composites with a conducting additive could be a practical approach for further improving the electrochemical performance of the active materials in LIBs.