In the kinetic process of Li ion batteries, ion diffusion in the electrode, called the rate-determining step, determines the speed of the primary electrochemical reaction. The relation among the mean diffusion time of Li ions ( τ ), the diffusion coefficient ( D ), and the diffusion length ( L ) is given as

Shortening the diffusion length is commonly used to improve the rate performance of the conventional Li ion battery materials. ^{[ 2 – 4 ]} For example, the conventional cathode material LiFePO ₄ has been studied extensively because of its high theoretical energy density of 580 W·h/kg. However, it suffers from low electronic and ionic conductivities. Wu et al. reported that a nanocomposite with highly dispersed nanoparticles of LiFePO ₄ in a nanoporous carbon matrix can be fully charged or discharged within a period of less than 30 s. ^{[ 2 ]} The extremely high power is enabled by nanometer-sized LiFePO ₄ particles, which shorten the Li ion diffusion path, and by quick Li ⁺ /e ^– diffusion, which arises from the nature of the nanoporous carbon matrix. ^{[ 2 ]}

Size reduction not only improves the rate performance of some electrode materials, but also endows some inactive materials such as rutile TiO ₂ with electroactivity. ^{[ 5 , 6 ]} Rutile is the most stable structure of TiO ₂ under standard conditions, but Li insertion into rutile is usually reported to be negligible. The capacity can be significantly improved by nanocrystallization. ^{[ 5 , 7 , 8 ]} Hu et al. reported observing high capacity, excellent capacity retention during cycling, and high rate performance for rutile TiO ₂ needles about 10 nm in diameter and 30 nm in length. ^{[ 5 ]}

Besides the reduced diffusion length, another reason for the higher intercalation/deintercalation rates of some nanomaterials is the increased contact area, which promotes Li ion exchange. The excellent performance of nanoscale Li ₄ Ti ₅ O ₁₂ is a suitable example. Li ₄ Ti ₅ O ₁₂ is an attractive anode material due to its low cost, zero strain, and operating voltage plateau which are sufficient to avoid the formation of lithium dendrites and solid electrolyte interface (SEI). However, it suffers from a moderate Li ion diffusion coefficient and poor electronic conductivity, which is also indicated by the band gap of about 2 eV calculated by ab initio study. ^{[ 9 ]} The nanocrystalline Li ₄ Ti ₅ O ₁₂ prepared by combustion synthesis exhibits high rate capability and good capacity retention, both of which can be attributed to the presence of highly porous nanostructures having BET surface areas of about 12 m ² /g. ^{[ 10 ]}

The electron exchange can also be improved by enhancing the contact area between the active materials and the conductive additives. Zhang et al. improved the effective contact area by connecting one-dimensional carbon nanofibers with zero-dimensional carbon black to build a conductive network, which is established within the Li ₄ Ti ₅ O ₁₂ particles by the penetrating multiple carbon nanofibers, and the carbon black particles attached onto the surface of the Li ₄ Ti ₅ O ₁₂ particles fill in the gaps between them. ^{[ 11 ]}

The materials with one-dimensional Li diffusion channel may exhibit high rate performance if the orientation of matter is controlled to improve the exposed area with high pore density for Li insertion/extraction. ^{[ 12 ]}

The diffusion coefficient is also affected by nanocrystallization in some cases. Based on their computational results for LiFePO ₄ , Malik et al. suggested that the kinetic benefit of small scale materials results from both shortened transport paths and enhanced diffusion constants of one-dimensional channel materials. The phenomenon will be introduced very briefly in the section below on theoretical calculation. ^{[ 13 ]}

The dynamic performance of any nanoscale electrodes should be dramatically improved in theory, but it is not actually the case for some electrode materials due to the thermodynamic instability that comes with size reduction.

Due to an abundance of dangling bonds, a large surface free energy, a high density of defects, and the high surface-to-volume ratio of nanostructured electrode materials, the risk of secondary reactions is dramatically high, leading to a short life cycle and consuming much of the Li supplied by the cathodes.

Nano LiCoO ₂ exhibits worse cyclability than bulk LiCoO ₂ due to the presence of SEI film, formed mainly in spontaneous chemical reactions between the solvent molecules and nanoscale LiCoO ₂ . ^{[ 14 , 15 ]} Furthermore, it has been found in many nanostructured transition metal oxides that thick SEI films formed during Li uptake may disappear completely upon Li extraction, which leads to capacity fading and safety problems. Therefore, surface modifications must be considered for nanostructured transition metal oxides. For instance, carbon coated Fe ₃ O ₄ nanospindles exhibit very high specific capacity, superior cycling performance, and high rate performance because the carbon coating enhances electronic conductivity and stabilizes the SEI films. ^{[ 16 ]}

The abundant agglomerates that lead to the irreversible fading of capacity and shortened cycle life will occur, and they occur during the preparation processes or electrochemical cycling.

Surface coating and the formation of nano/micro hierarchical structures are efficient techniques to avoid agglomeration, on account of the formation of highly dispersed nanocrystals in the matrix. ^{[ 16 , 17 ]} For example, Guo et al. proposed that a conducting 3D network (a sketch is shown in Fig.  1 ), a synthesis of a mesoporous TiO ₂ :RuO ₂ nanocomposite, would exhibit optimal high power density because of combining the advantages of nanoscale networks (negligible diffusion time, enhanced local conductivity, and possibly faster phase transfer reactions) and microscopic networks (good stability and ease of fabrication). ^{[ 17 ]}

Fig. 1.

	Figure Option View Download New Window
	Fig. 1. (a) Schematic of the desired design; the shaded areas represent 3D conductive networks. (b) Sketch of a realistic composite in which Li + /e – can transfer to most of the electroactive material particles through the 3D conductive networks. [ 17 ]

Lattice expansion dependent upon particle size is observed in some materials; however, explanations vary, including a change of bond length, a reduction of atomic charge, and so on. ^{[ 15 , 18 , 19 ]} According to magnetic susceptibility measurements, the fact that 20% of the cobalt at the surface layer is Co ²⁺ ions can explain the lattice expansion of nanocrystalline LiCoO ₂ , because the Co ²⁺ –O distance is longer than the Co ³⁺ –O distance. ^{[ 15 ]} Variation of the lattice parameter also impacts Li ion diffusion kinetics, since it changes the channel size.

The thermodynamic equilibrium voltage ( V ) is related to the difference of chemical potential (Δ μ ) between the reactants and products

Fig. 2.

	Figure Option View Download New Window
	Fig. 2. (a) Structure sketch and expected discharge curve for bulk LiCoO 2 , in which the site energy is considered to be a constant ε S . (b) Structure sketch and expected discharge curve for nanoscale LiCoO 2 . The fluctuation of the site energy is represented by δ . [ 15 ]

Defect energy not only impacts the thermodynamic equilibrium voltage of a given structure, but also results in the reversal of the stable morphology of a material, like Fe ₂ O ₃ . The phase transition from maghemite ( γ -Fe ₂ O ₃ ) to hematite ( α -Fe ₂ O ₃ ) has been observed in situ in XRD as the crystal size varies from 9 nm to 16 nm due to the Gibbs-energy change. ^{[ 23 ]}

Phase transition behavior is also connected with the size of material particles. Varied staging phenomena have been observed in different-sized particles of LiFePO ₄ , which is widely considered to be a typical first-order phase transition material. ^{[ 24 ]} The staging structure is an intermediate phase between LiFePO ₄ and FePO ₄ for large crystals or a uniform phase throughout the whole particle for small particles. The distinctive configuration, a thermodynamically metastable but kinetically controlled state, was also explained by density functional theory calculations. ^{[ 25 ]} The formation of the lithium staging configuration is mainly attributed to the interaction between the effective oxidation state of Fe redox and the arrangement of Li ions. ^{[ 25 ]} By calculating the magnitude of the overpotential, Ceder et al. determined that only minimal overpotential is required to enable the single-phase transformation path of LiFePO ₄ at room temperature and they explained the difference between larger particles stabilizing intraparticle two-phase coexistence and smaller particles favoring interparticle two-phase coexistence. ^{[ 26 ]} Kobayashi et al. indicated that the particle size determines which primary factor will dominate the electrochemical behavior of LiFePO ₄ . ^{[ 27 ]} Bulk miscibility dominates the electrochemical behavior of Li _x FePO ₄ with particle sizes larger than 40 nm, but the geometric surface portion becomes evident when the particles are smaller than 100 nm.

Despite the existence of thermodynamic instability, nanometer scale can play yet another favorable role in some aspects of thermodynamic behavior, such as improving the mechanical strength as an excellent strain accommodation during charge/discharge. A plenty of internal cavities or pores can tolerate the volume expansion/contraction associated with lithiation/delithiation. Silicon is an important candidate anode material for the next generation of Li ion batteries because of its extremely high theoretical capacity (4200 mA·h/g), realized by the formation of Li _4.4 Si. However, the reversible capacity of silicon anodes is very poor due to huge volume expansion (> 300%) during the lithiation of silicon, which pulverizes the electrode material, leading to fading capacity. The pulverization of Si resulting from volume changes can be mitigated by integrating particles smaller than 150 nm, as the expansion/contraction of single nanoparticles is much smaller than that of larger particles. ^{[ 28 – 31 ]} Li et al. reported that a composite of nanoscale silicon power and carbon black exhibits an extremely high reversible capacity of 1700 mA·h/g and excellent cyclic performance. ^{[ 28 ]} The smaller the particles, the larger the surface-to-volume ratio, accommodating a greater charge and more lithium ions. This fact significantly reduces the lithium ion diffusion distance during charging/discharging, which can greatly reduce the volumetric changes and increase the structural stability, because the structure at the surface is generally more favorable for the diffusion of lithium ions because the diffusion energy of lithium migration is generally higher in the bulk region than near the surface. ^{[ 32 ]}

The increased reversible capacity of nanomaterials originates both from good structural stability and from new lithium storage mechanisms.

One of the new mechanisms is the conversion mechanism, which can be used to explain the excellent lithium storage capacity of nanoscale transition metal oxides, fluorides, sulfides, nitrides, and other polyanion compounds. ^{[ 33 ]} For amorphous R VO ₄ ( R = In, Cr, Fe, Al, Y), a model based on the formation of Li–O bonds has been proposed to account for the large Li acceptance that was found in a survey of experimental results. ^{[ 34 ]} On this basis, Poizot et al. reported that the excellent capacity (700 mA·h/g) of nanoscale transition metal oxides M O ( M = Co, Ni, Cu, Fe) electrodes stems from the formation/decomposition of Li ₂ O that occurs with the reduction/oxidation of metal nanoparticles. For transition metals, thermodynamic calculations based on the conversion mechanism for different binary transition metal oxides and fluorides predicted an increase of cell voltage with increasing atomic number. ^{[ 35 ]}

With the generation of lithiated-state Li ₂ O or transition metal, the lithium storage capacity is commonly thought to be fully occupied, because it is assumed that the storage material cannot accommodate any more lithium. However, the capacity can be raised further by another lithium storage mechanism (interfacial lithium storage).

Interfacial lithium storage mechanism that Li ions and electrons store on the each side of the interface during lithiation process plays a large role in the overall capacity of nanostructural materials due to the comparatively large total interface area of the nanoparticles. Ab initio atomic and electronic structure calculations of Ti(0001)/Li ₂ O(111) indicated that the interface can store lithium, and a huge transfer of electrons to the Ti adatoms was clearly revealed by 2D difference electron density maps. ^{[ 36 ]} The interfacial lithium storage mechanism proposed by Jamanik and Maier was confirmed experimentally by the ⁶ Li magic angle spinning nuclear magnetic resonance of the lithiation process of nanocrystalline RuO ₂ . ^{[ 37 ]}

The third lithium storage mechanism resulting from size reduction is based on the space for lithium ions in the abundant three-dimensional defects such as nanopores or cavities. The size effects might be thought to enhance the properties of electrodes only, yet they also benefit the electrolytes of Li ion batteries.