Nanostructures in Nanoionics and Colloidal Chemistry: Overview and Problems

This chapter consists of two parts. In the first half of this chapter, some experimental facts for the problems related to enhanced ion dynamics in porous and related materials are summarized along with the history of research of the Lil-alumina composite. Historical view of how the research in nanoionics has been developed will be useful to understand what factors affect the problems and what kind of methods can be used. Some of the results seem to be contradicting each other so that further research and methods are required for the clarification of the mechanism.

In the second half of this chapter, experimentally relevant facts for the structures obtained from the coagulation of colloids/particles will be summarized, where the importance of dimensionality of the systems in colloidal systems and gels is shown. Furthermore, evidence of the coexistence of several length scales in gels, which means the existence of super aggregates, will be presented.

Molecular Dynamics of Nanostructures and Nanoionics: Simulations in Complex Systems Junko Habasaki

Copyright © 2021 Jenny Stanford Publishing Pte. Ltd.

ISBN 978-981-4800-77-8 (Hardcover), 978-1-003-04490-1 (eBook) www.jennystanford.com

Historical and Current Research on Nanoionics

The first topic is to show the historical and current status in the field of nanoionics. Some experimental facts and related simulation works so far reported will be explained. Especially, attention is paid to nanoionics with enhanced dynamics and factors modifying ionic properties in nanostructured composites for suggesting problems to be examined by molecular dynamics simulations.

Characteristics of nanostructured materials tend to be explained by assuming them to be coming from their large surface area as well as the large boundary regions. However, there are many other possible causes of changes in properties in nanostructured materials [1]. Furthermore, possible roles of large surface area and/or grain boundaries are not simple.

After the first report by Liang [2] for enhanced dynamics in Lil-Al₂0₃ composites, similar findings in other composites were reported by many authors. These findings have brought developments of studies of "surfaces and boundaries,” "chemical preparations of composites,” as well as developments of "percolation theories.” Therefore, the results of these studies will be useful to learn the history and current status of the field of nanoionics and related ones, although the explanation is not exactly in the chronological order. Many kinds of explanations have been proposed so far, regardless that quite similar behaviors of systems are commonly observed. One of the origins of this complexity seems to be coming from the dual (or more) roles of each component. For example, alumina and related components treated here are sometimes regarded as low-conductivity materials or insulators to separate conductive phases. However, at the same time, they are porous supports to hold and affect the conducting phases. Another possible cause may be the complexity of the experimental conditions to prepare and examine nanostructured materials. Each method seems to have its own characteristics to be considered to conclude.

For understanding dynamics in composites, methods to distinguish such roles seem to be required. Systematic studies for the role of modification of the system will be also helpful. Several proposals to explain the enhancement and distinguish several origins will be explained in this chapter. The effects of modification of dynamics in porous systems are discussed in Chapters 6 and 7. In Chapter 6, methods to separate possible mechanisms and effects of introducing pores by using MD simulations will be shown for the case of porous silicate systems. The methods used can be applied to more complicated nanostructured systems such as composites and films, confined systems with/without some modifications.

3.1.1 Experimental Observation for LiI–Alumina Composite

As already mentioned, the first important experimental facts to be argued in this field is the existence of enhanced dynamics found in several composites or mixtures. In 1973, Liang [2] reported enhanced dynamics of ions in the lithium iodide-aluminium oxide (Lil-alumina) system.

Liang [2] reported that the composite of lithium iodide- aluminium oxide showed the maximum conductivity of ~10"⁵ (S cm"¹) at around 45 mol % of Al₂0₃ content at room temperature, as shown in Fig. 3.1. After the discovery, this and related systems have been examined by many researchers [3-19].

Many theories and models have been proposed to explain enhancement. The space charge layer model [5-7], deformation- induced defect model [8-11], the effect of water [13, 14] and percolation theories [15, 16] are important ones, which affects developments of this research field. Other possible explanations can be found in our book of ionics, especially in the chapters of nanoionics and further applications [1]. Temperature dependence reported in [3] suggested that the enhancement is remarkable when it is concerned with the cooperative motions of ions at higher temperatures.

These explanations contain several factors and are not necessarily independent of each other.

Figure 3.1 Conductivity of UI-AI2O3 composite as a function of alumina content. Reprinted with permission from Liang, С. C. (1973),/ Electrochem. Soc., 120(10), pp. 1289-1292, doi:10.1149/1.2403248. Copyright (1973) Elsevier.

3.1.2 Space-Charge Layer Model-Geometrical Factors Related to Ionic Paths

In the space-charge layer model by Wagner [5], and that by Maier [6, 7], cations are trapped at the interfaces of two phases and cation vacancies increase within the space-charge layer due to a charge balance.

The concept of the model seems to be related to the percolation theory because the conduction path formed by the space-charge layer is affected by insulators introduced. The model seems to work well for several systems. Changes in the length scale may be expected from the model, and the method to obtain Debye length discussed in Section 3.7 is applicable for this purpose. Therefore, it will be interesting to examine the structure of the space-charge layers including length scales of it by MD simulations.

3.1.3 Deformation-Induced Defects Model

Although the space-charge model can explain the experimental fact in several cases, Dudney [9-11] reported that the space- charge layer could not explain successfully the enhancement of dynamics and proposed that the deformation-induced defects stabilized by inert phases cause the enhanced conductivity. It was found that the composites of AgCl and Al₂0₃ prepared by impregnation of an alumina fiber paper with molten AgCl did not show any enhancement, while the deformed one showed the enhancement [10]. It was also pointed out that the samples exhibiting enhanced conductivity so far reported were prepared as a pellet under pressure.

It is worth mentioning that one must consider the effects of pressure and tension remaining in the system.

The possible mechanism caused by deformation seems to be concerned with not only geometrical factors of paths but also the structure of cages discussed in Chapters 6 and 7.

3.1.4 Effect of Sizes of Particles in LiI–Alumina Composite

In 1979, Stoneham and coworkers [4] demonstrated that lithium iodide shows enhanced ionic conductivity when doped with a powder of the insulator, alumina. They extended Landauer's effective medium model [17] for electric resistance of binary systems to see if the observations were consistent with a high- conductivity layer forming on each non-conducting particle. They introduced a model, where the conducting region does not end abruptly but tails off into the bulk, and the model worked well. They have argued how the size of particles of powder affects the conductivity when high-conductivity layer surrounding insulator particles exists and has shown that the existence of the maximum of the enhancement. They suggest that the highest ionic conductivity will be reached with very fine alumina powder so that blockage is minimized. The effects of the size of particles seem to modify the geometrical factors related to ionic paths.

3.1.5 Existence of Distinct Sites

Ardel and coworkers [3] have examined the mixture of Lil and particles of A1₂0₃, experimentally. In this case, the system is prepared as the pellet treated under the press. Characterization of the system was done by several experimental methods such as X-ray diffractions, complex impedance, and high-resolution ⁷Li NMR spectroscopy. From these experiments, it was found that the observed enhancement in ionic conductivity by the addition of Al₂0₃ is accompanied with an increase in grain boundary resistance. By the high-resolution (MAS) NMR method, the existence of two or more distinct Li⁺ sites was found. It was also found that populations of different kinds of sites depend on the composition of mixing and temperature. One was assigned to the characteristic of bulk Lil and the rest to the surface/interface regions. Ionic conductivity is thus explained related to their populations. They also reported that the increase of Al₂0₃ concentration from 0 % to 50 % at temperatures below 90 °C is followed by a conductivity increase of only about 60 %, while above 90 °C conductivity enhancement of over a factor of two. They have found that at low temperatures the effect of alumina content on ionic conductivity in Lil-Al₂0₃ is less pronounced.

3.1.6 Percolation Model

Percolation theory can treat situations where conduction paths are separated by boundaries or pores.

Several versions of percolation models have been proposed so far [15,16].

In Fig. 3.2, a three-component bond-percolation model by Roman and coworkers [15] is shown. A remarkable feature of this model is the existence of two threshold concentrations, and the model can explain the existence of the maximum of the conductivity at a certain concentration.

In the figure, the two-phase mixture is represented on a square lattice for different concentrations, p, of the insulating material, which is represented by the shaded regions. In this figure, the highly conducting bonds are marked by bold lines. In Fig. 3.2a, the concentration, p, of the insulator is smaller than p'_c so that the path on the interface is not percolated. In the case of Fig. 3.2b, p is comparable to p'_c, which is the onset of interface percolation. In Fig. 3.2c, p is comparable to the second threshold pi for disruption of the conducting paths. In Fig. 3.2d, the value p is larger than p'l, and therefore portions of insulators spread widely.

Figure 3.2 The two-phase mixture on a square lattice for different concentration p of the insulating material, represented by the shaded regions. The highly conducting bonds are marked by bold lines, (a) p < Pc (b) p = pi onset of interface percolation, (c) p = p'l threshold for disruption of the conducting paths, and (d) p > p" Reprinted with permission from Roman, H. E., Bunde, A., Dieterich, W. (1986), Conductivity of dispersed ionic conductors: A percolation model with two critical points, Phys. Rev. B, 34, pp. 3439-3445.

Although the model, which includes several components, can reproduce the behavior similar to experiments, direct comparison with microscopic behavior of the system seems to be desired and molecular dynamics simulations seem to have the power to bring more insights for such behaviors.

Heitjans and Wilkening [18] have shown ⁷Li nuclear magnetic resonance spectra of nanocrystalline (l-x)Li₂0: xAl₂0₃ composites with different amounts (x) of alumina as shown in

Fig. 3.3. They have pointed out that a larger area fraction of the mobile ions was found when a higher number of conductor- insulator contacts concerning the total Li₂0 content were found. The result can be explained also by the percolation model. The existence of the localized fast ionic motion is considered in that figure.

Figure 3.3 ⁷Li nuclear magnetic resonance spectra of nanocrystalline (1-x) Li₂0: x A1₂0₃ composites with different amounts (x) of alumina (a) x = 0.2, island-like heterostructure, where small volume fraction is for alumina, (b) x = 0.5, where percolating diffusion pathways are formed and it corresponds to the dc-conductivity maximum, (c) x = 0.8, where isolated islands of Li₂0, which is fast but localized pathways are fonned. Spectra were recorded at 433 К and 58.8 MHz. Reprinted with permission from Heitjans, R, Wilkening, M. (2009), Ion dynamics at interfaces: Nuclear magnetic resonance studies, MRS Bull, 34, pp. 915-922, with some modifications.

3.1.7 A Length Scale Related to Enhanced Dynamics

Schreck and coworkers [19] have studied the enhanced ionic conductivity of thin films of Lil evaporated onto a planar sapphire (sapphire is an alumina oxide (oc-Al₂0₃), which usually containing trace amounts of elements such as Ca, Fe) surface. It was found that the specific conductivity of Lil adjacent to the sapphire film (with a thickness of 350 A) exceeded the bulk value by nearly one order. With distance from the surface, the value decreases exponentially. The conductivity of the film varies with temperature (25 °C й T й 120 °C) following activation energy of 0.40±0.04 eV. They argued that the value is in good agreement with the activation energy of bulk Lil in the extrinsic region. The corresponding "Debye-length," over which the conductivity drops to 1/e of its maximum value at the interface, was found to be about 300 A.

The Debye-length seems to be longer than the typical MD basic cell size, and hence one should be careful to design the MD simulations of such systems.

3.1.8 Effect of Impurity Such as Water

It has been reported that the enhancement is affected by how to prepare the sample as shown in the following examples. The effects of impurity, especially water brought during the experimental procedures, have been examined by several works.

Skarstad and coworkers [12] have compared Lil-H₂0 and Lil to learn if the enhancement is due to the presence of water. Measurements of the conductivity of Lil-H₂0 give values ~10'⁵ S cm'¹, while, higher conductivities, 10~⁴ S cm'¹, are observed for Lil and Lil-H₂0 mixed with Si0₂ or Al₂0₃. It means that the conductivity of the monohydrate is not high enough to explain the enhancement. That is, the effect cannot be explained by the presence of water alone.

This problem was also examined by Bjorkstam and coworkers [13] by comparing single crystals of Lil-D₂0 and Lil-H₂0, as well as upon pure and Si0₂ doped LiH-H₂0 powder. In that work, nuclear magnetic resonance studies of line narrowing (72), spin- lattice relaxation (71), and spectral changes with temperature have been performed to measure activation energies and correlation times for Li⁺ ion motion and water molecule reorientation and these results are compared with those from conductivity and structural experiments. The effect of water is found to be non-negligible for the enhancement.

3.1.9 Effect of Water in Related Systems

Enhancement is widely observed in related systems. The effects of water mentioned in the previous section are also observed in Li_xMn₂0₄. Chen and coworkers [14] have examined Li_xMn₂0₄ with 0.5 < x < 2.5. It was found that the lithium chemical diffusion coefficient (chemical diffusion coefficient is for diffusion under concentration gradient) in Li_xMn₂0₄ is fairly affected by the preparation method. If it was synthesized by this wet-chemical technique, at least 10 times higher value than that of Li_YMn₂0₄ was obtained by the solid-state reaction method. Comparing the enhancement by wet and dry methods, the effect of water on the enhancement is suggested.

The maximum of the conductivity and the smaller slopes in the Arrhenius plots are commonly found in some composites of Agl and М_хО^, (=A1₂0₃, Zr0₂, and Si0₂) with different compositions [20]. Comparable behaviors are also observed for nanocrystalline BaF₂ and CaF₂ and in BaF₂:CaF₂ composites [21].

There are many trials to understand the origin of the enhancement. Pre-factor and activation energy found in the Arrhenius plot seems to be useful to distinguish the possible mechanisms. Phipps and Whitmore [22] have observed the smaller (about 1/3 of bulk Lil) activation energy of the Lil sandwiched by Si0₂ plates as well as the increase of the pre-factor.

Yamada and coworkers [23] have examined the Lil-SiO ₂ system by XRD, geometric density, and a.c. impedance. They concluded that their result with nearly constant activation energy suggested that ionic conductivity was enhanced by not deformation-induced defects but space-charge layer at interfaces. They found that the maximum ionic conductivity of 5.8 * 10'⁶ S cm"¹ was observed when the amount of Lil was slightly smaller than the amount to fill pores. In that case, the maximum conductivity was obtained for the composite with the volume fraction of Si0₂ of 0.173. Although these works seem to support the existence of enhancement at the surface of some materials, when the adjacent layer of

Lil exists, the mechanism in different situations, further research, including the trapping effect in mesoporous systems and different sizes of pores, seems to be necessary to conclude the mechanism.

3.1.10 Lithium Silicate Glass Grown within Pores and in Composites

Similar enhancement of dynamics was observed in silicate glass within porous materials. Especially, systems containing lithium ions are important for designing high-conductivity materials towards solid-state batteries. In Section 3.1.6, alumina, silica, and other network formers are just considered as insulators to separate the ionically conducting phases, and hence the changes in the structures for the ionic conducting phase are not considered clearly. Different from these approaches, recently, the role of the free space in porous materials has been focused on in several papers.

3.1.11 Lithium Silicate in Porous Systems

For example, Saha and coworkers [24] have examined the conductivity of the system 23Li₂0-77Si0₂ in a pellet formed by ZnO nanorods. In this case, silicate glass was grown within the pores of a pellet formed by ZnO nanorods of a diameter of 70 nm, where lengths are changed from 80 to 270 nm. Remarkable enhancement of conductivity is found in such conditions. That is, nanoglass supported in nanorods shows three orders of lesser resistivity and 35% lower activation energy compared to its bulk counterpart. This effect was ascribed to an increase in free volume in the nano-dimensional glass. The ac conductivity variation at high frequency showed an exponent of 0.5 indicating two-dimensional movements of lithium ions in the nanoglass.

This effect of introducing pores by support materials is closely related to the results of molecular dynamics simulations of porous lithium silicate, which will be discussed in Chapters 6 and 7. The effect caused by free volume seems to be concerned with two factors: vacancies on the jump paths of ions and the caging of ions. The important difference between these factors is as follows. The former factor is mainly concerned with the geometrical conditions related to the jump paths, while in the latter, the deformation or introducing pores affects the jump rates of the of ions through structures of cages. To distinguish the mechanism by the geometry of jump paths and changes in caged dynamics, it is convenient to consider the time- dependent behavior of the mean squared displacement of ions (or corresponding frequency dependence of the conductivity spectra). That is, these factors can be distinguished by the time scale of events as shown in Chapters 6 and 7. In both cases, the roles of cooperative motions should be taken into account.

3.1.12 Ion Transport in the Dilithium Ethylene Dicarbonate (Li2EDC)

A complex system including Li ions has been studied by Borodin and coworkers [25]. That is, ion transport in the dilithium ethylene dicarbonate (Li₂EDC) component of the solid electrolyte interphase was examined by impedance spectroscopy and molecular dynamics (MD) simulations. When the melt is compared with the ordered system, the absolute value of the slope of the latter in Fig. 3.4 is smaller. That is, a decrease in the activation energy is observed. Snapshots of the structures of melt and the ordered system are shown in Fig. 3.4 and a clear ordering of Li ions is observed in Fig. 3.4c.

Figure 3.4 Snapshot from the MD simulations of Li₂EDC of the (a) ordered and (b) amorphous (molten phase) states at 450 К (Li* are highlighted as pink balls). A representative cluster from bulk Li₂EDC (ordered) with distances less than 2.4 A connected by dashed lines is also shown (c). Reprinted with permission from Borodin, 0., Zhuang, G. V., Ross, P. N., Xu, K. (2013), Molecular dynamics simulations and experimental study of lithium ion transport in dilithium ethylene dicarbonate, J. Phys. Chem. C, 117(15), pp. 7433-7444. Copyright (2013) American Chemical Society.

From such aligned structures of Li ions, it may be expected that the enhancement of ion dynamics is caused by the cooperative motions of ions [26].

Conductivity from MD simulations using a polarizable model for melts and ordered Li₂EDC materials is shown in Fig. 3.5. As shown in this figure, when temperature decreases, the Li⁺ diffusion coefficient between Li⁺ layers in the ordered sample decreases slower than the diffusion coefficient of melts.

Figure 3.5 Conductivity from MD simulations using a polarizable APPLE&P force field for melts and ordered Li₂EDC materials. Results from the MD simulations using a previous force field FF06 are also shown for comparison (crosses). AE (melt) = 84 kj/mol, AE (ordered) = 64 kj/mol. Reprinted with permission from Borodin, 0., Zhuang, G. V., Ross, P. N., Xu, K. (2013), Molecular dynamics simulations and experimental study of lithium ion transport in dilithium ethylene dicarbonate, J. Phys. Chem. C, 117(15), pp. 7433-7444. Copyright (2013) American Chemical Society.

At low temperatures, the Li⁺ diffusion across the layers is expected to become negligibly small compared to the diffusion within the Li⁺ layers. Heterogeneous and non-Gaussian motions of lithium ions have been observed at 393 K. The difference between polarizable and non-polarizable models has also been discussed. Heterogeneous dynamics in other ionic systems related to these results will be discussed in Chapter 5.

3.1.13 Ion Transport in Polymer Electrolyte-SiO_z Nanospheres in Polyethylene Oxide)

Polymer electrolyte with silica has been examined by Lin and coworkers [27]. They measured conductivities of some composite solid polymer electrolyte. Monodispersed Si0₂ nanospheres in poly(ethylene oxide) showed good ionic conductivity (1.2 x 10'³ S cm'¹ at 60 °C, 4.4 x 10"⁵ S cm"¹ at 30 °C), as well as electrochemical stability of the window up to 5.5 V. They have concluded that these systems show excellent rate capability as well as good cycling performance applicable to all-solid-state lithium batteries.

For a better understanding of the mechanisms of enhancements, following argument will be useful. Explanations so far proposed for the mechanism of enhancement seem to be related to the following factors.

Structural changes of ionic paths tend to be caused by the mixing of low conducting parts or insulator. In many papers, alumina or silica in composites is regarded as an insulator, which affects the paths of ions. These paths are affected by geometrical factors such as the structures of boundaries, layers, particle sizes, vacancies, and disorders.

Another possibility is that structural changes of cages are caused by introducing pores. It is because the insulators such as alumina or silica used in composite showing enhanced dynamics have a network structure, which is regarded as the porous support of ions in the ionic compounds (see Chapters 6 and 7).

3.1.14 Separation of Possible Factors Related to the Enhancement

Besides the factors mentioned in the previous sections, there are several effects found in nanostructured materials. It should not be forgotten that the difference of order and disorder of the structure in the system has a large effect (which can be several orders in magnitude) on the diffusivity and/or conductivities of ions [28-30]. Effects can be caused by the specific chemical or physical structure of materials.

Which factor (or factors) is (are) the most relevant among many possible factors? How can we distinguish the effect from others?

In the following chapters, such problems will be treated by MD simulations.

Here we briefly mention the outline of Chapters 4-7 to understand the relations among the chapters.

The dynamics in ionically conducting materials are complicated ones, which often deviate from Gaussian dynamics in several kinds of observations. Therefore, first, to examine the motions of ions in typical ionic conductors will be useful. This will be shown in Chapter 5. The characteristics of ionic motions explained here are used as the standard system to understand the effects of further modifications of systems.

In Chapter 5, from the results of MD simulations of lithium metasilicate glasses, fundamentals of ionics, including time scales and length scales found in the mean squared displacement in lithium silicate systems, will be explained. It is found that ionic motion is strongly heterogeneous and fast ions are accelerated by both short intervals of jumps as well as strong forward correlated motions in ion channels. The acceleration by the shortened time intervals of jumps is caused by the loosening of cages in a short time and length scales. While the forward correlated motions of ions are affected by the cooperativity of motions. As easily imagined, the latter motion is concerned with the dimensionality of the paths in longer time and length scales.

As shown in Fig. 3.6, the motion is accelerated by cooperative jumps of several Li ions and such motion is characterized [26] as Levy flight dynamics [31]. Such kind of acceleration by cooperative motions is commonly observed in recent MD simulation of fast ion conductors [32-35]. The trajectories of ions form the shape of ion channels as already shown in Fig. 2.9 in Chapter 2. That is, the changes of motions and paths (ion channels) related to the percolation theory are one of the possible explanations. This kind of motion can also play roles in other composites. For instance, the alignment of Li ions in Fig. 3.5c seems to be suitable for this kind of motions, although further confirmation is necessary.

How can we distinguish two mechanisms relevant to the acceleration of dynamics?

In Chapter 6, the effects of modification observed in a different time and length scale regions will be shown for porous lithium silicate systems. The treatment of these systems can be a good example of how many possible effects caused by perturbations of systems can be distinguished by using MD simulations. As shown in the experimental facts for lithium-containing systems shown above, enhancement of ionic motion is quite common in many systems. Therefore, it is probable that the comparable mechanism observed in porous lithium silicate found in MD simulations in the NVE condition can contribute to the enhanced dynamics in related composites. As shown in this example, we suggest that one of the possible methods to confirm the mechanism is to examine the time scales and length scales of events concerning the enhancement.

Figure 3.6 Trajectories of the lithium ions showing cooperative jumps projected on the x-y plane during 16 ps at 700 К in lithium metasilicate. Reprinted from Habasaki, J., Okada, I., Hiwatari, Y. (1997), Fracton excitation and Levy flight dynamics in silicate glasses, Phys. Rev. B, 55, pp. 6309-6315 with permission. Copyright (1997). American Physical Society.

Since the dynamics of ions are known to be heterogeneous in glasses or crystals, it is interesting to consider the effects of modification of such characteristics in the porous systems as well as in composites. The characteristics of non-Gaussian (NG) dynamics shown in Section 3.2.2 are like those found in the single alkali systems [36, 37]. Modification of non-Gaussianity in the porous system will be discussed in Chapter 7. The examination of heterogeneity in the system also provides a way to distinguish the mechanism of the enhancement.

For the development of the field of nanoionics, further research for the nanoscopic mechanism of the enhancement is expected and molecular dynamics simulation seems to be suitable for such treatments.

It is interesting to note that decreases in activation energy in the temperature dependence of conductivity have been reported for many systems showing enhanced dynamics.

In the case of fragile ionic liquid, non-Arrhenius behavior of the diffusivity is explained by the inflection of the behavior at T_c (or T_B) [38] in diffusivity against the inverse of temperature on a double-logarithmic scale. Above it, cooperative motions with long-ranged motion are dominant, while at lower temperatures localized motion with shorter length scales becomes dominant. In other words, it is related to the existence of heterogeneous dynamics, where the long-ranged cooperative jumps are suppressed at lower temperatures. This is due to the formation of more closely packed structures [39].

From this point of view, observed behavior in composites (and porous systems as shown in Chapter 6) is regarded as the result caused by the weakened suppression of the motions at lower temperatures by introducing pores (free volume).