Desktop version

Home arrow Mathematics

  • Increase font
  • Decrease font

<<   CONTENTS   >>

Classification of Nanostructured Materials and Effects of Nano-Sizing

Nanostructured materials (NSM) have useful properties such as high conductivity, high storage power of materials and energy if a suitable combination of constituents and nanoscopic structures are designed. Especially, enhanced dynamics found in nanoionics [1] is an important issue to be discussed.

In this book, complex systems such as nanoporous materials [2, 3] and colloidal solutions [4] are examined by molecular dynamics (MD) simulations. Before explaining the results of these works, some preparations for the treatment of these systems are necessary. First, the classification of the nanostructured materials is discussed in this chapter and it will be expanded to cover fractal and porous structures based on our several projects concerning complex systems. Then the general effects of nanosizing will be discussed. Here the term "fractal" does not necessarily mean the exact self-similar shapes, but it includes statistical ones. Details of the concept of the fractal will be explained later in Chapter 4.

What Are Nanostructured Materials?

Definitions of nanostructured materials are not the same if different researchers and fields are concerned. First, some methods found in the literature will be explained.

Classifications of Nanostructured Materials Found in the Literature

In 1995, Gleiter called the materials with a nanometer-sized (typically 1-10 nm) microstructure "nanostructured materials (NSMs)” [5, 6], where the structure elements discussed are mostly crystallites. In these articles, 12 typical structures are classified by combinations of four families (different chemical composition of crystallites) and three categories (different shapes of crystallites-layer-shaped, rod-shaped, and equiaxed crystallites).

Later, Pokropivny and Skorokhod [7] suggested classification based on the dimensionality of nanostructures themselves [k = 0,1,2,3) and of their components (/, m, n = 0,1,2,3) and a total of 36 classes are shown, with restricting the classification by 5 main ternary structures of kDlmn type built of 3 sort units. The system size L < 100~500 nm is considered there. For example, No. 35 (3D320) is for powder-layers composites.

As discussed in ref. [7], a general dependence of density of electron state (DOS) on the dimension of the nanostructure is well known. Namely, p(£)~AE, p[E) = const., p(£)~l/V (E-E0), and p(£)~<5(£-£’0) are for the 3-D, 2-D, 1-D and 0-D nanostructures, respectively. In general, diffusivity and conductivity also depend on the dimensionality as found in the Einstein equations. The dimension of the structure is also closely related to the surface area or related characteristics of nanoscale systems as discussed later. Thereby, similar classifications using dimensionality were used by several authors.

In 2011, Liu et al. [8] discussed the heterogeneous nanostructured electrode, where the nanostructured materials were also classified based on their structural complexity. That is, systems were classified from zero-dimensional (0-D) to three- dimensional (3-D). For example, 0-D includes core/shell (or core-shell) [9-11] nanoparticles, one-dimensional (1-D) includes coaxial nanowires, two-dimensional (2-D) includes graphene- based composites and three-dimensional (3-D) includes mesoporous carbon-based composites and the even more complex hierarchical 3-D nanostructured networks.

These classifications can treat "known systems" successfully and will be useful for many purposes, although suitable classification may depend on each purpose.

For example, by classification, one may have a clear picture of materials.

In the following sections, a similar scheme to classify complex nanostructured materials will be introduced. Although it depends on the same basis of dimensionality of nanostructures as in [7, 8], the combinations will not be restricted to the limited number of combinations and the classification will be expanded to further modification of systems.

The purpose of this trial is three-fold.

  • 1. Complicated NSMs tend to have several components, several structural units with different fractal dimensions [12-16] and length scales, different porosity (porosity is usually defined as a fraction of pores or voids in the material). They may have different physical and chemical properties such as colors, mechanical properties, heterogeneities and so on. Possible combinations of them seem to be infinite. Therefore, the expansion of the classification to include more systems with different combinations seems to be required, so that one can find out new combinations for designing materials. Accordingly, classification, which can include many unknown systems without the restriction of classifications, is desirable.
  • 2. In this book, ionically conducting glasses and colloidal solutions and its coagulation, as well as other complex systems, are examined. Furthermore, the concept of multifractal [13-16] is introduced because more than one characteristic region of the length scale is found in colloidal systems and gels [4,17,18].

Therefore, the classification of systems is better to be extended to use fractal dimensions, to treat disordered and/or fractal systems.

3. There are several methods to treat porous systems. Some of them are discussed here. One of the possible methods is to use the apparent dimension for typical porous systems.

An approach from a different direction is to use packing factor (or porosity) or fractal dimensions as parameters to control and characterize properties such as conductivity and mechanical properties.

The classification using these values can treat the porous systems systematically. In Chapters 6 and 7, it will be shown that the diffusivity (and hence conductivity) of ions is modified considerably by changes in the porosity.

Classification of Substructures by the Dimension of Elemental Structural Units and Dimension of Space

In this chapter, a classification based on the dimensionality will be extended for mixtures, fractal structures, porous structures, and dispersed structures. The outline of explanations of these concepts is shown in Fig. 2.1.

Elemental Units of Nanostructures

In ref. [7], nanostructures are distinguished from the nanostructured materials, which can be bulk. Similarly, we consider the whole structure of nanostructured material and substructures of them separately. Substructures are formed by the elemental nanostructural units shown in Fig. 2.2.

For useful classifications, one needs to choose the elemental unit and the length Я to characterize the nanostructured materials, where Я is a length scale determining the range of sizes to treat as nanomaterials. It can be typically 10-100 nm; however, there are some differences among researchers. If it is compared with the characteristic length scale of the phenomena, a clear definition of it will be required. If no description of Я is given, the natural way is to choose Я as 1-1000 nm exactly stated in the term "nanostructured materials."

Outlines of classification and expansion of it to fractal (multifractal) and porous systems

Figure 2.1 Outlines of classification and expansion of it to fractal (multifractal) and porous systems.

In Fig. 2.2, elemental units of the structures with different dimensionality are shown. They are named as 0-d~3-d with using small character d.

As in ref. [7], if all length scales, lx, ly, and I2 are less than or equals to X, the unit can be regarded as zero-dimensional (0-d). The unit of 0-d in Fig. 2.2 can be colloids, primary- particles, clusters. Combination of 0-d structures can be still in the nanoscale. Therefore, secondary particles in nano-size can be still regarded as 0-d structures. The 0-d units can form structures of different dimensionality as shown in Fig. 2.2. If two directions are less than X, the unit is regarded as 1-d, where structures are formed by combinations of 0-d units. If one direction (thickness) is less than X, it is regarded as 2-d, where the unit is formed by 0-d or 1-d units. 3-d units are not in the nanoscale but can be a part of the substructures in nanostructured materials.

This concept is similar to those in refs [7, 8] in the sense that it is based on the dimensionality of the structural units.

Schematic descriptions of elemental units of nanostructured materials, where the dimensionality is determined by its length scale of different directions. [0-d structures]

Figure 2.2 Schematic descriptions of elemental units of nanostructured materials, where the dimensionality is determined by its length scale of different directions. [0-d structures]: These elemental units are regarded as zero dimensional (0-d), which is atomic, or clusters or molecular levels. The elemental units can be primary particles, colloids, if lx ly lz are less than or equals to A. [1-d structures]: If a diameter of the unit is less than or equals to X, it can be regarded as a nanostructure unit [a nanofiber). The unit is regarded as 1-d, where structures are formed by combinations of 0-d units. Several length scales can be used to distinguish, for example, short and long structures. Here the value A is a length scale determining the range of sizes to treat as nanomaterials. [2-d structures]: If one direction [thickness) or a unit is less than or equals to A, it is regarded as 2-d, where the unit is formed by 0-d or 1-d units. Several sized ones can be distinguished if necessary. [3-d structures]. These structures are not in nano-size but can be a part of nanostructured materials.

Substructures of Nanostructured Materials

Substructures formed by these elemental units in each space dimension, D, are considered. Some examples for substructures (images) by this classification using dimension of structural units and that for space are shown in Fig. 2.3 as a combination of rows and columns. The essence of descriptions of elemental units in Fig. 2.2 is depicted in the bottom row of Fig. 2.3. Different from Fig. 2.2, substructures in Fig. 2.3 contain assembly and/or hierarchy structures of elemental units. All substructures shown in Fig. 2.3 can be regarded as building units of NSM. All possible combinations can be considered based on this kind of figure (including porous systems mentioned later).

Substructures of NSM

Figure 2.3 Substructures of NSM: Schematic description of classification of substructures of nanostructured materials based on the dimension of structural units, (0-d~3-d) and that of the (partial) space occupied by the substructure. Structures thus defined can be indexed by both dimensions. For example, arrays of columns forming a 3D structure can be indexed as 3D(ld). The difference in colors within each substructure is for a distinction of different chemicals and/or properties but not necessarily mean different constituents. If 1-d structures (sticks, rods), are in 3-D space and formed 3-D structures, one can use the index like 3D(ld). Elemental nanostructural units and their assemblies are included in the bottom row (below a red line). The combination of 0-d and 0-D can represent secondary particles. The core-shell-type particle can be also included in the class of 0D(0d). The rows for 3-d (above a green line) are not in nano-size but can be a part of the nanostructured materials. 3D(0d~2d) are not necessarily in nano-size but they can include nanostructured parts. Expansion of the classification, including mixing of these structures, fractal dimensions of assembly of structures, and contribution of pores, will be considered later.

Substructures thus defined can be indexed by both dimensions. If 1-d structures (sticks, rods), are located in 3-D space and formed 3-D structures, one can use the index like 3D(ld). Merit to use such indexing is not only to classify already-existing materials but also to find out missing combinations of building units with different characteristics. In these figures, space dimensions 0-D, 1-D and 2-D are for a partial space of 3-D.

<<   CONTENTS   >>

Related topics