Zero-dimensional particle

Nanocrystals are zero-dimensional particles and can be prepared by several chemical methods, typical of them being reduction of salts, solvothermal synthesis and the decomposition of molecular precursors, of which the first is the most common method used... 

Quantum size effects related to the dimensionahty of a system in the nanometer range suggests a plethora of future applications using novel material properties. Whereas three-dimensional systems have an infinite extent in all three directions, in layered systems, for example atomic monolayers and thin films, the dimensionality is two, i.e. they are characterized by a limited number of layers. Consequently, a one-dimensional material is represented by wires on an atomic or molecular scale and may be realized in fibers or polymers. Zero-dimensional particles are reduced in all directions to such an extent that the properties of the original bulk system cannot... 

Similar to zero-dimensional metal nanoparticles, most of the work on one-dimensional metal nanostructures focuses almost exclusively on gold nanorods. The high interest in anisometric gold nanoclusters arises from their unique optical and electronic properties that can be easily tuned through small changes in size, structure (e.g., the position, width, and intensity of the absorption band due to the longitudinal surface plasmon resonance is strongly influenced by the shell as well as the aspect ratio of the nanorods), shape (e.g., needle, round capped cylinder, or dog bone), and the inter-particle distance [157]. 

Synthesis forms a vital aspect of the science of nanomaterials. In this context, chemical methods have proved to be more effective and versatile than physical methods and have therefore, been employed widely to synthesize a variety of nanomaterials, including zero-dimensional nanocrystals, one-dimensional nanowircs and nanotubes as well as two-dimensional nanofilms and nanowalls. Chemical synthesis of inorganic nanomaterials has been pursued vigorously in the last few years and in this article we provide a perspective on the present status of the subject. The article includes a discussion of nanocrystals and nanowires of metals, oxides, chalcogenides and pnictides. In addition, inorganic nanotubes and nanowalls have been reviewed. Some aspects of core-shell particles, oriented attachment and the use of liquid-liquid interfaces are also presented. 

The special effects associated with materials made up of nanosized particles are also due to non-local interactions. Such effects were first noticed in the field of micro-electronics during efforts to decrease the size of devices to quasi one-dimensional or zero-dimensional structures [236]. One possibility for obtaining zero-dimensional structures is the inclusion of spherical semiconductor particles in a transparent dielectric medium. Such isolated microcrystals, typically of nanometer size are known as quantum dots. Best-known examples include particles of CdS and CdSe isolated in silicate glasses. 

A simple example of the wave equation, the one-dimensional particle in a box, shows how these conditions are used. We will give an outline of the method details are available elsewhere.The box is shown in Figure 2-3. The potential energy V x) inside the box, between x = 0 and x = a, is defined to be zero. Outside the box, the potential energy is infinite. This means that the particle is completely trapped in the box and would require an infinite amount of energy to leave the box. However, there are no forces acting on it within the box. 

Figure 5.17 shows a HREM image of a carbon allotrope having a zerodimensional (point) polymer of carbon observed at tire lower part of postshock sample I. The characteristic of the electron diffraction pattern of this type consists of two-dimensional asymmetric (hk) bands and symmetric (0001) reflections of tlie graphite structure and did not alter with tlie angle of tlie incident electron beam. In general, such patterns can be obtained when llie particle is a spherical shell, tlrat is, a zero-dimensional characteristic. Therefore,... 

Thus far, four mechanisms for the formation of concentric shell carbon particles as zero-dimensional carbon allotropes have been proposed. The first mechanism is the formation of a corannulene carbon framework followed by a spiral-shell growth [48], The second mechanism is that the regular concentric arrangements of carbon layers in the onion-like caibon sphere occur tlirough the solidification process of a carbon droplet under ultrafast condensation (49J. The third mechanism is due to a solid—>quasi-liquid—>solid process tliat is, reorganization of soot-containing tubular and polyhedral graphitic particles by... 

Chapter V,2). The coagulation occurs when the particles approach each other at distance Rmn, which is the sum of their radii. Due to coagulation the particles assume a new n + m-dimensional state. One thus can state that the concentration of m-dimensional particles at distance Rmn from the center of n-dimensional particle is equal to zero. Under such boundary conditions, assuming that particles are spherical, one can write eq. (IV.20) as... 

In the case of (a), the zero-dimensional (0-D) nanostructure is composed of nanoparticles whose fabrication requires the control of more than merely their diminutive size. For any practical applications such as electroactive components in electrodes, the processing conditions must be controlled so that the resulting nanoparticles have the following characteristics (a) identical size of aU particles (also referred to as monosized or quasi-monosized), (b) identical shape or morphology, and (c) identical or at least very similar chemical composition and crystal structure. Single crystalline nanoparticles are often referred to in the literature as nanocrystals. When the characteristic dimensions of nanoparticles are sufficiently small and quantum effects are observed, these nanoparticles are commonly... 

For convenience, we shall classify the molecular models according to their topological dimensionality, p. A molecular conformation defined by the set of nuclear position vectors is a zero-dimensional (OD) model. A one-dimensional (ID) model corresponds to a molecular skeleton, defined by the set of nuclear positions and their connectivity (bond) matrix. Contour surfaces of one-particle molecular properties such as electron density or electrostatic potential are topologically two-dimensional (2D) models embedded in three dimensions. Finally, we find a true three-dimensional (3D) model whenever an entire one-electron property over all space is involved. This model can be regarded as the continuum of all 2D isoproperty surfaces. The difference among the models is summarized in Figure 1. We shall deal with pD models in this work (p = 0,1, 2, 3). Each of them requires a different type of shape descriptor. 

The zero-dimensional structure mainly corresponds to nanoparticle or nanosphere. Conducting polymers can be coated on the surface of inorganic particles, and inorganic layers can also be coated onto polymer nanoparticles. Due to their low dimensions, the diffusion pathways of charges and ions would be reduced, thus enhance the electronic properties of composites. 

Stmctures consist not only of the three-dimensional objects that make up the objects and patterns in the stmcture but also of two-dimensional surfaces, one-dimensional fines, and zero-dimensional points associated with these objects. The qualitative microstmctural state is a fist of aU of the classes of object sets that are found in the stmcture. Surfaces, edges, and points arise from the incidence of three-dimensional particles or cells. Eor example, the incidence of two cells in space forms a surface. The kind of surface is made explicit by reporting the class of the two cells that form it The qualitative microstmctural state can be assessed or inferred by inspection of a sufficient number of fields to represent the stmcture. In many cases, one field will be enough for this qualitative purpose. In making this assessment, keep in mind that the process of sectioning the stmcture... 

Even though the expressions nanomaterials or nanocomposites are recent (and very successful), these industrial materials have existed for at least a century and apparently always existed in nature (in minerals and vegetables). These small particles range in size from a few to several tens of nanometres and are called quasi zero-dimensional mesoscopic systems, quantum dots, quantized or Q particles, etc According to Jordan et al. nano-sized inclusions are defined as those that have at least one dimension in the range 1 100 mn. In materials research, the development of polymer nanocomposites is rapidly emerging as a multidisciplinary research activity whose results could broaden the applications of polymers to the great benefit of many different industries. 

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