Shape term, definition

The K shape term definitely replaces the acentric factor, it being more general than the previously proposed acentric factor w. 

Chemicals exist as gases, liquids or solids. Solids have definite shapes and volume and are held together by strong intermolecular and interatomic forces. For many substances, these forces are strong enough to maintain the atoms in definite ordered arrays, called crystals. Solids with little or no crystal structure are termed amorphous. 

The term plastic is not a definitive one. Metals, for instance, are also permanently deformable and are therefore plastic. How else could roll aluminum be made into foil for kitchen use, or tungsten wire be drawn into a filament for an incandescent, light bulb, or a 100 ton ingot of steel be forged into a rotor for a generator. Likewise the different glasses, which contain compounds of metals and nonmetals, can be permanently shaped at high temperatures. These cousins to polymers and plastics are not considered plastics within the plastic industry or context of this book. 

Matter can also be categorized into three distinct phases solid, liquid, and gas. An object that is solid has a definite shape and volume that cannot be changed easily. Trees, automobiles, ice, and coffee mugs are all in the solid phase. Matter that is liquid has a definite volume but changes shape quite easily. A liquid flows to take on the shape of its container. Gasoline, water, and cooking oil are examples of common liquids. Solids and liquids are termed condensed phases because of their well-defined volumes. A gas has neither specific shape nor constant volume. A gas expands or contracts as its container expands or contracts. Helium balloons are filled with helium gas, and the Earth s atmosphere is made up of gas that flows continually from place to place. Molecular pictures that illustrate the three phases of matter appear in Figure 1-12. 

As surface area and pore structure are properties of key importance for any catalyst or support material, we will first describe how these properties can be measured. First, it is useful to draw a clear borderline between roughness and porosity. If most features on a surface are deeper than they are wide, then we call the surface porous (Fig. 5.16). Although it is convenient to think about pores in terms of hollow cylinders, one should realize that pores may have all kinds of shapes. The pore system of zeolites consists of microporous channels and cages, whereas the pores of a silica gel support are formed by the interstices between spheres. Alumina and carbon black, on the other hand, have platelet structures, resulting in slit-shaped pores. All support materials may contain micro, meso and macropores (see text box for definitions). 

Table 2.1 Some terms used to describe the shape of particles (qualitative definition).

One further effect of the formation of bands of electron energy in solids is that the effective mass of electrons is dependent on the shape of the E-k curve. If this is the parabolic shape of the classical free electron theory, the effective mass is the same as the mass of the free electron in space, but as this departs from the parabolic shape the effective mass varies, depending on the curvature of the E-k curve. From the definition of E in terms of k, it follows that the mass is related to the second derivative of E with respect to k thus... 

The three most important characteristics of an individual particle are its composition, its size and its shape. Composition determines such properties as density and conductivity, provided that the particle is completely uniform. In many cases, however, the particle is porous or it may consist of a continuous matrix in which small particles of a second material are distributed. Particle size is important in that this affects properties such as the surface per unit volume and the rate at which a particle will settle in a fluid. A particle shape may be regular, such as spherical or cubic, or it may be irregular as, for example, with a piece of broken glass. Regular shapes are capable of precise definition by mathematical equations. Irregular shapes are not and the properties of irregular particles are usually expressed in terms of some particular characteristics of a regular shaped particle. 

Problem 6.11 gives some very useful relationships between these parameters (damping coefTicient and time constant) and the shape of the response curve. There is a simple relationship between the peak overshoot ratio and the damping coefficient. Then the time constant can be calculated from the rise time and the damping coefficient. Refer to Prob. 6.11 for the definitions of these terms. 

Note 2 Short board-like shaped molecules usually form biaxial nematic mesophases. It is recommended that the use of the term disordered sanidic mesophases for such mesophases be discontinued (see Definition 3.3.1, Note 5). 

There are some very special characteristics that must be considered as regards colloidal particle behavior size and shape, surface area, and surface charge density. The Brownian motion of particles is a much-studied field. The fractal nature of surface roughness has recently been shown to be of importance (Birdi, 1993). Recent applications have been reported where nanocolloids have been employed. Therefore, some terms are needed to be defined at this stage. The definitions generally employed are as follows. Surface is a term used when one considers the dividing phase between... 

The solid state is characterized by definite shape and volume. The observed shape will be the one that maximizes favorable interactions between the atoms, ions, or molecules making up the structure. The preferred shape begins at the atomic or molecular level and is regularly repeated throughout the solid, producing a highly-symmetrical, three-dimensional form called a crystal. The network produced is termed the crystalline lot -t ice. 

---