Definitions, kinds

Unfortunately, most of the terms which the alchemists used to designate their Elements and Principles are terms which are now employed to designate specific substances. The word fire is still employed rather as a quality of many things under special conditions, than as a specific substance but earth, water, air, salt, sulphur, and mercury, are to-day the names applied to certain groups of properties, each of which is different from all other groups of properties, and is, therefore, called, in ordinary speech, a definite kind of matter. 

In addition to these advantages, the phlogistic theory was based on experiments, and led to experiments, the results of which proved that the capacity to undergo combustion might be conveyed to an incombustible substance, by causing it to react with some other substance, itself combustible, under definite conditions. The theory thus prepared the way for the representation of a chemical change as an interaction between definite kinds of substances, marked by precise alterations both of properties and composition. 

The Eqs. (23)-(25) permit for each concrete alloy to define the dependence character of solubility of interstitial impurity of definite kind on concentration a, temperature T, degree of long-range order rj, if energetic parameters a, a, p, P are known. 

In many cases it is possible to choose in many different ways the independent components of the sterns of a given kind for instance, take tems formed of hydrated crystals of sodium acetate and of an aqueous solution of sodium acetate we may take as independent components of the i stems of this kind water and hydrated sodium acetate we may take also, for independent components, water and anhydrous sodium acetate. But if the nature of the independent components of a definite kind of chemical i stems may, in certain cases, show a certain indefiniteness, the number of these independent components can show none it is easy to demonstrate the following theorem The number of independent components of systems of a given kind is always the same, whatever the manner of grouping the independent components of the elements which form the systems of the kind considered. 

Operators, or entities which operate on any function, that is, which when applied to this function, generate another function, can be represented in the most diverse ways. Heisenberg s matrices are simply one definite kind of representation of such operators another kind is the set of difhirential coefficients corresponding to the momentum components and the energy. In the latter kind of representation the Born-Jordan commutation laws admit of a simple interpretation here, by what we have just fvien, pq — qp simply means the application of the differential operator... 

Consider two distinct closed thermodynamic systems each consisting of n moles of a specific substance in a volnme Vand at a pressure p. These two distinct systems are separated by an idealized wall that may be either adiabatic (lieat-impemieable) or diathermic (lieat-condncting). Flowever, becanse the concept of heat has not yet been introdnced, the definitions of adiabatic and diathemiic need to be considered carefiilly. Both kinds of walls are impemieable to matter a permeable wall will be introdnced later. 

For tire purjDoses of tliis review, a nanocrystal is defined as a crystalline solid, witli feature sizes less tlian 50 nm, recovered as a purified powder from a chemical syntliesis and subsequently dissolved as isolated particles in an appropriate solvent. In many ways, tliis definition shares many features witli tliat of colloids , defined broadly as a particle tliat has some linear dimension between 1 and 1000 nm [1] tire study of nanocrystals may be drought of as a new kind of colloid science [2]. Much of die early work on colloidal metal and semiconductor particles stemmed from die photophysics and applications to electrochemistry. (See, for example, die excellent review by Henglein [3].) However, the definition of a colloid does not include any specification of die internal stmcture of die particle. Therein lies die cmcial distinction in nanocrystals, die interior crystalline stmcture is of overwhelming importance. Nanocrystals must tmly be little solids (figure C2.17.1), widi internal stmctures equivalent (or nearly equivalent) to drat of bulk materials. This is a necessary condition if size-dependent studies of nanometre-sized objects are to offer any insight into die behaviour of bulk solids. 

The same kind of spontaneous racemization oc curs for any as 1 2 disubstituted cyclohexane in which both substituents are the same Because such compounds are chiral it is incorrect to speak of them as meso compounds which are achiral by definition Rapid chair-chair interconversion however converts them to a 1 1 mixture of enantiomers and this mix ture IS optically inactive... 

Just as it is not necessary for polymer chains to be linear, it is also not necessary for all repeat units to be the same. We have already mentioned molecules like proteins where a wide variety of different repeat units are present. Among synthetic polymers, those in which a single kind of repeat unit are involved are called homopolymers, and those containing more than one kind of repeat unit are copolymers. Note that these definitions are based on the repeat unit, not the monomer. An ordinary polyester is not a copolymer, even though two different monomers, acids and alcohols, are its monomers. By contrast, copolymers result when different monomers bond together in the same way to produce a chain in which each kind of monomer retains its respective substituents in the polymer molecule. The unmodified term copolymer is generally used to designate the case where two different repeat units are involved. Where three kinds of repeat units are present, the system is called a terpolymer where there are more than three, the system is called a multicomponent copolymer. The copolymers we discuss in this book will be primarily two-component molecules. We shall discuss copolymers in Chap. 7, so the present remarks are simply for purposes of orientation. 

Step-growth polymerizations can be schematically represented by one of the individual reaction steps VA + B V —> Vab V with the realization that the species so connected can be any molecules containing A and B groups. Chain-growth polymerization, by contrast, requires at least three distinctly different kinds of reactions to describe the mechanism. These three types of reactions will be discussed in the following sections in considerable detail. For now our purpose is to introduce some vocabulary rather than develop any of these beyond mere definitions. The principal steps in the chain growth mechanism are the following ... 

In the extreme case where rjrj =0 because both rj and i2 equal zero, the copolymer adds monomers with perfect alternation. This is apparent from the definition of r, which compares the addition of the same monomer to the other monomer for a particular radical. If both r s are zero, there is no tendency for a radical to add a monomer of the same kind as the growing end, whichever species is the terminal unit. When only one of the r s is zero, say rj, then alternation occurs whenever the radical ends with an Mj unit. There is thus a tendency toward alternation in this case, although it is less pronounced than in the case where both r s are zero. Accordingly, we find increasing tendency toward alternation as rj 0 and rj 0, or, more succinctly, as the product X1X2 0. 

The systematic study of piezochromism is a relatively new field. It is clear that, even within the restricted definition used here, many more systems win be found which exhibit piezochromic behavior. It is quite possible to find a variety of potential appUcations of this phenomenon. Many of them center around the estimation of the pressure or stress in some kind of restricted or localized geometry, eg, under a localized impact or shock in a crystal or polymer film, in such a film under tension or compression, or at the interface between bearings. More generally it conveys some basic information about inter- and intramolecular interactions that is useful in understanding processes at atmospheric pressure as well as under compression. 

In vertical downward flow as well as in upward and downward inclined flows, the flow patterns that can be observed are essentially similar to those described above, and the definitions used can be applied. Experimental data on flow patterns and the transition boundaries are usually mapped on a two dimensional plot. Two basic types of coordinates are generally used for this mapping - one that uses dimensional coordinates such as superficial velocities, mass superficial velocities, or momentum flux and another that uses dimensionless coordinates in which some kind of dimensionless groups are used as coordinates. The dimensional coordinates maps are inherently limited to the range of data and flow conditions under which the experiments were conducted. In spite of this limitation, it is widely used because of its simplicity and ease of use. Figure 24 provides an example of such a map. 

The next problem area of micromechanics is initially very attractive in some respects. We look to the fundamental definition of a composite material made up in this case of, say, a fiber and a matrix and attempt to actually design that material. Let us change the proportions of fibers and matrix so that we get the kind of material behavior characteristics we want. That objective is admirable, but achieving that objective in all cases is not entirely realistic. 

There are many definitions of the word risk. It is a combination of uncertainty and damage a ratio of Itazards to safeguards a triplet combination of event, probability, and consequences or even a measure of economic loss or human injury in terms of both the incident likelihood and tlie magnitude of the loss or injuiy (AICliE, 1989). People face all kinds of risks eveiyday, some voluntarily and otliers involuntarily. Tlierefore, risk plays a very important role in today s world. Studies on cancer caused a turning point in tlie world of risk because it opened tlie eyes of risk scientists and healtli professionals to tlie world of risk assessments. 

The operation involved in the definition of the EPI is an exchange of atoms on sites i and j and it is a kind of localized perturbation. So the orbital peeling method provides an efficient means for obtaining the generalized phase shifts. 

According to the Hiickel criteria for aromaticity, a molecule must be cyclic, conjugated (that is, be nearly planar and have ap orbital on each carbon) and have 4n + 2 tt electrons. Nothing in this definition says that the number of p orbitals and the number of nr elections in those orbitals must be the same. In fact, they can he different. The 4n + 2 rule is broadly applicable to many kinds of molecules and ions, not just to neutral hydrocarbons. For example, both the cydopentadienyl anion and the cycloheptatrienyl cation are aromatic. 

Lipids are naturally occurring organic molecules that have limited solubility in water and can be isolated from organisms by extraction with nonpolar organic solvents. Fats, oils, waxes, many vitamins and hormones, and most nonprotein cell-meznbrane components are examples. Note that this definition differs from the sort used for carbohydrates and proteins in that lipids are defined by a physical property (solubility) rather than by structure. Of the many kinds of lipids, we ll be concerned in this chapter only with a few triacvlglycerols, eicosanoids, terpenoids, and steroids. 

Compounds are formed when atoms of two or more elements combine. In a given compound, the relative numbers of atoms of each kind are definite and constant. In general, these relative numbers can be expressed as integers or simple fractions. 

So far in this chapter our discussion has focused on thermochemistry, the study of the heat effects in chemical reactions. Thermochemistry is a branch of thermodynamics, which deals with all kinds of energy effects in all kinds of processes. Thermodynamics distinguishes between two types of energy. One of these is heat (q) the other is work, represented by the symbol w. The thermodynamic definition of work is quite different from its colloquial meaning. Quite simply, work includes all forms of energy except heat. 

Crystals have definite geometric forms because the atoms or ions present are arranged in a definite, three-dimensional pattern. The nature of this pattern can be deduced by a technique known as x-ray diffraction. Ihe basic information that comes out of such studies has to do with the dimensions and geometric form of the unit cell, the smallest structural unit that, repeated over and over again in three dimensions, generates the crystal In all, there are 14 different kinds of unit cells. Our discussion will be limited to a few of the simpler unit cells found in metals and ionic solids. 

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