Basic Concepts and Definitions

A polymer is a giant molecule made up of a large number of repeating units joined together by covalent bonds. The simple compounds from which polymers are made are called monomers. The word polymer is derived from the Greek words poly (many) and meros (parts). Polymer 

The styrene molecule is the monomer, and the resulting structure, enclosed in square brackets, is the polymer polystyrene. The unit in square brackets is called the repeating unit. Some polymers are derived from the mutual reaction of two or more monomers. For example, poly(hexamethylene adipamide) or nylon-6,6 is made from the reaction of hexamethylenediamine and adipic acid, as shown in the following equation  

For a molecule to be a monomer, it must be at least bifunctional. The functionality of a molecule refers to its interlinking capacity, or the number of sites it has available for bonding with other molecules. Reactions between monofunctional molecules use up the reactive groups completely and render the product incapable of further reactions, whereas the presence of two condensable groups in both hexamethylenediamine (-NH2) and adipic acid (-COOH) makes each of these monomers bifunctional with the ability to form polymers. In this respect, styrene is also a bifunctional monomer because the extra pair of electrons in the double bond can form two bonds with vinyl groups in other molecules. 

The number of repeating units in the polystyrene structure (1) is indicated by the index n. This is known as the degree of polymerization (DP). It specifies the length of the polymer chain. Oligomer is a very low 

In order to have any sort of estimation problem in the first place, there must be a system, various measurements of which are available. Rather than develop the notion of a system with a large amount of mathematical formalism, we prefer here to appeal to intuition and common sense in pointing out what we mean. 

The system is some physical object, and its behavior can normally be described by equations. The system can be dynamic (discrete or continuous) or static. Here, we will refer to a process under steady-state behavior. Later in this book we will extend our attention to considering dynamic or quasi-steady-state situations. 

Now let us consider exactly what we mean by estimation. Suppose that there is some quantity (possibly a vector quantity), associated with a system operation, whose value we would like to know at each instant of time. It may be that this quantity is not directly measurable, or that it can only be measured with error. In any case, we shall assume that noisy measurements, y, are available. Suppose, furthermore, that an experiment is designed to measure, or estimate, a set of system variables Xu X2. Xg. The set of variables can be written as the vector 

The most general situation is that in which the desired variables cannot be observed (measured) directly and must therefore be indirectly measured as functions of the direct observations. Thus, let us assume that the set of I measurements y can be expressed as a function of the g elements of a constant vector x plus a random, additive measurement error s. Then the process measurements are modeled as 

If = 0, then y = 0(x) and we say that the measurements are perfect. If 0, then they are noisy. In cases where 0 is assumed to be differentiable at a point x, we can define the matrix C  

In electrochemical terminology, the vessel in which electrochemical transformation occurs is called the cell. To bring the terminology in line with that of chemical reaction engineering, we refer to it as the electrochemical reactor (ECR). An ECR is one in which electrical energy is converted into chemical 

Examples of Difficult/Selective Organic Reactions Carried Out Electrochemicaiiy 

Since the success of the Monsanto process for adiponitrile, several challenging syntheses have been accomplished electrochemicaiiy. An important feature of many of these syntheses is that they cover particularly difficult or selective organic reactions. These include such classes of reactions as oxidation, reduction, carboxylation, dehalogenation, cyanation, etc., several specihc examples of which are listed in Table 21.1) (see Swann and Alkire, 1980, for more examples). 

The basic relationship applicable to all electrochemical reactions is Faraday s law that relates the amount of a substance reacted (kg) at the electrode surface to the charge passed  

Another important parameter associated with electrosynthesis is the amount of energy consumed. This refers to the electrical power in kWH required to produce a unit weight (kg) of the desired product and is given by 

We define a model as a functional relationship or relationships among various quantities involved in a physical process. The relationships may be expressed in the form of algebraic, differential, or integral equations, which need not necessarily possess an explicit analytical solution. In this sense the concept of a 

The quantities appearing in the equations are divided into input variables and output variables or responses of the model. The responses would be the predictions of experimentally observed entities or their known functions. Actual responses, typical for combustion research, are the intensity of a light beam, the voltage generated by a pressure transducer, etc. The researcher is interested, however, in concentrations of species as well as their logarithms and ratios, pressures, temperatures, ignition delay times, luminosity of flames, amounts of soot formed, etc. They can be taken for responses but only when the instrumental functions, i.e., the relationships between the actual responses and the entities considered, are known precisely. 

The input variables are subdivided into controllable variables and parameters. The controllable variables are those quantities whose values can be varied by the experimenter as, for example, initial and boundary conditions of experiments. Empirical and physical constants that are assumed to remain unchanged in a given set or a subset of experiments constitute the parameters of the model. To clarify an ambiguity that may arise from the above definitions let us consider a rate constant that is expressed in the Arrhenius form k = A Qxp — EJRT). In isothermal modeling the rate constant at the assumed temperature, /c, is a parameter. However, if temperature is a controllable variable of the model, then the preexponential factor A and the activation energy are the parameters. 

In modeling theory the term vector is customarily used to denote sets of functions, variables, or parameters (Dorny, 1975). In ordinary mathematical convention, Eq. (2.1) has the form of a vector function with m + p independent variables and / dependent variables . 

Of particular interest to combustion modeling are dynamic models, which are models formulated in terms of differential equations. For the sake of 

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The QET is not the only theory in the field indeed, several apparently competitive statistical theories to describe the rate constant of a unimolecular reaction have been formulated. [10,14] Unfortunately, none of these theories has been able to quantitatively describe all reactions of a given ion. Nonetheless, QET is well established and even the simplified form allows sufficient insight into the behavior of isolated ions. Thus, we start out the chapter from the basic assumptions of QET. Following this trail will lead us from the neutral molecule to ions, and over transition states and reaction rates to fragmentation products and thus, through the basic concepts and definitions of gas phase ion chemistry. 

The aim of this chapter is to describe the process of network formation using qualitative arguments together with simple mathematical tools. The intention is to provide a first approach to the subject that should enable the reader to get acquainted with the basic concepts and definitions of the network structure. 

For a better comprehension of the ED processes it is necessary to refresh a few basic concepts and definitions regarding the electrolytic cell and thermodynamic electrode potential, Faraday s laws, current efficiency, ion conduction, diffusivity, and transport numbers in solution. 

The basic concepts and definitions relating to sound propagation in a lossy material are reviewed. The material may be a viscoelastic polymer which converts the sound energy to heat by molecular relaxation, or the material may be a composite where sound is scattered by inhomogeneities (inclusions) in a host matrix material. 

Some basic concepts and definitions of terms used in the polymer literature are reviewed in this chapter. Much of the terminology in current use in polymer science has technological origins, and some meanings may therefore be understood by convention as well as by definition. Some of these terms are included in this chapter since a full appreciation of the behavior and potential of polymeric materials requires acquaintance with technical developments as well as with the more academic fundamentals of the field. An aim of this book is to provide the reader with the basic understanding and vocabulary for further independent study in both areas. 

Some basic concepts and definitions of statistics, chemometrics, algebra, graph theory, similarity/diversity, which are fundamental tools in the development and application of molecular descriptors, are also presented in the Handbook in some detail. More attention has been paid to information content, multivariate correlation, model complexity, variable selection, and parameters for model quality estimation, as these are the characteristic components of modern QSAR/QSPR modelling. 

We begin this chapter with a discussion of the basic concepts and definitions of MS followed by discussions of MS instrumentation and cUnical applications. 

Levine, R.J. Basic Concepts and Definitions. In Ethics and Regulation of Clinical Research, 2nd Ed. Levine,... 

Membrane-based reactive separation (otherwise also known as membrane reactor) processes, which constitute the subject matter of this book, are a special class of the broader field of membrane-based separation processes. In this introduction we will first provide a general and recent overview on membranes and membrane-based separation processes. The goal is to familiarize those of our readers, who are novice in the membrane field, with some of the basic concepts and definitions. A more complete description on this topic, including various aspects of membrane synthesis can be obtained from a number of comprehensive books and reviews that have already been published in this area [1.1, 1.2, 1.3,... 

Basic Concepts and Definitions. The task of relating thermometer output (i.e., magnitude of the variable dependent on temperature) to its temperature is achieved through calibration. Two general means of calibration are available (1) fixed-point calibration, and (2) compari-... 

This chapter presents the basic concepts and definition of risk (Section 3.1), a protocol for conducting transportation risk assessments (Section 3.2), and a prioritization process for identifying important issues and transportation scenarios requiring a more detailed risk analysis (Section 3.3). Due to the differences in safety and security definitions and risk assessment methodologies, the focus of Chapters 3, 4, and 5 is limited to transportation safety. Security concepts, definition, and assessment methods are presented separately in Chapter 6, with this chapter providing a high-level comparison of safety and security. 

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