Single fundamental principles

The process of vibrational excitation and deexcitation of a diatom in a collision with an atom represents a simplest example from the host of processes which are relevant to gas-phase chemical kinetics. Experimental techniques available now allow one to measure directly state-to-state energy transfer rate coefficients. Theoretically, it is possible to accomplish completely ab initio calculation of these coefficients. One can therefore, regard the existing models of the vibrational relaxation from a new standpoint as a means for helping to understand more clearly the dynamics of the energy transfer provided that all the models are related to a single fundamental principle. This is the Ehrenfest adiabatic principle as formulated by Landau and Teller in the application to the collisional vibrational transitions of diatomic molecules. 

It is a fundamental principle of quantum mechanics that electrons bound in an atom can have only discrete energy values. Thus, when an electron strikes an atom its electrons can absorb energy from the incident electron in specific, discrete amounts. As a result the scattered incident electron can lose energy only in specific amounts. In EELS an incident electron beam of energy Eq bombards an atom or collection of atoms. After the interaction the energy loss E of the scattered electron beam is measured. Since the electronic energy states of different elements, and of a single element in different chemical environments, are unique, the emitted beam will contain information about the composition and chemistry of the specimen. 

While many enzymes have a single substrate, many others have two—and sometimes more than two—substrates and products. The fundamental principles discussed above, while illustrated for single-substrate enzymes, apply also to multisubstrate enzymes. The mathematical expressions used to evaluate multisubstrate reactions are, however, complex. While detailed kinetic analysis of multisubstrate reactions exceeds the scope of this chapter, two-substrate, two-product reactions (termed Bi-Bi reactions) are considered below. 

In chemistry, as in many other sciences, statistical methods are unavoidable. Whether it is a calibration curve or the result of a single analysis, interpretation can only be ascertained if the margin of error is known. This section deals with fundamental principles of statistics and describes the treatment of errors involved in commonly used tests in chemistry. When a measurement is repeated, a statistical analysis is compulsory. However, sampling laws and hypothesis tests must be mastered to avoid meaningless conclusions and to ensure the design of meaningful quality assurance tests. Systematic errors (instrumental, user-based, etc.) and gross errors that lead to out-of-limit results will not be considered here. 

This review article describes progress made in scanning force microscopy of polymers during the last 5 years including fundamental principles of SFM and recent developments in instrumentation relevant to polymer systems. It focuses on the analytical capabilities of SFM techniques in areas of research where they give the most unique and valuable information not accessible by other methods. These include (i) quantitative characterisation of material properties and structure manipulation on the nanometer scale, and (ii) visualisation and probing of single macromolecules. 

This chapter describes the fundamental principles of heat and mass transfer in gas-solid flows. For most gas-solid flow situations, the temperature inside the solid particle can be approximated to be uniform. The theoretical basis and relevant restrictions of this approximation are briefly presented. The conductive heat transfer due to an elastic collision is introduced. A simple convective heat transfer model, based on the pseudocontinuum assumption for the gas-solid mixture, as well as the limitations of the model applications are discussed. The chapter also describes heat transfer due to radiation of the particulate phase. Specifically, thermal radiation from a single particle, radiation from a particle cloud with multiple scattering effects, and the basic governing equation for general multiparticle radiations are discussed. The discussion of gas phase radiation is, however, excluded because of its complexity, as it is affected by the type of gas components, concentrations, and gas temperatures. Interested readers may refer to Ozisik (1973) for the absorption (or emission) of radiation by gases. The last part of this chapter presents the fundamental principles of mass transfer in gas-solid flows. 

There is no single or simple way to purify all proteins. Procedures and conditions used in the purification of one protein may result in the denaturation of another. Further, slight chemical modifications in a protein may greatly alter its structure and thus affect its behavior during purification. Nevertheless, there are certain fundamental principles of protein purification on which most fractionation procedures are based. In all cases, the experimenter takes advantage of small differences in the physical and/or chemical properties of the many proteins in a crude mixture to bring about separation of the proteins from one another. Since the precise nature of these differences is not usually known in advance, the development of a purification procedure necessarily involves considerable trial and error. A procedure leading to a... 

An extremum principle minimizes or maximizes a fundamental equation subject to certain constraints. For example, the principle of maximum entropy (dS)v = 0 and, (d2S)rj < 0, and the principle of minimum internal energy (dU)s = 0 and (d2U)s>0, are the fundamental principles of equilibrium, and can be associated with thermodynamic stability. The conditions of equilibrium can be established in terms of extensive parameters U and. S, or in terms of intensive parameters. Consider a composite system with two simple subsystems of A and B having a single species. Then the condition of equilibrium is... 

The fundamental principle of the receptor models is that mass conservation can be assumed and the composition of source emissions are constant over the ambient and source sampling period. Therefore, the ratios between the components emitted by a single source are identical to the ratios between the resulting concentrations on the receptor location. Other assumptions required by the model are ... 

---