Important Concepts

Transport data of membranes can be expressed in terms of flux (mol/m s) or as flux normalised per unit of pressure (mol/m s Pa). Following the lUPAC convention this last parameter is called permeation (note in the literature the better term permeance is frequently used). Using permeation is meaningful 

9 — TRANSPORT AND SEPARATION PROPERTIES OF MEMBRANES WITH GASES AND VAPOURS 

It is convenient to distinguish between permeation measurements in which the flux is measured under a known (and constant) pressure gradient and those in which the flux of a component i is driven by a concentration difference between the membrane faces under a constant and equal total pressure at both sides (Wicke-Callenbach [3]). Either of these two main methods may be performed imder steady state or under transient conditions. Whether or not component fluxes cmd diffusivities measured with both methods give similar or different values depends on the conditions and on the type of the dominant diffusion mechanism. 

An overview of the transport mechanisms in porous membranes is given in Table 9.1. 

Viscous (Poiseuille) flow and molecular diffusion are non-selective. Nevertheless they play an important role in the macroporous substrate(s) supporting the separation layer and can seriously affect the total flow resistance of the membrane system. Mesoporous separation layers or supports are frequently in the transient-regime between Knudsen diffusion (flow) and molecular diffusion, with large effects on the separation factor (selectivity). 

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The fifth postulate and its corollary are extremely important concepts. Unlike classical mechanics, where everything can in principle be known with precision, one can generally talk only about the probabilities associated with each member of a set of possible outcomes in quantum mechanics. By making a measurement of the quantity A, all that can be said with certainty is that one of the eigenvalues of /4 will be observed, and its probability can be calculated precisely. However, if it happens that the wavefiinction corresponds to one of the eigenfunctions of the operator A, then and only then is the outcome of the experiment certain the measured value of A will be the corresponding eigenvalue. 

Conservation laws at a microscopic level of molecular interactions play an important role. In particular, energy as a conserved variable plays a central role in statistical mechanics. Another important concept for equilibrium systems is the law of detailed balance. Molecular motion can be viewed as a sequence of collisions, each of which is akin to a reaction. Most often it is the momentum, energy and angrilar momentum of each of the constituents that is changed during a collision if the molecular structure is altered, one has a chemical reaction. The law of detailed balance implies that, in equilibrium, the number of each reaction in the forward direction is the same as that in the reverse direction i.e. each microscopic reaction is in equilibrium. This is a consequence of the time reversal syimnetry of mechanics. 

This chapter has simnnarized some of the important concepts and results from what has become an exceedingly rich area of chemical physics. On the other hand, the very size of the field means that the vast majority of experimental and theoretical advances have been left out the books referenced in the introduction provide a much more complete picture of the field. 

The classical description of magnetic resonance suffices for understanding the most important concepts of magnetic resonance imaging. The description is based upon the Bloch equation, which, in the absence of relaxation, may be written as... 

We will now explain the meaning of the word identical used above. Physically, it is meant for particles that possess the same intrinsic attributes, namely, static mass, charge, and spin. If such particles possess the same intrinsic attributes (as many as we know so far), then we refer to them as physically identical. There is also another kind of identity, which is commonly refeiTed to as chemical identity [56]. As discussed in the next paragraph, this is an important concept that must be steessed when discussing the permutational properties of nuclei in molecules. 

End of Chapter Summaries highlight and con sohdate all of the important concepts and reac tions within a chapter... 

The summary provides the student with a brief review of the important concepts within the chapter. 

There are a number of important concepts which emerge in our discussion of viscosity. Most of these will come up again in subsequent chapters as we discuss other mechanical states of polymers. The important concepts include free volume, relaxation time, spectrum of relaxation times, entanglement, the friction factor, and reptation. Special attention should be paid to these terms as they are introduced. 

We shall devote a considerable portion of this chapter to discussing the thermodynamics of mixing according to the Flory-Huggins theory. Other important concepts we discuss in less detail include the cohesive energy density, the Flory-Krigbaum theory, and a brief look at charged polymers. 

Coordinate Indexing and Boolean Logic. Three methods of indexing have been prominent in the chemical Hterature in recent times. The first, articulated indexing, has been used in printed Chemicaly hstracts subject indexes from their earliest days until well into the 1990s. A number of important concepts are identified as permissible index entries, including specific compounds, material types, reactions, and processes. One or more modifying statements foUow each basic index entry. Thus, eg. 

Many have worked on plasma technology. Table 1 Hsts a few of the contributors (3—5) and the corresponding dates associated with their concepts. Table 1. Important Concepts in Gaseous Electronics... 

Another important concept in the discussion of photochromic systems is fatigue. Fatigue is defined as a loss in photochromic activity as a result of the presence of side reactions that deplete the concentration of A and/or B, or lead to the formation of products that inhibit the photochemical formation of B. The inhibition can result from quenching of the excited state of A or screening of active light. Fatigue, therefore, is caused by the absence of total reversibihty within the photochromic reaction (eq. 2). 

Another important concept is that of the critical ignition volume. During the propagation of the combustion wave, the flame volume cannot continually grow beyond a critical value without an additional supply of energy. The condition that controls the critical volume for ignition is reached when the rate of increase of flame volume is less than the rate of increase of volume of the combustion products. In this condition a positive exchange of heat between the flame and the fresh mixture is achieved. 

The basic approach is to direct the system to the safest operating level relative to people or the environment when any emergency condition is detected, including power loss. An important concept of process control safety is to have adequate redundancy to reduce unwanted shutdowns and maintain an adequate level of certainty that a safe state will result if a real emergency does occur. As far as possible, instruments should be of the fail-safe type. 

An important concept is the shadow cone, which is a region where no ions can penetrate due to the ion—nucleus repulsion (see Figure 2). This effect makes ion scattering surface sensitive. The size of the shadow cone / jCan be calculated for the classical Coulomb potential as ... 

Important concepts in neutron diffraction can be found in G. E. Bacon. Neutron Diffi oction. Clarendon Press, third edition, 1975. 

Mott played a major part, with his collaborator Frank Nabarro (b. 1917) and in consultation with Orowan, in working out the dynamics of dislocations in stressed crystals. A particularly important early paper was by Mott and Nabarro (1941), on the flow stress of a crystal hardened by solid solution or a coherent precipitate, followed by other key papers by Koehler (1941) and by Seitz and Read (1941). Nabarro has published a lively sequential account of their collaboration in the early days (Nabarro 1980). Nabarro originated many of the important concepts in dislocation theory, such as the idea that the contribution of grain boundaries to the flow stress is inversely proportional to the square root of the grain diameter, which was later experimentally confirmed by Norman Fetch and Eric Hall. 

There is no space here to go into the enormous body of experiment and theory that has emerged from von Hevesy s initiative. The reader is referred to an excellent critical overview by Seeger (1997). Important concepts such as the random-walk... 

The function (vm + Kvs) is termed the plate volume and so the flow through the column will be measured in plate volumes instead of milliliters. The plate volume is defined as that volume of mobile phase that can contain all the solute in the plate at the equilibrium concentration of the solute in the mobile phase. The meaning of plate volume must be understood, as it is an important concept and is extensively used in different aspects of chromatography theory. 

So by now it should be clear that what the process of clarification is all about is removing suspended solids from water. Important concepts that we have eluded to, but maybe not spelled out so clearly up to now are ... 

Exactly what type of lessons are learned cannot be foreseen. The size and diversity of site activities give rise to a wide variety of health and safety hazards. Individual sites need to document and disseminate information that could enhance their hazard recognition and mitigation. Effective documentation is an important concept that everyone needs to buy in to if the safety program is going to be effective. Wliy workers fail to document potential problems has been the subject of much debate. 

Let us comment on the developed schematic Monte Carlo (MC) code. Of course there are many clever ways to improve the execution speed. There is the important concept of neighbor lists, of clever implementation of numerical instructions, and so on. In developing a computer simulation one usually plugs in these enhancing concepts bit by bit. 

Another important concept is the notion of stabilization by means of coordination, A classic example is the. stabilization of the fugitive species cyclobutadiene, C4H4I by coordination to (Fe(CO)3l (p. 936). As the C atom is isoclectronic with (BH], so (C4H4] is isoelectronic with the borane fragment (BaH which is similarly stabilized by coordination to (Fe(CO)3l or the isoelectronic (Cofr/ -CsHs)) (see Panel on p. 174), Indeed it is a general feature of metallaboranc chemistry that such clusters are often much more stable than are the parent boranes themselves. 

Another important concept for batteries is resistance. Expressed in ohms, resistance is what limits current. For example, if a 12V car battery were connected to a circuit with 4 ohms resistance, the current would be 3 A. If the battery had a capacity of 90 A-h, it would supply 3 A for 30 hours. (Resistance of 4 ohms here refers to external resistance of the battery and the headlight circuit.) The greater the resistance of the circuit and cell itself, the less the current for a given applied voltage. 

Although important contributions in the use of electrical measurements in testing have been made by numerous workers it is appropriate here to refer to the work of Stern and his co-workerswho have developed the important concept of linear polarisation, which led to a rapid electrochemical method for determining corrosion rates, both in the laboratory and in plant. Pourbaix and his co-workers on the basis of a purely thermodynamic approach to corrosion constructed potential-pH diagrams for the majority of metal-HjO systems, and by means of a combined thermodynamic and kinetic approach developed a method of predicting the conditions under which a metal will (a) corrode uniformly, (b) pit, (c) passivate or (d) remain immune. Laboratory tests for crevice corrosion and pitting, in which electrochemical measurements are used, are discussed later. 

One often hears the phraise edge-of-chaos in discussions of AL, as in such and such a system appears poised at the edge-of-chaos. As this important concept is still a topic of some debate, we make a few comments regarding it. 

We note here an important concept introduced by Polya, that of the "corona" or "wreath product" of two permutation groups. If M is an w X M matrix, and G and H are permutation groups of degree m and n, consider all permutations of the mn elements of M obtained as follows ... 

A further important concept related to electronegativity and polarity is that of acidity and basicity. We ll see, in fact, that much of the chemistry of organic molecules can be explained by their acid-base behavior. You may recall from a course in general chemistry that there are two frequently used definitions of acidity the Brtfnsted-Lowry definition and the Lewis definition. We ll look at the... 

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