Important provisos

Relating deformation experiments to molecular mechanisms requires choices in experimental paths. Thus, to avoid premature fracture as well as necking instabilities and strain localization of flow in tension, experimental studies of plastic response are often conducted in compression. 

While mechanistic models of plastic flow consider simple shear or pure shear (extensional flow where mean normal stress is absent), in experiments fundamental shear information may need to be extracted from more complex 3D flow fields. This is done through the use of multi-axial flow formalisms that are based on the von Mises approach of relating the 3D response to an equivalent ID response described in Chapter 3. In this formalism the deviatoric shear response of the multi-axial field of stress and plastic strain is taken to represent shear flow in the mechanistic context where the effect of the accompanying mean normal stress is considered through its effect on the plastic resistance. There exists an experimental procedure for extracting deviatoric plastic-response information from a tensile-flow field that accomplishes this through the use of specially contoured bars with pre-machined neck regions where the concentrated extensional flow is monitored under conditions of imposed constant deviatoric strain rates (G Sell et al. 1992). 

Here the primary interest is in the plasticity of single-component glassy polymers well below the glass-transition temperature. We consider no heterogeneous blends and multi-component polymers. Some consideration of such polymers for purposes of toughening is deferred to Chapter 13. 

We note that, with few exceptions, the plastic responses of glassy polymers have direct parallels to the corresponding processes in non-polymeric atomic glasses discussed in Chapter 7. We make full use of the detailed mechanistic models presented there and develop in detail only phenomena of strain hardening arising from strain-induced segmental molecular alignment. 

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A very important point to keep in mind about any pair of enantiomers is that they will have identical chemical and physical properties, except for the signs of their optical rotations, with one important proviso All of the properties to be compared must be determined using achiral reagents in a solvent made up of achiral molecules or, in short, in an achiral environment. Thus the melting and boiling points (but not the optical rotations) of 5 and 6 will be identical in an achiral environment. How a chiral environment or chiral reagents influence the properties of substances such as 5 and 6 will be considered in Chapter 19. 

These geometry optimization procedures paid an additional dividend. With a true minimum in hand, it becomes possible to compute the vibrational spectrum of a given system. A straightforward formulation allows one to extract the normal vibrational modes of the system, complete with the corresponding frequencies, hut with the important proviso that... 

An important proviso in the calculation of a standard deviation is that the individuals should be independent. Thus if we made 10 batches of some material, and took duplicate samples from each batch, we could not calculate the standard deviation on the assumption that we made 20 observations. Clearly the duplicate observations on each batch are not independent of each other. The methods of dealing with this type of situation are discussed later (Chapter XII (j)). 

An important proviso in the use of control charts is that the control lines should be based upon at least 10 and, preferably, 20 batches otherwise the estimate of the mean range w is not very accurate. 

There is an important proviso, however, which is that the outlined procedure will only provide the rate constant being sought if there are no competing channels that can also serve to deactivate the reactant state. If the prepared reactant state can also involve itself in a proton-transfer reaction, say, that yields a dilferent product state, then the measured rate constant will be the siun of the rate constants of the two competing processes. The measured rate constant will only be identical to the electron-transfer rate constant if the competing side channels contribute negligibly to the total. It is never good practice to assume without evidence that the electron-... 

An important proviso for this is that the buffer equilibrium is established rapidly compared with the equilibrium under consideration. 

The same defect thermodynamics and diffusion theory can be applied to ionic crystals with one important proviso, which is the need to account for the charges on the ions (and hence effective charges on the defects), and that the crystal must remain electrically neutral overall. This means that the defects will occur as multiplets to satisfy this later condition. For example, in a MX crystal they will occur as pairs the Schottky pair- a cation vacancy and an anion vacancy the cation-Prenkel pair- a cation vacancy and an interstitial cation and the anion-Frenkel pair - an anion vacancy and an interstitial anion. The concentrations of the defects in the pair are related by a solubility product equation, which for Schottky pairs in an MX equation takes the form ... 

These research programmes involve the housefly, Musca domestica, and the tobacco whitefly, Bemisia tabaci. Both are based in the laboratory in the firm belief that for these and many other pests, much of the data needed for such descriptive modelling can be collected more quickly and with greater precision under laboratory conditions than in the field. There is, however, a very important proviso to this statement, since for laboratory experiments to be of direct practical relevance they must simulate closely both the ecology and control of insects under field conditions (.7). The purpose of this paper is to outline the philosophy and objectives of these two programmes and to highlight some achievements to date. 

The approximations of no extensive ionisation and ignoring the self ionisation of water apply equally to weak bases with piib values in the range 4.0 to 10.0, with the aU-important proviso provided the soiution is not too dilute again being necessary. 

An important proviso of this scheme is that under normal conditions the rate of synthesis of cysteine is limited by the availability of its sulfide precursor. Then, changes in the rate of formation of sulfide will be closely coupled to changes in the rate of cysteine formation. Evidence in support of the limitation of the rate of cysteine biosynthesis by the availability of sulfide includes the following, (a) The concentration of acid-volatile sulfide in L. minor growing on sulfate is about 11 fxM (Brunold and Schmidt, 1978), while the of cysteine synthase for sulfide is at least 180 f/M (Table II). This comparison suggests that cysteine synthase may normally be operating below its for sulfide, (b) Administration of H2S (18 ppm in the gas phase) to L. minor caused about a 50% increase in the steady-state concentration of soluble cysteine in the plants within a few minutes (Brunold and Erismann,... 

Of course there are the Important provisos that the complexatlon shift must be due solely to the aromatic ring current and that for aromatic-substrate complexes in solution a specific well-defined complex is formed. We wish to consider an example of the use of this technique in a drug-ligand interaction. 

However we must enter an important proviso, and that is that this concentration of Z must also be sufficient to capture A efficiently. For the nhotochemical scheme -... 

From measurements on the solubility of a substance in two different media, its relative activity coefficient in the two media may be deduced by the same reasoning embodied in the derivation of equation (3). This reasoning, however, involves the important proviso that the same solid phase must be in equilibrium with each of the two solutions under consideration. This condition is, in g eral, not fulfilled in solubility experiments on proteins the composition of protmn crystals is known to vary somewhat wth variation in the amount of salt, water and other substances in the medium in equilibrium with the (uystal. Nevertheless, these variations appear often to produce little change in tiie activity of the protein component of such a protein crystal, since independent measurements of the activity of proteins by other methods give results in general accord with those of the solubility method (on this subject see ref. 39, p. 619-622). 

Frahm stressed that calculated by (Eq. 4.1) may be taken as an approximation if no theoretical calculations on the bases of surface potential measurements are available. This important proviso was largely ignored the method has become popular because of its simplicity. The problem, however, is that it overestimates because it ignores the contribution of the micelle to solution conductivity above the... 

An important development in concrete mix design has been the addition of so-called supplementary cementitious materials. Two classifications apply to these compoimds Pozzolans, such as fly ash and silica fume, react with the cement hydration products, notably calcium hydroxide hydraulic materials, such as granulated blast furnace slag, undergo direct hydration reactions. As these materials are of lower cost than conventional cement and essentially represent environmental waste products, there are obvious incentives for blending them in concrete mixes. As pointed out by Hansson, these materials can improve the strength and durability of concrete, with the important proviso that the concrete is cured adequately. 

The spins involved in a coherence, in this case k and /, are often referred to as the active spins. The evolution of these x and y components of multiple-quantum coherences can be calculated in the same fashion as single-quantum coherence (Ij and Ij y) with several important provisos ... 

The Joint Committee consisted of eighteen members, nine from the Senate and nine from the House, with not more than five senators or five representatives from the same political party. The law vested the group with full jurisdiction over "all bills, resolutions, and other matters in the Senate or the House of Representatives relating primarily to the Commission or to the development, use, and control of atomic energy." An important proviso also required the Commission to keep the Joint Committee "fully and currently informed with respect to the Commission s activities." The Joint Committee could appoint its own staff as well as utilize the services, information, facilities, and personnel of the executive branch. ... 

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