Representation idealized

Figure 4.4 Idealized representation of a polymer crystal as a cylinder of radius r and thickness 1. Note the folded nature of polymer chains in crystal.

In Fig. 7.4.1, an idealized representation of tlie blast wave, tlie pressure pulse is shown as a function of tlie distance from tlie explosion center. Tlie sliape of tlie curve at A is not shown tlie cuix es at B tluough D and times 2 tluough 4 show tlie decrease in peak overpressure as tlie w ai e moves outward. Botli posilii e and negatii e pressures are observed in tlie curve at point D and dine 4. Figure 7.4.2 illustrates tlie variadon of overpressure P" widi dine at point D and Ij are die peak overpressure arrivid lime and duration dine, respectively. The modified Friedlander equadon is most conuiionly used to describe die overpressure curve. 

Figure 2.5 Idealized representation of an active cavity (a) situation at maximum boiling suppression (b) situation at incipient boiling. (From Dwyer, 1976. Copyright 1976 by American Nuclear Society, LaGrange Park, IL. Reprinted with permission.)... 

Fig. 3. An idealized representation of the supramolecular cylinder self-assembled from a single chain of the dendrimer derived from monomer 9 (R=OC12H25, n=3) in the hexagonal columnar phase, assuming one single backbone per cylinder, drawn to proportion with existing experimental data a tilted side view b top view. Reproduced with permission from references 5 a...

Fig. 2. Idealized representation of Bubble growth and collapse during transient cavitation.

Fig. 6. Idealized representation of tetrameric and pentameric cyclic species.

The scalar r represents the difference between the real measurement y, which is never perfect, and its ideal representation as the product cxa. 

Figure 2.9 Idealized representation of a linear pol3fmer resulting from radical poUmerization of a mono-O-methacroyl-sucrose (left) and a 1 1 copolymerization product with styrene. Di-O-substituted vinyl-sucroses are deemed to lead to cross-linked pol3miers (right).

The disconnection approach [5] is adopted in this work because it is amenable to backward chaining systems. The starting point is the target compound, which is, in this case, a Diels-Alder product. The target compound is broken or disconnected into two distinct parts called synthons. The synthons are the ideal representations of the actual reactants used to produce the target compound. Synthons embody the physical properties of the actual compounds they represent. 

Mislow and Bickart (258) have recently discussed the properties, and specified the limitations and essential features, of models that can be used for the prediction of chirality of a molecular system. In the simplified and idealized representation of molecular stracture, nonessential features are deliberately left out the model summarizes some selected aspects of the system and completely disregards or even falsifies, others. The model must be adequate to the time scale in which the phenomenon is observed. In particular, in mobile conformational systems it should refer to a time-averaged structure. In other words, the model can have a higher symmetry than that observed under static conditions (e.g., by X-ray diffraction in the crystalline state or by NMR under slow exchange conditions) (259). 

Figure 14.17 Idealized representation of defect-free (n,m)-SWNTs with open ends. Left a metallic conducting (10,10)-tube (armchair) middle a chiral, semiconducting (12,7)-tube right a conducting (15,0)-tube (zigzag). Armchair and zigzag tubes are achiral.

Many conditions are required for a chemical reaction to proceed. Conditions such as heat, light, and pressure must be just right for a reaction to take place. Furthermore, the reaction may proceed very slowly. Some reactions occur in a fraction of a second, while others occur very slowly. Consider the difference in the reaction times of gasoline igniting in a car s cylinder versus the oxidation of iron to form rust. The area of chemistry that deals with how fast reactions occur is known as kinetics (Chapter 12). Finally, not all reactions go to completion. The amount of product produced based on the chemical equation is known as the theoretical yield. The amount actually obtained expressed as a percent of the theoretical is the actual yield. In summary, it s best to think of a chemical equation as an ideal representation of a reaction. The equation provides a general picture of the reaction and enables us to do theoretical calculations, but in reality reactions deviate in many ways from that predicted by the equation. 

Figure 5.2 Idealized representation of the influence of temperature and chain length on a thermoplastic.

Figure 13.8 Schematic operation of a two-station rotaxane as a controllable molecular shuttle, and idealized representation of the potential energy of the system as a function of the position of the ring relative to the axle upon switching off and on station A. The number of dots in each position reflects the relative population of the corresponding coconformation in a statistically significant ensemble. Structures (a) and (c) correspond to equilibrium states, whereas (b) and (d) are metastable states. An alternative approach would be to modify station through an external stimulus in order to make it a stronger recognition site compared to station A.

The purple lines show the axis of the supercoil note the branching of the supercoil, (c) An idealized representation (c) of this structure. 

Figure 1 is an idealized representation of the structure proposed for zeolite 12 by Barrer and Villiger on the basis of x-ray powder data (5). The intersections of the straight lines represent point aluminum or silicon atoms, each of which is bonded to four tetrahedrally disposed oxygen atoms. 

Figure 17. An idealized representation of a cubic model. Restriction imposed on a ball trapped within a cube with different faces lacking. In models 1-10 various faces of the cube are absent. Such an absence increases the freedom the trapped ball experiences as one moves from model 10 to 2. The similarity between this situation and a guest within a restricted space is highlighted.

In Fig. 3 c the schematic volume-temperature curve of a non crystallizing polymer is shown. The bend in the V(T) curve at the glass transition indicates, that the extensive thermodynamic functions, like volume V, enthalpy H and entropy S show (in an idealized representation) a break. Consequently the first derivatives of these functions, i.e. the isobaric specific volume expansion coefficient a, the isothermal specific compressibility X, and the specific heat at constant pressure c, have a jump at this point, if the curves are drawn in an idealized form. This observation of breaks for the thermodynamic functions V, H and S in past led to the conclusion that there must be an internal phase transition, which could be a true thermodynamic transformation of the second or higher order. In contrast to this statement, most authors... 

It was postulated that the reaction occurs by the following steps which are illustrated below. The illustration is a greatly idealized representation of an aromatic ring of the lignin polymer. 

A final biomedical use for polyphosphazenes is as components in microspheres, vesicles, and micelles for use in drug-delivery applications. Microspheres are pseudo-spherical constructs that range in size from 1 to 600 microns. Vesicles (lipozomes) are hollow, water-filled bilayer spheres with diameters that range from 0.03 tolO microns. Micelles typically have diameters near 1 micron (100 nanometers). Idealized representations of these three structures are shown in Figure 3.23, together with the location of trapped drug molecules. 

Fig. 10.35 Idealized representation of the solid-melt suspension formed in the melting zone of CRNI twin extruders with staggered screw arrays. The mechanism of melting will he dissipative mix-melting. [Reprinted hy permission from R. J. Nichols and F. Kher-adi, Melting in CRT Twin Screw Extruders, Mod. Plastics, 61(2), 70 (1984).]...

While powerful contemporary techniques permit the use of molecular cavities of complex shape [3], it is instructive to note a few cases based on idealized representations of solute cavity and charge density. Cavities are typically constructed in terms of spherical components. Marcus popularized two-sphere models, [5,38] which can be used to model CS, CR, or CSh processes (see Section 3.5.2), where the two spheres are associated with the D and A sites, and initial and final charge densities are represented by point charges (qD and qA) at the sphere origins. If a single electron is transferred, Ap corresponds to A = 1 in units of electronic charge (e), and Aif is given by [5,38]... 

Crystallizers are made more flexible by the introduction of selective removal devices that alter the residence time distributions of materials flowing from the crystallizer. Three removal functions—clear-liquor advance, classified-fines removal, and classified-product removal— and their idealized removal devices will be used here to illustrate how design and operating variables can be manipulated to alter crystal size distributions. Idealized representations of the three classification devices are illustrated in Fig. 17. 

Fig. 1.1 Idealized representation of different structures of defect-free and opened carbon nanotubes (a) concentric MWCNT (b) metallic armchair [10,10] SWCNT (c) helical...

Figure 9.5. An idealized representation of an ordered dendritic network constructed by the procedure of Watanabe and Regen. 81 ...

Fig. 5.1 Idealized representation of the transient change in fiber and matrix stress that occurs during the isothermal tensile creep and creep recovery of a fiber-reinforced ceramic (the loading and unloading transients have been exaggerated for clarity). It is assumed that the fibers have a much higher creep resistance than the matrix. The matrix stress reaches a maximum at the end of the initial loading transient. After full application of the creep load, the matrix stress relaxes and the fiber stress increases. Upon specimen unloading, elastic contraction of the composite occurs, followed by a time-dependent decrease in fiber stress and increase in matrix stress. Overall, creep tends to increase the difference in stress between constituents and recovery tends to minimize the difference in stress. After Wu and Holmes.15...

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