Structural entity

These teclmiques differ mainly in the structural entities that contribute to the tenn. For light, the refractive... 

The most widely used method for the synthesis of thiazoles (see Chapter 4.19) is of this type and involves the reaction of a-halo compounds (Y = halogen in Scheme 2) with a reactive component containing an —C(=S)— structural entity. Reaction of the a-... 

Scheme 6 shows representative members of these three groups. Other combinations are possible and the design of an appropriate bielectrophile for use as a versatile synthon presents a considerable synthetic challenge, as by virtue of the structural entities involved they are extremely reactive. 

Complex ions, also called coordination complexes, have well-defined stoichiometries and structural arrangements. Usually, the formula of a coordination complex is enclosed in brackets to show that the metal and all its ligands form a single structural entity. When an ionic coordination complex is isolated from aqueous solution, the product is composed of the complex ion and enough counter-ions to give a neutral salt. In the chemical formula, the counter-ions are shown outside the brackets. Examples include the sulfate salt of [Ni (NH3)g, ... 

For a number of reasons, there are some important limitations to the extension of this principle. Biodegradation—as opposed to biotransformation—of complex molecules necessarily involves a number of sequential reactions each of whose rates may be determined by complex regulatory mechanisms. For novel compounds containing structural entities that have not been previously investigated, the level of prediction is necessarily limited by lack of the relevant data. Too Olympian a view of the problem of rates should not, however, be adopted. An overly critical attitude should not be allowed to pervade the discussions—provided that the limitations of the procedures that are used are clearly appreciated and set forth. In view of the great practical importance of quantitative estimates of persistence to microbial attack, any procedure—even if it provides merely orders of magnitude—should not be neglected. 

The presence of more complex substituent groups complicates the description of carbene structure. Furthermore, since carbenes are high-energy species, structural entities that would be unrealistic for more stable species must be considered. As an example, one set of MO calculations109 arrives at structure I as a better description of carbomethoxycarbene than the conventional structure J. 

The objective of traditional multistep synthesis is the preparation of a single pure compound, but combinatorial synthesis is designed to make many related molecules.57 The purpose is often to have a large collection (library) of compounds for evaluation of biological activity. A goal of combinatorial synthesis is structural diversity, that is, systematic variation in subunits and substituents so as to explore the effect of a range of structural entities. In this section, we consider examples of the application of combinatorial methods to several kinds of compounds. 

Except for biopolymers, most polymer materials are polydisperse and heterogeneous. This is already the case for the length distribution of the chain molecules (molecular mass distribution). It is continued in the polydispersity of crystalline domains (crystal size distribution), and in the heterogeneity of structural entities made from such domains (lamellar stacks, microfibrils). Although this fact is known for long time, its implications on the interpretation and analysis of scattering data are, in general, not adequately considered. 

Different kinds of heterogeneity can be imagined. In the most simple case only a few differing structural entities are found to coexist without correlation inside the volume irradiated by the primary beam. In this case it is the task of the scientist to identify, to separate and to quantify the components of such a multimodal structure. In an extreme case heterogeneity may even result in a fractal structure that can no longer be analyzed by the classical methods of materials science. 

Let us consider a template, i.e., the average representative particle or the average representative structural entity in a material with polydisperse structure. The template is described by its structure pr (r). The sample is full of dilated images... 

There shall be no correlation among different structural entities. Thus the observed correlation function of the material... 

This property is readily established from the definition of Fourier transform and convolution. In scattering theory this theorem is the basis of methods for the separation of (particle) size from distortions (Stokes [27], Warren-Averbach [28,29] lattice distortion, Ruland [30-34] misorientation of anisotropic structural entities) of the scattering pattern. 

Figure 8.12. The structural entity layer stack with infinite lateral extension (left) results in a ID scattering intensity (right)... 

A structural entity is a particle or an ensemble of arranged (i.e., correlated) particles that causes a distinct scattering pattern upon irradiation. Sometimes we call a structural entity made from several particles a cluster - not meaning that such particles are touching each other. 

D Structural Entities. In materials science, stmctural entities which can satisfactorily be represented by layer stacks are ubiquitous. In the field of polymers they have been known for a long time [156], Similar is the microfibrillar [157] structure. Compared to the microfibrils, the layer stacks are distinguished by the large lateral extension of their constituting domains. Both entities share the property that their two-phase structure is predominantly described by a ID density function, Ap (r3), which is varying along the principal axis, r3, of the structural entity. 

Synopsis of Experiment and Results. The material is irradiated during straining and relaxation. The example shows that a nanostructure which is hard to interpret from a series of scattering patterns may clearly reveal its complex domain structure after transformation to the CDF. Different structural entities are identified which respond each in a different way on mechanical load. The shape of the basic particles is identified (cylinders). The arrangement of the cylinders is determined. Thus the semi-quantitative analysis of the CDF provides the information necessary for the selection and definition of a suitable complex model which is required for a... 

If the structural entities are lamellae, Eq. (8.80) describes an ensemble of perfectly oriented but uncorrelated layers. Inversion of the Lorentz correction yields the scattering curve of the isotropic material I (5) = I (s) / (2ns2). On the other hand, a scattering pattern of highly oriented lamellae or cylinders is readily converted into the ID scattering intensity /, (53) by ID projection onto the fiber direction (p. 136, Eq. (8.56)). The model for the ID intensity, Eq. (8.80), has three parameters Ap, dc, and <7C. For the nonlinear regression it is important to transform to a parameter set with little parameter-parameter correlation Ap, dc, and oc/dc. When applied to raw scattering data, additionally the deviation of the real from the ideal two-phase system must be considered in an extended model function (cf. p. 124). 

Fig. 9.6), the orientation smearing must first be extinguished (Sect. 9.7) before the scattering of the perfectly oriented structural entities is retrieved. 

Properties and Application. The two independent statistical distributions of the two-phase stacking model are the distributions of amorphous and crystalline thicknesses, h (x) and ii2 x). Both distributions are homologous. The stacking model is commutative and consistent. If the structural entity (i.e., the stack as a whole) is found to show medium or even long-ranging order, the lattice model and its variants should be tested, in addition. As a result the structure and its evolution mechanism may more clearly be discriminated. 

The General Series Expansion for Stacks. In practice, ID scattering intensities can always be modeled by programming the obvious series expansion of such a structural entity every correlated distance along the stack axis is producing an attenuated oscillation according to Hk (5) that is weighted by the probability of its occurrence under consideration of the zero-sum rule and the related correlation-construction principle (p. 158, Fig. 8.30)... 

Analytical Expressions for Stacks of Finite Height. By virtue of the just mentioned general series expansion for stacks, even for structural entities built from a finite number of particles analytical solutions can be derived. For a structural entity from N particles of phase 1 the thickness distributions which are the components of the IDF are arranged... 

If the structural entities contain varying numbers of particles (solos, duos, trios,. ..), Ruland [84] deduces... 

At a first glance this subtraction appears to be a violation of the zero-sum rule. However, here an exception has to be made, because particles merge upon direct contact of adjacent structural entities, and thus the number of particles is reduced — just by the amount deduced by RULAND. 

Analytical Expressions for Lattice Models. Concerning the aforementioned paracrystalline lattice, an analytical equation has first been deduced by Hermans [128], His equation is valid for infinite extension. Ruland [84] has generalized the result for several cases of finite structural entities. He shows that a master equation... 

Hermans equation for the infinitely extended lattice is obtained. For a material built from finite structural entities containing an average of (N) particles Ruland obtains... 

In analogy to the treatment of the stacking model Jo (s) = 0 is valid, if the structural entities are embedded in matrix material. Compact material, again, may require a correction because of the merging of particles from abutting structural entities... 

The analytical structural model for the topology of the nanostructure is defined in Isr (5). For many imaginable topologies such models can be derived by application of scattering theory. Several publications consider layer topologies [9,84,231] and structural entities built from cylindrical particles [240,241], In the following sections let us demonstrate the principle procedure by means of a typical study [84],... 

Introduction. The following two chapters are devoted to the evaluation of the orientation of structural entities in the studied material, not to the analysis of the inner structure (topology) of these entities. First discussions of the problem of orientation smearing go back to Kratky [248,249], Unfortunately, the corresponding mathematical concepts are quite involved, and a traceable presentation would require mathematical reasoning that is beyond the scope of this textbook. Thus only ideas, results and references are presented. 

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