Hierarchical properties

The Cayley tree is a pictorial representation of a space that is called ultrametric. Each point of the ultrametric space can be put into correspondence with an element of the fractal set that is, the fractal set and ultrametric space are topologically equivalent sets. We remark that the main feature of an ultrametric space, as well as that of a fractal set, is its hierarchical property. 

Fig. 2. Conceptual image of hierarchy based on nanophotonics, and innovative optical security system utilizing the hierarchical structure. The important point is that, because induced optical near-fields are the result of interactions between nanometric structures, the hierarchical property can be designed by adjusting the size, shape, alignment, and composition of the nanometric structures.

Mechanical Properties. Although wool has a compHcated hierarchical stmcture (see Fig. 1), the mechanical properties of the fiber are largely understood in terms of a two-phase composite model (27—29). In these models, water-impenetrable crystalline regions (generally associated with the intermediate filaments) oriented parallel to the fiber axis are embedded in a water-sensitive matrix to form a semicrystalline biopolymer. The parallel arrangement of these filaments produces a fiber that is highly anisotropic. Whereas the longitudinal modulus of the fiber decreases by a factor of 3 from dry to wet, the torsional modulus, a measure of the matrix stiffness, decreases by a factor of 10 (30). 

One may now ask whether natural systems have the necessary structural evolution needed to incorporate high-performance properties. An attempt is made here to compare the structure of some of the advanced polymers with a few natural polymers. Figure 1 gives the cross-sectional microstructure of a liquid crystalline (LC) copolyester, an advanced polymer with high-performance applications [33]. A hierarchically ordered arrangement of fibrils can be seen. This is compared with the microstructure of a tendon [5] (Fig. 2). The complexity and higher order of molecular arrangement of natural materi-... 

A database (or data base) is a collection of data that is organised so that its contents can easily be accessed, managed, and modified by a computer. The most prevalent type of database is the relational database which organises the data in tables multiple relations can be mathematically defined between the rows and columns of each table to yield the desired information. An object-oriented database stores data in the form of obj ects which are organised in hierarchical classes that may inherit properties from classes higher in the tree structure. 

Advanced materials systems based on polymers, ceramics, and composites are constmcted by assembling components to create stmctures whose properties and performance are determined by the form, orientation, and complexity of the composite stmcture. The properties of these assemblages are determined not by the sum of weighted averages of the components but rather by synergistic effects in intercoimected phases. For this reason, the study of fabrication of hierarchical assemblages of materials, as well as the study of mechanisms for repairing defects in assembled stmctures, must be supported by fundamental research. 

A typical feature of expert systems that support frames is inheritance. Frames can be organized in a hierarchical structure. They can inherit properties (attributes) from frames that are higher in the hierarchy. The latter are therefore called parent frame and the former child frame. There are many varieties of the inheritance principle. Frames can have only one parent frame (simple inheritance) or may have multiple parent frames (multiple inheritance). All attributes can be inherited (full inheritance) or only a few, selected by the knowledge engineer, may be inherited (partial inheritance) by the child frames. An example of a simple inheritance organization of frames is shown in Table 43.1. The frame Organic Compound is the parent frame. The frames Ester and Acids are child frames of Organic Compound . A typical example of inheritance is instantiation. The frame Acetic acid is a child of Acids and, since no extra attributes are added, it is also an instantiation. 

Often the demand for such a complement of properties requires a hierarchical strategy in which only the broadest possible limits are satisfied by the less demanding design requirements. For example, topical administration assists in limiting toxicity while improving targeting and pharmacokinetic response. On the other hand, the requirements for effective... 

Friedel-Crafts acylation is widely used for the production of aromatic ketones applied as intermediates in both fine chemicals and pharmaceutical industries. The reaction is carried out by using conventional homogenous catalysts, which represents significant technical and environmental problems. The present work reports the results obtained in the Friedel-Crafts acylation of aromatic substrates (anisole and 2-methoxynaphthalene) catalyzed by Beta zeolite obtained by crystallization of silanized seeds. This material exhibits hierarchical porosity and enhanced textural properties. For the anisole acylation, the catalytic activity over the conventional Beta zeolite is slightly higher than with the modified Beta material, probably due to the relatively small size of this substrate and the weaker acidity of the last sample. However, the opposite occurred in the acylation of a bulky substrate (2-methoxynaphthalene), with the modified Beta showing a higher conversion. This result is interpreted due to the presence of a hierarchical porosity in this material, which favors the accessibility to the active sites. 

The catalytic activity of hierarchical and conventional Beta zeolites for acylation of 2-MN is displayed in Figure 2(a) The Beta (PHAPTMS) sample shows a superior catalytic activity than the conventional one, due to its enhanced textural properties. In this case, the bulky nature of both substrate and products may cause the existence of diffusional problems inside the zeolitic channels, which are attenuated in the modified Beta sample due to the presence of the hierarchical porosity. Regarding the product distribution (Figure 2(b)), two main products are observed and a third isomer, 8-A,2-MN isomer is produced just in minor amounts. Interestingly, the selectivity towards the desired isomer increases in the material obtained from silanized seeds, reaching values around 75%. Probably, the active sites located on the surface of the secondary porosity are able to catalyze also the formation of 6-A,2-MN by transacylation. However, this reaction is expected to be strongly hindered in the conventional Beta zeolite since it requires the participation of two bulky molecules as reactants. 

The Beta material prepared by seed silanization show interesting catalytic properties in aromatic acylation reaction, especially when using a bulky substrate, such as 2-methoxynaphthalene. The superior activity and selectivity exhibited by this sample has been related to the presence of a hierarchical porosity, which decreases the steric and diffusional hindrances, favoring the accessibility to the active sites and allowing the occurrence of the transacylation reaction. 

The nanometer- to micrometer-scale dimensions of supramolecular assemblies present many challenges to rigorous compositional and structural characterization. Development of adequate structure-property relationships for these complex hierarchical systems will require improved measurement methods and techniques. The following areas constitute critical thrusts in instrument development. 

Chirality is an essential property of life, which can be found throughout all biological self-assembled and self-organized architectures. Over many millennia nature has, through trial and error, learned how to utilize the chiral properties of the small building blocks, for example, amino acids and nucleic acids and how to express this structural property in a hierarchical process at the quaternary level. This expression of chirality at the quaternary level in turn... 

Schmidt, N. B., Joiner, T. E., Young, J., St Telch, M. J. (1995). The Schema Questionnaire Investigation of psychometric properties and the hierarchical structure of a measure of early maladaptive schemas. Cognitive Therapy and Research, 19, 295-321. 

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