Space-filling model, relationship

Fig. 10. The putative transition-state complex formed between the Fe protein MgADP AlFj and the MoFe protein. For simplicity only one a/3 pair of subunits of the MoFe protein is shown. The polypeptides are indicated by ribbon diagrams and the metal-sulfur clusters and MgADP AlFi" by space-filling models (MOLSCRIPT (196)). The figure indicates the spatial relationship between the metal-sulfur clusters of the two proteins in the complex.

Fig. 2 Supramolecular system consisting of a fullerene covalently linked to a calixarene [9] the authors say that the synthesis of the nanocup was a tribute to the French football team of 1998 (a) classical chemical representation (b) computer-generated space-filling model, showing the shape relationship of this supramolecular structure and (c) the football World Cup. Reproduced by permission of The Royal Society of Chemistry (RSC) and the Centre National de la Recherche Scientifique (CNRS)...

Space-filling model of the methane molecule. This type of model shows both the relative sizes of the atoms in the molecule and their spatial relationships. 

Figure 27. Side and top views of ca. one turn of the 14-helix extracted from the crystal structure of Gellman s trans-ACffC hexamer.239 A single S(14) H-bond circuit in the peptide backbone has been rendered as thick cylinders. Additionally, one residue has been rendered as a space filling model to provide a frame of reference between the two views and to more clearly show the spatial relationship between cyclohexyl groups.

A semi-quantitative structure-taste relationship has been derived97 and extended98 for carbosulphamates using Corey-Pauling-Koltun (CPK) space-filling models for measurements of parameters. Structure-taste relationships for heterosulphamates were developed... 

This relationship was of interest for several reasons. Firstly it indicated that the biological assay was sufficiently precise to enable the QSAR approach to be used Secondly the observation that only 2dkyl substituents R affected the activity whereas alkyl substituents in the R position apparently had little influence. This parallels the observations in the 6-thioxanthine series where a similar relationship was derived for the bronchodilating activity ( ) Thirdly, bulky substituents in the Rp position had a beneficial effect. Benzyl-substituted conqiounds e.g. (v) were more active than equation 1 indicated, possibly because the usual value of Es for benzyl did not reflect the buttressing effect of the adjacent triazole ring as revealed by a study of space-filling models ( ). 

Since the beginnings of organic chemistry, somewhere in the middle of the nineteenth century, chemists have sought to visualize the three-dimensional characteristics of the all-but-invisible molecules that participate in chemical reactions. Concrete models that could be held in the hand were developed. Many kinds of model sets, such as framework, ball-and-stick, and space- filling models, were devised to allow people to visualize the spatial and directional relationships within molecules. These hand-held models were interactive, and they could be readily manipulated in space. 

Gel structures are ubiquitous in foods and responsible for many of their physical properties. The space-filling network of polymers or aggregates provides solidlike properties in the presence of an enormous amormt of water. They are a form of solid water at ambient temperature and in fact they are used to immobilize free water in dietetic products. Gels have been extensively used as model systems to study strue-ture-property relationships due to their simple biphasic nature and the faet that the kinetics of structural changes can be continuously followed by oseiUatory rheometry. 

It is more complex to model water flow in the unsaturated zone than in the saturated zone because water flow in the vadose zone occurs only via water-filled pores, and the fraction of the pore spaces filled with water (the percent saturation) is highly variable. The water content 0 in a porous medium refers to the volumetric fraction that contains water it can range between zero and n, the porosity. The relationship between hydraulic conductivity and water content is complex and difficult to predict therefore, it is usually measured experimentally and expressed in the form of a K-6 curve, as shown in Fig. 3.21. One major complication in the K-6 relationship is hysteresis hydraulic conductivity differs depending on whether the porous media most recently have been dried or wetted to obtain a given moisture content. For dry material, regardless of its texture, hydraulic conductivity is low. 

We now wish to extend the considerations above dealing with several different structures extending simultaneously within the same space. Thus, for example, a macromolecule attached to carbon black at one point along its length may be cross-linked to other molecules at one or more points on either or both sides of the black particle, while another may pass fairly close to the black without contacting it and be equally cross-linked at the distant points. In order to be able to develop the mathematical relationships required for the development of this theory, it is necessary to represent the state of affairs by means of a highly idealized model. However, the model proposed here is believed to contain all the elements of a uniformly filled and cross-linked elastomeric compound. The possible existence of crystallization and inter-and intra-molecular forces other than main-chain carbon to carbon links, cross links and bonds between rubber and carbon black as hypothesized earlier, is specifically neglected. 

A simple model for the pore volume or the void space in a porous material is to assume it to be composed of a collection of cylindrical pores of radius r. Then a volume of a liquid that does not wet the pore wall surfaces can be forced under pressure to fill the void space. This liquid is invariably mercury because it has a high surface tension, thus the Hg penetration (or porosimetry) method is used to determine pore volumes and the pore size distribution of larger pores, i.e., those with radii larger than about 10 nm. The relationship between pore size and applied pressure. Pap, is obtained by a force balance, that is, the force due to surface tension is equated to the applied force ... 

Such considerations are pertinent to the molecular anatomy of membranes. The formulas of cholestanol and coprostanol (below) illustrate how very differently space is filled when at one time rings A and B are fused trans and at another cis (respectively). But a clear concept of thes( relationships can only be acquired by using molecular models. ... 

Equations 15.5a through 15.5c have been shown to accurately model dispersion in saturated porous media and for a stationary flow in unsaturated media. In transient conditions, however, the relationship between hydrodynamic dispersion coefficients and velocity becomes more complicated. In unsaturated media, the water content of the soil changes with the water flux. Hence, the structure of the water-filled pore space also changes with the water flux. The flow field, and therefore the distribution of pore velocities, depends on the saturation of the medium (Flury et al., 1994). As a consequence, dispersivity coefficients are strongly impacted by the volumetric water content. Usually, dispersivity is found to increase when the water content decreases as a result of the larger tortuosity of solute trajectories and a disconnection of continuous flow paths (Vanclooster et al., 2006). In some cases, especially when the activation of macropores significantly enhances pore-water variability, dispersivity is found to increase with volumetric water content. Currently, there is no unique validated theoretical model available for dispersivity in transient unsaturated flow. 

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