Models space-tilling

Ball-and-stick models are not as realistic as space-tilling models. Realistically portrayed atoms occupy more space, determined by their van der Waals radii, than do the atoms depicted in ball-and-stick models. 

The ball-and-wire display is used for model building. Although it is convenient for this purpose, other model displays show three-dimensional molecular structure more clearly and may be preferred. The space-tilling display is unique in that it portrays a molecule as a set of atom-centered spheres. The individual sphere radii are taken from experimental data and roughly correspond to the size of atomic electron clouds. Thus, the space-filling display attempts to show how much space a molecule takes up. 

It is convenient for many purposes to have models available for inspection in order to realize fully the three-dimensional aspect of molecular and lattice structures. "Ball-and-stick" models of various stages of sophistication are useful when it is necessary to be able to see through the structure under consideration. Space-tilling models of atoms with both covalent and van der Waals radii are particularly helpful when steric effects are important. The space-filling models and the more sophisticated stick models lend to be rather expensive, but there are several inexpensive modifications of the ball-and-slick" type available. It is extremely useful to have such a set at hand when considering molecular structures. 

Heme shown as (a) a structural drawing and as (b) a space-tilling model. The space-filling model shows the coplanar arrangement of the groups surrounding iron. 

Analogous to the spherical filler of radius R in the Kraus model, Bhattacharya and Bhowmick [31] consider an elliptical filler represented by R(1 + e cos 0), in the polar coordinate. The swelling is completely restricted at the surface and the restriction diminishes radially outwards (Fig. 40 where, qt and q, are the tangential and the radial components of the linear expansion coefficient, q0). This restriction is experienced till the hypothetical sphere of influence of the restraining filler is existent. One can designate rapp [> R( 1 + e cos 0)] as a certain distance away from the center of the particle where the restriction is still being felt. As the distance approaches infinity, the swelling assumes normality, as in a gum compound. This distance, rapp, however, is not a fixed or well-defined point in space and in fact is variable and is conceived to extend to the outer surface of the hypothetical sphere of influence. 

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