Interpenetrating molecular surfaces

Figure 4.3 An example of an interpenetrating molecular surface pair, such as a MIDCO and a MEPCO pair of the same molecule.

Molecular surfaces representing different physical properties are often markedly different. These differences, as interrelations among various molecular surfaces of the same molecule, can be easily represented by the pattern of interpenetration of two or several such surfaces. The same general technique of interpenetrating surfaces can be applied for two molecular surfaces of the same physical property of two different molecules. In this latter case, the interpenetrating surfaces provide a tool for direct shape comparisons. 

The nondifferentiability of these surfaces at the seams of interpenetrating spheres as well as the local nondifferentiability of solvent accessible surfaces or union surfaces, are a technical disadvantage. Local nondifferentiability limits the application of the shape group methods in their original form that requires second derivatives for curvature analysis. For example, at every point r of a VDWS where two or more atomic spheres interpenetrate one another, the surface is not smooth and is not differentiable. For such nondifferentiable molecular surfaces, alternative shape descriptors and shape codes have been introduced. 

Isolated atoms show spherical symmetry, and it is obvious to consider a molecule as a collection of atomic spheres of some appropriate defined vdW radii. Because the vdW radii of atomic spheres used for the representations of molecular space are usually much too large for modeling molecules by simply placing the atomic hard vdW spheres side by side, commonly one generates various fused sphere models for molecules, that is the atomic vdW spheres are interpenetrated one with another. Positions of these spheres may be described by their Cartesian coordinates according to the 3D stereochemical bond pattern of a particular molecule. The envelope of the outer surface of the vdW atomic fused spheres may be regarded as a formal vdW molecular surface. This envelope embeds a formal vdW molecular volume. 

Natural rubber displays the phenomenon known as natural tack. When two clean surfaces of masticated rubber (rubber whose molecular weight has been reduced by mechanical shearing) are brought into contact the two surfaces become strongly attached to each other. This is a consequence of interpenetration of molecular ends followed by crystallisation. Amorphous rubbers such as SBR do not exhibit such tack and it is necessary to add tackifiers such as rosin derivatives and polyterpenes. Several other miscellaneous materials such as factice, pine tar, coumarone-indene resins (see Chapter 17) and bitumens (see Chapter 30) are also used as processing aids. 

Three primary mechanisms have been suggested for enhanced adhesion via silane coupling agents.5 The classical explanation is that the functional group on the silane molecule reacts with the adhesive resin. Another possibility is that the polysiloxane surface layer has an open porous structure. The liquid adhesive penetrates the porosity and then hardens to form an interpenetrating interphase region. The third mechanism applies only to polymeric adherends. It is possible that the solvent used to dilute and apply the silane adhesion promoter opens the molecular structure on the substrate surface, allowing the silane to penetrate and diffuse into the adherend. 

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