Molecular chains geometry

Figure Bl.22.3. RAIRS data in the C-H stretching region from two different self-assembled monolayers, namely, from a monolayer of dioctadecyldisulfide (ODS) on gold (bottom), and from a monolayer of octadecyltrichlorosilane (OTS) on silicon (top). Although the RAIRS surface selection rules for non-metallic substrates are more complex than those which apply to metals, they can still be used to detemiine adsorption geometries. The spectra shown here were, in fact, analysed to yield the tilt (a) and twist (p) angles of the molecular chains in each case with respect to the surface plane (the resulting values are also given in the figure) [40].

The picture presented so far of the polyethylene chain being of a linear zig-zag geometry is an idealised one. The conformation of a molecular chain is in fact random provided that the bond tetrahedral angle remains fixed. This is best illustrated by considering a piece of wire with one bend at an angle of 109° 28 as shown in Fig. A.5a. 

Derivatives of Linear Chain Geometry. The molecular structure... 

An x-ray geometry is considered to be reasonably well reproduced if the RMS deviation of the atomic positions RMSxfz is less than 0.3 A. A chain geometry is taken to be well reproduced if the RMS deviation of the torsion angles at rotatable bonds RMSTa is less than 15°. A 3D molecular model is considered to be free of nonbonded interactions if the close contact ratio CCR (the ratio of the smallest nonbonded distance to the smallest acceptable value for this distance) is greater than 0.8. 

Alternatively, polysoaps with well defined chemical structures can be prepared by the polyaddition or polycondensation of non-amphiphilic reagents [56, 57, 119,120] (Fig. 2b). The surfactant fragments are formed in the course of the reaction only. This technique appears particularly attractive for polysoaps of main chain geometry (see below and Figs, le, 2e and 6d). The problems concerning the molecular weights are the same as for the polymerization of reactive surfactants, and the scope of useful chemical structures seems to be limited. 

Using differential geometry, a curve can be reconstructed from the knowledge of its curvature and torsional functions (the Frenet-Serret formulas). Therefore, these two functions give a concise shape description, provided one associates an everywhere-differentiable curve to the molecular skeleton. This approach has been employed in the analysis of protein shape. Moreover, this technique allows one to represent the dynamics of molecular chains or loops in terms of the deformation of elastic bodies. We return to this point when we discuss a number of purely topological descriptors of molecular curves. 

Chamberlain TW, Pfeiffer R, PeterUk H, Kuzmany H, Zerbetto F, Melle-Franco M, Staddon L, Champness NR, Briggs GAD, Khlobystov AN. Polyarene-functionaUzed fullerenes in carbon nanotubes towards controlled geometry of molecular chains. Small 2008 4 2262-70. 

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