Dihedral barriers

We can therefore conclude that differences in the structural relaxation between bead-spring and chemically realistic models can be attributed to either the differences in packing that we discussed above or the presence of barriers in the dihedral potential in atomistic models. To quantify the role of dihedral barriers in polymer melt dynamics, we now examine high-temperature relaxation in polymer melts. 

Finding that the scattering functions at low temperature are amenable to an MCT description, we are faced with a dilemma. On the one hand, the high-temperature mean-square displacement curves lead us to conclude that dihedral barriers constitute a second mechanism for time scale separation in super-cooled polymer melts besides packing effects. On the other hand, the... 

Fig. 7.16 Li" and anion diffusion in a PEPE5 showing influence of dihedral barriers on ion mobility...

Vn is often called the barrier of rotation. This is intuitive but misleading, because the exact energetic barrier of a particular rotation is the sum of all V components and other non-bonding interactions with the atoms under consideration. The multiplicity n gives the number of minima of the function during a 360° rotation of the dihedral angle o). The phase y defines the exact position of the minima. 

The functional form for dihedral angle (torsional) rotation is identical to that shown in equation (13) on page 175. The barrier heights are in kcal/mol and are in the file pointed to by the Fouri-erTorsion entry for the parameter set in the Registry or the chem. ini file, usually called tor.txt(dbf). If more than one term is... 

In Eq. (2), the dihedral tenn includes parameters for the force constant, Ky, the periodicity or multiplicity, n and the phase, 8. The magnimde of Ky dictates the height of the barrier to rotation, such that Ky associated with a double bond would be significantly larger that that for a single bond. The periodicity, n, indicates the number of cycles per 360° rotation about the dihedral. In the case of an bond, as in ethane, n would... 

The conformational distance does not have to be defined in Cartesian coordinates. Eor comparing polypeptide chains it is likely that similarity in dihedral angle space is more important than similarity in Cartesian space. Two conformations of a linear molecule separated by a single low barrier dihedral torsion in the middle of the molecule would still be considered similar on the basis of dihedral space distance but will probably be considered very different on the basis of their distance in Cartesian space. The RMS distance is dihedral angle space differs from Eq. (12) because it has to take into account the 2n periodicity of the torsion angle. 

There are two possible Cs conformations of the Sy homocycle exo and endo. The exo global minimum (Fig. 2) lies 15 kJ mol below the endo-form. Both conformers undergo facile pseudorotation through C2 transition states, with barriers of less than 4 kJ mol [54]. The exo-conformer possesses the geometry found in the sulfur allotropes y-Sy and 5-Sy [72]. This Cs structure has four bonds near the length of a normal S-S bond and one rather long bond of 215 pm with a dihedral angle of 0°. 

It is difficult to decide whether the discrepancy between the calculated and experimental data is due to a different conformational preference of the thietane dioxides in the liquid and the solid phase, or to the crude approximations included in the Karplus-Barfield equation. However, the relationship between vicinal coupling constants and dihedral angles appears qualitatively valid in thietane oxides and dioxides, particularly if trends instead of exact values are discussed . At any rate thietane dioxides, 1,3-dithietane dioxides and tetroxides maintain either planarity or a slightly distorted average vibrating conformation with a low barrier to ring planarity . 

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