Gauss linking number

We will now demonstrate the relation between helicity and the Gauss linking number. 

Fig. 5.8. Top Transverse relaxation curve calculated for a given cross-link density (diamonds) and multiparameter fits The Gauss-Lorentz fit (broken line) agrees well at short times. The biexponential fit (continuous line) agrees well at long times. Bottom T2 relaxation curves of the CH group for nine differently cross-linked samples of unfilled SBR samples. The effective number N,. of Kuhn segments per cross-link chain varies between 9.43 and 15.56 corresponding to vulcameter moments between 16.5 and 1 dNm. By renormalization of the time axis the master curve (top) has been obtained.

Figure 2 immediately leads to the definition of a bond any two atoms that are linked by lines of field are connected by a bond. Further, the number of lines (the electrostatic flux) is a direct measure of the strength of the bond. If the charges of the ions are set equal to their atomic valence (the number of electrons the atom uses for bonding), the electrostatic flux that forms the bond is called the bond valence. From this simple construction comes the most important rule of the bond valence theory the valence sum rule (Eq. 2 in [1]), which states that the valence of an atom is equal to the sum of the valences of the bonds it forms. This is Gauss law of electrostatics. 

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