Multinuclear NMR Studies of the Substitlent Effects in N-Phenyl-P,P,P-Triarylphospha-λ5-Azenes,Triaryl-Phosphines and Triarylphosphine Oxides

Abstract

A series of N-phenyl-P,P,P-triarylphospha-λ⁵-azenes (1) as well as their ^l5N labeled analogs was synthesized. The ¹³C, ³¹P, and ¹⁵N NMR spectra of this series and those of two other series of related compounds, namely triarylphosphines (2) and triarylphosphine oxides (3), were measured and are reported. Many satisfactory correlations using the mono-substituent parameter (MSP) and the Taft dual-substituent parameter (DSP) treatments with the ¹³C substituent chemical shifts (SCS), ³¹P SCS, ¹⁵N SCS and the one bond P-N, P-C and C-N coupling constants were observed and will be discussed. Thus, for example, the ³¹P and ¹⁵N chemical shifts in 1 correlated with [sgrave]^?with negative slopes while the ³¹P chemical shifts in 3 correlated with those in 1 with a slope of 2.0. The ¹³C chemical shifts in 1 correlated excellently with the corresponding ones in 3 with slopes very close to unity. The substituent effects on the chemical shifts of the various nuclei were shown to be mainly due to changes in the charge distribution on those nuclei. In 1 the one bond P-N and P-C coupling constants correlated with [sgrave]_p and [sgrave]_R respectively. The one bond P-C coupling constants of 1 correlated quite well with those of 3 with a slope of 0.93 while the corresponding correlation of 1 with 2 was quite poor. Taft DSP treatment of ¹J_PCin 1 and 3 were quite similar, ρI and ρR were both negative and ρR was much larger than ρI. Series 2 showed behavior which was different from that shown by 1 and 3 but similar to that shown by other systems with a lone electron pair on the atom bound to the phenyl ring. The substituent effects on the one bond P-N, P-C and C-N coupling constants will be discussed in terms of bonding and hybridization changes between the directly bonded nuclei.     

Degree-based topological indices of hexagonal nanotubes

There are several papers that determine one or a few chosen degree-based topological indices for hexagonal nanotubes. We present formulas, which can be used to compute any degree-based topological index for those nanotubes. Then we give exact values of the best-known degree-based indices for hexagonal nanotubes.     

Theoretical analysis of discrete contact problems with Coulomb friction

A discrete model of the two-dimensional Signorini problem with Coulomb friction and a coefficient of friction F depending on the spatial variable is analysed. It is shown that a solution exists for any F and is globally unique if F is sufficiently small. The Lipschitz continuity of this unique solution as a function of F as well as a function of the load vector f is obtained. Furthermore, local uniqueness of solutions for arbitrary F > 0 is studied. The question of existence of locally Lipschitz-continuous branches of solutions with respect to the coefficient F is converted to the question of existence of locally Lipschitz-continuous branches of solutions with respect to the load vector f. A condition guaranteeing the existence of locally Lipschitz-continuous branches of solutions in the latter case and results for determining their directional derivatives are given. Finally, the general approach is illustrated on an elementary example, whose solutions are calculated exactly.