The unusual chemical equilibria F3SSF ⇌ 2 SF2 and CF3SF2SCF3 ⇌ 2CF3SF

In order to understand more about the instability of sulfur difluoride, we have investigated the chemical interrelations between each of the monomers SF₂ and CF₃SF and the corresponding dimers F₃SSF and CF₃SF₂SCF₃. Thus we have found that SF₂ and CF₃SF exist in chemical equilibria with their dimers. These equilibria are unusual because they involve two different bonds (SF and SS). The equilibrium constants and dissociatíon enthalpies have been determined by i.r. and mass spectroscopic measurements.

The equilibrium between F₃SSF and SF₂ is disturbed by a decomposition reaction of these compounds yielding SF₄ and SSF₂. In both systems (1) and (2) the achievement of the equilibrium is comparatively slow at ?30 to 30 °C. The rates for dissociation and decomposition are strongly surface-dependent and the kinetics of the two processes have been studied separately. Under favorable conditions the half-lives at 298 K for the dissociation of F₃SSF and CF₃SF₂SCF₃ are found to be ca. 8.h and ca. 2 h, respectively, and for the decomposition of SF₂ to SF₄ and SSF₂ and CF₃SF to CF₃SF₃ and CF₃SSCF₃ (p?13 mbar) the values are ca. 10 h and 1 year respectively.     

Preparation and properties of perfluorochloromethyl-mercaptophosphoryldichlorides and -chlorophosphanes

In Arbuzov-type reactions CF_nCl_3?nSCl reacts with ROPCl₂ (R = CH₃, C₂H₅) to give CF_nCl_3?nSP(O)Cl₂ (n = 3,2,1,0). The corresponding reaction with CF₃SeX (X = Cl, Br) produces CF₃SeP(O)Cl₂ in good yields only in the presence of catalysts such as SbCl₅ or BCl₃. Reactions between P₄ and the sulfenylchlorides produce (CF_nCl_3?nS)_xPCl_3?n (n = 3,2,1 and x = 1,2). On heating CF_n′ Cl_3?n′ SP(O)Cl₂ (n′ = 2,1,0) decompose to P(O)Cl₃ and SCF_n′ Cl_2?n′. During this process fluorination of P(O)Cl₃ to P(O)F₃ by SCF₂ is observed. A Cl/Br exchange between CF_nCl_3?nSP(O)Cl₂ (n = 3,2) and PBr₃ was proved ¹⁹F? and ³¹P-NMR-spectroscopically.Chemical and physical properties of the newly synthesized compounds will be discussed.     

Reconfiguration graphs of shortest paths

For a graph $G$ and$a,b\in V\left(G\right)$, the shortest path reconfiguration graph of $G$ with respect to $a$ and$b$ is denoted by $S(G,a,b)$. The vertex set of $S(G,a,b)$ is the set of all shortest paths between $a$ and$b$ in $G$. Two vertices in $V\left(S(G,a,b)\right)$ are adjacent, if their corresponding paths in $G$ differ by exactly one vertex. This paper examines the properties of shortest path graphs. Results include establishing classes of graphs that appear as shortest path graphs, decompositions and sums involving shortest path graphs, and the complete classification of shortest path graphs with girth 5 or greater. We include an infinite family of well structured examples, showing that the shortest path graph of a grid graph is an induced subgraph of a lattice.     

Imidization reaction in polyvinylamides

Depending on their method of preparation, polyvinylamides can have nitrogen contents which vary from the theoretical value to considerably lower values. Cyanamer P-250, a polyacrylamide, manufactured by American Cyanamid Corporation, had a nitrogen content of 17.67% compared to the theoretical value of 19.7%. A polyacrylamide prepared in dioxane at 60°C and initiated by benzoyl peroxide, had a nitrogen content of only 15.5%. These low values are ascribed to loss of ammonia via intramolecular imide formation. We have found that when the intramolecular imidization reaction in poly acrylamide and in polymethacrylamide is driven to completion by heating the polymers in dilute solution, very close to 33% of the amide groups remain unreacted. Thus, unlike poly(methyl vinyl ketone) and poly(vinyl chloride), the poly-vinylamides do not obey Flory's statistical calculation for the random reaction of 1,3 groups in a head-to-tail polymer which predicts isolation of only 13.53% of the vinyl residues. Of the various possible explanations, the hypothesis of larger ring formation seems the most plausible, since specific interactions have been shown to exist between widely spaced amide groups in low molecular weight diamides. The infrared spectra of polyacrylimide and polymethacrylimide are presented and compared with those of the corresponding polyvinylamides. When the nitrogen content of polyacrylamide falls to the 14.9–15.4% N range due to imide formation, the polymer becomes water-insoluble. Because imidization stiffens the polymer chain and introduces weakly acidic groups, the imide content of a polyvinylamide should affect its compatibility with other polymeric systems.     

Band mixing in 49Cr and 47V: Importance of a correct treatment of hole excitations and the J2 term

Band mixing calculations treating correctly the $\text{j}{}^2$ term and hole excitations have been undertaken on the cross-conjugate pair ⁴⁷V, ⁴⁹Cr. It is found that such a treatment gives rise to appreciable differences from the usual band mixing calculations of nuclei in the lf-2p shell. The results are in good agreement with the experimental level schemes.     

Synthesis of time-optimal control of a second-order nonlinear process

The time-optimal control of a soft spring is discussed. The domain of controllability and the switching locus are described. It is shown that the switching locus changes in a discontinuous manner as the nonlinearity varies continuously.This research was partially supported by the Joint Services Electronics Program, Grant No. (4711) N00014-67-A-0226 ARPA 1129, and by NASA, Grant No. NGR 15-005-021.