On Classification of Modular Tensor Categories

We classify all unitary modular tensor categories (UMTCs) of rank ≤ 4. There are a total of 35 UMTCs of rank ≤ 4 up to ribbon tensor equivalence. Since the distinction between the modular S-matrix S and −S has both topological and physical significance, so in our convention there are a total of 70 UMTCs of rank ≤ 4. In particular, there are two trivial UMTCs with S = (±1). Each such UMTC can be obtained from 10 non-trivial prime UMTCs by direct product, and some symmetry operations. Explicit data of the 10 non-trivial prime UMTCs are given in Sect. 5. Relevance of UMTCs to topological quantum computation and various conjectures are given in Sect. 6.     

Deuterium solid echo line shape study of poly(ethylene oxide) dynamics in a blend with poly(methyl methacrylate)

Deuterium solid echo line shapes were measured on deuterated poly(ethylene oxide) (d₄PEO) in a blend with protonated poly(methyl methacrylate) to characterize chain dynamics of this component in the blend. Line shapes were observed as a function of temperature from 183 to 243 K and echo delay times from 10 to 100 μs on a blend containing 20 wt % d₄PEO. The line shapes and the associated relative intensities were quantitatively interpreted in terms of segmental motion and libration. The results of the interpretation are compared to an earlier study of deuterium spin‐lattice relaxation times over the temperature range of 313 to 413 K. A combined interpretation of both sets of data is developed based on bimodal distribution of correlation times that are separated by about 2 orders of magnitude in time. The faster mode is 30% of the correlation function with a stretched exponent near one while the slower mode is characterized by an exponent of 0.5. The source of the bimodal character is not revealed by the line shape and relaxation data but is consistent with the presence of two glass transition temperatures in this miscible blend and anomalous translational diffusion of diethyl ether through the blend. © 2005 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 43: 2433–2444, 2005     

REVERSIBLE SKELETAL SUBSTITUTION REACTIONS INVOLVING GROUP 13 HETEROPHOSPHAZENES

An unusual, reversible skeletal substitution reaction involving boron- and aluminum-based heterophosphazenes is described.     

PSEUDOHALOGEN CHEMISTRY. PART IV. HETEROLYTIC ADDITION OF THIOCYANOGEN TO ALKENES

Abstract

Thiocyanogen reacts slowly with alkenes, in the presence of a radical inhibitor in benzene or acetic acid in the dark at 25°, to yield α,β-dithiocyanates, α-isothiocyanates-β-thiocyanates and, in acetic acid, α-acetoxy-β-thiocyanates in varying proportions. The additions to alkyl alkenes are trans-stereospecific, and, in the case of the α-isothiocyanato-β-thiocyanates, non-regiospecific. The additions to aryl alkenes are trans-stereoselective and regiospecific, yielding the Markownikov-orientated α-isothiocyanato-β-thiocyanates. A heterolytic mechanism involving a two-step, kinetically controlled addition, with the formation of a cyano-sulfonium ion intermediate, e.g., 35, in the case of alkyl alkenes and an open carbonium ion, e.g., 36, in the case of aryl alkenes, is suggested. The diothiocyanate: isothiocyanato-thiocyanate ratios are discussed in terms of kinetic and steric control of reaction.     

Conformational Properties of the Phosphate Rings of Neutral Phosphoramidate Derivatives of Ribo- and 2′-Deoxyribonucleoside Cyclic 3′,5′-Monophosphates

Abstract

An investigation of the effects of changing the nature of X, nitrogen base (B), and amino substituent (R₂N) on the equilibrium 1?2 was carried out.

The influence of the above structural changes on the time-averaged coupling constants J_AP and J_BP, determined at 300 MHz, were used to follow changes in K_eq. With constant R₂N, small effects from variation of X and B were found. A large range in K_eq arose from changes in the steric size of R₂N. These results will be related to the question of the ease of chair to twist interconversion of the phosphate ring essential to the biological activities of the naturally occurring diesters, cAMP and cGMP.     

SOME HETEROCYCLIC PHOSPHOROCHLORIDATES AND THE FORMATION OF OTHER HETEROCYCLIC ORGANOPHOSPHORUS COMPOUNDS

Abstract

Pyrrolidine, morpholine, and β-hydroxyethylmorpholine have been phosphorylated with phosphorus oxychloride, phenylphosphorodichloridate, p-chlorophenylphosphorodichloridate and thiophosphoryl chloride. The resultant phosphorodichloridates have been condensed with a wied range of nucleophilic reagents, e.g. amines, hydrazines, phenols and isobutanol. Piperazine with phosphorus oxychloride (2 mols) gave the N(1) N(4)-diphosphorotetrachloridate, which was characterized as the tetracyclohexylamidate. β-Hydroxyethylpiperazine was similarly phosphorylated to the N,O-diphosphorotetrachloridate which was characterized as the tetraphenylhydrazidate.

Condensation of pyrrolidine (2 mols) with phosphorus oxychloride (1 mol) afforded N,N′-dipyrrolidinophosphorochloridate which was reacted with phenylhydrazide and sodium azide. The phosphoroazide with triphenylphosphine afforded the corresponding triphenylphosphinimine. N-Phenyl N′-pyrrolidinophosphorochloridate with aqueous pyridine gave the corresponding pyrophosphoramide and the stability of the pyrophosphoramide towards hydrolysis was examined. 1,2-Cyclohexanediol was phosphorylated with phenylphosphorodichloridate and thiophosphorylchloride. Trans-4-t-Butylcyclohexyl N,N′-diphenylhydrazinophosphorothioate by reaction with formaldehyde gave a tetra-azaphosphorine P-sulfide. Trans-4-t-Butylcyclohexyl N-phenyl N′-phenylphosphorodiamidic hydrazide reacted with 1,4-dibromobut-2-ene to give a 1,2-diazahex-4-ene.     

Synthesis of Amino Acid Derived Cyclic Phosphorus Ylides

Abstract

We recently reported the thermal elimination of Ph₃PO from suitably protected aminoacyl ylides 1 as a route to acetylenic amino acid analogues 2. Pyrolysis of ylides such as 3 with a free amino group takes a different course. Ethanol is eliminated to give the c h i d cyclic ylides 4 which can be viewed as 3-triphenylphosphoranylidene tetramic acids. Specific examples prepared include 4 (R = Me, Pri), the parent compound 5 (from glycine) and the six-membered ring compound 6 (from p-alanine). Using a similar approach, bicyclic ylides such as 7 (from proline) can be prepared. In the case of the glutamate derived ylide 8, thermolysis initially gives a mixturc of 9 and 10 but these both cyclise to the bicyclic product 11 with time. The structure and reactivity of these interesting cyclic ylides are now being examined.