Blue-Shift Hydrogen Bonds in Silyltriptycene Derivatives: Antibonding σ* Orbitals of the Si−C Bond as Effective Acceptors of Electron Density

Triptycene derivatives are widely utilized in different fields of chemistry and materials sciences. Their physicochemical properties, often of pivotal importance for the rational design of triptycene-based functional materials, are influenced by noncovalent interactions between substituents mounted on the triptycene skeleton. Herein, a unique interaction between electron-rich substituents in the peri position and the silyl group located on the bridgehead sp³-carbon is discussed on the example of 1,4-dichloro-9-(p-methoxyphenyl)-silyltriptycene (TRPCl) which exists in solution in the form of two rotamers differing by dispositions, syn or anti, of the Si−C_Ph (the C_Ph atom is from the p-methoxyphenyl group) bond against the peri-Cl atom. For the first time, substantial differences between the Si−C_Ph bonds in these two dispositions are identified, based on indirect experimental and direct theoretical evidence. For these two orientations, the experimental ¹J(Si,C_Ph) values differ by as much as 10 percent. The differences are explained in terms of effective electron density transfer from the peri-Cl atom to the antibonding σ* orbitals of the Si−X bonds (X=H, C_Ph) oriented anti to that atom. The electronic effects are revealed by an NBO analysis. Connections of these observations with the notion of blue-shifting hydrogen bonds are discussed.     

Proficiency assessment of laboratories undertaking hard coal analysis

The Institute for Chemical Processing of Coal in Zabrze, Poland, organized a proficiency testing round to determine the mass fraction of ash, total sulfur and total carbon and the value of gross calorific value. Forty-four participants from Polish heat and power plants, research entities and independent laboratories reported results. The performance of the participants was evaluated using z and E _n scores. Over 85 % of the participants reported satisfactory results indicating the high level of proficiency of the Polish laboratories in the field.     

Click‐chemistry of polymersomes on nanoporous polymeric surfaces

A facile click chemistry method of immobilizing surface‐functionalized polymer vesicles on casted polymeric PAN substrates is described. Microporous PAN membranes were subjected to hydrochloric acid hydrolysis to obtain surface carboxylates. The carboxylic groups were activated with EDC/NHS‐solution and were then reacted with propargylamine to introduce alkyne groups for CuAAC reactions. The alkyne functionality of the modified membrane surface was verified by reaction with an azide functional click dye both before and after the immobilization of azide‐functionalized ABA vesicles. The efficient postfunctionalization of the membrane with alkyne allowed quantitative coverage of the membrane surface with a polymersome monolayer, as confirmed by immobilization of polymerzomes loaded with a fluorescent dye. Polymersome monolayers immobilized on alkyne functionalized PAN‐membranes were characterized by cryo‐SEM and monolayers were confirmed by atom force microscopy. These methods opens up new avenues for preparing membrane based filtration and sensor technologies. © 2016 Wiley Periodicals, Inc. J. Polym. Sci., Part A: Polym. Chem. 2016 , 54, 2032–2039     

Topological equivalences between organic and coordination polymer crystal structures: an organic ladder formed with three-connected molecular and supramolecular synthons

[structure: see text] Crystal engineering of an organic ladder can be achieved with a T-shaped molecule, 4,4-bis(4'-hydroxyphenyl)-1-cyclohexanol, having three hydroxyl functionalities that can form O-H...O hydrogen-bonded helices. The topology of this network structure finds a parallel in three-connected coordination polymers.     

Topological density of ccc Boolean algebras--Every cardinality occurs

For every uncountable cardinal there is a ccc Boolean algebra whose topological density is .

     

Power residue problem on elliptic curves

Let E be an elliptic curve defined over a number field K, without complex multiplication, S a finite subset of E(K) and l a rational prime being good modulus for E/K. The main result of the paper asserts that if |S|l²+l and for almost all prime ideals P of _K S contains an element R satisfying R mod P = lQ with QE(_K/P) then S contains an element R which satisfies R=lQ with some QE(K). It improves the result of S.Wong [6], where the above statement is proved under the stronger assumption |S|l². Moreover we show that the bound |S|l²+l is optimal.     

Mercuric triflate catalyzed hydroxylative carbocyclization of 1,6-enynes

[reaction: see text] Hg(OTf)(2) exhibits remarkable catalytic activity for the hydroxylative cyclization of 1,6-enynes. The present procedure should involve a sequence of mercuration of a terminal alkyne, carbocyclization, hydration, and protodemercuration that regenerates the catalyst.     

On Transfer Operators for Continued Fractions with Restricted Digits

For any non-empty subset I of the natural numbers, let _I denotethose numbers in the unit interval whose continued fractiondigits all lie in I. Define the corresponding transfer operator for , where Re (rß) = _I is the abscissa of convergence of the series . When acting on a certain Hilbert space H_I, rß, weshow that the operator L_I, rß is conjugate to an integraloperator K_I, rß. If furthermore rß is real,then K_I, rß is selfadjoint, so that L_I, rß: H_I, rß H_I, rß has purely real spectrum.It is proved that L_I, rß also has purely real spectrumwhen acting on various Hilbert or Banach spaces of holomorphicfunctions, on the nuclear space C [0, 1], and on the Fréchetspace C [0, 1]. The analytic properties of the map rß L_I, rßare investigated. For certain alphabets I of an arithmetic nature(for example, I = primes, I = squares, I an arithmetic progression,I the set of sums of two squares it is shown that rß L_I, rß admits an analytic continuation beyond thehalf-plane Re rß > _I. 2000 Mathematics SubjectClassification 37D35, 37D20, 30B70.