Quantum General Relativity,Torsion and Uncertainty Relations

It is shown that in gravitational theories with torsion one is led to commutation rules corresponding to Landau-Peierls type uncertainty relations.     

A novel tridentate nitrogen donor as ligand in copper catalyzed ATRP of methyl methacrylate

A tridentate ligand, BPIEP: 2,6‐bis[1‐(2,6‐diisopropyl phenylimino) ethyl] pyridine, having central pyridine unit and two peripheral imine coordination sites was effectively employed in controlled/“living” radical polymerization of MMA at 90°C in toluene as solvent, Cu^IBr as catalyst, and ethyl‐2‐bromoisobutyrate (EBiB) as initiator resulting in well‐defined polymers with polydispersities M_w/M_n ≤ 1.23. The rate of polymerization follows first‐order kinetics, k_app = 3.4 × 10^?5 s^?1, indicating the presence of low radical concentration ([P*] ≤ 10^?8) throughout the reaction. The polymerization rate attains a maximum at a ligand‐to‐metal ratio of 2:1 in toluene at 90°C. The solvent concentration (v/v, with respect to monomer) has a significant effect on the polymerization kinetics. The polymerization is faster in polar solvents like, diphenylether, and anisole, as compared to toluene. Increasing the monomer concentration in toluene resulted in a better control of polymerization. The molecular weights (M_n,SEC) increased linearly with conversion and were found to be higher than predicted molecular (M_n,Cal). However, the polydispersity remained narrow, i.e., ≤1.23. The initiator efficiency at lower monomer concentration approaches a value of 0.7 in 110 min as compared to 0.5 in 330 min at higher monomer concentration. The aging of the copper salt complexed with BPIEP had a beneficial effect and resulted in polymers with narrow polydispersitities and higher conversion. PMMA obtained at room temperature in toluene (33%, v/v) gave PDI of 1.22 (M_n = 8500) in 48 h whereas, at 50°C the PDI is 1.18 (M_n = 10,300), which is achieved in 23 h. The plot of lnk_app versus 1/T gave an apparent activation energy of polymerization as (ΔE^≠_app) 58.29 KJ/mol and enthalpy of equilibrium (ΔH⁰_eq) to 28.8 KJ/mol. Reverse ATRP of MMA was successfully performed using AIBN in bulk as well as solution. The controlled nature of the polymerization reaction was established through kinetic studies and chain extension experiments. © 2005 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 43: 4996–5008, 2005     

Neutron interferometry in gravitational field with torsion

We consider the possibility of finding experimental evidence of the fifth force with the measurement of a phase shift of neutron beams via an interferometric apparatus and also a possible rotation of the polarization plane of polarized neutron beams when torsion is introduced in a gravitational field.     

Synthesis and characterization of poly(higher‐α‐olefin)s with a nickel(α‐diimine)/methylaluminoxane catalyst system: Effect of chain running on the polymer properties

Homopolymerization of octadecene‐1 at different reaction conditions has been studied. Significant chain running can be seen at higher polymerization temperatures. Interestingly, insertion of octadecene‐1 into a sterically hindered nickel‐cation/carbon (secondary) bond is observed. The microstructure of the polymer was established using NMR spectroscopy. The effects of chain running on polymer melting, crystallization behavior, and dynamic mechanical thermal properties were studied using DSC and DMTA. The extent of chain running (i.e., 2,ω‐, 1,ω‐enchainments) decreases with an increase in the carbon number of α‐olefins. © 2006 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 45: 191–210, 2007     

At what energy does gravity unite with grand unified theories in the early universe?

Unification of gravity with GUTs is usually expected at the Planck energyE _pl10¹⁹ GeV. However, the vastly different values of the two couplings atE _Pl ( _GUT 1, _grav 1) would make such unity (atE _Pl) implausible unless there is a drastic change in the behavior of either gravity or GUTs aroundE _Pl. We picture gravity and GUTs to be unified at energies >E_Pl with a single dimensionless coupling constant ( _U 1) and described by a scale-invariant action quadratic in the Weyl curvature (with Yang-Mills fields). Breaking of scale invariance atE _Pl then separates the interactions into gravity, now described by a Hilbert action with a dimensionalG and GUTs woth a dimensionless _GUT and YM action. Problems with Klein-Kaluza unification of gravity with GUTs are also discussed in this context.     

Gravity and CP violation

The non-conservation of CP symmetry in the decay of neutralK mesons was discovered almost three decades ago. The origin of this unique phenomenon is still not well understood. There have been attempts to link it with energy splitting of theK and in the earth's gravitational field. In this essay we examine these attempts critically. A more natural way in which a gravitational field can couple asymmetrically to the system is through torsion, which coupling to isospin can, in addition to parity violation, also give rise to a C violation. The magnitude of this effect is estimated in the vicinity of a kaon and found to give a CP-violating parameter of the right value. Moreover, it is predicted that the CP violating parameter for the new system is much smaller 10^–6. Implications for baryogenesis in the early universe is also studied. In this paper we work not with the Newtonian gravitational constantG but with a torsion coupling constant, which is energy-dependent and can be related to the Fermi weak interaction constant.     

Organoaluminum chemistry and its application to the initiation of carbenium ion polymerization

Organoaluminum compounds are weak Lewis acids, which specifically react with a number of reagents (or bases) and generate an electrophile (initiator)gegenion pair, reminiscent of classical Friedel—Crafts complexes. These complexes, under suitable reaction conditions, initiate polymerization of cationically polymerizable monomers producing useful high molecular weight polymers. In recent years a number of such organoaluminum-initiator systems have been systematically explored and their chemistry unravelled. As a consequence new insights have been gained which has led to newer applications of organoaluminum compounds in organic as well as new polymer synthesis.The present paper briefly summarizes the results in this area, especially from the point of view of initiator generation. Some recent results on the initiation of carbenium ion polymerizations using the oxyhalides of sulfur and phosphorous in conjunction with organoaluminum compounds are discussed.     

Acrylonitrile Copolymers Using Cobalt Acetylacetonate Triethylaluminum Initiator System. IV. Copolymerization with Styrene

The copolymerization of acrylonitrile with styrene was studied using homogeneous Ziegler-Natta initiator containing cobalt acetylacetonate and triethylaluminum in benzene at 50°C. The overall rate of polymerization shows an interesting dependence on triethylaluminum, monomer, and initiator concentrations. The overall activation energy for the polymerization was found to be 10 kcal/mol. The polymerization was susceptible to inhibition by added hydroquinone. These observations are explained based on a mechanism wherein acrylonitrile competes for complexation with both the catalyst sites and the Lewis acid. The catalyst sites appear to possess both coordinate anionic and free radical characteristics.