Cosmology and Description of Local Space-Time Properties by Einstein's Equations

We consider a theory in which the global and local space-time properties are described by different laws. One consequence of such a theory is that the only time-dependent cosmological models are such that their homogeneous and isotropic three-spaces are closed. In the framework of this theory the local space-time properties are approximately described bei Einstein's equations, but with Einstein's gravitational coupling number now being a function of the matter density filling the universe.     

A one-dimensional SiGe superlattice grown by UHV epitaxy

One-dimensional SiGe superlattices with periods ranging from 100 to 800 Å have been deposited on Si substrates by periodically varying the Ge content of a mixed Si_1-x Ge _x multilayer structure fromx=0 tox=0.15. The deposition was successful, employing and UHV evaporation technique at a substrate temperature of 750°C fulfilling the four conditions: Single crystal growth, no interdiffusion, two-dimensional growth, and pseudomorphic growth. It is shown that mismatch above 8 · 10^?3 favours growth by three-dimensional nucleation. The experimentally determined spacing of misfit dislocations is compared with theoretical results obtained by van der Merwe. The pseudomorphic growth behaviour of layers thinner than a critical thickness could be confirmed.     

The effect of vibrational energy on the reaction of molecular hydrogen with atomic oxygen

An upper bound of 6 × 10¹⁰ cm³/moles on the rate constant for the reaction of atomic oxygen with vibrationally excited H₂ has been deduced from laboratory observations and from detailed computer calculations. From this result it can be shown that no more than 30% of the vibrational energy of H₂ is effective in overcoming the activation energy for the O + H₂ reaction.     

Reconsidering glycosylations at high temperature: precise microwave heating

Current methods for glycosylation of complex alcohols, e.g. with glycosyl trichloroacetimidates, generally occur in the presence of a strong Lewis acid 'promoter', and at sub-ambient temperatures. However, the older literature reports high-temperature glycosylations, especially of phenols. We have described an efficient method for glycosylation of alcohols under neutral conditions, using as anomeric leaving group methyl 3,5-dinitrosalicylate (DISAL). Only a very few reports have described the use of microwaves to promote glycosylations, mainly of simple alcohols. Here we describe fast, high-temperature glycosylations using precise microwave heating in the synthesis of oligosaccharides, with both DISAL and widely used trichloroacetimidate glycosyl donors in the absence of strong Lewis acids. Also, we have applied microwave heating as a general protocol for evaluating new, potential glycosyl donors.     

Influence of the atmosphere on the thermal decomposition kinetics of the CaCO<Subscript>3</Subscript> content of PFBC coal flying ash

The thermal decomposition behavior of hard coal fly ash (HCA2), obtained from the combustion of an Australian hard coal in thermoelectric power plants, in different atmospheres (air, N₂ and N₂-H₂ mixture), was studied using thermogravimetry (TG), infrared-evolved gas analysis (IR-EGA), differential scanning calorimetry (DSC) and thermodilatometry (DIL) techniques. It was found that changing of the applied atmosphere affects the carbon content of the ash which results in different thermal decomposition behaviors. In air, the carbon content was oxidized to carbon dioxide before the decomposition of carbonate. In N₂ or in N₂-H₂ atmospheres, the carbon content acts as a spacer causing a fewer points of contact between calcium carbonate particles, thus increasing the interface area which results in a decrease of the carbonate decomposition temperature. Following the carbonate decomposition, the iron oxide content of the ash undergoes a reductive decomposition reaction with the unburned carbon. This oxidation-reduction reaction was found to be fast and go to completion in presence of the N₂-H₂ mixture than in the pure nitrogen atmosphere due to the reducing effect of the hydrogen. The kinetics of the carbonate decomposition step, in air and N₂-H₂ mixture was performed under non-isothermal conditions using different integral methods of analysis. The dynamic TG curves obeyed the Avrami-Erofeev equation (A₂) in air, and phase boundary controlled reaction equation (R₂) in N₂-H₂ mixture. The change in the reaction mechanism and the difference in the calculated values of activation parameters with the change of the atmosphere were discussed in view of effect of the atmosphere on the carbon content of the ash.     

Polarization Effects for Hydrogen-Bonded Complexes of Substituted Phenols with Water and Chloride Ion

Variations in hydrogen-bond strengths are investigated for complexes of nine para-substituted phenols (XPhOH) with a water molecule and chloride ion. Results from ab initio HF/6-311+G(d, p) and MP2/6-311+G(d, p)//HF/6-311+G(d, p) calculations are compared with those from the OPLS-AA and OPLS/CM1A force fields. In the OPLS-AA model, the partial charges on the hydroxyl group of phenol are not affected by the choice of para substituent, while the use of CM1A charges in the OPLS/CM1A approach does provide charge redistribution. The ab initio calculations reveal a 2.0-kcal/mol range in hydrogen-bond strengths for the XPhOH?OH(2) complexes in the order X = NO(2) > CN > CF(3) > Cl > F > H >OH >CH(3) > NH(2). The pattern is not well-reproduced with OPLS-AA, which also compresses the variation to 0.7 kcal/mol. However, the OPLS/CM1A results are in good accord with the ab initio findings for both the ordering and range, 2.3 kcal/mol. The hydrogen bonding is, of course, weaker with XPhOH as acceptor, the order for X is largely inverted, and the range is reduced to ca. 1.0 kcal/mol. The substituent effects are found to be much greater for the chloride ion complexes with a range of 11 kcal/mol. For quantitative treatment of such strong ion-molecule interactions the need for fully polarizable force fields is demonstrated.     

Molecular dynamics simulation of amphiphilic bistable [2]rotaxane langmuir monolayers at the air/water interface

Bistable [2]rotaxanes display controllable switching properties in solution, on surfaces, and in devices. These phenomena are based on the electrochemically and electrically driven mechanical shuttling motion of the ring-shaped component, cyclobis(paraquat-p-phenylene) (CBPQT(4+)), between a monopyrrolotetrathiafulvalene (mpTTF) unit and a 1,5-dioxynaphthalene (DNP) unit located along a dumbbell component. The most stable state of the rotaxane (CBPQT(4+)@mpTTF) is that in which the CBPQT(4+) ring encircles the mpTTF unit, but a second less favored metastable co-conformation with the CBPQT(4+) ring surrounding the DNP (CBPQT(4+)@DNP) can be formed experimentally. For both co-conformations of an amphiphilic bistable [2]rotaxane, we report here the structure and surface pressure-area isotherm of a Langmuir monolayer (LM) on a water subphase as a function of the area per molecule. These results from atomistic molecular dynamics (MD) studies are validated by comparing with experiments based on similar amphiphilic rotaxanes. For both co-conformations, we found that as the area per molecule increases the thickness of the LM decreases while the molecular tilt increases. Both co-conformations led to similar LM thicknesses at the same packing area. From the simulated LM systems, we calculated the electron density profiles of the monolayer as a function of area per molecule, which show good agreement with experimental analyses from synchrotron X-ray reflectivity measurements of related systems. Decomposing the overall electron density profiles into component contributions, we found distinct differences in molecular packing in the film depending upon the co-conformation. Thus we find that the necessity of allowing the tetracationic ring to become solvated by water leads to differences in the structures for the two co-conformations in the LM. At the same packing area, the value of the overall tilt angle does not seem to be sensitive to whether the CBPQT(4+) ring is encircling the mpTTF or the DNP unit. However, the conformation of the dumbbell does depend on the location of the CBPQT(4+) ring, which is reflected in the segmental tilt angles of the mpTTF and DNP units. Using the Kirkwood-Buff formula in conjunction with MD calculations, we find the surface pressure-area isotherms for each co-conformation in which the CBPQT(4+)@mpTTF form has smaller surface tension and therefore larger surface pressure than the CBPQT(4+)@DNP at the same packing area, differences that decreases with increasing area per molecule, which is verified experimentally.     

Quantification of the Magnetic Anisotropy of a Single-Molecule Magnet from the Experimental Electron Density

Reported here is an entirely new application of experimental electron density (EED) in the study of magnetic anisotropy of single-molecule magnets (SMMs). Among those SMMs based on one single transition metal, tetrahedral Co^II-complexes are prominent, and their large zero-field splitting arises exclusively from coupling between the d and d_xy orbitals. Using very low temperature single-crystal synchrotron X-ray diffraction data, an accurate electron density (ED) was obtained for a prototypical SMM, and the experimental d-orbital populations were used to quantify the d_xy-d coupling, which simultaneously provides the composition of the ground-state Kramers doublet wave function. Based on this experimentally determined wave function, an energy barrier for magnetic relaxation in the range 193–268 cm⁻¹ was calculated, and is in full accordance with the previously published value of 230 cm⁻¹ obtained from near-infrared spectroscopy. These results provide the first clear and direct link between ED and molecular magnetic properties.     

Integrability of Multicomponent Models in Multidimensional Cosmology

The multidimensional cosmological model describing the evolution of n Einstein spaces in the presence of multicomponent perfect fluid is considered. We define vectors related to the equations of state of the components. If they are orthogonal with respect to the minisuperspace metric, the Einstein equations are integrable and a Kasner-like form of the solutions is presented. For special sets of parameters the cosmological model is reduced to the Euclidean Toda-like system connected with some Lie algebra. The integrable vacuum (1+5+5)-model with two 5-dimensional Einstein spaces and non-zero Ricci tensors is obtained. Its reduction to a (1+5+3+2)-solution is given. For a special choice of the integration constant and one of the spaces (M₁ = S⁵) a non-singular solution with the topology is obtained.