Dynamical systems with relaxation time

We define mathematically a class of dynamical systems that exhibit relaxation corresponding to that observed in physical systems, and then show that this class is identical with the class ofK-mixing dynamical systems.     

On the initial layer solution of the Boltzmann equation with small Knudsen number

We extend our method of systematic removal of secular terms in a singular perturbation treatment of the Boltzmann equation with small Knudsen numbers to the initial layer. The requirement that the solution through the initial layer should connect smoothly to the normal solution removes an ambiguity noted in our previous paper. We show that removal of secular terms improves Grad's solution for the initial layer and reintroduces soundlike modes associated with higher moments, first found by Wang Chang and Uhlenbeck.     

Study of the α-relaxation of PVC, EVA and 50/50 EVA70/PVC blend

The dipole dynamics and α-relaxation behaviour of polyvinyl chloride PVC, poly(ethylene-co-vinyl-acetate) EVA₇₀ and blend of them EVA₇₀/PVC have been investigated by differential scanning calorimetry (DSC) and dielectric relaxation spectroscopy (DRS). The differential scanning calorimetry (DSC) thermograms measured on samples show a single glass transition in the analysed temperature range. These three polymers are wholly amorphous and pure PVC and pure EVA₇₀ are miscible in the ratio 1:1. The glass transition temperature T_g decreases significantly with presence of EVA₇₀. Furthermore, the values of apparent activation energies for molecular motions at the α-relaxation and the values of fragility index have also been determined for each sample using Moynihan expression for DSC results and Vogel-Fulcher-Tammann-Hesse (VFTH) form for DRS results. It is shown a large dependence of all the values of these parameters with the content of EVA₇₀. Comparing these three polymers, we found that the more fragile glass forming liquid is the PVC. Fragility decreases drastically with EVA₇₀ content. EVA₇₀ and EVA₇₀/PVC blend exhibit practically the same behaviour. The effect of inter- and intra-molecular interactions on fragility is discussed to explain these variations.     

The dielectric properties of water in its different states of interaction

A tutorial on dielectric (relaxation) spectrometry of liquids is given in this article. Some methods of measuring complex (electric) permittivity spectra are briefly described. Results for water are presented and related to characteristic properties of the liquid structure and to models of the molecular dynamics, particularly as resulting from computer simulation studies. Dielectric spectra for aqueous solutions of low weight electrolytes, polyelectrolytes, small molecules, and polymers are discussed to illustrate effects of kinetic depolarization, structure saturation, as well as positive, negative, and hydrophobic hydration. Reference is also made to fluctuations in the hydrogen bond network of mixtures of water with liquids that are completely miscible with this unique solvent.     

A comparative quantum-chemical analysis of electronic structures and spectroscopic parameters of cycloalkanes and cyclopolysilanes

A comparative quantum-chemical analysis of the electronic structures and spectroscopic parameters of the cycloalkanes C₃H₆, C₄H₈, C₅H₁₀, and C₆H₁₂ and their silicon analogs Si₃H₆, Si₄H₈, Si₅H₁₀ and Si₆H₁₂ was performed in the framework of the SCF MO LCAO method in the INDO approximation. Qualitative interpretation of “abnormal” ionization potentials and energies of electronic absorption spectra of cyclopolysilanes has been given. Translated fromIzvestiya Akademii Nauk. Seriya Khimicheskaya, No. 6, pp. 1105–1108, June, 1997.     

A Green's function approach to the photoelectron spectrum of bis(π-allyl)nickel[1]

The vertical ionization potentials of bis(-allyl)nickel (see (1) in Fig. 1) are calculated by means of the Green's function approach within a semiempirical INDO extension to the first transition metal series. The computed ionization potentials are in good agreement with an experimentally deduced assignment. In contrast to earlier theoretical and experimental studies, the 7a _u () level is predicted on top of the levels corresponding to the Ni 3d orbitals. Our approach leads to a complete assignment of the PE spectrum of (1) in the outer valence region.     

Dielectric relaxation of polystyrene with side-chain- and chain-end-labels

Polystyrenes with different concentrations of side groups with cyano groups were prepared and complex dielectric constants were measured in the range of the glass transition temperature and the frequency range of 10^–2–10⁷ Hz.The GPC and DSC measurements showed that the molecular weight of these polystyrenes was about 10500 g/mole and the glass transition temperatures were 89.5°C for all samples.The dielectric relaxation spectra obtained for the side group polystyrene labels and also the chain-end polystyrene labels prepared before [9] were analyzed to find out the degree of coupling of the chain-end and side-group labels with the cooperative reorientation of the polymeric matrix. The analysis of the spectra was carried out using the analysis method developed by Mansour and Stoll [6].The results obtained showed that both end- and side-group labels are strongly coupled with the segmental reorientation and relax with relaxation times longer than that of the segments.The value of logf _m = (logf _m(label)) – logf _m(matrix)) was obtained from the recently designed comparison diagram suggested by Mansour and Stoll [6, 14]. The value of logf _m depends on the label length in the case of chain-end labels.It was surprising to find that the side groups relax slower than the segments by only 0.9 decades. These results obtained implied that the label relaxes through a multistep relaxation mechanism of the side and end groups and not through a diffusion mechanism of the whole chain. In addition, the effective lengths of the relaxing units were determined using the empirical equation obtained before in the case of rodlike molecules in polyisoprene [7].     

Mineral–water interfacial structures revealed by synchrotron X-ray scattering

Chemical reactions occurring at the mineral–water interface are controlled by an interfacial layer, nanometers thick, whose properties may deviate from those of the respective bulk mineral and water phases. The molecular-scale structure of this interfacial layer, however, is poorly constrained, and correlations between macroscopic phenomena and molecular-scale processes remain speculative. The application of high-resolution X-ray scattering techniques has begun to provide substantial new insights into the molecular-scale structure of the mineral–water interface. In this review, we describe the characteristics of synchrotron-based X-ray scattering techniques that make them uniquely powerful probes of mineral–water interfacial structures and discuss the new insights that have been derived from their application. In particular, we focus on efforts to understand the structure and distribution of interfacial water as well as their dependence on substrate properties for major mineral classes including oxides, carbonates, sulfates, phosphates, silicates, halides and chromates. We compare these X-ray scattering results with those from other structural and spectroscopic techniques and integrate these to provide a conceptual framework upon which to base an understanding of the systematic variation of mineral–water interfacial structures.     

Deuterium relaxation time ofα-d-tryptophan included in cyclodextrin host molecules

Deuterium relaxation times ofd- andl--d-tryptophan included in -cyclodextrin derivatives were directly measured by deuterium NMR spectroscopy. The results showed that the molecular motion of the tryptophan molecule was strongly restricted even in the cavity of unmodified -cyclodextrin and the additional recognition groupings — ammonium and carboxylate — on -cyclodextrin did not affect the molecular motion of tryptophan, though the association constants were significantly enhanced.Deceased on March 22, 1987.     

Concerning the Thermal Diastereomerization of the Green Fluorescent Protein Chromophore

Summary. Two model compounds for the green fluorescent protein chromophore were prepared. One of them incorporates the natural 4-hydroxybenzylidene group of the natural tyrosin derived chromophore, the other one bears a methyl group instead of the hydroxy group. Whereas the photochemically prepared (E)-diastereomer of the first compound very effectively reverted thermally (room temperature) to the thermodynamically stable (Z)-diastereomer, the (E)-diastereomer of the second derivative proved to be stable even at elevated temperatures for more than a day. This finding can be rationalized by constructing the appropriate resonance structures showing that only in the first case an effective delocalization enables partial single bond character of the benzylidene double bond. From the standpoint of chemical etiology, only Nature’s choice of the tyrosin derived chromophore of the green fluorescent protein provides an efficient radiationless thermal relaxation channel for the unwanted photo-diastereomerization product formed after excitation besides the dominating fluorescence channel of its chromophore.