Reversible dynamics and the macroscopic rate law for a solvable Kolmogorov system: The three bakers' reaction

We investigate a piecewise linear (area-preserving) mapT describing two coupled baker transformations on two squares, with coupling parameter 0c1. The resulting dynamical system is Kolmogorov for anyc0. For rational values ofc, we construct a generating partition on whichT induces a Markov chain. This Markov structure is used to discuss the decay of correlation functions: exponential decay is found for a class of functions related to the partition. Explicit results are given forc=2^–n. The macroscopic analog of our model is a leaking process between two (badly) stirred containers: according to the Markov analysis, the corresponding progress variable decays exponentially, but the rate coefficients characterizing this decay are not those determined from the one-way flux across the cell boundary. The validity of the macroscopic rate law is discussed.     

Photophysical processes and photochemical reactions involved in poly(N-vinylcarbazole) and in copolymers with carbazole units

This paper is devoted to the analysis of the photochemical behaviour of copolymers with carbazole units exposed to long-wavelength radiation. These copolymers are constituted of two types of carbazolylethyl methacrylate units (CEM) with octyl methacrylate moieties (OMA). The exposure of copolymers and PVK to UV light results in dramatic modifications of the physical and photophysical properties of the polymer. These modifications can be correlated with modifications of the chemical structure of the matrix. The photoageing of copolymers and PVK has been analysed by fluorescence, ESR, UV-vis and infrared spectroscopies. The effects of crosslinking and chain scissions were determined by gel fraction measurements and size exclusion chromatography.     

Shortcut method for evaluation and design of a hybrid process for enantioseparations

Hybrid processes for enantioseparations have a considerable potential for reducing investment and operational costs. An example is the combination of simulated moving bed (SMB) chromatography and selective crystallisation. However, the design of integrated processes is a difficult task. A shortcut method is presented that can serve as a tool for design and estimation of the potential of such processes. The approach requires only limited experimental data and thus allows for systematic parameter studies. The method is based on the determination of the purity-performance characteristic of the SMB process and rigorous application of mass balances. The use of relative mass fluxes allows derivation of simple algebraic expressions for essential process parameters. The significant potential of combining SMB and crystallisation is demonstrated for the example of the separation of mandelic acid enantiomers.     

The application of the concept of reaction layer to the study of electrode processes coupled with the second-order chemical reactions at microelectrodes under steady-state conditions

Under steady-state conditions, the current equations of the second-order EC, ECE and DISPI reactions at microdisk, microspherical and microring electrodes are derived with the aid of the concept of the reaction layer. The conditions under which these equations would be valid are also discussed. Using these equations, methods to determine the kinetic parameters for the second-order EC, ECE and DISPI reactions are presented. The reduction of 2,6-diphenyl-pyrylium cation and oxidation of triphenylamine were investigated as examples of the second-order EC and ECE reactions.     

Characterization of Autocatalytic Reactions in Modified Cellulose/NMMO Solutions by Thermal Analysis and UV/VIS Spectroscopy

The thermal stability of cellulose/N-methylmorpholine-N-oxide (NMMO) solutions were investigated using UV/VIS spectrometry with a temperature programming cuvette and caloric measurements by means of the Systag calorimeter RADEX (mini-autoclave). Both analytical methods allow to characterize the influences of stabilizers and additives. With the temporal course of the optical density, temperature and pressure thermal runaway reactions with gas evolution and accumulation of chromophoric degradation products were recognized. Kinetic model calculations compared with UV/VIS measurements demonstrate the existence of autocatalytic reactions in cellulose/NMMO solutions. Varying the heating rate autocatalysis can be proved by dynamic caloric measurements as well.     

Optimal dynamic advertising policies for hereditary processes

In this paper, the Nerlove-Arrow model of optimal dynamic advertising policies is generalized by assuming a general probability distribution of the forgetting time, rather than the exponential one. A control problem with integrodifferential equations of motion is defined for which the transitory and steady-state properties of the optimal advertising policy are examined. The effects of assumptions like IHR-distributions and DHR-distributions, the existence of an upper bound for the forgetting time, etc., are explained. It is shown that there are two (in the case of an exponential distribution even three) different current-value adjoint functions associated with the problem, and relations between the two (three) are established. Also provided is a sensitivity analysis.Thanks are due to G. Feichtinger and S. Jorgensen for useful discussions.     

Mechanism of silicon film deposition in the RF plasma reduction of silicon tetrachloride

Plasma-chemical reduction of SiCl₄ in mixtures with H₂ and Ar has been studied by optical emission spectroscopy (OES) and laser interferometry techniques. It has been found that the Ar:H₂ ratio strongly affects the plasma composition as well as the deposition (r _D) and etch (r _E) rates of Si: H, Cl films and that the electron impact dissociation is the most important channel for the production of SiCl_x species, which are the precursors of the film growth. Chemisorption of SiCl_x and the reactive surface reaction SiCl_x+H–SiCl_(x–1)0+HCl are important steps in the deposition process. The suggested deposition model givesr _D [SiCl_x][H], in agreement with the experimental data. Etching of Si: H, Cl films occurs at high Ar: H₂ ratio when Cl atoms in the gas phase become appreciable and increases with increasing Cl concentration. The etch rate is controlled by the Cl atom chemisorption step.     

On the statistical independence of various column contributions to band broadening. Part 1: Second moment contributions from statistically independent,longitudinal diffusion in both phases

The total length-based second moment contribution from longitudinal sample diffusion in both phases on a column, σD , is derived by adding individual partial differential contributions to a partial differential equation accounting for the longitudinal diffusion processes only. Although each diffusion-dispersed sample part is equilibrated between two phases, the resulting σ,D (= 2D _mt _m + 2D _st _s) can be interpreted as the sum of two independent contributions in accordance with the variance addition rule. (D _m and D _s are the mean diffusion coefficients and t _mand t _s the mean residence times of the sample in the mobile and stationary phases, respectively.) The same σD expression is derived from the random walk model of Giddings by treating the diffusional process in each phase as statistically independent of the other processes. Under these conditions the broadening contribution from longitudinal diffusion in the mobile phase is shown to be independent of the velocity profile.     

Superstability estimates for anharmonic systems

We consider an anharmonic crystal described by variablesS _x ,x ^d ,S _x , with one-body interaction ¦S _x ¦ and nearest neighbor (n.n.) two body interaction ¦S _x –S _y ¦. We prove that, for ^d bounded, , where is the correlation function for the free boundary condition Gibbs state in ,>0 and are suitable constants independent of and . This generalizes previous results obtained in the case.Research partially supported by Consiglio Nazionale delle Ricerche.     

Low‐Temperature Facile Template Synthesis of Crystalline Inorganic Composite Hollow Spheres

This report presents a facile approach for the low‐temperature synthesis of crystalline inorganic‐oxide composite hollow spheres by employing the bulk controlled synthesis of inorganic‐oxide nanocrystals with polymer spheres as templates. The sulfonated polystyrene gel layer can adsorb the target precursor and induce inorganic nanocrystals to grow on the template in situ. The crystalline phase and morphology of the composite shell is tunable. By simply adjusting the acidity of the titania sol, crystalline titania composite hollow spheres with tunable crystalline phases of anatase, rutile, or a mixture of both were achieved. The approach is general and has been extended to synthesize the representative perovskite oxide (barium and strontium titanate) composite hollow spheres. The traditional thermal treatment for crystallite transformation is not required, thus intact shells can be guaranteed. The combination of oxide properties such as high refractive index, high dielectric constant, and catalytic ability with the cavity of the hollow spheres is promising for applications such as opacifiers, photonic crystals, high‐κ‐gate dielectrics, and photocatalysis.