Mathematical model of chemical oscillations arising in a homogeneous system of cysteine and oxygenated complexes of iron(II)

A mathematical model of the homogeneous oxidation kinetics of cysteine in the presence of oxygenated complexes of iron(II) with dimethylglyoxime and cytosine expressed in the form of a system of three nonlinear differential equations is analyzed. The model is simplified by stoichiometric analysis of the suggested kinetic scheme. As determined on the basis of qualitative analysis of the system of differential equations, a single stationary state with the singular point assigned to the focus—spatial saddle type, from which a bifurcation of the Andronov-Hopf type can occur, is implemented. Upon solving numerically the system of differential equations for different initial conditions, it is found that the mathematical model has a solution in the form of a limit cycle, and the process runs in an oscillatory mode at such initial concentrations of the catalyst and cysteine that are comparable to their contents at which chemical oscillations are observed in experiments.     

Capacitive-discharge-heated anisotropic pyrolytic graphite furnace used for atomic absorption spectrometry Part. 1 Thoeretical Modelling of the Heating Characteristics of the Furnace Surface and of the Gas Phase

A model of the temperature distribution in the tube wall and in the gas phase of an anisotropic pyrolytic graphite furnace heated by capacitive discharge technique is proposed. The heat loss from the graphite tube by conduction via the contact electrodes to the water-cooled electrode supports and by radiation to its surroundings are the main processes condidered. In calculating the gas temperature, heat transfer by conduction from the tube wall to the gas phase is the only mode taken into account. The instantaneous temperature of a graphite furnace is expressed in the form of a differential equation. A finite-difference form of the differential equation is used in a computer program to calculate the temperature at each time step. The computer simulation offers the capability of studying the factors affecting the characteristics of temperature/time profiles and the distribution of surface and gas phase temperatures of the furnace. The results of simulation studies of the effect of the capacitance and the initial voltage of the capacitor bank on the heating characteristics of the furnaces show a reasonable agreement with those obtained experimentally.     

An exponential Galerkin method for solutions of HIV infection model of CD4+ T-cells

In this study, we consider a nonlinear first order model about the infection of CD4⁺ T-cells by HIV. In order to solve it numerically, we present a new method based on exponential polynomials reminiscent of the Galerkin method. Considering the approximate solutions in the form of exponential polynomials, we first substitute these approximate solutions in the original model. Some relations are thus obtained, which we express in terms of matrices. Taking inner product of a set of exponential functions with these matrix expressions then yields a nonlinear system of algebraic equations. The solution of these equations gives the approximate solutions of the model. Additionally, the technique of residual correction, which aims to reduce the error of the approximate solution by estimating this error, is discussed in some detail. The method and the residual correction technique are illustrated with an example. The results are also compared with numerous existing methods from the literature.     

New method and results of Raman studies of non-diffusional reorientational dynamics of molecules in the nematic phase

The method of differential Raman spectroscopy is developed to the case of uniaxial liquid crystals, increasing the precision of the determination of relative broadening and splitting of the polarized components of Raman bands in liquid crystals. With the help of the new technique and on the basis of a more general treatment of rotational broadening of Raman bands, some typical liquid crystal materials, namely, 4-pentyl-4'-cyanobiphenyl (5CB) and trans-4-pentyl-(4-cyanophenyl)cyclohexane (5PCH) have been studied. It is shown that for a particular form of intramolecular vibration (for example the cyano stretching mode), it is possible to determine all independent orientational autocorrelation functions without applying model considerations of the rotational motion in the nematic phase. The deviations of the results of these studies from a simple diffusional model of orientational relaxation in the short-time limit are discussed.     

Evaluation of heats and entropies of fusion by quantitative differential thermal analysis method

The technique of dynamic differential calorimetry is discussed as a method for the quantitative determination of several thermodynamic properties of crystals. Some results on heats and entropies of fusion of binary tetrahedral semi-conductors are reported.     

Characterization of physical state of mannitol after freeze-drying: effect of acetylsalicylic acid as a second crystalline cosolute

Freeze-drying of mixed solutes is a preparative technique widely used in the pharmaceutical industry. The presence of an amorphous form or changes in the crystalline form can affect solid state stability. In this work, acetylsalicylic acid (AAS) was chosen as a model drug, and was mixed with mannitol, a commonly used bulking agent in formulation of tablets. Variations in the final freeze-dried crystalline forms were found after changing the ratios of the two co-solutes. Samples were analysed by powder X-ray diffractometry and differential scanning calorimetry. A major amorphous form and a minor crystalline delta-mannitol form were produced during the mannitol freeze-drying process. The crystal form of mannitol in the two-component system depended on the AAS:mannitol ratio. The AAS was mostly crystalline, regardless of the amount of mannitol present. A major delta-mannitol and a minor amorphous form were obtained when AAS was present in a high percentage (75% w/w). When AAS percentages of 50 and 25% (w/w) were present during the drying process, the mannitol was found in a highly crystalline form.     

High precision comparative polarography

A new cell assembly for use with the differential cathode ray polarograph is described togother with full practical details of its use in comparative polaragraphy. The difficulties of manipulating the cells and dropping mercury electrodes have been greatly reduced. Results obtained show that the coefficient of variation of a polarographic determination can be as low as 0.04%. Some general aspects of the technique are discussed.     

Analysis of two-dimensional models for liquid chromatographic reactors of cylindrical geometry

This work presents the analytical solutions of two-dimensional isothermal reactive general rate models for liquid chromatographic reactors of cylindrical geometry. Both irreversible and reversible reactions are considered. The model equations form a linear system of convection-diffusion-reaction partial differential equations coupled with algebraic equations for isotherms. Analytical solutions are derived by integrated implementation of finite Hankel transform, Laplace transform, eigen-decomposition technique, and conventional ordinary differential equations solution technique. To verify the analytical results, a high-resolution finite volume scheme is also applied to numerically approximate the model equations. The current results can be very useful to optimize and upgrade the liquid chromatographic reactors.     

EPDM accelerated sulfur vulcanization: a kinetic model based on a genetic algorithm

A simple closed form equation for the prediction of crosslinking of EPDM during accelerated sulfur vulcanization is presented. Such a closed form solution is derived from a second order non homogeneous differential equation, deduced from a kinetic model. The kinetic model is based on the assumption that, during vulcanization, a number of partial reactions occurs, both in series and in parallel, which determine the formation of intermediate compounds, including activated and matured polymer. Once written standard first order differential equations for each partial reaction, the differential equation system so obtained is rearranged and, after few considerations, a single second order non homogeneous differential equation with constant coefficients is derived, for which a solution may be found in closed form, provided that the non-homogeneous term is approximated with an exponential function. To estimate numerically the degree of crosslinking, kinetic model constants are evaluated through a simple data fitting, performed on experimental rheometer cure curves. The fitting procedure is a new one, and is achieved using an ad-hoc genetic algorithm, provided that a few points, strictly necessary to estimate model unknown constants with sufficient accuracy, are selected from the whole experimental cure curve. To assess the results obtained with the model proposed, a number of different compounds are analyzed, for which experimental or numerical data are available from the literature. The important cases of moderate and strong reversions are also considered, experiencing a convincing convergence of the analytical model proposed. For the single cases analyzed, partial reaction kinetic constants are also provided.     

Diode laser differential absorption spectrometry for measurements of some parameters of condensed media

A method of diode laser differential absorption spectrometry (DLDAS) is proposed. The method is based on the detection of absorption spectra variations caused by the changes of a parameter of a condensed media (temperature, composition of the components of a mixture, pH, etc.). Some simple theoretical background of the proposed technique is presented. The potentialities of the method are demonstrated in the experiments on remote contactless measurement of the temperature of aqueous solutions and measurement of the deviations of the composition of a mixture of dyes from the equilibrium state.     

Calorimetric study of the conformational relaxation times in polystyrene

The temperature dependence of the relaxation times of the structural relaxation process of polystyrene is determined by temperature-modulated differential scanning calorimetry (TMDSC) and by conventional differential scanning calorimetry (DSC) in the latter by modelling the experimental heat capacity curves measured in heating scans after different thermal histories. The good agreement between both measuring techniques in the temperature interval just above the glass-transition temperature is a guide for the interpretation of the results of the TMDSC technique in the glass-transition region. In addition, the same model applied to DSC scans is used to simulate the TMDSC experiment and the calculated response is compared with the measured scans. Received: 22 February 1999 Accepted in revised form: 11 June 1999     

Détermination du modèle thermocinétique d'un phénomène par convolution avec la fonction d'appareil optimisation des paramètres de ce modèle

The analysis of experiments on thermal reaction kinetics is complicated by the deformation of the signal due to the inertia of the microcalorimeter.A method is presented which calculates the thermogram by optimizing the parameters of a theoretical model. This model introduces the characteristics of the apparatus by a convolution technique. Since an experimental determination of the deformation due to the apparatus is used, it is unnecessary to assume an analytical form of this function as in previous methods of analysis by deconvolution.     

A novel scheme for structure determination in EXAFS

A novel scheme is introduced which allows bond distances to be determined from EXAFS data without the use of model compounds or calculated scattering phases. The basis for this method rests on the physical restrictions imposed on any functional form which is used to describe the scattering phases. These restrictions allows a differential equation to be set up in terms of the unknown phases. The abilityof this scheme to determine structural information is demonstrated for a series of model systems.     

Ternary water-salt system Sm(CCl<Subscript>3</Subscript>COO)<Subscript>3</Subscript>-Er(CCl<Subscript>3</Subscript>COO)<Subscript>v</Subscript>-H<Subscript>2</Subscript>O at 298 K

The system of samarium and erbium trifluoroacetates and water has been studied by the isothermal solubility technique at 298 K. The composition of the solids has been determined using the Schreinemakers wet residue technique. The refractive indices, specific volumes, and viscosities of liquid phases and the refractive indices of solid residues have been determined. A continuous solid solution is found to form in the system. Some thermodynamic parameters have been determined for this solid solution.     

Some Conceptual Issues For The Statement Of Quantum Problems In The Theory Of Molecular Structure And Transformations

Some conceptual issues are discussed in the context of the statement of quantum problems in the theory of molecular structure and properties. It is emphasized that the analysis of complex systems requires supplementary information from other fields of science in order to refine the problem definition. It is shown that the statements of quantum problems making them practically applicable for prediction can only result from a combination of the operator (differential equations) and matrix formalism, while these approaches are complementary rather than equivalent. A natural structure of vibronic wave functions is proposed in the form of a linear combination of well-defined basis functions.     

Numerical approximation of a nonisothermal two-dimensional general rate model of reactive liquid chromatography

A nonlinear and nonisothermal two-dimensional general rate model is formulated and approximated numerically to allow quantitatively analyzing the effects of temperature variations on the separations and reactions in liquid chromatographic reactors of cylindrical geometry. The model equations form a nonlinear system of convection-diffusion-reaction partial differential equations coupled with algebraic equations for isotherms and reactions. A semidiscrete high-resolution finite volume method is modified to approximate the system of partial differential equations. The coupling between the thermal waves and concentration fronts is demonstrated through numerical simulations, and important parameters are pointed out that influence the reactor performance. To evaluate the precision of the model predictions, consistency checks are successfully carried out proving the accuracy of the predictions. The results allow to quantify the influence of thermal effects on the performance of the fixed beds for different typical values of enthalpies of adsorption and reaction and axial and radial Peclet numbers for mass and heat transfer. Furthermore, they provide useful insight into the sensitivity of nonisothermal chromatographic reactor operation.     

Effect of the segmental mobility restriction on the thermoset chemical kinetics

The cure kinetics of an epoxy–amine commercial thermoset system have been investigated with the isothermal differential scanning calorimetry technique. In particular, a kinetic study has been performed in the glass–transition zone, in which diffusion phenomena compete with the chemical transformations and the overall reaction rate is partially slowed by the reduced segmental chain mobility. A generalized form of the Vogel equation has been formulated to account for the effect of the increasing glass–transition temperature on the chain mobility and, therefore, on the overall reaction rate. The kinetic model has been expressed with two factors representing the chemical reaction rate and the segmental mobility reduction. As the main result, the activation energy relative to the diffusion phenomena has been found to be very low, having a value of 42.5 K ≈ 0.356 kJ/mol, which is compatible only with the small‐angle rotation of the reactive unit. © 2002 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 40: 3757–3770, 2002