Peter Šimon

Single-step kinetics approximation employing non-arrhenius temperature functions

SummarySolid-state reactions ordinarily demonstrate a tangled interplay of various chemical and physical processes. The single-step kinetics approximation resides in substituting a generally complex set of kinetic equations by the sole single-step kinetics equation. It enables to describe the kinetic hypersurface in a simple way irrespective of the complexity of the overall process. The kinetic hypersurface is the dependence of conversion on temperature and time. The functions describing the temperature and conversion components of the hypersurface should be separable. For a complex process, the adjustable parameters in the temperature function have no mechanistic significance so that there is no reason to be confined to the Arrhenius relationship. Two groups of isoconversional methods based on non-Arrhenius temperature functions are presented and the corresponding formulas for isothermal, integral, differential and incremental isoconversional methods are derived. As an example of the method using the explicit expression of the conversion function, the first-order kinetics is treated. Comparing with the methods based on the Arrhenius relationship, the greatest advantage of the methods presented here is that the problems with calculating the temperature integral are eliminated since the corresponding integrals can be expressed in a closed form.

Thermal Properties of N-ethyl-N-phenyl-Dithiocarbamates and Their Influence on the Kinetics of Cure

The thermal properties (in the temperature range of 100–250°C) of N-ethyl-N-phenyldithiocarbamatecomplexes of Zn(II), Co(III), Ni(II), Cu(II) and Pb(II) and their influence on the kinetics of cure have been studied by differential scanning calorimetry (in nitrogen). It was found that Zn(II), Co(III) and Pb(II) dithiocarbamates melted without further effects, while the melting of Ni(II) and Cu(II) dithiocarbamates is accompanied with decomposition. From the kinetic point of view, the dithiocarbamates decrease the values of the reaction order and the values of rate constants follow this order (with respect to the metal ion): Zn(II)

Kinetics of polymer degradation involving the splitting-off of small molecules: Part 6—Dehydrochlorination of PVC in an atmosphere of HCl

Abstract High conversion kinetic runs of the thermal dehydrochlorination of PVC in an atmosphere of HCl have been treated employing a theory developed previously. Excellent agreement between theory and experiment has been reached for the immediate zip growth model. The kinetic parameters obtained by the non-linear least-squares method show that the activation energy and the pre-exponential factor of random elimination of HCl from PVC are identical with those for the inert atmosphere. In its interaction with degraded parts of the polymer chain, HCl catalyzes the initiation step of the zip reaction. HCl also causes the elongation of polyene sequences, mainly for temperatures below 220°C. The results suggest that the elongation occurs even for low concentrations of HCl in the polymer. The content of structural irregularities causing premature zip termination is small.

The mathematical incorrectness of the integral isoconversional methods in case of variable activation energy and the consequences

Kinetic parameters resulting from the application of isoconversional methods mostly depend on the degree of conversion. This paper shows that the integral isoconversional methods are mathematically incorrect if the activation energy depends on conversion. In this case, the incorrectness resides in improper separation of variables in the general rate equation. As a consequence, non-sensical snake-like shape of the conversion versus time curves is observed when the kinetic results are extrapolated to lower temperatures.

Thermal analysis of Micro, Nano- and Non-Crystalline Materials

Thermal Analysis of Micro-, Nanoand Non-Crystalline Materials: Transformation, Crystallization, Kinetics and Thermodynamics complements and adds to volume 8 Glassy, Amorphous and Nano-Crystalline Materials by providing a coherent and authoritative overview of cutting-edge themes in the field of crystalline materials. In particular, the book focuses on reaction thermodynamics and kinetics applied to solid-state chemistry and thermal physics of various states of materials. In this volume the fundamental and historical aspects of phenomenological kinetics and the equilibrium background of processes are detailed. Crystal defects, nonstoichiometry and nano-crystallinity, reduced glass-transition temperatures and glass-forming coefficients are covered. The determination of the glass transition by DSC, the role of heat transfer and phase transition in DTA experiments, and the explanation of DTA/DSC methods used for the estimation of crystal nucleation are reviewed. Structural relaxation and viscosity behaviour in glass and associated relaxation kinetics are also examined, together with the influence of preliminary nucleation and coupled phenomenological kinetics nucleation on both the strongly curved surfaces and nano-particles. The book investigates crystallization of glassy and amorphous materials including oxides, chalcogenides and metals, non-parametric and fractal description of kinetics, disorder and dimensionality in nano-crystalline diamond. Moreover, it analyzes thermal analysis of waste glass batches, amorphous inorganic polysialates and bioactivity of hydroxyl groups as well as reaction kinetics and unconventional glass formability of oxide superconductors. Written by an international array of distinguished academics, Thermal Analysis of Micro-, Nanoand Non-Crystalline Materials: Transformation, Crystallization, Kinetics and Thermodynamics is a valuable resource to advanced undergraduates, postgraduates, and researches working in the fields of applied material thermodynamics, thermal analysis, thermophysical measurements and calorimetry.

Kinetics of polymer degradation involving the splitting off of small molecules: Part 1—Basic concepts

A method of derivation of the kinetic equations for polymer degradation which involves the splitting off of low-molecular weight compounds based on the stochastic approach is suggested. The idea is that the degradation occurs via the zip mechanism and that the initiating step, i.e. the formation of an olefinic site in the polymer chain, occurs at random. Assuming that the polyenes formed in the course of the zip reaction can be considered as partitions dividing the polymer chain into non-dehydrochlorinated sequences, it has been shown that the lengths of sequences are distributed according to the most probable distribution. The method is tested on the mechanism of PVC degradation via the dehydrochlorination of a priori given sequences in oxygen-free conditions.

Thermochemical investigation of guest-host interactions in Werner clathrates of type [Ni(4-Etpy)4(NCS)2]·nG (G=naphthalene derivatives)

The stoichiometry of thermal decomposition and the thermochemistry were studied for [NiL4(NCS)2] (I) as a host complex, and for its clathrates of type [NiL4(NCS)2]·2G, where L=4-ethylpyridine and guest molecule G=1-methylnaphthalene in clathrate (II), 1-chloronaphthalene in (III) or 1-bromonaphthalene in (IV). For I, the loss of volatile components proceeds in three steps (−2L, −L, −L); the first steps for II–IV also involve the release of G (−2G, −2L). DSC and X-ray powder measurements indicated a phase transition in the host lattice, and allowed differentiation of the escape of G and L molecules. The enthalpy changes give the following sequence of thermodynamic stability for the studied chlathrates: I>II>III.

Kinetics of polymer degradation involving the splitting off of small molecules: Part 7—Thermooxidative dehydrochlorination of PVC

Abstract High-conversion kinetic runs of the thermooxidative dehydrochlorination of PVC have been treated employing a theory developed previously. Satisfactory agreement between theory and experiment has been achieved. The kinetic parameters obtained by the non-linear least-squares method show that the activation energy and the pre-exponential factor for random elimination of HCl from PVC are identical with those for an inert atmosphere. Oxygen catalyzes the initiation step of the zip reaction by interaction with degraded parts of the polymer chain; the process is very complex. The rate constant for the catalyzed initiation is proportional to the square root of the mole fraction of oxygen present in the dehydrochlorination atmosphere. Oxygen also affects the zip growth, the zip length decreasing with increasing oxygen pressure.

Some Fundamental and Historical Aspects of Phenomenological Kinetics in the Solid State Studied by Thermal Analysis

Chemical kinetics provides mathematical models for explaining and predicting the transformation rate of a chemical system. The fundamental concept of chemical kinetics is based on the law of mass action established by Cato M. Guldberg (1836–1902) and Peter Waage (1833–1900) in the latter half of the nineteenth century (Waage P, Guldberg CM, Studies concerning affinity. Forhandlinger: Videnskabs – Selskabet i Christinia: 35, English trans. (1986) J Chem Edu 63(12):1044–1047, 1864; Guldberg CM, Waage P Concerning chemical affinity. J Prakt Chem [2]. 19:69, 1879), where equilibrium constants were derived in terms of kinetic data and rate equations. The two different aspects, that is, equilibrium and kinetics, were encountered by the recognition that chemical equilibrium is a dynamic process in which rates of reaction for the forward and backward reactions must be equal, so that the chemical driving force of the forward reaction is compensated by that of the reverse reaction. Because the respective reaction rates are proportional to the product of active masses of the reactant species, the equilibrium constant K can be represented by the ratio of the affinity constants (rate constants) of the forward and reverse reactions, k and k′: K = k/k′. The law of mass action was lately reintroduced by J.H. van’t Hoff (1852–1911) from the aspect of chemical kinetics (van’t Hoff JH, Etudes de dynamique chimique. Frederik Muller, Amsterdam, 1884).

AN incremental integral isoconverzional method

An incremental integral isoconversional method for the determination of activation energy as a function of the extent of conversion is presented. The method is based on the treatment of experimental data without their transformation so that the resulting values of activation parameters should not be biased. The method was tested for recovering the activation energies from simulated data and employed for the treatment of experimental data of the NiS recrystallisation.An incremental integral isoconversional method for the determination of activation energy as a function of the extent of conversion is presented. The method is based on the treatment of experimental data without their transformation so that the resulting values of activation parameters should not be biased. The method was tested for recovering the activation energies from simulated data and employed for the treatment of experimental data of the NiS recrystallisation.