An exact treatment for non-linear relaxation processes governed by the rotational Smoluchowski equation

Recently the analysis of transient regimes of chemical reactions is paid much attention. This is due to the fact that the time-dependent relaxation modes prior to achieving steady states contain important information about the features of the reactions. During unsteady mode the changes in reactant concentrations and rate of the reaction in time are observed. These changes are due to their own relaxation processes, depending on the structure of the reaction mechanism. A complete study of the reaction mechanism involves the study of the relaxation characteristics both near and away from the stationary state. Linear relaxation time describes the local transient modes near the steady state and it is calculated as the time decrease deviations of reactant concentrations from steady-state values in the e-times. Non-linear relaxation time describes the overall behavior reactions and it can be evaluated through the reaction time from the initial state to a stationary. Depending on the structural features of reactions ratio to determine the non-linear relaxation time through of reactions parameters (rate constants stages and reactant concentrations) differ significantly. The establishment of such ratio for a particular reaction allows getting more information to identify the mechanism and the constituent rate constants of its stages. The mechanism of any catalytic reaction involves stages adsorption of one or more of the starting materials on the catalyst surface. As a rule these stages are initial remaining stages of chemical transformation of reactants adsorbed forms follow them. Therefore, it is necessary to have the data on these stages and rate constants of adsorption of reagents on the catalyst surface. Earlier by author the method for estimating the values of the rate constants of adsorption and desorption by linear relaxation times was described. This method was used for determine of mechanism and kinetic parameters of process of adsorption of carbon dioxide on the chromium oxide and gallium oxide catalysts. In this article the method for estimating the values of the rate constants of adsorption and desorption by non-linear relaxation times for this process is described. The previously found CO2 dissociative adsorption mechanism was proved by the obtained results. The intervals of values changes of the rate constants of adsorption and desorption of carbon dioxide on the gallium oxide and chromium oxide catalysts were defined.Forcitation:Kol’tsov N.I. Study of carbon dioxide adsorption on chromium oxide and gallium oxide catalysts on basis of non-linear relaxation times. Izv. Vyssh. Uchebn. Zaved. Khim. Khim. Tekhnol. 2018. V. 61. N 2. P. 46-52

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Non-linear dielectric spectroscopy for detecting and evaluating structure-property relations in a P(VDF-TrFE-CFE) relaxor-ferroelectric terpolymer

Applied Physics A ◽

10.1007/s00339-021-04876-0 ◽

2021 ◽

Vol 127 (10) ◽

Author(s):

Thulasinath Raman Venkatesan ◽

David Smykalla ◽

Bernd Ploss ◽

Michael Wübbenhorst ◽

Reimund Gerhard

Keyword(s):

Dielectric Spectroscopy ◽

Vinylidene Fluoride ◽

Paraelectric Phase ◽

Space Charge Polarization ◽

Relaxor Ferroelectric ◽

Relaxation Processes ◽

Structure Property ◽

Property Relations ◽

Non Linear ◽

Thermally Stimulated Depolarization

AbstractNon-linear dielectric spectroscopy (NLDS) is employed as an effective tool to study relaxation processes and phase transitions of a poly(vinylidenefluoride-trifluoroethylene-chlorofluoroethylene) (P(VDF-TrFE-CFE)) relaxor-ferroelectric (R-F) terpolymer in detail. Measurements of the non-linear dielectric permittivity $${\varepsilon _{2}^{'}}$$ ε 2 ′ reveal peaks at 30 and 80$$\,^\circ$$ ∘ C that cannot be identified in conventional dielectric spectroscopy. By combining the results from NLDS experiments with those from other techniques such as thermally stimulated depolarization and dielectric-hysteresis studies, it is possible to explain the processes behind the additional peaks. The former peak, which is associated with the mid-temperature transition, is found in all other vinylidene fluoride-based polymers and may help to understand the non-zero $$\varepsilon _\mathrm {2}^{'}$$ ε 2 ′ values that are detected on the paraelectric phase of the terpolymer. The latter peak can also be observed during cooling of P(VDF-TrFE) copolymer samples at 100$$\,^\circ$$ ∘ C and is due to conduction and space-charge polarization as a result of the accumulation of real charges at the electrode–sample interface.

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Non-linear relaxation methods

Journal of Electroanalytical Chemistry ◽

10.1016/s0022-0728(74)80314-1 ◽

1974 ◽

Vol 56 (1) ◽

pp. 1-25 ◽

Cited By ~ 21

Author(s):

S.K. Rangarajan

Keyword(s):

Linear Relaxation ◽

Relaxation Methods ◽

Non Linear

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Experimental and Theoretical Analysis of Non-linear Vibrational Relaxation of Polyatomic Molecules Strongly Excited by Resonant Laser Radiation

Laser Chemistry ◽

10.1155/lc.8.315 ◽

1988 ◽

Vol 8 (2-4) ◽

pp. 315-334

Author(s):

L. Carlomusto ◽

A. Cartelli ◽

S. Solimeno ◽

R. Velotta ◽

R. Bruzzese

Keyword(s):

Vibrational Relaxation ◽

Polyatomic Molecules ◽

Relaxation Processes ◽

Molecular Dissociation ◽

Molecular Gases ◽

Simple Theoretical Model ◽

Rough Approximation ◽

Resonant Laser ◽

Non Linear ◽

Made In

We present a very simple theoretical model aimed at the analysis of non-linear relaxation processes in molecular gases in the presence of partial molecular dissociation induced by vibrational–vibrational exchange between highly excited molecules. The model has a phenomenological character, since it analyzes the behavior of a system of anharmonic diatomic molecules, which is a very rough approximation of a polyatomic molecule such as SF6. Nonetheless, it provides an interesting key for the interpretation of a number of peculiar features characterizing our experimental observation, with which a comparison is made. In particular, the model takes realistic account of the influence of dissociation processes on the relaxation time.

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