Characteristic temperatures of non-isothermal rate signals of one-step processes

Abstract

Analytical expressions for the heights, and for the initial, the peak and the final temperature of the rate signals of bimolecular reactions, measured at constantly increased temperature, are derived. They are based on the specific time of the reaction, available from the activation data, and on the relative minimum rate used. DTA and non-isothermal u.v. absorption studies of 29 different organic reactions in solution reveal that the accuracy of the expressions is sufficient to reproduce the true position of peaks of one-step reactions on the temperature or time axis. A program for simple calculations, written in BASIC, is enclosed.In the approximate kinetic theory of the author [1,2], it is shown that the position and shape of the reaction rate peak of an elementary reaction of n-th order, generated for temperature rise proportional to time (T = m.t), can be calculated from the activation data (E, k~) via the specific time u at the maximum,using the heating rate rn (deg/min) and gas constant R. For a first-order process, this theory, which may be called "Theory of the Characteristic Rate Coefficients", is based on typical products of a specific rate coefficient with the u-parameter at characteristic points of the curve (onset, halfwidth points, peak, points of inflection, end), and has been shown to be very useful for the study and discussion of nonisothermal kinetic signals. For example, for a first-order process, the rate coefficients at start, maximum and end are obtained as follows [1,3], ko ~ Z__L (2a)Urne

Kinetic Analysis of Thermoluminescence

“…Fig. 15 describes the various quantities which appear in (32). The conductivity, u, is related to nc by the universal equation…”

“…15. The variables in (32) T -Lewandowski and McKeever [8] showed that in the generalized approach to TL and TSC (Section 2.5) one can evaluate Q ( T ) (17) by using the relation Q(T) = C (F + l)/ITL(T). (34) The coefficient C incorporates some constants the values of which are usually unknown.…”

The ‘Theorem of common kinetic runs’ in homogeneous non-isothermal reaction kinetics

“…It is unity for n= 1, but depends on co for n ~ 1. (TCRC -Theory of Characteristic Rate Coefficients [13]; cf. [16,17,231).…”

“…For the M-strings, such effects are caused by the co-dependent term (uk)m in the denominator of Eq. (7), used for a correction of M [13,14,27]. For some -mostly consecutive -mechanisms, stationarities cannot really be reached for both limiting elements (e.g.…”

“…Because the heating rate is an additional 'transmitter' parameter, there are now two 'response' quantities, available from an experiment, and for an elementary reaction nearly invariant with respect to the activation data. Both allow to calculate the reaction order, but are based on basically different features of the plot, namely on the asymmetry (shape index S [9,10]) and on the height (alternatively, halfwidth: Reaction type index M [11][12][13][14]; cf. [15][16][17]).…”