The effect of heating rate upon the coupling of complex reactions. I. Independent and competitive reactions

Theoretical curves of the rate of conversion vs. temperature at constant heating rate for first-order reactions with activation energies of 80, 160, 240 and 320 kJ mole^?1 are compared over a range of heating rates from 10^?9 to 10⁵ K s^?1 for independent and competitive reactions. Independent reactions with different activation energies may be separated from one another by either increasing or decreasing the rate of heating. The spectrum of derivative peaks for two competing reactions at various heating rates has a dispersion effect in the region of change from low to high activation energy reactions. The practical range of heating rates in thermal analytical experiments and the application of these model cases to the understanding of the kinetics of complex systems at high and low temperatures are discussed.     

A contribution to the theory of D.C. polarographic current-voltage curves: Electrode reactions with three parallel charge transfer processes

Equations of polarographic current-voltage curves are derived for electrode reactions with three parallel charge transfer processes coupled by two chemical reactions on the basis of the staeady-state assumption in the reaction layer. If the rate constants of the charge transfer processes are sufficiently different from one another, the current-voltage curve consists of three separated waves and the equation for each wave has the same form as for a simple electrode reaction with one pathway.     

Analysis of thermal decomposition behaviors with consecutive reactions by TG

Thermal decomposition behaviors of a fluororubber are observed with linear heating mode at constant rate, controlled rate mode and isothermal mode of TG/DTA, and, with isothermal mode of TG/mass-spectrometer. The results suggest that this material decomposes with, at least, three consecutive reactions. From the results of TG/DTA and TGMS in isothermal mode, it is considered that the first reaction is the first-order reaction, the second reaction is chain reaction and the last reaction is vaporization of residue. Supposing these three consecutive reactions, the decomposition behaviors of the rubber is simulated. The observed curves of fraction of mass loss, , against time, t, are well reproduced by the simulation. The relationship between d/dt and is reproduced also, though the differences between observed and the calculated values of d/dt are slightly larger than noise level of d/dt.     

Kinetic Study on Pyrolysis of Extracted Oil Palm Fiber. Isothermal and non-isothermal conditions

Pyrolysis of extracted oil palm fibers under isothermal and non-isothermal conditions was carried out in a thermogravimetric analyzer. Isothermal curves showed that increasing pyrolysis temperature resulted in a faster pyrolysis and a higher conversion of oil palm fibers into gaseous products. Raw material sizes (below 1.0 mm) had insignificant effects on the isothermal pyrolysis, but the fibers with a size fraction of 1.0 to 2.0 mm resulted in a lesser conversion. Two-step reactions were found in the non-isothermal pyrolysis as evidenced by the presence of two peaks in the derivative thermogravimetry curves. Raw material sizes had no obvious effects on the temperature at which the maximum rate of pyrolysis occurred, but affected the rate of sample mass loss. For the low and high temperature regimes, a three-dimensional diffusion mechanism and a first-order of reaction mechanism respectively were used to describe the non-isothermal pyrolysis kinetics of extracted oil palm fibers. This revised version was published online in July 2006 with corrections to the Cover Date.     

Effect of heating rate on the separation of various phenomena in the DSC technique

The value chosen for the heating rate plays an important role in the DSC technique. For example, the use of a low heating rate is of great help in determining the kinetic parameters of reactions more clearly. In this paper, the separation of peaks corresponding to heat flux-time curves of two various phenomena is especially studied. These peaks are shown in a typical cure reaction of epoxy resins. After determination of the kinetic parameters, DSC curves are simulated and a good agreement is found between theoretical and experimental curves. The effect of the heating rate on the separation factor of these peaks is studied, as well as its effect on the sensitivity of heat-flux measurement.     

Thermal analysis of sulfurization of polyacrylonitrile with elemental sulfur

Thermal analysis of sulfurization of polyacrylonitrile (PAN) with elemental sulfur was investigated by thermogravimetry and differential thermal analysis of the mixture of polyacrylonitrile and elemental sulfur up to 600°C. Due to the volatilization of sulfur, the different heating rate (10 and 20 K min⁻¹) and different mixture proportion of polyacrylonitrile and elemental sulfur were adopted to run the analysis. The different heating rates make the DSC curves of sulfur different, but make the DSC curves of PAN similar. In the DSC curve of sulfur for the heating rate of 20 K min⁻¹ around 400°C, a small exothermic peak occurs at 400°C in the wide endothermic peak around 380∼420°C, indicative of that there is an exothermic reaction around 400°C. In the DSC curves of the mixture, the peaks around 320°C are exothermic as the content of sulfur is below 3.5:1 and endothermic as the content of sulfur is over 4:1, indicating that one of the reactions between PAN and sulfur takes place around 320°C. In the TG curves of the mixture, the mass losses begin at 220°C, and sharply drop down from 280°C. The curves for the low sulfur content obviously show two steps of mass loss, and curves for the high sulfur content show only one step of mass loss, indicative of more sulfur is benefit for the complete sulfurization of PAN. This study demonstrates that the TG/DSC analysis can give the parameter for the sulfurization, even if the starting mixture contains the volatile sulfur.     

Primary Transformation Rate Measurements Through Differential Scanning Calorimetry

The primary crystallization of molten alloy systems at high undercooling is studied by a precise quantitative analysis of the calorimetric signal obtained during the transformation in terms of the reaction rate under isothermal and continuous heating regimes. It is shown that, under specific conditions, namely, stoechiometric primary precipitates, generalized relationships for the crystallization enthalpy and the reaction rate may be obtained.     

A novel approach to the explanation the effect of microwave heating on isothermal kinetic of crosslinking polymerization of acrylic acid

The effect of microwave heating (MWH) on the isothermal kinetic of crosslinking-polymerization of acrylic acid (CPAA) was investigated. The kinetic curves of CPAA were determined in the temperature range from 303 to 328 K. By applying the model-fitting method it was revealed that the isothermal kinetics of CPAA was described by the first order chemical reaction kinetics model under the MWH and by the second order chemical reaction rate model for the conventionally heated (CH) process. The values of the reaction rate constants of CPAA are about 40 times higher for the microwave heated system than for the conventional heating. The kinetic parameters (activation energy (E _a) and pre-exponential factor (lnA)) of the CPAA are significantly lower than the corresponding values for CH process. It was found that the increase in the reaction rate of CPAA for MWH was not a consequence of overheating neither the hot spots in the reaction system. Based on model of selective energy transfer between the reacting molecules and the heating bath a novel explanation of the established effects of MWH on the kinetics of CPAA is given. A quantized nature and value of activation energy was confirmed. The decrease in the value of activation energy of CPAA under microwave heating is explained by the increased value of energy of ground vibration level of resonant oscillator in the AA molecule (v = 1417 cm^?1) caused by the absorption of non-thermal energy of MW field.     

双(2,3-环氧环戊基)醚与芳香二胺的固化过程

本文用示差扫描量热法(DSC)、动态扭辮分析仪(TBA)对双(2,3-环氧环戊基)醚与芳香二胺的固化过程进行了研究。DSC扫描结果表明固化反应分两个阶段进行,对此两个阶段固化反应的机理进行了讨论。由TBA法测得的凝胶化时间对固化温度倒数作图符合Arrhenius关系式,但较高温度区与低温区的斜率却不相同。这一现象可能与体系在不同温度区所处的状态有关。最后,以实验数据绘出热固化相图,并作了简要讨论。     

Primary Transformation Rate Measurements Through Differential Scanning Calorimetry

Summary. The primary crystallization of molten alloy systems at high undercooling is studied by a precise quantitative analysis of the calorimetric signal obtained during the transformation in terms of the reaction rate under isothermal and continuous heating regimes. It is shown that, under specific conditions, namely, stoechiometric primary precipitates, generalized relationships for the crystallization enthalpy and the reaction rate may be obtained.     

Some methodological problems concerning nonisothermal kinetic analysis of heterogeneous solid–gas reactions

Isoconversional methods, those using only one curve α = α(T) (α is the conversion degree and T is the temperature), and invariant kinetic parameter method were applied to estimate the kinetic parameters from the following nonisothermal data: (1) simulated TG curves for a single reaction; (2) TG curves for thermal degradation of PVC; and (3) TG curves for the dehydration of CaC₂O₄·H₂O. The results obtained by applying various methods for the same system are compared and discussed. Finally, a procedure of kinetic analysis is suggested. Its application could lead to kinetic parameter values that can be used to predict either α = α(t) curves for other heating rates or α = α(T) curves for isothermal conditions. © 2001 John Wiley & Sons, Inc. Int J chem Kinet 33: 564–573, 2001     

Effects of the strain rate and temperature in stress–strain tests: study of the glass transition of a polyamide-6

In this work new insights are presented on the measurement of the tangent and secant moduli from stress–strain curves in polymeric systems. Expressions for the strain-rate and strain dependence of both moduli are derived for systems characterised by a distribution of relaxation times. The equivalent frequency of the stress–strain experiments is shown to be dependent on the strain rate and on the strain at which the measurements are carried out. Such considerations enable using quasi-static tensile stress–strain tests to study relaxational processes in polymeric materials. The tensile behaviour of a 30% glass fibre reinforced polyamide 6 was characterised at different strain rates and temperatures, covering the glass transition region. A master curve of the tangent modulus as a function of strain rate was successfully constructed by simple horizontal shifting of the isothermal data. The temperature dependence of the shift factors was well described by the WLF equation. It was also possible to fit the master curve considering a polymeric system with a distribution of relaxation times, relevant parameters such as the KWW β parameter being extracted. The results were found to be consistent with dynamic mechanical analysis results.     

几种聚醚胺改性蒙脱土对环氧树脂固化过程的影响

首先制备了五种聚醚胺改性蒙脱土(MMT), 并将这五种聚醚胺改性蒙脱土加入到双酚A 型环氧树脂E51 和聚醚胺D400体系中, 采用差示扫描量热法(DSC)考察了五种聚醚胺改性MMT对环氧树脂升温固化进程的影响. 随后, 优选一种EP/MMT 混合体系即EP/D400-T500-MMT 混合体系, 系统地研究了该体系与纯环氧树脂体系在130, 140, 150 及160 ℃等几个温度下的等温固化过程, 考察了等温固化时间对固化度和固化度变化速率的影响以及固化度与固化度变化速率之间的关系, 并利用Kamal 模型进行拟合计算了固化动力学参数. 研究结果表明, 与纯环氧树脂相比, 几种聚醚胺改性MMT 的固化放热峰均向高温迁移, 同时聚醚胺D400 协同插层MMT 降低了高分子量聚醚胺插层MMT 所导致的环氧树脂DSC 曲线的畸变情况; EP/D400-T500-MMT 混合体系和纯环氧体系的等温固化反应过程符合Kamal 模型;在相同的固化温度下, EP/D400-T5000-MMT 混合体系的反应速率常数k₁ 和k₂ 值以及反应级数m 均比纯EP 体系小, 而反应级数n 以及总反应级数m+n 值比纯EP 体系大, 表明两种聚醚胺协同插层的改性蒙脱土D400-T5000-MMT 的加入降低了环氧体系固化反应速率. 另外, EP/D400-T5000-MMT 混合体系的活化能E_a1 和E_a2 与纯EP 体系的相比也略有升高.     

On the apparent compensation effect found for two parallel reactions

The authors present a critical analysis of the use of an overall single reaction rate equation instead of the true rate equations corresponding to the decomposition of a substance according to two parallel reactions. Isothermal as well as nonisothermal decomposition are considered. An apparent compensation effect has been evidenced in both cases. It has been assigned to the dependence of the kinetic parameters on temperature (for the isothermal case), conversion, and heating rate (for nonisothermal one). © 1998 John Wiley & Sons, Inc. Int J Chem Kinet: 30: 673–681, 1998     

Controlled Rate Thermogravimetry: New usefulness of controlled rate thermogravimetry revealed by decomposition of polyimide

Curves obtained by controlled rate TG of polyimide film in air are quite different from those obtained by conventional constant rate heating TG. A two step mass loss was observed during the constant rate heating TG, while mass loss proceeded as a single step process in the controlled rate TG. To elucidate the cause for this difference, kinetic analysis was made, and it was found that the reaction mechanism in a lower temperature range is different from those in a higher temperature range. The lower temperature decomposition is a single step process, and the higher temperature decomposition is a two-step process. The reason for the difference is that only the low temperature single step process is observed in the controlled rate TG, while both reactions are observed in the constant heating rate TG along with the temperature increase. This speculation was confirmed by isothermal TG. These facts show us another usefulness of controlled rate TG. To analyze the three types of TG data together, the Friedman—Ozawa method was used, and it is demonstrated to be the most appropriate and reliable.This revised version was published online in November 2005 with corrections to the Cover Date.     

Reaction kinetics at linearly increased temperature. IV. Relationships between dta curves,rate curves and adiabatic calorimetry

A general concept is presented for the kinetic interpretation of DTA curves. This is based on the limiting conditions of a DTA measurement: either the kinetic cell constant is zero (adiabatic conditions), or infinite (rate curve). On the other hand, the self-heating effect (thermal feedback), based on the product of the reaction enthalpy with the reactant feed, may be absent (“ideal” kinetic DTA curve) or infinite (impulse reaction). Our recent formulae for the correction of the kinetic classification parameters, shape index and reaction type index, as well as other relationships and their utility, are successfully tested by application to ca. 2000 experimental DTA curves obtained in stirred solutions.The expressions reveal the influence of the activation parameters, heating rate, maximum signal height and cell constant and, therefore, allow a general discussion of the kinetics, independent of the experimental conditions.     

A method for constant-rate heating of milligram-sized samples

Heating a milligram-sized sample of material at a constant heating rate is usually achieved by controlling the temperature of an electric-resistance furnace with a proportional integral derivative (PID) controller. Here we present a new method for constant-rate heating that is based on a semi-empirical mathematical expression relating sample temperature, heating rate, and electric power supplied to the furnace. This method uses PID control only for second-order corrections of the heating rate. The linearity of the sample temperature vs. time curves obtained by applying this method to a simple furnace setup is the same as the linearity of the curves generated by modern commercial thermogravimetric analyzers.     

Thermokinetic Research Method for Simple-order Reactions. Double-thermoanalytical curve method

A novel thermokinetic research method for determination of the rate constant of a reaction taking place in a batch conduction calorimeter under isothermal conditions is proposed: the double-thermoanalytical curve method. The method needs only the characteristic time parameter t _m, the peak height Δ_m at time t _m and the peak area a*_m after time t _m for two thermoanalytical curves measured with different initial concentrations of the reactants: it conveniently calculates the rate constants. The thermokinetics of four reaction systems were studied with this method, and its validity was verified by the experimental results. This revised version was published online in July 2006 with corrections to the Cover Date.     

马瑞原油在空气和氮气中的热解-氧化性能

低温氧化是注空气采油及原位燃烧采油技术中的重要化学反应,为深入认识原油在有氧环境下复杂热反应过程中的低温氧化特性,我们采用热重/差热分析法(TG/DTA)研究了线性升温和等温条件下马瑞(Merey)原油的热反应行为。 结果表明,Merey原油在空气及线性升温条件下的受热过程分4个阶段:气化段、低温氧化段、热解段和高温氧化段;相邻阶段的物理、化学主导过程的重叠增加了分析原油热反应特征的难度。 升温速率提高,气化段和低温氧化段的终止温度不变;热解段和高温氧化段的终止温度以及热解段的峰温随升温速率的增加而升高。 N₂气与空气下Merey原油的热重/微分热重(TG/DTG)数据对比表明,升温速率越高,空气下的高温氧化段与热解段重叠程度越大,这有利于燃烧但会降低原油采收率。 空气下等温时的TG/DTA结果表明随升温速率增加,升温至300 ℃时的失重率降低,不利于原油轻组分的气化。 反应温度越高,气化过程时间越长,失重分数越大。 Merey原油在低于300℃时低温氧化反应不是主导反应。     

Bias in isothermal time-to-event studies due to approach to test temperature

Oxidative induction time (OIT), constant temperature stability (CTS) and isothermal crystallization are examples of isothermal time-to-event (TTE) measurements obtained using differential scanning calorimetry. In TTE experiments, a test specimen is heated/cooled at a constant rate from the setup temperature to an isothermal test temperature. Once the test temperature is achieved, a clock is started and the time to the thermal event (e.g., onset to oxidation, thermal decomposition or crystallization exotherm peak) is measured. Such TTE values may be used to rank stability of the material at the test temperature. Some portion of the reaction of interest, however, takes place during the pre-isothermal period as the test specimen approaches the test temperature. This amount of reaction is unmeasured and represents a bias in the resultant TTE value. An equation has been derived and numerically integrated to estimate this bias. This approach shows that the bias is dependent upon the activation energy of the test reaction, the heating/cooling rate used and the temperature range between the melting temperature and the test temperature. For commonly used heating rates, the bias for OIT and CTS tests is small. Further, the myth that isothermal crystallization kinetics determinations required high cooling rates is dispelled with the bias of less than 0.9 min resulting from heating rates as low as 10°C min^–1. Knowledge of magnitude of this bias permits the selection of experimental conditions without the expense of high heating/cooling rate apparatus or extra cost cooling accessories.