Thermogravimetric and dilatometric studies using Stepwise Isothermal Analysis and related techniques

The Stepwise Isothermal Analysis (SIA) technique, which was introduced by the author in the late seventies has proved to be very useful both in thermogravimetric and dilatometric studies. By this technique the heating and cooling programme is controlled by the rate of the reactions taking place in the sample, for instance thermal decompositions (TG) or sintering (dilatometry). By an advanced computer programme this control is achieved in the following way: The sample is heated at a constant heating rate until the reaction rate. i. e. the slope of the weight/length versus time curve, exceeds a preset limit at which point the heating is stopped. The reaction thereafter proceeds isothermally until the rate again becomes smaller than the limit where the heating is resumed. By this techniques the reactions thus characteristically take place in isothermal steps.This technique is especially useful in studies of thermal decompositions and it is believed that the decomposition températures determined by SIA is much more accurate than those determined by other techniques even for materials involving consecutive and close-lying reactions. One typical application of this technique is establishment of optimum conditions for removal of organic binders from ceramic powder compacts prepared for instance by dry pressing or injection moulding.The SIA technique is also very useful in kinetic studies and with the advanced computer systems available today rather sophisticated control and analysis of the data can be obtained. One example, which will also be discussed in the presentation, is a study of the decomposition of Ce-carbonate using first the standard technique described above by which the reaction mechanism could be established and then followed by the so-called Forced Stepwise Isothermal Analysis technique (FSIA) by which the activation energy could be obtained.Finally the SIA technique is also very useful in dilatometric sintering studies and to demonstrate this the result obtained both using SIA and the related constant shrinkage rate technique in a study of the initial sintering stage of CeO₂ will be presented.

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Zusammenfassung Das vom Autor Ende der siebziger Jahre eingeführte Verfahren der Stufenweisen Isothermischen Analyse (SIA) erwies sich sowohl bei thermogravimetrischen als auch bei dilatometrischen Untersuchungen als sehr nutzvoll. Bei diesem Verfahren wir das Heiz- und Kühlprogramm durch die Geschwindigkeit der in der Probe ablaufenden Reaktion- z.B. der thermischen Zersetzung (TG) oder des Sintern (Dilatometrie) — gesteuert. Diese Steuerung wird durch ein Computerprogramm auf folgende Weise erreicht: Die Probe wird mit einer konstanten Aufheizgeschwindigkeit aufgeheizt, bis die Reaktionsgeschwindigkeit, d.h. der Anstieg der Gewichts/Längen — Zeitkurve, einen gewissen Grenzwert überschreitet, wodurch der Aufheizvorgang gestoppt wird. Die Reaktion wird anschlie\end isotherm fortgesetzt, bis die Geschwindigkeit wieder kleiner als der Grenzwert wird, zu diesem Zeitpunkt setzt die Aufheizung wieder ein. Durch dieses Verfahren erfolgt die Reaktion somit in isothermen Stufen.Dieses Verfahren ist besonders bei der Untersuchung von thermischen Zersetzungen nutzvoll und man nimmt an, da\ die mittels SIA ermittelte Zersetzungstemperatur wesentlich genauer ist als im Falle von anderen Verfahren, besonders bei Substanzen mit konsekutiven und nahe beieinanderliegenden Reaktionen. Eine typische Anwendung dieses Verfahrens ist die Ermittlung der Optimumbedingungen für die Entfernung organischer Bindemittel aus Keramikpulverpre\lingen, die z.B. durch Trockenpressen oder Spritzgie\en hergestellt wurden. Ein Anwendungsbeispiel dafür wird hier diskutiert.Auch bei kinetischen Untersuchungen ist das SIA Verfahren sehr nutzvoll und mit den heute erhältlichen Computersystemen ist eine anspruchsvollere überwachung und Analyse der Angaben ist möglich. Ein ebenfalls in vorliegender Arbeit diskutiertes Beispiel ist die Untersuchung der Zersetzung von Ceriumkarbonat, wobei zuerst die obenbeschriebene Standardmethode angewendet wird, wodurch der Reaktionsmechanismus abgeschätzt werden kann. Im Anschlu\ erfolgt eine sogenannte Erzwungene Stufenweise Isotherme Analyse (FSIA), wodurch die Aktivierungsenergie ermittelt werden kann.Letztendlich ist das SIA Verfahren auch bei dilatometrischen Sinteruntersuchungen sehr nutzbringend. Um dies darzustellen, wird bei einer Untersuchung des ursprünglichen Sinterzustandes von CeO₂, sowohl das durch SIA als auch das durch das Verfahren der konstanten Abschreckgeschwindigkeit≓ erhaltene Ergebnis dargestellt.

     

Estimation of surface morphology of composite polymer particles prepared by the stepwise heterocoagulation method with ζ-potential measurement

 Core-shell composite polymer particle was prepared by the stepwise heterocoagulation of cationic small polymer particles (SPs) onto an anionic large polymer particle (LP), following heat treatment at temperatures which were higher than glass transition temperature (T _g=18 °C) of SP. At pH 9 ζ-potential of the hetero-coagulated particle (HP) was negative, but it changed to positive by the heat treatment and increased with the treatment time and finally attained to that of SP. The treatment time to attain the ζ-potential of SP became short by elevating the treatment temperature. This indicates that during the heat treatment, SP continued to melt on the surface of LP and finally formed a continuous shell. Received: 3 September 1997 Accepted: 29 October 1997     

The Harmonic and Anharmonic Force Fields of Nitrosyl Halides

Harmonic and anharmonic symmetry force constants matrices have been calculated using a stepwise coupling method for the twelve isotopic species of nitrosyl fluoride, chloride and bromide. The valence force fields derived from the above matrices were used to recalculate the normal frequencies and the potential energy distribution among force constants. The valence force fields are compared with others previously reported obtained by different methods.     

One-pot facile conversion of Baylis-Hillman adduct into N-alkyl 3-(E)-alkylidene-5-substituted sulfonylpiperidine-2,6-dione. Formal synthesis of tacamonine

A stepwise [3+3] strategy to N-alkyl 3-(E)-alkylidene-5-substituted sulfonylpiperidine-2,6-dione 1 used various N-alkyl α-substituted sulfonylacetamides 2 and α,β-unsaturated esters 3 as starting materials. α,β-Unsaturated esters 3 were generated by Baylis-Hillman reaction. A ring closure mechanism was proposed for the reactions. This method provides a convenient formal synthesis of tacamonine.     

Theoretical study of ester enolate–imine condensation route to β-lactams

The condensation reaction of the enolate of methyl acetate with formaldimine to afford a β-lactam was studied using the MP2-FC/6-31+G* level of theory taking into account the electrostatic effect of the solvent by means of a self-consistent reaction field continuum model. The reaction is a stepwise process with three main steps: the formation of the C3(SINGLE BOND)C4 bond, the closure of the β-lactam ring, and the elimination of the methoxide ion. The formation of the C3(SINGLE BOND)C4 bond is rate determining and according to our calculations is not a reversible step. © 1998 John Wiley & Sons, Inc. J Comput Chem 19: 1826–1833, 1998     

均匀设计中有重复试验的统计分析

本文先简要介绍有重复试验的回归分析理论及公式 ,再对一个例子重新给以计算及提出问题 ;最后笔者对此类数据的处理及 SAS统计软件包提出讨论意见 ,其中特别对常规的用平均数去取代试验结果的方法及当变量数超过样本数时用流行的逐步回归选取变量法提出批评。     

Stepwise Estimation of Random Processes

The problem of estimating a continuous-time random process from its observations at appropriately designed sampling points is considered. The quality of an estimator is measured by its integrated mean square error (IMSE). Here, sampling points are designed stepwisely to minimize the IMSE and the best linear unbiased estimator (BLUE) is so determined that the earlier calculations do not have to be repeated with addition of one or more new samples. For random processes whose covariance has a sharp corner at the diagonal, it is shown that essentially, an optimal one-step forward sampling location is one of the midpoints of intervals determined by the current and previous sampling points. Both analytical and numerical examples are considered. This revised version was published online in June 2006 with corrections to the Cover Date.     

Thermal degradation mechanism of poly(arylene sulfone)s by stepwise Py‐GC/MS

The thermal degradation of poly(ether sulfone) (PES) and polysulfone (PSF) was studied with a combination of thermogravimetric analysis and stepwise pyrolysis–gas chromatography/mass spectrometry techniques with consecutive heating of the samples at fixed temperature intervals (100 °C) to achieve narrow‐temperature pyrolysis conditions. The individual mass chromatograms of various pyrolysates were correlated with pyrolysis temperatures to elucidate the pyrolysis mechanism. The major mechanism for both PES and PSF was a one‐stage pyrolysis involving main‐chain random scission and carbonization. The major products SO₂ and phenol were released from the sulfone and ether groups in PES. The major products SO₂, phenol, and 1‐methyl‐4‐phenoxybenzene were released from the sulfone, ether, and isopropylene groups in PSF. In the PES, the thermal stability of the sulfone and ether groups was identical to the maximum thermogravimetric loss rate. In the PSF, the thermal stability was in the following order: sulfone < ether < isopropylene. The temperature of the maximum thermogravimetric loss rate was similar to the maximum evolution of phenol. However, there was a considerable difference in the thermal behavior of both polymers; the correlation of the polymer structure to the degradation mechanism is discussed. © 2000 John Wiley & Sons, Inc. J Polym Sci A: Polym Chem 38: 583–593, 2000     

Stepwise solution to an inverse problem for the radiative transfer equation as applied to tomography

An X-ray tomography problem is formulated and analyzed within the framework of a mathematical model based on the polychromatic stationary radiative transfer equation with no collision integral. It is assumed that the outgoing radiation density is only given, and the task is to find the surface of an internal inclusion on whose boundary the coefficients of the equation may have jump discontinuities. The uniqueness of the solution is proved, and the corresponding solution algorithm is outlined. A feature of this work is that the research technique is local in character. This makes it possible to use only some of the available data, and the procedure can be stopped at an intermediate stage of the reconstruction, which can be useful in applications.     

Theoretical investigation of the decomposition of acyl azides: Molecular orbital treatment

The thermal decomposition of formyl, acetyl, and benzoyl azides to the corresponding isocyanate and nitrogen has been treated theoretically using ab initio molecular orbital calculations at the Møller–Plesset type 2 (MP2)(full)/6‐31G* level. The reaction is stimulated by elongation of N N bond and is followed until the formation of the isocyanate and expulsion of nitrogen. The decomposition of formyl azide proved to be a concerted one‐step reaction without the formation of a nitrene intermediate. In contrast, the conversion of both acetyl and benzoyl azides to the corresponding isocyanate and nitrogen is a two‐step reaction, and a nitrene intermediate is formed. One transition state is located and identified during the course of the conversion of formyl azide, but two transition states are located and identified during the course of the conversion of acetyl and benzoyl azides. The thermodynamic functions, ΔE_r and ΔH_r, of the studied reactions are calculated. The results predict that the ease of conversion of the acyl azide to the isocyanate and nitrogen goes in the order: formyl azide > acetyl azide > benzoyl azide. © 2005 Wiley Periodicals, Inc. Int J Quantum Chem, 2006