Stepwise isothermal analysis

Stepwise isothermal analysis This has been described (46,47) as a method whereby reaction temperatures and mass loss steps can be accurately characterized by a complementary combination of simultaneous TG and DTA methods. The sample is heated at a slow, constant rate until a reaction is detected and, on reaching a specified (low) rate of mass loss, the temperature is maintained constant. When this rate process has been completed, indicated by diminution to a second specified (relatively much lower) rate, the slow rate of temperature increase is recommenced. Thus, each successive rate process is completed isothermally and both the mass loss (evidence of stoichiometry) and the temperature of that step are determined precisely. 

A valuable approach for measuring thermal degradation kinetic parameters is controlled-transformation-rate thermal analysis (CRTA) - a stepwise isothermal analysis and quasi-isothermal and quasi-isobaric method. In this method, some parameters follow a predetermined programme as functions of time, this being achieved by adjusting the sample temperature. This technique maintains a constant reaction rate, and controls the pressure of the evolved species in the reaction environment. CRTA is, therefore, characterised by the fact that it does not reqnire the predetermined temperature programmes that are indispensable for TG. This method eliminates the nnderestimation and/or overestimation of kinetic effects, which may resnlt from an incomplete understanding of the kinetics of the solid-state reactions normally associated with non-isothermal methods. 

Temperature-risiag elution fractionation (tref) is a technique for obtaining fractions based on short-chain branch content versus molecular weight (96). On account of the more than four days of sample preparation required, stepwise isothermal segregation (97) and solvated thermal analysis fractionation (98) techniques usiag variatioas of differeatial scanning calorimetry (dsc) techniques have been developed. 

Temperature may not always be raised in a linear fashion. In the case of CRT A (Controlled Rate Thermal Analysis), the heating rate is varied in such a manner as to produce a constant rate of mass loss. Alternatively a sinusoidal temperature rise is superimposed on the linear rise this is known as Modulated TG and allows the continuous calculation of activation energy and pre-exponential factor during a run. Sometimes a Temperature Jump (or stepwise isothermal) " is used, where temperature is held constant for a time, then jumped rapidly to a higher constant temperature (usually quite close in temperature). All of these procedures are supposed to help in the determination of kinetics of reaction. Another system accelerates the temperature rise when no mass loss is experienced, i.e. between reactions. The rate is slowed to a low value during mass loss. Some manufacturers call this High Resolution TG and an example follows. 

Comparison of chemiluminescence isothermal runs with oxygen uptake and DSC measurements has been at the centre of interest since practical industrial applications of the chemiluminescence method were attempted. It is a fact that the best comparison may be achieved when studying polymers that give a distinct induction time of oxidation typical for autoaccelerating curves of a stepwise developing oxidation. This is the particular case of polyolefins, polydienes and polyamides. The theoretical justification for the search of a mutual relationship between the oxidation runs found by the various methods follows directly from the kinetic analysis of the Bolland-Gee scheme of polymer oxidation. 

The analysis of these P(h) isotherms emphasises that stratified foam films are formed from both systems (I and II). A phenomenon not revealed so far is that spontaneous (under constant capillary pressure) and forced (under various capillary pressures) stepwise thinning can occur in the same single foam film. A question arises as to whether the film that acquired such a thickness is in thermodynamic equilibrium or is kinetically stabilised. It should be noted that these transitions occur only in the direction of increasing pressure, i.e. the process... 

Some isotherms of water vapours sorption-desorption are presented in Fig, 1. In the first cycle of sorption, the isotherms have a pronounced stepwise character, and the values of water vapour sorption are unusually low for wood specimens. This is connected with the strict drying conditions of the specimens 378K at a rapid rise in temperature) after the exposure procedure, which resulted in the fixation of the nonequilibrium structure. After saturation with water vapours and the subsequent vacuum treatment at 295K during the procedure of the sorption experiment, the second cycle of isotherms was carried out, and this state was regarded as an equilibrium one. Thus, the analysis of the specimens structure was performed on the basis of the sorption-desorption isotherms of the second cycle. 

For small disturbances of the adsorption layer from equilibrium, Lucassen (1976) derived an analytical solution (cf Section 6.1.1). An analysis of the effect of a micellar kinetics mechanism of stepwise aggregation-disintegration and the role of polydispersity of micelles was made by Dushkin Ivanov (1991) and Dushkin et al. (1991). Although it results in analytical expressions, it is based on some restricting linearisations, for example with respect to adsorption isotherm, and therefore, it is valid only for states close to equilibrium. 

Indeed, as Tnmg et al. [297] reported. X-ray diffraction analysis imam-biguously confirms the expansion of MNLL-53(A1, Cr) that accompanies absorption of normal alkanes into its interior. The breathing also manifests itself on the sorption isotherm as an unusual stepwise increase in the MOF capacity at rather low relative pressures. The same type of stepwise sorption isotherm for carbon dioxide at 196 K and clear-cut sorption—desorption hysteresis was also observed [298] for a flexible MOF formed by zinc carboxylate units joined by l,4-diazobicyclo[2,2,2]octyl groups in one direction and by 2-amino-1,4-benzenedicarboxylates in the other direction. The amino functions of the MOF were then converted into amide by modification with alkyl anhydrides of various lengths. Short alkyl chains thus introduced narrow the pores and the longer chains hold the pores... 

A sample can also be observed under isothermal conditions where the mass change is recorded as a function of time at a predetermined temperature. A third method of TG analysis is the jump method [4]. In this case the sample is held at a fixed temperature for a period of time until the temperature is discontinuously changed (or jumped), where again the mass change is observed as a function of time. The application of the jump method to the study of reaction rate kinetics is discussed in Section 5.3.3. If the chemical reaction under investivation proceeds slowly then the linear heating programme may be replaced by a stepwise programme so that the experimental conditions become quasi-isothermal [5]. 

Dynamic, isothermal, and stepwise temperature control makes it possible to design flexible temperature programs. Digital filtering via Fourier analysis enhances the signal-to-noise ratio, which helps to resolve small tan 8 values. Comprehensive, multidimensional calibration of the DMA system leads to reproducible test results for the modulus and damping (viscoelastic) behavior of a sample. 

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