Temperature instability

Of all the forms of induced instability, temperature fluctuations are most widely experienced by an unattended dispersion once it has been stored or applied. The caking of pharmaceuticals so that they will not pass through a hypodermic needle has been mentioned (7) another example is the failure of... 

Finally, Tallon [13] has suggested another instability point where the entropy of the superheated crystal becomes equal to that for a superheated diffusionless liquid (a glass) rather than that of the liquid. Since the glass has lower entropy than the liquid, this instability temperature is lower than that predicted by Fetch and Johnson [12],... 

In order to achieve passive safety with reactive material, the radius of the reactor tube is designed to be small to avoid any thermal explosion inside the tube. Using the Frank-Kamenetskii approach (see Chapter 13), the radius remains below the critical radius. Thus, even assuming a purely conductive heat transfer mechanism, corresponding to a worst case, no instable temperature profile can develop inside the reaction mass. The reactor can be shut down and restarted safely. 

An ideal baseline should be completely straight without any feature. This may not be the case, especially for samples with weak signals, due to a number of reasons. The cavity, the cryostat, or the capillary/cell may have a small amount of contamination, the signal of which may be reduced or even eliminated by cleaning. In addition, system instability (temperature variations, air drift, etc.) may also yield broad features in the baseline. 

As these signals are alternately added and subtracted into the summed FID, they cancel as long as we are careful to acquire an even number of scans for each t increment. This method depends for its success on precise subtraction of a very large signal, so it is sensitive to any instability (temperature change, vibration, variation in pulse widths, etc.) that occurs between one scan and the next. 

It is not clear, whether the experimentally observed random local freezing of the deuterons in the O-D—O bonds in deuteron glasses corresponds to a true thermodynamic phase transition or whether one deals with a dynamic phenomenon which only seems static because of the finite observation time of the experimental techniques. The recently observed42 splitting between the field-cooled and zero-field dielectric susceptibilities below an instability temperature Tf seems to speak for the occurrence of an Almeida-Thouless-like thermodynamic phase transition in deuteron glasses. It is well known that ID NMR and EPR allow a direct measurement of the Edwards-Anderson order parameter qEA only on time scales of 10 3-10 8 s and 2D exchange NMR possibly seems to be a better technique for such slow motions. 

Fig. 2.5. Schematic metastable polymorphous-phase diagram, which includes the instability temperature, T, the melting temperature, T0, and the glass temperature Tt, and defines the stability range of the crystal, liquid, and glass phases...

We now analyze the Eqs. (3.33) and (3.38). To the best of our knowledge, the exact analytical solution of these equations is impossible. To get (numerically) the curve td(af,ap) (actually td af = Up) since in the experiment [35] a/ = Up), we find the instability temperature t q) for the transition to the state with given q. The real transition, however, occurs to the state with the maximal value of t(q). The transition temperature td(af,ap) and corresponding domain wave-vector qd are found by taking the maximum of t(q). 

Disadvantages Instability Temperature Sensitivity Late Eluters ... 

As an example, consider the study by Banerjee et al. (1984) on the effect of electron irradiation on the order-disorder transformation in (DIJ Ni4Mo. Electron micrographs and diffraction patterns were obtained during in situ electron irradiations at 50-1050 K in a HVEM. At temperatures below 200 K, the alloy completely disorders. At 200-450 K, only SRO was observed, and the transition between LRO and SRO, which occurs via the completely disordered state, is consistent with the concentration-wave description of the SRO structure and supports the concept of spinodal ordering. It is believed that an interstitial mechanism is responsible for maintaining the SRO. Above 450 K, LRO persisted for samples initially in this state and SRO was only preserved up to 550 K for samples initially in that state. Between 550 and 720 K, a mixed SRO-LRO state occurred, and at temperatures above 720 K a complete transition to SRO was obtained. It is believed that maintenance of LRO requires a vacancy mechanism. At temperatures below 800 K the SRO-LRO transition occurred in a continuous fashion, while above 800 K a nucleation and growth mechanism was operative. This behavior is characteristic of an ordering transition of the first kind below and above the coherent instability temperature. 

The tendency to separate is expressed most often by the cloud point, the temperature at which the fuei-alcohol mixture loses its clarity, the first symptom of insolubility. Figure 5.17 gives an example of how the cloud-point temperature changes with the water content for different mixtures of gasoline and methanol. It appears that for a total water content of 500 ppm, that which can be easily observed considering the hydroscopic character of methanol, instability arrives when the temperature approaches 0°C. This situation is unacceptable and is the reason that incorporating methanol in a fuel implies that it be accompanied by a cosolvent. One of the most effective in this domain is tertiary butyl alcohol, TBA. Thus a mixture of 3% methanol and 2% TBA has been used for several years in Germany without noticeable incident. 

The effect can be important in mass-transfer problems (see Ref. 57 and citations therein). The Marangoni instability is often associated with a temperature gradient characterized by the Marangoni number Ma ... 

A similar Marongoni instability can be provoked in a single component system by a temperature gradient [31] as illustrated in Fig. XIII-2. The wavelength of the instability is approximately... 

Successful molecular dynamics simulations should have a fairly stable trajectory. Instability and lack of ec uilibratioii can result from a large time step, treatment of long-range cutoffs, or unrealistic coiiplin g to a temperature bath. ... 

This reaction is explosive and proceeds in low yield (—21%) because of the instability of the thioformamide that is destroyed as soon as it is cyclized with 1 (113,491). The thioformamide is better prepared directly in the reaction mixture by condensing phosphorus pentasulfide and for-mamide at room temperature, in dioxane solution, according to reaction 1 (491,492),... 

The Type N thermocouple (Table 11.60) is similar to Type K but it has been designed to minimize some of the instabilities in the conventional Chromel-Alumel combination. Changes in the alloy content have improved the order/disorder h ansformations occurring at 500°C and a higher silicon content of the positive element improves the oxidation resistance at elevated temperatures. 

Having assisted desolvation in this way, the carrier gas then carries solvent vapor produced in the initial nebulization with more produced in the desolvation chamber. The relatively large amounts of solvent may be too much for the plasma flame, causing instability in its performance and, sometimes, putting out the flame completely. Therefore, the desolvation chamber usually contains a second section placed after the heating section. In this second part of the desolvation chamber, the carrier gas and entrained vapor are strongly cooled to temperatures of about 0 to -10 C. Much of the vapor condenses out onto the walls of the cooled section and is allowed to drain away. Since this drainage consists only of solvent and not analyte solution, it is normally directed to waste. 

To achieve sufficient vapor pressure for El and Cl, a nonvolatile liquid will have to be heated strongly, but this heating may lead to its thermal degradation. If thermal instability is a problem, then inlet/ionization systems need to be considered, since these do not require prevolatilization of the sample before mass spectrometric analysis. This problem has led to the development of inlet/ionization systems that can operate at atmospheric pressure and ambient temperatures. Successive developments have led to the introduction of techniques such as fast-atom bombardment (FAB), fast-ion bombardment (FIB), dynamic FAB, thermospray, plasmaspray, electrospray, and APCI. Only the last two techniques are in common use. Further aspects of liquids in their role as solvents for samples are considered below. 

Instability in the flame leads to varying efficiencies in ion formation within the plasma (varying plasma temperature) and, therefore, to variations in measured isotope ratios (lack of accuracy). 

Remember that the hump which causes the instability with respect to phase separation arises from an unfavorable AH considerations of configurational entropy alone favor mixing. Since AS is multiplied by T in the evaluation of AGj, we anticipate that as the temperature increases, curves like that shown in Fig. 8.2b will gradually smooth out and eventually pass over to the form shown in Fig. 8.2a. The temperature at which the wiggles in the curve finally vanish will be a critical temperature for this particular phase separation. We shall presently turn to the Flory-Huggins theory for some mathematical descriptions of this critical point. The following example reminds us of a similar problem encountered elsewhere in physical chemistry. 

Catalyst Effectiveness. Even at steady-state, isothermal conditions, consideration must be given to the possible loss in catalyst activity resulting from gradients. The loss is usually calculated based on the effectiveness factor, which is the diffusion-limited reaction rate within catalyst pores divided by the reaction rate at catalyst surface conditions (50). The effectiveness factor E, in turn, is related to the Thiele modulus,

first-order rate constant, a the internal surface area, and the effective diffusivity. It is desirable for E to be as close as possible to its maximum value of unity. Various formulas have been developed for E, which are particularly usehil for analyzing reactors that are potentially subject to thermal instabilities, such as hot spots and temperature mnaways (1,48,51). 

Oxirene is probably a true intermediate, but is separated from ketene by only a very low barrier. Since its instability results from unimolecular isomerization rather than from attack of other molecules, the only viable current technique for its direct observation seems to be generation and spectroscopic examination in an inert matrix at temperatures near absolute zero. 

From N-oxides of aromatic bases oxaziridines were obtained only at very low temperatures, but oxaziridines were often postulated as intermediates in the photoconversion of such N-oxides (Section 5.08.3.1.2). Isolation of the more stable photoisomers of nitrones also causes some problems due to their thermal and photochemical instability leading to acid amides, e.g. (69TL2281), or, by fragmentation, to carbonyl compounds and products of stabilization of nitrenes, e.g. from (260) (69ZN(B)477). 

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