Thermal analogs

Oxidations initiated by thermally induced electron transfer in an oxygen-CT complex represent the thermal analog of the Frei photo-oxidation and are properly classified as hybrid type IlAOi-type IIaRH oxidations (Fig, 2), Such reactions require either zeolites with high electrostatic fields or substrates with low oxidation potentials. In addition, elevated temperatures are known to promote the thermally initiated electron-transfer step, although the possible intrusion of a classical free-radical initiation chain oxidation at higher temperatures must be considered. 

Table II presents some consequences of these analogies for a vapor phase and a condensed phase together with the thermal analogs. Here rti is the concentration of the vapor in molecules per unit volume, Nt is the mole fraction in the condensed phase, Vc is the molar volume of the substrate, p< is the partial pressure, and y< is the rational activity coefficient.

Wise and Frech " observed the formation of H2 as an intermediate in the oxidation of ammonia at 1096 °K, lending support to an initiation reaction such as (50). Later, Ordogh and Szabo reported studies of NH3 oxidation conducted mostly at 620-630 °C and initial pressures of 330-350 torr. They concluded that initiation took place via either reaction (50) or the thermal analog of reaction (41). 

Pyrolytic sources are trimethylamine (22), dimethylnitrosamine (16), dimethyl-nitramine (14), and tetramethyltetrazene (25, 31, 33), the pyrolyses proceeding according to the thermal analogs of Reactions 11, 12, and 13. A further probable source of these radicals is provided by the reaction between dimethylchloramine and copper-bronze in ether at 40° (19). 

Let us consider a thermal analogy. For this example, we define a local spin temperature which has a one to one correspondence with the spin polarization. Thus, if there is a small group of spins with no net polarization, we will say that its local spin temperature is infinite whereas if the small group of spins are all lined up (polarized) along the field we will say... 

Allows for quantum fluctuation description in analogy with thermal analogies. 

The developed bimorph beam model of IPMC was validated using the finite element method (FEM) and the used software was MSC/NASTRAN. As the software does not directly support the electromechanical coupling, the thermal analogy technique as described in [Lim et al. (2005) Taleghani and Campbell (1999)] was used. The simulated versus measured force-displacement relationship of an IPMC actuator is shown in Fig. 2.39. The relative errors for A = 0 between the calculated values and the measured data for 2V and 3V are 2.8% and 3.7%, respectively. The equivalent Young s moduli estimated from the equivalent beam model and the equivalent bimorph beam model are 1.01 GPa and 1.133-1.158 GPa, respectively, which are very close. However, the values from the equivalent beam model... 

For all numerical analyses, a commercial finite element analysis program, MSC/ NASTRAN [29], was used in conjunction with the equivalent bimorph beam model. A thermal analogy technique proposed by Taleghani and Campbell [30] was used to implement the electromechanical coupling effect into the finite element model. In the thermal analogy technique, the electromechanical coupling coefficient (dj/) is converted into the thermal expansion coefficient a/ as follows ... 

The operation of the heat flux DSC is based on a thermal equivalent of Ohm s law. Ohm s law states that current equals the voltage divided by the resistance, so for the thermal analog one obtains... 

Once these substitutions are made, the electrical formulas and intuition can be applied to thermal problems. Ohm s law, voltage dividers, parallel and series impedances and conductances, and capacitors charging through a resistor all have thermal analogs. 

The protons attached to C 2 of malonic acid are not directly involved m the process and so may be replaced by other substituents without much effect on the ease of decar boxylation Analogs of malonic acid substituted at C 2 undergo efficient thermal decar boxylation... 

Iron(III) bromide [10031-26-2], FeBr, is obtained by reaction of iron or inon(II) bromide with bromine at 170—200°C. The material is purified by sublimation ia a bromine atmosphere. The stmcture of inoa(III) bromide is analogous to that of inon(III) chloride. FeBr is less stable thermally than FeCl, as would be expected from the observation that Br is a stronger reductant than CF. Dissociation to inon(II) bromide and bromine is complete at ca 200°C. The hygroscopic, dark red, rhombic crystals of inon(III) bromide are readily soluble ia water, alcohol, ether, and acetic acid and are slightly soluble ia Hquid ammonia. Several hydrated species and a large number of adducts are known. Solutions of inon(III) bromide decompose to inon(II) bromide and bromine on boiling. Iron(III) bromide is used as a catalyst for the bromination of aromatic compounds. 

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