Temperature analog

Heat diffuses much like mass and is governed by similar equations. The temperature analog of Equation (8.12) is... 

Using in-boundary integral method for this Green s function gives us finite-temperature analog of the matrix given in Eq. (5),... 

The reaction between MAH, PE, clay and the catalyst must take place essentially simultaneously. If the clay is first reacted with MAH at elevated temperatures, analogous to the treatment of clay with silane coupling agents, a clay maleate half ester or diester is probably formed. The latter does not readily react with PE even in the presence of a free radical catalyst. 

Meldmm s acid 5-oxime, prepared by reaction of Meldrum s acid and NO followed by tautomerism of the nitroso group, thermolyzes at elevated temperatures analogously to give the highly reactive nitrosoketene <1997H(46)503, 1998H(47)383>, which has been characterized spectroscopically (Equation 15) <2002JRS443>. 

Die Reaktivitat von Halogenmethyl-l,2,4-oxadiazolen ist mit der von Benzylchloriden ver-gleichbar. Nukleophile Substitutionen z.B. mit Aminen verlaufen in guter Ausbeute zu Ami-nomethyl-1,2.4-oxadiazolen45,53. Aniline setzen sich bei hoherer Temperatur analog um69 z.B. ... 

Equation 2.14 gives the dependency of entropy on pressure and temperature. Analogous to Problem 2.1, show this dependency for an ideal gas. 

The ionic defects characteristic of the fluorite lattice are interstitial anions and anion vacancies, and the actinide dioxides provide examples. Thermodynamic data for the uranium oxides show wide ranges of nonstoichiometry at high temperatures and the formation of ordered compounds at low temperatures. Analogous ordered structures are found in the Pa-O system, but not in the Np-O or Pu-O systems. Nonstoichiometric compounds exist between Pu02 and Pu016 at high temperatures, but no intermediate compounds exist at room temperature. The interaction of defects with each other and with metallic ions in the lattice is discussed. 

Much less persistent radical cations with remarkable electronic structures can be produced by y-irradiation of small hydrocarbons in freon matrices at low temperatures. Analogously, such short-lived species can also be detected by CIDNP spectroscopy. Moreover, radical cations can be generated in zeolites. "... 

Variable-temperature Raman data for SbCl, have been interpreted in terms of a dimer at lower temperatures, analogous to that in (SbCl40Et)2, and a normal-co-ordinate analysis has been performed. Both 1 1 and 2 1 adducts can be formed between the pentachloride and NN -dimethyloxamide, which on heating lose hydrogen chloride to give respectively (131) and (132). A series of... 

Arenediazonium tetrafluoroborates can be converted into aryl azides under mild conditions, by reaction with Me3SiN3 in an ionic liquid at room temperature. Analogously, aryl bromides and iodides are formed with MesSiX (X = Br, I). 

Ti = Ti-i, but the temperature analog of Equation 8.32 provides a smoother estimate of the zero-slope condition. 

The formation of [HF2] is also observed when HF reacts with group 1 metal fluorides M[HF2] salts are stable at room temperature. Analogous compounds are formed with FICl, HBr and HI only at low temperatures. 

Stannane complexes can be prepared by photolysis at low temperatures, analogous to silane complexes on the MeCpMn(CO)2 fragment.82 In Eq. (11.31) the use of a nonpolar solvent such as pentane is crucial because the product thermally... 

We have seen that the nature of the polymorph that crystallizes depends on the relative rates of nucleation of the polymorphs. These kinetic factors also explain why solid state transformations in molecular crystals often display pronounced hysteresis [25]. For example, to induce the transition of the low-temperature enantiotrope to the high-temperature form, the former may have to be heated well above the transition temperature. Analogously, the absence of a solid state transformation... 

Molecular oxygen is the principal oxidant in the ordinary combustion of fuels. Burning is essentially a high-temperature analog of autooxidation, in which the spin barrier to the initiation step (Equation 4.67) is overcome by use of high temperatures. 

It is conceivable that a-azoxy radicals cyclize and then fragment at elevated temperatures, analogous to 33—>42. Although fragmentation of the alkoxy radical 102 would be rapid, the cyclization shown below is calculated to be endothermic by 32 kcal/mol. ... 

In the framework of the so-called mean-field theory, in which the fluctuations in the 1-d metal lattice are neglected, the energy gap 2A = 0 for T > Tp. Below the energy gap opens continuously with decreasing temperature, analogously to the BCS theory of superconductivity, and at T - 0, it has the value... 

The scope of aminocarbonylations was extended by the works from various groups. For example, Skoda-Fbldes and Kollar studied the carbonylation reactions of ferrocene derivatives in the presence of Pd(OAc)2/PPh3 [126-128]. Ferrocene amides and novel ferrocene a-ketoamides were synthesized in good yields based on palladium-catalyzed aminocarbonylation or double carbonylation of iodofer-rocene at 40-50 bar of CO. The double-carbonylated products were favored at 40-60 °C and amides were produced almost exclusively at 100 °C, as the selectivity of the reaction with less sterically hindered secondary amines is highly dependent on the reaction temperature. Analogous aminocarbonylation reactions of l,l -diiodoferrocene led to I -iodo-ferrocenecarboxamides and I -iodo-ferro-ceneglyoxylic amide-type products. 

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