Thermodynamic control INDEX

A theoretical study at a HF/3-21G level of stationary structures in view of modeling the kinetic and thermodynamic controls by solvent effects was carried out by Andres and coworkers [294], The reaction mechanism for the addition of azide anion to methyl 2,3-dideaoxy-2,3-epimino-oeL-eiythrofuranoside, methyl 2,3-anhydro-a-L-ciythrofuranoside and methyl 2,3-anhydro-P-L-eiythrofuranoside were investigated. The reaction mechanism presents alternative pathways (with two saddle points of index 1) which act in a kinetically competitive way. The results indicate that the inclusion of solvent effects changes the order of stability of products and saddle points. From the structural point of view, the solvent affects the energy of the saddles but not their geometric parameters. Other stationary points geometries are also stable. 

The most interesting studies included the evaluation of the reactivity of the same radicals for two different reaction paths, 16 and 17. The computational studies correctly selected path 16 as the most reactive one. However, the question remains is there sufficient selectivity to accomplish only transformation 16. The computed selectivity index was 0.0336 (0.1216-0.0980). These values assured the formation of products only through a five-memebered ring formation. This was in full agreement with experimenal results [128]. It is well known that a secondary radical is more stable than a primary radical. The calculations supported this by favoring the cyclohexyl radical by 7.7 kcal/mol over the cyclopentylmethyl radical. Therefore, formation of the six-membered ring product was thermodynamically controlled. 

These findings are in contrast to thermodynamics favoring in the case of naphthalene the formation of conjugated 1,2-isomers. Therefore, kinetic control has to be assumed. The site selectivity for the first as well as the second protonation step has been predicted by HMO theory. One approach refers to local charge densities [13,165] the other one uses localization energies as a reactivity index [166]. In any event, the inductive effect of the methylene group, formed in the first protonation step, has to be taken into account if two sites provide comparable reactivity indices. 

All the above ROMP/CT approaches rely on reaching the thermodynamic equi-Ubrium in order to produce homo-telechelic polymers with high degrees of end-functionalization. A polydispersity index of ideally 2.0 is thus inevitable for this method. A different approach in which a kinetically controlled homo-telechelic... 

Here, we follow a later, simpler formulation that illustrates the power of optimal control for finite-time thermodynamic processes [11]. We take as the control variable the set of temperatures at a given number of equally spaced heat-exchange points along the length of the distillation column. The (assumed) binary mixtme comes in as a feed at rate F and is separated into the less volatile bottom at rate B and the distillate, at rate D, that collects at the top of the colmrm. Let x be the mole fraction of the more volatile component in the liquid and y, the corresponding mole fi action in the vapom, and their subscripts, the indications of the respective points of reference. Thus the total flow rates, for steady flow, must satisfy F = D + B, and xpF = x D + xbB. We index the trays from 0 at the top to N at the bottom. Mass balance requires that the rate V +i of vapour coming up from tray n + 1, less the rate of liquid dropping from tray n, L , must equal D for trays above the feed point at which F enters, and must equal —B below the feed point. Likewise the mole fractions must satisfy the condition that Vn+iVn+i —XnLn = xpD above the feed and —xpB below the feed. The heat required at each nth tray is... 

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