The Reaction Space

4 Methods for Exploring the Reaction Space 4.1 The Reaction Space 

In the sections above, we have discussed methods for exploring the experimental conditions. For such experiments, it is assumed that the reaction system (substrate, reagent (s), solvent) is defined and that variations with respect to discrete variations is limited to alternative choices. We shall now discuss what can be done when 

We define the reaction space as the union of all possible discrete variations of the nature of the substrate, of the reagent (s) and of the solvent. For almost any given reaction, the number of such possible combinations will be overwhelmingly large. The problem is therefore to select subsets of representative test systems which ensure a sufficient spread of the critical properties of the system to permit general conclusions to be drawn. 

A problem is that discrete variations are prone to interaction effects, see Sect. 2.2. The ability to recognize such interaction effects is very important when new reactions are explored, otherwise the potential of the reaction for preparative purposes may be overlooked. It is therefore necessary to use multivariate strategies also for exploring the reaction space so that the joint influence of varying the substrate, reagent (s) and solvent can be evaluated. 

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The reasons for this lack of work are manifold The problem is quite complex and difficult to tackle. The information in reaction databases is inherently biased only known reactions, no reactions that failed, are stored. However, any learning also needs information on situations where a certain event will not happen or will fad. The quality of information stored in reaction databases often leaves something to be desired reaction equations are incomplete, certain detads on a reaction are often incomplete or missing, the coverage of the reaction space is not homogeneous, etc. Nevertheless, the challenge is there and the merits of success should be great ... 

Figure 4 Membrane reactor for 4-hydroxybenzoate production using phenolphosphate carboxylase. A membrane (A) separates the reaction space containing the enzyme (B) from water phase where the product is collected (C).

Here the energies of the reactants AC and B are linked (correlated) with the products, CB and A across the reaction space (reaction coordinate). When x = b/2, the three atoms form a transition complex, ACB. 

Fluoridated apatite crystals can grow using the dual membrane system involving on the one hand a calcium acetate solution and on the other hand a phosphate solution at physiological temperature with a pH of 6.5. lijima et al. showed that the combination of fluoride ions, added to the phosphate solution, and amelogenin (a major protein in the enamel extracellular matrix), present in the reaction space between the two membranes, controlled the transformation of octacalcium phosphate (OCP) into fine rod-like fluoridated apatite crystals with habit, size... 

The elementary reactions in Eqs. (1) are not necessarily linearly independent, and, accordingly, let Q denote the maximum number of them in a linearly independent subset. This means that the set of all linear combinations of them defines a 0-dimensional vector space, called the reaction space. In matrix language 0 is the rank of the S x A matrix (2) of stoichiometric coefficients which appear in the elementary reactions (1) ... 

The reaction takes place solely in the liquid phase, where B could be in excess. In such cases, it is frequently found that the reaction becomes of zero order with respect to (B), i.e. with respect to the component that is in excess in the reaction space or, in general, depending on the nature of the reaction with respect to the component whose concentration is relatively high. In these cases, the reaction rate becomes a function of only the liquid-phase concentration of A. 

The catalytic properties of Del-Ti-MWW have been compared with those of other titanosilicates in the epoxidation of cyclic alkenes (Table 4.4). The TON decreased sharply for TS-1, Ti-beta and 3D Ti-MWW with increasing molecular size of cyclic alkenes. Ti-MCM-41 with mesopores, however, showed higher TONs for cyclooctene and cyclododecene. This implies that the reaction space is extremely important for the reactions of bulky molecules. The delamination of Ti-MWW increased the TON greatly for not only cyclopentene but also bulkier cycloalkenes. Especially, the catalytic activity of Del-Ti-MWW was about 6 x higher than that of Ti-MWW for cyclooctene and cyclododecene. Del-Ti-MWW even turned out to be superior to Ti-MCM-41 in the epoxidation of bulky substrates. This should be due to the high accessibility of Ti active sites in Del-Ti-MWW. Thus the delamination was able to change Ti-MWW into an effective catalyst applicable to reactions of bulky substrates. 

In both cases, where the quencher is identical with the counterion or where the quencher is hydrophobic, confinement of the reaction space to the micelle size induces both an enhancement of the observed reaction as well as a reduction of the reaction order from two to one. 

For most types of kinetics, the stepwise changes in concentration results in a smaller average reaction rate than it would otherwise if the same feed materials were in a batch or plug (tubular) reactor. Therefore, to obtain the same output the volume of the reaction space must be larger, and in some instances much larger as in the case where only a single tank is used. By arranging several tanks in series the... 

For reactors of a larger diameter (e.g. more than 600 mm) it is more advisable to use a bundle of small tubes as heat exchangers. Such a distribution of heat exchange surfaces virtually does not inhibit fluidising and ensures that the heat is efficiently withdrawn from the whole surface of the apparatus. It should be also kept in mind that tube bundles allow one to select the reaction space and place rotating gas distribution devices between sections this considerably increases the coefficient of heat transfer and ensures a more uniform gas distribution in the reaction zone. 

The switching between dependencies (2.7) and (2.8) at the surface electron concentration ca. 1013 cm-2 may be explained as follows. According to the interpretation of the mass action law, the total probability of two particles A and B to enter the surface reaction is the product of the probability of particle B to appear in the reaction space S around particle A, which equals CB-S (where CB is the surface concentration of particles B), and the probability of this pair to react for time period t - P(t) [16] ... 

At CB-S > 1, the concentration of particles B is so high that particle B locates in the reaction space around particle A with probability ca. 1. At such large values of B concentration (CB > 1/S ), the reaction rate becomes independent of the B concentration. 

When using propanols for esterification, the alcohol and water form azeotropes making necessary secondary recovery and recycling of alcohol. An industrial process that is conducted in this way makes use of homogeneous catalyst (para-toluene sulfonic acid) lost after reaction [5]. A more efficient solution can found by employing an entrainer for breaking the azeotrope water/alcohol and superacid solid catalyst. Besides, the entrainer has a beneficial effect on the reaction rate, by increasing the amount of alcohol recycled to the reaction space [3]. 

It is interesting to note that supplementary reactions leading to impurities may take place outside the reaction space, mostly in the aqueous phase during the first separation steps of quench and absorption in water. Typical examples are the formation of propion-cyanhydrine and dinitrile-succinate favored by a basic pH ... 

The results given indicate the electrochemical method for the synthesis of nanostructured carbon materials to be promising. In the reaction space, dissipative self-assembly of carbon compounds takes place by the action of electric discharges. In this case, structures of new type can be formed, which are transitional between polycyclic aromatic hydrocarbons and fullerenes, nanotubes. 

When the dispersed phase, usually but not necessarily the cells, is of interest, no separation of phases need take place during sampling. The system must be opened in such a way that no infections can enter the reaction space either during sampling or between the sampling events. This requires the use of nonreturn valves and probably some repetitive sterilization procedure of the valve and exit line(s), as depicted in Fig. 18. 

Pharmacokinetics has been based on the concepts of classical chemical kinetics. However, the applicability of the rate equations used in chemical kinetics presupposes that the reactions are really reaction-limited. In other words, the typical time for the two chemical species to react when placed in close proximity (reaction time treac) is larger than the typical time needed for the two species to reach each other (diffusion time treaction space. When the condition treac > tdiff is met, then one can use the global concentrations of the reactant species in the medium to obtain the classical rate equations of chemical kinetics. This is so since the rate of the reaction is proportional to the global concentrations of the reactant species (law of mass action). The inequality freac > tdiff underlines the fact that the two reactant species have encountered each other more than one time previously in order to react effectively. 

The electrically feasible reaction conditions are (I) the extent of the reaction space and (2) the quantity of reactive ions in the latter, i.e. the concentration of the ions can be regulated in a purely electrical way and within the broadest limits. The highest dilutions can be realized just as well with weak currents and large electrode surfaces as the highest concentrations with strong currents and small surfaces. That most important factor of reaction kinetics, the reaction velocity, is thus determinatively influenced by these concentrations. The importance of the reaction velocity is especially fundamen-... 

Since, according to the preceding descriptions, the reaction space of electrolytic processes consists of an extremely thin layer in contact with the electrode—the contact surface of electrolyte and electrode—these processes can generally be regarded as reactions in heterogeneous systems. Nernst1 has proposed a theory for such systems, which has been tested experimentally by Brunner.2 The principle of this theory consists in basing the reaction velocities on the diffusion velocity. 

The gas-tight electrode stirrers are based on the same principle. They have the advantage of using the electrodes themselves,—which may have any shape,—for stirring. A fine division of the components is thus assured on the electrode surface the (reaction space). This matter is of great importance in a series of reactions, for instance in the simultane-... 

Carlson, R. and Lundstedt, T. Scope of Organic Synthetic Reactions. Multivariate Methods for Exploring the Reaction Space. An example by the Willgerodt-Kindler Reaction. Acta Chem. Scand., 1987, B41, 164-173. 

To solve highly nonlinear differential equations for systems far from global equilibrium, the method of cellular automata may be used (Ross and Vlad, 1999). For example, for nonlinear chemical reactions, the reaction space is divided into discrete cells where the time is measured, and local and state variables are attached to these cells. By introducing a set of interaction rules consistent with the macroscopic law of diffusion and with the mass action law, semimicroscopic to macroscopic rate processes or reaction-diffusion systems can be described. 

Fig. 1. V ariations of synthetic reactions are illustrated by the reaction space, the experimental space, and the response space...

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