Stepwise aggregation

To overcome aggregation, stepwise elongation of large peptides requires not only potent coupling reagents but also additional tools. In recent years, beneficial results have been obtained by means of PEG resins, pseudoprolines (TPro) and O-acyl isopeptide or depsipeptide methodology. 

The second strategy of unsupervised learning is based on cluster analysis. With this method, the objects are aggregated stepwise according to the similarity of their features. As a result, hierarchically or nonhierarchically ordered clusters are formed. In order to describe the similarity of objects, we need to learn about appropriate similarity measures. 

In the synthetic approaches described so far water was the reaction medium and, therefore the pH plays an important regulatory role. This is illustrated by the stepwise formation of the tetranuclear 4D and by the assembly of the octanuclear aggregate 8 which takes place at pH - 9. 

In dlfluorenylstrontlum Itself the solvation Is a stepwise process, l.e., Fl, Sr++,Fl- <— Fl",Sr F1" += Fl 11Sr4 11Fl (31). In the n - 2 bolaform salt the first separation step Is difficult, but once bound THF molecules force Sr to separate from the first Fl Ion, the cyclic structure probably opens up due to the shortness of the (CH2>2 chain. This would leave a free Fl Ion on one end of the chain. Since the conductance of the salt Is known to be very low, this latter species most likely will rapidly dimerize to form a non-conducting cyclic aggregate consisting of loose Ion pairs only,as shown In reaction 14. This aggregation shifts the equilibrium In favor of the loose Ion pairs. 

Another striking difference between aqueous and anhydrous, nonaqueous systems is the size of the aggregates that are first formed. As we have seen, n is about 50 or larger for aqueous micelles, while for many reverse micelles n is about 10 or smaller. A corollary of the small size of nonaqueous micelles and closely related to the matter of size is the blurring of the CMC and the breakdown of the phase model for micellization. Instead, the stepwise buildup of small clusters as suggested by Reaction (D) is probably a better way of describing micellization in anhydrous systems. When the clusters are extremely small, the whole picture of a polar core shielded from a nonaqueous medium by a mantle of tail groups breaks down. 

For the cases where gas phase cyclohexenes do not appear to be intermediates, the question arises as to the nature of the surface reaction. Thus, does cyclohexane simultaneously lose six hydrogen atoms via the sextet mechanism (T3) originally proposed by Balandin in 1929, or does the reaction take place in a stepwise fashion without desorption of intermediate products According to the sextet theory, the active catalyst unit is an aggregate of metal atoms which must be spaced within certain definite limits consistent with the geometry of the cyclohexane ring. While there... 

The presence of halide ligands in the molecules of bimetallic alkoxide complexes hinders apparently their decomposition with formation of oxoalkox-oderivatives. Examples are CunClZr2(OPr )9 [1664], CdHalZr OPti), [1508, 1687], Veith etal. [1687,1691] used the the stepwise replacement of Cl andl atoms for preparation of tiimetallic zirconates, [MnCdZr2(OPr )12]2, M11 = Ca, Sr, Ba These octanuclear aggregates contain linear [Ba(p-OR)2Cd(p-OR)2Cd(p-OR)2Ba] chains in the center and [Zr2Ba] triangles at the ends of each molecule (see also Section 4.7.3). 

It may be expected that other, highly structured solvents with a tri-dimensional network of strong hydrogen bonds, would also permit micelle formation by surfactants, but little evidence of such occurrences has been reported. On the other hand, surfactants in non-polar solvents, aliphatic or aromatic hydrocarbons and halocarbons tend to form so-called inverted micelles, but these aggregate in a stepwise manner rather than all at once to a definite average size. In these inverted micelles, formed, e.g., by long-chain alkylammonium salts or dinonyl-naphthalene sulfonates, the hydrophilic heads are oriented towards the interior, the alkyl chains, tails, towards the exterior of the micelles (Shinoda 1978). Water and hydrophilic solutes may be solubilized in these inverted micelles in nonpolar solvents, such as hydrocarbons. 

Figure 4. In (kj/k) vs. aggregation number j for various values of

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