Chain-ring distribution function

Fig. 11 Spatial distribution functions around the imidazolium rings of the cations of O atoms from tf2N anions (red isosurfaces) and C4 (ipso) atoms from toluene (white isosurfaces). Top row [C im [tf N], bottom row ( C C1im][tf,N]. Probability density around the butyl side chain is not shown, since it is not easy to plot it in the same referential due to conformational flexibility of the chain...

The probability of ring formation is calculated from the distribution function p(r) of the distance r between the two reacting atoms. In 1,6-dienes these are the C-2 and C-7 atoms [see (16-14)]. The distance between these two atoms is the distance between the ends of a chain with five bonds (six chain members). The distribution of the end-to-end distances Lof such a chain has been calculated for paraffins. The following has been found to be a good approximation for small end-to-end distances (0.33 < L < 1.3) ... 

The synthesis of polypeptides by ring-opening polymerization is an area that has been under study for more than five decades. Initially, this field suffered from limitations that necessitated excessive sample purification and fractionation to obtain well-defined polypeptides. Over the last 15 years, vast improvements in NCA polymerizations now allow the synthesis of a variety of block copolypeptides of controlled dimensions (molecular weight, sequence, composition, and molecular weight distribution). Many different block copolypeptides have now been prepared and used to form self-assembled structures with promising properties. The ability to easily adjust chain conformation and functionality in polypeptides, in combination with advanced synthetic methods that enable preparation of complex sequences, has opened up a new, promising field of materials with a wide range of tunable properties. 

Carothers work included both, KC and TC polymerization, but neither he nor his coworker Rory realized and discussed this difference. Under the conditions used by Carothers, the syntheses of polyesters and polyamides were TC polycondensations, whereas the syntheses of polyalkanes from 1,10-dibromodecane and sodium metal were perfect KCPs (see Chap. 3). In 1950, Stockmayer and coworkers published two papers [1,2] which dealt with the formation of cylics in ring-chain equilibria during synthesis or thermal degradation of polymers. The first paper was focused on the calculation of distribution functions of the cyclic oligomers, whereas the second... 

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