Cooperative Phenomena in Complexation Processes

It has been stated that many kinds of interaction forces act concertedly in the formation of intermacromolecular complexes. Thus, the free energy change of the reaction between two different macromolecular chains (AF°) is represented by the following equation  

Even relatively weak van der Waals and dipole-dipole interactions very often prove sufficient for maintaining the stabilization of some macromolecular associates in solution4965. This may be exemplified by the stereocomplexes or the associates of the right- or left-handed helices of poly (y-methyl-L(or -d)-glutamate) in organic solvents4975. 

The theoretical treatment of cooperativity in systems composed of oligomer and polymer has been discussed in detail by Kabanov et al.4985. The change in free energy (AF) in such systems is expressed by 

On the basis of these theroretical considerations, the following phenomena are expected to occur in oligomer-polymer reactions  

In Eqs. (51) and (52), a is comparable with a cooperative coefficient, representing the basic bonding constant. The values of A, B, a and ft are complied in Table 22. In the range of the chain lengths of these oligocations, the standard free energy change of complex formation decreases by about 0.6 kcal/mol upon the addition of one cationic residue. The difference of/3 (about 1.6 kcal/ mol) between two different types of cations may be due to the variation of the hydrophobidties between benzyl and methyl residues. 

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