Concentration-dependent collapse of a large polymer in a solution of incompatible polymers

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Abstract
DNA of high molecular weight is observed to collapse into a very compact particle in a salt solution in the presence of second neutral polymers, poly(ethylene oxide) [(EO) n ] of lower molecular weight, above a certain critical concentration. We show in a statistical mechanical way that the phenomenon is caused by the repulsive interaction between the DNA and (EO) n ’s. A self‐consistent (SC) potential is introduced to treat both intramolecular and intermolecular repulsive interactions of short‐range nature. Appearance of a bound state in this SC potential is necessary and sufficient condition for a collapsed state to be stable. The critical concentration of (EO) n is found to be proportional to the inverse degree of its polymerization. The average size of a DNA is expected to change from N 3/5 to N 1/3 at the transition point, where N is the number of base pairs in the DNA. The transition is of second kind.