Scaling Theory of Polyelectrolyte Nanogels* *Supported by China Earthquake Administration under Grant No. 20150112 and National Natural Science Foundation of China under Grant No. 21504014

Abstract

The present paper develops the scaling theory of polyelectrolyte nanogels in dilute and semidilute solutions. The dependencies of the nanogel dimension on branching topology, charge fraction, subchain length, segment number, solution concentration are obtained. For a single polyelectrolyte nanogel in salt free solution, the nanogel may be swelled by the Coulombic repulsion (the so-called polyelectrolyte regime) or the osmotic counterion pressure (the so-called osmotic regime). Characteristics and boundaries between different regimes of a single polyelectrolyte nanogel are summarized. In dilute solution, the nanogels in polyelectrolyte regime will distribute orderly with the increase of concentration. While the nanogels in osmotic regime will always distribute randomly. Different concentration dependencies of the size of a nanogel in polyelectrolyte regime and in osmotic regime are also explored.