Modeling Ionic and Sequence Effects on the Swelling Behavior of Polyampholyte Brushes

The structural responses of polyampholytes to various chemical stimuli are sensitive to the sequence of monomeric groups that bear positive and negative charges. A theoretical understanding is yet to be established to account for the sequence effects under diverse environmental conditions such as solution pH, salt concentration, and ion valence. As a first step toward delineating the underlying physics, in this work, we consider strong polyampholyte brushes with either a diblock or an alternating chain architecture and study their structure and swelling behavior in response to variations in salt concentration, ion size, and valency using a polymer density functional theory. As the salt concentration increases, an alternating brush displays a re-entrance behavior, characterized by an initial reduction of the brush height followed by a subsequent brush extension. The ion size effects become appreciable only at high salt concentrations, wherein a reduction of the ion size leads to an increased brush height. For a diblock brush, however, the brush height decreases monotonically with the addition of salt when the counterions to the lower block are significantly larger than the polymer segments. A re-entrance behavior is observed only when the ion diameter is equal to or smaller than that of the monomers. The nonmonotonic trend contradicts the so-called antipolyelectrolyte effect, which predicts an expansion of the polyampholyte brush upon the addition of salt. While the variation of the counterion size for the upper block generates a similar swelling behavior, the ion size has opposite effects on the degree of interblock association. These trends have been rationalized by considering the interplay of excluded-volume interactions with electrostatic and correlation effects. For both types of polyampholyte brushes, the salt effects become significantly more pronounced in the presence of divalent ions, with the alternating brush displaying a stronger dependence on the salt concentration.