Self-consistent theory of structures and transitions in weak polyampholytes

Weak polyampholytes are charged polymers, where the charge asymmetry can be tuned by varying the solution pH. We determine the size of a randomly charged weak polyampholyte in dilute solution as a function of charge asymmetry, Bjerrum length, salt concentration, pH, and degree of polymerization, using a self-consistent method. It is known that in the limiting cases of low and high charge asymmetries, polyampholytes behave as neutral polyampholytes and polyelectrolytes, respectively. We explore in detail the regime of intermediate charge asymmetry where a polyampholyte show non-monotonic change in the chain size as a function of Bjerrum length. A hierarchy of structures exists at different length scales, ranging from ideal coils at low Bjerrum length, extended rod-like state at intermediate Bjerrum length to globular states at high Bjerrum length. The transition between ideal coil and rod-like states is continuous, while that between rod-like and globular states is discontinuous. The addition of salt changes the nature of the rod-to-globule transition from discontinuous to continuous. The effective free energy shows a double minimum at intermediate charge asymmetry, indicating the coexistence of globules and extended states. The size as a function of the solution pH shows a minimum at the isoelectric point. The size of neutral polyampholytes at the isoelectric pH increases with the increase in the salt concentration. The size of charge excess polyampholytes far away from the isoelectric pH decreases with the increase in the salt concentration. Using a self-consistent variational theory, the size of a weak polyampholyte is determined as a function of the solution pH, Bjerrum length and ionic strenth. The variation of size as a function of the solution pH shows that weak polyampholytes behave like polyelectrolytes at low and high pH, and as neutral polyampholytes at the isoelectric pH. Our results show good agreement with simulations and experiments on weak polyampholytes. © 2011 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.