Excess chemical potential of dilute solutions of spherical polyelectrolytes

Abstract

The excess chemical potential of a dilute solution of spherical polyelectrolytes is calculated in the limit of the linear Debye-Hückel theory. The charge distribution within each polyelectrolyte is expanded in terms of its spherical harmonics. The calculation includes the effect of the finite radius of both of a pair of polyelectrolytes on the screening of their electostatic interactions. It is found that the term in the excess chemical potential of a minimum-salt protein solution that depends on the square root of the protein concentration arises from fluctuations in the net charge of each protein molecule. Fluctuations in the dipole moment of each protein molecule give rise to a term linearly proportional to the protein concentration. Interactions among the net charges Ze of protein molecules in a minimum-salt solution give rise to a concentration-independent term in the chemical potential of the form KT|Z̄|.