Effective potentials in polyelectrolyte solutions

Using Poisson-Boltzmann equation and linear response theory, we derive an effective interaction potential due to a fixed charge distribution in a solution containing polyelectrolytes and point salt. We obtain an expression for the effective potential in terms of static structure factor using the integral equation theories. To demonstrate the theory we apply it to Gaussian and rod-like polyelectrolytes and make connections to earlier theoretical works in some exact limits. We explore the role of both intra and inter polymer correlations, and the geometry of the polymers in the development of attractive regions in the effective potential as well as their effects on the screening lengths.