Polyelectrolytes in salt solutions: Molecular dynamics simulations

We present results of the molecular dynamics simulations of salt solutions of polyelectrolyte chains with number of monomers N = 300. Polyelectrolyte solutions are modeled as an ensemble of bead-spring chains of charged Lennard-Jones particles with explicit counterions and salt ions. Our simulations show that in dilute and semidilute polyelectrolyte solutions the electrostatic induced chain persistence length scales with the solution ionic strength as I^-1/2. This dependence of the chain persistence length is due to counterion condensation on the polymer backbone. In dilute polyelectrolyte solutions the chain size decreases with increasing the salt concentration as R ∝ I^-1/5. This is in agreement with the scaling of the chain persistence length on the solution ionic strength, l_p ∝ I ^-1/2. In semidilute solution regime at low salt concentrations the chain size decreases with increasing polymer concentration, R ∝ cp ^-1/4, while at high salt concentrations we observed a weaker dependence of the chain size on the solution ionic strength, R ∝ I ^-1/8. Our simulations also confirmed that the peak position in the polymer scattering function scales with the polymer concentration in dilute polyelectrolyte solutions as cp^1/3. In semidilute polyelectrolyte solutions at low salt concentrations the location of the peak in the scattering function shifts toward the large values of q* ∝ cp^1/2 while at high salt concentrations the peak location depends on the solution ionic strength as I^-1/4. Analysis of the simulation data throughout the studied salt and polymer concentration ranges shows that there exist general scaling relations between multiple quantities X(I) in salt solutions and corresponding quantities X(I₀) in salt-free solutions, X(I) = X(I₀)(I/I₀)^β. The exponent β =-1/2 for chain persistence length l_p, β = 1/4 for solution correlation length Ξ, and β =-1/5 and β =-1/8 for chain size R in dilute and semidilute solution regimes, respectively.