Electric potential and bending rigidity of a wormlike particle in electrolyte solution

Using the linearized Poisson-Boltzmann equation (LPB) we derive an asymptotic expansion for the electrostatic potential of charged torus immersed in solution of an electrolyte in the limit of high salinity and large major radius of the torus. The small parameter of this expansion is the ratio of the Debye length to the minor radius of the torus. We derive asymptotic expressions for the electrostatic free energy and for the electrostatic persistence length of a polyion of a finite thickness. We propose a simple interpolation formula, xi(el)=l(B)(sigma(0)/e)(2)bkappa(D)[1+kappa(D)/(4b)], that gives the electrostatic persistence length in terms of the Debye length kappa(D), the linear charge density (sigma(0)/e), and the thickness of the polyion, 2b. This formula reproduces the exact results from the LPB theory in the limits of high and low salt concentrations. For the entire range of salinities, our formula is in excellent agreement with the numerical LPB results for wormlike particles of varying thickness. For particles of vanishing thickness, this formula reduces to the classical Odijk-Skolnick-Fixman expression.