Department of Chemistry, St. Petersburg State University, Universitetsky prospect 26, 198504 St. Petersburg, Russia.
J Chem Phys. 2010 Feb 7;132(5):054902. doi: 10.1063/1.3298991.
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.
我们使用线性化泊松-玻尔兹曼方程（LPB），在高盐度和大环径的极限下，推导出了带电圆环在电解质溶液中的静电势的渐近展开式。这个展开式的小参数是德拜长度与圆环小半径的比值。我们推导出了有限厚度聚离子的静电自由能和静电持久长度的渐近表达式。我们提出了一个简单的插值公式，xi(el)=l(B)(sigma(0)/e)(2)bkappa(D)[1+kappa(D)/(4b)]，它用德拜长度 kappa(D)、线性电荷密度 (sigma(0)/e)和聚离子的厚度 2b 来表示静电持久长度。这个公式在高盐和低盐浓度的极限下再现了 LPB 理论的精确结果。对于整个盐度范围，我们的公式与不同厚度的蠕虫状粒子的数值 LPB 结果非常吻合。对于厚度为零的粒子，这个公式简化为经典的 Odijk-Skolnick-Fixman 表达式。
