A multiple decay-length extension of the Debye–Hückel theory: to achieve high accuracy also for concentrated solutions and explain under-screening in dilute symmetric electrolytes
The Poisson–Boltzmann and Debye–Hückel approximations for the pair distributions and mean electrostatic potential in electrolytes predict that these entities have one single decay mode with a decay length equal to the Debye length 1/κD, that is, they have a characteristic contribution that decays with distance r like e−κDr/r. However, in reality, electrolytes have several decay modes e−κr/r, e−κ′r/r etc. with different decay lengths, 1/κ, 1/κ′ etc., that in general are different from the Debye length. As an illustration of the significance of multiple decay modes in electrolytes, the present work uses a very simple extension of the Debye–Hückel approximation with two decay lengths, which predicts oscillatory modes when appropriate. This approach gives very accurate results for radial distribution functions and thermodynamic properties of aqueous solutions of monovalent electrolytes for all concentrations investigated, including high ones. It is designed to satisfy necessary statistical mechanical conditions for the distributions. The effective dielectric permittivity of the electrolyte plays an important role in the theory and each mode has its own value of this entity. Electrolytes with high electrostatic coupling, like those with multivalent ions and/or with solvent of low dielectric constant, have decay lengths in dilute solutions that substantially deviate from the Debye length. It is shown that this is caused by nonlinear ion–ion correlation effects and the origin of under-screening, i.e., 1/κ > 1/κD, in dilute symmetric electrolytes is analyzed. The under-screening is accompanied by an increase in the effective dielectric permittivity that is also caused by these correlations. The theoretical results for the decay length are successfully compared with recent experimental data for simple electrolytes in various solvents. The paper includes background material on electrolyte theory and screening in order to be accessible for nonexperts in the field.