DebyeHückelPotenzial

DebyeHückelPotenzial refers to the electrostatic potential around a charged ion in an ionic solution, taking into account the screening effect of mobile ions. It arises from the Debye–Hückel theory, which treats the ionic atmosphere in a mean-field approach and leads to a screened or Yukawa-type potential rather than the unscreened Coulomb potential.

In a dilute electrolyte, the potential at a distance r from a fixed ion of charge q is described by

φ(r) = (q / (4π ε ε0 r)) exp(-κ r),

where ε is the relative permittivity of the solvent, ε0 the vacuum permittivity, and κ the inverse Debye length. The Debye length λD = 1/κ characterizes the distance over which the electrostatic field is effectively screened. The inverse Debye length κ is given by

κ^2 = (e^2 / (ε0 εr kB T)) ∑i ni zi^2,

where ni is the number density of ion species i, zi its valence, e the elementary charge, εr the solvent's relative permittivity, kB the Boltzmann constant, and T the temperature. An equivalent formulation in terms of ionic strength I is κ ≈ sqrt( (2 N_A e^2 I) / (ε0 εr kB T) ).

DebyeHückelPotenzial is valid under the linearized Poisson–Boltzmann framework, which requires low electrostatic potentials (roughly below kBT/e) and sufficiently dilute solutions. It provides a first-order description of screening in electrolytes and underpins interpretations of activity coefficients and interionic interactions in electrochemistry, colloid science, and biophysics. Limitations include high ionic strength, multivalent ions with strong correlations, and nonlinear effects beyond the Debye–Hückel approximation.