DebyeHuckel

The Debye-Hückel potential models electrostatic interactions between charged particles in an electrolyte solution. It’s an approximation of the Poisson-Boltzmann equation, accounting for charge screening effects in ionic solutions.

\[U = \frac{q_i q_j}{4\pi\epsilon_0\epsilon_r} \frac{e^{-r/\lambda_D}}{r}\]

where:

  • \(q_i, q_j\) are the charges of the interacting particles

  • \(\epsilon_0\) is the vacuum permittivity

  • \(\epsilon_r\) is the relative permittivity of the medium

  • \(r\) is the distance between particles

  • \(\lambda_D\) is the Debye length, characterizing the screening effect

  • type: Bond2, DebyeHuckel

  • parameters: None

  • data:

    • id_i: int: Id of one particle

    • id_j: int: Id of the other particle

    • chgProduct: real: Product of charges \(q_i q_j\)

    • dielectricConstant: real: Dielectric constant of the medium \(\epsilon_r\)

    • debyeLength: real: Debye length \(\lambda_D\) \([distance]\)

    • cutOff: real: Cutoff distance for the interaction \([distance]\)

Example:

"debyeHuckelBonds":{
  "type":["Bond2","DebyeHuckel"],
  "parameters":{},
  "labels":["id_i", "id_j", "chgProduct", "dielectricConstant", "debyeLength", "cutOff"],
  "data":[[0, 1, -1.0, 78.5, 1.0, 10.0],
          [1, 2,  1.0, 78.5, 1.0, 10.0],
          [2, 3, -1.0, 78.5, 1.0, 10.0]]
}

Warning

In this potential, the charge product value is read from the potential data, and the charges of the particles are not used.