azplugins.wall

Overview

Colloid

Colloid wall potential.

LJ93

Lennard-Jones 9-3 wall potential.

Details

Wall potentials.

class hoomd.azplugins.wall.Colloid(walls)

Bases: WallPotential

Colloid wall potential.

Parameters:

walls (list [hoomd.wall.WallGeometry]) – A list of wall definitions.

Colloid is Lennard-Jones colloid wall potential, which is derived from integrating the standard Lennard-Jones potential between a spherical particle of radius \(a\) and a half plane:

\[U(r) = \frac{A \sigma^6}{7560} \left[\frac{7a-r}{(r-a)^7} + \frac{7a+r}{(r+a)^7} \right] - \frac{A}{6} \left[\frac{2ar}{r^2-a^2} + \ln\left(\frac{z-a}{z+a}\right) \right]\]

where:

  • \(\sigma\) - diameter of Lennard-Jones particles in the sphere and the wall

  • \(A\) - Hamaker constant, related to the Lennard-Jones parameters as

    \(A = 4 \pi^2 \varepsilon \sigma^6 \rho_{\rm w} \rho_{\rm c}\), where \(\rho_{\rm w}\) is the number density of particles in the wall, \(\rho_{\rm c}\) is the number density of particles in the sphere, and \(\varepsilon\) is the Lennard-Jones energy parameter.

Example:

walls = [hoomd.wall.Plane(origin=(0, 0, 0), normal=(0, 1, 0))]
colloid = azplugins.wall.Colloid(walls=walls)
colloid.params["A"] = dict(
    A=4 * numpy.pi ** 2,  # rho = 1, epsilon = 1, sigma = 1
    a=1.0
    sigma=1.0,
    r_cut=3.0,
)
params

The Colloid potential parameters. The dictionary has the following keys:

  • A (float, required) - Hamaker constant \(A\) \([\mathrm{energy}]\)

  • a (float, required) - Radius of particle \(a\) \([\mathrm{length}]\)

  • sigma (float, required) - Lennard-Jones particle size \(\sigma\) \([\mathrm{length}]\)

  • r_cut (float, required) - The cut off distance for the wall potential \([\mathrm{length}]\)

  • r_extrap (float, optional) - The distance to extrapolate the potential, defaults to 0. \([\mathrm{length}]\).

Type: TypeParameter [particle_type], dict]

class hoomd.azplugins.wall.LJ93(walls)

Bases: WallPotential

Lennard-Jones 9-3 wall potential.

Parameters:

walls (list [hoomd.wall.WallGeometry]) – A list of wall definitions.

LJ93 is Lennard-Jones 9-3 wall potential, which is derived from integrating the standard Lennard-Jones potential between a point particle and a half plane:

\[U(r) = A \left[\frac{2}{15} \left(\frac{\sigma}{r} \right)^9 - \left(\frac{\sigma}{r}\right)^3 \right]\]

where:

  • \(\sigma\) - diameter of Lennard-Jones particles in the wall

  • \(A\) - Hamaker constant, related to the Lennard-Jones parameters as

    \(A = \frac{2}{3} \pi \varepsilon \sigma^3 \rho\), where \(\rho\) is the number density of particles in the wall and \(\varepsilon\) is the Lennard-Jones energy parameter.

Example:

walls = [hoomd.wall.Plane(origin=(0, 0, 0), normal=(0, 1, 0))]
lj93 = azplugins.wall.LJ93(walls=walls)
lj93.params["A"] = dict(
    sigma=1.0,
    A=2 * numpy.pi / 3,  # rho = 1, epsilon = 1, sigma = 1
    r_cut=3.0,
)
params

The LJ93 potential parameters. The dictionary has the following keys:

  • A (float, required) - Hamaker constant \(A\) \([\mathrm{energy}]\)

  • sigma (float, required) - Lennard-Jones particle size \(\sigma\) \([\mathrm{length}]\)

  • r_cut (float, required) - The cut off distance for the wall potential \([\mathrm{length}]\)

  • r_extrap (float, optional) - The distance to extrapolate the potential, defaults to 0. \([\mathrm{length}]\).

Type: TypeParameter [particle_type], dict]