Interaction Potentials

This package defines several potentials that can be used out of the box. It is straightforward to implement your own potential, see Defining your own potentials. To evaluate the potential, call OrnsteinZernike.evaluate_potential(potential, r). For example:

using OrnsteinZernike, Plots
r = 0.9:0.01:4.0
potential = LennardJones(1.0, 1.0)
u = OrnsteinZernike.evaluate_potential(potential, r)
plot(r, u, xlabel="r", ylabel="u(r)", ylims=(-1,1), label=nothing)
Example block output

Implemented interaction potentials

Below is a list of implemented closures. We use the notation shown in the Theory section.

OrnsteinZernike.CustomPotential — Type
CustomPotential

Implements a potential that evaluates a user defined function.

Expects values f, and p, which respecively are a callable and a list of parameters. The function should be called f(r::Number, p) and it should produce either a Number, in the case of a single-component system, or an SMatrix, in the case of a multicomponent system.

Example:

f = (r, p) -> 4*p[1]*((p[2]/r)^12 -  (p[2]/r)^6)
potential = CustomPotential(f, (1.0, 1.0))
source
OrnsteinZernike.HardSpheres — Type
HardSpheres

Implements the hard-sphere pair interaction for single component systems $ u(r) = \infty$ for $r < 1$ and $u(r) = 0$ for $r > 1$, or $u_{ij}(r) = \infty$ for $r < D_{ij}$ and $u_{ij}(r) = 0$ for $r > D_{ij}$ for mixtures.

For mixtures expects either a vector $D_i$ of diameters for each of the species in which case an additive mixing rule is used $\left(D_{ij} = (D_{i}+D_{j})/2\right)$ or a matrix $D_ij$ of pair diameters.

Example:

potential = HardSpheres(1.0)

Example:

potential = HardSpheres([0.8, 0.9, 1.0])
Dij = rand(3,3)
potential = HardSpheres(Dij)
source
OrnsteinZernike.LennardJones — Type
LennardJones

Implements the Lennard-Jones pair interaction $u(r) = 4\epsilon [(\sigma/r)^{12} - (\sigma/r)^6]$.

Expects values ϵ and σ, which respecively are the strength of the potential and particle size.

Example:

potential = LennardJones(1.0, 2.0)
source
OrnsteinZernike.PowerLaw — Type
PowerLaw

Implements the power law pair interaction $u(r) = \epsilon (\sigma/r)^{n}$.

Expects values ϵ, σ, and n, which respecively are the strength of the potential and particle size.

Example:

potential = PowerLaw(1.0, 2.0, 8)
source
OrnsteinZernike.WCADivision — Type
WCADivision{P<:Potential, T, UC}

fields

  • potential::Potential
  • cutoff : ($r_{c}$)
  • U_c : $U(r=r_c)$

Splits the potential at the cutoff point using the WCA splitting rule. This means

\[u(r) = u_{SR}(r) + U_{LR}(r),\]

where $U_{LR}(r) = u(r)$ for $r > r_{c}$, and $U(r_{c})$ for $r < r_{c}$, and $USR(r) = 0$ for $r > r_{c}$, and $U(r) - U(r_{c})$ for $r < r_{c}$.

source