WCA (Weeks-Chandler-Andersen)

The WCA potential is a shifted and truncated version of the Lennard-Jones potential, providing a purely repulsive interaction. It is often used to model excluded volume effects in soft matter systems.

There are three types of WCA potentials implemented:

WCAType1

\[\begin{split}U = \begin{cases} 4\epsilon \left[ \left(\frac{\sigma}{r}\right)^{12} - \left(\frac{\sigma}{r}\right)^6 \right] + \epsilon & \text{if } r < 2^{1/6}\sigma \\ 0 & \text{if } r \geq 2^{1/6}\sigma \end{cases}\end{split}\]

WCAType2

\[\begin{split}U = \begin{cases} \epsilon \left[ \left(\frac{\sigma}{r}\right)^{12} - 2\left(\frac{\sigma}{r}\right)^6 \right] + \epsilon & \text{if } r < \sigma \\ 0 & \text{if } r \geq \sigma \end{cases}\end{split}\]

WCAType3

\[\begin{split}U = \begin{cases} \epsilon \left[ 5\left(\frac{\sigma}{r}\right)^{12} - 6\left(\frac{\sigma}{r}\right)^{10} \right] + \epsilon & \text{if } r < \sigma \\ 0 & \text{if } r \geq \sigma \end{cases}\end{split}\]

For all types:

\(\epsilon\) is the strength of the interaction
\(\sigma\) is the characteristic distance
\(r\) is the distance between particles

type: NonBonded, WCAType1 (or WCAType2 or WCAType3)
parameters:
- cutOffFactor: real: Interaction range as a multiple of sigma (typically 1.122462048309373 for Type1 and Type2, 1.0747892746492746 for Type3)
data:
- name_i: string: Type of particle i
- name_j: string: Type of particle j
- epsilon: real: Interaction strength \([energy]\)
- sigma: real: Characteristic distance \([distance]\)

Example:

"wca":{
  "type":["NonBonded","WCAType1"],
  "parameters":{
    "cutOffFactor":1.5,
    "condition":"all"
  },
  "labels":["name_i", "name_j", "epsilon", "sigma"],
  "data":[
    ["A", "A", 1.0, 1.0],
    ["A", "B", 0.8, 0.9],
    ["B", "B", 1.2, 1.1]
  ]
}

Note

The WCA potential provides a continuous, purely repulsive interaction that is computationally efficient and widely used in molecular dynamics simulations of soft matter systems.