\(\renewcommand{\AA}{\text{Å}}\)

# angle_style mwlc command

## Syntax

    angle_style mwlc

## Examples

    angle_style mwlc
    angle_coeff * 25 1 10 1

## Description

Added in version 4Feb2025.

The mwlc angle style models a meltable wormlike chain and can be used to model non-linear bending elasticity of polymers, e.g. DNA. mwlc uses a potential that is a canonical-ensemble superposition of a non-melted and a melted state (Farrell). The potential is

\[E = -k_{B}T\,\log [q + q^{m}] + E_{0},\]

where the non-melted and melted partition functions are

\[\begin{split}q = \exp [-k_{1}(1+\cos{\theta})/k_{B}T]; \\ q^{m} = \exp [-(\mu+k_{2}(1+\cos{\theta}))/k_{B}T].\end{split}\]

\(k_1\) is the bending elastic constant of the non-melted state, \(k_2\) is the bending elastic constant of the melted state, \(\mu\) is the melting energy, and \(T\) is the reference temperature. The reference energy,

\[E_{0} = -k_{B}T\,\log [1 + \exp[-\mu/k_{B}T]],\]

ensures that E is zero for a fully extended chain.

This potential is a continuous version of the two-state potential introduced by (Yan).

The following coefficients must be defined for each angle type via the angle_coeff command as in the example above, or in the data file or restart files read by the read_data or read_restart commands:

- \(k_1\) (energy)

- \(k_2\) (energy)

- \(\mu\) (energy)

- \(T\) (temperature)

## Restrictions

This angle style can only be used if LAMMPS was built with the EXTRA-MOLECULE package. See the Build package doc page for more info.

## Related commands

angle_coeff

## Default

none

(Farrell) Farrell, Dobnikar, Podgornik, Curk, Phys Rev Lett, 133, 148101 (2024).

(Yan) Yan, Marko, Phys Rev Lett, 93, 108108 (2004).