\(\renewcommand{\AA}{\text{Å}}\)

# angle_style mesocnt command

## Syntax

    angle_style mesocnt

## Examples

    angle_style mesocnt
    angle_coeff 1 buckling C 10 10 20.0
    angle_coeff 4 harmonic C 8 4 10.0
    angle_coeff 2 buckling custom 400.0 50.0 5.0
    angle_coeff 1 harmonic custom 300.0

## Description

Added in version 15Sep2022.

The mesocnt angle style uses the potential

\[\begin{split}E = K_\text{H} \Delta \theta^2, \qquad |\Delta \theta| < \Delta \theta_\text{B} \\ E = K_\text{H} \Delta \theta_\text{B}^2 + K_\text{B} (\Delta \theta - \Delta \theta_\text{B}), \qquad |\Delta \theta| \geq \Delta \theta_\text{B}\end{split}\]

where \(\Delta \theta = \theta - \pi\) is the bending angle of the nanotube, \(K_\text{H}\) and \(K_\text{B}\) are prefactors for the harmonic and linear regime respectively and \(\Delta \theta_\text{B}\) is the buckling angle. Note that the usual 1/2 factor for the harmonic potential is included in \(K_\text{H}\).

The style implements parameterization presets of \(K_\text{H}\), \(K_\text{B}\) and \(\Delta \theta_\text{B}\) for mesoscopic simulations of carbon nanotubes based on the atomistic simulations of (Srivastava) and buckling considerations of (Zhigilei).

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

- mode = buckling or harmonic

- preset = C or custom

- additional parameters depending on preset

If mode harmonic is chosen, the potential is simply harmonic and does not switch to the linear term when the buckling angle is reached. In buckling mode, the full piecewise potential is used.

Preset C is for carbon nanotubes, and the additional parameters are:

- chiral index \(n\) (unitless)

- chiral index \(m\) (unitless)

- \(r_0\) (distance)

Here, \(r_0\) is the equilibrium distance of the bonds included in the angle, see bond_style mesocnt.

In harmonic mode with preset custom, the additional parameter is:

- \(K_\text{H}\) (energy)

Hence, this setting is simply a wrapper for bond_style harmonic with an equilibrium angle of 180 degrees.

In harmonic mode with preset custom, the additional parameters are:

- \(K_\text{H}\) (energy)

- \(K_\text{B}\) (energy)

- \(\Delta \theta_\text{B}\) (degrees)

\(\Delta \theta_\text{B}\) is specified in degrees, but LAMMPS converts it to radians internally; hence \(K_\text{H}\) is effectively energy per radian^2 and \(K_\text{B}\) is energy per radian.

In buckling mode, this angle style adds the buckled property to all atoms in the simulation, which is an integer flag indicating whether the bending angle at a given atom has exceeded \(\Delta \theta_\text{B}\). It can be accessed as an atomic variable, e.g. for custom dump commands, as i_buckled.

Note

If the initial state of the simulation contains buckled nanotubes and pair_style mesocnt is used, the i_buckled atomic variable needs to be initialized before the pair_style is defined by doing a run 0 command straight after the angle_style command. See below for an example.

If CNTs are already buckled at the start of the simulation, this script will correctly initialize i_buckled:

    angle_style mesocnt
    angle_coeff 1 buckling C 10 10 20.0

    run 0

    pair_style mesocnt 60.0
    pair_coeff * * C_10_10.mesocnt 1

## Restrictions

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

## Related commands

angle_coeff

## Default

none

(Srivastava) Zhigilei, Wei, Srivastava, Phys. Rev. B 71, 165417 (2005).

(Zhigilei) Volkov and Zhigilei, ACS Nano 4, 6187 (2010).