# pair_style mesont/tpm command¶

## Syntax¶

pair_style mesont/tpm cut table_path BendingMode TPMType

• cut = the cutoff distance

• table_path = the path to the potential table

• BendingMode = the parameter defining the type of the bending potential for nanotubes: 0 - harmonic bending (Srivastava), 1 - anharmonic potential of bending and bending-buckling (Zhigilei1)

• TPMType = the parameter determining the type of the inter-tube interaction term: 0 - segment-segment approach, 1 - segment-chain approach (Zhigilei2, Zhigilei3)

The segment-segment approach is approximately 5 times slower than segment-chain approximation. The parameter BendingMode also affects the calculation of the inter-tube interaction term when TPMType = 1. In this case, when BendingMode = 1, each continuous chain of segments is additionally replaced by a number of sub-chains divided by bending buckling kinks.

## Examples¶

pair_style mesont/tpm 30.0 MESONT-TABTP_10_10.xrs 0 0


## Description¶

The tubular potential model (TPM) force field is designed for mesoscopic simulations of interacting flexible nanotubes. The force field is based on the mesoscopic computational model suggested in Ref. (Srivastava). In this model, each nanotube is represented by a chain of mesoscopic elements in the form of stretchable cylindrical segments, where each segment consists of multiple atoms. Each nanotube is divided into segments by a sequence of nodes placed on the nanotube centerline. This sequence of nodes determines the spatial position of the cylindrical segments and defines the configuration of the entire tube.

The potential force field that controls the dynamic behavior of a system of interacting nanotubes is given by the following equation defining the potential energy of the system:

$U = U_{str} + U_{bnd} + U_{vdW}$

where $$U_{str}$$ is the harmonic potential describing the stretching of nanotube (Srivastava), $$U_{bnd}$$ is the potential for nanotube bending (Srivastava) and bending-buckling (Zhigilei1), and $$U_{vdW}$$ is the potential describing van-der Waals interaction between nanotubes (Zhigilei2, Zhigilei3). The stretching energy, $$U_{str}$$ , is given by the sum of stretching energies of individual nanotube segments. The bending energy, $$U_{bnd}$$ , is given by the sum of bending energies in all internal nanotube nodes. The tube-tube interaction energy, $$U_{vdW}$$ , is calculated based on the tubular potential method suggested in Ref. (Zhigilei2). The tubular potential method is briefly described below.

The interaction between two straight nanotubes of arbitrary length and orientation is described by the approximate tubular potential developed in (Zhigilei3). This potential approximates the results of direct integration of carbon-carbon interatomic potential over the surfaces of the interacting nanotubes, with the force sources homogeneously distributed over the nanotube surfaces. The input data for calculation of tubular potentials are partially tabulated. For single-walled CNTs of arbitrary chirality, the tabulated potential data can be generated in the form of ASCII files TPMSSTP.xrs and TPMA.xrs by the stand-alone code TMDPotGen included in the tool directory of LAMMPS release. The potential provided with LAMMPS release, MESONT-TABTP_10_10.xrs, is tabulated for (10,10) nanotubes.

Calculations of the interaction between curved or bent nanotubes are performed on either segment-segment or segment-chain basis. In the first case, activated when parameter TPMType is equal to 0, the tubular potential is calculated for each pair of interacting mesoscopic segments. In this case, however, small potential barriers for inter-tube sliding are introduced. While relatively small, these barriers are still larger than the ones that originate from the atomic-scale corrugation in atomistic modeling of inter-tube interaction. The latter are too weak to prevent room-temperature rearrangements of defect-free CNT, while the artificial mesoscopic barriers due to the segment-segment interaction can impede sliding of nanotubes with respect to each other and affect the kinetics of structural rearrangements in a system of nanotubes at moderate mesoscopic temperatures. In the second case, activated when parameter TPMType is equal to 1, the inter-tube interaction term is calculated based on the segment-chain approach. In this case, for each NT segment, the list of its neighboring segments is divided into short continuous chains of segments belonging to individual nanotubes. For each pair of a segment and a chain, the curved chain is approximated by a straight equivalent nanotube based on the weighted approach suggested in Ref. (Zhigilei2). Finally, the interaction between the segment and straight equivalent chain is calculated based on the tubular potential. In this case, and in the absence of bending buckling (i.e., when parameter BendingMode is equal to 0), the tubular potential method ensures the absence of corrugation of the effective inter-tube interaction potential for curved nanotubes and eliminates any barriers for the inter-tube sliding. As a result, the tubular potential method can describe the spontaneous self-assembly of nanotubes into continuous networks of bundles (Zhigilei1, Zhigilei3).

The TMD force field has been used for generation of nanotube films, fibers, and vertically aligned forests of nanotubes. Mesoscopic dynamic simulations were used to prepare realistic structures of continuous networks of nanotube bundles and to study their structural and mechanical properties (Zhigilei1, Zhigilei3, Zhigilei4, Zhigilei5, Zhigilei6). With additional models for heat transfer, this force filed was also used to study the thermal transport properties of carbon nanotube films (Zhigilei7, Zhigilei8, Zhigilei8). The methods for modeling of the mechanical energy dissipation into heat (energy exchange between the dynamic degrees of freedom of the mesoscopic model and the energy of atomic vibrations that are not explicitly represented in the model) (Zhigilei10) and mesoscopic description of covalent cross-links between nanotubes (Banna) have also been developed but are not included in this first release of the LAMMPS implementation of the force field. Further details can be found in references provided below.

The MESONT package also provides TMDGen code designed to generate initial samples composed of straight and dispersed nanotubes of given chirality and length at a given material density, which is available in tools directory. In the generated samples, nanotubes are distributed with random positions and orientations. Both periodic and free boundary conditions are available along each axis of the system of coordinates. All parameters in the sample files generated with TMDGen are given in metal units.

## Restrictions¶

This pair style is a part of the MSEONT package, and it is only enabled if LAMMPS is built with that package. See the Build package doc page for more information.

This pair potential requires use of mesont atomic style.

This pair potential requires the newton setting to be “on” for pair interactions.

The cutoff distance should be set to be at least $$max\left[2L,\sqrt{L^2/2+(2R+T_{cut})^2}\right]$$ , where L is the maximum segment length, R is the maximum tube radius, and $$T_{cut}$$ = 10.2 A is the maximum distance between the surfaces of interacting segments. Because of the use of extended chain concept at CNT ends, the recommended cutoff is 3L.

Note

Because of their size, mesont style potential files are not bundled with LAMMPS. When compiling LAMMPS from source code, the file TABTP_10_10.mesont should be downloaded transparently from https://download.lammps.org/potentials/TABTP_10_10.mesont

The TABTP_10_10.mesont potential file is parameterized for metal units. You can use the carbon nanotube mesoscopic force field with any LAMMPS units, but you would need to create your own potential files with coefficients listed in appropriate units, if your simulation does not use “metal” units.

The chirality parameters set during system generation must match the values specified during generation of the potential tables.