Applying a generic and fast coarse-grained molecular dynamics model to extensively study the mechanical behavior of polymer nanocomposites: supplementary information and dataset

Abstract:
(from [1])

The addition of nano-sized filler particles enhances the mechanical performance of polymers. The resulting properties of the polymer nanocomposite depend on a complex interplay of influence factors such as material pairing, filler size, and content as well as filler-matrix adhesion. As a complement to experimental studies, numerical methods, such as molecular dynamics (MD), facilitate an isolated examination of the individual factors in order to understand their interaction better. However, particle-based simulations are, in general, computationally very expensive, rendering a thorough investigation of nanocomposites’ mechanical behavior both expensive and time-consuming. Therefore, this paper presents a fast coarse-grained MD model for a generic nanoparticle-reinforced thermoplastic. First, we examine the matrix and filler phase individually, which exhibit isotropic elasto-viscoplastic and anisotropic elastic behavior, respectively. Based on this, we demonstrate that the effect of filler size, filler content, and filler-matrix adhesion on the stiffness and strength of the nanocomposite corresponds very well with experimental findings in the literature. Consequently, the presented computationally efficient MD model enables the analysis of a generic polymer nanocomposite. In addition to the obtained insights into the mechanical behavior, the material characterization provides the basis for a future continuum mechanical description, which bridges the gap to the engineering scale. 

Contact:

Maximilian Ries
Institute of Applied Mechanics
Friedrich-Alexander-Universität Erlangen-Nürnberg
Egerlandstr. 5
91058 Erlangen

Software:

All MD simulations were performed with LAMMPS [2], version: 29 Oct 2020 / 20201029

Compiled with
Compiler: GNU C++ 4.8.5 20150623 (Red Hat 4.8.5-39) with OpenMP not enabled
C++ standard: C++11

Active compile time flags:
-DLAMMPS_GZIP
-DLAMMPS_SMALLBIG

Installed packages:
CLASS2, KSPACE, MANYBODY, MC, MOLECULE, MPIIO, OPT, VORONOI, USER-INTEL, USER-MISC, USER-MOLFILE, USER-NETCD

Polymer and polymer composite samples generated with self-avoiding random-walk algorithm [3]

Post-processing Matlab R2019b

Evaluation of polymer entanglements with Z1-Algorithm [4]

License:

Creative Commons Attribution 4.0 International

Context:

Data set supplementing  journal paper:

[1] M. Ries, J. Seibert, P. Steinmann, S. Pfaller. “Applying a generic and fast coarse-grained molecular dynamics model to extensively study the mechanical behavior of polymer nanocomposites”, Express Polymer Letters, 2022, 16.

This dataset contains the results presented in [1] and the necessary data to obtain those as well as supplementary information.

Content:

supplementary material:

supplementary_information.pdf

data:
    folder names vary depending on the context, explained in the following:

01_matrix

• 01_equilibration
  sample equilibration to different temperatures
  nomenclature: equil_<chains>-<chain_atoms>-box_<initial_box_length>-min_<SARW_distance>-angle_<SARW_angle>-T_<final_temperature>[-<batch_ID>]

  • chains: 200

  • chain_atoms: 200

  • initial_box_length: 100

  • SARW_distance: 0.9

  • SARW_angle: 50

  • final_temperature: 0.1-1.0

  • batch_ID: 2-5 

• 02_temperature_dependence
  uniaxial tension simulations to identify temperature dependence
  nomenclature: 01_UT_<chains>-<chain_atoms>-box_<initial_box_length>-min_<SARW_distance>-angle_<SARW_angle>-T_<final_temperature>

  • chains: 200

  • chain_atoms: 200

  • initial_box_length: 100

  • SARW_distance: 0.9

  • SARW_angle: 50

  • final_temperature: 0.1-1.0

• 03_directional_dependence
  uniaxial tension simulations to prove isotropy in Y and Z direction; X direction in 04_rate_dependence
  nomenclature: 03_UT_<chains>-<chain_atoms>-box_<initial_box_length>-min_<SARW_distance>-angle_<SARW_angle>-T_<final_temperature>-rate_<strain_rate>-<batchID>

  • chains: 200

  • chain_atoms: 200

  • initial_box_length: 100

  • SARW_distance: 0.9

  • SARW_angle: 50

  • final_temperature: 0.3

  • strain_rate: 5E-5

  • batchID: 1-5

• 04_rate_dependence
  uniaxial tension simulations to identify strain rate dependence
  nomenclature: 03_UT_<chains>-<chain_atoms>-box_<initial_box_length>-min_<SARW_distance>-angle_<SARW_angle>-T_<final_temperature>-rate_<strain_rate>[-<batchID>]

  • chains: 200

  • chain_atoms: 200

  • initial_box_length: 100

  • SARW_distance: 0.9

  • SARW_angle: 50

  • final_temperature: 0.3

  • strain_rate: 5E-4, 5E-5, 5E-6

  • batchID: 1-5

• 05_cyclic_loading
  sinusoidal uniaxial deformation
  nomenclature: 05_UT_<chains>-<chain_atoms>-box_<initial_box_length>-min_<SARW_distance>-angle_<SARW_angle>-T_<final_temperature>-rate_<strain_rate>-sin_<strain_amplitude>

  • chains: 200

  • chain_atoms: 200

  • initial_box_length: 100

  • SARW_distance: 0.9

  • SARW_angle: 50

  • final_temperature: 0.3

  • strain_rate: 5E-4

  • strain_amplitude: 0.01, 0.05, 0.15, 0.2

• 06_relaxation
  relaxation subsequent to time-proportional deformation
  nomenclature: 07_UT_<chains>-<chain_atoms>-box_<initial_box_length>-min_<SARW_distance>-angle_<SARW_angle>-T_<final_temperature>-rate_<strain_rate>-sin_<strain_amplitude>_relax

  • chains: 200

  • chain_atoms: 200

  • initial_box_length: 100

  • SARW_distance: 0.9

  • SARW_angle: 50

  • final_temperature: 0.3

  • strain_rate: 5E-4

  • strain_amplitude: 0.01, 0.05, 0.15, 0.2

• 07_simple_shear
  time-proportional simple shear deformation with different strain rates
  nomenclature: SS_P2VPSi-rate_<strain_rate>-<batchID>

  • strain_rate: 5E-4, 5E-5, 5E-6

  • batchID: 1-5

• 08_large_deformation
  uniaxial deformation up to 100% strain
  nomenclature: 02_UT_<chains>-<chain_atoms>-box_<initial_box_length>-min_<SARW_distance>-angle_<SARW_angle>-T_<final_temperatur>-strain_<max_strain>

  • chains: 200

  • chain_atoms: 200

  • initial_box_length: 100

  • SARW_distance: 0.9

  • SARW_angle: 50

  • final_temperature: 0.3

  • max_strain: 1

02_filler

• 01_Silica_equilibration
  sample equilibration

• 02_time_proportional
  time-proportional uniaxial and simple shear tests
  nomenclature: Silica_BV-<loadcase>_<direction>-strain_<max_strain>-rate_<strain_rate>

  • loadcase: uniaxial tension (UT), simple shear (SS)

  • max_strain: 0.1

  • direction: X, Y, Z (UT); XY, XZ, YZ (SS)

  • strain_rate: 5E-4, 5E-5, 5E-6

• 03_time_periodic
  time-periodic uniaxial and simple shear tests
  nomenclature: Silica_BV-<loadcase>_<direction>_sin-ampl_<strain_amplitude>-rate_<max_strain_rate>

  • loadcase: uniaxial tension (UT), simple shear (SS)

  • direction: X, Y, Z (UT); XY, XZ, YZ (SS)

  • strain_amplitude: 0.025

03_composite

• 01_equilibration
  sample equilibration
  nomenclature: equil_P2VPSi-rNP_<filler_radius>-nNP_<filler_number>-<batchID>

  • filler_radius: 2.5-10.0

  • filler_number: 1-160 (depending on filler_radius)

  • batchID: 1-5

• 02_uniaxial-tension
  uniaxial tension simulations
  nomenclature: UT_P2VPSi-rNP_<filler_radius>-nNP_<filler_number>-<batchID>

  • filler_radius: 2.5-10.0

  • filler_number: 1-160 (depending on filler_radius)

  • batchID: 1-5

• 03_filler-maxtrix-adhesion
  equilibration and uniaxial deformation of samples with mid and weak filler-matrix adhesion (for strong adhesion see 01_equilibration and 02_uniaxial-tension
  nomenclature: see above

• 04_IP_equilibration
  equilibration of samples to evaluate the microstructure for neat polymer and composites with filler radius 2.5-7.5
  nomenclature: P2VPSi-<chains>x<chain_atoms>_rNP_<filler_radius>-nNP_<filler_number>_pos_<filler_pos>-<batchID>

  • chains: 200

  • chain_atoms: 200

  • filler_radius: 0 (neat), 2.5, 5.0, 7.5

  • filler_number: 0 (neat), 1

  • batchID: 1-20

Each simulation directory contains:

• lammps input file (*.in) of the specific simulation

• data file (*.data) containing the initial sample configuration

• input.prm: input parameters of the specific simulation (read by the input file)

• meta.info: meta data of the specific simulation run

• LAMMPS_out:
  simulation results (lammps thermo_out) in tabulated form, an overview of columns is given below

  • thermo_out.Dat: raw output 

  • thermo_out_SG.Dat: smoothed output (Savitzky-Golay filter)

  • thermo_out_STD.Dat: standard deviation of raw output

Output quantities (columns of *.Dat files):
Please note that the normalized Lennard-Jones unit set is used, so all quantities are normalized to fundamental mass, length, energy, time and the Boltzmann constant. Thus all entries are unitless [1].

• Step: time step 

• Time: time 

• TotEng: total energy 

• PotEng: potential energy

• KinEng: kinetic energy 

• E_pair: pair energy 

• E_bond: bond energy 

• E_angle: angle energy 

• E_dihed: dihedral energy 

• Temp: temperature

• Press: hydrostatic pressure

• Pxx: xx component of pressure tensor 

• Pyy: yy component of pressure tensor 

• Pzz: zz component of pressure tensor 

• Pxy: xy component of pressure tensor

• Pxz: xz component of pressure tensor

• Pyz: yz component of pressure tensor

• Volume: volume of simulation box 

• Lx: box length in x direction  

• Ly: box length in y direction  

• Lz: box length in z direction  

• Density: density  

• c_RG: radius of gyration scalar 

• c_RG[1]: squared radius of gyration tensor (xx component)  

• c_RG[2]: squared radius of gyration tensor (yy component)  

• c_RG[3]: squared radius of gyration tensor (zz component)  

• c_RG[4]: squared radius of gyration tensor (xy component)  

• c_RG[5]: squared radius of gyration tensor (xz component)  

• c_RG[6]: squared radius of gyration tensor (yz component)  

• c_bondave[1]: bond energy averaged over all atoms  

• c_bondave[2]: bond distance averaged over all atoms  

• c_bondave[3]: squared bond distance averaged over all atoms  

• c_angleave[1]: angle energy averaged over all atoms  

• c_angleave[2]: angle averaged over all atoms degree

• c_angleave[3]: cosine of angle 

• c_angleave[4]: squared cosine of angle 

• c_MSD[1]: mean squared displacement x-direction  

• c_MSD[2]: mean squared displacement y-direction  

• c_MSD[3]: mean squared displacement z-direction  

• c_MSD[4]: total mean squared displacement  

• c_COM[1]: x coordinate of center of mass  

• c_COM[2]: y coordinate of center of mass  

• c_COM[3]: z coordinate of center of mass  

• v_strain_xx: xx component of engineering strain tensor   

• v_strain_yy: yy component of engineering strain tensor    

• v_strain_zz: zz component of engineering strain tensor    

• v_vMisesequivstress: von Mises equivalent stress 

• v_Cauchy_xx: xx component of stress tensor  

• v_Cauchy_yy: yy component of stress tensor

• v_Cauchy_zz: zz component of stress tensor

• v_Cauchy_xy: xy component of stress tensor 

• v_Cauchy_xz: xz component of stress tensor 

• v_Cauchy_yz: yz component of stress tensor 

• v_strain_xy: xy component of engineering strain tensor   

• v_strain_xz: xz component of engineering strain tensor   

• v_strain_yz: yz component of engineering strain tensor   

References:

[1] M. Ries, J. Seibert, P. Steinmann, S. Pfaller. “Applying a generic and fast coarse-grained molecular dynamics model to extensively study the mechanical behavior of polymer nanocomposites”, Express Polymer Letters, 2022, 16.

[2] S. Plimpton, “Fast parallel algorithms for short-range molecular dynamics,” Journal of computational physics, 1995, 117, 1-19.

[3] A. P. Thompson et al., “LAMMPS - a flexible simulation tool for particle-based materials modeling at the atomic, meso, and continuum scales,” Computer Physics Communications, vol. 271, p. 108171, 2022.

[4] M. Ries, V. Dötschel, J. Seibert, S. Pfaller. “A self-avoiding random walk algorithm (SARW) for generic thermoplastic polymers and nanocomposites”, Zenodo, 2022. https://doi.org/10.5281/zenodo.6245699