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