DOI: 10.5281/zenodo.6245700
title: Applying a generic and fast coarse-grained molecular dynamics model to extensively study the mechanical behavior of polymer nanocomposites: supplementary information and dataset

description: <strong>Abstract:</strong><br> (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. <strong>Contact:</strong> Maximilian Ries<br> Institute of Applied Mechanics<br> Friedrich-Alexander-Universität Erlangen-Nürnberg<br> Egerlandstr. 5<br> 91058 Erlangen <strong>Software:</strong> All MD simulations were performed with LAMMPS [2], version: 29 Oct 2020 / 20201029 Compiled with<br> Compiler: GNU C++ 4.8.5 20150623 (Red Hat 4.8.5-39) with OpenMP not enabled<br> C++ standard: C++11 Active compile time flags:<br> -DLAMMPS_GZIP<br> -DLAMMPS_SMALLBIG Installed packages<strong>:</strong><br> 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] <strong>License:</strong> Creative Commons Attribution 4.0 International <strong>Context:</strong> 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, <strong>2022</strong>, 16. This dataset contains the results presented in [1] and the necessary data to obtain those as well as supplementary information. <strong>Content:</strong> supplementary material: supplementary_information.pdf data:<br> folder names vary depending on the context, explained in the following: 01_matrix 01_equilibration<br> sample equilibration to different temperatures<br> nomenclature: equil_&lt;chains&gt;-&lt;chain_atoms&gt;-box_&lt;initial_box_length&gt;-min_&lt;SARW_distance&gt;-angle_&lt;SARW_angle&gt;-T_&lt;final_temperature&gt;[-&lt;batch_ID&gt;] 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<br> uniaxial tension simulations to identify temperature dependence<br> nomenclature: 01_UT_&lt;chains&gt;-&lt;chain_atoms&gt;-box_&lt;initial_box_length&gt;-min_&lt;SARW_distance&gt;-angle_&lt;SARW_angle&gt;-T_&lt;final_temperature&gt; 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<br> uniaxial tension simulations to prove isotropy in Y and Z direction; X direction in 04_rate_dependence<br> nomenclature: 03_UT_&lt;chains&gt;-&lt;chain_atoms&gt;-box_&lt;initial_box_length&gt;-min_&lt;SARW_distance&gt;-angle_&lt;SARW_angle&gt;-T_&lt;final_temperature&gt;-rate_&lt;strain_rate&gt;-&lt;batchID&gt; 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<br> uniaxial tension simulations to identify strain rate dependence<br> nomenclature: 03_UT_&lt;chains&gt;-&lt;chain_atoms&gt;-box_&lt;initial_box_length&gt;-min_&lt;SARW_distance&gt;-angle_&lt;SARW_angle&gt;-T_&lt;final_temperature&gt;-rate_&lt;strain_rate&gt;[-&lt;batchID&gt;] 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<br> sinusoidal uniaxial deformation<br> nomenclature: 05_UT_&lt;chains&gt;-&lt;chain_atoms&gt;-box_&lt;initial_box_length&gt;-min_&lt;SARW_distance&gt;-angle_&lt;SARW_angle&gt;-T_&lt;final_temperature&gt;-rate_&lt;strain_rate&gt;-sin_&lt;strain_amplitude&gt; 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<br> relaxation subsequent to time-proportional deformation<br> nomenclature: 07_UT_&lt;chains&gt;-&lt;chain_atoms&gt;-box_&lt;initial_box_length&gt;-min_&lt;SARW_distance&gt;-angle_&lt;SARW_angle&gt;-T_&lt;final_temperature&gt;-rate_&lt;strain_rate&gt;-sin_&lt;strain_amplitude&gt;_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<br> time-proportional simple shear deformation with different strain rates<br> nomenclature: SS_P2VPSi-rate_&lt;strain_rate&gt;-&lt;batchID&gt; strain_rate: 5E-4, 5E-5, 5E-6 batchID: 1-5 08_large_deformation<br> uniaxial deformation up to 100% strain<br> nomenclature: 02_UT_&lt;chains&gt;-&lt;chain_atoms&gt;-box_&lt;initial_box_length&gt;-min_&lt;SARW_distance&gt;-angle_&lt;SARW_angle&gt;-T_&lt;final_temperatur&gt;-strain_&lt;max_strain&gt; 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<br> sample equilibration 02_time_proportional<br> time-proportional uniaxial and simple shear tests<br> nomenclature: Silica_BV-&lt;loadcase&gt;_&lt;direction&gt;-strain_&lt;max_strain&gt;-rate_&lt;strain_rate&gt; 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<br> time-periodic uniaxial and simple shear tests<br> nomenclature: Silica_BV-&lt;loadcase&gt;_&lt;direction&gt;_sin-ampl_&lt;strain_amplitude&gt;-rate_&lt;max_strain_rate&gt; loadcase: uniaxial tension (UT), simple shear (SS) direction: X, Y, Z (UT); XY, XZ, YZ (SS) strain_amplitude: 0.025 03_composite 01_equilibration<br> sample equilibration<br> nomenclature: equil_P2VPSi-rNP_&lt;filler_radius&gt;-nNP_&lt;filler_number&gt;-&lt;batchID&gt; filler_radius: 2.5-10.0 filler_number: 1-160 (depending on filler_radius) batchID: 1-5 02_uniaxial-tension<br> uniaxial tension simulations<br> nomenclature: UT_P2VPSi-rNP_&lt;filler_radius&gt;-nNP_&lt;filler_number&gt;-&lt;batchID&gt; filler_radius: 2.5-10.0 filler_number: 1-160 (depending on filler_radius) batchID: 1-5 03_filler-maxtrix-adhesion<br> equilibration and uniaxial deformation of samples with mid and weak filler-matrix adhesion (for strong adhesion see 01_equilibration and 02_uniaxial-tension<br> nomenclature: see above 04_IP_equilibration<br> equilibration of samples to evaluate the microstructure for neat polymer and composites with filler radius 2.5-7.5<br> nomenclature: P2VPSi-&lt;chains&gt;x&lt;chain_atoms&gt;_rNP_&lt;filler_radius&gt;-nNP_&lt;filler_number&gt;_pos_&lt;filler_pos&gt;-&lt;batchID&gt; 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:<br> 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):<br> 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 <br> <strong>References</strong>: [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”, <em>Express Polymer Letters</em>, <strong>2022</strong>, 16. [2] S. Plimpton, “Fast parallel algorithms for short-range molecular dynamics,” <em>Journal of computational physics</em>, <strong>1995</strong>, 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,” <em>Computer Physics Communications</em>, vol. 271, p. 108171, <strong>2022</strong>. [4] M. Ries, V. Dötschel, J. Seibert, S. Pfaller. “A self-avoiding random walk algorithm (SARW) for generic thermoplastic polymers and nanocomposites”, <em>Zenodo</em>, 2022. https://doi.org/10.5281/zenodo.6245699
description: Sebastian Pfaller is funded by the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) - 396414850 (Individual Research Grant 'Identifikation von Interphaseneigenschaften in Nanokompositen'). Maximilian Ries, Paul Steinmann, and Sebastian Pfaller are funded by the DFG - 377472739 (Research Training Group GRK 2423 'Fracture across Scales - FRASCAL').