Evaluating the impact of filler size and filler content on the stiffness, strength, and toughness of polymer nanocomposites using coarse-grained molecular dynamics: dataset

Abstract: (from [1]) Their great versatility makes polymer nanocomposites an important class of engineering materials. In order to gain detailed insights into the nanoscale mechanisms underlying their macroscopic mechanical properties, molecular dynamics (MD) simulations are a valuable tool to complement experimental studies. In this work, we modify the analytical potential functions of an efficient bead-spring model representing a generic polymer nanocomposite to account for the breaking of covalent bonds. We perform uniaxial tensile simulations of double-notched specimens and validate the model using experimental trends for overall stiffness, strength, and toughness. First, we study the effects of sample size, notch geometry, strain rate, temperature, and molar mass for the pure thermoplastic matrix material. Second, we analyze the influence of filler size and filler content on the mechanical behavior of the polymer nanocomposite. With this study, we show that in both the development of new materials and the optimization of established materials, it is possible to gain important preliminary insights into the effects of pertinent material characteristics with a simple MD setup, which can then be further refined by increasing the complexity of the material description and the boundary conditions. Contact: Felix Weber Institute of Applied Mechanics Friedrich-Alexander-Universität Erlangen-Nürnberg Egerlandstr. 5 91058 Erlangen Germany Software: All simulations were performed with LAMMPS [2,3] (version 23 June 2022, patch_23Jun2022_update3) Compiler: GNU C++ 11.2.0 with OpenMP not enabled C++ standard: C++11 Active compile time flags: -DLAMMPS_GZIP -DLAMMPS_SMALLBIG Installed packages: BPM CLASS2 DPD-BASIC EXTRA-DUMP EXTRA-FIX EXTRA-MOLECULE INTEL KSPACE MANYBODY MC MISC MOLECULE MOLFILE MPIIO NETCDF OPT Moreover, we employ a self-avoiding random walker [4,5] implemented in MATLAB [6] for the initial positioning of the polymer chains and nanoparticles. License: Creative Commons Attribution 4.0 International Context: This dataset contains the results presented in [1] and the necessary data to obtain those. Content: Throughout this data set, LAMMPS lj units are used. The potentials were adapted from [7] in [1] and [8]. The files to reproduce our simulations and their results are structured as follows: 01_neat: Neat polymer systems 01_EQU: Equilibration simulations 02_UT: Uniaxial tensile simulations, including the notch insertion (token "initcrack") 1.1: Simulations for different sample sizes/numbers of chains (token "chains") at constant molar mass/number of beads per chain 1.3: Simulations for different widths of the Dirichlet boundary (token "diri") 2.1: Simulations for different critical bond lengths (token "bondcrit") 2.2: Simulations for different bond breaking probabilities (token "bondcprob") 3.1: Simulations for different crack widths (token "crackwidth") 3.2: Simulations for different crack lengths (token "crackdepth") 4: Simulations for different strain rates (token "strainrate") 5: Simulations for different temperatures (token "tem") 6: Simulations for different molar masses/numbers of beads per chain (token "chain-len") 02_PNC: Polymer nanocomposite (PNC) systems 01_EQU: Equilibration simulations 02_UT: Uniaxial tensile simulations for different filler radii (token "rF") and filler contents/numbers (token "nF"), including the notch insertion (token "initcrack") - parameter_study: Postprocessing of the MD results parameter_study.xlsx: Overview of the simulations with their respective parameters and statistical analysis of stiffness, strength, and toughness from filtered stress-strain curves (Savitzky-Golay filter applying a linear polynomial and frame length 21) .csv files of the single sheets of parameter_study.xlsx: samples.csv: Individual specimens averages.csv: Statistical analysis of the different samples corresponding to one batch Each simulation directory contains: LAMMPS input script (*.in) of the simulation input.prm: Input parameters of the simulation (read by the input script) LAMMPS data file (*.data, molecular style) of the investigated sample LAMMPS_out: Resulting LAMMPS data files, log files and simulation results in tabulated form additional files for the tensile tests: brokenbonds.dat: Fix print output for fix brokenbondsprint (step time brokenbondsPerStep brokenbondsSum) stressstrain.dat: Time-averaged data for fix dumpOpt (step v_strain_xx v_OBSstrain_xx v_Piola_xx) with the local strain at the crack tip v_OBSstrain_xx thermo_out.Dat: Thermodynamic output in condensed tabulated form thermo_out_SG.Dat: Thermodynamic output in condensed tabulated form, filtered by a Savitzky-Golay filter (linear polynomial, frame length 21) thermo_out_STD.Dat: Standard deviation between the filtered and unfiltered data job.out: Simulation log file meta.info: Meta data of the simulation run Naming convention: 01_neat: GTPm-[number of chains]_chains-[number of beads per chain]_chain_len-[temperature]_tem-[parameter value]_[parameter]-[sample] [parameter]: Parameter studied, i.e. diri/bondcrit/bondcprob/crackwidth/crackdepth/strainrate/tem (see above) [parameter value]: Value of the parameter studied [sample]: Sample ID 02_PNC: GTPm_rF-[filler radius]_nF-[number of fillers]_[sample] [sample]: Sample ID Output quantities (columns of *.Dat files): 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: mass density c_RG: radius of gyration 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_Piola_xx: xx component of the virial stress tensor normalized by the initial volume v_Piola_yy: yy component of the virial stress tensor normalized by the initial volume v_Piola_zz: zz component of the virial stress tensor normalized by the initial volume v_Piola_xy: xy component of the virial stress tensor normalized by the initial volume v_Piola_xz: xz component of the virial stress tensor normalized by the initial volume v_Piola_yz: yz component of the virial stress tensor normalized by the initial volume 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] F. Weber, V. Dötschel, P. Steinmann, S. Pfaller, M. Ries, "Evaluating the impact of filler size and filler content on the stiffness, strength, and toughness of polymer nanocomposites using coarse-grained molecular dynamics", Engineering Fracture Mechanics, vol. 307, p. 110270, 2024. [2] S. Plimpton, "Fast parallel algorithms for short-range molecular dynamics", Journal of computational physics, vol. 117, no. 1, pp. 1-19, 1995. [3] A. P. Thompson, H. M. Aktulga, R. Berger, D. S. Bolintineanu, W. M. Brown, P. S. Crozier, P. J. in 't Veld, A. Kohlmeyer, S. G. Moore, T. D. Nguyen, R. Shan, M. J. Stevens, J. Tranchida, C. Trott, S. J. Plimpton, "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] V. Dötschel, S. Pfaller, and M. Ries, "Studying the mechanical behavior of a generic thermoplastic by means of a fast coarse-grained molecular dynamics model", Polymers and Polymer Composites, vol. 31, pp. 1–11, 2023. [5] M. Ries, V. Dötschel, J. Seibert, and S. Pfaller, A self-avoiding random walk algorithm (SARW) for generic thermoplastic polymers and nanocomposites, Zenodo, 2022, https://doi.org/10.5281/zenodo.6245699. [6] The MathWorks, Inc., "Matlab. the language of technical computing", https://de.mathworks.com/help/matlab/. [7] V. Bocharova, A.-C. Genix, J.-M. Y. Carrillo, R. Kumar, B. Carroll, A. Erwin, D. Voylov, A. Kisliuk, Y. Wang, B. G. Sumpter, and A. P. Sokolov, "Addition of Short Polymer Chains Mechanically Reinforces Glassy Poly (2-vinylpyridine)–Silica Nanoparticle Nanocomposites", ACS Applied Nano Materials, vol. 3, no. 4, pp. 3427–3438, 2020. [8] 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, vol.16, no.12, pp. 1304–1321, 2022. Funding: The authors gratefully acknowledge funding by various sources: The overall research was funded by the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) - 377472739/GRK 2423/2-2023. Sebastian Pfaller is furthermore funded by the DFG projects 396414850 (Individual Research Grant 'Identifikation von Interphaseneigenschaften in Nanokompositen') and 505866713 together with the Agence nationale de la recherché (ANR, French Research Agency) – ANR-22-CE92-0049 (Individuel Research Grant 'BIO ART'). In addition, scientific support and HPC resources have been provided by the Erlangen National High Performance Computing Center (NHR@FAU) of the Friedrich-Alexander-Universität Erlangen-Nürnberg (FAU) under the NHR project b136dc. NHR funding is provided by federal and Bavarian state authorities. NHR@FAU hardware is partially funded by the DFG project 440719683.