Introduction

The initial goals of this project were to develop processing - structure linkages for semicrystalline polyethylene molecular dynamics (PE-MD) simulations. After analysis of our sample data revealed major issues, the focus of the project was shifted to the comparison of traditional crystallinity analysis tools (such as density and Herman’s Orientation) versus a new approach developed over the course of the term. This analysis technique is called Crystalline Degree and leverages two-point autocorrelations in the analysis of PE crystallinity.

Timeline

September 10th - 19th: In this first stage we were defining the project and understanding the data that we were given from Tony, originally generated by Xin Dong. The first step was to try and correlate the data files to simulations mentioned in the two papers released by Xin Dong. The Rundown of Data in Our Possession summarizes our efforts.

Concurrently Matlab codes were written to visualize the data at each timestep, which can be viewed in the Process-Structure Linkages in Semi-Crystalline PE post. At this point the goal was to generate process-structure linkages based on the parameters of density, Herman’s orientation, and crystalline orientation (using Euler angles). The main questions were deciding on the appropriate bin size to capture density and Herman’s Orientation accurately and how discretize the simulation (RVE) into smaller bins (SVEs) when the overall RVE dimensions changed with time.

September 20th - October 1st: During these weeks we investigated pair correlation functions as a way to analyze crystallinity. Pair correlations were performed between two chains within the simulation volume. The analysis showed a clear periodicity of the structure; however we were not able to resolve amorphous and crystalline regions directly. Thus we became skeptical about the usefulness of pair correlations on entire chains in the RVE. The Pair correlation functions for polymer chains post describes this effort.

October 2nd - 13th: During this stage codes were developed to analyze Herman’s orientation within an SVE and pair correlations continued to be developed. The post Pair Correlations for All Chains shows the pair correlation results for all 20 chains in our simulation with respect to the average pair correlation for all chains in the simulation. Additionally, the post Pair Correlations and Orientation Measurements presents the initial Herman’s results. At this time we began to consider the ideal SVE size to both accurately represent the crystallinity within each SVE and to show the spatial distribution of crystallinity in the RVE (through crystallinity maps and crystallinity autocorrelations). In addition, at this point we discovered through discussions with Dr. Karl Jacob and Xin Dong that only one of our data sets was physically representative of PE structure during deformation.

October 14th - 21st: In discussion with Dr. Kalidindi we considered the use of the autocorrelations of monomer locations in each SVE for crystallinity analysis. PE crystals have a representative signal in the monomer autocorrelation. Through the comparison of peak intensities and locations the ‘degree’ of crystallinity might be quantified.

In the Choosing between Structure Representations post we introduced this concept and demonstrated the two-tiered discretization of the simulation (from the RVE into SVEs and from each SVE into a microstructure function). In this post we also demonstrate the use of Herman’s Orientation in simulation data.

October 22nd - 27th: In the Detecting Chain Similarity through Pair Correlations in PCA Space post the pair correlations for each chain in the simulation were plotted in PC space. This post qualitatively demonstrated that chains close together in PC space also had similar shapes and pair correlations. While this approach showed promise, it wasn’t effective in identifying local crystallinity. Therefore we decided to focus on crystallinity analysis within each SVE instead of over the length of PE chains.

In the raw data each monomer is described by a set of coordinates. In order to more accurately represent the PE structure, each monomer was assigned a radius in the SVE. The Autocorrelations on Monomers with Specified Radius post shows the SVEs with volumized monomers and example autocorrelations for both semi- and perfectly-crystalline SVEs.

October 28th-November 20th: In this time we developed our capability to run LAMMPS simulations. The Recent Molecular Dynamics Simulations post provides details on an amorphous simulation that was performed. In addition, the first iteration of a crystalline degree analysis was developed and demonstrated in the Visualization of Crystallinity Results post. This method counted the number of vectors in the autocorrelation of an SVE exceeding some probability threshold. The post compares density, Herman’s Orientation and crystalline degree in the analysis of local crystallinity in a semicrystalline PE-MD simulation.

November 21st - December 8th: After a meeting with Dr. Surya Kalidindi and Dr. Karl Jacob a number of additional crystallinity analyses were investigated. These included the pair correlations of monomer locations and the use of autocorrelation peak intensities in the characterization of crystallinity. In addition, attempts were made to generate a variety of semicrystalline PE structures with which to test the crystallinity analyses. A number of these developments are captured in the Preliminary Results of Crystallinity Analyses post.

In the last week of the semester we settled on a final crystallinity analysis which counted the number of vectors in the autocorrelation that exceeded some probability threshold. This threshold was chosen in order to most accurately separate amorphous and crystalline regions in a variety of test structures. In addition, a uniaxial - strain amorphous simulation (to 4.0 engineering strain) was generated and analyzed using density, Herman’s Orientation and crystalline degree. This analysis indicated that Herman’s Orientation increased more with strain than the newly developed crystalline degree analysis. The results of these analyses are presented in the Final Presentation.

Future Work

  • Further investigate the use of pair-correlation peak locations and intensities in the analysis of crystallinity
  • Generate larger sets of amorphous and semicrystalline structures to better tune crystallinity analyses
  • Generate simulations with a variety of processing conditions and build processing-structure linkages
  • Author paper to present the results of this semester’s work

Division of Work

Throughout the project Noah acted as the coding and data analysis domain expert while Alex acted as the subject matter expert for simulations and polymers. The initial codes for Herman’s Orientation and Density were written by Alex then revised by Noah. Noah developed an integrated crystallinity analysis tool including codes to calculate pair correlations, two point statistics, and crystalline degree. As the semester progressed Alex performed additional simulations and generated theoretical structures for further analysis.

Collaborations

  • Meetings with Dr. Jacob to answer questions regarding polymer structure and crystallinity and help with direction of our project.
  • Xin Dong provided the initial semi-crystalline MD simulation data for analysis and answered various questions regarding the data and LAMMPS simulation.
  • Meetings with Dr. Fast and Dr. Kalidindi for coding advice and project direction.

Online Tools

  • Nanohub.org - We used the Polymer Builder tool to generate theoretical amorphous polyethylene structures of varying densities.
  • Amorphous Polymer Generator LAMMPS Script, Mark Tschopp - A series of online tutorials for LAMMPS from Mississippi State University. We used the script from the amorphous polymer deformation MD simulation and modified it for our purposes.
  • Various codes, including SpatialStatsFFT.m, for non-periodic 2-point statistics from Tony Fast
  • Use of PACKMOL and Avogadro for the development of theoretical semicrystalline structures.