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Crystallinity analysis in molecular dynamics
- 1. Crystallinity Analysis in Polyethylene Molecular Dynamics Noah Paulson - ME Alex Lohse - MSE ME8883 Materials Informatics 12/10/2014
- 2. Background and Motivation ● Crystallinity affects bulk polymer morphology and mechanical properties o The phenomena of crystallinity occurs with interactions at the molecular level ● Processing conditions alter crystalline development o quench rates, deformation rate, temperature ● Polyethylene crystallinity defined by specific arrangement of monomers in unit cell Polystyrene http://www.nationalboard.org/ http://neon.mems.cmu.edu/cramb/27- 100/lab/S00_lab2/lab2.html 2
- 3. Problem Statement ● Current analysis techniques do not account for spatial relationships between monomers o Density and Herman’s Orientation ● Develop a new analysis technique to measure local crystallinity in PE-MD simulations accounting for these spatial relationships http://www.doitpoms.ac.uk/tlplib/poly merbasics/images/Crystallinity.gif 3
- 4. The entire simulation volume is called the representative volume element (RVE) The discretized cells are called statistical volume elements (SVEs) Splitting Into SVEs 4
- 5. Density ● Traditional measure of morphology ● Accuracy issues with fine discretization Strain = 0.1 Temperature = 375K 5
- 6. Herman’s Orientation ● Measure of the orientation of a chosen axis to a reference axis Strain = 0.1 Temperature = 375K θ 6
- 7. Crystalline Degree To calculate crystalline degree (C°): 1. Represent monomers in SVE as voxelized spheres 2. Perform 2-pt autocorrelation (non-periodic) on monomers 3. Find number of vectors in autocorrelation which exceed 0.01 probability threshold 4. Normalize by maximum expected number of vectors exceeding 0.01 threshold for perfect PE crystals amorphous semicrystalline perfect crystal 7
- 8. Crystallinity Analysis Results Mass Density = ρ, Herman’s Orientation = θ, Crystalline Degree = C° ● 0.6 Threshold for crystallinity for θ from literature ● 0.4 Threshold for C° chosen from C° histogram ● By inspection, thresholds on C° and θ closely match 8 Density Herman’s Crystalline Degree
- 9. Measure Evolution with Strain https://www.dropbox.com/s/vi2cn82ritqumyi/amorphous_4strain_10e9-erate.mpg?dl=0 ● Herman’s orientation increases most with increasing strain ○ Due to alignment of amorphous chains ● Density stays mostly constant ● Crystalline Degree increases slightly 9 engineering strain
- 10. Future Work ● Investigation into pair-correlations for crystallinity analysis ● Development of processing- structure linkages for local PE crystallinity ● Officially release the analysis tools for PE-MD simulations on Github 10
- 11. Collaborative Interactions External Tools and Codes ● SpatialStatsFFT.m code for non-periodic 2-pt statistics - Dr. Tony Fast, GaTech ● Nanohub.org, Polymer Builder Tool - Benjamin Haley, Purdue Nano Collaboration Network (NCN) project ● Amorphous Polymer Generator LAMMPS script - Mark Tschopp, Cooperative Computing Group at Mississippi State University Thank You’s ● Trial PE-MD simulations and LAMMPS assistance from Xin Dong ● Consultation with Prof. Karl Jacob for PE-MD expertise, with Prof. Surya Kalidindi for data science expertise and Dr. Tony Fast for coding expertise ● ME8883 classmates for countless beneficial interactions in-class and online 11
- 12. References ● Dong, X. McDowell, DL. Kalidindi, SR. & Jacob, K. (2014). Polymer, 55, 4248–4257. ● Haley, BP, et. al. (2014), "Polymer Modeler" https://nanohub.org/resources/polymod. ● Hossain, D., et. al. Polymer, 2010, 51(25), 6071–6083. ● Ko, M. J., Waheed, N., Lavine, M. S., & Rutledge, G. C. (2004). The Journal of Chemical Physics, 121(6), 2823-2832. ● Niezgoda, S. R., Fullwood, D. T., & Kalidindi, S. R. (2008). Acta Materialia, 56(18), 5285–5292. ● Pant, P. V. K., Han, J., Smith, G. D., & Boyd, R. H. (1993). 99(1), 597–604. Questions? 12
- 13. Threshold Examples Perfect CrystalCrystalline RegionAmorphous Region 13
- 14. Crystallinity Autocorrelations 1.0 strain volume fractions: ρ = 0.67 θ = 0.76 C° = 0.67 0.1 strain volume fractions: ρ = 0.64 θ = 0.64 C° = 0.64 0.5 strain volume fractions: ρ = 0.66 θ = 0.61 C° = 0.58 ● All analysis techniques show periodicity of crystalline bands in the autocorrelations ● At high strain θ detects higher crystallinity throughout sample 14
Editor's Notes
- INCLUDE PRESENTATION NOTES BELOW SLIDES
- -The spatial relationships have will contain within them info about crystalline perfection, chain conformation, -Crystallinity can affect hardness, tensile strength and modulus, melting point, etc. -MD simulations are necessary to capture the effects of polymer crystallinity and understand how processing conditions will affect its nucleation. -In our case bi-axial and uniaxial stretching simulate a processing condition.
- -local crystallinity could be very important in recognizing transition, mesophase, regions which are not amorphous nor crystalline. This new measure could provide a way to capture this information. As we see later density contains high variance at small voxel size. Our measure is still accurate, perhaps giving a way to determine nucleation and growth sites/directions based on various processing conditions. -For amorphous simulation the order parameter increases, thus there is more noise and it becomes hard to threshold what is amorphous and what is crystalline.
- Polymer MD simulations with united atom talk about how at each timestep the we have monomer locations monomers form chains split up the simulation volume into spatial cells of a predetermined size talk about PE crystallinity talk about crystalline/amorphous examples in each cell we want to know if it is amorphous or crystalline or somewhere in-between
- crystalline regions have higher density and amorphous regions are lower. talk about how the size of the SVE impacts the accuracy of determination
- -Create animation where the two vectors come together and the angle between them is shown, highlight the fact that Herman’s is a measure of order, not of crystallinity -say that herman’s ranges from -½ for perfect amorphous to 1 for perfect crystalline -basically discuss how we measured herman’s with the every other monomer vectors
- covalent radius of the united atom PE monomer Walk through how Crystalline Degree is calculated
- Talk about the final step of thresholding the various measures to get a crystallinity map Talk about the high degree of alignment between the crystallinity analysis techniques Mention what this data is and where it comes from collaboration with Xin from Dr. Jacob’s lab Crystalline Degree Threshold : 0.4, Density Threshold : 0.862
- talk about how the autocorrelations change with increasing strain level depending on which crystallinity analysis is utilized at high-strain the Herman’s Orientation increases more than crystalline degree
- talk about how microstructure function is formulated we have monomer locations in each cell monomers are given some radius - talk about how this radius is chosen monomer material represented by 1s in 3D array the shape of the cell explain what the 2pt autocorrelation means in this case cite Tony’s spatialstatsfft code talk about how spatial cells with varying crystallinity show peaks at similar locations after the threshold in the autocorrelation threshold is applied by taking vectors with a probability exceeding some threshold as 1 and all others as 0
- talk about how the autocorrelations change with increasing strain level depending on which crystallinity analysis is utilized at high-strain the Herman’s Orientation increases more than crystalline degree