Crystallinity Analysis in

Polyethylene

Molecular Dynamics

Noah Paulson - ME

Alex Lohse - MSE

ME8883 Materials Informatics

12/10/2014

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.html2

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

The entire simulation

volume is called the

representative volume

element (RVE)

The discretized

cells are called

statistical volume

elements (SVEs)

Splitting Into SVEs

4

Density

● Traditional measure of

morphology

● Accuracy issues with fine

discretization

Strain = 0.1

Temperature = 375K

5

Herman’s Orientation● Measure of the

orientation of a chosen

axis to a reference axis

Strain = 0.1

Temperature = 375K

θ

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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

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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

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Density Herman’s Crystalline Degree

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

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engineering strain

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

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

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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?

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Threshold Examples

Perfect CrystalCrystalline RegionAmorphous Region

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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

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0.0 Engineering Strain

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2.0 Engineering Strain

16

3.5 Engineering Strain

17

4.0 Engineering Strain

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