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An Introduction to Wide Angle X-ray Scattering
(WAXS) of Polymers
Dr. Brian G. Landes
The Dow Chemical Company
989-638-7059
About Me….
Professional
• BS, MS, PhD Polymer Science
The Pennsylvania State University
• The Dow Chemical Company (33 years)
• Converted Products R&D
• Coating Materials R&D
• Packaging R&D
• Material Science
• Electronic Materials
• Analytical Sciences
• Public Policy
• National Light Sources (31 years)
Personal
• Coaching (Middle School, High School sports)
• Teaching (Technical, Career Development, Leadership)
• Hiking / Biking
• Eating
Discussion Outline
What we will discuss
• Introduction to polymer morphology and structure
• The Wide Angle X-ray Scattering (WAXS) experiment
• Common methods of quantitative analysis
• Challenges, tips in data analysis and interpretation
• Questions
What we won’t discuss (but can talk about)
• Basics of x-rays, instrumentation, crystal structure…
• Specialized approaches (ODF, residual stress….)
Good Starter Reference Materials
A basic primer on polymers and their properties
http://www.pslc.ws/mactest/maindir.htm
(University of Southern Mississippi)
Fundamental texts on diffraction theory applied to polymers and polymer morphology / structure
“X-ray Diffraction Methods in Polymer Science”, L. R. Alexander, Wiley-Interscience..
“X-ray Diffraction Procedures for Polycrystalline and Amorphous Materials”, Harold P. Klug and L. R.
Alexander, Wiley-Interscience, 1974.
“Macromolecular Physics “, Bernhard Wunderlich, Academic Press, 1973.
Volume 1: Crystal Structure, Morphology, Defects
Volume 2: Crystal Nucleation, Growth, Annealing
Volume 3: Crystal Melting
Some opening thoughts from Alexander
(X-Ray Diffraction Methods in Polymer Science)
• Polymers are never 100% crystalline. XRD is a primary technique to determine the degree of crystallinity.
• Synthetic polymers almost never occur as single crystals. The diffraction pattern from polymers is almost always either a
"powder" pattern (polycrystalline) or an oriented polycrystalline pattern.
• Crystallite size in polymers is usually on the nano-scale in the crystal thickness direction. The size of crystallites can be
determined using variants of the Scherrer equation.
• Polymers, due to their long chain structure, are highly susceptible to orientation. XRD is a primary tool for the determination of
crystalline orientation through the Hermans’ orientation function.
• Polymer crystals can contain a large number of defects. This leads to peak broadening, lattice expansion, and lower crystallinity.
• Polymer crystallites can be very small with a large surface to volume ratio which enhances the contribution of interfacial
disorganization on the diffraction pattern.
General Classifications
Long Range Order?
For the “No”, WAXS can still provide valuable information
No NoNoYes
Hierarchical Structure in Crystallizable Polymers
Spherulites Lamellar Stacks Lamellae Unit Cell(microns) (~100’s nm) (~5 – 50 nm) (0.1-1 nm)
WAXS
Crystalline Lamellae
Single lamellae Lamellar Stack
Sizes, shapes, orientation but NOT arrangement
Ch
ain
ax
is / c
-ax
is
Lateral / a,b-axes
Semicrystalline Models
Adjacent re-entry / lamellarFringed-micellar
• Small Angle Laser Light Scattering (SALLS) (~0.1 - 50m)
– Spherulite, Particle size
– Haze, Clarity
– Phase Transitions
• Small Angle X-ray Scattering (SAXS) (~1 – 100nm)
– Particle, Void size / distribution
– Lamella long period & thickness
– Orientation
– Phase Transitions
• Wide Angle X-ray Scattering (WAXS) (~1 - 40Å)
– Crystallinity
– Crystallite Size
– Structure
– Orientation
– Phase Transitions
Scattering Technologies for Polymer Morphology
The Scattering Experiment
The Scattering Experiment
Key Considerations
• Some quantitation of
polymer structure and
morphology can be
achieved with a 1-d
detector, but there are
significant limitations.
• Significant quantitation of
polymer structure and
morphology can be
achieved with a 2-d
detector and a robust
analysis platform.
Experimental Geometry for Data Acquisition
Transmission Geometry
• shape and size “friendly”
• spatially resolved information is possible
• optimal thickness for a hydrocarbon polymer is ~2 mm
• potentially limited sampling volume
Reflection Geometry
• large sampling volume
• thin film “friendly”.
• liquids (melts) easily handled
Transmission Wide Angle X-ray Scattering
CrystallinityPhase IDCrystallite SizePreferred orientation
crystalline
amorphous
With preferredorientation
No preferredorientation
What might we
observe using a
1-d detector?
Characteristic WAXS Patterns
Microcrystalline / liquid crystalline
Liquid Crystalline Order
http://pubs.rsc.org/services/images/RSCpubs.ePlatform.Service.FreeContent.ImageService.svc/ImageService/Articleimage/2007/CS/b612546h/b612546h-f3.gif
Crystal: 3-d lattice
Liquid Crystal: 1-d or 2-d lattice
Amorphous: No lattice
Chain Configuration Effects (polystyrene)
http://pslc.ws/macrog/images/tact05.gif
Chain Conformation Effects(Syndiotactic Polystyrene)
http://ars.els-cdn.com/content/image/1-s2.0-S0032386102006043-gr1.jpg
Determination of Percent Crystallinity
crystalline
amorphous
Ingredients for Success
• Collect data over the needed 2 range.
• Construct a reproducible baseline.
• Understand of the amorphous contribution.
• Minimize the number of peaks used to fit the data.
• Limit the adjustable parameters
• Choose the appropriate exponent (tails).
(There are commercial software packages that will make this easy)
This method of crystallinity determination becomes
more difficult at small apparent average crystallite size.
Would this pattern provide enough information to determine the percent crystallinity?
http://www.eng.uc.edu/~beaucag/Classes/Analysis/Chapter7Picts/Chapter726.GIF
Challenges• Is the 2 range wide enough?
(baseline, peaks, amorphous)
• Is the amorphous phase defined?
(symmetry, baseline)
Would this pattern provide enough information to determine the percent crystallinity?
Challenges• Is the 2 range wide enough?
(baseline, peaks, amorphous)
• Is the amorphous phase defined?
(symmetry, baseline)
• Is the background defined?
Factors / Conditions Effecting Polymer Crystallinity
The Effect of Branching
linear
branched
Defect Driven Changes in• Crystallinity
• AACS
• Lattice Parameters
When we can’t determine crystallinity
5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
Two-Theta (deg)
0
2500
5000
7500
Inte
nsity(C
ounts
)
5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21
Two-Theta (deg)
0
1000
2000
3000
4000
5000
6000
7000
Inte
nsity(C
ounts
)
Unstretched / Uniaxially Stretched Film Biaxially Stretched Film, complex part
90° to plane45° to plane
90° to plane45° to plane
(Radially integrated 2-d patterns)
Be careful to Understand Processing History
Higher Throughput Fitting Approach
Use a limited 2 range
or even a single peak
after a few full fits are
performed.
Using Temperature to Define Polymorphs(Polybutene-1 Structure)
Form II: 113 helical conformation with a tetragonal unit cell when crystallizing from the melt.
Form I: 31 helix conformation with trigonal unit cells, gradually forming at room temperature.
5 known polymorphs• melt (II)• melt Aging (I)• solution (III)• melt / pressure (II’, I’)
Higher Throughput Structure Ratios (Polybutene – 1)
9 10 11 12 13 14 15 16 17 18 19 20 21Two-Theta (deg)
[U080859] (MDI/JADE9)
time
72 hours
0 hours
Needed:• Known structure for each phase
• Single isolated peak for each phase
Effect of Temperature – Structural Transitions
Example:
Syndiotactic Polystyrene
• Polymorphs can be “stable” or
preferred over different
temperature ranges
• The temperature profile
(cooling rate, hold
temperatures, heating rate)
can determine which structure
is present
Crystallinity and Composition in Blends(Need the pure components)
4 5 6 7 8 9 10 11 12 13 14 15 16 17
Two-Theta (deg)
x103
5.0
10.0
15.0
20.0
25.0
30.0
Inte
nsity(C
ou
nts
)
[rak1a_waxs_182_0.chi]
[rak1a_waxs_182_1.chi]
[rak1a_waxs_182_2.chi]
[rak1a_waxs_182_3.chi]
[rak1a_waxs_182_4.chi]
[rak1a_waxs_182_5.chi]
BackgroundPEO/EAA (15)PEO/EAA (25)PEO/EAA (50)PEO (100)EAA (100)
Apparent Average Crystallite Size (AACS)
K ~0.9
D – AACS (Å)
- x-ray wavelength (Å)
- 0.5*(peak angle)
AACS Determination
Peak broadening is due to:
• Crystallite size
• Lattice strain
• Instrumental contribution
Procedure
• Perform peak fitting on reference (LaB6) in
same 2 region as sample peaks of interest.
• Perform pattern fitting on sample.
• Subtract reference peak half width from
sample peak half width
SampleLaB6
Use this one!
Different FWHM / Integral Breadth Contributions (Size or Size / Strain)
Crystallite Size and Strain
One reason the “Apparent” is in Crystallite Size(Polymer crystals can have a large population of defects)
Defects can either be trapped inside a crystalline lamellae or rejected to the lamellar surface or to an amorphous region.
The effects of either trapped or rejected defects on the lattice parameters and the degree of crystallinity can be similar for both scenarios.
Defects can include:• Branches• Comonomers• Configuration• Conformation• Solvent* (may result in a different structure)
The Effect of Temperature
https://www.imould.com/upload/remote/200941196505810.jpg
Increasing Temperature can lead to:• Decease in crystallinity (melting)• Change in crystal structure• Addition of a different crystal structure • Increase in crystallinity
Decreasing Temperature can lead to:• Increase in crystallinity• Change in crystal structure• Addition of a different crystal structure
Polymer Crystallization and Melting
Polyester
Using Temperature to define the amorphous contribution
General Considerations• Amorphous contribution is
shifted at elevated temperatures.
• Amorphous contribution may be
different at elevated temperatures.
• Quenching (fast cooling) can be
used to define the amorphous
contribution at room temperature.
Spatially resolved WAXS for Orientation and Crystallinity
(Process effects, skin / core)
450µm zone of high
orientation
Region-4
1500µm
Region-3 1100µm
Region-2
280µm
Region-1 skin
PP-200m PP-50mPP-600mPP-1500m
X-raydiffractionOptical
Change in orientation Change in orientation
Polymer surface1500 m in depth
50
55
60
65
70
75
0 500 1000 1500 2000
Cry
sta
lin
ity
Micron meter from surface
The Effects of Deformation on Morphology
http://www.kazuli.com/UW/4A/ME534/asgn3_files/image032.jpg
Common effects of deformation• Orientation• Decrease in AACS• Decrease in crystallinity• Increase in crystallinity (SIC)• Formation of an additional crystal structure• Transition to a different crystal structure
Stress Induced Crystallization
https://www.researchgate.net/figure/256149813_fig5_FIG-9-Stress-strain-curve-and-corresponding-diffraction-patterns-recorded
Some polymers (polyisoprene is a good example) will only exhibit crystallinity while under stress. Upon release of that stress the polymer reverts back to the amorphous state.
Development of Preferred Orientation
http://www.azom.com/images/Article_Images/ImageForArticle_13578(1).jpg http://www.kazuli.com/UW/4A/ME534/lexan2_files/image006.jpg
Key Considerations• Most fabricated articles possess preferred orientation
• Properties are directly related to orientation
Process induced order & orientation Post process induced order & orientation
Orientation During Processing & Post Processing
As spun Anneal / tension
Hermans’ Orientation Function
Key Considerations• Herman's orientation function (f)
is a mathematical construction
that allows a description of the
degree of orientation of a crystal
axis relative to some other axis
of interest (process axis).
• This function is valid
only for systems with
axial symmetry
Experimental Determination of ‘f’
Herman's orientation function 'f' has the properties that,
relative to the direction of interest, if 'on average' the chain
axis is:- completely aligned f = 1 randomly oriented f = 0
perpendicular f = - 0.5
Preferred Orientation
0
10000
20000
30000
40000
50000
0
27
.
55
82
.
11
0
13
8
16
5
19
3
22
0
24
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5
30
3
33
0
35
8
Degrees (Chi)
Inte
ns
ity
(a
rb. u
nit
s)
110
37
28
18
5
0
Increasingorientation
What if our sample does not possess axial symmetry?
What we see – and don’t see
http://www.jpk.com/index.media.d9d8546626c9edacaec7a6a69298e020v1.gif http://cdn.iopscience.com/images/0022-3727/40/23/R01/Full/jphysd245718fig02.jpg
Pole Figures to Represent 3D Texture
RD (MD) – roll or machine direction
TD – transverse direction
ND – normal direction
2
Each pole figure represents the alignment
Distribution of one crystallographic direction
Polyethylene Pole Figures
http://www.x-raywizards.com/Services/Texture/Application_Note_PT-002_Orientation-PE.pdf
MD MD
TD TDNDND
Representative Textures
Summary
Wide Angle X-ray Scattering (WAXS) is a powerful method for
quantitatively describing polymer morphology and structure.
The keys to applying it successfully are:
• Knowing your sample (chain microstructure, process history, thermal history).
• Recognizing potential limitations
(sample: texture, non-uniformity; method: resolution, sampling)
• Using consistent, physically meaningful analysis and modeling approaches.
• Reading the literature!
Accessing and Using Synchrotron Radiation
Dr. Brian G. Landes
The Dow Chemical Company
989-638-7059
Discussion Outline
• Synchrotron Basics
• Why conduct experiments at a beamline?
• Where are synchrotron sources?
• Acquiring beam time
• Types of experiments
• Preparation for beamline experiments
• Examples
Generation of Synchrotron Radiation
http://www.theage.com.au/ffxMedia/urlmedia_id_1058853142412_24HOW_IT_WORKS.jpg
A Range of Energies and Flux
Spectroscopies
Imaging
Scattering
Diffraction
Why do Experiments at a Synchrotron?
• X-ray intensity 101-1011 in-house equipment
• Continuum of X-ray energy selection
• Completely customizable experiments
• Simultaneous, in-situ, and time resolved studies
• High throughput capable
• Access to $MM worth of leading-edge instrumentation
• Interaction with globally recognized expertise and their networks!
Synchrotron Characteristics
• Intensity:
Brightness: photons sec-1 mrad-2 mA-1 per unit bandwidth
Brilliance : photons sec-1 mrad-2 mA-1 per unit bandwidth
per unit source area.
Comparison of X-ray Sources
Source Brilliance Expt. Time Project duration
Sealed X-ray tube 108 10 hours 10 months
Rotating anode tube 109 1 hour 1 month
NSLS bending magnet 1013 400 msec about 4 min
Insertion device 1015 4 msec about 2.4 sec
APS undulator 1019 0.0004 msec about 0.24 msec
3rd Generation: APS, ESRF, Spring-8
4th Generation: NSLS-II, APS-II
Advanced Photon Source (APS)Argonne Nat. LabChicago, Illinois
X-ray diffractionHard x-ray scatteringX-ray microtomography
National Synchrotron Light Source (NSLS-II)Brookhaven Nat. LabLong Island, New York
Soft X-ray spectroscopy
Advanced Light Source (ALS)Lawrence Berkeley Nat. LabBerkeley, California
Soft X-ray ImagingResonant Soft x-ray scattering
US National Light Sources
A Sample of other User Facilities
• USA• CHESS (Cornell High Energy Synchrotron Source, Ithaca, NY)
• SRC (Synchrotron Radiation Center, Madison, WI)
• SSRL (Stanford Synchrotron Radiation Laboratory, Menlo Park, CA)
• CAMD (Center for Advanced Microstructures and Devices, Baton Rouge, LA)
• Outside of USA• Australian Synchrotron (Melbourne, Victoria)
• CLS, (Canadian Light Source, Saskatchewan, Canada)
• ESRF (European Synchrotron Research Facility, Grenoble, France)
• DESY (Deutsches Elektronen Synchrotron, Hamburg, Germany)
• PAL (Pohang Accelerator laboratory, Pohang, South Korea)
• SLS (Swiss Light Source, Villigen, Switzerland)
• Spring-8 (Super Photon Ring 8, Nishi-Harima, Japan)
• SOLEIL (Optimized Source of LURE* Intermediary Energy Light, France)
• SRS (Synchrotron Radiation Source, Cheshire, UK)
http://www-als.lbl.gov/als/synchrotron_sources.html
Access to Light Sources
“Buy in”- cost- contract- guarantee access
“Rent” (General user)- not guaranteed access- proposal process
Preparing for a Successful Run
• Knowledge of scattering behavior of systems
• Ancillary analytical information
• Prepare materials / sample forms / devices
• Have a prioritized, detailed experimental protocol
• Bring appropriate staffing / expertise
• Minimize hardware rearrangements
• Have a plan for storage, reduction, analysis of data
• Communicate with beamline Scientists prior to arrival
• Make sure you are rested
During a “Run”
• Experimental set-up
• Hardware calibration
• Data acquisition, correction, transfer
• Experimental (hardware) tear down
• Data reduction
• Data Analysis
• Data Interpretation
• Reporting
What Types of Experiments can I do?
• Bulk, surface, interfaces, spatially resolved
• In-situ• Thermal (DSC, flame, cryo)• Mechanical (tensile, impact, tear, pressure)• Magnetic• Process (spinning, extrusion, molding, casting)• Solution (mixing, nebulizing, deposition)• Coupled
• Time-resolved
• High throughput
Examples of Compact Ancillary Devices for In-situ Studies
• Kinematic stage foundation
• Devices on kinematic mounts
• Swappable controllers
• Data streaming, reduction, analysis
Dow Confidential Information
Examples of other Ancillary Devices for In-situ Studies
Solvent cell
DSC cells
Instron Heated fiber
tensile cell
Extrusion
Cold finger
DSC Pans X 32 Capillaries X 8
• 6 cartridge heaters
• 3 PID loop controllers
• 3 independent thermocouples
• Compressed air / LN2 cooling
In-vacuum flow cell
Access to a Broad / Continuous q-range
WAXSMAXS
SAXSTriple detector System at the
Advanced Photon Source (DND-CAT)
Up to140 frames/second
Full coverage from 1.3Å to 6000Å
• RT to >2200˚C• Variable Tension
In-situ Processing(Production of Carbon Fiber)
Multi-level Structures in Carbon Fiber
I(q)
q
0.1Å-1
Carbon structureMicropore
• inter-layer distance
• average crystal size
• % crystallinity
• Average pore size
• Porosity
• Pore size distribution
SAXS
WAXS
Anisotropic WAXS and SAXS Patterns
SAXSWAXS
• Carbon / graphite• AACS• Preferred orientation
• Porosity• Pore size
Influence of Process on Structure and Properties
fiber
axis
La ┴
(100)
La ll
(100)
Lc
Low tension
High tension
No tension
Polymer core
(composition, formulation)
Stabilizing layer
(surfactants, additives)
Water
(co-solvents, additives)
High Viscosity Coatings
Interplay between
film formation and
structure development
(properties)
Phase segregation• Hard segments
• Soft Segments
Watching the Film Formation Process
71
Dynamics of Particle to Film Formation
Rapid optimization of chemistry, formulation and process to provide best performance and economics.
0.1 0.2 0.3 0.4 0.5 0.6 0.7Two-Theta (deg)
Materials Data, Inc. [u080859] Wednesday , February 03, 2010 01:41p (MDI/JADE9)Coating applied (t = 0)
Absence of scatteringFinal film
time
60
180
300
420
0.1 1 10 100 1000 10000
time (min)
d (
an
gstr
om
s)
0
500
1000
1500
Particle spacing
Hard Segment spacing
I (particle)
60
180
300
420
0.1 1 10 100 1000 10000time (min)
d (
an
gstr
om
s)
0
500
1000
1500
Water / surfactant
Water / surfactant / co-surfactant
Define Mechanisms and Key Variables to
Achieve desired Structure and Properties
AFM Image
AFM Image
Large Array Studies (and low viscosity systems)
• 10 position sample wells (50 samples with 5 goniometer mounts!)
• Adjustable fill → film thickness (variability and control)
• Normal beam transmission to grazing incidence
Quantitate Polymer/water ratio and Crystallinity with time
H2O
binder
t = 0
Rapid Comparison of Formulation Variables
Decreasing particle size
Hierarchical Structure in Photonic Polyethylene
Exposure to solvent…?
Blue Morpho Butterfly “Optical” PE
Heat Cool
Exposure to Temperature (Crystallinity?)
Effect of Temperature (Crystallinity)
4 5 6 7 8 9 10 11 12 13 14 15 16 17Two-Theta (deg)
[Max Intensity Scale = 12135.41] [u080859] (MDI/JADE7)
0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 1.1
Two-Theta (deg)
[Max Intensity Scale = 48634.39] [u080859] (MDI/JADE7)
SAXS WAXS
x, pixels
y,
pix
els
(log intensity)
200 400 600 800 1000
100
200
300
400
500
600
700
800
900
1000
SAXS
As Molded Heated 150C / 30 min
However….in very low q region (100’s nm)
No color change
Continuous color
change
time
ethanol,
hexane
WAXS
time
Color changes due to changes
In colloidal periodicity (200-400 nm)
SAXS (ethanol)
SAXS (hexane)
Effect of Solvent Exposure
Broad size scale resolution enabled fast definition of behavior
Processing Kinetics in Block Copolymers
VariablesTemperatureStrainStrain Rate
X-rays
Rheometer
0 seconds 32 seconds 180 seconds 501 seconds
As molded 18 seconds 37 seconds 110 seconds
240ºC
260º C
How Fast Can Structure Develop?
Preferred Orientation
0
10000
20000
30000
40000
50000
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.
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82
.
11
0
13
8
16
5
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5
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3
33
0
35
8Degrees (Chi)
Inte
ns
ity
(a
rb. u
nit
s)
110
37
28
18
5
0
Complete DOE of processParameters defined in 2 days.Post mortem studies wouldHave required months
In-situ Processing: Rheometry of Block Copolymers
Morphology Map of Sample 67G
0
20
40
60
80
100
120
140
160
180
200
0 50 100 150 200 250 300
Time (sec)
Lo
ad
(lb
)
Instron
In-situ Polyolefin Film Tear (WAXS)
Rotation, fine crystal slipCoarse deformationfibrillar-like crystalline phase
Pre-strain: isotropic crystal orientation
t ~ 2 mil
Morphology Map of Sample 67G
0
20
40
60
80
100
120
140
160
180
200
0 50 100 150 200 250 300
Time (sec)
Lo
ad
(lb
)
Instron
Lamellae Rotation
Increasing Lamellae Rotationmore perfect alignment
Additional Mechanism Develops•Fibrillar morphology•Microvoid development
Pre-strain: isotropic lamellae orientation
t ~ 2 mil
In-situ Polyolefin Film Tear (SAXS)
MV
In-situ Morphology Map
0
50
100
150
200
250
0 100 200 300
Time (sec)
Lo
ad
(lb
)
0
0.2
0.4
0.6
0.8
1
Instron
Long Period
AACS
HOF
Successful Use of Synchrotron X-Ray Sources
Collect the minimum data to answer question
Have a data analysis strategy in place
Data generation using an area detector
5 sec per frame for 8 hours (which is slow and low)
• 6000 2-d image
• 10’s of thousands 1-d data sets
Summary
Synchrotron technologies provide opportunities
for unique, ground breaking science. Dream it,
build it, do it – on a beamline!
