An Introduction to Wide Angle X-ray Scattering

(WAXS) of Polymers

Dr. Brian G. Landes

The Dow Chemical Company

989-638-7059

bglandes@dow.com

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

.

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0

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19

3

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0

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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

bglandes@dow.com

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

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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

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120

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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

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250

0 100 200 300

Time (sec)

Lo

ad

(lb

)

0

0.2

0.4

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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!