X-ray diffraction in polymer science
• 1) Identification of semicrystalline polymers and Recognition of
crystalline phases (polymorphism) of polymers
• 2)Polymers are never 100% crystalline. XRD is a primary technique
to determine the degree of crystallinity in polymers.
• 3) Microstructure: Crystallite size in polymers is usually on the nanoscale in the thickness direction. The size of crystallites can be
determined using variants of the Scherrer equation.
• 4) Orientation: 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.
1) Identification of semicrystalline polymers
Positions and Intensities of the peaks are used for identifying the material.
Unoriented PE
The diffraction of unoriented
samples in reflection
110
2θ = 21.4°
I
PE
polyethylene
200
2θ = 23.9°
The diffraction of unoriented samples in
transmission by using a flat film is characterized by
concentric circles called “Debye Scherrer Rings”
5
10 15 20 25 30 35 40
2θ (deg)
110
(2θ
θ=21.4°)
Rhkl = D tan 2θhkl
200
(2θ
θ=23.9°)
Unoriented PE
X ray diffraction of semicrystalline and amorphous
polymer
211
(20.3°)
I
300
110 (11.8°)
(6.2°)
310
220
amorphous
s-PS
syndiotattic
polystyrene
I
s-PS
syndiotactic
polystyrene
400
210
5
10 15 20 25 30 35 40
2θ (deg)
5
10 15 20 25 30 35 40
2θ (deg)
1) Identification of crystalline phases of polymers
Position and Relative intensities are the fingerprint of crystalline phases of polymer
211
s-PS
110
300
a
220
310 410
400
510
600
210
200
030
121
Intensity
220
041
331
020
210
111
_
410
_301
321
_101
111
132
020
210
111
_
121
_
_230
321
211
301
δ
102
_
112
_
302
322
δ
121
_
421
_
411
220
030 212
_302
322
_
010 210
10
15
γ
_
421
_
411
_
210
5
α
040
420
231
401
410
010
002
031
131
200
020
210
α
20
25
2θ (deg)
30
230
040
35
δDCE
40
b
Identification of crystalline phases of polymers also if they are present in mixture.
s-PS
(110)I
i-PB
Intensity
β
(211)I
tmax = 5 min
β
(300)I
Tmax = 320 °C
β
e
I
(220)I
Forma I
βα
Tmax = 310 °C
β
d
Forma I + II
α
α +β
Tmax = 300 °C
β
c
β
α
Forma I + II
α
(200)II
Tmax = 290 °C
b
α
α
(220)II
Tmax = 280 °C
a
0
(311)II
β
5
10
15 20 25
2ϑ (deg)
30
35
40
Forma II
5
10
15 20
2θ (deg)
25
30
X ray diffraction of semicrystalline polymer and inorganic
compound
inorganic compound
Polymer
211
(20.3°)
I
KBr
I
300
110 (11.8°)
(6.2°)
310
220
s-PS
syndiotattic
polystyrene
400
210
5
10 15 20 25 30 35 40
2θ (deg)
5
10
15
20
25
30
35
40
45
2 θ (deg)
50
55
60
65
70
75
80
30000
What about this spectra?
9.5
25000
28.6
Intensity (a.u.)
20000
15000
10000
17
5000
19
18.6
14.1
21.6
48.7
25.6
59.3
38.5
0
5
10
15
20
25
30
2θ(°)
35
40
45
50
55
60
Diffrazione dei raggi X del campione prima TGA
polimero
Diffrazione dei raggi X del campione dopo TGA
Carica inorganica
The peak positions, intensities, widths and shapes
provide important information about the structure of the
material
• amorphous / crystalline
• (polymer, inorganic/organic compound)
• crystalline phases
2)XRD a primary technique to determine the degree of crystallinity in polymers.
The determination of the degree of crystallinity implies use of a two-phase model, i.e. the
sample is composed of crystals and amorphous and no regions of semi-crystalline organization.
I = I crystalline + I amorphous
I
degree of crystallinity : xc
xc =
I crystalline
I crystalline + I amorphous
5
10
15
20
2θ
25
30
35
2) XRD : determination of degree of crystallinity in polymers.
The diffraction profile is divided in 2 parts: peaks are related to diffraction of crystallites,
broad alone is related to scattering of amorphous phase.
The assumption is that the areas are proportional to the
scattering intensities of crystalline and amorphous phases
Ia = diffracted
amorphous phase
Ib = diffracted
background
Ic = diffracted
crystalline phase
PE
Ic
Ia
Ib
intensity
of
intensity
of
intensity
of
Acr
xc =
Acr + KAam
K is a constant related to the different scattering factors of crystalline and
amorphous phases. For relative measures K = 1.
3) Microstructure: Crystallite size in polymers
The half-width of peaks is related to crystallite dimensions.
Half-width large correspond to smaller crystallites
Intensity
Contribution to broadening can be due to
lattice distortion, structural disorder as
well as instrumental effects.
5
10
15
20
25
2θ (deg)
30
Intensity
Half-width narrow correspond to bigger crystallites
5
10
15
20
25
2θ (deg)
30
Intensity
3) Microstructure: Crystallite size in polymers
B = half-width of peaks
B = ∆2θ = 2θ2 – 2θ1
Imax
Imax/2
b = broadening instrumental
β= broadening due to crystallites dimensions
B
2θ
2θ1
β=B−b
2θ2
2θ (deg)
b can be measured by the half-width of a peak
of crystalline compounds low molecular weight.
Crystallite size in polymers :
Lhkl =
Kλ
β ⋅ cosθ
Scherrer’s Equation
Lhkl = crystallite dimensions (in Å) along the direction perpendicular to the
crystallographic plane hkl.
β = half-width of peak related to the crystallographic plane hkl (rad).
K = constant (usually K = 0.89)
θ = diffraction angle of the hkl reflection.
λ
= wavelength used ( λCukα = 1.5418 Å.)
4)Orientation: Polymers, due to their long chain structure,are highly susceptible to orientation
Fiber
axes
Draw direction
X-ray
c
fiber
X-ray diffraction of oriented polymer: fiber pattern
y meridian
 360 x 
 -1 y 
cos 2θ = cos
 cos tan

2
π
R
R




Second layer l=2 (hk2)
First layer l=1 (hk1)
equator l=0 (hk0)
x
i-PP fiber
c=
lλ
sen(tan -1 ( y/R ))
c = periodicity along the chain axes
λ = wavelength used (CuKα = 1.5418 Å)
l = layer
x, y = distance of reflections from the center
along equatorial and meridian lines
R = chamber radius
X-ray diffraction of fibers annealed at different T
Distance from layers correspond to c axes
Helical
conformation
c=7.8 Å
Trans-planar
conformation
c=5.1Å
Oriented sPP fiber stretched at different ε
First layer l=1 (hk1)
equator l=0 (hk0)
ε = 50 %
ε = 100 %
ε = 200 %
ε=100(Lf-Li)/Li
Lf = final length
Li = initial length
ε = 500 %
The degree of orientation can be determined from the intensity
distribution of the corresponding diffraction on the Debye ring
by using the Hermans’ Orientation Function
fφ =
Azimutal scan: measuring the intensity at
2θ constant, by varying the χ angle.
(
)
1
3 cos 2φ − 1
2
Average cosine squared
value of φ angle
Z = draw axes
φc,Z
φa,Z
c
φb,Z
b
a
If the radiation is perpendicular to the fiber axes
χ
cos 2φhkl = cos 2 χhkl
2
χ
π/2
< cos 2χ hkl >=
2
(
)
I
χ
sen
χ
cos
χ dχ
∫
0
π/2
∫ I(χ)senχ dχ
0
Orientation with respect to draw
direction
parameter
parallel
random
perpendicular
<cos2φ>
f
1
1
1/3
0
0
-1/2
If χ = 0 for meridian reflection (00l)
<cos2φ00l> = 1 e fc = 1
The fiber is perfected oriented: fc = 1
Types of Orientation in polymers
Types of ORIENTATION
GEOMETRY
(Heffelfinger
& Burton)1
PREFERRED ORIENTATION
Crystallographic
elements
Reference
elements
1
Random
-
-
-
2
Axial
Crystallographic Axes parallel
to reference axes
c
draw axes
3
Planar
Crystallographic Axes on a
reference plane
c
film plane
4
Planar-axial
Crystallographic plane
Parallel to a reference axes
(100)
draw axes
5
Uniplanar
Crystallographic plane
Parallel to a a reference plane
(100)
film plane
c
draw axes
Uniplanaraxial
Crystallographic Axes parallel
to reference axes
and a Crystallographic plane
Parallel to a a reference plane
(100)
film plane
6
C. J. Heffelfinger, R. L. Burton J. Polym. Sci. 47, 289 (1960).
Uniplanar orientation: sps film
110
211
220
300
β
200
220
300 310
410
400
β
210
040
Intensity
220
E
101
111
410
040
25
2θ (deg)
Figure 1
C
010
δ
020
_
322
B
B
010
_
230
DCE clathrate
302
20
D
γ
030
_
411
_
111
β
240
170
δ
030
15
150
060
130
020
C
_
321
020
111
10
D
γ
132
_
411
_
2_30
321
600
110
002
040
_ 420 231
410 401
041
331
_
210
5
E
020
031
410 131
_
111
_
010 210
400
210
410 β
040
β ''
240
170
020
210
111
010
002
101
111
140
030
121
200
020
210
600
150
060
α
211
200
041
131
120 130
110
020
510
Intensity
110
β
α ''
30
020 111
040
35
030
A
40
DCE clathrate
A
040
5
10
15
20
25
2θ (deg)
Figure 2
30
35
40
Types of Orientation in polymers
Through
direction
End
direction
MD
TD
Edge
direction
end
through
Uniplanar orientation : (010)
010
edge
Rizzo, Lamberti, Albunia, Ruiz de Ballesteros, Guerra Macromol. 2002, 35, 5854
Albunia, Rizzo, Guerra Chem. Mat. 2009, 21,3370
Along the chain projections of packing of δ forms of
s-PS showing (010) planes parallel to the film surface
Film surface
010 planes
8.70Å
(010) planes correspond to rows of parallel helices with minimum
interchain distances (8.70Å) and maximum interplanar distances
(10.56Å)
s-PS co-crystals
a/2
R
L
0.87 nm
a
c
a
c
b
L
R
L
R
De Rosa, C.; Rizzo, P.; Ruiz de Ballesteros, O.; Petraccone, V.; Guerra G. Polymer, 1999, 40, 2103.
Chatani, Y.; Shimane, Y.; Inagaki, T.; Ijitsu, T.; Yukinari, T.; Shikuma, H. Polymer, 1993, 34, 1620.
Unique feature of s-PS: three uniplanar orientations
a
c
b
L
R
L
R
Solvent induced crystallization
on amorphous film
Bp < 110°C
Bp > 140°C
Rizzo, Spatola, Del Mauro, Guerra
Rizzo, Della Guardia, Guerra
Macromolecules 2005, 38, 10089
Macromolecules 2004, 37, 8043
a// c//
THF, CHCl3
a// c⊥
p-xylene, dichloroethane
Rizzo, Lamberti, Albunia, Ruiz, Guerra
Macromolecules 2002, 35, 5854
Rizzo, Costabile, Guerra
a⊥ c//
Film
thickness
Albunia, Rizzo, Tarallo, Petraccone,
Guerra Macromolecules 2008, 41, 8632
Macromolecules 2004, 37, 3071
Solution casting; Spin-coating
sPS Films: Orientation Upon Biaxial Balanced Drawing
E
D2
biaxial
stretch
(sPS)syndiotactic polystyrene
E
I
E
L
E
M
R
2.5x2.5
a// c//
Film surface
c
a
a// c010
planes
// Planes
8.70Å
a// c// planes correspond to rows of parallel helices with minimum interchain
distances (8.70Å) and maximum interplanar distances (10.56Å)
Paola Rizzo*, Alexandra R. Albunia Macromolecular Chemistry and Physics 2011, 212,1419-26
D1
Uniplanar orientation
E
D2
biaxial
stretch
E
I
E
L
E
M
R
2.5x2.5
(PET) polyethylene terephthalate
(100) uniplanar orientation
(a=4.56Å b=5.94Å c=10.75Å α=98.5° β=118° γ=112°) triclinic lattice
Bin, Y.; Oishi,K.; Yoshida, K.; Nakashima T.; Matsuo, M.; J. Polymer, 2004, 36,394-402
D1
Uniplanar orientation
E
(i-PP) polypropylene
D2
biaxial
stretch
E
I
E
L
E
M
R
2.5x2.5
A crystalline plane preferentially parallel to the film plane
Primary slip-plane:
- containing the chain axis
- and having the highest density
Paola Rizzo, Vincenzo Venditto, Gaetano Guerra, Antonio Vecchione Macromolecular Symposia 2002, 185, 53-63.
D1
Uniplanar orientation
A
E
D2
biaxial
stretch
E
I
E
L
E
M
R
D1
2.5x2.5
B
MD
(i-PP) polypropylene
TD
MD
C
ND
TD
MD
Paola Rizzo, Vincenzo Venditto, Gaetano Guerra, Antonio Vecchione Macromolecular Symposia 2002, 185, 53-63.
In the Schulz reflection method the goniometer is set at the Bragg angle
corresponding to the crystallographic planes of interest. A special specimen holder
tilted the sample with the horizontal axis (y rotation axis), while rotating it in its own
plane about an axis normal to its surface (j rotation axis) . The y rotation can be
varied from 0°to 90°, whereas the j rotation can be varied from 0°to 360°. The pole
figures are plotted on a polar stereographic projection using linear intensity scale.
Uniplanar orientation
(i-PP) polypropylene
E
D2
biaxial
stretch
E
I
E
L
E
M
R
2.5x2.5
D1
Iso-intensity lines indicate the relative
intensity of the pole related to the maximum
diffracted intensity (assumed equal to 10).
The presence on the diffraction rings of the pole figures of the (110) and (130) reflection
of intensity maxima along MD indicates some preferential c-axis orientation along TD.
It is worth noting that this minor axial orientation, which is related to a not perfect
balancing of draw ratios between the two drawing directions.
Paola Rizzo, Vincenzo Venditto, Gaetano Guerra, Antonio Vecchione Macromolecular Symposia 2002, 185, 53-63.
iPP:uniplanar-axial orientation
A
B
MD
TD
MD
ND
TD
MD
Paola Rizzo, Vincenzo Venditto, Gaetano Guerra, Antonio Vecchione Macromolecular Symposia 2002, 185, 53-63.
C
iPP:uniplanar-axial orientation
The pole figure of the (040) reflection shows a strong maximum in ND. Correspondingly,
the (110) and (130) pole figures show rings at latitude 72° and 46°, respectively.
These rings present more intense maxima along MD and less intense maxima along TD,
indicate the occurrence of a bimodal axial orientation, with prevailing orientation along TD.
Crystallites presenting (110) planes parallel to the film surface, associated with a c-axis
orientation along TD, can account for the two weak reflections at latitude of 72° along
MD, which are present on the (040) pole figure
Paola Rizzo, Vincenzo Venditto, Gaetano Guerra, Antonio Vecchione Macromolecular Symposia 2002, 185, 53-63.
iPP:uniplanar-axial orientation
The bimodal axial orientation, associated
with a major uniplanar orientation relative
to the (0k0) planes and minor uniplanar
orientations relative to the (110) and (130)
planes, can rationalize all the diffraction
peaks which occur in photographic patterns,
like those shown previously
Paola Rizzo, Vincenzo Venditto, Gaetano Guerra, Antonio Vecchione Macromolecular Symposia 2002, 185, 53-63.
Blown film of PE
(PE) polyethylene
a-axis (200) is preferentially oriented along the MD
It is evident that the a-axis (200) is preferentially oriented along the MD, because
poles with highest intensity are concentrated at the north and south ends of the (200)
pole figure.
In the (020) pole figure, poles with the highest intensity are concentrated in the center,
and spread along the TD. This suggests that b-axis is oriented in the ND-TD plane.
Chen, H. Y.; Bishop, M. T.; Landes, B. G.; Chum, S. P.; J. App. Polym. Sci., 2006, 101, 898-907
sPS:uniplanar-axial orientation
sPS:uniplanar-axial orientation
a⊥c ax
a// c ax
cax
sPS: uniplanar-axial orientation