x-ray diffraction in polymer · pdf filex ray diffraction of semicrystalline and amorphous...
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• 1) Identification of semicrystalline polymers and Recognition ofcrystalline 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 nano-scale 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 Hermansorientation function.
X-ray diffraction in polymer science
5 10 15 20 25 30 35 40
2002θ = 23.9°
I
2θ (deg)
PEpolyethylene
1102θ = 21.4°
1) Identification of semicrystalline polymersPositions and Intensities of the peaks are used for identifying the material.
hklhkl tanDR θ= 2
The diffraction of unoriented samples in transmission by using a flat film is characterized by concentric circles called “Debye Scherrer Rings”
Unoriented PE
200(2θθθθ=23.9°)
110(2θθθθ=21.4°)
The diffraction of unorientedsamples in reflection
Unoriented PE
X ray diffraction of semicrystalline and amorphous polymer
5 10 15 20 25 30 35 40
400
310
210
220
211(20.3°)
300(11.8°)
I
2θ (deg)
110(6.2°)
s-PSsyndiotattic polystyrene
5 10 15 20 25 30 35 40
I
2θ (deg)
s-PSsyndiotactic polystyrene
amorphous
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_
_
030220
_421
_322
_421
420040410
002
040
_111_111
_
101
_
041
031
020
200
510
600
410400210
310
210
210010
010
132
131030
220
200
210
211
220300
110
Inte
nsity
αααα
δδδδDCE
γγγγ
δδδδ
2θ (deg)
_410_321301
302
230
121
401231
331
_112102
210020
_121111
_
301
_321211
230
121
212_322302
411
411
210020
111
s-PS
Position and Relative intensities are the fingerprint of crystalline phases of polymer
1) Identification of crystalline phases of polymers
a b
αααα
δδδδ
0 5 10 15 20 25 30 35 40
T = 280 °Cmax
T = 290 °Cmax
T = 300 °Cmax
T = 310 °Cmax
T = 320 °Cmax
t = 5 minmax
β
β
β
α
β+α
β
β
β
β
β
α
αα
αα
e
d
c
b
a
Inte
nsity
2ϑ (deg)
s-PS
Identification of crystalline phases of polymers also if they are present in mixture.
5 10 15 20 25 30
Forma I + II
Forma I + II
Forma II
I
2θ (deg)
Forma I
(110)I
(300)I
(211)I(220)I
(200)II
(220)II
(311)II
i-PB
X ray diffraction of semicrystalline polymer and inorganic compound
5 10 15 20 25 30 35 40
400
310
210
220
211(20.3°)
300(11.8°)
I
2θ (deg)
110(6.2°)
s-PSsyndiotattic polystyrene
inorganic compound Polymer
5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80
I
2 θ (deg)
KBr
5 10 15 20 25 30 35 40 45 50 55 60
0
5000
10000
15000
20000
25000
30000
18.6
59.348.738.5
28.6
25.621.6
19
17
14.1
9.5
Inte
nsity
(a.
u.)
2θ(°)
What about this spectra?
polimero
Carica inorganica
Diffrazione dei raggi X del campione prima TGA
Diffrazione dei raggi X del campione dopo TGA
• amorphous / crystalline • (polymer, inorganic/organic compound)
• crystalline phases
The peak positions, intensities, widths and shapesprovide important information about the structure of the material
degree of crystallinity : xc
amorphousecrystallin
ecrystallin
II
Ixc +
=
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.
amorphousecrystallin III +=
5 10 15 20 25 30 35
I
2θ
The diffraction profile is divided in 2 parts: peaks are related to diffraction of crystallites, broad alone is related to scattering of amorphous phase.
amcr
cr
KAA
Axc +
=
K is a constant related to the different scattering factors of crystalline and amorphous phases. For relative measures K = 1.
PE
Ia = diffracted intensity of amorphous phaseIb = diffracted intensity of backgroundIc = diffracted intensity of crystalline phase
I c
Ia Ib
The assumption is that the areas are proportional to the scattering intensities of crystalline and amorphous phases
2) XRD : determination of degree of crystallinity in polymers.
5 10 15 20 25 30
Inte
nsity
2θ (deg)
5 10 15 20 25 302θ (deg)
Inte
nsi
tyThe half-width of peaks is related to crystallite dimensions.
Contribution to broadening can be due to lattice distortion, structural disorder as well as instrumental effects.
Half-width large correspond to smaller crystallites
3) Microstructure: Crystallite size in polymers
Half-width narrow correspond to bigger crystallites
B = ∆2θ = 2θ2 – 2θ1
2θ (deg)
β = B − bb = broadening instrumentalβ= broadening due to crystallites dimensions
B = half-width of peaksIn
tens
ityImax
Imax/2
2θ22θ1
B
2θ
Crystallite size in polymers:
cosθ
λ
⋅β= K
Lhkl 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.)
b can be measured by the half-width of a peak of crystalline compounds low molecular weight.
3) Microstructure: Crystallite size in polymers
4)Orientation: Polymers, due to their long chain structure,are highly susceptible to orientation
Draw direction
c
fiber
X-ray
Fiberaxes
X-ray diffraction of oriented polymer: fiber pattern
equator l=0 (hk0)
First layer l=1 (hk1)
Second layerl=2 (hk2)
i-PP fiber
))/((
λ
1- Rytansenc
l=
c = periodicity along the chain axesλλλλ = wavelength used (CuKαααα = 1.5418 Å)llll = layerx, y = distance of reflections from the center along equatorial and meridian linesR = chamber radius
meridiany
x
π=θ
R
ytancos
R
xcoscos 1-
2
3602
Distance from layers correspond to c axes
X-ray diffraction of fibers annealed at different T
Trans-planar conformation
c=5.1Å
Helical conformation
c=7.8 Å
ε = 50 % ε = 100 % ε = 500 %ε = 200 %
Oriented sPP fiber stretched at different ε
ε=100(Lf-Li)/Li
Lf = final length
Li = initial length
First layer l=1 (hk1)
equator l=0 (hk0)
Azimutal scan:measuring the intensity at 2θ constant, by varying the χ angle.
If χ = 0 for meridian reflection (00l)<cos2φ00l> = 1 e fc = 1
The fiber is perfected oriented: fc = 1
Orientation with respect to draw direction
parameter parallel random perpendicular
<cos2φ>f
11
1/30
0-1/2
The degree of orientation can be determined from the intensity
distribution of the corresponding diffraction on the Debye ring
by using theHermans’ Orientation Function
( )132
1 2 −= φφ cosf
Z = draw axes
a b
c
φa,Z φb,Z
φc,Z
χ
2χ ( )
χχχ
χχχχ>=χ<
χ=φ
∫
∫π
π
d)I(
d
2/
0
2/
0
2
2
22
sen
cossenI
cos
coscos
hkl
hklhkl
If the radiation is perpendicular to the fiber axes
Average cosine squared value of φ angle
Types of ORIENTATION GEOMETRY
(Heffelfinger& Burton)1 PREFERRED ORIENTATION
Crystallographic elements
Reference elements
1 Random - - -
2 AxialCrystallographic Axes parallel
to reference axesc draw axes
3 PlanarCrystallographic Axes on a
reference plane c film plane
4 Planar-axialCrystallographic plane
Parallel to a reference axes(100) draw axes
5 UniplanarCrystallographic plane
Parallel to a a reference plane (100) film plane
6Uniplanar-
axial
Crystallographic Axes parallel to reference axes
and a Crystallographic plane Parallel to a a reference plane
c
(100)
draw axes
film plane
C. J. Heffelfinger, R. L. Burton J. Polym. Sci. 47, 289 (1960).
Types of Orientation in polymers
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DCE clathrate
δδδδ
γγγγ
ββββ
αααα
240101
150
D
C
B
A
E
170111
060130
040
110020
030
210
Inte
nsity
040
Figure 2
2θ (deg)
111
020
020
010
010
040410
030
020
600
211
β410400
220
300
200
110
β
230_
5 10 15 20 25 30 35 40
DCE clathrate
δδδδ
γγγγ
ββββ ''
αααα ''
131041
240
150
101
002170
111
060
140
130120
040
110020
A
B
C
D
E
411_
321_230_
030
410
002
Figure 1
040
_
041
031
020
β
200
510
600
410400
210
310β
210
210010
010
132
131030
220
200
210
211
220300
110
Inte
nsity
2θ (deg)
121
401231
331
020
210020
111
_
111
302111_
111_
411
322_
321_
420040
410_
_
Uniplanar orientation: sps film
end
edge
through
Through direction
Edge direction
End direction
MD TD
Types of Orientation in polymers
010
Uniplanar orientation : (010)
Rizzo, Lamberti, Albunia, Ruiz de Ballesteros, Guerra Macromol.2002, 35, 5854
Albunia, Rizzo, Guerra Chem. Mat.2009, 21,3370
010 planes
8.70Å
Film surface
Along the chain projections of packing of δ forms of s-PS showing (010) planes parallel to the film surface
(010) planes correspond to rows of parallel helices with minimum interchain distances (8.70Å) and maximuminterplanar distances(10.56Å)
s-PSco-crystals
Chatani, Y.; Shimane, Y.; Inagaki, T.; Ijitsu, T.; Yukinari, T.; Shikuma, H. Polymer, 1993, 34, 1620.
De Rosa, C.; Rizzo, P.; Ruiz de Ballesteros, O.; Petraccone, V.; Guerra G. Polymer, 1999, 40, 2103.
c
a
0.87 nmRLa/2
ac
b L
LR
R
Unique feature of s-PS:three uniplanar orientations
ac
b L
LR
R
Solution casting; Spin-coating
Solvent induced crystallization on amorphous film
THF, CHCl3
Rizzo, Lamberti, Albunia, Ruiz, Guerra
Macromolecules2002, 35, 5854
p-xylene, dichloroethane
Rizzo, Costabile, Guerra
Macromolecules2004, 37, 3071
Bp > 140°CRizzo, Spatola, Del Mauro, Guerra
Macromolecules2005, 38, 10089
Bp < 110°CRizzo, Della Guardia, Guerra
Macromolecules2004, 37, 8043
Film
thickness
a// c// a⊥ c//a// c⊥
Albunia, Rizzo, Tarallo, Petraccone, Guerra Macromolecules 2008, 41, 8632
biaxial stretch
2.5x2.5 D1
D2
L M R
I
E
E E
E
sPS Films: Orientation Upon Biaxial Balanced Drawing
Paola Rizzo*, Alexandra R. Albunia Macromolecular Chemistry and Physics 2011, 212,1419-26
c
a
a// c//
010 planes
8.70Å
Film surface
a// c// planescorrespond to rows of parallel helices with minimum interchaindistances (8.70Å) and maximum interplanar distances (10.56Å)
a// c// Planes
(sPS)syndiotactic polystyrene
(PET) polyethylene terephthalate
biaxial stretch
2.5x2.5 D1
D2
L M R
I
E
E E
E
Bin, Y.; Oishi,K.; Yoshida, K.; Nakashima T.; Matsuo, M.; J. Polymer, 2004,36,394-402
(a=4.56Å b=5.94Å c=10.75Åα=98.5° β=118° γ=112°) triclinic lattice
(100)uniplanar orientation
Uniplanar orientation
Uniplanar orientation
A crystalline planepreferentiallyparallel to the film planePrimary 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.
(i-PP) polypropylenebiaxial stretch
2.5x2.5 D1
D2
L M R
I
E
E E
E
ND
MD
TD
TD MD
MDA
B C
(i-PP) polypropylene
Paola Rizzo, Vincenzo Venditto, Gaetano Guerra, Antonio Vecchione Macromolecular Symposia 2002, 185, 53-63.
Uniplanarorientationbiaxial stretch
2.5x2.5 D1
D2
L M R
I
E
E E
E
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.
(i-PP) polypropylene
Uniplanarorientationbiaxial stretch
2.5x2.5 D1
D2
L M R
I
E
E E
E
Paola Rizzo, Vincenzo Venditto, Gaetano Guerra, Antonio Vecchione Macromolecular Symposia 2002, 185, 53-63.
Iso-intensity lines indicate the relativeintensity 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) reflectionof 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 perfectbalancing of draw ratios between the two drawing directions.
ND
MDTD
TD MD
MDA
B C
Paola Rizzo, Vincenzo Venditto, Gaetano Guerra, Antonio Vecchione Macromolecular Symposia 2002, 185, 53-63.
iPP:uniplanar-axial orientation
Paola Rizzo, Vincenzo Venditto, Gaetano Guerra, Antonio Vecchione Macromolecular Symposia 2002, 185, 53-63.
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 uniplanarorientations relative to the (110) and (130) planes, can rationalize all the diffraction peaks which occur in photographic patterns, like those shown previously
(PE) polyethylene
a-axis (200) is preferentially oriented along the MD
Chen, H. Y.; Bishop, M. T.; Landes, B. G.; Chum, S. P.; J. App. Polym. Sci., 2006, 101, 898-907
Blown film of PE
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.
sPS:uniplanar-axial orientation
sPS:uniplanar-axial orientation
cax
a// c ax
a⊥c ax
sPS: uniplanar-axial orientation