Idea Transcript
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
f
1 1
1/3 0
0 -1/2
If χ = 0 for meridian reflection (00l) = 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