X-ray diffraction in polymer science - Polymer Technology Group [PDF]

XRD is a primary technique to determine the degree of crystallinity in polymers. • 3) Microstructure: Crystallite size

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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



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



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

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