• 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

5 10 15 20 25 30 35 40

_

_

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

5 10 15 20 25 30 35 40

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