X-ray diffraction in polymer science

(1)

• 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

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 Hermans

orientation function.

(2)

5 10 15 20 25 30 35 40 200 2θ = 23.9° I 2θ (deg) PE polyethylene 110 2θ = 21.4°

1) Identification of semicrystalline polymers

Positions and Intensities of the peaks are used for identifying the material.

hkl hkl

D

tan

R

=

2 θ

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 unoriented samples in reflection

(3)

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-PS

syndiotattic

polystyrene

5 10 15 20 25 30 35 40

I

2

θ

(deg)

s-PS syndiotactic polystyrene

amorphous

(4)

5 10 15 20 25 30 35 40 _ _ 030 220 _ 421 _ 322 _ 421 420 040 410 002 040 _ 111 _ 111 _ 101 _ 041 031 020 200 510 600 410 400 210 310 210 210 010 010 132 131 030 220 200 210 211 220 300 110 I n te n si ty α αα α δδδδ_DCE γγγγ δδδδ 2θ (deg) _ 410 _ 321 301 302 230 121 401 231 331 _ 112 102 210 020 _ 121 111 _ 301 _ 321 211 230 121 212 _ 322 302 411 411 210 020 111 s-PS

Position and Relative intensities are the fingerprint of crystalline phases of polymer

1) Identification of crystalline phases of polymers

a b

αααα

(5)

0 5 10 15 20 25 30 35 40 T = 280 °C_max T = 290 °C_max T = 300 °C_max T = 310 °C_max T = 320 °Cmax t = 5 min_max β β β α β + α β β β β β α α α α α e d c b a In te n si ty 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

2

θ

(deg)

Forma I (110)_I (300)_I (211)_I (220)I (200)_II (220)_II (311)_II

i-PB

(6)

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-PS syndiotattic 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

(7)

5 10 15 20 25 30 35 40 45 50 55 60 0 5000 10000 15000 20000 25000 30000 18.6 59.3 48.7 38.5 28.6 25.6 21.6 19 17 14.1 9.5

In

te

n

s

it

y

(

a

.u

.)

2

θ

(°)

(8)

polimero

Carica inorganica

Diffrazione dei raggi X del campione prima TGA

(9)

• amorphous / crystalline

• (polymer, inorganic/organic compound)

• crystalline phases

The

peak positions, intensities, widths and shapes

provide important information about the structure of the

material

(10)

degree of crystallinity :

x

_c

amorphous e crystallin e crystallin

I

x

_c

+

=

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.

amorphous

e

crystallin

I

=

+

5 10 15 20 25 30 35 I 2θ

(11)

The diffraction profile is divided in 2 parts: peaks are related to diffraction of crystallites, broad alone is related to scattering of amorphous phase.

am cr cr

KA

A

x

_c

+

=

K is a constant related to the different scattering factors of crystalline and

amorphous phases. For relative measures K = 1.

PE

I

_a

=

diffracted

intensity

of

amorphous phase

I

_b

=

diffracted

intensity

of

background

I

_c

=

diffracted

intensity

of

crystalline phase

I_c I_a _I b

The assumption is that the areas are proportional to the

scattering intensities of crystalline and amorphous phases

(12)

5 10 15 20 25 30 In te n si ty 2θ (deg) 5 10 15 20 25 30 2θ(deg) In te n si ty

The 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

(13)

B =

∆

2 θ

= 2

θ

₂

– 2

θ

₁

2θ (deg)

β

= B

−

b

b = broadening instrumental

β

= broadening due to crystallites dimensions

B =

half-width of peaks In te n si ty I_max I_max/2 2θ₂ 2θ₁ B 2θ

Crystallite size in polymers :

cos

θ

λ

⋅

β

=

K

L

_hkl

_{Scherrer’s Equation}

L_hkl = 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 ( λ_Cuk_α = 1.5418 Å.)

b can be measured by the half-width of a peak

of crystalline compounds low molecular weight.

(14)

4)Orientation

: Polymers, due to their long chain structure,are highly susceptible to orientation Draw direction c fiber X-ray Fiber axes

(15)

X-ray diffraction of oriented polymer: fiber pattern

equator l_{=0 (hk0)} First layer l_{=1 (hk1)} Second layer l_{=2 (hk2)} i-PP fiber

))

/

(

λ

1

-R

y

tan

sen

c

=

l

c = periodicity along the chain axes

λλλλ = wavelength used (CuK_αααα = 1.5418 Å)

l l l

l _{= layer}

x, y = distance of reflections from the center

along equatorial and meridian lines

R = chamber radius meridian y x             π = θ R y tan cos R x cos cos -1 2 360 2

(16)

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

(17)

ε= 50 % ε= 100 % ε= 200 % ε= 500 %

Oriented sPP fiber stretched at different

ε

=100(Lf-Li)/Li

Lf = final length Li = initial length

First layer l_{=1 (hk1)}

(18)

Azimutal scan: measuring the intensity at 2θconstant, by varying the χ angle.

If

χ

= 0 for meridian reflection (00

l

₎

<cos

2

φ

00l

> = 1 e f

_c

=

1 The fiber is perfected oriented: f

_c

= 1

Orientation with respect to draw direction

parameter parallel random perpendicular <cos2φ_> f 1 1 1/3 0 0 -1/2

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

(

3

1 )

2

1

₂

−

=

φ

cos

f

Z = draw axes a b c φ_a,Z φ_b,Z φ_c,Z χ 2 χ

( )

χ χ χ χ χ χ χ >= χ < χ = φ

∫

π π d ) I( d 2 / 0 2 / 0 2 2 2 2 sen cos sen I cos cos cos hkl hkl hkl

If the radiation is perpendicular to the fiber axes

Average cosine squared value of φ angle

(19)

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

6

Uniplanar-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).

(20)

5 10 15 20 25 30 35 40 DCE clathrate δδδδ γγγγ ββββ α αα α 240 101 150 D C B A E 170 111 060 130 040 110 020 030 210 I n te n si ty 040 Figure 2 2θ (deg) 111 020 020 010 010 040 410 030 020 600 211 β 410 400 220 300 200 110 β 230 _ 5 10 15 20 25 30 35 40 DCE clathrate δδδδ γγγγ ββββ '' α αα α '' 131 041 240 150 101 002 170 111 060 140 130 120 040 110 020 A B C D E 411 _ 321 _ 230 _ 030 410 002 Figure 1 040 _ 041 031 020 β 200 510 600 410 400 210 310 β 210 210 010 010 132 131 030 220 200 210 211 220 300 110 I n te n si ty 2θ (deg) 121 401 231 331 020 210 020 111 _ 111 302 111 _ 111 _ 411 322 _ 321 _ 420 040 410 _ _

(21)

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

(22)

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 maximum interplanar distances

(10.56Å)

(23)

s-PS co-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 nm R L a/2

a

c

b

L L R R

(24)

Unique feature of s-PS:

three uniplanar orientations

a

c

b

L L R R

Solution casting; Spin-coating

Solvent induced crystallization

on amorphous film

THF, CHCl₃

Rizzo, Lamberti, Albunia, Ruiz, Guerra

Macromolecules 2002, 35, 5854

p-xylene, dichloroethane Rizzo, Costabile, Guerra

Bp > 140°C

Rizzo, Spatola, Del Mauro, Guerra

Bp < 110°C

Rizzo, Della Guardia, Guerra

Film thickness

a

_//

c

_//

a

_//

c

_⊥

a

_⊥

c

_//

Albunia, Rizzo, Tarallo, Petraccone, Guerra Macromolecules 2008, 41, 8632

(25)

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

_//

c

_//

010 planes 8.70Å Film surface

a// c// planes

correspond to rows of parallel helices with minimum interchain distances (8.70Å) and maximum interplanar distances (10.56Å)

a

_//

c

_//Planes

(26)

(PET)

polyethylene terephthalate

Bin, Y.; Oishi,K.; Yoshida, K.; Nakashima T.; Matsuo, M.; J. Polymer, 2004, 36,394-402

(a=4.56Å b=5.94Å c=10.75Å

α

=98.5° β=118° γ=112°) triclinic lattice

(100)

uniplanar orientation

(27)

Uniplanar orientation

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.

(i-PP) polypropylene biaxial stretch 2.5x2.5 D1 D₂ L M R I E E E E

(28)

ND

MD

TD

TD _MD MD

A

B

_C

(i-PP) polypropylene

Uniplanar orientation

(29)

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.

(30)

(i-PP) polypropylene

Uniplanar orientation

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

(31)

ND

MD

TD

TD _MD MD

A

B

C

(32)

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

(33)

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

(34)

(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.