6_mptp_optical anisotropy of polymers

Polymer Engineering Department, DEP University of Minho, UM

4800-058 Guimarães, Portugal

Carla I. Martins

Master in Properties and Technology of Polymers

Polymer Properties

OPTICAL PROPERTIES AND MORPHOLOGY OF POLYMERS

Optical anisotropy of polymers

Transparencies prepared by Carla Isabel Martins and Maria Jovita Oliveira

1


Refractive index of polymer molecules

Refractive index and molecular organization

Interaction between polarized light and birefringent materials

- polarized light

- polarization colours

Birefringence measuring techniques

n1 > n2PE

n2The polarizability of the C-C bonds is higher thanthat of the C-H bonds

Optical anisotropy of polymersRefractive index of polymer

molecules

Polymer molecules are intrinsically anisotropic: the polarizability (and the refractive index) varies with the vibration direction of the light waves

Examples:

n1

2



Examples:

n1

of the phenil group (conjugated double bonds)

n1 < n2

PS

The polarizability of the C-C bonds is lower than thatn2

n1 > n2

PET



Examples:

n1

n2

3



The birefringence (n) is given by the difference between the two principal refractive indexes, n1(longitudinal) and n2 (transversal)

n1

n2

n = n1 - n2

Optical anisotropy of polymersRefractive index and molecular organization

Polymers with random organization of the molecules are optically isotropic

- Amorphous polymers solidified

or polimerized in quiescent conditions

The refractive index :- is independent of the polarization direction of the light- is the average of the two principal refractive indices of the molecule

The birefringence, n = 0

Examples:

- Melts of common polymers

n0

n0n0

4



Polymers with the molecules regularly arranged, deformed or under stress are optically anisotropic

Types of anisotropic polymers:

Polymers with molecular orientation (fibres, films, bioriented bottles, etc.)

Crystalline polymers

Block coplymers and fine polymer blends with phase organization

Sheared polymer melts

Stressed polymers

Liquid crystals



1. Polymers with molecular orientation

Example: Fibres

During the manufacturing process the molecules are aligned along the fibre axis

n1

n2

n2 ≠ n1

The material has uniaxial anisotropy. Therefore. it

is characterized by two principal refractive

indexes

5


Refractive index and molecular organization1. Polymers with molecular orientation

Example: Bioriented films

Uniaxial deformation

Biaxial deformation

Tenter frame film processing

Transversal

n2

Anisotropic biaxial material, therefore it is

characterized by three principal refractive

indexes

n1 ≠ n2 ≠ n3n3

Extrusion


Refractive index and molecular organization1. Polymers with molecular orientation

Example: Bioriented filmsThe molecules are aligned

along the extrusionand the transversal

directions

n1

Film plane

6

Picture taken between cross polarizers on the white light box

Integral hinge of PP

The anisotropy is generally biaxial and varies with the location in the part




Example: injection moulded parts

Molecular orientation

The anisotropy is generally biaxial and varies with the location in the part

HDPE

Molecular orientation

HDPE




Example: injection moulded parts

7

Molecular chain Lamellae Spherulite

The regular organization of the molecules creates anisotropy at lamellar and spherulitic levels

10 nm0,1- 1m

Severalm

1-200 m



2. Crystalline polymers

The birefringence of the spherulite is given by:n = nR – nT

SpherulitenR

nT

PE spherulites viewed under the polarizing microscope



2. Crystalline polymers

8

Hexagonal arrangement of butadiene rods in the PS matrix

Example: SBS triblock copolymer

TEM image of SBS:dark areas – PB, bright areas - PS

If the constituents have different refractive indexes and the dispersed phase is structurally organized

Form birefringence



3. Block copolymers and fine polymer blends with phase organization

www.cheque.uq.edu.au/.../clip_image001.jpg

Cross-Slot flow of PE in the Multi-Pass Rheometerhttp://www.cheng.cam.ac.uk/research/groups/polymer/news/news_old.html



4. Sheared polymer melts

9

http://www.cheque.uq.edu.au/.../clip_image001.jpg




































http://www.cheng.cam.ac.uk/research/groups/polymer/news/news_old.html



























































farm1.static.flickr.com/44/350194457_2174278a...



4. Sheared polymer melts

PC lens after injection moulding PC lens after injection moulding and with eyeglass frame

www.exponent.com/.../lensethumb.jpg

Under stress the intra and intermolecular distances change and that creates anisotropy



5. Stressed polymers

10

http://www.exponent.com/.../lensethumb.jpg














PS part stressed by bending the right side Strip of film stretched between crossed polarizers

www.oberlin.edu/.../optics/photoelastic.jpg



5. Stressed polymers

http://www.msm.cam.ac.uk/doitpoms/tlplib/anisotropy

Example:4-methoxylbenzylidene-4'-butylaniline (MBBA) transforms from crystalline to nematic liquid crystal at 20ºC, and from nematic to an isotropic liquid at 74ºC



6. Liquid crystals

11

http://www.oberlin.edu/.../optics/photoelastic.jpg




































Polarized Light



Single light waves are plane polarized:

The vibration direction of the electric field is perpendicular to the propagation direction of the wave and lies in a single plane (plane of polarization)

Polarization direction

Propagation direction

en.wikipedia.org

Polarizing device



Light may be polarized using several methods, one of them is by selective absorption of light waves

12

http://www.answers.com/topic/wire-grid-polarizer-svg-1

















Selective absorption

(dichroism)

Light polarized parallel to the chains is absorbed by the sheet; light polarized

perpendicularly to the chains is transmitted.

Polaroid sheet

Stretched polyvinyl alcohol doped with iodine

13

Optical anisotropy of polymersInteraction between polarized light and birefringent materials

Double refraction by anisotropic materialsWhen light waves pass through anisotropic materials they are split in two

Refracted light

Birefringent material

Unpolarized light

Anisotropic materials are birefringent

Properties of the refracted rays:1 – Generally follow different paths

2 – One of the rays (ordinary ray) follows the Snell’s Law

(the vibration direction is perpendicular to the propagation direction)

3 – The other ray (extraordinary ray) does not follow the Snell’s Law

(in general, the vibration direction is not perpendicular to the propagation direction)

Ordinary ray Extraordinary ray



Double refraction by anisotropic materials

Properties of the refracted rays:

4 – The two rays are polarized in perpendicular directions: the directions imposed by the material

5 – They travel at different speeds, according to the refractive index imposed by each vibration direction

Anisotropic material



Double refraction by anisotropic materials

14

The incident light (unpolarized) is polarized when passing at the polarizer; then it is double-refracted at the sample and forced to change its vibration direction; finally the refracted waves are set to vibrate in

the same plane (the analyzer plane) when they pass through the analyser.




Interaction between polarized light and birefringent materialsAnisotropic materials in crossed polarsMaterialWhite light

O

EP

PO

P

90-

P

PE

APE

PEA

90-PO

POA

15

MaterialWhite light

Final Amplitude (A) = 2P.cos.sen

The intensity of the light emerging from the analyser varies with the angle between the vibration direction of the incident light and the permited directions at the material.

For = 0º or 90º (A = 0) – light extinction For = 45º (A = P/2) - intensity is maximum

O

EP

PO

P

90-

P

PE

APE

PEA

PEA=P. sen .cos

90-PO

POA

POA=P.cos.sen

PO=P.cos PE=P.sen

Anisotropic materials in crossed polars



Extinction and maximum intensity positions

For = 0º (A = 0) – light extinction (the sample appears black)

P

AThe permitted directions coincide with the

vibration direction of the polarizer or analyser

16




For 45º> > 0º (A ≠ 0) – some light is transmitted - sample is visible

PA

A




For = 45º (A ≠ 0) – maximum light is transmitted –

sample is visible with maximum intensity

P

17



Extinction and maximum intensity positionsFor = 90º (A = 0) – light extinction (the sample appears black)

PA

The permitted directions coincide with the vibration direction of the polarizer or analyser




For 135º> > 90º (A ≠ 0) – some light is transmitted - sample is visible

P

A

18

For = 135º (A ≠ 0) – maximum light is transmitted –sample is visible with maximum intensity

P

A







For = 180º (A = 0) – light extinction (the sample appears black)

P

A

The permitted directions coincide with the vibration direction of the polarizer or analyser

19

The pair-waves leaving the analyser are out of phase:

OPD 2

OPD R t( n1 n2 ) t( n )

- angular phase difference

OPD – optical path difference or Retardation

(R) t – thickness of the slab of material

n1, n2 – refractive indexes

n - birefringence


OPD = t.(n1-n2)




Indicatrix and vibration direction in the material

Indicatrix- tridimensional model that shows the vibration directions and respective refractive indexes of the refracted waves

Isotropic materials - sphere The refractive index does not depend on the vibration direction of the light passing through

the material.

Y

n 0

Xn1n1

n1

X

20

Y

nono



Uniaxial materials – ellipsoid of revolution

The refractive indexes and the vibration directions are given by the axis of the section passing

through the centre of the ellipsoid, perpendicular to the propagation direction

Z = optic axis

X

ne


Uniaxial materialsFor light propagating through the Z axis the section

is circular. The refractive index is unique, independent of the vibration direction (radius of the

circle).

The material behaves as isotropic (n=0)

Z-axis is called the optical axis

Y

Xno

no

no

Z = optic axis

X

Y

ne

nono

Circular section


21

Uniaxial materials

n is maximum

Z = optic axis

Principal section

X

Y

Vibration direction of the o-ray

ne

nono no

ne Vibration direction of the e-ray



Uniaxial materialsFor light entering through any other direction (0º < < 90º)

the section is elliptic. The refractive index corresponding to

the e- ray (ne’) is intermediate between ne and no.

n (ne’ – no) is intermediate

Z = optic axis

Vibration direction

X

Y

ne

nono

of the o-ray Vibration direction of the e’-ray

no ne’



22



Uniaxial materials

The optical sign of the indicatrix can be positive or negative

Z = optic axis

Uniaxial positiveEx: PP fibres

ne ne > no

no

Z = optic axis

Uniaxial negativeEx: Acrylic fibres

ne < no

ne

no



Biaxial materials - triaxial ellipsoidAre characterized by three principal refractive indeces: n (maximum), n (minimum) and n

(intermediate)

Z

OA OA2Vz

YX

n

n

nn

n

n

n

n

n

The principal sections are elliptic: corresponds to light propagating through the principal axis.

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OA OA

2Vz

YX


Z

n

n

n

n

n

There are 2 circular sections in the biaxial indicatrix for light propagating through the

two optical axes (OA)

2V angle - this angle determines the (+ or -) sign and it is related to the velocities of the refracted rays




Biaxial materials

Are characterized by three principal refractive index: n (maximum), n (minimum) and n

(intermediate)

ZOA

OA

2Vz

YX

n

n

n

• If 2V is acute about Z: (+)

• If 2V is acute about X: (-)

• If 2V=90°, sign is indeterminate

• if 2V=0°, material is uniaxial

24

Material

Depending on the phase shift and relative amplitude, light emerging from the anisotropic material may have linear, elliptical, or circularly polarization

From: hyperphysics.phy-astr.gsu.edu/.../polcir.gif


Phase shift and polarization of refracted waves

= 0°, 180°(/2) or 360°()

When the phase shift is 0, 180, and 360 degrees, the resultant vector (the black line surrounding the waves) creates a black sine wave positioned at a 45-degree

angle between the orthogonal waves, or traces a straight line when the approaching waves are viewed along with the propagation direction (linearly

polarized light).http://www.olympusmicro.com/primer/java/polarizedlight/waveform3d/



25

http://www.olympusmicro.com/primer/java/polarizedlight/waveform3d/































Between zero and 90 degrees, the resultant vector forms an ellipse

= 45°




At 90 ° the ellipse becomes a circle (circularly polarized light)

= 90°(/4)

= 180°

= 226°

above 90 ° the light is again elliptically polarized

and the ellipse slowly collapses to form linearly polarized light (at 180 °)http://www.olympusmicro.com/primer/java/polarizedlight/waveform

3d/



26































































= 270°

At 270°, right-handed circularly polarized light is produced, which folds into elliptically polarized light between 270 ° and 360 °and, linearly

polarized light is again formed at 360 °

= 360° = 283°




Interference between waves may occur if they obey to these conditions: 1 – They have the same wavelength2 - Have the same propagation direction3 – Travel at the same speed4 – Vibrate in the same plane


OPD = t.(n1-n2)

dcssi.istm.cnr.it/Macchi/dottorato/Printing1.ppt

These waves can not interfere because they vibrate in perpendicular planes

After passing through the analyser the vibration plane becomes the same and interference can take place.



27
































Interference may be:

or partially constructive or partially destructive


Polarization colours with crossed polars

red

in green light

re

d

2re

d


Polarization colours with crossed polarsUnder crossed polars the condition for destructive interference is:

OPD = n n – integer - wavelength

With monochromatic light:

Destructive interference the sample appears black

Constructive interference the sample appears with the colour of the light

Quartz wedge

2re

d

3red4red

in red light OPD = e. n =n

3red4red

in green light

OPD increases withe continuously

28



With white light destructive or constructive interference occurs only to specific wavelengths, depending on which one satisfy the respective condition.

0




For large optical path differences (OPD), multiple constructive and destructive interference occur, leading to the sample to appears white.

29




Quartz wedgeOPD = e. n =n

The increase in thickness increases steadily OPD and changes the polarization colour

OPD = e. n =n

In the quartz wedge the increase in thickness increases steadily OPD and changes the polarization colour

Quartz wedge

/4Retardation

plate

1 Retardation

plate




30



With white light destructive or constructive interference occurs only to specific

wavelengths, depending on which one satisfy the respective condition.

Michel Levy Polarization Colours Chart

OPD (nm)


31

Methods for birefringence measurements

A. Direct measurement of refractive indices

Abbé refractometer

B. Measurement of Optical Path Difference (birefringence)

Michel Levy Chart (identification of the polarization colours) Compensation methods Wedge method (identification of interference fringes) Spectrophotometer method



How to measure birefringence?

1. Abbé refractometer

Direct measurement of refractive indexof a polymer

Abbé refractometer

32


1. Abbé refractometer T

he sample is sandwiched into a thin

layer between an illuminating prism and

a refracting prism.

The refracting prism is made of a glass

with a high refractive index (e.g., 1.75)

compared to the sample to be

measured

A light source is projected through the

illuminating prism, the bottom surface

of which is ground, so each point on

this surface can be thought of as

generating light rays traveling in all

directions.Abbé refractometer

n1

n2

n2 >> n1

light vibrating in all directions)Light traveling from point A to point B

will have the largest angle of incidence

(i) and thus the largest possible angle

of refraction (r) for that sample. All

other rays of light entering the refracting

prism will have smaller r and hence lie

to the left of point C (Snells law).

A detector placed on the back side of

the refracting prism shows an image of

light and dark regions

By calibrating the scale, the position of

the borderline can be used to

determine the refractive index of the

sample.

n


Roughened surface (generates

33

n1

n2

n2 >> n1


Roughened surface (generates light vibrating in all directions)

After determination of n in two different

directions, birefringence can be

determined as follow:

n12 = n2-n1

n13 = n3-n1

n12 + n23 + n31 =0

In plane and out of plane birefringence can be obtained!


Michel Levy Chart

OPD

The polarization colour is correlated to a specific OPD

What is the birefringence of a film showing the colour marked with X, when

the film is placed between cross polars under a white light box?

x

34

OPD of x = 700 m

Optical path diference – values directly taken from the chart, at the colour observed when the sample is placed between cross polars under white light source

x


Michel Levy Chart

Thickness of the sample t = 0.03 mm

Birefringence n = 0.023

Birefringence – It is measured by the oblique line intersecting the colour at the

corresponding thickness of the sample, as shown in the chart.

x


Michel Levy Chart

35


Michel Levy Chart

LIMITATIONS:

- The colour depends on the light source and on the sensitivity of the operator- It is difficult to

distinguish between identical colours of different orders

ADVANTAGES:

- It is economic, simple and fast

- It is very useful to confirm the results obtained from other more precise methods, such as using compensators.


Michel Levy Chart

How to distinguish between identical colours of different orders?

x x x

36


Michel Levy Chart


Using wave plates or retarders!

A wave plate or retarder is an optical device that alters the polarization state of a light wave travelling through it

Quarter-wave plate creates a quarter-wavelength phase shift and can change linearly polarized light to circular and vice versa. This is done by adjusting the plane of the incident light so that it makes 45° angle with the fast axis. This gives ordinary and extraordinary waves with equal amplitude.Lambda plate creates a wavelength phase shift (530 to 560 nm ) to the ordinary and extraordinary waves


Michel Levy Chart

Where to place the waveplates in the microscope?

37


Michel Levy Chart

Changes in polarization colour when using a quarter wave plate and a Lambda wave plate.


Looking at the colour changes after introducing a wave plate, it is better

distinguished the colour corresponding to the correct OPD of the sample


38

Concept of compensation

Slow vibration direction (higher refractive index)

Fast vibration direction (lower refractive index)

Polarization colour = Black

OPD1 + OPD2 = 0

OPD1 + OPD2 > OPD original

Polarization colour = away from black

Compensation method

The OPD of an anisotropic sample may be compensated if another one with equal

OPD is superimposed on it and the fast vibration direction of the first is aligned with the slow vibration direction of the

second.

No light will be transmitted above the analyser when compensation is

achieved. The colour will be black.


Compensation method

Example: Berek compensator

Thin plate of calcite (uniaxial cristal) cut perpendicularly to the optic axis, mounted on a axis that allows its rotation to a maximum of 30º.


39

Berek compensator

v2

v1

By varying the rotation angle, OPD varies due to:

- The increase in thickness

- The tilt of the indicatrix

May be used for precise measurement of the OPD of fibres,

films andthin cross-sections of moulded

parts

Birefringence measuring techniquesCompensation method

Compensator or retardation plate


Compensation methodsMeasurement of OPD with the polarized light microscope and

compensator

40

Compensation methodsMeasurement of OPD with the polarized light microscope and compensator

Method:

1. Place the sample between crossed polars at 45º from the extinction position (extinction position happens when a black field appears)

2. Insert the Berek compensator at the slot of the microscope

3. Tilt the compensator plate until a black fringe appears at the centre of the field

4. Record the tilt angle and repeat the process by tilting in the opposite direction

Note: compensation may not occur if the sample and the compensator have the fast and fast directions parallel to each other. In this case, rotate the sample 90º to the actual position.



Compensation methodsMeasurement of OPD with the polarized light microscope and compensator

i = (I1-I2)/2

I1 e I2 – angles measured at the compensator

OPD = C x (sen2 i + a sen4 i + b sen6 i + c sen8 i)

with:a = 0.20343836b = 0.07043622c = 0.02679496

C = 103.912 = 8165.824

Birefringence:

n

OPD sample thickness 41

Example: PC injection moulded discs

Procedure:

Cut a triangular wedge from the

sample with the edges aligned in pre-

defined directions

Polish the wedge surfaces to obtain

a very smooth finish


Wedge Method

Suitable for measuring OPD in rigid transparent polymers

Procedure: Cut a triangular wedge from the

sample with the edges aligned in pre-

defined

directions

Polish the wedge surfaces to obtain a

very smooth finish

Immerse the wedge in a liquid with a

refractive index similar to that of

the polymer (reduces diffusion at

the surfaces)

Observe the wedge in the

microscope between crossed polars

to identify the interference fringes.


Wedge Method

42


Wedge Method

Interference fringes in white light


Wedge Method

Interference fringes in green light

43

n2n3

n1

n2

n3n1

l1

l2

A’B’BA

l1

l2

t2 t1

OPD(A) = m = (n3-n1) t1

OPD(B) = (m+1) = (n3-n1) t2

t1=l1 tan t2=l2 tan

m – integern1, n2, n3 – principal refractive indeces

n /l2

l1tan


400 450 500 550 600

Wavelength (nm)

650 700 750

T (%

)

Minima occur when

m = OPD

Destructive interference

m = OPD 1/


Spectrophotometer

Testing conditions: The sample should be sandwiched between cross polars (for maximum intensity: -45º (P)/0º(S)/+45º(A)) and placed on the sample holder of the equipment. Set the mode of the equipment for Transmission mode in the visible light range of 400 to 700 nm.

Example: PS oriented rod500450400350300250200150100

500

44

m = OPD 1/

T (%

)

Wavelength (nm)5

0,001645

0,001736

0,001825

608

576

548

2

3

4

m (nm) 1/ (nm-1)

1 644 0,001553

y = 11019x - 16,118

0

1

2

3

4

0,0015 0,0016 0,0017

1/ (nm-1)

0,0018 0,0019

m

OPD = slop = 11019 nm

n 11019(nm ) 6,768 103

1628(m)

n

OPDt


45

500

450400350300250200150100 4 3 2 1500400 450 500 550 600

650700 750

6_mptp_optical anisotropy of polymers

Documents

isotropic amorphous

principal refractive

uniaxial anisotropy

polymer melts

molecular orientation

fine polymer

molecular orientation

bioriented filmsthe