Viscoelasticity, Creep and Oscillation Experiment · Oscillation Amplitude sweep Frequency sweep Time sweep Temperature sweep Expansion of the measurement range for oscillation Time

Viscoelasticity,

Creep and Oscillation Experiment

Basic Seminar

Applied Rheology

2

Repetition of some basic terms

Overview

Viscoelastic behavior

Experimental approach to viscoelasticity

Creep- and recovery

Oscillation

Amplitude sweep

Frequency sweep

Temperature sweep

Time sweep

Expansion of the measuremnent range for Oscillation

Time Temperature Superposition (TTS) principle

Cox-Merz Rule


3

Viscosity (dynamic) [Pa∙s]

Shear stress [Pa]

Deformation [-]

Shear rate [1/s].

Calculation of the dynamic viscosity


· =

4

y

A

F v

y

x

= F

A = Pa

N

m2

Force

Area =

= dv

dy =

d

dt =

m

s·m

1 s

·

= x y Distance

Displacement =

m

m

Calculation of the dynamic viscosity


5



Creep and recovery

Oscillation

Amplitude sweep

Frequency sweep

Time sweep

Temperature sweep

Expansion of the measurement range for oscillation


Cox-Merz Rule



Viscoelasticity

6

Reasons for viscoelasticity

Entenglements Network formation

Polymer solutions

Polymer melts

Emulsions

Suspensions


7

Appying Hookke‘s law to rheology

= F

A =

x

y

Result

Complex modulus G* G* = Pa

Purely elastic behavior

Spring


k = Spring constant = F

l

F

l

l

x

y

F A


8

Models for viscoelasticity

Maxwell

Model Voigt/Kelvin

Model Burgers Model

Viscoelastic Viscous Elastic

Dash pot Spring

F = k · l = · .

G* · =


9


Creep and recovery

Oscillation

Amplitude sweep

Frequency sweep

Time sweep

Temperature sweep



Cox-Merz Rule




Creep and recovery

Viscoelasticity

10


Creep and recovery

The viscoelastic behavior is observed by applying instantaneous shear

stress changes.

Non-destructive method (within the LVB)

Destinguishes between elastic and viscous properties

Determination of the time-dependent reaction to such changes

11

Time

= · ·

Irreversible deformation

Applied energy dissipates

completely

Rheometer input Viscous Sample


Creep and recovery

Sh

ear

str

ess

Defo

rmati

on

12

Time

F = k · l

Reversible deformation

Applied energy is stored

Elastic sample


Creep and recovery

Rheometer input

Sh

ear

str

ess

Defo

rmati

on

13

Time

Ela

sti

c p

art

Viscous part

1

2

3

2

3

2

1

1

Viscoelastic sample


Creep and recovery

Rheometer input

Sh

ear

str

ess

Defo

rmati

on

14

Time

Leveling

Sagging

Shear stability

Yield stress

0 Zero shear viscosity

e0 Equillibrium deformation

r Recoverable deformation

0 Retardation time

G0 Elastic modulus

Applications Ela

sti

c p

art

Viscous part

Results


Creep and recovery

Rheometer input

Sh

ea

r s

tre

ss

Defo

rmati

on

15

Leveling

Sagging

Shear stability

Yield stress




0 Retardation time

G0 Elastic modulus

Applications

Results

t

= t

.

=

.


Creep and recovery

Rheometer input

Time

Sh

ea

r s

tre

ss

Defo

rmati

on

16

Leveling

Sagging

Shear stability

Yield stress




0 Retardation time

G0 Elastic modulus

Applications

Results

e0


Creep and recovery

Rheometer input

Time

Sh

ea

r s

tre

ss

Defo

rmati

on

17

Leveling

Sagging

Shear stability

Yield stress




0 Retardation time

G0 Elastic modulus

Applications

Results

r


Creep and recovery

Rheometer input

Time

Sh

ea

r s

tre

ss

Defo

rmati

on

18

Leveling

Sagging

Shear stability

Yield stress




0 Retardation time

G0 Elastic modulus

Applications

Results

0


Creep and recovery

Rheometer input

Time

Sh

ea

r s

tre

ss

Defo

rmati

on

19

Leveling

Sagging

Shear stability

Yield stress




0 Retardation time

G0 Elastic modulus

Applications

Results

0

= G


Creep and recovery

Rheometer input

Time

Sh

ea

r s

tre

ss

Defo

rmati

on

20


Oscillation

Viscoelasticity

21

Oscillation

Principle of measurement

y

x1 x1

x2 x2

Two-Plates-Model

A usually sinosoidal oscilllation is being applied by the rheometer

Controllable parameters are the maximum amplitude ( xi) of the shear stress ( ) or

deformation ( ) as well as the (angular) frequency (f, ) and the temperature (T)

22

Sample

Stationäre Platte

Rotor

0 2 4 6

0

B

Y A

xis

Title

X Axis TitleTime

Rheometer input e.g. Plate Rotor

Rotor

Stationary plate

Oscillation


Sh

ear

str

ess

Defo

rmati

on

23

Shear stress (CS)

Deformation (CD) resp.

Purely elastic sample

Input

Response

Deformation

Shear stress resp.

Phase angle

= 0°

0 2 4 6

0

B

Y A

xis

Title

X Axis Title

0 2 4 6

0

B

Y A

xis

Title

X Axis Title

Time

Oscillation


Sh

ear

str

ess

Defo

rmati

on

24

0 2 4 6

0

B

Y A

xis

Title

X Axis Title

0 2 4 6

0

B

Y A

xis

Title

X Axis Title

0 2 4 6

0

B

Y A

xis

Title

X Axis Title

Purely viscous sample

Shear stress (CS)


Input

Response

Deformation

Shear stress resp.

Phase angle = 90°

Oscillation


Time

Sh

ear

str

ess

Defo

rmati

on

25

Shear stress (CS)


Viscoelastic sample

Input

Response

Deformation

Shear stress resp.

Phase angle

0 2 4 6

0

B

Y A

xis

Title

X Axis Title

0 2 4 6

0

B

Y A

xis

Title

X Axis Title0 2 4 6

0

B

Y A

xis

Title

X Axis Title

0°< < 90°

Time

Oscillation


Sh

ear

str

ess

Defo

rmati

on

26

0 2 4 6

0

B

Y A

xis

Title

X Axis Title Time

CS-Input

(t) = · sin( ·t)

Response

(t) = · sin( ·t - ) 0 2 4 6

0

B

Y A

xis

Title

X Axis Title

Shear stress

Deformation

Oscillation


Sh

ear

str

ess

Defo

rmati

on

27

Results I

Complex modulus

G* = G’ + i G’’ (i2 = -1)

Storage modulus

G’ (elastic part)

Loss modulus

G’’ (viscous part, damping)

= G*

G*

G”

G’

G’ = 0

= 90°

G’ > 0

G’’ > 0

Pure viscouse sample Viscoelastic sample

Real part

Imag

inary

part

Oscillation

28

G’ = G*

= G* G”

G’’ = 0

= 0°

G’ = 0

= 90°

Pure elastic sample Purely viscous sample

G’ = 0

= 90°

Results I

Oscillation

Complex modulus

G* = G’ + i G’’ (i2 = -1)

Storage modulus

G’ (elastic part)

Loss modulus


Real part

Imag

inary

part

29

G’ = G*

G’’ = 0

= 0°

Purely elastic sample Complex modulus

G* = G’ + i G’’ (i2 = -1)

Storage modulus

G’ (elastic part)

Loss modulus


Real part

Imag

inary

part

Results I

Oscillation

30

Phase angle (0° ≥ ≤ 90°)

Loss factor tan = G’’/ G’

Complex viscosity *= G* / i

Angular frequency = 2 f

(f = frequency)

Results II

Oscillation

31

Oscillation

Amplitude sweep

Viskoelastizität

32

Amplitude sweep

Increasing amplitude in shear stress (CS) or deformation (CD) with

constant frequency

Determination of the linear-viscoelastic range (LVR), where material

functions (G‘,G‘‘, ) are independent of the stress or the deformation

applied

Information about product stability

e.g. gel strength

Oscillation

33

Time

Increasing amplitude inshear stress (CS) or deformation (CD) with const. frequency

Amplitude sweep

Oscillation S

hea

r str

es

s

De

form

ati

on

34

Shear stress

Sto

rag

e m

od

ulu

s G

‘

10 Hz

1 Hz

0.1 Hz

Width of LVB is less

frequency depending

Width of the linear-

viscoelastic regime (LVB)

depends on the frequency

Plotted over

Plotted over

End of LVR

Amplitude sweep

Oscillation

35

Oscillation

Frequency sweep

Viskoelastizität

36

Frequency sweep

Variation of frequency with constant shear stress or deformation

respectively

Determination of material‘s structure

Determination of material’s properties, which cannot be

measured in shear

Oscillation

37

Time

Variation of Frequency with const. shear stress or deformation

Frequency sweep

Oscillation S

hear

str

ess

Defo

rmati

on

38

Viscous Flow

G’ < G’’

log Angular frequency

The samples behaves

mainly viscous over the

entire measuring range

log

Sto

rag

e m

od

ulu

s G

‘

log

Lo

ss m

od

ulu

s

G’’

For ideal viscous samples:

Slope G’( ) = 2

Slope G’’( ) = 1

Frequency sweep

Oscillation

39

G’ > G’’

Elastic Plateau

Examples:

Cross linked Polymers

Physical Networks

Sample behavior is

dominated by the elastic

properties

Frequency sweep

Oscillation


log

Sto

rag

e m

od

ulu

s G

‘

log

Lo

ss m

od

ulu

s

G’’

40


Cross-Over-Point G’ = G’’

In the region of low

frequencies the sample

behaves viscous

At high frequencies the

elastic behavior

predominates

Frequency sweep

Oscillation


log

Sto

rag

e m

od

ulu

s G

‘

log

Lo

ss m

od

ulu

s

G’’

41

The Cross-Over-Point

G’ = G’’ separates

viscous flow at low

frequencies and elastic

behavior at higher

frequencies

Cross-Over-Point

lo

g S

tora

ge m

od

ulu

s G

‘

log

Lo

ss m

od

ulu

s G

‘‘

Flow

Elastic

behavior

45°


Frequency sweep

Oscillation

Ph

ase a

ng

le

42

The location of the

cross over point

depends on:

Polymer Fluids

Broad distribution

High Mw

Narrow distribution

The average molecular

weight (Mw)

Low Mw

The molecular weight

distribution (MWD)

Frequency sweep

Oscillation lo

g S

tora

ge m

od

ulu

s G

‘

log

Lo

ss m

od

ulu

s G

‘‘


43

Frequency sweep

Oscillation

The location of the

cross over point

depends on:

Polymere Fluide

The temperature T

T T

c

c

The polymer

concentration c

(for polymer solutions)

lo

g S

tora

ge m

od

ulu

s G

‘

log

Lo

ss m

od

ulu

s G

‘‘


44

Oscillation

Temperature sweep

Viskoelastizität

45

Variation of the temperature with constant shear stress or deformation

and (angluar) frequency ,f

Temperature sweep

Determination of the glas transition, softening and melting

temperature

Investigation of chrystallization processes and sol-gel transitions

Determination of the temperature depending sample charteristics

Oscillation

46

Time

Variation of the temperatur with const. shear stress or deformation and

(agular) frequency ,f

Tem

pera

ture

Temperature sweep

Oscillation S

hear

str

ess

Defo

rmati

on

47

Temperature T

lo

g s

tora

ge m

od

ulu

s G

‘

log

lo

ss m

od

ulu

s G

‘‘

Glass transition Tg

Not cross linked

No positional order

Random orientation

Polystyrene

Examples:

Amorphous polymers

Polyvinylchloride

Polycarbonate

Temperature sweep

Oscillation

tan

48

Semi crystalline Polymers

Not cross linked

Partially ordered structure

Partially oriented

High Density Polyethylen

Polypropylen

Low Density Polyethylen

Glass transition Tg

Melting temperature Tm

Examples:

Temperature sweep

Oscillation

Temperature T

lo

g s

tora

ge m

od

ulu

s G

‘

log

lo

ss m

od

ulu

s G

‘‘

tan

49

Cross-linked Polymers

Via covalent or ionic bonds

cross-linked macro

molecules

Depending on the cross-link

density

Elastomers (wide-meshed)

Thermosets (close-meshed) Glass transition Tg

Examples:

Temperature sweep

Oscillation

Temperature T

lo

g s

tora

ge m

od

ulu

s G

‘

log

lo

ss m

od

ulu

s G

‘‘

tan

50



Viscoelasticity

Cox-Merz Rule




Creep and recovery

Oscillation

Amplitude sweep

Frequency sweep

Time sweep

Temperature sweep



51


log

Sto

rag

e m

od

ulu

s G

‘

lo

g L

os

s m

od

ulu

s

G’’

Viscous

Flow

Glass-

phase

Elastic

Plateau

Long Measurement

times limit the

measurement range

towards small

frequencies

Inertia effects of

rheometer limit the

measurement range

towards high

frequencies

Measuring range

Oscillation

Frequency sweep

52

100 0.01

10 0.1

1 1

0.1 10 0.17

0.01 100 1.67

0.001 1000 16.7 0.28

0.0001 10000 167 2.78 0.12

0.00001 100000 1670 27.8 1.2

0.000001 1000000 16700 278 12

Freq. [Hz] Time [s] Time [min] Time [h] Time [d]

Oscillation

Frequency sweep

53

= T1

= T3

T1 < T2 < T3

Time Temperature Superposition (TTS)

log

Lo

ss m

od

ulu

s G

‘‘

log

Sto

rag

e m

od

ulu

s G

‘ (·

··)

Standard frequency range

= T2

Performance

Several frequency

sweeps are being

performed at

different

temperatures

Expansion of the measurement range

54

lo

g S

tora

ge m

od

ulu

s G

‘

log

Lo

ss m

od

ulu

s G

‘‘

Expanded frequency range



55

lo

g S

tora

ge

mo

du

lus

G‘

log

Lo

ss

mo

du

lus

G‘‘


* = G* / i



log

Co

mp

lex

vis

co

sit

y

56

Determination of the

zero shear viscosity 0

Determination of the

viscosity at high

frequencies / velocities

and short relaxation

times




lo

g S

tora

ge

mo

du

lus

G‘

log

Lo

ss

mo

du

lus

G‘‘

log

Co

mp

lex

vis

co

sit

y

57

Cox-Merz Rule

* [rad/s] = [s-1]

Empiric Rule

Valid for numerous

unfilled polymer melts

and polymer solutions

Validity in the Non-

Newtonian may vary

Not valid for

dispersions,

suspensions and gels

log Shear rate [s-1] / log Angular frequency [rad/s].


log

Co

mp

lex

vis

co

sit

y

lo

g D

yn

am

ic v

isc

os

ity

58

Thank you for your attention

Any questions ?

Viscoelasticity, Creep and Oscillation Experiment · Oscillation Amplitude sweep Frequency sweep Time sweep Temperature sweep Expansion of the measurement range for oscillation Time

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