viscoelasticity, creep and oscillation...
TRANSCRIPT
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
Repetition of some basic terms
3
Viscosity (dynamic) [Pa∙s]
Shear stress [Pa]
Deformation [-]
Shear rate [1/s].
Calculation of the dynamic viscosity
Repetition of some basic terms
· =
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
Repetition of some basic terms
5
Viscoelastic behavior
Experimental approach to viscoelasticity
Creep and recovery
Oscillation
Amplitude sweep
Frequency sweep
Time sweep
Temperature sweep
Expansion of the measurement range for oscillation
Time Temperature Superposition (TTS) principle
Cox-Merz Rule
Viscoelastic behavior
Repetition of some basic terms
Viscoelasticity
6
Reasons for viscoelasticity
Entenglements Network formation
Polymer solutions
Polymer melts
Emulsions
Suspensions
Viscoelastic behavior
7
Appying Hookke‘s law to rheology
= F
A =
x
y
Result
Complex modulus G* G* = Pa
Purely elastic behavior
Spring
Viscoelastic behavior
k = Spring constant = F
l
F
l
l
x
y
F A
Viscoelastic behavior
8
Models for viscoelasticity
Maxwell
Model Voigt/Kelvin
Model Burgers Model
Viscoelastic Viscous Elastic
Dash pot Spring
F = k · l = · .
G* · =
Viscoelastic behavior
9
Experimental approach to viscoelasticity
Creep and recovery
Oscillation
Amplitude sweep
Frequency sweep
Time sweep
Temperature sweep
Expansion of the measurement range for oscillation
Time Temperature Superposition (TTS) principle
Cox-Merz Rule
Viscoelastic behavior
Repetition of some basic terms
Experimental approach to viscoelasticity
Creep and recovery
Viscoelasticity
10
Experimental approach to viscoelasticity
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
Experimental approach to viscoelasticity
Creep and recovery
Sh
ear
str
ess
Defo
rmati
on
12
Time
F = k · l
Reversible deformation
Applied energy is stored
Elastic sample
Experimental approach to viscoelasticity
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
Experimental approach to viscoelasticity
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
Experimental approach to viscoelasticity
Creep and recovery
Rheometer input
Sh
ea
r s
tre
ss
Defo
rmati
on
15
Leveling
Sagging
Shear stability
Yield stress
0 Zero shear viscosity
e0 Equillibrium deformation
r Recoverable deformation
0 Retardation time
G0 Elastic modulus
Applications
Results
t
= t
.
=
.
Experimental approach to viscoelasticity
Creep and recovery
Rheometer input
Time
Sh
ea
r s
tre
ss
Defo
rmati
on
16
Leveling
Sagging
Shear stability
Yield stress
0 Zero shear viscosity
e0 Equillibrium deformation
r Recoverable deformation
0 Retardation time
G0 Elastic modulus
Applications
Results
e0
Experimental approach to viscoelasticity
Creep and recovery
Rheometer input
Time
Sh
ea
r s
tre
ss
Defo
rmati
on
17
Leveling
Sagging
Shear stability
Yield stress
0 Zero shear viscosity
e0 Equillibrium deformation
r Recoverable deformation
0 Retardation time
G0 Elastic modulus
Applications
Results
r
Experimental approach to viscoelasticity
Creep and recovery
Rheometer input
Time
Sh
ea
r s
tre
ss
Defo
rmati
on
18
Leveling
Sagging
Shear stability
Yield stress
0 Zero shear viscosity
e0 Equillibrium deformation
r Recoverable deformation
0 Retardation time
G0 Elastic modulus
Applications
Results
0
Experimental approach to viscoelasticity
Creep and recovery
Rheometer input
Time
Sh
ea
r s
tre
ss
Defo
rmati
on
19
Leveling
Sagging
Shear stability
Yield stress
0 Zero shear viscosity
e0 Equillibrium deformation
r Recoverable deformation
0 Retardation time
G0 Elastic modulus
Applications
Results
0
= G
Experimental approach to viscoelasticity
Creep and recovery
Rheometer input
Time
Sh
ea
r s
tre
ss
Defo
rmati
on
20
Experimental approach to viscoelasticity
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
Principle of measurement
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
Principle of measurement
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)
Deformation (CD) resp.
Input
Response
Deformation
Shear stress resp.
Phase angle = 90°
Oscillation
Principle of measurement
Time
Sh
ear
str
ess
Defo
rmati
on
25
Shear stress (CS)
Deformation (CD) resp.
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
Principle of measurement
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
Principle of measurement
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
G’’ (viscous part, damping)
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
G’’ (viscous part, damping)
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 Angular frequency
log
Sto
rag
e m
od
ulu
s G
‘
log
Lo
ss m
od
ulu
s
G’’
40
Viscoelastic behavior
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 Angular frequency
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°
log Angular frequency
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
‘‘
log Angular frequency
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
‘‘
log Angular frequency
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
Expansion of the measurement range for oscillation
Time Temperature Superposition (TTS) principle
Viscoelasticity
Cox-Merz Rule
Repetition of some basic terms
Viscoelastic behavior
Experimental approach to viscoelasticity
Creep and recovery
Oscillation
Amplitude sweep
Frequency sweep
Time sweep
Temperature sweep
Expansion of the measurement range for oscillation
Time Temperature Superposition (TTS) principle
51
log Angular frequency
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
Expansion of the measurement range
Time Temperature Superposition (TTS)
55
lo
g S
tora
ge
mo
du
lus
G‘
log
Lo
ss
mo
du
lus
G‘‘
Expanded frequency range
* = G* / i
Expansion of the measurement range
Time Temperature Superposition (TTS)
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
Expanded frequency range
Expansion of the measurement range
Time Temperature Superposition (TTS)
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].
Expansion of the measurement range
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 ?