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VI CURSO DE INTRODUCCION A LA
REOLOGÍA
Madrid, 8-9 julio 2013
Prof. Dr. Críspulo Gallegos
Dpto. Ingeniería Química. Universidad de Huelva &
Institute of Non-Newtonian Fluid Mechanics (UK)
LINEAR VISCOELASTICITY
OUTLINE
1. Introduction
2. The Boltzmann superposition principle
3. Derivative models for the relaxation modulus
4. Relaxation spectrum
5. Small strain material functions
5.1. Stress relaxation
5.2. Creep
5.3. Small amplitude oscillatory shear
6. Some industrial applications
1. INTRODUCTION
Rheology
Solids Emulsions +
Foams Suspensions
Gels
(Polymer) Melts Liquid Crystals Macromolecular
solutions
Food
Detergents
Cosmetics
Paints
Pharmacy
Biological Fluids
Building Materials
Ink
Adhesives
Lubricants
Engineering Materials
Entanglement
in polymers
Structure/network
of colloids
1. INTRODUCTION
1. INTRODUCTION
• Rigid Solid (Euclidean)
• Linear elastic solid (Hookean)
• Non-linear elastic solid
• Viscoelastic
• Non-linear viscous fluid
• Linear viscous fluid (Newtonian)
• Inviscid fluid (Pascalian)
Rheological spectrum of materials
0
tf ,,
0
G
G
1. INTRODUCTION
1. INTRODUCTION
FUNCIONES
VISCOELÁSTICAS
INDEPENDIENTES
DEL ESFUERZO
APLICADO
DESTRUCCIÓN
ESTRUCTURAL
ESFUERZO
APLICADO
MATERIAL
CONSERVACIÓN
DE LA
ESTRUCTURA
> C
< C
VISCOELASTICIDAD
NO LINEAL
VISCOELASTICIDAD
LINEAL
ESTUDIO DE LA
ESTRUCTURA
(DESARROLLO DE
PRODUCTOS)
ESTUDIO DE
OPERACIONES BÁSICAS
(DESARROLLO DE
PROCESOS)
CONTROL DE CALIDAD
DE PRODUCTOS
INDUSTRIALES
1. INTRODUCTION
- Viscoelastic materials possess both viscous and elastic properties
in varying degrees.
- For a viscoelastic material, internal stresses are a function not only
of the instantaneous deformation, but also depend on the whole past
history of deformation. For real materials, the most recent past
history has much more influence (fading memory).
1. INTRODUCTION
- When a viscoelastic material is deformed, thermodynamic forces
immediately begin to operate to restore the minimum-energy state.
Movement from the rest state represents a storage of energy. This
type of energy is the origin of elasticity in many different materials,
i.e. polymer solutions, polymer melts, concentrated suspensions,
concentrated emulsions, asphalts, lubricating greases, etc.
- Linear viscoelasticity is the simplest response of a viscoelastic
material. If a material is submitted to deformations or stresses small
enough so that its rheological functions do not depend on the value
of the deformation or stress, the material response is said to be in the
linear viscoelasticity range.
2. THE BOLTZMANN SUPERPOSITION PRINCIPLE
Let’s consider the function γ(t) as representative of some cause (shear
strain) acting on a given material, and the shear stress, σ(t), the effect
resulting from this cause.
A variation in shear strain, occurring at time t1 will produce a
corresponding effect at some time later, t:
)()()( 11 tttGt
G (t-t1) is the relaxation modulus, which is a property of the material.
It is a function of the time delay between cause and effect.
This influence function is a decreasing function of (t-t1),
representing a “fading memory”, and is independent of the strain
amplitude.
2. THE BOLTZMANN SUPERPOSITION PRINCIPLE
Series of strain increments applied on a given material
(t1)
(t2)
(t3)
(t4) (t5)
TIME
SH
EA
R S
TR
AIN
0
0 t
1
t
4
t
3
t
2
t5
2. THE BOLTZMANN SUPERPOSITION PRINCIPLE
A series of N changes in the shear strain, each occurring at
different time, will all contribute cumulatively to the stress
at some later time:
If the change in strain occurs continuously:
)()()(1
ii
N
itttGt
t
tdttGt )'()'()( ')'()'()(.
dttttGt
t
t’: past time variable running from the infinite past to present time
2. THE BOLTZMANN SUPERPOSITION PRINCIPLE
For a material with a fading memory, there will be a time prior to
which all the strains which have previously occurred will have a
negligible contribution.
Thus, an experiment generally starts at some time (t = 0) when the
material is free of stresses. In this case:
t
tdttGt0
)'()'()(
2. THE BOLTZMANN SUPERPOSITION PRINCIPLE
The Boltzmann superposition principle can be generalized
for any type of deformation that can be applied on the material.
If the shear strain is replaced by the strain tensor, and the
shear stress by the stress tensor:
t
ijij tdttGt )'()'()(
')'()'()(.
dttttGt
t
ijij
3. DERIVATIVE MODELS POR THE RELAXATION MODULUS
The linear response of a given material to any type of deformation
can be predicted if the relaxation modulus has been experimentally
obtained.
It is previously necessary to correlate the evolution of the linear
relaxation modulus with time.
A classical approach to the description of the linear viscoelastic of real
materials is based upon an analogy with the response of combinations of
certain mechanical elements (a spring for elasticity, and a dashpot for
viscosity).
Such models are idealized and purely hypothetical, and are useful for
representing the behaviour of real materials only to the extent that the
observed response of the real material can be approximated by that of
the model.
Viscous flow Elastic deformation
G .
Viscoelasticity
Voigt
model
Maxwell
model
Burgers model
Spring
Dash pot
3. DERIVATIVE MODELS POR THE RELAXATION MODULUS
3. DERIVATIVE MODELS POR THE RELAXATION MODULUS
Maxwell’s model Voigt’s model visel
retG
visel
dt
drel
)/exp()( 0 tGtG
')'(/)'(exp)(.
0 dttttGt
t
ijij
λ: relaxation time (μ/G)
t’: past time variable running from the infinite past to present time
3. DERIVATIVE MODELS POR THE RELAXATION MODULUS
A large number of models can be formulated by combining different
numbers of springs and dashpots together in diverse ways, aiming to
simulate the evolution of the linear relaxation modulus of real
materials.
The Burgers model is a combination of a Maxwell element and a
Voigt element in series:
3. DERIVATIVE MODELS POR THE RELAXATION MODULUS
One of the most useful for viscoelastic fluids is the generalized
Maxwell model, which, in essence, assumes that, instead of a single
relaxation time, the fluid has a response characteristic of a whole
series, or distribution, of relaxation times.
Such a set of values is called a “discrete spectrum” of relaxation
times of the material.
3. DERIVATIVE MODELS POR THE RELAXATION MODULUS
In this case, the shear relaxation modulus is represented by the
following equation:
The linear constitutive equation can be written as:
)/exp()(1
ii
N
itGtG
')'(/)'(exp)(.
dttttGt
t
ijkkij
4. RELAXATION SPECTRUM
Another approach to the quantification of the linear relaxation
modulus is the use of a continuous relaxation spectrum H(λ).
Using it provides a continuous function of relaxation time, λ, rather
than a discrete set.
The relaxation modulus is now defined as:
)(ln/exp()()(
dtHtG
There are several methods to determine the linear relaxation spectrum
of viscoelastic materials from experimental data of different linear
viscoelasticity functions.
5. SMALL STRAIN MATERIAL FUNCTIONS
A number of small strain experiments are used in rheology.
Some of the more common techniques are stress relaxation, creep,
and sinusoidal oscillations.
In the linear viscoelastic region, all small strain experiments must be
related to one another through G(t), or through H(λ).
Different experimental methods are used because they may be more
convenient or better suited for a particular material or because they
provide data over a particular time range.
Furthermore, it is often not easy to transform results from one type
of linear viscoelastic experiment to another, and, consequently,
several functions are often measured.
5. SMALL STRAIN MATERIAL FUNCTIONS
5. SMALL STRAIN MATERIAL FUNCTIONS
Method Input Information
Stress relaxation test Const. deformation Material relaxation
Creep test Const. shear stress Deformation, flow
OSC Time test Const. frequency and Monitoring of
const. amplitude chemical reaction
OSC Amplitude sweep Stepwise increasing Network stability,
amplitude linear range
OSC Frequency sweep Stepwise increasing Frequency
frequency
dependence
OSC Temperature sweep const. frequency and Temperature
const. amplitude
dependence (gelation)
5. 1. STRESS RELAXATION
A sample is suddenly deformed
at a given strain, γ0 , and the
resulting stress is measured as
a function of time.
The relaxing stress data can be
used to determine G(t):
c
> c
0
)()(
ttG
5. 1. STRESS RELAXATION
GLASS
CROSSLINKING
G0
DILUTE
SOLUTIONS
AND
DISPERSIONS
log G
log t
POLYMERIC
LIQUID
RUBBER
Evolution of the linear relaxation modulus for different materials
5. 1. STRESS RELAXATION
Evolution of the linear relaxation modulus for different polymer
Systems. Viscoelastic liquids on left, viscoelastic solids on right
5. 1. STRESS RELAXATION
5. 1. STRESS RELAXATION
Evolution of the linear and non-linear relaxation modulus for enteral
pudding formulations
10-1
100
101
102
103
100
101
102
103
Strain%
0.8 %
1.0 %
5.0 %
10 %
50 %
100 %
200 %
300 %
400 %
500 %
G(t
)[P
a]
Time [s]
For linear polymers with a broad molecular weight distribution,
highly branched polymers, and many food gels and dispersions,
among others: mcttG )(
5. 2. CREEP
Creep experiments are useful for
certain practical applications
where long times are
involved.
A constant stress, σ0 , is
instantaneously applied on a
sample, and the resulting
strain is recorded versus time:
mainly
elastic
5. 2. CREEP
0.1 1.0 10.0 100.0
Shear Stress ‚ [Pa]
0.001
0.010
0.100
1.000
10.000
100.000
Defo
rma
tio
n
c
> c
ESTIMATION OF THE LINEAR VISCOELASTICITY RANGE
5. 2. CREEP
0 100 200 300 400 500
0
1x10-4
2x10-4
3x10-4
4x10-4
5x10-4
6x10-4
7x10-4
8x10-4
J(t)
(P
a)
time (s)
The strain values obtained
as a function of time can
be used to calculate the
compliance, J(t), as
follows:
0
)()(
ttJ
Typical creep behaviour for viscoelastic fluids
5. 2. CREEP
0 100 200 300 400 500
0
1x10-4
2x10-4
3x10-4
4x10-4
5x10-4
6x10-4
7x10-4
8x10-4
J(t)
(P
a)
time (s)
There is an initial elastic response.
The second region corresponds to
a retarded elastic response.
Finally, a constant shear rate is
reached.
A steady state creep compliance,
Je0, can be defined by
extrapolation of the limiting slope
in this last region to t = 0.
The creep compliance at long
times is given by: 0
0 /)( tJtJ e
5. 2. CREEP
A creep behaviour of a fluid represented by the Maxwell model will
follow the equation:
G
t
GtJ
1)( λ = η/G
At very short time, this behaviour is characterized by an elastic
response, and a purely viscous response at long time (t>> η/G).
5. 2. CREEP
- A creep behaviour represented by the Kelvin-Voigt model will
follow the equation::
τ = η/G (retardation time)
At very short time, this behaviour is characterized by a purely
viscous response.
)/exp(11
)( tG
tJ
5. 2. CREEP
tt
GGtJ )/exp(1
11)(
21
- In the case of the Burgers model:
5. 2. CREEP
- In most cases, a larger number of Kelvin-Voigt elements should be
added in series within the Burgers model, to fit the actual behaviour
of the material. The equation for the creep compliance would result:
tt
Gt
GGtJ .../exp(1
1)/exp(1
11)( 3
3
2
21
0
321
...111
eJGGG
5. 3. SMALL AMPLITUDE OSCILLATORY SHEAR
In this test, the material is submitted to a simple shearing
deformation, by applying a sine-wave-shaped input of stress or strain.
=0
(change of direction)
=0
(change of direction)
5. 3. SMALL AMPLITUDE OSCILLATORY SHEAR
phase shift
viscous
response el.
resp.
input
If a sinusoidal strain is applied,
the shear strain as a function of
time would be given by:
)sin()( 0 tt
γ0 is the strain amplitude and ω
is the frequency.
By differentiating, the evolution
of shear rate with time is given
by:
)cos()cos()( 0
.
0
.
wttt is the shear rate amplitude 0
.
5. 3. SMALL AMPLITUDE OSCILLATORY SHEAR
phase shift
viscous
response el.
resp.
input The resulting stress is
measured as a function of time
)sin()( 0 tt
σ0 is the stress amplitude and δ
is a phase shift, also known as
loss angle
The amplitude ratio, Gd, defined from the ratio between σ0
and γ0, and the loss angle, δ, are functions of frequency,
although they are independent of strain amplitude in the linear
viscoelasticity range.
5. 3. SMALL AMPLITUDE OSCILLATORY SHEAR
The results of an oscillatory shear test can be represented by the
frequency evolution of both the amplitude ratio and the loss angle.
However, they have not direct relationship with the material
functions traditionally used to characterize the linear viscoelasticity
behaviour of a given material.
For this reason, the stress data can also be analyzed by decomposing
the stress wave into two waves of the same frequency, one in phase
with the strain wave (sin ωt), and the other one 90º out of phase with
this wave (cos ωt):
tt cos''sin'''' '
0
''
0tan
5. 3. SMALL AMPLITUDE OSCILLATORY SHEAR
This mathematical treatment also suggests two different dynamic
moduli:
0
'
0'
G
0
''
0''
G
elastic, storage, or in-phase modulus
viscous, loss, or out-of-phase modulus
It is obvious that the loss tangent can be rewritten as:
'
''tan
G
G
5. 3. SMALL AMPLITUDE OSCILLATORY SHEAR
We can define the complex modulus, G*, as:
00 G
being G’ and G’’ its real and imaginary parts, respectively:
)('')(')( iGGG
From the previous relationships, it is obvious that the amplitude
ratio, Gd, is the magnitude of the complex modulus, G*:
22
0
0 )''()'(* GGGGd
)cos()('')sin()(')( 0 tGtGt
5. 3. SMALL AMPLITUDE OSCILLATORY SHEAR
For a purely elastic material, there is no viscous dissipation, no phase
shift, and the loss modulus is zero.
On the contrary, there is no energy storage for a purely viscous
liquid, being the loss storage modulus zero, and the loss angle 90º.
5. 3. SMALL AMPLITUDE OSCILLATORY SHEAR
LINEAR VISCOELASTICITY RANGE
The linear viscoelasticity functions,
G’, G” etc., do not depend on shear
stress (or strain)
The linear viscoelasticity range
depends on frequency
↓ω
5. 3. SMALL AMPLITUDE OSCILLATORY SHEAR
Another way to interpret the results obtained from small amplitude
oscillatory shear tests is in terms of a sinusoidal strain rate.
Two new material functions are then defined:
)sin()('')cos()(')( 0
.
ttt
''sin'
.
0
0
.
0
''
0 G
'cos''
.
0
0
.
0
'
0 G
The complex viscosity is:
)('')(')( i 22
.
0
0 )''()'(*
5. 3. SMALL AMPLITUDE OSCILLATORY SHEAR
The reciprocal of the complex modulus is also defined as an
additional oscillatory material function, the complex compliance, J*:
where the real and imaginary components of the complex
compliance are related to those of the complex modulus by:
)('')(')(*
1)(
iJJ
GJ
)('')('
)(')('
22
GG
GJ
)('')('
)('')(''
22
GG
GJ
5. 3. SMALL AMPLITUDE OSCILLATORY SHEAR
If a Maxwell model is used to represent the linear viscoelastic
response of a material submitted to small oscillatory shear, the storage
and loss moduli will be represented by the following equations:
22
22
1)('
GG 221
)(''
GG
At low frequencies, G’’ is much larger than G’, and the material
predominantly shows a viscous response.
At large frequency, the material shows a solid-like behaviour.
The critical crossover frequency, at which G’ = G’’, defines the
characteristic relaxation time of the material.
5. 3. SMALL AMPLITUDE OSCILLATORY SHEAR
Typical Maxwellian behaviour in oscillatory
testing, with the crossover point indicated (aqueous
surfactant solutions containing thread-like micelles)
5. 3. SMALL AMPLITUDE OSCILLATORY SHEAR
If a generalized Maxwell model is used to represent the linear
viscoelastic response of a material submitted to small oscillatory
shear, the storage and loss moduli will be represented by the
following equations:
N
i i
iiGG
122
22
1)('
N
i i
iiGG
1221
)(''
5. 3. SMALL AMPLITUDE OSCILLATORY SHEAR
G‘
G“
||
Frequency sweep tests in oscillatory shear for a biopolymer
solution
5. 3. SMALL AMPLITUDE OSCILLATORY SHEAR
Frequency sweep tests in
oscillatory shear for aqueous
xanthan gum solutions, at various
weight percentages
Frequency sweep tests in
oscillatory shear for PMMA (poly
methyl methacrylate), at 185ºC
5. 3. SMALL AMPLITUDE OSCILLATORY SHEAR
Oscillatory behaviour of 84
nm PMMA particles
in decalin, at various
effective phase volumes
Oscillatory behaviour of a
nonionic hexagonal
liquid crystalline phase
5. 3. SMALL AMPLITUDE OSCILLATORY SHEAR
Oscillatory behaviour of
two toothpastes
Oscillatory behaviour of a
lubricating grease at
room temperature
Unflocculated Emulsions
a) Otsubo-Prud’homme, 1994
b) Tadros, 1993
Weakly Flocculated Emulsions
c) Tadros, 1993
Flocculated Emulsions
d) Partal et al. 1996
e) Franco et al. 1995
5. 3. SMALL AMPLITUDE OSCILLATORY SHEAR
5. 3. SMALL AMPLITUDE OSCILLATORY SHEAR
0 5 10 15 20 25 30
0
200
400
600
800
1000
1200
Experimental data
Modified Princen Equation
GN
O (
Pa)
d4,3
(m)
)(31
32
0 bd
aG
PRINCEN EQUATION:
G0 = static shear modulus
= interfacial tension
= disperse phase volume fraction
Gc
dN
0
43
5. 3. SMALL AMPLITUDE OSCILLATORY SHEAR
The most general small oscillatory shear response of viscoelastic
complex liquid materials is shown below:
G’
G’’
1
2
3
4
5
Frequency, ω
G’
G
’’
5. 3. SMALL AMPLITUDE OSCILLATORY SHEAR
Different regions can be noticed:
1) Viscous or terminal region, where G’’ shows larger values than G’.
For frequencies low enough, G’’ varies linearly with frequency.
2) Transition to flow region. The crossover frequency at which G’’ =
G’ is usually denoted as a characteristic relaxation time of the
material.
3) Plateau region, where elastic behaviour predominates. This region
is characterized by higher and almost constant (slight increase
with frequency, actually) values of the storage modulus and a
minimum in the loss modulus at intermediate frequencies.
5. 3. SMALL AMPLITUDE OSCILLATORY SHEAR
4) Transition to glassy region. This region is related to high-frequency
relaxation and dissipation mechanisms, in which G’’ rises much
faster than G’. Another crossover frequency is noticed in this
region, which defines another characteristic relaxation time of the
material.
5) Glassy region, which is characterized by larger values of the loss
modulus and a further crossover frequency prior to a final solid-
like material response.
5. 3. SMALL AMPLITUDE OSCILLATORY SHEAR
The behaviour of a real system, especially a gel or very high
molecular weight polymer melt, can be simplistically modelled by
dividing it into Maxwell behaviour at low frequencies giving way
to Kelvin-Voigt behaviour at high frequencies:
5. 3. SMALL AMPLITUDE OSCILLATORY SHEAR
Temperature dependence of the storage ad loss moduli (at 6.28 rad/s) for: A)
Wheat gluten-based bioplastics, and B) Egg white-based bioplastics.
Temperature sweep tests
COLLOIDAL STRUCTURE FOR BITUMEN
• Bitumen: colloidal dispersion of
asphaltenes micelles peptizided by the
resin molecules.
• At every temperature, the asphaltene
core is insoluble. Peptization is provided
by a shell of resins that surrounds the
asphaltene core.The thickness of this
resin layer is temperature dependent.
•Temperature dependent transition is not
a sol-gel transition (no rubbery-like
plateau in G’). The liquid phase vitrifies
at low temperature (-20ºC).
6. SOME INDUSTRIAL APPLICATIONS
6. SOME INDUSTRIAL APPLICATIONS
AFM micrographs for
neat bitumen (A), and for
PMBs containing 2 (B),
8 (C) and 10 (D)
wt.% of MDI-PEG,
after a period of curing
of 11 months
A B
C D
Road distresses
Road
Good
Performance
Poor
Performance
Distresses
Loss of
structural
integrity
Destruction
of entire
pavement
Safe and
comfortable
ride over its design life
Problems difficult
to solve
with unmodified bitumen
6. SOME INDUSTRIAL APPLICATIONS
Road distresses: RUTTING
• Rutting: permanent
deformation due to the repeated
application of traffic loads.
• Rutting is associated with high
temperature and is more
prevalent in hotter
environments.
6. SOME INDUSTRIAL APPLICATIONS
Road distresses: LOW TEMPERATURE CRACKING
• Low temperature cracking appears
after a single thermal cycle down to
a critical temperature, or after a
series of thermal cycling above the
critical temperature.
• Uniformly spaced cracks initiate at
the pavement surface.
6. SOME INDUSTRIAL APPLICATIONS
Road distresses: FATIGUE CRACKING
• Fatigue cracking (alligator skin
pattern) is caused by repetitive loading.
• Every cycle of loading develops
accumulated stresses which are not
dissipated completely.
• Starts at the bottom of the road layer
and propagates to the surface.
•Appears in both types of climates.
6. SOME INDUSTRIAL APPLICATIONS
Tank Asphalt
RTFOT Residue
PAV Residue
Stiffness at 60 s
between 300 and 600 MPa?
m at 60 s
> 0.30?
Rotational Viscosity
135ºC
Viscosity < 3 Pa·s
Dynamic Shear Rheometer
Maximum Pavement Design Temp
G*/sinδ > 1.0 kPa 1/J’’
Dynamic Shear Rheometer
Maximum Pavement Design Temp
G*/sinδ > 2.2 kPa 1/J’’
Dynamic Shear Rheometer
Intermed Pavement Design Temp
G*·sinδ < 5.0 kPa G’’
Bending Beam Rheometer
Minimum Design Temperature + 10ºC
Stiffness at 60 s < 300 Mpa
m at 60 s > 0.30
Direct Tension Test
Minimum Design Temperature + 10ºC
strain at failure > 1.0%
pumpability
mixing
rutting
rutting
fatigue cracking
dissipated energy
polymer-modified
nonrecoverable deformation
thermal cracking
YES?
Newtonian Region
Viscoelastic Region
Low-temperature Region
Low-temperature Region
Viscoelastic Region
Viscoelastic Region
Flow Chart for Testing Required to Grade an Asphalt Cement for SUPERPAVETM
6. SOME INDUSTRIAL APPLICATIONS
Polymer modified bitumen
Bitumen modification by polymers mainly: Reduces its thermal susceptibility
Avoids rutting and cracking
Improves oxidation and ageing resistance
Reduces life cost of pavements
6. SOME INDUSTRIAL APPLICATIONS
POLYMER MODIFIED BITUMEN:
APPLICATIONS
Physical
modification:
SBS, SBR, EVA,
LDPE, etc.
Reactive (chemical) modification:
• polyethylene-co-methylacrylate
• methyl, ethyl, or butyl acrylate
• isocyanate-terminated polymers
• phenolic resins
Roofing:
Bitumen: 150/200
Polymer: 12-25% w/w
Paving:
Bitumen: 150/200 to 60/70
Polymer: 3-5% w/w
6. SOME INDUSTRIAL APPLICATIONS
10-6
1x10-4
10-2
100
102
104
106
101
102
103
104
105
106
107
108
109
1x10-4
10-2
100
102
104
10610
-1
100
101
102
103
A Bitumen-Laboratory
Bitumen-pilot plant
CTRMBs
anchor
4-blade
helical
pilot plant
G*
[Pa]
w·aT [rad·s
-1]
B
tan d
w·aT [rad·s
-1]
Master curves of the complex shear modulus (A) and loss tangent (B) for
unmodified bitumen and 9% CTRMBs processed in different devices at 180ºC
(reference temperature: 25ºC; temperature range: -10 – 75ºC)
RECYCLED EVA-BITUMEN
Linear viscoelasticity master curves of unmodified and
modified bitumen at 50ºC, for different EVA concentrations.
6. SOME INDUSTRIAL APPLICATIONS
10-7
1x10-5
10-3
10-1
101
103
105
10-3
10-2
10-1
100
101
102
103
104
105
106
107
108
109
10-7
1x10-5
10-3
10-1
101
103
105
10-2
10-1
100
101
102
103
104
105
106
107
108
109
Betún 150/200
Tref
=25ºC
Betún fresco
Betún procesado
0.5%
1%
3%
5%
7%
9%
Modelo Maxwell
G'
[Pa]
aT· [rad·s
-1]
Betún 60/70
G' [
Pa]
aT· [rad·s
-1]
260 280 300 320 34010
-5
10-4
10-3
10-2
10-1
100
101
102
103
104
Betún 150/200
Betún procesado
5% Polímero
aT
T [K]
Introduction
Bioplastics
Biopolymers
Plasticizers
Processing
Definition
Definitions of bioplastics according to European Bioplastics (European industrial association):
*Plastics based on renewable resources
*Biodegradable polymers which meet all criteria of
scientifically recognised norms for biodegradability and compostability of plastics and plastic products. In Europe
this is the EN 13432
Bioplastics represent a relatively new class of materials which have much in common with conventional plastics
6. SOME INDUSTRIAL APPLICATIONS
Introduction
Bioplastics
Biopolymers
6. SOME INDUSTRIAL APPLICATIONS
Introduction
Bioplastics
Biopolymers
Plasticizers
Processing
Proteins
Plasticizers
Polysaccharides Lipids
Wheat Gluten
Gliadin and Glutenin
Egg White
Albumen
Dough-like samples – Influence of temperature
Between 100º-135ºC G’ and G’’ increase, fact that may be attributed to protein aggregation
A slight increase in the linear viscoelastic functions above 40ºC
Results: Wheat gluten
Mixing
Thermosetting
Potential
Compression
Moulding
DSC: An exothermic event is found
between 40-60ºC. It would result from
a new rearrangement of protein
molecules (dissociation and unfolding)
20 40 60 80 100 120 14010
4
105
106
G' G''
0.5 G/EW, 10' mixing
G', G
''
(Pa
)
T (º C)
Dough-like samples – Influence of temperature
Up to 50ºC, G’ and G’’ T, reaching similar values G’ and G’’, which indicates an enhancement of the viscous properties of the blend
Above this T, G’ and G’’: this reveals a structural build-up due to protein denaturation and aggregation
Heat-induced gelation of globular proteins:
two-stage process (partial unfolding and
aggregation of unfolded protein molecules)
Results:
Egg white
Mixing
Thermosetting
Potential
Compression
Moulding
Compression Moulding: Influence of protein
nature
Glycerol / Wheat Gluten or Albumen
T (ºC)
Results:
Mechanical
Processing
Thermosetting
Potential
Compression
Moulding