Rheometer DMA Examples 2014 n

1

RHEOLOGICAL CHARACTERIZATION OF MATERIALS

USING RHEOMETER and DMA

Prof. Dr. Necati zkanCentral Laboratory

Middle East Technical University

EXAMPLES (DMA)

DYNAMIC MECHANICAL ANALYSIS (ELASTOMER)The dynamic mechanical properties (E, E, tan) of elastomers can be determined using Dynamic mechanical analysis (DMA). The ability of materials to store and dissipate mechanical energy upon deformation can be quantified using DMA. By using DMA, glass transition temperature (Tg) and elastomer melting point can also be determined. The DMA data allow the development of structure-property-performance relationships for an elastomer; in other words, how do changes in chemistry, processing or composition impact performance.STORAGE MODULUS: The solid-like or elastic portion of a viscoelastic material (elastomer, polymer, ...). It can be used for the determination of energy stored during deformation.E : stretching deformations (tensile)G: shearing, twisting, or torsional deformationsLOSS MODULUS: The liquid-like or viscous portion of a viscoelastic material (elastomer, polymer, ...). It can be used for the determination energy lost during deformation. The energy lost is in the form of heat.E : stretching deformations (tensile)G: shearing, twisting, or torsional deformationsTan Delta (tan): Indicative of the material's ability to dissipate energy, where tan = E"/E' = G"/G'. GLASS TRANSITION OF AN ELASTOMER: Temperature region over which the material changes from a rigid, glassy solid to a more flexible, elastomeric solid. RUBBERY REGION: The region above Tg where the modulus is nearly independent of temperature. HARD SEGMENT MELT: The temperature at which the solid-to-liquid transition of the hard segment occurs. It defines the upper use temperature of the elastomer.

2

Temp Cel100.00.0-100.0

E' (

Sto

rage

Mod

ulus

) M

Pa

1.0E+00

1.0E+041.0E+04

tanD

1.0000

0.8000

0.6000

0.4000

0.2000

0.0000

E"

MP

a

1.0E-04

1.0E+001.0E+00

- 6 4 .7 C e l1 . 0 0 0 H z

- 5 7 .0 C e l1 . 0 0 0 H z

- 4 1 .1 C e l1 . 0 0 0 H z

- 1 1 0 .5 C e l4 .5 E + 0 3 M P a

4 8 . 1 C e l1 . 1 E + 0 1 M P a

9 9 .3 C e l1 .1 E + 0 1 M P a

4 9 .6 C e l6 . 1 E -0 4 M P a

ELASTOMER

G = RT / Me (((( )))) (((( ))))

molg720mol

kg72.0M

m

J

mm

mN

m

NPa10x1.1

K)50273(KmolJ314.8

mkg1000x3

M

ETR3

MM

TR3E

e

3227

3

e

ee

====

============

++++

====

========

Onset ETg= -64.7 oC

Maximum ETg =-57.0 oC

Maximum tandTg = -41.1 oC

E = 3 RT / Me

Temp Cel200.0150.0100.050.00.0

E' (

Sto

rage

Mod

ulus

) M

Pa

1.6E+00

5.5E+03ta

nD

3.0000

2.0000

1.0000

0.0000

E"

MP

a

8.1E-07

1.8E+02

111.8Cel10.00Hz1.3E+03MPa

1 1 3 .2 C e l1 0 . 0 0 H z2 .5 E + 0 2 M P a

1 3 1 .3 C e l1 0 . 0 0 H z

Poly(methyl methacrylate) (PMMA)

Onset of E= 111.8 oCThe max of E= 113.2 oCThe max of tan =131.3 oC

3

Temp Cel200.0150.0100.050.00.0

E' P

a

1.0E+06

1.0E+101.0E+10

tanD

3.0000

2.5000

2.0000

1.5000

1.0000

0.5000

0.0000

E" P

a

1.0E+05

1.0E+091.0E+09

2 2 .7 C e l1 0 .0 0 H z4 .6 E + 0 9 P a

1 7 9 .7 C e l1 0 .0 0 H z3 .6 E + 0 6 P a

1 1 8 .9 C e l1 0 .0 0 H z3 .0 E + 0 8 P a

1 2 8 .1 C e l0 .5 0 0 H z

1 2 9 .5 C e l1 .0 0 0 H z

1 3 2 .4 C e l2 .0 0 0 H z

1 3 5 .3 C e l5 .0 0 0 H z

1 3 8 .0 C e l1 0 .0 0 H z

4 3 .1 C e l1 0 .0 0 H z0 .0 9 1 7

Frequency (Hz)

Tg (oC)

0.5 128.1 1.0 129.5 2.0 132.4 5.0 135.3 10.0 138.0

-1

-0.5

0

0.5

1

1.5

2

2.5

0.00242 0.00244 0.00246 0.00248 0.0025

1/T (1/K)

ln (

freq

uenc

y), (

s-1

)Slope=-EA/R

Slope = -48526R2 = 0.9928

EA=403 kJ/mol

Poly(methyl methacrylate) (PMMA)

Temp Cel100.050.00.0

E' (

Sto

rage

Mod

ulus

) M

Pa

4.4E+01

1.5E+04

tanD

1.5000

1.0000

0.5000

E"

MP

a

2.8E-03

3.5E+01B io d e g r a d a b le

30.8Cel

1.000Hz5.3E+03MPa

Biodegradable Polymer (Sample from Erin Bahegl)

4

ENERGY STORAGEAverage energy stored over a full cycle:

ENERGY DISSIPATIONEnergy dissipated per cycle:

(((( )))) (((( )))) G4

E20

S ====

(((( )))) (((( )))) GE 20d ====

0

10

20

30

40

50

60

70

80

90

0 20 40 60 80 100

Shear Rate or Frequency (s -1)

App

aren

t or C

ompl

ex V

isco

sity

(P

a.s)

SteadyDynamic

VISCOSITY MEASUREMENT (Steady and Dynamic Measureme nt)

SAMPLE: Powder suspension

EXAMPLES (Rheometer)

5

0.1

1

10

100

0.1 1 10 100


App

aren

t or C

ompl

ex V

isco

sity

(P

a.s)

SteadyDynamic



0.1

1

10

100

0.01 0.1 1 10 100


App

aren

t or C

ompl

ex V

isco

sity

(P

a.s)

SteadyDynamic

=0.56

&&

======== )()(* app

Modified Cox-Merz

Modified Cox-Merz Rule


6

0.1

1

10

100

0.1 1 10 100 1000

Shear Rate (s -1)

App

aren

t Vis

cosi

ty (P

a.s)

Newtonian Approximation

Power Law Approximation


0.1

1

10

100

0.1 1 10 100 1000

Shear Rate (s -1)

App

aren

t Vis

cosi

ty (P

a.s)

Measured

Model Fitting (Power Law)

(((( ))))

(((( ))))62.0app

n1app

2.12

k

====

====

&

&

MODEL FITTING

7

0.1

1

10

100

0.1 1 10 100 1000

Shear Rate (s -1)

App

aren

t Vis

cosi

ty (P

a.s)



n=0.38


0.1

1

10

100

0.1 1 10 100 1000

Shear Rate (s -1)

App

aren

t Vis

cosi

ty (P

a.s)



n=0.10


8

1

10

100

1000

0.1 1 10 100

Frequency (1/s)

G' (

Pa)

; G''

(Pa)

; *

(Pa.

s)

0

0.2

0.4

0.6

0.8

1

1.2

tan

G' G''

Complex Viscosity tand


PDMS

1

10

100

1000

10000

100000

0.1 1 10 100

Frequency (1/s)

G' (

Pa)

; G''

(Pa)

;

* (P

a.s)

0

1

2

3

4

5

6

tan

G'G''

Complex viscosity

tand

9

1

10

100

0.01 1 100 10000

Time (s)

G (t

), (P

a)

0

20

40

60

80

100

0 50 100 150 200

Time (s)

G (

t), (

Pa)

TRANSIENT MEASUREMENT (STRESS RELAXATION)SAMPLE: Powder suspension

Frequency = 5 HzStrain amplitude = 20 %Temperature = 25 oC

timelaxationEwhere

ttN

Re

exp)(

========

====

EXAMPLE:A parallel plate geometry was used to measure the d ynamic rheological properties of a polymer melt at 210 oC. A sinusoidal strain with a maximum strain ( o) of 0.05 was applied at an angular frequency ( ) of 5 s -1, and the corresponding stress ( o) and phase angle ( ) were measured as 2.8 MPa and 12 o, respectively. Calculate the following viscoelastic properties of the polymer melt at an angular frequency of 5 s -1.

a. Storage modulusb. Loss Modulusc. Complex modulusd. Complex viscosity

(((( ))))

(((( ))))

*GitycosvisComplex

GitycosviscomplexofPartaginaryIm

GitycosviscomplexofPartalRe

GG

tan

*GModulusComplex

sinGModulusLoss

cosGModulusStorage

0

0

0

0

0

0

====

====

====

====

========

========

========

Rheometer DMA Examples 2014 n

Documents

Transcript of Rheometer DMA Examples 2014 n