rheology of branched polymers - leibniz … of... · rheology of branched polymers overview: the...

RHEOLOGY OF BRANCHED POLYMERS

Overview: The Tube Model

Shear and elongational viscosity

Albena Lederer

Leibniz-Institute of Polymer Research Dresden

Member of Gottfried Wilhelm Leibniz Society WGL

Hohe Strasse 6, D-01069 Dresden, Germany

Rheology of branching

Flow visualisation of molten PE into a contraction - different flow fields when driven from a

larger to a smaller cylinder

HDPE (linear) LDPE (branched)

Newtonian

fluid

The tube model Monodispers linear polymers

Many chain system Tube model

Tube model of de Gennes, Doi and Edwards (1986)

Tube width a

Primitive lenght N.b

(N number of segments, b Kuhn lenght)

Monomer friction coef. x Perpendicular motions are confined

Curvilinear motions are permitted

Determination of stress relaxation modulus G(t) , e.g. G*(t)

The tube model Monodispers linear polymers

PS, PB and PI with similar degrees of entanglement

G‘(w) elastic modulus

G‘‘(w) dissipative modulus

in phase and out of phase stresses – structure information!

reptation

Tube distance

Diff constant of the chain

DP of enanglement

The tube model Monodispers star polymers

Broad range of relaxation times in the

branched polymer!

Reptation is suppresed

Fluctuations on the primitive length of the star arms

Unentangled loops

Number of entanglements of the arms Ma/Me

Linear PI

3-star PI

The tube model Monodisperse Comb polymers

Arm

retractions

Unentangled

backbones

H-shaped PI

(arm molecular weight 20 kg/mol, backbone 110kg/mol)

Model blends Star-star blends

PI 3-arm stars

M1=28 kg/mol

M2=114 kg/mol

Fast relaxation

Slow relaxation

Model blends Star-linear blends

PI star-linear

blend

fstar=0

0.4

0.65

0.9

1.0

Branched polymer melts Viscosity

Prediction of extension and shear viscosity of a branched polymer

Branched polymer melts Viscosity

extension viscosity

shear viscosity

LDPE

Hypebranched polymers Mechanical properties

a) b)a) b)

Storage modulus G’ and loss modulus G’’ vs. angular

frequency at 60°C for polyethylene

(chain walking mechanism with Pd-diimine catalyst)

highly branched topology nearly linear chain topology

Ye, Z.B.; Al Obaidi, F.; Zu, S.P. Macromol. Chem. Phys. 2004, 205, 897.

Hypebranched polymers Complex viscosity

0,1 1 10 100

102

103

104

105

co

mp

lex

vis

co

sit

y

[Pa

s]

frequency [rad/s]

OH terminated hb polyester

C12 terminated hb polyester

0,1 1 10 100

102

103

104

105

co

mp

lex

vis

co

sit

y

[Pa

s]

frequency [rad/s]

OH terminated hb polyester

C12 terminated hb polyester

Complex viscosity versus frequency of

OH- and C12- terminated aromatic hb

polyester

Schmaljohann, D.; Häußler, L; Pötschke, P.; Voit, B.I.; Loontjens, T.J.A. Macromol. Chem. Phys. 2000, 201, 49

Electron beam irradiation of linear PP

Formation of long chain branching-PP Advantageous property:

strain hardening / HMS behaviour

LCB Polypropylene Generation of LCB

CH3

CHCH2+

CH2 CH2

CH3

C CH

CH3

CH

CH3

CH2 CH

CH3

CH2

CH2

CH3CH

CH2 CH2

CH3

C CH

CH3

CH

CH3

CH2+

CH2 C

CH3 CH3

CHCH2

CH3

CHCH2 CH

CH3

CH2

Molar mass degradation by

ß-scission Molar mass increasing by

Branching reaction

Influence of the irradiation temperature

Faster decrease of the concentration of radicals induced by irradiation,

decrease of the addition reaction frequency,

increase of the rate of ß-scission reaction,

increase of the chain diffusion to the amorphous phase,

partial melting of pellets.

Rätzsch, M.; Arnold, M.; Borsig, E.; Bucka, H.; Reichelt, N. Progr. Polym. Sci. 2002, 27, 1195-1282.

LCB Polypropylene

ß-scission

low temperature

~25 °C

high temperature

up to 190 °C

Increasing of

ß-scission rate

e-beam

radiation

low branched PP

with large arms

high branched PP

with short arms

Speculation about

the structure of

modified products

Influence of the irradiation temperature LCB Polypropylene

Modification

Electron beam 1.5 MeV

sample

Heating Turbo molecular Pump

Inert gas

Experimental set-up

• isotactic polypropylene (iPP)

homopolymer Novolen PPH2150

(Basell Polyolefins)

• electron accelerator ELV-2

(Budker Institute of Nuclear Physics,

Novosibirsk, Russia)

• dose: 20 kGy, 100 kGy

(1.5 MeV; 2 mA)

• atmosphere: nitrogen

• temperature: 25 –190 °C

LCB Polypropylene

Characterization methods

Molecular Characterization by HT-SEC

at 150°C in 1,2,4-trichlorobenzene coupled with MALLS-detector

Molar mass M; radius of gyration <r2>

Principle of separation: hydrodynamic volume of molecules

branchlinear rr 22

branchlinear rr 22

branchlinear MM

branchlinear MM

LCB Polypropylene

<r2

> [

nm

2]

M [g/mol]

Linear iPP

Branched PP

linear

branch

r

rg

2

2

SEC-MALLS characterization

Auhl et al. Macromolecules 2004, 37 (25), 9465-9472

Increase of the

Irradiation dose

Decrease of the

molar mass

and

Increase of

the LCB

0,2

0,4

0,6

0,8

1,0

0 20 40 60 80 100 120 140 160

1x105

2x105

3x105

4x105

5x105

6x105

7x105

8x105

Nu

mb

er

of

LC

B p

er

100

0 m

ono

me

rs

Mw

irradiation dose d [kGy]

Mw

[g

/mo

l]

NLCB

LCB Polypropylene

5x105

106

2x106

3x106

103

104

virgin iPP

20 kGy: 100 kGy:

25°C 25°C

me

an

sq

ua

re r

adiu

s o

f g

yra

tio

n <

r2>

[n

m2]

molar mass M [g/mol]

Increase of the

Irradiation dose

Decrease of <r2>

Increase of

the LCB


SEC-MALLS characterization LCB Polypropylene

5x105

106

2x106

3x106

103

104

virgin iPP

20 kGy: 100 kGy:

25°C 25°C

80°C 80°C

mean s

quare

radiu

s o

f gyra

tion <

s2>

[nm

2]



5x105

106

2x106

3x106

103

104

virgin iPP

20 kGy: 100 kGy:

25°C 25°C

80°C 80°C

110°C 110°C

mean s

quare

radiu

s o

f gyra

tion <

s2>

[nm

2]



5x105

106

2x106

3x106

103

104

virgin iPP

20 kGy: 100 kGy:

25°C 25°C

80°C 80°C

110°C 110°C

150°C 150°C

mean s

quare

radiu

s o

f gyra

tion <

s2>

[nm

2]



5x105

106

2x106

3x106

103

104

virgin iPP

20 kGy: 100 kGy:

25°C 25°C

80°C 80°C

110°C 110°C

150°C 150°C

190°C

mean s

quare

radiu

s o

f gyra

tion <

r2>

[nm

2]


Increase of the

Irradiation

temperature

Decrease of <r2>


5,05,0

9

4

71

mmg

Assumption: trifunctional

randomly branched polymer

12

mm

MM S

Molar mass of the segments Ms:

(m+2) - number of the pieces between the branching points and the chain ends

(m-1) - number of the pieces between the branching points

Sugimoto et al. J. Appl. Polym. Sci.

1999, 73, 1493.;

Zimm et al. J. Chem. Phys. 1949, 17, 1301.

m - number of branching points


105

106

107

3x103

104

105

7x105

20 kGy: 100 kGy:

25°C 25°C

190°C 130°Cmola

r m

ass o

f seg

ments

MS [

g/m

ol]


Ms is nearly

constant in the

range between

5x105 - 3x106 g/mol


1x104

2x104

3x104

1,0x105

1,5x105

2,0x105

20 40 60 80 100 120 140 160 180 200

20 kGy

100 kGy

irradiation temperature T [°C]

mo

lar

ma

ss o

f se

gm

ent

MS [

g/m

ol]

Increase of the

Irradiation

temperature

Decrease of Ms

shorter chain

segments


1x104

2x104

3x104

1,0x105

1,5x105

2,0x105

20 40 60 80 100 120 140 160 180 200

20 kGy

100 kGy

irradiation temperature T [°C]

mo

lar

ma

ss o

f se

gm

ent

MS [

g/m

ol]

norm

aliz

ed h

ea

t flo

w [

W/g

]

exo

partial melt melt solid


Shear Flow Rheology by Plate-Plate rheometer

at 180°C, in nitrogen, cylindrical samples of 2 mm thickness and 25 mm diameter

Zero shear-rate viscosity 0

0

0

t

tJtJ

0lim

tJ

t

t

Qualitative determination of the branching topology

0 in dependence on Mw

J. Janzen, R. H. Colby J. Mol. Struct. 1999, 485-486, 569.

e

a

e

a

M

M

M

M

exp0

Rheology characterization LCB Polypropylene

105

2x105

4x105

6x105

8x105

106

102

103

104

105

106

3x106

T= 180°C

lg -15.4 + 3,5 x lg M

w

0 [P

a s

]

Mw [g/mol]

Low

branching

High

branching

Linear iPP

polyethylene:

Decrease of 0

Decrease of the

molar mass of LCB

and

Increase of the

number of LCB

(Mw~constant)

Inkson et al. Proc. XIVth Int. Congr. on Rheology, August 22-27, 2004, Seoul, Korea.

Shear Flow Rheology LCB Polypropylene

105

106

5x102

103

104

105

106

190°C170°C150°C

110°C 80°C25°C

150°C130°C

110°C80°C50°C

25°C

virgin iPP

linear iPP, T=180°C

lg -15,4 + 3,5 * lgM

W

ze

ro s

he

ar

vis

co

sity

0 [

Pa

s]

linear iPP

20 kGy & irrad. temp.

100 kGy & irrad. temp.

weight average molar mass Mw [g/mol]

Increase of the

Irradiation

temperature

Decrease of 0 (Mw~const.)

lower molar mass

and higher

number of LCB

More and shorter long chain branches (arms)

LCB Polypropylene Shear Flow Rheology

SEC-MALLS vs. Rheology LCB Polypropylene




Increase of the

Irradiation dose

Decrease of 0

At low LCB amounts

Increase of 0

At high LCB amounts

lower molar mass

and higher

number of LCB



Transient elongational viscosity vs. time

at different Henky strain rates Strain hardening factor:



•High sensitivity of detecting low amounts of branches in polymers of rheology measurements (strain

hardening/elongational viscosity and shear viscosity)

•Lower sensitivity of detection in solution (SEC) but qualitative calculations possible

Strain hardening factor:

rheology of branched polymers - leibniz … of... · rheology of branched polymers overview: the...

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