宋义虎+Universal+Contribution+of+Filler+to+Linear+Viscoelasticity+of+Filled+Polymer
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Yihu h SONG, Qiang ZHENG
Department of Polymer Science and Engineering Key Laboratory of Macromolecular Synthesis and Functionalization of Ministry of Education
Contribution of filler
● Strain amplification effect
Presence of hard and much less deformable filler inclusions in a soft and highly deformable matrix leads to hydrodynamic effects referring to a strain amplification factor Af > 1 Imposing a macroscopic strain to filled polymers Local strain of interstitial fluid = macroscopic strain multiplied by Af
The second class for solid‐like dispersions Using one modulus shift factor plus one frequency shift factor by choosing any concentration at > c as reference concentration Problem: breakdown in high‐ zone due to non‐Newtonian feature of the polymer melts?
Structural investigations show that filling may lead to
increase, decrease, or no change g in Tg, or even two Tg increase, or no change in molecular relaxation time
● Structural contribution
The filler phase form viscoelastic aggregates by interparticle aggregating and by absorbing polymer chain
Wolthers, 1997
Chain‐like aggregate microstructural rheological model Vi Viscoelasticity l ti it of f rigid i id aggregate t originated i i t d from f viscoelastic i l ti motion ti of f filler fill particles ti l
2010年复杂流体流变学学术研讨会
Linear rheology: Universal observations
10
6 5
G' / Pa G
Universal U i l Contribution C t ib ti of f Filler Fill t to Linear Viscoelasticity of Filled Polymers
A two phase model
The filler and the p polymer y contribute independently p y to modulus The total rheological response is the sum of the two independent contributions varying significantly with
depending on the polymer‐filler interactions
The first class fuild‐like dispersions Using one modulus shift factor by choosing =0 (dispersant) as reference concentration Problem: breakdown in low‐ zone where contribution from particle network seems dominative at high ?
+ one frequency shift factor (Trappe , 2000) LTS one frequency LTS: f shift hif f factor(Marcovich , 2004)
Proposing p g of a two p phase model Application of the model in terminal region Application of the model in nonterminal region
Background: plausible TCS
。
Background: plausible TCS
G', G'' / Pa
Trappe, Weitz, 2000 Hobbie, Fry, 2006 Romeo et al., 2008
Tan T
Marcovich, 2004
TCS applications CB dispersions p (Trappe, ( pp , Weitz,2000) , ) clay/8%PVC dispersions (Daga, 2006) MWCNT/PIB (Hobbie, 2007) SWCNT/PEO (Chatterjee, 2007) CB/PE ( (Jager, g Eggen, gg 2004) )
' " Gf* Gf1 iGf0
G'f(,) is very weakly dependent on G''f(,) is approximately independent of
Contribution of polymer to effective complex modulus of filled polymers = complex modulus Gm*(,) of polymer multiplied by Af, i.e. Af Gm*(,)
Under affine deformation assumption
Background: plausible TCS Problems for TCS
Linear dynamic rheology of filled polymers Contents
Amphibolous definitions for shift factors
Liquid q ‐like: one modulus shift factor ((Faitel‘son,, 1977)) solid‐like: one modulus shift factor
Linear dynamic rheology of filled polymers Contents
Proposing p g of a two p phase model Application of the model in terminal region Application of the model in nonterminal region
Faitel'son, , Yakobson, , 1977 Mongruel Cartault Mongruel, Cartault, 2006
chalk ( 0.15) in 8% solution l ti of f PIB in i cetane t
SBR/silica
PDMS/CaCO3
Xu, et al., 2008
unvaried
Network formation is assumed
physical jamming or percolation particle network the long‐lived chain bridges between the particles transient network or entrapped entanglements (due to polymer adsorption on the filler ) surface)
Frequency eque cy s shift t factor acto
Does filling influences molecular relaxation? from what filler concentration?
Do we need two master curves for understanding LTS t transition? iti ?
Linear rheology: plausible arguments
STL transition is related to polymer absorption on filler surface Absorption leads to
a decrease in effective segment an increase in effective filler volume fraction a formation of bound or occluded polymer shell a formation of restrained rubbery or even glassy shell around the filler inclusion a retardation in molecular relaxation on filler surface or in interfiller space due to motion restriction
Department of Polymer Science and Engineering Key Laboratory of Macromolecular Synthesis and Functionalization of Ministry of Education
Contribution of filler
● Strain amplification effect
Presence of hard and much less deformable filler inclusions in a soft and highly deformable matrix leads to hydrodynamic effects referring to a strain amplification factor Af > 1 Imposing a macroscopic strain to filled polymers Local strain of interstitial fluid = macroscopic strain multiplied by Af
The second class for solid‐like dispersions Using one modulus shift factor plus one frequency shift factor by choosing any concentration at > c as reference concentration Problem: breakdown in high‐ zone due to non‐Newtonian feature of the polymer melts?
Structural investigations show that filling may lead to
increase, decrease, or no change g in Tg, or even two Tg increase, or no change in molecular relaxation time
● Structural contribution
The filler phase form viscoelastic aggregates by interparticle aggregating and by absorbing polymer chain
Wolthers, 1997
Chain‐like aggregate microstructural rheological model Vi Viscoelasticity l ti it of f rigid i id aggregate t originated i i t d from f viscoelastic i l ti motion ti of f filler fill particles ti l
2010年复杂流体流变学学术研讨会
Linear rheology: Universal observations
10
6 5
G' / Pa G
Universal U i l Contribution C t ib ti of f Filler Fill t to Linear Viscoelasticity of Filled Polymers
A two phase model
The filler and the p polymer y contribute independently p y to modulus The total rheological response is the sum of the two independent contributions varying significantly with
depending on the polymer‐filler interactions
The first class fuild‐like dispersions Using one modulus shift factor by choosing =0 (dispersant) as reference concentration Problem: breakdown in low‐ zone where contribution from particle network seems dominative at high ?
+ one frequency shift factor (Trappe , 2000) LTS one frequency LTS: f shift hif f factor(Marcovich , 2004)
Proposing p g of a two p phase model Application of the model in terminal region Application of the model in nonterminal region
Background: plausible TCS
。
Background: plausible TCS
G', G'' / Pa
Trappe, Weitz, 2000 Hobbie, Fry, 2006 Romeo et al., 2008
Tan T
Marcovich, 2004
TCS applications CB dispersions p (Trappe, ( pp , Weitz,2000) , ) clay/8%PVC dispersions (Daga, 2006) MWCNT/PIB (Hobbie, 2007) SWCNT/PEO (Chatterjee, 2007) CB/PE ( (Jager, g Eggen, gg 2004) )
' " Gf* Gf1 iGf0
G'f(,) is very weakly dependent on G''f(,) is approximately independent of
Contribution of polymer to effective complex modulus of filled polymers = complex modulus Gm*(,) of polymer multiplied by Af, i.e. Af Gm*(,)
Under affine deformation assumption
Background: plausible TCS Problems for TCS
Linear dynamic rheology of filled polymers Contents
Amphibolous definitions for shift factors
Liquid q ‐like: one modulus shift factor ((Faitel‘son,, 1977)) solid‐like: one modulus shift factor
Linear dynamic rheology of filled polymers Contents
Proposing p g of a two p phase model Application of the model in terminal region Application of the model in nonterminal region
Faitel'son, , Yakobson, , 1977 Mongruel Cartault Mongruel, Cartault, 2006
chalk ( 0.15) in 8% solution l ti of f PIB in i cetane t
SBR/silica
PDMS/CaCO3
Xu, et al., 2008
unvaried
Network formation is assumed
physical jamming or percolation particle network the long‐lived chain bridges between the particles transient network or entrapped entanglements (due to polymer adsorption on the filler ) surface)
Frequency eque cy s shift t factor acto
Does filling influences molecular relaxation? from what filler concentration?
Do we need two master curves for understanding LTS t transition? iti ?
Linear rheology: plausible arguments
STL transition is related to polymer absorption on filler surface Absorption leads to
a decrease in effective segment an increase in effective filler volume fraction a formation of bound or occluded polymer shell a formation of restrained rubbery or even glassy shell around the filler inclusion a retardation in molecular relaxation on filler surface or in interfiller space due to motion restriction
