Y. H. Wen ( 溫玉合 ) and C. C. Hua ( 華繼中 )
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Y. H. Wen ( Y. H. Wen ( 溫溫溫 溫溫溫 ) ) and C. C. Hua ( and C. C. Hua ( 溫溫溫 溫溫溫 ) Department of Chemical Engineering, National Chung Cheng University Department of Chemical Engineering, National Chung Cheng University A Theoretical and Experimental A Theoretical and Experimental Investigation on Investigation on Short Short - - Time Stretch Rel Time Stretch Rel axation of Entangled Polymer Solutions axation of Entangled Polymer Solutions
description
A Theoretical and Experimental Investigation on Short - Time Stretch Relaxation of Entangled Polymer Solutions. Y. H. Wen ( 溫玉合 ) and C. C. Hua ( 華繼中 ) Department of Chemical Engineering, National Chung Cheng University. Introduction. Historical Sketch de Gennes (1971) - PowerPoint PPT Presentation
Transcript of Y. H. Wen ( 溫玉合 ) and C. C. Hua ( 華繼中 )
Y. H. Wen (Y. H. Wen ( 溫玉合溫玉合 )) and C. C. Hua (and C. C. Hua ( 華繼中華繼中 ))
Department of Chemical Engineering, National Chung Cheng UniversityDepartment of Chemical Engineering, National Chung Cheng University
A Theoretical and Experimental A Theoretical and Experimental Investigation on Investigation on ShortShort-- Time Stretch Relaxation of Time Stretch Relaxation of
Entangled Polymer Solutions Entangled Polymer Solutions
IntroductionIntroduction
Historical Sketch de Gennes (1971) Doi and Edwards (1986)
The tube (or reptation) model and its derivatives have proven very successful, especially in describing the linear viscoelasticity of entangled polymer liquids
Linearrelaxation
Chain Retraction(nonlinear relaxation)
A Story about Nonlinear ViscoelasticityA Story about Nonlinear Viscoelasticity
Orientation Relaxation(linear relaxation)
d
Reptation tim
5
e
s 45
PS/DEP solution (Mw=5.5x106 g/mol; PI=1.01; Zeq=77)
R
Rouse time
2.4 s
Chain Retraction(nonlinear relaxation)
d R eq/ 3Z
Dilute solution Concentrated solution
Rouse chain
Objectives of the current investigation:
The Rouse Model Prediction on
Short-time Chain Retraction
The Rouse Model Prediction on
Short-time Chain Retraction
Nonlinear Stress Relaxation Data in
Single-step Strain Flows
Nonlinear Stress Relaxation Data in
Single-step Strain Flows
For time scales <
The impact of polymer entanglement ?
R
Application of the Rouse chain in two distinct cases
Only terminal chain retraction is captured for the case of concentrated systems
Formulation Formulation ofof Stress Relaxation in Stress Relaxation in Single-Single-SS tep Sttep Strain Flowsrain Flows
(0)N
215( , ) ( )
4( ) ( )yx
yxG t t tG Q
22
R21
( ) 1 1exp( / )
( 0 ) 1
N
p
tt
Np
t
The Rouse model
where andeqN Zeq
( 0 )t E u
( )
( )
t
t
(0)
N
( )
yx
yx
G
Q
: shear stress
: D-E universal function (w/o IA assumption)
: plateau modulus
: strain: tube survival probability
: dimensionless chain stretching
eq
N
Z
: No. of Rouse modes: No. of entanglements per chain at equilibrium
Nonlinear stress relaxation modulus:
(rad/s)
10-3 10-2 10-1 100 101 102
G' a
nd
G"
(Pa
)
10-1
100
101
102
103
104
105
G'G"
e= 1.3 x 10-3 s; Zeq = 19
Experimentally Experimentally Determined Model ParametersDetermined Model Parameters
1weq
e,melt
MZ
M
eqZ
G
G
Number of entanglements per chain at equilibrium,
The Rouse time,eq
2R e ( )Z
φ: volume fraction of polymer
PS/TCP solution
Theory/Data ComparisonsTheory/Data Comparisons
eq RParameters: 42; 0.35 sZ eq RParameters: 118; 2.10 sZ
t (s)
10-1 100 101 102
G(t
,)
(Pa
)
100
101
102
103
Exp. (Zeq=42)
Rouse model
0.3
9
PS/DEP solution
t (s)
10-1 100 101 102 103
G(t
,)
(Pa
)
100
101
102
103
Exp. (Zeq=118)
Rouse model
0.4
9
PS/DEP solution
Self-consistently Renormalized Rouse ModesSelf-consistently Renormalized Rouse Modes
(a) t = 0 (at equilibrium)
A different number of entanglements per chain
N is a dynamic variable
A Renormalized Rouse model:2
2R2
1
( ) 1 1exp( / )
( 0 ) 1
N
p
tt
Np
t
eq
( )( )
( 0 )N t
tZ
tZ
where
(b) t = 0+
StretchingStretching
RetractionRetraction(c) t <
eq RParameters: 42; 0.35 sZ eq RParameters: 118; 2.1 sZ
t (s)
10-1 100 101 102 103
G(t
,)
(Pa
)
100
101
102
103
Exp. (Zeq=118)
Rouse modelRenormalized Rouse model
0.4
9
PS/DEP solution
t (s)
10-1 100 101 102
G(t
,)
(Pa
)
100
101
102
103
Exp. (Zeq=42)
Rouse modelRenormalized Rouse model
0.3
9
PS/DEP solution
t (s)
10-1 100 101
G(t
,)
(Pa)
100
101
102
103
104
Exp. (Zeq=19)
Rouse modelRenormalized Rouse model
0.5
10
PS/TCP solution
t (s)
10-1 100 101 102
G(t
,)
(Pa)
100
101
102
103
Exp. (Zeq=45)
Rouse modelRenormalized Rouse model
0.3
7
PαMS/PCB solution
t (s)
10-1 100 101
G(t
,)
(Pa
)
104
105
Exp. (Zeq=26)
Rouse modelRenormalized Rouse model
3.33
0.5
1,4-PB/FO solution
t (s)
0.1 1 10 100
G(t
,)
(Pa
)
101
102
103
Exp. (Zeq=17)
Rouse modelRenormalized Rouse model
0.3
5
PMMA/PCB solution
Theory/Data Comparisons for Theory/Data Comparisons for Various Polymer Various Polymer SpeciesSpecies
ConclusionsConclusions
The instantaneous entanglement property has a significant impact on short-time chain retraction of entangled polymer solutions.
Self-consistent mode renormalization leads to better agreement with experimental data.
Remaining discrepancies might result from (a) Inaccuracy of short-time relaxation data and/or (b) Tube pressure associated with a deformed polymer
network
AcknowledgementsAcknowledgements
National Science Council National Science Council (93-2116-E-194-001)
Excellency Project of the Ministry of Education of ROCExcellency Project of the Ministry of Education of ROC (91-E-FA04-2-4A)
