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Effect of Index on Curing Kinetics & Viscoelastic Properties of PU gels
Lifeng Wu
TRFA 2006 Annual Meeting
September 11, 2006
HUNTSMAN POLYURETHANES
Polyurethanes
Gel: a colloidal system consisting of a liquid which is dispersed in a solid polymeric matrix resulting in a soft, gelly, material.
Applications: Adhesives Energy absorbers, dampers
Gel
Polyurethanes
PU Gels
Hydrogel Poly(ethylene oxide) network swelled with water
Plasticizer gel PU network plasticized with phthalates
Polyol gel: PU network with excess multifunctional polyol
Monol gel*: Polyol mixture of diol and monol crosslinked with
multifunctional isocyanates
* US6908979 and US6914117 (Huntsman patents)
Polyurethanes
Polyol Gel
Materials: Rubinate 1209: prepolymer based on MDI (NCO% = 21.5) Jeffol G31-55: polyether triol (OHv = 55)
Jeffcat TD-33A: tertiary amine catalyst
OH
HO
HO
+NCOOCN
OH
NCO
H
O
OCNH
OCat.
Index: r [NCO]0/[OH]0
r = 0.5 – 1.0
Conversion: p ([NCO]0 – [NCO])/[NCO]0
Polyurethanes
Rheology
Rheology: study of the flow and deformation of matter.
AR 2000 Rheometer
G’: storage modulus
G”: loss modulus
: phase angle = tan-1(G”/G’)
G”
G’
liquid solid
Polyurethanes
Curing Rheology (r = 0.5, 0.6)
r = 0.5
1.0E-01
1.0E+01
1.0E+03
1.0E+05
1.0E+07
0 20 40 60 80 100
t (min)
G',
G"
(Pa
)
0
30
60
90
(
de
g)
G'
G"
r = 0.6
1.0E-01
1.0E+01
1.0E+03
1.0E+05
1.0E+07
0 20 40 60 80 100
t (min)
G',
G"
(Pa
)
0
30
60
90
(
de
g)
G'
G"
Gel Point: G’ = G”
Polyurethanes
Curing Rheology (r = 0.7, 0.8)
r = 0.7
1.0E-01
1.0E+01
1.0E+03
1.0E+05
1.0E+07
0 20 40 60 80 100
t (min)
G',
G"
(Pa
)
0
30
60
90
(
de
g)
G'
G"
r = 0.8
1.0E-01
1.0E+01
1.0E+03
1.0E+05
1.0E+07
0 20 40 60 80 100
t (min)
G',
G"
(Pa
)
0
30
60
90
(
de
g)
G'
G"
Similar behavior to r = 0.6.
Polyurethanes
Curing Rheology (r = 0.9, 1.0)
r = 0.9
1.0E-01
1.0E+01
1.0E+03
1.0E+05
1.0E+07
0 20 40 60 80 100
t (min)
G',
G"
(Pa
)
0
30
60
90
(
de
g)
G'
G"
r = 1.0
1.0E-01
1.0E+01
1.0E+03
1.0E+05
1.0E+07
0 20 40 60 80 100
t (min)
G',
G"
(Pa
)
0
30
60
90
(
de
g)
G'
G"
G” shows 2nd stage growth . High crosslink density
Polyurethanes
Curing kinetics
0
1
2
3
4
0 2 4 6 8 10 12 14
(1-r)t
Ln
[(1
-rp
)/(1
-p)]
k[H]0 = 0.28 min-1k[NCO][OH]
t
[NCO]
d
d
r)t(1k[OH])p-1
rp-1ln( 0
re
1et)p(r, r)t(1k[H]
r)t(1k[H]
0
0
Molecular weight*: Mw(r,p)
Crosslink density*: (r,p)
* Macosko and Miller, 1976
Gel Point
Polyurethanes
Viscosity at Initial Stage
1.0E-01
1.0E+00
1.0E+01
1.0E+02
1.0E+03
1.0E+04
0 2 4 6 8 10
t (min)
G"
(Pa
)
1.0E-01
1.0E+00
1.0E+01
1.0E+02
1.0E+03
1.0E+04
G' (
Pa
)
r = 0.5r = 0.6r = 0.7r = 0.8r = 0.9r = 1.0r = 1.0
Viscosity 0 = G”/ ( = 1 rad/s)
Polyurethanes
Initial Growth of Molecular Weight
1000
10000
100000
0 1 2 3 4 5 6
t (min)
Mw
(g
/mo
l)
1
10
100
1000
10000
G"
(Pa
)
r = 0.5r = 0.6r = 0.7r = 0.8r = 0.9r = 1.0r = 1.0
0 ~ Mw for unentangled polymers 0 ~ Mw
3.4 for entangled polymers
0 ~ Mw2
Entanglement
Polyurethanes
Crosslink Density –
0
0.2
0.4
0.6
0.8
1
0 20 40 60 80 100t (min)
r = 0.6 r = 0.7 r = 0.8
r = 0.9 r = 1.0
320 )
rp
1(2[OH]μ
0
0.2
0.4
0.6
0.8
1
0 20 40 60 80 100t (min)
1.0E+00
1.0E+01
1.0E+02
1.0E+03
1.0E+04
1.0E+05
1.0E+06
G"
(Pa)
r = 0.6 r = 0.7 r = 0.8
r = 0.9 r = 1.0 r = 0.9
r = 1.0
G"
Polyurethanes
Viscoelastic Properties (r = 0.5,0.6)
r = 0.5
1.0E+02
1.0E+03
1.0E+04
1.0E+05
1.0E+06
0.01 1 100 10000aT (rad/s)
G',
G"
(Pa
)
G'
G"
r = 0.6
1.0E+02
1.0E+03
1.0E+04
1.0E+05
1.0E+06
0.01 1 100 10000aT (rad/s)
G',
G"
(Pa
)
G'
G"
G’ ≈ G” ~ 0.5 (critical gel) G’ ~ 0 (low ),G” ~ 0.5
Polyurethanes
Viscoelastic Properties (r = 0.7,0.8)
r = 0.7
1.0E+02
1.0E+03
1.0E+04
1.0E+05
1.0E+06
0.01 1 100 10000aT (rad/s)
G',
G"
(Pa
)
G'
G"
r = 0.8
1.0E+02
1.0E+03
1.0E+04
1.0E+05
1.0E+06
0.01 1 100 10000aT (rad/s)
G',
G"
(Pa
)
G'
G"
G’ ~ 0, G” ~ 0.5
Polyurethanes
Viscoelastic Properties (r = 0.9,1.0)
r = 0.9
1.0E+02
1.0E+03
1.0E+04
1.0E+05
1.0E+06
0.01 1 100 10000aT (rad/s)
G',
G"
(Pa
)
70 °C
30 °C
50 °C
G'
G"
r = 1.0
1.0E+02
1.0E+03
1.0E+04
1.0E+05
1.0E+06
0.01 1 100 10000aT (rad/s)
G',
G"
(Pa
) 30 °C
50 °C
70 °C
G'
G"
r = 0.9
1.0E+02
1.0E+03
1.0E+04
1.0E+05
1.0E+06
0.01 1 100 10000aT (rad/s)
G',
G"
(Pa
)
70 °C
30 °C
50 °C
G'
G"
r = 1.0
1.0E+02
1.0E+03
1.0E+04
1.0E+05
1.0E+06
0.01 1 100 10000aT (rad/s)
G',
G"
(Pa
) 30 °C
50 °C
70 °C
G'
G"
G’ ~ 0, G” ~ 0 – 0.5
Polyurethanes
Plateau Modulus – G0
1.E+03
1.E+04
1.E+05
1.E+06
1.E+07
0.5 0.6 0.7 0.8 0.9 1
r
G0 (
Pa
)
1.E+03
1.E+04
1.E+05
1.E+06
1.E+07
0.5 0.6 0.7 0.8 0.9 1
r
G0 (
Pa
)
μRT2
1G0
Polyurethanes
Curing Rheology at High Indices
1.0E-01
1.0E+00
1.0E+01
1.0E+02
1.0E+03
1.0E+04
1.0E+05
1.0E+06
1.0E+07
0 20 40 60 80 100t (min)
G',
G"
(Pa
)
0
0.2
0.4
0.6
0.8
1
1.2
(
mo
l/L)
G'
G"
r = 1.0
Polyurethanes
r = 1.0
1.0E+02
1.0E+03
1.0E+04
1.0E+05
1.0E+06
1.0E+07
0.01 0.1 1 10 100 1000 10000aT (rad/s)
G',
G"
(Pa
)
30 min_G'
30 min_G"
G'
G"
Relaxation Behavior During Curing
r = 1.0
1.0E+02
1.0E+03
1.0E+04
1.0E+05
1.0E+06
1.0E+07
0.01 0.1 1 10 100 1000 10000aT (rad/s)
G',
G"
(Pa
)
30 min_G'
30 min_G"
90 min_G'
90 min_G"
G'
G"
G” ~ 0.5G” ~ 0
Polyurethanes
Mechanism: Dangling Chains
NCO
H
O
OCNH
O
NCO
H
O
OH
NCO
H
O
OCNH
O
G” ~ 0.5
G” ~ 0
Before transition:
After transition:
< 0.4 mol/L dangling chains > 50%
> 0.6 mol/L dangling chains < 25%
Polyurethanes
Conclusion
Before gel point: Initial and Mw growth is nearly independent of index:
log() ~ t
After gel point: index r crosslink density #dangling chain
G’(), G”() : r = 0.5: G’ ≈ G” ~ 0.5 (critical gel) r = 0.6 – 0.8: G’ ~ 0, G” ~ 0.5 r = 0.9, 1.0: G’ ~ 0, G” ~ 0 – 0.5 (2nd stage growth)
Polyurethanes
Effect of Conversion on Mw and
Macosko and Miller, 1976
Mw
