Transcript PVT Tim van Erp

Flow-induced crystallization
of polypropylene
STW progress, 21th of september 2011
Tim van Erp, Gerrit Peters
overview
• non-isothermal, multi-phase crystallization
• effects of cooling rate
• effects of pressure
• flow-induced (non-isothermal, multi-phase) crystallization
• experimental part
• modeling part; discussion on parameters
processing
structure
properties
PVT apparatus
A = Outer piston
B = Inner rotating piston
C = Sample
D = Teflon sealing ring
E = Cooling channels
F = Cooling channels
G = Thermocouples
for   0.99    Ri     Ro 
PVT :  
Ri
 0.95
Ro
processing protocol: FIC experiments
Annealing 10 min @ 250°C
Compressed air cooling @ ~1°C/s
Isobaric mode
Pressures: 100 – 500 – 900 – 1200 bar
Short term shearing of ts = 1s
Shear rates: 3 - 10 – 30 – 100 – 180 s-1
∆T = Tm(p) – Tshear = 30 - 60°C
analysis PVT data
normalized
specific volume
  s
 
 m  s

dimensionless
transition temperature

Tc,onset
TcQ,onset
analysis PVT data
Deborah number (‘strength of flow’)
De  aT ap
WLF Temperature shift
log  aT  
c1 Tshear  Tref 
c2  Tshear  Tref 
Pressure shift
normalized
specific volume
  s
 
 m  s

dimensionless
transition temperature

Tc,onset
Q
c ,onset
T
ap  exp    p  pref  
Shear temperature


Tshear  Tm0   0 p  T
results ∆T = 30°C
results ∆T = 60°C
dimensionless transition temperature
dimensionless
transition temperature

Tc,onset
TcQ,onset
flow regimes under non-isothermal conditions
from spherulitic morphology to oriented structures
flow regimes under non-isothermal conditions
saturation in crystallization temperature
overview
• non-isothermal, multi-phase crystallization
• effects of cooling rate
• effects of pressure
• flow-induced (non-isothermal, multi-phase) crystallization
• experimental part
• modeling part
• quiescent crystallization
• flow-induced crystallization
quiescent crystallization
space filling
Schneider rate equations
Avrami equation
nucleation density
individual growth rate
3  8
(3  8 N )
‘number’
2  G3
(2  4 Rtot )
‘radius’
1  G2
(1  Stot )
‘surface’
0  G1
(0  Vtot )
‘undisturbed volume’
 ln 1    0
‘real volume’
N T , p   Nmax exp  cN T  TNref  p  
2
Gi T , p   Gmax,i exp cG,i T  TGref ,i  p   


modeling flow effects on crystallization
flow-induced crystallization model
total nucleation density
(flow-induced) nucleation rate
shish length (L) growth
rate equations
Avrami equation
Ntot  Nq  Nf


4
Nf  g n  hmw
1


4
L  g l  avg
1
 2  4 Nf L
 1  G 2
 0  G 1
 ln 1    0  0
for   crit
‘length’
‘surface’
‘undisturbed volume’
‘real volume’
flow-induced crystallization model
total nucleation density
(flow-induced) nucleation rate
shish length (L) growth
rate equations
Avrami equation
experiment
Ntot  Nq  Nf


4
Nf  g n  hmw
1


4
L  g l  avg
1
for   crit
 2  4 Nf L
 1  G 2
 0  G 1
‘length’
‘surface’
‘undisturbed volume’
 ln 1    0  0
model
‘real volume’
flow-induced crystallization model
total nucleation density
(flow-induced) nucleation rate
shish length (L) growth
rate equations
Avrami equation
Ntot  Nq  Nf


4
Nf  g n  hmw
1


4
L  g l  av
g 1
 2  4 Nf L
 1  G 2
 0  G 1
 ln 1    0  0
gn  aT gn0
gl  aT gl 0
F. Custódio, PhD Thesis, 2008
very laborious and inaccurate work
gn  gn T , p 
gl  gl T , p
FIC regimes
total nucleation density
(flow-induced) nucleation rate
shish length (L) growth
Avrami equation
Ntot  Nq  Nf


4
Nf  g n  hmw
1


4
L  g l  avg
1
 ln 1    0  0
gn  gn T , p 
gl  gl T , p
prediction of FIC regimes
Mismatch between experimental results and model in oriented regime
a  1013 m3
Nf ,max  1050 m3
crit  41.5
gi  gi T , p
parameters gn and gl
gn  aT apgn0
aT, aP rheological shift factors
plane equation
aX  bY  cZ  d  0
scaling parameter
gl  10aT bP d
gn and gl arbitrary function of T and p?
aTl aPl gl 0
critical stretch
shish length (L) growth


4
L  g l  avg
1
HMW  crit
critical stretch
HMW (t )  crit
new definition for critical stretch criterium?
critical stretch
tflow
HMW (t )  crit

 HMW dt   crit
0
new definition for critical stretch criterium?
prediction of FIC regimes
Good agreement between experimental results and model
conclusions
• characterization of flow enhanced (point-like) nucleation
regime over wide range of processing conditions
• characterization of FIC of oriented structures regime
over wide range of processing conditions
• extended dilatometry (PVT) proven to be a powerfull tool
in characterizing flow induced crystallization