Transcript Slide 1

Multi-Scale Simulation of Polymer Processing
Kathryn Garnavish, David Kazmer, William Rousseau, & Yingrui Shang
University of Massachusetts Lowell
Consititutive Models
0 .9 8
0 .9 6
◦Momentum
  v  P


z  z  x
◦Heat
100
10
T 
 T
 T
2

C p 
v

k




2

t

x

z


2
1
10
100
1000
0 .9 4
0 .9 2
0 M P a F itte d
2 0 M P a F itte d
4 0 M P a F itte d
6 0 M P a F itte d
8 0 M P a F itte d
1 0 0 M P a F itte d
1 2 0 M P a F itte d
1 4 0 M P a F itte d
1 6 0 M P a F itte d
1 8 0 M P a F itte d
2 0 0 M P a F itte d
0 .9 0
0 .8 8
◦Relaxation
10
1.E+08
8
1.E+07
6
Exp.
Fitted
1.E+06
4
WLF
1.E+05
G'-Exp.
G"-Exp.
G'-Fitted
G"-Fitted
1.E+04
2
0
1.E+03
-2
0 .8 4
1.E+02
-4
0 .8 2
1.E+01
-6
0 .8 0
1.E+00
1.E-06
-8
0 .8 6
10000
0
50
100
Shear Rate (1/sec)

◦Viscoelasticity
Log(aT)
v   0
0 M P a E xp .
2 0 M P a E xp .
4 0 M P a E xp .
6 0 M P a E xp .
8 0 M P a E xp .
1 0 0 M P a E xp .
1 2 0 M P a E xp .
1 4 0 M P a E xp .
1 6 0 M P a E xp .
1 8 0 M P a E xp .
2 0 0 M P a E xp .
3
x
1.E+09
1 .0 0
1000
-3
t


◦Compressibility
S p e c ific V o lu m e (1 0 m /k g )

◦Viscosity
G', G" (Pa)
◦Mass
150
200
250
300
350
1.E-03
o
1.E+00
1.E+03
1.E+06
20
1.E+09

σ   P (  , T )I 
M  ( t )   ( )   

dG  ( t )   ( ) 
h ( I 1 , I 2 )  m exp(  n 1
1   ( t   )

1
C t ( )    ( t   )

0

2
2
m

dt
a
i 1
gi
T
i

1
0
20
( ) d 
80
e
15
70
i
Exp.
Sim.--Total
Sim.--Flow
Sim.--Cooling
60
I  3)
*
 ( t   )
1
t
 ( t )   ( )
I  3 )  (1  m ) exp(  n 2
*
170
220
270
320
25
M  ( t )   ( ) h ( I 1 , I 2 ) C
t
120
Temperature ( oC)
◦Birefringence
Optical Media
70
Frequency (rad/s)
T e m p e ra tu re ( C )
0

0
1 
-4
Dnrz (×10 )
 Develop & validate continuum polymer processing simulation with non-Newtonian,
non-isothermal, compressible flow, and thermoviscoelasticity
 Literature review of atomistic modeling of boundary conditions
 Specification of performance measures and end-use requirements
 Implement atomistic heat transfer boundary conditions (2005/06)
 Implement atomistic wall slip boundary conditions (2005/06)
 Implement molecular dynamic simulation for rheological development (2006/07)
 Validate against molding and extrusion processes (2006/07)
 Improve & define future work (2007/08)
Continuum Models
Path Difference (nm)
Research Tasks:
Conventional (Continuum) Approach:
Viscosity (Pa Sec)
Research Goal:
Develop and validate a multi-scale
polymer processing simulation for
concurrent engineering design and
manufacturing process development
50
40
Total
Flow Induced
Thermally Induced
10
5
0
30
-5
-0.5 -0.4 -0.3 -0.2 -0.1
20
0
0.1 0.2
0.3 0.4 0.5
z/d
10
0
-10
Dn 
Publications:
•Kathryn Elise Garnavish, An Investigation into Hesitation Defects from Oscillating
B. Fan, D. O. Kazmer, W.C. Bushko, R. P. Thierault, A. J. Poslinski, Birefringence
Prediction of Optical Media, Polymer Engineering & Science, v. 44, n. 4, April, 2004,
p. 814-824.
A.N. Smith and P. M. Norris, Microscale Heat Transfer, Chapter 18 of Heat Transfer
Handbook, eds. A. Bejan and A. D., Kraus, John Wiley & Sons, 2003.
K. S. Narayan* and A. A. Alagiriswamy, R. J. Spry, DC Transport Studies of
poly(benzimida-zobenzophenanthroline) a ladder-type polymer, Physical Review B,
v. 59, n. 15, p. 10054-8, 1999.
Fritch, L.W., ABS Cavity Flow – Surface Orientation and Appearance Phenomena
Related to the Melt Front, SPE Technical Papers, Vol. 21, 1979, pp. 15-20.
 J. S. Bergström and M. C. Boyce, Deformation of Elastomeric Networks: Relation
between Molecular Level Deformation and Classical Statistical Mechanics Models of
Rubber Elasticity, Macromoleclues, Vol. 32, pp. 3795-3808, 2001.
S. H. Anastasiadis and S. G. Hatzikiriakos, The Work of Adhesion of Polymer/Wall
Interfaces and the Onset of Wall Slip, J. Rheol., v. 42, n. 4, p. 795-812, 1998.
M. Doi, Challenges in polymer physics, Pure Appl. Chem., Vol. 75, No. 10, pp.
1395–1402, 2003.
Atomistic Modeling
of Heat Transfer
D 

-20
d
23
28
33
38
43
48
53
58
Radius (mm)
Atomistic Modeling
of Wall Slip
◦Boltzmann Transport Equation 
◦Wall slip condition characterized on
◦Modified Bose-Einstein distribution
meso-scale      /     1

to estimate Q=f(stress, compatibility,…)
◦On atomistic level, compare molecular
strain to wall adhesive forces

11
22
W
Atomistic Modeling
of Rheology
◦Incorporation of MD simulation
for rheological development 
<

1
1
No Slip
Dirichlet
Neumann
Adiabatic
0.9
0.8
0.9
Atomistic
0.7
0.6
0.5
0.4
0.3
0.7
0.6
0.5
0.4
0.3
0.2
0.2
0.1
0.1
0
0
0
1
2
3
4
5
Time (sec)
6
7
8
Free Surface
Atomistic
0.8
Dimensionless Inlet Pressure.
References:

C  ( t )   ( ) 
Nano-Scale Investigation:
Dimensionless Interface Temperature.
Flows, Univ. of Mass. Lowell, Dept. Plastics Engineering, 2005.
•William Rousseau, Effect of Shear Stress and Velocity Profile Development on Flow
Bore Wall Slip, Univ. of Mass. Lowell, Dept. Plastics Engineering, 2005.
•Bingfeng Fan and David Kazmer, Low Temperature Modeling of the TimeTemperature Shift Factor for Polycarbonate, Submitted to Advances in Polymer
Technology.

t
9
10
0
2
4
6
Time (sec)
8
10
Structural change of the microphase of
ABA tri block polymers under elongation.
ACKNOWLEDGEMENT: This research has been sponsored by the National Science Foundation under DMI-0425826.