using models to interpret experiments applications in molecular and mesoscopic modeling
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School of Chemical & Biomolecular Engineering
Using Models to Interpret Experiments
Applications in molecular and mesoscopic modeling
Martha Gallivan & Pete LudoviceInternational Center for Process
Systems Engineering Jim marveled at the realism of
his sodium and water simulation.
School of Chemical & Biomolecular Engineering
Why simulate? Relate proposed mechanism (scientific
understanding) and its mathematical version to macroscopic measurable properties using many-body simulations.
Models are often simple (e.g. pairwise potential), while the computations are complex.
Conclusions based on proposed mechanisms are qualitative. We cannot do many-body simulations in our
heads.
Test understanding quantitatively by running many-body simulations.
School of Chemical & Biomolecular Engineering
Motivation & Benefits
Radial distribution of species must be described to predict particle morphology
Continuum kinetics is only marginally applicable Miniemulsions use water instead of organic solvents
Miniemulsions can be used to make nanoparticles with internal structure.
Jonathan Rawlston, Joseph Schork, Charles Immanuel
School of Chemical & Biomolecular Engineering
Basis for Model
Spherical particle represented by FCC lattice (Clancy and Mattice)
Length scales from monomer radius of gyration to particle diameter are simulated
Model is based on discrete, intraparticle events, such as radical adsorption, propagation, chain transfer, termination, and monomer and polymer diffusion
Events are executed by changing state of lattice site between polymer or monomer, in simplest case
Discretize a particle into discrete monomer segments.
radical absorption
propagation
propagation
propagation
radical absorptiontermination
School of Chemical & Biomolecular Engineering
Features of Model and Simulation
Much faster than molecular dynamics Searching avoided by compiling a list of all possible events initially
and updating list after each execution Can be adapted to specific cases by adding rates for desired events Allows examination of dynamic and localized particle morphology
Compare to PDE distribution models for particle size distribution Moment equations PDE models for radial distribution within the particle
Must balance computational complexity and modeling goals.
School of Chemical & Biomolecular Engineering
Validation of Model
Model output compared to literature reports (Faldi, 1994)
Rates adjusted until agreement is achieved (parameter estimation)
Initially, propagation rate was fitted to experimental values, assuming a known radical concentration
Bond fluctuation rate was then tuned to produce realistic self-diffusion rate for methyl methacrylate (MMA)
Future plans for experiments when needed for model validation
Use bulk measurements, but not bulk rates.
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Also interest in RAFT chemistryand di- and triblock copolymers
School of Chemical & Biomolecular Engineering
Polymer DiffusionMove one mer at a time to achieve diffusion of the polymer chains.
Bond fluctuation Reptation
Chains are shifted through existing conformation, in either direction
Dramatically increased oligomer diffusion rates, allowed for fitting to literature data
Allows relaxation of conformation
Center of mass diffusion is computationally intensive
School of Chemical & Biomolecular Engineering
Reptation for center of mass diffusivity A constant reptation rate leads to correct scaling in diffusivity.
Simulation and Scaling Law, One Chain
y = 2.50E-05x-6.64E-01y = 2.65E-05x-7.13E-01
R2 = 9.87E-01
0.00E+00
5.00E-06
1.00E-05
1.50E-05
2.00E-05
2.50E-05
3.00E-05
0 2 4 6 8 10 12
Chain Length
Dif
fusi
vity
(cm
^2/
s)
ScalingLaw, 50 °C
Simulation
Scaling Law, 50 °C Simulation, 50 °C
School of Chemical & Biomolecular Engineering
Interplay between diffusion and propagationLocal regions of high conversion… polymer chain can’t get away from itself
Propagation Event Count vs Time
100
105
110
115
120
125
130
135
140
145
150
0 0.01 0.02 0.03 0.04 0.05 0.06
Time (s)
Pro
pa
ga
tio
n E
ven
t C
ou
nt
100 radicals
20 radicals
400 radicals
Vary diffusivity by a factor of 10
Propagation Event Count vs Time
100
105
110
115
120
125
130
135
140
145
150
0 0.0005 0.001 0.0015 0.002 0.0025
Time (s)
Pro
pa
ga
tio
n E
ve
nt
Co
un
tPropagation Event Count vs Time
100
105
110
115
120
125
130
135
140
145
150
0 0.002 0.004 0.006 0.008 0.01
Time (s)
Pro
pa
ga
tio
n E
ven
t C
ou
nt
School of Chemical & Biomolecular Engineering
Summary
Automatically get decay in diffusivity as chain length increases because the chain increasingly coils and blocks itself.
Even in the limit of high diffusivity, the propagation rate does not achieve the “well-mixed” limit. The local conversion near the radical is greater than the bulk
conversion.
Given this framework, the modeling becomes simpler. Rate constants are constant.
School of Chemical & Biomolecular Engineering
Polynorbornene
R
R
R
1 2
3 4 5
6
7
All 2, 3 polymerization All exo-exo polymerization
2,3 exo-exo erythro di-isotactic PNB 2,3 exo-exo erythro di-syndiotactic PNB
2,3 exo – exo configuration is assumed Orientation of bridging carbon (#7) is remaining variable
Goodall, B. L. from Late Transition Metal Polymerization Catalysis (Rieger, B; Saunders Baugh, L.; Kacker, S.; Striegler, S., Ed.) Wiley-VCH: Weinheim, Germany, p 101, 2003.
School of Chemical & Biomolecular Engineering
Alignment Explains WAXD
0
0.5
1
1.5
2
0 5 10 15 20 25 30
Perfectly Aligned2 Chains Fixed- 300° MD2 Chains Fixed- 500° MD2 Chains Fixed- 700° MD1 Chains Fixed- 500° MD1 Chains Fixed- 700° MDAmorphous
Inte
nsity
2-Theta
School of Chemical & Biomolecular Engineering
Alkyl Poly(norbornene)
Alkyl group randomly attached atpositions 5 &6
ExperimentSimulated (2 chains N=100)
Wilks, B.R., Chung, W.J., Ludovice, P.J., Rezac, M.E., Merkin, P. and A.J. Hill, Materials Research Society Proceedings,
752, 14 148 (2003).
School of Chemical & Biomolecular Engineering
Fractional Free Volume
0
0.1
0.2
0.3
0.4
0.5
0 0.5 1 1.5 2 2.5 3 3.5 4
FF
V
Penetrant Radius
0.8
1
1.2
1.4
1.6
1.8
2
2.2
0.8 1 1.2 1.4 1.6 1.8 2 2.2
Data 1
MethylButylHexyl
Me
thyl
Simulation
o-Ps0.8
1
1.2
1.4
1.6
1.8
2
2.2
0.8 1 1.2 1.4 1.6 1.8 2 2.2
Data 1
MethylButylHexyl
Me
thyl
Simulation
PNB
Side Chain
FFV
simulation
FFV
PALS
Methyl 0.160 0.150
Butyl 0.102 0.115
hexyl 0.090 0.102
Wilks, B.; Chung. W.J.; Ludovice P.J.; Rezac, M.; Meakin,P.; Hill, A., J. Polym. Sci.– Part B, Polym. Phys, 44, 215-233 (2005).
School of Chemical & Biomolecular Engineering
atacticpolypropylene
Space larger then energy cut-off to effectively convert 3D periodicity to 2D periodicity
Substrate
Objectives:- To predict spatial variation of density, mobility, CTE and Fractional Free Volume (FFV).
Mobility & CTE predicted from fluctuations; FFV predicted from Delaunay Tessellation
• Two models of a-polypropylene on graphite substrate were equilibrated for approximately 300 picoseconds through NPT-Molecular Dynamics Simulations. • Film thickness were around 3.5Rg, 7.5Rg (Mw= 4300; Rg= 20.5 Å).
Molecular Simulations of Films
School of Chemical & Biomolecular Engineering
Fractional Free Volume Distribution
L. Singh, P. J. Ludovice,
C. L. Henderson, SPIE (2004).
Film Thickness (Å)
Diff
usio
n C
oeffi
cie
nt
(cm
2/s
ec)
PHOST
10-12
10-11
10-10
10-9
10-8
0 2000 4000 6000 8000 10000 12000
~290 nm~ 100 Rg
Mw=12,000
Thickness at which Tg
effects observed
• Fractional Free Volume decreases as film thickness is decreased.• FFV distribution varies on a larger length scale than Tg .
Consistent with experiment, simulations predict:
0
0.05
0.1
0.15
0.2
0.25
0.3
0.35
0 1 2 3 4Penetrant Radius (Å)
FF
V
Film Thickness=3.5 Rg
Film Thickness=7.5 Rg
0
0.05
0.1
0.15
0.2
0.25
0.3
0.35
0 1 2 3 4Penetrant Radius (Å)
FF
V
Surface Region
Bulk Region
Substrate Region
School of Chemical & Biomolecular Engineering
Isoleucine Crystal Morphology
CHARMm force field with semiempirical charge calculations accurately reproduces morphology of isoleucine crystals
Givand, J., Ludovice, P.J.; Rousseau, R.W. J. of Cryst. Growth, 194, 228-238 (1998).
SimulatedCrystalMorphology
ExperimentalCrystalMorphology
School of Chemical & Biomolecular Engineering
Mesoporous Silicate (MCM-41)Surface
Area(m2/g)
Experimental 960
Cylinder approximation
586
Our Model 910
Density Gradient (White & co-workers)
257
Random Packing (Koh and co-workers)
1117
Cut quartz (He and Seaton)
280
Oxygen lattice (Maddox & Gubbins)
875-956Sonwane, C.; C.W. Jones, C.W.;. Ludovice, P.J. J. Phys. Chem. B, 109, 23395-23404 (2005).
School of Chemical & Biomolecular Engineering
Summary
Unique WAXD in PNB is due to alignment changing with MW
Changing alignment changes properties Alkylation of PNB changes packing and
therefore properties Solvent does not effect isoleucine crystal
morphology Amorphousness in MCM-41 mesoporous
silicates appears to cause increased surface area
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