School of Chemical & Biomolecular Engineering Using Models to Interpret Experiments Applications in...

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.


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.


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


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


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.


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.

C

C

H

3

C

O

O

C

H

3

C

H

C

O

O

(

C

H

2

)

3

C

H

3

C

C

H

3

C

O

O

(

C

H

2

)

3

C

H

3

"

M

M

A

"

"

B

A

"

"

B

M

A

"

Also interest in RAFT chemistryand di- and triblock copolymers


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


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


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


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.


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.


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


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).


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).


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


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


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


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).


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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