1. School of Chemical & Biomolecular Engineering Using Models to Interpret Experiments Applications in molecular and mesoscopic modeling Martha Gallivan & Pete Ludovice International Center for Process Systems Engineering Jim marveled at the realism of his sodium and water simulation.

2. School of Chemical & Biomolecular Engineering Why simulate? l Relate proposed mechanism (scientific understanding) and its mathematical version to macroscopic measurable properties using many-body simulations. l Models are often simple (e.g. pairwise potential), while the computations are complex. l Conclusions based on proposed mechanisms are qualitative. u We cannot do many-body simulations in our heads. l Test understanding quantitatively by running many-body simulations.

3. School of Chemical & Biomolecular Engineering Motivation & Benefits l Radial distribution of species must be described to predict particle morphology l Continuum kinetics is only marginally applicable l Miniemulsions use water instead of organic solvents Miniemulsions can be used to make nanoparticles with internal structure. Jonathan Rawlston, Joseph Schork, Charles Immanuel

4. School of Chemical & Biomolecular Engineering Basis for Model l Spherical particle represented by FCC lattice (Clancy and Mattice) l Length scales from monomer radius of gyration to particle diameter are simulated l Model is based on discrete, intraparticle events, such as radical adsorption, propagation, chain transfer, termination, and monomer and polymer diffusion l 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 radical absorption termination

5. School of Chemical & Biomolecular Engineering Features of Model and Simulation l Much faster than molecular dynamics l Searching avoided by compiling a list of all possible events initially and updating list after each execution l Can be adapted to specific cases by adding rates for desired events l Allows examination of dynamic and localized particle morphology Compare to l PDE distribution models for particle size distribution l Moment equations l PDE models for radial distribution within the particle Must balance computational complexity and modeling goals.

6. School of Chemical & Biomolecular Engineering Validation of Model l Model output compared to literature reports (Faldi, 1994) l Rates adjusted until agreement is achieved (parameter estimation) l Initially, propagation rate was fitted to experimental values, assuming a known radical concentration l Bond fluctuation rate was then tuned to produce realistic self-diffusion rate for methyl methacrylate (MMA) l Future plans for experiments when needed for model validation Use bulk measurements, but not bulk rates. Also interest in RAFT chemistry and di- and triblock copolymers

7. School of Chemical & Biomolecular Engineering Polymer Diffusion Move one mer at a time to achieve diffusion of the polymer chains. Bond fluctuation Reptation l Chains are shifted through existing conformation, in either direction l Dramatically increased oligomer diffusion rates, allowed for fitting to literature data l Allows relaxation of conformation l Center of mass diffusion is computationally intensive

8. School of Chemical & Biomolecular Engineering Reptation for center of mass diffusivity A constant reptation rate leads to correct scaling in diffusivity.

9. School of Chemical & Biomolecular Engineering Interplay between diffusion and propagation Local regions of high conversion… polymer chain can’t get away from itself 100 radicals 20 radicals 400 radicals Vary diffusivity by a factor of 10

10. School of Chemical & Biomolecular Engineering Summary l Automatically get decay in diffusivity as chain length increases because the chain increasingly coils and blocks itself. l Even in the limit of high diffusivity, the propagation rate does not achieve the “well-mixed” limit. u The local conversion near the radical is greater than the bulk conversion. l Given this framework, the modeling becomes simpler. Rate constants are constant.

11. School of Chemical & Biomolecular Engineering Polynorbornene All 2, 3 polymerization All exo-exo polymerization 2,3 exo-exo erythro di-isotactic PNB2,3 exo-exo erythro di-syndiotactic PNB l 2,3 exo – exo configuration is assumed l 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.

12. School of Chemical & Biomolecular Engineering Alignment Explains WAXD

13. School of Chemical & Biomolecular Engineering Alkyl Poly(norbornene) Alkyl group randomly attached at positions 5 &6 Experiment Simulated (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).

14. School of Chemical & Biomolecular Engineering Fractional Free Volume o-Ps PNB Side Chain FFV simulation FFV PALS Methyl0.1600.150 Butyl0.1020.115 hexyl0.0900.102 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).

15. School of Chemical & Biomolecular Engineering atactic polypropylene 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 3.5R g, 7.5R g (M w = 4300; R g = 20.5 Å). Molecular Simulations of Films

16. School of Chemical & Biomolecular Engineering Fractional Free Volume Distribution L. Singh, P. J. Ludovice, C. L. Henderson, SPIE (2004). Film Thickness (Å) Diffusion Coefficient (cm 2 /sec) PHOST 10 -12 10 -11 10 -10 10 -9 10 -8 020004000600080001000012000 ~290 nm ~ 100 R g M w =12,000 Thickness at which T g effects observed Fractional Free Volume decreases as film thickness is decreased. FFV distribution varies on a larger length scale than T g. Consistent with experiment, simulations predict:

17. 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). Simulated Crystal Morphology Experimental Crystal Morphology

18. School of Chemical & Biomolecular Engineering Mesoporous Silicate (MCM-41) Surface Area (m 2 /g) Experimental960 Cylinder approximation 586 Our Model910 Density Gradient (White & co-workers) 257 Random Packing (Koh and co-workers) 1117 Cut quartz (He and Seaton) 280 Oxygen lattice (Maddox & Gubbins) 875-956 Sonwane, C.; C.W. Jones, C.W.;. Ludovice, P.J. J. Phys. Chem. B, 109, 23395-23404 (2005).

19. School of Chemical & Biomolecular Engineering Summary l Unique WAXD in PNB is due to alignment changing with MW l Changing alignment changes properties l Alkylation of PNB changes packing and therefore properties l Solvent does not effect isoleucine crystal morphology l Amorphousness in MCM-41 mesoporous silicates appears to cause increased surface area