Using Models to Interpret Experiments Applications in molecular and mesoscopic modeling

1. Using Models to Interpret ExperimentsApplications 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. 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.

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

4. propagation propagation radical absorption radical absorption propagation termination Basis for Model Discretize a particle into discrete monomer segments. • 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

5. Features of Model and Simulation Must balance computational complexity and modeling goals. • 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

6. Validation of Model Use bulk measurements, but not bulk rates. • 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 Also interest in RAFT chemistry and di- and triblock copolymers

7. Polymer Diffusion Move 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

8. Reptation for center of mass diffusivity A constant reptation rate leads to correct scaling in diffusivity.

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

10. 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.

11. Polynorbornene 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.

12. Alignment Explains WAXD

13. Alkyl Poly(norbornene) Experiment Simulated (2 chains N=100) Alkyl group randomly attached at positions 5 &6 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. Fractional Free Volume 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). o-Ps

15. Molecular Simulations of Films • 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). Space larger then energy cut-off to effectively convert 3D periodicity to 2D periodicity Mobility & CTE predicted from fluctuations; FFV predicted from Delaunay Tessellation Objectives:- To predict spatial variation of density, mobility, CTE and Fractional Free Volume (FFV). atactic polypropylene Substrate

16. -8 10 -9 10 -10 10 Diffusion Coefficient (cm2/sec) PHOST -11 10 -12 10 0 2000 4000 6000 8000 10000 12000 Film Thickness (Å) Fractional Free Volume Distribution Thickness at which Tg effects observed L. Singh, P. J. Ludovice, C. L. Henderson, SPIE (2004). Mw=12,000 ~290 nm ~ 100 Rg Consistent with experiment, simulations predict: • Fractional Free Volume decreases as film thickness is decreased. • FFV distribution varies on a larger length scale than Tg .

17. Isoleucine Crystal Morphology CHARMm force field with semiempirical charge calculations accurately reproduces morphology of isoleucine crystals Experimental Crystal Morphology Simulated Crystal Morphology Givand, J., Ludovice, P.J.; Rousseau, R.W. J. of Cryst. Growth, 194, 228-238 (1998).

18. Mesoporous Silicate (MCM-41) Sonwane, C.; C.W. Jones, C.W.;. Ludovice, P.J. J. Phys. Chem. B, 109, 23395-23404 (2005).

19. 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