Processes with distributions are pervasive: - Molecular: molecular weight distribution in polymerization - Microparticle: particle size distribution in suspension polymerization - Biological: rupture frequency distributions in single- molecule pulling experiments This thesis presents a systematic approach to the modeling and control of these processes Systematic approach applied to diverse processes -Molecular distributions -Microparticle distributions -Biological distributions Common approach - Experiments/equipment - Parameter estimation - Sensitivity and uncertainty analysis - Model selection - Optimal control

1. A Systems Approach to the Modeling and Control of Molecular, Microparticle, and Biological Distributions Eric J. Hukkanen Dept. of Chemical & Biomolecular Engineering University of Illinois at Urbana-Champaign

3. Components of the Systematic Approach NO YES design constraints & performance criteria Robust Optimization optimized design Is model accurate? Hypothesis Mechanism Selection Experimental Data Collection Multiple Models Parameter Estimation Experimental Design experimental constraints Sensitivity & Uncertainty Analysis

5. Molecular Distribution Outline NO YES design constraints & performance criteria Robust Optimization optimized design Hypothesis Mechanism Selection Experimental Data Collection Multiple Models Parameter Estimation Experimental Design experimental constraints Sensitivity & Uncertainty Analysis Is model accurate?

8. Experiments/Equipment – Sensors ATR-FTIR Spectroscopy

14. Model Validation

18. Microparticle Distribution Outline NO YES design constraints & performance criteria Robust Optimization optimized design Hypothesis Mechanism Selection Experimental Data Collection Multiple Models Parameter Estimation experimental constraints Sensitivity & Uncertainty Analysis Is model accurate? Experimental Design

21. What is Suspension Polymerization? Monomer Reaction Aqueous Phase: Water, Surfactant Monomer Droplets: Monomer, Initiator Heat of Reaction Time Final Particles

22. Suspension Polymerization Droplets Particles In Situ Video Microscopy Optical Microscopy

24. Simulation of Polymerization Within Droplets

25. Simulation of Droplet Size Distribution using Population Balance Equation (PBE) Accounts for droplet breakage and coalescence and polymerization kinetics (i.e., increase in viscosity and volume contraction/expansion)

28. Comparison of Experiments and Model Predictions

30. Uncertainty Analysis – Moments Output

32. Biological Distribution Outline NO YES design constraints & performance criteria Robust Optimization optimized design Hypothesis Mechanism Selection Experimental Data Collection Multiple Models Parameter Estimation experimental constraints Sensitivity & Uncertainty Analysis Is model accurate? Experimental Design

35. Experiments/Equipment

36. Experiments/Equipment

37. Maximum Likelihood Parameter Estimates for Single-bond Microscopic Model Model not accurate (total residual = 0.4194)

39. Maximum Likelihood Parameter Estimates for Double-bond Microscopic Model Model much more accurate (total residual = 0.0687)