James B. Rawlings Research Group

Ethan A. Mastny B.S. Ch.E., Brigham Young University, 2002 Ph.D., University of Wisconsin-Madison, 2007 eamastny[AT]bevo[DOT]che[DOT]wisc[DOT]edu

Current Work

Crystallization applications range from small volume, high-value added products such as pharmaceuticals and photomaterials, to continuous high-throughput products such as fertilizers. In order to make high-quality products crystal producers must be able to control crystal size, habit, polymorph, and purity. Traditionally crystal engineering has relied upon empirical practices or models generated from experimental data.

In contrast to the traditional approach, this research develops the tools necessary for a bottom-up modeling approach of crystallization. This approach includes modeling the important phenomena of crystallization on molecular, microscopic, and macroscopic time and length scales. Techniques for communication between the models on these different time scales will be developed.

The overall objectives of this research are:

• Develop or identify molecular modeling methods that can efficiently and reliably determine important crystal growth characteristics, such as melting temperature, favorable polymorph, and growth rate of different faces.
• Develop methods for efficiently integrating information on different time and length scales, into a full multi-scale model.
• Develop operation and control strategies that integrate the multi-scale models.

The current focus of the project is to use molecular simulations to predict melting temperatures and pressures. A newly developed Monte Carlo algorithm which can directly calculate the Density of States (the number of possible configurations at a given energy) of a system is begin used to calculate the melting temperature of the Lennard Jones system and Sodium Chloride.

Density of states of the melting of an FCC Lennard Jones Crystal (left) and melting curve of the FCC Lennard Jones Crystal (right).

MPC of Stochastic Kinetic Models

Another current focus of research is modeling and control of gas reactions on a solid lattice. A well established method of simulating reactions on a surface is to simulate the individual reaction events that occur according to weighted probabilities. Under this framework, both macroscopic concentrations and the orientation of particles on the lattice affect the system behavior. During a gas reaction that occurs on a surface, adsorption, desorption, and reaction occur on one time scale, and diffusion occurs on a much faster time scale. Studying the transient response of a lattice gas becomes computationally intensive because the bulk of the computation time is spent simulating diffusion events. One focus of this research is to develop methods for quickly simulating these diffusion events, thereby enabling reaction events to occur.

These stochastic lattice gas models are also being used to study the control of inherently stochastic systems. The performance of Proportional Integral Derivative, Model Predictive Controllers, and Nonlinear Model Predictive Controllers on this stochastic lattice gas will be compared.

Lattice structure.

Publications

1

Ethan Allen Sturman Mastny.
Multiple-Time-Scale Order Reduction for Stochastic Kinetics and Molecular Simulation of Crystallization.
PhD thesis, University of Wisconsin-Madison, July 2007.

2

Ethan A. Mastny, Eric L. Haseltine, and James B. Rawlings.
Stochastic simulation of catalytic surface reactions in the fast diffusion limit.
J. Chem. Phys., 125(19):194715, November 2006.

3

Ethan A. Mastny, James B. Rawlings, and Yannis G. Kevrekidis.
Model-based control methodologies for catalytic surface reactions.
In Proceedings of the American Control Conference, Portland, Oregon, June 2005.

4

Ethan A. Mastny, James B. Rawlings, and Ioannis G. Kevrekidis.
Systems Engineering and Feedback Control of Stochastic Lattice Gas Reaction Models.
Annual AIChE Meeting, Austin, TX, November 2004.

5

Ethan A. Mastny, Eric L. Haseltine, James B. Rawlings, and Ioannis G. Kevrekidis.
Control of a kinetic Monte Carlo lattice gas model.
Annual AIChE Meeting, San Francisco, CA, November 2003.

Personal Web Page: www.che.wisc.edu/~eamastny