CE 400 Honors Seminar Molecular Simulation

1. CE 400 Honors SeminarMolecular Simulation Class 1 Prof. Kofke Department of Chemical Engineering University at Buffalo, State University of New York

2. Course Information • Instructor • Prof. Kofke • Office: 510 Furnas Hall • Contact: kofke@eng.buffalo.edu • Aims • To learn about molecular simulation • To better understand Nature • Assessment • Occasional assignments: 50% • Semester project: 50%

3. Discussion • Who are you? • Name, home town, major • What do you know? • Experience with computers and programming • Strength in physics (mechanics) and calculus • Knowledge of physical chemistry / thermodynamics • What do you expect? • Why did you select this course? • What do you think you’ll learn? • What is molecular simulation? • Molecular simulation: what’s it good for? • Accessible length and time scales?

4. Physical Properties • Quantify material behavior • Examples • What physical properties are needed for science and engineering, and why?

5. Physical Properties • Quantify material behavior • Examples • Density (sizing equipment) • Vapor pressure (separations equipment design) • Thermal conductivity (heat exchanger design) • Viscosity (pipe and pump sizing; analysis of flow systems, including complex media such as paint or blood) • Diffusivity (analysis of mixing; reacting systems) • Freezing/melting points (equipment/process design; handling of petroleum mixtures; cryogenic applications) • Solubility (design of mixtures; separations equipment design) • Heat capacity (heating/cooling, energy requirements) • Electronic/photonic properties (laser, LED device design) • Surface tension (wetting, colloidal systems, mixing, droplets, foams, aerosols)

6. Engineering Method • Desired to design and construct a material or process that achieves some goal • Example: Separation of methanol from water • Large catalog of general methods exists for many such goals • Adsorption, absorption, crystallization, distillation • Engineer selects an approach based on experience • Distillation • Design of equipment or material requires quantitative knowledge of material behavior • Vapor pressure of each component as a function of composition • Given physical property data, design of process can proceed routinely • Usually!

7. Physical Property Information • Experiment • The definitive source • Expensive and inconvenient for design purposes • Semi-empirical formulas • Intelligently interpolates or extrapolates experimental measurements • Two inputs to a semiempirical formula • Functional form • Parameters specific to the substance of interest • Example: Antoine formula for vapor pressure

8. Role of Molecular Simulation model and treatment Theory Experiment test treatment test model Simulation • Molecular simulation is the only means to “measure” the macroscopic behavior of a molecularly modeled system • Example • Model: molecules behaves as billiard balls (hard spheres) • Treatment: Carnahan-Starling equation for hard-sphere fluid

9. Test of Hard-Sphere Treatments Carnahan-Starling equation

10. What is Molecular Simulation? • Molecular simulation is a computational “experiment” conducted on a molecular model. • Many configurations are generated, and averages taken to yield the “measurements.” One of two methods is used: • Molecular dynamics Monte Carlo • Integration of equations of motion Ensemble average • Deterministic Stochastic • Retains time element No element of time • Molecular simulation has the character of both theory and experiment • Applicable to molecules ranging in complexity from rare gases to polymers to electrolytes to metals 10 to 100,000 or more atoms are simulated (typically 500 - 1000)

11. What is a Molecular Model? • A molecular model postulates the interactions between molecules • More realistic models require other interatomic contributions • Intramolecular • stretch, bend, out-of-plane bend, torsion, +intermolecular terms • Intermolecular • van der Waals attraction and repulsion (Lennard-Jones form) • electrostatic • multibody A typical two-body, spherical potential (Lennard-Jones model) Energy e Separation s

12. Boundary Conditions • Impractical to contain system with a real boundary • Enhances finite-size effects • Artificial influence of boundary on system properties • Instead surround with replicas of simulated system • “Periodic Boundary Conditions” (PBC) • Click here to view an applet demonstrating PBC

13. Etomica • GUI-based development environment • Simulation is constructed by piecing together elements • No programming required • Result can be exported to run stand-alone as applet or application • Application Programming Interface (API) • Library of components used to assemble a simulation • Can be used independent of development environment • Invoked in code programmed using Emacs (for example) • Written in Java • Widely used and platform independent • Features of a modern programming language • Object-oriented

14. Class Project • Design, construct, test and deploy a molecular simulation • Must demonstrate a non-trivial collective behavior • Incorporation of game-like features is encouraged • Work in teams of three students • Details to follow… • For now, think about possibilities