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

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

3. 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. 4 Physical Properties Quantify material behavior Examples –What physical properties are needed for science and engineering, and why?

5. 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. 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. 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. 8 Role of Molecular 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 Theory Experiment Simulation model and treatment test treatment test model

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

10. 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 dynamicsMonte 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. 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 Separation  

12. 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 PBCClick here

13. 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. 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