Introduction. Monday, January 6, 14

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1 Introduction 1

2 Introduction Why to use a simulation Some examples of questions we can address 2

3 Molecular Simulations Molecular dynamics: solve equations of motion Monte Carlo: importance sampling Calculate thermodynamic and transport properties for a given intermolecular potential 3 r 1 MD r 2 r n MC r 1 r 2 r n 3

4 Uses of Molecular Simulations Exact= in the limit of infinitely long simulations the error bars can be made infinitely small If one could envision an experimental system of these N particles that interact with the potential. The idea for a given intermolecular potential exactly compute the thermodynamic and transport properties of the system We assume the interactions between Diffusion coefficient the particles are known! Viscosity Pressure Heat capacity Heat of adsorption Structure. 4 4

5 Why Molecular Simulations Paul Dirac, after completing his formalism of quantum mechanics: The rest is chemistry. This is a heavy burden the shoulders of chemistry : 5 5

6 Intermolecular potential The intermolecular potential can: Mimic the experimental system as accurate as possible: Replace experiments (dangerous, impossible to measure, expensive, ) Make a model system: Test theories that can not directly be tested with experiment 6 6

7 If we know/guess the true intermolecular potential 7

Example 1: Mimic the real world Critical

8 Example 1: Mimic the real world Critical properties of long chain hydrocarbons To predict the thermodynamic properties (boiling points) of the hydrocarbon mixtures it is convenient (=Engineering models use them) to know the critical points of the hydrocarbons. 8 8

9 Critical points of long chain hydrocarbons Pentane Heptadecane 9 9

10 Hydrocarbons: intermolecular potential United-atom model Fixed bond length CH 2 CH 2 Bond-bending Torsion CH 3 CH 2 CH3 Non-bonded: Lennard-Jones 10 10

11 OPLS (Jorgensen) Model 11

12 Molecular dynamics: press enter and see But my system is extremely small, is the statistic reliable? Vapour-liquid equilibria Lectures on Free Energies and Phase Equilibrium Lectures on advanced Monte Carlo Molecular dynamics: press enter and see 12 Computational issues: How to compute vapour-liquid equilibrium? How to deal with long chain But C48 moves hydrocarbons? much slower than methane (C1). Do I have enough CPU time 12

13 Critical Temperature and Density 13 Nature 365, 330 (1993). 13

14 Example 2: Computational Carbon Capture 14

15 Carbon Capture and Sequestration 15

16 Amines in water: MEA Large amounts of pure water required Flue gas: 0.7 bar N2 0.1 bar CO2 ~30% energy penalty for regeneration 16

17 Metal Organic Frameworks BET surface areas up to 6200 m 2 /g Density as low as 0.22 g/cm 3 Tunable pore sizes up to 5 nm Channels connected in 1-, 2-, or 3-D Internal surface can be functionalized BASF production on ton scale Zn 4 O(1,4-benzenedicarboxylate) 3 MOF-5 17

change the pore topology crb dft sod mer rho Out of these many

18 Computation Challenge Chemical Flexibility of MOFs We can change the metal: Fe, Mg, Ca, Zn, Cu, etc We can change the linker We can change the pore topology crb dft sod mer rho Out of these many many millions of structures, which one is the best for Carbon Capture? 18

19 Separating CO 2 adsorption CO 2 /N 2 N 2 loading CO 2 N 2 Partial pressure CO 2 desorption 19

20 Working capacity & Henry coefficient Slope: Henry coefficient loading Flue gas at 40ºC desorption T working capacity 0.15 atm Partial pressure 1.0 atm 20

21 Increasing the working capacity: temperature loading Flue gas at 40ºC desorption Td T Td 0.15 atm Partial pressure 1.0 atm 21

22 Increasing the working capacity: pressure loading Pd 1atm Flue gas at 40ºC desorption Td 0.15 atm Partial pressure 1.0 atm We can increase the working capacity, but at which cost? 22

23 Performance metric: parasitic energy Energy penalty for Carbon Capture and Sequestration: compression work and the heating energy: Heating energy (Q): heat necessary to regenerate a given sorbent: Sensible heat: heats and cools bed. Provides driving force to produce CO 2 Desorption heat: desorbs CO 2 (equal to heat of adsorption, Δh). Sensible heat requirement Desorption heat requirement Compressor work (W comp ): Work to compress CO 2 to 150 bar (for transport) eq ( 0.75Q W ) W = η + carnot comp Parasitic energy calculated by discounting the heat requirement by the Carnot efficiency to simulate the effect of taking steam from a steam cycle 23

24 Zeolites 180 Known structures >3.000,000 hypothetical structures Which is the best for carbon capture? 24

25 Zeolites for Carbon Capture Equivalent Energy for those all silica structures with experimental data What is the best structure? What is the lowest energy? 25

26 Zeolites (MFI) CO 2 Open: simulations Closed: experiments N 2 (E. García-Pérez et al. Adsorption (2007) 13: ) 26

27 All known zeolites 27

What is the best zeolite structure? Hypothetical zeolites ~2.

within the +30 kj/mol Si energetic band above R-quartz in which

28 What is the best zeolite structure? Hypothetical zeolites ~ unique structures were enumerated, with roughly 10% within the +30 kj/mol Si energetic band above R-quartz in which the known zeolites lie Deem et al. J. Phys. Chem. C 2009, 113,

29 How to predict 1 million isotherms? CPU: one isotherm 5-10 days Control Logic CPU Cache ALU GPU ALU DRAM DRAM - Less than 20 cores - Designed for general programming - More than 500 cores - Optimized for SIMD (sameinstruction-multiple-data) problems GPU trade-off between memory, # threads, and work load Energy calculation in parallel Monte Carlo in parallel for different pressures J. Kim and B. Smit, J. Chem. Theory Comput. 8 (7), 2336 (2012) GPU: one isotherm in 1 minute 29

Screening: zeolites Screening: > 300,000

30 Screening: zeolites Screening: > 300,000 structures Identified many structures with a significantly lower parasitic energy compared to the current technology L.-C. Lin, et al, In silico screening of carbon-capture materials Nat Mater 11 (7), 633 (2012) 30

31 Example 3: make a model system Question: are attractive interactions needed to form a solid phase? but this experimentalist Your theory is WRONG refuses to use it disagrees with the YES: molecules that do not experiments have any attractive Attractive forces are needed for interactions vapourliquid equilibrium BUT: Theories predict this.. There no molecules with only attractive interactions How to test the theory? 31 My theory is RIGHT: 31

32 But we can simulate hard spheres.. Bernie Alder carried out Molecular Dynamics simulations of the freezing of hard spheres But,. did the scientific community accept this computer results as experimental evidence during a Gordon conference it was proposed to vote on it and it was voted against the results of Alder 32 32

A colloidal model system with an interaction tunable from hard

33 Experiments are now possible.. But not on molecules but on colloids: From the following article: A colloidal model system with an interaction tunable from hard sphere to soft and dipolar Anand Yethiraj and Alfons van Blaaderen Nature 421, (30 January 2003) 33 33

34 Molecular Dynamics MD Theory: r 1 r 2 r n Compute the forces on the particles Solve the equations of motion Sample after some timesteps 34 34

35 Monte Carlo What is the correct probability? Statistical Thermodynamics Generate a set of configurations with the correct probability Compute the thermodynamic and transport properties as averages over all configurations How to compute these properties from a simulation? MC r 1 r

36 Classical and Statistical Thermodynamics Problem: we have a set of coordinates and velocities -what to do with it? Statistical Thermodynamics The probability to find a particular configuration Properties are expressed in term of averages Free energies Thermodynamics: relation of the free energies to thermodynamic properties 36 36

New Materials and Process Development for Energy-Efficient Carbon Capture in the Presence of Water Vapor

New Materials and Process Development for Energy-Efficient Carbon Capture in the Presence of Water Vapor Randy Snurr, 1 Joe Hupp, 2 Omar Farha, 2 Fengqi You 1 1 Department of Chemical & Biological Engineering