L4_P02

1.021 , 3.021, 10.333, 22.00 : Introduction to Modeling and Simulation : Spring 2012 Part II – Quantum Mechanical Methods : Lecture 4

Application of QM Modeling to Solar Thermal Fuels

Jeffrey C. Grossman

Department of Materials Science and Engineering

Massac husetts Institute of T ec hnology

Par t II T opics

1. It ’ s a Quantum W orld: The Theor y of Quantum Mechanics

2. Quantum Mechanics: Practice Mak es P erf ect

3. Fr om Man y-Body to Single-Par ticle; Quantum Modeling of Molecules

4. Application of Quantum Modeling of Molecules: Solar Thermal Fuels

5. Application of Quantum Modeling of Molecules: Hydr ogen Storage

6. Fr om Atoms to Solids

7. Quantum Modeling of Solids: Basic Pr oper ties

8. Advanced Pr op . of Materials: What else can w e do?

9. Application of Quantum Modeling of Solids: Solar Cells Par t I

10. Application of Quantum Modeling of Solids: Solar Cells Par t II

11. Application of Quantum Modeling of Solids: Nanotechnolog y

Lesson outline

• Re vie w

• Interactiv e calculations and discussion on the H2

• First a pplication of QM modeling: Solar Thermal Fuels

• Interactiv e calculations and discussion on candidate fuels.

R e vi e w: Next? Helium

e -

r 1 r 12

-

H 1 = E 1

+ e

r 2 H 1

+ H 2

+ W ⇥ G ( → r 1

, → r 2 ) = E G ( → r 1

, → r 2 )

T 1 + V 1 + T 2 + V 2 + W ⇥ G ( → r 1 , → r 2 ) = E G ( → r 1 , → r 2 )

k 2 2

e 2 k 2 2 e 2

e 2 ⇥

0

— 2 m D 1 —

4 v s 0 r 1

— 2 m D 2 —

4 v s 0 r 2

+ 4 v s

r 12

G ( r 1 , r 2 ) = E G ( r 1 , r 2 )

cannot be solv ed anal yticall y p r oblem!

R e vi e w: The Multi- Elect r on Hamiltonian

H 1 = E 1 — D

—

G ( → r ) = E G ( → r )

Remember

the g ood old da ys of the

k 2 2 e 2 ⇥

The y ’ r e o v er!

1- electr on H-atom??

2 m 4 v s 0 r

N h 2

1 N N

Z i Z j e 2 h 2

n N n

Z e 2 1 n n e 2

R i

H     2

      2

   i

  

i  1

2 M i

2 m

2 i  1

j  1 i  j

R i  R j

r i

i  1 i  1 j  1

R i  r j

r i  r j

2 i  1 j  1

i  j

kinetic energ y of ions kinetic energ y of electr ons electr on-electr on interaction potential energ y of ions electr on-ion interaction

Multi-Atom-Multi-Elect r on Schrödinger Equation

H  R 1 , ..., R N ; r 1 , ..., r n    R 1 , ..., R N ; r 1 , ..., r n   E   R 1 , ..., R N ; r 1 , ..., r n 

Born-Oppenheimer App r o ximation

Electr ons and n uclei as “separate” systems

H  

h 2

2 m

n



i  1



2

r

N n Z e 2

   i 

i  1 j  1

1

2

n n

 

r i

e 2

 r j

i  j

i R i  r j

i  1

j  1

Born-Oppenheimer App r o ximation



Electr ons and n uclei as “separate” systems

H  

h 2

2 m

n



i  1



2

r

N n Z e 2

   i 

i  1 j  1

1

2

n n

 

r i

e 2

 r j

i  j

i R i

 r j

i  1 j  1

... but this is an a pp r o ximation!

• electrical r esistivity

• super conductivity

• ....

R e vi e w: Solutions

quantum chemistr y

density functional theor y

Molle r -Plesset per turbation theor y MP2

coupled cluster theor y CCSD(T)

Number of Atoms

Linear scaling DFT

DFT

R e vi e w: W h y DFT?

100,000

10,000

1000

100

MP2

QMC

CCSD(T)

10

Exact treatment

1

2003

2007

201 1

2015

Y ear

Image by MIT OpenCourseWare.

R e vi e w: DFT

w a v e function:

complicated!

G = G ( → r 1 , → r 2 , . . . , → r N )

elect r on

density:

easy!

n = n ( ⇤ r )

W alter K ohn

DFT 1964

see http://ocw.mit.edu/help/faq-fair-use/ .

All aspects of the elect r onic structur e of a system of interacting elect r ons, in the g r ound state , in an “external” potential, ar e determined b y n( r )

R e vi e w: DFT

ion

electr on density The g r ound-state energ y is a

functional

of the elect r on densit y .

E [ n ] = T [ n ] + V ii + V ie [ n ] + V ee [ n ]

kinetic ion-electr on

ion-ion electr on-electr on

The functional is minimal at the exact g r ound-state elect r on density n( r )

The functional exists... but it is unkno wn!

R e vi e w: DFT

E [ n ] = T [ n ] + V ii + V ie [ n ] + V ee [ n

kinetic ion-ion ion-electr on electr on-electr on

elect r on density n ( ⌅ r ) = Σ | c i ( ⌅ r ) | 2

i

E gr ound stat e = mi n E [ n

c

Find the w a v e functions that minimize the energ y using a functional derivativ e .

R e vi e w: DFT

Finding the minim um leads to K ohn-Sham equations

ion potential Har tr ee potential exchange-cor r elation

potential

equations f or non-interacting elect r ons

R e vi e w: DFT

Onl y one p r oblem: v xc not kno wn!

a pp r o ximations necessar y

local density general gradient a pp r o ximation a pp r o ximation

L D A GGA

R e vi e w: Self-consistent cycle

K ohn-Sham equations

-

n ( r ⌅ r )

= Σ | c i ( ⌅ r ) | 2

scf loop

i

R e vi e w: DFT calculations

scf loop

total energ y = -84.80957141 Ry total energ y = -84.80938034 Ry total energ y = -84.81157880 Ry total energ y = -84.81278531 Ry

total energ y = -84.81312816 Ry

exiting loop;

total energ y = -84.81322862 Ry r esult pr ecise enough

total energ y = -84.81323129 Ry

At the end w e get: 1) elect r onic charge density

2) total energ y


Structur e	Elastic	Vibrational	...
	constants	p r oper ties

R e vi e w: Basis functions

Matrix eigen value equation:

H 1 = E 1

H Σ c i c i = E Σ c i c i

⇥ = Σ c i c i

i

expansion in or thonormalized basis functions

i

∫

∫ d ⌥ r c H Σ Σ

i

c i c i = E d ⌥ r c c i c i

j j

i i

Σ H j i c i = E c j

i

H ⇤ c = E ⇤ c

R e vi e w: Plane w a v es as basis functions

plane w a v e expansion: G ( → r ) = Σ

j

c e i G ⇧ j · ⇧ r

j

plane wa v e

Cutoff f or a maxim um G is necessar y and r esults in a finite basis set.

Plane w a v es ar e periodic , thus the w a v e function is periodic!

Image by MIT OpenCourseWare.

periodic cr ystals: atoms, molecules: P erf ect!!! OK but be car eful!!!

Fi r st A pplication Exa mple: Sola r Chemical Fuels

Mate r ials will determine

the f utu r e of r ene w a b le ene r g y

Solar PV

Biofuels

Batteries

Thermoelectrics Solar Thermal

Hyd r ogen Storage

Thermoelectrics © D. J. Paul; hydrogen storage © Berkeley Lab; other images © sources unknown. All rights reserved. This content is excluded from our Creative Commons license. For more information, see http://ocw.mit.edu/help/faq-fair-use/ .

The Mate r ials Design Age

• Stone Age

• Ir on Age

• Br onze Age

• Industrial Age

• Plastic Age

• Silicon Age

• Materials Design

Let ’ s l ook at a sing le element:

carbo n

Nanotube architecture © John Hurt; graphene integrated circuit © Raghu Murali; other images © sources unknown. All rights reserved. This content is excluded from our Creative Commons license. For more information, see http://ocw.mit.edu/help/faq-fair-use/ .

Ca rbon in Ene r g y to Date

One Bar r el of oil (159 liters) =

1.73 MWh of energ y .

Sa me C: 10 5 X Imp r o v ement

That same 1 barrel could be used to make the plastic needed for thin-‐film solar cells.

The solar cells could generate ~16,000 MWh of energy over their lifetime, or 10,000 X as much

Sola r R esou r ce

P er ez et al.

Sola r Ene r g y Ha rv esting

Photo v oltaics

Solar Thermal

40000 TW

Photosynthesis

15 TW

Solar Thermal Fuels

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Sola r to Heat

Hot Water

Parabolic Dish / St i rl ing Engi n e e s s Reflectors (Parabolic Troughs)

Solar Towers (a.k.a. “Power Towers”)

From left (clockwise): SES SunCatcher solar dish © Stirling Energy Systems, barrels, reflectors, parabolic troughs, PS10 in Seville © sources unknown. All rights reserved. This content is excluded from our Creative Commons license. For more information, see http://ocw.mit.edu/help/faq-fair-use/ .

Solar Thermal: Sunlight-‐-‐>Heat: Concentrating

PS10, 11 MW Solar Tower (Sanlucar la Mayor, Seville)

Left : PS10, 11 MW Solar Tower in Sanlucar la Mayor, Seville © source unknown. Right : from Weiss, W. I. Bergmann, and G. Faninger. " Solar heat worldwide 2008: Markets and contributions to the energy supply 2006 " © International Energy Agency. All rights reserved. This content is excluded from our Creative Commons license. For more information, see http://ocw.mit.edu/help/faq-fair-use/ .

Ch a l l en ges wi t h S o l a r Th erma l Po wer:

• Losses in storage

• Auxiliary heating

• Highly reflective coatings + tracking

• Large footprint and cost

• N ot transportable, no distribution “as heat”

USA has not widel y adopted Solar W ater Heating.

USA

From Weiss, W. I. Bergmann, and G. Faninger. " Solar heat worldwide 2008: Markets and contributions to the energy supply 200 6 ." © International Energy Agency. Copyrighted content on this page is excluded from our Creative Commons license. For more information, see http://ocw.mit.edu/help/faq-fair-use/ .

Some Challenges with Solar Thermal

 Losses in storage

 Auxiliary heating

 Highly reflective (and clean) coatings

 T racking components

 Large storage facilities

 Not transportable, can’t be distributed “as heat”

11 MW Solar Tower in Sanlucar la Mayor, Seville © source unknown. All rights reserved. This content is excluded from our Creative Commons license. For more information, see http://ocw.mit.edu/help/faq-fair-use/ .

Sola r - Chemical :

Heat sto r ed in chemical bonds

Old Idea, BU T: ra p i d deg r adation for ALL cases.

Cha r ging

Heat

Discha r ging

Blast f r om the past (70’ s/80’ s)…

h 

+ 1.14 eV/molecule



N orbornadiene Quadricyclane

BUT : Poor cycling, rapid degradation for ALL cases.

“… a photochemical solar energy storage plant, although technically feasible, is not economically justified.”

Ind. Eng. Che m. Prod. Re s. De v., 1983, 22 (4), pp 627–633

Decomposition p r oducts

N orbornadiene:

h  Quadricyclane:

Starts to decompose Starts to decompose

at ~600K , or with 

repeated cycling

at ~500 K

+

 

Tolue ne

Cycloheptatriene

Cyclopentadiene Acetylene

(acetylene elimination via revers e D i el s - ‐ Al d er)

Stable up to ~1000 K

J. Phys. Che m. A 102, 9202-‐9212 (1998)

Ef for ts to p r ev ent decomposition

Images removed due to copyright restrictions. See article : Alexander D Dubonosov et al. Russian Chemical Reviews 71, no. 11 (2002): 917-27.

“donor-‐acceptor” norbornadienes: ~10 3 cy cle s

2, 3-‐disubstituted norbornadienes: can be cycled “many times”

N o magic bullet – always a trade-‐off between:

 quantum yield

 absorption efficiency

 stored energy

 thermal stability of the quadricyclane

 cyclability

Russian Che m. Re v. 71, 917-‐927 (2002)

Why r evisit sola r thermal f uels

Computational power for high-‐throughput materials design

Te chnolog y for atomic-‐scale en gi n eeri n g

now ?

+

Rapid computational screening of thousands of materials

Example: Time to perform calculations for 100, 000 known crystalline materials:

1980: 30 ye ar s

2012: f e w days

Potential to synthesize systems designed with atomic-‐scale control

The time is ripe to tackle this generation-‐old concept with a new “arsenal” of science/ technology capabilities.

A no v el a pp r oach to sola r thermal f uels

There are many, many photoactive molecules...

h 



DHA/VHF

...that are terrible solar thermal fuels.

E/Z−



h  h  Stilbene



spiropyran/merocyanine

Ca n w e tur n the m int o goo d ones ?

A ne w a pp r oach: combine photomolecule with template

h 

E a

 H

excited state

N

uncharge d

N

N N

charge d

The az oben z ene/CNT system

 Already synthesized*

 Photoactivity experimentally demonstrated*

 N ot previously con si d ered for en ergy storage

* e. g ., se e Fe ng , e t. al , J. Ap p l . Ph ys . ( 2007) ; Sim m ons e t. al , PRL (2007)

trans -azobenzene/CNT

Role of the CNT template

Intermolecular Separation (A)

Rigid substrate – fixes inter-‐molecular distances over long range, enabling:

 steric inhibition

  -‐stacking

 hydrophobic interactions

Enables design of spe cific intermolecular interactions – not available in free azobenzene

Stability

Stores More Energy

Energy density comparison


system	state	energy density (Wh/L)
Ru-fulvalene	solution (toluene)	0.02
azobenzene	solution (H 2 O)	0.000002
azobenzene	powder	90
azobenzene/CNT	soln. or powder	up to 690
Li-ion battery		200-600

h 



h 



Ne w Mate r ials for Sola r Thermal Fuels



Template Materials +

Ne w Chemistry Platform for Sola r Thermal Fuels

=

Photoactive Molecules

Sola r Thermal Fuel Ap p l i c a t i o n s

• Solar cooker: developing countries

• Solar cooker: hiking & outdoor / military

• Solar autoclave: developing countries

• Medical sanitation

• Milk pasteurization: rural

• Thin film window heating supplement

• On-‐site storage: power generation

• Gas/oil industry

• Military off-‐grid heat

• Building heating

• N ASA/maritime

• CSP auxiliary heat supply

• De-‐icing (windows, planes, power lines)

45

The Case for Sola r Coo k e r s

Problems with Cooking Off-‐Grid

‣ Cook ing fue l (e .g ., wood) is increasingly scarce, expensive, and time-‐intensive to find

‣ Smoke in not-‐well ventilated areas causes respiratory problems

Ex isti ng Solar O ve ns

‣ Can only cook while the sun is out

‣ Are cumbersome and heavy to transport

‣ Cannot be turned ‘ on’ and ‘ off’

Images of outdoor cookers and solar oven © sources unknown. All rights reserved. This content is excluded from our Creative Commons license. For more information, see http://ocw.mit.edu/help/faq-fair-use/ .

Solar Cooker: Using the Sun to Cook at N ight

St ove Top

Fuel Flow Dur i ng Cha r gi ng

Fuel Flow for cook i ng

Day Charging

N ight Cook ing

• Charging: slow flow through solar collector during the day.

• Cooking: device is turned upside down.

• Cost estimate <$200. Weight=<5 kg, floor space=1 sq. ft.

• 5 hours of charge time = boil liters of water or cook at 300C for ~1 hour.

47

Mate r ials Design Full Cycle

Simulation Synthesis P r ototype

Te s t i n g

Grossman Group, MIT.

So Why do W e Need QM?

h 

E a

 H

Solar radiation spectrum © Robert A. Rohde/Global Warming Art . License: CC-BY-SA. This content is excluded from our Creative Commons license. For more information, see http://ocw.mit.edu/help/faq-fair-use/ .

excited state

49

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