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
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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
• ....
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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
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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!
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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
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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 .
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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.
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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.
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Sola r Ene r g y Ha rv esting
Photo v oltaics
Solar Thermal
40000 TW
© source unknown. All rights reserved.
Photosynthesis
15 TW
Crescent Dunes, NV © source unknown. All rights reserved.
Solar Thermal Fuels
© source unknown. All rights reserved.
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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.
REN21. 2008. “ Renewables 2007 Global Status Report . ”© Deutsche GTZ GmbH. "All rights reserved.
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
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
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’
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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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