pathways to crystal nucleation and growthghf/cfdc_2008/robben-browning.pdf · andrea robben...
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![Page 1: Pathways to Crystal Nucleation and Growthghf/cfdc_2008/robben-browning.pdf · Andrea Robben Browning Glenn H. Fredrickson Michael F. Doherty Complex Fluids Design Consortium Annual](https://reader034.vdocuments.mx/reader034/viewer/2022050202/5f5608400e5fe738e217e7e6/html5/thumbnails/1.jpg)
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Pathways to Crystal Nucleation and Growth
Andrea Robben BrowningGlenn H. FredricksonMichael F. Doherty
Complex Fluids Design ConsortiumAnnual Meeting
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Background
• Organic crystals are found in everyday products and structure is critical to their usefulness
• Many molecules can form two or more solid structures (polymorphs)
• Polymorphs can have different properties (solubility, strength, etc.)
• Nucleation is the initial stage of polymorph formation
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Motivation
• Classical Nucleation Theory traditionally used– Nucleus shape and structure are inputs – Critical size is the output
• Appropriate surface energy at nucleus size scales is unknown
• Surface stress may also play a role• Gain understanding of nucleation mechanism for
development of nucleation theory• Current work
– Colloids– Stearic Acid in Hexane
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Colloid Particles
• Hard-core screened repulsive Yukawa pair potential • Solvent treated implicitly• Molecular Dynamics simulations
– NVT ensemble
– 32,000 particles in box (tested with 62,000)
• Seeded initial conditions– FCC or BCC polymorph seed– Variable seed size
• Unseeded, homogeneous, fully random initial conditions (for comparison with Weitz data)
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Yukawa Potential
σ = hard core diameter, 1/κ = screening length, ε = interaction energy when particles touch
σσκσε
r/
)]1r/(exp[u/
−−=
0
0.5
1
0 0.5 1 1.5 2 2.5 3
Screening length decreasing, 1/κσ dec.
pair
pote
ntia
l (u/
ε)
pair separation (r/σ)
Hard core
Large screening length
Small screening length
∞=εu/
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Phase Diagram for Weitz ExperimentsA. Hynninen and M. Dijkstra, Phy. Rev. E, 68, 021407 (2003)
0
0.05
0.1
0.15
0.2
0.25
0.3
0.35
0.4
0.45
0.5
0.35 0.4 0.45 0.5 0.55 0.6
Fluid
FCCBCC
T*= kBT/ε = 0.125
packing fraction (η)
scre
enin
g le
ngth
(1/
κσ)
expe
rimen
tal
cond
ition
s
σ = 2.52 µm
T = assume room temperature
ρparticle = assumed 1.196 g/cm3
ε = 3.29 x 10-20 J
1/κ = 0.126 µm
Giving: 1/κσ = 0.05
hard spheres
Simulations at 1/κσ = 0.05, 0.1, and 0.2, all at T* = 0.125
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T vs Packing Fraction Melting Curve for Weitz Experiments
0
0.05
0.1
0.15
0.2
0.25
0.25 0.3 0.35 0.4 0.45
Fluid
FCC StableBCC Metastable
Initial conditions for homogeneous nucleation experiments and simulations
packing fraction (η)
dim
ensi
onle
ss te
mpe
ratu
re (
T*)
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Critical Nuclei: Simulation & Experiment
Time for critical nuclei toappear = 0.03 secs of real time
Total time to end of run = 1 - 3 secsof real time (6 -7 days of computing time)
Nuclei sizes from simulations in range60 – 260 particles
More BCC content in simulated nucleithan experimental nuclei. Simulated nuclei lose BCC content as they grow
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Structure Analysis
• Neither experiments nor simulations give spherical or faceted nuclei
• Neither experiments nor simulations give perfect crystal structures for the nuclei
• Experiments (20 mins of observation) give – BCC 0 – 3%
– FCC 10 – 60%– HCP 20 – 30%– Amorphous 20 – 60% (mostly on exterior)
• Simulations (0.03 secs of observation) give– BCC 10 – 30% (decreases to 0% after further 2 -3 seconds of growth)
– FCC 15 – 45%– HCP 0 – 15%
– Amorphous 30 – 80%
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Effect of Undercooling - Seeded Simulations
0
0.02
0.04
0.06
0.08
0.1
0.12
0.14
0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5
FCC/fluid transition line
FCC/BCC transition line
BCC/fluid transition line
FCC StableBCC Metastable
FCC UnstableBCC Unstable
FCC StableBCC Metastable
FCC UnstableBCC Unstable
FCC MetastableBCC Stable
packing fraction (η)
dim
ensi
onle
ss te
mpe
ratu
re (
T*)
Simulations at 1/κσ = 0.2
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Results
0
0.02
0.04
0.06
0.08
0.1
0.12
0.14
0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5
FCC/fluid transition line
FCC/BCC transition line
BCC/fluid transition line
BCC seed-BCC crystal
BCC seed-FCC crystal
FCC seed-FCC crystal
FCC StableBCC Metastable
FCC UnstableBCC Unstable
FCC StableBCC Metastable
FCC UnstableBCC Unstable
FCC MetastableBCC Stable
packing fraction (η)
dim
ensi
onle
ss te
mpe
ratu
re (
T*)
“Crystal” means the entire solid box after 1 -3 seconds of real time
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0
0.02
0.04
0.06
0.08
0.1
0.12
0.14
0.16
0.18
0.2
0.25 0.3 0.35 0.4 0.45
BCC seed - FCC crystal
Fluid
FCC StableBCC Metastable
packing fraction (η)
dim
ensi
onle
ss te
mpe
ratu
re (
T*)
Simulations at 1/κσ = 0.05, if the interactions are very small the metastable seed won’t survive - seeding will not work
Seeded Simulations at WeitzConditions
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Take Home Message About Seeding
• The normal rule is “seed with the desired polymorph in order to grow crystals of that polymorph”
• Based on (limited) simulations, this strategy is not always successful. Success depends on– Strength of interparticle interactions (very weak interactions will
give the stable phase at all undercoolings – seeding with the metastable phase never works)
– For stronger interparticle interactions, success depends on degree of undercooling
- small undercoolings seeding with the metastable phase is successful
- large undercoolings seeding with the metastable phase is NOT successful
– It doesn’t take much deviation from hard spheres for seeding with the metastable phase to be successful at small undercoolings
⇒
⇒
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Stearic Acid
• Seeding technique developed for colloidal particle study • Stearic acid in hexane• Stearic acid has 4 polymorphs (A,B,C,E)
– 6 if include polytypes
• System exhibits a change in stable polymorph – C above 32°C, B below
– Change yields many conditions (temperature and concentration) of interest for polymorph selection
Form C in hexaneGarti, N; Sato,K. eds. Crystallization and Polymorphism of Fats and Fatty Acids. Marcel Dekker, 1988, 273.
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Form B and C Solubility in Hexane
0
2
4
6
8
10
12
15 20 25 30 35 40
BC
Sol
ubili
ty (
g/10
0g s
olve
nt)
T (ºC)Mirmehrabi, M. and S. Rohani. Can. J. Chem. Eng., 2004, 82, 335-342.
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Stearic Acid Form C
c
a
c
b
ab
a= 9.36 Åb= 4.95 Åc= 50.7 Å
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Simulation Details
• Molecular dynamics simulations– NPT ensemble– Gromacs software
• Explicit hexane solvent• United atom model
– CH3, CH2 groups
– Individual atoms in carboxylic acid group
• Current running conditions– 33 ºC, -73 ºC
– 0.073 mole fraction (128 g/L)• Solubility of polymorph C at 47 ºC
– Seeds of various sizes
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Seed Description
• Procedure was developed to equilibrate full crystal of Form C
• Seeds were created from equilibrated crystal
Long Axis View
6 molecules in form of 2 - complete bilayers, 2 - ½ bilayers
Perpendicular view
6 and 12 molecules in other directions
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Changes in Structure
128º
hexane/stearic acid
solution
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Changes in Structure
~90º
Change in angle may indicate “between” polymorph nucleus structure
hexane/stearic acid
solution
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Size of Stable Seeds
• Seeds with ≥ 7-9 layers in the other directions are stable – Seeds with ≤ 6 layers in other directions melt
– Valid for seeds with both 1 and 2 bilayers
• Stable seeds have ≥ 130 stearic acid molecules– ~50 Å in length
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0.75 ns
Steps of Dissolution
0.006 ns1.5 ns
Steps of dissolution follow energy trendMay indicate steps of nucleation
bilayersseparate
stearic acids dissolve from outside in
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Initial Growth
14 layers
Growth in other directions but not in bilayersSupports dissolution observations
Growth may be directional even at small scale
11 layers
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Questions Raised
• What are the steps of growth– Can affect nucleation mechanism
• How does shape affect the minimum seed size?– Shape is not given by Classical Nucleation Theory
• What does structure change indicate?– Possible transition to another polymorph
– Structure is not given by Classical Nucleation Theory
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Acknowledgements
• National Science Foundation Graduate Research Fellowship
• UC Regents Fellowship
• UCSB MRL Central Facilities
• CNSI Computing Facilities, Hewlett-Packard
• Dr. Patricia Soto Becerra
• Doherty Group– Ryan Snyder, Jacob Sizemore, Derek Griffin, Mike Lovette
• Fredrickson Group– Erin Lennon, Won Bo Lee
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26Malta V.; G. Celotti; R. Zannetti; A. Martelli. J. Chem. Soc. (B), 1971, 548-553.
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Critical Nuclei by Simulation with Surface Particles Removed to See the Core
Structure
Side view Top view
Nucleus 1
Nucleus 2 Nucleus 3
Nucleus 4