pathways to crystal nucleation and growth - ucsb …ghf/cfdc_2007/browning_cfdc_2007.pdf ·...
TRANSCRIPT
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Pathways to Crystal Nucleation and Growth
Andrea Robben BrowningGlenn H. FredricksonMichael F. Doherty
Department of Chemical Engineering University of California Santa Barbara
Complex Fluids Design Consortium Annual MeetingJanuary 23, 2007
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Presentation Overview
• Motivation
• Part 1: Model Particles– Simulations
– Comparison with colloidal experiments
• Part 2: Real Molecules– Initial seeded simulations
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Motivation for Project
• 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– Polymorph development not always determined by seed*
• Most nucleation is heterogeneous – What is learned in homogeneous nucleation can be applied
to heterogeneous nucleation
• Explore nucleation using– Simulations
*Yu, L. J. Am. Chem. Soc. 2003, 125, 6380-6381.
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Part 1: Model Particles
• Hard-core screened coulomb pair potential
– Spherically symmetric
• Molecular dynamics simulations – Seeded initial conditions
– Unseeded, homogenous nucleated simulations
• Direct comparison with experimental data (Weitz & coworkers)
σε
σσσκσε
<∞=
>−−
=
ru/
rr/
)]1r/(exp[u/
0
0.5
1
0 0.5 1 1.5 2 2.5 3
pair
pote
ntia
l (u/ε)
pair separation (r/σ)
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Model particle parameter space
Hynninen, A. ; Dijkstra, M. Phy. Rev. E 2003, 68, 021407.
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
Τ∗=0.125
packing fraction (η)
scre
enin
g le
ngth
(1/κσ)
Hard Core limit
Coulomb limit
Experimental conditions
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Simulation Details
• Molecular dynamics simulations– NVT ensemble– 10717 to 32000 particles
• Seeded initial conditions– FCC or BCC polymorph– Spherical shape– Variable seed size
– Structure of particles after box is fully crystalline is compared to
structure of the seed
– Results of simulations that are homogenously nucleated from fully
random initial condition are shown later
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Seed Evolution
packing fraction (η)
scre
enin
g le
ngth
(1/κσ)
FCCBCC
Fluid
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
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Seed Evolution
packing fraction (η)
scre
enin
g le
ngth
(1/κσ)
FCCBCC
Fluid
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
FCC seed-FCC crystal
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Seed Evolution
packing fraction (η)
scre
enin
g le
ngth
(1/κσ)
FCCBCC
Fluid
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
BCC Seed-BCC crystalFCC seed-FCC crystal
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Seed Evolution
packing fraction (η)
scre
enin
g le
ngth
(1/κσ)
FCCBCC
Fluid
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
BCC Seed-BCC crystalBCC Seed-FCC crystalFCC seed-FCC crystal
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0
0.05
0.1
0.15
0.2
0.25
0.3
0.35
0.4
0.45
0.5
0.2 0.3 0.4 0.5 0.6
BCC Seed-BCC crystalBCC Seed-FCC crystalFCC seed-FCC crystal
Seed Evolution-Low Temperature
packing fraction (η)
scre
enin
g le
ngth
(1/κσ)
FCC
BCC
Fluid
replot
T* = 0.05
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0
0.05
0.1
0.15
0.2
0.25
0.3
0.35
0.2 0.25 0.3 0.35 0.4 0.45 0.5 0.55
BCC Seed-FCC crystalBCC Seed-BCC crystalFCC Seed-FCC crystal
packing fraction (η)
Dim
ensi
onle
ss T
empe
ratu
re (
T*)
FCC
Fluid
Effect of UndercoolingScreening length=0.1
Melting line
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Initial Conclusions
• BCC can transform into FCC during crystal evolution
• FCC not observed to transform into BCC
• Undercooling can effect how polymorph develops– Seeding desired polymorph does not guarantee growing desired
polymorph
– Consistent with Yu’s observation of D-mannitol and D-sorbitol
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Comparison with Experiments
• Nucleation of colloidal particles observed by Weitz & coworkers using laser scanning confocal microscopy– Melting and freezing packing fractions comparable at
Τ∗=0.125 and screening length=0.05 • Same simulation procedure as in previous work but
without seeding- homogenous nucleation • Can compare simulations and experiments
– Shape– Size– Structure
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Model particle parameter space
Hynninen, A. ; Dijkstra, M. Phy. Rev. E 2003, 68, 021407.
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
Τ∗=0.125
packing fraction (η)
scre
enin
g le
ngth
(1/κσ)
Experimental conditions
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Comparison with Experiments
Side view Top view
Nucleus 1
Nucleus 2 Nucleus 3
Nucleus 4
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Comparison with Experiments
Gasser, U. et al. Science. 2001, 292, 258-261.
Nuclei from Weitzet. al. experiments
Nuclei from simulation
FCC/HCP structureFCC/HCP structure
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Results of Comparison with Experiments
• Particles in nuclei are primarily FCC coordinated
• No spherical nuclei observed– More elliptical in shape
• Nuclei have rough surface
• Minimum size for growth between 60 and 135 particles– Agrees with experimental result of between 60 and 160
particles
• Findings agree with experiments
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Part 1: Future Plans
• Surface stress and surface energy calculation • Develop predictive simulations for colloidal
experiments• Explore the effect of seed size on polymorph selection• Improved model for crystal nucleation useful in process
and product design– Be able to select and control the polymorph that is formed
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Part 2: Real Molecules
• Same techniques developed for particle study can be applied to molecular study
• First system studied is stearic acid in hexane• Stearic acid has 4 polymorphs (A,B,C,E)• 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 hexane
COOH
Garti, N; Sato,K. eds. Crystallization and Polymorphism of Fats and Fatty Acids. Marcel Dekker, 1988, 273.
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Polymorph C: Crystal Description
Long Axis View
6 molecules in form of 2 - complete bilayers, 2 - ½ bilayers
Perpendicular view
6 and 12 molecules in other directions
COOH
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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 – 0.073 mole fraction (128 g/L)
• Solubility of polymorph C at 47 ºC– Seed size 2 bilayers, 10 and 11 molecules in other directions
• ~400 stearic acid molecules
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Initial Condition
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Initial Condition- Seed
128º
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Seed after 1.5 ns
~90º
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Part 2: Future Plans
• Questions raised by initial simulation– What is the minimum seed size that does not dissolve?– How does shape effect the minimum seed size?– What does structure change indicate?
• Possible transition to another polymorph
• Future work– Smaller and larger seeds of different shapes– Higher concentrations or lower temperatures– Compare with polymorph B seeds
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Acknowledgements
• U.S. National Science Foundation Graduate Research Fellowship
• Doherty Group– Ryan Snyder, Jacob Sizemore, Derek Griffin, Mike Lovette
• Fredrickson Group– Erin Lennon, Won Bo Lee, Dr. Kirill Katsov
• Dr. Joan-Emma Shea and Dr. Patricia Soto Becerra