Experimental and theoretical
studies of the structure of binary
nanodroplets
Gerald Wilemski
Physics Dept.
Missouri S&T
Physics 1
Missouri S&T
25 October 2011
Acknowledgments
• Part I – Supersonic nozzle and small angle neutron scattering
(SANS) studies of nucleation and nanodroplet structure
•
•
•
Barbara Wyslouzil (OSU)
Reinhard Strey (Köln U),
Christopher Heath and Uta Dieregsweiler (WPI)
• Part II – Structure in binary nanodroplets from density
functional theory (DFT), lattice Monte Carlo (LMC), and
molecular dynamics (MD) simulations
•
Fawaz Hrahsheh, Jin-Song Li, and Hongxia Ning (Missouri S&T)
OUTLINE
Importance of structure for nanodroplets
Experimental overview
Experimental and theoretical results for
binary nanodroplets
SANS
Density Functional Theory
Lattice Monte Carlo
Molecular Dynamics
Conclusions
Nucleation occurs all around us…
simulation
reality
Organic matter is a common component
of atmospheric particles
Inverted micelle model for aqueous organic aerosols was
recently revived. (Ellison, Tuck, Vaida, JGR 1999)
Aqueous core + organic layer with polar heads (●)
Why is this important ?
Aerosols affect the Earth’s climate
Aerosols change the properties of clouds
Sites for chemical reactions:
heterogeneous chemistry, ozone
destruction
Fine particles (<100 nm) affect human
health
Particle structure influences particle activity
– nucleation and growth rates
Radiative forcing by
aerosols:
Direct (scattering and
absorption)
Indirect (affecting cloud
formation and cloud
properties)
Clouds effect the global
energy balance. They
modify earth’s albedo
and LW radiation.
How are small clusters involved?
V
L
growth
…
…
Nucleation rates
Critical cluster properties
Supersonic nozzle
10
-1
Log Normal Distribution
rg = 10.25 ± 0.05 nm
ln  = 0.184 ± 0.004
10
N = ( 4.91 ± 0.05 ) × 10
-2
11
-3
cm
-3
-1
I (cm )
10
10
10
Dp = 2-20 nm
-4
Nozzle A
Po = 59.7 kPa
To = 308.1 K
PD2O,o = 1.37 kPa
-5
3.75 m SDD
2.00 m SDD
10
-6
8 9
2
3
120
5
6 7 8 9
0.1
-1
q (Å )
-1.5
100
80
-2.0
60
-2.5
40
20
N2(g)
4
0.01
-3.0
0
0
20
40
60
80
100
120
H2O(g)
N2(g)
H2O(l)
neutron or X-ray
Beam (λ = 0.1 – 2 nm)
2
3
Experimental Setup at NIST
Is there evidence for structure
in larger nanodroplets?
Use small angle neutron scattering (SANS) to find out.
Well-mixed
Core-shell
Partly nested
or Russian doll
Core vs. Shell scattering
using contrast variation
In high q region
[q = (4π/λ)sin(θ/2)]
sphere
I  q–4
shell structure
I  q–2
Evidence for shell scattering
Wyslouzil, Wilemski, Strey, Heath, Dieregsweiler, PCCP 8, 54 (2006)
H2O – d-butanol/D2O – (h)butanol
Summary
• SANS: first direct experimental evidence for
Core-Shell structure in aqueous-organic
nanodroplets
Density Functional Theory
applied to nanodroplets
Treat nanodroplets as large critical nuclei in
supersaturated binary vapors. The species densities ρi
(r) vary with position r.
As a typical aqueous-organic system use nonideal waterpentanol mixtures modeled as hard sphere - Yukawa
fluids (van der Waals mixtures).
Use classical statistical mechanics to find the
unstable equilibrium density profiles: Solve EulerLagrange Eqs.
D. E. Sullivan, J. Chem. Phys. 77, 2632 (1982).
X. C. Zeng and D. W. Oxtoby, J. Chem. Phys. 95, 5940 (1991).
J.-S. Li and G. Wilemski, PCCP 8, 1266 (2006)
A droplet is a region with higher
density than the surrounding fluid
The red line shows
how the density (ρ)
varies with radial
position (r) within
the droplet.
This example is for
a pure droplet.
Two types of droplet structures
well-mixed
core-shell
1.0
1.0
Water
Pentanol
BDS
0.8
3
aP=1.001602
aW=1.178168
xP=2.64%
0.6
WW
WW
3
0.8
0.4
Water
Pentanol
BDS
0.6
0.4
0.2
0.2
0.0
0.0
0
1
2
3
4
Distance (nm)
5
6
aP=1.001602
aW=1.178168
xP=2.64%
0
1
2
3
4
Distance (nm)
5
6
Structural Phase Diagram from DFT
at 250 K
DFT predicts nonspherical
oil( )/water( ) droplets
Why interested in oil/water
droplets?
• Offshore natural gas wells produce
high pressure mixtures of methane,
water, and higher hydrocarbons (i.e., oils)
• Gas must be cleaned before pumping
to shore and clean-up may involve
droplet formation
DFT Summary
• DFT: provides a vapor activity “phase diagram” for
the nanodroplet structures
– bistructural region implies hysteresis for transitions
between well-mixed and core-shell structures
• Also predicts nonspherical shapes for droplets with
immiscible liquids
Lattice Monte Carlo Simulations of
Large Binary Nanodroplets
•
Generalize the lattice MC approach of Cordeiro and
Pakula, J. Phys. Chem. B (2005) for pure droplets
•
Each site of an fcc lattice is
occupied by a different particle
type (red or blue beads) or by
a vacancy.
•
Beads and vacancies interact repulsively
–
–
•
Ebv = 1, Erv = 2/3, Erb = 0, 0.5, 0.8
Red beads ↔ lower surface tension, higher volatility (~alcohol)
Blue beads ↔ higher surface tension, lower volatility (~water)
T range: 2.8 ≥ kT ≥ 2.0; Blue triple point is at kT= 2.8
Ideal binary droplet at kT=2.5
1400 ● + 3264 ● (Erb=0)
Nonideal binary droplet at kT=2.5
1400 ● + 3264 ● (Erb=0.5)
Density profile indicates surface enrichment of red beads.
Core-Shell droplet at kT=2.5
1400 ● + 3400 ● (Erb=0.8)
Interior depletion and surface enrichment of red beads.
Russian doll droplet at kT=2
1400 ● + 3400 ● (Erb=0.8)
Russian doll axial density profile at kT=2
1400 ● + 3400 ● (Erb=0.8)
Dimensionless Number Density
1.2
1.0
kT=2.0
N1=1400
0< r<1
0<r<1
component 1
component 2
N2=3400
0.8 E3=0.8
0.6
0.4
0.2
0.0
-20
-10
0
Axial (z) position
10
20
Core-Shell droplet at kT=2.5
formed by heating Russian Doll
1400 ● + 3400 ● (Erb=0.8)
Antonow’s Rule: Interfacial Tensions
and Wetting Transitions
γ(bv) < γ(rv) + γ(rb)
Partial wetting
γ(bv) = γ(rv) + γ(rb)
Perfect wetting
By Analogy with Antonow’s Rule
and Wetting Transitions
Partial wetting
Perfect wetting
heat
cool
Russian doll
γ(bv) < γ(rv) + γ(rb)
Core-shell
γ(bv) = γ(rv) + γ(rb)
Cool the Core-Shell droplet to
observe the dewetting transition
1400 ● + 3400 ● (Erb=0.8)
kT=2.5
The backside is more
evenly covered.
kT=2.4
There is a large dewetted patch;
the backside is evenly covered.
Cool the Core-Shell droplet to
observe the dewetting transition
1400 ● + 3400 ● (Erb=0.8)
kT=2.3
kT=2.2
As the temperature is reduced further, the droplet elongates.
Cool the Core-Shell droplet to
observe the dewetting transition
1400 ● + 3400 ● (Erb=0.8)
kT=2.1
T=2.0
kT=2.0
At the lowest temperatures dewetting and elongation are
pronounced.
LMC Summary
• LMC: the core-shell - Russian doll structural
change is a reversible wetting-dewetting transition
that modulates the shape of the nanodroplet
– May ultimately be a cause of droplet fission ?
• The RD droplet resembles the nonspherical
structure found with DFT for oil/water droplets
Molecular Dynamics (MD)
• Solve Newton’s equations of motion for
large numbers of interacting molecules
• Time step = 1 or 2 fs (10-6 ns)
• Average over 2 ns long trajectories to
calculate properties of interest
MD of nonane/water droplet
initial
Nonane molecules (blue-green)
surround a droplet of water (red-white).
final
The water droplet partly emerges
from the oil droplet.
Double click on the slide to see the simulation.
Grand Summary
• SANS: experimental evidence for Core-Shell
structure of aqueous-organic nanodroplets
• DFT: vapor activity “phase diagram” for CS and
well-mixed nanodroplet structures
• DFT: nonspherical droplet shapes
• LMC: core-shell - Russian doll structural transition
changes the shape of the nanodroplet
• MD: realistic simulations of droplets with large
numbers of molecules