Experimental and theoretical Experimental and theoretical studies of the structure of binary studies of the structure of binary

nanodroplets 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)

OUTLINEOUTLINE

Importance of structure for nanodropletsExperimental overview Experimental and theoretical results for

binary nanodropletsSANSDensity Functional TheoryLattice Monte CarloMolecular Dynamics

Conclusions

simulation

reality

Nucleation occurs all around us…Nucleation occurs all around us…

Organic matter is a common component of atmospheric particles

Aqueous core + organic layer with polar heads (●)

Inverted micelle model for aqueous organic aerosols was recently revived. (Ellison, Tuck, Vaida, JGR 1999)

Why is this important ?

Aerosols affect the Earth’s climateAerosols 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

Clouds effect the global energy balance. They modify earth’s albedo and LW radiation.

Radiative forcing by aerosols:

Direct (scattering and absorption) Indirect (affecting cloud formation and cloud properties)

How are small clusters involved?

… …

Critical cluster properties

growth

Nucleation rates

VV LL

Supersonic nozzleSupersonic nozzle

neutron or X-rayBeam (λ = 0.1 – 2 nm)

N2(g)

H2O(g)

120

100

80

60

40

20

0

120100806040200

-3.0

-2.5

-2.0

-1.5

N2(g)

H2O(l)

Dp = 2-20 nm 10-6

10-5

10-4

10-3

10-2

10-1

I (c

m-1

)

8 90.01

2 3 4 5 6 7 8 90.1

2 3

q (Å-1

)

3.75 m SDD 2.00 m SDD

Log Normal Distributionrg = 10.25 ± 0.05 nm

ln = 0.184 ± 0.004

N = ( 4.91 ± 0.05 ) × 1011

cm-3

Nozzle APo = 59.7 kPaTo = 308.1 KPD2O,o = 1.37 kPa

Experimental Setup at NIST

Is there evidence for structure Is there evidence for structure in larger nanodroplets?in larger nanodroplets?

Well-mixed Core-shell Partly nested or Russian doll

Use small angle neutron scattering (SANS) to find out.

CoreCore vs.vs. Shell Shell scattering scattering using contrast variationusing contrast variation

In high q region

sphere

I q–4

shell structure

I q–2

[q = (4π/λ)sin(θ/2)]

Evidence for shell scatteringEvidence for shell scattering

H2O – d-butanol/D2O – (h)butanolWyslouzil, Wilemski, Strey, Heath, Dieregsweiler, PCCP Wyslouzil, Wilemski, Strey, Heath, Dieregsweiler, PCCP 8, 8, 54 (2006)54 (2006)

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 water-pentanol mixtures modeled as hard sphere - Yukawa fluids (van der Waals mixtures). Use classical statistical mechanics to find the unstable equilibrium density profiles: Solve Euler-Lagrange 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 fora pure droplet.

Two types of droplet structureswell-mixed core-shell

1.0

0.8

0.6

0.4

0.2

0.0

W W

3

6543210

Distance (nm)

aP=1.001602

aW=1.178168

xP=2.64%

Water Pentanol BDS

1.0

0.8

0.6

0.4

0.2

0.0

W W

3

6543210

Distance (nm)

aP=1.001602

aW=1.178168

xP=2.64%

Water Pentanol BDS

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)

Density profile indicates surface enrichment of red beads.

1400 ● + 3264 ● (Erb=0.5)

Nonideal binary droplet at kT=2.5

Core-Shell droplet at kT=2.5

Interior depletion and surface enrichment of red beads.

1400 ● + 3400 ● (Erb=0.8)

Russian doll droplet at kT=2

1400 ● + 3400 ● (Erb=0.8)

Russian doll axial density profile at kT=2

1400 ● + 3400 ● (Erb=0.8) 0<r<1

-20 -10 0 10 200.0

0.2

0.4

0.6

0.8

1.0

1.2kT=2.0N1=1400

N2=3400

E3=0.8

0< r<1 component 1 component 2

D

imen

sio

nle

ss N

um

ber

Den

sity

Axial (z) position

Core-Shell droplet at kT=2.5formed by heating Russian Doll

1400 ● + 3400 ● (Erb=0.8)

Antonow’s Rule: Interfacial Tensions and Wetting Transitions

γ(bv) < γ(rv) + γ(rb) γ(bv) = γ(rv) + γ(rb)

Partial wetting Perfect wetting

By Analogy with Antonow’s Rule and Wetting Transitions

Russian doll Core-shell

Partial wetting Perfect wetting

heat

cool

γ(bv) < γ(rv) + γ(rb) γ(bv) = γ(rv) + γ(rb)

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)

As the temperature is reduced further, the droplet elongates.

kT=2.2kT=2.3

Cool the Core-Shell droplet to observe the dewetting transition

1400 ● + 3400 ● (Erb=0.8)

Cool the Core-Shell droplet to observe the dewetting transition

At the lowest temperatures dewetting and elongation are pronounced.

T=2.0kT=2.1 kT=2.0

1400 ● + 3400 ● (Erb=0.8)

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 final

Nonane molecules (blue-green) surround a droplet of water (red-white).

The water droplet partly emergesfrom 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