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

simulation reality 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 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

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 VL

Supersonic nozzle neutron or X-ray Beam (λ = 0.1 – 2 nm) N 2(g) H 2 O (g) N 2(g) H 2 O (l) D p = 2-20 nm

Experimental Setup at NIST

Is there evidence for structure in larger nanodroplets? Well-mixedCore-shellPartly nested or Russian doll Use small angle neutron scattering (SANS) to find out.

Core vs. Shell scattering using contrast variation In high q region sphere I  q –4 shell structure I  q –2 [q = (4π/λ)sin(θ/2)]

Evidence for shell scattering H 2 O – d-butanol/D 2 O – (h)butanol Wyslouzil, Wilemski, Strey, Heath, Dieregsweiler, PCCP 8, 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 ρ i (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 for a pure droplet.

Two types of droplet structures well-mixed core-shell

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 –E bv = 1, E rv = 2/3, E rb = 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= ● ● (Erb=0)

Density profile indicates surface enrichment of red beads ● ● (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 ● ● (Erb=0.8)

Russian doll droplet at kT= ● ● (Erb=0.8)

Russian doll axial density profile at kT= ● ● (Erb=0.8) 0<r<1

Core-Shell droplet at kT=2.5 formed by heating Russian Doll 1400 ● ● (Erb=0.8)

Antonow’s Rule: Interfacial Tensions and Wetting Transitions γ(bv) < γ(rv) + γ(rb) γ(bv) = γ(rv) + γ(rb) Partial wettingPerfect wetting

By Analogy with Antonow’s Rule and Wetting Transitions Russian dollCore-shell Partial wettingPerfect 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 ● ● (Erb=0.8)

As the temperature is reduced further, the droplet elongates. kT=2.2 kT=2.3 Cool the Core-Shell droplet to observe the dewetting transition 1400 ● ● (Erb=0.8)

Cool the Core-Shell droplet to observe the dewetting transition At the lowest temperatures dewetting and elongation are pronounced. T=2.0 kT=2.1 kT= ● ● (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 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