Green Engineering of Dispersed Nanoparticles: Measuring andModelingModeling Nanoparticle Forces

Kristen A. Fichthorn and Darrell VelegolDepartment of Chemical Engineering

The Pennsylvania State UniversityUniversity Park, PA 16802

Students: Yong Qin Gretchen Holtzer

R-8290501

Nanoparticles: Potential Building BlocksFor New and Existing Materials

• Catalysts

• Optical Materials

• Structural Materials

• Electronic Materials

Nano-Electronics

Difficult to Disperse or Assemble

“Bare” Nanoparticles

1 m5 nm

Conventional Colloids:Dispersant: ~1% volume

Nanoparticles:Dispersant: ~ 90% volume

A LOT OF WASTE! ! ! ! !

Nanoparticle Forces are POORLY UNDERSTOOD!

Colloidal Forcesfrom MolecularDynamics Simulations

• van der Waals and Electrostatic Forces:DLVO theory

• Solvation Forces:Solvent Ordering

• Depletion Forces:Entropic

How Do These Work forColloidal Nanoparticles?

Particle force light scattering (PFLS) for nanoparticle forces

Ofoli & Prieve, Langmuir,13, 4837 (1997)

0

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

0.45

0.5

0 500 1000 1500 2000 2500

time (ms)

(V-V

o)/

Vo

Fcrit = 0.3 pN 0.08

I N x mass2

800 nm particles

custom differentialelectrophoresis cell

Large-Scale Parallel MD Simulation

• Solvent: Lennard-Jones Liquid, n-Decane ( >105 Atoms)

• Nanoparticles: Solid Clusters of Atoms

• Solvophilic Nanoparticles: (εsf = 5.0εff)

• Solvophobic Nanoparticles: (εsf = 0.2εff)

Beowulf Cluster: Cruncher

Model Nanoparticles

Small Sphered = 4.9σ64 atoms

Large Sphered = 17.6σ

2048 atoms

Cubed = 13.2σ

2744 atoms

Icosahedrond = 4.0σ

55 atoms

Solvation Forces: Thermodynamic Integration

BSASAB

solvsolv

FFr

d

dUF

)(

j

i d

dUdAij

)(

Free Energy Change

Solvation Force

Mezei and Beveridge, Ann. N. Y. Acad. Sci. 482, 1 (1986).

Interactions for Spheres, Cubes

Solvophilic solvation forces are

oscillatory and comparable to van

der Waals forces

Solvophobic solvation forces

are attractive

-15.0

-10.0

-5.0

0.0

5.0

1.0 1.5 2.0 2.5 3.0 3.5 4.0

δ/σ

F·σ

/kT

Solvophilic

Solvophobic

van der Waals-30.0

-25.0

-20.0

-15.0

-10.0

-5.0

0.0

5.0

10.0

1.0 1.5 2.0 2.5 3.0 3.5 4.0

δ/σ

F·σ

/kT

Solvophilic

Solvophobic

van der Waals

Small Sphere

Large Sphere

-600.0

-400.0

-200.0

0.0

200.0

400.0

600.0

1.5 2.0 2.5 3.0 3.5 4.0 4.5

δ/σ

F·σ

/kT

van der Waals

Solvophilic

Cube

Fluid Ordering: Origin of Solvation Forces

Solvent ordering around nanoparticles can be observed in all solvophilic simulations

(Movie)

Solvophobic Nanoparticles: The Drying Transition

(Movie)

Derjaguin Approximation

222 S

Solv

CC D

F

A

A

-0.2

-0.1

0.0

0.1

0.2

0.3

0.4

0.5

0.5 1.5 2.5 3.5 4.5 5.5 6.5

δ/σ

ΔA

/(2A

cρc2

) or

FS

olv/(

πD

ρs2

)

(kT

σ4)

Small SphereLarge SphereCube

-0.04

-0.03

-0.02

-0.01

0.00

0.01

0.5 1.5 2.5 3.5 4.5 5.5 6.5

δ/σ

ΔA

/(2

Acρ

c2 ) o

r F

Sol

v /(π

Dρ

s2 )

(kT

σ4 )

Small SphereLarge SphereCube

Solvophilic Solvophobic

Derjaguin ApproximationDescribes the Envelope

Derjaguin Approximation Works

Influence of Surface Roughness on Solvation Forces

Particle orientation significantly affects the force profile: Particles will Rotate in Solution

-2.0

-1.0

0.0

1.0

2.0

3.0

4.0

5.0

6.0

0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5

Separation (σ)

Fo

rce

(kT

/σ)

Left

Center

Right

-2.0

0.0

2.0

4.0

6.0

8.0

10.0

0.5 1.5 2.5 3.5 4.5

δ/σ

F·σ

/kT

fixed

rotation

-0.4

-0.3

-0.2

-0.1

0.0

0.1

0.5 1.5 2.5 3.5 4.5

δ/σF

·σ/k

T

fixed

rotation

Solvophilic

Solvophobic

Rotation Reduces SolvophilicSolvation Forces

Nanocrystals Have PreferredOrientations

The Influence of Solvent Structure:n-Decane – Small Spheres

n-Decane Length Comparableto Nanoparticle Diameter

-4.0

-3.0

-2.0

-1.0

0.0

1.0

0.5 2.5 4.5 6.5 8.5 10.5δ/σ

F·σ

/kT

Solvophilic

Solvophobic

van der WaalsWeak SolvophilicForces

Step-LikeSolvophobicForces

Conclusions

• Current theories do not accurately describe forces for small nanoparticles

• Solvation forces can be important for colloidal nanoparticles

• Solvation forces are strongly dependent on particle size, shape, surface roughness, particle-solvent interactions, and solvent structure

• Solvent-nanoparticle suspensions can be engineered for stability, assembly, environmental impact……