OU NanoLab/NSF NUE/Bumm & Johnson Nano Particles High fraction of atoms at or near the surface. Surface Tension: liquids surfaces behave as though they

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OU NanoLab/NSF NUE/Bumm & Johnson

Nano Particles• High fraction of atoms at or near the surface.

• Surface Tension: liquids surfaces behave as though they are an elastic film.

• Kelvin Effect: higher vapor pressure over smaller droplets

• Ostwald Ripening: large particles grow at the expense of smaller particles

• Adsorption: impurities tend to stick to surfaces

• Surface charge: adsorption of ions can leave the nanoparticle electrically charged


Classification of NanoParticle Suspensions

DISPERSED PHASE (nanoparticle)

CONTINUOUS PHASE

(medium completely

surrounding the nanoparticle)

solid liquid gas

solidsolid suspension

(solid sol)

certain ceramics (Corel) & alloys, ruby glass

gel

jello, jelly, cheese,

certain rubbers,

Tygon tubing

solid foam

foam rubber,

marshmallow,

Styrofoam

liquidsuspension

(sol, in H2O hydrosol)

muddy water,

paint, ink

emulsion

mayonnaise,

milk

foam

shaving cream,

whipped cream

gassmoke

(aerosol)

smoke, dust

fog

(liquid aerosol)

fog, clouds

does not occur

(all gases are miscible)

No Examples


Homework Problem: What Fraction of Atoms are on the Surface?

A sphere of radius R is composed of atoms of radius a. Make the assumption that the surface atoms occupy a spherical shell 2a thick. Use the packing fraction to correct for the interstitial volume. You do not need to consider the granular nature of the particle any further (ignore packing, stacking, surface corrugations, etc.).

R–2a

RPacking fractions:FCC & HCP 0.740 BCC 0.680 SC 0.524

Find the number of gold atoms (a = 1.44 Å) in a gold nanoparticle and the fraction of gold atoms on the surface. The gold forms an FCC crystal.


Surface TensionFluids behave as though they have a surface composed of an elastic skin which is always in tension. There are many manifestations of surface tension you can observe everyday. Here are some fundamental properties of surface tension.

lF 2

The force by a planar soap film supported on a rectangular frame with one movable bar of length l. The factor of two is introduced because the soap film has two surfaces.

Fs l

The work required to create new surface area.

A

WAldW

d

d 2

Fs Fw

d

2A

surface tension γ units force/length typically given in dyne/cm


Pressure Difference Across a Curved Surface

Forces on a liquid sphere of radius r

rPPP outin

2

rPP

rrPP

rrPrP

FFF

F

outin

outin

outin

surfaceoutin

2

2

02

0

0

2

22

In this example there is only one surface. For a soap bubble, the force will be twice as great.

γ2πr

Pin

Pout

surface tension force

balance the forces:


γLV

γLS

γSV θV

S

L

Surface Tension: Wetting & Contact Angle

Contact Angle for a Sessile Drop

Young’s EquationHorizontal Tensions balance

criticalSVLS

LV

LVSVLS

LVSVLS

SVLVLS

r

r

r

2cos

0cos2

0cos2

0cos

0

•The critical surface tension γc is an intrinsic characteristic of the surface.

•Liquids with γ < γc completely wet the surface (θ = 0 º).

•Liquids with θ > 90º are said to not wet the surface (γLS > γSV) .

V vaporL liquidS solid

critical cos

contact angle


The Kelvin EquationThe surface tension causes an increased chemical potential for a molecule inside a droplet. This is manifested as an increase in the vapor pressure P of the liquid droplet compared to that of the bulk liquid P0. The is described by the Kelvin equation. Two radii of curvature appear in the result, r1 and r2. For a sphere both terms are equal, but for a cylindrical surface one term vanishes because one radius is infinite (flat).

210

11ln

rrRT

V

P

P

The other parameters are:γ the surface tension, the molar volume of the liquid, R the gas constant, and T the absolute temperature.

V

RTr

V

P

P 2ln

0

RTr

V

P

P

0

ln

sphere

cylinder


The Kelvin EffectAtoms of liquid on the surface of a small droplet are held less tightly compared to atoms on a flat (bulk) liquid surface. High curvatures effectively reduce the coordination number of the surface atoms making them easier to evaporate. Thus the liquid has a higher vapor pressure over small liquid droplets compared to bulk liquid. The effect of curvature on the vapor pressure of liquids is the Kelvin effect.

Positive curvature: liquid in drops has a higher vapor pressure that bulk.Negative curvature: liquid in pores has a lower vapor pressure than bulk.

The vapor pressure P relative to the bulk P0 can be found using the Kelvin equation, show here for spherical surfaces of radius r.

RTr

VPP

2exp0

The other parameters are:γ the surface tension, the molar volume of the liquid, R the gas constant, and T the absolute temperature.

V


Example: the Kelvin Effect on Water Drops

Equilibrium Vapor Pressure Increase Over Pure Water Dropletas a Function of Droplet Radius at T = 25 C

rp (μm) 1 0.3 0.1 0.03 0.01 0.003

P/P0 1.0011 1.0035 1.0107 1.0360 1.1118 1.4238

ΔP (%) +0.11 +0.35 +1.1 +3.6 +11 +42

Equilibrium Vapor Pressure Decrease of Pure Water inside a Poreas a Function of Pore Radius at T = 25 C

rp (μm) 1 0.3 0.1 0.03 0.01 0.003

P/P0 0.9989 0.9964 0.9895 0.9653 0.8994 0.7023

ΔP (%) −0.11 −0.35 −1.1 −3.5 −10 −30


Applications for Nanoparticles

• catalysis (high surface area, controlled crystal surfaces)

• optical properties (sun screen, hyperthermic cancer treatment, fluorescent tags)

• light scattering (smoke./fog screens)

• drug delivery (inhalation asthma, timed drug release.

• pesticide delivery (fogging and fumigation)

• magnetic recording (orient magnetic domain axis, important for hard drives, video & audio tapes)

• pigments, inks, paints (coloring and opacity)

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OU NanoLab/NSF NUE/Bumm & Johnson Nano Particles High fraction of atoms at or near the surface. Surface Tension: liquids surfaces behave as though they