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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

Nano Particles

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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

R–2a

R

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.).

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.

Packing fractions:

FCC & HCP0.740

BCC0.680

SC 0.524

Fs

l

2A

Fs

Fw

d

Fluids 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.

surface tensionγ units force/length typically given in dyne/cm

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.

The work required to create new surface area.

balance the forces:

Forces on a liquid sphere of radius r

Pout

surface tension force

Pin

γ2πr

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

γLV

V

γSV

θ

L

γLS

S

V vapor

L liquid

S solid

Contact Angle for a Sessile Drop

Young’s Equation

Horizontal Tensions balance

contact angle

- 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) .

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

The 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).

sphere

cylinder

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

Atoms 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.

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