1. 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
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2. Classification of NanoParticle Suspensions
DISPERSED PHASE (nanoparticle)
CONTINUOUS PHASE
(medium completely surrounding the nanoparticle)
solid
liquid
gas
solid suspension
(solid sol)
certain ceramics (Corel) & alloys, ruby glass
gel
jello, jelly, cheese,
certain rubbers,
Tygon tubing
solid foam
foam rubber,
marshmallow,
Styrofoam
suspension
(sol, in H2O hydrosol)
muddy water,
paint, ink
emulsion
mayonnaise,
milk
foam
shaving cream,
whipped cream
smoke
(aerosol)
smoke, dust
fog
(liquid aerosol)
fog, clouds
does not occur
(all gases are miscible)
No Examples
colloid, The Columbia Encyclopedia, Sixth Edition.  2001. 
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3. 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.).
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.
R–2a R
Packing fractions:
FCC & HCP 0.740
BCC 0.680 SC
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4. Surface Tension Fs l Fs Fw d 2A
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 tension γ units force/length  typically given in dyne/cm Fs l
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 Fw d 2A
The work required to create new surface area.
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5. Pressure Difference Across a Curved Surface
Forces on a liquid sphere of radius r
balance the forces:
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.
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6. Surface Tension: Wetting & Contact Angle
Contact Angle for a Sessile Drop
V vapor
L liquid
S solid
Young’s Equation
Horizontal Tensions balance
γLV
γLS
γSV θ V S L
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) .
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7. The Kelvin Equation sphere cylinder
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.
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8. The Kelvin Effect
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.
The other parameters are: γ the surface tension, the molar volume of the liquid, R the gas constant, and T the absolute temperature.
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9. Example: the Kelvin Effect on Water Drops
Equilibrium Vapor Pressure Increase Over Pure Water Droplet as 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 Pore as 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
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10. 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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