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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Classification of NanoParticle
Suspensions
DISPERSED PHASE (nanoparticle)
solid
CONTINUOUS
PHASE
(medium
completely
surrounding the
nanoparticle)
liquid
gas
solid
solid suspension
(solid sol)
certain ceramics (Corel)
& alloys, ruby glass
gel
jello, jelly, cheese,
certain rubbers,
Tygon tubing
solid foam
foam rubber,
marshmallow,
Styrofoam
liquid
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
gas
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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 0.524
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Surface Tension
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
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
F  2l
2A
The work required to create new surface area.
W  2ld  A
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dW

dA
Fs
Fw
d
Pressure Difference Across a Curved Surface
Forces on a liquid sphere of radius r
balance the forces:
Pout
surface tension force
F  0
Fin  Fout  Fsurface  0
Pin
γ2πr
Pinr 2  Poutr 2   2r  0
Pin  Pout r 2   2r
Pin  Pout 
In this example there is only one
surface. For a soap bubble, the
force will be twice as great.
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2
r
P  Pin  Pout 
2
r
Surface Tension:
Wetting & Contact Angle
Contact Angle for a Sessile Drop
Young’s Equation
Horizontal Tensions balance
  0
 LS   LV cos    SV  0
 LS   SV   LV 2r cos   0
 LS   SV
  LV cos   0
2r
 
 LV cos   LS SV   critical
2r
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V vapor
L liquid
S solid
γSV
V
S
γLV
contact angle
θ γ
LS
L
 cos    critical
•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 Kelvin Equation
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).
P V  1 1 
  
ln

P0 RT  r1 r2 
The other parameters are:
γ the surface tension,
V the molar volume of the liquid,
R the gas constant, and
T the absolute temperature.
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ln
P 2 V

P0 RTr
ln
P V

P0 RTr
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.
 2 V 

P  P0 exp 

RTr


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The other parameters are:
γ the surface tension,
V the molar volume of the liquid,
R the gas constant, and
T the absolute temperature.
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)
P/P0
ΔP (%)
1
0.3
0.1
0.03
0.9989
0.9964
0.9895
0.9653
−0.11
−0.35
−1.1
−3.5
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0.01
0.003
0.8994
0.7023
−10
−30
Applications for Nanoparticles
•
•
•
•
•
•
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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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