Surface

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Lecture 2 Surface Intermolecular Forces
van der Waals Forces
Full et al. (2000), Nature 405, 681-684
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Areas where Intermolecular Forces are important

• Examples
• Colloidal Stability in Dispersions/Emulsions
• - Attractive forces promote instability of
  dispersions
• - Repulsive forces are needed to stabilize
  dispersions

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Areas where Intermolecular Forces are important
Many observed phenomena in nature have their
basis in intermolecular forces!
Short-range forces have long-range (macroscopic)
effects. Identifying quantifying intermolecular
forces is key to the successful design of
stable/unstable systems as required
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Intermolecular Forces
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Intermolecular Forces Contrast with
gravitational forces
17th Century Newton postulated the law of
gravitation
19th Century Scientists postulated that one
simple force law would eventually account for all
intermolecular attractions
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Intermolecular Forces Contrast with
gravitational forces
Argument If Intermolecular Forces are not to
extend over long ranges, then n ? 3. How?
Consider a region of space where number density
of these molecules are ? (The region can be
solid/liquid/gas)
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Intermolecular Forces Contrast with
gravitational forces
The summation of all interaction energies of a
molecule with all other molecules in a spherical
system with size L is
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Intermolecular force potentials for n ? 3
For n lt 3, the size of the system is important
(E.g. Gravity Distant
planets and stars interact)
For n ? 3, intermolecular force potentials become
important
It is for this reason that Bulk properties of
material is size independent (unless in the
domains of intermolecular forces) (Boiling point
of water in a test tube boiling point of water
in a bucket)
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van der Waals Forces

• Reasoned out
• Molecules have finite volume (accounted by b)
• Attractive forces between the molecules
  (accounted by a)
• The relation predicted gas behavior across a
  larger pressure range

The attractive intermolecular forces between gas
molecules is now known as van der Waals forces
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van der Waals Forces
The three components that constitute van der
Waals Forces
The London component is the most dominant. n 6
indicates van der Waals forces are short range
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Keesom (dipole - dipole) component
- Dipole-dipole interactions are generally weak
- These weak dipole-dipole interactions becomes
significant when 2 interacting dipoles approach
each other closely. e.g. O-H, N-H, F-H
(These strong dipole-dipole interactions are the
well known Hydrogen Bond)
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Debye (dipole induced dipole) component
- Interaction of a polarizable molecule with a
dipole
- Polarizablility Electron cloud of molecule
responds to an electric field by a localized shift
- Debye interactions are independent of
temperature
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London (Dispersion) component
- The most important component of van der Waals
interaction
- Keesom and Debye interactions require the
presence of at least 1 permanent dipole, but
London interactions do not. - Hence, London
interaction exist between all molecules
- The London interaction component was always
known, but evolved only after the development
of quantum mechanics
- Provides molecular level reasoning that at room
temperature Small molecules (Ar, He, CH4) are
gases, Bigger molecules (hexane, decane) are
liquids, Even bigger molecules (C35H71) are
solids.
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Interactions between Surfaces and Particles -
Microscopic Approach -
1937 Hamaker calculated the total interaction
between two spherical particles by adding
contributions for each atom in the solid
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van der Waals Interaction Potential for various
configurations
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Example Considering only van der Waals
attraction, what is the force and energy of
adhesion between two particles of radius 1 ?m
with A 10-19 J ? (H H0 ? 3Å)
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Example Considering only van der Waals
attraction, what is the force and energy of
adhesion between two particles or radius 1 ?m
with A 10-19 J ? (H H0 ? 3Å)
Energy of adhesion
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Impinging air jets may be used to clean particles
from surfaces. The kinetic energy per unit
volume (J/m3) of an air jet at a surface, Er,
may be written as
Where r density of air (1.3 kg/m3), v air
velocity k proportionality constant (0.4
mm1.3) d distance from the jet nozzle (10 mm).
For a sphere adhered to a flat surface (A11
1x10-19 J), (1) What size of particle
(diameter) could a hurricane force wind
(v 15 m/s) remove from a surface? (2) What
size of particle can be removed at v 340 m/s
(speed of sound)? (3) What air velocity would
be required to remove a 1 mm particle and a
100 nm particle?
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But! we said all along... Intermolecular forces
potential exist when n ? 3
However, the potentials for the following cases
have n 1
Sphere Plate
Sphere Sphere
Why does this happen?
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Consider Sphere Plate Interaction
Integrate interaction of every element on the
sphere with the plate
The bulk material contributing to the interaction
terms causes n to collapse to 1, due to
integration of large number of individual sphere
elements with the plate
Reinforces the fact that van der Waals forces are
more significant for small molecules at small
distances
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The case of the Gecko Walk!
Spatulae
Check the Gecko feets microstructure
Seta
1 billion of them, all in the van der Waals domain
Satae
Feet microstructure enables the Gecko reach van
der Waals domains of attraction, hence
they scale walls with ease!
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This is also why...
Spatulae
Seta
Satae
Spiderman exists only in movies !
But Seriously, can we possibly make the Spiderman
costume?
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Estimation of A (Vacuum or non-vacuum media)
Combination Rules Allows quick approximation

• Limitations
• A may be a function of many other
  intermolecular forces
• Approach ignores many molecule interactions

Israelachvili Intermolecular and Surface Forces,
p. 200
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Values of Hamaker Constants for different material
Hamaker Constants (10-20 J)
Vacuum 25 20 18 15 13 12 13 6.5
n-Dodecane 1 6.8 5.0 3.6 2.6 1.9 2.1 0.15
Material 6H-SiC tetra-ZrO2 b-Si3N4 a-Al2O3 Y2O3 M
gO MgAl2O4 SiO2
Medium Water 13 8.8 7.0 5.2 4.0 3.2 3.5 0.83
Bergström, L (1997), Adv. Colloid and Interface
Sci., 70, 125
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Values of A in different media for selected
material

• Note the similarity in the magnitude A
• Typical values in vacuum (air) only vary from
  (0.4 to 4) x 10-19 J
• 1 ? 10-19 J is a good approximation for most
  dielectric materials

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van der Waals Force as a function of A
Sphere/Shpere
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van der Waals Force as a function of R
Sphere/Shpere
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DERJAGUIN APPROXIMATION

• Relates interaction energy of flat surfaces and
• interaction forces of curved surfaces
• Allows interactions to be calculated between
  different
• shapes

Important condition Range of distance where
surface forces are significant ltlt radius of
curvature
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Approach For concentric rings of radius x and
thickness dx, calculate the specific force
between a projection of that ring on the sphere
as if it were two plates of area 2pxdx separated
by H
Integrate from x 0 to x R
H0
H
x
dx
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For the Sphere/Plate interaction F(H)sph-plt
2?R W(H)plt W(H) is the energy/area between two
flat plates. Other geometries such as spheres
and cylinders may also be calculated W(H)plt-plt
Sphere/Plate F(H)sph-plt/2?R Sphere/Sphere
F(H)sph-sph/?R Crossed Cylinders F(H)cyl-cyl/2?R
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Theoretical Determination of Surface Tension (van
der Waals Approach)
H0 between liquid atoms at an interface ? 0.165 nm
Example for silica A 10-19 J and H0 0.3
nm gtheoretical A/(24pH02) 15 mJ/m2 but
gexperimental 30-73 mJ/m2 (H-bonding causes
the difference)
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Repulsive van der Waals
Medium Cyclohexane
F
Silica
Alumina
Silica or Alumina particle
TeflonAF
System1 Alumina Cyclohexane Teflon
A132-0.5510-20 J System 2 Silica Cyclohexane
Teflon A132-0.08910-20 J
Hamaker Constant Cyclohexane 5.210-20
J Silica 6.510-20 J Alumina
15.610-20 J Teflon 3.810-20 J
?
Lee et al. Colloids and Surfaces A, Volume 204,
Issues 1-3, 23 May 2002, Pages 43-50