The Surfaces Forces Apparatus SFA

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The Surfaces Forces Apparatus (SFA)

• Measuring surface forces in controlled vapor or
  immersed in liquids is directly measured using a
  variety of interchangeable force-measuring
  springs
• Both repulsive and attractive forces are
  measuring and a full force law can be obtained
  over any distance regimes

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The Surfaces Forces Apparatus (SFA)

• The distance resolution about 0.1nm (angstrom
  level)
• the force sensitivity about 10-8 N
• In Surfaces
• Two curved molecularly smooth surfaces of mica in
  a crossed cylinder configuration
• The separation is measured by use of an optical
  technique using multiple beam interference
  fringes
• The distance is controlled by use of a
  three-stage mechanism of increasing sensitivity (
  the coarse control 1µm the medium control 1nm
  a piezoelectric crystal tube 0.1nm )

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Use of SFA

• Identifying and quantifying most of
  fundundamental interactions occuring between
  surfaces on both aqueous solutions and nonaqueous
  liquids
• Including the attractive van der Waaals and
  repulsive electrostatic double layer forces,
  oscillatory forces, repulsive hydration forces,
  attractive hydrophobic forces, steric
  interactions involving polymeric systems and
  capillary and adhesion
• The extension of measurement into dynamic
  interaction and time-dependent effects and the
  fusion of lipid bilayers . etc

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The Atomic Force Microscope(AFM)
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The Atomic Force Microscope(AFM)

• Measuring atomic adhesion forces (10-910-10 N)
  between a fine molecular-sized tip and a surface
  ( 1µm lt Tip radii lt atom size )
• At finite distances, using very sensitive
  force-measuring springs (spring stiffness0.5
  Nm-1) and very sensitive ways for measuring the
  displacement (0.01nm)
• very short-range forces , but not longer range
  forces
• Interpreting the results is not always
  straightforward and exact due to the tip geometry

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THE FORCE LAWS FOR BODIES OF DIFFERENT
GEOMETRIES THE HAMAKER CONSTANT
Van der Waals energies for pairs of bodies of
different geometry
w(r) -C/r6 (for an interatomic
interaction) summation of the energies of all the
atoms in one body with all the aoms in the other
two body potentials for an atom near a
surface, for a sphere near a surface, or for flat
surfaces. For various geometries, the
interaction laws can be expressed in terms of the
conventional Hamaker constant. A p2Cr1r2 (When
the interaction is non-retarded and
additive) Typical values for the Hamaker
constants of condensed phases 10-19J (in
vacuum)
C 8 a2 8 v2 A 8Cr2 8 a2r2 8 v2/v2 8 constant
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THE FORCE LAWS FOR BODIES OF DIFFERENT
GEOMETRIES THE HAMAKER CONSTANT
(1)Find out adhesion force and energy between two
spheres of Radius R 1cm at a gap in between of
0.2 nm, 10nm respectively, A 10-19 J. Find
out the energy for R10nm sphere at the same
separations as above. (2) Find out the surface
energy of van-der Waals solid or liquid. Assume
the maximum approach of solid would be 0.2nm.
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THE LIFSHITZ THEORY OF VAN DER WAALS FORCES
Simple pairwise additivity Definition of A
ignore the influence of neighboring atoms on the
interaction between any pair of atoms. However,
in real system 1. The effective polarizability
of an atom changes when it is surrounded by other
atoms. 2. The existence of multiple
reflections. 3. In a medium
2
1
3
Lifshitz theory the atomic structure is ignored
the forces between large bodies are derived in
terms of bulk properties. All formulars for
VdWs interaction remain valid except using
calculated Hamaker constant.
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THE LIFSHITZ THEORY OF VAN DER VAALS FORCES
The interaction energy of a charge with a
molecule w(r) -C/rn -Q2a2/2(4peoe3)2r4
(a2 the excess polarizability of
molecule 2 in medium 3) When molecule 2 is
replace by medium 2, the interaction between the
charge in medium 3 and the surface of medium 2
W(D) -2pCr2/(n-2) (n-3)D(n-3)
-pQ2r2a2/2(4peoe3)2D ----- (11.2.3)
Then, a charge Q in a medium 3 at a distance D
from the plane surface of a 2nd medium
experiences a force as if there were an image
charge of strength -Q(e2-e3)/(e2e3) at a
distance D on the other side of the boundary.

-Q2 (e2-e3)
-Q2 (e2-e3)
F(D)
W(D)
----- (11.2.5)
(4peoe3)(2D)2(e2e3)
4(4peoe3) D (e2e3)
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THE LIFSHITZ THEORY OF VAN DER VAALS FORCES
Equating Eq. (11.5) with Eq. (11.3)
r2a2 2e2e3(e2-e3)/(e2e3)
Thus, Hamaker constant for the interaction of two
media 1 and 2
A p2Cr1r2
e2(inn) - e3(inn)
e1(inn) - e3(inn)
3kT

e2(inn) e3(inn)
e1(inn) e3(inn)
2
e2(in) - e3(in)
e1(in) - e3(in)
(e1 - e3) (e2 - e3)
3kT
3h


dn
e2(in) e3(in)
e1(in) e3(in)
(e1 e3)(e2 e3)
4
4p
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HAMAKER CONSTANTS CALCULATED ON THE BASIS OF THE
LIFSHITZ THEORY
e2(in) - e3(in)
e1(in) - e3(in)
(e1 - e3) (e2 - e3)
3kT
3h


dn
A
e2(in) e3(in)
e1(in) e3(in)
(e1 e3)(e2 e3)
4
4p
constant
constant
1

e(n)

(1-in/nrot)
(1-in2/ne2)
n2-1
(e-n2)
1

e(in)

(1n2/ne2)
(1n/nrot)
Since n1 gtgt nrot
e(in) 1 (n2-1)/(1n2/ne2)
Hamaker constant for two macroscopic phase 1 and
2 interacting across a medium 3
Ano Angt0 Assume the
absorption frequencies of all three media are
same.
A
(e1 - e3) (e2 - e3)
3hne (n12 - n32) (n22 - n32)
3kT


(e1 e3)(e2 e3)
8 2(n12 n32)1/2 (n22 n32)1/2 (n12 n32)1/2
(n22 n32)1/2
4
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HAMAKER CONSTANTS CALCULATED ON THE BASIS OF THE
LIFSHITZ THEORY
For the symmetric case
(e1 - e3)2
3hne (n12 - n32)2
3kT
Ano Angt0

A

(e1 e3)2
16 2(n12 n32)3/2
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(i) The VdWs force between two identical bodies
in a medium is always attractive, while that
between different bodies in a medium can be
attractive or repulsive (ii) The VdWs force
between any two condensed bodies in vacuum or air
is always attractive. (iii) The Hamaker constant
for two similar media interacting across another
medium remains unchanged if the media are
interchanged.