Chap'910 Intermolecular and interparticle Forces

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Chap.910 Intermolecular and interparticle Forces

• Dept. of Chemical Biomolecular Engineering,
  KAIST
• 2? ???, ???, ???

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9.1 Factors favoring the association of like
molecules or particles in a medium

• Intermolecular versus intramolecular bonds
• Intermolecular attractions
• attractions between one molecule and
• a neighboring molecule
• Intramolecular attractions
• attraction which hold an individual molecule
• together (for example, the covalent bonds)

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• ? For the binding energies of molecules A and B
  in contact
• WAA - A2 , WBB - B2 ( for like molecules )
• WAB - AB ( for unlike molecules )
• Where only for the purely Coulombic charge-charge
  interaction are the negative signs reversed

Dispersed state Wdisp - (3A23B218AB)
Associated state Wass - 12(A2B2)
? W Wass Wdisp - 9(A - B)2
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Dispersed Wdis -2AB
Associated Wass -(A2 B2)
?W -(A-B)2
Dispersed Wdis -2NAB
Associated Wass -2(N-n)AB-nA2-nB2
?W -n(A-B)2
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Generally

• ? For the binding energies of molecules A and B
  in contact
• ?W Wass-Wdisp -n(A-B)2
• n equal to the number of like bonds that
  have been formed in the process of association
• ?W lt 0 ( or Wasslt Wdisp ) lt (A-B)2 gt O
• ? There is always an effective attraction between
  like molecules or particles in a binary mixture.

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• ? For the interactions of like solute molecules
  and particles in a medium
• ?W -n(A-B)2 -n(v-WAA-v-WBB)2
• -n(A2B2-2AB) n(WAAWBB-2WAB)
• ?W ? -(vUA-vUB)2
• ?W the same as the interaction pair potential
  w(s) in the medium ( at contact )
• Reciprocity property for the specific case of
  van der Waals forces (?W /n)
• The interaction of two solute molecules in a
  solvent medium is coupled to the strength of the
  solvent-solvent interaction
• -nWAA, -nWBB Proportional to molar cohesion
  energies UA and UB

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Important Exceptions

• 1) for the Coulomb interaction between charged
  atoms or ions the dispersed state is favored
• ( since the sign of ?W is reversed )
• ex ) ionic crystals ( NaCl- )
• 2) H-bonding molecules the strength of the H
  bond between two different molecules cannot be
  expressed in terms of WAB -AB
• ex ) acetone molecules not form H bonds with
  another acetone molecule, but do so with water
  via its CO group
• ? miscible with water

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9.2 Two like surfaces coming together in a
medium surface and interfacial energy

• ? For two flat surfaces of A, each of unit area,
  in a liquid B
• ?W -2?AB
• ?AB the interfacial energy of the A-B interface
  (positive)
• ? Important thermodynamic relation valid for both
  solid and liquid interfaces
• ?AB ?A ?B WAB per unit area (?AB
  ?BA)
• ?AB ?A ?B - 2 v?A ?B (v ?A - v ?B)2
• ? Used to estimate the interfacial energy ?AB
  solely from the surface energies or surface
  tensions of the pure liquids, ?A and ?B, in the
  absence of any data on the energy of adhesion WAB

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9.3 Factors favoring the association of unlike
molecules, particles or surfaces in a third medium
? For two unlike molecules or particles A and B
coming together in the solvent medium composed of
molecules of type C ? The associated state of
like molecules has a lower energy than either (a)
or (b)
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?W Wass-Wdisp ?-AB-C2ACBC ?-(A-C)(B-C)

• If C is intermediate between A and B, two
  particles (or surfaces) will repel each other (
  van der Waals forces )
• - the most favored final state will be that of
  particles A associating with particles A, B with
  B and C with C.
• ? Extended to mixtures with more species
• There is always an effective attraction between
  like molecules or particles in a multicomponent
  mixture.
• Unlike particles may attract or repel each other
  in al solvent.

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9.4 Particle-surface interactions

• ? For a particle C near an interface dividing two
  immiscible liquid media A and B

?) Desorption the particle is repelled from the
interface on either side of it (negative
adsorption) ?) Adsorption the particle is
attracted to the interface from either side ?)
and ?) Engulfing the particle is attracted from
one side (left or right) but repelled from the
other (right or left)
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Schematic energy versus distance profiles
(assumed monotonic) for ?W ToTlt0
lt Note gt medium A solid ? particle C will
adsorb on it from B since it cannot be engulfed
by A
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• AgtCgtB or AltCltB the particle will be attracted
  to the interface from either side, leading to
  adsorption
• AgtBgtC or AltBltC ( B intermediate) the particle
  will be attracted to the interface from the left
  but repelled from the right (engulfing)
• BgtAgtC or BltAltC (A intermediate) it will be
  attracted from the right but repelled from the
  left (reverse engulfing or ejection)
• Negative adsorption from both sides cannot occur
  and that either adsorption or engulfing will be
  the rule

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9.5 Adsorbed surface films wetting and
non-wetting

• ? For the formation of thick adsorbed films on a
  solid surface
• (b) Wetting an adsorbed film of C develops and
  grows in thickness as the concentration of C in B
  approaches saturation (cos? gt1)
• (c) Unwetting resulting from repulsion between
  C and A in medium B above saturation (cos? lt-1)
• (d) Partial wetting intermediate case between
  the two above (-1 lt cos? lt1)

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• ? When the total surface energies of the whole
  system is minimized, the contact angle ? formed
  by these droplets is given by
• cos? (BC-2A)/(B-C)
• _at_ 0olt?lt180o only when A is intermediate between
  B and C
• ?AC ?BC cos? ?AB (Young equation)
• ?BC (1cos?) ?WABC ( Young-Dupre equation)
• ?WABC the adhesion energy per unit areas of
  surfaces A and C adhering in medium B.

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Finally

• Two particles or surfaces may have an adhesive
  energy minimum at contact
• If the force law is not monotonic the particles
  will remain separated
• ? repulsive before it becomes attractive closer
  in
• (i.e., they effectively repel each other).

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10. Interaction of Macroscopic particles or
Surfaces

• The net interaction energy is proportional to
  the size of the particles and very much larger
  than kT even at separations of 100nm or more
• Energy and Force decays much more slowly with
  the separation
• All manner of behavior depends on the specific
  form of the long-range distance dependence ( Fig.
  10 )
• The Particles can be trapped in some kinetic or
  metastable state due to sufficiently high energy
  barrier

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Fig. 10.1 Typical Interaction potentials
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10.2.1 Molecules - Surface Interaction

• The net interaction energy of a molecule and the
  planar
• surface of a solid made up of like molecules will
  be the sum of
• its interaction with all the molecules in the
  body

(For ngt3)
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10.2.2 Sphere - Surface and Sphere Sphere
Interactions

• For D gtgt R

• For D ltlt R

• n6

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10.2.3 Surface Surface Interaction

• n6

Per unit area
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10.3 Effective interaction Area of two spheres
The Langbein Approximation

• The effective area of interaction of a sphere
• with a surface the circular zone centred at a
• distanceD from the surfaces( inside the sphere )

for n6
The interaction of a sphere and a surface
the same as that of two planar surfaces at the
same surface separation D
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10.4 Interactions of large bodies compared to
those between molecules

• For two macroscopic bodies, the interaction
  energy generally decays much more slowly with
  distance
• ? the van der Waals energy between large
  condensed bodies decays is effectively of much
  longer range

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10.4 Interactions of large bodies compared to
those between molecules

• In contact b/n a small molecule and a wall
• In contact b/n a sphere of atomic dimensions

• In contact b/n two spheres
• Increasing of the size of a sphere above atomic
  dimensions

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10.5 Interaction Energy and Interaction Forces
Derjagun Approximation

• Assumption
• Two large spheres of radii R1 and R2
• R1gtgtD and R2gtgtD
• By integrating the force between small circular
  regions of area on one surface
• Surface to be locally flat

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10.5 Interaction Energy and Interaction Forces
Derjagun Approximation

• The force b.t.n two spheres is expressed in
  terms of the energy per unit area of two flat
  surfaces at the same separation D
• The distance dependence of the force b.t.n two
  curved surfaces can be quite different from that
  b.t.n two surfaces even though the same type of
  force is operating in both.

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Fig. 10. 4 Force laws betweem two curved
surfaces and two flat surfaces
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16.1 Indirect access for W(D)
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16.2 Direct access for W(D)
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16.2 Direct access for W(D)
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16.2 Direct access for W(D)
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16.2 Direct access for W(D)
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10.7 Direct measurements of Surface and
Intermolecular Forces

• The most unambiguous way to measure a force-law
• ? to position two bodies close together and
  directly measure the force between them
• ? very straightforward
• ? very weak challenge coming at very small
  intermolecular interaction
• ? surface separation controlled and measured to
  within 0.1nm

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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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The Surfaces Forces Apparatus (SFA)

• The force measurement
• The force A measured by expanding or contracting
  the piezoelectric crystal by a known amount
• The force B measured by optically how much the
  two surfaces have actually moved
• The difference of force b.t.n two positions
• Force A force B the stiffness of the
  force-measuring spring

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The Surfaces Forces Apparatus (SFA)

• The force and the interfacial energy
• The force b.t.n two curved surfaces scale R
• The adhesion or interfacial energy E per unit
  area two flat surfaces
• by the Derjaguin approximation
• For given R and sensitivity F,
• getting E ( an interfacial energy)

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The Surfaces Forces Apparatus (SFA)

• The 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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Total Internal Reflection Microscopy(TIRM)

• Measuring minute forces( lt10-15 N) between a
  colloidal particle and a surface
• Measuring the distance between an individual
  colloidal particle of diameter 10 µm hovering
  over a surface.
• A laser beam is directed at the particle through
  the surface made of transparent glass
• From the intensity of reflected beam
• ?deducing the equilibrium separation D0
• Providing data on interparticle interactions
  under conditions closely paralleling those
  occurring in colloidal systems

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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