10.3 effective interaction area of two spheres : the langbein approximation the effective area of...
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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
distance–D from the surfaces( inside the sphere )
RD
)n/(RDAeff
2
52
The interaction of a sphere and a surface = the same as that of two planar surfaces at the
same surface separation D
for n=6
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
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
6740 /C.)D(w
661 /C.)D(w
In contact b/n two spheres
Increasing of the size of a sphere above atomic dimensions
680 /C.)D(w
6261 /C)/R(.)D(w
10.5 Interaction Energy and Interaction Forces : Derjagun Approximation
[ Assumption ] Two large spheres of radii
R1 and R2
R1>>D and R2>>D
By integrating the force
between small circular
regions of area on one
surface
Surface to be locally flat
10.5 Interaction Energy and Interaction Forces : Derjagun Approximation
1. The force b.t.n two spheres is expressed in terms of the ener
gy per unit area of two flat surfaces at the same separation D
2. The distance dependence of the force b.t.n two curved surfac
es can be quite different from that b.t.n two surfaces even th
ough the same type of force is operating in both.
)D(WRR
RR)D(F
21
212
Fig. 10. 4 Force laws betweem two curved surfaces and two flat surfaces
16.1 Indirect access for W(D)
Thermodynamic data on gases, liquids and
solids
Physical data on gases, liquids and
solids
Thermodynamic data on liquids and liquid
mixtures
PVT data, B.PLatent heats of vaporizationlattice energy
Viscosity, diffusion. Compressibility, NMR X-ray, molecular beam scattering experiment
Phase diagrams solubilityPartitioning, miscibilityosmotic pressure
Short-range attractive potentials b.t.n molecules
Short-range interactions of molecules, especially repulsive forces giving molecular size, shape and structural role in condensed phase
Short-range silute-solvent and solute-solute interactions
16.2 Direct access for W(D)
16.2 Direct access for W(D)
Types Practical Applications Information
Adhesion measurement
Xerography, particle adhesion. Powder technology, ceramic processing
Particle adhesion forces and the adhesion energies of solid surfaces in contact ( attractive short-range forces)
Peeling measurement
Adhesive tapes, material fracture and crack propagation
Force-measuring spring or balance
Testing theories of intermolecular forces
The force macroscopic surfaces as a function of surface separation The full force law of an interaction
16.2 Direct access for W(D)
Types Practical Applications Effects
Contact AngleTesting wettability and stability of surface films, foams
Liquid-Liquid or Liquid-Solid adhesion energyInformation of states and adsorbed films, and of molecular reorientation time at interfaces
Equilibrium thickness of thin free films
Soap films, foams
A function of salt conc. or vapour pressureThe long-range repulsive forces stabilizing thick wetting films
Equilibrium thickness
of thin absorbed films
Wetting of hydrophilic surface by water, adsorption of molecules from vapor, protective surface coatings and lubricant layers, photographic films
16.2 Direct access for W(D)
Types Practical Applications Effects
Interparticle spacing in liquids
Colloidal suspensions, paints, pharmaceutical dispersions
The interparticle forces By changing the solution conditions and their mean separation By changing the quantity of solventsLimits to measure only the repulsive parts
Sheet-like particle spacing in liquids
Clay and soil swelling behavior, microstructure of soaps and biological membranes
Coagulation studies
Basic experimental technique for testing the stability of colloidal preparations
Information on the interplay of repulsive and attractive forces between particles in pure, sulfactant and polymer solutions
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
The Surfaces Forces Apparatus (SFA)
1. Measuring surface forces in controlled vapor or immersed in liquids is directly measured using a variety of interchangeable force-measuring springs
2. Both repulsive and attractive forces are measuring and a full force law can be obtained over any distance regimes
The Surfaces Forces Apparatus (SFA)
3. The distance resolution about 0.1nm (angstrom level)
the force sensitivity about 10-8 N
4. In Surfaces
a. Two curved molecularly smooth surfaces of mica in a crossed cylinder configuration
b. The separation is measured by use of an optical technique using multiple beam interference fringes
c. 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 )
The Surfaces Forces Apparatus (SFA)
5. The force measurement
a. The force A measured by expanding or contracting the
piezoelectric crystal by a known amount
b. The force B measured by optically how much the two
surfaces have actually moved
c. The difference of force b.t.n two positions
= [ Force A – force B ] * the stiffness of the force-
measuring spring
The Surfaces Forces Apparatus (SFA)
6. The force and the interfacial energy
a. The force b.t.n two curved surfaces scale = R
b. The adhesion or interfacial energy E per unit area two flat su
rfaces
by the Derjaguin approximation
c. For given R and sensitivity F,
getting E ( an interfacial energy)
R/FE 2
The Surfaces Forces Apparatus (SFA)
7. The use of SFA
a. Identifying and quantifying most of fundundamental interactions occuring between surfaces on both aqueous solutions and nonaqueous liquids
b. 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
c. The extension of measurement into dynamic interaction and time-dependent effects and the fusion of lipid bilayers . etc
Total Internal Reflection Microscopy(TIRM)
1. Measuring minute forces( <10-15 N) between a colloidal particle and a surface
2. Measuring the distance between an individual colloidal particle of diameter ~10 µm hovering over a surface.
3. A laser beam is directed at the particle through the surface made of transparent glass
4. From the intensity of reflected beam
deducing the equilibrium separation D0
5. Providing data on interparticle interactions under conditions closely paralleling those occurring in colloidal systems
The Atomic Force Microscope(AFM)
1. Measuring atomic adhesion forces (10-9~10-10 N) between a
fine molecular-sized tip and a surface ( 1µm < Tip radii <
atom size )
2. At finite distances, using very sensitive force-measuring
springs (spring stiffness=0.5 Nm-1) and very sensitive ways
for measuring the displacement (0.01nm)
3. very short-range forces , but not longer range forces
4. Interpreting the results is not always straightforward and
exact due to the tip geometry
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