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