2 Introduction Colloid stability: ability of a colloidal dispersion to avoid coagulation.Kinetic vs thermodynamic parameters.Two kinds of induced stability:(1) Electrostatic induced stability:(like) charges, repelvan der Waal’s forces, attract+verepulsivestableV-veattractiveunstableH=particle separation
3 (2) Polymer induced or Steric Stability: Stability is a result of a steric effect,where the two polymer layers oninteracting particles overlap andrepel one another.
4 Interparticle Repulsion Goal is to calculate repulsive potentialVR between two particlesYdHTwo possibilities for Y:Due to adsorption of charged speciesY remains constant, s decreasesDue to intrinsic charge on the particless constrained to remain constant,Y increases as overlap increases
5 Derjaguin Approximation Approximate sphere by a set of “rings”Assumes:Constant potential case.Sphere radius much larger thandouble layer thickness, ka>10.NO assumptions on potentials.dHa1a2Hlow potentials (D-H approx.)both particles the same.
6 Summary Simplest form of repulsive interaction: spherical like particleslow potentialslarge interparticle distances.As k increases, repulsion decreases, destabilisation occurs:increase in electrolyte concentrationincrease in counter-ion charge.Like charged particles stabilise, unlike charges destabilise.
7 Interparticle Attraction Van der Waal’s forces: exist for all particlesatom-sized and up.permanent dipole-permanent dipoleKeesom interactionpermanent dipole-induced dipoleDebye interactioninduced dipole-induced dipoleLondon or dispersion interactionALWAYS PRESENTalways attractive (?)long range ( nm)
8 Form of van der Waal’s Interactions (single particle)b includes contributions from London,Keesom and Debye forces.b = f(polarizability, dipole moment)Relative contributions:Compound m a b % % %Debye x1030 m3 x1077 Jm6Keesom Debye London
9 Van der Waal’s interactions between two particlesMust sum over each volume elementof a large particle -- introduces error!For two spheres close together (H<<a):Equal SpheresUnequal SpheresHamaker Constant!where...units of Joules
10 Hamaker constant determined by both polarizability and dipole moment ofmaterial in question...Material A(x 1020 J)Means of measuringdetermine froma and m(approximate and not always possible to get values)Measure using bulk properties:Surface tension is an obvious one
11 Direct Measurement of forces This is a difficult thing to do...Insert Fig here
13 Solvent Effects Previous results were in vacuum. Presence of a solvent between particleswill affect the overall Hamaker constant:3solvent3solvent123solvent3solvent12
14 Net result:If particles are the same reduces to...If particles are the same…Aeff is always positive -- i.e attractive.If A’s are similar, attraction is weak.If particles are different…Aeff is positive if A33>A11,A22 or A33< A11,A22 attractive.Aeff is negative if A11<A33<A22 i.e. repulsive interaction if the solvent Hamaker constant is intermediate to those of the particles.
15 Electrostatic Stabilisation We may combine the two expressions forthe potential experienced as follows…Effects of changing ALeast control, setby system.Effective overlong range.A=2x10-20 J5x10-20 J1x10-19 J2x10-19 JY = 100 mVk = 1x108 m-1a = 100 nm
16 Effects of changing Y (i.e. g): Much shorter rangeeffect.More effective at lowvalues of Y.Experimentally,we measure thezeta potential.A = 2x10-19 Jk = 1x108 m-1a = 100 nm
17 Effects of changing k (i.e. electrolyte concentration): This is the itemwe have mostcontrol over!Affects potentialsat short distances.For a 1:1 electro-lyte, the transitionis aboutmolar.A = 2x10-19 JY = 25 mVa = 100 nm
18 Critical Coagulation Concentration The Schulze-Hardy Rule C.C.C. is fairly ill-defined:The concentration of electrolyte which is just sufficient to coagulate a dispersion to an arbitrarily chosen extent in an arbitrarily defined time.At the C.C.C:dV/dH = 0 at V= 0VH
19 Assuming a symmetrical electrolyte (i.e. z+ = z-):As Y becomes large g®1small g®ze Y/4kTThus:c.c.c.µ 1/z6 at high potentialsc.c.c. µ 1/z2 at low potentialsEffect is independent of particle size!Strongly dependent on temperature!
20 Critical Coagulation Concentrations (mmol/L)Stronger dependency is typical ofadsorption in the Stern layer: softerspecies tend to adsorb better (morepolarizable) so have a slightlystronger effect.Any potential determining ion willhave a significant effect.
21 Kinetics of Coagulation No dispersion is stable thermodynamically.Always a potential well.Two steps in mechanism:(1) Colloids approach one anotherdiffusion controlled: perikinetic.externally imposed velocitygradient: orthokinetic(e.g. sedimentation, stirring, etc.).(2) Colloids stick to one another(assume probability of unity).Two forces then controlling approach:(1) Rapid diffusion controlled.(2) Interaction-force controlled(potential barrier, slows approach).
22 The Stability Ratio W= Rate of diffusion-controlled collision Rate of interaction-force controlled collisionW = large : particles are relatively stable.W = 1 : rate unhindered, particles unstable.Diffusion-controlled (Rapid) Rate:RR1R2R1+R2
23 Fick’s Second law can now be used: Which can be used to show that foridentical particles, the collision rate:Since 2 particles are involved, the reactionfollows second order kinetics:Thus, the rate constant is given by:Only binary collisionsoccur (dilute solution).Neglect solvent flow outof gap.For second relationshipStokes-Einstein is used.
24 The stability ratio can thus be given by: kslow will depend upon the potentialaround the particles.Can acquire an expression for kslow bymodifying Fick’s second law with an“activation energy”, V(R), where V(R)is the potential barrier previously dicussed.
25 Assume a (very simple) barrier such as the following...VVmax2a k-1particlestouchThen…
26 Critical Coagulation Concentration Can solve previous simple expressionfor W in terms of Vmax, determined fromwhen dV/dH = 0For water as dispersion mediumAgI Particle Coagulation
27 Plot is linearWhen log W =0 we are at the CCC, breaks in the curve appear as coagulation occurs at a rapid rate.Coagulation rates cannot be measured in this system beyond about log W = 4. Corresponds to an energy barrier of about 15 kT.Can use the slopes to analyze for Yo, if the particle size is known.