Colloidal Stability Introduction Interparticle Repulsion Interparticle Attraction Hamaker constant Measurement techniques Solvent Effects Electrostatic Stabilisation Critical Coagulation Concentration Kinetics of Coagulation

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, repel van der Waal’s forces, attract +ve repulsive stable V -ve attractive unstable H=particle separation

(2) Polymer induced or Steric Stability: Stability is a result of a steric effect, where the two polymer layers on interacting particles overlap and repel one another.

Interparticle Repulsion Goal is to calculate repulsive potential VR between two particles Yd H Two possibilities for Y: Due to adsorption of charged species Y remains constant, s decreases Due to intrinsic charge on the particles s constrained to remain constant, Y increases as overlap increases

Derjaguin Approximation Approximate sphere by a set of “rings” Assumes: Constant potential case. Sphere radius much larger than double layer thickness, ka>10. NO assumptions on potentials. dH a1 a2 H low potentials (D-H approx.) both particles the same.

Summary Simplest form of repulsive interaction: spherical like particles low potentials large interparticle distances. As k increases, repulsion decreases, destabilisation occurs: increase in electrolyte concentration increase in counter-ion charge. Like charged particles stabilise, unlike charges destabilise.

Interparticle Attraction Van der Waal’s forces: exist for all particles atom-sized and up. permanent dipole-permanent dipole Keesom interaction permanent dipole-induced dipole Debye interaction induced dipole-induced dipole London or dispersion interaction ALWAYS PRESENT always attractive (?) long range (0.2 - 10 nm)

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

Van der Waal’s interactions between two particles Must sum over each volume element of a large particle -- introduces error! For two spheres close together (H<<a): Equal Spheres Unequal Spheres Hamaker Constant! where... units of Joules

Hamaker constant determined by both polarizability and dipole moment of material in question... Material A (x 1020 J) Means of measuring determine from a and m (approximate and not always possible to get values) Measure using bulk properties: Surface tension is an obvious one

Direct Measurement of forces This is a difficult thing to do... Insert Fig. 1.27 here

Solvent Effects Previous results were in vacuum. Presence of a solvent between particles will affect the overall Hamaker constant: 3 solvent 3 solvent 1 2 3 solvent 3 solvent 1 2

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.

Electrostatic Stabilisation We may combine the two expressions for the potential experienced as follows… Effects of changing A Least control, set by system. Effective over long range. A=2x10-20 J 5x10-20 J 1x10-19 J 2x10-19 J Y = 100 mV k = 1x108 m-1 a = 100 nm

Effects of changing Y (i.e. g): Much shorter range effect. More effective at low values of Y. Experimentally, we measure the zeta potential. A = 2x10-19 J k = 1x108 m-1 a = 100 nm

Effects of changing k (i.e. electrolyte concentration): This is the item we have most control over! Affects potentials at short distances. For a 1:1 electro- lyte, the transition is about 10-2 - 10-3 molar. A = 2x10-19 J Y = 25 mV a = 100 nm

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= 0 V H

Assuming a symmetrical electrolyte (i.e. z+ = z-): As Y becomes large g®1 small g®ze Y/4kT Thus: c.c.c.µ 1/z6 at high potentials c.c.c. µ 1/z2 at low potentials Effect is independent of particle size! Strongly dependent on temperature!

Critical Coagulation Concentrations (mmol/L) Stronger dependency is typical of adsorption in the Stern layer: softer species tend to adsorb better (more polarizable) so have a slightly stronger effect. Any potential determining ion will have a significant effect.

Kinetics of Coagulation No dispersion is stable thermodynamically. Always a potential well. Two steps in mechanism: (1) Colloids approach one another diffusion controlled: perikinetic. externally imposed velocity gradient: 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).

The Stability Ratio W= Rate of diffusion-controlled collision Rate of interaction-force controlled collision W = large : particles are relatively stable. W = 1 : rate unhindered, particles unstable. Diffusion-controlled (Rapid) Rate: R R1 R2 R1+R2

Fick’s Second law can now be used: Which can be used to show that for identical particles, the collision rate: Since 2 particles are involved, the reaction follows second order kinetics: Thus, the rate constant is given by: Only binary collisions occur (dilute solution). Neglect solvent flow out of gap. For second relationship Stokes-Einstein is used.

The stability ratio can thus be given by: kslow will depend upon the potential around the particles. Can acquire an expression for kslow by modifying Fick’s second law with an “activation energy”, V(R), where V(R) is the potential barrier previously dicussed.

Assume a (very simple) barrier such as the following... V Vmax 2a k-1 particles touch Then…

Critical Coagulation Concentration Can solve previous simple expression for W in terms of Vmax, determined from when dV/dH = 0 For water as dispersion medium AgI Particle Coagulation

Plot is linear When 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.