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

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Introduction Colloid stability: ability of a colloidal dispersion to avoid coagulation. Kineticthermodynamic Kinetic vs thermodynamic parameters. Two kinds of induced stability: Electrostatic (1) Electrostatic induced stability: (like) charges, repel van der Waal’s forces, attract V +ve repulsive stable -ve attractive unstable 0 H=particle separation

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Steric Stability (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.

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

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Derjaguin Approximation Approximate sphere by a set of “rings” Assumes: Constant potential case. Sphere radius much larger than double layer thickness, a>10. NO assumptions on potentials. H a1a1 dH a2a2 low potentials (D-H approx.) both particles the same.

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

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

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Form of van der Waal’s Interactions includes contributions from London, Keesom and Debye forces. = f(polarizability, dipole moment) Relative contributions: Compound % % % Debye x10 30 m 3 x10 77 Jm 6 Keesom Debye London (single particle)

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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<
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Hamaker constant determined by both polarizability and dipole moment of material in question... Material A (x 10 20 J) Means of measuring determine from and (approximate and not always possible to get values) Measure using bulk properties: Surface tension is an obvious one

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

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Solvent Effects Previous results were in vacuum. Presence of a solvent between particles will affect the overall Hamaker constant: 3 solvent 3 solvent 3 solvent 3 solvent 1 12 2

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Net result: If particles are the same reduces to... If particles are the same… A eff is always positive -- i.e attractive. If A’s are similar, attraction is weak. If particles are different… A eff is positive if A 33 >A 11,A 22 or A 33 < A 11,A 22 attractive. A eff is negative if A 11
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Electrostatic Stabilisation We may combine the two expressions for the potential experienced as follows… = 100 mV = 1x10 8 m -1 a = 100 nm A=2x10 -20 J 5x10 -20 J 1x10 -19 J 2x10 -19 J Effects of changing A Least control, set by system. Effective over long range.

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Effects of changing (i.e. ): Much shorter range effect. More effective at low values of Experimentally, we measure the zeta potential. A = 2x10 -19 J = 1x10 8 m -1 a = 100 nm

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Effects of changing (i.e. electrolyte concentration): A = 2x10 -19 J = 25 mV a = 100 nm 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.

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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. 0 V H At the C.C.C: dV/dH = 0 at V= 0

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Assuming a symmetrical electrolyte (i.e. z + = z - ): As becomes large 1 small ze /4kT Thus: c.c.c. 1/z 6 c.c.c. 1/z 6 at high potentials c.c.c. 1/z 2 c.c.c. 1/z 2 at low potentials Effect is independent of particle size! Strongly dependent on temperature!

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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. Critical Coagulation Concentrations (mmol/L)

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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).

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The Stability Ratio 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 R1R1 R2R2 R 1 +R 2

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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.

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

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Assume a (very simple) barrier such as the following... V V max 2a -1 0 particles touch Then…

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

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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 o, if the particle size is known.

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