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Colloidal Stability Introduction Interparticle Repulsion Interparticle Attraction Hamaker constant Measurement techniques Solvent Effects Electrostatic.

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Presentation on theme: "Colloidal Stability Introduction Interparticle Repulsion Interparticle Attraction Hamaker constant Measurement techniques Solvent Effects Electrostatic."— Presentation transcript:

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

2 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

3 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.

4 Interparticle Repulsion Goal is to calculate repulsive potential V R between two particles H dd 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

5 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.

6 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.

7 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 ( nm)

8 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)

9 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<

10 Hamaker constant determined by both polarizability and dipole moment of material in question... Material A (x 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

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

12

13 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

14 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

15 Electrostatic Stabilisation We may combine the two expressions for the potential experienced as follows…  = 100 mV  = 1x10 8 m -1 a = 100 nm A=2x J 5x J 1x J 2x J Effects of changing A Least control, set by system. Effective over long range.

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

17 Effects of changing  (i.e. electrolyte concentration): A = 2x 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 molar.

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

19 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!

20 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)

21 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).

22 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

23 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.

24 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.

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

26 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

27 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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