Lecture 4 Suspension and emulsion stability

1 Suspension and emulsion stability Forces of attraction Steric repulsion Electrostatic repulsion Electrosteric repulsion Lecture 4. ACS 2007. Strength of interparticle forces . Rates of flocculation The time for half the particles to flocculate is: d 3W. t1/ 2 =. Since flocculation is a change in average 8 kT. particle size, the half life can be measured. And W, the stability ratio, determined.. U11 dH. The stability ratio depends on the W = d exp 2. interparticle forces: 0 kT H. Measurements on unstable dispersions showed that particles attract each other over distances comparable to particle sizes. ACS 2007 Lecture 4 - Suspension and emulsion stability 1. Hamaker model - Calculate the attraction between particles from molecular attractions Molecules in Molecules in particle 1 particle 2. H. 3. The intermolecular attraction is the U11 = 11r 6. London (dispersion) energy: 2. ACS 2007 Lecture 4 - Suspension and emulsion stability 2.

2 Hamaker equations for dispersion force attraction For two spheres (per pair): A11d G11 =. 24 H. For two flat plates (per unit area): A11. G11 =. 12 H 2. The A11 are the Hamaker constants. ACS 2007 Lecture 4 - Suspension and emulsion stability 3. Hamaker constants for some materials Substance A11 Polyvinyl acetate Methyl ethyl ketone (10-20 J) Polyvinyl alcohol Water , , Graphite Natural rubber Gold , , Polybutadiene Hexane Polybutene-1 Diethyl ether Silicon carbide 44 Quartz Acetone , Rutile (TiO2) 43 Polyethylene oxide Ethanol Silver , Polyvinyl chloride Ethyl acetate Germanium , Hydrocarbon Polypropylene oxide Chromiun (crystal) Pentane , Copper CaF2 7 PTFE Diamond Potassium bromide Liquid He Zirconia (n-ZrO2) 27 Hexadecane Silicon , Fused quartz Metals (Au, Ag, Cu) 25 40 Polymethylmethacryl Iron oxide (Fe3O4) 21 ate Selenium , Polydimethylsiloxane Aluminum , 14, Potassium chloride Chlorobenzene Cadmium sulfide Dodecane , Tellurium Decane Polyvinyl chloride Toluene Magnesia , 1,4-Dioxane Polyisobutylene n-Hexadecane Mica 10, Octane , Polyethylene Benzene Polystyrene , , n-Tetradecane , , Cyclohexane , Carbon tetrachloride , ACS 2007 Lecture 4 - Suspension and emulsion stability 4.

3 The affect of liquid between the particles The effect of an intervening medium calculated by the principle of Archimedean buoyancy: A121 = A11 + A22 2 A12. Introducing the approximation: A12 = [ A11 A22 ]. 1/ 2. Which leads to: A121 = ( A 1/ 2. 11 A 22 ). 1/ 2 2. and A123 = ( A111/ 2 A22. 1/ 2. )( 33 22 ). A1/ 2. A1/ 2. ACS 2007 Lecture 4 - Suspension and emulsion stability 5. Lifshitz Theory Problem with Hamaker theory: all molecules act independently Lifshitz theory: the attractions between particles are a result of the electronic fluctuations in the particle. What describes the electronic fluctuations in the particle? the absorption spectra: uv-vis-ir Result: nr A123. G123. nr = . 12 H 2. Where the Lifshitz constant depends on the absorption spectra of the solid particles. ACS 2007 Lecture 4 - Suspension and emulsion stability 6. Lifshitz calculations The absorption spectra is measured. Often a single peak in the UV and an average IR is sufficient.

4 That is two amplitudes and two wavelengths. The dielectric spectrum is calculated from the absorption spectrum. The only additional information needed is the static dielectric constant. ACS 2007 Lecture 4 - Suspension and emulsion stability 7. Calculation of Lifshitz constants ( 12 32 ). m The Lifshitz constant is a double summation . 3kT. of products of dielectric functions: A123 =. 2.. n = 0 m =1 m3. The dielectric functions are 1 ( i n ) 2 ( i n ) ( i ) 2 ( i n ). differences in dielectric constants 12 = and 32 = 3 n over a series of frequencies: 1 ( i n ) + 2 ( i n ) 3 ( i n ) + 2 ( i n ). 4 2 kT. The frequencies are: n = n h where k is the Boltzmann constant, T is the absolute temperature, h is Planck's constant, and the prime on the summation indicates that the n = 0. term is given half weight. At 21 C, 1 is 1014 rad/s, a frequency corresponding to a wavelength of light of about m. As n increases, the value of increases and the corresponding wavelength decreases, hence.

5 Takes on more values in the ultraviolet than in the infrared or visible. ACS 2007 Lecture 4 - Suspension and emulsion stability 8. Lifshitz calculation vs measurement Force - separation for TiO2 at the PZC. 100. 50. 0. F/R ( N/m). -50. -100. -150. -200. -10 0 10 20 30 40 50 60. Separation (nm). direction (0) IR(rad/s) CIR UV(rad/s) CUV. perpendicular 86 1 x 10. 14. 80 x 10. 15. Larson, I.; et al 14 15. parallel 170 1 x 10 163 x 10 JACS, 1993, 115,11885-11890. ACS 2007 Lecture 4 - Suspension and emulsion stability 9. Colloidal stability requires a repulsion force: Electrostatically stabilized Sterically stabilized All particles naturally attract each other. Electrical charges or attached polymer layers screen the attraction. ACS 2007 Lecture 4 - Suspension and emulsion stability 10. Steric stabilization ACS 2007. Criterion for Steric Stabilization H. Work is required to push the particles closer together than their polymer layers keep them apart.

6 In thermodynamic terms, this is: G 0 when H < 2t ACS 2007 Lecture 4 - Suspension and emulsion stability 12. Dispersion attraction between spheres A121d For two spheres: G121 =. 24 H. kT. 2t ACS 2007 Lecture 4 - Suspension and emulsion stability 13. Criterion for Steric Stabilization (1st order). A121d Kinetic energy > van der Waals attraction: kT >. 24(2t ). A . or t > 121 d 48kT . A121 (x 1020) J A121/48kT. Oil-water Polystyrene-water Carbon-oil TiO2 water ACS 2007 Lecture 4 - Suspension and emulsion stability 14. Polymer thickness sufficient for steric stabilization t ita n ia / w a t e r c a r b o n / o il p o ly s t y r e n e / w a t e r o il/ w a t e r ACS 2007 Lecture 4 - Suspension and emulsion stability 15. A simple theory for the polymer thickness . Radius of gyration for linear polymers: Rg MW 1/ 2. Molecular weight "Length" (nm). Rg 1,000 2. 10,000 6. 100,000 20. 1,000,000 60. A reasonable assumption is that the surface layer has a thickness equal to the radius of gyration.

7 ACS 2007 Lecture 4 - Suspension and emulsion stability 16. The Size of Polymers in Solution The radius of gyration of a freely-jointed chain, Rg, depends on the l n length of the monomer, l, and the number of monomer units, n: Rg =. 6. or The intrinsic viscosity of a polymer in solution is 1 solution . measured and related to its molecular weight: [ ] = lim . c 0 c . 1 . solvent . [ ] K ( MW ). 1/ 2. where K is gotten from the literature. MW is used to estimate the number of monomer units, n. or c* is the concentration where polymer molecules just fill the volume: 1/ 3. 1 3MW . [ ] = and Rg = No is Avogadro's number c* 4 N 0 c * . ACS 2007 Lecture 4 - Suspension and emulsion stability 17. Steric stabilization for spheres +. Steric G T. repulsion H. Coil diameter Dispersion attraction - ACS 2007 Lecture 4 - Suspension and emulsion stability 18. Configurations of adsorbed polymers Homopolymers Time Random copolymers Brush Anchor Block copolymers Two or three segments are common.

8 Grafted polymers Polymers may be attached to or grown from the surface. ACS 2007 Lecture 4 - Suspension and emulsion stability 19. Polymer Solution Phase Diagram Two phase region Temperature L. One phase region U. Two phase region Concentration Sterically stabilized dispersions are stable when the polymer is soluble the one phase regions. ACS 2007 Lecture 4 - Suspension and emulsion stability 20. Steric stabilization Ethylacetate Aqueous 141 nm silica particles- with grafted polymer. Pictures were taken at 0 C and 60 C. The particles phase-transfer with the change in polymer solubility. ACS 2007 Lecture 4 - Suspension and emulsion stability 21. Electrostatic stabilization ACS 2007. Electrostatic repulsion in aqueous dispersions The loosely held countercharges form electric double layers.. The electrostatic repulsion results from the interpenetration of the double layer around each charged particle. ACS 2007 Lecture 4 - Suspension and emulsion stability 23.

9 Stern's model for a charged particle Potential = exp( H ). - zeta potential e 2 ci zi2. = i Potential D 0 kT. Increased ionic strength Adsorbed surfactant layer 1/ Distance ACS 2007 Lecture 4 - Suspension and emulsion stability 24. The electrostatic repulsion between spheres 32n0 kT d 2. G r = exp( H ). 2. Effect of zeta potential 1. ( i) 0 50 100 150 200. in mV. i ACS 2007 Lecture 4 - Suspension and emulsion stability 25. Electrostatic stability of dispersions*. The total interaction between two spheres is the sum of the electrostatic repulsion and the dispersion attraction: 32n0 kT d 2 A121d + G = T. exp( H ) . 2 24 H. Electrostatic repulsion Total interaction G r H. 0. Secondary minimum *DLVO theory Dispersion attraction Primary minimum - ACS 2007 Lecture 4 - Suspension and emulsion stability 26. stability of dispersions as a function of electrolyte concentration 2000 nm oil drop in water 2000 nm titania particles in water (-100 mV zeta potential @ mM) (-100 mV zeta potential @ mM).

10 400 400. mM. 300 300. 1 mM. Energy (kT). mM. Energy (kT). 200 200. 5 mM. 2 mM. 100 10 mM 100. 3 mM. 0 0. 4 mM. 25 mM. -100 -100. 0 10 20 30 40 50 0 10 20 30 40 50. Distance (nm) Distance (nm). (Corrected from textbook.). ACS 2007 Lecture 4 - Suspension and emulsion stability 27. Critical coagulation concentration What concentration of salt (n0) eliminates the repulsive barrier? Increasing salt concentration Total Energy Separation d G t G t = 0 and =0. H = H0 dH H = H0. ( ) . 11 2 4 3. 4 DkT 2 3 1. n0 (molecules/cm ) =. 3 0. 6. exp ( 4 ) e A121 z 6 2 6. z The Schulze Hardy Rule: the stability depends on the sixth power of the charge on the ions! ACS 2007 Lecture 4 - Suspension and emulsion stability 28. Particle size effect in electrostatic stabilization 32n0 kT d 2 A121d G =. T. exp( H ) . 2 24 H. The larger the particles, the more stable the dispersion! ACS 2007 Lecture 4 - Suspension and emulsion stability 29.