Steric stabilization i the role of polymers

Transcription

1 Steric stabilization i the role of polymers Dispersions in liquids: suspensions, emulsions, and foams ACS National Meeting March 21 22, 2009 Salt Lake City Ian Morrison 2009

2 Ian Morrison 2009 Lecture 4 - Steric stabilization 1

3 Rates of flocculation Strength of interparticle forces The time for half the particles to flocculate is: 3 ηπ dw t 1/2 = 8 Φ kt Since flocculationl is achange in average particle size, the half life can be measured. And W, the stability ratio, be determined. The stability ratio depends on the interparticle forces: W 11 exp U = d kt 0 dh 2 H Ian Morrison 2009 Lecture 4 - Steric stabilization 2

4 Theories of dispersion energies Using a perturbation theory to solve the Schroedinger equation for two atoms, London found: Λab U( r) = 6 r hνahν b where Λ ab = αaαb hνa + hνb ν is a characteristic frequency and α is polarizability Casimir and Polder refined the theory to account for the finite speed of light, c: ( ) U r = 2 23hcα 2 7 4π r This retardation diminishes the attraction. F. London, The general theory of molecular forces, Trans. Faraday Soc., 33, 8, Casimir and Polder, Phys. Rev. 73, 360, Ian Morrison 2009 Lecture 4 - Steric stabilization 3

5 Hamaker model for the attraction between particles The intermolecular attraction is due 6 U to London (dispersion) energies: 11 = Λ11r 3 2 r Molecules l in particle 1 Molecules in particle 2 H Ian Morrison 2009 Lecture 4 - Steric stabilization 4

6 Hamaker equations for dispersion force attraction For two spheres (per pair): 11 Δ G A d 11 = 24H The A 11 are the Hamaker constants. For two flat plates (per unit area): A Δ G = 12π H Ian Morrison 2009 Lecture 4 - Steric stabilization 5

7 Hamaker constants for some materials Substance A 11 (10-20 J) Graphite 47.0 Gold 45.3, 45.5, 37.6 Silicon carbide 44 Rutile (TiO 2 ) 43 Silver 39.8, 40.0 Germanium 29.9, 30.0 Chromiun 29.2 Copper 28.4 Diamond 28.4 Zirconia (n-zro 2 ) 27 Silicon 25.5, 25.6 Metals (Au, Ag, Cu) Iron oxide (Fe 3 O 4 ) 21 Selenium 16.2, 16.2 Aluminum 15.4, 14, 15.5 Cadmium sulfide 15.3 Tellurium 14.0 Polyvinyl l chloride Magnesia 10.5, 10.6 Polyisobutylene Mica 10, 10.8 Polyethylene 10.0 Polystyrene 9.80, 6.57, , , 7.81 Polyvinyl acetate 8.91 Polyvinyl alcohol 8.84 Natural rubber 8.58 Polybutadiene 8.20 Polybutene Quartz 7.93 Polyethylene oxide 7.51 Polyvinyl chloride 7.5 Hydrocarbon 7.1 (crystal) CaF 2 7 Potassium bromide 6.7 Hexadecane 6.31 Fused quartz 6.3 Polymethylmethacryl 6.3 ate Polydimethylsiloxane 6.27 Potassium chloride 6.2 Chlorobenzene 5.89 Dodecane 5.84, 5.0 Decane 5.45 Toluene ,4-Dioxane 5.26 n-hexadecane 5.1 Octane 5.02, 4.5 Benzene 5.0 n-tetradecane 5.0 Cyclohexane , Carbon tetrachloride 4.78, 5.5 Methyl ethyl ketone 4.53 Water 4.35, 3.7, 4.38 Hexane 4.32 Diethyl ether 4.30 Acetone 4.20, 4.1 Ethanol 4.2 Ethyl acetate 4.17 Polypropylene py oxide 3.95 Pentane 3.94, 3.8 PTFE 3.8 Liquid He Ian Morrison 2009 Lecture 4 - Steric stabilization 6

8 The affect of liquid between the particles The effect of an intervening medium calculated by the principle of Archimedean buoyancy: A = A + A 2A Introducing the approximation: A [ A A ] 1/ Which leads to: ( 1/2 1/2 ) 2 A = A A and ( 1/2 1/2 )( 1/2 1/2 ) A = A A A A Ian Morrison 2009 Lecture 4 - Steric stabilization 7

9 Lifshitz theory Limitation of Hamaker theory: Lifshitz theory: all molecules act independently the attractions between particles are a result of the electronic fluctuations in the particle. What describes the electronic fluctuations in the particle? Result: the absorption spectra: uv-vis-ir A Δ G = 12π H nr nr The Lifshitz constant depends on the absorption spectra of the particles. Ian Morrison 2009 Lecture 4 - Steric stabilization 8

10 Data for Lifshitz calculations The absorption spectra is measured. Often a single peak in the UV and an average IR is sufficient. 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. Ian Morrison 2009 Lecture 4 - Steric stabilization 9

11 Lifshitz calculations The Lifshitz constant is a double summation of products of dielectric functions: A 3kT = ( ) Δ Δ n = 0 m = 1 m m The dielectric functions are ε1( iξn) ε2( iξn) ε3( iξn) ε2( iξn differences in dielectric constants ) Δ 12 = and Δ 32 = over a series of frequencies: ε 1 ( i ξ n ) +ε 2 ( iξ n ) ε 3 ( iξ n ) +ε 2 ( iξ n ) The frequencies are: ξ = n n 2 4π kt 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, ξ 1 is rad/s, a frequency corresponding to a wavelength of light of about 1.2 µm. As n increases, the value of ξ increases and the corresponding wavelength decreases, hence ξ takes on more values in the ultraviolet than in the infrared or visible. Ian Morrison 2009 Lecture 4 - Steric stabilization 10

12 Lifshitz calculation vs measurement Force - separation for TiO 2 at the PZC F/R (μn/m) Separation (nm) direction ε(0) ω IR (rad/s) C IR ω UV (rad/s) C UV perpendicular 86 1 x x parallel x x Larson, I.; et al JACS, 1993, 115, Ian Morrison 2009 Lecture 4 - Steric stabilization 11

13 Colloidal stability requires a repulsion force: Electrostatically stabilized Sterically stabilized Ian Morrison 2009 Lecture 4 - Steric stabilization 12

14 Steric stabilization Work is required to push polymer layers into each other. H When H < 2 t then ΔG 0 Ian Morrison 2009 Lecture 4 - Steric stabilization 13

15 Dispersion attraction between spheres Δ G = 121 A121 d 24H kt 2t Ian Morrison 2009 Lecture 4 - Steric stabilization 14

16 Criterion for Steric Stabilization (1 st order) kt > A d 24H The kinetic energy must be greater than the attractive energy: 121 Especially when the polymer layers just touch: For example: or t > A121 48kT d kt > A 121 d 48t A 121 (x ) J A 121 /48kT Oil-water Polystyrene-water Carbon-oil TiO 2 water Ian Morrison 2009 Lecture 4 - Steric stabilization 15

17 Polymer thickness for steric stabilization titania/water carbon/oil polystyrene/water oil/water Ian Morrison 2009 Lecture 4 - Steric stabilization 16

18 A simple theory for polymer thickness A reasonable assumption is that the surface coating has a thickness equal to the radius of gyration. Radius of gyration for linear polymers: r 1/ 2 2 1/ MW Molecular weight "Length" (nm) 2 r 1/ , , , ,000, Ian Morrison 2009 Lecture 4 - Steric stabilization 17

19 The Size of polymers in solution A polymer forms a random coil in solution. The polymer increases the viscosity of the solution in a manner approximately dependent on molecular size. This polymer size can be calculated from the intrinsic viscosity: r 2 1/2 2 MW = [ η ] 5 N 0 1/3 The intrinsic i i viscosity i is gotten by: or [ ] η = 1 c * Where MW is molecular weight and N 0 is Avogadro s number. 1 η solution = lim 1 c ηsolvent [ η ] c 0 where c* is the concentration where the viscosity it is not linear in concentration. ti or R = g l n 6 where l is the Kuhn length. Ian Morrison 2009 Lecture 4 - Steric stabilization 18

20 Steric stabilization a better model + T ΔG Coil diameter - Steric Se repulsion Dispersion attraction H Ian Morrison 2009 Lecture 4 - Steric stabilization 19

21 Configurations of adsorbed polymers Homopolymers Time Random copolymers Brush Anchor Block copolymers Two or three segments are common. Grafted polymers Polymers may be attached to or grown from the surface. Ian Morrison 2009 Lecture 4 - Steric stabilization 20

22 Polymers in solution - Phase Diagrams Two phase region Tempera ature Θ L One phase region Θ U Two phase region Concentration Sterically stabilized dispersions are stable when the polymer is soluble the one phase regions. Ian Morrison 2009 Lecture 4 - Steric stabilization 21

23 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. Ian Morrison 2009 Lecture 4 - Steric stabilization 22

24 Ian Morrison 2009 Lecture 4 - Steric stabilization 23