Electrostatic Forces & The Electrical Double Layer

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1 Electrostatic Forces & The Electrical Double Layer Dry Clay Swollen Clay Repulsive electrostatics control swelling of clays in water

2 LiquidSolid Interface; Colloids Separation techniques such as : column chromatography, HPLC, Paper Chromatography, TLC They are examples of the adsorption of solutes at the liquid solid interface. Liquid solid interfaces can be found everywhere and in any form and size, from electrode surfaces to ship hulls.

3 LiquidSolid Interface; Colloids Not so obvious examples for a solidliquid liquid interface is a colloid particle. Colloids are widely spread in daily use: Paint Blood Air pollution

4 LiquidSolid Interface; Colloids A very sensitive method to measure the amount of adsorbed material is by using a QCM (quartz crystal microbalance)

5 LiquidSolid Interface; Colloids Adsorption at low solute concentration: These isotherms can be either fitted by the langmuir isotherm Or the freundlich isotherm

6 LiquidSolid Interface; Colloids Stearic acid is adsorbed onto carbon black differently in different solvents:

7 LiquidSolid Interface; Colloids Different chain lengthes will show differences in adsorption behaviour:

8 LiquidSolid Interface; Colloids Traube s s rule:

9 LiquidSolid Interface; Colloids Composite adsorption isotherms:

10 Intermolecular Forces Interaction Force/Radius (mn/m) van der Waals Electrostatic Steric Depletion Hydrophobic Solvation Separation Distance (nm) Repulsive Forces (Above Xaxis) Attractive Forces (Below Xaxis)

molecular motor made of proteins Influencing proton release through protein is a key molecular approach to

11 Electrostatic Forces & The Electrical Double Layer Flagella EColi demonstrate tumbling & locomotive modes of motion in the cell to align themselves with the cell s rear portion Flagella motion is propelled by a molecular motor made of proteins Influencing proton release through protein is a key molecular approach to prevent EColi induced diarrhea Mingming Wu, Cornell University (animation) Berg, Howard, C. Nature 249: 7879, 1974.

12 Electrostatic Forces & van der Waals Forces jointly influence Flocculation / Coagulation Suspension of Al 2 O 3 at different solution ph Critical for Water Treatment Processes

13 Electrostatic Forces & The Electrical Double Layer 1) Sources of interfacial charge 2) Electrostatic theory: The electrical double layer 3) Electrokinetic Phenomena 4) Electrostatic forces

14 SOURCES OF INTERFACIAL CHARGE Immersion of some materials in an electrolyte solution. Two mechanisms can operate. (1) Direct Ionization of surface groups. H O M H O O O H O O M O H O O O H M H O 2 O O O (2) Specific ion adsorption OH O M O O

15 SURFACE CHARGE GENERATION (cont.) (3) Differential ion solubility Some ionic crystals have a slight imbalance in number of lattice cations or anions on surface, eg. AgI, BaSO 4, CaF 2, NaCl, KCl (4) Substitution of surface ions eg. lattice substitution in kaolin HO Si HO O Al O O Si O O OH Si O OH

16 ELECTRICAL DOUBLE LAYERS Ψ 0 SOLVENT MOLECULES COUNTER IONS x OHP CO IONS Helmholtz (100 years ago) proposed that surface charge is balanced by a layer of oppositely charged ions

17 Ψ 0 GouyChapman Model ( ) x Diffusion plane Assumed PoissonBoltzmann distribution of ions from surface ions are point charges ions do not interact with each other Assumed that diffuse layer begins at some distance from the surface

18 Ψ ζ Ψ 0 Stern (1924) / Grahame (1947) Model Gouy/Chapman diffuse double layer and layer of adsorbed charge. Linear decay until the Stern plane. Stern Plane Difusion layer Shear Plane Gouy Plane Bulk Solution x

19 Stern (1924) / Grahame (1947) Model In different approaches the linear decay is assumed to be until the shear plane, since there is the barrier where the charges considered static. In this courese however we will assume that the decay is linear until the Stern plane. Ψ ζ Ψ 0 OHP Difusion layer Shear Plane Gouy Plane Bulk Solution x

20 POISSONBOLTZMANN DISTRIBUTION 1 st Maxwell law (Gauss law): The total of the electric flux out of a closed surface is equal to the charge enclosed divided by the permittivity E = ( r) ρ ε ε Electric field is the differential of the electric potential E ( r) = Ψ Combining the two equations we get: Ψ r Which for one dimension becomes: () 0 r () r ρ( r = ε ε 2 ) 2 d Ψ dx Assuming Boltzmann ion distribution: 0 ( x) ρ( x) 2 = n ( x) ρ( x) 1 Z eψ kt Zen ( ZΨe kt Z e kt = = Z nee = e e ) 2 d Ψ i Ψ 2 i dx εε 0 εε 0 i εε 0 εε 0 r ρ Definitions E: Electric filed Ψ: Electric potential ρ: Charge density E Q : Energy of the ion x, r : Distance Boltzmann ion distribution E ezψ Q kt kt ( x) e = n Zee = ρ 0 0

21 POISSONBOLTZMANN DISTRIBUTION d 2 dx ψ 2 = 2Zen sinh ε ε r 0 Zeψ kt Z = electrolyte valence, e = elementary charge (C) n = electrolyte concentration(#/m 3 ) ε r = dielectric constant of medium ε 0 = permittivity of a vacuum (F/m) k = Boltzmann constant (J/K) T = temperature (K) PoissonBoltzmann distribution describes the EDL Defines potential as a function of distance from a surface ions are point charges ions do not interact with each other

22 POISSONBOLTZMANN DISTRIBUTION DebyeHückel approximation ZeΨ kt <<1 2Zen Zeψ sinh ε ε kt For then: 2 d ψ = 2 dx r 0 2Zen ε ε r 0 Zeψ = kt ( Ze) 2n ε ε kt 2 ( x) = κ Ψ( x) The solution is a simple exponential decay (assuming Ψ(0)=Ψ 0 and Ψ( )=0): Ψ( x)= Ψ 0 e κx DebyeHückel parameter (κ) describes the decay length κ = ( Ze) 2n ε ε kt r 0 2 r 0 2 Ψ

23 DOUBLE LAYER FOR MULTIVALENT ELECTROLYTE: DEBYE LENGTH DebyeHückel parameter (κ) describes the decay length 1/ 2 2 n e 2 κ = C iz i ε rε 0kT i= 1 Z i = electrolyte valence e = elementary charge (C) C i = ion concentration (#/m 3 ) n = number of ions ε r = dielectric constant of medium ε 0 = permittivity of a vacuum (F/m) k = Boltzmann constant (J/K) T = temperature (K) κ 1 (Debye length) has units of length

24 POISSONBOLTZMANN DISTRIBUTION Exact Solution For M 11 electrolyte Surface Potential (mv) Surface Potential (mv) ZeΨ kt <1 ZeΨ kt >1

25 DEBYE LENGTH AND VALENCY Debye Length κ 1, (nm) electrolyte 22 electrolyte 33 electrolyte Electrolyte Concentration (M) Ions of higher valence are more effective in screening surface charge.

26 ZETA POTENTIAL Point of Zero Charge (PZC) ph at which surface potential = 0 Isoelectric Point (IEP) ph at which zeta potential = 0 Question: What will happen to a mixed suspension of Alumina and Si3N4 particles in water at ph 4, 7 and 9?

27 ZETA POTENTIAL Effect of Ionic Strength Zeta Potential (mv) Alumina Increasing I.S ph

SPECIFIC ADSORPTION Free energy decrease upon adsorption greater than predicted by electrostatics Have the ability to shift the isoelectric point v and

28 SPECIFIC ADSORPTION Free energy decrease upon adsorption greater than predicted by electrostatics Have the ability to shift the isoelectric point v and reverse zeta potential Multivalent ions: Ca 2, Mg 2, La 3, hexametaphosphate, sodium silicate Selfassembling organic molecules: surfactants, polyelectrolytes 2

29 SPECIFIC ADSORPTION Ca 2 PO 4 3 ph Multivalent cations shift IEP to right (calcite supernatant) Multivalent anions shift IEP to left (apatite supernatant) Amankonah and Somasundaran, Colloids and Surfaces, 15, 335 (1985).

30 ELECTROKINETIC PHENOMENA Electrophoresis Movement of particle in a stationary fluid by an applied electric field. Electroosmosis Movement of liquid past a surface by an applied electric field Streaming Potential Creation of an electric field as a liquid moves past a stationary charged surface Sedimentation Potential Creation of an electric field when a charged particle moves relative to stationary fluid

31 ZETA POTENTIAL MEASUREMENT Electrophoresis ζ determined by the rate of diffusion (electrophoretic mobility) of a charged particle in an applied DC electric field. PCS ζ determined by diffusion of particles as measured by photon correlation spectroscopy (PCS) in applied field Acoustophoresis ζ determined by the potential created by a particle vibrating in its double layer due to an acoustic wave Streaming Potential ζ determined by measuring the potential created as a fluid moves past macroscopic surfaces or a porous plug

32 ZETA POTENTIAL MEASUREMENT Electrophoresis Smoluchowski Formula (1921) assumed κa >> 1 κ = Debye parameter a = particle radius electrical double layer thickness much smaller than particle v = µ Ε ε = r ε η ε 0 r ζ ε η 0 Ε ζ v = velocity, ε r = media dielectric constant ε 0 = permittivity of free space ζ = zeta potential, E = electric field η = medium viscosity µ E = electrophoretic mobility

33 ZETA POTENTIAL MEASUREMENT Electrophoresis Henry Formula (1931) expanded for arbitrary κa, assumed E field does not alter surface charge low σ 0 v µ 2εrε = 3η Ε 0 ζ f 2εrε = 3η 0 1 ζ f ( κa) Ε 1 ( κa) v = velocity ε r = media dielectric constant ε 0 = permittivity of free space ζ = zeta potential η = medium viscosity E = electric field µ E = electrophoretic mobility Hunter, Foundations of Colloid Science, p. 560

34 ZETA POTENTIAL MEASUREMENT Streaming Potential exp(zeζ / κa 2kT) << 1 κ = Debye parameter a = particle radius ζ = zeta potential Ε = Potential over capillary (V) ε r = media dielectric constant ε 0 = permittivity of free space (F/m) η = medium viscosity (Pa s) K E = solution conductivity (S/m) p = pressure drop across capillary (Pa) E = ε r ε 0 ηk ζ E p

35 Combined Effects of van der Waals and Electrostatic Forces DLVO Theory DLVO Derjaguin, Landau, Verwey and Overbeek Based on the sum of van der Waals attractive potential and a screened electrostatic repulsion potential arising between the double layer potential screened by ions in solution. The total interaction energy U of the system is: 2 AR 64πkTRnγ U ( x) = exp 2 12x κ Van der Waals (Attractive force) Electrostatics (Repulsive force) ( κx)

36 DLVO Theory 2 AR 64πkTRnγ U ( x) = exp 2 12x κ ( κx) A = Hamakar s constant R = Radius of particle x = Distance of Separation k = Boltzmann s constant T = Temperature n = bulk ion concentration κ= Debye parameter γ = tanh zeψ 4kT z = valency of ion e = Charge of electron Ψ = Surface potential

37 DLVO Theory 100 nm Alumina, 0.01 M NaCl, Ψ zeta =20 mv For short distances of separation between particles

38 DLVO Theory Hard Sphere Repulsion (< 0.5 nm) No Salt added J/m Energy Barrier x (distance) Secondary Minimum (Flocculation) Primary Minimum (Coagulation)

39 Discussion: Flocculation vs. Coagulation The DLVO theory defines formally (and distinctly), the often interused terms flocculation and coagulation Flocculation: Corresponds to the secondary energy minimum at large distances of separation The energy minimum is shallow (weak attractions, 12 kt units) Attraction forces may be overcome by simple shaking Coagulation: Corresponds to the primary energy minimum at short distances of separation upon overcoming the energy barrier The energy minimum is deep (strong attractions) Once coagulated, particle separation is almost impossible

40 Hard Sphere Repulsion (< 0.5 nm) J/m Effect of Salt Energy Barrier No Salt added Upon Salt addition x (distance) Secondary Minimum (Flocculation) Primary Minimum (Coagulation) Addition of salt reduces the energy barrier of repulsion. How?

41 Secondary Minimum: Real System 100 nm Alumina, Ψ zeta =30 mv

42 Discussion on the Effect of Salt The salt reduces the EDL thickness by charge screening Reduces the energy barrier (may induce coagulation) Also increases the distance at which secondary minimum occurs (aids flocculation) Since increased salt concentration decreases κ 1 (or decreases electrostatics), at the Critical Salt Concentration U(x) = 0

43 Effect of Salt Concentration and Type AR 12H 64πkTRnγ 2 κ 2 exp( κh ) = 0 H: Distance of separation at critical salt concentration At critical salt concentration, κh = 1. Upon simplification, we get: nα 1 z 6 Schultz Hardy Rule: n: Concentration Z: Valence Concentration to induce rapid coagulation varies inversely with charge on cation

44 Effect of Salt Concentration and Type For As 2 S 3 sol, KCl: MgCl 2 : AlCl 3 required to induce flocculation and coagulation varies by a simple proportion 1: 0.014: The DLVO theory thus explains why alum (AlCl 3 ) and polymers are effective (functionality and cost wise) to induce flocculation and coagulation

45 ph and Salt Concentration Effect Agglomerate Dispersion Dispersion Stability diagram for Si3N4(M11) particles as produced from calculations (IEP 4.4) assuming 90% probability of coagulation for solid formation.

46 REMARKS hydrophobic and solvation forces Due to the number of fitting parameters (ψ 0, A 132, spring constant, I.S.) and uncertainty in force laws (C.C. vs C.P., retardation) hydrophobic forces often invoked to explain differences between theory and experiment. Because hydrophobic forces involve the structure of the solvent, the number of molecules to be considered in the interaction is large and computer simulation has only begun to approach this problem. Widely accepted phenomenological models of hydrophobic forces still need to be developed.

Stability of colloidal systems

Stability of colloidal systems Colloidal stability DLVO theory Electric double layer in colloidal systems Processes to induce charges at surfaces Key parameters for electric forces (ζ-potential, Debye