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

Liquid-Solid 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.

Liquid-Solid Interface; Colloids  Not so obvious examples for a solid-liquid interface is a colloid particle.  Colloids are widely spread in daily use:  Paint  Blood  Air pollution

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

Liquid-Solid Interface; Colloids  Adsorption at low solute concentration:  These isotherms can be either fitted by the langmuir isotherm  Or the freundlich isotherm

Liquid-Solid Interface; Colloids  Stearic acid is adsorbed onto carbon black differently in different solvents:

Liquid-Solid Interface; Colloids  Different chain lengthes will show differences in adsorption behaviour:

Liquid-Solid Interface; Colloids  Traube´s rule:

Liquid-Solid Interface; Colloids  Composite adsorption isotherms:

Intermolecular Forces Repulsive Forces (Above X-axis) Attractive Forces (Below X-axis)

Electrostatic Forces & The Electrical Double Layer E-Coli 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 E-Coli induced diarrhea Mingming Wu, Cornell University (animation) Berg, Howard, C. Nature 249: 78-79, Flagella

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

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

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

(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 SURFACE CHARGE GENERATION (cont.)

ELECTRICAL DOUBLE LAYERS Helmholtz (100+ years ago) proposed that surface charge is balanced by a layer of oppositely charged ions COUNTER IONS CO IONS OHP SOLVENT MOLECULES Ψ0Ψ0 x

Gouy-Chapman Model ( ) Assumed Poisson-Boltzmann 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 Diffusion plane Ψ0Ψ0 x

Stern (1924) / Grahame (1947) Model Gouy/Chapman diffuse double layer and layer of adsorbed charge. Linear decay until the Stern plane Shear Plane Gouy Plane Difusion layer Bulk Solution Stern Plane Ψ0Ψ0 x ΨζΨζ

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 Shear Plane Gouy Plane Difusion layer Bulk Solution OHP Ψ0Ψ0 ΨζΨζ x

POISSON-BOLTZMANN 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” Electric field is the differential of the electric potential → → → → Combining the two equations we get: Which for one dimension becomes: Assuming Boltzmann ion distribution: Boltzmann ion distribution Definitions E: Electric filed Ψ: Electric potential ρ: Charge density E Q : Energy of the ion x, r : Distance

POISSON-BOLTZMANN DISTRIBUTION Z = electrolyte valence, e = elementary charge (C) n = electrolyte concentration(#/m 3 )  r = dielectric constant of medium  0 = permittivity of a vacuum (F/m) k= Boltzmann constant (J/K) T = temperature (K) Poisson-Boltzmann 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

POISSON-BOLTZMANN DISTRIBUTION Debye-Hückel approximation For then: The solution is a simple exponential decay (assuming Ψ(0)=Ψ 0 and Ψ(∞)=0): Debye-Hückel parameter (  ) describes the decay length

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

POISSON-BOLTZMANN DISTRIBUTION Exact Solution For M 1-1 electrolyte Surface Potential (mV)

DEBYE LENGTH AND VALENCY Ions of higher valence are more effective in screening surface charge.

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 Si 3 N 4 particles in water at pH 4, 7 and 9?

ZETA POTENTIAL -- Effect of Ionic Strength --

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 Self-assembling organic molecules: surfactants, polyelectrolytes SPECIFIC ADSORPTION

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

ELECTROKINETIC PHENOMENA Electrophoresis - Movement of particle in a stationary fluid by an applied electric field. Electro-osmosis - 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

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

Electrophoresis Smoluchowski Formula (1921) assumed  a >> 1  = Debye parameter a = particle radius - electrical double layer thickness much smaller than particle v = velocity,  r = media dielectric constant  0 = permittivity of free space  = zeta potential, E = electric field  = medium viscosity  E = electrophoretic mobility

ZETA POTENTIAL MEASUREMENT Electrophoresis Henry Formula (1931) expanded for arbitrary  a, assumed E field does not alter surface charge - low  0 v = velocity  r = media dielectric constant  0 = permittivity of free space  = zeta potential  = medium viscosity E = electric field  E = electrophoretic mobility Hunter, Foundations of Colloid Science, p. 560

ZETA POTENTIAL MEASUREMENT Streaming Potential  = Debye parameter a = particle radius  = zeta potential  = Potential over capillary (V)  r = media dielectric constant  0 = permittivity of free space (F/m)  = medium viscosity (Pa·s) K E = solution conductivity (S/m)  p = pressure drop across capillary (Pa)

DLVO Theory DLVO – Derjaguin, Landau, Verwey and Overbeek Combined Effects of van der Waals and Electrostatic Forces 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: Van der Waals (Attractive force) Electrostatics (Repulsive force)

DLVO Theory A = Hamakar’s constant R = Radius of particle x = Distance of Separation k = Boltzmann’s constant T = Temperature n = bulk ion concentration  = Debye parameter z = valency of ion e = Charge of electron Ψ = Surface potential

DLVO Theory For short distances of separation between particles 100 nm Alumina, 0.01 M NaCl,  zeta =-20 mV

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

Discussion: Flocculation vs. Coagulation The DLVO theory defines formally (and distinctly), the often inter-used terms flocculation and coagulation Flocculation: Corresponds to the secondary energy minimum at large distances of separation The energy minimum is shallow (weak attractions, 1-2 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

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

Secondary Minimum: Real System 100 nm Alumina,  zeta =-30 mV

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

Effect of Salt Concentration and Type H: Distance of separation at critical salt concentration At critical salt concentration,  H = 1. Upon simplification, we get: Schultz – Hardy Rule: Concentration to induce rapid coagulation varies inversely with charge on cation n: Concentration Z: Valence

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: Effect of Salt Concentration and Type The DLVO theory thus explains why alum (AlCl 3 ) and polymers are effective (functionality and cost wise) to induce flocculation and coagulation

pH and Salt Concentration Effect Stability diagram for Si 3 N 4 (M11) particles as produced from calculations (IEP 4.4) assuming 90% probability of coagulation for solid formation. Dispersion Agglomerate

REMARKS -- hydrophobic and solvation forces -- Due to the number of fitting parameters (  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.