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 length) Molecular factors affecting the electric forces Colloid stability (CCC, coagulation) Kinetics of aggregation

Colloidal stability o Colloidal stability = dispersion of colloidal particles, which do not aggregate (in the desired time limits) o Mechanic stability = dispersion of colloidal particles, which do not sediment Colloidal stability: V = f ( H ) Minima: instability aggregation (attraction forces dominate) Maxima: stability (repulsion forces dominate) V H = FdH

DLVO theory o DLVO theory (Derjaguin-Landau-Verwey-Overbeek) = the effect of the forces is simply additive between van der Waals and electrostatic forces (double layer energy) V V R + V A V(1) = stable colloidal dispersion V() = instable colloidal dispersion o Forces in colloidal systems are longer range than the intermolecular forces

DLVO theory o Critical coagulation concentration = concentration of the disperse phase for which: V V dv dh = 0 = 0 Example: spherical particles, equal radius, aprox. neutral (< 5mV for 1:1 electrolytes) ( kh ) = πrεε 0Ψ0 exp AR 1H Ψ 0 R k V R = zeta potential = radius of particles = Debye length V A Stability: balance between repulsion and attraction

Electric double layer in colloidal systems o Almost all particles are charged in HO/polar liquids. Change = f( ph, nature of the surface groups, salt concentration) o Most surfaces have negative charge - typically cations are more hydrated than the anions - anions adsorb at the surface o Hydration number = number of water molecules an ion can bind - divalent and trivalent cations are more solvated than monovalent cations. - monovalent cations are only weakly solvated -The charge at the interface is compensated by counter-ions

Electric double layer in colloidal systems o Double layer model= two regions are present at tha interface between a surface (planar, spherical) and the medium: - Stern layer = one short counter-ions plane (interaction with the interface) - Diffuse layer = counter-ions with a concentration that gradually decreases until an electroneutral solution

Net change: Electric double layer in colloidal systems - Stern layer + diffuse layer + surface = 0 - If the double layer of two particles overlap > the change of the Stern layer makes the particles to repel each-other Formation of osmotic pressure in the mid plane of the overalping layer

Processes to induce charges at surfaces a) Differential ions solubility b) Direct ionization of surface groups c) Isomorphous substitution d) Specific ions adsorption e) Anisotropic crystals

Processes to induce charges at surfaces o Isoelectric point, IEP= point in the interface region (around the particle/in front of the surface) where the charge is zero. o There are colloidal systems with more than one IEP (liquid crystals). Determine IEP: ζ = f ( ph ) - Zeta potential - IEP for surfaces f(surface treatment)

Key parameters for electric forces Electrical forces between nanoparticles Overlap of the diffuse double layer o DLVO Theory the repulsion potential: = π R Ψ exp ( kh ) V R εε 0 0 o Key parameters: - ζ potential, Ψ 0 - Debye length, k -1

ζ - potential Electrical double traverse with the nanoparticles Nanoparticles have counter-ions & solvent molecules attached ζ potential potential where the centre of the first layer of solvated ions moving relative to the surface is located ζ potential located at 0.5nm from the surface ζ > 30 mv stability (exceptions exist)

ζ - potential Various surface potentials Ψ 0 surface potential Ψ d Stern potential ζ potential ζ potential indicate the extent to which the ions from the solution are adsorbed into the stem layer Stern layer few Å the finite size of the charged groups / ions asociated with the surface

ζ - potential ζ << Stern Potential : Ψ d when exist high salt concentrations in practice: ζ = Ψ d Ψ 0 How to measure? electrophoresis v µ = [ ] 1 1 µ = m V s E 1 1 [ v ] = ms [ E] = Vm

ζ - potential o Small nanoparticles (Hückel model): Ψ 0 = 3µη εε 0 o Large nanoparticles (Smoluchowski model): Ψ 0 = µη εε 0 o Any size nanoparticles (Henry model): : Ψ 0 = 1.5µη εε f 0 ( kr)

ζ - potential µ < 0 Ψ 0 < 0 ζ = f(ph, salt conc.) o Nanoparticles aggregate close to the ph for IEP (V R 0) o nanoparticles (+) at ph < IEP o nanoparticles (-) at ph > IEP ζ when salt conc. salt enhance instability

ζ - potential ζ = f(ionic strength) High salt conc. compression of the double layer ζ to stabilize the nanoparticles o addition of small charged particles adsorb to the surface o change ph to be far from IEP flocculation (ζ 0) IEP should be avoided

Debye length Debye length thickness of the double layer (varying potential 3/k 4/k) Stern layer << diffuse layer: k 1 εε 0kBT εε 0k = = e N c z e N A i( B) T I B i A z i SO Ca 4 = + = + k 1 o few nm high salt conc. o few 10 nm low salt conc C salt k -1 repulsion

Debye length Simpler formula Example: H O solution 5 C k 1 0. nm [ ] ( mol L ) nm = 1 49 I = 1 i c i z i i c z i i k 1 1 0.49nm [ ] ( mol L ) nm = I

Debye length Important: what type of electrolyte is involved! Example: + SO4 Na + 1 4 c i i 6 Na SO z = ( C)( 1) + ( C)( ) = C CaCl 1Ca + + Cl c i i 6 z = ( 1C )( ) + ( C)( 1) = C + 4 Mg + 1 4 c i i 8 MgSO 1 SO z = ( 1C )( ) + ( 1C )( ) = C 3 AlCl 1Al + + 3 Cl 3 z = ( 1C )( 3) + ( 3C )( 1) = C NaCl 1 c i i 1 + 1 Na + Cl c i z i = ( 1C )( 1) + ( 1C )( 1) = C

Other expressions for k -1 [nm] Debye length

Debye length k -1 = f(salt conc., type of salt) k -1 k -1 for salt conc. for x:1 salt

Molecular factors affecting the electric forces nanoparticles approach double layers overlap nanoparticles repel each other Electrostatic double layer interactions decrease exponentialy with H 0 after a few k -1 (thickness of the double layer)

Molecular factors affecting the electric forces Monodisperse nanoparticles kr < 5 (Debye-Hückel approximation) V R = π R εε 0 Ψ 0 exp ( kh ) valid for single, symmetric electrolyte (1:1 or :) present in the medium Approximation valid when conditions more complex

Molecular factors affecting the electric forces V R for H V R for k -1 Effect of nanoparticles in a dispersion concentration of nanoparticles Faster decay of electrostatic repulsion The electrolyte Not particle-free solution aggregation

Molecular factors affecting the electric forces

Molecular factors affecting the electric forces Effect of salts (counter-ions) on stability Decrease the double layer instability coagulation Addition of electrolyte Repulsive forces Compression of the diffuse part of the double layer Possible ion adsorbtion into the Stern layer Van der Waals forces dominate Nanoparticles coagulate

Colloid stability a kinetic view V Effect of salt concentration on the energy salt concentration 1 Energy barriers 5 1: The repulsive force dominates and the colloid remains stable. : The secondary minimum starts appearing but the energy barrier is still very high, so the colloid is kinetically stable. 3: If the barrier is sufficiently low, the particles may even be able to cross it due to their thermal energy. H (nm) 4: Energy barrier has become zero, and fast coagulation is possible. The concentration at this point is called Critical Coagulation Concentration (CCC) at which coagulation can occur spontaneously. Hence, the colloid becomes unstable. 5: There is a large attractive Van-der Waals force, due to which there is no barrier and very fast coagulation takes place.

Critical Coagulation Concentration (CCC) Critical coagulation concentration (CCC) minimum concentration of an inert electrolyte coagulate a dispersion coagulation visible change in the dispersion appearence

Critical Coagulation Concentration (CCC) Schulze-Hardy rule role of salt in colloidal stability Strongly dependent on the valency of the counter-ions CCC 1 z CCC depends weakly on: Concentration of nanoparticles Nature of nanoparticles Charge number of counter-ions 6

Critical Coagulation Concentration (CCC) CCC values for various (nano)particles / electrolyte

Critical Coagulation Concentration (CCC) Schulze-Hardy rule: CCC DLVO theory: V = πrεε Ψ exp( κh ) 1 z CCC( saltii) = CCC( salti) 6 0 0 AR 1H V =0 z I z II 6 dv =0 dh CCC = 9.85 10 N ε ε k A z 4 3 0 6 Ae 3 5 B 6 T 4 γ 5 where: γ = e e zeψ o k T B zeψ o k T B 1 + 1 39 CCC 3.84 10 γ 4 = mol L ( A/ J) z / 6 for aqueous dispersions at 5 C

Critical Coagulation Concentration (CCC) From: CCC = 9.85 10 N ε ε k A z 4 3 0 6 Ae 3 5 B 6 T 5 γ 4 γ = e e ze ψ o k T B ze ψ o k T B + 1 1 High potential γ 1 CCC 1 6 z agree with Schulze-Hardy rule low potential γ ze 4k ψ 0 B T CCC ψ z 4 0 ψ 0 1 z CCC 1 6 z 3 CCC ε CCC independent with particle size The vanlency of counter-ions is very important to the collioid stability.

Critical Coagulation Concentration (CCC) the vanlency of counter-ions!! the influence of co-ions is very low. the influence of ion type?

Hofmeister series effectiveness of coagulation effectiveness of coagulation Precipitation at very high electrolyte concentration (salting-out effect) Purification of proteins Hydration of ions with different hydrophobicity dehydration of hydrophilic colloids precipitation

Kinetics of aggregation V Slow (potential-limited) coagulation V max H (nm) V 15 max k B T Thermal energy overcomes the repulsive potential energy barrier (curve 3) Smoluchowski model for slow coagulation: Second order dn dt = k n 1 n 1 n 0 = k t + obtain k by ploting 1/n as a funtion of t. n = number of particles per volume at some time t (m -3 ) k = reaction constant (m 3 number -1 s -1 ) n 0 = number of particles at start (t = 0) per unit volume (m -3 )

Kinetics of aggregation V Fast (diffusion-controlled) coagulation zero electrostatic barrier (by ion adsorption or by adding electrolyte) See curve 5 H (nm) The rate is limited only by the diffusion rate of particles towards one another and all collisions lead to adhesion Smoluchowski model for fast coagulation: k 0 = 4 k T B 3η medium 1 0.5 n 1 0 1 3η = kt1 t1 = = medium 0 0 n0 nk 4kBTn0 depend on temperature and viscosity of medium but not the particle size t 1/ is generally in the order of seconds to minutes

Kinetics of aggregation Stability ratio W k k 0 the total collisions between particles divided by W = the collisions of particles which result in a coagulation W is directly related to the maximum (barrier) of the potential energy function Reerink-Overbeek equation: W Fuchs equation: exp( Vmax 1 kbt k = e BT W = R dh κr H R V ) R = particle radius require numerical solutions W 5 10 easily obtained with modest potentials, about 15 k B T, debye length above 0 nm (curve 3). W = 9 10 corresponds to a V of about 5 k B T (very slow coagulation, rather stable dispersion, curve ).

Kinetics of aggregation Stability ratio W Theoretical repationships between W and electrolyte (1-1, -) concentration obtained by Fuchs equation 9 aγ logw = ψ d.06 10 logc z slow cogulation (potential-limited coagulation) a = effective ratius of particles linear relationship CCC! W = 1 fast cogulation (diffusion-controlled coagulation)

Kinetics of aggregation Stability ratio W W is able to be measured directly by estimating the apparent rates from static light scattering (SLS) or dynamic light scattering (DLS) with the relation: W fast fast = = aggregation of particles with a radius of 135 nm is induced with KCl Fast coagulation k 0 = dd dt H

From coagulation to sedimentation water treatment coagulation irreversible distabilized by electrolytes reach to a equilibrum state as a consequence of the height of the repusion energy barrier increasing with increasing particle size flocculation reversible clumped by polymers sendimentation sedimentation velocity see Lecture.

References: G. M. Kontogeorgis, S. Kill, Introduction to applied colloid and surface chemistry, Wiley-VCH, 016 D. F. Evans, H. Wennerstrom, The colloidal domain, Wiley- VCH, second edition, 014.