THE ADSORPTION OF MIXED SYSTEMS ON COLLOIDAL CARBON BLACK Scott Michael .

surfactant systems. However, the properties of these mixtures are complex and are atpresent not well understood.One of the driving forces for understanding surfactant behaviour in these rnixedsystems is the potential to optirnize their use and performance. Emulsion polyrnerizationis an example of a colloidal system that relies heavily on the properties of surfactants.The synthesis of the polymer and the final particie size distribution in the product areintncately linked to surfactant behavior in the colloidal system. Of fundamentalimportance is a thorough understanding of surfactant behaviour during the seeding orgrowing process of the primary particles. During this process seed particles are firstgenerated, these primary particles c m be aggregated to form the secondary particles.Surfactants play a prime role in both the growth of the pnmary particles and thesubsequent stabilization of the secondary particles. Control over the extent anduniformity of the secondary particle size is a result of a number of processes. Currentlythere exist some opposing ideas regarding the role of the surfactants during the particlegrowth and stabilization phases.Emulsion polyrnerization typically involves a number of different chemicals andfactors that exert influence on the final particle size distribution. Some of the moreimportant factors include shear rate. temperature, pH1 and type of surfactants.Recent research into narrowly dispersed aggregates at the Xerox Research Centreof Canada has provided a starting point to begin this investigation into mixed surfactantsystems. From the procedure developed at Xerox, narrowly dispersed aggregates areproduced fiom a pnmary particle size of 0.15 p with a final aggregafe size anywherebetween 5 and 10 Fm. The primas. particles are stablized with a mixture of anionic and

nonionic surfactants. Cationic surfactant is added to the systems to destabilize it and tobegin the aggregation process. There are several hypotheses directed at explaining thebehavior/roie of the individual surfactant components in the mixture.The surfactants in this system initially serve to keep the latex particles stable insoiution. Aggregation is induced by the addition of cationic surfactant, which causes theformation of a thick viscous gel. This gel is subsequently broken up at higher temperatureto form aggregates with a remarkably narrow size distribution. The restabilization isthought to be primarily a function of the aggregate size and of the surfactant concentrationand conformation on the particle surface. in order to M e r understand and explain theprocess, a method of determining the concentration and effect of individual surfactants int h i s complex mixture was required.This thesis describes a first attempt at obtaining analytical techniques fordetermining individual surfactant concentrations is such complex systems. A secondaryobjective of this research project was to investigate if narrow aggregate distributionscould be obtained by aggregating dispersions of colloidal carbon black.

CHAPTER 2. BACKGROUND AND THEORY2.1DLVO TheoryThe ability to control and manipulate colloidal stability has been the focus of alarge and concentrated effort for the past several decades. Depending on the applicationof a colloidal system, fme-control over the stability of the system can have a ciramaticinfluence on the end-use properties. In the area of colfoid science the theones ofDejaguin, Landau, Verwey and Overbeek (DLVO theory) are often used to defme andpredict the stability of a given system.The DLVO theory unified the theones goveming attraction and repulsion incolloidal particle systems. The theory deals with the potential energy of interactionbetween colloidal particles as a function of distance. It combines the attractive (van derWaals) and repulsive (electrostatic) energies between particles to predict the totalinteraction energy. The major contributing factors to the repulsive and attractive forcesacting between colloidal particles will be outlined next.2.1.1Electrostatic RepulsionElectrostatic repulsion arises between colloidal particles when two similarlycharged surfaces approach each other at a small distance of separation. The repulsion is adirect consequence of the interaction between the sirnilady charged surfaces.'There has been a vast amount of theoretical and experimental work directed atexplaining the nature of the electrical interface. The interface exists between the solid and

its surrounding solution environment. Repulsive electncal forces acting between thesurfaces of similarly charged colloids are often the primary means of stabilization within asystem.'Colloidal particles may acquire surface charge through one or a combination of thefollowing mechanisms: (i) preferential dissolution of surface ions. (ii) direct ionization ofsurface groups, (iii) substitution of surface ions, (iv) specific ion adsorption." The forcesacting between "charged surfaces" have their ongin in Coulomb's Law. This lawdescribes the interaction between point charges separated by a distance r in a vacuum.Coulomb's law m u t be modified in order to extend its applicability to colloicial systems.'The interaction of two charges in a vacuum, separated by distance r, can bedescribed by Equations 2.1 and 7.2whereFe1 elecûicaI force, Nq 1 ,qz electncal charges,&O permittivity of fiee space, kg" m*' s4 A'E dielectric constant of the mediumC

r separation distancew thebetween the centers of the charges, mwork necessary to bring two charges together fiom an infinitedistance, J.For charges of the same sign the work will be positive and the interaction will berepulsive. The quantity of work is defined as the "elecû-ical potential" at r due to thecharge q,, and is given the symbol Y.in order to describe systems of more practical interest Coulomb's law must bemodified by the Boltzmann distribution to account for al1 ions present in the system.which is descnbed by Equatior?2.3. If the surface has a negative electrical potential(negative surface charge), the concentration of positive charges in the region surroundingthe surface c m be calcuiated by the following expression:wherepositive ions surrounding the surface, moles L*'c, concentration ofCo concentration of positive ionsZ, charge one elementary electnc charge,Y surface potential, Vk BoItmiann constant, JT temperature. K.the ion, CK-'Cin the bulk medium, moles L"

One of the approximations often invoked to describe the electrical interface is toexpress the charge density of the surface as a fûnction of potential upon rnoving awayfiom the charged surface. Charge density is related to the surroundhg ion concentrationprofile as s h o w by Equation 2.4jwheredensity. C rn'jP' charge21 vaiencye eiementaryY surface potential,k Boltzmann constant, Jn1o concentrationT temperature,nurnberelectric charge. CVK-'of n type ions in the b u k medium, moles L-'K.Reiating Equation 2.4 to the potential results in the Poisson-Boltzmann (PB) equationThe Poisson equation implies that the potentiais associated with the variouscharges combine in an additive manner, whereas the Boltzmann distribution irnplies an

exponential relationship between the charges and the potential. The PB equation has noexplicit solution and must be soived for limiting cases. The solution to the abovedifferential equation under conditions of low surface potential and the condition ofelectroneutrality results in the Debye-Huckel approximation which is expressed asEquation 2.6,Wherey 0 thepotential at the particle surface, VK thereciprocai of the thickness of the double layer, m-'.The thickness of the double layer for surface potentials less than 25 mV is calculatedaccording to Equation 2.7The thickness of the double layer varies inversely with the concentration ofsolution electrolytes, and the square of the valency of the counter ion. By changing eitherthe concentration or the identity of the surroundhg electrolyte, the thickness of the doublelayer cm be manipulated. in systems whose stability is entirely dependent on electricdouble layer interactions this has important implications. This strong dependence on ionvalency and concentration is the basis for the Schulze-Hardy rule!The Schulze-Hardymle predicts the amount of inert electrolyte necessary to destabilize a colloidal system.

this arnount is most often referred to as the critical coagulation concentration (c.c.c). Atthe C.C.C. the surface charge of the particles will have been screened by the addedelectrolyte, this causes the attractive forces to dominate and the dispersion will becomeunstable.The solution taken as a whole will be electrically neutral. However in the vicinityof the charged surface, at the particle-solvent interface. there will exist an irnbalance ofelectrical charges. This charge irnbalance in the system depends heavily on the net chargeof the surface. The region of excess charge of opposite sign around a charged surface iscommonly referred to as the "ionic atmosphere" or "charge cloud" associated with thatpotential. This ionic atmosphere consists of a higher concentration of counter ions overCO-ionsas predicted fiom Equation 7.3. In colloidal systems the "charge cloud" inconjunction with the charged interface is commonly referred to as the "electncal doubielayer" associated with the particle.As a consequence of the dynarnic nature of a solution, the ions present in thedouble layer exist in a d i f i s e state. This results in a surrounding ionic environment thatis rapidly undergoing change. Taking account of this added complexity, Gouy andChapman developed a mode1 to describe the electrical double layer that relates thepotential of the surface to the diffise portion of the double layer.' It does not involve thessurnption of low potentials invoked in the Debye-Huckle approximation. A schematic ofthe interface is given in Figure 2.1.

FFUSE LAYER (MOBILE IONS)I\BOUND (IMMOBILE) COUNTER-IONSPARTICLE SURFACE IONSFigure 2.1 Schematic Drawing of the Electncal Double Layer(after Israelachvili 1992).

2.1.2Gouy-Chapman Mode1 of the Electrical InterfaceThe "Stem Layer" is the small space separating the ionic atmosphere around asurface rom the acnial diffuse double layer. and consists of tightly bound counter ionsthat are not ''fiee" to move with the thermal motion of the aqueous system. The StemLayer has a thickness on the order of a few angstroms, and its width accounts for the finitesize of charged groups and ions specifically associated with the surface.'It is assumed that the electrical potential in the solution surrounding the surfacedecreases exponentially with distance. This approximation is not valid at points close tothe surface, where the potential decreases much more rapidly due to the presence of boundcounter ions in the Stem Layer which are more effective at screening the surface charge.Several simplifjmg assumptions are employed to theoretically treat the nature of theinterface. These include: (i) ions fiom both the solution and the surface are treated aspoint charges, (ii) the surface is treated as a Mform charge, (iii) charges of opposite signc m approach infinitely closely. and (iv) the dielectric constant of the solvent is assurnedto remain constant throughout the double layer.The actual surface potential represented by y is replaced in the Gouy-Chapmanmodel with y,. This is the potential of the surface at the interface between the Stem planeand the solution. The Gouy-Chapman model accounts for the mobility of ions in aqueoussolution. The diffuse model of the double layer reflects the change in potential associatedwith the surface on moving away fiom the interface.No exact analytical expressions exist for solving the equations associated with thenature of the interface, recourse to nurnencal solutions or to various approximations areofien invoked. According to Overbeek. the rate of double layer overlap in typical

Brownian motion between particles is too fast for adsorption equilibrium to bemaintained.' Often models of the interface assume that the potential remains constantduring particle collision or that the surface charge remains constant; the true situation liesbetween these two assurnptions.Reerink and Overbeek developed an expression to calculate the interactionpotential caused by the overlap of the d i h e portion of two double layers. Thisinteraction is referred to as the electrostatic repdsion term (TlR). The main assumption intheir derivation is that the interparticle separation is large compared to the thickness of thedouble layers. For equal sph

Total nurnber of moles of solution before adsorption, moles Change in mole fraction of surfactant resulting from adsorption Mass of insoluble adsorbent, kg Amount adsorbed, mol rnS2 Number of moles of surfactant adsorbed. moles Surface area of substrate, m' Zeta potential, V Fluid density, kg m" Particle density, kg m-' Fluid viscosity. N s rn"