1 Introduction 2192 Surface Chemistry 220

2.1 Surface charge development 2202.2 Measurement of surface charge 221

3 The Electrical Double-Layer 2223.1 Helmholtz model 2223.2 Gouy-Chapman model 2223.3 Stern-Graham model 223

4 Zeta Potential (Electrokinetic Potential). . . 2244.1 Measurement of zeta potential 2244.2 Manipulation of zeta potential 225

5 Electrostatic Forces 2265.1 Calculation of electrostatic forces . . . 227

5.1.1 Boundary conditions 2275.1.2 The linearized

Poisson-Boltzmannapproach 228

5.1.3 Analytical formulae 2286 Manipulating Surface Behaviour by

Polymer Adsorption 2296.1 Solution behaviour of polymers 2296.2 Adsorption of polymer at the particle

surface 2306.3 Role of surface chemistry and

structure in polymer adsorption 2317 Manipulating Surface Behaviour by

Surfactant Adsorption 232

1 INTRODUCTION

Particulate processing plays a crucial role in industriessuch as mineral processing, chemicals, pharmaceutical,

7.1 Adsorption of surfactants at thesolid-liquid interface 2337.1.1 Mechanisms of

adsorption 2337.1.2 Contributions to the adsorption

energy 2337.2 Surfactant structures at the

solid-liquid interface 2368 Particle Processing 238

8.1 Dispersion of particles 2388.1.1 Characterization of the state of

dispersion 2398.1.2 Control of dispersion through

surface chemistry 2408.2 Selective flocculation of particles . . . 243

8.2.1 Design of selective reagentsbased on surfacechemistry 243

8.2.2 Modifying surface chemistryand structure to enhanceselectivity 244

8.3 Flotation of minerals 2468.3.1 Collector selection based on

surface charge 2468.3.2 Collector selection based on

surface reactions 2479 References 249

food processing, microelectronics and cosmetics, toname just a few. Many of the industrial applicationsinvolve particles, which are in the micron or thesub-micron size range. In such ranges, the surface

CHAPTER 10

Surface Chemistry in Dispersion,Flocculation and FlotationBrij M. Moudgil, Pankaj K. Singh and Joshua J. Adler

University of Florida, Gainesville, Florida, USA

Handbook of Applied Surface and Colloid Chemistry. Edited by Krister HolmbergISBN 0471 490830 © 2001 John Wiley & Sons, Ltd

properties or the surface chemistry controls theprocessing behaviour of the particles. It is imperativeto understand and manipulate the surface chemistry inorder to control the processing conditions to achieveconsistent and desired products. In this chapter, thesurface chemistry relevant to dispersion/flocculation andflotation processes is discussed.

The surface chemistry, and more specifically, thecharge development on the surface of particles in aque-ous systems is briefly reviewed. The manipulation ofsurface chemistry by the adsorption of organic reagents,such as surfactants and polymers, is also considered.Finally, to illustrate the importance of surface chemistryin particulate processing, the practical applications ofore flotation, dispersion of particles and selective floc-culation are discussed.

2 SURFACE CHEMISTRY

Solid surfaces are heterogeneous in nature, and mayhave sites with different energies. The presence of sur-face defects, and the different arrangement of the atomsin and around the surface defects, lead to surface siteswith wide ranging energies. Depending on the methodof preparation of the surface, the relative concentra-tions of atoms in the surface defects can be varied,thus resulting in different surface structure and ener-getics. Changes in the local environment can result indynamic restructuring of the surface. This rearrange-ment of surface atoms can occur on the chemisorptiontime-scale (~ 10~13 s), on the time-scale of catalyticreactions (seconds), and at longer times (hours). Thismakes the study of surfaces extremely complex. In cer-tain cases, both polar and non-polar sites can co-existon the same solid surface, thus leading to more com-plex surface structures. For example, on the surface ofsilicon oxide (SiO2), the Si-O-Si sites are hydropho-bic, whereas the Si-OH (silanol) sites are polar innature. In order to understand the surface phenomena,detailed information about the surface atomic structureand the chemical composition of a thin surface layeris required. For the study of solid surfaces in gases, anumber of experimental techniques have been used thatemploy heat, electric fields, electrons, photons, ions ormolecules in order to excite the surface. The responseof the surface to these excitations results in the emissionof electrons, photons, ions or molecules whose energy,mass, or direction can be measured. These techniqueshave significantly enhanced the understanding of sur-faces, but are limited in use because they all rely onthe use of high vacuum, i.e. 10~6 to 10~9 torr. Some of

the techniques that have been used include low-energyelectron diffraction (LEED), field-ion microscopy, elec-tron impact Auger spectroscopy, ion neutralization spec-troscopy, X-ray photoelectron spectroscopy, ultravioletphotoelectron spectroscopy, electron energy loss spec-troscopy (EELS), appearance potential spectroscopy andscanning tunnelling microscopy. The study of surfacesin aqueous environments becomes difficult, due to var-ious changes occurring at the interface, and the lackof instrumentation to detect such changes. The develop-ment of surface charges and the measurement techniquesare summarized in the following sections.

2.1 Surface charge development

When the solid surfaces are immersed in aqueous media,they exhibit a net surface charge. A great majorityof colloidal particles are charged by the followingmechanisms.

1. Ion adsorption Charge can develop at surfaces byunequal adsorption of oppositely charged ions. Ionadsorption may be positive or negative. Surfaces incontact with aqueous media are more often nega-tively charged due to the fact that cations are morehydrated when compared to anions. Hydrocarbon oildroplets and air bubbles exhibit net negative chargesbecause of negative adsorption of ions. Cationsmove away from the air-water and oil-water inter-face more than anions. Surface charge may also beestablished by the adsorption of charged surfactantmolecules. Preferential adsorption of one type of ionon the surface can occur due to either London-vander Waals interactions or hydrogen or hydrophobicbonding.

2. Ion dissolution Unequal dissolution of ions in thecase of ionic substances can lead to a net charge onthe substrate. A classical example of this mechanismis the silver iodide surface. When silver iodide isimmersed in an aqueous environment, dissolutionoccurs as AgI «* Ag+ + 1 ~ . Since the solubilityproduct for this equilibrium is relatively small (Ksp =aAg

+ai~ ~ 10~16), the concentrations of Ag+ andI~ in solution are small. The surface of the crystalconsists of an array of Ag+ and I~ ions in cubicclose packing, and no net charge develops when thenumber of each ion is the same. However, an equalnumber of each ion on the surface does not occur atthe concentration where there are equal numbers ofAg+ and I~ ions in the solution. Instead, due to theirhigher affinity for the surface, the iodide ions tend to

Figure 10.1. Schematic representation of charge developmentin SiC>2 tetrahedra by the substitution of a Si atom by anAl atom

be preferentially adsorbed at the surface. A detailedmathematical treatment of the AgI surface is givenin ref. (1).

3. Lattice imperfections and isomorphous substitutionsIn the case of most clay mineral systems, latticedefects result in very large charge densities. Thedefect in such cases is in the form of an isomorphousreplacement of one ionic species by another of lowercharge. For example, the replacement of a Si atomby an Al atom in the SiO2 tetrahedra will yield a netnegatively charged surface (Figure 10.1).

4. Ionization/Dissociation The ionization of groupssuch as carboxyl (-COOH), sulfate (-O.SO2.OH),sulfonate (-SO2-OH), sulfite (-O.SO.OH), amine(-NH2) and quaternary amine (-N+R3), may takeplace at the surface, thus resulting in the developmentof surface charges. The dissociation of these surfacegroups is pH dependent. This mechanism representsthe charge development in proteins and in, poly-mer latex systems, which have carboxyl, sulfate andsulfonate groups on their surfaces. In addition, thismechanism is applicable to the behaviour of oxidesurfaces. For a detailed description of such dissocia-tion models, the reader is referred to ref. (1).

2.2 Measurement of surface charge

The surface charge is measured by titrating the sur-face with the potential-determining ions (e.g. H+ andOH" ions for oxides, and Ag+ and I~ ions for silveriodide) for the surface. In such an experiment, a certainknown mass, m (typically < 1 g) of the particle is addedto a known volume, u(200 cm3 < v < 1000 cm3) of an"indifferent" electrolyte solution (e.g. 0.01M NaNO3),and the suspension is equilibrated for 30-60 min atfixed temperatures (22 or 25°C), followed by purgingwith nitrogen to expel any dissolved carbon dioxide.Care should be taken to purge out the dissolved car-bon dioxide completely, because this dissolved gas canlower the solution pH, thus resulting in incorrect mea-surements. A schematic of a typical set-up for measuringthe surface charge is shown in Figure 10.2.

Figure 10.3. Schematic representation of the typical resultsobtained from a surface titration experiment for the calculationof surface charge

After equilibration, the initial pH is noted. If theinitial pH is low, a base titration (e.g. 0.01M NaOH)is used to move to a higher final pH (pHfina]). If theinitial pH is high, an acid titration is used to move toa low pHfinal. The delay time between titrant additionfor complete reaction is usually between 5 and 30 min.A blank titration is also carried out on the electrolytesolution and the results obtained from the two titrationsare then superimposed. A typical result is shown inFigure 10.3. From such a figure, by subtracting the twocurves (i.e. subtract the blank electrolyte curve fromthe curve for electrolyte + solids), the relative amountsof OH~ or H+ adsorbed on the solid surface at anyparticular pH can be determined from the following

Background electrolyte

Electrolyte + solids

Volume of titrant

PH

Magnetic stirrer

Figure 10.2. Schematic of an experimental set-up used forsurface charge measurement

Sample for titrationWater in

Water jacket

Water out

Sealed cover

Titrant (acid/base)

NitrogenpH probe

equation:

- ( F + + r_, = ^ (io,)m(SSA)

where e is the charge on an electron, Na is the Avogadroconstant, [C] is the electrolyte concentration, V is theadditional amount of acid or base required for the samepH change in the presence of solid particles, and SSA isthe specific surface area.

The calculation is repeated for all pH values greaterthan initial pH, pH0, and the titrations are repeatedwith acid to cover the full pH range (if necessary).The relative amount of OH~ adsorbed is also equalto the relative surface charge (G0). The latter is thenplotted as a function of the pH for a particular electrolyteconcentration. The experiment is then repeated for otherelectrolyte concentrations (e.g. 0.1 M and 0.3M NaNO3).The results can then be plotted on the same graph, asshown in Figure 10.4. The common intersection point(CIP) (Figure 10.4(a)) is also the point of zero charge(PZC) (Figure 10.4(b)), since it is only at the PZC thatthe relative surface charge (OQ) is independent of thebackground electrolyte concentration. The CIP is thentranslated to a0 = 0 to generate a plot of the absolutevalues of a0 at any given pH.

Some of the experimental considerations required inorder to obtain accurate results are as follows:

• The background electrolyte used should be "indiffer-ent".

• The surfaces of the particles should be insoluble.• Sufficient delay time should be allowed between

titrant additions.• The pH probe used for the experiments should be very

accurate (±0.01 pH units or better).

3 THE ELECTRICALDOUBLE-LAYER

Surface charge on a particle results in an unequaldistribution of ions in the polar medium in the vicinityof the surface. Ions of opposite charge (counterions) areattracted to the surface, and ions of like charges (co-ions) are repelled away from the surface. This unequaldistribution gives rise to a potential across the interface.The exact distribution of the counterions in the solutionsurrounding the charged surface is very important, sinceit determines the potential decay into the bulk from thecharged surface. Electrostatic attraction, thermal motionand forces other than electrostatic (specific adsorption)influence the counterions in the vicinity of the surface.

Several models have been proposed for the distri-bution of ions in the vicinity of the surfaces, and aresummarized below.

3.1 Helmholtz model

In 1879, von Helmholtz proposed that all of the coun-terions are lined up parallel to the charged surface at adistance of about one molecular diameter (Figure 10.5).The electrical potential decreases rapidly to zero withina very short distance from the charged surface in thismodel. Such a model treated the electrical double-layer as a parallel-plate condenser, and the calcula-tions of potential decay were based on simple capacitorequations. However, thermal motion leads to the ionsbeing diffused in the vicinity of the surface, and thiswas not taken into account in the Helmholtz model.

3.2 Gouy- Chapman model

This model, proposed by Gouy (1910 and 1917) andChapman (1913), consists of a diffuse distribution of thecounterions, with the concentration of such ions fallingoff rapidly with distance near to the surface, because

Figure 10.4. Schematic showing the conversion of relative sur-face charge (a) into absolute surface charge (b). The commonintersection point (CIP) defines the point of zero charge (PZC)

Surfa

ce ch

arge Point of zero charge (PZC)

Increasing salt

PH

PH

Common intersection point (CIP)

Relat

ive su

rface

cha

rge

Figure 10.5. Schematic representation of the Helmholtz modelof the electrical double-layer: (a) distribution of counterions inthe vicinity of the charged surface; (b) variation of electricalpotential with distance from the surface

of the screening effect, and then falling off gradually(Figure 10.6). Such a model is accurate for planarcharged surfaces with low surface charge densities, anddistances far away from the surface, but is inaccurate forsurfaces with high surface charge densities, especiallyat small distances from the charged surfaces, since ittreats the ions as point charges and neglects their ionicdiameters.

3.3 Stern-Graham model

This model, shown in Figure 10.7, divides the double-layer into two parts, i.e. (i) a fixed layer of stronglyadsorbed counterions, adsorbed at specific sites on thesurface, and (ii) a diffuse layer of ions similar to thatof the Gouy-Chapman model. The fixed layer of ionsis known as the Stern layer, and the potential decaysrapidly and linearly in this layer. The potential decay ismuch more gradual in the diffuse layer. In the case ofspecifically adsorbing ions (multivalent ions, surfactants,etc.) the sign of the Stern potential may be reversed.

Figure 10.7. Schematic representation of the Stern-Grahammodel of the electrical double-layer: (a) distribution of coun-terions in the vicinity of the charged surface; (b) variation ofelectrical potential with distance from the surface

Mathematical treatment of the electrical double-layeris given in refs (1) and (2) and the interested readeris referred to these books for detailed mathematicaldescriptions of the various models.

Distance from surface

SolutionSurface

Poten

tial

Distance from surface

SolutionSurface

Poten

tial

Distance from surface

Poten

tial

Surface

Solution

Figure 10.6. Schematic representation of the Gouy-Chapmanmodel of the electrical double-layer: (a) distribution of coun-terions in the vicinity of the charged surface; (b) variation ofelectrical potential with distance from the surface

4 ZETAPOTENTIAL(ELECTROKINETIC POTENTIAL)

Zeta potential is the potential of the surface at theplane of shear between the particle and the surroundingmedium as the particle and medium move with respectto each other. In the presence of an applied electric field,the charged surface (and the attached material) tends tomove in the appropriate direction, while the counterionsin the mobile part of the double-layer would have a netmigration in the opposite direction. On the other hand,an electric field would be created if the charged surfaceand the diffuse part of the double-layer were made tomove relative to each other. The plane of shear is beyondthe Stern plane, and the zeta potential facilitates easyquantification of the surface charge. The pH at whichthe calculated zeta potential value is zero is known asthe isoelectric point (IEP).

4.1 Measurement of zeta potential

The zeta potential of a particle is calculated from elec-trokinetic phenomena such as electrophoresis, streamingpotential, electro-osmosis and sedimentation potential.Each of these phenomena and the determination of zetapotential by using each technique will be discussedbriefly in this section.

1. Electrophoresis This is the movement of a chargedsurface along with the adsorbed ions, in relation toa stationary liquid under the influence of an appliedelectric field. The electrophoresis cell consists of ahorizontal glass tube with inlet and outlet taps and anelectrode at each end. Platinum black electrodes areemployed for salt concentrations in the range from10~3 to 10~2 mol dm~3, or otherwise appropriatereversible electrodes such as Ag/AgCl or Cu/CuSO4

must be used so as to avoid gas evolution. A flatmicroelectrophoresis cell is shown in Figure 10.8.The mobility of the particle is viewed under themicroscope at a "stationary plane" in the cell, wherethe electro-osmatic flow of the liquid caused by thecharged surface of the cell is compensated by thereturn flow of the liquid. For a cylindrical cell, thestationary plane is located at 0.2 and 0.8 of thetotal depth, with the exact location depending on thewidth/depth ratio.The electrophoretic mobility is calculated from thetime that a particle takes to travel a fixed distance.The zeta potential, § (potential at the shear plane),is calculated by using the Smoluchowski equation

Illuminating light source

Figure 10.8. Schematic of a vertically mounted flat microelec-trophoresis cell

for spherical particles, which can be treated as pointcharges, as follows:

UE = — (10.2)

where UE is the mobility under an applied potentialE, s is the permittivity of the electrolyte medium,and T] is the viscosity of the medium.Electrophoretic-mobility-measurement-based instru-ments are more suited for the determination of zetapotentials of fine particles.

2. Streaming potential The liquid in the capillary of aporous plug carries a net charge given by the mobilepart of the electrical double-layer. When the liquidflows through the capillary or the plug, it gives rise toa streaming current and consequently a potential dif-ference. An apparatus suitable for studying streamingpotentials is illustrated in Figure 10.9.The streaming potential can be measured by using amicrometer instead of an electrometer. To minimize

Sample in Sample out

Plug

Electrometer

Perforated electrodes

Figure 10.9. Schematic of an apparatus for measuring stream-ing potential

Sample

Microscope

Sample

ElectrodeElectrode

Figure 10.10. Schematic of the capillary method used for themeasurement of electro-osmosis

electrode polarization, an alternating streaming cur-rent can be generated by forcing the liquid throughthe plug by a reciprocating pump.If E is the potential difference developed across acapillary of radius a and length /, for an appliedpressure difference /?, we can write the following:

E = ^ - (10.3)

where s is the permittivity of the medium, f is thezeta potential, 77 is the viscosity of the liquid, and K0

is the conductivity of the electrolyte solution.3. Electro osmosis This technique involves the move-

ment of a liquid relative to a stationary chargedsurface (e.g. a capillary or porous plug) by the appli-cation of an electric field. Experimentally, zeta poten-tials may be measured by this method by means ofan apparatus such as that shown in Figure 10.10. Thepotential is supplied by electrodes, as shown in theschematic, and the transport of liquid across the tubeis observed through the motion of an air bubble inthe capillary providing the return flow. For water at25°C, a field of about 1500 V/cm is needed to pro-duce a velocity of 1 cm/s if the surface potential (^r0)is 100 mV.

4. Sedimentation potential This is the creation of anelectric field when charged particles move relative toa stationary fluid. This technique is the least com-monly used for the determination of zeta potential,because of several limitations associated with themeasurement and calculation of the zeta potential.

A selection of some of the commercially availableinstruments for measuring zeta potential, and the rel-evant techniques employed by these, is presented inTable 10.1.

4.2 Manipulation of zeta potential

The zeta potential has wide ranging applications inparticulate processing. However, control of the zeta

Table 10.1. Commercially available instruments for measuringzeta potential, and the corresponding techniques employed

Instrument Technique

Zeta Meter 3.0+ ElectrophoresisRank Brothers Mark II ElectrophoresisZpi, Inc.- Zeta Reader ElectrophoresisLaval Lab Zetaphoremeter III ElectrophoresisMicromeritics Zeta Potential Electrophoresis

Analyser 1202

Laval Lab Zetacad Streaming potentialBrookhaven-BI-EKA (Electro Streaming potential

Kinetic Analyser)

Dispersion Technology (DT200, AcoustophoresisDT300, DT 1200)

AcoustoSizer II Acoustophoresis

Brookhaven Zeta Plus/Zeta Pals Laser Doppler/Photoncorrelation (PCS)

Coulter Delsa 440 SX Laser Doppler/Photoncorrelation (PCS)

In Capillary

Electrode

Plug

Electrode

Alumina

Silica

Zeta

pot

entia

l (m

V)

pH

Figure 10.11. Variation of the zeta potential as a function ofpH for silica and alumina

potential within a specific range is necessary in orderto control such processing. In this present section, theuse of solution pH and ionic condition for manipulatingthe zeta potential will be illustrated.

1. pH The variation of the zeta potential with pH isshown in Figure 10.11. It can be seen that at low pHvalues the zeta potential is positive and as the pH isincreased, the zeta potential decreases, goes throughzero at a pH known as the isoelectric point (IEP),and finally becomes negative as the pH is furtherincreased. The IEPs of some common oxides andminerals are presented in Table 10.2.

PH

Figure 10.12. Illustration of the effect of increasing ionicstrength on the zeta potential for alumina

2. Ionic strength In the presence of indifferent ions, thezeta potential is reduced and goes towards zero asthe ionic strength is increased (Figure 10.12). How-ever, in the presence of specifically adsorbing ions,depending on the nature of such ions, the IEP shiftsand the sign of the zeta potential may be reversed(Figure 10.13 (3)). In this figure, for calcite in apatitesupernatant, the specifically adsorbing ion is PO4

3",and we see that the IEP shifts to lower pH and thesign of the zeta potential is reversed. In case of apatitein caleite supernatant, Ca2+ acts as the specificallyadsorbing ion and shifts the IEP to a higher pH value.

PH

Figure 10.13. Effects of specifically adsorbing ions on the zetapotentials of calcite and apatite (after ref. (3))

5 ELECTROSTATIC FORCES

The presence of surface charges leads to the develop-ment of a potential gradient in the vicinity of the sur-face. The Poisson-Boltzmann (PB) distribution, whichassumes ions as point charges and non-interacting,defines the potential distribution as a function of thedistance from the surface as follows:

d2x/f 2Zen (Ze$\ / i n ..T T = sinh —-f- (10.4)dx2 ers0 \ kT J

where Z is the electrolyte valency, e the elementarycharge (C), n the electrolyte concentration (#/m3), Ex thedielectric constant of the medium, E0 the permittivity ofa vacuum (F/m), k the Boltzmann constant (J/K), and Tthe temperature (K).

When solved, the PB equation gives the potential(^r), the electric field (differential of the potential) andthe counterion density at any distance (x) away from thesurface.

The Debye-Huckel parameter (/c) describes thedecay length of the electrical double-layer, while theinverse of the parameter, /c"1, which is known as theDebye length, indicates the distance away from thesurface where the distribution of ions in the solutionis affected by the presence of a charged surface:

V E,£okT )

where all of the symbols are as defined above forequation (10.4). Figure 10.14 shows the variation of the

Zeta

pote

ntial

(mV)

Zeta

pot

entia

l (mV)

Increasingionic strength

Table 10.2. Isoelectric points (IEPs) of some common oxidesand minerals

Material

QuartzSol-gel silicaAluminaTitaniaZirconiaHematiteMagnesiaMolybdenum oxideVanadium oxideZinc oxideChromium oxideTin oxideCalcium carbonateMulliteKaolin (edge)ApatitePotassium feldspar

Chemical formula

SiO2

SiO2

Al2O3

TiO2

ZrO2

Fe2O3

MgOMoO3

V2O5

ZnOCr2O3

SnO2

CaCO3

3Al2O3 • 2SiO2

Al2O3 • SiO2 • 2H2O10CaO • 6PO2 • 2 H2OK2O • Al2O3 • 6SiO2

IEP

2.02.58-95-64-68-912.0

0.5-10.5-1

9.06-74-59-106-86-74-63-5

Electrolyte concentration (M)

Figure 10.14. Variation of the Debye length with electrolyteconcentration for different z-z electrolytes

Debye length as a function of the electrolyte concentra-tion for electrolytes with different valences. The extentof the double-layer decreases with increasing electrolyteconcentration due to the shielding of surface charge,with ions of higher valences being more effective inscreening such charge.

The overlap of similar electrical double-layers leadsto a repulsive interaction, which will be summarizedin the following sub-section. A schematic showingthe overlap of electrical double-layers is presented inFigure 10.15, where part (b) illustrates the potentialdistribution after overlapping of such layers. In thisfigure, the dashed lines show the potentials expectedfrom single double-layers, while the continuous linerepresents the potential due to the overlap. The expectedpotential due to the latter is higher, thus leading toa higher counterion concentration, which results ina higher osmotic pressure, which tends to push theparticles further apart.

5.1 Calculation of electrostatic forces

5JJ Boundary conditions

1. Constant potential surfaces Under the assumptionof a constant potential, the potential distributionnear the surface remains constant. In order tomaintain electro-neutrality, as the electrical double-layers overlap, the concentration of the counterion

Figure 10.15. Schematic representations of the potential dis-tribution between two approaching surfaces, shown (a) before,and (b) after overlap of the electrical double-layer; overlapleads to a higher potential between the planes, thus resultingin repulsion

increases. This increase leads to more counterionadsorption on the approaching surfaces, thus resultingin a decrease of the Stern charge. As a result, sucha model predicts the minimum repulsion. Surfacesthat develop charge by ion adsorption (AgI, NaCl,KCl, air bubbles, etc.) are best represented by thisboundary condition.

2. Constant charge surfaces In these systems, as thesurfaces approach each other, the charge on the sur-faces remains constant, thus resulting in a maximumpredicted repulsion between them. This model is theclosest fit for surfaces that develop charges throughsite dissociation (Al2O3, TiO2, latex, microbes, etc.).

3. Charge regulated surfaces In reality, most surfacesdisplay an intermediate behaviour between constantcharge and constant potential. For example, silica(SiO2) can develop surface charge by both sitedissociation and ion adsorption:

Surface dissociation SiOH < • SiCT + H+

(10.6)

Ion adsorption SiO -Na+ < > SiO~ + Na+

(10.7)Information about the number of sites per unit areafor each site is needed to calculate the surface charge.Because of the complexity of the charge-regulationmodel, many experiments under different conditions(pH, ionic strength, etc.) are needed in order to

Deby

e len

ght,

K 1 (n

m)

Distance from surface

Poten

tial

Poten

tial

Distance from surface Distance from surface

Poten

tial

Poten

tial

extract the dissociation constants for the (surface)reactions responsible for surface charge development.The charge-regulated-surface assumption predicts themagnitude of the repulsion to be between that ofconstant charge and constant potential.

5.1.2 The linearized Poisson-Boltzmannapproach

In order to calculate the repulsive interaction due to theoverlap of the electrical double-layers (EDLs), the PBequation (equation (10.4)) needs to be solved numeri-cally, which is difficult and computationally intensive.An easier approach is to produce analytical formulae byusing a series of approximations. The PB equation canbe written in terms of series expansion terms; for low-surface-charge and low-ionic-concentration conditions,even the first term of the expansion results in a more orless accurate estimate of the repulsive interaction.

5.1.3 Analytical formulae

Based on the above simplifications, analytical formulaecan be produced for the calculation of the electrostaticenergy of interaction between two flat surfaces. Appro-priate formulae for two different models, i.e. constantpotential and constant charge, are given as follows:

Constant potential (4)

^V(#)flt/flt = 2ZzmkT [j^J ~[l~ t a n h ~Y )

(10.8)Constant charge (4)

Wa(H)m/m = 2Z2^kT (^) I (co th^- l )

(10.9)where Wflt/flt is the energy between two flat plates (J/m2),H the separation distance (m), Z the valency, nx the ionconcentration (#/m3), k the Boltzmann constant (J/K),T the temperature (K), e the electron charge (C), ^8 theStern potential (V), and K the Debye-Huckel parameter(m-1).

For large separation distances, Wf = Wa, and isgiven by the following equation (4):

64nkTWV (//)pit/plt = Wa (H)pu/pu =

K

x tanh2 (7^)e-*H (10.10)V 4kT )

Separation distance (nm)

Figure 10.16. Variation of the electrostatic interaction energywith separation distance for different surface potentials, calcu-lated by using the constant-potential assumption (ionic strength,0.001M; K~Y, 905 nm)

Figure 10.16 illustrates the variation of the electrostaticinteraction energy (mN/m) as a function of separationdistance for three different surface potentials by usingthe constant-potential assumption. As mentioned ear-lier, the constant-charge assumption will yield higherrepulsion energies in all cases. It can be seen that asthe separation distance increases, the interaction energydecreases. In addition, the interaction energy decreaseswith decreasing surface potential. Figure 10.17 depictsthis by showing that as the ionic strength of the solu-tion is increased, the Debye length decreases, and hencethe range of the interaction energy also decreases due toshielding of the surface charges.

Intera

ction

force

/ rad

ius (m

N/m)

Inter

actio

n fo

rce

/ rad

ius (m

N/m)

Separation distance (nm)

Figure 10.17. Variation of the electrostatic interaction energywith separation distance for different ionic strengths, calculatedby using the constant-potential assumptions (̂ r8» 30 mV)

So far, only basic concepts have been outlined aboutthe surface charge behaviour and its implications con-cerning interactions between charged surfaces. Mostapplications demand a control of interaction forcesand/or surface behaviour, e.g. dispersion/agglomerationor the wettability of particulate systems. This is achievedby the use of polymer/surfactant or particulate coat-ings on core particles. The manipulation of surfacebehaviour and/or interactions by polymeric coatings isdiscussed next.

6 MANIPULATING SURFACEBEHAVIOUR BY POLYMERADSORPTION

The word polymer is derived from the Greek, with"poly" meaning many and "mer" meaning part. Accord-ing to the IUPAC definition, "A polymer is a substancecomposed of molecules characterized by the multiplerepetition of one or more species of atoms or groupsof atoms (constitutional repeating units), linked to eachother in amounts sufficient to provide a set of propertiesthat do not vary markedly with the addition of one or afew of the constitutional repeating units". Polymers aremade from repeating units of chemical species known asmonomers, with typical molecular weights between 50and 100 Da. Some of the polymers used in particulateprocessing are illustrated in Figure 10.18.

Polymers at particle surfaces play an importantrole in a range of technologies such as stabilization,flocculation, enhanced oil recovery and lubrication. Inorder to control and optimize these technologies, it isvery important to understand the adsorption of polymersat the particle surfaces.

6.1 Solution behaviour of polymers

In order to understand the role played by polymersat interfaces in particle processing, it is important tounderstand the solution behaviour of such materials. Thetwo major theories concerning this are briefly describedbelow.

1. Flory-Huggins theory This theory calculates thefree energy of mixing of pure amorphous polymerswith pure solvent. The entropy and the enthalpyof mixing can be calculated separately, and thefollowing relationship applies:

AGM = AHM - TASM (10.11)

where AGM is the total free energy change, AHM

is the enthalpy change, and ASM is the change inentropy, all with respect to mixing.

The entropy of mixing was originally calculatedby Flory using a lattice approach, but it can alsobe derived by using a free volume approach. Theentropy of mixing, ASM, can be denoted by thefollowing equation (1):

ASM = -k(ni\nvi +n2\nv2) (10.12)

where k is the Boltzmann constant, n\ the numberof solvent molecules, n2 the number of polymermolecules, v\ the volume fraction of the solvent inthe polymer solution, and V2 the volume fraction ofthe polymer.

The enthalpy of mixing is calculated by con-sidering mixing to be a quasi-chemical reaction (1)between the dissimilar solvent contacts and segmentcontacts, which can be expressed as follows:

1 - 1 + 2 - 2 = 2 ( 1 - 2 ) (10.13)

Equation (10.13) depicts the formation of two sol-vent-polymer contacts (1-2) from a solvent-solventcontact (1-1), and a polymer segment-segment(2-2) contact. An interaction parameter, / i , isdefined where xi&T is the difference in energy ofa solvent molecule immersed in pure polymer, rela-tive to that in pure solvent. For n\ solvent molecules,

Polyethylene oxide) (PEO)

Polypropylene oxide) (PPO)

Poly(vinyl alcohol) (PVA)

Poly(acrylic acid) (PAA)

Poly(methacrylic acid) (PMAA)

Polyacrylamide (PAM)

Figure 10.18. Some common polymers used in particulateprocessing

the energy change is ti\X\kT. The probability of asolvent molecule being in contact with a polymersegment in a polymer solution is i>2, and hence theenthalpy of mixing, A//M , can be denoted by thefollowing equation [I]:

AHM = H1V2XIkT (10.14)

Therefore, by combining equations (10.11), (10.12)and (10.14), the free energy of mixing is given by:

AGM Z=IcT(H1InV1 +«2lnv2+AIiV2Xi) (10.15)

It can be seen that the dominating reason for disso-lution of a polymer is the increase in entropy of thesolvent (e.g. water) molecules.

2. Free volume theory In the Flory-Huggins theory,Xi was considered primarily as an enthalpy term,although it was later shown experimentally that formany non-aqueous polymer-solvent systems, posi-tive values of Xi, which oppose the mixing of solventand polymer, are determined by entropic considera-tions. The enthalpy terms are relatively small, andthe sign can vary depending on the conditions (1). Inaddition, it was found that Xi depends on the polymerconcentration, and varies between 0.1 and 0.5, withXi becoming more positive as the polymer concen-tration increases. The Flory-Huggins theory predictsthat the mixing would be favoured as the tempera-ture increases, since the mixing is entropy driven.However, phase separation has been observed formost polymer solutions near the critical point of thesolvent. (The latter is defined as the temperature atwhich the transition takes place from a good solventto a poor solvent)Most of the shortcomings of the Flory-Hugginstheory have been overcome by the use of the freevolume theory (1). The entropic contribution to Xiwas attributed to the difference in free volumebetween the solvent and the polymer. The increasein the value of Xi with concentration was explainedon the basis of the ordering of the solvent moleculeson increasing the segment concentration. The phaseseparation near the critical temperature of the solventwas attributed to the decrease in entropy on mixingthe solvent and polymer under such conditions.

An important length-scale associated with polymer solu-tions is the root-mean-square radius of the polymer coilin the solution. For an unperturbed coil, this is knownas the unperturbed radius of gyration, Rg, and is givenby the following (1):

s V6 V6

where n is the number of segments, / the effectivesegment length, M the molecular weight and M0 thesegment molecular weight. Equation (10.16) is validso long as the solvent is "ideal" for the polymer, i.e.there are no interactions, either attractive or repulsive,between the segments in the solvent. In real (non-ideal)solvents, the effective size of a coil can be larger orsmaller than the unperturbed radius Rg, and is sometimesreferred to as the Flory radius, /?F, where R¥ = aRg, anda is the intramolecular expansion factor, which dependson the nature of the solvent.

6.2 Adsorption of polymer at the particlesurface

The free energy of the overall process must befavourable in order for a polymer to adsorb at a parti-cle surface. The different factors contributing to the freeenergy change, when polymer adsorption takes place,are as follows (5):

• the adsorption energy, due to contacts of the polymersegments with the surface

• the conformational entropy of the chains• the entropy of mixing of chains and solvent• the polymer-solvent nearest-neighbour interactions

Adsorption takes place only if the energy of a seg-ment-surface interaction is lower than that of a sol-vent-surface interaction (the first factor given above).A quantitative measure for this energy is the dimen-sionless parameter Xs, which is defined such that thenet effect of the exchange of a solvent molecule on thesurface and a segment in the bulk solution is —xskT.For polymer adsorption to take place, x* n a s to bepositive and the adsorption energy is proportional tothe number of adsorbed segments. Polymers bond withsurfaces through a variety of mechanisms, includingelectrostatic interactions, hydrogen bonding, hydropho-bic interactions and specific chemical bonding, and thefree energy for adsorption can be given by the followingformula:

AG°ds = AG°lec + AG°hem + AG«ydrophoblc

+ AGtb o n d i n g + --- (10.17)

Depending on the surface chemistry, and the natureand energetics of the sites on the surface of the particle,different factors contribute to the adsorption energy. Inorder to control polymer adsorption on surfaces, theinterplay between the different adsorption mechanismsshould also be considered.

The second and third factors listed above representthe entropy loss occurring upon adsorption, and hencecan be considered as the opposing forces for polymeradsorption. The second accounts for the reduction of theinternal degrees of freedom within the chains when theyadsorb, while the third is related to the conflgurationalentropy loss, which occurs when the homogeneouspolymer solution is separated into a polymer-rich surface"phase" and a solution that becomes enriched withrespect to the solvent.

The final factor results from the mutual interactionbetween segments and solvent molecules. In a poor sol-vent, the segment-solvent interaction is unfavourable.This forces the polymer out of the solution, thus promot-ing adsorption. In a good solvent, the segment-solventinteraction is favourable, while the aggregation of seg-ments is unfavourable and as a result the adsorbedamount is less.

At equilibrium, in order to minimize the energy theadsorbed layer consists of polymer chains with severalstretches of segments in the surface layer (trains),with the parts connecting the trains sticking out intothe solution (loops). Moreover, at the chain ends,freely dangling tails may protrude into the solution.(Figure 10.19). The relative amount of the polymersegments, in trains, loops and tails, depends on theenergetics of the polymer adsorption process discussedearlier.

6.3 Role of surface chemistry andstructure in polymer adsorption

For a particular polymer functionality, the adsorptiondepends on the nature and energetics of the adsorptionsites that are present on the surface. The adsorptionof polymers via electrostatics, chemical bonding andhydrophobic attraction is relatively well understood,

and most of the unexpected adsorption behaviour isattributed to hydrogen bonding, which is ubiquitousin nature. In this section, the dependence of hydrogenbonding on the surface chemistry will be presented, toillustrate how, by clever manipulation of the surfacechemistry, hydrogen bonding can be controlled andpredicted.

For a hydrogen-bonding polymer such as polyethy-lene oxide) (PEO), whose ether oxygen linkage actsas a Lewis base, it was illustrated that not only doesthe number of hydrogen-bonding sites differ from onesurface to another, but the energy of such sites alsovaries (6). Based on adsorption studies of PEO onsilica and other oxides (6), it was demonstrated thatthe amount of adsorbed polymer depends on the natureof the Br0nsted acid sites on the particles. (Br0nstedacids are defined as proton donors.) Hence, the moreelectron-withdrawing is the underlying substrate, thenthe greater is the Bronsted acidity, and thus the lowerthe isoelectric point of the material. It can be seenfrom Figure 10.20 that SiO2, MoO3 and V2O5 stronglyadsorb PEO, whereas oxides with a point of zerocharge (pzc) greater than that of silica, such as TiO2,Fe2O39Al2O3 and MgO, did not exhibit significantadsorption of PEO. However, within a single system(silica) it has been found that PEO will adsorb to

Satur

ation

ads

orpti

on d

ensit

y (m

g/m2)

PHpzc

Figure 10.20. The effect of surface-Br0nsted acidity on theadsorption of a hydrogen-bonding polymer, poly(ethyleneoxide) (PEO) (after ref. (6)). ("Reprinted from InternationalJournal of Mineral Processing, 58, S. Mathur, P. Singh andB. M. Moudgil, Advances in selective flocculation technologyfor solid-solid separations, Page 212, Copyright (2000), withpermission from Elsevier Science")

Figure 10.19. Structure of an adsorbed polymer layer at thesolid-liquid interface

Trains

Tails

Tails

Loops

sol-gel-derived silica but not to glass or quartz at highpH values (6). This suggests that not only is the typeof Bronsted acid site important, but that its strength, asdetermined by the surface molecular architecture, alsoinfluences the adsorption process. It was also proventhat by surface modification, using techniques suchas calcination and re-hydroxylation (7), the nature andenergetics of the surface sites could be modified. Uponcalcination of silica surface to 800°C, the number of

isolated surface hydroxyl groups and three-memberedsilicate rings increased, thus resulting in a higher surfaceacidity. These changes led to higher adsorption of thePEO polymer (Figure 10.21) (7). Based on the polymerfunctionality, it may be possible to predict the surfacemolecular architecture or the surface sites that arerequired for the polymer to adsorb. Table 10.3 correlatesthe polymer functionalities with the nature of the surfacesites on which they adsorb (Lewis acid, Br0nsted acid,etc.).

7 MANIPULATING SURFACEBEHAVIOUR BY SURFACTANTADSORPTION

A surfactant (surface-active agent) is a substance which,when present at low concentrations in a system, adsorbson to the surface or interface of the system, and alters, toa marked degree, the surface or interfacial free energiesof the surface. Surface-active agents have a molecularstructure consisting of two distinct groups, namely thehead and the tail. The tail is a structural unit that hasvery little attraction for the solvent, and is known asa lyophobic group. The head has a strong attractionfor the solvent, and is called the lyophilic group. Thiskind of structure, consisting of lyophobic and lyophilic

Ceq (mg/l)

Figure 10.21. Adsorption of PEO on sol-gel silica afterdifferent treatments (calcined at 800° C; rehydroxylated) (afterref. (7))

r (m

g/m2)

Table 10.3. Correlation of polymer functionality with the surface absorption sites: PEO, poly(ethylene oxide); PVA,poly (vinyl alcohol); PAA, poly (aery lie acid); PAM, polyacrylamide(non-ionic); PAH, polyalamine

Polymer Repeat unit Functionality Adsorbs (to) Adsorption site

PEO

PVA

PAA

PAM

PAH

Ether

Hydroxyl

Carboxylic acid

Amide

Amine

SiO2

SiO2

Fe2O3, Al2O3, TiO2

Fe2O3, Al2O3, TiO2

SiO2

Br0nsted

Br0nsted

Lewis

Lewis

Br0nsted

Next Page