Journal of Colloid and Interface Science 297 (2006) 170–181www.elsevier.com/locate/jcis

Electrokinetic behavior and colloidal stability of polystyrene latex coatedwith ionic surfactants

A.B. Jódar-Reyes a,∗, J.L. Ortega-Vinuesa b, A. Martín-Rodríguez b

a Departamento de Física, Facultad de Veterinaria, University of Extremadura, Avda. Universidad s/n, 10071 Cáceres, Spainb Biocolloid and Fluid Physics Group, Department of Applied Physics, University of Granada, Av. Fuentenueva s/n, 18071 Granada, Spain

Received 17 July 2005; accepted 7 October 2005

Available online 10 November 2005

Abstract

This work is focused on analyzing the electrokinetic behavior and colloidal stability of latex dispersions having different amounts of adsorbedionic surfactants. The effects of the surface charge sign and value, and the type of ionic surfactant were examined. The analysis of the elec-trophoretic mobility (µe) versus the electrolyte concentration up to really high amounts of salt, much higher than in usual studies, supports thecolloidal stability results. In addition, useful information to understand the adsorption isotherms was obtained by studying µe versus the amountof the adsorbed surfactant. Aggregation studies were carried out using a low-angle light scattering technique. The critical coagulation concen-trations (ccc) of the particles were obtained for different surfactant coverage. For latex particles covered by ionic surfactants, the electrostaticrepulsion was, in general, the main contribution to the colloidal stability of the system; however, steric effects played an important role in somecases. For latices with not very high colloidal stability, the adsorption of ionic surfactants always improved the colloidal stability of the dispersionabove certain coverage, independently of the sign of both, latex and surfactant charge. This was in agreement with higher mobility values. Severaltheoretical models have been applied to the electrophoretic mobility data in order to obtain different interfacial properties of the complexes (i.e.,zeta potential and density charge of the surface charged layer). 2005 Elsevier Inc. All rights reserved.

Keywords: Interfaces and colloids; Polystyrene latex; Ionic surfactant; Electrophoretic mobility; Colloidal stability; Diffuse potential; Zeta potential;Electrolyte concentration

1. Introduction

It is well known that the adsorption of surfactants changesthe hydrophobic/hydrophilic character of the surface on whichthey are adsorbed. In the case of ionic surfactants, they also al-ter the surface charge. As a result, ionic surfactants are broadlyused as stabilizers/destabilizers of colloidal dispersions in sev-eral fields (i.e., industry, medicine, biology, mineral processing,and treatment of wastewater) [1,2].

In principle, a colloidal dispersion with low affinity for themedium (as polystyrene latex particles in water) is thermo-dynamically unstable and tends to aggregate spontaneously.However, if repulsive interactions take place among the par-ticles, this aggregation is slow enough to consider the system

* Corresponding author. Fax: +34 927257153.E-mail address: ajodar@unex.es (A.B. Jódar-Reyes).

0021-9797/$ – see front matter 2005 Elsevier Inc. All rights reserved.doi:10.1016/j.jcis.2005.10.033

as kinetically stable. This is the mean of the term “colloidalstability.” In the case of polystyrene latex, the synthesis proce-dure leads to some polar and/or charged groups on the surfaceof the particles. This causes the colloidal stability of the sys-tem by means of the repulsion originated by the overlappingof the electric double layers of the particles. Van der Waalsattractive forces are also present. When ionic surfactant mole-cules are adsorbed on latex, they modify the balance of theseforces, above all, those related to electrostatic contributions.The adsorption of chains on particles with the same sign ofcharge should increase the electrostatic repulsion. However,the adsorption on opposite charged surfaces would give riseto the charge cancellation and, as a consequence, to the desta-bilization of the system. Overcoming the adsorbed surfactantamount necessary to destabilize the system, stable complexescould be found again. Other contribution to the repulsive in-teraction among complexes is the steric interaction (osmosis

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and mixing [3,4]). This contribution could be strong enoughto maintain the colloidal stability of the complexes in absenceof electrostatic repulsion (at high electrolyte concentration).Analysing how the ionic surfactants modify the properties of amodel system (with known characteristics) will help to under-stand their role on different surfaces. Polystyrene latices cov-ered by nonionic surfactants (Triton X-100 and Triton X-405)have been already extensively studied [5]. The case of ionicsurfactant-polystyrene latex complexes is analyzed in this work.Latices with different surface charge sign and value were ex-amined. In addition, the effect of the type of surfactant (pos-itive and negative) was considered. A study of the electroki-netic behavior of such ionic surfactant–latex complexes wasperformed from two points of view. On the one hand, the elec-trophoretic mobility as a function of the adsorbed surfactantamount was analyzed, which gave information about differenttrends observed in the adsorption isotherm published in a pre-vious paper [6]. On the other hand, the mobility of particleswith different surfactant coverage was studied by increasingthe electrolyte (NaCl) concentration. Higher salt concentrationsthan those usually reported were reached in this work. Thismakes it interesting for understanding the charging of aqueous-hydrophobic interfaces, which is especially important in manyindustrial and biological systems where moderate or high ionicstrengths are required [7]. These measurements were also veryuseful to understand the colloidal stability results. The studyof the aggregation of the complexes by adding NaCl was doneby means of nephelometry. The critical coagulation concentra-tion (ccc) was obtained for complexes with different surfactantcoverage. Finally, a theoretical treatment of the electrophoreticmobility data allowed us to calculate different magnitudes re-lated to the interface of the covered latex systems, that is,the zeta potential and the surface density charge of the com-plexes.

2. Materials and methods

2.1. Reagents

All chemicals used were of analytical grade. NaCl salt waspurchased from Merck. The water was purified by a Milli-QAcademic Millipore system. Buffered solutions (borate forpH 9, phosphate for pH 7, and acetate for pH 5) present aconstant ionic strength of 2 mM. Nonbuffered solutions wereobtained by adding to water the amount of HCl or NaOH nec-essary to get the required pH. Ionic strength was kept constantwhen mixing of these solutions was necessary.

2.2. Latex particles

Two different polystyrene latices, synthesized in our lab-oratories, were used in this work. They were an anionic la-tex, namely, Lx(COOH), with weak acid groups on the sur-face coming from the iniciator 4,4′-azobis(4-cyanopentanoicacid) (ACPA), and an amphoteric latex, Lx(anfo), with positivecharge at acid pH and negative one at basic pH. This amphoteric

Table 1Characteristics of latices. PDI: polydispersity index, σ0: surface charge density

Latex Mean diameter (nm) PDI σ0 (mC/m2)

Lx(COOH) 364±13 1.004 −150±3 (pH 7)

−205±3 (pH 9)

Lx(anfo) 320±15 1.007 139±3 (pH 5)

−62±2 (pH 9)

character is due to the synthesis conditions, where azo N,N ′-dimethylenisobutyramidine hydrochloride (AMDBA) was usedas an initiator. These amphoteric polystyrene particles presenta more hydrophobic surface than those synthesized with otherinitiators [6]. Their main characteristics are shown in Table 1.The mean diameter of the particles was obtained by transmis-sion electron microscopy photographs (H-7000 FA Hitachi mi-croscope), which were automatically analyzed with the Bolerosoftware (AQ Systems), averaging over 500 particles per sam-ple. The polydispersity index of these latices (very close to unit)points out that the particle size distribution can be consideredextremely narrow. The surface charge density was determinedby conductometric and potentiometric automatic titrations em-ploying a pH meter (Crison Instruments, Model 2002), a con-ductometer (Crison Instruments, Model 525), and a Dosimat665 (Methrom) to add the titrant agent. Both latices presenta charge dependency on the pH. More details about the syn-thesis and characterization of these latices can be found else-where [6].

2.3. Surfactants

An anionic surfactant (sodium dodecylbenzenesulfonic, re-ferred to as NaDBS) and a cationic surfactant (Domiphen bro-mide or dodecyldimethyl-2-phenoxyethyl ammonium bromide,referred to as DB), both from Aldrich, were used in this study.They were well characterized as shown in Ref. [6]. The mole-cular weight was 348.48 g/mol for NaDBS, and 414.48 g/molfor DB. The critical micelle concentration, that is, the surfac-tant concentration at which micelles start forming, was obtainedin our lab by using several techniques [6]. Surface tension(ADSA-P technique, pendant drop method) provided the mostaccurate results. The cmcs in pH 7 buffer (2 mM) at 23 ◦Cwere (0.86 ± 0.03) mM for NaDBS, and (0.50 ± 0.03) mMfor DB. Dynamic light scattering measurements were used fordetermining the radius of the micelles [6]: (2.16 ± 0.04) nm forNaDBS, and (1.05 ± 0.03) nm for DB.

2.4. Methods

2.4.1. Adsorption isothermsThe adsorption isotherms were determined in a previous

work [6] by means of a spectrophotometric technique. Prelim-inary studies showed that there was surfactant desorption bydilution. Therefore, prior performing the kinetic or stability ex-periments where a particle concentration lower than that of theoriginal sample was required, the original pools were dilutedin surfactant solutions until reaching the corresponding equilib-rium surfactant concentration.

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2.4.2. Electrophoretic mobilityA Zeta Sizer IV (Malvern Instruments) was used to obtain

the electrophoretic mobility at low ionic strength for those ex-periments where the effect of the adsorbed surfactant amountwas studied. They were measured at 25 ◦C in buffered solutions.However, the analysis of the effect of the salt concentration(NaCl) was done in nonbuffered solutions and up to very highelectrolyte concentrations. This is why a device prepared formeasuring at such extreme conditions (ZetaPALS, BrookhavenInstruments) was used. This apparatus is based on the prin-ciples of phase analysis light scattering (PALS) [8,9] and isspecially useful at high ionic strength when the mobility isvery low. The particle concentrations in the experimental cellwere 3.00 × 10−3 and 1.67 × 10−3 mg/ml for Lx(anfo) andLx(COOH) respectively. The mobilities were measured 10 minafter mixing of particles and electrolyte solution.

2.4.3. Colloidal stabilityColloidal stability was studied by using a low-angle light-

scattering technique. Scattering light intensity was measuredat 10◦ for 120 s. A rectangular scattering cell with a 2 mmpath length was used. Equal volumes (1 ml) of NaCl and non-buffered latex solutions were mixed and introduced into the cellby an automatic mixing device. The latex dispersions used forthese experiments were diluted enough to minimize multiplescattering effects. The particle concentrations in the scatteringcell were 0.18 and 0.11 mg/ml for Lx(anfo) and Lx(COOH)respectively. The light scattered at low angle behaved linear forthe first steps of the coagulation. The stability ratio, also calledFuch’s factor (W) [10], is a criterion broadly used to study thestability of colloidal systems. It can be obtained by the follow-ing expression:

(1)W = kr

ks,

where the rate constant kr corresponds to rapid coagulation ki-netic, and ks is the rate constant for slow coagulation regime.The ratio of both constants is equal to that of the initial slopes inour coagulation experiments. The critical coagulation concen-tration (ccc) can be easily obtained by plotting the logarithm ofW versus the logarithm of the salt concentration and locatingthat point where logW reduces to zero.

3. Results and discussion

Different adsorbent surfaces were used in order to analysethe influence of the latex surface charge (sign and value) onthe electrophoretic mobility of the latex–surfactant complexes:Lx(COOH) at pH 9 and 7, and Lx(anfo) at pH 9 as negativesurfaces, and Lx(anfo) at pH 5 as a positive surface. The ad-sorbed surfactant amount of the complexes at such conditionsis known through the adsorption isotherms presented in a pre-vious work [6].

The results for each ionic surfactant will be presented sep-arately. We will distinguish between the case in which surfaceand surfactant have opposite charge sign and the case in whichthey have the same sign.

Fig. 1. Electrophoretic mobility of complexes as a function of the adsorbedamount of NaDBS on the surfaces: Lx(COOH) at pH 9 (1), Lx(COOH) atpH 7 (2), Lx(anfo) at pH 9 ("), Lx(anfo) at pH 5 (%).

3.1. Electrophoretic mobility as a function of theadsorbed amount

3.1.1. Anionic surfactant: NaDBSConsidering the electrophoretic mobility data shown in

Fig. 1, the influence of the surface characteristics was analyzedas follows:

(a) Surface and surfactant with opposite sign of charge.When NaDBS adsorbed on a positive surface (Lx(anfo) atpH 5), the mobility changed from positive, at low coverage, tonegative above certain adsorbed amount. Electrostatic bindingof surfactant anions to positively charged surface groups up tosurface neutralization explains the decrease in mobility values.At adsorbed amounts corresponding to the intermediate plateauin the adsorption isotherm (around Γ = 1.25 µmol/m2) [6],which are higher that the amount necessary to destabilize thesystem (Γ = 1.07 µmol/m2) [6], the mobility was negative. Asthe theoretical number of charged groups necessary to cancelthe surface charge is 1.44 µmol/m2, the electrostatic bindingat low surfactant concentrations was not 1:1. Therefore, the ad-sorption of other components of the solution (probably ions)could take place [11,12]. The fact that the mobility at the in-termediate plateau was negative, explains that the adsorptionof new negative chains is hindered in this region due to elec-trostatic repulsion between the adsorbed surfactants and thoseapproaching from the solution. The mobility became more neg-ative by adsorbing more surfactant. These results are similarto those obtained by Galisteo et al. [13] for alkyl sulfates ona cationic latex. They found a sharp increase in the mobil-ity above certain coverage that was explained by assuminghemimicelle formations on the surface. The rearrangement ofthe chains is also assumed for this system (see Ref. [6]), how-ever, the increase in mobility is not so sharp. This could beexplained again by counterion condensation [11,12].

(b) Surface and surfactant with the same sign of charge.If the original surface was negatively charged, the mobilityremained negative when NaDBS was adsorbed, as expected.However, differences were found depending on the type of sur-face. In the case of Lx(COOH) at pH 9, the mobility of the com-

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Fig. 2. Electrophoretic mobility of complexes as a function of the adsorbedamount of DB on the surfaces: Lx(COOH) at pH 9 (1), Lx(COOH) at pH 7 (2),Lx(anfo) at pH 9 (∅), Lx(anfo) at pH 5 (%).

plex became more negative by adsorbing NaDBS. Therefore,even though electrostatic repulsion existed between surface andsurfactant, adsorption took place by means of hydrophobic at-traction, as discussed in Ref. [6]. However, for a less chargedsurface, Lx(COOH) at pH 7, the mobility increased in absolutevalue up to certain coverage, after that, became slightly morepositive. Again, counterion condensation could reduce the ef-fective charge. The more negative mobility values of the com-plexes formed with Lx(COOH) at pH 9 explain the differencesin affinity found in the adsorption isotherms of this latex at pH 9and 7 (see Ref. [6]). The fact that the affinity of the adsorptionisotherm for Lx(anfo) at pH 9 was higher than for Lx(COOH)was mainly attributed to the higher hydrophobicity of the am-photeric surface [6]. However, the lower mobility in absolutevalue of the complexes formed with this latex at low coverageshowed that the electrostatic repulsion is also lower than thatof the Lx(COOH) at pH 7 and 9. The mobility became morenegative by adsorbing more NaDBS up to the surfactant asso-ciation started [6]. After this, counterion condensation reducedthe mobility in absolute value.

3.1.2. Cationic surfactant: DBThe electrokinetic behavior of the complexes formed using

the cationic surfactant is shown in Fig. 2.(a) Surface and surfactant with opposite sign of charge. The

mobility of all the negatively charged latices became positiveabove certain DB coverage. Electrostatic binding of cationicsurfactant to the negative surface groups together with the hy-drophobic attraction surfactant tail-surface explain these re-sults. However, the hydrophobicity of the surface and the valueof the surface charge influenced the electrokinetic behaviorof the complexes. The mobility for complexes formed withLx(COOH) at pH 9 remained negative up to DB coveragehigher than for the other surfaces. This explains that the ad-sorption at DB concentrations in the range (0.1–0.3) cmc washigher for this Latex at pH 9 than at pH 7 (for which the com-plexes already present a positive mobility). The mobility datafor Lx(COOH) at pH 9 showed that the charge neutralizationtook place around Γ = 2.0 µmol/m2. This means that, consid-

ering the surface charge density of the latex, the adsorption atthat point occurred at the 1:1 ratio. This result is in agreementwith the lowest colloidal stability of the complex at such a cov-erage (see below). After neutralization, the mobility becamemore positive by adsorbing more surfactant up to the maxi-mum coverage was reached. The theoretical number of chargedgroups necessary to cancel the surface charge for Lx(COOH) atpH 7 is 1.56 µmol/m2. However, the change in the sign of themobility took place at slightly lower coverage. Therefore, theelectrostatic binding at low surfactant concentrations was not1:1 and other components of the solution (ions) could be ad-sorbed [11,12]. The higher hydrophobicity of the Lx(anfo) atpH 9 led to a higher maximum adsorbed amount of surfactantthan on the other surfaces [6]. As a result, complexes formedwith Lx(anfo) at pH 9 presented higher mobility at high cover-age than those formed with the other latices.

(b) Surface and surfactant with the same sign of charge.For a surface positively charged, the mobility remained posi-tive by adsorbing a cationic surfactant. There was no significantchange in the mobility by increasing the adsorbed amount ofDB. As seen in the corresponding adsorption isotherm [6], themaximum surfactant adsorbed amount was relatively low. Thehydrophobic attraction was not able to overcome the electrosta-tic repulsion above certain coverage and a plateau was reached.

Unlike nonionic covered polystyrene particles, for which theelectrophoretic mobility decreases (in absolute value) as a resultof the adsorption of surfactant [14], we can see that the chargeof the ionic surfactant alters this result. We have observed thatthe mobility increases (in absolute value) by adsorbing surfac-tant in some cases.

3.2. Electrophoretic mobility as a function of theelectrolyte concentration

The electrophoretic mobility of the complexes was deter-mined for increasing NaCl concentrations in nonbuffered so-lutions. High electrolyte concentrations were used in order toreach mobility values near zero. All these µe results will becompared with the colloidal stability of the complexes in Sec-tion 3.3.

3.2.1. Anionic surfactant: NaDBS(a) Surface and surfactant with opposite sign of charge. The

results corresponding to the positive surface (Lx(anfo) at pH 5),are shown in Fig. 3. When the anionic surfactant was adsorbedon the positively charged surface above certain coverage nec-essary to charge neutralization, the complexes showed a neg-ative mobility. This negative mobility was relatively high (inabsolute value) up to very high salt concentrations. In agree-ment with other works [13], a maximum (in absolute value)was appreciated in all the curves (for every surfactant–latexcomplex presented in this work). Such a maximum is usuallyfound in the case of bare polystyrene beads [15,16], however, amonotonic decrease of mobility with increasing ionic strengthis observed for protein-latex complexes [17]. There exist sev-eral theories to explain this maximum in the case of bare latex:preferential ion adsorption [18,19], hairy layer (surface rough-

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Fig. 3. Electrophoretic mobility as a function of NaCl concentration forLx(anfo) at pH 5 (positive charge) and different adsorbed amount of sur-factant: Bare particles (2), ΓNaDBS = 1.75 µmol/m2 ("), ΓNaDBS = 2.40µmol/m2 (F), and ΓDB = 1.28 µmol/m2 (1).

Fig. 4. Electrophoretic mobility as a function of NaCl concentration forLx(COOH) at pH 9 (negative charge) and different adsorbed amount ofsurfactant: Bare particles (2), ΓNaDBS = 0.5 µmol/m2 ("), ΓNaDBS =1.98 µmol/m2 (F), ΓDB = 0.46 µmol/m2 (1), ΓDB = 2.0 µmol/m2 (!), andΓDB = 2.89 µmol/m2 (E).

ness) [20,21], or anomalous surface conductivity (conductivitybehind the slip plane) [22–24]. When an ionic surfactant is ad-sorbed, a new reason based on the hairy layer model couldbe considered: at low ionic strength, the electrostatic repulsionamong the adsorbed chains provokes that they are extendedto the aqueous phase. The shear plane where the ζ -potentialis defined would be far away from the surface. By increas-ing the electrolyte concentration, the chains could collapse to-ward the surface because of the screening of the surfactantcharge. Therefore, the shear plane is shifted nearer the sur-face and the ζ -potential increases. At higher ionic strength thedouble layer squeezes and the electrokinetic potential dimin-ishes. On the other hand, the anomalous surface conductivity(also known as additional surface conductivity) of a protein ad-sorbed layer is comparable with the diffuse layer conductivityand its importance in electrophoresis has been shown [25–27].By taking this into account, the role of the additional sur-face conductivity in the electrokinetic behavior of surfactant–latex complexes must be analyzed. This will be done in Sec-tion 3.4.

Fig. 5. Electrophoretic mobility as a function of NaCl concentration forLx(COOH) at pH 7 (negative charge) and different adsorbed amount ofsurfactant: Bare particles (2), ΓNaDBS = 0.15 µmol/m2 ("), ΓNaDBS =2.18 µmol/m2 (F), ΓDB = 1.52 µmol/m2 (1), ΓDB = 2.18 µmol/m2 (!),and ΓDB = 2.60 µmol/m2 (E).

Fig. 6. Electrophoretic mobility as a function of NaCl concentration forLx(anfo) at pH 9 (negative charge) and different adsorbed amount of surfactant:Bare particles (2), ΓNaDBS = 2.36 µmol/m2 ("), ΓDB = 2.12 µmol/m2 (1),and ΓDB = 3.31 µmol/m2 (!).

(b) Surface and surfactant with the same sign of charge.At low ionic strength (2 mM), the mobility of the complexesformed with Lx(COOH) at pH 9 (Fig. 1) became slightly morenegative by adsorbing NaDBS. However, the influence of thesurfactant coverage on the mobility was more significant athigh electrolyte concentrations (Fig. 4). Data for Lx(COOH)at pH 7 are shown in Fig. 5. At low ionic strength (see Fig. 1),the mobility value seemed not to be influenced by the adsorbedamount of NaDBS. However, relevant differences were foundat high ionic strength (Fig. 5). In addition, at very low cover-age (ΓNaDBS = 0.15 µmol/m2) the mobility of the complex athigh electrolyte concentrations was lower than that of the bareparticles. This was also observed for nonionic surfactants on la-tex [14], and it was explained by means of the displacement ofthe share plane toward the bulk due to the chains present on thesurface. At higher coverage, the net charge density of the par-ticles increases leading to higher µe values, finding a similarbehavior to that found at pH 9.

The increase in mobility caused by adsorbing NaDBS wasvery significant in the case of Lx(anfo) at pH 9 as shown in

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Table 2Critical coagulation concentration of complexes formed with NaDBS on different surfaces

Lx(anfo) at pH 5 Lx(COOH) at pH 9 Lx(COOH) at pH 7 Lx(anfo) at pH 9

ΓNaDBS(µmol/m2)

ccc(mM)

ΓNaDBS(µmol/m2)

ccc(mM)

ΓNaDBS(µmol/m2)

ccc(mM)

ΓNaDBS(µmol/m2)

ccc(mM)

0.00 230±20 0.00 550±20 0.00 460±20 0.00 109±201.75 680±20 0.50 590±20 0.15 580±20 2.36 580±202.40 640±20 1.98 620±20 2.18 620±20

Fig. 6. The mobility remained different from zero up to reallyhigh electrolyte concentrations, while the µe of the bare parti-cles rapidly reduced to zero when increasing the ionic strength.

3.2.2. Cationic surfactant: DB(a) Surface and surfactant with opposite sign of charge.

These results (Figs. 4–6) were in agreement with those foundfor the negative surfactant and the positive surface (Fig. 3).Above the coverage necessary to neutralize the negative chargeon the surface, the adsorption of more surfactant led to a changein the sign of the mobility. This mobility became more positiveby adsorbing more DB, and above certain coverage, was evenhigher in absolute value than the mobility of the bare particlesat high electrolyte concentrations. The results for Lx(COOH) atpH 9 are shown in Fig. 4. At low surfactant coverage, when themobility was still negative, differences only appeared at highelectrolyte concentration. The mobility became zero at higherNaCl concentration for the bare particles. The mobility wasstrongly reduced at ΓDB = 2.0 µmol/m2. At higher coverage,the mobility was lower than for the bare latex in absolute value,however, it became zero at the same NaCl concentration.

All the Lx(COOH)-DB complexes analyzed at pH 7 (Fig. 5)presented positive mobilities. These values became zero at anelectrolyte concentration much lower than the corresponding tothe negative bare latex case. There were no significant differ-ences by increasing the adsorbed amount of DB. However, datafor the maximum coverage were missed and they are expectedto be positive up to higher electrolyte concentrations (as seen inFig. 4 for pH 9).

The results for Lx(anfo) at pH 9 (Fig. 6) showed that thecomplexes had a positive mobility that was higher than that ofthe bare latex (in absolute value) above certain coverage at lowand high ionic strength.

(b) Surface and surfactant with the same sign of charge.When the surface was positive, Lx(anfo) at pH 5 (Fig. 3), themobility became more positive by adsorbing DB and remaineddifferent from zero up to very high electrolyte concentrations.This difference could not be appreciated at low electrolyte con-centration (2 mM), as seen in Fig. 2.

3.3. Colloidal stability

The critical coagulation concentration was determined forthe complexes analyzed in Section 3.2. The comparison be-tween colloidal stability and mobility data must be carefullydone, as the particle concentration used in mobility experimentsis two orders of magnitude lower than that used in colloidal sta-bility experiments. That is why bare particles are expected to

Fig. 7. Stability factor as a function of NaCl concentration for Lx(anfo) atpH 5 at different NaDBS coverage: ΓNaDBS = 0 µmol/m2 (2), ΓNaDBS =1.75 µmol/m2 ("), and ΓNaDBS = 2.40 µmol/m2 (P).

present mobility values close to zero at electrolyte concentra-tions much lower than the ccc.

3.3.1. Anionic surfactant: NaDBSThe ccc obtained for all the latices under study at different

NaDBS coverage are shown in Table 2.We will analyse again separately the case in which surface

and surfactant have opposite sign and the case in which theyhave the same sign.

(a) Surface and surfactant with opposite sign of charge. Theexperimental data from which the ccc is obtained for Lx(anfo)at pH 5 at different NaDBS are presented in Fig. 7. It is worthto highlighting that even thought the Lx(anfo) at pH 5 is posi-tive, the colloidal stability of the complexes formed adsorbinga negative surfactant was much higher than that of the bare la-tex above certain coverage. The electrokinetic behavior of thetwo complexes analyzed (Fig. 3) was similar up to high elec-trolyte concentration. This similarity was also found in stabilityresults (Fig. 7). Therefore, the electrostatic contribution to thecolloidal stability of these complexes was more important thanthe steric contribution.

(b) Surface and surfactant with the same sign of charge.If the surface was negatively charged, the ccc was alwayshigher when NaDBS was adsorbed (see Table 2). In the case ofLx(COOH) at pH 9, the important differences found in the elec-trokinetic behavior at the two studied NaDBS coatings (Fig. 4)were not reflected in the corresponding stability results. By sig-nificantly increasing the surfactant coverage, the electrokineticcharge remained different from zero up to much higher elec-trolyte concentrations. However, only small differences werefound between the cccs. For Lx(COOH) at pH 7, at very low

176 A.B. Jódar-Reyes et al. / Journal of Colloid and Interface Science 297 (2006) 170–181

Table 3Critical coagulation concentration of complexes formed with DB on different surfaces

Lx(anfo) at pH 5 Lx(COOH) at pH 9 Lx(COOH) at pH 7 Lx(anfo) at pH 9

ΓDB(µmol/m2)

ccc(mM)

ΓDB(µmol/m2)

ccc(mM)

ΓDB(µmol/m2)

ccc(mM)

ΓDB(µmol/m2)

ccc(mM)

0.00 230±20 0.00 550±20 0.00 460±20 0.00 109±20

1.28 460±20 0.46 450±20 1.52 83±10 2.12 90±502.00 100±10 2.18 105±10 3.31 320±502.89 200±10 2.60 80±10

Fig. 8. Stability factor as a function of NaCl concentration for Lx(COOH) atpH 7 at different NaDBS coverage: ΓNaDBS = 0 µmol/m2 (2), ΓNaDBS =0.15 µmol/m2 ("), and ΓNaDBS = 2.18 µmol/m2 (P).

coverage (ΓNaDBS = 0.15 µmol/m2) the mobility of the com-plex at high electrolyte concentrations was lower than that ofthe bare particles (Fig. 5). However, the ccc and the stabilitydata (Fig. 8) showed that the colloidal stability was higher. Inthis case, this stability must be mainly due to steric effects.When comparing the two studied coverage, the electrokineticand stability behaviors were more in agreement than in the caseof Lx(COOH) at pH 9. For Lx(anfo) at pH 9, the mobility wasdifferent from zero at the NaCl concentration correspondingto the ccc. That means that the existing electrostatic repulsionwas not enough to prevent coagulation. It should be noted thatthe ccc values of the complexes with the maximum adsorbedamount (see adsorption isotherms in Ref. [6]) were indepen-dent of the sign and value of the surface charge (Table 2). Thus,stability of fully coated particles only depended on the proper-ties of the outer part of the adsorbed surfactant layer.

3.3.2. Cationic surfactant: DBThe results for DB complexes on the different surfaces are

shown in Table 3.(a) Surface and surfactant with opposite sign of charge. If

the surface presents a negative charge, a minimum in the col-loidal stability is found at certain DB coverage (see Table 3).The complex with the lowest stability always presented a posi-tive mobility that became zero at a lower electrolyte concentra-tion than the bare latex did (Figs. 4–6). The electrostatic contri-bution seems to be important for the colloidal stability of thesecomplexes. For Lx(COOH) at pH 7, ccc values did not showa clear minimum by increasing the DB coverage. However,

Fig. 9. Stability factor as a function of NaCl concentration for Lx(COOH)at pH 7 at different DB coverage: ΓDB = 0 µmol/m2 (2), ΓDB = 1.52µmol/m2 ("), ΓDB = 2.18 µmol/m2 (P), and ΓDB = 2.60 µmol/m2 (!).

Fig. 10. Stability factor as a function of NaCl concentration for Lx(anfo) atpH 5 at different DB coverage: ΓDB = 0 µmol/m2 (2), and ΓDB = 1.28µmol/m2 (").

the lower stability for the complex at ΓDB = 1.52 µmol/m2

was observed in the stability data (Fig. 9). When the surfaceis Lx(COOH), the colloidal stability of the complex is lowerthan that of the bare latex. However, in the case of Lx(anfo) atpH 9, the complexes were more stable. This is a consequenceof the high stability of the bare Lx(COOH).

(b) Surface and surfactant with the same sign of charge. Ifthe surface is positive (Lx(anfo) at pH 5), the colloidal stabil-ity of the complex is higher than that of the bare latex (Fig. 10).Differences in the electrokinetic behavior (Fig. 3) are in agree-ment with the differences in the stability data. Once more, theelectrostatic contribution plays an important role on the col-loidal stability of these complexes.

A.B. Jódar-Reyes et al. / Journal of Colloid and Interface Science 297 (2006) 170–181 177

For DB surfactant, the highest stability corresponds to acomplex formed with the surface that reaches the lowest maxi-mum adsorbed amount, this is Lx(anfo) at pH 5 (see adsorptionisotherms in Ref. [6]). The mobility of such a complex alsobecame zero at higher NaCl concentration than the other com-plexes did.

3.4. Determination of zeta potential from electrophoreticmobility data

Different theories have been used in order to obtain theζ -potential of surfactant-colloidal particle complexes fromelectrophoretic mobility data [12,28,29]. Even though it is lim-ited to particles with κa � 1, where a is the particle radius andκ−1 is the Debye length, and low ζ -potential, Smoluchowskiequation is commonly used for this conversion [30].

(2)µe = εrε0

ηζ,

where εr is the relative dielectric constant of the solution, ε0the dielectric constant of vacuum, and η is the viscosity of thesolution.

Other authors prefer to use a relationship established fromthe solution of the full electrokinetic equations for the liquidflow, ionic flow, and the potential distribution, whose numericalcalculation was improved by O’Brien and White [31]. An ap-proximate analytic expression for the mobility was proposed byOhshima et al. [32] covering the whole range of ζ -potential andvalid for κa > 10. For a symmetric electrolyte with valency z,this equation results in

Em = sgn(ζ )

{3

2ζ̃ − 3F

1 + FH + 1

κa

[−18

(t + t3

9

)K

+ 15F

1 + F

(t + 7t2

20+ t3

9

)

− 6(1 + 3m̃)(1 − e−ζ̃ /2) + 12F

(1 + F)2H

+ 9ζ̃

1 + F(m̃G + mH)

(3)− 36F

1 + F

(m̃G2 + m

1 + FH 2

)]},

where sgn(ζ ) is the sign function, sgn(ζ ) > 0, if ζ > 0, andsgn(ζ ) < 0, if ζ < 0. Em is the dimensionless electrophoreticmobility, defined as

Em = 3ηze

2εrε0kBTµe

and ζ̃ is the reduced ζ -potential defined as

ζ̃ = ze|ζ |kBT

,

where kB is the Boltzmann constant, T the absolute tempera-ture, and e is the electron charge.

F = 2(1 + 3m)(eζ̃/2 − 1),

κa

G = ln1 + exp(−ζ̃ /2)

2,

H = ln1 + exp(ζ̃ /2)

2,

K = 1 − 25

3(κa + 10)exp

[− κa

6(κa − 6)ζ̃

],

t = tanhζ̃

4,

m = 2εrε0kBT NA

3ηzλ∞ ,

m̃ = 2εrε0kBT NA

3ηzλ̃∞ ,

where λ∞ and λ̃∞ are the limiting ionic molar conductivitiesof counterions and coions, respectively. This theory has beenrecently applied to SDS-polystyrene latex complexes [12], SDScovered graphite particles, and CTAB covered graphite particles[30].

Finally, as mentioned in Section 3.2.1, the additional sur-face conductivity (Kσ i) of the surfactant adsorbed layer couldplay an important role in the electrokinetic behavior of thesurfactant–latex complexes. To account for this phenomenon,ζ -potential of such complexes and electrophoretic mobility datahave been related by using the following expression [24] for1–1 electrolyte:

(4)Em = 3Du

1 + 2Du

[2 ln 2 − 2 ln

(1 + e

eζ2kBT

)] + 3ζ

2,

where Em is the dimensionless electrophoretic mobility as de-fined in Eq. (3).

The Dukhin number (Du) is defined through the conductivitybeyond the slip plane (Kσd), and the conductivity behind theslip plane (Kσ i) as [24]

Du = Kσd

aKL + Kσ i

aKL ,

where a is the radius of the particle, and KL is the bulk conduc-tivity given by

KL = (λ̃∞ + λ∞)c,

where λ∞ and λ̃∞ are the limiting ionic molar conductivitiesof counterions and coions, respectively, and c is the bulk elec-trolyte concentration (in mol/m3).

By assuming that Kσ i mainly comes from the counterionswithin the surfactant layer, and by identifying their diffusivity(Dσ ) with their bulk value (D), we have

Kσ i = eDσ i

kBT,

where σ i is the surface charge density in the Stern layer calcu-lated from the adsorbed surfactant amount (Γ ). The diffusivityof the ions is related with the dimensionless parameter m de-fined in Eq. (3) by means of

D = 2εrε0

3ηm

(kBT

e

)2

.

178 A.B. Jódar-Reyes et al. / Journal of Colloid and Interface Science 297 (2006) 170–181

Fig. 11. Theoretical predictions on ζ -potential for surfactant-Lx(anfo) pH 5complexes. Ohshima (Eq. (3)): bare particles (short dash–dot line), ΓNaDBS =1.75 µmol/m2 (dash line), ΓNaDBS = 2.40 µmol/m2 (dash–dot line), ΓDB =1.28 µmol/m2 (dash–dot–dot line). Including additional surface conductivity(Eq. (4)): ΓNaDBS = 1.75 µmol/m2 (2), ΓNaDBS = 2.40 µmol/m2 ("), andΓDB = 1.28 µmol/m2 (1). Surface potential of bare latex (Eq. (5)) (dot line).

The conductivity beyond the slip plane can be calculated byusing the following expression derived by Bikerman for 1–1electrolyte [24]:

Kσd = 2e2NAc

kBT κ

[D̃

(e− eζ

2kBT − 1)(1 + 3m̃)

+ D(e

eζ2kBT − 1

)(1 + 3m)

],

where D̃ and D are the bulk diffusivity of coions and counteri-ons, respectively, and m̃ and m where defined in Eq. (3).

In this work, we have applied Eqs. (2)–(4) to the ex-perimental mobility data of the different complexes to ob-tain the dependence of their ζ -potential on the electrolyte(NaCl) concentration. The following magnitude values corre-sponding to T = 298 K were used: εr = 78.54, ε0 = 8.85 ×10−12 C/(V m), η = 8.937×10−4 kg/ms, λ∞(Na+) = 50.15×10−4 �−1 m2 mol−1, λ∞(Cl−) = 75.85×10−4 �−1 m2 mol−1,λ∞(Br−) = 78.06 × 10−4 �−1 m2 mol−1 (Na+ and Cl− areconsidered as counterions or coions in Eqs. (3) and (4) depend-ing on the sign of the complex mobility). For a given valueof µe, Eq. (3) can be numerically solved for the ζ -potential.However, in some cases, there exist two solutions, and addi-tional information is required to choose the correct ζ -potential.The maximum in the µe–ζ -potential curve disappears whenEq. (4) is used. However, in some cases, at low electrolyteconcentrations, Eq. (4) predicts mobility values lower (in ab-solute value) than the experimental ones up to unrealistichigh ζ -potential values. In these cases, Eq. (4) does not givea solution for the µe–ζ -potential curve, and the correspond-ing data are missed in the ζ -potential–κa plot (see Fig. 11,ΓDB = 1.28 µmol/m2 (�)). The fact that κa > 10 made resultsfrom Smoluchowski (Eq. (2)) and Ohshima (Eq. (3)) theories besimilar. Therefore, only data from Eqs. (3) and (4) are plottedin Figs. 11–14.

With the aim of comparing the value of the calculated elec-trokinetic or zeta potential (potential at the slip plane and re-lated with the electrokinetic charge) of the different complexes

Fig. 12. Theoretical predictions on ζ -potential for surfactant-Lx(COOH) pH 9complexes. Ohshima (Eq. (3)): bare particles (short dash–dot line), ΓNaDBS =0.50 µmol/m2 (dash line), ΓNaDBS = 1.98 µmol/m2 (dash–dot line), ΓDB =0.46 µmol/m2 (dash–dot–dot line), ΓDB = 2.00 µmol/m2 (short dash line), andΓDB = 2.89 µmol/m2 (short dot line). Including additional surface conduc-tivity (Eq. (4)): ΓNaDBS = 0.5 µmol/m2 (2), ΓNaDBS = 1.98 µmol/m2 ("),ΓDB = 0.46 µmol/m2 (1), ΓDB = 2.00 µmol/m2 (!), and ΓDB = 2.89µmol/m2 (>). Surface potential of bare latex (Eq. (5)) (dot line).

Fig. 13. Theoretical predictions on ζ -potential for surfactant-Lx(COOH) pH 7complexes. Ohshima (Eq. (3)): bare particles (short dash–dot line), ΓNaDBS =0.15 µmol/m2 (dash line), ΓNaDBS = 2.18 µmol/m2 (dash–dot line), ΓDB =1.52 µmol/m2 (dash–dot–dot line), ΓDB = 2.18 µmol/m2 (short dash line), andΓDB = 2.60 µmol/m2 (short dot line). Including additional surface conductiv-ity (Eq. (4)): ΓNaDBS = 0.15 µmol/m2 (2), ΓNaDBS = 2.18 µmol/m2 ("),ΓDB = 1.52 µmol/m2 (1), ΓDB = 2.18 µmol/m2 (!), and ΓDB = 2.60µmol/m2 (>). Surface potential of bare latex (Eq. (5)) (dot line).

with the potential (ψd) related with the diffuse charge density(σd) of the bare latices, the following expression proposed byOhshima et al. [33] was used:

σd = 2εrε0κkBT

esinh(yd/2)

[1 + 1

κa

(2

cosh2(yd/4)

)

(5)

+ 1

(κa)2

8 ln(cosh(yd/4))

sinh2(yd/2)

]1/2

,

where yd = eΨd/kBT . The ψd potential as a function of theelectrolyte concentration for each latex separately at differ-ent NaDBS and DB coverage are shown in Figs. 11–14 forκa > 10.

A.B. Jódar-Reyes et al. / Journal of Colloid and Interface Science 297 (2006) 170–181 179

Fig. 14. Theoretical predictions on ζ -potential for surfactant-Lx(anfo) pH 9complexes. Ohshima (Eq. (3)): bare particles (short dash–dot line), ΓNaDBS =2.36 µmol/m2 (dash line), ΓDB = 2.12 µmol/m2 (dash dot line), and ΓDB =3.31 µmol/m2 (short dash line). Including additional surface conductivity(Eq. (4)): ΓNaDBS = 2.36 µmol/m2 (2), ΓDB = 2.12 µmol/m2 (1), andΓDB = 3.31 µmol/m2 (!). Surface potential of bare latex (Eq. (5)) (dot line).

The maximum (in absolute value) in the ζ -potential versusionic strength curve was not always predicted by both theories.By accounting for the additional surface conductivity, the ζ -potential becomes higher (in absolute value) than that predictedby Ohshima approximation up to high electrolyte concentra-tions [24].

It is worth to highlighting that the experimental conditionsin this work allowed us to reach electrolyte concentrations atwhich ζ -potential for bare particles was zero, but ψd poten-tial remained different from zero. In model colloids, ψd po-tential and ζ -potential should tend to coincide by increasingionic strength. However, our results did not behave in thatway. In Fig. 14 it can be seen that covering Lx(anfo) at pH 9with NaDBS at ΓNaDBS = 2.36 µmol/m2 and applying Eq. (4),ζ -potential of the complexes and ψd potential of the bare parti-cles coincide at intermediate electrolyte concentrations.

3.5. Theoretical prediction on interface properties of thesurfactant–latex complexes

It is possible to theoretically predict different properties ofthe solid/liquid interface of the surfactant–latex complexes byusing experimental mobility data presented above. This can bedone by applying a theoretical treatment developed by Ohshimaet al. [34–38] for polyelectrolyte covered colloidal particlesto the variation in µe with the electrolyte concentration curveobtained for the different surfactant–latex complexes. The the-ory can be summarized as follows. Consider a colloidal par-ticle with a polyelectrolyte layer adsorbed on its surface. Thecharged groups of this superficial layer of thickness d are dis-tributed at an uniform density N . These charged groups have avalency of z. The particle surface is assumed to be plane withthe applied electric field parallel to it. The charged colloidalparticles are moving in a liquid containing a symmetrical elec-trolyte of valency ν and bulk concentration n. In these cases,the above authors, using two Poisson–Boltzmann equations andhydrodynamics considerations, found an analytical expression

for the electrophoretic mobility of such a system [34]. Never-theless, it is quite difficult to calculate µe theoretically throughthat equation, as there is an integral that seldom holds an analyt-ical solution. Anyway, Ohshima and Kondo managed to obtainvarious simpler expressions for the mobility of structured inter-faces. They were tested and discussed by Ortega and Hidalgo[17] concluding that the best equation to be applied to protein–latex complexes is the following (valid for all potential valueand for d > 1 nm):

(6)µe = εrε0

η

ΨDON/λ + Ψ(0)/κm

1/λ + 1/κm+ zeN

ηλ2,

where

ΨDON = kBT

νeln

[zN

2νn+

((zN

2νn

)2

+ 1

)1/2],

Ψ(0) = ΨDON − kBT

νetanh

νeΨDON

2kBT,

κm = κ

[1 +

(zN

2νn

)2]1/4

.

The equation has been expressed considering a negativelycharged polyelectrolyte layer. If positive, the absolute valuemust be taken. σ is the amount of fixed charged contained inthe surface charged layer per unit area (σ = zeNd), and λ is ahydrodynamic parameter equal to

λ =(

γ

η

)1/2

,

where η and γ are the viscosity of the fluid and the frictionalcoefficient of the adsorbed polyelectrolyte layer, respectively.Even though these equations are applicable to the case in whichthe surface of the latex is not charged, it can be shown [17]that they are also valid for charged surfaces by including thischarge in the value of the N parameter. By assuming that atmaximum coverage the thickness of the surfactant adsorbedlayer is equal to the micelle radius (d > 1 nm), we can com-pare the average charge density (σ ) of complexes formed bythe same surfactant but different surfaces. The results for com-plexes formed by the different latices presented in this work atmaximum NaDBS coverage in the presence of NaCl are shownin Fig. 15, where the electrophoretic mobility is plotted ver-sus κa. For these complexes, N could change with the surfacecharge, but λ coincides. Value for d also coincides for thosecomplexes and was set at 2.16 nm. λ and N were used as thefitting parameters. The last experimental point in all cases wasremoved in the fitting procedure.

N value contains information on the latex surface charge andon the surfactant adsorbed layer charge. In Table 4 we presentthe amount of fixed charge in the surface layer per unit area(σ ) predicted by Ohshima theory (Eq. (6)) for the data shownin Fig. 15, together with the latex surface charge (σ0) and thecharge corresponding to the experimental surfactant coverage(ΓNaDBS). From the obtained values of ζ -potential (Eqs. (3)and (4)) we can compute the charge density in the slip layerusing Eq. (5). The maximum values in absolute value (σ max

ζ

180 A.B. Jódar-Reyes et al. / Journal of Colloid and Interface Science 297 (2006) 170–181

Table 4Surface density charges corresponding to different NaDBS–latex complexes at maximum coverage

Latex σ0 (mC/m2) ΓNaDBS (mC/m2) σ (mC/m2) σmaxζ (Eq. (3)) (mC/m2) σmax

ζ (Eq. (4)) (mC/m2) Ψ σd (mV)

Lx(COOH) pH 7 −150±3 −210 −113.86 −38.11 −64.00 −53.5pH 9 −205±3 −190 −135.3 −50.94 −73.78 −60.6

Lx(anfo) pH 5 139±3 −231.3 −89.71 −55.56 −88.42 −44pH 9 −62±2 −227.4 −158.41 −52.25 −85.88 −68.8

Note. σ0 = latex surface charge; ΓNaDBS = charge corresponding to the experimental NaDBS coverage; σ = fixed charge in the surface layer predicted by Ohshimatheory (Eq. (6)). The maximum charge density in the slip layer (σmax

ζ (Eq. (3)), σmaxζ (Eq. (4))) and the potential by using σ in Eq. (5) (Ψ σ

d ) are also presented.

Fig. 15. Electrophoretic mobility of NaDBS–latex complexes versus NaClconcentration (expressed as κa): Experimental data: Lx(COOH) pH 7,ΓNaDBS = 2.18 µmol/m2 (1); Lx(COOH) pH 9 ΓNaDBS = 1.98 µmol/m2

(2); Lx(anfo) pH 9, ΓNaDBS = 2.36 µmol/m2 ("); and Lx(anfo) pH 5,ΓNaDBS = 2.40 µmol/m2 (!). Respectively, solid, dash, dot and dash–dotlines correspond to the theoretical fit by using Ohshima’s theory (Eq. (6)) withd = 2.16 nm and λ = 3.3 nm−1. N (expressed as σ ) values are listed in Table 4.

(Eq. (3)) and σ maxζ (Eq. (4))) for the complexes at maximum

NaDBS coverage are also shown in Table 4. These values aremuch lower (in absolute value) than the corresponding σ , σ0,ΓNaDBS values when Ohshima approximation (Eq. (3)) is used.However, by accounting for the additional surface conductiv-ity (Eq. (4)), the predicted charge density in the slip layer σ max

ζ

(Eq. (4)) becomes closer to the corresponding σ , σ0, ΓNaDBS(even for Lx(anfo) at pH 5, σ max

ζ (Eq. (4)) ∼ σ ).Ohshima theory (Eq. (6)) predicts a continuous decrease of

the mobility (in absolute value) with increasing ionic strength,reaching a “plateau” at high electrolyte concentrations, whichis not in agreement with the experimental data. It can be alsoseen in Table 4 that the charge predicted by Ohshima theory isalways lower than expected. However, qualitatively, it demon-strates that σ values are not only due to the charge in thesurfactant adsorbed layer, but also to the surface charge. Thehighest surfactant adsorbed amount corresponds to the Lx(anfo)pH 5 complex, but the theory predicts the lowest σ (in absolutevalue), which is in agreement with the assumption of partialneutralization of the negative surfactant adsorbed charge due tothe positive surface charge of the latex. This partial neutraliza-tion is not observed in the σmax

ζ data. We can use Eq. (5) forcalculating the potential corresponding to the fixed charge inthe surface layer predicted by Ohshima theory. The results areshown in Table 4. These potentials would be closer to the realsurface potential than those obtained from σ0.

For DB surfactant, we only have data at maximum coveragefor Lx(anfo) pH 5. In this case, d = 1.05 nm and the best set ofparameters predicted by Ohshima theory is λ = 3.3 nm−1 andσ = 26.2 mC/m2. It is worth to highlighting that the λ para-meter, that characterizes the degree of friction exerted on theliquid flow in the surface layer, results similar for both NaDBSand DB from the fitting procedure.

4. Summary

Looking through the mobility and colloidal stability resultscorresponding to the different complexes analyzed, we can con-clude that the electrostatic repulsion is the main responsible forthe colloidal stability of the latex-ionic surfactant complexes.Above certain adsorbed amount, the complexes are always col-loidally stable at low electrolyte concentrations. That meansthat even though the surfactant is adsorbed on a surface with op-posite sign of charge, overcoming the amount needed to cancelthe surface charge, stable complexes can be found. In the caseof latex with not very high colloidal stability, the complexes aremore stable than the bare particles. This is in agreement withhigher mobility values.

Acknowledgments

Financial support from ‘Comisión Interministerial de Cien-cia y Tecnología,’ Projects MAT2003-01257 and AGL2004-01531/ALI (European FEDER support included) is gratefullyacknowledged.

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