Journal of Colloid and Interface Science 410 (2013) 188–194

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Journal of Colloid and Interface Science

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AFM forces between mica and polystyrene surfaces in aqueouselectrolyte solutions with and without gas bubbles

0021-9797/$ - see front matter � 2013 Elsevier Inc. All rights reserved.http://dx.doi.org/10.1016/j.jcis.2013.08.001

⇑ Corresponding author. Fax: +56 41 2204691.E-mail address: petoledo@udec.cl (P.G. Toledo).

Jorge H. Saavedra a, Sergio M. Acuña b, Pedro G. Toledo a,⇑a Chemical Engineering Department and Surface Analysis Laboratory (ASIF), University of Concepción, PO Box 160-C, Correo 3, Concepción, Chileb Department of Food Engineering, University of Bio-Bio, PO Box 447, Chillán, Chile

a r t i c l e i n f o a b s t r a c t

Article history:Received 2 May 2013Accepted 2 August 2013Available online 11 August 2013

Keywords:AFMHydrophilic–hydrophobic interactionNanobubblesVapor cavitiesExtended DLVOHydrophobic force

Force curves between a flat mica substrate and a polystyrene microsphere were measured with an atomicforce microscope (AFM) in carefully degassed water and aqueous NaCl, CaCl2, and AlCl3 solutions. The pHof the water used does not change significantly with degassing treatment, and its value remains close to6. Electrolyte concentration ranges from 10�4 to 10�2 M and pH from 4.7 to 5.1. We have found that therepulsive long-range electrostatic force between mica and polystyrene is attenuated by the presence ofelectrolytes and counterbalanced by a long-range attractive force, which we referred to as a hydrophobicforce, which is longer-ranged than the ever present attractive van der Waals force. This force, whichincludes the adhesive bridging of residual air bubbles and newborn vapor cavities, and any otherunknown forces, is reasonably well represented by a unique exponential law. Prefactor and decayinglength are not very sensitive to electrolyte type, concentration, and pH, suggesting that any new forceincluded in the law, in addition to adhesive bridges, should obey a non-classical electrostatic mechanism.However, we also know that liquid/solid contact angle and liquid/vapor surface tension increase withelectrolyte concentration and valence increasing the stability of bubbles and cavities which in turnincrease the bridging force. Clearly, these effects are hidden in the empirical force law.

� 2013 Elsevier Inc. All rights reserved.

1. Introduction

Nonsymmetrical hydrophilic–hydrophobic interactions in elec-trolyte solutions are central in many industrial processes, for in-stance, in flotation operations for which hydrophobic forcesdetermine the fate of particle–bubble interactions. The origin andcharacteristics of this non-DLVO hydrophobic surface have beenthe subject of intense research activity in the last 30 years. Despitethis enormous effort, the origin of the force is not yet resolved. Sev-eral explanations for its origin, strength, and range are available,i.e., this force originates from the structuring of water betweentwo hydrophobic surfaces [1]; from an electrostatic mechanismincluding polarization of water close to hydrocarbon–water inter-faces [2], from adsorbed but laterally mobile ions [3], and fromelectric fields associated with large ordered crystalline domains[4]; from the metastability of water films separating two hydro-phobic surfaces, which produces vapor cavities that give rise tocapillary bridges between the surfaces [5–12]. Sakamoto et al. in-stead propose that air bubbles which are introduced during thepreparation of solutions are responsible and therefore proposed a

method of degassing [13]. The interaction between hydrophobicsurfaces shows extremely long-range interactions, in some casesreaching 300 nm [9], 600 nm [14], and 1200 nm [4], and forces ofso high intensity that are not easy to explain. Most of the studiesof hydrophobic interactions have been made in symmetricalhydrophobic-hydrophobic systems [1,4,5,11–37] and compara-tively few in asymmetrical hydrophilic–hydrophobic systems[4,9,15–17,38–42]. This paper presents the results of direct AFMmeasurement of force curves between a flat mica substrate and apolystyrene microsphere in water and in aqueous NaCl, CaCl2,and AlCl3 solutions. Electrolyte concentration ranges from 10�4

to 10�2 M and pH from 4.7 to 5.1. Measurements were made withand without gas bubbles at ambient conditions. We have foundthat the repulsive long-range electrostatic force between micaand polystyrene is attenuated by the presence of electrolytes andcounterbalanced by a long-range attractive force. This force, whichis longer-ranged than van der Waals forces, includes the adhesivebridging of residual air bubbles and newborn vapor cavities andany other unknown forces, is reasonably well represented by a un-ique exponential law. Prefactor and decaying length are not verysensitive to electrolyte type, concentration, and pH, suggesting thatany new force included in the law, if any, should obey a non-clas-sical electrostatic mechanism. However, we also know that liquid/

J.H. Saavedra et al. / Journal of Colloid and Interface Science 410 (2013) 188–194 189

solid contact angle and liquid/vapor surface tension increase withelectrolyte concentration and valence increasing the stability ofbubbles and cavities which in turn increase the bridging force.Clearly, these effects are hidden in the empirical force law.

2. Methods

Three types of water were used as ambient fluid to measureinteraction forces: bi-distilled (Jencons Scientific Ltd., England),tetra-distilled (Heraeus Schott, Germany), and milli-Q (Milli-pore,USA). Water was used ‘‘as received’’ and after two processes ofdegassing; sonication in an ultrasonic bath (Branson UltrasonicCorporation, USA) for three hours and three cycles of boiling for15 min, followed by rapid freezing with liquid nitrogen, evacuatedby a vacuum pump, and subsequent melting at ambient conditions[13]. The pH of the water used does not change significantly withtreatment, and its value remains close to 6 (5.8 in bi-distilledwater, 5.6 in tetra-distilled water, and 5.5 in milli-Q water). All pre-vious measurements have been performed at atmospheric pressureand ambient temperature of 20 �C. Interaction forces were alsomeasured in electrolyte solutions as ambient fluid; such solutionswere prepared in degassed milli-Q water in vacuum. NaCl, CaCl2,and AlCl3 (analytical chemical grade, Merck, Germany) were usedin concentrations ranging from 10�4 to 10�2 M. Experiments werecarried out without any buffering, and pH ranges from 4.7 to 5.1.Under these conditions, mica surfaces in water or in aqueous solu-tions were negatively charged. All glassware used in the prepara-tion of solutions previously was detergent and alkali washedwith final thorough rinsing in bi-distilled water.

The AFM used in this study was a Multimode Atomic ForceMicroscope (Veeco, USA) equipped with a Nanoscope IIIa SPM con-trol station, fluid cell (0.1 cm3), silicone pad for vibration isolationand acoustic enclosure. Muscovite mica substrates typically1 � 1 cm2 were used. Freshly cleaved mica sheets were obtainedat time of use from a native muscovite mica block available inour laboratory. The flat substrates were glued to AFM stubs beforeuse. Polystyrene probes were prepared by adhering a polystyrenemicrosphere of approximately 20 lm in diameter (Duke ScientificCorporation, USA) to the end of a contact Si3N4 tipless V-shaped,200 lm long, 0.6 lm thick cantilever (Thermo, USA) with NorlandOptical Adhesive 61 (Norland Products, USA). A simple adaptationof Huntington and Nespolo protocol for attaching microspheres toAFM cantilever tips was implemented in a Dimension 3100 (Veeco)atomic force microscope [43]. The size of the microspheres wasdetermined by SEM (ETEC, Autoscan). Probes were UV-heated en-ough to secure the microsphere-cantilever bonding. Spring con-stants of individual cantilevers were determined by the methodof standards (standards provided by Park Scientific) with theDimension 3100 AFM microscope and were typically 0.14 N/m.SEM and AFM images verified the quality of the modified cantile-vers. Prior to force measurement, the mineral and polystyrene sur-faces were thoroughly rinsed in high-purity water (18.6 MO/cm)and then with ethanol and then again with pure water. Surfaceroughness, assessed by AFM imaging with the Dimension 3100,was typically subnanometer in size for both substrate andmicrosphere.

Samples were manipulated with tweezers to avoid contamina-tion. Once substrate and probe were appropriately mounted, thecell was flooded with ambient fluid. The system was allowed toreach equilibrium for few minutes before probe and substrate wereapproached one to another. Measurement of a typical force curvetook less than 20 min; during this time, the AFM roughness ofthe substrate remained unaltered. AFM allows continuous mea-surement of cantilever deflection vs. position as probe and sub-strate approach each other, commonly named extension, or

separate, commonly named retraction. Data were provided byNanoscope IIIa DI v4.42 instrument software (Veeco). To convertthese data into force vs separation curves, we used commercialsoftware and own routines based on the procedure of Duckeret al. [44,45]. Detail of this procedure was published previously[46]. Extension and retraction driving speeds were low (0.5 Hz)in order to minimize hydrodynamic contribution to the measuredforce. Typically, four or five force data points per nanometer wereacquired. Forces are reported normalized by the microsphere proberadius, that is, as interaction energy between mica and polystyreneflat surfaces by virtue of Derjaguin’s approximation [47]. Interac-tion curves between the sphere and the flat substrate in waterwere measured at two different points, three measurements perpoint, whereas for the interaction in electrolyte solutions, curveswere measured several times but at a single point.

3. Results and discussion

Here, we are interested in the forces that arise in the approach-ing of a colloidal polystyrene microsphere to a flat mica substratein aqueous electrolyte media with and without bubbles.

3.1. Non-degassed water

Fig. 1 shows approaching force curves between a flat mica sur-face and a polystyrene microsphere probe in bi-distilled, tetra-dis-tilled, and Milli-Q water, all them ‘‘as received.’’ Dissolved airappears as bubbles. Fig. 1a shows six approaching force curves inbi-distilled water: three of them measured at one point on the sub-strate, the other three at a different point. Results show a strongrepulsion as the surfaces approach. In the long range, this repulsionis attributable to electrostatic effects, bubbles adhered onto thesurface of the polystyrene probe acquire charge in water and thusa surface potential. Mica has a surface potential of around �50 mV,and the polystyrene has a zeta potential between �30 and �60 mV[48], which is very similar to zeta potentials that have been mea-sured on the surface of a bubble [49]. In shorter distance ranges,comparable to the size of bubbles, the repulsive effect is enhancedby compression of such air bubbles between the approaching sur-faces. Repulsion reaches a peak at a distance of �15 nm. Then,unexpectedly, the surfaces jump into contact. Extensive literatureis available on this ‘‘hydrophobic’’ force and working mechanism;however, no generally acceptable explanation is available. For thedata here, it is plausible to argue that this attractive force has itsorigin in two mechanisms: the electrical fields of unalignedcharges on both surfaces at very short distance cooperate to pro-duce an attractive force [50] and the breaking of large bubbles intonanobubbles that migrate away from the contact area thus elimi-nating the hindrance to the contact. Thecontinuous approach be-tween the mica and polystyrene may end up with a fewnanobubbles trapped between the surfaces. The approaching forcecurves are not significantly different at the two points studied. Fordistances of 5 nm and less, repulsive forces become stronger againdominating the interaction. The origin of this very short-rangeforce is better understood and is related to hydration and waterstructuring [53]. Fig. 1b shows the results for the interaction be-tween mica and polystyrene in tetra-distilled water. Approachingforce curves are similar to those obtained in bi-distilled water.Repulsion values obtained are similar, and jumps occur at the samerange of separation distances, i.e., 10–15 nm. There were no differ-ences between the force curves measured at different points on thesubstrate. Fig. 1c shows results for the mica-polystyrene interac-tion in milli-Q water. It is clear that these curves differ significantlyfrom those obtained in bi-distilled and tetra-distilled water.Approaching force curves present repulsion values significantly

D (nm)0 20 40 60 80 100

F/R

(mN

/m)

-0.2

0.0

0.2

0.4 Position 1Position 2

(a) D (nm)

0 20 40 60 80 100

F/R

(mN

/m)

-0.2

0.0

0.2

0.4 Position 1Position 2

(b) D (nm)

0 20 40 60 80 100

F/R

(mN

/m)

-0.2

0.0

0.2

0.4 Position 1Position 2

(c) Fig. 1. Approaching AFM force curves between a flat mica substrate and a polystyrene microsphere in three types of water ‘‘as received’’. (a) Bi-distilled, (b) Tetra-distilled,and (c) Milli-Q. Six force curves measured at two points on the substrate.

190 J.H. Saavedra et al. / Journal of Colloid and Interface Science 410 (2013) 188–194

lower than for the previous cases. Furthermore, in this case, theapproaching force curves differ between measuring points. Forone point, the jump to contact occurs at a separation distance ofaround 15 nm, while for the other occurs at a distance of about30 nm. At the center are bubbles attached to the polystyrene sur-face that may take a different configuration at different points onthe substrate, changing in size among other possibilities [11,51].

The key result thus far is that we have not measured thestrength of the approaching force between the surfaces of interestbut between the surfaces mediated by air bubbles. The differencesbetween the three types of water are significant and are attributedto bubbles whose sizes appear to play an important role in the sta-bility of the system. Large bubbles being compressed between thesurfaces disintegrate and/or easily escape from the contact of thesurfaces, as a result the force curves show less repulsion and sur-faces jump to contact at longer distances.

3.2. Degassed water by sonication

Fig. 2a shows approaching force curves between the flat micaand the polystyrene microsphere in bi-distilled water that hasbeen degassed by sonication for a period of 3 h. In Fig. 2a at all sep-aration distances between the surfaces, in addition to electrostaticrepulsion, results show repulsion either by deficient degassing

D (nm)

F/R

(mN

/m)

0.0

0.2

0.4

0.6

0.8

Position 1Position 2

(a) D

F/R

(mN

/m)

-0.10

-0.05

0.00

0.05

0.10

0 20 40 60 80 100 0 5 10

Fig. 2. Approaching AFM force curves between a flat mica substrate and a polystyrene miand (c) Milli-Q. Six force curves measured at two points on the substrate.

and/or certain ‘‘stability’’ of bubbles on the polystyrene surface,and bubbles do not disintegrate nor move away from the contactof the surfaces. Fig. 2b and c show almost identical approachingforce curves in tetra-distilled and milli-Q water degassed by ultra-sound; these curves, however, are very different from those mea-sured in bi-distilled water (Fig. 2a). Repulsion is not observed inthese last force curves but instead a small short-range attractionat separation distances close to 3 nm. This was observed at thetwo points on the substrate. The insert in Fig. 2c reveals that thisattraction leads to a jump to contact between the surfaces.

3.3. Degassed water by cycles of boiling-freezing-melting

Fig. 3 shows approaching force curves for the mica-polystyrenesystem in degassed water by cycles of boiling, fast freezing byusing liquid nitrogen, and melting. This figure shows similar re-sults for the three types of water used. Repulsion is not observedduring the approach, and notably at distances between 3 and5 nm, a jump to the contact of the surfaces occurs, this effect weassociate with genuine attractive hydrophobic and van der Waalsinteractions. Hydration forces and few nanobubbles trapped be-tween the surfaces determine the extension of the jumps. Resultsin water subject to this degassing treatment did not differ signifi-cantly at different points on the substrate.

(nm)

Position 1Position 2

(b) D (nm)

15 20 25 0 5 10 15 20 25

F/R

(mN

/m)

-0.10

-0.05

0.00

0.05

0.10Position 1Position 2

D (nm)0 2 4 6 8 10

F/R

(mN

/m)

-0.03-0.010.010.030.05 Milli-Q - Set 1

(c)

crosphere in three types of water sonicated for 3 h. (a) Bi-distilled, (b) Tetra-distilled,

D (nm)

F/R

(mN

/m)

-0.10

-0.05

0.00

0.05

0.10

Position 1Position 2

(a) D (nm)

F/R

(mN

/m)

-0.10

-0.05

0.00

0.05

0.10

Position 1Position 2

(b) D (nm)

0 5 10 15 20 25 0 5 10 15 20 25 0 5 10 15 20 25

F/R

(mN

/m)

-0.10

-0.05

0.00

0.05

0.10

Position 1Position 2

(c) Fig. 3. Approaching AFM force curves between a flat mica substrate and a polystyrene microsphere in three types of water treated by boiling-freezing-boiling cycles. (a) Bi-distilled, (b) Tetra-distilled, and (c) Milli-Q. Six force curves measured at two points on the substrate.

J.H. Saavedra et al. / Journal of Colloid and Interface Science 410 (2013) 188–194 191

Results here suggest that the presence of large bubbles attachedto at least one of the interacting surfaces interferes in the forcemeasurement in hydrophilic–hydrophobic systems. Dependingon water type, electrostatics, and size and stability of bubbles,interaction between the surfaces shows pure repulsion, repulsionfollowed by attraction, or simply attraction leading to jumps tothe contact of the surfaces. The literature on hydrophilic–hydro-phobic systems is considerable less extensive than on hydropho-bic-hydrophobic systems. To explain the measured attraction, wecited cooperation of electrical fields from nonaligned charges onthe surfaces, although this is valid for the very short range only.What else can be invoked? Bubbles cannot be observed directlyin our experiments; yet our degassing treatments indirectly provetheir existence. According to Christenson et al. [5], cavitationshould not be ruled out as a possible mechanism for growing vaporcavities due to spinodal decomposition of water between the twointeracting surfaces. Such decomposition is driven by the highchemical potential of water which is unable to maximize formationof hydrogen bonds in zones close to the contact. Closely related isthe fact that the literature has suggested that chemical heterogene-ities on the interacting surfaces improve the stability of bubbles[52]. If such is the case for the mica substrate here, then survivingair nanobubbles and newborn vapor cavities may also contributeto the attraction by building adhesive bridges between the twosurfaces. Clearly, the cavities are characteristics of the system,but the air bubbles are not; the latter are exogenous to the system.In the analysis of our force data, we consider all these forcesalthough we may have not included all possible contributions. Re-sults for any degassed water by ultrasound (except bi-distilled)and by cycles of boiling-freezing-melting reveal that the approach-ing force curves are similar, characterized by the absence of long-range interaction, a clear short-range attraction between 2 and5 nm, and a strong repulsion near contact, suggesting that thesetwo degassing treatments are effective in removing large gas bub-bles which if present interfere with the measurement of the force.

3.4. Electrolytes

The following results are for the interaction between mica andpolystyrene in carefully degassed solutions of NaCl, CaCl2, andAlCl3 with concentrations of 0.0001, 0.001, and 0.01 M and pH from4.7 to 5.1. For each electrolyte and concentration, Fig. 4 shows asingle approaching force curve representative of six, measured attwo different points on the substrate. High reproducibility of the

force curves indicates the appropriateness of the degassing treat-ment. Most remarkable is that all measured curves show a jumpto the contact of the surfaces at a separation distance which in-creases with electrolyte concentration and especially with electro-lyte valence. This dependence is clearly seen in Table 1, whichsummarizes the averages for the jump distance DD and the totaladhesive force which we calculate as F = kDD, k being the elasticconstant of the cantilever used. There is no interaction betweenthe surfaces at large separation; however, it is also remarkable thata small repulsive force is manifested at the beginning of the jump,and such force is more noticeable if the electrolyte has smallcharge and is diluted. The repulsive long-range electrostatic andshort-range hydration forces between these two surfaces as ex-pected are attenuated by the presence of electrolytes but alsocounterbalanced by a long-range attractive force. We do not knowexactly the origin of this force; however, we estimate that residualair bubbles and newborn vapor cavities contribute to it. It shouldbe added that liquid–vapor surface tension, as the adhesive force,increases with electrolyte concentration and valence.

3.5. DLVO theory and the hydrophobic force

For many systems, the continuum DLVO theory [53] has beenfound to describe satisfactorily the surface interactions down toseparations of 1–2 nm. Key features of the theory are the repulsiveelectric double-layer force and the attractive van der Waals forcethat operates in the range over 1–2 nm. Any ‘‘extra’’ DLVO forcecan be isolated by subtracting the theory from the data measured,and it is the best one can do. In favor is the known fact that DLVOworks amazingly well at short distances by a fortuitous cancelationof two or more opposite effects. Nonretarded van der Waals attrac-tions between mica and polystyrene were calculated here throughthe Lifschitz theory

FR

����vderW

¼ A

6D2 ð1Þ

where A is the Hamaker constant which we estimate as1.76 � 10�20 J [53] and D is the distance between the interactingsurfaces. Constant surface charge and constant surface potentialmodels can be used to estimate repulsive double-layer interactionsbetween mica and polystyrene. Constant charge and constant po-tential, respectively, over predicts and under predicts the interac-tion force, a well-known fact. For the analysis here, we prefer theconstant charge model (edl-CC) that works better down to shorter

D (nm)0 20 40 60 80 100

F/R

(mN

/m)

-0.4

-0.3

-0.2

-0.1

0.0

0.1

NaCl 0.0001 MNaCl 0.001 MNaCl 0.01 M

D (nm)0 20 40 60 80 100

F/R

(mN

/m)

-0.4

-0.3

-0.2

-0.1

0.0

0.1

CaCl2 0.0001 MCaCl2 0.001 MCaCl2 0.01 M

D (nm)0 20 40 60 80 100

F/R

(mN

/m)

-0.4

-0.3

-0.2

-0.1

0.0

0.1

AlCl3 0.0001 MAlCl3 0.001 MAlCl3 0.01 M

D (nm)0 20 40 60 80 100

F/R

(mN

/m)

-0.4

-0.3

-0.2

-0.1

0.0

0.1

NaCl 0.0001 MCaCl2 0.0001 MAlCl3 0.0001 M

D (nm)0 20 40 60 80 100

F/R

(mN

/m)

-0.4

-0.3

-0.2

-0.1

0.0

0.1

NaCl 0.001 MCaCl2 0.001 MAlCl3 0.001 M

D (nm)0 20 40 60 80 100

F/R

(mN

/m)

-0.4

-0.3

-0.2

-0.1

0.0

0.1

NaCl 0.01 MCaCl2 0.01 MAlCl3 0.01 M

Fig. 4. Approaching force curves between a flat mica substrate and a polystyrene microsphere in degassed milli-Q water in a range of solutions at 20 �C. Each curve isrepresentative of six independent AFM measurements at two points on the substrate. Electrolytes are NaCl, CaCl2, and AlCl3. Concentrations range from 10�4 to 10�2 M andpH from 4.7 to 5.1.

192 J.H. Saavedra et al. / Journal of Colloid and Interface Science 410 (2013) 188–194

separation distances between the surfaces. Repulsive double-layerinteractions at constant surface charge were calculated by solvingthe expression first derived by Gregory [54]

FR

����edl�CC

¼ 2p 2nkBTj

2�y lnBþ �y cothðjD=2Þ

1þ �y

� �� ln �y2 þ cos hðjDÞ þ B sin hðjDÞ

� �þ jD

� �

ð2Þ

where

Table 1Adhesion force between mica and polystyrene surfaces measured in electrolytesolutions at 20 �C. Electrolytes are NaCl, CaCl2, and AlCl3. Concentrations range from10�4 to 10�2 M, and pH ranges from 4.7 to 5.1. The adhesive force is calculated asF = kDD, where k = 0.14 N/m is the elastic constant of the cantilever and DD is thesurface-to-surface distance at the jump to the contact of the surfaces, which we readdirectly from the force curves in Fig. 4.

Medium Concentration (M) DD (nm) F (mN/m)

Water �5 � 10�6a 5.22 ± 1.24 0.05 ± 0.01NaCl 1 � 10�4 10.0 ± 1.41 0.11 ± 0.03

1 � 10�3 11.67 ± 1.86 0.14 ± 0.031 � 10�2 15.17 ± 1.60 0.16 ± 0.02

CaCl2 1 � 10�4 15.33 ± 2.58 0.14 ± 0.021 � 10�3 18.33 ± 2.73 0.23 ± 0.041 � 10�2 21.17 ± 1.33 0.30 ± 0.03

AlCl3 1 � 10�4 20.33 ± 0.82 0.28 ± 0.011 � 10�3 22.50 ± 0.55 0.30 ± 0.011 � 10�2 24.67 ± 1.03 0.33 ± 0.01

� Water used is bi-distilled with a conductivity of 18.6 MO/cm and a concentrationroughly estimated in 10�6 M from material dissolved from the glassware.

�y ¼ ðy1 þ y2Þ=2; yj ¼ zewj=kBT; j2 ¼ 2e2nz2=ekBT; B

¼ 1þ �y2 csc h2ðjD=2Þh i1=2

where yj is the reduced potential of surface j, z the electrolyte va-lence, e the electron charge, wj the potential of surface j, kB theBoltzmanns constant, T the absolute temperature, j the Debye-Hüc-kel reciprocal length parameter, e the permittivity of the medium,and D the separation between the two surfaces. Surface potentialsfor mica in the various solutions employed here were reported pre-viously [55]. Polystyrene surface potentials are not available for theaqueous media of interest here. We know that polystyrene surfacesare not strictly neutral because they bare negative residual charges[10,35]. Vinogradova et al. [35] used polystyrene surface potentialsbetween �30 and �60 mV to fit DLVO to polystyrene-polystyreneinteraction; they mentioned that these potentials are comparableto zeta potentials measured on bubbles [49]. Considering that zetapotentials for polystyrene in KCl solutions ranges from �28 to�60 mV [48], we use this last range in the hope to embrace the truepolystyrene potential in the various solutions employed here.

Fig. 5 shows that an ‘‘extra’’ DLVO attractive force is required tofit the experimentally measured curves. The DLVO model does be-come an extended DLVO model (eDLVO). The quality of the fit wejudge first by the ability of the eDLVO model to capture the begin-ning of the jump and second by the ability to represent as rigor-ously as possible the long-range tail of the measured force. Noattempt is made to fit short-range forces. Thus, the eDLVO modelis given by

J.H. Saavedra et al. / Journal of Colloid and Interface Science 410 (2013) 188–194 193

FR

����eDLVO

¼ FR

����edl�CC

� FR

����vderW

� FR

����H

ð3Þ

Unexpectedly, the excess attractive force needed, which wereferred to as an hydrophobic force (H), is reasonably well repre-sented by a unique exponential law for the system immersed inpure water at pH 5.1 and in aqueous NaCl, CaCl2, and AlCl3 solu-tions, with concentrations from 10�4 to 10�2 M and pH from 4.7to 5.1. The adhesion force in all cases in Fig. 5 conforms to the law

FR

����H

¼ 3 exp�D6

� �ð4Þ

D (nm)

F/R

(mN

/m)

-1.0

-0.5

0.0

0.5

1.0

1.5NaCl 0.0001 Mvan der WaalsFh / ReDLVO60eDLVO28

D

F/R

(mN

/m)

-1.0

-0.5

0.0

0.5

1.0

1.5CavaFh

eDeD

D (nm)

F/R

(mN

/m)

-1.0

-0.5

0.0

0.5

1.0

1.5NaCl 0.001 Mvan der WaalsFh / ReDLVO60eDLVO28

D

F/R

(mN

/m)

-1.0

-0.5

0.0

0.5

1.0

1.5CavaFh

eDeD

D (nm)

F/R

(mN

/m)

-1.0

-0.5

0.0

0.5

1.0

1.5NaCl 0.01 Mvan der WaalsFh / ReDLVO60eDLVO28

D

F/R

(mN

/m)

-1.0

-0.5

0.0

0.5

1.0

1.5CavaFh

eDeD

0 10 20 30 40 50 0 10 20

0 10 20 30 40 50 0 10 20

0 10 20 30 40 50 0 10 20

Fig. 5. Extended DLVO fits to measured force curves between a flat mica substrate and a pat 20 �C. Concentrations range from 10�4 to 10�2 M and pH from 4.7 to 5.1. The constantelectrolyte and concentration. For polystyrene we use two limits to embrace its true potenFH/R is the extra DLVO attractive force required to fit the experimentally measured forcepotential respectively �28 mV and �60 mV.

where F/R is in mN/m and D in nm. The repulsive long-range elec-trostatic force between mica and polystyrene is attenuated by thepresence of electrolytes and counterbalanced by the long-rangeattractive force in Eq. (4). This force includes the adhesive bridgingof residual air bubbles and newborn vapor cavities and any otherunknown forces. Quantitative differences in the fits in Fig. 5 shouldbe expected. Prefactor and decaying length in Eq. (4) are not verysensitive to electrolyte type, concentration, and pH, suggesting thatany new force included in Eq. (4), in addition to adhesive bridges,should obey a non-classical electrostatic mechanism.

However, we also know that liquid/solid contact angle and li-quid/vapor surface tension increase with electrolyte concentration

(nm)

Cl2 0.0001 Mn der Waals / RLVO60LVO28

D (nm)

F/R

(mN

/m)

-1.0

-0.5

0.0

0.5

1.0

1.5AlCl3 0.0001 Mvan der WaalsFh / ReDLVO60eDLVO28

(nm)

Cl2 0.001 Mn der Waals / RLVO60LVO28

D (nm)

F/R

(mN

/m)

-1.0

-0.5

0.0

0.5

1.0

1.5AlCl3 0.001 Mvan der WaalsFh / ReDLVO60eDLVO28

(nm)

Cl2 0.01 Mn der Waals / RLVO60LVO28

D (nm)

30 40 50 0 10 20 30 40 50

30 40 50 0 10 20 30 40 50

30 40 50 0 10 20 30 40 50

F/R

(mN

/m)

-1.0

-0.5

0.0

0.5

1.0

1.5AlCl3 0.01 Mvan der WaalsFh / ReDLVO60eDLVO28

olystyrene microsphere in degassed milli-Q water in NaCl, CaCl2, and AlCl3 solutionscharge model is used [54]. Surface potential for mica is taken from Ref. [55] for eachtial, �28 mV and �60 mV. Hamaker constant for mica-polystyrene is 1.76 � 10�20 J.curves. eDLVO28 and eDLVO60 are the extended DLVO fits for polystyrene surface

194 J.H. Saavedra et al. / Journal of Colloid and Interface Science 410 (2013) 188–194

and valence increasing the stability of bubbles and cavities whichin turn increase the bridging force [56]. Clearly, these effects arehidden in the empirical law given by Eq. (4). Similar force lawshave been proposed in the literature for the few asymmetrical sys-tems studied thus far, some of which are very different to ours, forinstance, for the interaction of a dimethyl-dioctadecyl-ammonium(DODA) monolayer-coated surface and a bare mica surface [42], fora stainless steel surface and a silanated glass sphere [39], and for asilanated glass bead and a silanated silica plate with different con-tact angles [56].

4. Conclusion

Remarkable is that all our measured force curves between micaand polystyrene in carefully degassed water and electrolyte solu-tions show a jump to the contact of the surfaces at a separation dis-tance which increases with electrolyte concentration andespecially with electrolyte valence. Our force data show that an‘‘extra’’ DLVO attractive force is required to fit the experimentallymeasured curves. Unexpectedly, the excess attractive force needed,which we referred to as a hydrophobic force, is reasonably wellrepresented by a unique exponential law. The repulsive long-rangeelectrostatic force between mica and polystyrene is attenuated bythe presence of electrolytes and counterbalanced by the long-rangehydrophobic force. This force which is longer-ranged than theattractive van der Waals force includes the adhesive bridging ofresidual air bubbles and newborn vapor cavities and any other un-known forces. Bubbles cannot be observed directly in our experi-ments; yet our degassing treatments indirectly prove theirexistence. Cavities are characteristics of the system, but air bubblesare not; the latter are exogenous to the system. Prefactor anddecaying length of the hydrophobic force law are not very sensitiveto electrolyte type, concentration, and pH, suggesting that any newforce involved, in addition to adhesive bridges, should obey a non-classical electrostatic mechanism. However, we also know thatliquid/solid contact angle and liquid/vapor surface tension increasewith electrolyte concentration and valence increasing the stabilityof bubbles and cavities which in turn increase the bridging force.Clearly, these effects are hidden in the empirical force law.

Acknowledgement

Financial support from CONICYT-Chile through project FONDE-CYT 1101023 is gratefully appreciated.

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