Unifying Model for the Electrokinetic and Phase Behavior of Aqueous

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Unifying Model for the Electrokinetic and Phase Behavior of Aqueous Suspensions Containing Short and Long Amphiphiles Andr
e R. Studart,*,† Rafael Libanori,† Aitor Moreno,‡ Urs T. Gonzenbach,§ Elena Tervoort,§ and Ludwig J. Gauckler§ †

Complex Materials, Department of Materials, ETH Zurich, 8093 Zurich, Switzerland Laboratory of Inorganic Chemistry, Department of Chemistry and Applied Biosciences, ETH Zurich, 8093 Zurich, Switzerland § Nonmetallic Inorganic Materials, Department of Materials, ETH Zurich, 8093 Zurich, Switzerland ‡

bS Supporting Information ABSTRACT: Aqueous suspensions containing oppositely charged colloidal particles and amphiphilic molecules can form fluid dispersions, foams, and percolating gel networks, depending on the initial concentration of amphiphiles. While models have been proposed to explain the electrokinetic and flotation behavior of particles in the presence of long amphiphilic molecules, the effect of amphiphiles with less than six carbons in the hydrocarbon tail on the electrokinetic, rheological, and foaming behavior of aqueous suspensions remains unclear. Unlike conventional long amphiphiles (g10 carbons), short amphiphiles do not exhibit increased adsorption on the particle surface when the number of carbons in the molecule tail is increased. On the basis of classical electrical double layer theory and the formerly proposed hemimicelle concept, we put forward a new predictive model that reconciles the adsorption and electrokinetic behavior of colloidal particles in the presence of long and short amphiphiles. By introducing in the classical Gouy
Chapman theory an energy term associated with hydrophobic interactions between the amphiphile hydrocarbon tails, we show that amphiphilic electrolytes lead to a stronger compression of the diffuse part of the electrical double layer in comparison to hydrophilic electrolytes. Scaling relationships derived from this model provide a quantitative description of the rich phase behavior of the investigated suspensions, correctly accounting for the effect of the alkyl chain length of short and long amphiphiles on the electrokinetics of such colloidal systems. The proposed model contributes to our understanding of the stabilization mechanisms of particle-stabilized foams and emulsions and might provide new insights into the physicochemical processes involved in mineral flotation.

’ INTRODUCTION Aqueous suspensions containing colloidal particles and amphiphilic molecules are widespread and can be found in applications ranging from food and pharmaceutics, to mineral processing and oil recovery, to the fabrication of new functional materials.1
5 Because of their surface active nature, amphiphilic molecules often lead to aqueous suspensions exhibiting rich colloidal behavior. For systems comprising oxide particles and amphiphiles of opposite charges, electrostatically stabilized fluid dispersions are typically obtained at low amphiphile concentrations due to the particle’s high zeta potential. At intermediate amphiphile concentrations, the amount of amphiphiles physically or chemically adsorbed on the particles is sufficient to partially screen their surface charges and to render their surface less hydrophilic. This phenomenon is widely exploited in mineral flotation6
11 and in the stabilization of foams and emulsions using surface active particles.3,12
23 At high amphiphile concentrations, the modified particles can extensively agglomerate throughout the suspension, forming particle clusters and gels.18,23 Further addition of long amphiphiles leads to the formation of r 2011 American Chemical Society

bilayers or reversed micelles on the surface to minimize the exposure of the hydrophobic moieties in the aqueous phase. This usually reverses the particle electrokinetic charge, renders the particle hydrophilic again, and eventually refluidizes the system.7,11 The adsorption of amphiphilic molecules on the surface of oxide particles usually occurs via electrostatic interactions or chemical reactions between the amphiphile polar group and the hydrophilic groups on the particle surface,7,24
27 as well as through lateral hydrophobic interactions between the alkyl chains of the adsorbed molecules28 and interactions between the amphiphile tail and the particle surface. Typical examples of electrostatically adsorbed amphiphiles are protonated alkyl ammonium ions adsorbed on negatively charged silica and deprotonated alkyl sulfate (or sulfonate) ions adsorbed on positively charged alumina particles.7,11,28
30 Amphiphiles that adsorb on the surface through chemical reactions include, for example, alkyl Received: June 24, 2011 Revised: August 8, 2011 Published: August 19, 2011 11835

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Langmuir thiols and xanthates on gold and sulfides24 and alkyl silanes on oxide surfaces. Lateral interactions between the hydrocarbon chains of long amphiphiles play a major role in the adsorption behavior and the resulting surface chemistry of oxide particles.7,28
32 At concentrations much lower than those required for complete monolayer formation, lateral interactions between the hydrophobic alkyl chains increase adsorption significantly because of the formation of two-dimensional patches on the surface. These patches, known as hemimicelles, consist of densely packed surfactant molecules aligned perpendicular to the particle surface, with the polar head groups attached to the solid
liquid interface and the alkyl chains oriented toward the aqueous solution. This and other similar structures formed by long amphiphiles on the particle surface33,34 have been generally termed “solloids”.35 Under favorable physical or chemical interactions between amphiphiles and particles, the critical concentration needed for hemimicelle formation on the surface (HMC) is orders of magnitude lower than the concentration needed to form surfactant micelles in bulk water (CMC).28 The sharp increase in adsorption observed at the HMC results in a strong increase in the hydrophobicity of the particle (e.g., contact angle in water) and an abrupt decrease of the absolute zeta potential.35,36 This combined effect favors the adsorption of the modified particles at fluid interfaces.37 Given the relatively low free energy gained per
CH2 group upon lateral association of the alkyl chain (∼1 kBT), hemimicelle formation has been mostly observed for amphiphiles containing at least eight carbons in the hydrocarbon tail.11,29,35,36 Surprisingly, amphiphiles with unusually short alkyl chains (2
6 carbons) have recently been shown to also increase the hydrophobicity of the surface of oxide particles and to favor their adsorption to fluid interfaces. Short fatty acids and alkyl amines with less than six carbons in the hydrocarbon chain are observed to efficiently decrease the hydrophilicity of the surface of a wide range of oxide particles, allowing for the stabilization of novel foams and emulsions.20,21 As opposed to the short-chain alkyl xanthates used in flotation processes, such carboxylic acids and amines do not form strong chemical bonds at the particle surface.20,21 In a recent paper, Meguias-Alguacil et al.38 have also shown that short-chain carboxylic acids render the alumina surface less hydrophilic and increase its contact angles up to 70°. Further amphiphile addition presumably leads to the unusual formation of bilayers that hydrophylize the surface again. The concentration of amphiphiles needed to reverse the contact angles scales inversely with the chain length. All of these previous studies reveal that colloidal suspensions containing short amphiphiles exhibit phase behavior that resembles that observed for long-chain surfactants. However, the adsorption of short amphiphiles on particle surfaces of opposite charge does not depend on the length of the molecule’s hydrocarbon chain,18 which is in strong contradiction to the increased adsorption of long amphiphiles with longer hydrocarbon tails.35,36 In this article, we present a theoretical analysis of the electrokinetic and phase behavior of aqueous suspensions containing oppositely charged oxide particles and amphiphilic molecules of various chain lengths. On the basis of the Gouy
Chapman theory and the original hemimicelle concept, we reconcile in a new unifying model the adsorption and electrokinetic behavior of colloidal particles in the presence of both short and long amphiphilic molecules (e6 and g10 carbons, respectively). On the basis of the proposed model, we obtain scaling relationships that allow for the quantitative prediction of the concentrations of

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short amphiphiles at which abrupt changes occur in the behavior of the colloidal suspensions. Prior to the theoretical treatment, earlier18,21,34 and new results on the adsorption of short amphiphiles on alumina particles and the resulting phase behavior of colloidal suspensions are presented so as to allow for a comparative analysis to well-established systems containing long-chain surfactants.

’ ADSORPTION OF SHORT AMPHIPHILES ON OXIDE PARTICLES The colloidal suspensions with short amphiphiles analyzed in this study typically consist of 35 vol % 200 nm alumina particles and 0.005
0.180 mol/L of carboxylic acids with 2
6 carbons in the alkyl chain dissolved in water at pH 4.75. This pH is close to the pKa of the carboxylate groups of the investigated amphiphiles: 4.87, 4.83, 4.83, and 4.89 for propionic, butyric, valeric, and enanthic acids, respectively.39 Thus, at pH 4.75, the alumina particles are positively charged and about one-half of the amphiphilic molecules are negatively charged, with the other half remaining uncharged. Because of the opposite charges, the amphiphiles adsorb electrostatically on the surface of the alumina particles, as shown in Figure 1. Ligand exchange reactions between the molecule’s carboxylate group and the hydroxyl groups on the oxide surface favor the adsorption of amphiphiles at this pH. 40 The number of molecules adsorbed on the surface does not depend on the length of the carboxylic acid but solely on its initial (c) and equilibrium (ceq) concentrations (Figure 1). The maximum number of molecules adsorbed on the particle surface approaches 3.5 μmol/m2 for the highest initial amphiphile concentration of 0.180 mol/L achieved with propionic acid. Because this surface density is lower than the typical density of reactive
OH groups present on polycrystalline alumina surfaces (4.25 μmol/m2),41 we conclude that the amount of adsorbed carboxylic acids is not sufficient to fully compensate for the positive charges arising from the protonated
OH2+ surface groups. When plotted against the amphiphile equilibrium concentration, the adsorption data can be described by a Langmuir isotherm curve with a maximum amount adsorbed (Γmax) of 4.02 μmol/m2 and an adsorption constant (k) of 55.16 L/mol (Figure 1b). Such a Γmax value is close to the typical surface density of reactive
OH groups (4.25 μmol/m2), confirming that the adsorption process is primarily driven by the electrostatic attraction between the charged surfaces and amphiphiles. The adsorption constant is at least one order of magnitude lower than that observed for molecules adsorbing through strong ligand exchange reactions on alumina surfaces,42 suggesting a rather weak adsorption of the amphiphiles. The observation that the amount of amphiphiles adsorbed on the surface is not influenced by the molecule’s hydrocarbon chain length was confirmed by additional adsorption experiments using quantitative 1H NMR spectroscopy (Bruker Avance 700 MHz spectrometer). In this experimental series, the competitive adsorption of carboxylic acids with two and four carbons in the alkyl chain on the surface of alumina particles was assessed by measuring the concentration of amphiphiles remaining in the supernatant of aqueous suspensions containing 10 vol % α-Al2O3 particles (Ceralox, HPA-0.5w/MgO, Tucson, AZ), 10 mM propionic acid (number of carbons, m = 2), and 10 mM valeric acid (m = 4) in deuterated water at pH 4.75. Prior to the NMR analysis, the suspensions were equilibrated for 24 h and afterward 11836

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Figure 2. Low-frequency sections of the 1H NMR spectra of the supernatant of aqueous suspensions containing 10 vol % alumina particles, 10 mM propionic acid (PA), and 10 mM valeric acid (VA) at pH 4.75 in the absence (a) and presence (b) of an inert back electrolyte (100 mM KNO3). Graph (c) shows the spectrum obtained for the reference sample containing only the carboxylic acids in deuterated water. Relative integrals are indicated above the corresponding methyl triplet signals.

propionic and valeric acids to 0.34 and 0.38, respectively. However, such high fractions of adsorbed carboxylic acids, even in the presence of a 10-fold higher concentration of KNO3, suggests that the hydrophobic interactions between the alkyl chains lead to the preferential adsorption of the amphiphiles on the alumina surface. The results indicating similar adsorption behavior of carboxylic acids with different chain lengths are in good agreement with the data shown in Figure 1.18,21

Figure 1. Adsorption behavior of short-chain carboxylic acids on alumina particles at pH 4.75. (a) and (b) show the adsorption data plotted against the initial and equilibrium amphiphile concentrations, respectively. The Langmuir isotherm equation and fitting parameters used to describe the amphiphile adsorption behavior are shown as an inset in (b). Data were obtained for 35 vol % alumina suspensions in the absence of inert electrolyte.18,21

centrifuged for 3 min at a rotation speed of 14 000 rpm (Eppendorf MiniSpin, Hamburg, Germany) to remove the supernatant. Reference samples containing only 10 mM of the amphiphiles in deuterated water were also analyzed. The effect of an inert back electrolyte on the adsorption of the carboxylic acids on the alumina particles was also evaluated by analyzing samples containing 100 mM KNO3. The NMR spectra of the supernatants reveal that valeric and propionic acids adsorb to a similar extent on the alumina particles (Figure 2). The results show that 54 and 58% of the initially added propionic and valeric acids eventually adsorbed on the alumina particles. Considering that only half of the carboxylic acid molecules are deprotonated and electrostatically attracted to the particle surface at pH 4.75, adsorbed fractions of 0.54 and 0.58 indicate a high affinity of these amphiphilic molecules toward the alumina particle surface. The presence of 100 mM KNO3 as an inert electrolyte reduced the fractions of adsorbed

’ PHASE BEHAVIOR OF AQUEOUS SUSPENSIONS CONTAINING SHORT AMPHIPHILES The adsorption of amphiphiles on the particle surface leads to remarkable changes in the colloidal behavior of the aqueous suspensions. This is illustrated in Figure 3 for suspensions containing alumina particles and different concentrations of carboxylic acids of various chain lengths. The first major change occurs at a critical amphiphile concentration c1* at which the apparent surface tension of the suspension decreases significantly (Figure 3a). Such a decrease is attributed to the adsorption of carboxylate-coated particles at the air
water interface. The hydrocarbon chain of the adsorbed carboxylate molecules increases the hydrophobicity of the particle, favoring their adsorption at the air
water interface. Partially hydrophobized particles adsorbed at the interface replace part of the high-energy air
water interfacial area, decreasing the apparent surface tension of the suspension. The critical amphiphile concentration c1* required for particle adsorption decreases for increasing tail lengths. No significant reduction in apparent surface tension is observed in suspensions containing acetic acid or inert electrolytes such as NaCl. Although a fraction of amphiphiles added to the suspension remains in the bulk water (Figures 1 and 2), control experiments showed that the sharp decrease in apparent surface tension shown in Figure 3a is not related to the adsorption of free molecules at the air
water interface.20,21 11837

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Figure 4. The critical carboxylic acid concentrations c1* and c2* corresponding to the onset of particle adsorption at the air
water interface () and the onset of particle agglomeration throughout the suspension (+) as a function of the number of carbons in the alkyl chain (m). The empty, half-filled, and filled circles indicate the conditions leading to fluid dispersions, foams, and gel networks, respectively.

Figure 3. (a) Apparent surface tension and (b) apparent viscosity at a shear rate of 100 s
1 of 35 vol % alumina suspensions containing various concentrations of short-chain carboxylic acids at pH 4.75. (c) Air content of foams prepared by mechanical shearing of the same alumina suspensions. The critical amphiphile concentrations c1* and c2* for valeric acid are indicated in (a) and (b) as an example (number of carbons, m = 4). Data were obtained from Gonzenbach et al.18,21

Further addition of amphiphiles beyond a second critical concentration c2* leads to a marked increase in the suspension's apparent viscosity (Figure 3b). Similar to the apparent surface tension data, amphiphiles with longer tail lengths require lower concentrations to cause the abrupt increase in apparent viscosity. The observed viscosity increase is a clear indication of strong particle agglomeration in the suspension, even though the c2* values are significantly lower than those needed for coagulation using acetic acid or inert electrolytes (∼0.2 mol/L). A comparison of the apparent surface tension and viscosity data (Figure 3a,b) also shows that the amphiphile concentrations required to increase the suspension viscosity (c2*) are 2
10-fold higher than those needed to promote the adsorption of modified particles at the air
water interface (c1*). Interestingly, suspensions containing amphiphile concentrations between c1* and c2* result in ultrastable particle-stabilized foams upon mechanical frothing (Figure 3c). For such intermediate concentrations, the degree of hydrophobicity of the

modified particles is high enough to induce their adsorption at the air
water interface while sufficiently low to avoid extensive agglomeration throughout the suspension. Given the dependence of c1* and c2* on the carboxylic acid tail length, the range of amphiphile concentrations leading to foam stabilization is shifted to lower values as the length of the molecule’s hydrocarbon chain is increased (Figure 3c). The diagram shown in Figure 4 summarizes the amphiphile concentrations at which the aqueous alumina suspensions are dispersed, foamed, or agglomerated for amphiphiles of different chain lengths. The lower and upper limits of the concentration range leading to stable foams correspond, respectively, to the concentration needed for the onset of particle adsorption at the air
water interface (c1*) and to the concentration required for the onset of particle agglomeration in the suspension (c2*). As the amphiphile concentration is increased, stable foams are obtained when the surface modified particles are able to adsorb at the air
water interface. However, once the concentration leading to particle agglomeration is achieved, the suspension becomes so viscous that air can no longer be incorporated into the system (Figure 4). The adsorption of short carboxylic acids on the surface of alumina particles also has a pronounced effect on the particle’s surface charge, as indicated by the zeta potential data shown in Figure 5 for 2 vol % alumina suspensions containing amphiphiles of different chain lengths at pH 4.75. The addition of amphiphiles decreases the zeta potential of the alumina particles by screening the positive electrical charges on the particle surface. Remarkably, the concentrations at which the screening effect takes place decrease as the amphiphile hydrocarbon tail is increased. The decrease in zeta potential with the addition of amphiphiles occurs at concentrations significantly lower than those required to impart the same screening effect using inert electrolytes (Figure 5). These results clearly indicate that hydrophobic interactions between the adsorbed amphiphiles have a major effect on the electrical potential on the particle surface. 11838

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Figure 5. Zeta potential of alumina particles at pH 4.75 as a function of the concentration of different short-chain carboxylic acids. Data were obtained from 2 vol % suspensions.18,38

Such specific interactions are strong enough to even revert the particle surface charge at high amphiphile concentrations38 (Figure 5).

’ THEORETICAL ANALYSIS The strong dependence of the surface activity of particles coated with short-chain carboxylic acids on the number of carbons in the amphiphile tail closely resembles the effect of the chain length of long amphiphiles on the flotation behavior of oxide particles.7,28,31 While the tail of amphiphiles containing less than seven carbons seems in principle too short to result in appreciable hydrophobic interactions between hydrocarbon chains,11,28,29 the apparent surface tension, foaming, and rheological properties presented above suggest that short-chain amphiphiles might also be able to associate through such hydrophobic interactions. To further evaluate this hypothesis, we theoretically analyze the potential impact of hydrophobic interactions between amphiphiles and their resulting association on the behavior of aqueous alumina suspensions containing carboxylic acids with 2
6 carbons in the hydrophobic tail. The hemimicelle model, originally proposed by Gaudin and Fuerstenau, 28 assumes that long amphiphiles exhibiting an opposite charge with respect to the particle surface adsorb as counterions in the Stern layer around the particle. According to the model, long amphiphiles with a higher number of carbons in the hydrocarbon tail adsorb to a larger extent on the particle surface because of hydrophobic interactions between the chain’s alkyl groups in water. The increased adsorption of long amphiphiles (>6 carbons) for increases in hydrocarbon tails has been experimentally verified in different oxide/amphiphile systems. 35,36 However, the data shown in Figures 1 and 2 confirm that the adsorption of short carboxylic acids on the surface of alumina particles does not depend on the molecule’s chain length. Yet, the chain length of both short and long amphiphiles clearly affects the critical concentrations needed to change the colloidal behavior of aqueous suspensions.

Figure 6. Proposed mechanism for the effect of amphiphilic electrolytes of different tail lengths on the electrical potential (ψ) of oppositely charged particles in water. Adsorption in the Stern layer is governed primarily by electrostatic attraction and thus leads to an equal reduction of the surface potential ψ0 to the Stern potential ψδ, regardless of the chain length of the amphiphiles. However, stronger hydrophobic interactions between amphiphilic electrolytes with longer alkyl chain result in a denser cloud of counterions within the diffuse layer, leading to a more pronounced screening of the Stern potential, ψδ. This lowers the zeta potential ζ while keeping the total amount of counterions adsorbed within the Stern and diffuse layers constant. ζ corresponds to the electrical potential at the shear plane s. Non-amphiphilic counterions (e.g., Cl
) are indicated by white circles with a negative charge, whereas co-ions were intentionally omitted to simplify the scheme. The amphiphile concentration considered here is lower than that required for charge reversal (Figure 5).

To solve this contradiction, we propose that associative hydrophobic interactions between the alkyl groups of short amphiphiles lead to a more compressed diffuse layer of amphiphilic counterions around the particle surface, without necessarily increasing the overall concentration of surface adsorbed molecules (Figure 6). This hypothesis is assessed here by comparing theoretical predictions and experimental data on the effect of amphiphilic counterions on the zeta potential of charged particles, assuming that attractive hydrophobic interactions occur between the amphiphiles within the diffuse part of the electrical double layer. For that purpose, we first develop a modified version of the classical Poisson
Boltzmann equation that accounts for hydrophobic interactions between amphiphilic electrolytes within the diffuse layer. While more detailed analyses of the effect of electrolytes on the electrical properties of oxide surfaces under high ionic strengths are available, 43,44 we show that the less accurate Debye
H€uckel approximation to classical 11839

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double layer theory is powerful enough to predict the overall colloidal behavior of concentrated suspensions of oxide particles and amphiphilic molecules. According to Boltzmann’s law, the volumetric number density of ions around electrically charged particles (ni) is given by the following:45 ni ¼ n0i e
zi qψ=kB T

ð1Þ

n0i

where and zi are the number density and valence of ions in the bulk solution, respectively; q is the elementary electrical charge (1.6  10
19 C); ψ is the local electrical potential; kB is the Boltzmann constant (1.38  10
23 J/K) and T is the temperature. Similarly to the original hemimicelle model, the attractive hydrophobic interactions between the alkyl chains are taken into account by introducing an additional hydrophobic energy term in the Boltzmann factor of eq 1, leading to the following relationship: ni ¼ n0i e
ðzi qψ þ Eh Þ=kB T

ð2Þ

where Eh is the total energy gained per molecule through the hydrophobic association of their hydrocarbon chains and the term ziqψ is the electrostatic energy gained by the counterion by positioning itself within the diffuse layer. As proposed in the Gouy
Chapman theory, the volumetric density of ions given by eq 2 can be combined with the Poisson equation describing the electrical potential as a function of the local charge density to obtain the following relationship (see Supporting Information): !1=2 z2i q2 n0i 2 2
Eh =kB T ∇ ψ ¼ k ψe with k ¼ ð3Þ εr ε0 kB T i

∑

where k is the inverse of the Debye screening length, εr is the relative permittivity of the liquid medium (80 for water), and ε0 is the permittivity of vacuum (8.85  10
12 C2/(N m2)). Solving eq 3 taking the Stern potential ψδ as the electrical potential at a distance (r0 + δ) from the particle center as boundary condition yields the following: ðr0 þ δÞ ψδ e
jðr
r0
δÞ ψðrÞ ¼ r j ¼ ke
Eh =2kB T

with ð4Þ

where r is the distance from the particle center. Equation 4 can be rearranged to give the following explicit relationship between the electrical potential ψ(r) and the bulk electrolyte concentration ceq: ln ψðrÞ ¼ ln½ðr0 þ δÞψδ =r
ðz2i q2 =εr ε0 kB TÞ1=2 e
Eh =2kB T ðr
r0
δÞc1=2 eq ð5Þ Whereas the sum of the volumetric number density of ions in the bulk solution (∑in0i ) equals 2ceq for completely ionized electrolytes, only one-half of the amphiphilic electrolyte is deprotonated at the pH of 4.75 used in all the experiments (pH = pKa of the carboxylic acid group). To take this into account, eq 5 was obtained assuming ceq = ∑in0i . Equation 5 enables the prediction of the zeta potential of particles in the presence of different concentrations of amphiphilic

Figure 7. Linear dependence of the natural logarithm of the zeta potential (ln ζ) on the square root of the amphiphile concentration (c1/2) for (a) short-chain carboxylic acids adsorbed on positively charged alumina particles at pH 4.75 and (b) long-chain alkyl ammonium acetates adsorbed on negatively charged silica particles at pH 6.5
6.9. Data in (a) and (b) were obtained from Gonzenbach et al.18 and Somasundaran et al.,46 respectively.

electrolytes. Considering that the zeta potential ζ corresponds to the electrical potential at the shear plane located at a distance s from the particle surface (Figure 6), the following relationship can be obtained from eq 5: ln ζ ¼ ln½ðr0 þ δÞψδ =ðr0 þ sÞ
ðz2i q2 =εr ε0 kB TÞ1=2 e
Eh =2kB T ðs
δÞc1=2 eq

ð6Þ

On the basis of this theoretical analysis, a linear dependence of ln ζ with respect to c1/2 eq should exist if the deprotonated amphiphilic molecules act indeed as counterions around the particles. This assumes that the hydrophobic interactions between amphiphiles of one particular length can be described by a constant hydrophobic energy term Eh. Because the zeta potential data were obtained from 2 vol % suspensions, the initial amphiphile concentration c is similar to the equilibrium concentration and thus was taken as ceq in eq 6. An analysis of the experimental zeta potential data based on this theoretical framework confirms that the amphiphilic molecules decrease the zeta potential by adsorbing as counterions in the diffuse layer around the particles, as indicated by the linear dependence between ln ζ and c1/2 shown in Figure 7 for amphiphiles of different chain lengths. For comparison, zeta 11840

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Figure 8. Linear relationship between the natural logarithm of
(d ln ζ)/ (dc1/2) (or ln p) and the number of carbons (m) in the alkyl tail of shortchain carboxylic acids (full circles) and long-chain ammonium acetates (empty squares). The continuous lines are linear fittings whose slopes correspond to the free energy (ϕ) gained through hydrophobic interactions between alkyl groups of the hydrocarbon chain.

potential results previously reported by Somasundaran et al.46 for long amphiphilic electrolytes adsorbed on oppositely charged quartz particles are also plotted in Figure 7. We conclude that both short and long amphiphilic molecules reduce the zeta potential by adsorbing as counterions within the diffuse layer surrounding the charged particles. The ln ζ versus c1/2 graphs also provide information about the energy Eh associated with hydrophobic interactions between the amphiphiles’ hydrocarbon tails. Eh is equal to mϕ, where m is the number of carbons in the amphiphile tail and ϕ is the free energy gained per
CH2
group upon lateral hydrophobic association of the alkyl chain in water. By replacing Eh with mϕ in eq 6 and taking the negative derivative, p, of ln ζ with respect to c1/2 eq , one arrives at the following relationship in logarithmic form: ! " # d ln ζ ϕ 1 z2i q2 ðs
δÞ2 m þ ln ln p ¼ ln
1=2 ¼
2kB T 2 εr ε0 kB T dceq ð7Þ Plotting ln p as a function of the number of carbons m in the amphiphile hydrocarbon tail allows us to experimentally assess the free energy ϕ gained per
CH2
group through hydrophobic interactions between the amphiphilic molecules. A linear relationship between ln p and m is obtained for both short and long amphiphiles, with the slope corresponding to the normalized energy term
ϕ/2kBT (Figure 8). Free energies ϕ of
1.0588 and
1.0012 kBT are obtained from the ln p versus m graphs for the short and long amphiphilic molecules, respectively. Remarkably, these ϕ values are in very close agreement with the free energy of
1 kBT gained per
CH2
group during the formation of micellar amphiphilic structures in bulk water.31,46 Our analysis suggests that the enhanced ability of amphiphilic molecules to screen the electrical potential of charged particles (Figure 5) can indeed be attributed to the formation of a denser cloud of counterions within the diffuse part of the double layer due to attractive hydrophobic interactions between the molecules’ alkyl chains. Moreover,

these results show that carboxylic acids containing between two and six carbons in the alkyl chain are strongly influenced by attractive hydrophobic interactions, despite their unusually short hydrocarbon tail. The ligand exchange reactions on the particle surface and the cooperative association between charged and uncharged amphiphiles expected at pHs around the pKa value of the carboxylate group are also expected to enhance the adsorption of the short-chain amphiphilic molecules investigated here. Importantly, this interpretation of the effect of amphiphilic electrolytes on the zeta potential of charged particles does not rely a priori on a higher surface coverage of the amphiphiles within the Stern layer (Figure 6). For amphiphilic electrolytes containing 2
6 carbons in the hydrocarbon chain, the energy gained through hydrophobic association (Eh) is higher but still in the same order as the electrostatic energy ziqψ experienced by hydrophilic electrolytes (1 ziqψ < Eh < 4 ziqψ). In this case, the hydrophobic energy gained by positioning amphiphilic molecules in close proximity to each other in the diffuse layer increases the volumetric density of counterions around the particle but is not high enough to avoid competitive adsorption with hydrophilic counterions. As a result, short amphiphiles adsorb to a similar extent regardless of the molecule’s chain length. In contrast, the hydrophobic energy Eh for amphiphiles containing 10
18 carbons in the tail is substantially higher than the electrostatic energy ziqψ gained by hydrophilic electrolytes present in the diffuse layer (6 ziqψ < Eh < 12 ziqψ). Under this condition, the competitive adsorption of hydrophilic electrolytes becomes progressively less important as the chain length (and Eh) of the hydrophobic electrolyte increases, thus leading to an increased adsorption of the amphiphiles for increasing the number of carbons in the tail. In this case, although the effect of the amphiphiles on the electrokinetic behavior of the particle can still be interpreted in terms of an increase of the volumetric density of counterions (Figure 7), the diffuse layer is likely sufficiently thin to make plausible the original assumption by Gaudin and Fuerstenau that the amphiphiles adsorb primarily in the Stern layer.28 In this context, our theoretical treatment offers a more detailed picture of the electrical double layer around oxide particles in the presence of amphiphilic counterions and eventually reconciles apparently contradicting experimental data for long and short amphiphiles. By rearranging eq 6, one can also correlate the bulk concentration of amphiphiles needed to reduce the particle zeta potential to any arbitrary value (c ζ) with the number of carbons in the amphiphile tail, as follows: !  " # ϕ εr ε0 kB T ψ ðr þ δÞ 0 m þ ln ln cζ ¼ ln2 δ kB T ζðr0 þ sÞ z2i q2 ðs
δÞ2 ð8Þ While a direct estimate of the concentrations of amphiphiles needed to reduce the particle zeta potential to a particular value requires knowledge of the electrical Stern potential ψδ and of the distance s at the shear plane, a simpler scaling relationship can be obtained by applying eq 8 to any pair of amphiphiles with specific numbers of carbons in the chain (m), as follows: cm2 ¼ eðm1
m2 Þ cm1

ð9Þ

where c*m1 and c*m2 are the concentrations of amphiphiles with, respectively, m1 and m2 carbons in the alkyl tail required to reduce the particle zeta potential to a constant arbitrary value. 11841

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Figure 9. Bulk concentrations of amphiphiles (cζ/2) required to halve the zeta potential of particles as a function of the number of carbons in the alkyl chain (m) for short-chain carboxylic acids adsorbed on alumina particles (full circles) and long-chain ammonium acetates adsorbed on silica particles (empty squares).

To derive eq 9, we assume a constant relative permittivity εr of the liquid medium regardless of the amphiphile chain length. Estimates of the relative permittivity of the solution within the diffuse layer for the different carboxylic acids show that this assumption leads to errors lower than 11% for the critical concentrations predicted using eq 9. To illustrate the predictive character of this scaling relationship, theoretical estimates obtained from eq 9 for amphiphiles with different number of carbons, m, are compared with the experimentally determined amphiphile concentrations needed to reduce the zeta potential by half of its initial value in the absence of electrolytes (Figure 9). To estimate the critical concentration c*m2 for an amphiphile containing m2 carbons in the tail, prior knowledge of a reference critical concentration c*m1 for another amphiphile with m1 carbons is required. In Figure 9, predictions of c*m2 were obtained from the scaling relationship taking the experimental concentration of propionic acid required to halve the zeta potential as the reference c*m1 value in eq 9. Figure 9 shows good agreement between theoretical and experimental values, confirming that eq 9 allows for the quantitative prediction of the amphiphile concentrations needed to change the zeta potential of the charged particles. According to the proposed model, amphiphiles with more carbons in the hydrocarbon chain lead to a higher volumetric density of counterions in the diffuse part of the electrical double layer, thus requiring a lower concentration in the bulk to reduce the zeta potential to any arbitrary value, as exemplified in Figure 9. The screening of the particle electrical potential combined with the presence of hydrophobic species on the particle surface enhance the affinity of the oxide particles toward the air
water interface. Once a critical concentration of amphiphiles is achieved in the bulk (c > c1*), the zeta potential becomes sufficiently screened to allow for the adsorption of the slightly hydrophobized oxide particles at the air
water interface, thus decreasing the apparent surface tension of the suspension (Figure 3a). By further increasing the amphiphile concentration (c > c2*), the absolute zeta potential continues to decrease until the electrical double layer is no longer thick enough to avoid particle agglomeration. This ultimately

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Figure 10. Phase behavior of aqueous alumina suspensions containing short-chain carboxylic acids at pH 4.75 as a function of the number of carbons (m) in the alkyl chain. The dashed lines indicate the critical amphiphile concentrations c1* and c2* predicted by the proposed scaling relationship (eq 9). Predictions were obtained by taking the experimental critical concentrations of propionic acid as the reference c*m1 value in eq 9. Sparsely hatched, gray, and densely hatched areas indicate the conditions leading to fluid dispersions, foams, and gel networks, respectively. Figure 4 provides a detailed description of the symbols shown here.

leads to a sharp increase in the suspension's apparent viscosity (Figure 3b). Stable foams are obtained at intermediate amphiphile concentrations (c1* < c < c2*), at which particles are sufficiently hydrophobic to adsorb at the air
water interface and the electrical double layer is still thick enough to prevent extensive particle agglomeration in the bulk aqueous phase (Figure 3c). Given the fact that the sharp transitions in the phase behavior of aqueous suspensions containing amphiphilic electrolytes result from the aforementioned changes in the particle zeta potential, the scaling relationship depicted in eq 9 should also enable the quantitative prediction of the critical amphiphile concentrations c1* and c2* indicated in Figure 4. A close agreement between experiments and theory is observed when the theoretical predictions for c1* are plotted directly on the original experimental diagram (Figure 10). Despite the high particle concentration of 35 vol % of such suspensions, the experimental data are correctly described by theoretical estimates based on the initial rather than the equilibrium concentration of amphiphiles. This surprising correlation probably reflects the complex nonequilibrium nature of such concentrated suspensions, whose behavior is ultimately dictated by the initial rather than the equilibrium conditions of the system. Figure 10 shows that the critical concentration c2* can also be accurately predicted by the suggested scaling law in the case of short amphiphiles (m = 2 and 3). Poorer agreement was found for longer carboxylic acids (m = 4 and 6), probably because of the local formation of micelles or immiscible phases during the addition of high concentrations of valeric and enanthic acids in water (Figure 10). We expect eq 9 to be also applicable to emulsified colloidal systems,15,16 although the partition of amphiphiles between the oil and aqueous phases has to be considered in this case. 11842

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Langmuir The predictive power of the scaling relationship shows that the proposed model captures the essential physicochemical mechanisms governing the phase behavior of aqueous suspensions containing both short and long amphiphilic electrolytes. This contributes to our current understanding of these complex colloidal systems and makes it possible to delineate the phase behavior of other unknown particle
amphiphile combinations with little experimental effort.

’ CONCLUSIONS The rich electrokinetic and phase behavior of suspensions containing particles and amphiphilic electrolytes of opposite charge can be theoretically explained and predicted by incorporating an additional energy term associated with attractive hydrophobic interactions between electrolytes into the classical Gouy
Chapman model of the electrical double layer. We show that such attractive hydrophobic interactions between the amphiphile’s hydrocarbon tail lead to denser clouds of amphiphilic counterions within the diffuse part of the electrical double layer as compared to that expected for nonhydrophobic electrolytes. This interpretation explains the effect of amphiphiles on the electrokinetic and phase behavior of colloidal suspensions without the assumption that amphiphilic molecules with increasing hydrocarbon chain lengths necessarily adsorb to a larger extent on the particle surface. We show that a compression of the diffuse layer without an enhanced adsorption of longer amphiphiles is expected when the energy gained through hydrophobic association (Eh) is higher but still in the same order as the electrostatic energy (ziqψ) that causes nonhydrophobic electrolytes to adsorb in the diffuse layer (1 ziqψ < Eh < 4 ziqψ). This is the case for amphiphilic molecules containing 2
6 carbons in the hydrocarbon chain. The effect of longer amphiphiles (g10 carbons) on the electrokinetics of colloidal particles can also be explained in terms of a compression of the diffuse part of the electrical double layer. However, the fact that in this case the hydrophobic energy is much higher than the electrostatic energy (Eh > 6 ziqψ) results in a preferential adsorption of amphiphiles in the diffuse layer, which is ultimately reflected in an increased adsorption for amphiphiles with increasing tail length. On the basis of the proposed model, we obtain scaling relationships that can quantitatively predict the effect of the hydrocarbon tail length on the bulk amphiphile concentrations required to screen the particle surface potential. Because the screening of the surface charges eventually leads to the adsorption of particles at the air
water interface and, later on, to extensive particle agglomeration, the scaling relationship proposed in this study can be used to predict the colloidal behavior of aqueous suspensions containing amphiphilic electrolytes. The proposed model reconciles previous experimental results for both short and long amphiphilic electrolytes and has important implications in the stabilization of wet foams and emulsions using colloidal particles and the fabrication of materials from particle-stabilized colloidal systems and might provide new insights into the flotation of mineral particles. ’ ASSOCIATED CONTENT

bS

Supporting Information. Electrical potential of charged particles in the presence of amphiphilic electrolytes. This material is available free of charge via the Internet at http://pubs.acs. org.

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’ AUTHOR INFORMATION Corresponding Author

*E-mail: [email protected].

’ ACKNOWLEDGMENT We thank CIBA Specialty Chemicals (Switzerland) for the financial support, Prof. Dr. Douglas W. Fuerstenau and Prof. Thomas W. Healy for their valuable comments on the manuscript, Philip Sturzenegger, Rahel N€ageli, and Claudia Strehler for their contribution to the experimental work, and Prof. Dr. Nelson Studart and Dr. Randall M. Erb for fruitful discussions. ’ REFERENCES (1) Binks, B. P.; Horozov, T. S. Colloidal Particles at Liquid Interfaces; Cambridge University Press: Cambridge, U.K., 2006; p 518. (2) Studart, A. R.; Studer, J.; Xu, L.; Yoon, K.; Shum, H. C.; Weitz, D. A. Langmuir 2011, 27 (3), 955–964. (3) Studart, A. R.; Gonzenbach, U. T.; Akartuna, I.; Tervoort, E.; Gauckler, L. J. J. Mater. Chem. 2007, 17 (31), 3283–3289. (4) Taylor, P.; Liang, W.; Bognolo, G.; Tadros, T. F. Colloids Surf. 1991, 61, 147–165. (5) Annable, T.; Buscall, R.; Ettelaie, R.; Shepherd, P.; Whittlestone, D. Langmuir 1994, 10 (4), 1060–1070. (6) Moudgil, B. M.; Singh, P. K.; Adler, J. J. In Handbook of Applied Surface and Colloid Chemistry; Holmberg, K., Ed.; John Wiley & Sons Ltd.: West Sussex, U.K., 2002; Vol. 1, pp 219
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