Ionic Nature of a Gemini Surfactant at the Air/Water InterfaceChi M. Phan,*,† Cuong V. Nguyen,†,‡ Hiromichi Nakahara,§ Osamu Shibata,§ and Thanh V. Nguyen∥

†Department of Chemical Engineering, Curtin University, Perth, Western Australia 6845, Australia‡Military Academy of Logistics, Long Bien, Hanoi, 1263, Vietnam§Department of Biophysical Chemistry, Graduate School of Pharmaceutical Sciences, Nagasaki International University, Sasebo,Nagasaki 859-3298, Japan∥School of Chemistry, University of New South Wales, Sydney, New South Wales 2052, Australia

ABSTRACT: The ionic state of an adsorbed geminisurfactant at the air/water interface was investigated using acombination of surface potential and surface tension data. Thecombined model was developed and successfully described theexperimental data. The results verified the existence of threeionic states of the gemini surfactant in the interfacial zone.Furthermore, the model can quantify the adsorbed concen-trations of these species. At low concentrations, the fullydissociated state dominates the adsorption. At high concen-trations, the fully associated state dominates, accounting for upto 80% of the total adsorption. In the middle range, theadsorption is dominated by the partially associated state, whichhas a maximum percentage of 80% at a critical micelleconcentration of 0.5. The variation in the ionic state is a unique characteristic of gemini surfactants, which can be the underlyingmechanism for their advantages over conventional surfactants.

1. INTRODUCTION

The behavior of an ionic surfactant at the interface is animportant factor for its successful application, for instance, indetergency and foaming. Although adsorption has beendescribed theoretically by the Gibbs adsorption isotherm,such analysis does not provide sufficient details at the molecularlevel, such as molecular arrangement or ionic charges.1

Recently, results have highlighted the deficits of the conven-tional analysis2−5 for ionic surfactants.Among the ionic surfactants, gemini is a relatively new class

of surfactants. Because of their ionic structure, geminis have anumber of advantages over single-head surfactants.6 Inparticular, geminis have a significantly low critical micelleconcentration (CMC). It has been shown that the CMC of thegeminis can be 1 or 2 orders of magnitude lower than that ofthe corresponding single-head surfactant.7 The low CMCimplies dramatic savings in chemicals for industrial applications.However, the behavior of geminis at the interface remainspoorly understood.6 The application of the conventional Gibbsadsorption equation to gemini surfactants is particularlyproblematic, as briefly presented below.For single-surfactant systems, the general form of the Gibbs

equation is presented in the following form8,9

γ− Γ =nRT c

dd ln b (1)

where cb is the bulk concentration, γ is the surface tension, Γ isthe adsorbed concentration, and n is the prefactor that dependson the nature of the surfactant.Conventional theory indicates that n equals 3 for fully

dissociated geminis. On the other hand, other studies havesuggested that the prefactor should be 2 for geminis. Theconflicting hypotheses between the two cases have beenreviewed in detail.7 The variation in n can over- orunderestimate the adsorbed concentration by 50% for thesame surface tension data. A later study with neutronreflectometry (NR), however, pointed to more complicatedbehavior. The obtained prefactors of most geminis at the CMCwere neither 2 nor 3.10 Indeed, the prefactor varies with thesurfactant concentration.11 The data demonstrated that differ-ent ionic states of geminis coexist in the systems. With multiplestates, a simple form such as eq 1 is no longer obtainable.Instead, a complicated theoretical framework was proposed forsuch systems, with multiple parameters.10,12 Verification of sucha model remains challenging, especially when relying on theequilibrium surface tension and NR data.This study aims to provide a detailed description of gemini

adsorption from a different approach: a combination of surfacepotential and dynamic surface tension. With multiple ionicstates at the interface, the adsorbed geminis expectedly have a

Received: September 22, 2016Revised: November 3, 2016Published: November 4, 2016

Article

pubs.acs.org/Langmuir

© 2016 American Chemical Society 12842 DOI: 10.1021/acs.langmuir.6b03484Langmuir 2016, 32, 12842−12847

profound impact on the surface charge. It should be noted thatthe surface charge is a decisive factor for application processesof surfactants, such as in foaming.13 The surface potential dataare complemented by the dynamic surface tension. Fromprevious dynamic modeling,14 we have been able to quantifythe total adsorbed concentrations without relying on the Gibbsequation. In this study, the modeled adsorption is combinedwith the surface potential data to clarify the ionic nature of theadsorbed geminis.

2. THEORETICAL FRAMEWORKAlthough the absolute surface charge of the air/water interfaceremains unclear,15 experimental methods are available tomeasure the change in the surface potential due to thepresence of surfactants. It has been found that the surfacepotential can change by as much as 400 mV for ionicsurfactants.16,17 To quantify the change in the surface potential,an arrangement between the surfactants and counterions needsto be considered at a molecular level.In the literature, the ionic distribution at the air/water

interface has been proposed by various researchers. Generally,the proposals depict the adsorption in separate ionic layers.16,18

The surfactant molecules are located further outside because ofthe hydrophobicity of the surfactant tails. The counterions,which are governed by the electrostatic attraction of thesurfactant head, are mostly located further inside of the liquidphase. Although the overall arrangements are well accepted, thequantitative verification remains unsatisfactory. There are twoimportant theories for the ionic charge at the interface. The firsttheory is based on ionic-binding equilibrium,18 in which thecounterion can react with the head of the surfactants. The ionicbinding can be quantitatively described by a reaction constant,as in the binding of aqueous ions with a solid surface.19 Thesecond model includes the dipole moment of the adsorbedsurfactant molecules on the overall potential change,16 whileneglecting the binding reactions. Both models require someparameters that are not easy to verify experimentally.Furthermore, these models need to use the Gibbs equationto quantify the adsorbed concentrations. As mentioned above,the application of Gibbs equation with multiple ionic states isnot practical for gemini surfactants.10

For gemini surfactants, with their multiple ionic states, theionic binding model is required. In this case, the relativequantities between the three ionic states can be mathematicallydescribed by the reaction equilibria. It should be noted that themodel18 inherently indicated a coexistence of multiple ionicstates of surfactants, which has been verified recently with alkyltrimethylammonium bromide.2 In this study, the ionic structureis proposed for the cationic geminis as follows: the surfactantadsorption is governed by the equilibrium between the tails andthe surface. The counterions, Br− in this case, also concentratenear the surface because of the Coulombic attraction to thesurfactant heads. Most of the anions are fully hydrated andlocated further inside of the liquid phase. Some of the anionscan penetrate the surfactant layers because of ionic binding withthe surfactant heads. These anions are partially hydrated. Theequilibria between ionic species are governed by the reactionconstants.The change in the surface potential (Figure 1) is given by

ψ ψ ψΔ = − = = +V V V0 t s w (2)

where ψt is the potential at the interfacial layer (V), ΔV is thechange in the surface potential (V), V is the surface potential of

the surfactant solution, and V0 is the surface potential of purewater.The total surface potential, ψt, has two components: the

potential due to the surfactant charge (ψs) and the potentialdue to the disruption of water arrangement (ψw). In thisinstance, ψw accounts for the impact of the surfactant tails onthe water surface potential. It has been shown that the watersurface molecules can create a potential due to their asymmetricarrangement.20 Simulations indicated that the potential can beas low as −600 mV.21 Hence, the surfactant tails can increasethe potential by disrupting the water order.16 In general, it isexpected that ψw is less significant than ψs. At lowconcentrations, however, ψw can be comparable to ψs.It is noteworthy that our model does not employ a diffuse

layer (or Gouy−Chapman layer), in which the anionsconcentrate on the surface with a smooth and exponentiallydecreasing trend. As discussed in the literature, such a modelignores the finite radius of hydration anions and is notappropriate for high surface potentials, >50 mV.1 The cationicsurfactants can increase the surface potential by up to 300 mV.Furthermore, the surface charge, which is given by adsorbedsurfactants, is on the order of 10−6 mol/m2. At high ionicsurface concentrations, such a double electrical diffuse layer isnot appropriate.1 The model in this study is effectively aDonnan equilibrium.22 In this case, anions are concentrated onan anionic zone with a finite width on the order of a fewangstroms. The ionic zone is fully penetrable by ions in thebulk. The total charge of the zone is equal, with opposite sign,to that of the surfactant zone. Consequently, ψs is directlyrelated to the surface charge, which is induced by the surfactantas

ψ σλ

ε ε=s

s

s 0 (3)

where σ is the surface charge density (C/m2), εs is thepermittivity of the double electrical layer, ε0 is the vacuumpermittivity, and λs is the thickness of the double electrical layer(m).In eq 3, λs has the same scale as the radius of the hydrated

anions. The permittivity of the charged zone is smaller thanthat of water.

Figure 1. Molecular arrangement of the adsorbed gemini surfactant atthe air/water interface.

Langmuir Article

DOI: 10.1021/acs.langmuir.6b03484Langmuir 2016, 32, 12842−12847

12843

In the next section, the ionic-binding equilibria are used toderive the relationship between the adsorbed molecules and thesurface charge, σ. The equilibrium involves adsorption of thesurfactant and the ionic-binding process. First, the adsorption isdriven by the interaction between the aqueous surface and thesurfactant tails. The adsorption of the surfactant molecules isgoverned by the equilibrium between the occupied and emptysites18

=Γ

Γk

css

o b (4)

where Γs is the adsorbed surfactants (which equals the numberof occupied sites) and Γo is the number of empty sites. Becausethere is a limited number of available adsorption sites

Γ = Γ + Γmax o s (5)

where Γmax is the total number of available sites. By substitutingin eq 5, the adsorbed surfactant is governed by the Langmuirisotherm

Γ = Γ+k c

k c1s maxs b

s b (6)

The adsorbed surfactant can have different ionic states. For adibromide gemini surfactant, GeBr2, there are three ionic states:Ge2+, GeBr+, and GeBr2. It should be noted that because of thelow bulk concentration the surfactant is fully dissociated in thebulk (i.e., existence in the form of Ge2+ only). The ionicbinding of Br− with the adsorbed surfactant has two associationsteps

+ ↔

+ ↔

+ − +

+ −

Ge Br GeBr

GeBr Br GeBr

k

k

2

2

1

2(7)

The equilibria between these species are given by18

ψ

ψ

=Γ

Γ−

=Γ

Γ−

+

+ −

+ −

⎛⎝⎜

⎞⎠⎟

⎛⎝⎜

⎞⎠⎟

kc

e

k T

kc

e

k T

exp

exp

t1

GeBr

Ge Br B

2GeBr

GeBr Br

t

B

2

2

(8)

where Γi (i = Ge2+, GeBr+, and GeBr2) are the surfaceconcentrations of the corresponding species and k1 and k2(M−1) are the reaction constants. The value of k1 should besignificantly higher than k2 (because ionic binding with Ge2+ isenergetically easier than binding with GeBr+). If both k1 and k2are zero, the system reduces to a single and fully dissociatedspecies, Ge2+. It should be noted that the surface concentrationsare in mol/m2, whereas cBr− is the Br

− concentration in the bulk

(M). The correction term, − ψ( )expe

k Tt

B, is included to account

for the energy required for the ions to move from the bulk tothe surfactant layer. The implication of this correction term hasbeen discussed previously.18 Qualitatively, a higher potential atthe interface will make it easier for the anion to bind at theinterface, and vice versa. The total adsorbed surfactant is givenby

Γ = Γ + Γ + Γ+ +s Ge GeBr GeBr22 (9)

The surface charge at the interface is

σ = Γ + Γ+ +eN (2 )a Ge GeBr2 (10)

where e is the charge per electron (1.602 × 10−19 C) and Na isthe Avogadro constant (6.022 × 1023 mol−1). Solving theequilibria and eq 5, one can obtain

σ+ +

++ +

Γ =⎡⎣⎢

⎤⎦⎥eN

K K KK

K K K2

1(1 ) (1 )a

1 2 1

1

1 2 1s

(11)

where = ψ− ( )K k c exp

e

k T2 2 Brt

Band = ψ

− ( )K k c expe

k T1 1 Brt

B. Com-

bining with eq 3, the potential is given by

ε ελ

ψ ψ

+ ++

+ +Γ

− − =

⎡⎣⎢

⎤⎦⎥eN

K K KK

K K K2

1(1 ) (1 )

( ) 0

a1 2 1

1

1 2 1t

s 0

st w

(12)

Equation 12 can be solved numerically for ψt. The aboveframework has six parameters: ks, Γmax, k1, k2, ψw, and λs/εsε0.Generally, the system needs to be solved by fitting with thesurface tension and the surface potential. In such an approach,the Gibbs equation has to be employed. This study employs adifferent approach by utilizing dynamic modeling that is basedon the Langmuir isotherm and the diffusion process.23 Thedynamic modeling does not require the Gibbs equation andgives consistent values for ks and Γmax. Consequently, the otherfour parameters are found by fitting against the surfacepotential data.

3. EXPERIMENTAL SECTIONA synthesized gemini surfactant, [C12H25N(CH3)2−(CH2)3−N-(CH3)2C12H25]Br2,

14 was used for this study. The surface tension,both dynamic and equilibrium, has been successfully modeledpreviously. In this work, the change in the surface potential wasmeasured using an ionizing electrode (Figure 2), as described in the

literature.21,24 The surfactant was purified by crystallization twicebefore the measurement. The measurements were repeated at leastthree times at each concentration.

4. RESULTS4.1. General Observations. From previous modeling, the

values of ks and Γmax were obtained: 24.8 × 10−3 M−1 and 3.37× 10−6 mol/m2, respectively.14 The adsorbed concentration, Γs,is plotted with the surface potential data in Figure 3.It can be seen that the surface potential followed the same

trend as that of other cationic17 surfactants: the potential

Figure 2. Experimental setup for surface potential.

Langmuir Article

DOI: 10.1021/acs.langmuir.6b03484Langmuir 2016, 32, 12842−12847

12844

dramatically increases before reaching a plateau. Theconcentration at which the trend changes was around 5 ×10−6 M, or ∼0.5% of the CMC (0.95 mM). In other words, thesurface charge reached saturation faster than the surfacetension. The data qualitatively indicated that adsorption of asingle species (either Ge2+, GeBr+, or GeBr2) cannot describethe change in the surface potential. Because the surfacepotential changes rapidly at cb < 5 × 10−6 M, more data werecollected in the lower range (shown in the inset). It should benoted that the data exhibit a clearer trend than the reportedvalues of sodium dodecyl sulfate (SDS).16,24 The surfacepotential of SDS (being an anionic surfactant) was reduced to−100 mV.4.2. Modeling in a Limiting Case. Before employing the

full equation, it is worth considering a simplified case: ψw = 0.In this instance, eq 12 reduces to

ε ελ

ψ

+ ++

+ +Γ

− =

⎡⎣⎢

⎤⎦⎥eN

K K KK

K K K2

1(1 ) (1 )

( ) 0

a1 2 1

1

1 2 1t

s 0

st

(13)

with

ψ ψ= =− −

⎛⎝⎜

⎞⎠⎟

⎛⎝⎜

⎞⎠⎟K k c

e

k TK k c

e

k Texp and exp2 2 Br

t

B1 1 Br

t

B

By using a bisection method, the above equation can besolved for ψt. The equation has only three parameters: k1, k2,and λs/εsε0. It can be seen that the model can describe thechange in the surface potential in the middle range (Figure 4 isplotted on a logarithmic scale to improve clarity). However, themodel underpredicts the data at lower concentrations. It shouldbe noted that in the lower range the surfactant concentration iscomparable to water self-ionization (10−7 M). Consequently,the contribution of hydronium/hydroxides at the interface iscomparable to the surfactant contribution. The issue ofhydronium/hydroxides adsorption remains hotly debated inthe literature and is not addressed in this study. Consequently,

the model can be improved by incorporating a nonzero ψw topredict the data in the lower range.

4.3. Full Model. Equation 12 is solved using all fourparameters. The fitting to the experimental data is presented inFigure 5. It can be seen that the model can fit the whole rangeof experimental data.The inclusion of ψw (best-fitted value at 58 mV) can predict

the data at low concentrations very well. The data indicatedthat the surfactant influence on interfacial water molecules has apositive impact on the surface potential. This result isconsistent with the data reported in the literature.16 Thisvalue also indicated that the surface potential of surfactant-freewater is negative. The two kinetics were consistent with theassociation constants from alkylammonium bromide.25 Itshould be noted that k2 is about 2 orders of magnitude smallerthan k1, as expected. From the best-fitted value of λs/εsε0, onecan estimate the separate distance in the double electrical layer.Assuming a value of εs of 10, the distance λs is 6.2 Å, which ison the same order of hydration shell radius as that of halideanions.26 In summary, the obtained values were consistent withthe physical constraints.At high concentrations, >70% of CMC, the experimental data

increase slightly whereas the model indicates a small reduction.

Figure 3. Surface potential and adsorbed concentration.

Figure 4. Surface charge and predicted ψt in a limiting case.

Langmuir Article

DOI: 10.1021/acs.langmuir.6b03484Langmuir 2016, 32, 12842−12847

12845

This can be explained by the formation of micelles.Theoretically, micelles can form at concentrations belowCMC, albeit at low quantities. The equilibrium between theisolated surfactant and the micelles is well-established.27

Formation of micelles in the vicinity of the CMC is alsoresponsible for the inconsistency of the conventional theory foranionic4 and cationic3 surfactants. It should be noted that theoptima (in this case, a maxima) in the surface potential is notunusual for ionic surfactants. Previously, a minima at around1% CMC was reported for the anionic surfactant, SDS. Theminima for SDS was confirmed independently using a vibratingprobe16 and our ionizing electrode.24

The distribution between the three ionic states was alsoobtained from the model. It can be seen that the model predictsa significant fraction of GeBr+ in the middle range (Figure 6).

In particular, GeBr+ has a maximal percentage of 80% at ∼0.5%CMC. An apparent prefactor can also be computed forcomparison with the conventional form (eq 1)

′ =Γ + Γ + Γ + Γ

Γ

+ +

n Ge GeBr GeBr Br

t

22

(14)

It can be seen that n′ = 3 only at very low concentrations. Forthis surfactant, n′ is almost 1 at the CMC. Using theconventional equation, this indicates that the surfactant behavesas if it is a nonionic surfactant at high concentrations. As

mentioned earlier, the adsorption of the geminis cannot beexplained consistently by the conventional theory. Neutronreflectometry (NR)/tensiometry in combination with eq 1 hasbeen applied to 17 geminis. The apparent prefactor, around theCMC, varies from 0.7 to 3.2.10 The decreasing n with increasingconcentration is consistent with the reported trend ofgeminis.11 It should be noted that the estimation of n fromapplication of NR and eq 1 has a large error, ±0.4.Furthermore, the neutron reflection is insufficient at lowconcentrations for effective measurement. Whereas directcomparison with NR is not possible, the result from Figure 6is consistent with the behavior of geminis reported in theliterature.Although many cationic geminis have been synthesized and

reported in the literature,7 the correlation between the spacer ofthe gemini and its adsorption remains unclear. For instance, thevariations in the CMC6 and the specific occupied surface area7

are not explainable using the conventional theory. The modelin this study indicates that the influences of the spacer onadsorption have to be quantified through the values of k1 andk2. The developed model presents a new approach to study theionic behavior of gemini surfactant solutions. Furtherinvestigation on different geminis is carried out to clarify therole of the spacer on the adsorption behavior.Finally, the new model is compared with the current models

for multiple species,2,10 which employ the Gibbs adsorptionequation. In the new model, the two ionic forms, GeBr+ andGeBr2, exist only in the interfacial zone, not the bulk. Theconventional model, in contrast, requires the existence ofGeBr+ and GeBr2 in the bulk, albeit mathematically. Therequirement is because the surface tension of each species isrepresented by Γi/ln ci (if ci is zero, then Γi does not contributeto the surface tension of the system). Physically, GeBr+ andGeBr2 may not exist in the bulk at all. As mentioned earlier,with the increasing cb, micelles are formed instead of GeBr+ orGeBr2. The new model, on the other hand, includes thesespecies through the reaction equilibrium (eq 7) and dynamicsurface tension. Hence, the new model is physically moreconsistent. In this case, the existence of GeBr+ or GeBr2 isstrictly an interfacial effect. Hence, this model is applicable toother systems, in which certain species exists in the interfacial,not in the bulk. A well-known system with such an effect is theinterfacial assembly of trianion and cationic surfactants.28 Insuch a system, an interfacial assembly was formed at theinterface by electrostatic binding and cannot be described bythe conventional theory. Furthermore, the experimentalverification of the conventional theory relies on NR data,which are not obtainable at low concentrations. The newmethod utilizes the surface potential, which can effectivelycapture the dramatic changes at low concentrations.

5. CONCLUSIONSThe ionic binding model can successfully describe the changein the surface potential by the adsorbed gemini surfactant. Theexperimental data and the modeling results verified theexistence of multiple ionic conditions in the interfacial zone.The model provides a number of advantages over theconventional theory, which was developed for a single ionicstate. First, the model is easier to validate with surface potentialdata. Unlike NR, the surface potential can be obtained reliablyat low concentrations. Second, the proposed model does notrequire assumptions regarding the associated species, GeBr+

and GeBr2, in the bulk. Most importantly, the model can

Figure 5. Change in the surface potential ψt (k1 = 1.34 M−1, k2 = 0.017M−1, λs/εsε0 = 7 m2/F).

Figure 6. Distribution between the three ionic states as a function ofFt.

Langmuir Article

DOI: 10.1021/acs.langmuir.6b03484Langmuir 2016, 32, 12842−12847

12846

correctly predict the surface charge at the interface, which canbe a decisive factor in applications. The method can be appliedto other geminis to quantify the influence of the spacer on thesurface behavior.

■ AUTHOR INFORMATION

Corresponding Author*E-mail: c.phan@curtin.edu.au.

ORCIDChi M. Phan: 0000-0002-1565-8193Cuong V. Nguyen: 0000-0003-3997-0939NotesThe authors declare no competing financial interest.

■ REFERENCES(1) Butt, H.-J.; Graf, K.; Kappl, M. Physics and Chemistry of Interfaces;Wiley-VCH: Weinheim, 2003.(2) Phan, C. M. Dissociation of Ionic Surfactants at the Air/WaterInterface: Complete or Partial? J. Phys. Chem. B 2016, 120, 7681−7686.(3) Li, P. X.; Thomas, R. K.; Penfold, J. Limitations in the Use ofSurface Tension and the Gibbs Equation to Determine SurfaceExcesses of Cationic Surfactants. Langmuir 2014, 30, 6739.(4) Xu, H.; Li, P. X.; Ma, K.; Thomas, R. K.; Penfold, J.; Lu, J. R.Limitations in the Application of the Gibbs Equation to AnionicSurfactants at the Air/Water Surface: Sodium Dodecylsulfate andSodium Dodecylmonooxyethylenesulfate Above and Below the CMC.Langmuir 2013, 29, 9335−9351.(5) Phan, C. M.; Nguyen, C. V.; Yusa, S.-i.; Yamada, N. L. SynergisticAdsorption of MIBC/CTAB Mixture at the Air/Water Interface andApplicability of Gibbs Adsorption Equation. Langmuir 2014, 30,5790−5796.(6) Menger, F. M.; Littau, C. A. Gemini surfactants: A new class ofself-assembling molecules. J. Am. Chem. Soc. 1993, 115, 10083−10090.(7) Zana, R. Dimeric and oligomeric surfactants. Behavior atinterfaces and in aqueous solution: A review. Adv. Colloid InterfaceSci. 2002, 97, 205−253.(8) Adamson, A. W.; Gast, A. P. Physical Chemistry of Surfaces; Wiley,1997.(9) Rosen, M. J.; Kunjappu, J. T. Surfactants and InterfacialPhenomena, 4th ed.; Wiley: Hoboken, 2012.(10) Li, P. X.; Dong, C. C.; Thomas, R. K.; Penfold, J.; Wang, Y.Neutron Reflectometry of Quaternary Gemini Surfactants as aFunction of Alkyl Chain Length: Anomalies Arising from IonAssociation and Premicellar Aggregation. Langmuir 2011, 27, 2575−2586.(11) Li, Z. X.; Dong, C. C.; Thomas, R. K. Neutron ReflectivityStudies of the Surface Excess of Gemini Surfactants at the Air−WaterInterface. Langmuir 1999, 15, 4392−4396.(12) Wegrzyn ska, J.; Para, G.; Chlebicki, J.; Warszyn ski, P.; Wilk, K.A. Adsorption of Multiple Ammonium Salts at the Air/SolutionInterface. Langmuir 2008, 24, 3171−3180.(13) Murray, B. S. Stabilization of bubbles and foams. Curr. Opin.Colloid Interface Sci. 2007, 12, 232−241.(14) Nguyen, C. V.; Nguyen, T. V.; Phan, C. M. Dynamic adsorptionof a gemini surfactant at the air/water interface. Colloids Surf., A 2015,482, 365−370.(15) Chaplin, M. F. Theory vs Experiment. What is the Charge at theSurface of Water? Water 2009, 1, 1−28.(16) Warszyn ski, P.; Barzyk, W.; Lunkenheimer, K.; Fruhner, H.Surface Tension and Surface Potential of Na n-Dodecyl Sulfate at theAir−Solution Interface: Model and Experiment. J. Phys. Chem. B 1998,102, 10948−10957.(17) Nakahara, H.; Shibata, O.; Moroi, Y. Examination of SurfaceAdsorption of Cetyltrimethylammonium Bromide and SodiumDodecyl Sulfate. J. Phys. Chem. B 2011, 115, 9077−9086.

(18) Kalinin, V. V.; Radke, C. J. An ion-binding model for ionicsurfactant adsorption at aqueous-fluid interfaces. Colloids Surf., A 1996,114, 337−350.(19) Yates, D. E.; Levine, S.; Healy, T. W. Site-binding model of theelectrical double layer at the oxide/water interface. J. Chem. Soc.,Faraday Trans. 1 1974, 70, 1807−1818.(20) Fan, Y.; Chen, X.; Yang, L.; Cremer, P. S.; Gao, Y. Q. On theStructure of Water at the Aqueous/Air Interface. J. Phys. Chem. B2009, 113, 11672−11679.(21) Nguyen, C. V.; Phan, C. M.; Ang, H. M.; Nakahara, H.; Shibata,O.; Moroi, Y. Molecular Dynamics Investigation on Adsorption Layerof Alcohols at the Air/Brine Interface. Langmuir 2015, 31, 50−56.(22) Cevc, G. Membrane electrostatics. Biochim. Biophys. Acta, Rev.Biomembr. 1990, 1031, 311−382.(23) Phan, C. M.; Le, T. N.; Nguyen, C. V.; Yusa, S.-i. ModelingAdsorption of Cationic Surfactants at Air/Water Interface withoutUsing the Gibbs Equation. Langmuir 2013, 29, 4743−4749.(24) Nakahara, H.; Shibata, O.; Moroi, Y. Examination of surfaceadsorption of sodium chloride and sodium dodecyl sulfate by surfacepotential measurement at the air/solution interface. Langmuir 2005,21, 9020−9022.(25) Geng, Y.; Romsted, L. S. Ion Pair Formation in Water.Association Constants of Bolaform, Bisquaternary Ammonium,Electrolytes by Chemical Trapping. J. Phys. Chem. B 2005, 109,23629−23637.(26) Yang, L.; Fan, Y.; Gao, Y. Q. Differences of Cations and Anions:Their Hydration, Surface Adsorption, and Impact on Water Dynamics.J. Phys. Chem. B 2011, 115, 12456−12465.(27) Tanford, C. The hydrophobic effect and the organization ofliving matter. Science 1978, 200, 1012−1018.(28) Menger, F. M.; Shi, L. Electrostatic Binding among Equilibrating2-D and 3-D Self-Assemblies. J. Am. Chem. Soc. 2009, 131, 6672−6673.

Langmuir Article

DOI: 10.1021/acs.langmuir.6b03484Langmuir 2016, 32, 12842−12847

12847