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Journal of Colloid and Interface Science 267 (2003) 151154www.elsevier.com/locate/jcis

Testing the GouyChapman theory by means of surface tensionmeasurements for SDSNaClH2O mixtures

C. Marcus Persson,a,b, A. Petra Jonsson,a,b Magnus Bergstrm,a,b and Jan Christer Eriksson a,b

a Institute for Surface Chemistry, SE-11486 Stockholm, Swedenb Department of Chemistry, Surface Chemistry, Royal Institute of Technology, Drottning Kristinas vg 51, SE-100 44 Stockholm, Sweden

Received 10 December 2002; accepted 18 July 2003

Abstract

Surface tension isotherms were measured for sodium dodecyl sulfate (SDS) at different concentrations of added salt (NaCl). The freeenergy of the surfactant monolayer was assessed by invoking the GouyChapman theory for the charged head groups, the hydrophobic(Tanford) free energy of transfer of the hydrocarbon chain, and the hydrocarbon chain configurational free energy according to Gruens cal-culations and finally macroscopic contact terms. In particular, the effect of an increased salt concentration in bulk was examined. Theoreticalpredictions compare well with the experimental findings, and good agreement was found with respect to both the variation of free energy ofthe monolayer and the surface pressure behavior. Thus, at least for a liquid-expanded monolayer of SDS, the GouyChapman model yieldsa satisfactory account of the electrostatic contribution to the thermodynamic properties at different salt concentrations of NaCl. 2003 Elsevier Inc. All rights reserved.

Keywords: Surface tension; Surface pressure; Ionic surfactant; SDS; GouyChapman

1. Introduction

In various ways the GouyChapman theory of chargedinterfaces, assuming a smeared-out surface charge and ne-glecting ionion correlation and volume effects, has beenshown to hold for 1:1 salts. A main reason is presumablythat the size and ionioncorrelation effects approximatecan-cel [1]. The intuitive model of an adsorbed surfactant layerat the airwater interface as being composed of a hydro-carbon part, liquid-like in its properties, and a polar part ofwhich the head groups mix with the adjacent solution has re-

cently been verified through sum frequency generation spec-troscopy and ellipsometric measurements [2,3]. Thus, we arejustified in adhering to the molecular model of a surfactant-laden 1/v interface presented by Eriksson and Ljunggren [4]for which the free energy of the electrostatic double layer iscalculated according to the GouyChapman model. In thepresent study we compare the prediction of the moleculartheory as to the effect of added salt (NaCl) with the corre-sponding experimental results.

* Corresponding author.

E-mail address: [email protected] (C.M. Persson).

2. Material and methods

Sodium dodecyl sulfate (SDS) was purchased fromSigma and repeatedly recrystallized in ethanol. Sodiumchloride was obtained from Merck (Suprapur) and used asreceived. Surface tension was measured with a Krss K12tensiometer, employing the Wilhelmy plate method. The wa-ter used in the experiments was obtained from a MilliporeRiOs-8 and Milli-Q Plus 185 purification system and finallyfiltered through a 0.2-m Millipak filter.

3. Theory

We consider a liquid-expanded monolayer in which thehydrocarbon part of the monolayer behaves as a liquid hy-drocarbon and adhere largely to the approach taken in [4].The following film free energy contributions are taken intoaccount: the one caused by the hydrophobic effect, theconfigurational free energy of the hydrocarbon chains, thechanges in the macroscopic tensions, and the free energy ofthe electrostatic double layer.

The free energy gain in transferring a hydrocarbon chain

from the bulk solution at mole fraction x2 to the interface has0021-9797/$ see front matter 2003 Elsevier Inc. All rights reserved.doi:10.1016/S0021-9797(03)00761-6
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152 C.M. Persson et al. / Journal of Colloid and Interface Science 267 (2003) 151154

been quantified by Tanford [5] and is for a straight saturatedC12 hydrocarbon chain given by

(1)Tan/kT =19.96 lnx2,where k is the Boltzmann constant and T the absolute tem-perature (295 K). The attachment of the hydrocarbon chains,packed to the bulk-phase densities, to the polar groups re-siding in water imposes constraints on their configurationaldegrees of freedom. This free energy contribution, gconf, ascalculated by Gruen [6] and Szleifer et al. [7] relative to bulkhydrocarbon agrees well with experimental results [4] for adodecyl chain. Thus we can use the numerical fit [4]

gconf/kT = 3.126301 1.155336L+ 0.1827336L2(2) 0.01407631L3+ 0.0004774232L4,

where L is the thickness of the interface, determined by L=V/a2, V being the molar volume of the hydrocarbon chain(351 3/molecule) and a2 being the average molecular area.

As a condensed monolayer is formed some changes in themacroscopic surface tensions will occur. gm is the change inmacroscopic surface energies and is given by

(3)gm = hva2 + hwa2,where hv is the surface tension of the hydrocarbonvaporinterface formed and hw the surface tension value of thehydrocarbonwater interface. We next invoke the approxi-mation

(4)0 = hv + hw,where 0 is the surface tension value of water at zero SDS

concentration.The free energy due to a layer of surfactant ions and

its counterions is calculated by the GouyChapman theory,which is based on the PoissonBoltzmannapproximation as-suming a smeared-out surface charge. Accordingly, we have

(5)gel = 2kT lnS+

S2 + 1

2kT

(S2 + 1) 1

S

,

where S, the reduced charge parameter, is defined by

(6)S=

2

8RT 0rc,

where is the surface charge density, R the ideal gas con-stant, r the relative dielectric constant for the solution,0 the (vacuum) permissivity constant, and c the total saltconcentration in the bulk. The net free energy change perDS ion in the monolayer becomes

(7)= gDS = a2,where DS is the chemical potential of the dodecyl sulfateion.

The surface tension, , is also given by the derivative

(8)=

dg

da2T,all

.

According to the above scheme, the surface pressure isdetermined by

(9) =(conf+ el),i.e., of the sum of the configurational and electrostatic com-ponent of the surface pressure where

conf=dgconf

dL

dL

da2

T ,all

.

4. Gibbs surface tension equation

Assuming the surfactant and the salt to be fully dissoci-ated results in the following conditions:

(10)cDS = cSDS,(11)cNa+ = cSDS + cNaCl = ctot.

Furthermore assuming the activity factors to be given by theDebyeHckel limiting law yields the following expressionsfor the chemical potential of SDS:

SDS =DS +Na+

(12)

=0SDS +RT lnf2 +RT ln cDS +RT lncNa+ .

Hence,

(13)

dSDS =RTdlnf2 + dln cSDS + dln(cSDS + cNaCl)

,

where lnf =1.17ctot.

Accordingly, using Eq. (11),(14)dlnf2 =1.17

dcSDSctot

.

Finally, we obtain

(15)dSDS =RT

2cSDS + cNaClcSDS + cNaCl

1.17cSDSctot

dlncSDS.

Insofar as NaCl remains negligibleand the changes in NaClare minor the Gibbs surface tension equation is simply (con-stant T)

(16)d=SDS dSDS.

Thus the surface excess, DS (SDS = DS) is readily ob-tained from Eqs. (15) and (16).

However, DS accounts for the amount adsorbed in themonolayer (mDS) plus a small negative contribution due tothe exclusion of DS ions from the diffuse part of the doublelayer. Taking this small contribution into account transformsEq. (16) for the salt-free case into

(17)mDS = SDS(1 x),where x , the fraction of DS in the diffuse part of the doublelayer, is given by [8]

(18)

1

+x

1 x =1

S

S2+ 1 1

.


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C.M. Persson et al. / Journal of Colloid and Interface Science 267 (2003) 151154 153

Fig. 1. Surface tension isotherms for SDS at different concentrations ofNaCl. From right to left, 0, 10, 30, 50, 100, and 300 mM.

This effect becomes smaller and smaller as the salt con-centration is increased. The reason is that the extent of the

diffuse double layer decreases while also the concentrationof DS in the bulk decreases for a given adsorbed amount.At 30 mM NaCl concentration the effect is negligible. Thechange in the activity factor with SDS concentration alsodecreases as the background concentration of NaCl is in-creased. This is due to the fact that the change in total ionconcentration becomes smaller and smaller.

5. Results and discussion

The surface tension isotherms measured at different NaClconcentrations are displayed in Fig. 1. The decrease in SDSconcentration for a given adsorption density as the salt con-centration of NaCl is increased is clearly seen. This is due tothe decrease in the free energy of forming a charged mono-layer as the ionic strength of the solution is increased asevident from Eq. (5).

The surface pressure isotherms of SDS at different bulkconcentrations of NaCl, 0 and 30 mM, are displayed inFig. 2. These results verify that the simple GouyChapmanmodel of the interface combined with the Gruen expressionfor the configurational contribution account well for the ob-served surface pressure isotherms especially at higher saltconcentrations of NaCl. The less good agreement in the ab-

sence of salt could be due to trace amounts of impurities(dodecanol). This effect is expected to be less severe as thesalt concentration is increased since the surface activity ofSDS increases significantly. Another possibility is that DS,which is the coion in the salt-free case, is large and hy-drophobic in contrast to Cl, which acts as coion at highersalt concentrations.

The change in free energy due to an increase in the saltconcentration at a constant molecular area is readily cal-culated from (assuming all other free energy contributionsremain the same when changing the salt concentration)

(19)g 0DS = gel 19.96kT+ gconf+ gcontact + pg,

Fig. 2. The surface pressure isotherms for SDS in 0 (upper thick line) and30 mM NaCl (lower thick line). The thin lines are calculated according tothe model (the upper for 0 mM and the lower for 30 mM NaCl).

Fig. 3. The free energy according to Eq. (19) (filled symbols, theory, puttingpg = 0) and Eq. (20) (unfilled symbols, experiment). The circles are for amolecular area of 50 2 and the squares for a molecular area of 40 2.

where gconf+gcontact presumably are independent of the saltconcentration and pg is a constant independent of the ad-sorption density. It includes the free energy changes upontransferring the polar group from the bulk to the inter-face apart from purely electrostatic contributions. The cor-responding change, dominated by the change in gel, in theelectrostatic free energy can also be computed from the ex-perimental data by employing Eq. (7). In this way we obtain

(20)g 0DS = a2 + lnfxDS .

The surface tension values at a constant molecular area(40 and 50 2) and the corresponding SDS mole fractionwere inserted in Eq. (20). Because the salt concentration in-creases significantly we used the experimentally determinedvalues of the activity factor obtained from [9]. The theoret-ical values, obtained from the GouyChapman theory, andthe experimentally determined ones are shown in Fig. 3 fortwo molecular areas, 40 and 50 2. We note that the dif-ference between the experimental and the theoretical points,pg, is nearly constant for a given molecular area as well ascomparing the two molecular areas (0.85kT). This supportsthe use of Eq. (19), which is based upon adding various free

energy contributions. For instance, the fact that a given ad-


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154 C.M. Persson et al. / Journal of Colloid and Interface Science 267 (2003) 151154

sorption density of SDS occurs at lower SDS concentrationswhen the salt concentration is raised is readily explainedby the decrease in free energy of forming a charged mono-layer as predicted by the GouyChapman theory. For theSDS/NaCl monolayer case this theoretical approach workswell, especially when considering that no adjustableparame-

ters but the head group constant pg are involved. However,to generalize our findingsonewould need to study additionalcharged monolayers systems. It might well turn out that allthat is needed to fully capture the behavior of other similarmonolayer systems would be to invoke other values for thehead group constant pg encompassing different counterions.

6. Conclusions

To conclude, we have verified that the GouyChapmantheory of the electrical double-layer that was developed al-

most a century ago provides a next-to-quantitative accountof the electrostatics of monolayers of SDS in the liquid-expanded range. The inherent features of an evenly distrib-uted, smeared-out surface charge and volumeless counter-and coions may well seem unrealistic, yet the model cov-ers two important entropic effects, viz. the lateral and thevertical mixing of the counterions with the solvent, ulti-

mately giving rise to an approximate surface pressure equalto 2kT/a2 for large values of the Sparameter. Apart from asmall (constant) head group contribution, the monolayer freeenergy itself is also reproduced by the model used here fordifferent salt concentrations as well as at different packingdensities.

Acknowledgment

This work was supported by the Competence Centre forSurfactants Based on Natural Products, SNAP.

References

[1] R. Kjellander, S. Marcelja, J. Phys. Chem. 90 (1986) 1230.[2] S.R. Goates, D.A. Schofield, C.D. Bain, Langmuir 15 (1999) 1400.[3] G.R. Bell, S. Manning-Benson, C.D. Bain, J. Phys. Chem. B 102 (1998)

218.

[4] J.C. Eriksson, S. Ljunggren, Colloids Surf. 38 (1989) 179.[5] C. Tanford, The Hydrophobic Effect, 2nd ed., Wiley, New York, 1980.[6] D.W.R. Gruen, E.H.B. Lacey, in: K.L. Mittal, B. Lindman (Eds.), Sur-

factants in Solution, Vol. 1, Plenum, New York, 1984.[7] I. Szleifer, A. Benshaul, W.M. Gelbart, J. Phys. Chem. 94 (1990) 5081.[8] J.C. Eriksson, Finn. Chem. Lett. 105 (1982).[9] Handbook of Chemistry and Physics, 78th ed., CRC Press, Boca Raton,

FL, 19971998.

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