JOURNAL OF COLLOID AND INTERFACE SCIENCE 182, 214–219 (1996)ARTICLE NO. 0453

Linear Compression of an Adsorbed Monolayer ofSodium Dodecyl Sulfate and Dodecanol

PETER PETROV AND PAUL JOOS1

Department of Chemistry, University of Antwerp, U.I.A., Universiteitsplein 1, B-2610 Wilrijk, Belgium

Received December 11, 1995; accepted April 3, 1996

established for this surfactant. An example of such a sys-A theory is presented to describe the increase in the surface tem is sodium dodecyl sulfate (SDS) with a minor com-

pressure of a mixed adsorbed monolayer under linear compres- ponent (dodecanol ) . Experiments below and above thesion. This mixed monolayer contains a very soluble surfactant CMC are carried out.and a less soluble one as a minor component. This theory is asimplification of a more general one with two not very soluble

THEORYsurfactants. The presented theory is verified by experimentswith SDS and dodecanol. Good agreement between theory and

A mixed monolayer containing surfactant 1 (SDS), whichexperiment is obtained. For micellar systems, the minor compo-is very soluble, and a minor component, surfactant 2 (dode-nent is solubilized in the micelles and the compression curvescanol) , is allowed to equilibrate, and afterward it is com-are different from those for concentrations below the CMC.pressed with a constant speed and the resulting increase inFrom the compression data the elasticity of the monolayer as

a function of time is obtained. q 1996 Academic Press, Inc. surface pressure is measured.Key Words: compression of monolayer SDS and dodecanol; elas- Since surfactant 1 is very soluble, we may assume that

ticity of mixed monolayers. diffusion equilibrium is established between the bulk andthe subsurface; in other words, the subsurface concentrationof component 1, c s

1 , is equal to the bulk concentration,INTRODUCTION c 0

1 . But since the adsorption of surfactant 1 depends on theconcentration of both surfactants we have by inversion

In previous papers (1, 2 ) we considered the increasein surface pressure, by linear compression with constant

dc s1 Å 0 Å S Ìc1

ÌG1DG2

DG1 / S Ìc1

ÌG2DG1

DG2 . [1]speed, of an adsorbed monolayer initially in equilibrium.For doing this we first considered a one-surfactant system( 1) . Since a continuously deformed surface gives rise to

By introducing the partial diffusion relaxation time t11 andconvection, a convective term must be accounted for inthe cross diffusion relaxation time t12 , defined asthe diffusion equation. This equation was integrated fol-

lowing the method of Levich (3 ) . From the experimentaldata, the Gibbs elasticity and diffusion relaxation time

√t11 Å

1√D1S ÌG1

Ìc1DG2

,√t12 Å

1√D1S ÌG2

Ìc1DG1

, [2]for a one-surfactant system were obtained. Next we con-sidered a system containing two surfactants (2 ) . Here

Eq. [1] can be written astwo convective diffusion equations must be integrated.They are linked by the condition of a local equilibriumbetween the surface and the subsurface, since the adsorp- DG1√

t11

/ DG2√t12

Å 0. [3]tion of a surfactant depends on its concentration and alsoon the concentration of the other surfactants. This resultsin addition parameters: the partial Gibbs elasticity, the As shown previously (2) , the convection diffusiontwo partial diffusion relaxation times, and two cross dif- equation for the not very soluble component, surfactantfusion relaxation times. 2, results in

We now consider a simplified situation where one sur-factant is very soluble. During surface deformation, diffu-

DG1S 4tpt21

D1/2

/ DG2F1 / S 4tpt22

D1/2Gsion equilibrium between the bulk and the subsurface is

1 To whom correspondence should be addressed. Å G e2 [ f ( t) 0 1]. [4]

2140021-9797/96 $18.00Copyright q 1996 by Academic Press, Inc.All rights of reproduction in any form reserved.

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215COMPRESSION OF SDS–DODECANOL MONOLAYERS

However, the change of adsorption DG1 and DG2 is notHere DG1 Å G1 0 G e1 , G1 being the adsorption of surfac-

directly measurable, so we can measure only the overalltant 1 and G e1 its equilibrium adsorption, and similarly

increase in surface pressure, DP. The increase in the surfaceDG2 Å G2 0 G e2 for surfactant 2. t21 and t22 are again

pressure iscross and partial diffusion relaxation times, defined as

DP Å S ÌPÌG1DG2

DG1 / S ÌPÌG2DG1

DG2 . [14]√t21 Å

1√D2S ÌG1

Ìc2DG2

,√t22 Å

1√D2S ÌG2

Ìc2DG1

, [5]

From Eqs. [12], [13], and [14] we obtainand the function

DP

f ( t) 0 1Å e

f ( t) Å V0

V. [6]

Å0(G e

2 /√t12)(ÌP /ÌG1)G2

/ (G e2 /

√t11)(ÌP /ÌG2)G1

1/√t11 / (4t /p)1/2 (1/

√t11t22 0 1/

√t12t21)

.This function depends on the kind of deformation, since V0

is the initial surface area and V is that after time t . For linear [15]deformation of the surface,

We note that

V Å V0 /dV

dtt . [7]

f ( t) 0 1 Å V0 0 V

VÅ 0 DV

V[16]

For a monolayer compressed with a constant speed, dV /dt and that the modulus of elasticity, e, is defined asis a constant and we have

e Å 0 DP

DVV, [17]V Å V0(1 / at) , [8]

andwhere

e01 Å G e1S ÌPÌG1

DG2

, e02 Å G e2S ÌPÌG2

DG1

. [18]a Å 1V0

dV

dtõ 0. [9]

Hence Eq. [15] becomesHence

DP(1 / at)0at

Å ef ( t) Å 1

1 / at. [10]

Å e02 0 (G e2 /G e

1 )(t11 /t12) 1/2e01

1 / (4t /pt22) 1/2[1 0 (t11t22 /t12t21) 1/2 ]. [19]

The parameter t in [4] is given by

In general when component 1 is also not very soluble wehave obtained (2) the expressiont Å *

t

0

f 2( t)dt Å t

1 / at. [11]

From Eqs. [3] and [4] we obtain

DG1 Å 0G e

2 [ f ( t) 0 1]√t12

e Å

e01 / e02 / S4tp D

1/2FS e01√t22

/ e02√t11D

0 SG e2

G e1

e01√t12

/ G e1

G e2

e02√t21DG

1 / S4tp D

1/2S 1√t11

/ 1√t22D

/ 4tp S 1√

t11t22

0 1√t12t21

D

. [20]1 1

1/√t11 / (4t /p)1/2[1/

√t11t22 0 1/

√t12t21]

, [12]

DG2 ÅG e

2 [ f ( t) 0 1]√t11

1 1

1/√t11 / (4t /p)1/2[1/

√t11t22 0 1/

√t12t21]

. [13]This expression reduces to Eq. [19] for t11 r 0 and t12 r 0.

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216 PETROV AND JOOS

FIG. 1. Equilibrium surface tension of SDS solution as a function of concentration: — , according to Elworthy and Mysels (5) (pure sample);– s – , present impure sample; ---, surface tension as a function of concentration according to Eq. [22].

EQUILIBRIUM SURFACE TENSION OF followed with G` Å 6 1 10010 mol cm02 and a constant ai

depending on the chain length. We assume that dodecanolSDS–DODECANOL MIXTURESalso follows ideal surface behavior with the same saturationadsorption, and (by extrapolation) a2 Å 3.7 1 1009 molThe apparatus for compressing the SDS–dodecanolcm03 .monolayer, initially in equilibrium, is the same as that de-

The equilibrium surface tension concentration curve forscribed previously (1, 4) .SDS (data of Elworthy and Mysels) follows regular behaviorThe used SDS sample contains some dodecanol as a minorwith a saturation adsorption G` Å 7.68 1 10010 mol cm02component. This sample was obtained from Sigma [Sigma(G` is twice the saturation adsorption of SDS), a1 Å 1.6 1ultra with purity ú99% (gas chromatography)] . In Fig. 11006 mol cm03 , and an interaction parameter H Å 1.14 (6).the equilibrium surface tension as a function of the concen-

In order to not overcomplicate the equations, e.g., to usetration for this sample is shown. A sharp minimum is ob-Eq. [21], we approximate the surface tension concentrationtained at a concentration c Å 7 1 1006 mol cm03 , somewhatcurve for pure SDS by the von Szyszkowski equation,lower than the CMC of pure SDS (CMC Å 8 1 1006 mol

cm03) , as expected. As a comparison we have shown theequilibrium surface tension as a function of concentration

P Å RT G`lnS1 / c1

a1D [22]taken from Elworthy and Mysels (5) . At high concentra-

tions, the difference in the equilibrium surface pressure be-tween the pure SDS (Elworthy and Mysels) and our sample

(with G` Å 6 1 10010 mol cm02 and a1 Å 1 1 1006 molis about DP Å 10 mN m01 .cm03) , to describe this curve near the CMC.For a surfactant mixture, showing ideal behavior if both

From Eqs. [21] and [22] we obtain the difference in sur-components have equal saturation adsorptions, the surfaceface pressures between the pure and impure samples:pressure as a function of concentration follows an extended

von Szyszkowski equation,

DP Å RT G`lnF1 / c2a1

a2(a1 / c1) G . [23]P Å RT G`lnS1 / c1

a1

/ c2

a2D , [21]

For c1 Å 7 1 1006 mol cm03 , DP Å 10 mN m01 , and weobtain c2 Å 2.82 1 1008 mol cm03 . Hence as a rough esti-G` being the saturation adsorption, c1 and c2 the concentra-

tions of surfactant 1 and 2, and a1 and a2 the constants of mate, the SDS sample contains 0.4% dodecanol. As anotherestimate, the ratio of the adsorptions of SDS (1) and dodeca-distribution for surfactants between bulk and surface.

For the higher alcohols up to decanol ideal behavior is nol (2) obtained from the Langmuir equation is

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217COMPRESSION OF SDS–DODECANOL MONOLAYERS

ment between theory and experiment is quite good. TheG1

G2

Å c1a1

c2a2

Å 0.92. [24] parameters e0 and tD are given in Table 1.For submicellar solutions until c1 Å 4 1 1006 mol cm03 ,

e0 increases slightly and tD decreases with increasing con-Consequently the adsorptions are nearly equal, not with-centration, as expected. However, for a concentration c1 Åstanding the fact that the SDS sample is 99.6% pure! Its6 1 1006 mol cm03 , still below but quite near the CMC, e0remains true that these data rely on bold approximations.is rather low and the relaxation time high. The reason for thisNevertheless we expect that the order of magnitude is stillis still obscure. Perhaps during compression the dodecanolcorrect and the adsorption of dodecanol is important evenconcentration in the layer below the surface increases andfor samples of such purity.as a consequence the formation of micelles is enhanced. Ithas been shown (8) that in the presence of dodecanol theDYNAMIC SURFACE TENSION OFCMC decreases. At a concentration just above the CMC (c1SDS–DODECANOL MIXTURESÅ 8 1 1006 mol cm03 or 1.14 1 CMC) e0 is still lower andtD is high. The concentration of dodecanol as monomers inCompression curves at different relative compressionthe bulk decreases, resulting in smaller values for e0 .rates, a, were measured at SDS concentrations of 1 1 1006 ,

For concentrations fairly above the CMC (c1 Å 1.5 12 1 1006 , 4 1 1006 , and 6 1 1006 mol cm03 and also for1005 mol cm03 or 2.14 1 CMC) two compression curvesconcentrations above the CMC, 8 1 1006 and 1.5 1 1005

are given (see Fig. 3) . At this concentration the SDS micellemol cm03 (or 1, 2, 4, 6, 8, and 15 mol m03) . The experimen-concentration is higher and solubilization of dodecanol intal results are analyzed through Eq. [19] written asthese micelles is nearly complete. In this case the concentra-tion of SDS monomers is equal to the CMC values (71 1006

DP Å 0 at

1 / at

e0

1 / (4t /ptD)1/2 , [25] mol cm03) . The difference between the surface pressure ofthe pure system without dodecanol and that of our contami-nated sample is DP É 2 mN m01 . For the concentration of

where e0 and tD are short symbols fordodecanol as monomers, making the same calculation asbefore gives c2 Å 4.3 1 1009 mol cm03 . The total concentra-tion of dodecanol is 6 1 1008 mol cm03 . This means thate0 Å e02 0

G e2

G e1St11

t12D1/2

e01 [26]93% of the dodecanol is solubilized in the SDS micelles.The adsorption of dodecanol is very low and upon compres-

and sion the increase in surface pressure is nearly zero for a longtime, called lag time, t0 . The same situation is observedfor myristic acid (9) , where upon compression the surface1√

tD

Å F1 0 St11t22

t12t21D1/2G 1√

t22

. [27] pressure starts to rise at a molecular area A Å 60 A2 (corre-sponding with G Å 2.78 1 10010 mol cm02) .

Because the concentration of dodecanol is so low, theThe parameters e01 , e02 , t11 , t12 , t21 , and t22 are essen-relaxation time is very high and we have nearly insolubletially thermodynamics parameters, depending on the concen-monolayer behavior. This means that when the surface pres-tration but not on the way in which the surface is deformed.sure starts to rise (at time t Å t0) Eq. [25] is followed withThe same holds for e0 and tD.tD r ` . The result is a very low elasticity, e0 Å 0.23 mNOne can expect an increase in e0 and a decrease in tDm01 . With this value of e0 the compression curves are calcu-with increasing SDS concentration (the concentration of do-lated for t ú t0 . For t £ t0 , e0 É 0.decanol being proportional to that of SDS). This is easy to

The same behavior, but not so clearly expressed, is ob-see if we assume ideal surface behavior and equality of theserved at a concentration of c1 Å 8 1 1006 mol cm03 .saturation adsorption of both surfactants (see the Appendix) .

It should be noted that the diffusion relaxation time inThe resultant values may not be accurate, but qualitativelythis case (tD Å 3050 s) is rather lower than expected (seethe trend remains.Table 1). We obtain tD (together with e0) as an adjustableIn Fig. 2 the compression curves for a SDS concentrationparameter from the fitting procedure of experimental datac1 Å 1 1 1006 mol cm03 (c1 Å 1 mol m03) are givenwith Eq. [25]. For this concentration (c1 Å 8 1 1006 molfor different compression rates. The compression curves forcm03) it seems that the behavior of adsorbed dodecanolother submicellar concentrations (2 1 1006 , 4 1 1006 , andchanges from almost insoluble monolayer behavior at the6 1 1006 mol cm03) are quite similar and are not givenhighest relative compression rate a to slightly soluble mono-here. Compression curves for micellar solution (1.5 1 1005

layer behavior at lower compression rates. It makes question-mol cm03) are given in Fig. 3.able the correct value of tD, identical for all compressionFor each concentration, the compression curves are fitted

by Eq. [25] using the same parameters e0 and tD. The agree- rates. However, we give a value for tD which leads to the

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218 PETROV AND JOOS

FIG. 2. Compression curves (increase in surface pressure, DP, as a function of time, t) of SDS–dodecanol monolayers with a SDS concentrationc 0

1 Å 1 1 1006 mol cm03 at different compression rates: a Å 02.38 1 1002 s01 (s) ; a Å 01.41 1 1002 s01 (n) ; a Å 06.19 1 1003 s01 (h) ; a Å03.20 1 1003 s01 (m) . The solid lines are calculated according to Eq. [25].

least error in fitting procedures for all speeds but do not is far more surface active than SDS. A rough calculationclaim that this is the most realistic one. shows that our sample of SDS is 99.6% pure; nevertheless,

the adsorption of dodecanol is on the same order of magni-tude as the adsorption of SDS. The SDS is very soluble, andCONCLUSIONthis implies that the diffusion equilibrium of SDS betweenthe subsurface and the bulk is established in the time domainA soluble monolayer of SDS contaminated with dodeca-

nol at the water/air surface has been investigated. Dodecanol of the experiment. The dynamic effects observed are elastic-

FIG. 3. Compression curves of SDS–dodecanol monolayers with a SDS concentration c 01 Å 1.5 1 1006 mol cm03 at different compression rates: a

Å 02.44 1 1002 s01 (s) and a Å 01.41 1 1002 s01 (l) . The solid lines are calculated according to Eq. [25] with tD r ` and for t ú t0 .

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219COMPRESSION OF SDS–DODECANOL MONOLAYERS

TABLE 1 Next, the relation between adsorptions and concentrations isKinetic Parameters for the Mixed SDS–Dodecanol given by

Monolayers Obtained from Eq. [25]c1

a1

Å G1

G` 0 G1 0 G2

,c2

a2

Å G2

G` 0 G1 0 G2

. [A-3]c01 e0 tD

(mol m03) (mN m01) (s)

From this we obtain1 7.0 25502 7.3 21004 8.7 6306 3.7 5900

√t11 Å

1√D1S ÌG1

Ìc1DG2

Å (G` 0 G1 0 G2) 2

a1

√D1(G` 0 G2)

,8 1.15 (3050)a

15 0.23 ` √t22 Å

1√D2S ÌG2

Ìc2DG1

Å (G` 0 G1 0 G2) 2

a2

√D2(G` 0 G1)

,a Disputable value.

ity due to the presence of the minor component. The theory √t12 Å

1√D1S ÌG2

Ìc1DG2

Å (G` 0 G1 0 G2) 2

a1

√D1G1

,presented is a simplification of a previous one for a mixedsurfactant system. For the present system the difference oftensioactivities is given by a1 /a2 É 270. This means that √

t21 Å1√D2S ÌG1

Ìc2DG1

Å (G` 0 G1 0 G2) 2

a2

√D2G2

. [A-4]the exchange between the surface and the bulk for SDS ismore than 1004 times faster than that for dodecanol.

For concentrations above the CMC (2.14 1 CMC) nearlyall of the dodecanol is solubilized in the micelles. Adsorption This results in e0 given by Eq. [26],of dodecanol is low and the diffusion relaxation time high,and the surface shows nearly insoluble monolayer behavior,

e0 Å RT G` G2

G` 0 G2

, [A-5]with respect to dodecanol.

where we have the approximation G e2 /G e

1 É G2 /G1 , and inAPPENDIXtD given by Eq. [27],

It is expected that e0 increases and tD decreases withincreasing concentrations of SDS, keeping in mind that un- √

tD Å(G` 0 G1 0 G2)(G` 0 G1)

a2

√D2

. [A-6]der our experimental conditions the ratio of SDS and dodeca-nol is a constant: c2 Å kc1 (k being a proportionality constantand for our sample roughly estimated as kÉ 3.4 1 1003 ; see If c1 increases (and accordingly c2 increases) , G2 in-Equilibrium Surface Tension of SDS–Dodecanol Mixtures) . creases. Then from Eq. [A-5] it is clear that e0 increasesThis can easily be shown, by assuming ideal surface behavior with increasing concentrations of SDS. In the same way itwith G`

1 Å G`2 Å G` . The relation between surface pressure follows from Eq. [A-6] that if c1 (and c2) increases, G1 and

and adsorption is given by G2 increase and consequently tD decreases with increasingSDS concentrations.

P Å 0RT G`lnS1 0 G1

G`0 G2

G`D . [A-1] REFERENCES

1. Petrov, P., and Joos, P., J. Colloid Interface Sci., in press.2. Petrov, P., and Joos, P., J. Colloid Sci., in press.From this it follows that3. Levich, V. G., in ‘‘Physicochemical Hydrodynamics,’’ pp. 540–542.

Prentice-Hall, Englewood Cliffs, NJ, 1962.4. Horozov, T., and Joos, P., J. Colloid Interface Sci. 173, 334 (1995).

e01 Å G1S ÌPÌG1DG2

Å RT G` G1

G` 0 G1 0 G2

,5. Elworthy, P., and Mysels, K., J. Colloid Interface Sci. 21, 331 (1966).6. Fang, J. P., and Joos, P., Colloids Surf. 65, 113 (1992).7. Lucassen-Reynders, E. H., J. Phys. Chem. 70, 1777 (1966).8. Shinoda, K., Nakagawa, T., Tamamushi, B., and Isemura, T., in ‘‘Col-e02 Å G2S ÌPÌG2

DG1

Å RT G` G2

G` 0 G1 0 G2

. [A-2]loidal Surfactants.’’ Academic Press, New York, 1966.

9. Joos, P., and van Uffelen, M., J. Colloid Interface Sci. 172, 77 (1995).

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