nelabeling

chains ato the pureinterface.

iously on,

Journal of Colloid and Interface Science 262 (2003) 235–242www.elsevier.com/locate/jcis

The structure of mixed nonionic surfactant monolayers atthe air–water interface: the effects of different alkyl

chain lengths

J. Penfold,a,∗ E. Staples,b I. Tucker,b R.K. Thomas,c R. Woodling,c and C.C. Dongc

a ISIS Facility, Rutherford Appleton Laboratory, CLRC, Chilton, Didcot, Oxon, United Kingdomb Unilever Research, Port Sunlight Laboratory, Quarry Road East, Bebington, Wirral, United Kingdom

c Physical and Theoretical Chemistry, University of Oxford, South Parks Road, Oxford, United Kingdom

Received 18 April 2002; accepted 9 January 2003

Abstract

The structure of mixed nonionic surfactant monolayers of monodecyl hexaethylene glycol (C10E6) and monotetradecyl hexaethyleglycol (C14E6) adsorbed at the air–water interface has been determined by specular neutron reflectivity. Using partial isotopic(deuterium for hydrogen) of the alkyl and ethylene oxide chains of each surfactant, the distribution and relative positions of thethe interface have been obtained. The packing of the two different alkyl chain lengths results in structural changes compared tsurfactant monolayers. This results in changes in the relative positions of the alkyl chains and of the ethylene oxide chains at theThe role of the alkyl chain length is contrasted with that of the ethylene oxide chain length, determined from results reported prevthe nonionic surfactant mixture of monododecyl triethylene glycol (C12E3) and monododecyl octaethylene glycol (C12E8) (J. Penfold, et al.J. Colloid Interface Sci. 201 (1998) 223). 2003 Elsevier Science (USA). All rights reserved.

ur-,3].

ica-uses orpurein

sur-tionvelynsiol in-uentthethe

, the

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o ac-the

ad-ingle

1. Introduction

The study of surfactant mixtures is of considerable crent interest, for both practical and theoretical reasons [2The many domestic, industrial, and technological appltions of surfactants usually involve mixtures. This is becamixtures provide a synergistic enhancement of propertieperformance, or because commercial surfactants are imThat is, they often contain mixtures of different alkyl chalengths, different isomers, and in the case of nonionicfactants different ethylene oxide chain lengths. Adsorpand micellization of mixed surfactants have been extensistudied using a range of techniques, such as surface te[4] and have been the result of considerable theoreticaterest [5–7]. The ideal solution approach [5] and subseqadaptation of regular solution theory [6,7] have formedbasis of the theoretical approach to surfactant mixing. Inpseudo-phase approximation or regular solution theory

* Corresponding author.E-mail address: j.penfold@rl.ac.uk (J. Penfold).

0021-9797/03/$ – see front matter 2003 Elsevier Science (USA). All rights rdoi:10.1016/S0021-9797(03)00061-4

.

n

departure from ideality is characterized by a single intetion parameter,β , and a central assumption is that the excentropy of mixing is zero [7]. Recent neutron reflectivand surface tension measurements on the adsorption ofmixed surfactant systems [8,9], notably sodium dodesulfate/n-dodecyl-N ,N -dimethylamine (SDS/Betaine) anSDS/n-dodecyl-β-D-Maltoside (Maltoside) are not well described by the pseudo-phase approximation. The correlabetween structure and composition in these mixed surtant systems suggest that structural changes and espechanges in hydration are important. Some modificationthe regular solution approach have been developed tocommodate such issues [10]. Blankschtein and co-wor[11,12] have developed a more fundamental approach wis aimed at removing the phenomenological nature of relar solution theory, but retaining thermodynamic rigor. Ththeory as well as an analogous approach by Hines [13based on a two-dimensional gas approach and takes intcount molecular detail. These considerations establishimportance of the structural details of mixed surfactantsorbed layers and their changes compared to a pure scomponent surfactant monolayer.

eserved.

236 J. Penfold et al. / Journal of Colloid and Interface Science 262 (2003) 235–242

ues,icalera

ailsity,vide

ntra20]ntspictheity.ur-pplynon-

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The development of modern experimental techniqsuch as neutron and X-ray reflectivity [14,15] and the optprobes of sum frequency [16] and second harmonic gention [17], provides the opportunity to probe structural detin adsorbed monolayers. In particular neutron reflectivthe technique used in this study, has been shown to proinformation about adsorbed amounts over a wide concetion range (from less than to greater than the cmc) [18–and about structural details [21–23] in single surfactaand surfactant mixtures. Hydrogen/deuterium(H/D) isotosubstitution of parts of the surfactant molecules and ofsolvent provides a high degree of selectivity and sensitiv

To investigate in more detail the role of structure in sfactant mixing we have, in the first instance, chosen to athese techniques to the study of the structure of mixedionic surfactant monolayers, in which the mixing is closeideal. We have previously reported the variation in surfcomposition for the nonionic mixture C12E3/C12E8 with sur-factant concentration [20]. The ability to measure adsoramounts over a wide concentration range provided theexperimental verification of the abrupt change in surfcomposition at the mixture cmc due to changes in the disution of the two surfactant species between the bulk soluand the monolayer as a result of mixed micelle formatMore recently we reported [1] measurements of the stture of the mixed C12E3/C12E8 monolayer at the cmc. Ithis case, for a mixture of two surfactants with identical alchain lengths, but rather different headgroup sizes, we wable to show that the frustration caused by the packing otriethylene and octaethylene headgroups results in a chin the structure compared to the pure monolayer of eisurfactant. Compared to the pure monolayer the alkyl cdistributions of both surfactants are more extended, theethylene glycol group is less hydrated, and the octaethyglycol group is less extended and more hydrated.

In this paper we contrast those results for C12E3/C12E8with similar measurements for a different nonionic mixtuC10E6/C14E6. In this case the ethylene oxide chain lenis fixed, and we contrast the role of varying the alkyl chlength on the surface packing. The structure of a surfacmonolayer of C10E6/C14E6 at the air–water interface, witan approximately equimolar composition at the interfacecompared with the structure of pure C10E6 and C14E6 mono-layers at an equivalent area/surfactant molecule. Meaments were made for a 97.3 mole% C10E6/2.7 mole% C14E6mixture at a total surfactant concentration of 4.2 × 10−4 M(∼cmc) and were compared with the C10E6 and C14E6monolayers at 10−4 M. Partial deuterium labeling of thalkyl and ethylene oxide chains and of the solvent was uto obtain the structural details of the adsorbed monolaye

2. Neutron reflectivity

Specular neutron reflectivity provides information abinhomogeneities normal to an interface or surface. Its

-

-

e

-

ory is described in detail elsewhere [24], and its applicato the study of surfactant adsorption has been recentlviewed [14]. The basis of a neutron reflectivity measuremis that the variation of specular reflection withQ (the wavevector transfer defined asQ = (4π/λ)sinθ , whereθ is theglancing angle of incidence andλ is the neutron wavelengthis simply related to the composition or concentration proin the direction normal to the surface. In the kinematicproximation [25] the specular reflectivityR(Q) is given by

(1)R(Q) = 16π2

Q2

∣∣ρ(Q)∣∣2,

where ρ(Q) is the one-dimensional Fourier transformρ(z), the average scattering length density profile indirection normal to the interface,

(2)ρ(Q) =∞∫

−∞ρ(z)exp(iQz) dz

and

(3)ρ(z) =∑

i

Ni(z)bi.

The neutron refractive index is formally related to tscattering length density by,

(4)n(z) = 1− λ2∑

i

Ni(z)bi/2π,

where Ni is the number density of speciesi, and bi itsscattering length. The key feature of the neutron reflecity technique for studying surfactant adsorption is thatneutron scattering properties of D and H are vastly differHence H/D isotopic substitution can be used to maniputhe scattering length distribution and refractive index. Tis particularly powerful in determining structure or invetigating surfactant mixtures, where by selective deuteraparticular components or fragments can be highlighteisolated. This enables adsorbed amounts in complextures and detailed surface structure to be determined.

At the simplest level, neutron reflectivity can be useddetermine adsorbed amounts in single and multicompomixtures, with good accuracy and over a wide concentrarange. For a deuterated surfactant in null reflecting w(nrw; water with a refractive index of unity (the sameair) and a 92 mole% H2O/8 mole% D2O mixture), thereflectivity arises only from the layer of deuterated surfacat the interface. The reflectivity can be analyzed to sufficaccuracy by assuming that it arises from a single laof uniform or homogeneous composition [26]. Usingoptical matrix method [27,28], this yields a scattering lendensity and thickness, such that

(5)ρ = b

τA,

whereb andA are the scattering length and area/molecof the surfactant at the interface, andρ andτ are the scattering length density and thickness obtained from the m

J. Penfold et al. / Journal of Colloid and Interface Science 262 (2003) 235–242 237

chrn,m aary

ule

recttionenensity

rs

rs

ofthece,rel-ce.ingure] thaturef dif

sians),

sian

o bemp-are

ichthe

two

-lene, in

therce,he

in-.5areedffi-

tivityurede-

ity[29]

fit. A similar approach is used for mixtures, where eacomponent in the mixture is selectively deuterated in tuand the resultant reflectivity is then treated as arising frosingle layer of homogeneous composition [26]. For a binmixture this gives

(6)ρ = b1

A1τ+ b2

A2τ,

wherebi andAi are the scattering lengths and area/molecof each component.

To analyze the reflectivity from the C10E6/C14E6 mixedmonolayer in terms of the structure of the monolayer a dimethod of analysis based on the kinematic approximais used [29]. By separately labeling the alkyl and ethyloxide chains of each surfactant the scattering length deprofile can be written as

ρ(z) = bc(10)nc(10)(z) + be(10)ne(10)(z) + bc(14)nc(14)(z)

(7)+ be(14)ne(14)(z) + bsns(z),

where the subscriptsc(10), c(14), e(10), e(14), ands referto the alkyl and ethylene oxide chains of the C10E6 andC14E6 and to the solvent. Substituting into Eq. (1) gives

R(Q) = 16π2

Q2

[b2c(10)hc(10) + b2

c(14)hc(14) + b2e(10)he(10)

+ b2e(14)he(14) + b2

s hs + 2bc(10)be(10)hc(10)e(10)

+ 2bc(14)be(14)hc(14)e(14) + 2bc(10)be(14)hc(10)e(14)

+ 2bc(14)be(10)hc(14)e(10) + 2bc(10)bc(14)hc(10)c(14)

+ 2be(10)be(14)he(10)e(14) + 2bc(10)bshc(10)s

+ 2be(10)bshe(10)s + 2bc(14)bshc(14)s

(8)+ 2be(14)bshe(14)s],

where the fivehi factors are the self-partial-structure factogiven by

(9)hi(Q) = ∣∣n̂i(Q)∣∣2

and the tenhij factors are cross-partial-structure factogiven by

(10)hij (Q) = Re{n̂i (Q)n̂j (Q)

},

and ni(Q) is the one-dimensional Fourier transformni(z). The self-partial-structure factors relate directly todistributions of the individual components at the interfawhereas the cross-partial-structure factors relate to theative positions of the different components at the interfaFrom a series of different reflectivity measurements, usdifferent labeled combinations, the different partial structfactors can be extracted. We have shown elsewhere [30simple analytical functions describe these partial strucfactors, and this approach has been applied to a range oferent systems [14].

The surfactant self-terms are described as a Gausdistribution (for the alkyl and ethylene oxide distribution

t

-

and the solvent as a tanh distribution, such that

(11)ni(z) = ni

(exp

(−4z2/σ 2i

)),

(12)ns(z) = n0[1/2+ (1/2) tanh(z/ζ )

].

The surfactant self-partial-structure factors for a Gausdistribution are then given by

(13)hi(Q) = 1

A2i

exp(−Q2σ 2

i /8),

whereAi is the area/molecule of componenti andσi is itswidth. The solvent partial structure factor is given by

(14)hs(Q) = n20

(ζπ

2

)2

cosech2(

ζπQ

2

),

wheren0 is the bulk solution number density andζ is thewidth of the solvent distribution.

The cross-partial-structure factors have been shown ta good approximation independent of any model assutions [30]. The cross-term between two distributions thatexactly even distributions about their centers is given by

(15)hij = ±(hihj )1/2 cosQδij

and the cross-term between two distributions, one of whis even and the other of which is odd (for example,solvent), is given by

(16)his = ±(hihs)1/2 sinQδis,

whereδij , δis is the distance between the centers of thedistributionsi, j or i, s.

For the pure C10E6 and C14E6 monolayers a similar approach is used, where labeling either the alkyl and ethyoxide chains and the solvent gives rise to six factorsa way similar to Eqs. (7) and (8), to givehc(10)(hc(14)),he(10)(he(14)), hs , hc(10)s(hc(14)s), he(10)s(he(14)s), hc(10)e(10)(hc(14)e(14)).

3. Experimental details

The specular reflectivity measurements were made onSURF reflectometer [31] at the ISIS pulsed neutron souusing the “white beam time of flight” method. That is, tmeasurements were made in theQ range of 0.048 to 0.5 Å−1

in a single measurement at a fixed glancing angle ofcidence of 1.5◦, using a neutron wavelength band of 0to 6.8 Å, and where the different neutron wavelengthsdistinguished by time of flight. The data were normalizfor the incident beam spectral distribution and detector eciency, and they were established on an absolute reflecscale by reference to the reflectivity from the surface of pD2O, using standard procedures [32]. A flat background,termined by extrapolation to high values ofQ (Q ∼ 0.3 to0.5 Å−1) was subtracted from all the measured reflectivprofiles. This has been shown to be a valid procedurefor such data.

238 J. Penfold et al. / Journal of Colloid and Interface Science 262 (2003) 235–242

nts-the

gena-

se,de

aresur-The

re

ofsi-

weresur

r to

d.im-l thed theopri

t

theas

-sted

the

er of

tant

a

2.ionctant

ntlyror.

rthe

e ine

esstheasethe

vet the

thstentfaceforThe

e-ixed

High purity water was used for all the measureme(Elga ultra-pure), and the D2O was obtained from Fluorochem. All glassware and the Teflon troughs used forreflectivity measurements were cleaned in alkaline deter(Decon 90), followed by copious washing in ultra-pure wter. All the measurements were made at 25◦C, compared tothe cloud points of 60◦C and 45◦C for C10E6 and C14E6.With the exception of the hydrogeneous C10E6 and C14E6,which were obtained from Nikkol and columned before uall the surfactants were custom synthesized, and thetails of the preparation, purification, and characterizationgiven elsewhere [33]. The surface tension of the purefactant components and the mixture were measured.measured cmc values for C10E6 and C14E6 were 9×10−4 Mand 10−5 M, respectively, and the cmc values of the mixtuthat were measured were consistent with ideal mixing.

Neutron reflectivity measurements were made for 10−4 MC10E6 and 10−4 M C14E6, and for a 97.3 mole% C10E6/2.7mole% C14E6 mixture at a total surfactant concentration4.2×10−4 M. The concentrations and the mixture compotion were chosen such that the structural comparisonsmade at an equivalent area/molecule, and such that theface composition for the mixture was roughly equimolaensure maximum sensitivity. As the C14E6 is significantlymore surface active than the C10E6 (the cmc’s are differ-ent by∼102) an extreme solution composition is requireThis makes the surface very sensitive to small levels ofpurities and extreme care was taken to ensure that alsurfactants were highly pure (see earlier discussion), ansurface compositions was cross-checked by the apprate neutron reflectivity measurements. For the pure C10E6and C14E6 monolayers the reflectivity from five differenisotopically labeled combinations were measured, dCnhE6,and dCndE6 in nrw, and dCnhE6, dCndE6, and hCnhE6 inD2O. For the C10E6/C14E6 mixture 15 different isotopicallylabeled combinations were measured, dC10hE6/dC14hE6,dC10hE6/hC14hE6, hC10hE6/dC14hE6, dC10dE6/hC14hE6,hC10hE6/dC14dE6, dC10dE6/dC14hE6, dC10hE6/dC14dE6,and dC10dE6/dC14dE6 in nrw, and hC10hE6/hC14hE6,d10ChE6/hC14hE6, hC10hE6/dC14hE6, dC10dE6/hC14hE6,dC10dE6/dC14hE6, dC10hE6/dC14dE6, and hC10hE6/dC14dE6 in D2O. The nomenclature adopted to describedifferent isotopically labeled surfactants is summarizedfollows: dC10hE6, CD3(CD2)9(OCH2CH2)6OH, dC10dE6;CD3(CD2)9(OCD2CD2)6OH; and hC10hE6, CH3(CH2)9(OCH2CH2)6OH; and similarly for C14E6. The neutron scattering lengths for the different labeled components are liin Table 1.

4. Results and discussion

The model parameters obtained from the analysis ofreflectivity profiles in nrw for 10−4 M dC10hE6, 10−4 MdC10dE6, 10−4 M dC14hE6, and 10−4 M dC14dE6 usingEq. (5) and treating the adsorbed layer as a single lay

t

-

-

-

Table 1Scattering lengths and volumes of the isotropically labeled surfaccomponents and solvent used in this study

Scattering length Volume(×10−5 Å) (Å3)

D2O 19.2 30.0C10H21 −12.1 294.0C10D21 207.0 294.0C14H29 −15.4 400.0C14D29 287.0 400.0(OCH2CH2)6OH 26.9 380.0(OCD2CD2)6OH 287.0 380.0

Table 2Model parameters (τ,ρ, andA) for single uniform layer model fits for datin nrw

Sample τ ρ A

(Å) (×10−6 Å−2) (Å2)

10−4 M dC10hE6 17.0 1.8 76.0± 210−4 M dC10dE6 21.7 3.1 72.010−4 M dC14hE6 21.9 3.1 48.010−4 M dC14dE6 27.1 4.0 52.04.2× 10−4 M 97.3 mole%dC10hE6/hC14hE6 24.5 0.93 103.0dC10dE6/hC14hE6 28.4 1.6 106.0hC10hE6/dC14hE6 22.8 1.7 80.0hC10hE6/dC14dE6 27.2 2.6 81.0

uniform composition or density are summarized in TableThe measurements in nrw provide principally informatabout the adsorbed amount and the extent of the surfalayer. The results show that the area/molecule for C10E6and C14E6 at 10−4 M are 74± 2 Å2 and 50± 2 Å2,respectively, and the variation between the two differeisotopically labeled surfactants is within experimental erThe thickness of the adsorbed layer is 17 Å for dC10hE6and 22 Å for dC14hE6, which are typical of the layethicknesses obtained for such surfactants [14], anddifferences between 17 and 22 Å reflects the increaschain length from C10 to C14. The measurements for thfully deuterated surfactants (dC10dE6, dC14dE6) give anincrease in thickness to 22 and 27 Å, respectively for C10E6and C14E6. This thickness now reflects the overall thicknof the adsorbed layer rather than just the extent ofalkyl chain from the previous measurements. The increin thickness is not as large as might be expected foraddition of the E6 chain and is indicative of the extensioverlap between the alkyl and ethylene oxide chains ainterface as previously reported [1,23].

For the C10E6/C14E6 mixture measurements in nrw, wiboth or either surfactant deuterated, provide a self-consiestimate of the amount of each surfactant at the interusing Eq. (6). The results for alkyl chain labeling andthe fully deuterated surfactants are listed in Table 2.area/molecule for the C10E6 is 104±3 Å2 and that for C14E6is 80± 2 Å2, and both are within experimental error indpendent of isotope. The mean area/molecule in the m

J. Penfold et al. / Journal of Colloid and Interface Science 262 (2003) 235–242 239

ules

the

r-hainr togainain

theurers.utrtial(7)–cturdns

-fiveine

etionivi-stsul-tioners

pi-the

oth

yleeen

re-

ainib-lonicfor

tionionsd

aes

,rwtureturede-tors

monolayer is∼45 Å2 and is comparable to the area/molecof the pure C10E6 and C14E6 monolayers. This correspondto a surface composition of 43 mole% (±1 mole%) C10E6compared to a solution composition of 97.3 mole% C10E6.This reflects the substantially higher surface activity forC14E6, and the measured composition at 4.2 × 10−4 M isconsistent with the predictions of ideal mixing. The diffeences between the thicknesses obtained from the alkyl cdeuterated and fully deuterated surfactants are similathat obtained from the pure surfactant monolayers and areflect the extent of alkyl chain and ethylene oxide choverlap. The thicknesses obtained for the C14E6 deuteriumlabeled are similar to those obtained for the pure C14E6monolayers. Whereas, the extent of the C10E6 in the mixedmonolayer is significantly thicker than for the pure C10E6monolayer. The values are closer to those obtained forC14E6 and give an indication of the change in the structof the mixed monolayer compared to the pure monolaye

The most direct way to gain more information abothe structure of the adsorbed layer is the method of pastructure factors, as described earlier in the paper [Eqs.(10)]. This approach has been used to determine the struof the C10E6 and C14E6 monolayers, and of the mixeC10E6/C14E6 monolayer, using the isotopic combinatiodescribed in the experimental section.

For the C10E6 and C14E6 only three different isotopically labeled surfactants were available, and so onlyof the reflectivities required to unambiguously determthe partial structure factorshc(10)(hc(14)), hc(10)(he(14)), hs ,hc(10)s(hc(14)s), hc(10)e(10)(hc(14)e(14)) were measured. Thpartial structure factors were extracted using a variaof the approach, by simultaneously fitting the reflectties using a trial distribution which is modified by leasquares until the best solution is obtained [34]. The retant number density distributions (plotted as volume fracdistributions) are shown in Fig. 1. The key parametare σc(10)(σc(14)), σc(10)(σe(14)), ζs , δc(10)e(10)(δc(14)e(14)),δc(10)s(δc(14)(s)), and δe(10)s(δe(14)s) (summarized in Ta-ble 3); and these quantify the extent of the different isotocally labeled components and their effective positions atinterface. The width of the ethylene oxide chains for bC10E6 and C14E6, σe(10) andσe(14), are similar,∼17 Å, andclose to that previously observed for C12E6 [23]. The widthof the alkyl chain distribution for C10E6, σc(10), is similarto that for C12E6, 17 Å, whereas the distribution for C14E6,σc(14), is larger, 19 Å, reflecting partially the longer alkchain length. A significant contribution to the width of thcomponents is due to capillary waves, and this has not bremoved from the values in Table 3 or Fig. 1. It was pviously estimated to be∼9 Å for C12E6 [23] and adds inquadrature with the intrinsic width. The ethylene oxide chdistributions are almost coincident with the solvent distrution (δe(10)s, δe(14)s ∼ 2 Å), and there is significant alkychain/ethylene oxide chain overlap as seen in other nonisurfactant structures [1,23]. This is substantially largerC10E6 than for C14E6; δc(10)e(10) is 7 Å for C10E6 as opposed

e

Fig. 1. Volume fraction distributions of C10E6 and C14E6 ethylene oxideand alkyl chains and solvent for 4.2 × 10−4 M 97.3 mole% C10E6/2.7mole% C14E6: (· · ·) solvent, (—) C10E6 alkyl chain, (–·–) C10E6 ethyleneoxide chain, (– –) C14E6 alkyl chain, (–··–) C14E6 ethylene oxide chain(and as per labeling in the figure). The center of the solvent distribuis arbitrarily defined as zero. The distribution shows the relative positof the C10E6 and C14E6 alkyl and ethylene oxide chains in the mixemonolayer.

Table 3Model parameters for fits to partial structure factors for 10−4 M C10E6,10−4 M C14E6, and 4.2× 10−4 M 97.3 mole% C10E6/2.7 mole% C14E6

10−4 M 10−4 M 4.2× 10−4 M 97.3 mole%C14E6 C10E6 C10E6/2.7 mole% C14E6

σc(10) – 16.0 18.5σe(10) – 17.0 17.0σc(14) 19.0± 1 – 19.5σe(14) 17.0 – 17.0ζs 7.5± 0.5 6.0 7.0δc(10)e(10) – 7.0 11.0δc(14)e(14) 13.0± 0.5 – 11.0δc(10)c(14) – – 0.0δe(10)e(14) – – 0.5δc(10)s – 10.0 13.0δc(14)s 14.0 – 13.0δe(10)s – 2.0 2.0δe(14)s 2.0 – 1.5

to 13 Å for C14E6. It has previously been shown that forrange of C12En nonionic surfactants this overlap increaswith increasing ethylene oxide chain length [35].

For the C10E6/C14E6 mixture 15 different reflectivitiesfrom the different isotopically labeled combinations in nand D2O, were measured; and hence the 15 partial strucfactors were extracted unambiguously. The partial strucfactors are well described by the model distributionsscribed by Eqs. (11)–(15), and the partial structure facand the model fits forhc(10)s , hc(14)s , hc(10)c(14), he(10)s ,he(14)s , hc(10)e(10), andhc(14)e(14) are shown in Fig. 2.

The key model parameters for the mixture areσc(10),σe(10), σc(14), σe(14), ζs , δc(10)e(10), δc(14)e(14), δc(10)e(14),δe(10)c(14), δc(10)s, δc(14)s , δe(10)s, andδe(14)s, and these are

240 J. Penfold et al. / Journal of Colloid and Interface Science 262 (2003) 235–242

ter-

yers

ex-tent

aint,ysisle isf theions. 1.

re

thelentclearing.ed

xidee

esenein

the

ent

geap,

lynt,r

yltheisicateits

with

(a)

(b)

(c)

Fig. 2. Partial structure factors (plotted asQ2hij (Q) for 4.2 × 10−4 M97.3 mole% C10E6/2.7 mole% C14E6). (a) (•) hc10s , (Q) hc14s, (b) (•)he10s , (Q) he14s , and (c) (•) hc10e10, (Q) hc14e14. The solid lines arecalculations as described in the text.

also summarized in Table 3. For both the pure C10E6 andC14E6 monolayers and the mixed C10E6/C14E6 monolayersthe relative positions of the different components at the in

face are over determined. For the pure surfactant monola

(17)δc(n)s − δe(n)s = δc(n)e(n)

and for the mixed C10E6/C14E6 monolayer

(18)δc(10)s − δe(10)s = δc(10)e(10),

(19)δc(14)s − δe(14)s = δc(14)e(14),

(20)δc(10)s − δc(14)s = δc(10)c(14),

and

(21)δe(10)s − δe(14)s = δe(10)e(14).

The values reported in Table 3 are within the quotedperimental error and are consistent with the self-consisconstraints described by Eqs. (18)–(21). A further constrestablished from the simple single layer model analto derive adsorbed amounts, is that the area/molecuconstant and known, and hence so the stoichiometry osurface layer. The resultant number density distribut(plotted as volume fraction distributions) are shown in FigIn Fig. 3 the volume fraction distributions for C10E6 andC14E6, along with the equivalent distributions for the puC10E6 and C14E6 monolayers are plotted.

A comparison of the key structural parameters fortwo surfactants in the mixed monolayer with the equivaparameters for the pure surfactant monolayers providesevidence of the structural changes that occur on mixFor the C14E6 the width of the alkyl and ethylene oxidlayers (σc(14), σe(14)) are similar in the pure and mixemonolayer. This is also the case for the ethylene ochain of the C10E6, σe(10). This is in marked contrast to thwidth of the alkyl chain for C10E6, σe(10), which comparedto the pure C10E6 monolayer is∼2.5 Å thicker in themixed C10E6/C14E6 monolayer. The other major differencare associated with the position of the alkyl and ethyloxide chains relative to the solvent distribution, andtheir positions relative to one another. The positions ofethylene oxide groups,δe(10)s and δe(14)s (for both C10E6and C14E6), are unaltered on mixing and almost coincidwith the solvent distributions, being slightly offset by∼2 Å.The position of the alkyl chain for the C14E6 relative tothe solvent,δc(14)s , is almost unaltered on mixing (a chan∼1 Å), but the alkyl chain–ethylene oxide chain overlδc(14)e(14), has increased (by∼2 Å). However, there is amuch larger change for the C10E6 on mixing, and the alkychain–ethylene oxide chain overlap,δc(10)e(10), decreases b∼4 Å. The position of the alkyl chain relative to the solveδc(10)s, changes by∼3 Å: that is, the alkyl chain is furthefrom the solvent on mixing.

In the mixed monolayer the distribution of the alkand ethylene oxide chains and of the solvent for bothC10E6 and C14E6 are almost completely coincident. Thisachieved by the changes described previously and indthat the C10E6 adjusts its position at the interface andconformation to a greater extent than the C14E6 to achievethe optimal packing. These changes contrast markedly

J. Penfold et al. / Journal of Colloid and Interface Science 262 (2003) 235–242 241

lingrentheievere

sitionth

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lventuced

is in

andgly-the

ani-lkyle ar-ly

(a)

(b)

Fig. 3. (a) Volume fraction distributions of solvent and C10E6 alkyl andethylene oxide chains in a pure monolayer (10−4 M) and the mixedC10E6/C14E6 monolayer (4.2 × 10−4 M 97.3 mole% C10E6/2.7 mole%C14E6): (· · ·) solvent in pure monolayer, (– –) in mixed monolayer; (–··–)ethylene oxide chain in pure monolayer, (–·–) in mixed monolayer; (—)alkyl chain in pure monolayer, (– –) in mixed monolayer (and as per labeon the figure). The comparison between the distributions of the diffecomponents of C10E6 in the pure and mixed monolayer shows how tC10E6 adjusts its position and conformation at the interface to achoptimal packing with the C14E6. The center of the solvent distributions aarbitrarily defined as zero. (b) Same as Fig. 3a, except comparing C14E6in the pure monolayer (10−4 M) with C14E6 in the C10E6/C14E6 mixedmonolayer. The symbols are the same as in Fig. 3a. In this case the poand conformation of the C14E6 are essentially unaltered on mixing wiC10E6.

those previously reported for the C12E3/C12E8 nonionicmixture [1] where the packing of the different ethyleoxide chains has a different impact on the structure. ForC12E3/C12E8 nonionic mixture the difference in headgrosize resulted primarily in changes in the ethylene oxstructure on mixing (see Fig. 4). In Fig. 4 the volume fractdistributions for C12E3 and C12E8 in the mixed C12E3/C12E8

(a)

(b)

Fig. 4. (a) Volume fraction distribution of solvent and C12E3 alkyl andethylene oxide chains in a pure C12E3 monolayer (5.5 × 10−5 M) andin a mixed C12E3/C12E8 monolayer (5× 10−5 M 30 mole% C12E3/70 mole% C12E8), from Ref. [1]: (· · ·) solvent in pure monolayer, (– –mixed monolayer; (–··–) ethylene oxide chain in pure monolayer, (–·–)in mixed monolayer; (—) alkyl chain in pure monolayer, (– –) in mixmonolayer. (b) Same as Fig. 4a, except comparing C12E8 in pure monolayer(1.8 × 10−4 M) with C12E8 in the mixed C12E3/C12E8 monolayer. Thesymbols are the same in both figures, and the center of the sodistribution is arbitrarily defined as zero. These results are reproddirectly from Ref. [1] for comparison with the results for the C10E6/C14E6mixture and show how in this case the significant change on mixingthe ethylene oxide chain of the C12E8 component.

mixed monolayer are compared with the pure C12E3 andC12E8 monolayers.

The frustration caused by packing the triethyleneoctaethylene glycol groups resulted in the octaethylenecol group being less extended and more hydrated andtriethylene glycol group being less hydrated. This reorgzation of the ethylene oxide groups resulted in both achains becoming more extended. In this case it could bgued that the C12E8 structure was adjusted to more closeaccommodate the structure of the C12E3 on mixing.

242 J. Penfold et al. / Journal of Colloid and Interface Science 262 (2003) 235–242

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5. Summary

Neutron reflectivity, in combination with H/D isotopsubstitution, has been used to determine the detailed sture of adsorbed nonionic surfactant monolayers atair–water interface for C10E6 and C14E6 at 10−4 M, andfor a 97.3 mole% C10E6/2.7 mole% C14E6 mixture at 4.2×10−4 M. The role of the difference in alkyl chain lengton surfactant packing is contrasted with that of the etene oxide chain length, from data previously reportedC12E3/C12E8 mixtures. For the C10E6/C14E6 mixture therelative position of the alkyl and ethylene oxide chainsaltered on mixing, and the largest impact is upon the C10E6.For C10E6 the molecule is partially dehydrated on mixinthe alkyl chain ethylene oxide overlap decreases, andalkyl chain is more extended. In contrast, mixing C12E3 andC12E8 has a greater impact upon the C12E8 where the ethylene oxide chain is less extended and dehydrated, andalkyl chains are more extended.

We have demonstrated that, even in mixtures whbehave closely to ideal, measurable changes in the comation of the molecules and their levels of hydration canobserved. Such results provide the information and theportunity to refine the theories of surfactant mixing to tainto account such changes. In particular we have quantthe changes that arise from a mismatch in alkyl chain lenin nonionic surfactant mixtures and contrasted thosesome previous reported changes arising from a mismatethylene oxide chain length

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