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Colloids and Surfaces A: Physicochem. Eng. Aspects 375 (2011) 130–135

Contents lists available at ScienceDirect

Colloids and Surfaces A: Physicochemical andEngineering Aspects

journa l homepage: www.e lsev ier .com/ locate /co lsur fa

quilibrium and surface rheology of two polyoxyethylene surfactants (CiEOj)iffering in the number of oxyethylene groups

ablo Ramíreza,∗, Luis María Péreza, Luis Alfonso Trujilloa, Manuela Ruiza, José Munoza, Reinhard Millerb

Departamento de Ingeniería Química, Facultad de Química, Universidad de Sevilla c/P, García González, 1, E41012 Sevilla, SpainMax-Planck-Institut für Kolloid-und Grenzflächenforschung, Am Mühlenberg 1, 14424 Potsdam, Germany

r t i c l e i n f o

rticle history:eceived 9 September 2010eceived in revised form 27 October 2010ccepted 28 November 2010vailable online 9 December 2010

eywords:

a b s t r a c t

A study of equilibrium adsorption properties and surface dilational rheology of two polyoxyethylenesurfactants of technical grade have been carried out. It has been shown, that equilibrium adsorption andsurface rheology are greatly influenced by the oxyethylene chain. To explore the equilibrium properties, apendant drop profile tensiometer was used. The equilibrium surface pressure isotherms can be explainedin the framework of the reorientation model. The increase in the number of oxyethylene units leads tohigher surface activity at low concentration when the surfactants adsorb in the state of maximum molar

on-ionic surfactantsdsorption equilibriumurface dilational rheologyscillating drop methodrop profile analysis

area. However, at higher concentration the adsorbed surfactant molecules reorient to a state of minimummolar area. In this state the surface activity is, on contrary, lower for C10EO14 due to higher hydrophilicity.Dilational rheology was studied by means of the oscillating drop method. The surfactant with higher EOunits showed an enhanced elasticity. Moreover, whereas C10EO6 experimental data can be interpreted onthe basis of the diffusional theory and a diffusion coefficient of 4 × 10−10 m2 s−1 was estimated, C10EO14

mayer s

behavior is more complexto that expected for polym

. Introduction

Polyoxyethylene surfactants are widely used in industrial appli-ations such as coating, food products, agricultural formulations,ersonal care, petroleum industry applications, and in generalo stabilize foams and emulsions [1–3]. Therefore, many studiesave been carried out regarding the surface properties of theseurfactants, namely equilibrium adsorption [4–18], dynamic sur-ace tension [19–22] and surface rheology [7,23–27]. Furthermore,ome works have related their surface properties with technicalpplications as foam and emulsion stabilizers [28–30].

Polyoxyethylene surfactants are usually denoted as CiEOj, wherestands for the number of carbon atoms in the hydrophobic tail andaccounts for the number of oxyethylene (EO) units. The influencesf the hydrocarbon chain length as well as the number of EO groupsn the adsorption of these nonionic surfactants at the air/water12,16,25,27] and oil/water [13,25,27] interfaces have been previ-

usly reported. Recently, a series of papers explored the influencef the number of EO groups on the adsorption, dynamic and sur-ace rheology properties of Triton-type surfactants [5,21,23,31].owever, although many studies have been carried out within

∗ Corresponding author. Tel.: +34 954 557180; fax: +34 954 556447.E-mail address: pramirez@us.es (P. Ramírez).

927-7757/$ – see front matter © 2010 Elsevier B.V. All rights reserved.oi:10.1016/j.colsurfa.2010.11.074

be due to the multitude of possible adsorption conformations and is closerurfactants.

© 2010 Elsevier B.V. All rights reserved.

the series of C10EOj surfactants, to the best of our knowledge,the surface rheology of surfactants with j > 8 has not been yetreported.

Surface rheology is of key importance in many technical appli-cations as foam, emulsion, coating, etc. The main parameter usedto describe the surface rheology is the surface dilatational vis-coelasticity modulus. This modulus is a complex number whosereal part, called the storage modulus, represents the surface elas-ticity, whereas the imaginary part, loss modulus, is related to theviscosity of the surface.

It is essential to describe accurately the adsorption processto interpret correctly surface rheology data. The adsorption ofoxyethylene based surfactants is well described by using thereorientation model [6,10,11,13,17]. Recently, more rigorous reori-entation models have been developed, accounting for the surfacecompressibility in the state of minimum molar area [5,7].

In the present work adsorption and surface rheology propertiesof two technical-grade non ionic surfactants with the same alkylchain length and different numbers of EO groups have been stud-ied. The reorientation model was used to describe the adsorption

process of both surfactants. However, surface rheology data haveto be interpreted differently. It will be shown that whereas C10EO6can be interpreted in the framework of diffusional relaxation pro-cess, C10EO14 surface rheology is closer to that of non ionic polymersurfactants.

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P. Ramírez et al. / Colloids and Surfaces A:

. Materials and methods

.1. Materials

Two poly(oxy ethylene)-based nonionic surfactants have beentudied, both of them with the same alkyl chain, but differing inhe number of oxyethylene groups. Hexaethylene glycol mono n-ecyl ether (C10EO6) and tetradecaethylene glycol n-decyl etherC10EO14) are technical grade surfactants and were kindly pro-ided by BASF and used as received. The solutions were preparedith Milli-Q water. All glassware was cleaned with a sulfuric acid

olution of 8 g l−1 of ammonium peroxodisulphate.

.2. Interfacial tension and rheological measurements (droprofile tensiometer)

Surface tension measurements were performed with a drop pro-le analysis tensiometer (CAM200, KSV, Finland). The drop was

ormed inside a thermostated cuvette at 20 ◦C and controlled usingcustom-built control unit consisting of a syringe with a piston that

s driven by a stepper motor. The control procedure was as follows:nce the drop was formed the contour of the drop was acquirednd then the drop initial area was calculated. Every 10 s the areaas calculated and the actual and initial value were compared. If

he values differed then the stepper motor drove the piston in theespective direction to correct the difference.

Oscillation perturbations were made using the PD 100 modulerom KSV. This module consists of a chamber filled with the solu-ion to be measured where there is a piezoelectric device calibratedith the pc sound card which produces harmonic oscillations. The

esults of oscillating experiments were analyzed as follows. First,he oscillating area was fitted to a time-dependent sine function

= A0 + Aa sin(ωt + �A) (1)

here ω is the frequency in rad s−1, A0 is the unperturbed droprea, Aa is the surface area amplitude and �A is a phase angle usedo fit experimental data when the start of the oscillation does notoincide with the first experimental surface area recorded. A0, Aa

nd �A were used as fit parameters. Then, the measured surfaceensions were fitted according to the following equation:

= �0 + �a sin(ωt + ��) (2)

here ω was the frequency in rad s−1, and �0 is the surface ten-ion prior to the harmonic perturbations, �a is the amplitude ofhe surface tension and �� is equal to: �� = �A + �, where � is thehase angle shift between the sinusoidal area perturbation and theurface tension response. Fitting of results was made by using theolver package from Excel. From the phase angle shift, � the storageodulus, E′ and the loss modulus, E′′ may then be calculated from

= E′ + iE′′ =∣∣E∣∣ cos � + i

∣∣E∣∣ sin � (3)

here

E| = A0�a

Aa(4)

Prior to each measurement the surface tension of water, �w,as measured and it was checked that its value was constant and

etween 72 and 73 mN m−1. Surface pressure values are calculateds: ˘ = �w − � .

. Theory

The theoretical models used to describe both the adsorption andurface elasticity have been previously developed [6,11,18,32,33].herefore, only the main equations will be summarized here.

ochem. Eng. Aspects 375 (2011) 130–135 131

3.1. Surface pressure isotherms

The software package IsoFit, [34] has been used to fit surfacepressure isotherm data to the reorientation model. In this modelthe molecules are supposed to be in two different states charac-terized by their partial molar areas, ˝1 and ˝2, where ˝1 > ˝2.Therefore, total surface concentration, � , is given by adding sur-face concentrations of molecules adsorbed in each state � 1 and� 2, respectively: � = � 1 + � 2. Furthermore, the mean molar area isdefined as ˝� = ˝1� 1 + ˝2� 2. The Szyszkowski–Langmuir equa-tion was used as equation state:

˘ = −RT

˝ln(1 − �˝) (5)

while the adsorption isotherm was given by:

bc = �2

(1 − �˝)˝2/˝ (6)

where c is the surfactant bulk concentration and b is the adsorptionequilibrium constant in state 2 (smaller molar area). The ratio ofadsorption in these two states was defined by the generalized Joosequation [35]

�1

�2= exp

[˝1 − ˝2

˝

](˝1

˝2

)˛

exp

[−˘(˝2 − ˝1)

RT

](7)

Here, ˘ is the surface pressure, R is the gas constant, T is theabsolute temperature, and ˛ is a constant related to the additionalsurface activity of state 1, since the adsorption equilibrium in state1 can be higher than the one in state 2.

3.2. Surface dilatational elasticity

The surface dilatational modulus, E, is defined as the change insurface tension, � , with small area variations. This dilatational mod-ulus (E) can be expressed as a complex number (see Eq. (3)) wherethe real part is the storage modulus, representing the surface dila-tional elasticity, whereas the imaginary part is the loss modulus,that is related to the dilational viscosity (�d), since E′′ = ω�d, whereω is the angular frequency. The real and imaginary part of this com-plex number can be expressed by using the absolute value of thesurface dilatational modulus, |E|, and the phase angle, �:

E′ =∣∣E∣∣ cos � (8)

E′′ =∣∣E∣∣ sin � (9)

In the theoretical framework based on bulk diffusion in the lin-ear surface elastic regime, |E| and �, are defined as follows [33]:

∣∣E∣∣ = E0√1 + 2� + 2�2

(10)

� = arctg

[�

1 + �

](11)

where, � = (ω0/ω)1/2, E0 = d˘/d ln � , is the limiting elasticity andω0 = D/2(d� /dc)2 is the characteristic diffusion frequency. � is thesurface concentration of the surfactant, D is the diffusion coefficientand c is the bulk concentration.

Once the equilibrium surface pressure isotherm is fitted to asuitable model, E0 and d� /dc can be calculated. Therefore if themain relaxation process is diffusion, experimental |E| and � valuescan be fitted to Eqs. (10) and (11) just selecting the right diffusioncoefficient value.

132 P. Ramírez et al. / Colloids and Surfaces A: Physicochem. Eng. Aspects 375 (2011) 130–135

Fig. 1. Surface pressure isotherms for C10EO6 (triangles) and C10EO14 (squares) sur-factants at the air/water interface at 20 ◦C. Experimental data were fitted to thereorientation model with the parameters given in Table 1.

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4

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scdtitaocwsi

TP

ig. 2. Dynamic surface tension of C10EO6 (triangles) and C10EO14 (circles) solutions.he bulk concentrations were 5 × 10−3 mol m−3 for C10EO6 and 3 × 10−3 mol m−3 for10EO14.

. Results and discussion

.1. Surface pressure isotherms

To obtain the equilibrium surface pressure isotherms (Fig. 1),urface tension measurements were taken between 30 min foroncentrated solutions and 3 h for diluted ones. Fig. 2 shows theynamic surface tension for solutions of low surfactant concentra-ion. It is clearly seen that for both surfactants the equilibrium values reached in the available experimental time window. Experimen-al data were fitted according to the reorientation model explainedbove. The parameters which provided the best fit between the-retical model and experimental data are reported in Table 1. As

an be observed the maximum molar surface area, ˝1 increasedith the number of oxyethylene units (EO), whereas ˝2 was only

lightly affected, despite it could be expected that both parametersncreased with j. Parameters ˛ and b exhibited opposite behav-

able 1arameters used to fit surface pressure isotherms to the reorientation model.

Surfactant ˝1, m2 mol−1 ˝2, m2 mol−1 b, m3 mol−1 ˛

C10EO6 9 × 105 3 × 105 100 2C10EO14 16 × 105 3.2 × 105 54 4

Fig. 3. Indicatrix of 5 × 10−3 mol m−3 (triangles) and 0.12 mol m−3 (circles) of C10EO6

surfactant. Dotted and solid lines are the expected theoretical values from Eq. (12)with E0 calculated from equilibrium measurements.

iors with increasing j (the number of EO groups). The rise of ˛with j indicates the higher surface activity of the surfactant witha larger number of oxyethylene groups at the first stage of theadsorption process, when ˝1 is reached. This may be ascribed toa partial adsorption of EO groups as can be deduced from Fig. 1,where the reduction of the surface tension was more pronouncedfor C10EO14 at low concentrations. On the contrary, b decreases withj, which may be associated with the decrease of the surface activityof surfactants with longer oxyethylene chains in the state of lowermolar area, since their hydrophilic character increases. Therefore,the change in the relative surface activity of surfactants with differ-ent number of oxyethylene groups results in the appearance of anintersection point in the surface pressure isotherms. This intersec-tion is observed at a concentration of 0.02 mol m−3 and a surfacepressure of 12 mN m−1 (Fig. 1). This behavior has been also shownin previous works and, interestingly, the value of the intersectionsurface pressure coincides with that reported for Triton surfactantsin [5].

4.2. Surface dilational viscoelasticity

The viscoelastic properties of layers of polyoxyethylene alcoholsat the air–water interface were studied by means of harmonic per-turbations within the lineal range. From the experimental data |E|and � were determined for each surfactant as function of concen-tration and frequency. Furthermore, from Eqs. (8) and (9) the lossand elastic modulus were calculated.

The plot of E′′ as a function of E′, called indicatrix, is a useful toolto determine if the surface elasticity is governed by a diffusionalmechanism [24]. The corresponding plot of the loss shear modulus(G′′) versus the storage shear modulus (G′) is called in bulk rheol-ogy Cole–Cole plot and it has proven useful to discriminate betweenfluid-like and structured (highly elastic) materials [36]. Fluid-likesolutions exhibit half circles, whereas materials with a long relax-ation time show open curves with only one zero point. This plotturns out to be quite sensitive to the influence of temperature onthe viscoelasticity of polymeric systems [37]. It is interesting to notethat the original graph consisted of a plot of the imaginary part ofthe complex dielectric constant ε′′ against the real part ε′ [38].

If Eqs. (10) and (11) apply then E′′ as a function of E′ is given by

[24]

E′2 + E′′2 = E0(

E′ − E′′) (12)

Figs. 3 and 4 show the indicatrix for two concentrations ofC10EO6 and C10EO14, respectively. The lines represent the behavior

P. Ramírez et al. / Colloids and Surfaces A: Physicochem. Eng. Aspects 375 (2011) 130–135 133

Fsw

piemtlts

cq

Fmfa

ig. 4. Indicatrix of 3 × 10−3 mol m−3 (circles) and 0.3 mol m−3 (triangles) of C10EO14

urfactant. Dotted and solid lines are the expected theoretical values from Eq. (12)ith E0 calculated from equilibrium measurements.

redicted from Eq. (12) with E0 determined from the adsorptionsotherm, since E0 = d ln ˘/d ln � . It can be clearly checked that thexperimental results for C10EO6 fit fairly well with the theoreticalodel, whereas the behavior of C10EO14 cannot be explained on

he basis of diffusion relaxation. Furthermore, the low values of theoss modulus and the fact that they do not depend on either surfac-ant concentration or on frequency, is characteristic of polymeric

urfactants [39].

Figs. 5 and 6 show |E| and � as a function of surfactant bulkoncentration for C10EO6 and C10EO14, respectively, at three fre-uencies, 0.02 Hz, 0.1 Hz and 0.5 Hz.

ig. 5. Experimental (symbols) and theoretical (lines) dependencies of the dilationalodulus, |E| and phase angle, �, on the C10EO6 solution concentration for three

requencies: 0.02 Hz (circles, and dot-dashed lines), 0.1 Hz (triangles and solid lines)nd 0.5 Hz (squares and dashed lines).

Fig. 6. Experimental (symbols) and theoretical (lines) dependencies of the dilationalmodulus, |E| and phase angle, �, on the C10EO14 solution concentration for threefrequencies: 0.02 Hz (circles, and dot-dashed lines), 0.1 Hz (triangles and solid lines)and 0.5 Hz (squares and dashed lines).

For C10EO6 a maximum of |E| at intermediate surfactant concen-tration can be clearly observed, whose value increases and shiftstowards higher concentrations with increasing frequency. On theother hand, the phase angle increases with surfactant concentrationeventually reaching values which are not far from 45◦. Interestingly,the phase angle increases faster at lower frequencies. All these fea-tures are common for non ionic surfactants whose main relaxationprocess is diffusion, and agree with the indicatrix shown above.Therefore, the experimental values obtained can be fitted by usingEqs. (10) and (11). E0 and d� /dc as a function of concentrationcan be calculated from Eqs. (5) to (7) of the reorientation modelwith the parameters given in Table 1, the only adjustable parame-ter being the diffusion coefficient. The solid lines in Fig. 5 illustratethe calculated |E| and � values as a function of surfactant concen-tration, assuming a diffusion coefficient of 4 × 10−10 m2 s−1. Thisvalue agrees with the diffusion coefficient determined by dynamicsurface tension for this type of surfactants [19,20,25].

The results obtained for C10EO14 were rather different to thoseexhibited by C10EO6. They did not fit the diffusional model as illus-trated in Fig. 6, where theoretical values calculated as explainedabove and using a coherent diffusion coefficient of 1 × 10−10 m2 s−1

were shown. |E| did not show a maximum value in the concen-tration range studied. Furthermore, the experimental phase anglesobtained were much lower than those predicted by the diffusionalmodel and did not depend on the experimental frequency used.According to these results it is concluded that the storage modulus

and the loss modulus do not depend on frequency in the studied fre-quency range and the former is comparatively higher. This impliesa slow relaxation process similar to the obtained for polymeric sur-factants [24,39]. Furthermore, a similar behavior has been obtainedfor Triton with larger number of oxyethylene units (TX165) [23] and

134 P. Ramírez et al. / Colloids and Surfaces A: Physic

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ig. 7. Surface dilational elasticity, E′ , and surface dilational viscosity, �d , as a func-ion of concentration of C10EO6 (squares) and C10EO14 (circles). Open and closedymbols stand for the experimental results at the lowest frequency used (0.02 Hz)nd the highest one (0.5 Hz), respectively.

t was related to the behavior of surfactant mixtures as describedn [40]. Therefore, it is likely that the dilational rheology of this sur-actant is strongly influenced by the molecules with large numberf EO units.

In Fig. 7 the dilatational elasticity and viscosity of both surfac-ants as a function of concentration for the lowest and highestrequencies employed have been plotted. It is seen that the dila-ional elasticity of C10EO14 (E′ = |E|cos �) is higher than the valuesor C10EO6, at every concentration and independent of frequency.n the contrary the dilational viscosity (�d = E′′/ω = (|E| sin �) /ω)t low frequencies is higher for the C10EO6 surfactant. It is alsobserved that the dilational viscosity is very small at the highestrequency for both surfactants. Therefore, the surfactant with thearger number of EO groups form a more elastic layer, especiallyt lower bulk concentrations when according to the reorienta-ion model the molar area of C10EO14 is higher than that of10EO6.

. Conclusions

The equilibrium adsorption properties as well as the surfaceheology of two technical-grade polyoxyethylene alcohols with dif-erent ethoxylation numbers were studied.

The equilibrium surface tension can be described on the basisf the reorientation model. An increase in the EO number of theon-ionic surfactants studied results in a rise of the molar area

f the molecules in the state of higher molar area, and in a risef the activity in that state being indicated by the parameter ˛ inhe model used (see Table 1). Conversely, when the number of EOroups is reduced the surface activity increases at high concentra-ions, i.e., when surfactants are in the state of minimum molar area.

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ochem. Eng. Aspects 375 (2011) 130–135

As a consequence, an intersection in the surface tension isothermis produced.

From surface rheology measurements it is concluded that theC10EO6 surfactant form a viscoelastic layer at the water/air surface,controlled by the diffusion of surfactant molecules. Combining theprevious equilibrium results and the rheological data, a diffusioncoefficient of 4 × 10−10 m2 s−1 was estimated according to a diffu-sional transport. However, the dilational rheology measurementsof C10EO14 could not be interpreted in the same way. The so-calledindicatrix and the concentration dependence of the phase angle atseveral frequencies support that the surface rheology of this sur-factant is closer to the behavior of polymeric surfactants than thatof small non-ionic surfactants, and it is likely due to the presenceof homologues with a large number of oxyethylene units.

Comparison of dilatational elasticity and viscosity of both sur-factants indicates that elasticity is enhanced by increasing thenumber of EO groups.

Acknowledgements

This paper reports part of the results obtained in projectCTQ2007-66157PPQ sponsored by the Spanish Ministerio de Cien-cia y Tecnología and the European Commission (Feder Programme).The authors kindly acknowledge the financial support received. L.M. P. also acknowledges the Universidad de Sevilla for its financialsupport (Beca PIF IV Plan Propio de Investigación).

References

[1] B.E. Chistyakov, Surfactants – chemistry, interfacial properties, applications, in:D. Möbius, R. Miller (Eds.), Studies in Interface Science, Elsevier, Amsterdam,2001.

[2] L.L. Schramm, Emulsions, Foams and Suspensions: Fundamentals and Applica-tions, Wiley-VCH, Weinheim, 2005.

[3] T.F. Tadros, Applied Surfactants: Principles and Applications, Wiley-VCH, Wein-heim, 2005.

[4] J.S. Cheng, Y.P. Chen, Correlation of the critical micelle concentration for aque-ous solutions of nonionic surfactants, Fluid Phase Equilib. 232 (2005) 37–43.

[5] V.B. Fainerman, S.V. Lylyk, E.V. Aksenenko, A.V. Makievski, J.T. Petkov, J. Yorke, R.Miller, Adsorption layer characteristics of Triton surfactants. 1. Surface tensionand adsorption isotherms, Colloids Surf., A 334 (2009) 1–7.

[6] V.B. Fainerman, R. Miller, E.V. Aksenenko, Adsorption behavior of oxyethylatedalcohols at the solution/air interface, Langmuir 16 (2000) 4196–4201.

[7] V.B. Fainerman, S.A. Zholob, J.T. Petkov, R. Miller, C14EO8 adsorption charac-teristics studied by drop and bubble profile tensiometry, Colloids Surf., A 323(2008) 56–62.

[8] M. Ferrari, L. Liggieri, F. Ravera, Adsorption properties of C10E8 at thewater–hexane interface, J. Phys. Chem. B 102 (1998) 10521–10527.

[9] J.B. Jeong, J.Y. Kim, J.H. Cha, J.D. Kim, The effect of polydispersity on the static anddynamic behavior of dodecyl ethoxylates at the air–water interface, ColloidsSurf., A 207 (2002) 161–167.

10] R. Miller, E.V. Aksenenko, L. Liggieri, F. Ravera, M. Ferrari, V.B. Fainerman, Effectof the reorientation of oxyethylated alcohol molecules within the surface layeron equilibrium and dynamic surface pressure, Langmuir 15 (1999) 1328–1336.

11] R. Miller, V.B. Fainerman, H. Möhwald, Adsorption behavior of oxyethylatedsurfactants at the air/water interface, J. Colloid Interface Sci. 247 (2002)193–199.

12] M. Ueno, Y. Takasawa, H. Miyashige, Y. Tabata, K. Meguro, Effects of alkylchain length on surface and micellar properties of octaethy-leneglycol-N-alkylethers, Colloid Polym.Sci. 259 (1981) 761–766.

13] M.A. Valenzuela, M.P. Garate, A.F. Olea, Surface activity of alcohols ethoxylatesat the n-heptane/water interface, Colloids Surf., A 307 (2007) 28–34.

14] R. Varadaraj, J. Bock, P. Geissler, S. Zushma, N. Brons, T. Colletti, Influence ofethoxylate distribution on interfacial properties of linear and branched ethoxy-late surfactants, J. Colloid Interface Sci. 147 (1991) 396–402.

15] V.B. Fainerman, E.V. Aksenenko, J.T. Petkov, R. Miller, Adsorption layer charac-teristics of mixed oxyethylated surfactant solutions, J. Phys. Chem. B 114 (2010)4503–4508.

16] J. Penfold, E. Staples, I. Tucker, L. Thompson, R.K. Thomas, Adsorption ofnonionic mixtures at the air–water interface: effects of temperature and elec-trolyte, J. Colloid Interface Sci. 247 (2002) 404–411.

17] L. Liggieri, M. Ferrari, A. Massa, F. Ravera, Molecular reorientation in theadsorption of some CiEj at the water–air interface, Colloids Surf., A 156 (1999)455–463.

18] V.B. Fainerman, R. Miller, R. Wüstneck, A.V. Makievski, Adsorption isothermand surface tension equation for a surfactant with changing partial molar area.1. Ideal surface layer, J. Phys. Chem. 100 (1996) 7669–7675.

Physic

[

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P. Ramírez et al. / Colloids and Surfaces A:

19] H.C. Chang, C.T. Hsu, S.Y. Lin, Adsorption kinetics of C10E8 at the air–waterinterface, Langmuir 14 (1998) 2476–2484.

20] J. Eastoe, J.S. Dalton, Dynamic surface tension and adsorption mechanisms ofsurfactants at the air–water interface, Adv. Colloid Interface Sci. 85 (2000)103–144.

21] V.B. Fainerman, S.V. Lylyk, E.V. Aksenenko, L. Liggieri, A.V. Makievski, J.T. Petkov,J. Yorke, R. Miller, Adsorption layer characteristics of Triton surfactants. Part 2.Dynamic surface tension and adsorption, Colloids Surf., A 334 (2009) 8–15.

22] B.V. Zhmud, F. Tiberg, J. Kizling, Dynamic surface tension in concentrated solu-tions of CnEm surfactants: a comparison between the theory and experiment,Langmuir 16 (2000) 2557–2565.

23] V.B. Fainerman, E.V. Aksenenko, S.V. Lylyk, A.V. Makievski, F. Ravera, J.T. Petkov,J. Yorke, R. Miller, Adsorption layer characteristics of Tritons surfactants. 3.Dilational visco-elasticity, Colloids Surf., A 334 (2009) 16–21.

24] F.K. Hansen, Surface dilatational elasticity of poly(oxy ethylene)-based surfac-tants by oscillation and relaxation measurements of sessile bubbles, Langmuir24 (2008) 189–197.

25] L. Liggieri, M. Ferrari, D. Mondelli, F. Ravera, Surface rheology as a tool forthe investigation of processes internal to surfactant adsorption layers, FaradayDiscuss. 129 (2005) 125–140.

26] E.H. Lucassen-Reynders, A. Cagna, J. Lucassen, Gibbs elasticity, surface dilationalmodulus and diffusional relaxation in nonionic surfactant monolayers, ColloidsSurf., A 186 (2001) 63–72.

27] L. Liggieri, V. Attolini, M. Ferrari, F. Ravera, Measurement of the surface dila-tional viscoelasticity of adsorbed layers with a capillary pressure tensiometer,J. Colloid Interface Sci. 255 (2002) 225–235.

28] N. Buchavzov, F. Ravera, S. Hess, Y. Liu, U. Steinbrenner, C. Stubenrauch, Inter-facial tensions, partition coefficients, and interfacial elasticities: measures foremulsion stability? Tenside Surfactants Deterg. 44 (2007) 230–238.

[

[

ochem. Eng. Aspects 375 (2011) 130–135 135

29] E. Santini, L. Liggieri, L. Sacca, D. Clausse, F. Ravera, Interfacial rheology of Span80 adsorbed layers at paraffin oil–water interface and correlation with thecorresponding emulsion properties, Colloids Surf., A 309 (2007) 270–279.

30] C. Stubenrauch, R. Miller, Stability of foam films and surface rheology: anoscillating bubble study at low frequencies, J. Phys. Chem. B 108 (2004)6412–6421.

31] V.B. Fainerman, A.V. Mys, E.V. Aksenenko, A.V. Makievski, J.T. Petkov, J. Yorke, R.Miller, Adsorption layer characteristics of Triton surfactants. 4. Dynamic surfacetension and dilational visco-elasticity of micellar solutions, Colloids Surf., A 334(2009) 22–27.

32] V.B. Fainerman, E.H. Lucassen-Reynders, R. Miller, Adsorption of surfactantsand proteins at fluid interfaces, Colloids Surf., A 143 (1998) 141–165.

33] J. Lucassen, M. van den Tempel, Dynamic measurements of dilational propertiesof a liquid interface, Chem. Eng. Sci. 27 (1972) 1283.

34] http://www.thomascat.info/thomascat/Scientific/AdSo/AdSo.htm.35] P. Joos, G. Serrien, The principle of Braun-le Chatelier at surfaces, J. Colloid

Interface Sci. 145 (1991) 291–294.36] R. Lapasin, S. Pricl, Rheology of Industrial Polysaccharides. Theory and Appli-

cations, B.A.P.C. Hall, London, 1995.37] C.D. Hang, Rheology and processing of polymeric materials, in: Polymer Rhe-

ology, O.U. Press, Oxford, 2007.38] K.S. Cole, R.H. Cole, Dispersion and absorption in dielectrics. I. Alternating cur-

rent characteristics, J. Chem. Phys. 9 (1941) 341–351.

39] B.A. Noskov, S.Y. Lin, G. Loglio, R.G. Rubio, R. Miller, Dilational viscoelasticity of

PEO–PPO–PEO triblock copolymer films at the air–water interface in the rangeof high surface pressures, Langmuir 22 (2006) 2647–2652.

40] E.V. Aksenenko, V.I. Kovalchuk, V.B. Fainerman, R. Miller, Surface dilational rhe-ology of mixed surfactants layers at liquid interfaces, J. Phys. Chem. C 111 (2007)14713–14719.