Correlation between wetting, adhesion and adsorption in the polymer–aqueous solutions of ternary surfactant mixtures–air systems

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Applied Surface Science xxx (2013) xxx– xxx

Contents lists available at ScienceDirect

Applied Surface Science

j ourna l ho me page: www.elsev ier .com/ locate /apsusc

orrelation between wetting, adhesion and adsorption in theolymer–aqueous solutions of ternary surfactant mixtures–airystems

atarzyna Szymczyk, Anna Zdziennicka ∗, Joanna Krawczyk, Bronisław Janczukepartment of Interfacial Phenomena, Faculty of Chemistry, Maria Curie-Skłodowska University, Maria Curie-Skłodowska Sq. 3, 20-031 Lublin, Poland

r t i c l e i n f o

rticle history:eceived 6 May 2013eceived in revised form 4 October 2013ccepted 10 October 2013vailable online xxx

eywords:urface tensionurface excess concentrationurfactantsernary mixtures

a b s t r a c t

The correlation between the wettability of polymers and adsorption of ternary mixtures including CTAB,TX-100 and TX-114 at the polymer–aqueous solution interface as well as the adhesion of aqueous solutionof these mixtures to apolar polytetrafluoroethylene (PTFE), monopolar polymethyl methacrylate (PMMA)and nylon 6 was considered on the basis of the contact angle measurements and the literature data ofthe solutions surface tension. From these considerations it appeared that the efficiency and effectivenessof the adsorption at the PTFE–water interface are comparable to those at the water–air one, but forthe PMMA–water and nylon 6–water interfaces they are lower than those for the water–air one for agiven series of solutions. The efficiency and effectiveness are reflected in the composition of the mixedmonolayer at the polymer–solution interface which even for the PTFE–solution interface is somewhatdifferent from the water–air interface. The properties of the mixed monolayer at these interfaces influence

ettabilitydhesionolymers

the critical surface tension of polymer wetting which for PTFE is somewhat higher but for PMMA andnylon 6 considerably lower than their surface tension. From these considerations it also appeared thatthe work of adhesion of aqueous solutions of ternary mixtures of surfactants to the PTFE surface does notdepend on the composition and concentration of solution contrary to PMMA and nylon 6. The adhesionwork of these solutions to the PMMA and nylon 6 surface can be determined on the basis of van Oss et al.and Neumann et al. equations.

. Introduction

In many applications of surfactants for example, such as in cos-etics, detergency and enhanced oil recovery the reduction of theater contact angle on a given solid surface to the proper low value

s necessary [1–4]. However, it is impossible to be achieved by a sin-le surfactant but only by the addition of the mixture of differentypes of surfactants to water.

The reduction of the water contact angle depends on the prop-rties of the mixed monolayer at the water–air, solid–water andolid–air interfaces, which, in turn, is connected with the composi-ion and structure of this layer [1]. The composition and structuref such a layer at these interfaces influence the wettability ofolids and in the case of multicomponent mixtures of surfactantshey are not quite established, particularly at the solid–solution

Please cite this article in press as: K. Szymczyk, et al., Correlation betweenof ternary surfactant mixtures–air systems, Appl. Surf. Sci. (2013), http://d

nterface. In our previous paper we presented the studies deal-ng with the mutual influence of Tritons (TX-100 and TX-114) andetyltrimethylammonium bromide (CTAB) on their adsorption and

∗ Corresponding author. Tel.: +48 81 537 56 70; fax: +48 81 533 3348.E-mail address: [email protected] (A. Zdziennicka).

169-4332/$ – see front matter © 2013 Elsevier B.V. All rights reserved.ttp://dx.doi.org/10.1016/j.apsusc.2013.10.059

© 2013 Elsevier B.V. All rights reserved.

composition of the monolayer at the water–air interface [5]. Itappeared that the composition of the unsaturated and saturatedmonolayer of the ternary mixtures at the water–air interface andthe behaviour of the particular surfactant in this monolayer aredifferent. In the range of surfactants mixture concentration corre-sponding to the unsaturated monolayer at the water–air interface,the adsorption of CTAB from the mixture is comparable to itsadsorption from the single solution, and the adsorption of TX-100from the mixture is higher than that from the single solution andincreases similarly to CTAB with the increase of the concentration insolution. However, in the saturated monolayer CTAB decreases theTX-100 adsorption compared to that from the single solution of TX-100. It is in accordance with the behaviour of TX-100 in the binarymixture of CTAB and TX-100 [6]. In the case of TX-114 its adsorptionfrom the mixture of surfactants is lower than from a single solu-tion, however, only in the range of concentration of the mixture inthe bulk phase corresponding to the unsaturated monolayer at thewater–air interface. At the concentration of mixture corresponding

wetting, adhesion and adsorption in the polymer–aqueous solutionsx.doi.org/10.1016/j.apsusc.2013.10.059

to the saturated monolayer, the mole fraction of TX-114 is higherthan in a single solution. However, the maximal surface excess con-centration of surfactant in the ternary mixtures is smaller than thatof single solutions. The changes of the composition of the mixed

dx.doi.org/10.1016/j.apsusc.2013.10.059


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onolayer at the water–air interface in comparison to the bulkhase and independent adsorption of each surfactant from singleolution influence on the synergetic effect in the reduction of waterurface tension confirmed by the efficiency of adsorption despitemaller effectiveness of ternary mixtures compared to individualurfactants.

The behaviour of the surfactants in the mixed monolayer at theater–air interface should influence on the wettability of poly-ers. On the other hand, the adsorption of particular surfactant

rom the aqueous solution of ternary mixtures of surfactants at theolymer–water interface also plays a very important role. In the lit-rature it is possible to find that the adsorption of surfactants andheir mixtures at the apolar polymer–water interface is similar tohat at the water–air one, but in the case of monopolar polymerss smaller [1,7–10]. However, it is practically impossible to find theelationship between the composition of the multicomponent layert the polymer–water and water–air interfaces and the wettabilityf polymers.

It follows from the thermodynamic rules that complete wettingf the solid by the liquid takes place if the work of adhesion of thisiquid to the solid surface is equal or higher than liquid cohesion

ork. On the other hand, the work of liquid adhesion to the solidurface is connected with the surface tension of solid and liquid.hus, it is the relationship between the adhesion work and the sur-ace tension of solid and liquid as well as it is connected with theritical surface tension of solid wetting. In the case of aqueous solu-ions of surfactants, this relationship depends also on the propertiesf the adsorbed surfactants layer at the three interfaces: solid–air,olid–solution and solution–air.

The purpose of our paper was to discuss the relationshipetween the work of adhesion of aqueous solutions of ternary mix-ures of surfactants (TX-100 + TX-114 + CTAB) to PTFE, PMMA andylon 6 surfaces and the surface tension of these polymers as wells the critical surface tension of their wetting taking into accounthe properties of the mixed adsorbed monolayer at the solution–airnd polymer–solution interfaces. For this purpose the contact anglef aqueous solutions of TX-100, TX-114 and CTAB mixtures onhe apolar polytetrafluoroethylene (PTFE), monopolar polymethyl

ethacrylate (PMMA) and nylon 6 was measured.

. Experimental

.1. Materials

Doubly distilled and deionized water (Destamat Bi18E), p-1,1,3,3-tetramethylbutyl)-phenoxypolyoxyethylene glycols, Tri-on’s: TX-100, TX-114 (Sigma–Aldrich), were used without purifi-ation. Cetyltrimethylammonium bromide (CTAB) (Sigma–Aldrich)as purified by the method described in the literature [11]. For

he contact angle measurements the ternary mixtures of TX-100n = 1), TX-114 (n = 2) and CTAB (n = 3) were prepared in two differ-nt ways: the first is that the total concentrations of two surfactantsn the ternary mixture were the same as the third one but the moleraction of one surfactant in the binary mixture in the bulk phaseas equal to 0.2, 0.4, 0.5, 0.6 and 0.8 and the second that the total

oncentration of the binary mixture in the ternary mixture wasonstant and equal to 5 × 10−7, 1 × 10−6, 1 × 10−5 and 5 × 10−5 M,nd the concentration of the third surfactant changed in a wideange corresponding to that in the single solution in which the sur-actants were presented in the monomer and aggregated forms.ll the aqueous solutions of ternary surfactant mixtures at a given


oncentration and composition lower than 1 mM were preparedrom the stock solution (1 mM). Then from it the solutions in theoncentration range from 1 × 10−4 M to 1 × 10−3 M were prepared.ext from the solution at the concentration equal to 1 × 10−4 M the

PRESS Science xxx (2013) xxx– xxx

solutions in the concentration range from 1 × 10−5 M to 1 × 10−4 Mwere prepared and so on. The stock solution was prepared bymass using an analytical balance (model XA105, Mettler-Toledo)with the error ±0.01 mg. The standard uncertainties (u(C)) changedfrom 1.5 × 10−12 to 1.5 × 10−7 for CTAB and from 1.3 × 10−12 to1.3 × 10−7 M for TX-100 and TX-114 in the range of the studiedconcentrations.

The plates used for the contact angle measurements were pre-pared from polytetrafluoroethylene (PTFE), polymethyl methacry-late (PMMA) and nylon 6. PTFE was obtained as a result offree-radical polymerization of tetrafluoroethylene in the presenceof peroxides as initiators by the Nitrogen Industrial Plant in Tarnów(Poland). The procedure of preparation and cleaning of PTFE, PMMAand nylon 6 plates is described in detail elsewhere [12]. The qual-ity of the surface of each plate was controlled by a polarizingmicroscope (Nikon, ECLIPSE E 600 POL) and next the selectedplates without cracks and roughness were additionally controlledby determination of the contact angle on the four sides of thewater drop settled on the PTFE, PMMA or nylon 6 surfaces. If thedifferences between the values of the contact angle measured ondifferent sides of the water drop did not exceed ±1◦ and the aver-age values of the contact angle obtained for PTFE or PMMA or nylon6 were close to those in the literature [12,13] then such plates wereused for investigations.

2.2. Contact angles measurements

The measurements of the advancing contact angles of aqueoussolutions of surfactants studied on PTFE, PMMA and nylon 6 plateswere carried out using the sessile drop method by the DSA 30 mea-suring system (Krüss), in a thermostated chamber at 293 ± 0.1 K.For each studied system of PTFE (PMMA, nylon 6)–solution–air atleast 30 independent drops were used for the determination of theaverage values of the advancing contact angles. Good reproducibil-ity was found for the contact angle measurements. The standarddeviation for each set of values was less than ±1.1◦.

3. Results and discussion

3.1. Wettability of polymers

As follows from the contact angle (�) isotherms of aqueous solu-tions of TX-100 + TX-114 + CTAB mixtures on the PTFE, PMMA andnylon 6 surfaces wettability of a given polymer depends on the con-centration (C) and the mole fraction of the given surfactant in themixture in the bulk phase (˛) of the ternary mixtures of surfactants(Figs. 1–6, S1–S48). The dependence between the contact angle andthe composition (˛) of ternary mixtures of surfactants shows thesynergetic effect in the reduction of water contact angle on PTFE,PMMA and nylon 6 surface at the concentration of the ternarymixtures from 0 to that corresponding to the minimal value of �(Figs. 7–9, S49–S54). It is evident particularly at the mole fraction ofCTAB in the mixture in the bulk phase close to 0.1 independently ofthe composition of Tritons. Unfortunately contrary to nylon 6 com-plete wetting of PTFE and PMMA surfaces by the studied solutionsdid not occur.

According to the Young equation [1,2]:

�SV − �SL = �LV cos � (1)

the contact angle depends on the surface tension of solid (�SV) and


liquid (�LV) as well as the solid–liquid (�SL) interface tension. Unex-pectedly, in the case of PTFE for all studied mixtures, it is possibleto describe the dependence between � and log �LV (Fig. S55) as wellas between � and log �SL (Fig. S55) by the second order polynomial


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Fig. 1. A plot of the contact angle of the aqueous solution of TX-100 + TX-114 + CTABmixture (�) on PTFE surface vs. logarithm of the total ternary mixture concentration(Ct

f

�

a

�

rdlwtt

Fmt0i

Fig. 3. A plot of the contact angle of the aqueous solution of TX-100 + TX-114 + CTABmixture (�) on nylon 6 surface vs. logarithm of the total ternary mixture concentra-

The electron–donor parameter of the PMMA and nylon 6 surface

C123). For each mixture the mole fraction of TX-114 was constant and equal to 0.5.urves 1, 2, 3, 4 and 5 correspond to the mole fractions of CTAB in the mixture inhe bulk phase equal to 0.1, 0.2, 0.25, 0.3 and 0.4.

unctions which have the form:

= −(151.13 ± 3.59)(log �LV)2 + (641.67 ± 12.14) log �LV

− 559.75 ± 10.19 (2)

nd

= (11.10 ± 0.26)(log �SL)2 + (26.66 ± 0.64) log �SL

+ 36.05 ± 0.38 (3)

However, the dependence between � and log �SL is the mirroreflection of � vs. log �LV (Fig. S55). It means that there are someifferences in the composition and/or orientation of the adsorbed


ayer of surfactants at the PTFE–water interface compared to theater–air one. As mentioned above, at the constant �SV the con-

act angle depends on both �SL and �LV. The summing up effect ofhe changes of �SL and �LV under the influence of the adsorption

ig. 2. A plot of the contact angle of the aqueous solution of TX-100 + TX-114 + CTABixture (�) on PMMA surface vs. logarithm of the total ternary mixture concentra-

ion (C123). For each mixture the mole fraction of TX-114 was constant and equal to.5. Curves 1, 2, 3, 4 and 5 correspond to the mole fractions of CTAB in the mixture

n the bulk phase equal to 0.1, 0.2, 0.25, 0.3 and 0.4.

tion (C123). For each mixture the mole fraction of TX-114 was constant and equal to0.5. Curves 1, 2, 3, 4 and 5 correspond to the mole fractions of CTAB in the mixturein the bulk phase equal to 0.1, 0.2, 0.25, 0.3 and 0.4.

of the ternary mixtures of surfactants at the polymer–water andwater–air interfaces can be expressed as the sum of log �SL andlog �LV. In fact, this effect is expressed by the linear dependencebetween � and the sum of log �SL and log �LV (Fig. S56) which hasthe form:

� = (38.62 ± 0.04)(log �LV + log �SL) − (24.96 ± 0.11) (4)

Surface properties of PMMA and nylon 6 are somewhat differ-ent from those of PTFE because the polar groups such as −CO,−OCH3 are present on the PMMA surface and −CO and −NHon nylon 6 [14,15]. Oxygen in these groups can behave as anelectron–donor in the contact with water molecules or another sub-strate with active hydrogen and the hydrogen bond can be formed.


tension has a considerably higher value than the electron-acceptorone [13,16]. Thus, the contribution of the electron-acceptor param-eter to the PMMA surface tension can be practically neglected and

Fig. 4. A plot of the contact angle of the aqueous solution of the ternary TX-100 + TX-114 + CTAB mixture (�) on PTFE surface at the constant mole fraction of CTAB in thebinary CTAB + TX-100 mixture equal to 0.5 and the logarithm of TX-114 concentra-tion (C2). Curves 1, 2, 3 and 4 correspond to the constant concentration of the binaryCTAB + TX-100 mixture in the bulk phase equal to 5 × 10−7, 1 × 10−6, 1 × 10−5 and5 × 10−5 M, respectively.


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4 K. Szymczyk et al. / Applied Surface Science xxx (2013) xxx– xxx

Fig. 5. A plot of the contact angle of the aqueous solution of the ternary TX-100 + TX-114 + CTAB mixture (�) on PMMA surface at the constant mole fraction of CTAB inthe binary CTAB + TX-100 mixture equal to 0.5 and the logarithm of TX-114 con-cba

PoBcpnTsstafttb

F1tcba

Fig. 7. The contact angle values of the aqueous solution of the ternary TX-100 + TX-114 + CTAB mixture (�) and single surfactant on PTFE surface at the concentrationof solution equal to 1 × 10−6, 2 × 10−6, 2 × 10−5 and 1 × 10−4 M, respectively.

entration (C2). Curves 1, 2, 3 and 4 correspond to the constant concentration of theinary CTAB + TX-100 mixture in the bulk phase equal to 5 × 10−7, 1 × 10−6, 1 × 10−5

nd 5 × 10−5 M, respectively.

MMA is called monopolar solid whose surface tension resultsnly from the Lifshitz–van der Waals intermolecular interactions.ecause on the nylon 6 surface there are the −NH groups, whichan interact with the adherent medium as the electron-acceptorart of Lewis acid–base interactions, thus the acid parameter ofylon 6 surface tension is somewhat higher than that of PMMA.he presence of polar groups on the PMMA and nylon 6 surfaceshould influence on the relation between the contact angle and theurface tension of aqueous solution of ternary mixtures of surfac-ants and the polymer–solution interface tension. For both PMMAnd nylon 6, contrary to PTFE, the changes of the contact angle as aunction of the logarithm from the surface tension of the solution of

Please cite this article in press as: K. Szymczyk, et al., Correlation between wetting, adhesion and adsorption in the polymer–aqueous solutionsof ternary surfactant mixtures–air systems, Appl. Surf. Sci. (2013), http://dx.doi.org/10.1016/j.apsusc.2013.10.059

ernary mixtures and logarithm of the polymer–solution interfaceension as well as the sum of log �SL and log �LV cannot be describedy one function for all studied mixtures (Figs. S57–S62).

ig. 6. A plot of the contact angle of the aqueous solution of the ternary TX-100 + TX-14 + CTAB mixture (�) on nylon 6 surface at the constant mole fraction of CTAB inhe binary CTAB + TX-100 mixture equal to 0.5 and the logarithm of TX-114 con-entration (C2). Curves 1, 2, 3 and 4 correspond to the constant concentration of theinary CTAB + TX-100 mixture in the bulk phase equal to 5 × 10−7, 1 × 10−6, 1 × 10−5

nd 5 × 10−5 M, respectively.

Fig. 8. The contact angle values of the aqueous solution of the ternary TX-100 + TX-114 + CTAB mixture (�) and single surfactant on PMMA surface at the concentrationof solution equal to 1 × 10−6, 2 × 10−6, 2 × 10−5 and 1 × 10−4 M, respectively.

Fig. 9. The contact angle values of the aqueous solution of the ternary TX-100 + TX-114 + CTAB mixture (�) and single surfactant on nylon 6 surface at the concentrationof solution equal to 1 × 10−6, 2 × 10−6, 2 × 10−5 and 1 × 10−4 M, respectively.


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their mixtures concentration using the following equation [1,2]:

�i = − Ci

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(∂�SL

∂Ci

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= − 12.303mRT

(∂�SL

∂ log Ci

)T,nj /= i

(8)



.2. Critical surface tension of polymers wetting and their surfaceension

It is interesting that for PTFE there is linear dependence betweendhesion and surface tension (Fig. S63) which can be describedy one linear equation for all studied aqueous solutions of ternaryixtures of surfactants:

LV cos � = −(1.0013 ± 0.000815)�LV + (46.5491 ± 0.040614)

(5)

The critical surface tension of PTFE wetting determined fromhis dependence is equal to 23.26 mN/m. The value 23.26 mN/m isomewhat higher than that of the surface tension of PTFE deter-ined from the contact angle of n-alkanes (20.24 mN/m) [17] and

s practically close to that determined from the contact angle foriquids having high surface tension [12].

To find out the reason for the differences between critical surfaceension of PTFE wetting by aqueous solution of ternary surfactants

ixture and its surface tension, the values of �SV were calculatedrom the Neumann et al. [18] equation:

cos � + 12

=√

�SV

�LVexp−ˇ(�LV−�SV)2

(6)

here is the constant which does not depend on the kind of theolid and is assumed to be equal to 0.000115 (m2/mJ)2. It appearedhat �SV is not constant and depends on the concentration, compo-ition and kind of ternary mixtures of surfactants (Figs. S64–S69),hereas at the concentration of surfactant mixtures corresponding

o the unsaturated monolayer at the water–air interface [5] andigher than CMC of particular components of the mixtures [19],alues of �SV calculated from Eq. (6) differ insignificantly. Thesealues are somewhat lower than that of the surface tension of PTFE20.24 mN/m) [17]. On the isotherms of PTFE surface tension cal-ulated from Eq. (6) there is observed a wide minimum which isn the range of CMC values of particular components of the mix-ures [19]. It is difficult to understand that the PTFE surface tensionan be decreased to the value of 15 mN/m by the adsorption ofater and/or surfactant molecules on the PTFE surface around the

olution drop settled on the PTFE surface.In the case of PMMA and nylon 6, contrary to PTFE, it is impossi-

le to describe changes of the adhesion tension against the surfaceension of the studied solutions by one linear function (Figs. S70nd S71). The critical surface tension of PMMA and nylon 6 wet-ing determined from this dependence is ranged from 29.90 to1.16 mN/m for PMMA and from 31.02 to 31.50 mN/m for nylon, respectively and practically does not depend on the compositionf ternary mixtures of surfactants. The values of the critical sur-ace tension of PMMA and nylon 6 wetting are considerably lowerhan those of their surface tension (39.21 mN/m and 40.26 mN/m)20,21] and even the Lifshitz–van der Waals component of PMMAnd nylon 6 surface tension (36.66 mN/m and 36.48 mN/m) [13]. Inur earlier considerations [20] the possibility of surfactants to pen-trate into the PMMA surface from the settled solution drop wasather excluded. On the other hand, it should be remembered that athe drop–air interface there are adsorbed surfactant molecules andheir amounts and orientation can be changed after drop attachingo the polymer surface. As a result, the surface tension of PMMAnd nylon 6 can be probably changed under the drop settled on theurface. To obtain the answer to this question we calculated thealues of PMMA and nylon 6 surface tension from the Neumann


t al. equation (Eq. (6)) [18] taking into account the surface tensionf aqueous solutions of CTAB + TX-100 + TX-114 mixtures at differ-nt compositions and their contact angle on the PMMA and nylon

surfaces [5]. Unexpectedly, it appeared that the surface tension

PRESS Science xxx (2013) xxx– xxx 5

of PMMA and nylon 6 calculated in this way depends on the kind,concentration and composition of the surfactants ternary mixtures(Figs. S72–S83).

However, the minimal values of �SV for PMMA and nylon 6 prac-tically do not depend on the kind and composition of the ternarysurfactants mixtures and for PMMA they are in the range from 29.22to 30.66 mN/m and for nylon 6 from 30.59 to 32.45 mN/m, respec-tively. These values are close to the critical surface tension of PMMAand nylon 6 wetting. It is interesting that �SV for PMMA and nylon6 calculated from Eq. (6) for the contact angle of “pure” water isequal to 41.35 and 42.86 mN/m, respectively and is comparable tothe surface tension of these polymers determined by using the vanOss et al. [21,22] approach to the interfacial tension for the contactangle of model liquids. The changes of �SV values for PMMA andnylon 6 calculated from Eq. (6) as a function of the compositionand concentration of the ternary surfactant mixtures suggest thatthe surface layer of the surfactant under the settled drop influencesthe polymer–solution interface tension.

3.3. Adsorption of ternary mixtures of surfactants at thepolymer–solution interface

The reduction of the water surface tension as well as thechanges of the polymer–water interface tension under the adsorp-tion of ternary mixtures of surfactants at the water–air andpolymer–water interfaces plays a main role in the changes of thecontact angle on the polymer surface as a function of the concen-tration and composition of ternary mixtures of surfactants.

As it be seen from Eq. (5) for PTFE the slope of the linear depend-ence between �LV cos � and �LV for all solutions studied is equal to−1. However, in the case of PMMA (Fig. S70) and nylon 6 (Fig. S71),it is impossible to describe this dependence by one linear functionfor all ternary mixtures of surfactants at different compositions.The slope of this dependence is considerably higher than that forPTFE and is in the range from −0.23 to −0.28 for PMMA and from−0.15 to −0.21 for nylon 6.

The slope of the linear dependence between adhesion andsurface tension is directly connected with the adsorption of thesurfactants at the solution–air, polymer–solution and polymer–airinterfaces which can be seen from the Lucassen–Reynders equation[23]. This equation has the form:

d(�LV cos �)d�LV

= �SV − �SL

�LV(7)

where � SL, � LV and � SV are the surface excess concentrations ofthe surface active agents at the solid–solution, solution–air andsolid–air interfaces, respectively.

As follows from this equation it is possible to determine the ratioof (�SV − �SL) to � LV. However, if for aqueous solution of the surfaceactive agents in the total range of their concentration � SV is con-stant, then it is possible to determine � SL knowing � LV. Of course,� SL can be directly determined from the Gibbs isotherm adsorptionequation knowing the changes of �SL as a function of surfactant or


where m is the number depending on the kind of surfactant whichwas assumed to be equal to 1 for Triton’s and 2 for CTAB, R is a gasconstant and T is the temperature.


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If the surface tension of solid is constant in the range of aqueousolution of surfactants or their mixtures then:

i = − Ci

mRT

(∂(− cos ��LV

)∂Ci

)T,nj /= i

= − 12.303mRT

(∂(− cos ��LV

)∂ log Ci

)T,nj /= i

(9)

The calculated maximal values of the Gibbs surface excess con-entration of the ternary surfactants mixtures at the PTFE–solutionnterface are close to those at the solution–air one, but at theMMA–solution and nylon 6–solution interfaces they are lowerhan those at the solution–air ones. Because the maximal Gibbsurface excess concentration is a measure of the effectivenessf surfactants adsorption, we can state that the effectiveness ofdsorption of ternary mixtures is lower than that of single surfac-ants and depends on the composition of ternary mixtures (Figs.84–S86). Probably the effectiveness of adsorption of ternary sur-actant mixtures at the polymer–solution interface depends on theolyoxyethylene chains in the Triton’s molecules which can rollp in a different way. This suggestion is confirmed by the loweralues of maximal surface excess concentration of the studied mix-ures at the nylon 6–solution interface to that of PMMA–solution. It

eans that the minimal area occupied by one molecule at the nylon–water interface is larger than at the PMMA–water one with theame composition of ternary mixtures in the bulk phase. As men-ioned above apart from CO the NH groups are present on theylon 6 surface. The NH group can form the hydrogen bond withhe oxyethylene chains and therefore, the chains are rolled up to amaller degree than at the PMMA–water interface.

The minimal area occupied by one molecule at the interface inach case cannot be proportional to the efficiency of surfactantsdsorption at a given interface. In other words, the effectivenessf surfactant or their mixtures adsorption does not always changen the same way as efficiency of adsorption depending on the kindf surfactant or mixture and their composition. A measure of thefficiency of adsorption is the standard Gibbs free energy of adsorp-ion (�Gads

◦). In the literature it is possible to find many approacheso determine the Gibbs surface free energy of adsorption. Some ofhem are based, for example the Langmuir one, on the adsorptionata corresponding to low concentration of surfactant solutionshich is sometimes difficult to determine. The others e.g. as thatroposed by Rosen are based on the data dealing with the satu-ated monolayer at the solution–air or solid–solution interfaces.he main problem to use these data is whether a monolayer is reallyormed and aggregation process occurs in the layer. It seems thator these reasons the Gu and Zhu isotherm adsorption equation isery useful for �Gads

◦ determination. This equation has the form24,25]:

= �∞KCn

1 + KCn(10)

here � is the Gibbs surface excess concentration of surfactant athe solid–solution interface, � ∞ is the limited Gibbs surface excessoncentration of surfactant at the solid–solution interface, K is thequilibrium constant of the surface aggregation process and n is theverage aggregation number of the surface aggregate.

Eq. (10) can be transformed to the logarithmic form:( )


og�

�∞ − �= log K + n log C (11)

A plot of log[� /(� ∞ − � )] vs. log C permits evaluation of K and when the data give a straight line. When n = 1 then K = 1/a and


Eq. (10) becomes the Langmuir adsorption isotherm equation. Thea constant in the Langmuir equation at 293 K fulfils the condition:

a = 55.4 exp�Gads

◦

RT(12)

For �Gads◦ calculations we used the values of � ∞ taken from

the literature [26].The values of �Gads

◦ calculated from Eq. (12) for thepolymer–solution interface depend on the composition of theternary mixtures (Figs. S87–S89). In the case of PTFE the efficiencyof the adsorption at the PTFE–water and water–air interfaces is sim-ilar but for the PMMA/nylon 6–water interface it is lower than thatat the water–air one. �Gads

◦ of the ternary mixtures adsorption atthe PTFE–water interface does not indicate that there is a synergeticeffect in the efficiency of adsorption of these mixtures compared tothe binary mixture of the surfactant (Figs. S87–S89). However, inthe case of PMMA and nylon 6 there is an evident synergetic effectin the efficiency of the adsorption of ternary surfactant mixture par-ticularly at the CTAB mole fraction in the mixture in the bulk phaseequal to 0.1. The presence of the synergetic effect in the efficiencyof adsorption of ternary mixtures at the PMMA/nylon 6–waterinterface indicates that there is greater influence of the interac-tions between the hydrophilic groups of surfactant with PMMA andnylon 6 surface than that of PTFE. The changes of the efficiency of theternary mixtures adsorption at the PMMA/nylon 6–water interfaceare somewhat different as a function of the mixture composition.This probably results from the presence of different hydrophilicgroups on the PMMA and nylon 6 surfaces [14,15]. The influ-ence of interactions of the hydrophilic groups of surfactant withPMMA and nylon 6 surfaces on their adsorption is confirmed bythe comparison of the efficiency and effectiveness of adsorptionat the polymer–water interface. In the case of PTFE there is pro-portional dependence between the efficiency and effectiveness ofadsorption contrary to PMMA and nylon 6. The mutual influenceof particular components of the mixtures on their adsorption atthe polymer–water interface is different. However, adsorption ofeach surfactant of the mixture depends on the composition of thebinary mixtures. Of course, in all cases the efficiency of adsorptionof a given surfactant decreases with the increase of the concentra-tion of binary mixture. The changes of this efficiency as a functionof the binary mixture concentration are almost linear and the linesare parallel for each studied system. The changes of the efficiency ofCTAB adsorption to the smaller extent depend on the compositionof the binary TX-100 + TX-114 mixture compared to the influenceof the given Tritons adsorption on the composition of CTAB andthe other Triton’s mixtures. Thus, at the mole fraction of CTAB inthe ternary mixture lower than 0.5 its greatest influence on theefficiency of adsorption of ternary mixtures at the polymer–waterinterface is observed. On one hand, it probably results from largerhydrophobic interactions between the tails of CTAB and polymersand on the other hand from possibility of attractive interactionsbetween the hydrophilic parts of CTAB and Tritons. These interac-tions probably cause dehydration of the oxyethylene groups andthe adsorption of pairs of CTAB and each Triton’s molecules ona given surface. It should be reflected in the composition of thesurface layer at the polymer–water interface.

3.4. Composition of the ternary mixed monolayer at thepolymer–water interface


surfactant at the polymer–solution interface (Xi), the values of � iwere used in the following equations:

�0NA0 +∑

�iNAi = 1 (13)


ING Model

A

urface

wm

X

pwa

tpc1ecuodmi

obfot[ctthatiitfgmlcTitoslarif1sfgbmcpHrIiC



here � 0 is the surface concentration of water, A0 and Ai are theinimal surface areas per a molecule of water and surfactant, and:

i = �i∑�i + �0

(14)

The mole fraction of the area occupied by surfactants at theolymer–water interface was calculated in two ways, that is with orithout � 0. Xi calculated in the latter way referred to the part of the

rea occupied by the particular surfactants only in their mixtures.To show the mutual influence of surfactants in the ternary mix-

ure on the adsorption of each component of this mixture at theolymer–air interface, the mole fraction of surfactants at the totaloncentration of the ternary mixture equal to 7.5 × 10−7, 1.5 × 10−6,.5 × 10−5 and 7.5 × 10−5 M and the composition of each surfactantqual to 0.33 in the bulk phase was considered. The studied totaloncentration of the mixture corresponded to the unsaturated, sat-rated monolayer and to the minimal values of the surface tensionf the aqueous solution of the mixture. This mutual influence waseduced by the comparison of the mole fraction of surfactants in theixed monolayer on the assumption that this surfactant adsorbs

ndependently.The composition of the unsaturated and saturated monolayer

f the ternary mixture at the polymer–water interface and theehaviour of the particular surfactant in this monolayer are dif-erent. As mentioned earlier it can be expected that the adsorptionf surfactants can occur through individual adsorption of surfac-ants and the pairs between the nonionic and cationic surfactants6]. It is more probable that at the PTFE–water interface the pairs ofationic and nonionic surfactants are formed because the adsorp-ion of CTAB from the mixture is comparable to its adsorption fromhe single solution. The adsorption of TX-100 from the mixture isigher than from the single solution in the unsaturated monolayernd increases similarly to CTAB with the increase of concentra-ion in solution (Figs. S90–S92). However, the TX-100 adsorptions lower compared to that from the single solution of TX-100. Its in accordance with the behaviour of TX-100 in the binary mix-ure of CTAB and TX-100 [6]. In the case of TX-114 its adsorptionrom the ternary mixture of surfactants is lower than from the sin-le solution, however, only in the range of concentration of theixture in the bulk phase corresponding to the unsaturated mono-

ayer at the water–air interface. At the concentration of the mixtureorresponding to the saturated monolayer, the mole fraction ofX-114 is higher than in its single solution (Fig. S91). However,t should be mentioned that the maximal surface excess concen-ration of surfactants in the ternary mixtures is smaller than thatf single solutions (Figs. S84–S86) [26]. It means that the maximalurface excess concentration of TX-114 in the mixed monolayer isower than in the single monolayer. Thus, we can state that thedsorption of TX-114 at the concentration of ternary mixtures cor-esponding to the saturated monolayer at the water–air interfaces inhibited to a smaller degree in comparison with the adsorptionrom the single solution. Different behaviour of TX-114 and TX-00 in the ternary mixed monolayer at the PTFE–water interfacehould result from different interactions between TX-100 and CTABrom those of TX-114 and CTAB hydrophilic groups. Some investi-ators [27,28] stated that each oxyethylene group can be hydratedy two or more molecules of water. Additionally, most of waterolecules can be mechanically trapped in the polyoxyethylene

hains of nonionic surfactants, with 5.2 to 10.5 water moleculeser oxyethylene unit [29]. The other investigators stated that the3O+ ions are adsorbed on the oxyethylene groups and for these


easons TX-100 and TX-114 behave as cationic surfactants [1].n such a case the counterion of the cationic surfactant shouldnfluence on the interactions between the hydrophilic groups ofTAB and TX-100/TX-114 as suggested in the literature [30]. This


influence can result also from the possibility of strong electrostaticion–dipol interactions between the hydrophilic groups of CTAB andTX-100/TX-114. Because TX-100 differs from TX-114 only by thenumber of the oxyethylene groups it seems that the interactionsbetween CTAB and the hydrophilic groups of TX-100 are higherthan those of CTAB and TX-114. Therefore, it is more probable thatat the concentration of the surfactant corresponding to the satu-rated mixed monolayer the adsorption of the pairs of CTAB–TX-100molecules is more probable than that of CTAB–TX-114 one andtherefore the TX-100 adsorption is inhibited to a larger degree thanthat of TX-114. So, the adsorption of each surfactant in the pair isdifferent from that in the single solution.

Considering the composition of the saturated mixed monolayerat the PTFE–water interface, it can be stated that it does not practi-cally depend on the concentration of the ternary mixture in the bulkphase corresponding to this monolayer. However, the area occu-pied by the Tritons molecules in the saturated monolayer decreaseswith the increase of the mixture concentration in the bulk phase.

The behaviour of the ternary mixtures of surfactants at thePMMA–water and nylon 6–water interfaces is somewhat differentfrom that at the PTFE–water one. However, in all cases the contentof TX-114 in the mixed monolayer is the largest and that of CTAB isthe smallest (Figs. S90–S92). It should be also stressed that in thesaturated monolayer at the polymer–water interface the mole frac-tion of TX-114 is higher than in the hypothetical mixtures when thesurfactant adsorbs independently. However, the surface area occu-pied by one molecule for each surfactant is considerably lower thanin the case of the single solution. On the basis of the composition ofthe adsorbed monolayer at the PMMA/nylon 6–water interface it isdifficult to determine the influence of the particular polar groups onthe surface on the composition of the monolayer as it was found inthe case of the efficiency of the adsorption process at these inter-faces because the composition of the monolayer is not related tothe area occupied by one molecule at the interface.

3.5. The work of adhesion of aqueous solutions of ternarymixtures of surfactants to the polymer surface

To explain the effect of the mixed adsorbed surfactants layer onsurface properties of the studied polymers, the work of adhesionof aqueous solutions of these mixtures to the polymer surface wascalculated.

According to the thermodynamic rules, the work of liquid adhe-sion to the solid surface (Wa) fulfils the condition [31]:

Wa = �SV + �LV − �SL (15)

where �SV, �LV and �SL are the solid–air, liquid–air and solid–liquidinterface tension.

If the contact angle of the liquid on the solid surface fulfils theYoung equation (1) then the work of adhesion of liquid to the solidsurface can be determined from the Young–Dupre equation, whichhas the form [31]:

Wa = �LV(

cos � + 1)

(16)

In the case of PTFE, as mentioned above, there is one lineardependence between the adhesion and surface tension of the aque-ous solutions of ternary mixtures of surfactants whose slope isequal to −1 (Fig. S63). If so, then from Eqs. (15) and (16) it resultsthat:

�LV cos � = −�LV + Wa (17)


Eq. (17) can be rewritten in the following form:

cos � = −1 + Wa1

�LV(18)


ARTICLE ING Model


8 K. Szymczyk et al. / Applied Surface

Fig. 10. A plot of work of adhesion (Wa) of aqueous solutions of TX-100 + TX-1fb

dsioettslttcticwapa

F1fb

14 + CTAB mixtures to PMMA surface calculated from Eq. (16) (points 1–5) androm Eq. (21) (dash lines 1′–5′) vs. logarithm of total concentration of mixture in theulk phase (C123) at the mole fraction of TX-114 equal to 0.5.

On the basis of Eq. (18) we can state that if there is a linearependence between cos � and the reciprocal of the surface ten-ion of these solutions (Fig. S63) and this line crosses the cos � axisn −1 then the slope of this linear dependence is equal to the workf adhesion of this solution to the given solid. In the case of PTFExists one such dependence which does not depend on the concen-ration and composition of the studied solutions. The constant inhe linear equation describing the dependence between the adhe-ion and surface tension (46.55 mJ/m2) is close to the slope of theinear dependence between cos � and the reciprocal of the surfaceension (46.46 mJ/m2). Thus, the work of adhesion of these solu-ions to the PTFE surface does not depend on the concentration andomposition of aqueous solutions of CTAB + TX-100 + TX-114 mix-ures. It was explained earlier that the constant value of Wa for PTFEs not a general rule but results from similar work of adhesion of theomponents of the studied solutions to the PTFE surface [10]. Theork of adhesion of aqueous solutions of ternary mixtures to PMMA


nd nylon 6 surface calculated from Eq. (16) depends on the com-osition of the mixtures and their concentration (Figs. 10 and 11nd Figs. S93–S102).

ig. 11. A plot of work of adhesion (Wa) of aqueous solutions of TX-100 + TX-14 + CTAB mixtures to nylon 6 surface calculated from Eq. (16) (points 1–5) androm Eq. (21) (dash lines 1′–5′) vs. logarithm of total concentration of mixture in theulk phase (C123) at the mole fraction of TX-114 equal to 0.5.


The work of adhesion of liquid to solid surface can be also calcu-lated on the basis of van Oss et al. [22,23] approach to the interfacialtension. According to this approach the work of adhesion can beexpressed by the following equation [21]:

Wa = 2

(√�LW

S �LWL +

√�+

S �−L +√

�−S �+

L

)(19)

where the subscripts S and L refer to the solid and liquid, LW to theLifshitz–van der Waals component of the solid or liquid surface ten-sion and “+” and “–” to the electron-acceptor and electron-donorparameters of the acid–base component of the solid or liquid sur-face tension, respectively.

In the case when the adsorbed surface layer at the solid–liquidinterface can be formed then according to the Schrader suggestion[32] Eq. (15) assumes the form:

Wa = �LV + �SV − �SL − �e (20)

where �e is the pressure of the adsorbed layer at the solid–liquidinterface.

It means that if we detach the drop of solution settled on thesolid surface, then the surface tension of solid will be not �S but�S − �e. Taking into account Eqs. (19) and (20) we obtain:

Wa = 2

(√�LW

S �LWL +

√�+

S �−L +√

�−S �+

L

)− �e (21)

Because the interactions of water molecules with the PMMA andnylon 6 surface play an important role thus, for the Wa calculation itwas assumed at the first approximation that the electron-acceptorand electron-donor parameters of the acid–base component of thesurface tension of the studied aqueous solutions are similar. Forthese calculations the values of the components and parametersof PMMA and nylon 6 surface tension were taken from literature[10,13]. Taking into account the fact that the work of adhesion ofthe aqueous solution of ternary mixtures to the PTFE surface is con-stant we assumed that the Lifshitz–van der Waals component of thestudied solutions is constant and equal to that of water (21.8 mN/m)[33]. The values of �e used for Wa calculations in Eq. (21) werededuced on the basis of �SV values determined from Eq. (6). Weassumed that these values correspond to the surface tension ofPMMA and nylon 6 with the adsorbed film under the drop settled ontheir surface. Thus, �e equal to the difference between the surfacetension of PMMA or nylon 6 surface calculated from Eq. (6) usingthe water contact angle, and the surface tension corresponds to agiven concentration of the ternary surfactant mixtures. It appearedthat the values of Wa for �LW

L = 21.8 mN/m calculated from Eq. (21)are very close to those determined from the Young–Dupre equation(Eq. (16)) [31]. Thus, it confirms that probably the values of PMMAand nylon 6 surface tension calculated from the Neumann et al.equation (Eq. (6)) [18] deal with the surface tension of PMMA andnylon 6 under the solution drop settled on their surface and do notprove that a surfactants adsorbed layer is formed around the drop.

4. Conclusions

The results reported in this paper showed that the synergeticeffect in the reduction of the contact angle of water on the PTFE,PMMA and nylon 6 surfaces takes place in the presence of the TX-100 + TX-114 and CTAB mixtures in the range of their concentrationfrom 0 to that corresponding to the minimal contact angle. Thiseffect was confirmed by the standard Gibbs surface free energy ofadsorption determined on the basis of the Gu and Zhu adsorption


isotherm. The changes of the contact angle of all solutions studiedon the PTFE surface against the PTFE–solution and/or solution–airinterface tensions can be described by one second order polynomialfunction and against the sum of logarithm of the solution surface


ING Model

A

urface

ttc

ihbnsi

tcPt

stoHttest

s6e

A

He

A

fj

R

[

[

[

[

[

[

[

[

[

[

[

[[

[

[

[

[

[

[[[[



ension and the PTFE–solution interface tension by the linear equa-ion. In the case of PMMA and nylon 6 these changes depend on theomposition of ternary mixture of surfactants.

The composition of the mixed monolayer at the PTFE–waternterface is somewhat different from that at the water–air one,owever, the surface excess concentration is almost the same atoth interfaces. In the case of the systems including PMMA andylon 6 the surface excess concentration of the ternary mixture ofurfactants and its composition at the polymer–solution interfaces considerably different from that at the solution–air one.

The critical surface tension of PTFE wetting by the aqueous solu-ions of TX-100 + TX-114 + CTAB mixtures does not depend on theomposition and is somewhat higher than the surface tension ofTFE determined from the contact angles of n-alkanes and is closeo that determined from the contact angle of other liquids.

The critical surface tension of PMMA and nylon 6 wetting by thetudied solutions is considerably lower than the surface tension ofhese polymers and even the Lifshitz–van der Waals componentsf this tension determined from the contact angle of model liquids.owever, the critical surface tension of these polymers is close to

heir surface tension calculated from the contact angles for the solu-ions of ternary mixtures at high concentration using the Neumannt al. equation. Contrary to PMMA and nylon 6 the work of adhe-ion of studied solutions to the PTFE surface does not depend onhe composition and concentration of the solutions.

It is possible to determine the work of adhesion of aqueousolutions of ternary surfactants mixture to the PMMA and nylon

surfaces on the basis of the van Oss et al. and Neumann et al.quations.

cknowledgment

The financial support from the Polish Ministry of Science andigher Education, Project No. N N204 352040 is gratefully acknowl-dged.

ppendix A. Supplementary data

Supplementary data associated with this article can beound, in the online version, at http://dx.doi.org/10.1016/.apsusc.2013.10.059.

eferences

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