Correlation between the Adsorption of the Fluorocarbon Surfactants at

Nov 16, 2012 - Correlation between the Adsorption of the Fluorocarbon Surfactants at the Polymer–Solution and Solution–Air Interfaces and the Para...
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Correlation between the Adsorption of the Fluorocarbon Surfactants at the Polymer−Solution and Solution−Air Interfaces and the Parameter of the Interfacial Interaction Katarzyna Szymczyk* Department of Interfacial Phenomena, Faculty of Chemistry, Maria Curie-Skłodowska University, Maria Curie-Skłodowska Sq. 3, 20-031 Lublin, Poland S Supporting Information *

ABSTRACT: Using the literature data of the surface tension and contact angle of the fluorocarbon surfactants Zonyl FSN-100 (FSO100) and Zonyl FSO-100 (FSO100) on polytetrafluoroethylene (PTFE) and polymethyl methacrylate (PMMA), the values of the interfacial tension at the PTFE/PMMA−solution interface were calculated. Because of the possibility of the existence of the surfactant film on the PMMA surface, these calculations for PMMA were performed in two ways, that is with the assumption that the surface tension of PMMA is constant and that it is changed proportionally to the values of the surface tension of aqueous solution of surfactants. Next, the values of the Gibbs surface excess concentration, activity, and monomer mole fraction of the studied surfactants at the PTFE/PMMA−solution interface were determined and correlated with the Lucassen-Reynders equation. Also the values of the parameter of the interfacial interaction were calculated on the basis of the Girifalco and Good and Neumann et al. approaches.

1. INTRODUCTION The important ability of surfactants to promote wetting of solids has been studied extensively and technologically for decades.1−6 The wettability of the surface of solids depends on the surface tension of solid and liquid as well as solid−liquid interfacial tension. The amount of the adsorbed surfactants at the solid−air, water−air, and solid−water interfaces, and the orientation of their molecules in the surface layers change the values of these tensions making more or less wetting of the surface a given solid. In the case when the surfactants can interact with the solid surface or penetrate a solid, the changes of the solid surface tension by chemisorptions or absorption, which depend on the concentration of surfactants, strongly influence the wettability of the solid.1,7 Adsorption of nonionic hydrocarbon surfactants at different interfaces has been studied for many years due to its industrial relevance.7−9 These uncharged compounds play an important role in many technological processes such as detergency, flotation, paint, lubrication, and enhanced oil recovery. On the other hand, the behavior of the fluorocarbon nonionic surfactant solutions has been scarcely investigated so far in spite of considerable interest in the physicochemical properties of surface active fluorocarbon derivatives.10−14 This interest has increased further since fluorocarbon-based emulsions have been proposed and approved as the first artificial injectable oxygentransport fluid for human use.10,11 In order to improve stability and oxygen carrying as well as delivering ability of the emulsions and to achieve better clinical efficacy and biological acceptance, the development of new surfactants is a focal point.15,16 There is, therefore theoretical and practical interest in carefully characterizing the properties of these highly surface active compounds. Also the wetting behavior of fluorocarbon surfactants, as well as their stability in harsh thermal or chemical environments, makes them useful in industrial applications © 2012 American Chemical Society

including for example paints, coatings, polymer technology, metal working and uranium recovery. However, the process of wetting of polymeric solids like polytetrafluoroethylene (PTFE) and polymethyl methacrylate (PMMA) with aqueous solutions of fluorocarbon surfactants has not been solved completely yet and it is difficult to find the relationship between the concentration of the surfactants at the surface layer at the water−air and polymer−water interfaces in the thermodynamic equilibrium state and the work of solution adhesion to the polymer surface or cohesion which influences the wettability of these polymers.3,17−19 This relationship for smooth and flat surfaces is commonly determined by plotting the adhesion tension (γLV cos θ) against the surface tension (γLV).20 In earlier studies, it was proved that the relationship between these tensions for different kinds of hydrocarbon surfactants and their binary mixtures is linear for PTFE and PMMA, but the slope of this relationship is equal to −1 for PTFE and is higher than −1 for PMMA.21,22 In the case of aqueous solution of classical surfactants for which the Gibbs surface excess concentration at the water−air and polymer− water interfaces is practically equal to the total concentration, it is possible to determine the relative adsorption at the polymer− water interface compared to that of at the water−air one from the Lucassen-Reynders equation.23 If the slope of the plot of the adhesion tension versus the surface tension is equal to −1, it means that the concentration of the surface active agents at the water−air and polymer−water interfaces is the same. In the previous paper24 dealing with wettability of PTFE and PMMA by the aqueous solution of the fluorocarbon nonionic Received: Revised: Accepted: Published: 15601

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where γSV is the solid surface tension and θ is the contact angle. For the calculation of γSL, the relationship between the solid−liquid interfacial tension and the solid and liquid surface tension should be known. In the literature, there are two basic approaches to this problem. The first is based on the assumption that the solid−liquid and liquid−liquid interfacial tension is a function of components or components and parameters of the surface tension of phases being in contact.3,26 The second approach represented by Neumann et al.27−29 is based on the assumption that the solid−liquid interfacial tension is a function of solid and liquid surface tension. Both basic approaches took into account the parameter of interphase interaction proposed by Rayleigh30 and next theoretically derived by Good et al.31,32 Fowkes3,26 assumed that this parameter is equal to unity if across the solid−liquid (or liquid−liquid) interface the dispersion forces are interacting. However, van Oss et al.6,33,34 assume this parameter as equal unity if across the interface only the interactions by Lifshitz− van der Waals forces take place. Such case takes place if the surface tension of solid and/or liquid results only from the dispersion intermolecular interactions according to Fowkes or Lifshitz−van der Waals ones as suggested van Oss et al. If the solid surface tension results from the dispersion (γdLV) or the Lifshitz−van der Waals (γLW LV ) intermolecular interactions only then its surface tension can be calculated from the following equations:

surfactants, Zonyl FSN-100 (FSN100) and FSO-100 (FSO100) in the thermodynamic equilibrium state, it was shown that at their concentrations corresponding to the unsaturated monolayer at the water−air interface, the constants in the relationship between the adhesion and the surface tension for the PTFE surface are higher than −1, but considerably smaller at a higher concentration. This means that the behavior of fluorocarbon surfactants in the surface layer at the PTFE−solution interface is quite different from that of the hydrocarbon surfactants, and in such case adsorption at this interface is not the same as at the water−air interface, like the structure of the surface layer. It is interesting that in the case of PMMA the relationships between γLV cos θ and γLV have positive slopes. According to the Lucassen−Reynders equation,23 these positive slopes indicate that PMMA wetting is impaired by the solutions of FSN100 and FSO100, and perfluoroalkyl surfactant chains are much poorer wetting agents than the hydrocarbon one. On the other hand, these positive slopes of the curves indicate that the Gibbs surface excess concentration of surfactants at the PMMA−air interface (ΓSV) is higher than zero and that of the Gibbs surface excess concentration of the surfactants at the PMMA−water interface (ΓSL) or that ΓSL < 0. If we assume that ΓSV is higher than zero, we must take into account the fact that there is motion of the surfactant molecules from the droplet on the solid surface or the diffusion of surfactant molecules to the surface layer. From this point of view, based on the values of contact angles and surface tension discussed in the previous paper,24 it was interesting to consider in more detail the adsorption of the fluorocarbon surfactants, FSN100 and FSO100, at the polymer−water interface in comparison to their adsorption at the water−air interface. These considerations were based on the Gibbs equation of the isotherm of adsorption which allowed to determine the Gibbs surface excess concentrations of surfactants in the monolayer at the polymer−water interface and to use them in the Lucassen-Reynders equation23 and the Sprow and Prausnitz25 equation to determine the activity of surfactants at interfaces. Also the values of surface tension of the PTFE and PMMA surfaces determined in different ways allowed to calculate the PTFE/PMMA−solution interfacial tension and next the parameter of the interfacial interaction, ϕ.

γSV =

γSV =

RT dC

=−

[γLV(cos θ + 1)]2 LW 4γLV

(4)

LW LW γLV(cos θ + 1) = 2( γLV γSV +

+ − γLV γSV +

− + γLV γSV )

(5)

For this purpose, the contact angle values for water, glycerol, formamide ethylene glycol, and diiodomethane were used (Supporting Information Table S1). On the basis of the detailed studies dealing with the PMMA surface tension and its components, they found out that the Lifshitz−van der Waals component γLW SV = 36.68, the electron-acceptor parameter of the acid−base component γ+SV = 0.16, the electron-donor parameter of the acid−base component γ−SV = 10.02, and the surface tension γSV = 39.21 mN/m, respectively.36 Knowing the values of the surface tension of PTFE and PMMA determined in this way, it is possible to determine the PTFE−liquid and PMMA−liquid interfacial tension from eq 2.

dγSL 1 dγSL 1 =− RT d ln C 2.303RT d log C (1b)

where C represents the concentration of surfactant, γLV is the surface tension, and γSL is the solid−solution interfacial tension and can be calculated, among others, from the Young equation:1,7 γSL = γSV − γLV cos θ

(3)

According to Fowkes, PTFE can be treated as a solid whose surface tension results only from dispersion of intermolecular interactions. Taking this fact into account and the values of the contact angle of n-alkanes from n-hexane to n-hexadecane, Jańczuk et al.35 calculated the dispersion component of PTFE surface tension (eq 3). The average value of this component was equal to 20.24 mN/m35 and was equal that calculated from eq 4. Because the surface tension of PMMA results from the apolar and polar intermolecular interactions,3 the PMMA surface tension as well as components and parameters of this tension were determined, among others by Jańczuk et al.36 from the equation:

(1a)

C dγSL

d 4γLV

3,26

2. CALCULATIONS The Gibbs surface excess concentration of the surfactants at the water−air and polymer−water interface can be determined on the basis of the adsorption isotherms using the Gibbs equation (1). For the dilute solution (10−2 mol/dm3 or less) containing the nonionic surfactant the Gibbs equation can be written in the form: C dγLV dγLV 1 dγLV 1 Γ SLV = − =− =− RT dC RT d ln C 2.303RT d log C Γ SSL = −

[γLV(cos θ + 1)]2

(2) 15602

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In turn, Neumann et al.27−29 analyzing the contact angles of different liquids on the polymers measured by Zisman et al.18,19 showed that there is the linear dependence between the parameter of interphase interaction and the polymer−liquid interfacial tension, and based on this, they proposed the equation of state which was modified by them.27−29 Taking into account this approach to the interfacial tension in Young equation (eq 2), they obtained the following relation: cos θ = −1 + 2

γSV γLV

interface to that in the bulk phase, molar surface area, and polymer−solution interfacial tension. However, it should be taken into account that the activity of a given component of solution can be defined in two different ways: symmetrical (a) and asymmetrical (a*). Thus, a for the solvent and the solute approaches unity if x → 1 (x is the molar fraction of solvent or solute) and a* = x for the solvent when x → 1 but for the solute when x → 0. In the case of aqueous solutions of surfactant, the dependence between its surface tension and the activity of water and surfactant in the surface layer and the bulk phase can be expressed, among others by the Sprow and Prausnitz equation25 which for the polymer−solution interface assumes the following forms:

2

e−β(γLV − γSV)

(6)

where β is the constant equal to 0.000 15. On the basis of eq 6, it is possible to calculate the values of γSV knowing the values of γLV and θ. Taking into account the same values of contact angle as were used in the Fowkes3,26 and van Oss et al. approach,6,33,34 the PTFE and PMMA surface tension was calculated. In the case of PTFE the calculated values of γSV for the series of n-alkanes are in the range of 19.96−20.57 mN/m. Unfortunately, the surface tension of PMMA depends on the kind of liquid whose contact angle was used for calculation and is in the range 35.74−42.30 mN/m. Taking into account the surface tension of PTFE and PMMA calculated in this way, it is also possible to determine the PTFE−liquid and PMMA−liquid interfacial tension and then the Gibbs surface excess concentration of a given surfactant at these interfaces, ΓSLV and ΓSSL. On the basis of the values of ΓSSL at the polymer−solution interface which is practically equal to the total concentration at this interface, it is possible to calculate the composition of surface layer, namely the mole fraction of surfactant 1 (XS) forming 1 m2 surface plane using the following equations:37 W ΓSL NAoW + Γ SSLNAoS = 1

XS =

γSL = γSW +

γSL = γSS +

γSL = γSW +

γSL = γSS +

(11)

a *S RT ln WB * ωW aW S RT aS* ln B ωS aS*

(12)

(13)

where γSW is the polymer−water interfacial tension, γSS is the polymer−surfactant interfacial tension, ωW is the molar area of water at the polymer−solution interface, ωS is the molar area of surfactant at the polymer−solution interface, aSW and aBW or aW *S B and aW * are the activity of water in the surface layer and bulk phase, and aSS and aBS or a*S S and a*WB are the activity of surfactant in the surface layer and bulk phase, respectively. It is known that the polymer−surfactant interfacial tension depends on the orientation of the surfactant molecules at the interfaces, and therefore, it is difficult to determine it by using the surface tension data of surfactants different for tails and heads and polymer surface tension.33,34,41 Thus, it is difficult to apply eqs 11 or 13 for determination of the surfactant activity in the surface layer, knowing its activity in the bulk phase. It is known that ∑αi=1 aI = 1 if symmetrical definition of the activity is considered. In this case the activity of surfactant can be determined on the basis of eq 10. As the adsorption process of the surfactant at the polymer−solution interface was considered for the dilute solution at the first approximation, it can be assumed that the activity of surfactants in the bulk phase is very small and that of water is close to unity. In such a case eq 10 can be expressed as

(8)

where ΓW SL is the Gibbs surface excess concentration of water at the polymer−solution interface, ΓSSL is the Gibbs surface excess concentration of surfactant at the polymer−solution interface, N is the Avogadro number, AW o is the minimal possible area occupied by water molecules at the interface, and ASo is the minimal possible area occupied by surfactant molecules at the polymer−solution interface. AW o is commonly assumed on the basis of adsorption data as equal to 10 Å2, but it is possible to determine ASo, among others, from the Joos equation of state38 which for the aqueous solutions of surfactants can be written in the form:

γLV, Γ∞ W

aS RT ln SB ωS aS

or

Γ SSL

⎛ −Π ⎞ C ⎛ −Π ⎞ exp⎜ =1 ∞ ⎟ + exp⎜ ∞⎟ ⎝ RT Γ W ⎠ ⎝ RT Γ S ⎠ aS

(10)

and

(7)

W ΓSL + Γ SSL

aS RT ln W B ωW aW

(9)

Γ∞ S

where Π = γW − and are the maximal possible Gibbs surface excess concentration of water and surfactant at 0B 0S the interface, respectively, and aS = exp[(μ0S S − μS )/RT]ω (μS and μ0B are the standard potentials of surfactant in the surface S layer and bulk phase, γW is the surface tension of water at 293 K). The calculated values of mole fraction of surfactants at the polymer−solution interface contrary to the bulk phase cannot be equal to their activity. According to the definition of the chemical potential39,40 of ith component of solution, there is the relationship between the ratio of this potential in the surface layer at the solid−solution

γSL = γSW +

RT S ln aW ωW

(14)

From this equation, it is possible to determine the activity of water in the surface region at the polymer−solution interface and next evaluate the activity of surfactant at this interface: S aSS = 1 − aW

(15)

For smooth solids combining the Gibbs adsorption equation with that of Young’s Lucassen-Reynders,23 the relationship is derived between the Gibbs surface excess concentration of 15603

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the shape of the PTFE−solution interfacial tension isotherms for the studied fluorocarbon surfactants is quite different from those for the systems including hydrocarbon surfactants,21 as well as the isotherms of surface tension of aqueous solutions and contact angle on the PTFE surface.24 The values of γSL decrease even at the concentrations higher than those of critical micelle concentration (CMC) of the surfactants determined from the surface tension measurements (CMC FSN100 = 6.88 × 10−5, CMC FSO100 = 9.37 × 10−5 M).24,42 These differences for the values of γSL calculated on the assumption that γSV is constant were explained on the basis of the van Oss at al. approach6,33,34 to the interfacial tension and calculation of the Lifshitz−van der Waals component of the surface tension, LW γLW LV . Because on the curves of γLV −log C, there was a minimum at the concentration equal to 5.01 × 10−5 and 7.77 × 10−5 M for FSN100 and FSO100, respectively, and the values of γLW LV corresponding to this minimum were lower than the surface tension of the hydrophobic groups of the surfactants mentioned above, it was concluded that the surface tension of PTFE is changed as a function of surfactants concentration, and/or the film pressure is not equal to zero and depends on the surfactant concentration.24 It is interesting that at the same concentration 24 where there was a minimum on the γLW there LV −log C curves, is also a minimum on the γSV−log C curves if the values of γSV were calculated from eq 6 (Supporting Information Figure S1), and these values of γSV are close to those of γLW LV for a given concentration in the bulk phase. Also at the concentrations close to these minima, there is an intersection point in the relationship between the adhesion and surface tension (Figure 1, curves 5 and 6) and the slope of the γLV cos θ−γLV curves at the concentration corresponding to the unsaturated monolayer at the water−air interface24 is equal to −0.5, contrary to the nonionic hydrocarbon surfactants, TX100 and TX165, having a similar number of oxyethylene oxide groups, for which the slope of γLV cos θ−γLV curves is close to −1 (Figure 1, curves 7 and 8). According to eq 16, this means that the Gibbs surface excess concentration of the studied fluorocarbon surfactants at the solution−air interface is different from that of the PTFE− solution one. This conclusion is confirmed by the values of the surfactant Gibbs surface excess concentration calculated from eqs 1a or 1b (Supporting Information Figure S2). Also the average value of the ratio of ΓSL to ΓLV for a given concentration of FSN100 and FSO100 is equal to 0.48 which confirms that for PTFE and the studied surfactants ΓSV ≈ 0. Because the values of ΓSL and ΓLV for a given surfactant are different, the mole fraction of the surfactants at the PTFE− solution interface calculated from eq 8 is also different from that at the solution−air interface (Supporting Information Figure S3). The minimal surface area per molecule of the surfactant at both interfaces is also different for a given surfactant, that is ASo for FSN100 and FSO100 at the water−air interface is equal to 33.95 and 30.91 Å2, and 44.96 and 43.55 Å2 at the PTFE−solution one, respectively. It can be expected that the activity of the surfactant at a given concentration in the bulk phase can not be the same at the polymer−solution interface in comparison to that at the solution−air interface. The calculated values of activity (Supporting Information Figure S3) confirm this suggestion, and additionally, these values increase with the concentrations corresponding to the saturated monolayer at the water−air interface, where the values of the mole fraction of FSN100 and FSO100 are constants. These changes suggest that the specific interaction between the surfactant molecules, their molecules with water, and the PTFE surface takes place. The

surface active agents at the solid−solution (ΓSL), solution−air (ΓLV), and solid−air (ΓSV) interfaces, and the differential of adhesion tension (γLV cos θ) with respect to the surface tension of solution (γLV), which has the form: d(γLV cos θ ) dγLV

=

ΓSV − ΓSL ΓLV

(16)

where θ is the contact angle in the solid-solution drop-air system. The slope of the plot of γLV cos θ versus γLV consequently provides information about the surfactant excess concentrations at the three interfaces.23 It is possible to obtain the linear or nonlinear dependence between the adhesion and surface tension.31 The slope of the plot γLV cos θ vs γLV can be positive or negative. Generally, plotting γLV cos θ vs γLV, it is possible to determine the ratio of (ΓSV − ΓSL) to ΓLV, but if ΓSV ≈ zero that of ΓSL to ΓLV. When the slope of γLV cos θ−γLV curve is equal to −1, it means that for ΓSV ≈ zero the surface excess of surfactant concentration at the solution−air interface is equal to that of the solid−solution one. Thus, analyzing eq 16 gives a possibility to determine only the ratio of (ΓSV − ΓSL)/ ΓLV or ΓSL/ΓLV if ΓSV = 0. Knowing the values of γLV, γSL, γSV, and θ, on the basis of the Girifalco and Good approach31,32 to the interfacial tension and the Young equation (eq 2), it is possible to calculate the parameter of the interfacial interaction, ϕ, from the relation: ϕ=

γLV(cos θ + 1) 2 γSVγLV

(17)

3. DISCUSSION PTFE. The values of the PTFE−solution interfacial tension, γSL, (Figure 1, curves 1 and 2) calculated from eq 2 with the assumption that the surface tension of PTFE, γSV, is constant and equal to 20.24 mN/m and on the basis of the values of γSV calculated from eq 6 (Figure 1, curves 3 and 4), indicate that

Figure 1. Dependence of the values of interfacial tension, γSL, at the PTFE−solution interface calculated for γSV = 20.24 mN/m (curves 1 and 2) and from the Neumann approach (curves 3 and 4) for FSN100 (curves 1 and 3) and FSO100 (curves 2 and 4), respectively, on log C (C represents the concentration of FSN100 and FSO100), and γLV cos θ on the surface tension (γLV) of FSN100 (curve 5), FSO100 (curve 6), TX100 (curve 7), and TX165 (curve 8). 15604

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of the probe liquid. This means that as the molecular size increases, the contribution of dispersion interactions to the total intermolecular forces increases. The ϕ−γSL curves for FSN100 and FSO100 (Figure 2, curves 1 and 2) (γSL calculated from eq 2 on the assumption that the surface tension of PTFE, γSV, is constant and equal to 20.24 mN/m) can be divided into two linear parts. The constants of these parts are presented in Table 1. The minimal values of the

confirmation of this suggestion are the values of the parameter of the interfacial interaction, ϕ, which are calculated from eq 17 and are presented as a function of PTFE−solution interfacial tension (γSL) (Figure 2). It appears that there is no one linear

Table 1. Slopes and Intercepts for the ϕ = f(γSL) Straight Relationships for FSN100 and FSO100 on PTFE (γSV = 20.24 mN/m) ϕ = A + BγSL FSN100

FSO100

A

B

A

B

0.110 0.973

0.011 −0.019

0.054 0.1000

0.012 −0.024

ϕ parameter are equal to 0.417 and 0.368 for FSN100 and FSO100, respectively, and correspond to the concentration in the bulk phase equal to 3.74 × 10−5 and 7.93 × 10−5 M. These concentrations are close to those with the minimum on the 24 γLW LV −log C and Wa−log C curves and also to the minimum of the values of the PTFE surface tension determined on the basis of the contact angle of water, formamide, and diodomethane measured on the FSN100 and FSO100 films formed during 1 min.44 It is worth emphasizing that the values of ϕ for FSN100 and FSO100 in the studied concentration range are smaller not only than those of the intermolecular interaction parameter for hydrocarbon TX100 and TX165 (Figure 2, curves 5 and 6) but also than the values of this parameter for n-alkanes (ϕ close to 1) and different kinds of liquids (Supporting Information Table S1) on the PTFE surface.32,45,46 At the concentrations corresponding to the saturated monolayer of the fluorocarbon surfactants at the water−air interface24 and close do CMC, the values of ϕ are also smaller than those for water (0.593). On the other hand, the values of ϕ parameter calculated from eq 6 for FSN100 and FSO100 are much greater not only than those determined on the basis of the constant value of the PTFE surface tension but also than the values of ϕ for TX100 and TX165 (Figure 2, curves 3 and 4). It is interesting that Girifalco and Good32 at the water− perfluorodibutyl ether interface at 293 K estimated one of the lowest values of the molecular interaction parameter among a large number of studied different liquids, but this value equal to 0.55 was only slightly smaller than ϕ for water. On the other hand, Gardon47 stated that the ϕ parameter can be greater than unity only if the two phases are partially miscible, otherwise ϕ ≤ 1. For completely immiscible phases, it is a product of two components: ϕ = ϕIϕV where ϕV is unity if the molar volumes of the two components are the same. The value of ϕI depends on the nature of the interaction forces at two phases. If the two liquids are of different polarity, ϕI is less than unity, but for the extreme case of the interfacial free energy between water and nonpolar organic liquids the lowest value of ϕI is about 0.5.47 So, the values of ϕ presented in Figure 2 for aqueous solutions of FSN100 and FSO100 calculated with the assumption that the surface tension of PTFE is constant and equal to 20.24 mN/m and also from the Neumann equation (eq 6) are not real and suggest that this tension is changed as a function of surfactants concentration and that molecules of surfactants can penetrate into the PTFE surface and introduce oxyethylene

Figure 2. Dependence of the values of the interaction parameter across the PTFE−solution interface (ϕ) calculated for γSV = 20.24 mN/m (FSN100-curve 1, FSO100-curve 2, TX100-curve 5, TX165curve 6), from the Neumann approach (FSN100-curve 3, FSO100curve 4), and for FSN100 (curves 7 and 8) and FSO100 (curves 9 and 10) in different fractions of tails in the contactable area on the PTFE− solution interfacial tension (γSL) calculated from eq 2.

dependence between the ϕ parameter and γSL calculated for γSV = 20.24 mN/m for the studied fluorocarbon surfactants contrary to the belief by Neumann et al.27−29 who obtained the linear dependence for nine polymers on the surface of which the contact angle was measured by Zisman et al.18,19 only for “pure” liquids. For this linear relationship (ϕ = A + BγSL), Neumann obtained the value of A as equal to 1 and B as equal to −0.0075.27 It is interesting that for the values of γSL calculated on the basis of the values of the surface tension of PTFE determined from the Neumann equation (eq 6), there is the linear relationship between the ϕ parameter and γSL, and the constants A and B in this relationship are equal to 1.0035 and −0.0085, respectively. On the other hand, in the case of TX100 and TX165 (Figure 2, curves 5 and 6) and other hydrocarbon surfactants,21 the curves ϕ−γSL, at the first approximation, can be described by one exponential equation and the values of ϕ at the PTFE− solution interface increase as the interfacial tension decreases. In the literature, it can be found that ϕ is different from 1 when the specific interactions occurred within the liquid or solid phase, but not across the interface.31,32 These interactions include, among others, hydrogen bonding and metallic bonds as well as cation−anion interactions. Mangipudi43 tested the solid polymer surfaces using various probe liquids and reached the following conclusions: (i) the value of ϕ depends more on the probe liquid than on the nature of the solid surface, (ii) using liquids with predominant dispersive interactions ϕ is close to unity (London dispersive forces are dominant), (iii) ϕ is small if the association effects of the probe liquid (water, formamide, etc.) due to H-bonding are dominant, and (iv) the value of ϕ is moderate when the molecular size of the probe liquid is relatively large (larger than water). Mangipudi also noted that the value of ϕ increases with the increasing the molecular size 15605

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perpendicular, the fraction of area occupied by tails is equal to 0.8 and 0.83 for FSO100 and FSN100, respectively. Taking these values into account, new more reasonable ones of ϕ were calculated as a sum of the interactions between the hydrocarbon tail with the PTFE surface and the hydrophilic head with the PTFE and they are presented in Figure 2. The values of ϕ calculated in such a way are close to those of molecular interaction parameter of different kinds of liquids and PTFE surface found in the literature.45,50 From the presented studies, it is clear that the values of ϕ are strongly dependent on the way of the determination of the surface tension of a given solid. As was mentioned earlier, all approaches to the solid−liquid interfacial tension are more or less based on the ϕ parameter and were tested mostly on the solid−liquid drop-air systems in which the influence of the adsorbed film at the solid−air interface was ignored. In the case of PTFE−aqueous solution of fluorocarbon drop-air system, the changes of the surface tension of PTFE around the solution drop settled on its surface and also under the solution drop cannot be excluded, as indicated by the above results of ϕ parameter. However, the changes of this parameter values as a function of fluorocarbon surfactant concentration can be treated as the results of PTFE surface tension changes under adsorption or absorption and proper orientation of surfactant molecules in the surface layer at the PTFE−solution interface but the ϕ values probably do not reflect the real intermolecular interaction across the PTFE− solution interface. PMMA. Similarly to the PTFE surface the behavior of FSN100 and FSO100 molecules at the PMMA−water interface is different from that of hydrocarbon surfactants.21 The γLV cos θ−γLV curves for PMMA (Supporting Information Figure S5) and the above-mentioned surfactants can be divided into two parts and each of them can be approximately described by a linear function. At the concentration of FSN100 and FSO100 corresponding to the unsaturated monolayer at the water−air interface,24 the γLV cos θ values for these systems decrease (Figure S5) proportionally to γLV decrease and the relationships between γLV cos θ and γLV have positive slopes (0.274 and 0.277). The statement mentioned above suggests that the Gibbs surface excess concentration of surfactants at the PMMA−air interface is higher than zero and their Gibbs surface excess concentration at the PMMA−water interface, or that ΓSL < 0. To prove which suggestion is more probable, ΓSL should be calculated from eq 1b. However, the PMMA− solution interfacial tension calculated on the assumption that the surface tension of PMMA is constant (39.21 mN/m)36 increases in the surfactant concentration range 0−10−4 M (Figure 3, curves 1 and 2), and it is impossible to calculate the values of ΓSL. This situation suggest the existence of the film of not only water molecules but also the surfactant ones on the PMMA surface. The confirmation of this suggestion is the ratio of the minimal possible area occupied by the surfactant molecules at the water−air interface and the area of the molecule calculated by summarizing the area occupied by −CF3, −CF2, and oxyethylene oxide groups48 (FSN100 183.06 Å2 and FSO100 137.57 Å2). Thus the values of γSL calculated on the basis of eq 6 (Figure 3, curves 9 and 10) which are much smaller than those calculated for the constant γSV are not real. If there was not a film of the surfactant molecules, these ratios (0.185 and 0.224 for FSN100 and FSO100, respectively) should be equal to the values of the slopes in the relationship between the adhesion and surface tension (Supporting Information Figure S5). Because of the existence of this film,

groups causing that the PTFE surface can interact by polar forces. In the earlier studies on the basis of the contact angle of water, formamide and diiodomethane, it was proved that the surface tension of PTFE is changed under the influence of the fluorocarbon surfactants film on its surface at different concentrations in the bulk phase and depends on the time of solution contact with the polymer surface.44 Taking into account the calculated values of the Lifshitz−van der Waals component of the surface tension of the PTFE covered by the surfactant film formed during 1 min and 24 h of the solution contact with PTFE and assuming that the surface tension of hydrophobic groups is equal to the proper perfluoroalkane,48 the values of the PTFE−solution interfacial tension, γSL, were calculated from the Fowkes equation which is of the form: LW LW γSL = γSV + γLV − 2 γSL γLV

(18)

but on the assumption that only dispersion intermolecular interactions are present across the interface. Next, the new values of ϕ were calculated at the concentration of surfactants ranging from 10−6 to 10−3 M by using the relation: γSL = γSV + γLV − 2ϕ γSVγLV

(19)

These values of ϕ (Supporting Information Figure S4) for the PTFE surface covered with the surfactant film formed during 1 min interactions with the aqueous solution of surfactant at the concentrations corresponding to the saturated monolayer at the water−air interface are almost constant for these two surfactants and the average value of the intermolecular interaction parameter is equal to 0.994. On the other hand, van Oss et al.33,34 using the measured surface tension of the hydrophilic ethylene oxide (EO), as well as the hydrophobic, polyethylene (PE) of POE at 293 K calculated the surface tension components and parameters of + ethylene oxide (EO) as equal to: γLW EO = 43 mN/m, γEO = 0, and γ−EO = 80 mN/m, respectively.49 Taking into account these + − values of parameters and those of γLW SV , γSV, γSV, and γSV of PTFE covered with the fluorocarbon surfactant film formed during 1 min and 24 h of their aqueous solutions contact with the surface, the values of γSL were calculated from the relation + − − + LW LW γSL = γSV + γLV − 2 γLV γSV + 2 γLV γSV + 2 γLV γSV

(20)

and next the values of the parameter of the interfacial interaction, ϕ, from eq 19. The values of ϕ calculated in such a way (Supporting Information Figure S4) in the concentration range of aqueous solution equal to 10−6−10−3 M change from 1 to 0.807 and from 1 to 0.868 if the film of fluorocarbon surfactant is formed during 1 min, but if the film is formed during 24 h, the values of ϕ are in the range 1−0.338 and 0.759−0.215 for FSN100 and FSO100, respectively. As the measurements of the used values of the contact angles were performed immediately after the deposition of the solution drop on the PTFE surface and the most probable values of ϕ parameter are obtained for PTFE covered with the fluorocarbon surfactant film formed during 1 min, the values of ϕ calculated for these films were taken into account in further calculations. In the earlier studies, it was shown that the fraction of tails in the contactable area of these surfactants with the parallel orientation is equal to 0.29 and 0.25 respectively.44 However, if it was assumed that at the minimum value of the Lifshitz−van der Waals component, the tails are oriented parallel toward the PTFE−solution interface and heads 15606

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Figure 3. Dependence of the values of interfacial tension, γSL, at the PMMA−solution interface calculated for γSV = 39.21 mN/m (FSN100−curve 1 and FSO100−curve 2), for γSV recalculated proportionally to the values of the surface tension (FSN100−curve 3 and FSO100−curve 4) and next calculated to the values γSL (FSN100−curve 5 and FSO100−curve 6) as well as for γSV and γSL calculated from the Neumann approach (curves 7−10) on log C (C represents the concentration of FSN100 and FSO100).

Figure 4. Dependence of the values of the interaction parameter across the PMMA−solution interface (ϕ) calculated for γSV = 39.21 mN/m (FSN100−curve 1, FSO100−curve 4, TX100−curve 8, and TX165−curve 8), for γSV recalculated proportionally to the values of the surface tension (FSN100−curve 2 and FSO100−curve 4), for γSV from the Neumann approach (FSN100−curve 3 and FSO100−curve 6), and for FSN100 (curves 9 and 10) and FSO100 (curves 11 and 12) in different fractions of tails in the contactable area on the PTFE− solution interfacial tension (γSL) calculated from eq 2.

the values of ΓSV cannot be equal to zero and should change with the concentration of surfactants in the bulk phase. The existence of the water and surfactant molecules film around the aqueous solution of the fluorocarbon surfactant confirms the surface tension of PMMA data obtained from the Neumann et al. equation27,29 (Figure 3, curves 7 and 8). These data indicate that the PMMA surface tension changes as the function of surfactant concentration. Although the values of PMMA surface tension calculated from eq 6 probably do not express the real ones, their relative changes should be connected with the film of water and surfactant molecules presence on the PMMA surface. To calculate the values of ΓSV, first the values of γSV were determined in such a way that they were changed proportionally to the values of the surface tension of aqueous solution of surfactants24 and they are presented in Figure 3 (curves 3 and 4). On the basis of values of γSV not only ΓSV (Figure S5) but also the values of γSL were determined (Figure 3, curves 5 and 6) as well as those of ΓSL for the PMMA surface (Figure S5). Knowing the values of ΓSV, ΓSL (Figure S5), and ΓLV (Supporting Information Figure S2) for a given surfactant, it was possible to calculate the values of (ΓSV − ΓSL)/ΓLV (eq 16). The average values of (ΓSV − ΓSL)/ΓLV for FSN100 and FSO100 and the concentrations smaller than those of CMC are equal to 0.261 and 0.294, respectively, and are in a good agreement with the values of slopes in the relationship between γLV cos θ and γLV (Figure S5). The possibility to form the surface layer by the fluorocarbon surfactants at the PMMA−air interface influences on the composition of the surface layer at the PMMA−solution interface and the activity of surfactants at this interface (Supporting Information Figure S6) as well as the values of the parameter of the interfacial interaction, ϕ (Figure 4). As follows from Figure 4, the ϕ values calculated in two different ways, that is on the basis of the values of γSL calculated on the assumption that the surface tension of PMMA is constant (Figure 4, curves 1 and 4) and taking into account the presence of the surfactant film (Figure 4, curves 2 and 5), achieve the

minimum as the function of PMMA−solution interfacial tension at the concentrations close to CMC which may be connected with the change of PMMA surface tension under the influence of the film covering its surface. Curves 1, 2, 4, and 5 of ϕ−γSL plots for PMMA and FSN100 and FSO100 (Figure 4), contrary to TX100 and TX165 (curves 7 and 8), can be divided into two parts and each of them can be approximately described by a linear function (Table 2). The minimal values of ϕ Table 2. Slopes and Intercepts for the ϕ = f(γSL) Straight Relationships for FSN100 and FSO100 on PMMAa ϕ = A + BγSL FSN100

FSO100

A

B

A

B

2.699 0.735 −6.690 0.979

−0.074 −0.005 0.454 −0.017

2.003 1.024 0.085 0.986

−0.048 −0.017 0.046 −0.023

γSV = 39.21 mN/m and recalculated proportionally to the values of the surface tension. a

calculated on the assumption of the existence of the surfactant film at the interface are equal to 0.698 and 0.687 for FSN100 and FSO100, respectively, and are much higher than those calculated on the basis of the constant value of the PMMA surface tension. All the values of ϕ calculated for FSN100 and FSO100 are lower than 1 and than the values of the molecular interaction parameter at the PMMA−solution interface calculated for water, ethylene glycol, formamide, glycerol, and diiodomethane (Supporting Information Table S2). On the other hand, the values of ϕ calculated on the basis of γSV determined from the Neumann equation (Figure 4, curves 3 and 6) are much more higher than the all values of ϕ parameter calculated for FSN100 and FSO100 as well as for hydrocarbon TX100 and TX165. Also the shape of ϕ−γSL curves for ϕ 15607

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calculated on the basis of the Neumann equation, which can be described by one exponential function, are different from the others presented in Figure 4. As mentioned earlier, this indicates that the surface of PMMA under the influence of surfactant adsorption becomes more hydrophobic than the “pure” surface, but the influence of the fluorocarbon surfactants on the properties of the PMMA surface are quite different from those of hydrocarbon ones. Similarly to PTFE, it was proved that the surface tension of the PMMA changes under the influence of the FSN100 and + − FSO100 films,44 taking into account the values of γLW SV , γSV, γSV, and γSV for PMMA calculated on the basis of the contact angle of water, formamide, and diiodomethane, the values of ϕ were determined in two ways, that is as an interaction between the hydrocarbon tails and oxyethylene groups with the PMMA surface (Supporting Information Figure S7). Next, taking into account the same values of the fraction of tails in the contactable area of these surfactants as in the case of the PTFE surface, new values of ϕ were calculated and are presented in Figure 4 (curves 9−12). The values of ϕ determined in such a way are higher than those of the molecular interaction parameter for the water and PMMA surface and are found in the range of ϕ values for different kinds of liquids.45,50 However, to explain the changes of this parameter with the increasing concentration of the fluorocarbon surfactants in the bulk phase further studies should be carried out.

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ASSOCIATED CONTENT

S Supporting Information *

Tables S1 and S2 and Figures S1−S7 as mentioned in the text. This material is available free of charge via the Internet at http://pubs.acs.org/.

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AUTHOR INFORMATION

Corresponding Author

*Phone: (48-81) 537-5538. Fax: (48-81) 533-3348. E-mail: [email protected]. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS The author wishes to express her gratitude to Professor Bronisław Jańczuk (Department of Physical Chemistry, M. Curie-Skłodowska University, Lublin, Poland) for helpful criticism during the preparation of this paper and his great interest in its progress.

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REFERENCES

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4. CONCLUSIONS The calculations of the Gibbs surface excess concentrations and the mole fractions of the fluorocarbon surfactants, Zonyl FSN100 and FSO-100, at the water−air and PTFE/PMMA−water interfaces indicate that the adsorption of these surfactants at these interfaces is not the same and that they are the specific interactions between the surfactant molecules, their molecules with water, and PTFE/PMMA surface. This is confirmed by the values of the activity of surfactants at the interfaces, adhesion tension, and the parameter of the interfacial interaction, ϕ, at the PTFE/PMMA−water interfaces. Because the values of ϕ for the studied surfactants, calculated on the assumption that the surface tension of PTFE and PMMA was constant, were smaller not only than those of intermolecular interaction parameter for different hydrocarbon surfactants but also than the values of this parameter for n-alkanes and different kinds of liquids, it was shown that more reliable values of this parameter can be obtained if the calculations are performed separately for the head and tail of the fluorocarbon surfactants, taking into account their fraction in the contactable area as well as the values of components and parameters of PTFE and PMMA surface tension under the influence of the FSN100 or FSO100 films absorbed on these surfaces. Also the calculation of the surface tension of the studied polymers on the basis of the Neumann approach and next the interfacial tensions and parameter of intermolecular interactions across the interfaces confirm that the changes of the surface tension of PTFE and PMMA around the solution drop settled on their surface and also under the solution drop cannot be excluded and that the values of ϕ are strongly dependent on the way of determination of the surface tension of a given solid. 15608

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