Quantification of deexcitation processes for analyzing liquid surfaces

Nuclear Instruments and Methods in Physics Research B 340 (2014) 44–50

Contents lists available at ScienceDirect

Nuclear Instruments and Methods in Physics Research B journal homepage: www.elsevier.com/locate/nimb

Quantification of deexcitation processes for analyzing liquid surfaces H. Morgner Wilhelm Ostwald Institute for Physical and Theoretical Chemistry, University Leipzig, Linnestreet 2, D-04103 Leipzig, Germany

a r t i c l e

i n f o

a b s t r a c t

Article history: Received 10 March 2014 Received in revised form 23 June 2014 Accepted 24 June 2014 Available online 6 August 2014

In the last two decades the mathematical tools for quantitative data evaluation have been developed for several surface spectroscopic techniques like Angular Resolved X-ray Photoelectron Spectroscopy (ARXPS), Neutral Impact Collision Ion Scattering Spectroscopy (NICISS) and Metastable Induced Electron Spectroscopy (MIES). Provided that the experimental data are of good quality, quantitative data processing can add a lot to the information that can be gained from surface spectroscopy. We give a selection of references that contain information on these methods. The emphasis of this contribution aims at providing motivation to apply quantitative data evaluation by presenting a few examples. We try to demonstrate, that careful data evaluation may lead to interesting insight into basic concepts as well as to results that are useful for practical applications. Ó 2014 Elsevier B.V. All rights reserved.

Keywords: NICISS ARXPS MIES Micelle formation Bimodal free energy distribution of molecules

1. Introduction For many decades the only experimental tool for studying liquid surfaces has been tensiometry [1]. The advent of surface spectroscopy which has been pioneered by Siegbahn [2] has added more detailed information on liquid surfaces, e.g. concentration depth profiles, thus revealing the 3-dimesional structure of liquid surfaces. Surface spectroscopy does not render the conventional method of surface tensiometry superfluous, but in contrast, the combination of spectroscopy and tensiometry allows understanding the properties of liquid surfaces in more depth than has been possible before. The meaningful combination of both pieces of information is made possible by the Gibbs equation [1] which reads for a binary system of components A, B.

dr ¼ CeA  dlA

ð1aÞ

or

dr ¼ CeB  dlB

ð1bÞ e

where r denotes the surface tension, C the surface excess and l the chemical potential of the components. The surface excess can be determined from the concentration depth profiles cA ðzÞ, cB ðzÞ and its definition is given here for component A as

CeA ¼

Z 0

1

  xA cA ðzÞ  cB ðzÞ dz xB

E-mail address: [email protected] http://dx.doi.org/10.1016/j.nimb.2014.06.026 0168-583X/Ó 2014 Elsevier B.V. All rights reserved.

ð2Þ

Thus, the advent of surface spectroscopy has turned Ce into a measurable quantity. In consequence, the chemical potential l of either or both components can be determined in a straightforward manner from experiment without any model assumptions. This is of particular interest for surfactant solutions, as the low bulk concentration of surfactants renders conventional methods (e.g. variation of the solvent vapor pressure) for measuring chemical potentials invalid. Recently, some progress has been made along this line: for the first time has it been possible to study the mutual influence of two surfactants [3] quantitatively on the basis of experimental data. The paper is organized as follows. The next section introduces the three experimental techniques, results of which are discussed. The mathematical methods used to end up with quantitative data evaluation are briefly described and references given. Thus, the reader interested in these methods can find detailed information in the literature. The scope of the present paper goes beyond mere data processing. We will observe that in some cases rigorous treatment of surface spectroscopic data can not only yield unexpected information on the entire system, i.e. on bulk properties, but may as well lead to reconsidering theoretical concepts. We will discuss three systems, the first motivating us to inspect the common concept of micelle formation, the second illustrating that the surface of a liquid system may force matter into a very unusual state of matter, and the last system demonstrating that basic considerations may in some cases be closely related to technical applications.

H. Morgner / Nuclear Instruments and Methods in Physics Research B 340 (2014) 44–50

2. Experimental techniques employed In the present contribution we will discuss results from three experimental techniques: 1. X-ray photoelectron spectroscopy (=XPS) which has been applied to liquid surfaces for the first time by Siegbahn [2]. The angular resolved version of this technique (ARXPS) has matured into determining depth profiles in great detail without the need to formulate a model structure, e.g. [4]. Based on the concept of a mean free path of the emitted electrons the observation depth varies in a predictable way with the angle under which the electrons are detected. Thus, the spectra vary with emission angle for different species in a different way reflecting the concentration depth profile of every species. In XPS the chemical shift allows to distinguish different chemical environments for one and the same element. Thus, when evaluating XPS data (and thereby ARXPS data) one can identify one and the same element in different chemical environments as different species. Accordingly, concentration depth profiles can be reconstructed separately for different molecular groups, even if one deals e.g. with hydrocarbon compounds. Carbon atoms within a saturated hydrocarbon chain have a binding energy of ca. 284 eV while a carbon atom pertaining to a carboxylic acid has a binding energy that is ca. 3.4 eV higher. Compared to the energy resolution of the technique that can easily be tuned to be better than a few tenth of an eV, the two species can be unambiguously distinguished. This method has been employed in Ref. [4] for exploring the surface of the solution TBAI/FA (tetrabutylammonium iodide dissolved in the polar solvent formamide) by exploiting the chemical shift between carbon atoms within the solvent and carbon atoms within the solute. The careful evaluation of the experimental spectra is, however, only the first step towards the reconstruction of a reliable concentration depth profile, as has been described in Ref. [4]. Several authors content themselves with observing qualitatively whether a given component is enriched in the surface or not, e.g. [5–7]. In the present contribution we will demonstrate that careful quantitative data evaluation can lead to interesting information that sometimes may even invoke a challenge to theoretical concepts. 2. Neutral impact collision ion scattering spectroscopy (NICISS) is based on the backscattering of projectiles (often He+ ions with a kinetic energy of several keV). Recording energy loss and scattering angle allows calculating the mass of the target atom that has been hit. NICISS is a reliable technique to determine depth profiles of selected elements in the surface near range in case of amorphous samples. Thus, this method can be used to check results from ARXPS and vice versa. Even though the spectra measured in NICISS allow for a coarse estimate of the concentrations depth profiles without data processing, the detailed quantitative data evaluation requires several steps. First of all, one has to separate the signal caused by the reflected projectiles from the background due to recoiled light atoms. This can be done because the reflected projectiles yield a structured pattern while the recoil signal from light atoms (usually hydrogen) forms a broad unstructured background. Further, the kinetic energy distribution of the projectiles broadens the spectra. The last aspect that has to be taken into account rests in the statistical nature of the stopping power. All three influences can be mathematically handled to good accuracy. If so, very detailed information about the (laterally averaged) concentration depth profile can be obtained, see Ref. [8,9]. 3. Metastable Induced Electron Spectroscopy (=MIES) is distinguished by perfect surface sensitivity and, thus, complements the first two techniques. MIES allows determining the composi-

45

tion of the top layer, but is as well sensitive to the orientation of the molecules in this layer. The mathematical tools for quantitative evaluation of MIES data are described in Ref. [10]. In particular the decomposition of spectra from inhomogeneous surfaces into contributions from separate, identifiable species is discussed in this review article. 3. Results and discussion 3.1. Solution of a nonionic surfactant in a polar solvent: challenge to common understanding of micelle formation and to familiar thermodynamic concepts The surface properties of the solution of the nonionic surfactant 1-palmitoyl-2-oleoyl-sn-glycero-3-phosphocholine (POPC) in the polar solvent 3-hydroxipropionitrile (HPN) have been investigated by the surface spectroscopy NICISS and by surface tensiometry. The data can be found in Ref. [11]. The spectroscopic measurements allowed determining the surface excess of the surfactant. Combining these results with surface tension data via the Gibbs equation, the chemical potential lPOPC of the surfactant could be determined over a large range of concentrations, starting at more than one order of magnitude below the critical micelle concentration (CMC) to an order of magnitude above the cmc. Inspection of the chemical potential shows that up to the cmc the solution displays ideal solution behavior. Above the cmc the chemical potential and the surface tension remain constant, cf. [11]. Insofar, the behavior of the system follows the expected behavior. However, in a small range above the cmc an unusual feature could be observed. The surface tension displays a local minimum which leads via the Gibbs equation to a local maximum of the chemical potential lPOPC . The literature knows two different comments with respect to this phenomenon, cf. Ref. [12]. Several authors claim that the occurrence of a local minimum in the surface tension is an unambiguous indication for the presence of a surface active impurity. As this impurity is to be understood as impurity with respect to the surfactant, its concentration is much smaller than the surfactant concentration and, thereby, extremely low. Thus, it escapes detection by bulk related analytical techniques. The only method to get rid of such an impurity is the observation of purification protocols. The ability to employ surface spectroscopy gave an advantage in this respect: a surface active impurity is best identified by means of surface spectroscopy. No trace of such impurity could be found, cf. [11]. If an impurity was present, its properties had to be almost identical to the properties of the surfactant POPC. Thus, an explanation of the phenomenon without reference to an impurity has been sought. It has been formulated a few years later in Ref. [13]. The treatment in this paper assumed a hindrance against micelle formation. Not all surfactant molecules exceeding the critical micelle concentration lead to the formation of micelles. Thus, micelle formation is delayed to concentrations larger than the nominal cmc. A later experimental paper reported the same effect for the somewhat different surfactant 1,2-dioleoyl-sn-glycero-3phosphochline (DOPC) dissolved in the same solvent HPN [14]. This time the effect was identified by the spectroscopic technique MIES and was found to be even more pronounced than in case of POPC/HPN. Again, the theory from Ref. [13] proved fruitful in describing the effect. (see Fig. 1). The systems discussed are characterized by the presence of altogether three phases: the bulk monomer solution, the surface and the micelles. The micelles are comparatively small (about 17 POPC molecules per micelle) such that the total area of the interface between monomer solution and micelles is extremely large. This goes along with an inhomogeneous distribution of matter. Thus, strong capillary forces are present. One may conclude that

46

H. Morgner / Nuclear Instruments and Methods in Physics Research B 340 (2014) 44–50

surfactant properties in POPC/HPN 9000

POPC not involved in micelle formation

ideal solution

chemical potential [J/mol]

8500

8000

7500

POPC involved in micelle formation 7000

exp. data employed in fit additional exp. data

6500

fit within fluctuation model 6000 1.E-04

2.E-04

3.E-04

4.E-04

5.E-04

6.E-04

7.E-04

8.E-04

concentration [mol/kg] Fig. 1. The chemical potential lPOPC of the surfactant POPC near the critical micelle concentration. Data are taken from Ref. [11]. The theoretical explanation for the local maximum of lPOPC in Ref. [13] requires that the energetic situation of the POPC molecules is described by a bimodal distribution. E.g. at cPOPC = 3  104 about half the POPC molecules are involved in micelle formation (red line), while the rest is not (blue curve). Below the cmc and well above the cmc the POPC molecules experience only a homogeneous broadening of their free energy. The colored vertical bars are a measure for the relative amount of molecules in either mode. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)

the phenomena described show up for systems whose behavior is dominated by capillary forces.

A few years ago we have studied by means of MIES the surface of several binary mixtures of polar solvents [15] by the combination of surface tensiometry and of the surface spectroscopy MIES. As all mixtures investigated are miscible in all proportions, the bulk molar fraction could be varied over the full range from zero to unity. It turned out that the MIE spectra of the mixtures Smix ðEel Þ could be reproduced by a linear combination of the spectra taken for the pure liquids SA ðEel Þ and SB ðEel Þ.

Smix ðEel Þ ¼ aA  SA ðEel Þ þ aB  SB ðEel Þ

ð3Þ

The meaning of the coefficients aA and aB was identified as representing the fraction of the surface covered by either of the components. For all mixtures of the three liquids formamide (FA), 3-hydroxipropionitrile (HPN), polyethyleneglycol (PEG) we made the observation that the surface tension when plotted as function of the surface fraction obtained from MIES via Eq. (3) rather than as function of the bulk molar fraction, can be fitted to high precision by a straight line. For the mixture HPN/FA this outcome is displayed in Fig. 2. It has been argued in Ref. [15] that this linearity proves that the topmost layer is identical to the entire surface layer. For comparison we have defined another quantity that characterizes the surface. It is the molar fraction within the top surface layer (or surface molar fraction). It can be computed from the surface fractions a via the relations. 2

xsurf A

2

aA  n3A aB  n3B ¼ and xsurf ¼ 2 2 2 2 B aA  n3A þ aB  n3B aA  n3A þ aB  n3B

ð3Þ

where nA, nB are the molar densities of the pure components. Eq. (3) assumes that the molar areas of the molecules are proportional to 2 n3 , i.e. that no preferential orientation prevails. It is important to note that any definition of the surface molar fraction depends on a model assumption. Thus, we choose a definition which is easily computed from the data available. It is interesting to note that

surface tension [mN/m]

3.2. Binary mixture of two polar solvents

binary mixture HPN/FA

62 60 58 56 54

plotted against surface fraction plotted against surface molar fraction

52 50 0

0.2

0.4 0.6 surface fraction HPN

0.8

1

Fig. 2. Binary mixture of HPN and FA. The surface tension when plotted against the surface fraction of either component yields a straight line with great accuracy. The plot against the surface molar fraction clearly indicates that linearity is less well satisfied if the surface tension is plotted against the molar fraction in the surface layer. Adopted from Ref. [14].

the surface tension displays a noticeable deviation from linearity if plotted against the molar fraction in the surface, cf. Fig. 2. Once the top surface layer is identified with the entire surface, one can easily evaluate the surface excess of both components and thereby via the Gibbs. Eq. (1) the variation of the chemical potentials of both components as function of the composition. Both chemical potentials are normalized to zero for the pure liquids. Once the chemical potentials are obtained one can compute the Gibbs energy of mixing via

DGmix ¼ xBA  lBA þ xFA  lFA

ð4Þ

The Gibbs energy is plotted in Fig. 3. Comparison with the curve of the ideal solution indicates that the interaction between the species is similarly attractive as would correspond to an ideal solution. The same quantity can be evaluated for the surface layer by setting surf surf DGsurf mix ¼ xBA  lBA þ xFA  lFA

ð5Þ

Its plot as function of the surface molar fraction in Fig. 3 looks quite similar to the plot of the respective bulk entity. We conclude that for this system the energetic situation in the surface does not differ very much from that in the bulk.

H. Morgner / Nuclear Instruments and Methods in Physics Research B 340 (2014) 44–50

surface molar fraction HPN 0

0.2

0.4

0.6

0.8

1

0.6

0.8

1

0

Gibbs energy of mixing [J/mol]

-200

Gmix[ideal] Gmix[bulk]

-400

Gmix[surface] -600 -800 -1000 -1200 -1400 -1600 -1800 0

0.2

0.4

bulk molar fraction HPN Fig. 3. Binary mixture HPN/FA. Plotted is the Gibbs energy of mixing DGmix computed for the bulk (blue) and DGsurf mix for the surface layer (red). The Gibbs energy of mixing for an ideal mixture is given for comparison. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)

binary mixture BA/FA

surface tension [mN/m]

60

55

50

45

40 0

0.2

0.4

0.6

0.8

1

surface fraction BA Fig. 4. Plotted is the surface tension of the mixture BA/FA as function of the surface fraction aBA of benzylalcohol. Three piecewise linear sections can be discerned. Adopted from Ref. [14].

While the difference in surface tension between the three liquids HPN, FA and PEG does not exceed 10 mN/m, we will address now a system in which the respective surface tensions differ by almost 20 mN/m. It is the binary mixture of benzylalcohol (BA) and formamide (FA). Again the surface tension as well as the surface fraction are measured over the entire range of concentrations. Plotting for this system the surface tension as function of the surface fraction leads to a surprise: the curve turns out to be linear, but piecewise linear. No less than three linear parts of the plot could be detected. The intersections occur at aBA ¼ 0:79 and aBA ¼ 0:96. The interpretation of this phenomenon will be postponed until we have derived some information on energetic properties. Again the chemical potentials of both components have been computed via the Gibbs equation. Making use of Eq. (4) the Gibbs energy of mixing can be determined. It is plotted in Fig. 5 together with the corresponding curve for an ideal mixture. Now we

47

address the Gibbs energy of mixing of the surface layer via Eq. (5). The result is added in Fig. 5. It turns out that its behavior differs distinctly from the bulk curve. The most eye-catching feature is the surf abrupt change of slope at xsurf BA ¼ xBA ðaBA ¼ 0:79Þ ¼ 0:69. This value of the surface molar fraction has been computed via Eq. (3) and corresponds to the first intersection at aBA ¼ 0:79 in Fig. 4. The surf position xsurf BA ¼ xBA ðaBA ¼ 0:96Þ ¼ 0:93 which is related to the second intersection in Fig. 4 is indicated as well by a dashed line (Fig. 5 right panel). The shape of the Gibbs energy of mixing DGsurf mix in the interval between the intersections is well described by a straight line. This behavior is unexpected and according to our knowledge has not been observed before. If one looks out for an explanation relying on similar findings in the thermodynamic behavior of bulk material, one feels reminded of a miscibility gap. In order to illustrate this statement we inspect the schematic features of a miscibility gap in a binary liquid mixture. The related graphs are found in Fig. 6. The left panel displays the Gibbs energy of mixing DGmix . The miscibility gap is indicated by vertical dashed lines. These represent the composition of the two phases that are coexisting in the gap. Within the gap the quantity DGmix takes on the shape of a straight line with the slope changing at the borders of the gap. The related chemical potentials are shown in the right panel of the figure. Within the gap we have two phases in equilibrium and, thus, the chemical potentials of both components remain constant within the gap. From the scheme of the bulk miscibility gap in Fig. 6 we are led to the conclusion that the linear part of the surface Gibbs energy DGsurf mix in Fig. 5 may be indicative of a miscibility gap. This would be unexpected as the bulk system has clearly no miscibility gap, cf. Fig. 5. We inspect now in Fig. 7 the behavior of the chemical potential of the component BA which represents the majority species surf between the intersection points at xsurf BA ¼ 0:69 and xBA ¼ 0:93 identified in Fig. 4. Between the marked points the chemical potential lBA is well represented by a straight line. If the range between the marked points were a classical miscibility gap of the surface subsystem, the chemical potential ought to be constant, cf. Fig. 6. Thus, we have to observe that the conventional picture of a miscibility gap does not apply. Indeed, at second glance we can hardly expect the standard picture to hold. The subsystem ‘surface’ is in direct contact to the bulk. The bulk determines the chemical potential of the entire system including the surface subsystem. As the bulk does not have a miscibility gap, the value of the chemical potential lBA necessarily varies with the bulk molar fraction xBA (or surface fraction aBA ) between the two marked points. This would lead to the following picture: even if we stick to the notion that we identify the range between the marked points as a surface miscibility gap and, thus, assume the existence of two phases located at the marked points, the conventional requirement of constancy of the chemical potentials within the gap can not apply. We rather have to accept that spontaneous separation into two surface phases must differ from the normal case as the 2 surface phases must have different chemical potentials. Still, the concept of two phases in the surface of the binary mixture would necessarily call for a linear variation of the chemical potential lBA within the surface miscibility gap, as observed. It is obvious that the concept of a surface miscibility gap and the related phase separation in the presence of a single homogeneous phase in the bulk leads to the existence of two energetically different situations (i.e. the two surface phases with different values of the chemical potentials). This is unusual, but does not contradict the concepts of thermodynamics. We know that the value of a thermodynamic quantity like the chemical potential does not apply likewise to all molecules at a time, but that the values are well defined only after averaging over time, in agreement with the ergodic principle. The unusual fea-

48

H. Morgner / Nuclear Instruments and Methods in Physics Research B 340 (2014) 44–50

bulk molar fraction BA 0

0.2

0.4

0.6

binary mixture BA/FA 0.8

1 12BA:1FA

molar Gibbs energy [J/mole]

Gm[bulk] ideal Gibbs molar energy Gm[surface]

-200

molar Gibbs energy [J/mol]

-200

-700

-1200

-1700

7BA:3FA

-700

-1200

-1700

-2200

-2200 0

0.2

0.4

0.6

0.8

0.6

1

0.7

0.8

0.9

1

surface molar fraction BA

surface molar fraction BA

Fig. 5. Left panel: for the mixture BA/FA the Gibbs energy of mixing is plotted as function of the bulk molar fraction. Comparison with the curve for the ideal mixture indicates that the interaction between the components is less attractive than for an ideal mixture, but obviously the components are miscible in all proportions. In addition the Gibbs surf energy of mixing for the surface DGsurf mix is displayed. Right panel: DGmix with blown up horizontal scale. Further discussion is found in the text.

miscibility gap in binary mixture A,B

miscibility gap in binary mixture A,B

0.2

0

Gmix for homogeneous system ideal mixture Linear (Gmix in real system)

0.1

-0.2

phase2

-0.4

phase1 -0.1

chemical potential

Gibbs energy of mixing / RT

0

-0.2 -0.3 -0.4 -0.5

-0.6 -0.8 -1

phase1

-1.4

-0.6

-1.6

-0.7

-1.8

-0.8

phase2

-1.2

component A component B

-2 0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

molar fraction xA

1

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

molar fraction xA

Fig. 6. Schematic picture of a miscibility gap for a binary mixture A/B. The Gibbs energy of mixing is plotted as function of the bulk molar fraction in the left panel. The right panel shows the chemical potentials.

ture in the present case consists in the fact that the distribution over which the averaging is to be carried out is a bimodal one while in the general case one has a monomodal distribution (homogeneous broadening). Finally, we inspect the chemical potential of the other component lFA between the two marked points, cf. Fig. 8. Taking into account the error bars, the data may not explicitly contradict a linear dependence, but clearly do the data not call for a linear dependence. This observation is in contrast to the notion of two phases in the surface. This observation may represent a warning that the explanation of the unusual phenomena displayed in Figs. 4, 5 and 7 in terms of a surface miscibility gap is only a first approach to a maybe more complex theoretical concept.

3.3. TBABr/POPC/HPN: the interaction of two surfactants Recently we have studied a solution containing two very different surfactants dissolved in a polar solvent. The nonionic surfactant 1-palmitoyl-2-oleoyl-sn-glycero-3-phosphocholine (POPC) and the ionic surfactant tetrabutylammonium bromide (TBABr) were simultaneously dissolved in the polar solvent 3-hydroxipropionitrile (HPN). The concentration of TBABr was varied from zero to 1.3 mol/kg which is close to the solubility limit, while the POPC concentration remained below 4  8104 mol/kg. The goal of the work has been gaining insight into the interaction between two surfactants [3]. Again the surface tension and the surface excess have been measured. But in this case the number of measurements was quite substantial as all quantities had to be recorded for a

49

H. Morgner / Nuclear Instruments and Methods in Physics Research B 340 (2014) 44–50

activity coefficient of POPC

binary mixture BA/FA 1000

12BA:1FA

-1000

1.0

-2000

c(TBABr) [mol/kg HPN]

chem. pot. BA [J/mol]

3.5

1.2

7BA:3FA

0

-3000 -4000 -5000 -6000 -7000 -8000

0.020 0.8

1.0 6.0

0.6

0.4

3.5

0.10

0.2

-9000 0

0.2

0.4

0.6

0.8

16

1

10

surface molar fraction BA

0.0 0.0000

Fig. 7. Binary mixture BA/FA. The chemical potential of BA is plotted as function of surf the surface molar fraction xsurf BA . The behavior between the intersections xBA ¼ 0:69 and xsurf BA ¼ 0:93 identified in Fig. 4 is found to be linear, but not constant. Outside the range between the intersections the chemical potential does not show any unusual properties.

2.0 0.0001

0.0002

0.0003

0.0004

c(POPC) [mol/kg HPN] Fig. 9. The ternary system POPC/TBABr/HPN. The activity coefficient fPOPC ðcPOPC ; cTBABr Þ of POPC is plotted as function of the concentrations of both surfactants. Data are taken from Ref. [3].

binary mixture BA/FA 12BA:1FA

1000

7BA:3FA

chem. pot. FA [J/mol]

0 -1000 -2000 -3000 -4000 -5000 -6000 0.6

0.7

0.8

0.9

1

surface molar fraction BA Fig. 8. Binary mixture BA/FA. The chemical potential of FA is plotted as function of surf the surface molar fraction xsurf BA . The behavior between the intersections xBA ¼ 0:69 and xsurf BA ¼ 0:93 appears not to be linear, as is displayed by comparison to the best fit of a straight line (red line). The thin black line indicates ideal behavior. Further discussion in the text. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)

2-dimensional set of parameters, namely the concentrations of both surfactants cPOPC and cTBABr. The experiments provided the three quantities rðcPOPC ; cTBABr Þ, CePOPC ðcPOPC ; cTBABr Þ and e CTBABr ðcPOPC ; cTBABr Þ which are related by the Gibbs equation which reads for the ternary system.

dr ¼ CePOPC  dlPOPC þ CeTBABr  dlTBABr

ð6Þ

For the two binary systems the chemical potentials are evaluated in a straightforward way via

dlPOPC ¼

dr

CePOPC

and dlTBABr ¼

dr

CeTBABr

The task is then to reconstruct the chemical potentials in the entire 2-dimensional plane ðcPOPC ; cTBABr Þ. Given the fact that for almost all points in the ðcPOPC ; cTBABr Þ plane the concentration of TBABr exceeds that of POPC by orders of magnitude, a perturbation

method could be used leading to reliable results [3]: the Gibbs Duhem equation allows to predict that the chemical potential of TBABr is hardly affected by POPC which is present only in low concentration. Thus, at the end we had to reconstruct only the chemical potential of POPC as function of both concentrations ðcPOPC ; cTBABr Þ. From the chemical potential lPOPC ðcPOPC ; cTBABr Þ we have computed the activity coefficient fPOPC ðcPOPC ; cTBABr Þ which is defined by lPOPC ¼ RT lnðfPOPC ðcPOPC ; cTBABr Þ  cPOPC Þ. In Fig. 9 the activity coefficient of POPC is plotted. Its value is normalized to unity for the binary system POPC/HPN below the cmc, i.e. in a parameter regime where the system POPC/HPN forms an ideal solution. The presence of TBABr leads to results that depend strongly on the concentration of POPC. Well below the cmc the activity coefficient decreases by almost two orders of magnitude with increasing concentration of TBABr. On the other hand, near and above the cmc the presence of TBABr increases the activity coefficient of POPC by more than one order of magnitude. Thus, the ionic surfactant TBABr has a tremendous effect on the behavior of the nonionic surfactant POPC which shows up in the variation of the activity coefficient by more than three orders of magnitude. At low concentration POPC is effectively removed from the solution by the presence of the ionic surfactant. The most likely explanation for this behavior is the formation of mixed aggregates. A possible scheme of such an aggregate can be conceived as follows: the POPC molecules are wrapped into a layer of ionic surfactants and, thus, are shielded from interaction with the solvent. If the number of both species in the aggregate is similar then the concentration of TBABr is hardly affected by the formation of aggregates while the monomer concentration of POPC can be strongly diminished. This would be a convincing explanation for the observed increase of the surface tension when adding TBABr to a weakly concentrated POPC/HPN solution, cf. Ref. [3]. Which model could explain the increase of the activity coefficient at higher POPC concentration? quite obviously, the formation of aggregates does not occur. If one starts with a pure POPC/HPN solution above the cmc, then adding even small amounts of TBABr lead to the dissolution of POPC micelles without initiating the formation of mixed aggregates. Here, a different model applies: the combination of TBABr/HPN behaves as one solvent of much higher polarity than corresponds to pure HPN, thus increasing the activity of POPC [3].

50

H. Morgner / Nuclear Instruments and Methods in Physics Research B 340 (2014) 44–50

4. Conclusions The first two systems presented lead to the observation that in some ranges of the parameter space molecules of the system display a bimodal distribution of their energetic situations. For the POPC/HPN system this is the range of concentrations shortly above the cmc where POPC molecules hindered from micelle formation have a significantly different value of the chemical potential compared to POPC molecules that are involved in micelle formation, either by being inside a micelle or in its immediate environment. The two configurations are apparently separated by some sort of energy barrier, even though the nature or size of this barrier could not be characterized. The binary mixture BA/FA displays in a range of bulk molar fractions features that are reminiscent of a miscibility gap in the surface even though the bulk shows miscibility at all proportions. The features observed within this concentration range have motivated discussing a bimodal distribution of energetic situations of molecules at the surface while the bulk is characterized by a single value of the chemical potential. While the concept of a bimodal distribution of (free) energy is not in contrast to thermodynamics, it still is unusual. A more thorough theoretical understanding would be desirable. The findings presented may be considered as challenge to thermodynamic concepts. One may tentatively generalize that those systems that experience the strong influence of capillary forces may in certain parameter ranges require a revision of common concepts of thermodynamics. On the other hand, the third system discussed demonstrates that the detailed investigation of surface phenomena may shed

light onto an improved understanding of the mutual influence of surfactants. In industrial applications hardly ever a single surfactant is used. Rather well chosen mixtures of surfactants are employed, the basis for choosing the mixture usually being empirical [16]. The development of a firm theoretical basis would be worthwhile. Data from carefully evaluated surface spectroscopic measurements could prove helpful in complementing bulk measurements [16].

References [1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11] [12] [13] [14] [15] [16]

A.W. Adamson, Physical Chemistry of Liquid Surfaces, John Wiley, 1982. H. Siegbahn, K. Siegbahn, J. Electr. Spectr. Rel. Phenom. 2 (1973) 319–325. H. Pohl, R. Manzoor, H. Morgner, Surf. Sci. 618 (2013) 12–19. F. Eschen, M. Heyerhoff, H. Morgner, J. Vogt, J. Phys. Condens. Matter 7 (1995) 1961–1978. K.R. Lovelock, C. Kolbeck, T. Cremer, N. Paape, P.S. Schulz, P. Wasserscheid, F. Maier, H.-P. Steinrück, J. Phys. Chem. B 113 (2009) 2854–2864. C. Kolbeck, T. Cremer, K.R. Lovelock, N. Paape, P.S. Schulz, P. Wasserscheid, F. Maier, H.-P. Steinrück, J. Phys. Chem. B 113 (2009) 8682–8688. S. Men, B.B. Hurisso, K.R. Lovelock, P. Licence, Phys. Chem. Chem. Phys. 14 (2012) 5229–5238. G. Andersson, Phys. Rev. A 75 (2007) 032901. G. Andersson, H. Morgner, H. Pohl, Phys. Rev. A 78 (2008). 032904/1-8. H. Morgner, Adv. At. Mol. Opt. Phys. 42B (2000) 387–488. Th. Krebs, G. Andersson, H. Morgner, J. Phys. Chem. B 110 (2006) 24015–24020. S.-Y. Lin, Y.-Y. Ling, E.-M. Chen, Ch.-T. Hsu, Ch.-Ch. Kwan, Langmuir 15 (1999) 4370–4376. H. Morgner, J. Phys. Chem. B 112 (2008) 1383–1390. H. Pohl, H. Morgner, J. Phys. Chem. B 114 (2010) 12847–12850. K. Kirmse, H. Morgner, Langmuir 22 (2006) 2193–2199. F. Schambil, M.J. Schwuger, in: J. Falbe (Ed.), Surfactants in Consumer Products, Theory, Technology and Applications, Springer Verlag, New York, 1987.