The investigation of liquid surfaces by electron spectroscopy

Journal of Electron Spectroscopy and Related Phenomena, 68 (1994) 71 L-177 0368.2048/94/$07.00 0 1994 - ElsevierScience B.V. All rights reserved

The investigation of 1iqGd w-faces by electron spectroscopy Harald Morgner

Institute of Experimental Physics, Science Stockumer Strasse 10, D-58448 Witten

Department,

University

Wittenperdecke

We evaluate electron spectrometric data taken from the surface of the solution of 0.5m tetrabutylammoniumiodide in the polar solvent formamide. In agreement with expectation we find strong enhancement of the salt in the topmost layer of the liquid. We describe how to derive the segregation depth profile of the salt making use of the fact that different electron spectroscopies lead to different observation depths. In addition we show how mean free paths of electrons in liquids can be determined with unprecedented accuracy by combining electron spectroscopy and conventional techniques likes surface tension measurementa

1 .IM’RODWCI’3ON Studies of liquid surfaces with electron spectroscopy are comparetively scarce even though the microscopic understanding of these systems could benefit to the same extent as is the cass for surfaces of solids. The short mean free path Xe of slow electrons in condensed matter ensures that electrons leaving the surface must originate from a site which is separated from the very surface by at most a few times Xe. This holds for XPS, UPS, AES and EELS. Indeed, these techniques have been used by a small number of groups for the investigation of liquid surfaces. The first such study was published by R and K.Siegbahn on formamide using XPS [ll, followed by a large number of works by H.Siegbahn and coworkers on several liquid surface% e.g. solutions of surfaces active salts [2-41. Two groups have made we of the He1 resonance line to perform UPS on liquid surfaces [S-S]. Ballard showed that AES and EELS (with energy losses in the eV range) could reproducibly be carried out on these Byeterns C7-Jeven though there

SSDT 0368-2048(94)02 186-4

remains the need to understand the precise contribution of these methods to the diagnosis of liquid surfacea The above mentioned spectroscopies have in common that their surfaces sensitivity is governed by the value of the mean free path length Xe of the emitted electrons. There is, however, one electron spectroscopy that is distinguished in that its observation depth is not related to a mean free electron path. It is MIES (=Metastable Induced Electron Spectroscopy), a technique which monitors exclusively the topmost layer of a surface [a]. The energy needed for electron emission is supplied by the excitation energy (19.819 eV) of met&able helium atoms He*(ls2q3S). The surface sensitivity of MtES goes so far that even the orientation of the molecules in the topmost layer can be determined [8]. Using a combination of MIES and UPS (HeI) we have been able to investigate several properties of liquid surfaces. We have determined the orientation of molecules in the topmost layer of pure liquids like formamide (FA) [8] and benzylalcoho1 (BA) [S,lO]. Other liquids like hydroxipropionitrile (HPN) do not show a prefer-

red orientation at the surface [ill. For binary liquid mixtures MIES allows to measure the composition of the topmost layer. We found strong enrichment. of benzylaicoho1 by a factor of up to 8 at the surface of a BA/E’A mixture [12]. On the other hand, TJF’Ssamples a layer of a few Angstriim. Combining both sets of data all owed us to determine the concentration depth profile if assuming an analytical expression n,dz)

= nLJ!k+

nzf*

em’/’

for the depth depending concentration of the component BA [123. Here the concentration profile is described by only two parameters; the excessz;;centration at the very surface n and the characteristic length B. R+lthin this approach the surface excess is easily evaluated as mrf *a r (2) = nBA One must realize, however, that the absolute value of s can be determined only if the Ups obaertvation depth X’ is known. Unfortunately, this is not the case since available data on the mean free path of electrons in organic matter are not very reliable in that they scatter within an order of magnitude [13]. Thus, instead of the quantity s itself only the ratio s/X’ can be determined. In this example

communication of our attempt

we

present

leads to an enhancement of the salt molar fraction at the surface by a factor as large as 15 for small bulk concentrations below 0.2 molality 041. We combine the MIES data 041 and XF’S data taken by HSiegbahn [3] with newly measured UPS data 051. The respective experiments were performed at the Berlin sy-nchrotron radiation facility BESSY. The observation depth X’ has been varied in two ways, first, by varying the photon energy and, hence, the energy of the emitted electrons. The second method to control the effective observation depth has been employed before by Siegbahn for liquid surfaces [31: measuring electrons under an angle o( with respect to the surface normal results in the decreased observation depth x7 = xe * COBo(

(3)

2. TEEORY We consider a liquid consisting of two components A and B. The concentration of A as function of distance z from the surface is written as n*(Z)

=

nidk

+ niXC(Z)

an

-firstly, to determine concentration depth profiles without assuming an analytical function for their shape -secondly, to estimate more accurately the mean free path X of electrons which serves as scaling length of the concentration profile, irrespective of whether an analytical function is chosen or not. The system we investigate is a solution of the salt tetrabutylammoniumiodide (TBAI) in formamide (FA). The hydrophobicity of the positive ion TBA+ causes segregation of the salt to the surface which

with nitik being the known number density of A in the bulk of the mixture and nix”(z) describing the deviation of the actual density from the bulk value. Its value is positive for surface active specieg but negative for the other component. Electron spectroscopy with an effective observation depth X’ of the liquid leads to a contribution from component A which is equivalent to a signal from N molecules of species A if no weakening o3 the signal via a limited free path length would occur

NA = f dz aA

I?/”

113

The analoguous definition shall hold for component 3. Usually, the excess concentration n exc z is described by an analytical an&z. %()ommonly ussd shapes are exponential (cf. eql) or step functions [2,3]. As discussed by Siegbahn [3], the determination of nixc(z) without a mathematical ansatz requires experimental data of extreme precision. Our own experience supports this statement. In order to evaluate presently available data and still not to influence the outcome of a profile by a rigid choice of a trial function we use the ansatz

qz, = nidk for

+AznLxc

(k)

(6)

(k-l)Az $ z < kAz, k=l,..,lO

This histogram ansatz is rather flexible, but requires large sets of data in order to determine the increased number of parametera Using q(6) th e observed ratio of the contributions of both molecules to the electron energy spectrum is described as R = c N, / NB (71 Here c accounts for a possible difference between the ionization cross sections of A and B. If X’ is varied via observation angle (x then c remains constant as long as effects of angular distributions can be excluded This is the case if the bands considered for A and B in the electron spectra have the same angular distribution. In case of the valence electron spectra evaluated below we found c to depend on the photon energy but not on the emission angle. The C(ls) core electron spectra we evaluate assuming c=l. With above formulation of the problem, and the parameters n6*xc (k), nT(z) for any energy o emrtted e ectrons- the mean free path X, and eventually c ha-

ve to be fitted to experimental data. These data are given as ratios according to eq(7). A reduction of parameters is carried out by assuming the liquid to be compact, i.e.

Gxc(z) = - nr”

(z)

vA/vB

being the volumes of the EZecy$eS: %is is an approximation that appears necessary at the moment, but is not to severe and may be overcome in the future. In consequence of eq(8) we have c(k)

=

- nr

(k)

vA/vB

(9)

The width AZ of the 10 layers introduced in eq(6) has been varied in the initial stages of the work but then set to the fixed value AZ = 0.05 * Xe(lOOOj where Xt (1000) denotes the mean free path of electrons emitted with 1OOOeV kinetic energy. This refers to the situation of Siegbahn’s XPS data on C(ls) [31. x, (1000) serves as scaling length in our treatment. Thus, not only AZ but as well the electron path lengths i\= for the smaller kinetic energies in our UPS data are measured in units of this quantity. Xe(lOOO) itself will be evaluated at the end by comparing with surface tension measurements. We follow two strategies to determine the still large number of parameters: 10 values for the excess concentration n i’=(k), k= l,..,lO plus the energy depending parameters c and he 1 Method1 consists in simply selecting all necessary parameters via a random number generator. Then the quantities R from eq(7) can be determined and be compared to their experimental counterparta Combinations of parametirs that lead to an averaged relative deviation

which exceeds a preset limit, are rejected. Among the accepted sets of parameters we compute the mean values and the standard deviationa This method is simple and has the advantage that it is unlikely that one ends up in a local minimum of F in the multidimensional (i.e. 15-16 dimensional) parameter space. The acceptance rate depends on the bounds between which the random number generator selects trial parameter values. The results shown below are obtained from 80 parameter sets being accepted out of 50000. Methodll aimes at reducing the number of parameters with nonlinear influence. Starting with eq(7) and making use of eq(8)and (9), reqectively, we obtain for the quantity N, R* nidk - I&__~ = -_-_____-___-_ NA 1 +RVA&

01)

On the other hand we can evaluate via the ansatz (6) as

NA= ,?nldk +

1’

E

,qcc

The parameters X= (and eventually c) are varied systematically or again via random number generator. Once theee are chosen, the values of the n .,,(k) can be determined from e&3) through a linear least sqnares fitting routine which is straightforward. Accordingly, the error depends only on the few parameters X, and c and can be minimized much easier. In the course of the evaluation of the data we found that we have to add further constraints on the nix=(k) in order to avoid unphysical results E.g. the concentration can not dro below zero which requires n cxc(k) 2 -nAJk for all k In order to reta,i$ the advantages of a Ii: near fit we account for this problem by adding additional linear equations to (13) I [nr(k-l)-2ny(k)+ny(k+l)] for k E[2,9]

NA

+

(eAZ&)

free path ‘he _ In case of valence electron spectroscopy we have in addition to deal with c, yet to be determined. For a given electron energy the actual observation depth X’ depends on the known electron emission angle a via q(3).

(k) ,-kAa/X’

k-1

= 0 04

We found that ~4 0.05 avoids unphysical results but does not limit the flexibility of our ansatz. Of course, increasing E to values > 1 tends to reduce the concentration depth profile more and more to a linear interpolation between surface and bulk concentration.

which can written as a system of linear equations for the parameters nftxc(k):

3. Rmurim ?

a(j,k)

nF(k)

=

b(j)

(13)

kd

with

a(j,k) =

b(j)

(eAzP” -1) ck W”

=NA

/A’ -

upk

Here, j is the numbering of the experimental values R = R(j). Associated with every j is a known value of electron energy and an unknown value of mean

We have applied the above outlined procedure to two sets of data from a solution of tetrabutylammoniumiodide (THAI) in formamide (FA). The molality of the solution is 0.5. The first set of data, i.e. measured ratios R according to from valence e+(5) and (71, originates electron spectroscopy Cl51 taken with photon energies between 25eV and 66eV

yielding electron energies between 15eV and 50eV. The second set of data is derived from C(ls) core electron spectroscopy CM] with photon energies between 17eV and 97eV above threshold In both cases we have incorporated the MIES result [lO,l4) which we treat as having the observation depth X7=0 and the respective ratios from XPS [3]. The XPS related mean free path of the Xt(lOOO) serves as scaling electrons length throughout. the fitting procedure.

0.00 0.06 0.04 0.02 02&(1000)

0

0-

mide.

x’/xe(looo)

Fig.1

RJLtiO

of

big

dots

data. from

x’b=N~~/NFA

observation from

Evaluated AR.UF%

R(

Big

1 an

depth

valence circle

is from

A’.

electron MIES,

XPS

Fig.1 shows the ratios R/c= N JNFA as function of the normalized oEe rvatlon depth A’/>, (1090) as obtained from the valence electron spectroscopy data. Note that for every electron energy the parameters c and X are fitted as well. The full line is the” back calculation of the quantity R=R(X’) from the determined TFMI concentration profile. The latter is presented in figs. The abscissa is the dietance from the surface, again in units of Xc(lOOO). The shaded bars visualize the result from the fitting methodI. Their lower and upper values represent the mean minus and plus the standard deviation, respectively :

profile

function

number

Other

densitiy

nTBAI(z)

of

surface. n is given

bulk

0

function

Density as

the

d

_i

Fig.2 TBAI

0:&5 of

distance in of

explanationa

units pure

from of

the

forma-

in text.

The standard deviation does not show the correlation between adjacent values of the histogram. One value being large leads to a small value with its neighbore. This can be read of the fact that the integrated excess concentration F,exedk)

(15)

k==l

has only a small standard deviation of a few percent. The result from methodII is shown for comparison. The fitted values are indicated by thick lines. The agreement between the two methods is satisfactory within the standard deviation of methodI. The values from methodI.I suggest that the enhancement of TBAI near the surface is followed by a depletion layer. Comparison of both methods shows that we can not deny, but certainly not positively claim such a depletion zone. It is, however, safe to state that the excess concentration of TBAI is de&bed by step function rather than by an exponential, but is not identical to either (see fig.2)

Df.51, i.e. constant, plifies to

r =

that f can be treated as a then the Gibbs equation sim-

/v

3

vFA ________T?E________--*

vFAkXSA1+

%YB&%3Alj

%rBAI-----d-i ---

RT dsTBm

!

0

Fig.3

RJLtio

function ARUPS

from

C(h)

Big

circle

data.

dots

R( X’WJTBsu/NFA obacrvation depth

of

Eva1 uated big

1

1

x’/x,(looo)

0

from

core ie from

aa A’.

electron MUSS,

We address now to the absolute length of our scaling parameter Xt(lOOO). It can be determined in the following way. The Gibbs equation relates the surface excess r to the thermodynamic quantities surface tension y and activity a= f X with X being the bulk molar fraction of the dissolved component and f the activi ty coefficient vFA /v TBAI _ _l_------______-I____ ‘FA/

%33AI+ *

*

%&=&I)

1 ----___ du

R’r dln aTBM

Now, surface tension measurements as carried out in our lab [lo] are sufficient to determine the surface excess r. The integrated excess concentration from eq.(15) is related to the surface excess Via

XF’S

The data from core electron spectroscopy are displayed in fig.3. For reasons unknown, the data scatter more strongly than in fig.2 around the function FL=R(X’) calculated from the fitted profile. Only method II has been employed in this case. The agreement with the first set of data is good. The same holds for the fitted concentration profile.

r =

on

since in the fitting procedure all lengths are consistently measured in units of X,(1000)_ The above expression allows to determine

Xe(iOOOj =

45 d @wn)

(1%

We are now in the position to give an absolut value for the thickness of the surface layer with enhanced TI3AI concentration. We obtain * 10 bgstr6m which is about the diameter of the TBA+ ion. A similar result has been obtained before by Siegbahn [3] on the basis of the XPS data. It is interesting to note, however, that in [3] X (1000) was taken to have a value of 25AngstrSm and that the shape of ncxc(z) had to be assumed beforehand.

(16)

If we assume that the bulk molar fraction of the slblt (which is X=0.022, computed from 0.5 mol TBAI being diesolved in lkg FA * 22 mol FA) is sufficiently low that Benry’e law holds

4. SVMMARY Summarizing we can state that the present study presents a distinct progress towards a more detailed understanding of the liquid surface as a 3-dimensional object. On the other hand our results

demonstrate that it is worthwhile to make efforts for improving the accuracy of the experimental data. As an example we point out that our interesting finding of a depletion zone that follows the layer of enhanced concentration depends on the method of data evaluation. Both methods of data treatment give good agreement with the experimental data within the estimated experimental error and thus the depletion zone can not be considered a fact.

8. W.Keller, H.Morgner and W.A.Miiller, Mol. Phys. 57 (1986) 623 9. K. Roth, PhD Thesis 1990, University Witten/Herdecke 10. XOberbrodhage, PhD Thesis University WittenjHerdecke 11. KRichter, PhD Thesis sity Witten/Herdecke

1992,

1992, Univer-

12. H.Morgner, J.Oberbrodhage, K.R.ichter and K.Roth, Mol.Phya73 (1991) 1295 13. M-P.&ah and W.A.Dench, terface Anal. 1 (19’79) 2

Surf.

In-

14. HMorgner, J.Oberbrodhage, K.Richter and K.Roth, J.Phya: Condena Matter 3 (1991) 5639 The work on electron spectroscopy of liquid surfaces has. been enabled by grants from the German Science Foundation (DFG) and from the Federal Ministery of Research and Technology (BMFT)

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R.Moberg Spectr.

and Rel

RMoberg,F.B6kman,OBohman and HSiegbahn, Report 1219 (1990), Upp sala University

5. L.Nemec, HJ.Gaehrs, D elahay, J.Chem Phya

L.Chia and P. 66 (1977) 4450

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15.

F.Eschen, M.Heyerhoff, HMorgner and M.Wulf (1993) in preparation

16.R.A.Alberty, “Physical Chemistry”, John Wiley& Sons, New York, 1987