Langmuir 1993,9, 2630-2640
2630
Calorimetric Studies of the Surface Aggregation of Adsorbed Molecules in Ionic Surfactant Adsorption onto the Heterogeneous Oxide Surfacest J. Narkiewicz-Michalek and W. Rudzinski’ Department of Theoretical Chemistry, Faculty of Chemistry UMCS, P1.M. Curie-Sklodowskiej, Lublin, Poland 20-031
S. Partyka Laboratoire de Physico-Chimie des Systemes Polyphases, LA 330, U.S.T.L.,Place Eugene Bataillon, 34060 Montpellier Cedex, France Received December 21, 1992. In Final Form: March 22,199P
A review is given of our extensive experimentalstudies of the calorimetriceffects accompanying ionic surfactant adsorption on the heterogeneous surfaces of some oxides. Then equations are developed for the heats of surfactant adsorption, corresponding to two models of surfactant adsorption: one of them assumingthat the surfaceaggregationof adsorbed surfactant molecules is a two-dimensionalcondensation and the second one assuming that this is a two-dimensionalmicellization. The obtained experimentaldata for heats of adsorption are compared next with the theoretical predictionsarising from these two models. There are systemswhere the assumption of two-dimensional condensation,along with the model of perfect random topography seems to explain the behavior of the experimentalheats of adsorption. There are also systems where it is difficult to discriminate one aggregation mechanism in favor of the other one. A simultaneous analysis of experimental isotherms and heats of adsorption seems to suggest that the hydrophobic phase formed at lower surface coverage is a noncondensed ‘swelling” phase.
Introduction The adsorption of surfactants from aqueous solutions onto polar surfaces is a process of great practical importance (flotation, washing, purification of wastewaters, biological systems, ). So it is no surprise that the investigation of surfactant adsorption was the subject of hundreds of publications and is extensively carried out in many laboratories in the world. These investigations led scientists to establish some fundamental features of that adsorption mechanism. Thus, at very small surface concentrations, the adsorption proceeds via attachment to the surface of single monomers by their polar heads, and a certain number of CH2 segments. As the surface concentration increases, the growing competition for the available surface area will decreasethe (statistical)number of CH2segments by which monomer molecule is attached to the surface. The changing conformation of the adsorbed surfactant molecules will favor the hydrophobic interactions between the more or less vertically oriented hydrophobic moieties. Then, at a certain concentration, called “critical” concentration, a sudden increase in the adsorption isotherm is observed, due to the formation of surface aggregates having a compact hydrophobic core. This was shown by Levitz1*2 and by Somasundaran and co-worker@ using a special fluorescence technique to monitor that aggregation.
Though the above described mechanism of surfactant adsorption onto polar surfaces is now generally accepted, the nature of that process is still not well understood. Cases and co-workersGg see that process as a twodimensional condensation of monomers or dimers attached to the surface by one polar head. They apply next the Tiemkin (Bragg-Williams) isotherm equation developed for the one-site occupancy adsorption with nearestneighbor interactions between adsorbed molecules. That equation predicts a two-dimensional condensation to occur, manifested by a vertical discontinuity on the predicted theoretical adsorptionisotherm. Such discontinuities have really been observed by Cases and co-workers in some of the investigated adsorption systems. Sometimes it was a series of steps, as shown in the work by Cases and coworkers?~~ These vertical steps were ascribed by Cases to two-dimensional condensations on a patchwise heterogeneous surface, composed of a certain number of distinct homogeneous patches. The lack of such vertical steps in some systems was explained as being due to a large number (an almost continuum spectrum) of various patches. That model of the surface aggregation has been refined next by Schechter and co-workerslOJ1considering more carefully the bilayer character of adsorption. They emphasize that the aggregates which result from the two-dimensional phase transition tend to be bilayer, much like lipid membranes, when charged surfactants adsorb from aque-
t Forwarded for publication in the special issue of Langmuir devoted to the international symposium Effects of Surface Heterogeneity in Adsorption and Catalysis on Solids. * Author to whom the correspondence should be addressed. e Abstractpublished in Advance ACS Abstracts, August 16,1993. (1) Levitz, P. Proceeeue d‘aasociation de molecules non ioniques: adsorption a l’interface solide hydrophile-em et micellisation en phase aqueuee. Ph.D. Thesis, 1985. (2) Levitz, P.J. Phys. Chem. 1986,90,1302. ( 3 ) Somasundaran, P.; Turro, N. J.; Chandar, P. Colloids Surf. 1986, 20,146. (4) Somasundaran, P.; Kunjappu, J. T. Miner. Metall. Process. 1988, May.
(6) Somasundaran, P.; Kunjappu, J. T.; Kumar, Ch. V.; Turro,N. J.; Bartan, J. K . Langmuir 1989,5,216. (6) Cases, J. M.; Mutaftachiev, B. Surf. Sci. 1968, 9, 67. (7) Rakotonarivo, E.; Bottero, J. Y.; Cases, J. M. Colloids Surf. 1984, 9, 273; 1985, 16,163. (8)Cases, J. M.;Doerler, N.; Francois,M. XVZZnternational Mineral Processing Congress; Forssberg, E., Ed.; GEDIM St. Etienne, France, 1988, p 1477. (9) Cases, J. M.; Vierae, F. Langmuir 1992,8,1251. (10) Scamehom,J.F.;Schechter,R.S.;Wade,W.H.J. ColloidZnterface Sci. 1982, 85, 463. (11) Harwell, J. H.; Hoskins, J. C.; Schechter, R. S. Langmuir 1986, 1 , 251.
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0743-7463/93/2409-263~~04.00l0 0 1993 American Chemical Society
Adsorbed Molecules on Heterogeneous Oxide Surfaces
ous solution on oppositely charged surfaces. Their calculations suggested that very little of the surface was ever covered by a monolayer. While accepting that hypothesis, one has to assume the formation of infinite (in two dimensions) aggregates, as the 2D condensation means simply a phase separation in two dimensions. The dimensionsof these aggregateswould be limited in practice only by the dimensions of the homogeneous microdomains. The fluorescence spectroscopy investigations by Somasundaran and co-workers showed that the aggregation number is finite and changes with the adsorbed amount. This, on the other hand, would suggest similarities between the surface aggregation and the micellization occurring in bulk surfactant solutions. Thus, in some of our recently published W O ~ ~ weS , treated the surface aggregation like a two-dimensional micellization. Though the driving force for such twodimensional micellization is the same, i.e., these are the hydrophobic attractive interactions, the nature of this process is somewhat different. The two-dimensional condensation assumed by Cases and Schechter must result into phase separation, Le., formation of aggregates infinite in two dimensions. (Limited practically by surface geometry.) Micellization is a process leadingto the formation of surface aggregates of finite dimensions. However, as the presence of solid surface must affect stronglythat surface aggregation,deep similaritiesbetween the surface aggregation and the bulk micellization may be put into question. Trying, thus, to understand the nature of that surface aggregation,we have decided to investigate first which features of the actual adsorption systems are predicted by the model of two-dimensional condensation and which predictions diverge from the experiment. So,in our latest work16wehave shown that, surprisingly, the concept of the 2D condensation explains very well the dependence of the critical bulk concentration on the length of the aliphatic chain. The critical bulk concentration is that one at which the sudden (not necessarily vertical) step occurs on the experimentaladsorption isotherm. That intriguing theoretical finding has encouraged us to investigate the model of 2D condensation in more detail. We have shqwn in our previous p u b l i ~ a t i o n s that l~~~ adsorption calorimetry is a powerful tool to investigate the mechanism of surfactant adsorption. So, we now investigate to what extent the studies of the calorimetric effede accompanyingsurfactantadsorption may advocate for the model of 2D condensation. This is the purpose of the present work. Theory We used the simple Koopal approachle as the starting point in our consideration. That approach is based on the following assumptions: (1)The surfactant molecule is a chain containing one charged group (valency T ) and (r - 1)apolar segments. As the first approximation each CH2 group of the aliphatic chain can be considered as one segment. (2) In the adsorbed state each chain of, in total, r segments has a sequence of m segments adsorbed in the (12) Partyka, S.;Rudzineki, W.; Brun, B.; Clint, J. H.Lagmuir 1989,
5. 297.
(13) Narkiewicz-Michalek, J.; Rudzinski, W.; Keh,E.; Partyka, S. Colloid8 Surf. 1992,62,273. (14) Narkiewicz-Michalek, J. Ber. Buns.-Gee. Phya. Chem. 1990,94,
787. .-..
(16)Narkiewicz-Michalek, J. Ber. Buns.-Gee. Phy8. Chem. 1991,95, 86. (16) Koopal, L. K.;Wilkinson, G. T.; Raleton, J. J. Colloid Interface Sci. 1988,126,493.
Langmuir, Vol. 9, No.10, 1993 2631
first layer as a train, and the remaining (r - m) segments protrude into the solution as a tail. (3) Due to Coulombic attraction the charged head segment has a strong electrostatic affinity to the surface, so that all adsorbed head segmentsare present in the first adsorbed layer (closest to the surface). (4) In a poor solvent, as water is for surfactants, segments tend to cluster together. The segment density distribution is therefore assumed to be homogeneous (step function), and extends over r / m layers each with a volume fraction 4j equal to 41. Only for such simplified segment density distribution (4i) is the calculation of the free energy of mixing relatively simple. ( 5 ) The surfactant chain is flexible both in the solution adsorbed state. ~ and ~ ~in the ~ With these assumptions Koopal et al.I8 developed the following isotherm equation
where the subscript asterisk (*) refers to the equilibrium bulk solution and W is a combinatorial factor the simplest form of which is the following:
w = x,(n-Al (2) In eq 2 XO is the fraction of the nearest neighbors in the same lattice layer and XI is that one in each of the adjacent layers, hence 2x1 + ho = 1. The last exponential term on the right-hand side of eq 1 describes the interactions between the surfactant and surface, ( m g i ) , then between the adsorbed surfactant molecules, [2rg'(41 - 4,)1, and between the polar head and the surface (-7Y1). Above z i is the weighted average net adsorption energy per segment mz,' = (x,P + X 1 x 9 + ( m - l)(x," + X1xa0)
(3) where xsP is the polar segment (p)-surface (8) interaction energy, xw is the "exchange energy" parameter for polar segment-water (PO) interaction, and the meaning of x0. and x a p is now obvious. The meaning of z' is as follows:
z'= ( x , + X + O1 +
(1--;)y-
Finally Y1is the reduced potential e+l/kT, where $1 is the potential at the plane through the centers of the adsorbed polar heads. The potential + l ( x ) can be interpreted as a sum of two contributions, the first originating from the plane charge itself and the second from the image charge (5)
where a0 is the area of a unit cell (the molecular cross section of a segment), usis the surface charge density sign included, e = ere0 with €0 the dielectric permittivity of vacuum and cr that of water, T is the valency of the adsorbing ion, and K is the reciprocal Debye length, which in the presence of a symmetrical indifferent electrolyte can be given as K = e(2n+2/&T)1/2 (6) where no is the number of ions per unit volume, z is the valency of the indifferent electrolyte, and k is the Boltzmann constant.
Narkiewicz-Michakk et al.
2632 Langmuir, Vol. 9, No. 10,1993
For most surfactants water is a poor solvent and the maximum value of q5# is given by the bulk critical micelle concentration. Hence, for most practical situations 4a 4;,c the chemical potential of monomer in aggregate is lower. So, at 4* = 4*,ca vertical rise on the adsorption isotherm will be observed from to a constant value rbhyer. Harwell et al. believe that the bilayered coverage represents complete saturation of the surface. Here again a difference is to be emphasized between their concept of aggregation and the model of two-dimensional condensation. In the model of twodimensionalcondensationnot all solid surface is saturated at 4; = d;,c. Harwell et al." next accept the model of patchwise surface. The surface charge usis the characteristic which determines 4*,cfor some patch. Thus, for each solution of a given surfactant concentration and a counterion concentration, there corresponds a surface charge density sufficient to stabilize an admicelle. The adsorption on the patches with lower charge density will be described by the isotherm rI,whereas all the other patches will be completely covered by admicelles. Accordingly,the total adsorption isotherm of surfactant rt is given by the sum (28) Pashley, R.M.; Israelachvili, J. N. Colloids and Surf. 1989,2,169.
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2638 Langmuir, Vol. 9, No. 10, 1993
where u8cis the minimum charge density which stabilizes the existence of admicelles. Then rI is assumed to be Henry's isotherm, though it may be another isotherm equation as well. Of course, it may be also the isotherm eq 11 developed here by us. Thus, our theoretical treatment could be combined with the approach proposed by Harwell et al. Therefore, it seems worthwhile to consider the behavior of the heats of adsorption, predicted by their approach. For a homogeneous surface Qatwill, in general, vary with coveragein the initial region from zero to a criticalcoverage rc= F(4,,J and then should be pretty constant, for r > rC,like the heat of bulk micellization. In the case of a patchwise heterogeneous surface, the observed heat of adsorption will be given by the following average
(33) where Qat"& is the heat of admicelle formation and Qst(u,) is to be evaluated from the isotherm equation FI(u,,$,). Then because Qat(a8)is the function of coverage,in general, the observed heat of adsorption QEtshould no longer have a linear section, when plotted as the function of the adsorbed amount. Let us remark at this moment that assuming the model of two-dimensional condensation, along with patchwise topography, will also lead us to the conclusion that there should be no linear section in the experimental Q,t(r) curves. At the same time (it has been already mentioned), the experimentally observed isotherms should not have a vertical step. Thus, a simultaneous inspection into the shape of an experimental adsorption isotherm, and the corresponding heat of adsorption, allows us to judge to which extent their behavior does support an assumption about surface topography and the mechanism of the surface aggregation. We may summarize our conclusion as follows: 1. A very sharp increase at a certain surface coverage rc= I'(4,,J on an experimental isotherm, together with a pretty constant section on the corresponding heat of adsorption curve, will be evidence of random topography. Whether this is a two-dimensional condensation,or a twodimensional micellization, will depend on how much the aggregation changes the molecular status of the aggregating molecules. 2. The larger the deviation of the experimentalisotherm from a steplike function, the larger deviations from the model of random topography. These deviations will also lead to less and less marked section in the corresponding heat of adsorption curve, within which the heat of adsorption is constant. It should, however,be emphasized that the above discussed behavior may be associated either with a two-dimensional condensation or with a twodimensionalmicellization on surfaces exhibiting patchwise topography to a certain extent. It may even be a slightly patchwise character, associated with weak lateral electrical fields. Such small potential gradients may not practically affect the adsorption of simple ions but may strongly affect the two-dimensional aggregation. (As we have already mentioned, the systems of interacting molecules are very sensitive to even weak external fields in the physical regimes where these systems may undergo a phase transition.) But then, there still arises a next question concerning the structure of the hydrophobic phase, formed in the initial coverage region (0, $Its).
According to some widely spread views, surface aggregates exist even at very small surface coverages. So, it has been assumed for a long time that because of the hydrophobicnature of the surface, these aggregates must be hemimicelles(monolayeredaggregates). It was not until 1982 that the structure of the aggregates of adsorbed surfactant began to be systematicallyreexamined. In 1982 Scamehorn et al.lO have presented a theoretical model of the formation of the surfactant aggregate on the surface. Their theoretical approach started from Cases' concept of two-dimensional condensation but was modified to allow bilayered formation to occur subsequent to either monolayered aggregate (condensed phase) formation or simultaneous formation. Then, the model of patchwise topography was accepted along with a Gaussian distribution of adsorption energies. That approach, applied to the adsorption systems they were studying, led them to the conclusion that even at low coverages the adsorbed surfactant layer was built up primarily by the patchwise formation of essentially bilayer aggregates. Three years later (in 1985),Harwell et al." arrived at a similar conclusion by assuming that the bilayer aggregates are admicellesand developing a theoretical approach based on the model of pseudophase separation. The principles of their approach and the corresponding fundamental equations have been discussed above. Later on, Yeskie and HarwelP have shown that, the path leading to the formation of bilayered aggregates should be preferred on surfaces with high surface charge densities. On the contrary, low surface charge densities will favor the path leading to monolayered aggregates. However, Yeskie and Harwell do emphasize that "the equations derived in (their)paper do not address whether or not any surfactant aggregate will, in fact, form at a given set of conditions. They only address whether a monomer in a hypothetical aggregate at those conditions would be at a lower chemical potential in a hemimicelle or in an admicelle." In particular, their treatment does not address the question whether monomers which are neither hemimicelles nor admicelles might have a lower chemicalpotential in some conditions. As the existence of bilayered aggregates at higher surface coverages seems to be commonly detected, the problem which deserves further experimental and theoretical study can be formulated as follows. Does the formation of the bilayered aggregates proceed directly from adsorbed monomers or via hemimicelles which are formed first? In other words, what is the nature of the hydrophobic surface phase, formed in the initial region of surface coverages. Looking for a suitable experimental data for analysis, one should focus the attention on these physical regimes where the possibility of existence of bilayered structures should be small. It seems that we have such a system in our data collection. It is shown in Figures 7 and 8. There we can see two sets of experimental data: one measured at pH values ranging from 8 to 7 and the other one measured at pH = 4.1. Let us focus our attention on the data measured at pH = 8-7 first. One can easily deduce from these figures that, at surface coverage of about 50 pmol-g1a quite sudden switch takes place from one adsorption mechanism to another. Then at pH = 4.1 the adsorption terminates at 50 pmo1-g' indicating, thus, that only one of these two types of adsorption is now observed. There is no doubt that the second type of adsorption starting at r > 50 pmol-g-l is simply the formation of (29) Yeskie, M.A.; Harwell, J. H.J. Phys. Chem. 1988,92, 2946.
Adsorbed Molecules on Heterogeneous Oxide Surfaces
Langmuir, Vol. 9, No. 10,1993 2639 to the chemical potential ps due to the heterogeneity of the silica surface. Thus we accept Koopal's block profile model for CH2 mers as a fundamental approximation, but then we multiply +It in the term
I
2
0
C lmM1
6
Figure 7. Adsorption isotherms of ClrHaN(CHS)firadsorbed on silica at 25 "C, at pH varying between 8.2 and 7.0 (0)and at constant pH = 4.1 (+I. The solid lines were drawn by hand to help eye. The arrows indicate corresponding cmc values.
-101
0
I
I
I
I
02
04
0.6
08
I
by a certain factor 5 > 1to account for the fact that the total occupancy of lattice sites in the first lattice plane next to surface will be higher than in the other lattice planes. When r and m are large, that correction may be negligible. On the contrary, it will be essential for small m. Generally speaking, it will be a function of m and r, but we will introduce it into our equations as a certain effective constant 5. Otherwise, it would make our equations very complicated. In spite of a large number of the unknown physical parameters appearing in our equations for r and QBt,the list of the independent best-fit parameters is rather short. In the isotherm equation, the best-fit parameters are cyp, Po, rm,t, PI, and P2 defined as follows:
As we are not sure which kind of medium e and K are to be referred to, we will also treat y = eKao as another bestfit parameter. The isotherm equation takes then the form
10
r/rlllax
Figure 8. Heats of adsorption of CuHd(CHs)aBr on silica at 26 O C , at pH varying between 8.2 and 7.0 (0) and at constant pH = 4.1 (+). The solid lines were drawn by hand to help eye. bilayered structures. So what we observe at pH = 4.1 is just a solely monolayer formation. Thus, we have a unique chance to study separately the mechanism of the first type of adsorption, making the surface hydrophobic. The maximum amount adsorbed at pH = 4.1 is just not 2, but 3 times lower than that adsorbed at high pH values where bilayered aggregatesexist. This would suggestthat the monolayer is not a condensed phase. So, if such an aggregation does not occur, there must be also another adsorption mechanism, characterizedby a still lower value of adsorption potential. Of course, it goes without saying, that it will be adsorption of single monomers. Then, in the absence of a phase transition, small deviations from the random model of silica surfaces should not be important. Consequently the adsorption isotherm and the corresponding heat of adsorption at pH = 4.1 should be well described by our eqs 11and 26. However, before applying these equations to fit the experimental isotherm and heat of adsorption of TTAB on silica at pH = 4.1, a certain modification in these equations is to be made. Namely, in the original Koopal's approach the polar head is assumed to occupy only one lattice site, just like the -CH2 group (mer). (The dimensions of the auxiliary theoretical lattice of sites are dictated by the dimensions of the CH2 mer.) The polar group of our surfactant is much larger than CH2 mer, so we must introduce a certain correction to account for this difference. As the polar group is always located in the first lattice plane, the above mentioned difference will affect mainly the contribution
The lack of and gap on our list of parameters is due to the assumption that the charged nitrogen atom surrounded by three methyl groups does not interact strongly with water molecules or with CH2 segments. So, we simply put these parameters equal to zero in our numerical bestfit exercises. As for parameter , , ' l the physical values of l/r, should lie between 5 and 10 A2. Another controlling factor is the calculated value of w which should range from kT to 2kT. (In the present approach w is the function of coverage.) Then, a a and apshould be chosen in such a way that the tangent of the calculated isotherm in the limit 4*,41t 0 should be one-half or less. (Such values are found in the experiments for ionic surfactants adsorbed on oxides.) Considering the structure of the polar group of TTAB, the factor 5 should vary between 3 and 1. Coming now to the related equation for the heat of adsorption, we have only two parameters more
-
and
and the contribution to the heat of adsorption due to the
2640 Langmuir, Vol. 9, No. 10,1993
Narkiewicz-Michakk et al.
Table I. Best-Fit Parameters Leading to the Theoretical Isotherm and Heat of Adsorption, Fitting the Experimental Data Presented in Figures 9 and LO. Pl PZ PS(de&) P4 (deg-9 xm a&T a*kT E BKao (OV-lemol-1) rm (@mol& 6.04 0.0 0.001 0.019 1.65 0.92 0.85 1.9 88987.0 688.0
The cmc value used in our calculation was equal to 4.2 m M as suggested by the calorimetric investigations of bulk micellization, and the aggregation number was taken from literatureg0as equal to 68.
-
L
1
1,
2.0
20
10
10
I
0
1
3
2
5
4
CimMI
Figure 9. Agreement between experimental (m) and theoretical (-) adsorption isotherms of TTAB on silica a t constant pH = 4.1. The theoreticalcurve wasobtainedbyusing theparametera collected in Table I. The arrow indicates the cmc value.
/
1
/---------
h
051
i
0
I
1
I
02
OL
06
, 06
Figure 11. log(m) (-) and w (- - -) plotted aa a function of the relative coverage I'/I', for the system TTAB on silica a t constant pH = 4.1,calculated by using the parameters collected in Table I.
-
I
0
'=E- 20Y I
I
a"l510-
5-
0
02
OL
06
08 r/rlllOX
Figure 10. Agreement between experimental (m) and theoretical
(-) heats of adsorption of TTAB on silica a t constant pH = 4.1. The theoretical curve was calculated by using the parameters collected in Table I.
interactionswith the surfacetakesnow the followingsimple form: (37)
Thus, trying to fit simultaneously the experimental adsorption isotherm and the experimental heat of adsorption curve, we did not have much field of maneuver in choosing our best-fit parameters. They are listed in Table I, and the agreement with the experiment is shown in Figures 9 and 10. Figure 11 shows m and w as functions of the relative coverage I'/I'". Because the thickness of the adsorbed layer (block) increases not only due to the increasing number of the adsorbed molecules but also due to their changing orientation from the flat to a vertical one, we may call it a "swelling" adsorbed phase. Bdhmer et al.3l-33 have developed a computer program to study the adsorption of ionic surfactants on oxides in (30) Nagarajan,N.;Ruckenstein,E. J.Colloid Interface Sci. 1979,71, 580. (31) B6hmer, M. R.; Koopal, L. K. Langmuir 1992,8, 2649.
terms of a lattice approach. They applied the self-consistent field approach, originally developed by Scheutjens and Fleer34*3s to study polymer adsorption. The adsorbed phase is not longer assumed a priori to have a block profiie, but the density profile of CH2 mers and of coadsorbed ions is calculated as a function of the distance from the surface. It is, however, interesting to see (Figures 6 and 7 in the work by BBhmer et al.9, that in conditions where strong preferences exist for monolayer adsorption, the calculated density profile has really a blocklike profile. BBhmer et al. argue that "simple models often fail to give an accurate prediction of adsorbed amounts ...."But then, there appears the question, what "simple models" means in our case. More detailed calculations of the density profile surely make real progress toward a more realistic treatment. At the same time, however,neglecting lateral energetic inhomogeneity of the first lattice plane (solid surface) must be seen as a serious simplification. The shape of the heat of adsorption curve in Figure 10 is typical for adsorption on heterogeneous surfaces. The authors of the present publication have doubts if the present approach by BBhmer et al. could reproduce that shape. We continue our theoretical analysis of the large body of experimental data on the heats of surfactant adsorption obtained in the CNRS laboratory in Montpellier, and we believe that the calorimetric studies may bring one to a new level of understanding the mechanism of surfacant adsorption. Acknowledgment. The research was supported by KBN, Research Grant No. 2 0870 91 01. (32) Bdhmer, M. R.; Koopal, L. K. Langmuir 1992,8, 2660. (33) B6hmer, M. R.; Koopal, L. K. Langmuir 1992,8, 1594. (34) Scheutjene,J. M. H.M.;Fleer, G. J. J.Phy.9.Chem. 1979,83,1619. (35) Scheutjene,J. M. H.M.; Fleer, G. J. J. Phye. Chem. 1980,84,178.
