Langmuir 1994,10, 3754-3764
3754
A New Theoretical Approach to Adsorption of Ionic Surfactants at Water/Oxide Interfaces: Studies of the Mechanism of Cationic Surfactant Adsorption L. Eajtar, J. Narkiewicz-Michalek,* and W. Rudzinski Department of Theoretical Chemistry, Faculty of Chemistry, Maria Curie-Sklodowska University, P1. Marii Curie-Sklodowskiej 3, 20-031 Lublin, Poland
S. Partyka Laboratoire de Physico-Chimie des Systemes Polyphases, LA 330, USTL, Place Eugene Bataillon, 34060 Montpellier Cedex, France Received March 14, 1994. In Final Form: July 6, 1994@ The adsorptionisotherms of cationic surfactants adsorbed from nearly neutral solutions on polar surfaces show, as a rule, two steps: one at small surface coverages and the other one terminating at a plateau corresponding to the crictical micelle concentration. The second step is generally believed to be due to the formation of bilayered surface aggregates (admicelles). The first step corresponds to the formation of a monolayer-like hydrophobic phase which may well be composed of single noncondensed monomers or to the creation of monolayered aggregates (hemimicelles). In order to study such two-step isotherms and the corresponding heats of adsorption, we have generalized our new theoretical approach for the case when the two kinds of surface aggregates coexist on a solid surface. The extended theoretical treatment can be applied also to monomer-admicelle surface equilibria by putting equal to one the aggregation number of hemimicellesin appropriate theoretical expressions. The obtained theoretical expressions for adsorption isotherms and heats of adsorption were next fitted to the experimental data obtained at CNRS Laboratory in Montpellier. Our computer exercises showed that when agreement with experiment was achieved, the calculated aggregation number ofhemimicelleswas unity. This suggeststhat the first step on the isotherms of cationic surfactants is due to single monomer adsorption, in accordance with such an assumption often expressed in literature, but not sufficientlydocumented. The aggregation numbers determinedby computer are smaller than those found previously by us for zwitterionic surfactants and are much smaller than the surface aggregation numbers found experimentally for anionic surfactants adsorbed at the waterfoxide interface.
Introduction Because of its great practical importance, the adsorption of ionic surfactants at oxidelelectrolyte interfaces is a subject of extensive experimental and theoretical studies in many laboratories in the world. Great progress has been made in understanding some fundamental features of these adsorption systems. A generally accepted view about the mechanism of adsorption in these systems is as follows: At very small surface concentrations, the adsorption proceeds via attachment of single monomers to the surface by their polar heads and a certain number of CH2 segments. As the surface concentration increases, the growing competition for the available surface area decreases the (statistical) number of CHZ (hydrophobic) segments 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”, 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
* To whom the correspondence should be addressed. Abstract published in Aduance A C S Abstracts, September 1, 1994. (1)Levitz, P. Processus d’association de molecules non ioniques: adsorption a l’interface solide hydrophile-eau et micellisation en phase aqueuse. Ph. Thesis, 1985. (2)Levitz, P.J . Phys. Chem. 1986,90,1302. @
and Somasundaran and c o - ~ o r k e r s ~using - ~ a special fluorescence technique to monitor that aggregation. Though the above described mechanism of surfactant adsorption onto polar surfaces is now generally accepted, certain important features of that process are still not well understood. Cases and c o - w ~ r k e r s ~see - ~ that process as a twodimensional condensation of monomers or dimers attached to the surface by one polar head. That model of the surface aggregation has been refined next by Schechter and coworkerslOJ1considering more carefully the bilayer character of adsorption. Recently Narkiewicz-Michalek12has shown that the model of 2D condensation explains very well the dependence of the “critical” bulk concentration on the length of the hydrophobic (aliphatic) chain of surfactant. At the same time there are certain features ofthat spontaneous surface aggregation which can hardly be explained by the model of 2D condensation. (3)Somasundaran, P.;Turro, N. J.;Chandar, P. Colloids Su$. 1986, 20,145. (4)Somasundaran, P.;Kunjappu, J. T. Miner. Metall. Process. 1988, May. (5)Somasundaran, P.;Kunjappu, J. T.; Kumar, Ch. V.; Turro, N. J.; Barton, J. K. Langmuir 1989,5 , 215. (6) Cases, J. M.; MutaRschiev, B. Suq. Sei. 1968,9,57. (7)Rakotonarivo, E.; Bottero, J. Y.; Cases, J. M. Colloids Suq. 1984, 9,273;1985,16,153. (8)Cases, J.M.; Doerler, N.; Francois, M. XVI International Mineral Processing Congress; Forssberg, E., Ed.; 1988;p 1477. (9) Cases, J. M.; Villieras, F. Lungmuir 1992,8, 1251. (lO)Scamehom, J. F.; Schechter, R. S.; Wade, W. H. J. Colloid Interface Sei. 1982,85, 463. (11)Harwell, J. H.; Hoskins, J. C.; Schechter, R. S. Langmuir 1985, 1, 251. (12)Narkiewicz-Michalek, J. Ber. Bunsen-Ges. Phys. Chem. 1991, 95,85.
0 1994 American Chemical Society
Adsorption of Ionic Surfactants 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 dimensions of these aggregates would be limited in practice only by the dimensions of homogeneous surface microdomains. Meanwhile, the fluorescence spectroscopy investigations by Somasundaran and co-workers showed that the aggregation number was finite and changed with the adsorbed amount. This, on the other hand, suggests similarities between the surface aggregation and micellizationoccurringin the bulk surfactant solutions. Thus, in some of our recently published work^'^-'^ we attempted to treat the surface aggregation like a twodimensional micellization. Of course, as the presence of a solid surface must affect strongly that surface aggregation, deep similarities between the surface aggregation and bulk micellization may be put into question. These intriguing similarities and differences between the behavior of these systems observed in the experiment, and predicted by the 2D condensation and (or) micellization models, have driven us to propose a new theoretical approach to describe the adsorption in these systems.16It combines certain features of the models of surface micellization and 2D condensation. Thus, the adsorbed phase is viewed as a mixture of 2D lipid-membrane-like aggregates of various dimensions. It is assumed next that they interact only via “excluded area” interactions as is true in the case of concentrated micellar solutions. Depending on whether these are monolayered- or bilayered-likeaggregates, they are called “hemimicelles”or “admicelles”,respectively. At the same time, it is assumed that these aggregates are the result of local 2D condensations on a heterogeneous surface characterized by a surface topography intermediate between “patchwise”and “random”. Such heterogeneous surfaces are called “partially correlated”. This new approach has led us to a successful quantitative description of both experimental isotherms and heats of adsorption of zwitterionic surfactants onto oxide surfaces. The experimental isotherms of adsorption in this case are S-shaped, indicating, thus, that only one kind of adsorption mechanism governs the behavior of these systems. The analysis ofthe density ofthe adsorbed phase at the plateau of the isotherm suggested that these were ”admicelles” present on the silica surface. The excellent agreement between the theory and experiment suggested that the existence of other adsorbed forms, i.e., monomer or “hemimicelles”could be safely ignored. At the same time the numerous computer exercises made by us showed that our new approach could not reproduce the appearance of two steps on an experimental adsorption isotherm. Meanwhile, the appearance of two steps is a rule in adsorption of cationic surfactants on silica, which is most commonly used in these adsorption experiments. Figure 1 shows the adsorption isotherms measured in the CNRS 300 Laboratory in M0ntpel1ier.l~ The second step proceeding the plateau on these adsorption isotherms must be associated with the formation of the bilayered aggregates (admicelles). Such a conclusion must be drawn from the analysis of the maximum density of the adsorbed phase at the plateau (13) Partyka, S.;Rudzihski,W.;Brun,B.;Clint, J. H.Langmuir 1989, 5.297. (14)Narkiewicz-Michalek,J.; Rudzidski, W.; Keh, E.; Partyka, S. Colloids Su$. 1992,62, 273. (15)Narkiewicz-Michalek, J. Ber. Bunsen-Ges. Phys. Chem. 1990,
-94. -, 787 . - .. (16) Lajtar, L.; Narkiewicz-Michalek,J.; Rudzifiski,W.; Partyka, S. Langmuir 1993,9, 3174. (17) Bouzerda, M. Ph.D. Thesis, CNRS Lab 330 Montpellier, 1991.
Langmuir, Vol. 10,No. 10,1994 3755
1
5‘0 1
E 4.0
p:
z
2
-
3.0-
L-
2.0 -
i
c
0.0 0.0
I
I
4.0
8.0
12.0
t,
16.0
I
20.0
C(mM)
Figure 1. Adsorption isotherms of DTA+ (U) and TTA+ (0) ions measured on silica RP 63-876 at 25 “C and pH 8.2. The solid lines were drawn by hand to help the eye. Results are from Bouzerda.’’
’E
‘-
o
-
DTA’
-1 3 L-
0
8
12
16 C(mM) Figure 2. Adsorption isotherms of DTA+ ( 0 )and Br- ( 0 )ions measured on B.D.H. silica at pH 8. The solid and dashed lines
were drawn by hand to help the eye. Results are from Bijsterbosch.20
of adsorption isotherm, contact angle measurement~,’~J~ and electrokinetic experiment^.'^^^^ Perhaps the most impressive proof comes from the counterion adsorption.20 Figure 2 shows an example of such measurements. One can see that the adsorption of Br- counterions is associated with the second step. Of course, these are positively charged polar heads of the surfactant molecules in the second layer which are the adsorption centers for Br- ions. The first step terminates at a more or less distinct plateau which may constitute up to 30%of the maximum adsorbed amount in these systems. The nature of that first adsorption mechanism is an intriguing question, in view of the following findings. According to some widely spread views, surface aggregates exist even at very small surface coverages. In the case of anionic surfactant adsorption the fluorescence decay spectroscopy experiments by Somasundaran and co-workers provided a solid support for that view. Analyzingthe adsorption isotherms of anionic surfactants onto alumina in 1982,Scamehorn et presented a theoretical model of the formation of the surfactant aggregates on the surface. Their theoretical approach started from Cases’ concept of two-dimensional condensation but was modified to allow bilayered formation to occur either subsequent to monolayered aggregate (condensed phase) (18) Brode, P. F., I11 Langmuir 1988,4, 176. (19) Elton, G.A.Proceedings ofthe International Congress ofsurface Activity, 2 n d Butterworth: London, 1957; Vol. 3, p 161, London. (20) Bijsterbosch, B. H.J . Colloid Interface Sci. 1974, 47, 186.
tajtar et al.
3756 Langmuir, Vol. 10, No. 10, 1994 5.0 I
I
I
I
TTA+
0.0
-
0.2
I
\ '
0
1
0.4
0.6
0.8
et
1.o
-
c
c
?
211 L '
0.0 0.0
.
. , r 1.0
2.0
I
I
3.0
4.0
2
3
4
5
C(mM1
Figure4. Adsorptionisotherm and heat of adsorptionof TTA+ ions adsorbed on silica RP 63-876 at 25 "C and pH 4.1. The solid lines are theoretical curves calculated for the model of 2D condensation on the heterogeneous surfacepresented in ref 22. 5.0
6.0
C(mM 1
Figure 3. Adsorption isotherms of TTA+ ions on silica RP 63-876 at 25 "C: (0)pH 8.2; (D) pH 4.1. The solid lines were drawn by hand to help the eye. Results are from B0uzerda.l' formation or simultaneously. Then, the model of patchwise topography was accepted along with a Gaussian distribution of adsorption energies. That approach applied to the adsorption systems which they were studying, led them to the conclusion, that even a t low coverages the adsorbed surfactant layer was built up primarily by the patchwise formation of essentially bilayered aggregates. Three years later (1985), Harwell et al." arrived at a similar conclusion, assuming that the bilayer aggregates are admicelles and developing a theoretical approach based on the model of pseudophase separation. Later on, Yeskie and HanvelP have shown that the path leading to the formation of bilayered aggregates should be preferred on the surfaces with high surface charge densities. On the contrary, low surface charge densities will favor the path leading to the monolayered aggregates. However, Yeskie and Harwell did emphasize, that "the equations derived in (their)paper did not address whether or not any surfactant aggregate would, in fact, form a t 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 of whether monomers which are neither hemimicelles nor admicelles may have a lower chemical potential in some conditions. As the existence ofbilayered aggregates a t high 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 surfacephase,formedin the initial regionof surface coverages, and leading to the first step on the adsorption isotherm? When looking for suitable experimental data for analysis, one should focus attention on these physical regimes where the possibility of existence of bilayered structures should be small. We have found such a system in our data collection. I t is shown in Figure 3. (21)Yeskie, M. A.; Hanvell, J. H. J. Phys. Chem. 1988,92,2346.
There one 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 this figure that, at surface coverage of about 50pmol*g-l,a quite sudden switch takes place from one adsorption mechanism to another. Then at pH 4.1 the adsorption terminates at 50 pmo1.g-I 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 a t r > 50 pmo1.g-I is simply the formation of bilayered structures. The absence of such bilayered structures at low pH values can be explained on the grounds of the theoretical considerations of Yeskie and Harwell.21 We discussed it in more detail in our previous publication.22 Concerning this one-step isotherm measured at pH 4.1, we postulated that the adsorbed phase consisted of monomers which were not hemimicelles. This is because the maximum amount adsorbed at pH 4.1 is just not 2, but 3 times lower than the maximum adsorption at high pH values where bilayered aggregates exist. This suggests that the monolayer is not a condensed phase. The simultaneously measured differential isosteric heat of adsorption decreased exponentially with the growing adsorbed amount indicating, thus, an adsorption on a heterogeneous solid surface. So we applied the Narkiewicz-Michalek12 theory of multisite-occupancy adsorption on heterogeneous surfaces to develop suitable expressions for adsorption isotherm and isosteric heat of adsorption. With a relatively small number ofbest-fit parameters, we could fit simultaneously our theoretical expressions to the experimental isotherms and heats of adsorption. This is shown in Figure 4. Comparing the two isotherms in Figure 3 it would be natural to assume that also at the higher pH values between 7 and 8, the first step corresponds to adsorption of monomers which are not hemimicelles. Meanwhile, an inspection into the corresponding experimental heats of adsorption does not provide obvious evidence for that. Except for the first few points corresponding to very small surface coverages, the heat of adsorption increases with the adsorbed amount. This is shown in Figure 5. I t is well-known that calorimetric effects of adsorption are much more sensitive to the nature of an adsorption system than experimental adsorption isotherms. As the behavior of the heats of adsorption at pH 7-8 is, in a sense, opposite to that observed at pH 4.1,there arises the following important question: (22) Narkiewicz-Michalek,J.;Rudziriski, W.; Partyka, S.Langmuir 1993,9,2630.
Langmuir, Vol. 10, No. 10,1994 3757
Adsorption of Ionic Surfactants m n L”.”,
-10.01 0.0
I
I
I
0.2
0.L
1
I
0.6
0.8
1.0 et
Figure 6. Heats of adsorption of DTA+ (U) and TTA+ ( 0 )ions on RP 63-876 silica measured at 25 “C and pH 8.2. Results are from B0uzerda.l’ 1
Figure 6. Surface phase seen from above. The black circles
denote the monolayered aggregates(hemimicelles)whereas the white ones denote the bilayered aggregates (admicelles).
Does the first step of the two-step adsorption isotherms, found in the adsorption from neutral solutions or at pH > 7, still correspond to single monomer adsorption or is it due to the formation of hemimicelles? Trying to answer this important question, we have accepted the following investigation strategy. Namely, we have generalized our new theory of surfactant adsorption to the case when the adsorbed phase is a mixture of hemimicelles and admicelles. This is schematically shown in Figure 6 . The aggregates composed of black disks are hemimicelles, whereas those composed of white disks are admicelles. Providing we have to deal with the equilibrium between single monomers and admicelles, we will have only single black disks in Figure 6 , but the principles of the new generalized theory remain unchanged. One has to put equal to unity the aggregation number of the “hemimicelles” in appropriate theoretical expressions. In the next section we will develop the expressions for adsorption isotherms and heats of adsorption, assuming that the adsorbed phase is a mixture of aggregates of two kinds. Next we will fit the obtained expressions to the experimental data to find the (best) values for the aggregation numbers of these two kinds of aggregates. This should give the answer to the question of whether the hydrophobic phase corresponding to the first step on the adsorption isotherm is built up from single monomers or hemimicelles.
11. New Theoretical Approach to the Surface Aggregation According to the model presented in our previous publication,16the surface phase can be viewed as a mixture of oblate aggregates built up from monomers (elementary disks) and defined by only two parameters: S, (the cross section area) and 1, (the number of nearest-neighbor pairs in the aggregate. Thus, it is possible within the frames of that model to consider different structures of the aggregates described by the above parameters. Let us assume that the adsorbed phase is a mixture of two kinds of aggregates: monolayered and bilayered. The monolayered aggregates that form mainly at low surface coverages are composed of monomers oriented in such a manner that the hydrophilic groups of the surfactants are next to the charged mineral oxide surface, with the surfactant tail groups forming a hydrophobic film in contact with the aqueous solution. Aggregates of this structure are commonly referred to as “hemimicelles”.The bilayered aggregates, termed “admicelles”, are viewed as a classical bilayer of monomers. The orientation of surfactant molecules in the first layer is the same as in a hemimicelle, but the molecules in the second layer are postulated to adsorb on those of the first in the opposite orientation (with polar groups directed toward the water phase). The surface aggregates have oblate, disklike shapes, the structure of which is related to the following assumption. Of all the possible structures which an aggregate composed of a fured number of monomers may have, the most probable one will be the structure characterized by the highest cohesive force, in other words, the structure characterized by the largest number of the nearest neighbor attractive interactions. The two assumed structures of surface aggregates are schematically shown in Figure 6 . While considering the interactions between the surface aggregates, we neglect all possible interactions between the aggregates but the “excluded volume” interactions in a mixture of hard disks. The theoretical considerations presented below are the generalization of our new theory of surfactant adsorption for the case when two kinds of surface aggregates exist on a solid surface. We will use two indices ((inand “s” to relate different quantities to a given surface disk. The subscript “i”will denote the number of monomers in a hemimicelle or in one layer of an admicelle. Thus, it will determine the radius of a hard disk R, and its cross-section area S,.The superscript “s”, (s = a, h), will refer a given quantity to a hemimicelle or an admicelle. For a hemimicelle i, 1, is the number of the pairs composed oftwo nearest neighbor monomers. Thus, for an admicelle the number of these pairs will be 21,. Let w; denote the energy of the lateral interactions in the aggregate. It will be given by the following equation
where 1
dS={ 2
fors=h f o r s =a
(2)
and w is the energy of interaction between two neighboring monomers. That pair interaction is a sum of the attraction between two hydrophobic moieties and of the repulsion between their polar heads. Let us assume further, that the adsorption energy of the aggregate i is given as
3758 Langmuir, Vol. 10,No. 10, 1994
Lajtar et al.
When s = h, eh = €1, where €1 is the adsorption energy of a monomer attached by its polar head to the solid surface. For s = a, ea = €1 €2 where €2 is the adsorption energy of the surfactant molecule in the second layer. So far, our considerationhas been based on a model of an energetically homogeneous surface. The total adsorbed amount of surfactant N = LXiiS8Nis will be a function of the chemical potential of monomer in the equilibrium bulk phase pb
+
pb = p:
+ kT l n x
(4)
where x is the concentration of monomers in the bulk solution. Except for the surfactant concentrations close to the critical micelle concentration (cmc), eq 4 is a good formula to calculate pb. Of course, we could use a more precise relation between pb and x , but this problem is not essential for the fundamental part of our present consideration. The condition of the thermodynamic equilibrium in our system takes the following form
Above, Si is the cross-section area of the ith disk, Ri is its radius, and S is the total surface area. While calculating si we used the approximation
4i - 1 s. = -
l
3
which is fully correct fori = 1,7,19,...,i.e., when the disks are fully symmetrical. From eqs 4,5,and 8, we obtain the equation system for the individual adsorption isotherms rt, and for the total adsorption isotherm r
where where ,ut is the surface chemical potential ofthe aggregate of type (i,s), and (Nis} is the distribution of monomers among various surface aggregates. We start our theoretical consideration by writing the expression for the canonical partition function for the adsorbed phase Q
K t = [A3 (q)-'ldsifisS1 exp(
i8
+kTdsliw)
(12)
where
and q is the internal molecular partition function of the surfactant molecule in the bulk phase. From the fluorescence decay experiments published by it follows that the highest Somasundaran and co-~orkers,~ aggregation numbers detected exceed 300. It means, we have to solve a system of more than 600 nonlinear equations. In the particular case of our equation system 11,it is possible to reduce that numerical problem to that of solving a system of two nonlinear equations. We introduce for this purpose two new variables 5 and q, defined as follows
2 is the configurational integral for the mixture of hard
With this notation, the equation system 11takes the form
ies
+ dsl,ws
s i=l
disks, qs is the molecular internal partition function of a monomer in the surface aggregate, and A is the thermal wavelength of the monomer. The Scaled Particle Theory (SPT) yields the following expression for the chemical potential ofthe surface aggregate of type (i,s), pis S
d; = (x)'"Kt exp(-cri - p i )
= (1- Old;,
(14) So, according to eqs 9a-c we have l-
+
kT
(15b) Introducing eq 13 yields the desired system of two equations
where
r3
s
i
the solution ofwhich yields 5 and q determining in a unique
Langmuir, Vol. 10,No. 10, 1994 3759
Adsorption of Ionic Surfactants manner the distribution of adsorbed molecules among surface aggregates of various sizes and structures. Having evaluated the values of 5 and p, from the equation system 16, we calculate now
p,s=h,a
k,i=l,2
,..., n
cL
Having evaluated r$ and from equation systems 21 and 22 we can calculate the isosteric heat of adsorption from eq 19. Similarto the case of adsorption isotherm, the numerical problem formulated above can be reduced to solving a system composed of two equations with the unknown 5 and p. Derivation of the expression for the isosteric heat of adsorption as a function of these two variables was discussed in detail in our previous publication.16 For the model presented above this expression takes the form
i.e.
and finally
1
+cCd:si s
i
s
i
where
111. Heats of Adsorption Heats of adsorption reveal many important features of surfactant adsorption, which can hardly or never be seen and in the behavior of experimental adsorption isotherms. It was demonstrated in our previous p u b l i c a t i o n ~ ~that ~-~~,~~ a simultaneous analysis of experimental adsorption isotherms and heats of adsorption allows for the discrimination between different models of surfactant adsorption. Below, we are going to develop theoretical expressions for the heat of adsorption corresponding to the model of surfactant adsorption based on the scaled particle theory. The differential molar heat accompanying the adsorption of surfactant molecules, Qst, is given by
cc
dk "sk
s
+ 0.5
k
IV. Analysis of Experimental Adsorption Q*t s
i
(19)
cim
Isotherms and Heats of Adsorption Let us consider in more detail the quantity Kis defined in eq 12. According to what was shown in our previous publication, li can be approximated by the linear relationship, 1, = /3li /32, and Ki" in eq 12 may be written in the form
+
The derivatives l-$- = ( K i s / H 9 and = ( X i s / aIn x ) can be calculated from the equation system ( l l ) , which we rewrite for that purpose to the following form:
F:
=In
r:
- 6"i l n x - 1nK: - In (1 - 0 )
+
The differentiation of the above equation system with respect to In x yields the following system of equations
p,s=h,a
k , i = l , 2 ,..., n
whereas differentiation with respect to T gives
where the exponentialterm represents the whole potential energy of the ith surface aggregate. Our numerical exercises based on the above discussed approach showed that an assumption of a constant value of the interaction parameters c and o led to a rapid two-dimensional condensation-like aggregation at a certain value of the surfactant concentration in the bulk phase. Formation of aggregates of finite dimensions occurs when one assumes that the values of o andor c decrease with the increasing aggregate size. As previously we assume that both parameters decrease linearly with the growing aggregate size i, i.e. w=o,,-Aoi
(26a)
3760 Langmuir, Vol. 10, No. 10, 1994
tajtar et al. Table 1 parameters
The decrease of o with i is due to the same effects which are responsible for the finite size of micelles in bulk solutions. We believe, however, that the decreasing with i value of Es is the main effect governing the formation of surface aggregates. In our previous publication we have discussed impressive experimental evidence for that. There we also postulated that the decrease of ?c with i was due to the "partially correlated" topography of the really existing heterogeneous oxide surfaces. Equations 26 represent Taylor expansions of the unknown functions w(i) and Es(i), cut after the second term. With these assumptions we arrive at the followingexpressions for Ki"
where as= dsSlA-2 e x p@2@0[ T }
While calculating the isosteric heat of adsorption, we will still have to consider the derivatives ( a In Ki"laT). With the approximation accepted in eq 26,we have
h," ch aQ l/K DTAB (25"C)4.5 13.45 5.0 1 x lo-" 29.442 1.35 41 -23.5 -8.5 'M'AB (25"C) 2.8 15.10 4.2 5 x lo-" 32.430 1.40 40 -22.5 4.0 'M'AB (35"C)3.2 15.10 4.7 1 x 32.730 1.72 41 surfactant
ah
bh
unit of surface area. Taking into account eq 9a we obtain
where N A is the Avogadro number. The appearance of the plateau on the experimental adsorption isotherms of surfactants is connected with the fact that when cmc concentration is reached, the bulk concentration of monomer (chemical potential of surfactant) does not increase much. In the case of ionic surfactants, the calculation of the monomer concentration can, to a good approximation, be done by using the mass action law
where K,, is the equilibrium constant for the formation of the micelles of size n from n single surfactant molecules, x,, is the mole fraction of the surfactant in the micelles, and x is the mole fraction of monomer. The equilibrium constant is given by
-AGmic In K,, = -- -n ln(cmd55.5)
RT
where
a In as aT
(30)
Having found the parameters as,bs,cs, and S1fitting-best the adsorption isotherm, we calculated the derivative (a In aslaT) from the equation
a In as
(33)
The derivative (i3c8/aT)was calculated from eq 32 and the derivative (abslaT)was treated as a best-fit parameter, for we did not know the temperature dependence of the molecular partition functions qs and q. Now it is necessary to establish the relation between our theoretical quantities ri8,and the experimentally measured adsorption Tt expressed usually in moles per
(36)
where cmc is expressed in mol-dm-l. To test our model, we used the adsorption isotherms and heats of adsorption of two cationic surfactants DTAB and 'ITAB adsorbed on silica, measured in the CNRS Laboratory in Montpellier. The adsorption isotherms of these surfactants are characterized by two plateaus similar to those of DTAB and CTAB on B.D.H. silica measured by BijsterboschZ0and of alkylpyridiniums on silica gel measured by Gao et aLZ3 The results of fitting our theoretical expressionsto the experimentaldata are shown in Figures 7-9 and the best-fit parameters are collected in Table 1. The values of cmc and bulk aggregation numbers necessary for evaluating the monomer concentration corresponding to a given total concentration of the surfactant in the bulk phase were taken from literat~re.'~*~~ In Figures 7 and 8 the theoretical and experimental adsorption isotherms of DTAB and TTAB at 25 "C are presented. The dashed lines in these figures show the contribution to the total adsorption coming from the monolayered and bilayered aggregates. One can see that our theory fits well the experimental adsorption isotherms in the whole concentration range. Figure 9 shows the experimental and theoretical differential heats of adsorption. Here the fit is worse, especially in the region of very small surface coverages where the heat of adsorption decreases due t o the heterogeneity of the surface. However, the essential features of the heat behavior a t intermediate and higher surface coverages are quite well reproduced. Thus, the (23)Gao, Y.;Du, J.; Gu, T. J . Chem. Soc., Faraday Trans. 1 1987, 83,2671. (24)Rao, I. V.;Ruckenstein, E. J . Colloid Inerface Sei. 1987, 119, 211.
Adsorption o f Zonic Surfactants
DTA'
L--
-
Langmuir, Vol. 10, No. 10,1994 3761
/+---1
-1
I 0
0 .o
/
/
5.0
I
I
15.0
10.0
20.0 ClmC)
Figure 7. Agreement between experimental(W) and theoretical (-) adsorption isotherms of DTA+ ions adsorbed on silica RP 63-876 at 25 "C and pH 8.2. The solid line is the theoretical
curve calculated by using parameters collected in Table 1.The dashed lines denote contributions to the total adsorption isotherm coming from hemimicelle (- - -) and admicelle (- - -) adsorption.
TTA'
0.0 1 0.0
,
4.0 5.0 C(mMI Figure 8. Agreement between experimental(0)and theoretical
2.0
1.0
3.0
adsorption isotherms of TTA+ions adsorbed on silica RP 63-876 at 25 "C and pH 8.2. The solid line is the theoretical curve calculated by using parameters collected in Table 1.The dashed lines denote contributions to the total adsorption isotherm coming from hemimicelle (- - -1 and admicelle (- - -) adsorption. (-)
- 20.0
1
c
0.0
-10.0 I 0.00
I
I
I
0.25
0.50
0.75
I
1.00 0t
Figure 9. Agreement between experimental and theoretical
heats of adsorption of DTA+ (0)and TTA+ (0)ions adsorbed on silica RP 63-876 at 25 "C and pH 8.2. The solid lines are the theoretical curves calculatedby using parameters collected in Table 1. energetic effect is endothermic in the region of monolayer adsorption and exothermic when the formation of bilayered aggregates takes place. The reason for this is a growing hydrophobic interaction between hydrocarbon chains of surfactant molecules when the admicelles are formed on the surface. A simultaneous inspection into the shape of experimental adsorption isotherms, heats of adsorption and corresponding theoretical mean surface aggregation numbers, presented in Figure 10, leads us to the conclusion
0.01 0.0
I
1.o
0.5 et
Figure 10. Average aggregation numbers of the DTA+ and TTA+ surface aggregates calculated by using parameters collected in Table 1 and plotted as a function of the relative surface coverage et = rn,,,=.
that at low surfactant concentrations the monolayer forms from single monomers attached to the surface by their polar heads and with nonpolar hydrocarbon chains oriented upward to the bulk solution. The average aggregation number found while fitting best the theoretical expressions to the experimental data is equal to unity for both analyzed surfactants in the monolayer coverage region. The large values of the parameter ch obtained from the calculations cause the free energy of the monolayered aggregate to decrease quickly with the increasing aggregation number and the formation of hemimicelles does not occur. The rapid increase of adsorbed amount at low bulk concentrations is caused by the strong electrostatic and specificinteraction between positively charged polar heads of surfactant molecules and the negatively charged surface of silica. If the adsorption were only due to the electrostatic attraction, the surface active cation could only neutralize the negative charge on the silica surface and could not make the surface charged positively. Meanwhile, the electrophoretic mobility measurements show" that the isoelectric point is reached in our systems at the surface coverage of about 0.62 p m ~ l - m -which ~ , is lower than that corresponding to the first plateau on the adsorption isotherm (l.lpmol.m-2). Beyond the isoelectric point the electrophoretic mobility increases continuously due to some additional specific adsorption of surfactant in the Stern layer and becomes practically constant when the admicelles form on the surface. The formation of a monolayer at low surfactant concentrations is responsible for the growing hydrophobicity of silica particles. Eltonlg measured contact angles of water droplets of DTAB solutions on a fused silica plate and found a maximum of 92" at a concentration of about M. This concentration corresponds to the beginning of the first plateau on the adsorption isotherm of DTAB. The formation of bilayered aggregates starts at a concentration of about l/4 cmc. The mean surface aggregation number increases gradually to the value of about 6 for TTAB and about 7 for DTAB at the plateau of the isotherm. These values are much smaller than those obtained by us for zwitterionic surfactants adsorbed on silica from almost neutral solutions.16 This result is not surprising. The head groups in the zwitterionic surfactants carry the charges of opposite signs and the nonadsorbed parts of the polar heads play a role very similar to that of adsorbed counterions. This reduces to a great extent the electrostatic repulsion between the head groups
3762 Langmuir, Vol. 10, No. 10, 1994
Lajtar et al.
0.60 81
-0.375
,
I
!
',
_-.-.___
1
0.615 1.000
AGGREGATION NUMBER 2i
0.60-
~
\
._
a 0.45 -
-.-.-
TTA' 125OCl
---- TTA' OTA'
i3s0c) (25OCi
AGGREGATION NUMBER 2i
Figure 11. Distributions of the surface areas occupied by bilayered surface aggregates (admicelles)formed by TTA+ions among their aggregation numbers calculated by using parameters from Table 1for different values of the relative surface coverage et.
Figure 12. Distributions of the surface areas occupied by bilayered surface aggregates (admicelles)formed by DTA+ and "A+ ions among their aggregation numbers calculated by using parameters from Table 1for et = 1(plateau of the adsorption isotherm).
and favors the formation of bilayered aggregates with higher aggregation numbers even at low surfactant concentrations. In the case of cationic surfactant adsorption in the absence of extra salt, the situation is different. At low surfactant concentrations the monolayer of individually adsorbed monomers exists on the polar surface. The attractive hydrophobic interactions between apolar chains which are responsible for the surface aggregation are not sufficient to overcome the strong attraction of surfactant cations to the negatively charged surface sites, and that is why the aggregation does not occur under these conditions. The beginning of the formation of bilayered aggregates at higher surfactant concentrations is reflected by the appearance of the second step on the adsorption isotherm. As the formation of admicelles starts, the adsorption in a monolayer maintains initially unchanged and then begins to decrease. At the second plateau on the isotherm about 15%of the adsorbed surfactant is still present in a monolayer. The full bilayer cannot be formed because the cmc is reached before this could occur. The increasing number of head groups located on the solution side of the admicelle makes the surface progressively hydrophilic, which is reflected in the experimentally observed decrease of the contact angle and a reduction of flotability. An interesting conclusion can be drawn from Figure 11. Here the distributions of the surface areas occupied by different aggregates among their aggregation numbers are shown for different values of the relative surface coverage et = F a m m .One can see that with the increasing value of et the height of the distribution increases but its position on the abscissa axis and its width do not change much. It means that in the region where bilayered aggregates form the adsorbed amount increases due to creation of new aggregates but the sizes of these aggregates remain unchanged. For three different relative surface coverages of TI",the most probable aggregation number of admicelles is equal to 8. Let us mention here that the calculated average aggregation numbers of cationicsurfactants adsorbed from almost neutral solution on silica surface and plotted as a function of the relative surface coverage differ significantly from those obtained by us for zwitterionic surfactants adsorbed on silica and the experimental mean aggregation numbers found by Chandar et al.25for sodium dodecyl sulfate adsorbed on alumina. The most pronounced difference is observed in the region of initial surface coverages where the mean aggregation numbers of zwit-
terionic surfactants and of SDS rapidly increase whereas those of cationic surfactants are constant and equal to unity, indicating that no aggregation takes place in this region of surface coverages. Moreover, the mean aggregation numbers corresponding to the plateau of the adsorption isotherm of cationic surfactants are much smaller than the appropriate aggregation numbers of zwitterionic surfactants and SDS. These differences are mainly due to the strong attractive (Coulombic) interactions of cationic surfactants with the silica surface at low surface coverages and the strong repulsion between similarly charged polar heads in the absence of indifferent electrolyte. Both these factors hinder the formation aggregates in a wide range of initial surface coverages and favor the formation of small surface aggregates at higher surface coverages. In Figure 12 we have shown three distributions of aggregate sizes corresponding to the plateau of adsorption isotherms of DTAB and TTAl3 at 25 "C and of TTAB at 35 "C. The distributions for DTAB and "TAB at the same temperature are very similar suggestingthat the structure of the adsorbed layer at the plateau of the isotherm is the same for these both surfactants. It is consistent with the maximum adsorbed amount which is almost identical for both these surfactants at 25 "C and does not depend on the length of the hydrocarbon chain. At 35 "C the distribution for TTAB is shifted to the smaller aggregation numbers. It means less compact structure of the adsorbed phase and thus a smaller adsorbed amount at the plateau of the isotherm. It may be concluded that our new theoretical approach to ionic surfactant adsorption at waterloxide interface generalized for the case when the two kinds of surface aggregates (monolayered and bilayered ones) coexist on a solid surface can be successfully used to describe twostep isotherms of cationic surfactants adsorbed from neutral solutions on a silica surface. A two-step character of these isotherms indicatesthat two different mechanisms govern the adsorption in these systems. The simultaneous theoretical analysis of experimental adsorption isotherms and heats of adsorption based on our new approach showed undoubtedly that the second step observed at higher surface coverages was associated with the formation of bilayered aggregates (admicelles). However, the calculated average aggregation number of these admicelles is small, and that is why they cannot be experimentally detected. Thus, our theory offers the only possibility to determine the sizes of the surface aggregates formed by cationic surfactants at waterloxide interface. The calculated average aggregation number of monolayered aggregates that form in a wide range of initial coverages is equal to unity, indicating that the monolayer
(25) Chandar, P.; Somasundaran,P.;Turro, N. J . Colloid Interface Sci. 1987, 117, 31.
Adsorption of Ionic Surfactants phase is built up by head on adsorption of vertically oriented single monomers which are not hemimicelles. As there are some discrepancies observed between the experimental and theoretical heats of adsorption at very low surface coverages, it should be noted that our theoretical model may not describeproperly the adsorption in the region where not only the polar head but also the alkyl chain is in direct contact with the solid surface. In this case the model of multisite-occupancyadsorption on a heterogeneous surface should be more adequate.12,22 There exists strong experimental evidence that the adsorption in the region oflow surfacecoveragesis strongly affected by the dispersion of active cation-surface interactions. First of all, the log-log plots of the experimental isotherms tend to be linear at very small surfacecoverages, but the tangent of that limiting slope is often less than unity. In the case of our systems these tangents are equal to 0.36 for DTAB and 0.42 for TTAB and indicate adsorption on a strongly heterogeneous surface, characterized usually by the Freundlich isotherm equation. Moreover,the decrease of differential heats of adsorption with the increasing adsorbed amount, observed usually at the lowest surface coverages, also advocatesthe crucial role of the surface heterogeneity effects in adsorption of cationic surfactants on polar surfaces. In the ref 16, we adopted the model of a “partially correlated”heterogeneous surface to explain the decrease of the potential energy of an aggregate with its growing size. There we came to the conclusion that the decreasing tendency in the potential energy should be strong in the first stage of adsorption where small surface aggregates were formed and smaller in the second stage where the sizes of the aggregates on the surface were larger. This is why the c values obtained by us for the monolayered aggregates that form first are much larger than those for the bilayered aggregates. Recently Bohmer and have applied the selfconsistent field lattice theory to study the adsorption of ionic surfactants onto polar surfaces. Their theory allows for calculation of the density of different segments of a surfactant molecule and of adsorbed co-ions and counterions as a function of the distance from the surface. As this theory is based on a mean field approximation in each lattice layer, it cannot be used to calculate inhomogeneities parallel to the surface which are necessary to describe the process of surface aggregation. Finally, it seems necessary to comment on the differences between the large surface aggregation numbers of anionic surfactants found experimentally and the small ones of cationic surfactants predicted here by us. To our knowledge experimental studies of the surface aggregation of adsorbed cationic surfactant molecules by means of fluorescence spectroscopyhave not been reported yet. One of the possible reasons is that detecting such small surface aggregates might be difficult at the present accuracy of this experimental technique. Of course, we do not exclude that the assumptions and simplifications accepted in our theoretical approach might have led us to a certain underestimation of the surface aggregation numbers. Nevertheless,we believe that these numbers are low indeed. Thus, the question which still remains open is why the surface aggregation numbers of anionic surfactants are large whereas those of cationic surfactants are small. The main reason which we believe is the difference in the mechanism of adsorption of anionic and cationic surfactants at oxide/electrolyte interface. (26) Bohmer, M. R.; Koopal, L. K. Langmuir 1992,8,1594. (27) Bohmer, M. R.; Koopal, L.K. Langmuir 1992,8,2649.
Langmuir, Vol. 10, No. 10,1994 3763 Except for the region of very low surface coverageswhere the hydrophobic moieties are attached to the surface, the mechanism of the adsorption of simple ions and surfactants in the double electriclayer formed at oxidelelectrolyte interface must have some important features in common. Like simple ions, (Na+,K+, Ca2+,C1-, Nos-), the polar heads of surfactant molecules are adsorbed initially within the electrical double layer. However, as in the case of the simple ions, the mechanism of adsorption of anions and cations is much different. Anions adsorb on a purely electrostatic basis, due to the coulombic interactions with the doubly protonated surface oxygens called the surface complexes SOH2+. According to the popular “surface complexation model” the simple anions A- are attracted electrostatically to the surface complexes SOH2+,to form new surface complexes SOHz+A-. (For the sake of simplicity we consider here 1:l electrolyte.) In the case of anionic surfactants, the relatively weak Coulombic interactions attract the polar heads (anions) to the surface, but the predominant interactions between their hydrophobic moieties force the polar heads to accept a “noncomensurate” arrangement with respect to the position of SOHz+ complexes on the surface. That “noncomensurate” arrangement is dictated rather by closepacking tendencies, similar to those found in the bulk solution. And there, the aggregation numbers are large. In the case of simple cation adsorption, in addition to the weak Coulombic interactions, cations form also real chemical bonds to the surface oxygens (complexes),SO-. It has been realized only recently that these chemical bonds play a dominant role in simple cation adsorption within the electrical double layer. The same must be true also in the case of adsorption of the polar heads of cationic surfactants. As they form strong chemical bonds to the negative surface complexes SO-, they are fully immobilizedon these surface sites. Even at pH > pzc the calculated amount of the free surface complexes is small because their large portion is engaged into formingthe SO-Me+ c o m p l e x e ~ . ~ ~ J ~ Thus, the relatively long distances between SO- sites on the oxide surfacecreate serious difficulties forthe adsorbed surfactant molecules to accept the arrangement favored by the hydrophobic interactions. Consequently only certain parts of their hydrophobic moieties, if any, can interact. In other words, there must exist a certain ensemble of closely lying free surface oxygens SO- on an oxide surface, that a micellelike aggregate could be formed on the surface. Assuming that the free surface oxygens are distributed randomly on the oxide surface, the probability of finding n closely lying free surface oxygens SO- will decrease with n as ( x s o - ) ~function, where XSO- is the fraction of fully ionized surface oxygens. Roughly speaking, the probability of finding of a surface aggregate composed of n monomers attached to the free surface oxygens SO- is expected to decrease rapidly with n like ( x s o - ) ~function. One will face a similar situation in the case of adsorption of zwitterionic surfactants at pH > pzc. At such pH values the zwitterionic surfactants will adsorb by their cationic polar heads. We have analyzed such adsorption systems in our previous publication. Although the calculated surface aggregation numbers were 2 or 3 times larger, they were still of 1 order smaller than the surface aggregation numbers found experimentally in the case of anionic surfactants. In spite of the unfavorable conditions for the formation of surface aggregates in the case of adsorption of cationic (28) Rudziliski, W.; Charmas, R. Langmuir 1991, 7, 354. (29) Rudzinski, W.; Charmas, R. Langmuir 1992,8, 1154.
3764 Langmuir, Vol. 10, No. 10, 1994
surfactants (or zwitterionic surfactants at pH > pzc), large hydrophobic moieties will facilitate the formation of such surface aggregates. And this is the reason why we predicted somewhat larger surface aggregation numbers in the case of the zwitterionic surfactants adsorption, investigated in our previous publication. Large hydrophobic moieties create strong tendencies to surface aggregation, even under unfavorable conditions. It means, large hydrophobic moieties decrease strongly the probability of existing monomers on the surface. Accordingly
Lajtar et al. we did not observe the first step on the experimental isotherms of adsorption of the investigated zwitterionic surfactants. We conclude our considerations in this paper as follows: In the case of adsorption of cationic surfactants, the conditions for the formation of surface aggregates are much different from those accompanying the formation of their micelles in bulk solutions. Therefore, one has to expect large differences to exist between the surface and bulk aggregation numbers.
