0 Copyright 1989 American Chemical Society
The ACS Joumal of
Surfaces and Colloids MARCHIAPRIL, 1989 VOLUME 5, NUMBER 2
Art i d e s Calorimetric Studies of Adsorption of Anionic Surfactants onto Alumina S. Partyka,* W. Rudzinski, and B. Brun Laboratoire de Physico-Chimie des Systemes Polyphases U.S.T.L.,L A 330, Place Eugene Bataillon, 34060 Montpellier, Cedex, France
J. H. Clint British Petroleum Company, B. P . Research Centre, Chertsey Road, Sunbury-on- Thames, Middlesex T W 1 6 7LN, U.K. Received October 29, 1987. In Final Form: March 21, 1988 The adsorption isotherm and heat of adsorption of the isomerically pure sodium salt of n-alkylbenzenesulfonate, C7H,$hS03Na, onto alumina are reported. The experimental heat of adsorption curve reveals some interesting features of adsorption mechanism, manifested by very high heats of adsorption at very small surface coverages and a sharp peak at very high surface coverages. Equations are developed for the adsorption isotherm and heat of adsorption, taking into account the possibility of various surfactant structures existing on the alumina surface. Based on the developed equations, the numerical analysis of our experimentaldata suggests the following adsorption mechanism. The adsorption must be considered as running on an energetically heterogeneous solid surface. The very high values of the heat of adsorption at small surface coverages indicate the formation of two-dimensional aggregates from monomers or dimers, whereas the sharp peak at the very high surface coverages indicates a transition of these two-dimensional aggregates into three-dimensional-like aggregates.
Introduction The first concepts concerning the mechanism of adsorption of anionic surfactants onto such polar surfaces as alumina come from the works of Fuerstenau, Somasundaran, and co-workers.ls2 According to their concepts, the initial rise in adsorption with no change in l-potential is just a simple exchange of surfactant ions with the indifferent counterions of the supporting electrolyte in the double layer. Then, at a certain surfactant concentration known as hmc (hemimicelleconcentration), a sudden rise in the slope of the adsorption isotherm is observed, accompanied by a dramatic decrease in electrophoretic mobility. That second stage of adsorption is associated with the formation of double-layer structures on the surface called “hemimicelles”. Initially it was not clear whether
* Author to whom correspondence should be addressed.
they are dimers oriented perpendicularly toward the solid surface or two-dimensional micelle-like aggregates, which may be thought of as a result of two-dimensional condensation of the dimers. What was only sure from the beginning was that the interactions between the hydrophobic moieties are the main driving force for adsorption at this second stage. The observations of contact angle3 and sedimentation rate4provided further support for that adsorption mechanism. When the surfactant concentration (adsorbed amount) increases still further, or pH is decreased so that the {-potential indicates pzc, the slope of the isotherm decreases again. That stage of adsorption (1) Somasundaran, P.; Fuerstenau, D. W. J. Phys. Chem. 1966,70,90. ( 2 ) Wakamatau, T.;Fuerstenau, D. W. Adu. Chem. Ser. 1968,79,161. (3) Wakamatau, T.;Fuerstenau, D. W. Trans. AIME 1973,254,123.
(4) Somasundaran, P.;Goddard, E. D.Mod. Aspects Electrochem. 1979, 13, 207.
0 1989 American Chemical Society Q743-7463/S9/24Q5-0297~Q1.5Q~Q
Partyka et al.
298 Langmuir, Vol. 5, No. 2, 1989
corresponding to small positive and negative values of l-potential is distinguished as the third stage. In addition to the decreasing slope in the adsorption isotherm, the main reason for distinguishing that adsorption stage is the recognition there of repulsive forces between solid surface and surfactant molecules. Then, the simple ion-exchange concept may not be used to explain the adsorption mechanism in that range; nor does it solely involve the strong chain-chain attractive hydrophobic interactions. In the latter case, the obvious question arises as to why the micelle-like aggregates appear on the solid surface first. In fact, the mechanism of adsorption at this stage is still very poorly understood. In addition to several questions which still remain open, there has appeared a new one, coming from our recent calorimetric experiments. This is the intriguing peak on the experimental heat curve (see Figure 2) at the highest investigated surface coverages. One simple explanation might follow from the view which is sometimes expressed that at very high surface coverages a reorganization in the structure of the surface aggregates may take place. That view encouraged some authors to distinguish a fourth stage of adsorption corresponding to the highest surface covera g e ~ .That ~ hypothesis, assuming a rapid transition from two-dimensional- to three-dimensional-like aggregates, leaves, however, two important questions open. The first question concerns the high heat effect accompanying that transition (up to 17 kJ mol-'), which can hardly be compared even with the heat of micellization in the bulk solution (a few kilojoules per mole). The next question follows from the obvious thermodynamic argument that, after a sudden change in the heat of adsorption at the start of that phase transition, it should remain more or less constant up to the end of that transition. The occurrence of surface aggregates at higher surface coverages was documented well by the thermodynamic analysis of the temperature dependence of adsorption isotherms done by Somasundaran and Fuerstenau.6 Recently, it has been confirmed also by the direct fluorescence experiments carried out by Somasundaran and co-workers.' These experiments, however, can detect only the existence of a dense hydrophobic core, so the form of the surface aggregates remains still an open question. Thus fluorescence experiments may not be sensitive to the above mentioned transition. Solving the problem of the appearance of that intriguing peak might, therefore, be a good key to understanding some basic features of adsorption of anionic surfactants onto the polar surfaces.
Experimental Section The alumina used in our experiment was the Linde (A) highpurity sample purchased from Union Carbide Corp. Its BET surface area was found to be equal to 15 m2g-*. As the anionic surfactant we used an isomericallypure sodium salt of n-alkylbenzenesulfonate, C7H15PhS03Na. The adsorption isotherm was obtained by measuring the surfactant concentration in the solution before and after contact with 2 g of alumina in glass vials at 35 OC. After about 14 h of shaking the supernatant was separated by centrifugation and analyzed in order to measure the surfactant equilibrium concentration. The equilibrium concentrations were determined by UV absorption using calibration curves established at the same experimental conditionsas those used for isotherm experimental ( 5 ) Harwell, J. H.; Schechter, R.; Wade, W. H. In Solid-Liquid Interactions in Porous Media; Cases, J. M., Ed.; Technip: Paris, 1985; p 371. (6) Somasundaran, P.; Fuerstenau, D. W. Trans. SME 1972,252,8. (7) Chandar, P.; Somasundaran, P.; Turro, N. J. J. Colloid Interface Sci. 1987, 117,31.
e-----
I
0
I
--d
I
I
I 15
10
2 5
2.0
3 0
BULK C O N C E N T R A T I O N / m o l kg-'
Figure 1. Experimental adsorption isotherm of the surfactant The broken lines are drawn to emphasize the trends in C7 (0). the experimental data.
4
I 0 5
0 0
I 1 0
RELATIVE LMOUNT ADSORBED
Figure 2. Experimental heats of adsorption (0)shown as functions of the adsorbed amount. The so-called "relative adsorbed amount" is the value of the adsorbed amount I? divided by this value for the last highest point measured on the adsorption isotherm rmax.
I
001
I
002
T
I 0 03
I
0 04
I
1
005
BULK C O N C E N T R A T I O N I mol hg-' Figure 3. Experimental heat of dilution of the surfactant C7 as a function of its bulk concentration. The solid line represents the smoothed experimental curve.
points. The adsorption isotherm measured in this way is shown in Figure 1. Then we measured the related heat of adsorption in the way which has been described in detail in our previous publication.* This is shown in Figure 2 as a function of the relative adsorbed amount W/r-). (8) Partyka, S.; Lmdheimer, M.; Zaini, S.; Keh, E.; Brun, B. Langmuir 1986, 2, 101.
Langmuir, Vol. 5, No. 2, 1989 299
Calorimetric Studies of Anionic Surfactant Adsorption
_ _0
0 5
10
1 5
CONCENTRATION ( X i h k l m ) )
RELATIVE
Figure 4. Monitored pH change accompanying the adsorption of the surfactant C7. Here X,b(m)is the bulk micellization concentration.
t
40
+ 20 > E
where p," and are the surface chemical potentials of the aggregates and water, 6 is the fraction of the surface sites covered by the aggregates E , and E , are the "specific" adsorption energies of the aggregates and water, j," and j,, are appropriate surface molecular partition functions, 7 is the Flory parameter related to the flexibility and the symmetry number of surface agggates, k is the Boltzmann constant, and T is the absolute temperature. Equation 1can be generalized for the case of a nonideal adsorbed phase by multiplying 6 and (1- 6) by y t and yw8, the surface activity coefficients of the aggregates and water, respectively. Nowadays it is already widely realized that the crystallography and the stoichiometry of actual solid surfaces do not represent simple extrapolation of appropriate bulk properties. For many obvious reasons these properties vary across a solid surface. That variation causes in turn a variation in the value E , - ne, when considering various surface areas (occupied by one surfactant molecule). Therefore, our theoretical adsorption isotherm 6 must be averaged additionally over all possible values of E = E , ne,, which are "detected" by one surfactant molecule. So let x ( e ) denote the differential distribution of the configurational surface states of surfactant molecules among various values of E , normalized to unity
pn
- 40 5
6
7
pH OF EQUILIBRIUM
pzc
9
10
11
BULK SOLUTION
Figure 5. Monitored changes in the {-potentialon changing pH value for the alumina sample investigated. The shaded area corresponds to the pH region in which the adsorption of C7 was investigated. To understand the behavior of the heats of adsorption better, we have also performed an auxillary calorimetric experiment. In Figure 3 the curve of dilution of the C7HI6PhSO3Na (referred to hereafter as C7 surfactant for convenience) in water is shown. Figure 4 shows the changes of pH of the equilibrium bulk solution accompanying the adsorption of the C7 surfactant, whereas Figure 5 shows our measurements of {-potential as a function of pH.
Theory We assume fmt that only one kind of surface aggregates exists on our alumina surface. It occupies n adsorption sites which are assumed to be the surface points where hydrogen bonds can be formed according to the mechanism proposed by Rosen and co-workers?JO While being adsorbed, the aggregate displaces from the inner Helmholtz layer previously adsorbed species which may be protons, hydroxyls, or water molecules. From the data presented in Figure 4 we deduce that a large number of adsorbed polar heads do not change greatly the pH of the bulk solution in contact. We assume thus that these are mostly water molecules, which are removed from IHP in this pH range. In the absence of Coulombic interactions, the application of Flory's approach yields the following isotherm equation:'l (9) h n , M. J. Surfactants and Interfacial Phenomena; Wiley: New York, 1987; p 34. (IO) Rosen, M. J. J. Am. Oil Chem. SOC.1975,52,431.
where AEis the physical domain of E . As in the previous works by Rudzinski-and colleagues,11J"21 we will consider here the domain to be the infinite interval (-, + m ) for the purpose of mathematical convenience. That assumption does not introduce any significant error until the region of extremely small concentrations of one of the components is considered." We will also apply here the Rudziiiski-JagieHo approach to evaluate the averaged surface coverage 6,
While using the simplest form of the Rudziiiski-Jagido approach, we obtain1'
6t = -X(cJ
(4)
where
(11) Rudzibski, W.; Eajtar, L.; Wolfram, E.; Pasli, P. J . Colloid Interface Sci. 1983, 96,339. (12) Cases, J. M.; Mustaftschiev, B. Surf. Sci. 1968, 9, 57. (13) Cases, J. M.; Goujon, G.; Smani, S. In AIChE Symp. Ser. 1976, 71. 100. (14) Goujon, G.; Cases, J. M.; Mustaftchiev, B. J. J. Colloid Interface Sci. 1976, 56, 587. (15) Cases, J. M.; Canet, D.; Doerlier, N.; Poirier, J. E. In Adsorption at the Gas-Solid and Liwid-Solid Interface;Rouquerol, J., Sing, K. S., Eds.; Elsevier: Amsterd-am, 1982. (16) Rudzhiski, W.;Narkiewicz, J.; Partyka, S. J.Chem. SOC., Faraday Trans. 1 , 1982, 78, 2361. (17) Rudzibski, W.; Zajac, J.; Narkiewicz, J.; Partyka, S. In R o c . Znt. Conf. Fundamentals of Adsorption; Myers, A. L.,Belfort, J., Eds.; AIChE New York. 1983. (18)Rudzihski, W.; Narkiewicz, J.; Schollner, R.; Herden, H.; Einicke, W. D. Acta Chim. Hung. 1982, 113, 207. (19) Rudzibski, W.; Zajac, J.; Hsu, C. C. J. Colloid Interface Sci. 1985, 103, 528. (20) Rudzibski, W.; Zajac, J.; Dekany, I.; Szanto, F. J . Colloid Znter'faceSci., in press. (21) Rudzibski, W.; Zajac, J. Acta Chim. Hung., in press.
Partyka et al.
300 Langmuir, Vol. 5, No. 2, 1989 e, is the function of the chemical potential and temperature found from the condition
[ 3... =O
6(y-yo) describing a homogeneous surface characterized by the adsorption energy c = 6. Recently RudzSski et al.= have published a theoretical rationalization for that adsorption energy distribution. Thus, it is to be expected that the distribution (eq 8) should represent well the dispersion of the fraction of the adsorption energy (e/n) associated with one adsorption site. Then, in the case of multioccupancy adsorption, the dispersion of the ensembles of n adsorption sites among various values of e, is given by the following recurrence e x p r e ~ s i o n : ~ ~
We now approach an important consideration in our analysis. This is the effect of the surface “topography” of an energetically heterogeneous solid surface. So far two extreme topographies have been considered. The first one is the “patchwise” surface topography accepted initially in the works of Cases and c o - ~ o r k e r s ~ ~ - ~ ~ and very recently by Schechter et aL5 According to this where x,(e,) is the differential distribution of the number model, the adsorption sites having the same adsorption of ensembles composed on n adsorption sites among varenergy are grouped on a heterogeneous surface into large ious values of e,. One can show that the most probable “patches”. These patches are so large that the contribution value of E,, denoted here by eo, is simply equal to nyo. from the states of the system in which two interacting Then, the effect of n on the shape of the distribution molecules are adsorbed on different patches to a system function X, is described by the changing value of the k-th partition function is neglected. Thus, the adsorption central moment mk, which is defined as system is considered as a collection of independent subsystems with homogeneous surfaces being only in thermal and material contact. There is no doubt that in the case of some solid surfaces, The most pronounced effect of n on the shape of X, is for instance, the minerals investigated by Cases and cothat coming from the change of the second central moworkers, the patchwise model is a good representation of ment, being simply the variance of the distribution functhe nature of surface energetic heterogeneity. There are, tion however, materials like charcoals, silica, and alumina where such a patchwise model can hardly be accepted. Rudziiiski c, = n1I2c (11) and co-workers investigating the calorimetric effects of adsorption of nonelectrolyte mixtures on these surfaces We will neglect in our further consideration the changes have demonstrated that in this case another model of in the form of X , caused by the changes in higher central surface topography can successfully be applied. This is moments. the “random” mode1.11J6-20 Fuerstenau et al.,25 Scamehorn et a1.,26and Levitz2’ According to that model, the surface sites having difsuggested that the formation of surface aggregates may be a process similar to that taking place in the bulk solution. ferent adsorption energies are distributed on a heterogeIt seems, however, that certain structures may not exist neous surface completely at random. In other words, there is no spatial correlation on the solid surface between adin the bulk solution, since only the presence of the solid sorption sites having the same adsorption energy. Thus, surface stabilizes their existence. While considering the in the general case of a nonideal adsorbed phase, our adsimilarities, we will assume, as in case of bulk solutions of anionic surfactants, that the dispersion of the degree of sorption system must be considered as a thermodynamic entity. aggregation on the surface will not be very large. So, we Different topographies lead to different results of intecan write gration in eq 3. This is because in the case of the patchwise p; = mpO : mkT In x,b (12) surface topography the surface activity coefficients are functions of e through O(e) for a given patch, whereas in where x,b is the surfactant concentration in the equilibrium the case of the random surface topography they are bulk solution. functions of the averaged quantities Ot and are therefore So far, we have not discussed the role of the electric treated as constants while performing the differentiation forces acting on the adsorbed surfactant molecules. The outlined in eq 6. After performing that differentiation we increasing number of adsorbed polar heads induces some arrive at the following expression for cc: changes in the distribution of the surface charge, which causes a transfer of protons from the equilibrium bulk solution to the surface phase. The changing value of {potential must, in turn, affect the adsorption of surfactant molecules. While investigating the calorimetric effect of adsorption The effect of electric forces on adsorption at solid/soof nonelectrolyte liquid mixtures of small molecules, lution interfaces is an extremely complicated phenomenon. Rudziiiski et a1.21and Wightman et a1.22found that the The unusual dimensions of the surface aggregates and their Gaussian-like function x(y) special features compared with the other simple ions present introduce a new degree of complexity. Looking ( l / c ) exp[b - Y O ) / C l (8) xb)= for a simple solution, we assume that only these polar [1 + explb - Yo)/CIl2 represents well the dispersion of E in many adsorption (23) Rudzifiski, W.; Michalek, J.; Brun, B.; Partyka,S. J. Chromatogr. systems, including those with alumina surfaces. In eq 8 198’7.406. 295. , ..-, - -. c represents the width (variance) of the distribution (24) Marczewski, A. W.; Derylo-Marczewska,A.; Jaroniec, M. J. Colloid Interface Sci. 1986, 109, 310. function, which is centered at y = yo. When c 0 our (25) Fuerstenau, D. W.; Healey, T. W.; Somasundaran, P. J . Phys. function (eq 8) degenerates into the Dirac 6 distribution Chem. 1964,68, 3565.
+
-
(22) Wightman, J. P. J. Colloid Interface Sci. 1985, 108, 995.
(26) Scamehorn, J. F.; Schechter, R. S.;Wade, W. H. J . Colloid I n terface Sci. 1982, 85, 436. (27) Levitz, P. Ph.D. Thesis, Universite d’Orleans, 1985; p 112.
Calorimetric Studies of Anionic Surfactant Adsorption heads which are closest (bound) to the surface are affected by the changing values of {. Thus, we will write :p
= pL,b - zeJ/,gz
where the meanings of $d, X,and A, are the same as in the monograph by Hough and Renda1.28 Having determined the function of pH(x,b) experimentally, one may include the electric interactions very easily. Thus in the pH region investigated by us, the function [(pH) as reported by Fuentenau is only slightly dependent upon surfactant concentration. So, as a next approximation we will assume l(pH) to be the same as in the absence of surfactant molecules. Then, in the narrow surfactant region investigated by us, it may be well represented by LY
teractions between the adsorbed aggregates. Its origin is related to Qin,defined as
(13)
where z is the valency of the polar head ion and e is the fundamental unit of charge. We will accept here the Debye-Hiickel approximation = $d exp(-XAl) (14)
r = -a(pH - PZC)@;
Langmuir, Vol. 5, No. 2, 1989 301
> 0, 0 < j3 < 1
(15)
Of course, instead of the approximate relation of eq 15 we might introduce another one coming from the theories relating the pH value to the value of l-potential. That small improvement would be achieved at the expense of introducing new unknown parameters. Although eq 15 should be generally valid for alumina, the parameters LY and j3 may vary to some extent from one sample of alumina to another. For that reason we have performed our own measurements of the pH({) function of our sample, and the results are shown in Figure 5. Then we have found that the function pH(~,b),monitored experimentally by us during our adsorption experiment, may be well approximated by the formula
when a = 0.01, b = 280, and bl = 0.7. The solid line in Figure 4 shows the agreement between experimental and approximate calculated values of pH(x,b). The obtained agreement is excellent, but at present we do not know yet its theoretical origin. We will investigate that problem in our future publications. Meanwhile, we would like to remark that the empirical character of the formula (eq 16) by no means limits its applicability here. When combined with eq 15 it introduces into our consideration the electric interactions in the svstem without introducing new unknown parameters. "Using the notation
In order to find the explicit form of Qh we must accept some approach leading to analytical expressions for the surface activity coefficients y: and yws. The simplest possibility is offered by Flory's mean-field approach, which has already been accepted here, leading to the following expression for Qin: W
Qin
It introduces only one parameter more into our consideration, w , related to the interactions between two aggregates being nearest neighbors. The approach was used extensively by Cases and co-workers12-1Sinvestigating adsorption systems with patchwise surface topography. It was also used very recently by Harwells et al. in their interesting work on adsorption of ionic surfactants on solid surfaces exhibiting a patchwise surface topography. For that reason we will accept it also. The related molar differential heat of adsorption Q is now calculated easily according to the usual formula
After performing the differentiation in eq 18, one arrives at the following expression for Q:
Q = 80+ Qh + Qin
The other two contributions are related solely to the situation on the adsorbent surface. These are the contribution due to the energetic surface heterogeneity Qh
and Qin-the contribution coming from the interactions between the adsorbed molecules. In addition, we have the contribution Qel from the electric interactions in the adsorbed phase Qei
= DiJ'i(X,b) + D2$2(~,b)
where
--
W
mkT
et
; D
D1 = "[D m
+
e
> 0 (18)
+
D2="[-(-)+&)] 1 da m T dT The functions
where
+ Qel
(23) where Qo is the nonconfigurational contribution given by the expression
D = -ea(bl)@exp(XAl) we arrive at the isotherm equation
=ZTet
and
(26)
$(%)I a
db
(28)
t2are defined as
1 jsSvsS wW PsbO l n K = - nyo + - In -+ -+ - (19) mkT m n(jws)n mkT kT
and where the term (we,/mkT)represents the lateral in(28) Hough, D. B.; Rendal, H. M., In Adsorption From Solution at the Solid Liquid Interface; Parfitt, G. D., Rochester, C. H., Eds.; Academic: London, 1983; p 247.
(30)
We now approach a very interesting point in our analysis. Namely, when the factor (n/m)(c/kT)is not far from
Partyka et al.
302 Langmuir, Vol. 5, No. 2, 1989
unity, and both D = 0 and w = 0, our eq 18 reduces to the well-known Stern-Langmuir equation. Rendal et alSBused that equation as a starting point and generalized it next to account for the electric interactions in the adsorbed phase. That generalized equation was then successfully used by these authors to correlate the experimental adsorption isotherms of anionic surfactants at lower surface coverages, where monomer adsorption must be predominant. It is now generally accepted that adsorbed monomers lie horizontally on adsorbent surfaces (even in the case of ionic adsorbents), occupying thus a large number of adsorption sites. So, it may surprise one that this apparent multisite occupancy adsorption is not governed by the term In [8,/(1 - OJn] but by the Langmuir-like term In [e,/(l e,)] developed statistically for single-site-occupancy adsorption. The lack of the exact linear relationship between In [e,/(l - e,)] and In x,b was ascribed to electrical interactions. Our theoretical treatment brings, thus, a first explanation for that apparent contradiction. In the more general case ( D = 0, w # 0), our eq 18 resembles very much the Frumkin-Fowler-Guggenheim isotherm equation used by Lyklema and co-workersmand by Cases and c o - ~ o r k e r s . ~to~describe - ~ ~ * ~the ~ adsorption at higher surface coverages as well. We believe that the aggregate which is formed first is a result of the two-dimensional condensation of dimers or monomers which exist at bulk concentrations smaller than mol kg-'.' The question of whether the formation of the two-dimensional aggregates proceeds via dimers or directly from the monomer state still needs some further investigation. Their assumed structure implies the existence of hydrophobic lateral interactions, which are responsible also for their creation. However, at the highest surface coverages, the strong competition for the surface sites available for adsorption must favor the creation of more dense and bulky aggregates. Their formation may proceed both via inclusion of new monomers into the already existing structures and/or through making the aggregate more three-dimensional. In our further consideration we will distinguish only between the exactly two-dimensional aggregates and the three-dimensional-like ones. We assume that both kinds of aggregates exist in the concentration region investigated by us. The changing concentration in the equilibrium bulk solutions changes both their number on the surface and their relative proportions. To handle the problem mathematically, we will apply here the approach which has been developed by Rudziiiski et al.32to describe the adsorption from multicomponent liquid mixtures onto heterogeneous solid surfaces. Here, the two kinds of surface aggregates will be treated as two different components. Before the explicit form of adsorption equations is written, a certain correction must be discussed concerning the hydrophobic interactions between the two-dimensional aggregates. Namely, in the absence of the three-dimensional aggregates, the constant w would have been proportional to the maximum number of the nearest neighbors-surface aggregates corresponding to factor 1- 63t, where 0%denotes the fraction of the alumina surface occupied by the three-dimensional aggregates. 02t will denote later the (29) Rendal, H. M.; Smith, A. L.; Williams, L. A. J. Chem. SOC., Faraday Trans. I 1979, 75, 669. (30) Van der Schee, H. A.; Lyklema, J. J . Phys. Chem. 1984,&?, 6661.
(31) Cases, J. M.; Poirer, J. E.; Canet, D. In Solid-Liquid Interactions i n Porous Media; Cases, J. M., Ed.; Technip: Paris, 1985; p 335. (32) Rudzidski, W.; Michdek, J.; Pilon, K.; Suprynowicz, Z. J. Chem. Soc., Faraday Trans I 1985, 81, 553.
fraction of the surface occupied by two-dimensional aggregates. According to what has been said above about our adsorption model, the application of Rudzidski's approach from multicomponent liquid mixtures onto heterogeneous solid surfaces leads us to the following system of adsorption equations:
F , = -In x,b - In K2 + -- In m 2 kT 1 - Bzt - 03t n2lI2
f92t
n3If2 e3t + F3 = -in xsb- In K3 + - - In m3 kT 1 - 62t - 03t a exp(bx,b) B n3 = 0 (32) m3 kT 1 + a exp(bx,b)
]
The solution of these equations yields the fractions of the surface area occupied by the two-dimensional, and the three-dimensional-like aggregates, 0%and 03t. In the concentration region investigated here, Le., above hmc, we neglect in our consideration the presence of monomers. Now let us consider the expression for the heat of adsorption corresponding to the physical situation assumed above. Let us remark to that end that, on an incremental change in the total surface coverage et = (elt + Ozt), the fraction Ari
i
will represent the fraction of the surfactant molecules adsorbed in the i-th form. Then, the molar differential heat of adsorption Qt is expressed as
aF1/a@,,
...
aF1/ax2
a ~ /ax: , ... ... LaF, /as,, ... aF, /ax: aF, /a@,, ...
a@it _ - (-1)
ax:
[
/a@,, a ~ /a@,, , ... aF, /a@,, aF,
... ...
aF, /as.,
... ...
... aF,
aF,
1
/a@,,
...I
(35)
... aF, /a@, ... aF, /ae,, ... aFz /a@, ... aF2/a@,,
... ...
,..
... aF, /a@, ...
aF, /a@,,
The other derivative with respect to temperature is evaluated as
After the equation system of eq 31 and 32 is solved, the total adsorbed amount r(x,b)is evaluated as (37)
where M is the total number of adsorption sites existing
Langmuir, Vol. 5, No. 2, 1989 303
Calorimetric Studies of Anionic Surfactant Adsorption
surfactant set no.
KZ
K3
35
25
1
c7
Table I. Parameters Used in Numerical Calculations mzlnz mslns cn3IkJ w/kJ D l k J QoJkJ 2.0
2.3
2.5
2.0
fix c7
2
31
37
c7
3
35
25
C18
4
160
290
2.0 fix 2.0 fix 2.0 fix
2.3
2.3
1.3
2.3
2.5
2.0
5.5
15.0
3.0
on our alumina sample (expressed practically in the same units in which the adsorbed amount is expressed). The heterogeneity contribution Qhi now takes the form n11/2c Qhi = -In mi
(
);
1 - Bzt - eat eit
i = 1, 2
QozIkJ
DllkJ
DzlkJ
12.5
0.0
0.0
fix
fix 0.0 fix
0.0 fix 3.4
-1.0
0.0 fix
10.5
14.5
0.0 fix 17.0
-1.0
10.5
12.5
0.0 fix
0.0
20.0
10.5
0.0 fix 0.5 fix 0.0 fix
2.0
fix 0.0 fix 1
I
(38)
whereas the interaction contribution Qh2 due to the hydrophobic interactions between the two-dimensional aggregates reads (39) Finally, we believe that showing separately certain contributions to Qt may be very instructive for drawing conclusions about the investigated adsorption mechanism. Thus, while presenting the results of our analysis of our experimental heats of adsorption, we will distinguish the following contributions: (1)the contribution Qit due to the presence of the aggregate “i”
(2) the nonconfigurational contribution QOtfrom both kinds of the surface aggregates
(3) the total contribution due to the energetic heterogeneity of the alumina surface, Qht
(4) the interaction contribution due to the hydrophobic interactions between the two-dimensional aggregates, Qht Qint
= CAriQini i
(43)
and (5) the electric contribution Qelt Qelt
= CAriQeli
(44)
I
Results and Discussion While analyzing our experimental data we required our expressions for the adsorption isotherms and heats of adsorption to fit the experimental data simultaneously. So, the following parameters had to be determined in our numerical calculations: K2,K3,m3/n3, cn21/2,cn3ll2,w , D, D,, D2, QO1,and Qoz. The parameter mz/n2was always assumed to be equal to 2. The parameter /3, estimated from the function pH({), was equal to 0.8. One may argue that the list of the best-fit parameters is rather long. That impression could be understood if only the adsorption isotherms had been analyzed. However, we have at our disposal the data obtained from two independent experimental sources to be fitted simultaneously. One of them-the heat of adsorption-is particularly sensitive to the nature of the adsorption systems,
BULK C O N C E N T R A T I O N x 1 0 2 1 mol kg-’
Figure 6. Agreement between the experimental adsorption isotherm of C7 (0) and the theoretical one (-) calculated by means of eq 31,32, and 37 using parameter set no. 1. (- - -) is the fraction of the surface 0 occupied by the two-dimensional agwhereas (--) is the fraction of alumina surface gregates e)(, occupied by the three-dimensional aggregates, est. much more sensitive than are the adsorption isotherms, The reason for that is very well known in thermodynamics. However, to rely only on formal best-fit exercises could be risky. Therefore, we have chosen the following strategy for our theoretical-numerical analysis. First, we used a best-fit procedure to find approximate values of the parameters giving a reasonable fit to experimental data. Starting from these parameters, we next performed numerous model investigations to see the way in which the parameters influence the agreement with experiment. In particular, we observed which parameters reproduce well the peaks on the experimental heats of adsorption. In Table I we have collected the sets of the parameters which, in our opinion, reproduce not only the numerical values of the majority of the experimental points but also the observed trends in the experimental data. Thus, our calculations were partially best-fit exercises and partially model investigations. Our first intention was to show that the expressions developed in the previous section can explain satisfactorily the complicated behavior of the experimental data. In the course of our calculations we have discovered that the parameters D and w are strongly correlated. From the physical condition D > 0 and w > 0, it follows that the way in which the electric forces affect the surfactant adsorption is reciprocal to the effect of the lateral hydrophobic interactions between the two-dimensional aggregates. This confirms the widely accepted view that the lateral hydrophobic interactions are one of the main driving forces for anionic surfactant adsorption. Since the parameters w and D were highly correlated, we have performed our calculation twice, by assuming the two extreme physical situations: w = 0, D # 0 and w # 0, D = 0. The comparison with experiment is shown in Figures 6-9. One can see in these figures that the obtained agreement is not much different, but the assumption that w = 0 and D # 0 reproduces the position on the heat of adsorption curve better. The conclusion which we draw from this
304 Langmuir, Vol. 5, No. 2, 1989
Partyka et al.
$ 1 0
1 0
05 R E L A T I V E ADSORBED
AMOUNT
Figure 7. Agreement between the experimental heats of adand the theoretical ones, Qt (-), corresponding sorption of C7 (0) to parameter set no. 1 and calculated by means of eq 33-36. (- - -) is the contribution Qa defined by eq 40 due to the adsorption of the two-dimensional aggregates. (--) is the contribution to the total heat of adsorption due to the presence of the threedimensional aggregates, Q3t.
RELATIVE ADSORBED A M O U N T
1
Figure 10. Nonconfigurational contribution Qa (- - -) to Qt, defined in eq 42, in the case of C7 adsorption, calculated with parameter set no. 1.
;; z o f
. 2
I
1
RELATIVE
ADSORBED
AMOUNT
I
Figure 11. Behavior of the functions (--) and q2 (- - -) compared with the behavior of the heterogeneity contributionQht (-), in the case of the surfactant C7 and the parameter set no. 1.
BULK C O N C E N T R A T I O N X 1 O 2
mol k9-l
Figure 8. Agreement between the experimental adsorption isotherm of C7 and the theoreticalone correspondingto parameter set no. 2. The notation is as in Figure 6.
0
10
05 RELATIVE
ADSORBED
AMOUNl
Figure 9. Agreement between the experimental values of the heat of adsorption of C7 and the theoretical ones calculated with parameter set no. 3. The notation is as in Figure 7. model investigation is that the nature of the lateral hydrophobic interactions and the electric ones is almost exactly reciprocal and that the hydrophobic interactions prevail. Figure 10 demonstrates, that the peak on the heat of adsorption curve is a combined effect of nonconfigurational contribution, Qat, and the contribution Qht coming from the energetic surface heterogeneity. This should not suprise w since an extensive cancellation takes place between
the electric and hydrophobic interactions; their contribution to the total heat effect may not be so essential. Figure 11 shows separately the functions $1and which might represent the combined effect coming from the electric and hydrophobic interactions. The assumption that $z makes a significant contribution could only worsen the obtained agreement. From Figure 11one can deduce that any linear combination of the functions and $2 could not produce the sharp peak on the heat of adsorption curve. Our calculation appeared to be very sensitive to the parameter mln. This reflects probably the competition for the free available adsorption sites. That competition must obviously favor the thee-dimensional-likeaggregates. The decrease in the parameter cn1lZmeans that the three-dimensional aggregates occupy a smaller number of adsorption sites when counted per aggregate. That, probably, is the response of the surface aggregates to the repulsive forces exerted by the surface on the polar heads attached to the surface. Let us finally consider the remarkable decrease in the average aggregation number m accompanying that transition expressed by the aggregation ratio m3/m2= 0.74. This would mean that the transition discussed above proceeds via a destruction of very large two-dimensional “patches” of the bilayer aggregates and a subsequent formation of smaller, more three-dimensional aggregates. Acknowledgment. We express our thanks to D. Cot for technical assistance in preparing this publication. We also wish to thank the British Petroleum Company plc for permission to publish this paper. Registry No. Cy,33660-91-2;CIS, 27177-79-3; A1203,1344-28-1.
