Langmuir 1994,10,3268-3278
3268
Adsorption of Ionic Amphiphiles as Bilayers on Charged Surfaces Per Wangnerud* and Bengt Jonsson Thermochemistry and Division of Physical Chemistry 1, Chemical Center, Lund University, P.O. Box 124,S-22100 Lund, Sweden Received March 17,1994. In Final Form: July 5, 1994@ A model for the adsorption of ionic amphiphiles in the form of a bilayer at an oppositely charged surface is presented. The treatment is based on an earlier model developed by Jansson and Wennerstrom for the association of ionic amphiphiles in aqueous solution. The electrostatic effects are treated by using the Poisson-Boltzmann equation. In addition to the electrostatic interaction, the influence of dispersion forces, solvation, and steric interaction on the interaction between the bilayer and the surface are also considered. From the model expression for the free energy of the system it is possible to calculate the critical amphiphile concentrationfor formation of a bilayer at the surface and the concentrationdependence of the thickness of the bilayer. It is found that the critical concentration strongly depends on the charge density of the surface; at low charge densities the electrostatic interaction between the surface and the bilayer is too small to stabilize the bilayer at amphiphile concentrationsbelow the cmc. The outcome of the model is compared with experimental results obtained by in situ ellipsometry for the alkyltrimethylammonium bromide/SiOz system. It is concluded that at low to neutral solution pH it is questionable if a bilayer is formed at the surface. At high solution pH, implying high charge densities of the surface, the bilayer adsorptionmodel is able to describe the effect of changes of the electrolyte concentration,co-ion valence, and alkyl chain length on the adsorption of alkyltrimethylammonium bromides on SiO2.
Introduction The most characteristic property of mixtures of surfactants and water is the association of the amphiphiles into various kinds of aggregates. At low amphiphile concentrations, the aggregates present are comparatively small micelles while liquid crystalline aggregates, e.g. lamellar bilayers, are formed a t higher concentrations. The major cause for the association of the amphiphiles into aggregates is the drive of the system to diminish the contact area between the hydrocarbon parts of the amphiphiles and the surrounding water. The major factor opposing the aggregation is the decrease in the configurational entropy of the polar head group and, if any, the accompanying counterion. In the case of ionic surfactants, the electrostatic repulsion between the charged head groups a t the surface of the aggregates is of course also of importance. Although an amphiphilic aggregate consisting of a large number of interacting molecules is a very complex system, relatively simple thermodynamic models describe the properties of these systems rather we1l.l For association of ionic surfactants, the model developed by Jonsson and Wennerstrom, here denoted the PBCM model, is very useful for the understanding of systems containing micellar or liquid crystalline aggregates. Substantial simplifications of the real system are, of course, introduced in this model in order to obtain simple and useful equations, but the major contributions to the free energy under most conditions likely are treated in a correct manner, since the model rather accurately describes several characteristics of these systems. In the original PBCM model it is only possible to treat the interaction between aggregates in solution, but in this work we have modified the model so that the interaction between a charged solid surface and an amphiphile aggregate can be considered. As a representative of the various types of aggregates, e.g. micelles, disks, and bilayers, that can possibly form at the surface or in the solution region adjacent to the surface, we have in this work choosen to treat the formation of an amphiphile
* To whom correspondence
should be addressed. Abstract published inAdvance ACSAbstracts,August 15,1994. (1)Jonsson, B.;Wennerstrom, H. J. Phys. Chem. 1987,91, 338. @
bilayer. This choice is partly due to the simple relations for the electrostatic interaction that are obtained for this particular aggregate geometry and partly due to that we in this work mainly are interested in the adsorption behavior from intermediate adsorption densities up to the adsorption plateau above the cmc, O.S(cmc) < cBUd< 1.3(cmc),and the bilayer structure is usually the most stable type of aggregate at high surfactant concentrations. Work in the direction of describing the intermicellar and the surface-micelle interactions for spherical micelles in the solution adjacent to a charged solid surface is in progress. In a previous work2we have treated the initial adsorption, cS+, cmc, where the amphiphiles are adsorbed primarily as monomers and dimers. The influence of important factors such as the surface charge density, the ionic strength, and the alkyl chain length on the adsorption behavior of amphiphiles has been studied experimentally by measurements of adsorption isotherms for alkyltrimethylammoniumbromides on silica at various conditions. The adsorption isotherms have been determined by means of in situ ellips~metry.~-~ The fact that the adsorbent used in ellipsometric measurements is smooth and nonporous is an advantage of this technique compared with conventional solution-depletion methods where a more or less porous powder is used as adsorbent since the interpretation then is facilitated. The experimental observations are presented in the next section. Then follows a description ofthe way the different energy contributions that affect the adsorption are treated, the computational procedure, and the bilayer adsorption model. In the final section the predictions of the bilayer model are compared with the experimentally observed influence of the different factors mentioned above.
Experimental Observations Materials. The instrument used was a modified Rudolph thin-film ellipsometer. A detailed description of the instrument Oxidized silicon slides and data treatmentis given el~ewhere.~J with a 30 nm thick surface layer of Si02were used as adsorbents. (2) Wlingnerud, P.; Jbnsson, B. Langmuir, in press. (3) Wangnerud, P.; Olofsson, G. J . Colloid Interface Sci. 1992,153, 392. (4)Landgren, M.;Jonsson, B. J . Phys. Chem. 1993,97,1656. ( 5 ) Tiberg, F.; Landgren, M. Langmuir 1993, 9, 927.
0743-746319412410-3268$04.50/0 0 1994 American Chemical Society
Adsorption of Ionic Amphiphiles
Langmuir, Vol. 10, No. 9, 1994 3269 6
l
'
L
1
*
'
o o o o o o 0
'
0
c!
'
m
a
l
a
a
0
E
I
a
a
a a 0
10 mM NaBr pH 9.3 H,O pH9.7
0
1 2 Concentration/ mmol.dm"
3
Figure 1. Influence of pH on the adsorption of C14TAB on Si02 from 10 mmol~dm-~ NaBr. Procedure. The experimental procedures were identical to what has been reported previ~usly.~ The values for the molar refraction of dodecyl- and tetradecyltrimethylammonium bromides (in the following abbreviated as &TAB and c14TAB, respectively) were obtained from measurements of the refractive index of surfactant solutions in the concentration range 0-20% by weight a t a wavelength of 589 nm and corrected to the actual wavelength, 400 nm, ofthe measurements by using an electronic absorption frequency of 3 x 1015s - ~ .The ~ correction results in an increase of the molar refraction of %4%, and the values used for the ratio of molar mass to molar refraction were 3.46 and 3.41 g ~ m for - ~&TAB and &TAB, respectively. Results. Adsorption isotherms for c14TAB in 10 "01-dm-3 NaBr on Si02 determined a t various pH are shown in Figure 1. Si02 surfaces have, due to ionizable silanol groups, a variable negative surface charge that increases with pH, the isoelectric point being about 2-3.7J' Increasing the solution pH has a great influence on the adsorption of cationic surfactants on silica.3*9Jo As shown in Figure 1,the adsorption density increases considerably with pH, and the overall shape of the isotherm is changed when the pH of the solution is changed. At low pH they are S-shaped, while in the presence of NaBr the adsorption isotherm becomes distinctly convex a t high pH. However, independent of solution pH, the isotherms shown in Figure 1 level off a t a surfactant concentration of about 1.6 mm~l-dm-~, which agreed well with the break point in the surface ~ A similar tension curve for c14TAB in 10 m m ~ l - d m -NaBr. change in isotherm shape with an increase in pH was observed by Bijsterbosch for the adsorption of ClzTAB on Cab-0-Si1 M5 silica gello and has also been observed for the adsorption of octylbenzenesulfonate on alumina.ll Due t o the small surface area used, ellipsometric measurements are rather sensitive to the presence of impurities3J2and the weak maxima seen in some of the adsorption isotherms might be due to desorption of coadsorbed organic impurities after the cmc. The influence of the supporting electrolyte concentration on the adsorption of c14TAB on Si02 is shown in Figure 2. The adsorption isotherms in pure water at low pH (not shown) are S-shaped3as in the presence of NaBr. However, the adsorption isotherm determined in water at high pH is linear, while the - ~ shows correspondingisotherm determined in 10 m m ~ l d mNaBr a convex shape. Reducing the concentration of supporting electrolyte shifts the adsorption isotherm to higher concentrations of surfactant, but the cmc is also shifted to higher concentrations, and the plateau adsorption has only a slightly lower value in pure water as compared to the solution containing additional salt. The break point in the adsorption isotherm for c14TAB in water occurs a t a surfactant concentration of about 3.5 mmol~dm-~ and agrees (6)Israelachvili,J. N. Intermolecular and Surface Forces;Academic Press: London, 1985. (7) Iler, R. K. The Chemistry of Silica; Wiley: New York, 1979. (8) Scales, P. J.; Grieser. F.: Healv, T. W.; White, L. R.; Chan, D. Y. C. Langmuir 1992,8,965. (9)Partyka, S.;Lindheimer, M.; Faucompre, B. Colloids Surf. 1993, 76,267. (10)Bijsterbosch, B. H. J. Colloid Interface Sci. 1974,47, 186. (11)Denoyel, R.; Rouquerol, J. J. Colloid Interface Sci. 1991,143, 555. (12)Amebrant,T.;Backstrom,K; Jonsson, B.;Nylander,T . J . Colloid Interface Sci. 1989,128, 303.
0
1
2 3 4 Concentration mm01.dm.~
5
Figure 2. Adsorption isotherms for C14TA.B on Si02 in the presence of 10 mmol~dm-~ NaBr and without any extra electrolyte present, respectively.
a 5 mM C a r z pH 9.0 ,
0
0.5
,
i
1
.
i
1.5
.
,
2
,
,
2.5
Concenaation / m m ~ i . d m - ~
Figure 3. Influence of the valence of the surfactant co-ion: adsorption isotherms for on Si02 from 10 m m ~ b d m - ~ NaBr and 5 m m ~ l a d m -CaBrz. ~ well with reported cmc values for &TAB in pure water of 3.5 and 3.6 m m ~ l - d m - ~ . ~ ~ J ~ The effect of increasing the valence of the surfactant co-ion on the adsorption isotherm is illustrated in Figure 3 by the adsorption isotherms for c14TAB on Si02 determined in 10 mmol~dm-~ NaBr and 5 mm~ladm-~ CaBrz, respectively. Since we, in this work, are interested in the adsorption behavior ofthe surfactant all the way up to and above the cmc, a CaBrz was choosen in order to have the concentration of 5 "01-dm-3 same concentration of bromide ions and therefore also about the same cmc in both solutions. Changing the surfactant co-ionfrom Na+ to Ca2+results in a shift of the adsorption isotherm to higher surfactant concentrations. The effect is largest at low surfactant concentrations; at higher concentrations the isotherm determined in CaBrz solution approaches the isotherm determined in NaBr solution and both isotherms show a break point at approximately the same surfactant concentration. Not only the valence, but also the identity of the surfactant co-ion may have an influence on the adsorption of ionic surfactants onto oppositely charged surfaces. Replacing Na+by C1TA+(that resembles the surfactant head group) as the surfactant co-ion has an influence on the initial stage of the adsorption process. At higher adsorption densities the influence of the surfactant co-ion on the adsorption is negligible; see ref 15. The adsorption isotherms for &TAB and c14TAB on Si02 from pure surfactant solutions are shown in Figure 4. Just as in the case for the value of the cmc,16the alkyl chain length has a profound influence on the concentration dependence of the adsorption behavior of ionic surfactants on oppositely charged surface^.^^-^^ Adding two methylene units to the surfactant alkyl chain results in a decrease of the cmc in pure water from about 15 mmol*dm+ for C12TAB14J6to about 3.5 mmol~dm-~ for c14TAB. (13)Sepulveda, L.; C o f i s , J. J . Phys. Chem. 1986,89, 5322. (14)Limos, P.;Zana, R. J . Colloid Interface Sci. 1981,84, 100. (15)Wangnerud, P.;Berling, D.; Olofsson, G. J . Colloid Interface Sci., in press. (16)Lindman, B.;Wennerstrom, H. Topics in Current Chemistry; Springer: Berlin, 1980. (17)Wakamatsu, T.;Fuerstenau, D. W. Adu. Chem. Ser. 1968,79, 161. (18)Somasundaran,P.; Healy,T. W.; Fuerstenau,D. W. J . Phy. Chem. 1964,68,3562.
Wangnerud and Jonsson
3270 Langmuir, Vol. 10,No.9,1994
“
E0
4
4
0
53 2
24° r
0 O
C,,TAB pH 9.7
I
x
t
Figure 5. Schematic representation of the model system used to calculate the influence of the electrostatic interaction on the stability of an amphiphilic bilayer adjacent t o an oppositely charged solid surface. The adsorption behavior of C12TA.Band c14TAB on Si02 shows a similar trend, and after the concentration axis is rescaled (not shown) by dividing the surfactant concentration by the cmc for the actual case, the two isotherms almost overlap. However, the slope of the c14TAB isotherm is still somewhat higher, and the adsorption density of C14TAB a t concentrations above the cmc is about 10%higher than that of C12TA.B. The modest increase of the adsorption density is in reasonable agreement with previously reported results for the adsorption of C,TAB on Si02 surface~.~JO~~~
Different Energy Contributions that Affect the Amphiphile Adsorption In the model it is postulated that a bilayer of cationic surfactant is formed at, or in close proximity to, a negatively charged surface, e.g. a Si02 surface. From calculations using the developed model, we can then conclude whether or not the suggested structure is stable with respect to the charge densities of the inner and the outer parts of the bilayer and the distance between the bilayer and the charged solid surface. In the calculations we consider only the thermodynamic properties of the bilayer, and therefore we cannot prove that this is the most stable structure. Other structures, such as spherical micelles or disklike aggregates, can of course, depending on surface charge density and amphiphile concentration, be more stable than the bilayer. In order to estimate the influence of the electrostatic interaction on the stability of an amphiphilic bilayer adjacent to an oppositely charged surface, we have used the model system shown in Figure 5 to describe the bilayer formation. The adsorbed bilayer is represented by the hatched area in Figure 5, and it is the location of the head group that determines whether the amphiphile belongs to the outer, I, or inner, 11, monolayer. There is no rkstriction on the location of the amphiphile alkyl chain in the model, and the alkyl chains from the two monolayers can interpenetrate freely. Moreover, we assume that the area of the bilayer is sufficiently large so that boundary effects can (19)Bohmer, M. R.; Koopal, L. K. Langmuir 1992,8, 2660. (20) Wahlgren, M. C.; Amebrant, T.; Askendal, A.; Welin-Klintstrom, S. Colloids Surf. A: Physico. Chem. Eng. Aspects 1993,70, 151.
be neglected, which implies that the formation of the bilayer at the surface can be regarded as a “phase separation”. This means that the bilayer is formed at a certain critical amphiphile concentration and then covers the whole solid surface. At amphiphile concentrations above this critical concentration the thickness of the bilayer increases; i.e. the average area per head group decreases, but the total area of the bilayer remains constant. The major driving force for formation of a bilayer is the drive for minimum contact area between the hydrocarbon parts of the amphiphiles and the surrounding water. However, also the electrostatic intercations within the bilayer and between the bilayer and the charged surface are of importance. At low amphiphile concentrations these two contributions to the gain in free energy for formation of a bilayer will not be large enough to overcome the loss in entropy due to the gathering of the amphiphile monomers needed to form the bilayer. This entropy loss decreases with increasing amphiphile concentration, and at a certain concentration, the critical surface bilayer concentration (csbc), the formation of a bilayer at the surface, will be possible. Above this concentration the bilayer will extend over all the charged solid surface. The distribution of amphiphiles between monolayer I and I1 will vary with the distance, L , between the bilayer and the charged surface; see Figure 5. The major cause for the inhomogenous distribution of amphiphiles between the two layers is the electrostatic interactions among the charged amphiphile head groups and between the head groups and the surface. The critical concentration of amphiphile, csbc, and the concentration dependence of the thickness of the bilayer will be calculated from the model. Another issue considered in our calculations is whether there will be a layer of water in between the bilayer and the charged surface. In the model it is assumed that the free energy, G , of a system consisting of a bilayer having an area A and residing at a distance L from a charged surface can be divided into the following portions. 1. The Hydrophobic Effect. The main reason for the association of amphiphilic molecules into micellar or bilayer type of aggregates is the strong interaction between water molecules, obstructing the mixing of water and nonpolar compounds. Solubility data for homologous series of substituted hydrocarbons show that the difference in standard free energy of 1mol of such molecules in an aqueous solution and in a nonpolar environment, Ghe,often is a linear function of the number of carbon atoms, nc, in the alkyl chain:
Ghe Kl
+ 1.4RTnC
where the value of Kl depends on the functional group of the substituted hydrocarbon. The difference in energy for the alkyl chain of an amphiphilic molecule in an aqueous solution and in the interior of a bilayer is, however, somewhat less than the value indicated by eq 1. There are two main reasons for this. (a)The alkyl chain is not completely removed from water contact, but there is always some contact between the hydrocarbon part of the amphiphile and the surrounding water. Thus, a term that depends on the contact area between the bilayer and the surrounding water must be added to eq 1: (b) There is an important difference between an amphiphilic molecule in a bilayer and a hydrocarbon molecule in the interior of a nonpolar environmentin that the head group of the amphiphile is more or less anchored at the surface of the bilayer. As a consequence, the amphiphiles
Adsorption of Ionic Amphiphiles
Langmuir, Vol. 10, No. 9,1994 3271
are conformationally restricted in the aggregate. Both the number of possible configurations of the surfactant head group and the number of possible conformations for the alkyl chain are reduced. The number of attainable conformations of the alkyl chain of an amphiphile in a bilayer depends on the area per amphiphile, i.e. the thickness of the bilayer. Due to the complexity of the system it is unfeasible to obtain a simple expression for the variation in conformational entropy of the alkyl chain with the area per amphiphile from a molecular description of the system. Instead, it has proven to be fruitful to describe this contribution to the free energy of a bilayer as a series expansion in A, which is truncated after the two first terms: Gconf = K3 + K44 (3) Summation of these three contributions, eqs 1-3, gives the following expression for the gain in free energy for transfer of the hydrocarbon part of an amphiphile from aqueous solution to a bilayer: hse -
(4) - (namph,I + namph,II) *pamph + YM The constant of proportionality, y , has been measured as s18 x J.m-2 for lamellar liquid crystalline aggregates of several different surfactant-water systems. 2A is the interfacial area of the bilayer toward the surrounding solution. Boundary effects a t the edges of the bilayer are neglected. 2. The Electrostatic Free Energy for Formation of a Bilayer and the Free Energy of Interaction between the Bilayer and the Charged Surface. Regarding the distribution of charges in the system, the following assumptions are made in the model calculations: Charges are found at the solid surface, at the surfaces of the outer and the inner amphiphile monolayers, and in the surrounding solution as mobile ions. The distribution of ions in the solution is calculated by means of the Poisson-Boltzmann equation. The charge density of the solid surface is assumed to remain constant, independent of distance between the bilayer and the solid surface (thus, we neglect the possibility that the surface may titrate) while the charge densities of the two amphiphile monolayer surfaces are allowed to vary with distance from the surface. The electrostatic contribution to the free energy of the system can be divided into two parts, an energy term,
where e is the charge density and t,!J the electrostatic potential a t a distance x from the charged solid surface (see Figure 5), and EO+ is the permittivity of the system, and an entropy term,
water in each region, the following expressions are obtained for the electrostatic contribution to the chemical potential of water in regions I and 11:
(7b)
+
where Ci,buh, ci(L b), c&), and ci(0) denote the concentrations of ionic species i in the bulk solution, at the surface of the outer monolayer, a t the surface of the inner monolayer, and a t the charged interface, respectively (see Figure 5). 00, a ~and , UII denote the charge densities ofthe interface, the outer monolayer, and the inner monolayer, respectively. The equation for the chemical potential of the free ions is obtained from the derivative of the equation for the free energy. The result is
pi = p i *
+ RT In("it:)
where pi* is the standard chemical potential of ion i in the aqueous solution. Concerning the electrostatic contribution to the chemical potential of the amphiphiles in the two monolayers, two cases can be distinguished: (a) The area per molecule in the layer can be varied; i.e. the amphiphiles are not close packed. (b)The amphiphiles in the layer are close packed; i.e. the area per amphiphile is constant, at a minimum value. For case a, the electrostatic contributions to the chemical potential of the amphiphile in the outer and the inner monolayers can be written as
+
where F is the Faraday constant and +(L b ) and v ( L ) are the electrostatic potentials at the surface of the outer and the inner monolayers, respectively. In eqs 9a and b it is implicitly assumed, and will be from now on, that the charge of the amphiphile is +l. For the case of a close-packed monolayer, when the area per amphiphile is constant, the corresponding expressions are
-TSm, = A R T C s,"ci i
where R is the universal gas constant, T the absolute temperature of the system, ci the concentration of ionic species i, and co the concentration of water, %55.5 m ~ l - d m - ~The . ideal entropy of mixing for the ions and the water molecules is also included in eq 6. Differentiating eqs 5 and 6 with respect to the number of molecules in the different regions gives the electrostatic contribution to the chemical potential of each component in the different regions. Since these differentiations are rather involved, they are given in the appendix, and only the resulting expressions are given here. From the derivative of the electrostatic free energy the ideal entropy of mixing with respect to the amount of
+
where Aamphis the area per amphiphile in a close-packed monolayer. (aG,l+,daA) gives the area dependence of the free energy in the system. The equation for (aG,l+,daA) is (see appendix)
3. Dispersion Forces. The interaction between the bilayer and the solid surface due to dispersion forces can
Wangnerud and Jonsson
3272 Langmuir, Vol. 10,No.9,1994
potential of water in region I1 is then
be calculated from the expression given below:
pEzo= - Khf -eapj'hf
whereA123 is the effectiveHamaker constant ofthe system and A the interfacial contact separation.6 For the system SiO2-H2O-hydrocarbon, A123 is about 5 x J, calculated from data given in ref 6. For a large variety of compounds, a value of 1.65 A for A gives a good agreement between experimental surface energies and those calculated on the basis of the Lifshitz theory.6 The contribution of the dispersion energy to the chemical potential of water in region I1 is given by disp
pH''
- A123
- 63tco
1 ( ( L A)3 ( L
+
+
6nCo ( L
+ A)3i f L + A < < b (13)
For the amphiphiles in the bilayer this contribution to the chemical potential is disp
=--
PA
+ A + b)3
(14)
where V m p h is the molar volume of the amphiphile. The contribution from the dispersion energy to pa,f can be of importance a t low surface excess when the adsorbed layer is comparatively thin. For a 20 A thick layer of CI4TA+ molecules, the contribution of the dispersion energy to the chemical potential of the amphiphile is less than 0.003RT and is therefore neglected in the model. The contribution to aGlaA from the dispersion energy can be written as
-A''
+
3L A i f L A
