Langmuir 1994,10, 3542-3549
3542
Ionic Surfactants at the Charged Solid/WaterInterface: Significance of Premicellar Aggregation Per Wangnerud* and Bengt Jonsson Thermochemistry and Physical Chemistry 1, Chemical Center, Lund University, Box 124, 221 00, Lund, Sweden Received March 14, 1994. In Final Form: July 11, 1994@ The initial adsorption of alkyltrimethylammoniumbromides (CnTAB, n = 10,12,and 14)on silica has been determined as a function of alkyl chain length a t high solution pH. The isotherms showed a strong chain length dependence at low adsorption densities. The influence of the identity and valency of the surfactant co-ion on the initial adsorption was investigated by determination of the isotherms in 10 mmol~dm-~ Br- solutions containing Na+, Ca2+,and ClTA+ (that resemble the surfactant head group). The dependence of the adsorption on ionic strength and alkyl chain length is interpreted in terms of formation of small surfactant aggregates in the solution region adjacent to the charged oxide surface. A thermodynamic model, based on the Poisson-Boltzmann equation, that accounts for the formation of surfactant oligomersand the electrostatic binding ofthese aggregatesin the diffise layer has been developed. A qualitative agreement between calculated and experimental isotherms was found if only electrostatic interaction between the surface and the surfactant aggregates was considered.
Introduction The hydrocarbon chain plays a dominant role in the adsorption of ionic surfactants onto oppositely charged solid surfaces, and the influence of the chain length on the adsorption has been demonstrated by a variety of methods, for example, by electrokinetic ~ t u d i e s , lflotation -~ b e h a v i ~ rand , ~ adsorption measurement^.^ Even at bulk concentrations well below the critical micelle concentration, cmc, a strong dependence of the adsorption on alkyl chain length can be observed also for adsorption onto surfaces normally not regarded as hydrophobic. This is illustrated in Figure 1 by the adsorption isotherms for a homologous series of alkyl trimethylammonium bromide surfactants, CnTAB. For a number of surfaces, e.g. polystyrene,’ AgI,8g9etc., the strong dependence on alkyl chain length can a t least partly be explained by a direct hydrophobic or dispersion interaction between the surface and the hydrocarbon part ofthe surfactant. However, in most cases the dependence on the alkyl chain length is too strong to be explained by a direct interaction between the hydrocarbon part and the surface alone. We will in this work develop a n alternative explanation to the strong chain length influence by assuming self-association of the amphiphilic molecules into dimers, trimers, etc. The fraction of surfactants present as dimers or oligomers in bulk solutions is usually very low but may, due to electrostatic interactions, be considerably higher in the region adjacent to a charged interface. Besides the two aforementioned possibilities, specificbinding of the surfactant head group @
Abstract published in Advance ACS Abstracts, September 1,
1994. (1)Fuerstenau, D.W. J. Phys. Chem. 1966,60, 981. (2)Somasundaran, P.;Healy, T. W.; Fuerstenau, D. W. J.Phys. Chem. 1964,68,3562. (3)Debacher, N.;Ottewill, R. H. Colloids Surf. 1992,65, 51. (4)Fuerstenau, D.W.; Healy, T. W.; Somasundaran, P. Trans.AZME 1964,321. (5)Wakamatsu, T.;Fuerstenau, D. W. Adv. Chem. Ser. 1968,79, 161. (6)Wangnerud, P.;Olofsson, G. J. Colloid Interface Sei. 1992,153, 392. (7)Connor, P.;Ottewill, R. H. J.Colloid Interface Sci. 1971,37,642. (8)Ottewill, R. H.; Rastogi, M. C. Trans.Faraday Soc. 1960,56,880. (9)de Keizer, A.;Fokkink, L. G. J. Colloids Surf. 1990,51, 323.
4 L
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,
, , , , , . , (
,
, , , , . , , ,
,
,
0 105
104 103 ConcenuatianI mol.dm.’
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Figure 1. Influence of alkyl chain length on the adsorption of C,TAB onto Si02 from 2.7 mm~l-dm-~ CaBrz at p H 9.6 as measured by ellipsometry.6 Only the initial part of the isotherms are shown, and the adsorption increases until the cmc’s, indicated by arrows, are reached in the solution: (W) CsTAB, (0)CMTAB,( 0 )CizTAB.
may also contribute to the adsorption. Depending on the system of interest, the relative importance of the different contributions will vary. In this work we will focus on the effect ofthe self-associationof the surfactants in the diffuse layer on the adsorption of surfactants. The most characteristic property of ionic surfactants in solution is the self-association which arises from the tendency of the system to strive for minimum contact area between the hydrocarbon parts and water. In bulk solution of long-chain surfactants,most of the surfactants are present as monomers below the cmc, and a t concentrations higher than the cmc additional surfactants associate into large micelles. Thus, i t is usually not necessary to consider dimers and oligomers in the treatment of aggregation in bulk systems. The equilibrium between the different aggregates will differ considerably in the vicinity of a charged interface from that of the bulk solution due to the electrostatic interaction. I t has been known for a long time that, even though the bulk concentration of surfactant is well below the cmc, the local concentration near the charged surface may be considerably higher than the cmc.l0J1 The variation in concentra(10)Gaudin, A. M.; Fuerstenau, D. W. Trans.AZME 1955,202,958. (11)Ter-Minassian-Saraga Discuss. Faraday SOC.1976,59,179.
0743-7463/94/2410-3542$04.50/00 1994 American Chemical Society
Langmuir, Vol. 10,No. 10,1994 3543
Ionic Surfactants at the Solid I Water Znterface 0.1
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tion of a monovalent ion (C14TA+monomer) with distance from a charged interface calculated accordingto the GouyChapman theory is shown in Figure 2. The bulk concentration of C14TA+ is 0.1 m m ~ l - d m - the ~ , supporting electrolyte is 10 mmol~dm-~ of NaBr, and the surface charge density is set to -0.01 el&. As can be seen in the figure, the local monomer concentration exceeds the cmc within a region extending about 13 A out into the solution. To our knowledge, the possibility of formation of small surfactant aggregates in the solution layer outside the charged surface has not been discussed. If the local concentration of surfactant was the determining factor whether micelles would form or not, the concentration of monomer could not exceed the cmc but instead micelles would start to form at this concentration. However, it is not the local concentration of surfactant that is decisive for the onset of micelle formation but the average concentration within a region with a spatial extension on the order ofthe size of a micelle. Large micelles will not form a t low surfactant concentrations where the cmc is exceeded only within a short distance from the surface, but instead the surfactant molecules will associate into smaller aggregates such as dimers and other oligomers. In this work the adsorption behavior of CloTAB-Cl4TAB a t the SiOz/aqueous solution interface was studied experimentally and a thermodynamic model developed that describes the effect of self-association of the surfactants into oligomers on the adsorption at the solidlliquid interface.
Experimental Section Samples of tetradecyl-and dodecyltrimethylammonium bromides of 99% purity (Sigma Chemical Co., St. Louis, MO) and decyltrimethylammoniumbromide (Kodak Eastman) were further purified by repeated recrystallizationfrom ethanoyacetone mixtures followed by dryingunder reduced pressure at 65 "C for 12 h. Calcium bromide, tetramethylammonium bromide, and sodium bromide of analytical quality were used without further treatment. The water used was of reagent grade produced by a Milli-Q fdtration system (Millipore). A hydrophilic, macroporous silica (SpherosilX-015, IBF, France) with a specific area of 25 m2g-l as specified by the manufacturer was used as adsorbent. The adsorption isotherms were determined by the solutiondepletion method. The surface excess was calculated according to
. ) . . . . I
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103 Concenwtion/ m 0 1 . h . ~
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Figure 2. Concentrationprofile of C14TA+outside a negatively NaBr as charged surface in the presence of 10 mm~l-dm-~ calculated by the Poisson-Boltzmann equation for a surface charge density of -0.01 e/&!. The bulk concentration of c14TAf is 0.1mm~l-dm-~. The cmc of &TAB at this ionic strength is indicated by the horizontal line.
,
'
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Figure 3. Adsorption isotherm of C14TA.Bon Spherosil silica CaBrz. The vertical lines indicate the four from 5 mm~l-dm-~ different regions often found for adsorption isotherms of ionic surfactants on oppositely charged surfaces. where Cbt and C, are the total and the equilibrium concentrations of surfactant,Vthe solutionvolume, m the amount of adsorbent, and A the specific area of the adsorbent. In all measurements 0.3 g of adsorbent and 10 cm3 of surfactant solution were mixed in test tubes that were sealed by parafilm, and the mixtures were slowly rotated for 2 h. The adsorbent was separated from the solution by centrifugationfor 3 min at 3000 rpm. Equilibrium concentrations of surfactant in the supernatant solutions were determined spectrophotometricallyby following the procedure developed by Few and Ottewill.12 All concentrationdeterminations were repeated twice. The initial pH of the solutions was adjusted to 9 0.1. Due t o the slightly increased ionization of the silanol groups on adsorption of the oppositely charged surfactant,the solution pH decreased to about 8.5 at a coverage of 1pmol.m-2 in the experiments involving monovalent electrolyte.
*
Results The entire adsorption isotherm of C14TAB on Spherosil silica in 5 m m ~ l / d m -CaBrz ~ is shown in a doublelogarithmic plot in Figure 3. The characteristics of the isotherm are the same as have been reported for isotherms of anionic surfactants adsorbed onto metal oxides such as A120313-15and Ti02.16J7 These isotherms are often referred to as "four-region isotherms" due to the different regions, indicated in the figure, that appear in a double-logarithmic plot. The slope ofthe C14TAB isotherm in region I, at the lowest adsorption densities, is considerably less than unity, jndicating that surface heterogeneities are present.ls The adsorption density in this region is low, less than 1%of the maximum adsorption, and disturbances have a large influence on the isotherm shape in this region. Figure 4 shows the initial part of the C14TAB isotherm on a linear scale together with the adsorption isotherms of CloTAB and ClzTAB in the same adsorption region. The adsorption isotherms are linear in this region, but extrapolation does not give zero intercept but a residual adsorption of about 0.025 ,umol*m-2. The isotherms obtained by subtraction of the residual adsorption of 0.025 ,umol.m-2 from the isotherms shown in Figure 4 are represented on a double-logarithmic scale in Figure 5. (12)Few, A. V.;Ottewill, R. H. J. Colloid Sci. 1956,11, 34. (13)Somasundaran,P.;Fuerstenau, D. W. J.Phys. Chem. 1966,70, 90. (14)Somasundaran,P.;Kunjappu,J. T. Colloids Surf 1989,37,245. (15)Scamehom, J. F.; Schechter, R. S.; Wade, W. H. J. Colloid Interface Sci. 1981,85,463. (16) Bohmer, M. R.; Koopal, L. K. Langmuir 1992,8,2649. (17)Fuerstenau, D.W.; Jang, H. M. Langmuir 1991,7,3138. (18)Narkiewicz-Michalek,J. Ber. Bunsen-Ges. Phys. Chem. 1990, 94, 787.
Wangnerud and Jonsson
3544 Langmuir, Vol. 10, No.10, 1994
107
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0
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10.~
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Figure 6. Influence of the valency of the surfactantco-ion on the initial adsorption of c14TA.B. Adsorption in the presence of 10 mm~ledm-~ NaBr and 5 mmol~dm-~ CaBr2.
10.1 N
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Figure 5. Isotherms of CloTAB, CI~TAB,and c14TAB from Figure 4, corrected for the adsorption to the anomalous sites. By subtracting the residual adsorption, we implicitly assume that the surfactants adsorbed to the anomalous sites do not interfere with the further adsorption process. The slopes of the CloTAB and &TAB isotherms are approximately unity, but the C12TAB isotherm is shifted to lower concentrations of surfactant with respect to the CloTAB isotherm. The behavior of C14TAB deviates somewhat from that ofthe two other surfactants, the slope of the isotherm is higher than unity, and it is more displaced to laever concentration with respect to the other isotherms. Electrostatic interactions are of great importance in the adsorption of ionic surfactants onto oppositely charged surfaces, and consequently,the concentrationand valency of the surfactant co-ion are important parameters governing the initial adsorption of the surfactant. Figure 6 shows the initial adsorption ofC14TAB onto Spherosil silica from solutions of 10 m m ~ l - d m NaBr -~ and 5 mmol~dm-~ CaBrz. Increasing the valency of the surfactant co-ion gives a lower adsorption, and the isotherm is shifted to higher concentration of the surfactant. In addition to the general electrostatic interaction, ion specific effects may influence the interaction between the surface and the different ions present in the system. In order to investigate the importance of nonelectrostatic interactions in the C,TAB/Si02 system, the adsorption of c14TAB was measured in 10 mmol~dm-~ CITAB, that resembles the surfactant head group. As can be seen in Figure 7, the isotherm determined in the presence of C1TAB is shifted to higher concentrations of surfactant compared to the isotherm determined in NaBr solution, indicating that the surfactant head group has a higher affinity for the silica surface than the sodium ion.
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105
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103
/ mol,dm.'
Figure 7. Influence ofthe head group on the initial adsorption of C14TAB. Adso tion in the presence of 10 mm~ladm-~ NaBr and 10 mmol.dm3 C1TAB.
The Model The association of long-chain surfactants into aggregates in bulk solution is a highly cooperative process where the strong cooperativity of the process favors the formation of large micelles and the fraction of small aggregates such as dimers or trimers is therefore low. The size distribution of the micelles is already, at concentrationsslightly above the cmc, rather narrow since large micelles forms at the expense of the smaller aggregates. In the vicinity of a charged interface where the concentration of amphiphile varies strongly with distance from the surface, large aggregates will not be favored in the same way as in a bulk solution. There are two main reasons for this. (a) Since there is a continuous formation and ruption of micelles in a solution, each part of a micelle will be in equilibrium with the free amphiphiles in the solution surrounding the micelle. Therefore, it is the average concentration and not the highest concentration in this region that determines whether a micelle will form or not. The concentration of amphiphile decreases rapidly with distance from a charged surface, and therefore, a small aggregate at the surface will be surrounded by a solution of an average concentration higher than that of a large aggregate. (b)The surface charge density of a large micelle is often higher than that of the oppositely charged surface. This means that at small separations the micelle willbe repelled when it comes closer than a certain equilibrium distance from the surface. A smaller aggregate has a lower surface
Ionic Surfactants at the Solid I Water Interface
Langmuir, Vol. 10, No. 10, 1994 3545
charge density and is, therefore, less or not a t all repelled by the surface; see ref 19. The local concentration of surfactant in the vicinity of the surface can be considerably higher than the cmc even at very low bulk concentrations (cf. Figure 21, and clearly hydrophobic interaction will occur among the surfactants in the region adjacent to the surface. However, due to the reasons given above, ordinary micelles will not be the first type of aggregates formed a t the interface, but much smaller aggregates will dominate in the initial stage of the adsorption process. This effect will be most pronounced when the solid surface is highly charged, since the higher the charge density the steeper is the concentration gradient of mobile ions outside the charged interface. A thermodynamic model to describe the association of surfactants in the vicinity of a charged surface and to calculate the surface excess of the surfactants a t low adsorption densities is developed. In the model amphiphiles are described as monomers, dimers, and trimers at the concentrations studied. The energy contributions to the formation of the oligomers and the interactions between the surface and the small aggregates have been modeled in the following way. TheAmphiphile-Amphiphile Interaction. (1)The reduction of the unfavorable hydrocarbon-water contact is the major driving force for amphiphile aggregation. The difference in free energy for a hydrocarbon molecule in a water solution and in a nonpolar environment, the hydrophobic effect, has been measured for a variety of hydrocarbons, and the results from these measurements show that the difference amounts to approximately 1.4kT per CH2group and somewhat more per CH3 group.2oFor a homologous series of compounds, the difference in energy per mole can be written a s
where R is the gas constant, T the temperature, a a characteristic constant for the homologous series, and nc the number of carbon atoms in the alkyl chain. The alkyl chain dependence in eq l a is due to the increased hydrocarbon-water contact area as the alkyl chain length increases, and a n alternative way to express this dependence is pl,he= constant
+ yAcnc
(1b)
where Ac is the area a methylene group exposes toward the water and y is a proportionality constant. The value of y is about 0.02 J.m-2.21-23 The change in free energy on formation of a small aggregate such as a dimer or a trimer is, however, much smaller than the value indicated by eqs l a and l b since the hydrocarbon-water contact is not completely eliminated when a dimer or a trimer is formed. The difference in hydrophobic free energy for a n alkyl chain in a n oligomer and a n alkyl chain in the monomeric state is proportional to the fraction of the area of the alkyl chain removed from water contact. Thus, the simplest way to estimate the hydrophobic interaction between the amphiphilic molecules in a n oligomer is to estimate the (19) StPlberg, J.; Jonsson, B.; Horvhth, C. Anal. Chem. 1991,1867. (20) Tanford, C. The Hydrophobic Effect; John Wiley: New York, 1980. (21) Jonsson, B.; Wennerstrom, H. J.Colloid Interface Sci. 1981,80, 482. (22)Tanford, C.J. Phys. Chem. 1974,78, 2469. (23) Parsegian, V. A. Trans. Faraday SOC.1966,62, 848.
difference in hydrocarbon-water contact areas for the individual and the associated molecules.
A,, denotes the interfacial area of a n aggregate, i is the number of monomers in the aggregate, and A,, is the interfacial area of a monomer. However, it is not straightforward to estimate the interfacial area, Aagg, of small aggregates such as dimers and trimers since the shape of the aggregate is not well defined. Depending on the way the interfacial areas are estimated and the choice ofparameter values, one arrives a t values for in the range 0.5-1RTnc for dimer formation and in the range 1-2RTnc for trimer formation. In the following calculations we have used - A P ~ , = ~ 0.8RTnc and - A P ~ , = ~ 1.5RTnc. These values were obtained by using y = 0.02 J-m-2 and assuming that the mean shape of the aggregates is spherical.
(2) The electrostatic interaction between the charged amphiphiles in a micellar aggregate has been discussed previously by use of the Poisson-Boltzmann equation in ref 24. For smaller aggregates such as dimers or trimers, the obtained results may be written as (4a)
where a2 and a3 are the average separations between two charges in a dimer and trimer, e is the unit charge, cOcr is the dielectric permittivity, and K is the inverse Debye length. For the surfactants and electrolyte concentrations used in this work, the electrostatic contributions to the chemical potential of a dimer and a trimer are about 1RT and 3RT, respectively. The Aggregate-Surface Interaction. (1)The volume of a n oligomer and the distribution of the charged head groups over the aggregate surface must be accounted for in a n exact description of the electrostatic interaction between a surfactant oligomer and a charged surface. Such a detailed description is outside the scope of this article. Therefore we will, regarding the electrostatic interaction between the aggregate and the surface, treat the dimer and trimer as divalent and trivalent point charges, respectively. With this approximation the electrostatic interaction between the charges in a n aggregate, at a distance x from the surface, and all other charges in the system may be written as
where i is the number of charges in the aggregate, F the Faraday constant, and qXx) the mean electrostatic potential a t a distancex from the surface. The Poisson-Boltzmann equation will later be used to estimate @(XI. (24) Jonsson, B.; Wennerstrom, H. J. Phys. Chem. 1987,91, 338.
Wangnerud and Jonsson
3546 Langmuir, Vol. 10,No. 10, 1994 The chemical potentials of the monomers, dimers, and trimers (i = 1-3) in the solution adjacent to the surface may now be obtained from the sum of the different contributions:
p l = pt
p, = 2p:
p3 = 3p:
c,(x) + F @ ( x )+ RT In (-)55.55
i
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c,(x> + RT(3 - 1 . 5 ~+~3F~ @(x) ) + RT In (55.55)
Thus,
KOCi,bulk
where Ci(bu1k) is the bulk concentration of monovalent, divalent, and trivalent ions. Introducing the quantity u(x),where
u(x)= exp( -F @(x)/RT)
(10)
and integrating the PB equation once allows eq 9 to be simplified to the following expression: -
l),/I
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JI
s””---du = duldx 1
Zti-1.5
du (13)
+ ( u - NC,+ + ( u + 3)C3+)
The integrals can in some special cases be solved analytically (see Appendix) but must generally be solved by a numerical procedure. But before this integration can be done, the value of the surface potential 4(0)or uomust be found. This can be done by use of the boundary condition of d@/& at the Si02 surface. At A: = 0 the following equations are valid
where u is the surface charge density of the Si02 surface. By combination ofeqs 11,12, and 14,the followingequation valid at x = 0 can be constructed and used to obtain the uo value. &IOO&
To be able to calculate the amount of the monomers, dimers, and trimers in the ion distribution outside the charged surface, the Poisson-Boltzmann equation, eq 9, was used to obtain the distance dependence of the electrostatic potential:
= -KO&&
Ci,bulk
(6a)
(2) Other possible interactions between amphiphile and surface, e.g. between the surfactant head group and specific surface sites or between the alkyl chain and the surface, are assumed to be short-range and are therefore neglected in the solution adjacent to the surface. At equilibrium, the chemical potentials are constant throughout the system. Moreover,the chemical potentials of the dimers and trimers, p~ and p3, are related to p1 via
dx
from the integrals given below:
=
This nonlinear equation may, when C3+ 0, be solved analytically (see Appendix) but must in most cases be solved by a numerical procedure, for example, the Newton-Raphson method. The surface excess of monomers, dimers, and trimers can be calculated from eqs 13and 15unless the amphiphile binds specifically to the surface. To be able to describe systems where specific binding takes place, one may proceed a s follows. Assume that the specific interaction between the surface and each amphiphile in the small aggregates per molar basis can be approximated by
where k1 and k2 are characteristic constants for the system of interest. The equations for the chemical potentials of the monomers, dimers, and trimers at the charged Si02 surface may then be written as p1= pol +
+ e@(O>+ RT In (rl,suflo)(17a)
+ ( u - 1)(C2++ ( u + 3)C3+) (11)
where (12) and I is the ionic strength of the system. The surface excess of monomers, dimers, and trimers, ri,dub, in the diffuse layer adjacent to the Si02 surface can be obtained
where ri,su& the amount of bound monomers, dimers, or trimers per unit area and To is the amount of adsorption sites per unit area. For simplicity we will assume that the number of amphiphile adsorption sites is equal to the number of charged sites a t the surface. The chemical potential for each type of aggregate, pi, will a t equilibrium
Ionic Surfactants at the Solid I Water Interface 10.7
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Langmuir, Vol. 10, No. 10, 1994 3547 I
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Figure 8. Calculated adsorption isotherm of C14TA+(-) on a surface with a charge density of -0.01 el& in the presence of 5 mmol~dm-~ CaBrz. The contributions of monomer (-1, dimer (- - -), and trimer (- -) adsorption to the total surface excess are also shown.
.
.
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Figure 9. Effect of the alkyl chain length on the adsorption: calculated surface excess ofCloTA+(-1, C12TA+(- -), and c14TA+ (- - -) in the presence of 5 mmol~dm-~ CaBrz.
layer, and the slope of the adsorption isotherm is close to unity. As the concentration of surfactant is increased, be equal both in the aqueous solution and at the surface, the contribution of dimers to the adsorption increases which gives the following expressions for ri,surf: progressively, and the adsorption isotherm bends upward; i.e. the slope becomes larger than unity. At still higher ri,surf = roexp(-i(e#(O)/lzT A~O,,~)?.))ci(bulk)/55.55 solution concentration, the concentration of trimers in the region adjacent to the surface becomes significant and (18) adsorption of dimers and trimers dominates over monomer adsorption. The model calculations clearly show that The specific binding of amphiphile will also affect the surfactant-surfactant interaction becomes important surface charge density, 0,in eq 15 since already a t extremely low adsorption densities of long3 chain surfactants. In the calculations presented above, 0 = -To xiri,surf about 50%of the surfactants are adsorbed as dimers at (19) a n adsorption density of 2 x mol.m-z, which should F i=l be compared to the maximum adsorption densities on the order of 3-5 x lod6mol.m-z often found for adsorption of If eqs 18 and 19 are inserted into eq 15, uo may be ionic surfactants onto oppositely charged surface^.^^^^^^^ determined also for this type of system, and then ri,dub can Slopes of the adsorption isotherms in log-log form larger be calculated as previously described for systems where than unity at adsorption densities less than 10+ mol*m-z specific interaction is absent. have been observed experimentally, besides our results Summation of the different types of surface excess gives in Figure 5 , also for adsorption of anionic surfactants onto the total surface excess of surfactant: positively charged surface^.^^^^* 3 The formation of surfactant aggregates is a result of the decrease in unfavorable water-hydrocarbon contact (20) and therefore is strongly dependent on the hydrocarbon chain length ofthe surfactant. The influence of surfactant chain length on the adsorption behavior is shown in Figure Discussion 9. The calculated adsorption isotherms for CloTA+, (212The surface excess of C14TA+ as a function of the TA+,and C14TA+converge at low surfactant concentrations surfactantconcentration in 5 m m ~ l d m CaBrZ, -~ calculated where monomer adsorption is dominating also for C14according to the model presented in the previous section, TA+. is shown in log-log form in Figure 8. Although significant As can be seen in the figure, the contribution of dimer progress has been made during the last two decades, the adsorption to the surface excess of amphiphile is rather charge behavior of Si02 surfaces is still not fully underlow for CloTA+ in the concentration interval shown, in stood. Due to the possibility of a porous layer at the contrast to the C14TA+ adsorption where aggregate surfacez6or adsorption of the supporting electrolyte,z6the formation is dominating. The calculated adsorption actual charge density of the surface is not well known. isotherms shown in Figure 9 are in qualitative agreement The surface charge density is the only unknown parameter with the experimentally determined isotherms shown in in the model calculations shown in Figure 8, and a value Figure 5. The steep increase in adsorption density of C14of -0.01 el& corresponding to 1.7 x mol of charged TAB that was observed experimentally is less pronounced sites per mzwas assigned to this parameter. I t is assumed in the model calculations. A probable explanation for this that the interaction between the surfactant and surface deviation is that specific interaction between the surfacis solely electrostatic; i.e. there is no specific binding of tant and the surface was not taken into account in these the surfactant ion to the surface (exp(Aposud)= 0). Thus, calculations; see below. the calculated surface excess of surfactant is entirely due As can be seen in Figure 6, the adsorption of surfactant is strongly influenced by the valency of the other surfaceto accumulation of the surfactants in the diffuse layer. counterions in the system. A divalent electrolyte will At sufficiently low concentration, the surfactants are present almost exclusively as monomers also in the diffuse reduce the surface potential much more effectively than
+
+
(25)Kleijn, J. M.Colloids Surf. 1990,51, 371. (26)Hunter, J. H.Foundations of Colloid Science II; Clarendon Press: Oxford, 1989.
(27)Partyka, S.;Lindheimer,M.; Faucompre, B.Colloids Su$. 1998, 76,267. (28)Bohmer, M.R.;Koopal, L. K. Langmuir 1992,8,2660.
Wangnerud and Jonsson
3548 Langmuir, Vol. 10, No. 10, 1994
-eP
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1; 5
Concenttation 1moi&i3
Figure 10. Influence of the valency of the surfactant co-ion on the initial adsorption: the calculated surface excess of &TA+ - ~ and 5 mm~l-dm-~ CaBrz. in the presence of 10 m i n ~ l d m NaBr a monovalent electrolyte. This effect is clearly seen in the model calculations. The calculated surface excesses of C14TAB in solutions containing 5 m m ~ l - d mCaBrz -~ and 10 mmol~dm-~ NaBr are shown in Figure 10. In the foregoing calculations it was assumed that the interaction between the surface and the mobile ions in the system was solely electrostatic; i.e. the preferential accumulation of amphiphiles in the diffuse layer was entirely due to formation of small surfactant aggregates. However, the adsorption isotherm of C14TAB determined in ClTAB solution was shifted to somewhat higher surfactant concentrations compared to the isotherm in NaBr solution (Figure 7). The most straightforward explanation for the difference between the two isotherms is a stronger specific binding of the C1TA+ion to the Si02 surface compared to the Na+ ion. A higher affinity of ClTA+ than of K+ for the Si02 surface was deduced by Rutland and PashleyZ9 from electrokinetic measurements. Since C1TA+ binds specifically to the Si02 surface, there should be a corresponding contribution to the adsorption of CloTA+-C14TA+ as these surfactants differ from C1TA+ only by the length of the hydrocarbon chain. The influence of the strength of the specific interaction on the calculated surface excess of C14TA+at the charged Si02 surface in a 5 m m ~ l - d m solution -~ of CaBrz is shown in Figure 11. A comparison between the experimentally observed adsorption isotherm for C14TAB in Figure 3 and the model calculations shown in Figure 11indicates that the specific interaction between C14TA+ion and the surface probably is on the order of -In 2RT. If this value is used also in the calculation of the surface excesses of CloTAB and C12TAB, the adsorption isotherms shown in Figure 12 are obtained. Summary
Model calculations as well as experimental results show that hydrophobic interaction is important at very low adsorption densities of long-chain surfactants, less than 1/1000 of the amount required for formation of a compact monolayer. The dependence of the adsorption on the hydrocarbon chain length at this low coverage is explained by formation of small surfactant aggregates in the solution region adjacent to the surface. The most important factors in the developed model are the hydrophobic interaction (29) Rutland, M. W.; Pashley, R. M. J. Colloid Interface Sci. 1989, 130, 448.
1; 3
COnWItratIOrI 1mol dm
Figure 11. Effect of the strength of the specific interaction between surfactant and surface: the calculated surface excess of C14TA+ in the presence of 5 m m o l ~ l m -CaBr2 ~ for three different values of the specific interaction parameter, A p o s ~ exp(-AposUdRT) = 0, exp(-Apos&RT) = 2, exp(-AposUdRT) = 5. 10'
I
10.9
1 1d.5
I
1
/. / . L
/
';
/
1A-4
1b3
ConcenmtlonI m01.dm.~
Figure 12. Calculated adsorption isotherms of CloTAB (-), &TAB (- -1, and C14TAB(- - -). Parametervalues as in Figure 9 except for the specific interaction contribution,Aposurf,which was set to -In 2RT in the calculations presented above. between the adsorbing surfactants (aggregate formation) and the electrostatic interaction between the surface and the surfactants. However, to obtain a better quantitative agreement between the calculated and the experimentally determined isotherms for the C,TAB/Si02 system, it was necessary to include a small specific interaction term. We conclude that at relatively high surface charge densities and low surfactant concentrations large micelles cannot be formed in the vicinity of the surface even though the local concentration of surfactant may exceed the cmc in the region closest to the surface. Therefore the selfassociation process in the interfacial region is less cooperative than in the bulk solution, and surfactant oligomers play a more prominent role in the aggregation at the solifliquid interface than in bulk solution. Model calculations including formation of dimers and trimers have been performed in order to investigate the influence of surfactant association into small aggregates on the adsorption behavior. At higher surfactant concentrations larger aggregates may form at the interface, and this is the subject of a subsequent paper. Appendix
If the formation of trimers is neglected, the surface excess of monomer and dimer in the diffuse layer outside the Si02 surface can be calculated as follows:
Ionic Surfactants at the Solid I Water Znterface
1
= KOcmon(bulk) fo)
&I
+ (u2- U ) C 2 +
Langmuir, Vol. 10, No. 10, 1994 3549
du
where the value of uo can be calculated from
+ 3(-) F
1 - cos(Yl3)J1
z
Koa,,
uo =
(21)
where '1
Y = arccos
+ 4.5-(-) c+ I
F
Kooya
2'
(22)
