Langmuir 2000, 16, 2469-2474
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Size of Cationic Surfactant Micelles at the Silica-Water Interface: A Fluorescent Probe Study Cecilia Stro¨m, Per Hansson,† Bengt Jo¨nsson, and Olle So¨derman* Department of Physical Chemistry 1, Center for Chemistry and Chemical Engineering, Lund University, P.O. Box 124, S-221 00 Lund, Sweden Received July 6, 1999. In Final Form: November 29, 1999 We present what is, as far as we are aware of, the first time-resolved fluorescence quenching study of the state of adsorbed cationic surfactants on a silica surface. Three different monovalent and one divalent cationic surfactant are investigated. We employ pyrene as fluorescent probe and quenchers that in themselves are surfactants, viz., alkylpyridinium chlorides. Essential to the analysis of the data is knowledge of the distribution of the quencher between the micelles and the aqueous subphase. We use previously obtained relations that give us this quantity. The results show unequivocally that all of the studied surfactants are adsorbed as discrete micelles with aggregation numbers close to those found in bulk solutions for the same surfactants. The aggregation numbers increase with the amount of adsorbed surfactant.
Introduction The adsorption of surfactants at a solid interface in contact with a water solution of the surfactant continues to attract considerable interest.1-8 One crucial question pertains to the size and structure of the adsorbed aggregates. Over the years, a rather detailed understanding of the aggregation properties of surfactants in water solutions has been built up, and it seems natural that many of the concepts with regard to the driving force of the aggregation processes can be carried over to the problem of describing aggregation at surfaces. However, few methods exist that are capable of conveying information about the (equilibrium) state of the surfactant aggregates on solid surfaces. This is due to the fact that in a typical experimental situation one has to deal with the problem that an overwhelming proportion of the surfactant is present in the bulk solution. Thus, in any technique that relies on monitoring the surfactant as such, one has to be able to subtract the contribution from nonadsorbed molecules. Alternatively, one has to use a technique that directly probes the adsorbed aggregates. One such technique is fluorescence quenching. 9,10 The technique, which is by now a standard method for the determination of micellar aggregation numbers in bulk micellar phases, relies on measuring the fluorescence of a probe molecule in the presence of a quencher molecule. The fact that the method relies on adding both a fluorescent probe and a quencher † Present address: Department of Physical Chemistry, Uppsala University, Box 532, S-752 21 Uppsala, Sweden.
(1) Thomas, R. K. Prog. Colloid Polym. Sci. 1997, 103, 2216. (2) Fragneto, G.; Thomas, R. K.; Rennie, A. R.; Penfold, J. Langmuir 1996, 12, 6036. (3) Grant, L. M.; Tiberg, F.; Ducker, W. A. J. Phys. Chem. B 1998, 102, 4288. (4) Kiraly, Z.; Borner, R. H. K.; Findenegg, G. H. Langmuir 1997, 13, 3308. (5) Manne, S.; Gaub, H. E. Science 1995, 270, 1480. (6) Manne, S. Prog. Colloid Polym. Sci. 1997, 103, 2226. (7) Manne, S.; Scha¨ffer, T. E.; Huo, Q.; Hansma, P. K.; Morse, D. E.; Stucky, G. D.; Aksay, I. A. Langmuir 1997, 13, 6382. (8) Stro¨m, C.; Jo¨nsson, B.; So¨derman, O.; Hansson, P. Colloid Surf. 1999, in press. (9) Zana, R. In Surfactant Solutions: New Methods of Investigation; Zana, R., Ed.; Marcel Dekker: New York, 1987; Vol. 22; p 241. (10) Almgren, M. In Kinetics and Catalysis in Microheterogeneous Systems; Gra¨tzel, M., Kalyanasundaram, K., Eds.; Marcel Dekker: New York, 1991.
molecule is a drawback, because the addition may perturb the system. Thus, it becomes important to chose the probe and quencher with care. As regards the probe molecule, there is essentially only one alternative available, namely, pyrene. Pyrene is hydrophobic and, therefore, solubilizes in the interior of the surfactant aggregates, and provided that the bulk concentration of the surfactant is below cmc, the probe will be exclusively present in the adsorbed micelles. Pyrene is usually present in very low concentrations (10-6-10-7 M), and therefore, its presence is not expected to perturb the macroscopic properties of the system. To what extent the micelles in which one pyrene resides are perturbed is an open question. The same considerations hold for the quencher. Provided that a hydrophobic molecule is used as quencher it will be solubilized in the micelles. Therefore, pyrene has often been used also as a quencher, in that one utilizes the formation of excimers between an excited pyrene and a ground-state pyrene. This approach has been applied to the adsorption of nonionic surfactants to various substrates.11,12 Investigations of charged surfactants are less frequent. As far as the present authors are aware of, one anionic surfactant (sodium dodecyl sulfate) at the alumina-water interface has been investigated.13 Evidence in favor of both discrete and infinite (which implies aggregation numbers in excess of a few 100) surfactant micelles on the surfaces has been found. For instance, in the case of SDS adsorption to alumina, the data were interpreted in terms of the formation of hemimicelles on the surface with aggregation numbers that increased with increasing adsorption density at the surface. One problem with the use of pyrene as quencher is that it is present in rather high amounts (typically on average one molecule per micelle), leading to the risk of introducing artifacts. Ideally, one would like to use a quencher whose properties are similar to that of the investigated surfactant. With this in mind, it was suggested to use alkylpyridinium surfactants as quencher.14 In particular, this choice is suitable if one is investigating aggregation (11) Levitz, P.; Damme, H. v.; Keravis, D. J. Phys. Chem. 1984, 88, 2228. (12) Levitz, P.; van Damme, H. J. Phys. Chem. 1986, 90, 1302. (13) Chandar, P.; Somasundaran, P.; Turro, N. J. J. Colloid Interface Sci. 1987, 117, 31. (14) Hansson, P.; Almgren, M. J. Phys. Chem. 1995, 99, 16684.
10.1021/la990885w CCC: $19.00 © 2000 American Chemical Society Published on Web 01/27/2000
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numbers in quaternary ammonium surfactants, to which the alkylpyridinium surfactants bear a close resemblance. One advantage of this approach is that it is possible to estimate the distribution of the quencher between the micellar and aqueous subphases, which is necessary in order to obtain the aggregation numbers. This problem was addressed by Hansson et al.,15 and relations that can be used to accurately estimate this quantity were presented. Silica is an often used substrate in studies of surfactant adsorption. Silica is negatively charged (at least at pH values above the isoelectric point, which is approximately 2). Therefore, many studies have been devoted to the characterization of cationic surfactant adsorption to silica.16 Adsorption isotherms have been measured, and several theoretical studies have been carried out in which both the adsorption isotherms and the state of the adsorbed surfactant has been treated (see, e.g., earlier works1,5,7,17). In contrast to this, very few studies have appeared dealing with the experimental characterization of the surfacebound aggregates. Manne and co-workers have used atomic force microscopy (AFM) and from such measurements deduced that the quaternary ammonium surfactants (such as C14TAB) form discrete micelles with aggregation numbers corresponding roughly to those of spherical micelles.5,6 A related study pertaining to the state of adsorbed micelles of a number of symmetric and asymmetric gemini-surfactants on mica is reported by Manne et al.7 Of relevance in the present context are also the neutron reflection studies reported by Thomas1 and Fragneto et al.2 By using selective deuterium labeling of different parts of C16TAB, the neutron reflection data could be interpreted in terms of bilayer fragments of thickness 32 Å. In addition, the neutron data imply that the surface is far from completely covered by a bilayer. Thus, the data do not exclude the presence of discrete aggregates adsorbed on the surface, which could be discussed in term of deformed adsorbed micelles. As discussed by Stro¨m et al.,8 one reason the (charged) micelles may be deformed is to optimize the interaction with the (charged) silica surface. In this study, we have performed fluorescence quenching measurements, using pyrene as fluorescent probe, on three different monovalent cationic surfactants, viz., dodecyl-, tetradecyl-, and hexadecyltrimethylammonium bromide (henceforth referred to as DoTAB, TTAB, and CTAB, respectively) and one divalent cationic surfactant, viz. dodecyl-1,3-propylene-pentamethyl-bis(ammonium chloride) (DoPPDAC, CH3-(CH2)11-N+(CH3)2-(CH2)3-N+(CH3)3 + 2Cl-). By comparing the adsorption properties of the divalent surfactant with the adsorption of monovalent surfactants, the importance of the electrostatic driving forces in the adsorption process is elucidated. We have previously presented the adsorption isotherms for DoPPDAC to silica as measured with ellipsometry.8 In addition, a thermodynamic model for the adsorption process of DoPPDAC to the silica surface was developed. In this model, it is assumed that the adsorbed aggregates are micelles with a spherical shape. Methods Materials. Dodecyl-, tetradecyl-, and hexadecyl trimethylammonium bromide were obtained from Serva. DoPPDAC was (15) Hansson, P.; Jo¨nsson, B.; Stro¨m, C.; So¨derman, O. J. Phys. Chem. 1999, submitted for publication. (16) Wa¨ngnerud, P. Adsorption of ionic surfactants on charged solid surfaces, Thesis, Lund University, Lund, Sweden, 1994. (17) Wa¨ngnerud, P.; Olofsson, G. J. Colloid Interface Sci. 1992, 153, 392.
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Figure 1. Adsorption isotherms for DoTAB (O), TTAB (0),17 and DoPPDAC (4).8 The data are plotted vs the surfactant concentration in the bulk, divided by the relevant cmc values. The following cmc values were used: For DoTAB, cmc ) 15.3 mM; for TTAB, cmc ) 3.5 mM; and for DoPPDAC, cmc ) 48.0 mM. synthesized by Synthelec AB (Lund, Sweden) using as starting material dodecyl-1,3-propylene-bis(ammonium chloride), which was a kind gift from Berol Nobel AB, Sweden. As quencher, we use N-hexadecylpyridinium chloride (C16PC) from Merck, which was used as supplied, and N-dodecylpyridinium chloride (C12PC) from Aldrich, which was recrystallized several times from acetone. Pyrene from Aldrich was recrystallized twice from ethanol. Spherosil XO 15 porous silica (IBF, Villeneuve-la-Garenne) was a kind gift from the Division of Thermochemistry, Lund. According to the manufacturer, it has a specific area of 25 m2 g-1, whereas BET measurements indicated a surface area of 23.45 ( 0.13 m2 g-1. Sample Preparation. An appropriate amount of pyrene dissolved in ethanol was added to a suitable container. After careful evaporation of the ethanol with nitrogen, a surfactant solution containing a precisely known amount of quencher was added together with the Spherosil silica (and, when appropriate, sodium bromide). The pH was adjusted to 9 by adding small volumes of a concentrated sodium hydroxide solution. The sample was stirred in the closed container for 24 h prior to measurements. During that time, it was necessary to readjust the pH a few times. All samples contained 0.18 g silica. For DoTAB, TTAB, and DoPPDAC, samples were prepared at compositions corresponding to three points along the binding isotherms (cf. Figure 1), whereas for CTAB, one composition was studied. The binding isotherms for DoTAB and TTAB have previously been determined by ellipsometry by Wa¨gnerud and Olofsson.17 The same method was used for the determination of the adsorption isotherm of DoPPDAC.8 The adsorbed amount of CTAB was estimated from the adsorption isotherms of DoTAB and TTAB. A natural question is whether one would expect any differences in the adsorption isotherms as determined on silica gels by, for instance, solutiondepletion methods and the silica wafers used in the ellipsometry studies. This question was addressed by Wa¨gnerud and Olofsson,17 where it was concluded that the adsorption isotherms for silica gel and silica were similar under comparable conditions. To match the conditions under which the isotherms were obtained, the total amount of surfactant in each system was always orders of magnitude larger than the total amount of fixed charges on the silica surfaces. This was achieved by varying the volume of the surfactant solution. For example, in the case of CTAB, where the equilibrium concentration of free unimeric surfactant is very low, it was necessary to work with 1 L of solution. After equilibration, the silica gels were allowed to sediment to the bottom of the vessels and then were transferred to 1 cm quartz cells together with a fraction of the solution. Fluorescent Quenching Experiments. Fluorescence decays were recorded with the single-photon counting technique. The
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experimental setup has been described in detail elsewhere.18 The probe was excited at 325 nm by positioning the cell with the Spherosil silica sediment in the path of the laser beam. The emission was detected front-face and separated from the scattered light using an interference filter (400 nm). For each investigated system, the fluorescence decay in the absence of quencher was recorded. As a check, the emission from solutions in equilibrium with the silica particles were investigated. From these results, it is clear that the aqueous solution only contained trace amounts of free pyrene. Thus, the contribution to the signal from pyrene dissolved in the aqueous domains in the porous silica is negligible.
Fluorescence Quenching Relations describing the time-evolution of the fluorescence intensity of an excited probe are available for systems of different degrees of complexity.9,19 The situation of interest here is the rapid quenching observed in small discrete micelles containing probes and quenchers. Moreover, we will consider the case where the probe and the quencher are stationary; i.e., their residence time in the micelle is much longer than the fluorescence lifetime, τ0. The relevant relation describing the fluorescence decays is then given by20,21
F(t) ) F(0)exp{-t/τ0 + 〈n〉[exp(-kqt) - 1]}
(1)
where F(0) is the fluorescence intensity at the time of the excitation event (t ) 0), 〈n〉 is the average number of quenchers per micelle, kq is the first-order quenching rate constant, and nkq is the quenching frequency in a micelle with n quenchers. Although kq derives from an approximate description of the intramicellar quenching kinetics in small micelles,22 〈n〉 is independent of the kinetic description but is related to the assumption of a Poisson distribution of the quenchers among the micelles. In fact, at long times (t . 1/kq), eq 1 becomes single-exponential and can be written on a general form:
F(t) ) F(0)exp{-t/τ0}P0
(2)
where P0 denotes the fraction of quencher free micelles. Equation 2 describes the contribution to the fluorescence decay curve (for all times) from excited probes in quencherfree micelles. With a Poisson distribution of quenchers in the micelles P0 is given by P0 ) exp(-〈n〉). Note that, if F(0) can be accurately estimated from the quenched fluorescence decay curve, 〈n〉 can be obtained even if the description of the quenching process is poor. The Poisson distribution was introduced by Turro and Yekta 23 when analyzing static fluorescence data. Other distributions have also been used. 9 However, in most cases, the Poisson (or random) distribution appears to be a good approximation. Deviations are expected when there are net interactions between the quenchers confined to the same micelle. This situation was demonstrated by Bales and Stenland 24 and has been analyzed in some detail recently by Almgren and co-workers,25 who used a nearest-neighbor description of the interactions. One (18) Almgren, M.; Hansson, P.; Mukhtar, E.; van Stam, J. Langmuir 1992, 8, 2405. (19) Almgren, M. Adv. Colloid Interface Sci 1992, 41, 9. (20) Infelta, P. P.; Gra¨tzel, M.; Thomas, J. K. J. Phys. Chem. 1974, 78, 190. (21) Tachiya, M. Chem. Phys. Lett. 1975, 33, 289. (22) van der Auweraer, M.; Dederen, J. C.; Gelade´, E.; De Schryver, F. C. J. Chem. Phys. 1981, 74, 1140. (23) Turro, N. J.; Yekta, A. J. Am. Chem. Soc. 1978, 100, 5951. (24) Bales, B. L.; Stenland, C. J. Phys. Chem. 1993, 97, 3418. (25) Almgren, M.; Hansson, P.; Wang, K. Langmuir 1996, 12, 3855.
Table 1. Values of R (cf. eq 5) Used in This Worka S/Qb
R
DoTAB/C12PC TTAB/C16PC CTAB/C16PC DoPPDAC/C16PC
0.67 0.038 0.47 4 × 10-4
a Values Are Taken from Hansson et al.15 combination.
b
Surfactant/quencher
important conclusion from that study was that only large interactions result in serious deviations from the Poisson distribution. As noted in the Introduction, surfactant molecules will be used as quenchers in this work. The reason for this choice is that on account of the chemical resemblance to the main surfactant the disturbances introduced by the quencher is minimized. As noted elsewhere,14 ideal mixing in the micelles of the components in a binary surfactant mixture results in a binomial distribution, which in the limit of a large excess of one of the components becomes identical to the Poisson distribution. When employing surfactant molecules as quenchers, it is convenient to treat them as cosurfactants. The average aggregation number is then given by
N)
〈n〉 XQ
(3)
where XQ is the mole fraction of quenchers in the micellar subphase (below N denotes the average aggregation number). Thus,
XQ )
[Q]mic [Q]mic + [S]mic
(4)
where [Q]mic and [S]mic are the concentration of quencher Q and surfactant S in micelles, respectively. To summarize, time-resolved fluorescence quenching experiments provide accurate estimates of 〈n〉, from which N can be calculated if XQ is known. In the next section, we will consider different approaches of calculating XQ. Quencher Distribution The problem of obtaining values of XQ was recently addressed by Hansson et al.15 In the general case, it can be shown that XQ is given by15
XQ )
RQCtot Ctot + Cf,S(R - 1)
(5)
where R is given by the standard chemical potentials of Q or S in the micelle and in the water subphase plus the contribution from the hydrophobic effect to the chemical potential of the components in the micelle (see further discussion by Hansson et al.15). Ctot is the total concentration of Q and S, and Cf,S is the concentration of S as monomers in the bulk solution. RQ is the mole fraction of Q in the surfactant mixture. Knowledge of R and Cf,S thus makes it possible to calculate XQ. Values of R were obtained from PoissonBoltzmann calculations as described by Hansson et al,15 and values of Cf,S were obtained from the adsorption isotherms and the (known) total amounts of S in the samples. The values used in this work are collected in Table 1. For the special case of micelles in equilibrium with an infinite bulk solution of the components (surfactant and
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Table 2. Relevant Parameters Used in the Calculations of Na surfactant
Ctot (mM)
DoPPDAC DoPPDAC DoPPDAC DoTAB DoTAB DoTAB DoTAB DoTAB DoTAB DoTAB TTAB TTAB TTAB TTAB TTAB CTAB
14.7 30.0 40.4 5.09 10.1 14.1 5.09 5.09 5.09 10.1 1.01 1.99 3.01 3.09 1.01 0.801
Csalt (mM) RQ × 100 0 0 0 0 0 0 50b 75b 100b 10 0 0 0 0 5 0
0.21 0.14 0.13 2.0 2.0 2.0 2.0 2.0 2.0 2.0 0.37 0.37 0.37 0.17 0.37 0.97
Cfree (mM)
Γ XQ × 100 (µmol/m2)
14.0 29.3 39.1 4.05 8.50 12.1 4.05 4.05 4.05 8.50 0.914 1.83 2.79 2.90 0.85 0.801
4.2 5.4 4.1 2.7 2.7 2.8 2.7 2.7 2.7 2.7 2.8 3.2 3.4 1.7 1.9 2.1
1.0 1.7 2.2 2.0 3.2 4.1 2.0 2.0 2.0 3.2 2.1 3.5 4.9 5.3 4.0 ≈5c
a Adsorption isotherms used in obtaining Γ (see, however, footnotes b and c) were taken from works by Stro¨m et al.8 and Wa¨ngnerud and Olofsson.17 b The adsorbed amounts for DoTAB in the presence of NaBr have been obtained using the adsorption isotherm without salt. c Estimated from the amounts adsorbed of DoTAB and TTAB.
quencher), the thermodynamic model underlying eq 5 and conservation of mass gives15
(
)
Cbulk,Q XQ )R Cbulk,S 1 - XQ
(6)
where Cbulk,Q,S is the bulk concentration of Q or S. Furthermore, by introducing the mole fraction Ri of component i in the surfactant mixture, we obtain because Cbulk,i ) RiCbulk,tot
XQ )
1 1 - RQ 1+R RQ
(
)
(7)
The conditions for which eq 7 is valid were fulfilled for CTAB in the present investigation. By combining eqs 3 and 5 (or eqs 3 and 7 in the case of CTAB) the aggregation numbers for the surface-bound micelles can be obtained once 〈n〉 has been estimated. The relevant parameters used are collected in Tables 1 and 2. Adsorption Isotherms To calculate the surface-bound micellar aggregation numbers, we also need access to the surfactant adsorption isotherms. In Figure 1, we present such data for DoTAB, TTAB, and DoPPDAC (data taken from works by Stro¨m et al.8 and Wa¨ngnerud and Olofsson17). The following features of the isotherms are of relevance for this work. The adsorbed amounts for the first points on the isotherms at dilute concentrations are roughly 1.2 and 0.6 µmol m-2 for the monovalent and divalent surfactants, respectively. These amounts correspond approximately to charge neutralization of the silica surface. Although there are some uncertainties regarding the influence of pH and salt concentrations on the charge density of silica,26-29 it would appear that a reasonable charge density at the pH used in the present work and in the determination of the isotherms is 1/150 Å2.27 This value leads to (26) Wa¨ngnerud, P.; Jo¨nsson, B. Langmuir 1994, 10, 3268. (27) Bolt, G. H. J. Phys. Chem. 1957, 61, 1166. (28) Scales, P. J.; Grieser, F.; Healy, T. W.; White, L. R.; Chan, D. Y. C. Langmuir 1992, 8, 965. (29) Tadros, T. F.; Lyklema, J. J. Electroanal. Chem. 1968, 17, 267.
Figure 2. One representative fluorescence decay curve for each surfactant studied. For each surfactant (as indicated in the figure), two curves are shown: one without quencher and one with quencher. The total concentration (cf. Table 2) of each surfactant is as follows: DoPPDAC, Ctot ) 40.4 mM; DoTAB, Ctot ) 10.1 mM; TTAB, Ctot ) 1.01 mM; and CTAB, Ctot ) 0.801 mM. The amount of pyrene in each sample is roughly 1 pyrene/ 50 (surface-bound) micelles. The curves have been arbitrarily displaced in the vertical direction. The rapid initial decrease in the CTAB case is partly due to scatting of the laser pulse (please note that the pyrene concentration is lowest in the CTAB case).
charge neutralization at 1.1 and 0.55 µmol m-2 for the monovalent and divalent surfactant, respectively. This fact implies that the surfactant is aggregated at the surface for most of the surfactant concentrations for which the isotherm is determined in Figure 1. The adsorbed amount increases up to the cmc value where it reaches a plateau value. This value is higher for the monovalent case than for the divalent case, which implies that the aggregation number of the micelles formed by the former is larger than those formed by the latter and that the surface concentrations of micelles is larger for the monovalent case. Results and Discussions Time-resolved fluorescence experiments, using pyrene as fluorescent probe, were performed on DoTAB, TTAB, CTAB, and DoPPDAC. In addition, some measurements were performed for DoTAB and TTAB in the presence of NaBr. Some representative fluorescence decay curves are presented in Figure 2. The decay curves obtained without quencher present are all essentially monoexponential,
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Table 3. Results from the Fluorescence Quenching Experiments surfactant
C (mM)
CNaBr (mM)
N on surf.
N in bulka
DoPPDAC DoPPDAC DoPPDAC DoTAB DoTAB DoTAB DoTAB DoTAB DoTAB DoTAB TTAB TTAB TTAB TTAB TTAB CTAB
14.7 30.0 40.4 5.1 10.1 14.1 5.1 5.1 5.1 10.1 1.0 2.0 3.0 3.1 1.0 0.8
0 0 0 0 0 0 50.0 75.0 100.0 10.0 0 0 0 0 5 0
25 23 34 40 59 82 54b 54 64 60 53 72 115 143 92 93
20/40 60/60
80/80
75/120
a
Bulk aggregation number from the same probe/quencher combination used in this work. The two values given correspond to values close to cmc and values at concentrations at 30 mM above cmc (from Stro¨m et al.8 and Hansson et al.15). b The aggregation numbers for DoTAB in the presence of NaBr have been obtained using the adsorption isotherm without salt.
whereas the curves with quencher added all display a rapid initial decay of the fluorescence intensity followed by an exponential decay at longer times (cf. eq 2). The initial part of the decay curves originates from micelles containing both an excited probe and one (or more) quencher, and the exponential part corresponds to micelles containing only a excited probe. Note also that the slope of the decay curves at longer times is the same as that obtained without quencher. Taken together, these features give strong indication for the presence of discrete surfacebound aggregates for all of the systems studied here. We consider this as the principal result of this study. In addition, the probe/quencher does not migrate between micelles during the measuring time. The obtained aggregation numbers are presented in Table 3. Given in Figure 3a,b are the results in graphical form. Before discussing the features of the obtained aggregation numbers, we will make some remarks about the uncertainty in the obtained aggregation numbers. The errors entailed in fitting the fluorescent decay curves are small (at the most they amount to 5%). This is a random error. In the present analysis, the main source of uncertainty derives from the assumptions used in obtaining the distribution of the quencher between the micelles and the aqueous subphase. We judge the uncertainty here to be around 10% and at the maximum 20%. It should be noted that this source of error is systematic; thus, all of the aggregation numbers for a given surfactant/quencher combination might systematically deviate from the correct values. However, this means that trends observed with increasing surfactant concentration or the addition of salt are probably valid although the absolute numbers of N may be incorrect. When turning to the data in Figure 3, the following features are noteworthy. In the absence of salt (cf. Figure 3a), the aggregation numbers are on the same order of magnitude as those found in bulk. For the case of DoTAB and TTAB, there is a rather pronounced increase in N with surfactant concentration, whereas the increase of N for DoPPDAC with concentration is milder. The first micelles formed on the surface are rather small. As discussed by Stro¨m et al.,8 this feature can be explained by the effort of the micelles to match their charge density to that of the surface. Because the surface charge density
Figure 3. Derived aggregation numbers for micelles on silica for the studied surfactants. (a) Aggregation numbers as a function of bulk surfactant concentrations. The symbols are DoTAB (O), TTAB (0), DoPPDAC (4), and CTAB (×). (b) Data for DoTAB (O) and TTAB (0) as a function of added NaBr. The different surfactant concentrations used are indicated in the figure.
is comparatively low, this leads to small micelles. As the surfactant concentration increases, the shielding of the head group interactions increases, which leads to an aggregate growth. The effect is analogous to that found in bulk solutions upon increasing the surfactant concentration. The fact that the divalent surfactant shows a milder increase of N reflects the driving force of this surfactant to maintain small aggregation numbers, again as observed in bulk.30 It is interesting to note that the aggregation number determined for the monovalent cases in bulk at the cmc is lower than that found for the surfacebound micelles at a surfactant concentration equal to the cmc. This can be explained by the electrostatic interaction of the micelle with the surface that increases the driving force for the micelles to grow. For the divalent case, the same state of affairs applies (although our measurements were not performed at concentrations close to the bulk cmc in this case). The influence of added salt on the aggregation number has been investigated for DoTAB and TTAB. As can be seen in Figure 3b, for DoTAB, the aggregation numbers increase mildly with increasing salt for a given surfactant concentration. For TTAB, the increase is more pronounced. Again, the results can be rationalized in terms of the increased shielding of the surfactant in the micelle upon increasing the salt concentration, which brings about an increase in the aggregation numbers. (30) Hagsla¨tt, H.; So¨derman, O.; Jo¨nsson, B.; Johansson, L. B.-Å. J. Phys. Chem. 1991, 95, 1703.
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Finally, it is of interest to relate the results in this work to other work in this field. Manne and co-workers have studied the state of adsorbed micelles by AFM, using precontact repulsive forces. Their studies of TTAB indicate that nearly spherical aggregates are formed on silica.5 The nearest-neighbor distance between the micelles at pH 9.9 and at a bulk concentration of twice the cmc is 5.6 ( 0.6 nm. This value together with the adsorbed amount allows us to compute an aggregation number for the imaged micelles. From Figure 1, the adsorbed amount of TTAB at the plateau is 5.2 µmol m-2. This yields an aggregation number of 85 ( 18 (assuming that the micelles are arranged in a two-dimensional hexagonal lattice), which should be compared with our data at the highest surfactant concentration used, viz., 140 (cf. Table 2). Our analysis thus yields somewhat higher values of N. The reason for this is unclear. For the case of DoPPDAC adsorbed on the cleavage plane of mica, the AFM images clearly show a hexagonal packing of spherical micelles, with a nearest-neighbor
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distance of 5.1 ( 0.4 nm.7 This value together with the adsorbed amount at the plateau allows us to compute an aggregation number for the imaged micelles. By using the amount adsorbed at the plateau in Figure 1 and with a hexagonal arrangements of the micelles on the surface, we obtain 38 ( 6, which is in agreement with the value obtained here. One should note that mica has a higher charge density and as a consequence we are underestimating the adsorbed amount by using data from silica. In conclusion, our data is reasonable agreement with and supports the conclusions of the AFM work of Manne and co-workers. Acknowledgment. This work was financially supported by the Swedish Board for Industrial and Technical Development and the Swedish Natural Science Research Council. LA990885W
