Adsorption Behavior of Two Binary Nonionic Surfactant Systems at the

5042

Langmuir 1996, 12, 5042-5047

Adsorption Behavior of Two Binary Nonionic Surfactant Systems at the Silica-Water Interface Johanna Brinck* and Fredrik Tiberg† Physical Chemistry 1, Center for Chemistry and Chemical Engineering, Lund University, P.O. Box 124, S-221 00 Lund, Sweden Received March 18, 1996. In Final Form: June 19, 1996X The adsorption of the mixtures C14E6-C10E6 and C12E5-C12E8 onto a silica surface has been studied by in situ null ellipsometry. Both equilibrium and kinetic features have been investigated. The adsorption isotherms of the two mixed systems exhibit different characteristics which can be attributed to the magnitude of the difference in critical micelle concentrations (cmc’s) of the individual components in each pair. The isotherm of the C14E6-C10E6 system exhibits a maximum at low total concentrations, while the C12E5C12E8 system acts as a single surfactant system with similar cmc but intermediate adsorbed amount compared with those of the individual components. The study of the kinetic behavior of the mixtures reveals that the adsorption characteristics are similar for the two systems, while during desorption they behave very differently. The amount of the C14E6-C10E6 system adsorbed exhibits a maximum upon rinsing. The difference in desorption behavior between the two systems can be understood from the individual surfactant characteristics and the knowledge we have gained from studying the equilibrium adsorption behavior.

Introduction The special property of surfactants that makes them so interesting is their amphiphilicity. This property enables them to form a multitude of different structures in solution depending on concentration and surrounding media. Another consequence of their amphiphilicity is their tendency to adsorb at interfaces. The behavior at solidliquid interfaces is of special importance for many industrial applications such as detergency, wetting, flotation, and dispersion stability. Almost all surfactants used in practical applications are polydisperse. Commercial polyethylene glycol monoalkyl ethers (CnEm) are generally subject to a distribution of not only the number of oxyethylene groups but also the hydrocarbon chain length. There are many reasons for this wide use of more or less polydisperse surfactants; one being the cost of purification and another the fact that by mixing surfactants it is sometimes possible to enhance the properties of the preparation. In order to understand the effects of polydispersity in nonionic surfactant systems, it is necessary to study welldefined mixtures. These mixtures are of considerable academic interest not only because of their own varied behavior or their suitability as model systems but also for the reason that they can provide an understanding of more complicated systems (e.g., block copolymers) where the behavior may be too complex to be interpreted directly. The many interesting questions connected with the field of mixed surfactants have resulted in a great deal of research activity and several books on the subject.1-3 The adsorption of pure nonionic surfactants has been studied extensively through the years (e.g., refs 4-7). In our own previous studies of this subject, time-resolved * To whom correspondence should be addressed. E-mail: [email protected]. † Present address: Institute for Surface Chemistry, P.O. Box 5607, S-114 86 Stockholm, Sweden. X Abstract published in Advance ACS Abstracts, September 1, 1996. (1) Mixed Surfactant Systems; Ogino, K., Abe, M., Eds.; Marcel Dekker: New York, 1993; Vol. 46. (2) Phenomena in mixed surfactant systems; Scamehorn, J. F., Ed.; American Chemical Society: Washington, DC, 1986; Vol. 311. (3) Mixed surfactant systems; Holland, P. M., Rubingh, D. N., Ed.; American Chemical Society: Washington, DC, 1992; Vol. 501.

S0743-7463(96)00260-0 CCC: $12.00

ellipsometry has proved to be a useful tool, providing us with not only the amount adsorbed but also the mean optical thickness of the adsorbed layer of surfactants. The parameters measured can be determined with a time resolution of about 1-3 s, which makes it possible to study the evolution of adsorbed layers with time.8,9 When it comes to the adsorption of mixed nonionic surfactants at a solid-liquid interface, studies are more sparse,9,10 but a large number of studies have been carried out on naturally polydisperse nonionic surfactants (e.g., refs 11-13). In this study, we chose the two pairs C14E6C10E6 and C12E5-C12E8 as model systems to study the effects of polydispersity on adsorption at hydrophilic silica surfaces. In the first pair, the surfactants differ in the size of the hydrophobic tail, the consequence being that the critical micelle concentrations (cmc’s) differ by approximately 2 orders of magnitude. In the second pair, the polydispersity lies in the size of the hydrophilic headgroup, which results in a small difference between the cmc’s of the individual surfactants. The variation in hydrophobic and hydrophilic chain lengths leads to substantial differences in the plateau adsorption of the individual surfactants within each pair which facilitates the evaluation of the experimental data. Materials and Methods Materials. A series of monodisperse polyethylene glycol monoalkyl ethers (CnEm; C10E6, C12E5, C12E8, and C14E6) were purchased from Nikko Chemicals and used without further purification. Polished silicon slides (p-type, boron-doped, resistivity 1-20 Ω‚cm) were purchased from Okmetic Ltd. The wafers were (4) Clunie, J. S.; Ingram, B. T. In Adsorption from solution at the solid/liquid interface; Parfitt, G. D., Rochester, C. H. Ed.; London Academic: London, 1983; pp 105-152. (5) von Rybinski, W.; Schwuger, M. J. In Nonionic surfactants; Schick, M. J., Ed.; Marcel Dekker: New York, 1987; Vol. 23, pp 45-107. (6) Cases, J. M.; Villieras, F. Langmuir 1992, 8, 1251-1264. (7) Levitz, P. Langmuir 1991, 7, 1595. (8) Tiberg, F.; Jo¨nsson, B.; Lindman, B. Langmuir 1994, 10, 37143722. (9) Tiberg, F.; Jo¨nsson, B.; Tang, J.; Lindman, B. Langmuir 1994, 10, 2294-2300. (10) Huber, K. J. Colloid Interface Sci. 1991, 147, 321-332. (11) Aston, J. R. Ph.D. Thesis, University of Melbourne, Australia, 1987. (12) Hsiao, L.; Dunning, H. N. J. Phys. Chem. 1955, 59, 362-366. (13) Kuno, H.; Abe, R. Kolloid-Z. 1961, 177, 40-44.

© 1996 American Chemical Society

Adsorption of Mixtures

Langmuir, Vol. 12, No. 21, 1996 5043

Table 1. Refractive Index Increment (dn/dc),14 Critical Micellar Concentration (cmc),15 Critical Surface Aggregation Concentration (csac), and Plateau Adsorption (Γp) 9 surfactant

dn/dc

cmc, mmol‚L-1

C10E6 C12E5 C12E8 C14E6

0.129 0.131 0.142 0.135

0.90 0.057 0.092 0.010

Γp

csac, mmol‚L-1

mg/m2

µmol/m2

0.70 0.050 0.060 0.0060

1.1 2.3 0.97 2.5

2.5 5.7 1.8 5.2

oxidized thermally in a saturated oxygen atmosphere at 920 °C for ≈1 h, followed by annealing and cooling in a flow of argon. This procedure resulted in a SiO2 layer thickness of ≈300 Å. The oxidized wafers were then cut into slides with a width of 12.5 mm and cleaned in a mixture of 25% NH4OH (pro analysi, Merck), 30% H2O2 (pro analysi, Merck), and H2O (1:1:5 by volume) at 80 °C for 15 min, followed by cleaning in a mixture of 32% HCl (pro analysi, Merck), 30% H2O2 (pro analysi, Merck), and H2O (1:1:5 by volume) at 80 °C for 15 min. The slides were then rinsed twice, first in doubly distilled Millipore water and then in ethanol (spectrographically pure, 99.5%, Kemetyl). They were then stored in ethanol until used. Just before the slides were placed in the ellipsometer cuvette, they were treated in a plasma cleaner (Herrick Scientific Corp. Model PDC-3XG) for 5 min. The plasma treatment was performed at a pressure of 0.03 mbar at a power of 30 W. Method. The optical properties of the adsorbed surfactant layer were determined by means of in situ null ellipsometry. The instrument used in this study was a modified, automated Rudolph Research thin-film ellipsometer, Model 43603-200E. It is equipped with five-phase stepper motors from Berger-Lahr, Model VRDM 566, and controlled by a personal computer. The light source used was a xenon arc lamp, and the experiments were performed at a wavelength of 4015 Å, using an interference filter to select the wavelength. The fused quartz cuvette needed for measurements in liquid ambient media was made by Hellma, Germany. The angle of incidence is determined by the angle between the two cuvette walls which the light passes through (≈67.7°). To obtain accurate measurements of the thickness and the amount of material adsorbed, it is necessary to know the optical properties of the oxidized silicon substrate. By studying the bare substrate in two different ambient media, air and water, it is possible to calculate the complex refractive index (N2 ) n2 + jk2) of the bulk silicon (Si) and the thickness (d1) and the refractive index (N1 ) n1) of the silica (SiO2) layer. Typical values of these parameters are n2 ) 5.505 ( 0.005, k2 ) -0.37 ( 0.03, d1 ) 300 Å, and n1 ) 1.48 ( 0.03, varying somewhat from batch to batch. The measurements in different media were performed by fourzone null averaging to eliminate systematic errors due to imperfections in the optical components. The water used in these experiments was doubly distilled Millipore water with a pH of approximately 5.8. The surfactant was added to the temperature-controlled cuvette (25.0 ( 0.1 °C) where stirring was performed at 300 rpm. During the experiment the ellipsometrical angles Ψ and ∆ were determined in one zone as a function of time. When Ψ and ∆ were calculated, corrections were made for imperfections revealed during four-zone averaging. The mean optical thickness (df) and the refractive index (nf) of the film were then calculated from these angles. By using de Feijter’s formula16

Γ)

(nf - no)df dn/dc

with dn/dc as determined by Chiu et al.,14 the amount adsorbed could be calculated. The parameter no in this formula is the refractive index of the ambient bulk solution. When steadystate conditions had been established, rinsing at a continuous flow of 10 mL/min was initiated. (14) Chiu, Y. C.; Chen, L. J. Colloids Surf. 1989, 41, 239-244. (15) Mukerjee, P.; Mysels, K. J. Critical Micelle Concentration; National Bureau of Standards (U.S.): Washington, DC, 1971. (16) de Feijter, J. A.; Benjamins, J.; Veer, F. A. Biopolymers 1978, 17, 1759.

Figure 1. Adsorption isotherms of the equimolar C14E6-C10E6 system and of the pure surfactants. The concentration of the mixed system, as presented in the figure, is the concentration of C14E6, which equals half the total concentration of surfactant. Solid lines are drawn only to guide the eye. More detailed descriptions of the instrument and the procedure for characterization of thin films adsorbed on layered substrates can be found in previous publications.17,18 When the adsorbed amount of the binary systems was converted from mg/m2 to µmol/m2, it was assumed that the composition in the adsorbed layer varied linearly with the amount adsorbed, which indeed seems to be the case for the surfactants studied.9

Results Equilibrium Features. The equilibrium results presented include two typical isotherms of the C14E6-C10E6 and the C12E5-C12E8 systems and also a more detailed study of the dependence of adsorption on the total composition for the same systems. The changes in adsorption with total concentration and composition are interpreted in terms of changes in the surface micellar composition. The adsorption isotherms of the system 1:1 (molar ratio) C14E6-C10E6 and those of the individual surfactants are shown in Figure 1. In contrast to the pure surfactants, the mixed system exhibits an isotherm with a maximum located around the bulk cmc of the mixture. In the region below this maximum, the behavior of the mixed system is very similar to that of the pure C14E6. However, as the concentration is increased above the bulk cmc of the mixture, the amount adsorbed decreases. The adsorption isotherms of the system 1:1 C12E5-C12E8 and the individual surfactants are shown in Figure 2. The isotherm of the mixed system is very similar to those of the individual surfactants. The total concentration at which adsorption begins to increase is close to the csac (critical surface aggregation concentration) for the two pure surfactants. As the concentration is increased further, an adsorption plateau, intermediate to the corresponding adsorption of the individual surfactants, is reached. In Figures 3 and 4, the dependence of adsorption on the total composition for the two binary systems can be seen. The data are presented as isotherms in order to show the effects of changes in the composition of the bulk more clearly. All the measurements were performed at concentrations well above the cmc of the mixture. By treating the micelles as a pseudo phase and assuming that the mixing in the micelles is ideal, it was possible to calculate the composition of the micelles.19 The calculated molar fractions of C14E6 and C12E5 in the aggregates are shown (17) Tiberg, F.; Landgren, M. Langmuir 1993, 9, 927-932. (18) Landgren, M.; Jo¨nsson, B. J. Phys. Chem. 1993, 97, 1656-1660. (19) Clint, J. H. J. Chem. Soc., Faraday Trans. 1 1975, 71, 13271334.

5044 Langmuir, Vol. 12, No. 21, 1996

Figure 2. Adsorption isotherms of the equimolar C12E5-C12E8 system and of the pure surfactants. The concentration of the mixed system, as presented in the figure, is the concentration of C12E5, which equals half the total concentration of surfactant. Solid lines are drawn only to guide the eye.

Figure 3. The amount adsorbed (Γ) of the C14E6-C10E6 system (filled diamonds) for the total molar fractions specified to the right of the figure and the amounts of pure surfactants adsorbed (open circles) given on the left y-axis. The calculated fraction of C14E6 in the mixed micelles (broken lines) for the molar fractions specified on the right (X1,mic, given by eqs 1-3 in the Appendix) is given on the right y-axis. The concentrations of the mixed systems are presented as the concentrations of C14E6 on the x-axis. The solid lines of the pure surfactant isotherms are drawn only to guide the eye.

Figure 4. The amount adsorbed (Γ) of the C12E5-C12E8 system (filled diamonds) for the total molar fractions specified to the right of the figure and the amounts of pure surfactants adsorbed (open circles) given on the left y-axis. The calculated fraction of C12E5 in the mixed micelles (broken lines) for the molar fractions specified on the right (X1,mic, given by eqs 1-3 in the Appendix) is given on the right y-axis. The concentrations of the mixed systems are presented as the concentration of C12E5 on the x-axis. The solid lines of the pure surfactant isotherms are drawn only to guide the eye.

by broken lines for each of the different total compositions specified to the right. It is clear from the experimental data shown in Figure 3 that the general behavior of the C14E6-C10E6 system, with a maximum adsorption at low total concentrations, remains unchanged when varying the total composition. Adding C10E6 to the 1 mM C14E6 solution to the molar fractions specified resulted in a marked decrease in adsorption. The more C10E6 added, the lower the adsorp-

Brinck and Tiberg

Figure 5. Evolution of the amount adsorbed (Γ) with time for the binary system C14E6-C10E6 with a total surfactant concentration of 2 mM and a C14E6 molar ratio of 0.5, and for the pure surfactants with concentrations well above the cmc. The surfactants were injected at t ) 0 and continuous rinsing was initiated at about 3000 s.

tion. The trend is the same for the measurements performed with 0.1 mM C14E6, but in this case the decrease in adsorption upon the addition of C10E6 was much smaller. The isotherm of the C12E5-C12E8 system also retained its major features as the total composition was varied; the adsorption not being very sensitive to changes in concentration. The effect of adding more C12E8 to pure C12E5 systems was a decrease in adsorption; the decrease being about the same for high total concentrations as for low. Kinetic Features. In this section, two typical adsorption-desorption cycles for the C14E6-C10E6 and the C12E5C12E8 systems are presented. They will be compared with those of the pure systems and interpreted in the discussion with the aid of individual surfactant characteristics and equilibrium adsorption data presented in this article. Figure 5 shows the adsorption-desorption cycle for the C14E6-C10E6 system with a total surfactant concentration of 2 mM and a C14E6 molar ratio of 0.5. Also presented are the curves for the corresponding pure substances. The two pure surfactants both show the same general characteristics, an initial linear increase in adsorption which then levels off to finally reach an adsorption plateau. The desorption is dominated by a linear decrease in the amount adsorbed with time, during which nearly all of the surfactants are desorbed. The mixed system exhibits similar adsorption behavior, but very different desorption behavior, i.e., the amount adsorbed increases upon rinsing and reaches a maximum. The rate of desorption after this maximum is the same as that of pure C14E6. The adsorption-desorption cycle of the binary system C12E5-C12E8 with a total surfactant concentration of 2 mM and a C12E5 molar ratio of 0.5 is shown in Figure 6. Corresponding pure surfactant adsorption-desorption cycles are also shown. In this case, the adsorption and the desorption behavior of the mixed system resembles that of the pure systems. Discussion Equilibrium Features. The understanding of the adsorption of monodisperse nonionic surfactants of the type studied here is now rather good. At very low concentrations, when only monomers are present, the adsorption at a silica-water interface is low. However, above a critical concentration not far from the cmc (csac), the adsorption increases strongly within a narrow concentration interval. At higher concentrations, closer to the bulk cmc, the adsorption levels off, and plateau values are generally reached around the cmc. In this region the amount of CnEm surfactants adsorbed increases with

Adsorption of Mixtures

Figure 6. Evolution of the amount adsorbed (Γ) with time for the binary system C12E5-C12E8 with a total surfactant concentration of 2 mM and a C12E5 molar ratio of 0.5, and for the pure surfactants with concentrations well above the cmc. The surfactants were injected at t ) 0, and continuous rinsing was initiated at about 3000 s.

decreasing m/n ratio.9,20 Hydrophilic surfactants with relatively large headgroups, such as C12E8 and C10E6, exhibit low plateau adsorption values because they form small discrete aggregates on the surface surrounded by water, whereas more hydrophobic surfactants, such as C14E6 and C12E5, form larger aggregates, resulting in higher plateau adsorption (in µmol/m2).9,20-22 It is important to bear in mind, when studying surfactant mixtures, that as the total concentration changes, the monomer concentration, the monomer composition, and also the micellar composition vary continuously.19,23 In the C14E6-C10E6 system, the two components have cmc’s which differ by nearly 2 orders of magnitude (0.01 and 0.9 mmol‚L-1 for C14E6 and C10E6, respectively). The consequence of this is that the bulk micelles consist of almost only the more hydrophobic C14E6 molecules at low total concentrations, but as the total concentration increases, the representation of the more hydrophilic C10E6 molecules in the micelles increases. In the isotherm shown in Figure 1, the adsorption starts to increase at a C14E6 concentration, which is approximately the same as the csac for the pure surfactant, indicating that the C10E6 molecules hardly contribute to the initial formation of surface aggregates. The mixed system behaves like pure C14E6 up to a total concentration where the properties of the adsorbed layer of the mixed system are the same as those of the pure surfactant at its adsorption plateau. Increasing the total concentration further results in a decrease in the amount adsorbed. This is interpreted as being the consequence of an increase in the C10E6 molar fraction in the surface aggregates. Due to less efficient packing of these surfactants in the surface aggregates,9 the adsorption decreases with increasing C10E6 content in the adsorbed layer. An interesting feature in Figure 1 is that the incorporation of C10E6 into the micelles starts at a concentration far lower than its own csac. If we calculate the monomer concentrations for the equimolar system (by assuming ideal mixing in the micelle and using a phase separation model, eqs 1 and 2 in the Appendix19) as a function of the total concentration, we find that the monomer concentra(20) Bo¨hmer, M. R.; Koopal, L. K.; Janssen, R.; Lee, E. M.; Thomas, R. K.; Rennie, A. R. Langmuir 1992, 8, 2228-2239. (21) Levitz, P.; Van Damme, H.; Keravis, D. Collect. Colloq. Semin. (Inst. Fr. Pet.) 1985, 42 (Interact. Solide-Liq. Milieux Poreux), 473483. (22) Levitz, P.; Van Damme, H. J. Phys. Chem. 1986, 90, 13021130. (23) Harwell, J. H.; Scamehorn, J. F. In Mixed surfactant systems; Ogino, K., Abe, M., Eds.; Marcel Dekker Inc.: New York, 1993; Vol. 46, pp 263-281.

Langmuir, Vol. 12, No. 21, 1996 5045

tion of C10E6 is a monotonically increasing function which equals cmc(C10E6)/2 in the limit of high concentration. The monomer concentration of C14E6, on the other hand, reaches a maximum at the cmc of the mixed system and then decreases upon further addition of surfactant also toward a limiting value of cmc(C14E6)/2. In the C12E5-C12E8 system, the two surfactants have cmc’s of the same magnitude (0.057 and 0.092 mmol‚L-1). The tendency of the two surfactants to form aggregates at a given concentration can be expected to be approximately the same. This means that the composition of the aggregates will be similar to the composition in the bulk. Indeed, in the equimolar isotherm in Figure 2, the C12E5-C12E8 system behaves very much like a pure surfactant with a csac similar to those of the two individual surfactants and intermediate plateau adsorption. As expected, an increase in total concentration results in minor changes of the surfactant composition in the aggregates. Correspondingly, there will be only minor changes in adsorption over a large concentration interval ranging from the cmc of the mixed system, and upward. Ideal solution theory has proved useful in describing bulk surfactant systems with similar headgroups.19,24,25 The correlation between the amount adsorbed and the calculated micellar composition for the two different mixed systems in Figures 3 and 4 confirms the evolution of surface aggregate composition (adsorption) with concentration, as described for the equimolar systems discussed above. In the case of the C14E6-C10E6 system, the calculated composition of the bulk aggregates ranges from a very high C14E6 content, at low total concentration, to the overall bulk molar fraction of C14E6, in the limit of high total concentration. The same calculations for the C12E5-C12E8 system show only very small changes in composition with increasing concentration. The correlation between the calculated micellar composition in the bulk and the adsorption or surface aggregate composition indicates that the surface and bulk aggregates are quite similar for the two systems studied. It should be noted that any discrepancy between the adsorption and calculated composition can be interpreted as the result of either (or both) of the following two situations: nonideality in the interactions between the two surfactants or, in case of ideal behavior in bulk, small dissimilarities between bulk and surface aggregates, mainly due to packing restrictions caused by the presence of the planar interface and surfactant-surface interactions. The most common way of presenting the adsorption of mixed surfactant systems is to plot the adsorption as a function of total concentration with the molar fraction kept constant. A different approach is to start from the fact that the micellar phase can be treated as a pseudophase and treat the adsorption as a function of the concentrations of both components in a phase diagram. The major features can be presented in a schematic phase diagram as in Figure 7. The phases considered are those formed at the surface and not those in the bulk. There are two main regions: one where only monomers are present, and one where surface aggregates also are formed. At the border (the broken line) between these two regions there is a concentration interval where the adsorbed layer is not yet complete. This zone is broader for systems with less cooperative adsorption, such as C12E8. For the C14E6-C10E6 system, the adsorption can be estimated from calculations of the micellar composition as seen in Figure 3. In Figure 8, the corresponding (24) Meguro, K.; Ueno, M.; Esumi, K. In Nonionic surfactants; Schick, M. J., Ed.; Marcel Dekker: New York, 1987; Vol. 23; pp 109-184. (25) Holland, P. M. In Mixed surfactant systems; Holland, P. M., Rubingh, D. N., Eds.; American Chemical Society: Washington, DC, 1992; Vol. 501, pp 31-44.

5046 Langmuir, Vol. 12, No. 21, 1996

Figure 7. Schematic surface phase diagram of the C14E6C10E6 system. The rings show the experimental critical surface aggregation concentrations of the pure and the mixed systems. The broken line is drawn only to guide the eye.

Figure 8. Calculated amount adsorbed of the C14E6-C10E6 system (given by eqs 1-4 in the Appendix) as a function of the concentrations of both components. The symbols represent isoadsorption lines, i.e., the concentrations at which the total adsorption was equal to, for example, 4 µmol/m2.

calculated adsorption is presented in iso-adsorption curves for concentrations of both components up to 1 mM. The lower concentration limit is the cmc for the mixed system. As was demonstrated in a recent publication by Manne and Gaub, surfactants adsorbed at a surface can assume the same type of well-defined spherical, cylindrical, or bilayer-like structures as those found in the bulk.26 For the particular system discussed here, the aggregate region can be assumed to contain subregions of more planar aggregates in the limit of high C14E6 micellar molar fraction, while the C10E6-rich aggregates are smaller, due to different geometric packing constraints for the two surfactants. By addition of lines for different constant total compositions, it is easy to go back to the traditional isocomposition isotherms and study, for example, the variation of isotherm shape with composition or the variation of aggregate structure with total concentration. Kinetic Features. The number of studies on the adsorption kinetics of nonionic surfactants onto hydrophilic solids is to our knowledge rather small cf. refs 8, 27, and 28, but as can be seen in a previous publication, the adsorption and desorption kinetics of monodisperse nonionic CnEm surfactants are nevertheless quite well understood.8 The dependence of the adsorption and desorption modes and rates on a large number of parameters, such as the surfactant characteristics (e.g., csac, diffusion (26) Manne, S.; Gaub, H. E. Science 1995, 270, 1480-1482. (27) Klimenko, N. A.; Permilovskaya, A. A.; Tryasorukova, A. A.; Koganovskii, A. M. Kolloid. Zh. 1975, 37, 972-975. (28) Partyka, S.; Zaini, S.; Lindheimer, M.; Brun, B. Colloids Surf. 1984, 12, 255-70.

Brinck and Tiberg

Figure 9. Possible course of desorption for the 1 mM C14E6-1 mM C10E6 system (cf. Figure 5). The line represents the estimated surface composition and concentrations during rinsing.

constants, micellar association, and dissociation constants) and hydrodynamic properties of the system (influencing the size of the stagnant layer outside the surface), makes it difficult to extend the understanding to binary systems in a simple way. Nevertheless, as is shown below, some important features can be understood from our knowledge about the individual surfactants and by comparing the kinetics with the equilibrium behavior of the mixtures. In the adsorption and desorption cycles presented, we have found a major difference between the behavior of the two mixed systems. The C14E6-C10E6 system exhibits a maximum in the amount adsorbed with time during the process of rinsing, while the C12E5-C12E8 system shows a more single-surfactant-like desorption. When we start to rinse in a system with 1 mM C14E6 and 1 mM C10E6, there will be a lowering of the concentration in the stagnant layer outside the surface. Due to the very large C10E6 monomer concentration gradient (Cmon(C10E6) ≈ 0.35 mM; Cmon(C14E6) ≈ 0.006 mM, according to the ideal solution theory) it is likely that the transport of surfactant from the stagnant layer will rapidly be dominated by monomer transport out of C10E6. Both the lowering of the total concentration and the increase in C14E6 molar fraction would, under equilibrium conditions, imply a higher adsorbed amount (Figure 3). The increased equilibrium adsorption would be the result of a change in the surface micellar composition toward more C14E6. This creates a deficit of C14E6 in the surface region, which in turn causes a decrease in the chemical potential of C14E6 close to the surface. The chemical potential gradient now formed within the stagnant layer gives rise to back diffusion of C14E6 to the surface, increasing the amount adsorbed. As the rinsing continues, there will eventually be a net desorption when the concentration close to the surface has become low enough.8 Due to the high C14E6 content at the surface, the desorption will follow the mode and rates of pure C14E6. In Figure 9 we have tried to show how the surface composition and concentration might change during rinsing for the mixed system 1 mM C14E6-1 mM C10E6. The fact that there must be diffusion of C14E6 toward the surface during the initial process of rinsing, and not just redistribution of the surfactants in the immediate surface region between monomer and micellar forms, can be illustrated by the following example. For the 1 mM C14E6-1 mM C10E6 system, the amount adsorbed at equilibrium is about 4.2 µmol/m2. Assuming that the composition in the adsorbed layer varies linearly with the amount adsorbed, we have 63 molar % C14E6 in the adsorbed layer, that is 2.6 µmol/m2. At maximum adsorption during rinsing, we have 4.9 µmol/m2 and 89 molar % C14E6 in the adsorbed layer, that is 4.4 µmol/m2

Adsorption of Mixtures

C14E6. Thus 4.4 - 2.6 ) 1.8 µmol/m2 C14E6 must be transported to the surface during the initial process of rinsing. In a very simple model, the equilibrium concentrations of the two components within the stagnant layer (excluding the immediate surface region) can be said to be 1 mM. This means that in order to increase the adsorption from 4.2 to 4.9 µmol/m2, we need a number of C14E6 molecules equivalent to all those present within a distance of (1.8 µmol/m2)/(1 mmol/dm3) ) 1.8 µm away from the surface. As can be seen from this extremely simplified example, the transport of C14E6 to the adsorbed layer cannot be limited to the immediate surface region. It might be expected that the adsorption step of the C14E6-C10E6 system, as well as the desorption step, would be affected by the surfactant characteristics: but in what way? The course of adsorption from a low surfactant concentration solution can be expected to be determined mainly by monomer diffusion since the micellar concentration is low. In this case, the two surfactant monomer gradients over the stagnant layer would determine the adsorption step, and when the C10E6 monomer concentration in the bulk is significantly higher than that of C14E6, we would expect stepwise adsorption. Initially, the C10E6 molecules will dominate close to the surface, but there will be a continuous transport to the surface of more and more C14E6 which eventually evens out the total concentrations of the two components, and during this process, the adsorption increases monotonically. At high total concentrations, it is difficult to separate the effects of the two surfactants partly because the adsorption process is too rapid and partly because the micellar diffusion contribution to the transport of surfactant through the stagnant layer will be significant. The micellar contribution will be in the form of the release of monomers. The presence of a maximum during desorption, with an amount adsorbed approaching that of pure C14E6, suggests that the equilibration process at the surface is relatively fast in comparison with the mass transfer of the two surfactants away from the surface region out into the bulk. In the case of the C12E5-C12E8 system, a decrease in concentration in the stagnant layer does not imply any change in the amount adsorbed at equilibrium. In the isotherms in Figures 2 and 4, there are only minor changes in adsorption (surface aggregate composition) due to changes in the total concentration. Furthermore, the surfactants are transported away from the surface equally fast, due to approximately equal monomer concentrations and micellar molar fractions, which means there will not be any change in the total composition within the stagnant layer that could cause surface aggregate composition to change with a change in the amount adsorbed at equilibrium as a result. Conclusions By using null ellipsometry we have studied the adsorption of the two binary systems C14E6-C10E6 and C12E5C12E8 onto a silica surface. These systems were chosen in order to reveal the effects of different sorts of polydispersity on the adsorption; the first pair being polydisperse in the sense of different sizes of hydrophobic tails, the second in the sense of different sizes of the hydrophilic headgroups. Our results show that the effect of the polydispersity on the equilibrium and kinetic adsorption behavior of these two systems can be attributed to the relation between the cmc’s of the individual components. The variations in the equilibrium adsorption with total concentration and total composition are largely due to changes in aggregate composition. The large difference in cmc between C14E6 and C10E6 causes major changes in aggregate composition with increasing total concentration which results in an

Langmuir, Vol. 12, No. 21, 1996 5047

isotherm with a maximum at low concentrations. The small difference in cmc between C12E5 and C12E8 makes the isotherms flat and less dependent on total concentration. Our study of the kinetic behavior reveals surprising results concerning the desorption process. While the C12E5-C12E8 system shows single-surfactant-like kinetic behavior, the C14E6-C10E6 system presents a maximum in adsorption upon rinsing. This phenomenon can be related to the individual surfactant characteristics and the equilibrium adsorption behavior and is coupled to a change in the composition of the adsorbed layer during rinsing. The change in composition is made possible by the transport of C14E6 molecules toward the surface during the initial rinsing process. The presence of a maximum during rinsing shows that the equilibration process at the surface must be relatively fast in comparison with the mass transfer of the surfactants away from the surface region during rinsing. Acknowledgment. The authors would like to thank Bengt Jo¨nsson for his continuous support and numerous interesting discussions. This work was sponsored by the Swedish Research Council for Engineering Sciences (TFR) and the Swedish National Board for Technical Development (NUTEK). Appendix The monomer concentrations and micellar composition in a binary nonionic surfactant system can be calculated assuming ideal mixing in the micelle and using a pseudophase model.19 Under such conditions, the following expressions give the monomer concentrations of the two surfactants

c1,mon )

-(Ctot - δ1) + x(Ctot - δ1)2 + 4c1δ1 cmc2 2 -1 cmc1

(1)

c2,mon )

-(Ctot - δ2) + x(Ctot - δ2)2 + 4c1δ2 cmc1 2 -1 cmc2

(2)

[ [

] ]

where c1 and c2 are the total concentrations of the two surfactants 1 and 2, respectively

Ctot ) c1 + c2, δ1 ) cmc2 - cmc1 and δ2 ) cmc1 - cmc2. To calculate the fraction of component 1 in the mixed micelles, the following equation can be used:

X1,mic )

c1 - c1,mon Ctot - c1,mon - c2,mon

(3)

Assuming that the composition in the adsorbed layer varies linearly with the amount adsorbed, theoretical values for the amount adsorbed can be calculated according to

Γtot ) Γplateau,1X1,mic + Γplateau,2X2,mic

(4)

where X1,mic and X2,mic denote the micellar molar fractions of the two surfactants 1 and 2, respectively, and Γplateau,1 and Γplateau,2 are the plateau adsortions of the pure surfactants. LA960260N