Experimental Observations on the Scaling of Adsorption Isotherms for

Abstract Image. The self-assembly of nonionic surfactants in bulk solution and on hydrophobic surfaces is driven by the same intermolecular interactio...
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Experimental Observations on the Scaling of Adsorption Isotherms for Nonionic Surfactants at a Hydrophobic Solid-Water Interface Nitin Kumar,*,†,‡,§ Stephen Garoff,†,§ and Robert D. Tilton*,‡,§ Departments of Physics and Chemical Engineering and Center for Complex Fluids Engineering, Carnegie Mellon University, Pittsburgh, Pennsylvania 15213 Received July 18, 2003. In Final Form: February 12, 2004 The self-assembly of nonionic surfactants in bulk solution and on hydrophobic surfaces is driven by the same intermolecular interactions, yet their relationship is not clear. While there are abundant experimental and theoretical studies for self-assembly in bulk solution and at the air-water interface, there are only few systematic studies for hydrophobic solid-water interfaces. In this work, we have used optical reflectometry to measure adsorption isotherms of seven different nonionic alkyl polyethoxylate surfactants (CH3(CH2)I-1(OCH2CH2)JOH, referred to as CIEJ surfactants, with I ) 10-14 and J ) 3-8), on hydrophobic, chemically homogeneous self-assembled monolayers of octadecyltrichlorosilane. Systematic changes in the adsorption isotherms are observed for variations in the surfactant molecular structure. The maximum surface excess concentration decreases (and minimum area/molecule increases) with the square root of the number of ethoxylate units in the surfactant (J). The adsorption isotherms of all surfactants collapse onto the same curve when the bulk and surface excess concentrations are rescaled by the bulk critical aggregation concentration (CAC) and the maximum surface excess concentration. In an accompanying paper we compare these experimental results with the predictions of a unified model developed for selfassembly of nonionic surfactants in bulk solution and on interfaces.

1. Introduction Surfactant self-assembly in solution and on hydrophobic interfaces is driven by the amphiphilic nature of the surfactant molecules. At the critical aggregation concentration (CAC), surfactants in bulk solution self-assemble to form association colloids of varying size and shape.1 The same types of intermolecular forces that drive the formation of these bulk aggregates are also responsible for surfactant self-assembly on hydrophobic interfaces. However, the relationship among the surfactant molecular structure, self-assembly in solution, and self-assembly at hydrophobic interfaces is not clearly understood. This paper is motivated by the lack of systematic studies of surfactant self-assembly on chemically homogeneous and uniform hydrophobic solid surfaces. Such experimental data is necessary to understand the relationship among molecular structure and self-assembly in bulk and on interfaces. Nonionic alkyl polyethoxylate surfactants (CH3(CH2)I-1(OCH2CH2)JOH, CIEJ) are extensively used as model surfactants.2 The self-assembly of CIEJ surfactants has been investigated on a variety of hydrophobic solid surfaces, such as polystyrene,3-5 polystyrene latex,6,7 * To whom correspondence should be addressed. E-mail: Nitin Kumar [email protected] and [email protected]. † Department of Physics, Carnegie Mellon University. ‡ Department of Chemical Engineering, Carnegie Mellon University. § Center for Complex Fluids Engineering, Carnegie Mellon University. (1) Israelachivili, J. N. Intermolecular and Surfaces Forces; Academic Press: New York, 1991. (2) Schick, M. J. Nonionic Surfactants; M. Dekker: New York, 1987. (3) Howse, J. R.; Steitz, R.; Pannek, M.; Simon, P.; Schubert, D. W.; Findenegg, G. H. Phys. Chem. Chem. Phys. 2001, 3, 4044-4051. (4) Geffroy, C.; Stuart, M. A. C.; Wong, K.; Cabane, B.; Bergeron, V. Langmuir 2000, 16, 6422-6430. (5) Kjellin, U. R. M.; Claesson, P. M.; Linse, P. Langmuir 2002, 18, 6745-6753. (6) Zhao, J.; Brown, W. J. Colloid Interface Sci. 1996, 179, 281289.

poly(methyl methacrylate),3,8,9 and silane monolayers.5,10-13 These solid surfaces differ from each other in terms of surface chemistry and surface inhomogeneities. There are few systematic studies using chemically homogeneous and uniform surfaces.14,15 In comparison, a large amount of literature is available for self-assembly at the air-water (AW) interface16-22 due to the ease with which consistent AW interfaces can be produced. Similarly, extensive research has been carried out for self-assembly in bulk solution.20,23-31 (7) Jodar-Reyes, A. B.; Ortega-Vinuesa, J. L.; Martin-Rodriguez, A.; Leermakers, F. A. M. Langmuir 2002, 18, 8706-8713. (8) Gilchrist, V. A.; Lu, J. R.; Keddie, J. L.; Staples, E.; Garrett, P. Langmuir 2000, 16, 740-748. (9) Steinby, K.; Silveston, R.; Kronberg, B. J. Colloid Interface Sci. 1993, 155, 70-78. (10) Haidara, H.; Vonna, L.; Schultz, J. J. Adhes. Sci. Technol. 1999, 13, 1393-1403. (11) Stalgren, J. J. R.; Eriksson, J.; Boschkova, K. J. Colloid Interface Sci. 2002, 253, 190-195. (12) Grant, L. M.; Tiberg, F.; Ducker, W. A. J. Phys. Chem. B 1998, 102, 4288-4294. (13) Kumar, N.; Tilton, R.; Garoff, S. Langmuir 2003, 19, 53665373. (14) Fragneto, G.; Lu, J. R.; McDermott, D. C.; Thomas, R. K.; Rennie, A. R.; Gallagher, P. D.; Satija, S. K. Langmuir 1996, 12, 477-486. (15) Thritle, P. N.; Li, Z. X.; Thomas, R. K.; Rennie, A. R.; Satija, S. K.; Sung, L. P. Langmuir 1997, 13, 5451-5458. (16) Lu, J. R.; Thomas, R. K.; Penfold, J. Adv. Colloid Interface Sci. 2000, 84, 143. (17) Subramanyam, R.; Maldarelli, C. J. Colloid Interface Sci. 2002, 253, 377-392. (18) Pan, R.; Green, J.; Maldarelli, C. J. Colloid Interface Sci. 1998, 205, 213-230. (19) Dong, C.; Hsu, C.-T.; Chiu, C.-Y.; Lin, S.-Y. Langmuir 2000, 16, 4573-4580. (20) Meguro, K.; Ueno, M.; Esumi, K. In Nonionic Surfactants; Schick, M. J., Ed.; Marcel Dekker: New York, 1987. (21) Prosser, A. J.; Franses, E. I. Colloids Surf., A: Physicochem. Eng. Aspects 2001, 178, 1-40. (22) Kumar, N.; Couzis, A.; Maldarelli, C. J. Colloid Interface Sci. 2003, 267, 272-285. (23) Sjo¨blom, J.; Stenius, P.; Denielsson, I. In Nonionic Surfactants; Schick, M. J., Ed.; Marcel Dekker: New York, 1987. (24) Nagarajan, R.; Ruckenstein, E. Langmuir 1991, 7, 2934-2969.

10.1021/la035310k CCC: $27.50 © 2004 American Chemical Society Published on Web 04/28/2004

Scaling of Adsorption Isotherms

To fill this void for hydrophobic solid-water (SW) interfaces, we have measured adsorption isotherms for various CIEJ surfactants (I ) 10-14, J ) 3-8) on selfassembled monolayers (SAM) of octadecyltrichlorosilane (OTS). When deposited on polished silica surfaces, OTS SAMs result in uniform and chemically homogeneous hydrophobic surfaces.32 The comparison of adsorption isotherms reveals a systematic effect of the surfactant molecular structure on self-assembly at the SW interface. The results for the SW interface are compared with available literature data for the AW interface. The surfactant molecular structure has a similar effect on both AW and SW interfaces. A strong relationship between self-assembly in bulk solution and SW interface is evident from the existence of a common adsorption isotherm for all surfactants in the CIEJ series. In the accompanying paper, a unified model for self-assembly in solution and at hydrophobic interfaces is developed and compared with the experimental results obtained in this paper. 2. Experimental Section 2.1. Materials. Octadecyltrichlorosilane (OTS, CH3(CH2)17SiCl3, (95% purity)), HPLC-grade hexadecane, and chloroform were purchased from Sigma Aldrich Co. Nochromix and sulfuric acid (98%) were purchased from Fischer Scientific. C10E3, C10E6, C12E3, C12E4, C12E6, C12E8, and C14E3 were purchased from Fluka, Inc. The manufacture’s specified purity for all surfactants was greater than 99%. All chemicals were used as received without any further purification. All water was purified by a Millipore Milli Q Plus system and had resistivity of 18 MΩ cm. Polished single-crystal silicon wafers were purchased from International Wafer Service. 2.2. Preparation of Hydrophobic Substrates. Prior to the OTS monolayer deposition, silicon substrates were cleaned by sonicating in a mixture of Nochromix and sulfuric acid for 30 min followed by a water rinse. Dry nitrogen was used to dry the substrates. Approximately 20-50 nm thick silicon oxide layers were thermally grown on the Si wafer by baking at 1000 °C in air for 15-20 min prior to the OTS monolayer deposition. The thick oxide layer enhances the sensitivity of the optical reflectometry measurements.33 The substrates were again cleaned with Nochromix and water, followed by drying with nitrogen. The dry substrates were immersed for 30 min in a 4 mM OTS solution prepared in a solvent mixture of hexadecane-chloroform (90:10 by volume). The excess solvent was removed from the substrates by rinsing with chloroform, followed by further sonication in chloroform for approximately 15 min. The OTS monolayers were then heated at 60 °C for approximately 30 min. The monolayer preparation and adsorption experiments were conducted under ordinary laboratory conditions at 25 °C. This procedure ensures the formation of complete and uniform (25) Puvvada, S.; Blankschtein, D. J. Chem. Phys. 1990, 92, 37103724. (26) Vasilescu, M.; Caragheorgheopol, A.; Caldararu, H. Adv. Colloid Interface Sci. 2001, 89-90, 169-194. (27) Penfold, J.; Staples, E.; Tucker, I. J. Phys. Chem. B 2002, 106, 8891-8897. (28) Nagarajan, R. Langmuir 2002, 18, 31-38. (29) Danino, D.; Talmon, Y.; Zana, R. J. Colloid Interface Sci. 1997, 186, 170. (30) Kim, J. H.; Domach, M. M.; Tilton, R. D. J. Phys. Chem. B 1999, 103, 10582-10590. (31) Kim, J. H.; Domach, M. M.; Tilton, R. D. Colloids Surf., A: Physicochem. Eng. Aspects 1999, 150, 55-68. (32) Kumar, N.; Maldarelli, C.; Steiner, C.; Couzis, A. Langmuir 2001, 17, 7789-7797. (33) Tilton, R. D. In Polymer -Colloid Interactions: Techniques and Applications; John Wiley and Sons: New York, 1999; pp 331-363.

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OTS monolayers.32 The advancing and receding angles of water on the hydrophobic substrates were measured to be 105 ( 2° and 95 ( 2°, respectively 2.3. Measurement of Adsorption by Optical Reflectometry. We used optical reflectometry to measure the surfactant adsorption isotherms on OTS monolayers. This technique, based on the change in the interfacial refractive index profile that is caused by adsorption, has frequently been used to determine adsorption of polymers, surfactants, proteins, etc., on thin films prepared atop Si wafers.33,34 We used the instrument described by Furst el al35 and further modified by Velegol et al.36,37 The reader may consult the cited publications for detailed discussions of the technique. The OTS-coated wafer serves as one wall of a rectangular slit flow cell. Water was degassed immediately prior to the experiment by boiling and quenching. Before introducing the surfactant solution to the flow cell, degassed water was passed over the substrate for a few hours while monitoring the reflectivity to determine whether any surface-active impurities are present or any OTS desorbs from the SAM. Substrates that did not produce a constant reflectivity during this initial pure water rinse were abandoned. The equilibrium surface excess concentration (Γ) at a particular bulk solution concentration was determined from the reflectivity 10-15 min after the signal had reached a constant value. Surface excess concentrations at different bulk concentrations were obtained by sequentially flowing solutions with different concentrations. Most of the surface excess concentration data was obtained with the incident p-polarized laser beam fixed in the Brewster Angle configuration. The accuracy of results measured at fixed incident angles was verified by measuring reflectivity as a function of incident angle at a particular surface concentration in a manner described by Pagac et al.38 The values of surface concentration from scanning angle measurements and fixed angle measurements were usually within 5% of each other. To verify the reversibility of adsorption, we varied the sequence in which we changed the bulk solution concentration. The surface excess concentration at any particular bulk concentration was found to be independent of the prior adsorption history on the surface. The same procedure was followed for every surfactant. This verified that the self-assembly of these surfactants on the OTS SAM is reversible and that the adsorption isotherms reported here are equilibrium isotherms. The following values of optical constants were used to calculate surface excess concentrations from optical reflectometry data. Refractive indices of silicon oxide, water, and silicon are 1.46, 1.333, and 3.882+0.019i, respectively.35 The values of dn/dC for all surfactants, except C14E3 were taken from Chiu et al.39 dn/dC for C14E3 was obtained by extrapolating dn/dC values of C10E3 and C12E3. Surfactant solutions in all cases were sufficiently dilute that their refractive indices did not differ significantly from pure water. (34) Berglund, K. D.; Przybycien, T. M.; Tilton, R. D. Langmuir 2003, 19, 2705-2713. (35) Furst, E. M.; Pagac, E. S.; Tilton, R. D. Ind. Eng. Chem. Res. 1996, 35, 1566-1574. (36) Velegol, S. B.; Tilton, R. D. Langmuir 2001, 17, 219-227. (37) Velegol, S. B.; Tilton, R. D. J. Colloid Interface Sci. 2002, 249, 282-289. (38) Pagac, E. S.; Prieve, D. C.; Tilton, R. D. Langmuir 1998, 14, 2333-2342. (39) Chiu, Y. C.; Chen, L. J. Colloids Surf. 1989, 41, 239.

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3. Results and Discussion The choice of the hydrophobic surface is extremely important as the surface chemistry and hydrophobicity play a major role in interfacial self-assembly.12,40,41 As mentioned in the Introduction, silane SAMs have been used as model hydrophobic surfaces that are chemically homogeneous and smooth.32,42-46 Fragneto et al.14 and Thritle et al.15 used hydrophobic UTS (Undedecyltrichlorosilane, CH2dCH-(CH2)8SICl3) and OTS SAMs as hydrophobic surfaces to study the structure of densely packed layers of various CIEJ surfactants. When self-assembled on silica surfaces, the silane end of the molecules adhere to the silica surface, forming monolayers with the hydrocarbon chains aligned almost normal to the surface. The hydrocarbon chains are packed densely on the surface. The main advantage offered by the silane monolayers over other hydrophobic surfaces, such as polymer films, is that they could be deposited freshly on silica surfaces with very high reproducibility. SAMs deposited over clean and smooth surfaces are chemically homogeneous and have a roughness similar to that of the substrate (∼1-5Å in the case of polished silicon wafers).32 At equilibrium, the chemical potential of surfactant molecules present in bulk as monomers, or in aggregates, or on interfaces should be same. Below the critical aggregation concentration (CAC), the chemical potential of surfactant in solution is given by µ0B + kT ln X, where X is the mole fraction of surfactant in bulk solution. The surfactant concentration in solution is so low that the solution can be treated as an ideal solution. Above the CAC, the chemical potential of surfactant does not vary significantly. Thus, all adsorption isotherm data in this paper are shown with a logarithmic scale for bulk solution concentration up to and including the CAC. Equilibrium thermodynamics requires that the surfactant’s assembly on the SW interface be reversible. In the Experimental Section we discussed the procedure adapted to confirm the reversibility of adsorption on OTS surfaces. Figure 1 shows the adsorption isotherms of C10E3, C12E3, and C14E3. The adsorption isotherms of C10E6 and C12E6 are shown in Figure 2. The two figures demonstrate the effect of the number of carbons in the hydrophobic group (I). The adsorption isotherms of all surfactants exhibited some common features. No abrupt changes in slope are observed for any surfactant. Below the CAC, Γ increases monotonically with bulk concentration (C). The value of Γ, attained at the CAC above which the surfactant chemical potential becomes independent of bulk concentration, is defined as the maximum surface concentration (Γmax) or maximum packing. The minimum area per unit molecule (Amin) is defined as (Amin ) 1/Γmax). The values of Amin and Γmax for all surfactants are summarized in Table 1. The plot of Amin vs I for CIE3 and CIE6 surfactants is shown in Figure 3. Figure 3 also shows the values of Amin for various CIEJ surfactants on UTS monolayers (40) Johnson, R. A.; Nagarajan, R. Colloids Surf., A: Physicochem. Eng. Aspects 2000, 167, 21-36. (41) Johnson, R. A.; Nagarajan, R. Colloids Surf., A: Physicochem. Eng. Aspects 2000, 167, 37-46. (42) Richter, A. G.; Yu, C. J.; Datta, A.; Kmetko, J.; Dutta, P. Colloids Surf., A: Physicochem. Eng. Aspects 2002, 198-200, 3-11. (43) Lee, S.-W.; Mao, C.; Flynn, C. E.; Belcher, A. M. Science 2002, 296, 892-895. (44) Kojio, K.; Tanaka, K.; Takahara, A.; Kajiyama, T. Bull. Chem. Soc. Jpn. 2001, 74, 1397-1401. (45) Yang, X. M.; Peters, R. D.; Kim, T. K.; Nealey, P. F.; Brandow, S. L.; Chen, M.-S.; Shirey, L. M.; Dressick, W. J. Langmuir 2001, 17, 228-233. (46) Richter, A. G.; Yu, C. J.; Datta, A.; Kmetko, J.; Dutta, P. Phys. Rev. E: Stat. Phys., Plasmas, Fluids, Relat. Interdiscip. Top. 2000, 61, 607-615.

Figure 1. Adsorption isotherms of C10E3 (O), C12E3 (∆), and C14E3 (b) showing the effect of the hydrophobic group. CAC is indicated by arrows.

Figure 2. Adsorption isotherms of C12E6 (0) and C10E6 (∇). CAC is indicated by arrows. Table 1. Bulk and Interfacial Self-Assembly Characteristics C12E3 C12E4 C12E6 C12E8 C10E3 C14E3 C10E6

CAC51 (mol/L)

Γmax (mol/m2)

Amin (Å2/molecule)

5 × 10-5 6.4 × 10-5 8.7 × 10-5 10 × 10-5 4.6 × 10-4 6.3 × 10-6 8.9 × 10-4

6.03 ( 0.1 × 10-6 3.28 ( 0.1 × 10-6 3.17 ( 1 × 10-6 2.1 ( 0.1 × 10-6 4.86 ( 0.2 × 10-6 6.14 ( 0.1 × 10-6 2.78 ( 0.1 × 10-6

27.5 ( 0.5 50.5 ( 1.5 52.3 ( 1.6 75.0 ( 3.5 34.1 ( 1.4 27.0 ( 0.5 59.6 ( 2.1

measured by Thritle et al.,15 whose values are in excellent agreement with ours. For the CIE3 series, Amin decreases, i.e., surfactant self-assembles more densely, as I increases from 10 to 12. Further increase in hydrocarbon chain length from 12 to 14 does not significantly change Amin. For the CIE6 series, Amin decreases as I increases from 10 to 12. Further increase in I from 12 to 14 increases Amin. Finally, as I increases from 14 to 16, there is no significant change in Amin value. The surface activity of a surfactant is a measure of the ability of the surfactant to assemble on a hydrophobic interface. A more surface-active surfactant would achieve a certain surface concentration at a lower bulk concentration. Figures 1 and 2 show a systematic change in surface activity with changes the in the structure of the hydro-

Scaling of Adsorption Isotherms

Figure 3. Plot of Amin (Å2/molecule) as a function of the length of the hydrophobic group (I) for various CIE3 and CIE6 surfactants; (b) present work for CIE6; (2) present work for CIE3; (O) CIE6, data from Thritle et al.15

phobic group. An increase in I results in higher surface activity for the CIE3 as well as the CIE6 series. The solubility of the hydrophobic group decreases with increasing I. Thus, the free energy decrease that occurs as the surfactant assembles on the hydrophobic interface increases with I, and therefore, the surface activity increases.47 When I increases from 10 to 12 or 12 to 14, the bulk concentration at which a certain surface excess concentration is achieved is reduced by a factor of approximately 10. This effect of an increase in chain length on the self-assembly on the SW interface is similar to the self-assembly in bulk2 and on the AW interface.19,48,49 The surface activity for AW interface also increases by a factor of approximately 10 with two-carbon increase in hydrophobic chain.20,50 The CAC also decreases by a factor of approximately 10 with an increase of 2 carbon atoms in the hydrocarbon chain (Table 1).20,51 The effect of changes in the hydrophilic group is shown in Figure 4, where the adsorption isotherms for four surfactants in the C12EJ series, C12E3, C12E4, C12E6, and C12E8, are shown. Similar to the isotherms for the CIE3 and CIE6 series shown in Figures 1 and 2, the isotherms for the C12EJ series increase monotonically up to the CAC. Figure 5 and Table 1 show the values of Amin for different C12EJ surfactants. Figure 5 also shows the values of Amin for C12EJ surfactants measured by Thritle et al.15 and Fragneto et al.14 Their results for C12E4, C12E6, and C12E8 agree very well with our results. As the length of the hydrophilic ethoxylate chain (J) decreases, Amin decreases systematically and Γmax increases. All surfactants with the exception of C12E6 follow this pattern. Due to the steric repulsion among the ethoxylate chains, surfactants with larger J have a larger headgroup area, and as a result they pack less densely compared to the surfactants with smaller J.47 As with variation in I, we see systematic changes in the surface activity with variation of J. The adsorption isotherms of C12E4 and C12E6 almost overlap with each (47) Kumar, N.; Garoff, S.; Tilton, R. Langmuir 2004, 20, 44524464. (48) Hsu, C.-T.; Chang, C.-H.; Lin, S.-Y. Langmuir 1999, 15, 19521959. (49) Karakashev, S. I.; Manev, E. D. J. Colloid Interface Sci. 2002, 248, 477-486. (50) Sokolowski, A.; Burczyk, B. J. Colloid Interface Sci. 1983, 94, 369. (51) Huibers, P. D. T.; Lobanov, V. S.; Katritzky, A. R.; Shah, D. O.; Karelson, M. Langmuir 1996, 12, 1462-1470.

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Figure 4. Adsorption isotherm of C12EJ series exhibiting the effect of hydrophilic PEO chain: (∆) C12E3, (∇) C12E4, (0) C12E6, (]) C12E8. CAC is indicated by arrows.

Figure 5. Plot of Amin vs J for C12EJ surfactants: (0) present work, (2) Thritle et al. and Fragneto et al.

other. The adsorption isotherm of C12E8 is below the isotherm of C12E6. The relative position of adsorption isotherms shows that C12E3 is the most surface active. C12E4 and C12E6 have almost identical surface activities. C12E8 is the least surface active. Similar results are predicted by the model that we have developed in the accompanying paper.47 While some attempts have been made to relate the selfassembly in solution and on hydrophobic interface,40 definite experimental evidence for this elusive connection is not available in the literature. Our results show that the changes in the molecular structure of surfactants result in similar changes in surface activity and CAC. Considering this, it is natural to make an attempt to connect the adsorption isotherms with CAC by scaling the adsorption isotherms for different surfactants shown in Figures 1, 2, and 4. A rescaled bulk concentration C* is defined as C* ) C/CAC, and a rescaled surface concentration is defined relative to the surface concentration at the CAC, Γ* ) Γ/Γmax. The values of Γmax and CAC are shown in Table 1. The rescaled isotherms are shown in Figure 6. It is particularly notable that although the raw isotherms for all the surfactants span a wide range of bulk and surface concentrations (Figures 1,2, and 4), the rescaled isotherms

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Figure 6. Rescaled isotherms of various surfactants: (∆) C12E3, (∇) C12E4, (0) C12E6, (]) C12E8, (O) C10E3, (b) C14E3; (- - - -) Langmuir fit, (;;) Frumkin fit. The adsorption isotherms of all surfactants collapse onto the same curve.

collapse onto the same curve. This collapse of the adsorption isotherms onto common isotherm is strong experimental evidence of a very close relationship between the self-assembly in bulk and at a hydrophobic interface. The theoretical model developed in the accompanying paper also predicts this collapse of the adsorption isotherms. The common isotherm of CIEJ surfactants on hydrophobic silane monolayers suggests that all CIEJ surfactants selfassemble on a hydrophobic surface in a similar manner. For practical purposes, the rescaled common isotherm can be fit using some of the common models available in the literature. The Frumkin model is expressed as

C)

Γ ReKΓ/Γ∞ Γ Γ∞ 1Γ∞

(

)

(1)

KΓ*/Γ∞*

Γ* R*e Γ∞* Γ* 1Γ∞*

(

computed from the value of Amin. Figures 3 and 5 show that the value of Amin depends mainly on the number of EO units, J. The value of I does not significantly affect Amin. Later in this paper we show that Amin varies with J as Amin ) 25.4J1/2 Å2/molecule for J ) 4-12. Thus, Γ∞ ) Γ∞*/(25.4 J1/2) ) 1.3/(25.4 J1/2) molecule/Å2 ) 1/(19.5 J1/2) molecule/Å2 The other Frumkin model parameters for any CIEJ (I ) 10-16, J ) 4-12) surfactant in eq 1 could be evaluated as follows

Γ∞ ) 1/(19.5 J1/2) molecule/Å2 )

where K, Γ∞, and R are the model parameters associated with the intermolecular interactions, maximum surface excess concentration, and surface activity, respectively. To fit the rescaled isotherms, the parameters in eq 1 are rescaled as C* ) C/CAC, R* ) R/CAC, Γ∞* ) Γ∞/Γmax, Γ* ) Γ/Γmax.

C* )

Figure 7. Amin for C12EJ surfactants on AW and SW interface: (0) present work for hydrophobic SW interface, (2) Fragneto et and Thritle et al.14,15 on hydrophobic SW interface, (O) AW interface by Lu et al.16 Solid line is a fit to Amin on SW interface data by Amin ) 25.4 J1/2 Å2. Dashed line is fit to Amin on AW interface by Amin ) 22.2 J1/2 Å2.

)

(2)

We would like to point out important differences between Γ∞ and Γmax. Γmax is the maximum surface excess concentration physically attained at CAC. Γ∞ is the molecular packing parameter that signifies the maximum surface excess concentration achievable only at infinite surfactant concentration. Thus, Γ∞ is the physically unrealizable surface excess concentration. The Langmuir model is a specific case of the Frumkin model where K ) 0. The rescaled isotherm data in Figure 6 is fitted by ℵ2 minimization using C* and Γ* as experimental measurements and R*, K, and Γ∞* as model parameters. The best fits to the Langmuir and Frumkin models are also shown in Figure 6. The Frumkin model provides a more satisfactory fit to the experimental data. The model parameters for the Frumkin model are ln(R*) ) -5.53, Γ∞* ) 1.3, K ) 5.52. Because the value of Γ∞ was scaled by Γmax () 1/Amin), the packing parameter for any CIEJ surfactant could be

8.49 × 10-6 J-1/2 mol/m2 K ) 5.53 R ) (CAC)e-5.3

(3)

With these parameters and experimentally determined CAC of any other CIEJ surfactant,51,52 the adsorption isotherm for any member of the CIEJ series could then be predicted. In the Introduction we mentioned that the same types of intermolecular forces drive nonionic surfactant selfassembly on both AW and hydrophobic SW interfaces. Therefore, one may expect their self-assembling characteristics to be similar on SW and AW interfaces. In Figure 7 we compare the values of Amin for various C12EJ surfactants on the AW interface that were obtained using neutron reflectivity by Lu et al.16,53 This figure also shows the values of Amin for C12EJ surfactants on hydrophobic SW interfaces that are shown in Figure 5. We have not plotted the exceptional case of C12E6. For all the CIEJ surfactants, there is a systematic effect of the change in the PEO headgroup both on SW and AW interfaces. The value of Amin is progressively smaller for shorter PEO chains. For all surfactants with J > 3, Amin on the AW interface is less than that on the SW interface. The (52) Rosen, M. J. Surfactants and Interfacial Phenomena; John Wiley & Sons: New York, 1989. (53) Lu, J. R.; Su, T. J.; Li, Z. X.; Thomas, R. K.; Staples, E. J.; Tucker, I.; Penfold, J. J. Phys. Chem B 1997, 101, 10332-10339.

Scaling of Adsorption Isotherms

difference between the values of Amin on AW and SW interface becomes smaller as J decreases. Finally, for C12E3, Amin is less for the SW interface than the AW interface. The Amin for both AW and SW interface can be satisfactorily described by Amin ) FJ1/2. For the AW interface, FAW ) 22.2 ( 0.2 Å2 as shown by the dashed line. This relation fits Amin for all surfactants from J ) 2 to 12. For SW interface, with FSW ) 25.4 ( 1.5Å2 fits the data for all C12EJ surfactants examined except for C12E3. Thus, a similar scaling law with respect to the length of the ethoxylate chain is followed on AW and SW interfaces. While the square-root scaling of Amin has been reported previously for AW interface,54 to our knowledge this is the first time similar scaling behavior has been established for hydrophobic solid-water interface. The C12EJ surfactants (with J > 3) assemble more densely on the AW interface than on the SW interface. This can be attributed to the fact that hydrocarbon chains are able to penetrate out of the aqueous environment at the AW interface but not at the rigid SW interface. At the SW interface, a significant amount of water molecules remain mixed in the adsorbed surfactant layer.14,15,47 The chemistry of the surface has a large effect on surfactant self-assembly on solid interfaces. The CIEJ surfactants have been observed to form aggregates, e.g., hemi-micelles, etc, on solid hydrophilic surfaces, such as silica, instead of uniform monolayers.12,41,55 On such surfaces, the formation of aggregates below the CAC is attributed to strong interactions between ethoxylate chains and solid surface. The formation of surface aggregates usually results in an abrupt change in the slope of the adsorption isotherms.12,55,56 For planar and uniform hydrophobic surfaces, the direct evidence12,14,15 as well as indirect evidence40 show that the CIEJ surfactants selfassemble as a uniform layer. Our results also confirm this conclusion. None of the adsorption isotherms for the surfactants we studied showed any abrupt change in slope within the concentration range examined (0.005-1 CAC). The surface excess concentration increases smoothly with the bulk concentration. The absence of any abrupt change and more importantly a common isotherm for all surfactants, irrespective of their molecular structure, are consistent with the self-assembly of CIEJ surfactants as uniform monolayers on hydrophobic silane monolayers. In Figures 3 and 5 we observed that C12E6 does not follow the pattern followed by the other surfactants. In (54) Sedev, R. Langmuir 2001, 17, 562-564. (55) Tiberg, F. J. Chem. Soc., Faraday Trans. 1996, 92, 531-538. (56) Li, B.; Ruckenstein, E. Langmuir 1996, 12, 5052-5063.

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Figure 3 a minimum in Amin is observed for C12E6 in CIE6 homologous series. In Figure 5 for the C12EJ series, Amin for C12E6 is lower than the expected from the J1/2 scaling followed by other surfactants. On the AW interface, C12E6 does not show any unusual behavior. This unusual characteristic of C12E6 could be regarded as some experimental error at first glance. However, the comparison of our maximum packing results with those of Thritle et al. and Fragento et al. (Figures 3 and 5) shows the excellent agreement between results obtained by two very different experimental techniques that respond to different characteristics of the adsorbed layers (optical reflectometry and neutron reflectometry). Thus, the unusually low value of Amin for C12E6 on hydrophobic silane monolayers interface is evidently correct. The reason for this exceptional behavior of C12E6 is not yet clear. 4. Conclusion The adsorption isotherms for CIEJ surfactants at hydrophobic solid-water interfaces show a systematic variation with the sizes of the hydrophobic and hydrophilic groups. Surfactants with larger hydrophobic groups have lower CAC, are more surface-active, and adsorb on the SW interface to a higher surface concentration. On the other hand, surfactants with a larger hydrophilic group are less surface-active and adsorb on SW interface to a lower surface concentration. For any CIEJ surfactant, the hydrophilic ethoxylate group mainly controls the maximum surface concentration. The minimum area per molecule follows a square-root relationship with J. CIEJ surfactants follow similar scaling with J on hydrophobic SW and AW interfaces. All CIEJ surfactants examined, with the exception of C12E3, assemble to a higher surface excess concentration on the AW interface than on the hydrophobic SW interface. The adsorption isotherms for all the CIEJ surfactants collapse onto a single common isotherm when the bulk and surface concentrations are rescaled with the respective values at CAC. This shows that there is a direct relationship between the selfassembly in bulk and on interfaces. In the accompanying paper, we develop a model to predict the self-assembly of CIEJ surfactants in bulk solution as well as at both AW and hydrophobic SW interfaces. The model predictions compare favorably with the experimental results of this paper. Acknowledgment. The authors would like to thank Air Products and Chemicals, Inc. for their financial support. LA035310K