Redox-Dependent Surface Tension and Surface Phase Transitions of

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Redox-Dependent Surface Tension and Surface Phase Transitions of a Ferrocenyl Surfactant: Equilibrium and Dynamic Analyses with Fluorescence Images Sammy S. Datwani,‡,§ Van Nguyen Truskett,‡,| Craig A. Rosslee,† Nicholas L. Abbott,† and Kathleen J. Stebe*,‡ Department of Chemical Engineering and Department of Materials Science and Engineering, The Johns Hopkins University, Baltimore, Maryland 21218, and Department of Chemical Engineering, University of Wisconsin, Madison, Wisconsin 53706 Received September 26, 2002. In Final Form: June 9, 2003 The surface tension data for the surfactant Fc-CH2-N+(CH3)2-(CH2)14CH3-Br- (where Fc represents the ferrocenium cation) display the signatures of a surface gaseous-surface liquid expanded transition with binodals that depend on the oxidization state of the Fc headgroup. The phase transition is imaged using fluorescence microscopy. The equilibrium and dynamic surface tension data (obtained by the pendant bubble method) are analyzed in terms of an equilibrium model that accounts for surface phase transitions and electrostatic interactions and a dynamic model that accounts for the mass transfer kinetics of surfactant adsorption to the interface. The dynamic surface tension of the reduced form of the surfactant is controlled by bulk diffusion to the interface. The dynamic surface tension of the oxidized form of the surfactant is diffusion-controlled at dilute concentrations, but not at more elevated concentrations where adsorptiondesorption barriers are important. The kinetic constants are determined from these data, yielding an adsorption kinetic constant β ) 9.2 × 10-1 m3/(mol s) and a corresponding desorption kinetic constant R ) 1.9 × 10-6 s-1. This value for β is similar to those found for poly-ethoxylated surfactants, but the desorption kinetic constant is slower, indicating that desorption of this surfactant is highly hindered.

1. Introduction Active control over surface tension can be achieved by altering a reactive surfactant in situ to create a molecule that differs in surface activity from the original molecule. Such control can be achieved by reacting a redox-active group incorporated into the molecule using electrochemical techniques,1-3 or by optically addressing a surfactant with a light-sensitive reactive site which can be reversibly altered.4 The rate of response of the surface tension to a change in a reactive surfactant is controlled not only by the reaction rate itself but also by the rates of surfactant exchange between the interface and the bulk solution. When they are rate limiting, these transport rates determine the rate of response of the surface tension. The active control of surface tension has widespread potential applications. For example, redox-active surfactants have been used to generate Marangoni stresses to pump fluids in microfluidic channels.5,6 Optically reactive surfactants have been used to deposit drops on demand4 by reducing the surface tension to cause droplets to detach when desired. * To whom correspondence should be addressed. E-mail: kjs@ jhu.edu. Phone: (410) 516-7760. Fax: (410) 516-5510. † University of Wisconsin. ‡ The Johns Hopkins University. § Present address: Eksigent Technologies, 2021 Las Positas Ct., Suite 16, Livermore, CA 94550. | Present address: Molecular Imprints Inc., 1807-C W. Baker Lane, Austin, TX 78758. (1) Gallardo, B. S.; Metcalfe, K. L.; Abbott, N. L. Langmuir 1996, 12, 4116. (2) Gallardo, B. S.; Hwa, M. J.; Abbott, N. L. Langmuir 1995, 11, 4209. (3) Abbott, N. L. Prog. Polym. Sci. 1997, 103, 300. (4) Shin, J.; Abbott, N. L. Langmuir 1999, 15, 4404. (5) Gallardo, B. S.; Gupta, V. K.; Eagerton, F. D.; Jong, L. I.; Craig, V. S.; Shah, R. R.; Abbott, N. L. Science 1999, 283, 57. (6) Bennett, D. E.; Gallardo, B. S.; Abbott, N. L. J. Am. Chem. Soc. 1996, 118, 6499.

In this work, the dynamic surface tension of the surfactant Fc-CH2-N+(CH3)2-(CH2)14CH3-Br- (where Fc indicates the ferrocenyl headgroup) is studied as a function of redox state using pendant bubble tensiometry.7 The equilibrium and dynamic surface tension data exhibit signature behavior for a surfactant undergoing a surface phase transition from the surface gaseous to the liquid expanded state.8 This phase change is confirmed using fluorescence microscopy.9,10 The pendant bubble data are analyzed using a surface equation of state which is appropriate for charged surfactants undergoing a surface phase change, that is, the Davies equation augmented with a second virial coefficient to capture nonelectrostatic attractive interactions.11,12 A Maxwell construction is performed on this equation of state to locate the surface binodals, allowing this single surface equation of state to be applied to the surface tension in the gaseous (G), coexistence, and liquid expanded (LE) states.13 Since these binodals change in a pronounced manner with the redox state of the surfactant, the state of the monolayer can be changed by oxidation of the surfactant. The dynamic surface tension has a prolonged induction period before the surface tension reduces. The length of this induction period corresponds to the time required for the surface concentration to pass through G-LE coexistence, so the surface concentration at the end of this period corresponds to the surface binodal concentration for the LE state. The length of the induction time is compared to that predicted for a diffusion-controlled model for the surface tension evolution, which agrees well with the (7) Lin, S.; McKeigue, K.; Maldarelli, C. AIChE J. 1990, 36, 1785. (8) Lin, S. Y; McKeigue, K.; Maldarelli, C. Langmuir 1991, 7, 1055. (9) Henon S.; Meunier, J. J. Chem. Phys. 1993, 98, 9148. (10) Pollard, M. L.; Pan, R.; Steiner, C.; Maldarelli, C. Langmuir 1998, 14, 7222. (11) Davies, J. T. Proc. R. Soc. London 1958, 245, 417. (12) Davies, J. T. Proc. R. Soc. London 1958, 245, 429. (13) Ferri, J. K.; Stebe, K. J. J. Colloid Interface Sci. 1999, 209, 1.

10.1021/la020813w CCC: $25.00 © 2003 American Chemical Society Published on Web 09/03/2003

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Figure 2. Pendant bubble apparatus setup. A pendant bubble is formed in a surfactant solution placed in the path of a collimated beam of light. The bubble silhouette is projected onto a CCD camera, digitized, and stored for analysis. The chemical structure of FcCH2N+(CH3)2(CH2)14CH3Br- was characterized by 1H NMR (DMSO): 4.5 (2H, Fc-CH2-N(CH3)2), 4.4 (4H, Hferrocene), 4.2 (5H, Hferrocene), 3.1 (2H, N(CH3)-CH2), 2.8 (6H, N(CH3)2), 1.7 (2H, CH2-CH2), 1.2 (24H, CH2-CH2-CH2), 0.85 (3H, CH2-CH3). EI-MS: m/z 454.2 ((M - Br)+). Purity was confirmed by the absence of minima in the surface tension plots of FcCH2N+(CH3)2(CH2)15CH3Br- and Fc+CH2N+(CH3)2(CH2)15CH3Br-. 2.2. Electrochemistry. The surfactant S+ was oxidized to S2+ using standard electrochemical procedures which are described briefly here. The reversible redox reaction of the surfactant headgroup that is exploited is

Fc0 H Fc+ + eFigure 1. (a) Chemical structures of Fc-CH2-N (CH3)2(CH2)14-CH3, termed S+ and S2+, for the reduced and oxidized forms, respectively. (b) Rotating disk voltammogram for a platinum rotating disk electrode in 1.0 × 10-6 mol/cm3 solution for a rotating rate w ) 500 rpm and a scan rate v ) 10 mV/s for the surfactant S+ (Fc-CH2-N+(CH3)2-(CH2)14-CH3Br-).

(1)

+

experiments for the reduced form of the surfactant. The induction time for the oxidized form of the surfactant agrees well with a pure diffusion-controlled model at dilute concentrations but becomes far longer at more elevated concentrations as adsorption-desorption barriers become important. Applying a pure kinetic-controlled model at elevated concentrations allows the kinetic constants for the surfactant in the oxidized state to be evaluated. The behavior of the ferrocenyl surfactant studied here can be compared in terms of its latitude in controlling surface tension and its dynamics to previous studies, in which ferrocene was incorporated at the opposite end of a quaternary amine surfactant to create a bolaform surfactant.2 2. Materials and Methods 2.1. Surfactant Synthesis. The surfactant S+ (Fc-CH2N+(CH3)2-(CH2)14-CH3Br-; Fc ) [η5-C5H5]Fe[η5-C5H5]) was synthesized by mixing 1-bromopentadecane (Aldrich) and (dimethylaminomethyl) ferrocence (Aldrich) on a 1:1 mole basis and keeping the mixture under constant reflux at 55-60 °C for 2 h. The chemical structures of the oxidized and reduced form of this molecule are presented in Figure 1a. Reflux was performed in a nitrogen atmosphere to minimize the formation of any oxidized byproduct, S2+ (Fc-CH2-N+(CH3)2-(CH2)14-CH3Br-; Fc ) [η5-C5H5]Fe+[η5-C5H5]). Purification was achieved by repeated recrystallization of S+ with acetone (Fisher Scientific) until no further change in the equilibrium surface tension of aqueous solutions of S+ was obtained.

where Fc0 denotes the electrically neutral ferrocene molecule and Fc+ denotes the ferrocenium cation. The reaction vessel is a two-compartment fritted glass cell with a platinum gauze electrode (5.0 cm × 5.0 cm, 52 mesh, Alfa Aesar) contained in each compartment. A solution of S+ was placed in one compartment. The second compartment was filled with 100 mM Li2SO4 solution, pH 2.0. The surfactant S+ was oxidized to S2+ by application of an oxidizing potential to the working electrode placed in the surfactant solution. Figure 1b is a cyclic voltammogram (CV) performed over the voltage range of interest for a 1 mM solution conducted at a 1.6 mm diameter platinum disk electrode versus a saturated calomel electrode (SCE). The CV shows the half wave potential to be ∼485 mV. This CV was used to select the oxidizing potential (300 mV), which was well below the oxidation potential for water. The oxidizing potential was controlled using a potentiostat (Bioanalytical Systems) and a saturated Ag/AgCl (3000 mM NaCl) reference electrode. Application of 300 mV to the Pt gauze electrode immersed in a solution of 1.0 × 10-6 mol/cm3, 100 mM Li2SO4, pH 2.0, for 6 h caused the surfactant S+ to oxidize to S2+. The solution undergoes a gradual visible color change from yellow (reduced) to green and, eventually, to blue (oxidized). To ensure that the surfactant solution was completely oxidized, the equilibrium surface tensions of surfactant solutions of S2+ were measured until no change occurred with further application of an oxidizing potential. All surfactant solutions were prepared in the reduced state in 100 mM Li2SO4 titrated to pH 2.0 with H2SO4 using filtered and deionized water (Millipore). To limit oxidation of S+ to S2+ in air, all solutions were degassed with filtered nitrogen before surfactant was added. The surfactant and all aqueous surfactant solutions were stored in a nitrogen environment. 2.3. Surface Tension Measurement. The surface tension evolution caused by the adsorption of the ferrocenyl surfactant Fc-CH2-N+(CH3)2-(CH2)14-CH3Br- in aqueous solution was studied for the surfactant in both the reduced and oxidized states using the pendant bubble technique. The pendant bubble apparatus is shown in Figure 2. A quartz cell is filled with the surfactant and electrolyte solution. This cell is aligned perpen-

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dicularly to a collimated beam of visible light. A bubble is rapidly formed at the tip of a Teflon-coated stainless steel inverted needle which is immersed in the surfactant/electrolyte solution. The collimated beam of light casts a silhouette of the bubble onto a CCD camera; using the camera and a frame grabber, digital images of the bubble silhouette are obtained. The locus of the bubble shape is determined using an edge detection routine and matched to a numerical solution of the Young-Laplace equation to determine the surface tension. For dynamic surface tension experiments, a bubble is formed rapidly and the CCD camera is set to record images at given time intervals. The surface tension corresponding to each image is determined. The long-time asymptotes of the surface tension profiles are reported as the equilibrium surface tension. When the surfactant was studied in its reduced valence state, the pendant bubble experiments were performed under a nitrogen atmosphere to prevent surfactant oxidation. 2.4. Fluorescence Microscopy. The growth of the LE state to cover the interface during the induction period was made visible using fluorescence microscopy. The interface of the surfactant solution was first aspirated to remove any initially adsorbed surfactant. A fluorescent dye, 4-hexadecylamino-7-nitrobenz-2oxa-1,3-diazole (NBD-HDA, obtained from Molecular Probes) was then spread from chloroform onto the interface at approximately 5000 Å2 per molecule, an area per molecule orders of magnitude in excess of that for which this probe would fluoresce because of its own G-LE transition.14 When excited at a wavelength of 488 nm from an argon ion laser (Spectra Physics), this dye fluoresces when in contact with disordered hydrophobes and is quenched when in contact with water. The visualization technique relies on sequestering the fluorophore among the disordered liquid hydrocarbon environment provided by the disordered tailgroups in the LE state. In regions of the interface covered in the G state, the fluorophore is quenched by contacting with water between the sparse chains. In monolayers that can form surface states that are more highly ordered than the LE state (e.g., LC or S states), the fluorophore is expelled by the ordered hydrocarbon chains and therefore does not fluoresce in those states. The ferrocenyl surfactants studied here cannot form these more highly ordered states because of their bulky headgroups and their net charge. Therefore, the evolution from a dark surface to a bright surface of the excited fluorophore corresponds to the growth of the LE phase as the surfactant adsorbs on the interface. Fifteen minutes was allowed to elapse before images of the interface were acquired in order to allow the chloroform to evaporate after spreading the dye. Images were acquired using an epifluorescence microscope (Karl Zeiss) equipped with a 10× objective which projected the image onto a CCD camera (XC-77 Hamamatsu). Digitized images were captured on a PC equipped with an imaging board (PIXCI-SV) and analyzed using XCAP software (Epix).

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Figure 3. The equilibrium surface tension isotherms of the reduced form (S+) of Fc-CH2-N+-(CH3)2-(CH2)14-CH3 (squares) and the oxidized form (S2+) of Fc-CH2-N+-(CH3)2(CH2)14-CH3 (circles). The surface equation of state fit to the equilibrium data (constants in Table 1). The dashed line indicates the reduced fit, and the symbol / indicates the coexistence concentration. The solid line indicates the oxidized fit, and the symbol † represents the coexistence concentration.

3. Results and Discussion 3.1. Equilibrium Surface Tension Data. The equilibrium surface tension γ for (Fc-CH2-N+(CH3)2-(CH2)14CH3Br-) is presented in Figure 3 as a function of bulk concentration of surfactant C1∞ for the surfactant in both the reduced (S+) and oxidized (S2+) states. These data clearly demonstrate the potential of these molecules to be used in active control of the surface tension. For example, at a bulk concentration of 3.0 × 10-7 M, the change in redox state creates a 15 mN/m difference in the equilibrium surface tension. Another feature apparent in these data is that the surface tension remains elevated at dilute concentrations and drops steeply at elevated concentrations. The concentration at which these steep drops occur is a strong function of the redox state, and the slope of these curves beyond that point also differs with the redox state. 3.2. Dynamic Surface Tension Data, the Induction Period, and G-LE Phase Transitions. In Figure 4, (14) Lucassen, J.; Akamatsu, S.; Rondelez, F. J. Colloid Interface Sci. 1991, 144, 434.

Figure 4. (a) The family of dynamic surface tension relaxations of S+. The fastest to slowest relaxations correspond to surfactant concentrations of 5.0 × 10-7, 1.0 × 10-7, 1.0 × 10-8, 5.0 × 10-9, 2.0 × 10-9, 1.0 × 10-9, and 5.0 × 10-10 mol/cm3, respectively. (b) The family of dynamic surface tension relaxations for S2+. The fastest to slowest relaxations correspond to surfactant concentrations of 5.0 × 10-7, 1.0 × 10-7, 2.0 × 10-8, 1.0 × 10-8, 5.0 × 10-9, 1.0 × 10-9, and 5.0 × 10-10 mol/cm3, respectively.

the dynamic surface tension traces for the reduced S+ and oxidized S2+ forms of the surfactant are presented. In both redox states, the dynamic surface tension shows a prolonged induction period during which the surface tension remains elevated before it drops abruptly. This induction period results from the surfactant passing through the G and coexisting G-LE states as it assembles by adsorption at the air-liquid interface.8 Assuming


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an upward shift of the π-A isotherm and should change the binodal area per molecule for the surfactant as a function of the redox state. In Figure 5b, π is recast in terms of the surface tension versus the time-evolving surface concentration for a soluble surfactant. When an interface is formed in contact with the surfactant solution, adsorption causes the surface concentration to increase from zero. For 0 < Γ < ΓG, the surface tension decreases slightly as adsorption proceeds, where ΓG ) 1/AG. Typically, this decrease in surface tension is small (roughly 0.1 mN/m). Once Γ becomes equal to ΓG, further adsorption drives the interface into the coexistence region. Islands of LE phase form at ΓLE, where ΓLE ) 1/ALE. The surface tension remains fixed as adsorption proceeds until the entire interface is covered with surfactant in the LE phase. Only after this time does the surface tension decrease. Thus, the induction period tind ends when the interface is completely covered with liquid expanded phase, that is,

Γ(t)tind) ) ΓLE

Figure 5. (a) A π-A isotherm for a soluble surfactant undergoing a surface phase transition. ALE corresponds to the area per molecule in the liquid expanded phase, and AG corresponds to the area per molecule in the gaseous phase. (b) Schematic of the γ versus Γ(t) isotherm for a surfactant undergoing a surface phase transition. ΓLE corresponds to the surface concentration in the liquid expanded phase, and ΓG corresponds to the surface concentration in the gaseous phase. (c) A π-A isotherm for the ferrocenyl surfactant in the reduced state (S+, left curve) and oxidized state (S2+, right curve).

monolayer adsorption, the surface pressure π and area per molecule A are given by

π ) γ0 - γ(Γ)

A)

1 Γ

(2)

As A is reduced (i.e., as Γ is increased), π rises weakly for a surfactant which is in the G phase until A equals the binodal area per molecule for this phase, AG. Further compression of the monolayer causes islands of the LE phase to form on the interface at its binodal area per molecule, ALE. For AG < A < ALE, the surface pressure π remains fixed at the coexistence pressure. Finally, when the entire interface is covered with the LE phase, further compression causes the surface pressure to rise steeply (shown schematically in Figure 5a). The greater the surfactant valence, the larger the repulsion between the surfactants at a given area per molecule. This should cause

(3)

For times less than tind, the surface tension remains elevated, close to its initial value. For times greater than tind, the surface tension drops steeply. The induction time for Fc-CH2-N+-(CH3)2-(CH2)14-CH3 in both redox states versus C1∞ is reported in Figure 7. 3.3. Fluorescence Imaging of the Growth of the LE Phase. Fluorescent images of the growing LE phase for the surfactant S2+ throughout the induction period were obtained. Regions of the interface covered with G phase are dark, while those covered in LE phase are bright. The fluorescent images for the surfactant S2+ undergoing the G-LE transition are shown in Figure 6. Islands of LE phase grow on the interface initially covered in G as surfactant adsorbs. The LE phase grows at the expense of the G phase until the interface is entirely bright. The time required for this evolution corresponds to the induction time for this solution; that is, only after the interface is covered in LE state does the surface tension reduce. This confirms the definition of tind in eq 3. 4. Analysis and Discussion 4.1. Equilibrium. The equilibrium data are compared to the augmented Davies equation which accounts for both electrostatic and nonelectrostatic interactions:

Γeq ) Γ∞

βC1∞ R Γeq βC1∞ z1FΨs +K exp + RT Γ∞ R

(

)

(4)

where K is the second virial coefficient describing nonelectrostatic nearest neighbor interactions in the interface, z1 is the valence of the surfactant, F is Faraday’s constant, and Γ∞ and β/R are the maximum packing and the tendency to adsorb at the interface, respectively. The values for K, Γ∞, and β/R are fit to the equilibrium data for both the reduced and oxidized states. These constants are given in Table 1. The surface potential Ψs is related to the surface charge density σ by an extended Gouy-Chapman relationship for nonequivalent species:15

{∑ [ ( ) ]} 4

σ ) zFΓ ) -2(RT)1/2

Ci∞ exp

i)1

-ziFΨs RT

1/2

-1

(5)

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Figure 6. Fluorescence images of S2+ bulk surfactant concentration of 5.0 × 10-10 mol/cm3 depicting the G/LE phase transition. The induction time for the solution is 1 h. Table 1. Equilibrium Parameters for S parameter

reduced

oxidized

z1 Γ∞ (mol/m2) β/R (m3/mol) K κh C1* (mol/m3) AG ) 1/ΓG (Å2/molecule) ALE ) 1/ΓLE (Å2/molecule)

+1 6.78 × 10-6 3.30 × 103 -7.0 28.7 2.43 × 10-4 184 25.8

+2 2.09 × 10-6 4.90 × 105 -7.0 8.7 1.38 × 10-4 392 86.1

where C2∞ is the bulk concentration of the surfactant counterion, and C3∞ and C4∞ are the bulk concentrations of the fully disassociated ions from the added salt (where C3∞ corresponds to the co-ion, and C4∞ to the counterion). The permittivity of water is set to 80 in the simulations. The three fitted parameters (K, Γ∞, and β/R) are obtained by minimizing the error between these data and the augmented Davies equation subject to a Maxwell construction, as explained further below. The surface equation of state for the equilibrium surface tension γeq is

[(

) ( )

-

∫0

Γeq K Γeq γeq ) γ0 + RTΓ∞ ln 1 Γ∞ 2 Γ∞

2

Ψs

on the interface can be estimated by taking the inverse maximum coverage. This calculation indicates that the divalent form of the surfactant spans a larger area per molecule than the reduced form (79.4 versus 24.5 Å2/ molecule at maximum surface coverage). This may correspond to an actual geometric reorientation of the headgroup in the divalent form. (Note that in studies where electrostatic interactions among headgroups are not accounted for explicitly, the effect of electrostatic repulsion is often lumped into a larger effective headgroup area. That is not the case here; in these simulations, headgroup electrostatic repulsions have been explicitly addressed.) The Debye length κ-1 (which is the characteristic thickness of the diffuse double layer formed by charged species in solution) for solution conditions in this study (100 mM Li2SO4, pH 2.0) is 8 Å. A more useful parameter which captures the role of electrostatics in these simulations is the ratio of the adsorption depth hion (which is the characteristic depth below the interface depleted of ionic species) to the Debye length.

κhion ) κ

]

∇Ψ dΨ (6)

The minimum area per molecule of the surfactant adsorbed

Γ∞ 4

(7)

Ci∞ ∑ i)1 This ratio, which decreases with ionic strength, indicates the importance of electrostatic interactions in influencing


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the equilibrium amount of the surfactant adsorbed.15,16 In these simulations, κhion ) 28.7 when the surfactant is in its reduced form and κhion ) 8.7 when the surfactant is in the oxidized form based on the maximum packing parameter for each surfactant. Because the concentration of the surfactant is far less than that of the added salts, this ratio is independent of the surfactant concentration. A negative value for K (in eqs 4 and 6) indicates attractive interactions among the adsorbed surfactants. When these attractions are sufficiently pronounced, the adsorbed surfactant separates into G and LE states.13,17,18 The greater the electrostatic charge, the weaker the net attraction, resulting in an upward shift in the phase bell. A Maxwell construction is applied to eq 6 to locate the binodal surface areas (and hence binodal surface concentrations) and the coexistence surface tension γ* according to

∫AA

G

LE

γ dA ) γ*(AG - ALE)

(8)

The surface tension remains constant at the tie line value γ* for ΓG < Γ < ΓLE, obeying the solid curve in Figure 5a. The coexistence bulk concentration C* is also located by the Maxwell construction as the bulk concentration which is in equilibrium with both the G and LE states according to eq 4. The results from the Maxwell construction fitted to the equilibrium data are shown as the lower solid curve in Figure 5a for the surfactant in the reduced state. If the values for K, Γ∞, and β/R are fixed and the valence is increased from +1 to +2, increased electrostatic repulsion results in an upward shift of the isotherm, as shown by the upper solid curve in Figure 5a. However, because of the larger headgroup area spanned by the oxidized surfactant and the differing surface activity, the phase bell shifts to the right as well as upward. The π-A isotherms which correspond to the values for Γ∞ and β/R fit to the surface tension data in each redox state are presented in Figure 5c. Because of this rightward shift, there is a pronounced difference between the binodals as LE LE a function of redox state, that is, ALE OX > ARED or ΓOX < LE ΓRED. Recall that the induction period in the dynamic surface tension ends once the surface concentration becomes equal to ΓLE. For purely diffusion-controlled mass transfer to the interface, this difference in binodal surface concentrations suggests that the induction period for the oxidized state should be shorter than that for the reduced state at a given bulk surfactant concentration. While this is observed at dilute concentrations, the induction period is far longer for the divalent species at higher concentrations. Below, this trend is analyzed in terms of a kinetic barrier to surfactant adsorption which slows the adsorption of the oxidized form of the surfactant appreciably enough to govern the surfactant transport at high concentrations. 4.2. Diffusion-Controlled Model for the Dynamic Surface Tension. The transient pendant bubble data are modeled for the reduced form of the surfactant assuming diffusion-controlled transport of surfactant to the interface of the bubble, which is approximated as a sphere of radius a.13,15,16 When a bubble is formed in a (15) Datwani, S. S.; Stebe, K. J. J. Colloid Interface Sci. 1999, 219, 282. (16) Datwani, S. S.; Stebe, K. J. Langmuir 2001, 17, 4287. (17) Aratono, M.; Uryu, S.; Hayami, Y.; Motomura, K.; Matuura, R. J. Colloid Interface Sci. 1984, 98, 33. (18) Frumkin, A. Z. Phys. Chem. 1925, 116, 446.

surfactant solution of bulk concentration C1∞, the concentration is initially uniform. Surfactant near the interface adsorbs, depleting the sublayer concentration C1s. This depletion causes surfactant to diffuse toward the interface. For surfactant adsorbing into a single phase at the interface, the surface concentration Γ(t) evolves according to

Γ(t) )

2xD [C xt xπ 1∞

∫0xtC1s(t - τ) dxτ] + t D [C t - ∫0 C1s dτ] a 1∞

(9)

where D is the surfactant diffusivity in solution. This equation relates Γ(t) to the instantaneous surface concentration C1s(t). In the diffusion-controlled limit, the interface is in equilibrium with the instantaneous sublayer concentration. Therefore, Γ(t) and C1s(t) are also related by the adsorption isotherm:

Γ(t) ) Γ∞

βC1s(t) R βC1s(t) z1FΨs(t) Γ(t) +K exp + RT Γ∞ R

(

)

(10)

and the surface potential Ψs evolves in equilibrium with the surface charge density according to

σ(t) ) zFΓ(t) )

{∑ [ (

-2(RT)1/2

4

i)1

Cis(t) exp

) ]}

-z1FΨs(t) -1 RT

1/2

(11)

subject to the initial conditions that

C1s(t)0) ) Γ(t)0) ) 0

(12)

In this treatment, the surfactant diffusion is assumed to be rate limiting. The diffusion of counter- and co-ions in solution is assumed to be rapid.15,19 When the interface is formed, C1s and Γ increase monotonically from zero according to eqs 9-12, and the surface tension reduces in equilibium with the adsorbed surface concentration according to eq 6. This proceeds until Γ ) ΓG and C1s ) C*, when the interface enters twophase coexistence. At that time, Γ increases by forming liquid expanded phase. Domains of liquid expanded phase grow until the entire interface is covered in the LE state. Defining the fraction of the interface covered with liquid expanded phase as Φ, the surface concentration evolves through the phase transition according to a lever rule:

Γ(t) ) ΓG(1 - Φ(t)) + ΓLE(Φ(t))

Φ(Γ)ΓG) ) 0.0 (13)

During the phase transition, Γ(t) is determined by eq 9 subject to the constraint that C1s remains fixed at C*; Φ(t) is determined by eq 13, and the surface tension remains fixed at γ*. Once Φ(t) ) 1.0, the surface concentration again evolves according to a single-phase evolution. For Γ > ΓLE, C1s and Γ again increase according to eqs 9-11, and γ evolves according to eq 6 until equilibrium is attained. Because the electrostatic terms make the equations stiff, numerics and data are compared only until the end of the induction period, rather than running the numerics to equilibrium. Since the induction period is clearly related (19) MacLeod, C. A.; Radke, C. J. Langmuir 1994, 10, 3555.

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to a given surface concentration, this suffices to fix the controlling mass transfer mechanisms. 4.3. Kinetically Controlled Model for the Dynamic Surface Tension. For surfactants that adsorb according to a kinetically controlled mechanism, the surfactant adsorbs from a solution with a sublayer concentration that is reduced from the uniform bulk concentration C1∞ by a Boltzmann distribution in the surface potential. Thus, eq 10 is replaced with

(

)

-z1FΨs(t) dΓ(t) ) β exp C1∞(Γ∞ - Γ(t)) dt RT Γ(t) Γ(t) (14) R exp K Γ∞

( )

where the electrostatic potential is determined by eq 11 and the initial conditions in eq 12 become

Γ(t)0) ) 0

(15)

Surfactant adsorbs according to eq 14 until Γ ) ΓG, when the interface enters two-phase coexistence. At that time, Γ increases by forming liquid expanded phase with the surface tension fixed at γ*. Domains of liquid expanded phase grow until the entire interface is covered in the LE state. The surface concentration evolves through the phase transition according to a lever rule:

{

[ ( )] [ ( )] } [ ( )] }

z1FΨG s dΦ (1 ) βC1∞ (Γ∞ - ΓG) exp dt RT z1FΨLE s Φ) - (Γ∞ - ΓLE) exp Φ RT

(ΓG - ΓLE)

{[ ( )]

ΓG G ΓLE LE Γ (1 - Φ) + exp K Γ Φ Γ∞ Γ∞

R exp K

(16)

This equation reflects the fact that the electrostatic energy barrier to adsorption and the van der Waals energy barrier to desorption differ in the surface liquid and gaseous phases. For Γ > ΓLE, Γ again increases according to 14, and γ evolves according to eq 6 until equilibrium is attained. 4.4. Comparison of Model to Experimental Data. In Figure 3, the isotherm fit to the surface tension data is compared to the equilibrium surface tension data as a function of bulk concentration. The model curve predicts that the surface tension remains elevated until the bulk concentration C* (indicated by the asterisk in Figure 3), beyond which it drops steeply. This is the bulk concentration at which G and LE states coexist at the interface. The slope of γ versus log C1∞ is associated with the surface excess concentration Γ through the Gibbs adsorption equation for an ideal solution of a single surface-active species:

dγ ) -RTΓ d ln C1∞

(17)

Figure 7. (a) The induction time versus C1∞ for the ferrocenyl surfactant in the reduced (S+) state. The filled circles indicate the induction times reported for the dynamic surface tension profiles in Figure 4a. The dashed curve indicates the induction time predicted by the diffusion-controlled adsorption analysis with D fixed at 8.0 × 10-6 cm2/s. (b) The induction time versus C1∞ for the ferrocenyl surfactant in the oxidized (S2+) state. The filled triangles indicate the induction times reported for the dynamic surface tension profiles in Figure 4b. The dashed curve indicates the induction time predicted by the diffusion-controlled model with D fixed at 6.8 × 10-10 m2/s. The dotted line indicates the induction time predicted by the kinetically controlled model, with β ) 9.2 × 10-1 m3/(mol s) and a corresponding R ) 1.9 × 10-6 L/s.

surface binodal concentration of the surfactant in a surface liquid expanded state, ΓLE. Before discussing the detailed analysis of the dynamic data, the gross features of the data in Figure 7 can be understood from approximate mass transfer arguments. A short term expansion for the diffusion-controlled model (simply truncating eq 9 at order t1/2) yields the following relationship between induction time and bulk concentration: 2

tind ≈

π ΓLE 4D1 C 2

(18)

1∞

The change in slope apparent at C* is consistent with a first-order phase change occurring in the interface.20 Approaching the coexistence concentration C* from below, the slope corresponds to the surface binodal concentration of the surfactant in a surface gaseous state, ΓG. Approaching C* from above, the slope corresponds to the

suggesting a line with a slope of -2 should approximate the graph of induction time as a function of the logarithm of the bulk concentration shown in Figure 7 for a diffusioncontrolled mechanism. In contrast, an approximation of a kinetically controlled adsorption argument for very early times yields

(20) See: Ter Minsassian Saraga and Prigogine. In Defay, R.; Prigogine, I. Surface Tension and Adsorption; John Wiley & Sons: New York, 1966.

∂Γ ≈ βC1∞Γ∞ ∂t

(19a)


Langmuir, Vol. 19, No. 20, 2003 8299

Table 2. Fit Dynamic Parameters DS+ ) 8.0 × 10-10 m2/s βS2+ ) 9.2 × 10-1 m3/(mol s) DS2+ ) 6.8 × 10-10 m2/s

or

tind ≈

ΓLE 1 Γ∞ βC1∞

(19b)

suggesting a line with a slope of -1 should approximate the data in Figure 7 for a kinetically controlled mechanism. For the reduced form of the surfactant, the graph indeed goes roughly with a slope of -2, indicating that diffusion is probably the controlling mechanism. For the oxidized form, the dilute-concentration data fall steeply, but the high-concentration data fall with a slope closer to -1, indicating a shift in controlling mechanism from diffusioncontrolled adsorption at dilute concentrations to kinetically controlled adsorption at higher concentrations. This shift typically occurs at high concentration because diffusion time scales, which can be long at low concentrations, decrease with concentration faster than do kinetic time scales, so sorption kinetics are often apparent only at high concentrations. (For a detailed discussion of the shift in mechanism with bulk concentration for nonionic surfactants, see Pan et al.21 who studied the adsorption and desorption kinetics of ethoxylates in pendant bubble experiments.) The shift to kinetic control is favored for the oxidized form of the surfactant for two reasons not explored in those studies. First, the maximum packing of the surfactant in the oxidized state is reduced, so less surfactant can fit on the interface. This reduces the diffusion time scale. Second, the increased valence of the surfactant increases the surface charge density and therefore also increases the electrostatic repulsion that slows adsorption to the interface. The diffusion-controlled surface tension model described in section 4.2 is solved numerically to find the length of the induction time as a function of bulk concentration. The predictions of the numerical integrations are shown in Figure 7. They agree well with the experimentally measured value for the reduced form of the surfactant and with the dilute concentrations of the oxidized surfactant. The kinetic-controlled surface tension model described in section 4.3 is also solved numerically and compared to the high-concentration data for the oxidized form of the surfactant. Recall that the ratio β/R is fixed by the equilibrium adsorption isotherm. An adsorption kinetic constant β ) 9.2 × 10-1 m3/(mol s) (Table 2) is fit to the data, with a corresponding desorption kinetic constant of R ) 1.9 × 10-6 s-1. These kinetic constants are still scarce in the literature. Pan et al. report an adsorption kinetic constant for C12E6 of β ) 4.0 m3/(mol s) and a desorption kinetic constant of 1.4 × 10-4 s-1. While the values for the product βΓ∞ are comparable, the desorption of the ferrocene surfactant in this study is far slower. The activation energy for desorption has been estimated to increase by 1.1 RT per methylene group,21 so the 15 carbons in the long saturated chain could contribute to a significant hindering of desorption kinetics. 4.5. Comparison to the Bolaform Surfactants. A family of ferrocenyl surfactants with a bolaform structure Fc-(CH2)n-N+(CH3)3 have been studied in terms of their equilibrium surface tension as a function of n, the (21) Pan, R.; Green, J.; Maldarelli, C. J. Colloid Interface Sci. 1998, 205, 213.

Figure 8. (a) Hypothesized structure of adsorbed Fc-(CH2)15N+-(CH3)3Br-, termed B+ and B2+, for the reduced and oxidized forms, respectively. (b) The equilibrium surface tension isotherms of the reduced form (B+) of Fc-(CH2)15-N+(CH3)3Br(squares) and the oxidized form (B2+) of Fc-(CH2)15-N+(CH3)3Br- (circles). The surface equation of state fit to the equilibrium data (constants in Table 1). The dashed line indicates the reduced fit, and the symbol / indicates the coexistence concentration. The solid line indicates the oxidized fit, and the symbol † represents the coexistence concentration.

hydrocarbon chain length.2 In the reduced state, these surfactants have a single ionic headgroup (the -N+(CH3)3 moiety) and a long hydrophobic chain formed by the remainder of the molecule. In the oxidized state, the Fc group also becomes positively charged, causing it to become strongly hydrophilic as well. In this case, if the hydrocarbon chain length is sufficiently long, it may be possible for both headgroups to remain in the aqueous phase, with the hydrocarbon chain forming a bridge between them (see Figure 8a). This argument was invoked to explain

8300


Datwani et al.

Table 3. Equilibrium Parameters for B parameter

reduced

oxidized

z1 Γ∞ (mol/m2) β/R (m3/mol) K κh C1* (mol/m3) AG ) 1/ΓG (Å2/molecule) ALE ) 1/ΓLE (Å2/molecule)

+1 8.30 × 10-6 4.20 × 102 -7.0 35.2 2.36 × 10-3 169 21.1

+2 1.84 × 10-6 5.70 × 103 -7.0 7.83 9.58 × 10-4 398 98.5

the equilibrium surface tension data for the bolaform surfactant Fc-(CH2)15-N+(CH3)3Br-. In Figure 8b, the equilibrium surface tension data for this surfactant (termed B for bolaform) are reproduced. Except for a rightward shift which is commensurate with a lower surface activity of B, the general forms of the isotherms for S (reported in Figure 3) and B are the same. The slope at high bulk concentration of these graphs can be related to the maximum packing or minimum area per molecule in the adsorbed monolayer. The oxidized state of B indeed corresponds to the surfactant spanning a larger area per molecule, in keeping with the configuration suggested in Figure 8a. Also, the areas per molecule of both the S and B forms are similar in the reduced (S+ and B+) and oxidized (S2+ and B2+) forms of the surfactants (Table 3). The bolaform surfactants are considerably far less surface active. This feature actually makes them a preferred structure for the rapid manipulation of surface tension using redox-active surfactants. This can be best understood by considering the characteristic diffusion time scale τD:

τD )

2 1 Γeq D1 C 2

the time required for the surfactant to adsorb to create a liquid expanded state. The equilibrium pendant bubble data are analyzed using a Davies equation of state augmented with a term to capture attractive interaction in the interface. A Maxwell construction is performed on this equation to locate the surface binodals of the surfactant as a function of redox state. A comparison of this model to the data indicates that upon oxidation, the surfactant valence, the surface activity, and the maximum packing change with the redox state. By comparison of the length of the induction time in the dynamic surface tension data to appropriate mass transfer models, the reduced form of the surfactant is shown to have diffusion-controlled transport, while the oxidized form is shown to undergo a shift of controlling mass transfer mechanism from diffusion control at dilute concentrations to kinetic control at elevated bulk concentrations. The kinetic constants for adsorption obtained from this analysis are comparable to those obtained for shorter chained nonionic surfactants in the literature, but the desorption kinetic constant is orders of magnitude smaller, suggesting that attractive interactions in this saturated 15 carbon chain strongly retard desorption. The surfactant studied here is compared to the bolaform ferrocenyl surfactants studied previously in the literature. The bolaform surfactants were much less surface active, were highly soluble, and therefore had rapid mass transfer from the interface in the concentration ranges of interest. They are appropriate for applications in which rapid equilibration between the interface and solution is desirable. The single-headgroup ferrocenyl surfactants studied here are potentially useful for creating highly nonequilibrium interfaces.

(20)

1∞

The surface concentrations that can be attained are comparable, but the bulk concentrations required to attain them are far higher for the bolaform surfactants. Thus, the characteristic time required to diffuse from solution to the interface for the bolaform surfactants is orders of magnitude less than for the single-headgroup surfactants studied here. In contrast, the slow mass transfer dynamics for the S form of the surfactants creates new opportunities for manipulating highly nonequilibrium states in the interface. Imagine a bubble formed and equilibrated with a 10-6 M solution of the S+ surfactant, with an equilibrium surface tension of roughly 55 mN/m, and a monolayer with an area per surfactant molecule of roughly 30 Å2/ molecule. If the surfactant were then rapidly oxidized from the vapor phase, a monolayer of oxidized surfactant could be created with a surface concentration in excess of that which could be attained by adsorption from the bulk solution. The large repulsion in the interface could drive the surface tension to very low values that would persist until the oxidized surfactant desorbed from the interface. These transient nonequilibrium low surface tension states will be explored in a later study. 5. Conclusions The equilibrium and dynamic surface tension of a redoxactive ferrocenyl surfactant, Fc-CH2-N+-(CH3)2(CH2)14-CH3, are probed. Dynamic pendant bubble data have an induction time that depends strongly on the bulk concentration of surfactant. Fluorescence microscopy is used to verify that this induction period corresponds to

Acknowledgment. The authors acknowledge Mr. Scott Goosman for help with the fluorescence microscopy. Nomenclature Ai Amin Ai eq ALE AG a B+ B2+ Ci∞ Ci C1s C* D F heq hion h∞ i k K R S+ S2+

area per molecule of component i minimum area per molecule of component i equilibrium area per molecule of component i liquid expanded phase binodal area per molecule of surfactant gaseous phase binodal area per molecule of surfactant radius of pendant bubble reduced form of the bolaform surfactant oxidized form of the bolaform surfactant concentration of component i, in the bulk phase concentration of component i outer sublayer concentration of component 1 coexistence bulk concentration of component 1 surfactant bulk diffusion coefficient Faraday’s constant adsorption depth adsorption depth of ionic species bulk depletion depth component i dimensionless bulk concentration or adsorption number second virial coefficient in the interface gas constant reduced form of the single-headgroup surfactant oxidized form of the single-headgroup surfactant

Redox-Dependent Surface Tension t T zi R β Γ Γ∞ Γeq Γi eq ΓLE ΓG

time temperature valence of species i kinetic constant for desorption kinetic constant for adsorption surface concentration of adsorbed surfactant maximum surface concentration equilibrium surface concentration equilibrium surface concentration of species i binodal surface concentration for LE state binodal surface concentration for G state

Langmuir, Vol. 19, No. 20, 2003 8301 γ γeq κ µ1 π σ Ψ Ψs

surface tension equilibrium surface tension dielectric permittivity the inverse Debye length chemical potential of component 1 in solution surface pressure surface charge density electrostatic potential electrostatic potential at the surface

LA020813W

Redox-Dependent Surface Tension and Surface Phase Transitions of

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