Adsorption kinetics of ammonium perfluorononanoate at the air–water interface

The adsorption of the fluorocarbon surfactant, ammonium perfluorononanoate (APFN) has been studied in an overflowing cylinder (OFC).

The equilibrium adsorption isotherm, determined by drop shape tensiometry, is well-described by the Volmer isotherm.

The dynamic surface excess at the expanding surface of the OFC was measured by neutron reflectometry (NR).

The dynamic surface excess was in good agreement with the predictions of a diffusion-controlled adsorption model.

Significant Marangoni effects were observed.

The relationship between the mass transport equation in the OFC and the short and long-time asymptotes of the Ward–Tordai equation is noted.


The overflowing cylinder is a useful platform for studying adsorption kinetics and Marangoni effects (i.e., surface-tension-driven hydrodynamic flows) in surfactant solutions.1–15

The overflowing cylinder provides an extremely stable, continuously expanding, air–water interface with a surface age in the range of 0.1–1 s.

The large flat surface of the OFC is well-suited for a range of sensitive surface analytical techniques.

In the presence of surfactants, surface tension gradients lead to large accelerations of the surface: the surface velocity can increase by more than an order of magnitude compared with pure water.

More remarkably still, the interfacial properties are determined autonomously by the surfactant and become independent of the bulk flow rate or the dimensions of the cylinder (within certain limits).1,11

Although the range of timescales accessible in the OFC is less than in some other methods, such as the maximum bubble pressure (MBP) technique,16,17 the well-defined hydrodynamics and time-independence of the OFC allow precise testing of kinetic models for adsorption and provide a valuable complement to more traditional methods.

We have shown recently8 that adsorption of the cationic surfactants CnTAB (CH3(CH2)n−1N+(CH3)3Br, n = 12–16) at the surface of the OFC is diffusion-controlled at all concentrations below the critical micelle concentration (c.m.c.).

For C14TAB + NaBr, a model was developed incorporating micellar diffusion and adsorption was shown to be diffusion-controlled with fast micelle breakdown kinetics above the c.m.c.8

For C16TAB + NaBr, micelle breakdown kinetics become important and a rate constant for micelle breakdown was deduced.14

In this note, we present data on the adsorption of the fluorocarbon surfactant ammonium perfluorononanoate (APFN) in an OFC.

This study is the first on the adsorption kinetics of a perfluorocarboxylate surfactant at the air–water interface.

Perfluorocarboxylate surfactants are highly surface-active molecules and can reduce the surface tension of water to <20 mN m−1.18,19

Synergistic effects in surfactant mixtures result in even lower surface tensions.

Studies of the kinetics of adsorption of mixtures of APFN with hydrocarbon surfactants (where the interactions are primarily antagonistic) will be described elsewhere.

In this preliminary study, we look at the adsorption kinetics of pure APFN.

The specific choice of APFN for this study was dictated by the desirability of a Krafft point that is below room temperature and by a critical micelle concentration (c.m.c. = 8.9 mM) that is not too high.18,19

To model adsorption kinetics, one needs reliable data on both the equilibrium and dynamic properties of a surfactant.

In the Results section, we first present measurements of the equilibrium surface tension and deduce the adsorption isotherm.

We then present measurements of the dynamic surface excess, Γdyn, on the OFC by neutron reflectometry at the spallation neutron source, ISIS.

To interpret Γdyn, we need also to know the surface expansion rate, which is measured by laser Doppler scattering.

The surface expansion rate, θ, was found to be in the range θ = 1–3 s−1, which therefore defines the timescale over which information on the adsorption kinetics is accessible.

The experimental values of Γdyn are then compared with the predictions of a diffusion-controlled adsorption model and found to be in excellent agreement.

Finally, we draw an analogy between the kinetics of the overflowing cylinder and adsorption to a stagnant interface.

Experimental section


Ammonium perfluorononanoate was prepared by neutralisation of heptadecafluorononanoic acid (Fluorochem, 99%) with ammonium hydroxide solution (Aldrich, 28% NH3 in water, 99.99+%) followed by freeze-drying and recrystallisation (3 times) from dichloromethane/isopropanol.

The tetra-ammonium salt of ethylenediamine tetra-acetic acid (EDTA) was prepared as either 74 or 130 mM aqueous solutions by neutralisation of EDTA (Aldrich, 99.999%) with 4 equivalents of ammonium hydroxide solution.

Ultra-high purity (UHP) water was obtained from a variety of water polishing systems.

Overflowing cylinder

The design and operation of the overflowing cylinder has been described in detail previously.1

Briefly, a gravity-fed solution flows upwards in a stainless steel cylinder (8 cm in diameter) and overflows the rim.

The flow at the surface is radially outwards from a stagnation point at the centre of the cylinder.

The surface expansion rate, θ = d lnA/dt (where A is the area of an element of surface) is approximately uniform over the surface of the cylinder.

Measurements on the OFC were conducted at a temperature of 298 K and a volume flow rate of 17 cm3 s−1, corresponding to a mean vertical velocity in the cylinder of 0.34 cm s−1.

The total fluid volume in the OFC and pumping system was 1.6 dm3.

Surface tensiometry

Surface tensions were measured at 298 K by axisymmetric drop shape analysis (ITConcept, Longessaigne, France).

Bubbles of air with a typical volume of 5 μl were formed in aqueous solutions of APFN containing 1 mol% of the tetra-ammonium salt of EDTA to complex calcium ions (the EDTA will be present in solution with varying degrees of ionisation, with the speciation dependent on the APFN concentration).

EDTA was not added to the solutions for dynamic measurements by NR and LDV (see below), since trace ions do not have time to exert a measurable effect on the expanding air–water interface.

Bubbles were allowed to equilibrate for 1–45 min before measurements were taken.

The drift in the surface tension values was <0.1 mN m−1 min−1; 2–3 readings were acquired at each concentration.

Tetra-ammonium EDTA was tested to ensure that it was not surface-active at the concentrations employed here.

Laser Doppler velocimetry (LDV)

A 10 mW HeNe laser beam was split into two equal parts, focused, and recombined on the surface of the OFC.

The APFN solution was seeded with a few mg of 2-μm TiO2 particles.

When these particles pass through the interference fringes formed by the crossed laser beams they scatter light with an intensity that is modulated at a frequency (in the range of 104 Hz) that is determined by the spacing of the fringes and the velocity of the particles.

Experimental details may be found elsewhere.1

The surface velocity, us(r) was measured as a function of the radial position, r, and the surface expansion rate deduced from θ = r−1d(rus)/dr.

θ was almost constant across the central 5 cm of the cylinder: the value at r = 0 is reported.

Neutron reflectometry (NR)

Neutron reflection experiments on the OFC were carried out on the SURF beamline at the spallation neutron source ISIS (Didcot, UK) according to a protocol that has been described in detail previously.3,15

The reflectivity was calibrated with a sample of pure D2O in the OFC before the sample runs and checked with a second calibration after the runs were complete.

The calibration factors differed by 2%.

The sample solutions were prepared in null-reflecting water (nrw = 0.08 D2O: 0.92 H2O by mole).

Reflectivity profiles were acquired for between 20 min for the highest concentration of APFN and 130 min for the lowest concentration.

The raw time-of-flight data were binned into intervals with a width of 5% of the momentum transfer and normalised by the calibration factor determined from the D2O runs.

The profiles were analysed on a simple three-layer model (air/monolayer/water) to yield a thickness, τ, and scattering length density, ρ, of the adsorbed monolayer.

These two parameters are strongly correlated, but the surface excess can be determined reliably from the equationwhere bi is the scattering length of atom i and ni is the number of times that atom i appears in the molecular formula for the surfactant.

Assuming that the ammonium counterion is fully exchanged with solvent and that all the counterions contribute to the reflectivity, the scattering length of APFN, ∑nibi = 165.3 fm.

In studies of anionic surfactants with the tetramethyl ammonium counterion, Thomas and coworkers found that a fraction of the counterions in the electrical double layer (up to 90% in one case) were not detected by NR.20,21

However, since the scattering length density of NH4+ in nrw is close to zero, the counterions make very little contribution to the reflectivity here.

Neutron reflection can be used to determine the equilibrium adsorption isotherm of surfactants,15,22 but due to the limited availability of beamtime, surface tensiometry was used instead (see above).

Results and discussion

Equilibrium adsorption

The equilibrium adsorption isotherm of APFN was determined by surface tensiometry.

The presence of divalent counterions, especially Ca2+, is known to interfere with interpretation of surface tension data for anionic surfactants,23 so the tetra-ammonium salt of EDTA was added to the APFN solutions at a level of 1% of the surfactant concentration (by mole) to complex any trace Ca2+ ions present in the surfactant or leached from the glassware.

To determine the appropriate level of EDTA, we measured the surface tension of a 0.7-mM solution of APFN containing varying concentrations of EDTA.

In the presence of trace divalent ions, the surface tension is expected to show a maximum with increasing EDTA concentration: at low concentrations, divalent ions complex to the surfactant at the interface and lower the surface tension; at high concentrations EDTA increases the ionic strength, which screens the electrostatic repulsions between adsorbed APFN molecules, increases the extent of adsorption and lowers the surface tension.

For 0.7-mM APFN, the surface tension was constant at low EDTA concentrations and decreased at concentrations of EDTA above 8 mol%.

A value of 1 mol% falls within the plateau region.

The ammonium salt of EDTA was used in preference to the commercially available tetrasodium salt so as not to add a second counterion to the system.

The surface tension of APFN as a function of bulk concentration, c, is shown in Fig. 1.

The Debye–Hückel Limiting Law was employed to convert the bulk concentrations into activities.

Various adsorption isotherms were explored to fit the surface tension data.

The most appropriate isotherm is the van der Waals’ isotherm with counterion binding.24,25

To determine the four unknown parameters in this model with confidence it is usually necessary to make measurements both with and without added electrolyte.

For APFN, however, we found that the interaction parameter between adsorbed molecules was very small, so the simpler Volmer isotherm could be used eqn. (2).where K1 = 4.6 × 103 m3 mol−1, K2 = 1.2 × 10−3 m3 mol−1, Γ = 5.74 μmol m−2 and the concentrations of the surfactant ion (c1) and counterion (c2) immediately below the surface (z = 0) are determined by Gouy–Chapman theory.

For the ammonium salt, counterion binding is weak (K2 is very small); the isotherm is thus insensitive to the exact value of K2 and can be determined with reasonable confidence in the absence of data with added electrolyte.

The equivalent surface tension isotherm is shown as a solid line in Fig. 1.

The intersection between this isotherm and a linear fit to the surface tension above the c.m.c. yields a value for the c.m.c. of 8.9 mM.

This value is in agreement with a c.m.c. of 9.1 mM26 obtained by electrical conductivity.

The value of Γ at the c.m.c. is 4.3 μmol m−2; the limiting value of Γ < Γ because micelle formation places a cap on the chemical potential of the surfactant.

Γ−1 is the excluded area per molecule, A0, in the van der Waals’ model.

The value we obtain for A0 = 0.29 nm2 is very close to the cross-sectional area of a helical fluorocarbon chain (0.27 nm2)27.

Dynamic surface excess

Sample reflectivity profiles are shown in Fig. 2 for three concentrations of APFN, together with theoretical fits to a three-layer model (air, monolayer, nrw).

The dynamic surface excess obtained from such fits is plotted against the bulk concentration in Fig. 3.

The equilibrium isotherm from surface tensiometry is shown as a solid line.

We would expect agreement between Γe and Γdyn at high concentrations where the mass transport to the surface is fast on the timescale of the OFC.

However, the limiting value of Γdyn = 4.7 μmol m−2 above the c.m.c. is significantly higher than the tensiometric value of 4.3 μmol m−2.

It is not uncommon for there to be a small difference in scaling factors between surface coverages determined by NR and tensiometry, even in measurements on static surfaces.

There are several possible reasons for this discrepancy23 including impurities in the surfactant, approximations in the isotherm used to fit the surface tension data, and errors in the determination of the calibration factor in the NR experiments.

In the case of NR measurements on the OFC, obtaining an accurate calibration is complicated by the fact that the surface of the D2O calibration sample is significantly more curved than the surface of the surfactant solutions.

This curvature defocuses the reflected neutron beam and reduces the transmission through the final slit before the detector.

The consequence is that the scale factor is too small and the surface excesses of the surfactant are more or less uniformly overestimated.

To mitigate this effect, the footprint of the neutron beam on the OFC is limited to 20 × 20 mm.

There are no equilibrium NR measurements on APFN in large planar troughs for comparison with the OFC data, but we can compare with measurements on the 8-carbon homologue, APFO.

In the presence of 0.1 M ammonium chloride, Simister et al.28

Downes et al.,29 and Lu et al30. all reported a value of Γe = 4.1 ± 0.2 μmol m−2 for APFO at the c.m.c.

While APFN may have a slightly higher surface excess at the c.m.c. than APFO, it is unlikely to be 15% higher.

We therefore assign the discrepancy in Fig. 3 to an underestimation of the scale factor in the NR measurements.

To enable comparison of the equilibrium and dynamic surface excesses, the NR data were scaled (by 0.9) to agree with the surface tension isotherm at high surfactant concentration (dotted line in Fig. 4).

The dynamic surface excesses then fall slightly below the equilibrium values at lower surfactant concentrations, as would be expected on physical grounds.

Marangoni effects

The surface expansion rate determined by LDV is shown in Fig. 5 as a function of the bulk concentration of APFN.

Surface accelerations are observed at all concentrations of APFN, with a maximum at 1.5 mM.

The general shape is characteristic of monomeric surfactants (cf. C14TAB8).

At low concentrations, there is very little adsorbed surfactant and hence the gradients in surface excess and consequently in surface tension are small.

At high surfactant concentrations, mass transport to the surface is fast and the surface is close to equilibrium: again large surface tension gradients do not arise.

Adsorption kinetics

Analysis of mass transport and convection at a surface under constant dilation yields a relationship between Γdyn, θ, the diffusion coefficient, D, the bulk concentration, c, and the subsurface concentration, cs, at the edge of the electrical double layer.4,31,32

In the absence of added electrolyte, the effective diffusion coefficient D = 2DPFNDNH4/(DPFN + DNH4), where DPFN = 5.2 ± 0.2 × 10−10 m2 s−1 is the self-diffusion coefficient of perfluorononanoate and DNH4 = 1.96 × 10−9 m2 s−1 is the diffusion coefficient of ammonium ions.33

(DPFN was determined by I. Furó by pulsed field gradient NMR of a 3-mM APFN solution in H2O at 295 K.) If adsorption is diffusion-controlled, then the interface is locally at equilibrium: i.e. the relationship between Γdyn and cs is the same as between Γe and c.

For a mixed kinetic-diffusion model, Γdyn (cs) < Γe(c).

The diffusion-controlled values of the surface excess are shown with a solid line in Fig. 4.

For each pair of experimental parameters, θ and c, there are an infinite number of values of Γ and cs that satisfy eqn. (3).

However, in eqn. (3), Γdyn is a monotonically decreasing function of cs, while in the equilibrium isotherm Γe is a monotonically increasing function of c = cs.

Consequently, there is only one pair of values, Γ and cs, that simultaneously satisfy the mass transport equations and the local equilibrium isotherm.

This value of Γ is plotted in Fig. 4.

As one would anticipate, the calculated values of the dynamic surface excess fall below the equilibrium values, since there has to be a concentration gradient to replenish the surfactant removed from the surface by dilation.

The difference between Γdyn and Γe is greatest at low concentrations, where Γ is most sensitive to changes in cs, and near the maximum in θ, where the mass transport away from the surface by dilation is greatest.

The theoretical difference between Γdyn and Γe is never greater than 0.2 μmol m−2, or about 5% of a monolayer of APFN.

In the diffusion-controlled model, the difference, Δσ, between the dynamic surface tension, σdyn, and equilibrium surface tension, σe, is <2 mN m−1 and increases with increasing θ.

Since it is surface tension gradients that drive Marangoni effects, it is not surprising that there is a correlation between θ and Δσ.

We note that much larger values of Δσ (≤30 mN m−1) are observed with more efficient surfactants, such as the cationic surfactant, CTAB [CH3(CH2)15N+(CH3)3Br], or the non-ionic surfactant, C12E8 [CH3(CH2)11(OCH2CH2)8OH].

The maximum surface expansion rates for these surfactants are twice as high as for APFN.

While this observation is intuitively reasonable, we do not yet have a sufficiently good understanding of the boundary conditions in the OFC to make quantitative predictions of surface expansion rates from the adsorption isotherm and transport properties of a surfactant alone.

A comparison of the predicted and experimental values of Γdyn shows quantitative agreement (Fig. 4).

We have shown in a previous paper that electrostatic barriers to adsorption are not expected to be important at strain rates accessible on an OFC.8

The agreement we observe here with a diffusion-controlled model shows that, on the timescale of the OFC, there are no steric barriers to adsorption for APFN either.

Relationship to kinetic measurements at a static liquid surface

Finally, we comment briefly on the relationship between steady-state adsorption with convection on an OFC and adsorption at a clean surface in the absence of convection.

In the latter case, the extent of adsorption is given by the classic Ward–Tordai equation34(where t is the time since creation of the clean surface and τ is a dummy variable of integration).

At long times, we can take cs outside of the integral and eqn. (4) becomes17

Comparing eqns. (3) and (5), we see that there is an equivalence between the surface expansion rate, θ, and (2t)−1 in the long-time asymptote of the Ward–Tordai equation.

Consequently, measurements made on the OFC should map onto measurements of stagnant adsorption onto a clean surface in the long-time limit if the substitution t = (2θ)−1 is made.

For the experiments presented here, cs > 0.85c at all concentrations (see Fig. 6), so the long-time asymptote should be a good approximation.

One would therefore predict agreement with dynamic surface tension measurements made by, for example, the MBP method.

Similarly, to obtain the short-time asymptote of eqn. (4) (cs → 0), we neglect the back-diffusion term and obtainwhich once again has the same form as the mass-transport equation in the OFC (eqn. (3)), with substitution t = (2θ)−1.

While there is no direct parallel between the Ward–Tordai equation and eqn. (3) in the general case, since the mapping between θ and ½t holds in both the long-time and short-time limits, it is unlikely to lead to large errors at intermediate times.

We note, however, that eqn. (3) holds under all conditions (below the c.m.c.) while eqns. (5) and (6) apply only in their respective asymptotic limits.


An analysis of the kinetics of adsorption of the fluorocarbon surfactant, APFN, at the air–water interface shows that adsorption is diffusion-controlled at all concentrations below the c.m.c.

The small deviations of the dynamic surface from equilibrium (Δσ ≤ 2 mN m−1, ΔΓ ≤ 0.2 μmol m−2) are nevertheless sufficient to yield surface expansion rates in an OFC of up to 3 s−1, six times greater than pure water at the same flow rate.

Significant Marangoni effects can occur even when interfaces are very close to equilibrium.

Under these conditions (ccs) there should be a direct correspondence between data from the OFC and from adsorption measurements at stagnant surfaces.