Langmuir 1998, 14, 979-981
979
Evidence for Activation-Diffusion Controlled Dynamic Surface Tension with a Nonionic Surfactant Julian Eastoe,* James S. Dalton, and Philippe G. A. Rogueda† School of Chemistry, University of Bristol, Bristol BS8 1TS, U.K.
Peter C. Griffiths Department of Chemistry, University of Wales Cardiff, P.O. Box 912, Cardiff CF1 3TB, U.K. Received November 14, 1997. In Final Form: January 9, 1998 Dynamic surface tensions (DSTs) of aqueous solutions of a glucamide nonionic surfactant, di-(C6-Glu), below its critical micelle concentration, have been measured by a maximum bubble pressure method as a function of temperature, from 10 to 50 °C. Du Nouy tensiometry was used to determine the temperature dependence of the equilibrium surface tension and surface excess, while the self-diffusion coefficient for monomeric di-(C6-Glu) was obtained by pulsed-field-gradient spin-echo NMR (D ) 2.7 × 10-10 m2 s-1 at 25 °C). With these measured values, the final stages of the DST decays are shown to be consistent with an activation-diffusion controlled adsorption mechanism, and an apparent activation energy Ea of about 80 kJ mol-1. This conclusion supports the arguments of Liggieri et al. (J.Colloid Interface Sci. 1993, 156, 109).
Introduction Dynamic surface tension (DST or γ(t)) is an important property of surfactant solutions, and number of different models have been proposed to account for the decay1. Although it is generally accepted that the initial adsorption is purely diffusion controlled, there is still some controversy about the underlying mechanism closer to equilibrium. This letter shows that below the critical micelle concentration (cmc) of a nonionic surfactant, the final stages of the γ(t) decay as a function of temperature are consistent with Arrhenius-like behavior and an activation-diffusion controlled adsorption mechanism. This surfactant is the dichain glucamide, (C6H13)2C[CH2NHCO(CHOH)4CH2OH]2 (di-(C6-Glu)), and recently its adsorption properties have been studied in detail.2-7 Owing to the hydrophilic -OH groups the adsorption isotherm and micelle phase of this surfactant are much less temperature sensitive than those for a comparable ethyleneoxide CiEj nonionic.3,4,7 For example, with di(C6-Glu) there is no cloud point up to 90 °C. Extensive du Nouy measurements, over the range 10-50 °C, show that both the cmc and the maximum adsorbed amount Γmax are essentially constant, and they may be taken as (1.35 ( 0.05) × 10-3 mol dm-3 and (2.75 ( 0.25) × 10-6 * To whom correspondence should be addressed: e-mail,
[email protected]; tel. U.K., +117-9289180; fax U.K., +1179250612. † Current address: Astra Charnwood, Bakewell Rd., Loughborough, Leics LE11 5RH, U.K. (1) Dukhin, S. S.; Kretzschmar, G.; Miller, R. Dynamics of Adsorption at Liquid Interfaces; Elsevier: Amsterdam, 1995. (2) Briggs, C. B. A.; Newington, I. M.; Pitt, A. R. J. Chem. Soc., Chem. Commun. 1995, 3, 379. (3) Eastoe, J.; Rogueda, P.; Harrison, W. J.; Howe, A. M.; Pitt, A. R. Langmuir 1994, 10, 4429. (4) Eastoe, J.; Rogueda, P.; Howe, A. M.; Pitt, A. R.; Heenan, R. K. Langmuir 1996, 12, 2701. (5) Cooke, D. J.; Lu, J. R.; Lee, E. M.; Thomas, R. K.; Pitt, A. R.; Simister, E. A.; Penfold, J. J. Phys. Chem. 1996, 100, 10298. At the cmc Thomas et al.’s measurements of the surface excess Γ were 2.52 × 10-6 mol m-2 by neutron reflectivity and 2.75 × 10-6 mol m-2 by tensiometry using the Gibbs isotherm. (6) Eastoe, J.; Dalton, J. S.; Rogueda, Ph. G. A.; Crooks, E. R.; Pitt, A. R.; Simister, E. A. J. Colloid Interface Sci. 1997, 188, 423. (7) Rogueda, Ph. G. A. Ph.D. Thesis, University of Bristol, 1996.
mol m-2.5-7 Furthermore, the isotherms obtained by both tensiometry and neutron reflectivity5-7 clearly show that Γ is invariant down to cmc/10. All of these properties make di-(C6-Glu) an ideal surfactant for studying the effects of temperature on dynamic surface tension, and because it is nonionic, electrostatic effects can also be ignored. With the Ward and Tordai equation, which assumes a diffusion-only mechanism for the time dependence of the adsorption Γ(t),8 eq 1 can be derived9 to account for the decay in the long time limit with nonionic surfactants.
γ(t)tf∞ ) γeq +
RTΓ2 π 2c Dt
1/2
( )
(1)
The parameters γeq, c, Γ, and D represent the equilibrium tension, bulk concentration, surface excess, and monomer diffusion coefficient of the surfactant. For di-(C6-Glu) Γ is known accurately,4-7 and here the self-diffusion coefficient D has been measured independently by pulsed-field-gradient spin-echo NMR (PFGSENMR). If the adsorption were purely diffusion controlled, then eq 1 should account for the end of the tension decays. Recently it has been shown that eq 1 is valid for investigating the adsorption mechanism.10 This can be done via an effective monomer diffusion coefficient Deff, which is often less than D for the pure monomer, obtained say by PFGSE-NMR.6 Liggeri et al.11,12 suggested that if (8) Ward, A. F.; Tordai, L. J. Chem. Phys. 1946, 14, 453. (9) Fainerman, V. D.; Makievski, A. V.; Miller, R. Colloids Surf., A 1994, 87, 61. (10) Miller, R.; Makievski, A. V.; Fainerman, V. B.; Bree, M.; Liggieri, L.; Ravera, F. Colloids Surf., A 1997, 122, 269. The characteristic time td of a diffusion-controlled process may be given as td ) (1/D)(Γ/c)2 and for di-C6-Glu at 5 × 10-4 mol dm-3 td ) 0.11 s and 50td ) 5.6 s. On the t-1/2 axis of Figure 2 these times correspond to 3.0 and 0.42 s-1/2, respectively. In this range either eq 1 or 3 can be used to test if the adsorption is essentailly diffusion controlled. (11) Ravera, F.; Liggieri, L.; Steinchen, A. J. Colloid Interface Sci. 1993, 156, 109. (12) Liggieri, L.; Ravera, F.; Passerone, A. Colloids Surf., A 1996, 114, 351. Note in refs 11 and 12 the relevant equation is defined as Deff ) D exp(-2Ea/RT) making the activation barrier calculated in this paper, using eq 2, twice as large.
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980 Langmuir, Vol. 14, No. 5, 1998
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the mechanism was mixed diffusion-activation, then Deff should obey an Arrhenius-like equation
Deff ) D exp(-Ea/RT)
(2)
with Ea the activation barrier. Their calculations show that raising Ea can cause a significant decrease in the adsorption Γ(t), especially in the long time limit. A number of reports have recently appeared in support of this mechanism, for both surfactants6,11-14 and also polymers.15,16 The results presented here for di-(C6-Glu) confirm that eqs 1 and 2 account for the temperature dependence of DST decays. To be sure that all surfactant was present as monomer and eliminate any possible effects of micelles,17 the concentration of di-(C6-Glu) was 5.0 × 10-4 mol dm-3, and this is 0.37 × cmc. Experimental Section The di-(C6-Glu), a gift from Kodak European Research R and D, Harrow U.K., was stored in a desiccator over refreshed P2O5 until used. 1H and 13C NMR spectra were consistent with the expected chemical structure. The du Nouy γ vs ln(concentration) plot was characteristic of a pure surfactant and agreed well with previous results.3-7 Water was from a Milli-Q reverse-osmosis purification system. Surface tensions were measured as described previously6 using a Kru¨ss K10 du Nouy apparatus and a Lauda MPT1 MBP tensiometer. These instruments were calibrated over the range 73-22 mN m-1 against various standards (as in ref 6), and this defined the absolute uncertainties in γ as (0.1 mN m-1 (du Nouy) or (0.20 mN m-1 (MBP). The sample cells were thermostated using a Grant LTD6G circulator bath, and the uncertainties were (0.1 °C up to 30 °C rising to (0.5 °C at 50 °C. The self-diffusion coefficient for monomeric di-(C6-Glu) below the cmc, at 8.0 × 10-4 mol dm-3 and 25 °C, was measured as D ) 2.70 × 10 -10 m2 s-1 using a pulsed-field gradient NMR method described previously.18
Figure 1. Dynamic surface tensions for solutions of di-(C6glu), below the cmc at 5 × 10-4 mol dm-3, as a function of temperature (T in °C): 10.0 (]); 20.0 (9); 30.0 (4); 40.0 (b); 50.0 (0).
Results and Discussion The variation of equilibrium tension γeq with temperature T was measured by du Nouy tensiometry. At 10 °C γeq was 41.0 mN m-1, and it consistently decreased to 36.9 mN m-1 at 50 °C. Figure 1 shows the corresponding γ(t) data for di-(C6-Glu) as a function of T. These γ(t) curves were reversible and reproducible, and it is clear that increasing T gives rise to a faster decay. Between 20 and 50 °C the DST decays were essentially complete, and the final points were close to the du Nouy γeq values. For example, at 20 °C the last DST measurement at 20 s was 1.8 mN m-1 above γeq, whereas at 50 °C this difference was 0.7 mN m-1. The apparent drop in tension at the start of the decay is consistent with the effect of temperature on the surface tension of water and also the earlier onset of adsorption at higher temperatures. These DST data are plotted as a function of t-1/2 in Figure 2. As expected for a diffusion-type process, the data are linear at long times. The lines are least-squares fits for t > 0.25 s (i.e., t-1/2 < 2), with the intercepts equal to the measured equilibrium tensions γeq. The gradients (13) Eastoe, J.; Dalton, J.; Rogueda, P.; Sharpe, D.; Dong, J.; Webster, J. R. P. Langmuir 1996, 12, 2706. (14) Lin, S.-Y.; Tsay, R.-Y.; Lin, L.-Y.; Chen, S.-I. Langmuir 1996, 12, 6530. (15) Um, S.-U.; Poptoshev, E.; Pugh, R. J. J. Colloid Interface Sci. 1997, 193, 41. (16) Cho, D.; Narsimhan, G.; Franses, E. I. J. Colloid Interface Sci. 1997, 191, 312. (17) Fainerman, V. B.; Makievski, A. V. Koll. Zh. (English) 1992, 54, 890, 897. (18) Griffiths, P. C.; Stilbs, P.; Paulsen, K.; Howe, A. M.; Pitt, A. R. J. Phys. Chem. 1997, 101, 915.
Figure 2. Dynamic surface tension data of Figure 1 plotted vs t-1/2. The lines are least-squares fits to the data as t f ∞ with the intercept equal to the measured equilibrium value γeq. The symbols represent the same temperatures as those given in Figure 1. Table 1. Gradients of Dynamic Surface Tension Decays and Diffusion Coefficients as a Function of Temperature for di-(C6-glu) Solutions at 5 × 10-4 mol dm-3 T/°C
gradient/mN m-1 s1/2
1010 Deff/m2 s-1
1010 D/m2 s-1
Deff/D
10 20 30 40 50
15.1 9.6 6.6 3.7 2.0
0.032 0.086 0.20 0.66 2.32
2.56 2.65 2.74 2.83 2.93
0.013 0.033 0.072 0.232 0.793
of these fitted lines are given in Table 1, and they consistently decrease with temperature. Values for the effective diffusion coefficients Deff, derived from these slopes using Deff ) (RTΓ2π1/2/2c gradient)2, are also given in Table 1. The measured monomer coefficient D (2.70 × 10 -10 m2 s-1 at 25 °C) was used to estimate the D values at the other temperatures, assuming the Stokes-Einstein equation.19 These D values are given in Table 1, along with the ratios, Deff/D. The observed decrease in gradient dγ/d t-1/2 with T goes hand-in-hand with an increase in the apparent diffusion coefficient Deff. At 50 °C the ratio Deff/D
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Langmuir, Vol. 14, No. 5, 1998 981
Figure 3. Dynamic surface tensions of di-(C6-glu) at 5 × 10-4 mol dm-3; 10.0 °C (]) and 50.0 °C (b). The lines are calculations, described in the text, using Equation 1 and measured values.
is very close to 1, suggesting a near diffusion-controlled adsorption at this higher temperature. Alternatively, the Hansen equation
γ(t)tf∞ ) γeq +
RTΓ2 1 c πDt
1/2
( )
(3)
could also be used to analyze the long-time DST decays of Figure 2, and Miller et al. have recently made a comparison of eqs 1 and 3 for this purpose.10 The diffusion coefficients derived from eq 3 are lower than those in Table 1 by a factor of π2/4 () 2.47). However, this does not change the conclusion that only at 50 °C is the DST close to diffusion-controlled. Figure 3 shows the γ(t) curves for 10 and 50 °C, with calculations using eq 1, the monomer diffusion coefficients D (Table 1), and the equilibrium tensions γeq at the different temperatures. At 50 °C eq 1 accounts for the measurements well, at least from 0.01 s onward. For the lower temperature there are obvious discrepancies in the range 0.2-10 s and the calculated tensions are too low. Clearly temperature has a more important effect on the measured DSTs than on those predicted by the diffusiononly theory (eq 1), even taking into account the combined effects of T and D(T). Figure 4 shows a plot of ln(Deff/D) vs 1/T in line with eq 2, and the gradient gives Ea ) 78 ( 1 kJ mol-1.20 (Note this value would be 39 kJ mol-1 if Ea was defined as in refs 11 and 12). For a pre-cmc solution of the poly(ethylene oxide) nonionic, Triton X-100 at 1.55 × 10-4 mol dm-3, Miller et al. have also shown that the gradient dγ/dt-1/2 decreases with temperature.21 For example at 30 °C the slope was 17 mN m-1 s1/2, whereas at 70 °C it was 8 mN m-1 s1/2. These changes are also consistent with an activation barrier, which can be estimated as around 40 kJ mol-1 for that surfactant.21 (19) Atkins, P. W. Physical Chemistry, 5th ed.; Oxford University Press: Oxford, 1994. The Stokes-Einstein equation gives a linear dependence of D on T. However, even if D was proportional to xT (kinetic theory of gases), a very similar value for Ea is obtained, 80 kJ mol-1. (20) Using the effective diffusion coefficients derived using eq 3 gave the same activation energy but a slightly lower intercept.
Figure 4. Arrhenius-type plot of ln(Deff/D) vs 1000/T for a di-(C6-Glu) solution at 5 × 10-4 mol dm-3. The fitted line corresponds to Ea ) 78 kJ mol-1.
Recently, dynamic surface tensions for nine different CiEj and di-(Cn-Glu) nonionic surfactants, spanning cmc’s from 1.0 × 10-2 to 5 × 10-5 mol dm-3, were studied as a function of concentration, but at fixed temperature.6 For all of these compounds, including the di-(C6-Glu), the final parts of the γ(t) curves were also consistent with a mixed diffusion-activation adsorption, and they suggested a mean activation energy of 10 kJ mol-1. This difference in Ea, as compared to the value found here, is not unexpected, because in the previous work the temperature dependence of eqs 1 and 2 was not tested. Conclusions The effect of temperature on the gradients of dynamic surface tension decays of a nonionic sugar surfactant, di(C6-Glu), are consistent with an activation-diffusion controlled adsorption mechanism, as proposed by Liggieri et al.11,12 For this surfactant, below its cmc, the activation barrier appears to be of the order of 80 kJ mol-1, and this is somewhat higher that earlier estimates of ∼10 kJ mol-1.6 The origin of this adsorption barrier may that the molecules must be oriented favorably and/or do work against the surface pressure. In the absence of any molecular theory for DST an activation barrier can be used to account for all these possibilities, since only molecules with a sufficient energy Ea can adsorb into the layer and effect the tension. It is hoped that these new results stimulate fresh theoretical effort to understand the origin of this adsorption barrier. Acknowledgment. This work was supported by EPSRC through a research grant (GR/ K04774) and studentships (J.S.D.). Kodak European Research R and D and the University of Bristol are thanked for a studentship (Ph.G.A.R.), and for the gift of the di-(C6Glu) sample. LA971241W (21) Miller, R.; Fainerman, V. B.; Schano, K.-H.; Hofmann, A.; Heyer, W. Tenside, Surfactants, Deterg. 1997, 34, 357. From those DST data Ea for Triton X-100 was estimated using D ) 2.6 × 10-10 m2 s-1 and Γ ) 2.65 × 10-6 mol m-2.
