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Articles Surface Pressure Effect of Poly(ethylene oxide) and Sugar Headgroups in Liquid-Expanded Monolayers C. Marcus Persson,* U. R. Mikael Kjellin, and Jan Christer Eriksson Department of Chemistry, Surface Chemistry, Royal Institute of Technology, SE-100 44 Stockholm, Sweden, and Institute for Surface Chemistry, Box 5607, SE-114 86 Stockholm, Sweden Received December 3, 2002. In Final Form: July 1, 2003 Surface tension isotherms were recorded for six different but chemically closely related surfactants. The surfactants studied have three types of headgroups, tetra(ethylene oxide) (E4), penta(ethylene oxide) (E5), and maltopyranoside (Mal). For each headgroup, two hydrocarbon chain lengths were investigated, decyl (C10) and dodecyl (C12). By utilizing the Gibbs surface tension equation, surface pressure versus molecular area isotherms as well as the corresponding adsorption isotherms were generated for all six surfactants. By considering the various contributions to the free energy of the interface, theoretical surface pressure isotherms have been derived which are compared with the experimental ones in the molecular area interval especially studied here, from 60 Å2/molecule down to the molecular area obtained at the critical micelle concentration. Mainly two contributions to the free energy give rise to changes of the surface pressure with the area/molecule. The first contribution is related to restricting the hydrocarbon chain configurations, and the second one to the interactions between the polar groups and the surrounding solvent, water. It was found that the surface pressure effect of the maltoside headgroup is close to the one calculated for hard disks whereas the ethylene oxide headgroup behaves more like short polymer chains for which the Flory-Huggins theory is approximately valid. Surprisingly, we have found that the shorter carbon chain (C10) generates a higher surface pressure than the longer one (C12).
Introduction The molecular mechanisms responsible for the surface tension lowering due to adsorption of surfactants at the air-water interface have been studied by means of various theoretical approaches.1-3 Recently,4,5 investigations based on sum frequency spectroscopy and ellipsometric measurements have shown that the hydrocarbon part of the monolayer has a density similar to that of a bulk hydrocarbon at packing densities where the hydrocarbon part of the monolayer covers the entire interface. This is in agreement with simulations carried out for hydrocarbon monolayers using the rotational isomeric state model.6,7 Thus, as more surfactants become adsorbed at the interface, the thickness of the hydrocarbon layer sandwiched between the bulk phases increases linearly with the surface density. Eriksson and Ljunggren1 demonstrated that the surface pressure versus molecular area plots derived by Motumura et al.8 for dodecylammonium chloride in water can be quantitatively accounted for by * Corresponding author. Address: Institute for Surface Chemistry, Box 5607, SE-11486 Stockholm, Sweden. Tel: +46 8 7909941. Fax: +46 8 208998. E-mail:
[email protected]. (1) Eriksson, J. C.; Ljunggren, S. Colloids Surf. 1989, 38, 179. (2) Zoeller, N.; Lue, L.; Blankschtein, D. Langmuir 1997, 13, 5258. (3) Prosser, A. J.; Franses, E. I. Colloids Surf., A 2001, 178, 1. (4) Goates, S. R.; Schofield, D. A.; Bain, C. D. Langmuir 1999, 15, 1400. (5) Bell, G. R.; Manning-Benson, S.; Bain, C. D. J. Phys. Chem. B 1998, 102, 218. (6) Gruen, D. W. R.; Lacey, E. H. B. In Surfactants in solution; Mittal, K. L., Lindman, B., Eds.; Plenum Press: New York, 1984; Vol. 1. (7) Szleifer, I.; Benshaul, A.; Gelbart, W. M. J. Phys. Chem. 1990, 94, 5081. (8) Motumura, K.; Iwanaga, S.-I.; Hayami, Y.; Uryu, S.; Matuura, R. J. Colloid Interface Sci. 1981, 80, 32.
invoking two main effects, one associated with the headgroup interactions and one with the interactions among the hydrocarbon chains. The surface pressure due to the ionic headgroups, that is, the electrostatic surface pressure, was accounted for by the well-known GouyChapman theory. This surface pressure component is largely of entropic origin stemming from the mixing of counter- and co-ions with water in the diffuse part of the electric double layer. The second component is the hydrocarbon chain conformational surface pressure, arising upon compression of the hydrocarbon chain tails, thus altering their conformational state.6,7 For a straight C12 chain, this component only contributes appreciably at surface densities below 48 Å2/molecule as calculated by a mean-field statistical-mechanical approach.6,7 In this paper, we compare the experimentally derived surface pressure versus molecular area isotherms for three commonly used types of nonionic surfactants with two different chain lengths, decyl (C10) and dodecyl (C12), in order to quantify the respective surface pressure components. Experimental Section Chemicals. Penta(ethylene oxide) n-dodecyl ether (C12E5), penta(ethylene oxide) n-decyl ether (C10E5), tetra(ethylene oxide) n-dodecyl ether (C12E4), and tetra(ethylene oxide) n-decyl ether (C10E4) were obtained from Nikkol and used as received. n-Decylβ-D-maltopyranoside (C10Mal) and N-dodecyl-β-D-maltopyranoside (C12Mal) were obtained from Anatrace (>99% pure) and used as received. The water used in all experiments was of highpurity grade obtained from a Millipore Milli-Q purification system and a final filtration through a 0.2 µm filter. The surface tension of pure water was between 72.5 and 72.6 mN/m in all experiments.
10.1021/la026943m CCC: $25.00 © 2003 American Chemical Society Published on Web 08/27/2003
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Table 1. C10E4 C12E4 C10E5 C12E5 C10Mal C12Mal
k1
k2
1/k3
R2
64.367 66.244 60.679 63.214 69.785 72.126
0.003 917 0.003 997 4 0.003 666 7 0.003 715 3 0.003 593 2 0.003 615 9
0.018 796 0.000 978 47 0.025 11 0.001 522 9 0.055 405 0.002 696 4
0.9998 0.9998 0.9999 0.9999 0.9998 0.9998
Experimental and Numerical Procedures. The surface tensions of the surfactant solutions were measured with a Kru¨ss K12 tensiometer employing the Wilhelmy plate method. The plate made of platinum was roughened in order to ascertain a zero contact angle against the solution. All glassware and the platinum plate were cleaned prior to the measurements with warm (≈80 °C) bichromosulfuric acid for about 15 min and then thoroughly rinsed with water. The measurements were made at room temperature, that is, 22 ( 0.2 °C, and the ambient atmosphere was nearly saturated with water by inserting beakers of water inside the measurement chamber. The surface tension values reported were recorded when the surface tension had stayed constant for >60 s. Assuming ideal bulk phase behavior, the surface excess at the air-water interface of the surfactant, Γ2, is given by the Gibbs surface tension equation,
Γ2 ) -dγ/(RT d ln c2)
(1)
where c2 is the surfactant concentration. To be precise, we are here considering a Gibbsian surface phase of zero thickness located so as to make the surface excess of water equal to zero. The average area per molecule, a2, in the interface is related to the surface excess through the obvious relation
a2 ) 1/(Γ2NA)
(2)
with NA denoting the Avogadro number. The experimental surface tension isotherms were fitted to eq 3 below. This equation was used because it proved to give the best fits (highest correlation coefficient, R2) of the analytical expressions tried (second- and third-order polynomials etc.).
γ ) k1 - RTk2 ln(ck3 + 1)
(3)
The constants k1, k2, and k3 were determined numerically and are given in Table 1. Like the Szyszkowski expression, eq 3 when combined with eq 1 yields a Langmuir type of adsorption equation. Hence, we obtain
Γ2 ) k2k3c/(1 + ck3)
(4)
Theory Let us consider a soluble surfactant monolayer in equilibrium with its solution phase. As the appropriate excess free energy function of the interface, we take the grand potential, Ω ≡ Fs - N2µ2, with Fs denoting the Helmholtz free energy and µ2 the surfactant chemical potential. The corresponding free energy differential is
dΩ ) γ dA - S dT - N2 dµ2
(5)
where the Gibbs model of the interface still is employed (ΓH2O ) 0). A stands for the surface area, S for the surface entropy, and N2 for the number of surfactant molecules in the interface. Integration at constant T and µ2 yields
range, from 60 Å2/molecule down to the packing obtained at the critical micelle concentration (cmc) (≈40-45 Å2/ molecule). In this range, the coherent nonpolar layer between the headgroups and the vapor phase has a density about the same as that of bulk hydrocarbon.3,4 This is of course hardly surprising, as the vapor phase is a poor solvent for the hydrocarbon chains. Next we consider the different contributions to upon transferring the surfactant from the bulk to the monolayer. Then we have to correct for the changes in the surface free energy occurring upon forming the adsorption layer out of bulk hydrocarbon. Thus, we have
contact ) a2γhv + (a2 - apg)γhw
(7)
where γhv is the macroscopic surface tension of the hydrocarbon-vapor interface (∼20 mN/m) and γhw is the surface tension of the hydrocarbon-water interface (∼50 mN/m). apg stands for the cross-section area of the headgroup which shields some of the hydrocarbon-water contact area from the underlying bulk water and is assumed to remain constant in the area interval studied. The main driving force behind surfactant adsorption is the hydrophobic effect, which is a consequence of the unfavorable situation for water molecules in the vicinity of hydrocarbon chains. As hydrocarbon chains are being transferred to the monolayer, the number of these unfavorable contacts diminishes, resulting in a significant free energy gain of the system. To begin with, we account for the free energy gained by transferring a hydrocarbon chain from the bulk solution at the mole fraction x2 to bulk hydrocarbon by means of the expressions
Tan(C12) ) -(19.96 + ln x2)kT
(8)
Tan(C10) ) -(16.98 + ln x2)kT
(9)
where -19.96 kT and -16.98 kT are the standard free energy changes as derived according to Tanford9 for C12 and C10 hydrocarbon chains, respectively. The next contribution to consider is the free energy associated with the headgroups (mix). This contribution is mainly of entropic nature and originates from the mixing of the headgroups with water. At very dense surface packings, additional contributions from the differences in headgroup-headgroup, water-water, and headgroup-water interactions are also expected to contribute. Finally, we have the chain conformational contribution, conf, which is a consequence of anchoring the hydrocarbon tails to the headgroups present at the hydrocarbon interface resulting in restrictions on the number of accessible conformational states. As shown by molecular dynamic simulations using the rotational isomeric state model, the hydrocarbon chains have a preferred state where the conformational free energy has a minimum, which occurs at an area of 48 Å2/molecule for a straight C12 chain.6 Thus, this surface pressure component changes sign at 48 Å2/molecule from being attractive at larger areas to becoming repulsive at smaller areas. The surface pressure is now given by
(6)
π ) -(d/da2)T,µ2 ) -(d(contact + mix + conf)/da2)T,µ2 (10)
where is the Ω-potential/molecule. Now, in particular we consider a surfactant interface in the liquid-expanded
(9) Tanford, C. The hydrophobic effect, 2nd ed.; Wiley and Sons: New York, 1980.
Ω ) N2 ) γA
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or, using eq 7
π ) γ0 - γ ) γ0 - (γhv + γhw) - dmix/da2 dconf/da2 ) γ0 - (γhv + γhw) + πmix + πconf (11) Furthermore, we put γ0 ) γhv + γhw where γhv ) 22.5 and γhw ) 50 mN/m. Surface force measurements between bilayers of C12E410 have shown that even such a relatively small headgroup as E4 behaves in a polymer-like fashion, a conclusion also supported by molecular dynamics simulations.2 Thus, we may assume that the headgroup properties of the short ethylene oxide (EO) chains attached to a monolayer can be approximated by means of the Flory-Huggins model. On this basis, we arrive at the following free energy expression for the headgroup free energy:
Figure 1. Surface tension as a function of concentration for C10E5, C10E4, C10Mal, C12E4, C12E5, and C12Mal.
Mφ1 mix )M-1+ ln φ1 + ln φpg - χM + Mχφ1 (12) kT φpg where the volume fractions of water and the polar group are given by φ1 ) 1 - apg/a2 and φpg ) apg/a2. The molecular surface areas are defined by apg ) vpg/tw and aw ) vw/tw, respectively, where vpg and vw are the molecular volumes of the headgroup and water, tw being the thickness of the headgroup layer and M ) vpg/vw ) apg/aw. tw is around 3.6 Å/EO, the volume/EO is around 65 Å3,11 and χ ) 0.2 kT. (M - 1) - χM accounts for the circumstance that the pure oligomer standard state is located (M - 1) - χM kT-units above the extrapolated Φpg ) 1 standard state primarily used here. Equation 12 gives the following surface pressure expression:
(
) ( )
apg a2 - apg πmix M M-1 )ln - χM 2 kT apg a2 a2 a
(13)
2
One obvious deficiency of the Flory-Huggins model is however that the ends are not supposed to be fixed. Taking this into account, as shown in the Appendix, leads to the following free energy expression:
(
) (
) ( ) ( )
a2 - ras a2 - ras ras mix )M-1+M ln + ln + kT ras a2 a2 a2 - ras χM - χM (14) a2 where the ethylene oxide group nearest the hydrocarbon chain is restricted to the interface. In eq 14, a common lattice site area, as, has been invoked as the volumes of a single CH2 group, an ether oxygen, and a water molecule are roughly of the same order. The corresponding surface pressure expression becomes
(
)
ras a2 - ras πmix M M-1 )ln - χM 2 (15) kT ras a2 a2 a 2
On the other hand, surface force profiles for sugar surfactants on a hydrophobic substrate show that the range of the surface forces generated by the headgroups is considerably shorter than for ethylene oxide based (10) Lyle, I. G.; Tiddy, G. J. T. Chem. Phys. Lett. 1986, 124, 432. (11) Lu, J. R.; Thomas, R. K.; Penfold, J. Adv. Colloid Interface Sci. 2000, 84, 143.
Figure 2. Surface tension as a function of log c for the six surfactants. The solid line is the fit according to eq 3 to the experimental data.
surfactants.12-14 Thus, it is not unreasonable to assume that the lateral interactions within the layers approximately obey a hard disk behavior. The following analytical free energy expression is consistent with numerical hard disk simulations:15,16
( ) ( )
mix φpg φpg ) ln + -1 kT φ1 φ1
(16)
which, upon differentiation, yields the attractively simple surface pressure equation
πmix 1 ) kT a2Φ12
(17)
Results The surface tension versus concentration isotherms for the six surfactants investigated are shown in Figure 1. The fits to the experimental data, which were used to evaluate the adsorbed amount, are displayed in Figure 2, and the corresponding adsorption isotherms in Figure 3. The cmc, area/molecule at the cmc, and the value of the surface tension at the cmc are presented in Table 2. (12) Waltermo, Å.; Claesson, P. M.; Johansson, I. J. Colloid Interface Sci. 1996, 183, 506. (13) Claesson, P. M.; Kjellin, U. R. M. In Modern Characterization Methods of Surfactant Systems; Binks, B. P., Ed.; Surfactant Science Series, Vol. 83; Marcel Dekker: New York, 1999. (14) Persson, C. M.; Claesson, P. M.; Lunkenheimer, K. J. Colloid Interface Sci. 2002, 251, 182. (15) Erpenbeck, J. J.; Luban, M. Phys. Rev. A 1985, 32, 2920. (16) Nilsson, U. Thesis, Lund University, Lund, Sweden, 1992.
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Figure 3. Adsorption isotherms for the six surfactants.
Figure 4. The free energy, pg + mix, of bringing the different headgroups from the bulk to the interface. Table 2. The cmc, γcmc, and acmc Derived from Figures 1 and 2 surfactant
cmc [mM]
γcmc [mN/m]
acmc [Å2/molecule]
C12E5 C12E4 C10E5 C10E4 C12Mal C10Mal
0.064 0.05 0.73 0.73 0.17 2.1
29.7 27.6 29.9 29.2 35.3 37.3
45.8 42.4 46.8 43.5 46.7 47.4
The trends for the hydrophobic and hydrophilic groups shown in Table 2 follow the ordinary behavior for the maltosides and poly(ethylene oxides). The cmc is only slightly raised when the headgroup size of the ethylene oxide chain is increased, whereas the acmc is somewhat more affected. The maltoside headgroup is more hydrophilic than the penta(ethylene oxide) headgroup, which is reflected in a higher cmc, whereas acmc increases in the order E4 < Mal ≈ E5. The difference in hydrophilicity can be further explored by writing the full free energy expression for . We have
) γa2 ) Tan + conf + mix + contact + pg (18)
pg includes the transfer of the headgroups from the bulk at infinite dilution to the hypothetical standard state Φpg ) 1 in the interface. For example, for the hard disk expression used to describe the headgroup behavior of Mal as given by eq 14, here the reference state for mix is Φpg ) Φ1. pg + mix reveals which headgroup is most hydrophilic; that is, it contains information regarding the difference in the free energy upon transferring the headgroup from solution to the interface at an average area/molecule of a2. Now we can calculate pg + mix for the three surfactants (eqs 7, 8, 18, and 19). This is done in Figure 4 where it is clearly seen that the free energy of transferring Mal from the bulk to the interface at an average area/molecule a2 is the highest (2 kT more than for E5). From eqs 14 and 16, we can calculate mix for the respective headgroups and thus obtain pg as a function of a2. This is displayed in Figure 5, and we note that pg is nearly constant over the whole a2 regime as required. The surface pressure isotherms derived for the six surfactants are displayed in Figure 6. By comparing the C10 and C12 chains for a given headgroup, we note that the shorter chains consistently generate a higher surface pressure than the longer ones. Taking the difference in
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Figure 5. pg as a function of a2 for the three different headgroups.
Figure 6. Surface pressure as a function of area/molecule for the six surfactants.
surface pressure at a certain area for two surfactants with identical headgroups gives the relative surface pressure effect between the decyl and dodecyl chains. This difference in surface pressure is displayed in Figure 7. We note that the difference in surface pressure generated from 60 Å2/ molecule down to 50 Å2/molecule for C10 and C12 chains is rather constant, 3 mN/m, while at areas/molecule of
