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Langmuir 2001, 17, 562-564
Notes Limiting Area per Molecule of Nonionic Surfactants at the Water/Air Interface R. Sedev* I.-N.-Stranski-Institut fu¨ r Physikalische und Theoretische Chemie, Technische Universita¨ t Berlin, Strasse des 17. Juni 112, D-10623 Berlin, Germany Received April 15, 2000. In Final Form: October 23, 2000
Introduction It is well-known1-4 that ethoxylated nonionic surfactants adsorbed at the water/air interface comply with the rule 1/2
A/N
) constant
(1.1)
where A is the limiting area per molecule and N is the number of ethylene oxide (EO) segments in the surfactant tail. Forty years ago van Voorst Vader1 gave an explanation of this behavior which is still reproduced in modern surfactant literature.2-4 Although experimental evidence supports the above prediction, the original formulation1 appears to be incorrect. In the present Note we reiterate the arguments of van Voorst Vader, show them to be inadequate, and derive an improved version based on scaling formulas valid for flexible chains in good solvent.5 The “correct” result is quite close to the version of van Voorst Vader and also agrees with the data available. van Voorst Vader’s Description Consider a saturated adsorption layer at the water/air interface (Figure 1). We focus on an element which comprises only one surfactant molecule and some water. The hydrophobic head is assumed to float on the aqueous surface. The volume of the element (excluding the head) is
V ) AL ) NVEO + NWVW
(1.2)
where N is the number of EO segments in the surfactant tail, VEO is the volume of such a segment, NW is the number of water molecules, and VW ()30 Å3) is the volume of a water molecule. Since the surfactant concentration in the layer is rather high (even for dilute solutions), van Voorst Vader assumed that only hydration water remains in the layer.1 If all water molecules are bound to the surfactant tail, then * Present address: Ian Wark Research Institute, University of South Australia, Mawson Lakes, SA 5095, Australia. Phone: +(61 8) 8302 3225. Fax: +(61 8) 8302 3683. E-mail: rossen.sedev@ unisa.edu.au. (1) van Voorst Vader, F. Trans. Faraday Soc. 1960, 56, 1078. (2) Lange H., Jeschke, P. Surface Monolayers in Nonionic Surfactants; Schick, M. J., Ed.; Marcel Dekker: New York, 1987. (3) Nikas, Y. J.; Puvvada, S.; Blankschtein, D. Langmuir 1992, 8, 2680. (4) Alexandridis, P.; Hatton T. A. Colloids Surf., A 1995, 96, 1. (5) de Gennes, P. G. Scaling Concepts in Polymer Physics; Cornell University Press: Ithaca, NY, 1979.
Figure 1. Saturated surfactant layer at the water/air interface (A, area per molecule; L, thickness of the hydrophilic tail).
V ) N(VEO + RVW)
(1.3)
where R ) NW/N is the hydration number of the poly(ethylene oxide) (PEO) chain. It was further assumed that the hydrophilic tail behaves like a Gaussian coil and keeps its characteristic size unperturbed inside the saturated adsorption layer.1 Thus
L ) 2RG ) 2aN1/2
(1.4)
where RG is the radius of gyration and a ()2.1 Å6) is an effective monomer size.5 It follows from eqs 1.3 and 1.4
VEO + RVW A ) 1/2 2a N
(1.5)
We refer to the constancy of A/N1/2 predicted by eq 1.5 as the van Voorst Vader rule. Numerous series of ethoxylated nonionic surfactants, including “polymeric surfactants” (triblock PEO-PPO-PEO copolymers, PPO ) poly(propylene oxide)) have been found to follow this rule. The results from fitting the equation A ) KNx to various data sets are collected in Table 1. The values of the exponent x are scattered, and there are discrepancies between different authors, but all are reasonably close to 1/2. The prefactor K has never received much attention. Available data suggest the values VEO ) 65 Å3 17 and R ) 3,18,19 which when introduced into eq 1.5 (6) Flory, P. J. Statistical Mechanics of Chain Molecules; Interscience Publishers: New York, 1969. (7) Schick, M. J. J. Colloid Sci. 1962, 17, 801. (8) Ohba, N.; Takahashi, A. Proc. Int. Congr. Deterg., 5th 1968, 2, 481. (9) Schott, H. J. Pharm. Sci. 1969, 58, 1521. (10) Lange, H. Kolloid-Z. Z. Polym. 1965, 201, 131. (11) Katz, J. L. J. Colloid Interface Sci. 1976, 56, 179. (12) Lu, J. R.; Thomas, R. K.; Penfold, J. Adv. Colloid Interface Sci. 2000, 84, 143. (13) Barry, B. W.; El Eini, D. I. D. J. Colloid Interface Sci. 1976, 54, 339. (14) Crook, E. H.; Fordyce, D. B.; Trebbi, G. F. J. Phys. Chem. 1963, 67, 1987. (15) Hsiao, L.; Dunning, H. N.; Lorenz, P. B. J. Phys. Chem. 1956, 60, 657. (16) Alexandridis, P.; Athanassiou, V.; Fukuda, S.; Hatton, T. A. Langmuir 1994, 10, 2604. (17) Bailey, Jr., F. E.; Koleske, J. V. Poly(Ethylene Oxide); Academic Press: New York, 1976. (18) Caragheorgheopol, A.; Caldararu, H.; Dragutan, I.; Joela, H.; Brown, W. Langmuir 1997, 13, 6912. (19) Tirosh, O.; Barenholz, Y.; Katzhendler, J.; Priev, A. Biophys. J. 1998, 74, 1371.
10.1021/la000572x CCC: $20.00 © 2001 American Chemical Society Published on Web 12/23/2000
Notes
Langmuir, Vol. 17, No. 2, 2001 563
Table 1. Best Fit Parameters for the Equation A ) KNx (Cj ) Aliphatic Chain with j Carbon Atoms; OP ) Octylphenol; NP ) Nonylphenol; PO ) Propylene Oxide; EO ) Ethylene Oxide; SER ) Standard Error of Regression) surfactant type
j
K (Å2)
x
SER (Å2)
ref
C12(EO)j C12(EO)j C12(EO)j C12(EO)j C16(EO)j OP(EO)j NP(EO)j EOjPO56EOj (25 °C) EOjPO56EOj (35 °C)
4, 7, 14, 23, 30 5-8, 28 5, 7, 9, 12 2-6, 8, 12 17, 32, 44, 63 1-10 9, 10, 15, 20, 30, 100 19, 30, 37, 129 19, 30, 37, 129
13 ( 2 25.0 ( 1.3 18.3 ( 0.4 23.5 ( 1.1 8(2 22.7 ( 1.1 17.9 ( 0.8 9(2 7.1 ( 1.3
0.61 ( 0.06 0.49 ( 0.02 0.54 ( 0.01 0.46 ( 0.02 0.68 ( 0.07 0.48 ( 0.03 0.51 ( 0.01 0.44 ( 0.05 0.46 ( 0.04
5 1 1 2 5 2 1 4 3
7 8, 9 10, 11 12 13 14 15 16 16
yield K ) 37 Å2. The order of magnitude is correct even though the actual values of K are about half that large. Thus eq 1.5 is in good agreement with the experimental results and is often quoted in modern surfactant literature.2-4 Nevertheless the assumptions made in its derivation appear to be incongruous as detailed below.
(10-25 water molecules per EO unit) in the adsorbed layer is an argument in favor of the scaling description of PEO chains used below. Water is a good solvent for PEO and accordingly the undisturbed radius of gyration, RF, is given by the Flory formula:5
Criticism and Reformulation
RF = aN3/5
The crucial assumption made in the derivation of eq 1.5sthat only bound water is present in adsorbed layers seems exaggerated. Contemporary data about the hydration of PEO chains show that typically three water molecules are bound per EO segment18,19 (though hydration numbers ranging from 1 to 5.5 have been reported for various ethoxylated surfactants20). Lu et al.21-24 have investigated in great detail the structure of alkyl ethoxylates at the water/air interface and have consistently found that about two water molecules are associated with any EO group. This implies a volume fraction of about 40% poly(ethylene oxide) in the layer. However neutron reflectivity studies of amphiphilic block copolymers adsorbed at the same interface detected a much lower volume fraction: ca. 17% for EO98PO69EO9825 (experiments were actually done at the water/hexane interface, but the authors insisted on the hexane having not altered the conformation adopted by the molecule at the water/air interface), 8-15%26 and about 16%27 for several PEOPPO-PEO copolymers at the D2O/air interface, and 16.7% for an insoluble PS-PEO diblock copolymer spread on the free surface of D2O.28 The two data sets are not necessarily incompatible: the longest chain examined by Lu et al.24 has only 12 EO units while the result of Currie et al28 pertains to a chain composed of 750 EO units. Furthermore it has been repeatedly stressed that the water distribution along the chain is not uniform (e.g., refs 18 and 23). Thus the assumption made by van Voorst Vader that only hydration water is present in the layer is not supported, at least for longer PEO chains. As a matter of fact it is hard to conceive of a flexible chain being flexible in a solvent composed only of molecules firmly bound to the chain itself. Therefore the larger amount of water (20) van Os, N. M.; Haak, J. R.; Rupert, L. A. M. Physico-Chemical Properties of Selected Anionic, Cationic, and Nonionic Surfactants; Elsevier: Amsterdam, 1993. (21) Lu, J. R.; Lee, E. M.; Thomas, R. K.; Penfold, J.; Flitsch, S. L. Langmuir 1993, 9, 1352. (22) Lu, J. R.; Li, Z. X.; Su, T. J.; Thomas, R. K.; Penfold, J. Langmuir 1993, 9, 2408. (23) Lu, J. R.; Li, Z. X.; Thomas, R. K.; Staples, E. J.; Tucker, I.; Penfold, J. J. Phys. Chem. 1993, 97, 8012. (24) Lu, J. R.; Su, T. J.; Li, Z. X.; Thomas, R. K.; Staples, E. J.; Tucker, I.; Penfold, J. J. Phys. Chem. B 1997, 101, 10332. (25) Phipps, J. S.; Richardson, R. M.; Cosgrove, T.; Eaglesham, A. Langmuir 1993, 9, 3530. (26) Clifton, B. J.; Cosgrove, T.; Richardson, R. M.; Zarbakhsh, A.; Webster, J. R. P. Physica B 1998, 248, 289. (27) Sedev, R.; Steitz, R.; Findenegg, G. H. Submitted for publication in Physica B.
(1.6)
Equation 1.6 also describes the scaling behavior of the adsorption layer thickness, but only at low surface coverage, when separate coils are anchored at the interface and do not interfere with each other (L = RF)sthe “mushroom” regime.29 In this case the area per molecule is estimated as the projection of the swollen coil: A = RF2 ∝ Ν6/5, which is very different from the experimental findings (Table 1). The scaling behavior of the layer thickness at saturation adsorption is markedly different. In the limit of high surface coverage the layer becomes a polymer brush.29,30 The PEO chains are terminally attached to the interface (via the hydrophobic “buoy”) and stretch into the solution in order to compensate the increased osmotic pressure (monomer-monomer interaction) inside the brush layer. The thickness of such a brush is29-31
L = a5/3
N A1/3
(1.7)
Thus the PEO chain does not retain its characteristic bulk size (RF) when incorporated into the adsorption layer. Interestingly differential scanning calorimetry measurements have led to the speculation that the hydration of the PEO chain increases when it elongates from a random coil to a brush.19 Equation 1.7 describes a grafted chain at fixed surface coverage, i.e., A.31 Recently experimental evidence was gathered that it also holds for PEO chains anchored at the water/air interface,32,33 but the area per molecule has to be determined independently. Generally A varies with the length of the tail and reflects the equilibrium condition of the self-assembly process. In the wake of a model used to derive the aggregation number of a micelle formed by an AB copolymer in selective solvent,31 we assume that the free energy per adsorbed molecule is composed of two terms: (28) Currie, E. P. K.; Wagemaker, M.; Cohen Stuart, M. A.; van Well, A. A. Macromolecules 1999, 32, 9041. (29) de Gennes, P. G. Macromolecules 1980, 13, 1069. (30) Alexander, S. J. Phys. (Paris) 1977, 38, 983. (31) Halperin, A.; Tirrell, M.; Lodge, T. P. Adv. Polym. Sci. 1992, 38, 31. (32) Sedev, R. Colloids Surf., A 1999, 156, 65. (33) Sedev, R.; Exerowa, D.; Findenegg, G. H. Colloid Polym. Sci. 2000, 278, 119.
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Notes
F ) Fint + Fconf
(1.8)
Uneven water distribution along the PEO chain as well as interpenetration between the hydrophobic and hydrophilic parts of the molecule are ignored. The interfacial free energy, Fint, can be written as constant + (A - A1)γ where A1 (
