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Structure of Partially Fluorinated Surfactant Monolayers at the Air-Water Interface† A. J. Jackson,*,‡,| P. X. Li,‡ C. C. Dong,‡ R. K. Thomas,‡ and J. Penfold§ Physical and Theoretical Chemistry Laboratory, South Parks Road, Oxford, OX1 3QZ, U.K., and ISIS, Rutherford-Appleton Laboratory, Chilton, Didcot, OX11 0QX, U.K. ReceiVed September 5, 2008. ReVised Manuscript ReceiVed October 29, 2008 Partially fluorinated cationic surfactants of the form CnF2n+1CmH2mN(CH3)Br have been prepared, and their behavior at the air-water interface has been studied using surface tension measurements and neutron reflectometry. The degree of fluorination has been varied while keeping the overall chain lengths similar. The results are compared with those previously obtained for C16H33N(CH3)Br (C16TAB). The structural studies show a decrease in molecular orientation with increasing fluorination. The mean tilt away from the surface normal varies from 55° for C16TAB to 25° for C8F17C6H12N(CH3)Br. The interfacial layer roughness is observed to be lower than that expected for a pure fluorocarbon surfactant.
Introduction There is not as yet a definitive model relating the structure of surfactants to the surface tension of their solutions in water. The qualitative picture is that the hydrophobic part of the surfactant (usually a hydrocarbon) forms a liquidlike hydrocarbon layer on the surface. This has a much lower surface tension than water, and the amount by which the tension is lowered from that of water then depends on the effectiveness with which this liquidlike layer covers and shields the aqueous surface. The main factor that would be expected to prevent the most effective coverage by the hydrocarbon layer is repulsion between the head groups, which will attenuate the layer. Conversely, an intermediate layer that also shields the hydrocarbon layer from water (e.g., ethoxy groups) might be expected to assist in the reduction of surface tension. A further complication occurs when the hydrophobic part of the surfactant is made up of two hydrophobic units of different type (e.g., aromatic rings and saturated hydrocarbon chains or fluorocarbon and hydrocarbon chains). The surface energies of the pure hydrophobic species are quite different, and the surface activity can be expected to depend on which fragment dominates the surface. Although surfactants containing groups of different hydrophobicity are widely used (e.g., linear alkyl benzene sulfonates and partially fluorinated surfactants), we know little about the relation between the position of the two groups in the molecule and the overall surface behavior. Studies of the structure of surfactant layers of these mixed hydrophobe types of surfactant at the air-water interface could shed some light on the important underlying mechanisms. We have a second reason for examining the surface structure of layers of more complex types of surfactants. As part of a study of surfactant mixing at interfaces,1-7 we have been aiming to † Part of the Neutron Reflectivity special issue. * Corresponding author. E-mail:
[email protected]. ‡ Oxford University. § ISIS. | Now jointly at The NIST Center for Neutron Research, Gaithersburg, MD 20899 and the Department of Materials Science and Engineering, University of Maryland, College Park, MD.
(1) Hines, J. D.; Thomas, R. K.; Garrett, P. R.; Rennie, G. K.; Penfold, J. J. Phys. Chem. B 1997, 101, 9215–9223. (2) Hines, J. D.; Fragneto, G.; Thomas, R. K.; Garrett, P. R.; Rennie, G. K.; Rennie, A. R. J. Colloid Interface Sci. 1997, 189, 259–267.
Table 1. Critical Micelle Concentrations and Limiting Surface Tension at the cmc for Fluorocarbon-Capped Surfactants cmc ( 0.03 mM
γlim ( 0.2 mN/m
T (K)
1.13 0.83 1.07 0.37 0.92
25.6 22.3 24.0 20.2 38.0
303 303 298 308 298
fC4hC11TAB fC5hC10TAB fC6hC8TAB fC8hC6TAB hC16TAB
Table 2. Area Per Molecule (A), Surface Excess (Γ), and Mean Thickness of a Surfactant Monolayer for Partially Fluorinated Surfactants and C16TAB Obtained from Neutron Reflectivity Measurements, Area Per Molecule (As), and Surface Excess (Γs) Calculated from Surface Tension Measurements Γ ( 10-6 Γs ( 10-6 A ( 2/Å2 mol m-2 τ ( 2/Å As ( 2 /Å2 mol m-2 fC4hC11dTAB fC5hC10dTAB fC6hC8dTAB fC8hC6dTAB dC16dTAB
39 42 39 43 44
4.26 3.95 4.26 3.86 3.69
28 26 27 28 22
58 53 47 50 59
2.86 3.13 3.53 3.32 2.80
select pairs of surfactants with strong interactions between the hydrophobic groups but with otherwise similar characteristics (e.g., size, head group, and critical micelle concentration (cmc)). This is because deficiencies in the regular solution model of interfacial mixing are often difficult to disentangle from the experimental error when there is a large difference in the cmc. A possible combination is fluorocarbon and hydrocarbon, which is known to exhibit a strong tendency to demix.8-10 However, only a limited range of pure fluorocarbon surfactants is generally available, and the structural differences between fluorocarbon and hydrocarbon surfactants of similar cmc are very large. In (3) Hines, J. D.; Thomas, R. K.; Garrett, P. R.; Rennie, G. K.; Penfold, J. J. Phys. Chem. B 1998, 102, 8834–8846. (4) Penfold, J.; Staples, E.; Cummins, P.; Tucker, I.; Thompson, L.; Thomas, R. K.; Simister, E. A.; Lu, J. R. J. Chem. Soc., Faraday Trans. 1996, 92, 1773– 1779. (5) Penfold, J.; Staples, E.; Cummins, P.; Tucker, I.; Thomas, R. K.; Simister, E. A.; Lu, J. R. J. Chem. Soc., Faraday Trans. 1996, 92, 1549–1554. (6) Penfold, J.; Staples, E. J.; Tucker, I.; Thompson, L. J.; Thomas, R. K. Physica B 1998, 248, 223–228. (7) Penfold, J.; Staples, E.; Tucker, I.; Thomas, R. K. J. Colloid Interface Sci. 1998, 201, 223–232. (8) Mukerjee, P.; Mysels, K. J. ACS Symp. Ser. 1975, 9, 329. (9) Mukerjee, P.; Handa, T. J. Phys. Chem. 1981, 85, 2298–2303. (10) Mukerjee, P.; Yang, A. Y. S. J. Phys. Chem. 1976, 80, 1388.
10.1021/la802928f CCC: $40.75 2009 American Chemical Society Published on Web 01/15/2009
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Table 3. Layer Thicknesses (τ) and Head-Group-Adjusted Thicknesses (τc) for fCnhCmTABs Compared with Their Calculated Hydrophobic Chain Lengths (lc), with Molecular Volumes (V) Also Shown fC4hC11TAB fC5hC10TAB fC6hC8TAB fC8hC6TAB
τ(1Å
τc ( 1 Å
lc ( 0.5 Å
V ( 8 Å3
28 26 27 28
25 23 24 25
20.5 19.2 19.2 19.2
640 640 635 650
partially fluorinated materials, the outer part of the hydrophobic chain can be fluorinated, and the remainder of the hydrophobic chain length can be adjusted to create values of the cmc that approximately match those of a corresponding pure hydrocarbon surfactant. For example, the surfactants C4F9C11H22N(CH3)3Br (fC4hC11TAB) and hC16TAB have identical head groups, almost identical chain lengths, and approximately the same cmc, but they have quite different surface activities and they would be expected to interact repulsively. The use of partial fluorination allows for the simplest possible approach, namely, varying the degree of interaction and chain stiffness through the introduction of groups without changing the basic geometry of the surfactant. We have shown in earlier studies3 that clues to the reasons for deviations from regular solution theory may come from structural changes in the layer that are associated with mixing. Neutron reflectometry is a powerful tool for the study of interfaces on the nanometer scale.11 In addition to determining interfacial layer thickness, the use of isotopic and elemental substitution allows detailed structural and compositional information about the interfacial layer to be obtained. A further requirement for our compounds was therefore that we should also be able to label the structures with deuterium in a way that would allow neutron reflection to lead to a description of the structure of the individual and mixed layers. Fluorine has similar neutron scattering characteristics to deuterium; therefore, by labeling the head group trimethyl functionality with deuterium we can use neutron reflection to determine the mean distance between the head group and the fluorocarbon group in the partially fluorinated surfactant. Hence, we have prepared a series of surfactants of the form CnF2n+1CmH2mN(CH3)Br (fCnhCmTAB) with unlabeled (fCnhCmhTAB) and deuterium-labeled (fCnhCmdTAB) head groups. The comparison of the structure of the pure partially fluorinated surfactants and their hydrocarbon counterparts turns out to be interesting in its own right, and we report the results here. We report the results of the experiments on the mixtures in a second paper.
Experimental Details Synthesis. The compounds studied were C4F9C11H22N(CH3)3Br (fC4hC11TAB), (CF3)2C3F5C10H20N(CH3)3Br (fC5hC10TAB), C6F13C8H16N(CH3)Br (fC6hC8TAB), and C8F17C6H12N(CH3)3Br (fC8hC6TAB), which were prepared as follows. The partially fluorinated alcohols were prepared by the addition of a perfluoroalkyl iodide (Fluorochem) across the terminal double bond of the appropriate n-alkenol12,13 (Aldrich). The n-perfluoroalkyl iodide was not available to synthesize fC5hC10TAB, thus the branched compound was used. The iodide was eliminated to give the saturated partially fluorinated alcohol,14 which was purified by preparative medium-pressure liquid chromatography (MPLC) on a silica column with a 50/50 mixture of diethyl ether and petroleum spirit as eluent. The alcohol was brominated, and following purification by MPLC, (11) Lu, J. R.; Thomas, R. K.; Penfold, J. AdV. Colloid Interface Sci. 2000, 84, 143–304. (12) Huang, W. Y. J. Fluorine Chem. 1992, 58, 1–8. (13) Huang, W. Y. J. Fluorine Chem. 1986, 32, 179–195. (14) Barton, D.; Jang, D. O.; Jaszberenyi, J. J. Org. Chem. 1993, 58, 6838– 6842.
the resulting alkyl bromide was reacted directly with trimethylamine in methanol to form the alkyl trimethylammonium bromide. The final trimethylammonium salts were initially recrystallized from acetone. Recrystallization before experimental work was from a hot ethanol/diethyl ether mixture followed by filtration under suction and rinsing with cold ethanol. Neutron Reflection. Neutron reflection measurements were performed on the reflectometers CRISP and SURF at the RutherfordAppleton Laboratory (Didcot, U.K.). The instruments and the procedure for making the measurements have been described fully elsewhere.15-17 Measurements were made at an incident angle of 1.5°, which gave a range of momentum transfer, κ () (4π sin θ)/λ, where θ is the glancing angle of incidence), from 0.5 to 3.5 nm-1, and a flat incoherent scattering background was subtracted. The level of the incoherent background, on the order of R ) 10-6, combined with the weak reflectivity from the samples to limit the useful range of κ to 0.5 to 2 nm-1. The conversion of measured signal to absolute intensity was made by calibration with D2O. Data analysis using the optical matrix method was performed using the program AFit by P. N. Thirtle. Kinematic approximation calculations were made using routines written by the authors for use with SigmaPlot (version 8 from SPSS Inc.). Surface Tension. The surface tension measurements were performed on a Kru¨ss K10T digital tensiometer and a Camtel CIT100 interfacial tensiometer by the du Nou¨y ring method with a platinum/iridium ring. The apparatus was calibrated with high-purity water (72.0 mN m-1 at 298 K), and the measured surface tensions were corrected using the equation of Zuidema and Waters.18
Results Surface Tension. Surface tension was used to establish the surface purity of all of the samples and to determine the surface activity and cmc. The surface purity was established by repeated recrystallization of the surfactants until no mimimum was observed in the surface tension at the cmc. Table 1 gives values of the cmc’s and limiting surface tensions (at the cmc) of all of the compounds studied. There are some interesting differences from the corresponding n-alkyl surfactants. For example, partially fluorinated fluorocarbon surfactants fC4hC11TAB and fC5hC10TAB have very similar cmc’s at 1.13 and 0.83 mM, respectively, to that of C16TAB at 0.92 mM, but the surface tension is considerably lower (25.6 and 22.3 mN m-1 for the fluorocarbon surfactants versus 38 mN m-1 for C16TAB). The significantly lower value for the fC5 compound may be as much to do with the terminal branch as with the extra group. The main reason for these differences in surface tension is almost certainly that the outer region of the saturated surfactant layer is largely composed of fluorocarbon and hydrocarbon in the two types of chains where the surface tension of a fluorocarbon is well known to be lower than that of a hydrocarbon. However, one could expect that disorder in the surfactant layers might promote mixing of the groups within the layer and hence reduce the tendency to form distinct layers. Adsorbed Layer Area Per Molecule. Neutron reflection experiments not only enable the determination of the structure of an adsorbed surfactant layer but, as we have shown elsewhere,11,19,20 are also capable of giving a more reliable measure of the amount of adsorbed surfactant than that obtained using surface tension measurements, especially for cationic (15) Penfold, J.; Ward, R. C.; Williams, W. G. J. Phys. (Paris) 1987, E20, 1411. (16) Penfold, J. Physica B 1991, 173, 1–10. (17) Penfold, J.; Ward, R. C.; Williams, W. G. ISIS Annu. Rep. 1995, 104. (18) Zuidema, H.; Waters, G. Ind. Eng. Chem., Anal. Ed. 1941, 13, 312. (19) An, S. W.; Lu, J. R.; Thomas, R. K.; Penfold, J. Langmuir 1996, 12, 2446–2453. (20) Simister, E. A.; Thomas, R. K.; Penfold, J.; Aveyard, R.; Binks, B. P.; Cooper, P.; Fletcher, P. D. I.; Lu, J. R.; Sokolowski, A. J. Phys. Chem. 1992, 96, 1383–1388.
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Table 4. Segment Volumes (V) and Scattering Length Densities (SLD) Used in Fitting the Reflectivity Data SLD × 10-6 Å-2
V ( 5 Å3
V ( 5 Å3
SLD × 10-6 Å-2
fC4 fC5 fC6 fC8
200 230 280 350
3.87 4.15 4.05 4.26
hC11 hC10 hC8 hC6
300 270 215 160
-0.31 -0.31 -0.31 -0.31
hTAB H2O
140 30
0.18 -0.52
dTAB D2O
140 30
6.69 6.36
Table 5. Fitting Parameters for fC4hC11TAB contrast
σFC/Å
σHC/Å
σH/Å
cmc cmc cmc cmc
fC4hC11hTAB/D2 O fC4hC11dTAB/D2 O fC4hC11hTAB/NRW fC4hC11dTAB/NRW
8 8 7 7
11 12 11/12 11/12
cmc/10
all
6
6
δW/Å
A/Å2
σW/Å
δFC/Å
δHC/Å
10 10 10 10
6 6 6 6
-14 -14 -14 -14
-8 -6 -6/-8 -6/-8
-10 -10 -10 -10
(0.5) (0.5) (0.5) (0.5)
39 39 39 39
8
6
-11
-5
-3 (-0.5)
59
Table 6. Fitting Parameters for fC5hC10TAB contrast
σFC/Å
σHC/Å
σH/Å
σW/Å
δFC/Å
δHC/Å
δW/Å
A/Å2
cmc cmc cmc
fC5hC10hTAB/D2 O fC5hC10dTAB/D2 O fC5hC10dTAB/NRW
9 9 9
14 14 14
14 14 14
8 8 8
-13 -13 -13
-7 -6 -7/-6
-10 (-0.5) -10 (-0.5) -10 (-0.5)
42 42 42
cmc/3
all
8
12
12
11
-11
-5
-6 (-0.5)
50
Table 7. Fitting Parameters for fC6hC8TAB contrast
σFC/Å
σHC/Å
σH/Å
σW/Å
δFC/Å
δHC/Å
δW/Å
A/Å2
all
9.5
8.5
12
10
-13.5
-6
-4(0.5)
39
cmc
Table 8. Fitting Parameters for fC8hC6TAB contrast
σFC/Å
σHC/Å
σH/Å
σW/Å
δFC/Å
δHC/Å
δW/Å
A/Å2
all all
10 10
12 10
12 10
9 15
-13 -12.5
-4 -5
-7 (-1.5) -2 (-1.5)
53 64
cmc/2 cmc/6
Table 9. Summary of Structural Fitting Parameters at the Lowest Area Per Molecule Studied surfactant
concentration/mM
σFC/Å
σHC/Å
σH/Å
σW/Å
δFC/Å
δHC/Å
δW/Å
A/Å2
fC4hC11TAB fC5hC10TAB fC6hC8TAB fC8hC6TAB
1.13 0.83 1.07 0.19
7.5 9 9.5 10
11.5 14 8.5 12
10 14 12 12
6 8 10 9
-14 -13 -13.5 -13
-7 -6.5 -6 -4
-10 (0.5) -10 (-0.5) -4 (0.5) -7 (-1.5)
39 42 39 53
Table 10. Fitting Parameters for C16TAB at the cmc
the surface excess Γ by
contrast
σC
σH
σW
δC
δW
A
dC16dTAB/NRW dC16dTAB/D2 O hC16hTAB/D2 O dC16hTAB/D2 O dC16hTAB/NRW
16.5 16.5 16.5 16.5 17.5
14 14 14 14 14
5 5 5 10/5 5
-8.5 -8.5 -8.5 -8.5 -8.5
-10 -10 -10 -10/-12 -10
44 44 44 44 39
Lu et al.
16.5
14
6.5
-8
-2
44
surfactants. The amount of these partially fluorinated surfactants adsorbed at the surface can be obtained from measurements of each surfactant with a deuterated head group in null reflecting water (NRW) (i.e., a mixture of 9 mole % D2O in H2O that has the same neutron refractive index as air) and fitting of the reflectivity data to a single-layer model. This allows the calculation of the area per surfactant molecule at the interface from
A)
∑ i bi Fτ
(1)
where Σibi is the scattering length of the surfactant, F is the scattering length density of the layer in the optical matrix model, and τ is the layer thickness. The area per molecule is related to
A)
1 NAΓ
(2)
where NA is Avogadro’s number, with the two concepts being equivalent in this simple case of a single surfactant species. We will use the area per molecule in our discussions. In all cases, a value of 3 Å was used for the intrinsic air-water interfacial roughness, and any roughness imposed by the presence of the surfactant is included in the calculated layer thickness. The areas per molecule and mean thicknesses of the layer at the cmc are compared in Table 2 with those of C16TAB. The layer thickness at the cmc is similar across all four surfactants, with fC5hC10TAB being slightly lower at 26 Å. The area per molecule at the cmc is similar for fC5hC10TAB and fC8hC6TAB (42 Å2 and 43 Å2, respectively), with fC4hC11TAB being lower at 39 Å2. It should be noted that these values differ significantly from those calculated using the Gibbs equation. This sort of discrepancy has been noted for a number of ionic surfactants,11,19,20 and because the neutrons provide a direct measure of the surface coverage, the values from the reflectivity measurements will be used in the following discussions.
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Figure 1. Reflectivity profiles and fits for fC4hC11TAB at four contrast conditions: fC4hC11hTAB/NRW (open black circles/long dashes), fC4hC11dTAB/NRW (closed black circles/solid line), fC4hC11hTAB/ D2O (open gray circles/short dashes), and fC4hC11dTAB/D2O (closed gray squares/dashed-dotted line).
A comparison of the layer parameters of the fCnhCmTAB’s at their cmc’s with those of C16TAB, a well-characterized hydrogenated surfactant21-23 of similar chain length, reveals interesting differences. C16TAB has a layer thickness of 22 Å and an area per molecule of 44 Å2, and it is thinner and has a slightly larger area per molecule than any of the four fCnhCmTAB’s. The orientation of C16TAB in the surface layer is known to be tilted away from the surface normal, with the tilt being greater in the outer part of the chain.23 The calculation of the tilt from single layer fits requires a comparison of the fully extended chain length of the surfactant hydrophobes with the measured layer thickness. Tanford’s formula24 for calculating the fully extended length of a linear hydrocarbon chain, lmax ) 1.5 + 1.265nc (where nc is the number of carbon atoms in the chain), can be employed here by noting that the C-C bond length in a fluorocarbon chain is the same as that in a hydrocarbon chain.25 In the case of branched fC5hC10TAB, molecular modeling26 was used to provide a value for the length. It was found that the fC5 segment has the same length as fC4. When comparing the chain length to the thickness, the head group (21) Lu, J. R.; Hromadova, M.; Simister, E.; Thomas, R. K.; Penfold, J. Physica B 1994, 198, 120–126. (22) Lu, J. R.; Hromadova, M.; Simister, E. A.; Thomas, R. K.; Penfold, J. J. Phys. Chem. 1994, 98, 11519–11526. (23) Lu, J. R.; Li, Z. X.; Smallwood, J.; Thomas, R. K.; Penfold, J. J. Phys. Chem. 1995, 99, 8233–8243. (24) Tanford, C. J. Phys. Chem. 1972, 76, 3020. (25) Kissa, E. Fluorinated Surfactants; Marcel Dekker: New York, 1994; Vol. 50. (26) http://www.bioinformatics.org/ghemical.
Figure 2. Volume fraction profiles derived from kinematic reflectivity fits for monolayers of partially fluorinated surfactants at their lowest measured area per molecule. (A) fC4hC11TAB, (B) fC5hC10TAB, (C) fC6hC8TAB, and (D) fC8hC6TAB. The monolayer components are the fluorocarbon segment (solid line), hydrocarbon segment (solid gray line), head group (dashed-dotted line), and water (short-dash line). The total volume fraction is shown by long dashes.
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Figure 3. Division of C16TAB into C2 segments showing the correlations with partially fluorinated surfactants used in comparisons of the mean tilt from the surface normal.
dimensions must be taken into account. The previous work on C16TAB21 suggests a value of 3 ( 1 Å, about equivalent to that for C2H4. In each case (Table 3), the fully extended length of the hydrophobic chain is less than the adjusted layer thickness, suggesting that the chains are fully extended in the layer and upright (i.e., with no tilt). This might be expected given the tendency of fluorocarbon and hydrocarbon to demix; tilting would increase the interaction between fluorocarbon and hydrocarbon segments. However, any roughness imparted to the surface by the presence of surfactant is included in the layer thickness, and the interfacial roughness is known to increase with decreasing surface tension. Thus, using a single-layer fit, we cannot distinguish between the conclusion that the chains are extended and upright from one where the chains are tilted and the layer is very rough. We will show below that roughness is the major contributor to the greater thickness. Despite this, the smaller areas per molecule that the partially fluorinated surfactants exhibit suggest that they are indeed more upright than C16TAB.
Figure 4. Orientation of partially fluorinated surfactants (solid line) at the interface compared with C16TAB (dashed line): (A) fC4hC11TAB, (B) fC5hC10TAB, (C) fC6hC8TAB, and (D) fC8hC6TAB.
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Table 11. Comparison of Head-Fluorocarbon Separation (δFC) Values from Modeling with Fully Extended Chain Lengths (lc) Calculated from Tanford’s Formula Using nc CH2 Units δFC ( 0.5 Å
lc/Å
nc
(lc - δFC) ( 0.5 Å
14.0 13.0 13.5 13.0
18.0 16.7 15.4 14.2
13.0 12.0 11.0 10.0
4.0 3.7 1.9 1.2
fC4hC11TAB fC5hC10TAB fC6hC8TAB fC8hC6TAB
Table 12. Head-segment Separations for fCnhCmTABs and Their Equivalents in C16TAB δFC/Å C16TAB equiv/Å δHC/Å C16TAB equiv/Å fC4hC11TAB fC5hC10TAB fC6hC8TAB fC8hC6TAB
14.0 13.0 13.5 13.0
11.2 (11) 10.25 9.3 (9.63) 8.9 (9.75)
7.0 6.5 6.0 4.0
6.0 5.5 (5.25) 4.55 (4.45) 3.6 (3.5)
Adsorbed Layer Structure. The measurements of the singleisotope species in NRW described above give only very limited structural information because of the comparable contributions from roughness and structural thickness. Because the roughness is expected to increase with decreasing surface tension, it then becomes difficult to judge whether the partial fluorination changes the structure of the layer. As we have shown previously, the use of multiple different isotopic species of surfactant and solvent can be used to explore the relative positions of fragments within the layer largely independently of interfacial roughness. Whereas the adsorbed surfactant layer can be described in terms of a series of slabs and the aforementioned fragment correlations are implicit in such a model, they can be examined more carefully and explicitly using the kinematic approximation. Here, the reflectivity can be described in terms of a series of partial structure factors,27,28 and either a set of measurements from a series of labeled compounds can be combined to give the partial structure factors directly or a set of partial structure factors can be fitted to the measured reflectivity. The latter, with the application of appropriate distributions for each component in the interface, requires fewer isotopic labels and avoids the problems of systematic errors and poor statistics from which the extraction of partial structure factors from data suffers. In this case, we make use of Gaussian distributions to describe the surfactant head group, hydrocarbon and fluorocarbon chain fragments, and a water distribution that is space-filling up to a certain distance into the surfactant layer and decaying as a halfGaussian thereafter.29 The reflectivity is given by
R)
16π2 κ2
[∑ bi2|Fˆi|2 + ∑ 2bibj|FˆiFˆj|] i
zf e zi e zhead (3)
iej
where Fˆi represents the Fourier transforms of the number density profiles of the components and bi represents their scattering lengths. It is often found that truncation errors in numerical Fourier transforms can be troublesome, and this problem can be eliminated by considering the Fourier transform of the scattering length density gradient instead
R)
16π2 κ4
[∑ i
bi2|Fˆ i′|2 +
∑ 2bibj|Fˆ i′Fˆ j′|]
isotopic compositions (contrasts). The partially fluorinated cationic surfactants were studied at four contrasts with a deuterated and protonated head group in NRW and D2O. The surfactant layer has been modeled using four componentss the fluorocarbon segment, FC, the hydrocarbon segment, HC, the head group, H, and the water, W. As discussed above, the surfactant components have been represented by Gaussian distributions, and the water has been represented by a distribution that is space-filling up to a cutoff value and then decays as a half-Gaussian. The surfactant components are thus each described by two values, the width of the Gaussian distribution (σFC, σHC, and σH) and the distance of the center of the distribution from the center of the head group distribution (δFC and δHC). The water distribution is strongly affected by the surfactant distributions, and the two parameters that are used in the calculation do not relate closely to the actual distribution, which can only be shown either diagramatically or as a table of data. Therefore, in addition to the parameters necessary to produce the fit, σW (the distance between the space-filling cutoff and the head group) and σW (the width of the half-Gaussian component), the distance from the head group to the position in the interface where the net adsorption of water is zero has been calculated. This is equivalent to the position of the dividing surface in the Gibbs treatment.30 In the tables of results, this value is given in parentheses with the value of δW. In addition to these surfactants, the data originally published by Lu et al.21 for C16TAB has been reanalyzed using the above method. This first provides some measure of validation of the fitting method because the only major difference that should occur is in the shape of the water distribution. Second, the C16TAB data can then be directly compared with the other cationic surfactants. In all cases, the fitting proceeded from an initial reasonable set of parameters, using the area per molecule calculated using the single-layer optical matrix fits, by a process of trial and error. Rather than perform the fit against the reflectivity, the more stringent test of fitting against Rκ4 was used. This removes the κ4 factor from the reflectivity (eq 4) and leaves data that is more directly related to the structure of the interface. The most important constraint on the selection of model parameters is that they should be physically reasonable. A simple result of this is that the fluorocarbon segment should be further from the head group than the hydrocarbon segment and both should be further out of the surface plane than the head group
(4)
iej
To study the structure of the layers using this approach, it is necessary to measure the reflectivity of a number of different (27) Crowley, T. L. D. Phil. Thesis, University of Oxford, 1984. (28) Crowley, T. L.; Lee, E. M.; Simister, E. A.; Thomas, R. K. Physica B 1991, 173, 143–156. (29) Jackson, A. J.; Li, Z. X.; Thomas, R. K.; Penfold, J. Phys. Chem. Chem. Phys. 2002, 4, 3022–3031.
(5)
where zi is the position of component i in the layer. The position of the head group has been taken as the zero value for z, and the air side of the interface has been taken as having negative z values. Another manifestation of the requirement of physicality is the necessity that the δ values are not greater than the fully extended chain length of the relevant section or partial section. Thus δHC must not be larger than 0.5lc + lhead, where lc is the chain length of the hydrocarbon segment of the partially fluorinated surfactant and lhead is a length accounting for the part of the head group that is included in δHC. The case of δFC is somewhat more complicated because simple geometry shows that the constraint should be
δFC e (lh + lhead)sin θh + 0.5lf
(6)
where (30) Gibbs, J. W. The Collected Works of J. Willard Gibbs; Longman Press: New York, 1931.
Partially Fluorinated Surfactant Monolayers
sin θh )
δHC 0.5lh + lhead
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(7)
and θh is the angle of tilt between the hydrocarbon segment of the hydrophobic chain and the surface plane. These constraints, although not explicitly included in the fitting routines, were respected during the fitting process. Having found a fit for a given set of data, the parameters were tested and adjusted appropriately to give a fit within the constraints. The molecular volumes of the segments are required as fixed parameters in the calculation of the volume fractions of the nonsolvent components and therefore indirectly determine the water distribution. The volumes of the hydrocarbon segments were calculated using Tanford’s method24 and from literature values of the density of hydrocarbons.31,32 The fluorocarbon volumes used were calculated from literature values for the density of flurorocarbons.33-35 Table 4 shows the values used in the reflectivity calculations. We will discuss the determination of the structure of fC4hC11TAB in some detail. Four isotopic compositions were used to determine the structure at the cmc. The chosen combinations were fC4hC11hTAB/D2O, fC4hC11dTAB/D2O, fC4hC11hTAB/NRW, and fC4hC11dTAB/NRW, resulting in the reflectivity profiles and fits shown in Figure 1. The correlation between the fluorocarbon fragment and the head group is well determined by the fC4hC11dTAB/NRW combination, and that between the fluorocarbon fragment and water is determined by fC4hC11hTAB/D2O. Somewhat surprisingly, the correlation of the hydrocarbon fragment with the other components of the layer can be well determined despite not using the chain deuterated species (the preparation of which would have presented a more difficult synthetic challenge). It is unclear exactly what the reasons for this are, but they must essentially result (a) from the strong well function in the scattering length density profile that the exclusion of strongly scattering material from the middle of the layer produces in the fC4hC11dTAB/D2O combination and (b) from having a strongly scattering fragment on the air side of the layer (a hydrocarbon layer on the outside would be essentially invisible). The reflectivity profiles (Figure 1) of the two contrasts are very similar and in the case of those measured at the cmc required slightly different parameters for the hC11 segment to provide satisfactory fits (Table 5). Both sets of parameters fitted the NRW contrasts because there is no measurable contrast between the hC11 and solvent, a factor that influences the fits in D2O. When it is not possible to use the same model parameters to fit all contrasts, the aim should be to minimize the differences between contrasts. In this case, the flurorocarbon parameters were largely fixed by the fC4hC11dTAB/NRW contrast, leaving the other parameters to be determined from the contrasts. The structure of the layer at cmc/10 was determined using only three of the isotopic compositions, with the fC4hC11hTAB/NRW combination giving a signal that was too weak to be worth analyzing. The data at cmc/10 fit (Table 5) to one set of parameters at all three contrasts. However, it was necessary to allow the area per molecule to vary in the range of 58 to 60 Å2. The measurements and data analysis for the other three partially fluorinated surfactants followed the same pattern as for (31) American Petroleum Institute. Selected Properties of Hydrocarbons; Technical Report, National Bureau of Standards, 1949. (32) Kurtz, S. J.; Sankin, A. In Physical Chemistry of the Hydrocarbons; Farkas, A., Ed.; Academic Press: New York, 1953; pp 1-80. (33) Brown, J. A.; Mears, W. H. J. Phys. Chem. 1958, 62, 960–962. (34) Burger, L. L.; Cady, G. H. J. Am. Chem. Soc. 1951, 73, 4243–4246. (35) Reed, T. I. J. Fluorine Chem. 1964, 5, 133–236.
fC4hC11TAB. As with fC4hC11TAB, it was necessary to fit the two fC5hC10TAB/D2O profiles measured at the cmc using slightly different parameters for the hC11 segment. The NRW contrasts fit both sets of parameters. The measurements made at cmc/3 were fit to a single set of parameters (Table 6). In the case of fC6hC8TAB, all four measured contrasts were fit with one set of parameters (Table 7). It was possible to fit all of the contrasts for fC8hC6TAB to one set of parameters at both of the coverages studied (Table 8). The most notable aspect of these results is the relatively high penetration of water into the layer. The position of zero water adsorption excess is 1.5 Å into the air side of the interface. Given that one might expect that greater fluorination would lead to a lower degree of hydration of the layer, this seems to be anomalous behavior and is discussed further in the general comparison. Table 9 give a summary of the structural parameters at the lowest measured area per molecule. In the cases where different contrasts required different parameters, Table 9 gives their average.
Discussion C16TAB was previously studied21,23 at its cmc (0.92 mM), where it has an area per molecule of 44 ( 2. The results of fitting the data from that study are shown in Table 10. The first three contrasts in the Table were all fit to the same set of parameters with an area per molecule of 44. In the case of the dC16hTAB/ NRW contrast, the fitted area per molecule is lower at 39. The dC16hTAB/D2O contrast is mainly sensitive to the interaction of the head group with the solvent. In this case, there is a range of solvent parameters giving similar solvent distributions, which provides a fit to the data. Hence as σW varies from 10 to 5 Å, δW varies from -10 to -12 Å (i.e., decreasing the distribution width requires a corresponding increase in the cutoff to counteract it). Comparison with the original calculations21 (Table 10) shows that the widths and separation of the chain (σC and δC) and head (σH and δH) segments are consistent within error. To describe the water distribution across the interface, the original study21 used a tanh distribution defined by
[ 21 + 21 tanh( ζz )]
nw ) nw0
(8)
where nw0 is the number density of bulk water and ζ is the width parameter of the distribution. Compared to such a distribution, the water distribution calculated here falls off more rapidly, resulting in less interfacial water. However, the difference is not large. The structures of the four partially fluorinated cationic surfactants(Figure2)sfC4hC11TAB,fC5hC10TAB,fC6hC8TAB, and fC8hC6TABsare broadly similar, as would be expected from their similar molecular structure. Although some allowance must be made for the differing areas per molecule, a number of structural trends can be clearly distinguished. The σ values (Table 9) contain contributions from both the intrinsic thickness of the distributions and the roughness, where the degree of roughness will increase with decreasing surface tension. In the case of the fluorocarbon segment, the two effects act in the same direction, and σFC does increase slightly from fC4 to fC8. In the case of the hydrocarbon fragment, the effects act in opposite directions, and now fC5hC10TAB has the largest σHC. However, the lower surface coverage for fC8hC6TAB could be significant, and if we assume that roughness changes inversely with area per molecule, which is fairly typical of a single smallmolecule species, then scaling to an area of 43 Å2 yields a σHC value of 15 Å, giving fC8hC6TAB the thicker hydrocarbon fragment. The trend in and size of σh matches those of σHC, and
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because the head group is much smaller, this suggests that the distribution widths are dominated by roughness that increases with the size of the fluorinated group. A comparison of the δFC values with the appropriate fully extended chain lengths (Table 11) suggests that the surfactant chains are not as fully extended and upright in the interfacial layer as the uniform layer model suggested. Because δ is independent of roughness, the fully extended lengths of appropriate hydrocarbon chains can be calculated from Tanford’s formula,24 incorporating an additional 1.5 Å to account for the head group. The difference between the values of δFC and lc decreases as the fluorination increases and the hydrocarbon segment length decreases. This implies that the hydrophobic chains become more upright as the level of fluorination increases. Because fluorocarbon chains are stiffer, having fewer gauche defects on average than hydrocarbons, the overall flexibility of the chain is decreasing from fC4hC11TAB to fC8hC6TAB, which may contribute to fC8hC6TAB being more upright than fC4hC11TAB. Further evidence of this behavior can be seen in the comparison of the δFC and δHC values for the fluorocarbon surfactants with the separation of comparable segments of C16TAB from the head group (Table 12). The comprehensive structural study of C16TAB by Lu et al.23 divided the hexadecyl chain into C2 segments by selective deuteration, and the separation of each of these segments from the head group was calculated. To compare the partially fluorinated surfactants with C16TAB, their fluorocarbon and hydrocarbon segments must be correlated with segments in C16TAB. The correlations are shown diagrammatically in Figure 3. The fluorocarbon segment of fC4hC11TAB can be correlated with the position of C2h(7)sthe seventh C2 segment from the head groupsbecause the fC4 segment occupies C(12) to C(15) of the chain and the center of that is the equivalent of C(13)-C(14), which is C2h(7). The hydrocarbon segment of fC4hC11TAB is more complex. The center of the hC11 chain is the position of C(6), with C(1) to C(5) on one side and C(7) to C(11) on the other. C(6) falls within the C2h(3) segment, and its position can be taken as being three-quarters of the distance into C2h(3). This position has been calculated on the basis of the separation of C2h(4) from C2h(3) using
δC6 )
δC2h(4) - δC2h(3) + δC2h(3) 4
(9)
The correlations for the other fluorocarbons are more straightforward.ThebranchedfluorinatedsegmentoffC5hC11TAB is the same length as a straight-chain fC4 segment, and hence its center falls halfway between C2h(6) and C2h(7) and can be calculated as the mean of their positions. The center of the hC10 segment equates to the position of C2h(3) but could also be calculated as the mean of C2h(1-5). In Table 12, the values given are those of the C2 segment that matches the center of the fluorocarbon segment of the molecule or the position calculated with the minimum number of C2 segment positions. The values in parentheses represent the means for the whole length of the segment. In fC6hC8TAB, the fC6 segment is equivalent to the position of C2h(6) or the mean of C2h(5-7) with the hC8 segment being equivalent to the mean of C2h(2-3) or C2h(1-4). The fC8 segment of fC8hC6TAB equates to the mean of C2h(5-6) or C2h(4-7) whereas the hC6 segment position is either that of C2h(2) or the mean of C2h(1-3). These comparisons allow a calculation of the orientation of the C16 chain that is directly comparable to the partially fluorinated surfactants. The mean surface orientation of the
hydrophobic chains can be calculated from simple geometry. Whereas the study of the structure of C16TAB shows that the C16 chain is not fully extended over greater than a C2 segment, it will be assumed for the purposes of the calculation that each segment (e.g., the C11 segment in fC4hC11TAB) is fully extended. Making this assumption for the C16TAB data effectively allows comparison with a notional scheme whereby C16TAB is deuterated to match the fluorination in the partially fluorinated surfactants. The fluorocarbon segments are known to be stiffer than an equivalent hydrocarbon chain, so the assumption of full extension is probably valid for those segments. The results of these calculations, shown in Figure 4, reveal that the partially fluorinated cationic surfactants are more vertically oriented in the interfacial layer than C16TAB. The hydrophobic chains become more upright with increasing fluorination, with fC4hC11TAB and fC5hC10TAB having similar mean chain orientations of about 45° from the surface normal, fC6hC8TAB having a 36° mean orientation, and fC8hC6TAB being closest to upright with a 25° mean orientation. These values are all more upright than C16TAB, which averages about 55°. The significantly lower surface free energies of fluorocarbons combined with the tendency of fluorocarbon and hydrocarbon to demix should cause the fluorocarbon segment to occupy the outer region of the interface. In doing so, the chains as a whole will be more vertically oriented at the interface. The higher-resolution study of C16TAB23 showed that the four carbons next to the head group (those immersed in water) are tilted only a relatively small amount from the surface normal, about 30°, presumably because of packing constraints close to the head group. A similar phenomenon almost certainly occurs here because, despite the strong tendency of the fluorocarbon to obtain the outer region of the interface, the hydrocarbon segment is more upright than the fluorocarbon. The degree of hydration of the interfacial layers of the partially fluorinated cationic surfactants is notable for the fact that it increases with increasing fluorination. The position of zero surface excess of water shifts from 0.5 Å to the water side of the interface for fC4hC11TAB and fC6hC8TAB to 1.5 Å to the air side of the interface for fC8hC6TAB. Although fC8hC6TAB is at a higher area per molecule, comparison with the results for fC5hC10TAB at 50 Å2 shows that the comparison remains valid and the fC8hC6TAB interfacial layer is wetter than that of the other three. This variation is, at first glance, counterintuitive because one might expect the increasing fluorination to cause less water to be associated with the interfacial layer as a result of the increasing hydrophobicity of the surfactant chain. However, the switch to a hydrocarbon segment that is shorter than the fluorocarbon segment may imply that the packing is now dominated by the fluorocarbon. This may reduce the ability of the hydrocarbon chains to pack as closely as in the other surfactants, prevent the formation of a dense water-excluding hydrocarbon region, and result in greater penetration of water into the surfactant layer. Most notable about the structural parameters for the partially fluorinated surfactants is that the capillary wave roughness is much lower than expected from simple assumptions about surface tension. The contribution of capillary waves to the roughness can be taken to be inversely proportional to the surface tension, so lower surface tension should increase the roughness. However, here we see that the roughness of all segments is lower than that for C16TAB with the underlying hydrocarbon segment and head group displaying a larger roughness than does the overlying fluorocarbon layer. It is possible that the driving force for the steeper molecular tilt and decreased roughness is thermodynamic
Partially Fluorinated Surfactant Monolayers
and related to the tendency of the fluorocarbon and hydrocarbon segments to demix. In minimizing the interaction between the two components of the hydrophobe, the molecules must adopt a more upright orientation and lower roughness.
Conclusions Cationic surfactants with partially fluorinated hydrophobes where the fluorination is terminal form monolayers at the air-water interface that are more closely packed, with more upright mean molecular orientation, than an equivalent hydrogenated surfactant (C16TAB). The interfacial roughness measured for these surfactants is much lower than expected and lower than that of C16TAB. This latter effect is an interesting result and
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may result from a minimization of interaction between fluorocarbon and hydrocarbon components. Such behavior may have implications for the behavior of mixed surfactant systems comprising partially fluorinated surfactants and hydrogenated equivalents. Acknowledgment. We thank the EPSRC for support, ISIS for access to neutron reflectometry instruments, and the ISIS instrument scientists for their assistance. A.J.J. thanks Kodak Ltd for funding through the EPSRC CASE scheme and L. Simister and A. Pitt for valuable discussions and support. LA802928F
