Direct Determination by Neutron Reflectometry of the Distribution of

Hydrogenous and deuterated isomers of poly(ethylene oxide) have been capped at one end by a C6F13 fluorocarbon group. For the three molecular weights ...
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Langmuir 2003, 19, 7768-7777

Direct Determination by Neutron Reflectometry of the Distribution of Hydrophobically End Capped Polyethylene Oxide at the Air/Water Interface† Randal W. Richards* and Jordan Sarica Interdisciplinary Research Centre in Polymer Science and Technology, University of Durham, Durham, DH1 3LE, United Kingdom

John R. P. Webster and Stephen A. Holt ISIS Science Division, Rutherford Appleton Laboratory, Chilton, Didcot, Oxon OX11 0QX, United Kingdom Received October 22, 2002. In Final Form: January 8, 2003 Hydrogenous and deuterated isomers of poly(ethylene oxide) have been capped at one end by a C6F13 fluorocarbon group. For the three molecular weights investigated (ca. 2000, 5000, and 10 000 g mol-1), the surface tensions of the aqueous solutions decrease over the concentration range 10-7 to 10-2 g mL-1, the lowest surface tension observed being ca. 20 mN m-1. Neutron reflectometry has been used to determine the nature, thickness, and composition of the surface excess region. At high concentrations of polymer in solution, the surface excess region has a two-layer organization, the lower layer consisting of micelles at the underside of an upper layer at the air-water interface. For the lowest molecular weight polymer, the upper layer attains a thickness that is more than twice the radius of gyration of the polymer, indicative of a highly extended configuration and adsorption to the interface by the fluorocarbon end group. The upper layer dimensions for the two higher molecular weight polymers are of the same order as their radii of gyration, and it appears that adsorption is due to both the fluorocarbon end and ethylene oxide segments in the molecule. Although the surface excess concentration for these two polymers is considerably less than that of the 2000 g mol-1 polymer, all have surface excess concentrations that are at least 2 orders of magnitude greater than for unmodified poly(ethylene oxide). Small-angle neutron scattering has been used to define the nature of the micelles, but the low concentrations and consequent weak signals meant that insufficient detail was in the scattering to allow a quantitative description. However, the micelles of the higher molecular weight polymers appear to have a more diffuse organization than those formed by the lowest molecular weight polymer.

Introduction Tethering polymers to an interface by one end has been a focus of interest for a number of years.1-5 Their role in stabilizing colloidal dispersions has been appreciated for a considerable time;5 more recently the possibility of using tethering to inhibit protein adsorption, influence lubrication, and control viscoelastic moduli of membranes at fluid interfaces6,7 and evaluation of their use as self-regulating flow control valves have been explored.8-10 An aspect of particular interest has been the extent to which tethered polymer layers can be described as brushlike layers, and the factors that promote such behavior have been explored and predictions compared with experimental data.1,2,11-14 * To whom correspondence should be addressed. † Part of the Langmuir special issue dedicated to neutron reflectometry. (1) Alexander, S. J. Phys. (Paris) 1977, 38, 977. (2) de Gennes, P. G. Macromolecules 1980, 13, 1069. (3) Fleer, G. J.; Cohen Stuart, M. A.; Scheutjens, J. M. H. M.; Cosgrove, T.; Vincent, B. Polymers at Interfaces; Chapman and Hall: London, 1993. (4) Jones, R. A. L.; Richards, R. W. Polymers at Surfaces and Interfaces; Cambridge University Press: Cambridge, 1999. (5) Hunter, R. J. Foundations of Colloid Science; Oxford University Press: Oxford, 1987; Vol. 1. (6) Kent, M. S. Macromol. Rapid Commun. 2000, 21, 243. (7) Szleifer, I.; Carignano, M. A. Macromol. Rapid Commun. 2000, 21, 423. (8) Sevick, E. M.; Williams, D. R. M. Macromolecules 1994, 27, 5285. (9) Kumaran, V. Macromolecules 1993, 26, 2464. (10) Barrat, J.-L. Macromolecules 1992, 25, 832. (11) Carignano, M. A.; Szleifer, I. Macromolecules 1995, 28, 3197.

Although much of the theory is concerned with the interfacial pressure developed in tethered polymer layers and the nature of any changes as the interfacial organization changes from “pancake” to brush, a key parameter is the thickness of the layer (or brush height) and its dependence on surface coverage. Various systems have been used to provide experimental data, via small-angle neutron scattering,15-19 neutron reflectivity, and the earlier force-distance experiments,6,20-35 neutron reflec(12) Barentin, C.; Joanny, J. F. Langmuir 1999, 15, 1802. (13) Szleifer, I.; Carignano, M. A. Adv. Chem. Phys. 1996, 94, 165. (14) Szleifer, I. Europhys. Lett. 1998, 44, 721. (15) Aubouy, M.; Fredrickson, G. H.; Pincus, P.; Raphaeel, E. Macromolecules 1995, 28, 2979. (16) Aubouy, M.; Guiselin, O.; Raphael, E. Macromolecules 1996, 29, 7261. (17) Auroy, P.; Auvray, L.; Leger, L. Phys. Rev. Lett. 1991, 66, 719. (18) Auroy, P.; Auvray, L.; Leger, L. Macromolecules 1991, 24, 2523. (19) Auvray, L.; Auroy, P.; Cruz, M. J. Phys. I 1992, 2, 943. (20) Baranowski, R.; Whitmore, M. D. J. Chem. Phys. 1998, 108, 9885. (21) Bisterbosch, H. D.; de Haan, V. O.; de Graaf, A. W.; Mellema, M.; Leermakers, F. A. M.; Cohen-Stuart, M. A.; van Well, A. A. Langmuir 1995, 11, 4467. (22) Currie, E. P. K.; Wagemaker, M.; Cohen Stuart, M. A.; van Well, A. A. Macromolecules 1999, 32, 9041. (23) Baranowski, R.; Whitmore, M. D. J. Chem. Phys. 1995, 103, 2343. (24) Factor, B. J.; Lee, L. T.; Kent, M. S.; Rondelez, F. Phys. Rev. E 1993, 48, R2354. (25) Field, J. B.; Toprakcioglu, C.; Dai, L.; Hadziioannou, G.; Smith, G.; Hamilton, W. J. Phys. II 1992, 2, 2221. (26) Karim, A.; Satija, S. K.; Douglas, J. F.; Ankner, J. F.; Fetters, L. J. Phys. Rev. Lett. 1994, 73, 3407.

10.1021/la026730x CCC: $25.00 © 2003 American Chemical Society Published on Web 03/06/2003

Determination of Distribution of End-Capped PEO

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Chart 1. Schematic Molecular Structure of Polymers

tivity providing the most direct access to such aspects as layer composition and thickness. Considerable attention has been devoted to polymers at solid-liquid interfaces, but the most extensive studies have been on spread polymer films at fluid interfaces. In most cases, the spread polymer is a block or graft copolymer with the insoluble component acting as an anchor. Such spread films provide a flexible means of varying the surface concentration merely by compressing the film. However, Szleifer14 has pointed out that some aspects of the behavior of the tethered polymer in these situations may not be due merely to the surface density of tethered chains but also result from repulsions between the insoluble anchor block and the soluble tethered portion. Rather than spread a polymer film, it would be more convenient to have a surface layer self-assemble at an interface to a sufficiently high surface density that brush formation is favored. Poly(ethylene oxide) (PEO) is a polymer that, in aqueous solution, forms a surface excess layer.36 It is not however a brushlike layer; a rather flat layer structure develops37 that can be likened to the oftcited pancake organization. Modification of poly(ethylene oxide) by attaching a hydrophobic group to one end dramatically changes the association behavior of the polymer and the surface tension of aqueous solutions. The distinctive viscoelastic and fluorescence properties and eventual gelation of poly(ethylene oxide)s capped at both ends in solution have been reported.38-40 When fluorocarbons were the end caps, in addition to micelle formation, enhanced adsorption of the polymer to both the aqueous solution and the bulk solid-air interfaces was noted from surface tension and X-ray photoelectron spectroscopy (XPS) data.41,42 The conclusion was that the polymer was (27) Kent, M. S.; Lee, L. T.; Factor, B. J.; Rondelez, F.; Smith, G. S. J. Chem. Phys. 1995, 103, 2320. (28) Kent, M. S.; Factor, B. J.; Satija, S.; Gallagher, P.; Smith, G. S. Macromolecules 1996, 29, 2843. (29) Lee, L.-T.; Factor, B. J.; Rondelez, F.; Kent, M. S. Faraday Discuss. 1995, 98, 139. (30) Levicky, R.; Koneripalli, N.; Tirrell, M.; Satija, S. K. Macromolecules 1998, 31, 3731. (31) Liu, Y.; Schwarz, S. A.; Zhao, W.; Quinn, J.; Sokolov, J.; Rafailovich, M.; Iyengar, D.; Kramer, E. J.; Dozier, W.; et al. Europhys. Lett. 1995, 32, 211. (32) Mansfield, T. L.; Iyengar, D. R.; Beacage, G.; McCarthy, T. J.; Stein, R. S. Macromolecules 1995, 28, 492. (33) Miller, A. F.; Richards, R. W.; Webster, J. R. P. Macromolecules 2000, 33, 7618. (34) Miller, A. F.; Richards, R. W.; Webster, J. R. P. Macromolecules 2001, 34, 8361. (35) Perahia, D.; Wiesler, D. G.; Satija, S. K.; Milner, S. T. Phys. Rev. Lett. 1994, 72, 100. (36) Glass, J. E. J. Phys. Chem. 1968, 72, 4459. (37) Lu, J. R.; Su, T. J.; Thomas, R. K.; Penfold, J.; Richards, R. W. Polymer 1996, 37, 109. (38) Xu, B.; Li, L.; Yekta, A.; Masoumi, Z.; Kanagalingam, S.; Winnik, M. A.; Zhang, K.; Macdonald, P. A.; Menchen, S. Langmuir 1997, 13, 2447. (39) Zhou, J.; Zhuang, D.; Yuan, X.; Jiang, M.; Zhang, Y. Langmuir 2000, 16, 9653. (40) Alami, E.; Almgren, M.; Brown, W.; Francois, J. Macromolecules 1996, 29, 2229.

attached to the surface by the fluorocarbon end, especially as the observed surface tensions of the aqueous solutions were much lower than that of a pure PEO melt. At high surface density, and if adsorption by one end is preferred, the possibility of a brushlike adsorbed layer becomes distinct. However, there has been no direct evidence for this in such solutions of end-fluorinated polymer. We report here the organization at the air-solution interface determined by neutron reflectivity of poly(ethylene oxide), capped at one end by a fluorocarbon sequence of modest size (Chart 1). The influence of both polymer molecular weight and bulk concentration of polymer on the composition and dimensions of the surface excess layer of polymer have been investigated, and we compare the results with theoretical predictions and with the available data for the surface excess layer of unmodified poly(ethylene oxide). Background Theory. A neutron reflectivity experiment provides the variation in reflectivity (reflected beam intensity divided by incident beam intensity) as a function of scattering vector, Q ()4π sin θ/λ where θ is the grazing angle of incidence and λ is the neutron wavelength), for a beam of neutrons incident on a smooth surface. The Q dependence of the reflectivity is determined by the variation in scattering length density, F, normal to the surface, and because the scattering length density is directly related to the composition, neutron reflectivity data can be interpreted to provide the composition profile normal to the surface. The most widely applicable analysis method is that based on the optical matrix description of reflectivity, where the near-surface region is modeled by a series of stratified layers whose thickness and composition will reproduce the reflectivity profile.43 Because layer thickness and scattering length density are coupled, the uniqueness of the model producing the fit may sometimes be questionable. When the reflectivity is small, that is, no greater than ca. 10-2, the kinematic approximation can be used,44 the reflectivity being given by

R(Q) )

16π2 F(Q)2 Q2

(1)

where F(Q) is the one-dimensional Fourier transform of the scattering length distribution normal to the surface. For the case of an aqueous polymer solution with a surface excess layer, the kinematic approximation for the reflec(41) Su, Z.; Wu, D.; Hsu, S. L.; McCarthy, T. J. Macromolecules 1997, 30, 840. (42) Su, Z.; McCarthy, T. J.; Hsu, S. L.; Stidham, H. D.; Fan, Z.; Wu, D. Polymer 1998, 39, 4655. (43) Penfold, J.; Thomas, R. K. J. Phys.: Condens. Matter 1990, 2, 1369. (44) Lu, J. R.; Thomas, R. K.; Penfold, J. Adv. Colloid Interface Sci. 2000, 84, 143.

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tivity is

R(Q) )

Table 1. Molecular Weights, Radii of Gyration, and Fluorocarbon Content of End-Functionalized Polymers

16π2 2 (bp hpp(Q) + bw2hww(Q) + 2bpbwhpw(Q)) Q2 (2)

where hii is the self-partial structure factor which is the one-dimensional Fourier transform of the number density distribution of species normal to the interface, p signifying polymer, w signifying water. Interpreting the self-partial structure factors by suitable models gives the spatial dimensions and composition of the near-surface region. The cross partial structure factor, hij, can give insight into the center-to-center separation of the near-surface polymer and water layers. To extract each of these three partial structure factors requires neutron reflectivity data at three different contrasts obtained by various combinations of hydrogenous and deuterated polymer and subphase. Thus deuterated polymer in null reflecting water (a mixture of light and heavy water with zero net scattering length density, signified by NRW) gives hpp directly because all other partial structure factor contributions to eq 2 are zero. Hydrogenous polymer in heavy water makes the water partial structure factor term dominant, and the combination of deutero polymer in heavy water lifts the contribution of the cross partial structure factor. By solving simultaneously each of the three expressions for R(Q), the individual partial structure factors can be obtained. For reflectivities greater than ca. 5 × 10-2, a correction has to be applied45,46 to the data before they can be expressed in the kinematic approximation form of eq 2. In general, this correction is usually needed only for those systems where the solvent is deuterated. In these cases, the reflectivity to use in eq 2 is given by

polymer

Mn/g mol-1

2KHPEO-C6F 2KDPEO-C6F 5KHPEO-C6F 5KDPEO-C6F 10KHPEO-C6F 10KDPEO-C6F

2553 2323 5363 4933 9643 9823

Rg/Å 18 28 42

fluorocarbon ends per molecule 1.1 0.9 1.1 0.83 0.9 0.8

In all of the above equations, Qc is the scattering vector associated with critical reflection between the two bulk phases. All of the data reported here pertain to the organization of the fluorocarbon end modified poly(ethylene oxide) only but have been obtained by the solution of the series of simultaneous equations of the form of eq 2.

On complete conversion of the monomer (typically after 1 week at 343 K), the living polymer was terminated by addition of degassed acetic acid, giving a polymer with a hydroxyl group at one end. Molecular weights were determined by size exclusion chromatography using dimethyl formamide as solvent and both mass and light scattering detection. End functionalization was carried out according to the procedure detailed by Xu et al.38 In brief, tridecafluorooctylisophorone monoisocyanate was prepared by reaction of tridecafluoro-1-octanol with excess isophorone diisocyanate. The hydroxylterminated poly(ethylene oxide) was dried under a vacuum at 383 K in a reaction flask, and after cooling dry ethylene glycol dimethyl ether was added to the flask followed by a solution of the tridecafluorooctylisophorone monoisocyanate and the whole contents were heated to reflux with stirring. Three drops of dibutyl tin laurate were added as catalyst, and the reaction was refluxed under dry nitrogen for 8 h. After cooling, the contents were poured into excess hexane, and the crude polymer was recovered and washed by refluxing separately in hexane and methyl tert-butyl ether before being dissolved in refluxing ethyl acetate and allowed to crystallize on cooling. Three molecular weights of polymer are discussed here, ca. 2000, 5000, and 10 000 g mol-1; for each a hydrogenous and a deuterated version were synthesized. For ease of reference, the notation nKSPEO-C6F will be used, where n signifies the molecular weight (n ) 2, 5, or 10) and S the isotopic species (D or H). The extent of functionalization by the fluorocarbon for each polymer was determined by 19F NMR using added 1,4-difluorobenzene as an internal calibrant; these data together with the molecular mass of each polymer are reported in Table 1. Surface Tension. Surface tension data for aqueous solutions of each polymer at 298 K were obtained using a Kru¨ss tensiometer and a platinum Wilhelmy slide. Solutions were prepared in ultrapure water (80 MΩ cm-1 resistivity), and data were recorded when a constant value of the surface tension was obtained. In most cases, equilibrium values required 3 h to be achieved. Neutron Reflectometry. Neutron reflectometry data on aqueous solutions of the end-fluorinated polymers were collected using the SURF reflectometer at the ISIS pulsed neutron source, Rutherford Appleton Laboratory, Didcot, U.K. Solutions were placed in Teflon troughs inside sealed containers with quartz inlet and outlet windows for the incident and reflected neutron beams. Data were converted to absolute reflectivity using calibration factors obtained from fitting to the reflectivity from heavy water. The range of scattering vector (Q) explored was 0.017 e Q/Å-1 e 0.6, this being achieved by using three different angles of incidence of the neutron beam. Three isotopic combinations were used: deutero polymer in NRW, hydrogenous polymer in heavy water, and deutero polymer in heavy water. The range of concentrations used was 10-7 g mL-1 e c e 10-2 g mL-1, although the highest concentration that could be used for the 2KPEO-C6F polymers was 10-3 g mL-1. At higher concentrations, phase separation was evident as oily droplets visible to the naked eye dispersed throughout the aqueous phase.

Experimental Section

Results

Polymer Synthesis. Poly(ethylene oxide) was synthesized by anionic polymerization under a high vacuum using diphenyl methyl potassium as initiator and tetrahydrofuran as solvent.

Surface Tension. The dependence of surface tension on polymer concentration for all three molecular weights is shown in Figure 1. At very low concentrations, the surface tension is essentially that of pure water. For 2KHPEO-C6F and 5KHPEO-C6F, the surface tension falls rapidly until a fairly sharp break is observed at higher concentrations, whereafter the surface tension is constant.

R(Q) ) Rk(Q) +

[

]

1 + (1 - Qc2/Q2)1/2 2 2 RExpt(Q) - Rs(Q)

[

1 - Rs(Q)

]

(3)

where Rk(Q), Rs(Q), and RExpt(Q) are the reflectivities calculated by the kinematic approximation, the exact optical matrix method, and the observed reflectivity, respectively. Rk(Q) and Rs(Q) apply to the bulk phases only, that is, air and water, and are given by

Rk(Q) ) Rs(Q) )

[

16π2 (Fw - Fair)2 Q4

]

1 - (1 - Qc2/Q2)1/2

2

1 + (1 - Qc2/Q2)1/2

(45) Lu, J. R.; Simister, E. A.; Lee, E. M.; Thomas, R. K.; Rennie, A.; Penfold, J. Langmuir 1992, 8, 1837. (46) Lu, J. R.; Lee, E. M.; Thomas, R. K.; Penfold, J.; Flitsch, S. L. Langmuir 1993, 9, 1352.

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Figure 1. Surface tensions of aqueous solutions of fluorocarbon end capped poly(ethylene oxide)s.

Figure 3. Reflectivity data for 2KDPEO-C6F in null reflecting water for selected concentrations of the bulk solution.

Figure 2. Reflectivity data at a concentration of 10-3 g mL-1 in null reflecting water. Solid lines are fits to the data from the use of optical matrix analysis.

Figure 4. Reflectivity data at a concentration of 10-5 g mL-1 in null reflecting water. Solid lines are fits to the data from optical matrix analysis.

For 10KHPEO-C6F, the decline in surface tension is not so monotonic but a fairly definite break is observed at a concentration of ca. 5 × 10-4 g mol-1. The surface tension of unmodified poly(ethylene oxide) exhibits quite different behavior, a constant value of ∼60 mN m-1 being rapidly obtained on increasing the concentration of PEO in solution. Neutron Reflectometry. The neutron reflectivities from solutions of each of the polymers are quite different to each other. Figure 2 shows the reflectivity for DPEOC6F in NRW for each molecular weight at a concentration of 10-3 g mL-1. Evidently the reflectivity from the 2KDPEO-C6F is significantly different from that of the 5KDPEO-C6F which also exhibits differences to the reflectivity of 10KDPEO-C6F. These differences are more evident in the double logarithmic plot for these same data shown in the inset to Figure 2. The 5KDPEO-C6F reflectivity has some evidence of a residual fringe in the data but by no means as definitive as observed for the 2KDPEO-C6F polymer. The reflectivity for the 10KDPEO-C6F polymer is very similar to that observed for unmodified poly(ethylene oxide) solutions, that is, a continuous smooth decay of the reflectivity with no distinguishing features until background signal is reached. Figure 3 shows the variation of reflectivity with concentration for the 2KDPEO-C6F polymer. For the three highest concentrations in Figure 3, the reflectivities are very similar. At a concentration of 10-4 g mL-1, the fringe located at ca. Q ) 0.07 Å-1 becomes slightly less well defined; this loss of definition continues as the concentration decreases (data sets not shown in Figure 3)

further to 5 × 10-5 g mL-1, and at a concentration of 10-5 g mL-1 and below there is no evidence for a fringe at all in the reflectivity. Figure 4 shows the reflectivity for all three molecular weight polymers all at the same bulk concentration of 10-5 g mL-1. The evidence for a strong fringe in the data for the 2KDPEO-C6F has disappeared, but the shape of the reflectivity is very different still to that of the higher molecular weight polymers. For these latter, although the reflectivity is mainly a smooth decay, there is a weak maximum for each centered at Q ≈ 0.1 Å-1 indicative of a near-surface layer that is not as diffuse as that normally seen for adsorbed polymer layers at fluid interfaces. Although not shown in the figures, the reflectivity for 10KDPEO-C6F changes but little as the bulk concentration is reduced until a concentration of 10-6 g mL-1 is reached whereat the reflectivity begins to decrease in magnitude. Discussion Optical Matrix Analysis. To aid subsequent analysis of the partial structure factors, optical matrix analysis of the reflectivity data was undertaken using the minimum number of layers to fit the reflectivity data. Each layer was characterized by a thickness, a scattering length density, and a mean square Gaussian roughness between each layer. We focus on the 2KDPEO-C6F polymer being the polymer that provides reflectivity data with the most “structure” in it. For bulk solution concentrations up to 10-5 g mL-1, a single uniform layer model is sufficient; at higher concentrations a second thicker but less concentrated layer is needed. The fits to the reflectivity data

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Figure 5. Number density distributions from optical matrix analysis of reflectivity data for aqueous solutions of 2KDPEOFC6F with the bulk concentrations indicated.

using these models are included as the solid lines in Figures 2 and 4. The parameters of each layer thickness, scattering length density, and interfacial roughness have been converted to a number density distribution of 2KDPEO-C6F using the relation

F(z) ) bn(z) where F(z) is the scattering length density at a distance z from the surface, b is the scattering length, and n(z) is the number density of polymer molecules. Examples of the number density distribution are given in Figure 5. The upper (near air) layer shows a decrease in number density and an increase of thickness as the bulk concentration increases above 10-5 g mL-1, indicative of a stretching of the adsorbed polymer molecules rather than incorporation of more polymer into the layer. At these lower concentrations, the interface with the bulk aqueous phase is somewhat diffuse. At higher concentrations where a second layer is definitely evident, several aspects regarding the upper layer are apparent: (a) the layer thickness becomes constant, (b) the number density of the upper layer becomes constant, and (c) a sharp interface develops between the upper and lower layers. The latter suggests a low degree of interpenetration between the layers. Kinematic Approximation Analysis. Reflectivity data for each combination of deuterated and hydrogenous polymer and water were expressed in the form of eq 2 using the appropriate scattering lengths for each combination and after incorporating the corrections where D2O was the solvent. These equations were then solved for the partial structure factors, but only those for the polymer, hpp, are discussed here. Partial structure factors obtained for 2KDPEO-C6F at selected concentrations are shown in Figure 6. At low concentrations of polymer, the partial structure factor increases with Q, a maximum being evident for some concentrations. For solution concentrations greater than ∼3 × 10-5 g mL-1, the partial structure factors are radically different; two maxima are evident, that centered at higher Q being of larger amplitude than that at lower Q. The maximum in the partial structure factor at higher Q does not move in Q as the concentration increases and is coincident with the single maximum observed for lower concentration solutions. The maximum at lower Q moves slightly to lower Q values as the solution concentration increases, and at the highest concentration the position of the maximum is cut off by the low Q limit of the scattering vector range.

Figure 6. Partial structure factors for 2KDPEO-C6F at selected solution concentrations: (a) 10-3 g mL-1, (b) 3 × 10-5 g mL-1, and (c) 10-5 g mL-1.

Fits to the low concentration solution partial structure factors are obtainable using either a single uniform density layer of polymer at the surface or a Gaussian distribution of polymer molecules. The quality of the fits are indistinguishable between either of the model functions, but the Gaussian distribution is a more physically viable description of the distribution. For a single Gaussian distribution given by

n(z) ) n1 exp(-4z2/σ2)

(4)

where σ is the full width at half-height of the distribution

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and defines the layer thickness, the partial structure factor is

Q2hpp(Q) ) n12

(

)

πQ2σ2 -Q2σ2 exp 4 8

(5)

For solutions with concentrations greater than 3 × 10-5 g mL-1, that is, where the partial structure factors exhibited two maxima, a double Gaussian distribution was found to give the best fit to the data. This distribution is given by

( )

n(z) ) n1 exp

(

)

-4(z + δ)2 -4z2 + n exp 2 σ2 τ2

n1 and n2 being the number density of polymer molecules at the maximum of each Gaussian peak that have full widths at half-height of σ and τ, and δ is the distance between the maxima. The partial structure factor is given by

(

)

2 2

-Q τ 8

(

) (

πQ2σ2 -Q2σ2 πQ2τ2 exp exp + n22 4 8 4 -Q2(σ2 + τ2) στπQ2 exp + n1n2 cos(Qδ) 2 16

Q2hpp(Q) ) n12

)

The best nonlinear least-squares fits of these model partial structure factors to the data are shown in Figure 6 as the solid lines. The fits were obtained by adjusting n1, n2, σ, and τ with δ ) (σ + τ)/2, the number of parameters depending on whether a single or double Gaussian was used. These same models were also applied to the selfpartial structure factors obtained for the 5KDPEO-C6F and the 10KDPEO-C6F; for the latter polymer the quality of the fits was not as good and attributable to the rather more diffuse distribution of the polymer at the air-water interface for these higher molecular weight polymers. However, a single-layer model was not appropriate for the 10KDPEO-C6F polymer at any concentration and only valid for the two lowest concentration solutions of 5KDPEO-C6F. The dependences of the number density and distribution full widths at half-height (σ and τ) on solution concentration are shown in Figures 7 and 8. The behavior of the number density at distribution maximum is dependent on the polymer; for the 2KDPEO-C6F, the upper layer number density (n1) increases rapidly to a constant value of ca. 1.5 × 10-4 Å-3 whereas the lower layer number density (n2) increases gradually to what appears to be a constant value of ∼7 × 10-5 Å-3. Number densities of the 5KDPEO-C6F polymer for the upper layer are less than half the magnitudes of those of the 2KDPEOC6F polymer, a more gradual increase to the constant value of 6 × 10-5 Å-3 being evident. The lower layer has a constant number density of 2 × 10-5 Å-3 and attains this value over a very narrow range of bulk solution concentration. Number densities of the 10KDPEO-C6F polymer are further reduced, a constant value being observed over the whole range of concentration. The upper layer has a number density of 2 × 10-5 Å-3, and that of the lower layer is 5 × 10-6 Å-3, an order of magnitude smaller than the 2KDPEO-C6F lower layer number density. The behavior of the full widths is somewhat different for each polymer; for the 2KDPEO-C6F, the upper layer width (σ) increases smoothly until the first appearance of a second layer and thereafter it remains constant. The second layer width (τ) increases continuously over the concentration range 3 × 10-5 to 10-3 g mL. Full widths for the 5KDPEOC6F polymer do not show such distinct behavior; both upper

Figure 7. Number densities at the maximum of each Gaussian fitted to experimental partial structure factors as a function of solution concentration: (a) 2KDPEO-C6F, (b) 5KDPEO-C6F, and (c) 10 K DPEO-C6F.

and lower layers have much the same values of the distribution width over the range where two layers are evident. There is some evidence for a decrease in the upper layer width as the concentration decreases to 10-5 g mL-1, but at lower concentrations the distribution width increases to approximately the same value as for higher concentrations. For concentrations less than 10-6 g mL, only a single layer is evident. The distribution width behavior of the 10KDPEO-C6F polymer has some similarities with that of the 5KDPEO-C6F, that is, the lower layer width is roughly constant at 44 ( 4 Å and is present over the whole concentration range. The upper layer distribution width shows a small increase from 25 to 35

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Figure 9. Comparison of number density distributions from optical matrix fits and fits to partial structure factors for 2KDPEO-C6F: (a) 10-6 g mL-1 and (b) 10-4 g mL-1.

PEO-C6F polymer, and this may be due to the more diffuse nature of the layers for the polymer. The lower magnitudes of the number density combined with the larger layer dimensions for this polymer are certainly indicative of a diffuse distribution of the polymer at the air-solution interface. The number density and distribution width are combined in the surface excess, Γ,

Γ)

Figure 8. Widths of Gaussian distributions (σ and τ) as a function of polymer concentration: (a) 2KDPEO-C6F, (b) 5KDPEO-C6F, and (c) 10KDPEO-C6F.

Å over the concentration range explored but is essentially constant at the larger value for concentrations of 5 × 10-5 g mL-1 and above. The number density distributions from the double Gaussian fits to the partial structure factors and those calculated from the optical matrix fits are quite similar to each other, Figure 9. Generally, the double Gaussian distributions are somewhat broader especially at the airsolution interface, and this is attributable to fixing the roughness at this interface in the optical matrix fits to the root-mean-square (rms) amplitude of capillary wave fluctuations on a water surface, that is, 2.5 Å. The greatest disparity between the two distributions is for the 10KD-

xπ (n σ + n2τ) 2 1

and the total adsorption isotherms for each polymer are compared in Figure 10a, the adsorption isotherm for the upper layer alone being given in Figure 10b. Included in these plots are the surface excess values calculated from neutron reflectivity data37 for a 0.1% solution of unmodified poly(ethylene oxide) with molecular weights of 89 000 and 17 800 g mol-1; the surface excess for these polymers at ca. 10-13 mol cm-2 is at least 2 orders of magnitude smaller than those observed for the fluorocarbon end modified polymers investigated here. For all polymers, the polymer in the upper layer makes the major contribution to the surface excess layer, the 10KDPEO-C6F polymer having a constant surface excess over the whole range of concentration. A gradual increase to a constant surface excess of ∼5 × 10-11 mol cm-2 is noted for the 5KDPEOC6F, but the lowest molecular weight polymer has a continuous increase in the surface excess with no indication of a constant value being approached. Upper Adsorbed Layer. For the upper layer surface excess alone, the general behavior for the two higher

Determination of Distribution of End-Capped PEO

Langmuir, Vol. 19, No. 19, 2003 7775

Figure 11. Upper layer thickness normalized by the radius of gyration of equivalent molecular weight PEO as a function of the normalized surface coverage, σ*.

the magnitude of the scaling exponent depends on the range of σ* and the nature of the interaction between polymer segments and the surface, values from 0.2 to 3 being predicted. The contribution of the repulsion to brush formation arises from the frequent use of spread films of amphiphilic copolymers at air-liquid interfaces to provide grafted polymer chains to the interface remarked on earlier. Figure 11 shows that all values of σ* bar the very lowest concentration solution for the 2KDPEO-C6F are greater than 2. To obtain the scaling exponent, σ/Rg was plotted as a function of σ*, and Figure 11 shows that the 10KDPEO-C6F and 5KDPEO-C6F polymers follow the same scaling relation which is quite different from that of the 2KDPEO-C6F. Least-squares fits to these data give Figure 10. (a) Adsorption isotherms calculated for both layers at the air/water interface. (b) Adsorption isotherms calculated for the upper layer alone.

molecular weight polymers is much the same, the surface excess values being only marginally smaller than the total surface excess. For the 2KDPEO-C6F, the upper layer adsorption isotherm is now more like that observed for low molecular weight surfactants, that is, a rapid increase at low concentrations with an asymptotic value being approached at high concentrations. From these upper layer surface excess values, the normalized interfacial grafting density can be calculated:

σ* ) πRg2ΓNA1016 where Γ has units of mol cm-2 and the radius of gyration, Rg, is in angstroms. The radius of gyration of the polymers was assumed to be that of unmodified PEO, and values were calculated using the experimental relation obtained by Kawaguchi et al.47 The transition to a brushlike layer for polymers grafted to an interface is predicted to take place at σ* ) 2,14,27,48,49 and the exponent in the scaling relation between brush layer thickness and σ* should be 0.33.4 This scaling exponent is derived for a parabolic distribution of segment density characteristic of a brushlike layer, and the transition to a brushlike layer has been predicted to be either first order or smooth. Additionally, Szleifer has argued on the basis of single-chain mean field theory that (47) Kawaguchi, S.; Imai, G.; Suzuki, J.; Miyahara, A.; Kitano, T.; Ito, K. Polymer 1997, 38, 2885. (48) Currie, E. P. K.; Leermakers, F. A. M.; Cohen Stuart, M. A.; Fleer, G. J. Macromolecules 1999, 32, 721. (49) Ligoure, C. J. Phys. II (Paris) 1993, 3, 1607.

2KDPEO-C6F

σ ∼ σ*0.85 Rg

5KDPEO-C6F/10KDPEO-C6F

σ ∼ σ*0.3 Rg

It could be argued that there is no evidence for extension to brush layer formation in the case of the 10KDPEOC6F polymer because the values of σ/Rg are always less than 1. Strictly it is the brush height, h, that should be used rather than σ, and h is a parameter in the parabolic number distribution characteristic of brushlike layers.50,51 For other distributions, various moments have been used to characterize the brush height11,13,23,27 and consequently there could be some uncertainty regarding the magnitude of the layer thickness. However, the values of σ from the fits to the partial structure factors are very similar to the layer thickness values obtained from the optical matrix fits to the reflectivity data and justify our use of σ here as the effective layer thickness. Nonetheless, the exponent of 0.3 obtained for the high molecular weight we believe is fortuitous and not symptomatic of brush formation. For these two polymers, the maximum extension is 1.5Rg, and this does not constitute significant stretching of the polymer to be classified as a brushlike layer. The thickness of the upper layer for both the 10KDPEO-C6F and 5KDPEO-C6F is ca. twice that of the equivalent layer thickness for unmodified poly(ethylene oxide) adsorbed at the air-water interface, and since the surface excess is orders of magnitude larger, it is clear that the low surface (50) Milner, S. T.; Witten, T. A.; Cates, M. E. Macromolecules 1989, 22, 853. (51) Milner, S. T.; Witten, T. A.; Cates, M. E. Macromolecules 1988, 21, 2610.

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energy, hydrophobic fluorocarbon end group is enhancing the adsorption to the air/water interface. There is significantly less adsorption of ethylene oxide segments to the interface, and a more extended, but not stretched, arrangement is adopted. For the 2KDPEO-C6F, there is evidently very strong stretching that is much larger than that observed by Kent et al. for higher molecular weight polystyrene immersed in ethyl benzoate at much higher values of σ*;6,27 consequently the scaling exponent is much larger. Additionally we note that the upper layer thickness grows as the concentration of polymer in solution increases up to ca. 5 × 10-5 g mL-1, and together with the low values of the surface tension observed at the highest concentrations, it seems that the polymer is adsorbed to the airwater interface by the fluorocarbon end. At the lowest concentrations, the layer thickness is indicative of a pancakelike layer where both ethylene oxide segments and the fluorocarbon end of the polymer molecule are adsorbed at the surface. As the concentration increases, the adsorbed ethylene oxide segments are displaced by the fluorocarbon ends of polymer molecules being adsorbed from the bulk solution and the molecular weight of this polymer is sufficiently low that all ethylene oxide units can eventually be displaced from the interface at a sufficiently high concentration. At this point, no further PEO can be adsorbed and since the polymer concentration exceeds its critical micelle concentration, micelles are formed in the bulk. The dependence of the surface excess concentration in the upper layer of the 2KDPEO-C6F polymer mirrors the surface tension behavior reasonably well, with an asymptotic surface excess concentration being approached in the same concentration range as the surface tension approaches a constant value. This also true to a much lesser extent for the 5KDPEO-C6F polymer but with a continued fall in surface tension as the surface excess concentration remains constant. This latter behavior is also evident for the 10KDPEO-C6F where there is a decrease in surface tension but no change at all in the surface excess concentration in either layer. It appears that the lowest molecular weight polymer is adsorbed to the interface by the fluorocarbon end whereas the higher molecular weight polymers adsorb by a combination of fluorocarbon ends and ethylene oxide segments, with the lower surface energy fluorocarbon ends replacing the ethylene oxide segments at higher concentrations, thereby reducing the surface tension with no change in the surface excess concentration. Lower Adsorbed Layer. We now consider the nature of the lower layer. For two higher molecular weight polymers, this layer is quite diffuse, very much so in the case of the 10KDPEO-C6F polymer, as the number density distributions in Figure 12 show. The thickness and composition of this lower layer for the 10KDPEO-C6F and 5KDPEO-C6F polymers are constant. This is not so for the 2KDPEO-C6F polymer; the thickness appears to be increasing over the whole concentration range although the number density of the polymer approaches an asymptotic value. All polymers show evidence of micelle formation from the surface tension data, and since the second layer is observed at concentrations that correspond to, or are greater than, these critical micelle concentrations and the dimensions of this layer far exceed the radii of gyration of the polymers, the most probable explanation is the adsorption of micelles at the underside of the original adsorbed layer of individual molecules. In an attempt to obtain some knowledge of the size and nature of these micelles, small-angle neutron scattering data were collected for each polymer at a concentration of 10-3 g mL-1 and are shown in Figure 13. The scattering from the two

Richards et al.

Figure 12. Number density distribution of 10KDPEO-C6F at the concentrations of bulk solutions indicated.

Figure 13. Small-angle neutron scattering data for each polymer in aqueous solution at a concentration of 10-3 g mL-1.

higher molecular weight polymers is quite different to that of the 2KDPEO-C6F, suggesting that the micelles have distinctly different morphology. From double logarithmic plots of these data, the scaling relation between scattering cross section and scattering vector gives exponents of -1.5 and -2 for the 5KDPEO-C6F and 10KDPEO-C6F, respectively. The latter exponent is that for a flexible random coil, while the former is near the scaling expected for wormlike micelles. (Cylindrical micelles should have a scaling exponent of -1.52) No such scaling exponent can be obtained from the scattering for the 2KDPEO-C6F. It is possible to fit many models to these data (spherical, cylindrical, Gaussian coils) because the scattering cross section rapidly falls to background due to the very low concentrations. Moreover, in the Q range where the signal-to-noise ratio is acceptable, there are no distinctive features that would enable discrimination between the various possibilities. Consequently, all we can reliably obtain from these data are the radii of gyration of the micelles; from both Guinier and Zimm plots of the data, these were 110, 122, and 336 Å in order of increasing molecular weight. These values are far larger than the radius of gyration expected for single molecules. The reflectivity data, the sharpness of the transition from upper layer to lower layer, and the small-angle scattering data for the 2KDPEO-C6F polymer suggest that the micelles for this polymer have a well-defined morphology. On the other hand, the number density distributions for the two higher molecular weight polymers indicate (52) Hamley, I. W.; Pedersen, J. S.; Booth, C.; Nace, V. M. Langmuir 2001, 17, 6386.

Determination of Distribution of End-Capped PEO

significant overlap between the two layers, suggesting a less well defined micellar structure that is partially mixed with tails from molecules in the upper layer which have a slightly extended configuration compared to PEO with no fluorocarbon ends. Conclusions The adsorption of poly(ethylene oxide) from aqueous solutions to the air-water interface is considerably enhanced by a hydrophobic fluorocarbon group placed at one end of the molecule. The nature of the surface excess layer is dependent on both the molecular weight of the polymer and the solution concentration. For a molecular weight of ca. 2000 g mol-1, a single layer is evident at low concentrations. The thickness and concentration of this layer increase with an increase in the bulk concentration of the solution, and a considerable stretching of the molecules is implicated since the final thickness is more than twice the radius of gyration of the polymer. Above a bulk concentration of 3 × 10-5 g mL-1, a second layer is formed below the first layer and the thickness of this layer increases as the bulk solution concentration increases still further. The total surface excess of this polymer increases continuously with increasing bulk concentration. The surface excess associated with the upper layer approaches an asymptotic value at a concentration of ca. 3 × 10-5 g mL-1, and this behavior mirrors the dependence of surface tension on concentration. For higher molecular weight polymers, there is still considerably more polymer adsorbed than for unmodified poly(ethylene oxide). The adsorbed layers have lower thicknesses than the polymer with a much lower molecular weight, suggesting that as well as fluorocarbon ends being adsorbed, some of the ethylene oxide units are also adsorbed at the air-water interface, promoting a “flatter”

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structure. The surface excess region has a two-layer structure for much of the bulk concentration range explored, and there is little variation in the dimensions of these layers. For the polymer with molecular weight in the region of 10 000 g mol-1, the layer thicknesses are of the same magnitude as the radius of gyration. For this polymer, the surface excess (both total and that attributable to the upper layer alone) is constant although the surface tension decreases over much of the concentration range. This suggests that at higher bulk concentrations the adsorbed ethylene oxide segments are displaced from the interface with the air by the lower surface energy fluorocarbon groups. The surface excess layers are much more diffuse for these higher molecular weight polymers, and there is some mixing of polymer molecules in the upper and lower layers. From the dependence of the layer thickness on normalized grafting density, the scaling exponent for the two higher molecular weight polymers is 0.3, as predicted for a brushlike polymer layer. However, because the layer thickness is at most only 1.5 times the radius of gyration, a stretched brushlike layer is not supportable as a description of the organization. For the polymer with molecular weight of 2000 g mol-1, the scaling exponent is 0.85, characteristic of a highly stretched configuration, which supports adsorption at the interface of this polymer being due to the fluorocarbon ends. Acknowledgment. J.S. thanks the University of Durham for the award of a studentship that enabled this research project. CCLRC is thanked for the provision of neutron beam facilities of ISIS at the Rutherford Appleton Laboratory. LA026730X