Surface and Bulk Collapse Transitions of Thermoresponsive Polymer

pubs.acs.org/Langmuir © 2009 American Chemical Society

Surface and Bulk Collapse Transitions of Thermoresponsive Polymer Brushes Xavier Laloyaux,* Bertrand Mathy, Bernard Nysten, and Alain M. Jonas* Institute of Condensed Matter and Nanosciences, Universit
e catholique de Louvain, Place Croixdu Sud 1, 1348 Louvain-la-Neuve, Belgium Received June 25, 2009. Revised Manuscript Received October 7, 2009 We elucidate the sequence of events occurring during the collapse transition of thermoresponsive copolymer brushes based on poly(di(ethyleneglycol) methyl ether methacrylate) chains (PMEO2MA) grown by atom-transfer radical polymerization (ATRP). The collapse of the bulk of the brush is followed by quartz crystal microbalance measurements with dissipation monitoring (QCM-D), and the collapse of its outer surface is assessed by measuring equilibrium water contact angles in the captive bubble configuration. The bulk of the brush collapses over a broad temperature interval (∼25
C), and the end of this process is signaled by a sharp first-order transition of the surface of the brush. These observations support theoretical predictions regarding the occurrence of a vertical phase separation during collapse, surf with surface properties of thermoresponsive brushes exhibiting a sharp variation at a temperature of Tbr . In contrast, bulk surf occurring on average ∼8
C below Tbr and the bulk properties of the brush vary smoothly, with a bulk transition Tbr ∼5
C below the lower critical solution temperature (LCST) of free chains in solution. These observations should also be valid for planar brushes of other neutral, water-soluble thermoresponsive polymers such as poly(N-isopropylacrylamide) (PNIPAM). We also propose a way to analyze more quantitatively the temperature dependence of the QCM-D response of thermoresponsive brushes and deliver a simple thermodynamic interpretation of equilibrium contact angles, which can be of use for other complex temperature-responsive solvophilic systems.

Introduction Stimuli-responsive polymers are macromolecules able to respond predictably to specific environmental changes.1-3 When densely grafted on surfaces, such macromolecules form dense responsive brushes a few tens of nanometers thick,4,5 leading to smart surfaces with applications in actuation,6,7 motion control,8 tuning of biointeractions,9 stimuli-gated filtration,10 and sensing.11 Responsive polymer brushes offer a way to transduce and amplify changes in their environment (pH, temperature, light, solvent, etc.) most often by undergoing a sharp modification of the conformation of the chains and of associated properties. For example, when using polymers displaying a lower critical solution temperature (LCST) in a suitable solvent, thermoresponsive polymer brushes are obtained. Below the critical point, the polymer chains interact preferentially with the solvent and adopt a swollen, extended conformation. Above the critical point, the polymer chains collapse as they become more solvophobic. The detailed pathway of the collapse transition of brushes grafted onto flat surfaces is still under debate. This is because most *Corresponding authors. E-mail: [email protected]; alain. [email protected]. (1) Gil, E. S.; Hudson, S. A. Prog. Polym. Sci. 2004, 29, 1173–1222. (2) Schmaljohann, D. Adv. Drug Delivery Rev. 2006, 58, 1655–1670. (3) Winnik, F. M.; Whitten, D. G.; Urban, M. W. Langmuir 2007, 23, 1–2. (4) Luzinov, I.; Minko, S.; Tsukruk, V. V. Prog. Polym. Sci. 2004, 29, 635–698. (5) Minko, S. Polym. Rev. 2006, 46, 397–420. (6) Zhou, F.; Shu, W.; Welland, M. E.; Huck, W. T. S. J. Am. Chem. Soc. 2006, 128, 5326–5327. (7) Huck, W. T. S. Mater. Today 2008, 11, 24–32. (8) Santer, S.; Kopyshev, A.; Donges, J.; Yang, H.-K.; R€uhe, J. Adv. Mater. 2006, 18, 2359–2362. (9) Ebara, M.; Yamato, M.; Aoyagi, T.; Kikuchi, A.; Sakai, K.; Okano, T. Biomacromolecules 2004, 5, 505–510. (10) Alem, H.; Duwez, A.-S.; Lussis, P.; Lipnik, P.; Jonas, A. M.; DemoustierChampagne, S. J. Membr. Sci. 2008, 308, 75–86. (11) Abu-Lail, N. I.; Kaholek, M.; LaMattina, B.; Clark, R. L.; Zauscher, S. Sens. Actuators, B 2006, 114, 371–378.

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thermodynamic characterization methods fail as a result of the small number of polymer chains grafted onto flat substrates. However, a better knowledge of this pathway is crucial for implementing real-world applications. For instance, responsive brushes grafted onto cantilevers can be used to bend the cantilever reversibly,6,11 which allows the conversion of thermal or chemical energy into mechanical work. In this case, the power that can be delivered by this micromechanical device depends on the sharpness of the transition undertaken by the bulk of the brush. In contrast, when using thermoresponsive brushes to control cell adhesion and spreading,14 the transition of the outer surface of the brush becomes central. Likewise, when responsive brushes are used to move small objects as proposed by R€uhe et al.,8,15 the surface-energy component of the brush is predominant and the surface transition of the brush is again of more importance than its bulk transition. At this stage, one should recall an important general result from the mean-field theory of responsive polymer brushes,16 showing that the collapse transition of a planar brush is not a thermodynamic phase transition but only a cooperative conformational transition. This means that the temperature dependence of the collapse transition should not be sharp however slowly the system may be heated or cooled. Although initially derived for polymers exhibiting an upper critical solution temperature (UCST), this conclusion should be valid for polymers displaying a LCST as well, such as thermoresponsive neutral water-soluble polymers including poly(N-isopropylacrylamide) (PNIPAM), (12) Jonas, A. M.; Glinel, K.; Oren, R.; Nysten, B.; Huck, W. T. S. Macromolecules 2007, 40, 4403–4405. (13) Lutz, J. F. J. Polym. Sci., Part A: Polym. Chem. 2008, 46, 3459–3470. (14) Wischerhoff, E.; Uhlig, K.; Lankenau, A.; Borner, H. G.; Laschewsky, A.; Duschl, C.; Lutz, J.-F. Angew. Chem., Int. Ed. 2008, 47, 5666–5668. (15) Santer, S.; R€uhe, J. Polymer 2004, 45, 8279–8297. (16) Zhulina, E. B.; Borisov, O. V.; Pryamitsyn, V. A.; Birshtein, T. M. Macromolecules 1991, 24, 140–149.

Published on Web 10/20/2009

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Scheme 1. Schematic Representation of the Vertical Phase Separation for a Collapsing Thermoresponsive Brusha

a The surface of the brush collapses at a higher temperature T than the collapse of its bulk, which happens at Ttr. The variation of monomer concentration with vertical distance φ(z) is also drawn schematically, together with the location of the Gibbs dividing interface defined so that the vertically and horizontally shaded areas are equal. φbr0 is the monomer concentration of the reference brush used for the thermodynamic developments. Both the Gibbs dividing interface and φbr0 vary with T.

poly(ethylene oxide) (PEO), and the di(ethylene glycol) methyl ether methacrylate-based copolymers13 (PMEO2MA) that we will be using in the present study. These neutral water-soluble polymers can be described by a two-state model in which the monomer units are in dynamic equilibrium between two interconverting states (i.e., a hydrophobic and a hydrophilic state).17 A self-consistent field theory of brushes of such two-state polymers was proposed by Halperin and co-workers.18 The results are similar to those derived from a mean-field treatment of thermoresponsive polymer brushes having a concentrationdependent effective solvent-polymer interaction parameter, χeff(T, φ), increasing with both temperature, T, and monomer volume fraction, φ.19 This is the case for PNIPAM.20 According to mean-field theories of polymer brushes,21 the monomer concentration in a swollen brush decreases away from the substrate along its perpendicular direction (defined as the vertical direction in the sequel). For real brushes, termination reactions during polymerization will also contribute to decrease φ with distance from the substrate, z. The dependence of solvent quality on monomer concentration and temperature then results in an incomplete collapse of the brush when it is heated in water: the collapse first occurs at the bottom of the swollen brush, which is denser in monomer units, and then progresses toward its external more dilute surface as the temperature is increased. During the heating process, the theoretical model thus predicts that the monomer volume fraction changes from a dilute layer to a bilayer concentration profile and then to a more contracted single layer, resulting in the vertical phase separation schematically shown in Scheme 1. Importantly, the model indicates that the surface properties of the brush should essentially be affected at the end of the collapse process, at a higher temperature than the bulk of the brush. That the collapse transition occurs over a relatively large range of temperatures is supported by a series of experimental results, (17) Baulin, V. A.; Halperin, A. Macromolecules 2002, 35, 6432–6438. (18) Baulin, V. A.; Zhulina, E. B.; Halperin, A. J. Chem. Phys. 2003, 119, 10977– 10988. (19) Baulin, V. A.; Halperin, A. Macromol. Theory Simul. 2003, 12, 549–559. (20) Afroze, F.; Nies, E.; Berghmans, H. J. Mol. Struct. 2000, 554, 55–68. (21) Milner, S. T. Science 1991, 251, 905–914. (22) Balamurugan, S.; Mendez, S.; Balamurugan, S. S.; O’Brien, M. J.; Lopez, G. P. Langmuir 2003, 19, 2545–2549. (23) Liu, G.; Zhang, G. J. Phys. Chem. B 2005, 109, 743–747. (24) Annaka, M.; Yahiro, C.; Nagase, K.; Kikuchi, A.; Okano, T. Polymer 2007, 48, 5713–5720. (25) Montagne, F.; Polesel-Maris, J.; Pugin, R.; Heinzelmann, H. Langmuir 2009, 25, 983–991.

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essentially obtained on PNIPAM brushes.22-25 Direct experimental evidence supporting the vertical phase separation process is scarcer. So far, the main experimental result in favor of a vertical phase separation was obtained by neutron reflectometry (NR) on PNIPAM brushes in deuterated water.26 Upon heating or cooling through the transition, the experimental monomer volume fraction changed from a single layer to a distinct bilayer and then back to a single layer. The bilayer profile was observed in a narrow temperature range close to the collapse transition. However a recent NR study of PMEO2MA copolymer brushes, although confirming that the collapse occurs over a wide temperature range, failed to observe this bilayer structure and proposed an alternate model wherein the collapse occurs homogeneously and progressively over the whole polymer brush.27 If this is true, then the surface of the brush should also undergo a progressive and broad transition, contrasting with the predictions of the model of vertical phase separation. Considering the importance of a detailed knowledge of the collapse transition with respect to the applications mentioned above and the fact that contradictory results were obtained so far on brushes of two closely related polymers (PNIPAM and PMEO2MA), there is clearly room for further study. This article thus focuses on elucidating the sequence of events occurring during the collapse transition of thermoresponsive polymer brushes based on PMEO2MA chains.12 These brushes, which are grown by atom-transfer radical polymerization (ATRP) from silicon oxide surfaces, display a collapse transition in water at temperatures close to physiological ones12 and offer interesting opportunities for biological or bioinspired applications14,28 and nanotechnology.29,30 The LCST of free PMEO2MA-rich chains in water decreases with polymer concentration in a way similar to that for PNIPAM,31 hence both polymers should behave similarly in brushes. The collapse of the bulk of the brush is followed by quartz crystal microbalance measurements with dissipation monitoring (QCM-D), and the collapse of the outer (26) Yim, H.; Kent, M. S.; Satija, S.; Mendez, S.; Balamurugan, S. S.; Balamurugan, S.; Lopez, G. P. Phys. Rev. E 2005, 72, 051801. (27) Gao, X.; Ku^cerka, N.; Nieh, M.-P; Katsaras, J; Zhu, S; Brash, J. L.; Sheardown, H. Langmuir 2009, 25, 10271-10278. (28) Glinel, K.; Jonas, A. M.; Jouenne, T.; Leprince, J.; Galas, L.; Huck, W. T. S. Bioconjugate Chem. 2009, 20, 71–77. (29) Jonas, A. M.; Hu, Z.; Glinel, K.; Huck, W. T. S. Macromolecules 2008, 41, 6859–6863. (30) Jonas, A. M.; Hu, Z.; Glinel, K.; Huck, W. T. S. Nano Lett. 2008, 8, 3819– 3824. (31) Lutz, J.-F.; Akdemir, O.; Hoth, A. J. Am. Chem. Soc. 2006, 128, 13046– 13047.

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surface of the brush is assessed by measuring equilibrium water contact angles in the captive bubble configuration. This is, to the best of our knowledge, the first time that such techniques have been combined to probe the differences between surface and bulk properties of thermoresponsive brushes. After the Experimental Section, we present how quantitative structural and thermodynamical data on the collapse of brushes can be extracted by these two methods. Then we compare the collapse of the bulk and surface of the brushes and discuss whether our results support the model of vertical phase separation.

Experimental Section Materials. 2-(2-Methoxyethoxy)ethyl-methacrylate (MEO2MA), oligo(ethyleneglycol)methylether-methacrylate (OEGMA300 and OEGMA475), with molar masses of 300 and 475 g/mol, respectively, were purchased from Aldrich and used as received. Absolute ethanol from Fluka was used without further purification. Milli-Q water (resistivity 18.2 MΩ cm) was obtained from a Millipore system. Copper(I) chloride (99.995þ%) (Cu(I)Cl), copper(II) chloride (99.999þ%) (Cu(II)Cl2), and 2,20 -bipyridyl (99þ%) (bipy) were from Aldrich. Single-side-polished silicon wafers (Æ100æ orientation) were from ACM (France). Quartz crystal sensors covered with a layer of SiO2 (QSX 303) were purchased from Q-Sense (Sweden) and rinsed with ethanol before use. The different steps of the surface preparation are described below and are identical for silicon wafers and the QCM-D sensors, unless stated otherwise. Brush Growth. Brushes were grown according to a previously published protocol.12 Si wafers were cleaned in piranha solution, whereas quartz sensors were cleaned by UV/ozone treatment for 30 min to avoid full immersion in the strongly oxidizing piranha bath. (Caution! Piranha solution is a strong oxidant that reacts violently with organic compounds.) The substrates were then silanized with an ATRP silane initiator (2-bromopropan-2-yl 4-(trichlorosilyl)butanoate) as described previously;12 the thickness of the initiator monolayer was determined by X-ray reflectometry to be 1.1 ( 0.2 nm. Different series of polymer brushes were synthesized by controlled radical polymerization using either pure MEO2MA or a mixture of MEO2MA and either OEGMA300 or OEGMA475 in the feed solution, keeping the total molar content in methacrylate constant. For each series of brushes, a set of initiatorcovered silicon substrates were immersed in the feed solution in an oxygen-free atmosphere (Schlenk tubes) and removed at increasing times to check the polymerization kinetics. When the ellipsometrydetermined thickness reached about 100 nm, the polymerization was stopped and the resulting ∼100-nm-thick brush was used for further experiments. The brush growth rates on silicon substrates and QCM-D sensors were similar, showing that the differences in the cleaning procedures used for both types of substrates are of no importance. The grafting density of PMEO2MA brushes was evaluated in previous work to be ∼0.3 nm-2;29 the polydispersity of the chains could not be measured but is expected to be small because the brush growth is well controlled.12 Ellipsometry. The film thickness was measured with a spectroscopic ellipsometer (Uvisel from Horiba-Jobin-Yvon, France) at an angle of incidence of 70
and in a wavelength range from 400 to 850 nm. The ellipsometric data were fitted by the DeltaPsi 2 software of the apparatus. The ellipsometric model consists of three layers: silicon (bulk), native silicon oxide (0.15 nm thickness), and a polymer brush. The complex index of refraction of Si and native SiO2 were taken from tabulated data provided by the manufacturer. The complex index of refraction of the brushes, n - jk, was modeled by a transparent Cauchy layer with n(λ) = A þ 104Bλ-2 þ 109Cλ-4 and k(λ) = 0 with A, B, and C three-fit parameters. The measurement was carried out three times at different spots on the substrate. The evaluated ellipsometric thickness of the polymer brushes was compared to the thickness measured by X-ray reflectometry: both measurements generally 840 DOI: 10.1021/la902285t

agreed to within better than 10%. The brush thickness on the QCM-D sensor was likewise evaluated by a model using four layers: gold, titanium, silicon oxide, and polymer (Cauchy layer). The values of the index of refraction of Ti, Au, and SiO2 were again tabulated values. X-ray Reflectometry (XRR). XRR was measured with a two-circle goniometer (Siemens D5000) with 30 cm radius and 0.002
positioning accuracy. The incident beam (Cu KR radiation, λh = 0.15418 nm) was obtained from a rotating anode (Rigaku, Japan) operated at 40 kV and 300 mA, fitted with a collimating mirror (Osmic, Japan) delivering a parallel beam of about 0.0085
angular divergence. The beam size was defined by a 40-μm-wide slit placed 17.5 cm away from the focal spot. The sample was fixed at the center of the goniometer with an automated procedure using a vertical stage of 1 μm resolution. The intensity was scaled to unit incident intensity and corrected for spillover at very low angles of incidence. The film thickness was obtained from the pseudo-autocorrelation function of the electron density, obtained by Fourier transforming the experimental data multiplied by (sin θ/λh)4, where θ is the angle of incidence measured from the sample plane.32

Quartz Crystal Microbalance with Dissipation Monitoring (QCM-D). QCM-D measurements were performed in water with a Q-Sense E4 microbalance. The AT-cut quartz crystal sensor with 14 mm diameter was oscillating at its fundamental frequency (5 MHz) or one of its overtones. All overtones were acquired, although the third overtone was generally selected for analysis unless mentioned otherwise. The thickness of the silicon oxide layer covering the sensor was evaluated by ellipsometry on five different sensors to be 23 ( 2.5 nm. The quartz sensor was mounted in a flow module with one side exposed to the solution. The module temperature was maintained to a precision of 0.02
C. Data collection was realized in two ways: static and dynamic. For static measurements, the system temperature was increased by steps and equilibrated for at least 50 min at each step before performing the acquisition. For dynamic measurements, the temperature was ramped at rates from 0.2 to 2
C/min while continuously acquiring data. The QCM-D data were collected between 15 and ∼45
C. Equilibrium Contact Angle Measurements. Contact angle measurements were performed in the captive air bubble configuration within a water-filled temperature-calibrated home-built cell, as described elsewhere.12 The cell was placed on a Linkam TMS91 hot stage to control the temperature. An air bubble of about 1 mm diameter was trapped below the sample immersed face-down in water, and images of the bubble were taken with a digital camera. The temperature was increased in steps with an equilibration time of ∼1 h before taking a measurement. The bubble shape was fit near the triple line by arcs of a circle, and the left and right contact angles were averaged to obtain the contact angle. No significant difference was found upon heating or cooling the sample, testifying to the reversibility of the brush response. Because of refraction through the glass windows of the cell, the absolute values of equilibrium contact angles are not precise to better than a few degrees. However, the relative precision and repeatability of the measurements in a given set of measurements is on the order of 0.2
.

Data Analysis Extracting the Temperature Dependence of the Bulk of the Brush by QCM-D. QCM-D is a technique generally used to monitor adsorption processes at the gas or liquid/solid interface,33 but it can also monitor more complex processes such as the swelling of a brush23,24,34,35 and can more generally measure the (32) Arys, X.; Laschewsky, A.; Jonas, A. M. Macromolecules 2001, 34, 3318– 3330. (33) Marx, K. A. Biomacromolecules 2003, 4, 1099–1120. (34) Domack, A.; Prucker, O.; R€uhe, J.; Johannsmann, D. Phys. Rev. E 1997, 56, 680–689. (35) Zhang, Y.; Du, B.; Chen, X.; Ma, H. Anal. Chem. 2009, 81, 642–648.

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viscoelastic, mechanical, or dielectric properties of films.36 It is used here to follow the temperature dependence of the hydration and dehydration process of the bulk of the polymer brush. By applying a proper oscillating voltage, the QCM-D quartz sensor is made to vibrate at its resonance frequency f1 and odd overtones fn (n = 1, 3, 5,...). After the application of the oscillating excitation, the damping of the vibration is monitored during the relaxation period of the sensor, giving access to the dissipation factor D that is defined as D = (τπf1)-1 where τ is the time constant for the amplitude decay after switching off the power source.35,39 The deposition of extra material on the sensor surface (e.g., by grafting a polymer brush, changes the resonance frequency. If the layer is thin, rigid, uniform enough, and in vacuum, then the frequency shift (Δf) can be related to the absorbed mass by the Sauerbrey equation40 Δm ¼ -C

Δf n

ð1Þ

where Δm is the sensed mass per piezoelectrically active area, C is a constant depending on the sensor parameters (17.7 ng/(cm2 Hz) in our case), and n is the overtone number. Most of the time, the fundamental resonance frequency f1 is noisy because of energy trapping or piezoelectric stiffening.41 Therefore, the third overtone f3 was generally selected here. When the sensor is immersed in a fluid and/or if the deposited layer is viscoelastic, as is the case here, the Sauerbrey equation breaks down. The response of a piezoelectric sensor covered by a viscoelastic layer immersed in a bulk liquid was proposed some time ago,34,37-39 as reviewed recently.36 Assuming that the swollen brush can be modeled as a single average homogeneous layer, the frequency shift with respect to the bare sensor, Δf, and dissipation factor shift, ΔD, can be linked to the temperature-dependent thickness hbr(T), density Fbr(T), shear viscosity ηbr(T), and shear modulus μbr(T) of the polymer brush as follows


ηL ðTÞ þ hbr ðTÞ Fbr ðTÞω δL ðTÞ #   ηL ðTÞ 2 ηbr ðTÞω2 -2hbr ðTÞ δL ðTÞ μbr 2 ðTÞ þ ηbr 2 ðTÞω2 Δf ðTÞ ≈ Cf

" ΔDðTÞ ≈ CD

ð2Þ

#   ηL ðTÞ ηL ðTÞ 2 μbr ðTÞω þ 2hbr ðTÞ δL ðTÞ δL ðTÞ μbr 2 ðTÞ þ ηbr 2 ðTÞω2 ð3Þ

where ω = 2πfn (s-1). The constants Cf =- (2πFshs)-1 and CD = 2πfnFshs, where hs is the thickness of the quartz crystal and Fs is its density, can be determined easily and are considered to be temperature-independent under our conditions. δL(T) = [2ηL(T)/FL(T)ω]1/2 (m) is the water viscous penetration depth. The temperature dependence of the water viscosity, ηL(T), and that of the water density, FL(T), were taken from the literature42 and interpolated over our experimental temperature range as (36) Johannsmann, D. Phys. Chem. Chem. Phys. 2008, 10, 4516–4534. (37) Nakamoto, T.; Moriizumi, T. Jpn. J. Appl. Phys. 1990, 29, 963–969. (38) Granstaff, V. E.; Martin, S. J. J. Appl. Phys. 1994, 75, 1319–1329. (39) Voinova, M. V.; Rodahl, M.; Jonson, M.; Kasemo, B. Phys. Scr. 1999, 59, 391–396. (40) Sauerbrey, G. Z. Phys. 1959, 155, 206–222. (41) Diethelm, J. Macromol. Chem. Phys. 1999, 200, 501–516. (42) Lide, D. R., Ed. CRC Handbook of Chemistry and Physics, 87th ed.; Taylor and Francis: Boca Raton, FL, 2007.

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(1.68 - 0.024T)10-3 (Pa s) and 1004 - 0.3T (kg/m3), respectively, with T in
C. Equations 2 and 3 are valid for a homogeneous film of thickness hbr(T) resting on the quartz sensor. This is clearly at odds with the model of vertical phase separation that assumes a bilayer profile for the film (Scheme 1). In addition, for a film exhibiting a profile of solvent concentration, the very notion of film thickness is somewhat blurred because different layers will contribute differently to the response of the sensor depending on their viscoelastic properties and mechanical coupling. It was demonstrated that the acoustic thickness of a swollen polymer brush determined by QCM may be quite higher than the optical thickness determined by ellipsometry because the quartz sensor is more sensitive to dilute regions in the tail of the concentration profile.34 Therefore, the thickness hbr appearing in eqs 2 and 3 will not be taken literally in the sequel but will provide us with some average measure of changes occurring in the brushes, which will allow us to define the temperature range over which the bulk of the brush collapses. Four unknown temperature-dependent physical quantities in eqs 2 and 3 describe the brush in an intermediate configuration between the swollen and collapsed states: hbr(T), ηbr(T), μbr(T), and Fbr(T). However, the density of the swollen brush can be computed from a knowledge of the density of the dry brush and of water and from the thicknesses of the dry and swollen brushes. Denoting the thickness and density of the dry brush as hdry br and Fdry br , respectively, one obtains Fbr ðTÞ ¼

hdry hbr ðTÞ -hdry br br Fdry FL ðTÞ br þ hbr ðTÞ hbr ðTÞ

ð4Þ

Furthermore, the remaining three physical quantities do not vary independently from each other. For instance, when the brush swells, hbr increases while the shear modulus and viscosity of the layer should decrease. Therefore, the temperature variation of these parameters was described by a single empirical sigmoidal curve hbr ðTÞ -hcoll μ ðTÞ -μcoll η ðTÞ -ηcoll ¼ - br ¼ - br jΔhj jΔμj jΔηj ! 1 T -Ttr ¼ erfc pffiffiffi 2 2σ tr

ð5Þ

where erfc(x) is the complementary error function, Ttr is the temperature at which half of the brush has collapsed, and σtr is a measure of the breadth of the transition (formally, this parameter is the standard deviation of the Gaussian whose integral reproduces the shape of the temperature profile). |Δh| is the difference in brush height between the swollen and collapsed states, hcoll is the height of the brush in the collapsed state, and similar definitions apply for |Δμ|, |Δη|, μcoll, and ηcoll. Equations 4 and 5 allow us to represent the temperature variation of the data by eight unknown parameters only. Other parameters appearing in these equations refer to the dry brush and can be measured by X-ray reflectometry or ellipsometry. The density of the dry brushes was measured from the critical angle for total external reflection on the X-ray reflectograms and 3 was found to be Fdry br = 1.2 ( 0.1 g/cm . The dry thicknesses of the brushes were obtained by ellipsometry. It is thus possible to fit eqs 2 and 3 simultaneously to the experimental data while constraining the fit by using eqs 4 and 5. The fit parameters are Ttr, σtr, hcoll, μcoll, ηcoll, |Δh|, |Δμ|, and |Δη|. Two supplementary fit parameters DOI: 10.1021/la902285t

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were added to the list, consisting of constant shifts of ΔD and Δf that take into account small calibration errors. These result from the fact that shifts in D and f arise from clamping/unclamping the sensors in the cell, which was required because the brushes were not grown in situ within the QCM-D cell. The fit results are the temperature variation of the brush height, of its shear modulus, and of its shear viscosity. No attempt was made to fit different overtones simultaneously because this would have required a knowledge of the spectrum of relaxation times of the brush in its different swollen states. Considering our goal, the simplicity of our one-layer model, and the restrictions on the meaning of hbr alluded to above, it was considered useless to undertake a complete analysis of the viscoelastic spectrum. Extracting the Surface Behavior of the Brush from Equilibrium Contact Angles. Because contact angles are measured in the captive bubble configuration, it is possible to wait at each temperature until equilibrium is attained before measuring the contact angle. At equilibrium, the chemical potential of water is identical in the brush in contact with the liquid or the gas, in the liquid water, and in the air bubble that is filled with saturated water vapor. Under these circumstances, equilibrium thermodynamics applies. It is of utmost importance to realize that measurements performed in the classical droplet-on-solid configuration usually do not provide equilibrium contact angles because the droplet evaporates before the vapor pressure of water reaches equilibrium in the gas phase. What follows should thus not be used to analyze out-of-equilibrium contact angle measurements. In the sequel, we use the conventions defined by Gibbs for surface thermodynamics.43,44 We consider three reference phases: the infinitely thick swollen brush in equilibrium with water, an infinite volume of liquid water, and an infinite vapor-saturated gas. Note that we ignore the presence of air in the reference gas phase and we also neglect its low concentration in the other phases. There is only one reference phase for the ideal brush, irrespective of its location below the liquid or gaseous water. This is because if we had introduced two reference phases for the brush then the total number of phases np in the ideal reference system would have been four (the two reference brush phases plus liquid and gaseous water). There are only two species in the system, water molecules and grafted polymer chains (i.e., nc = 2). Therefore, Gibbs’ phase rule45 would have predicted the number of degrees of freedom of our ideal system to be nc þ 2 - np = 0,46 which is obviously wrong. Our choice of only one reference brush phase leads to np = 3 and nc þ 2 - np = 1, indicating that the ideal system has one degree of freedom and may exist over a range of temperatures T, with the pressure p being fixed by the selection of T. This formal analysis corresponds to the obvious fact that water, having a single chemical potential independent of its state, must swell the reference brush identically in the vapor or liquid phases. Note that the concept of a swollen reference brush phase may appear to be somewhat cumbersome because self-consistent field theory predicts that the monomer concentration is not constant in the vertical direction but adopts a parabolic profile instead,21 whereas the definition of a phase requires constant properties throughout space. However, recent molecular dynamics simulations show that the segment density profile of dense brushes such (43) Gibbs, J. W.; Van Name, R. G.; Longley, W. R.; Bumstead, H. A. Collected Works of J. Willard Gibbs; Longmans, Green and Co.: New York, 1928. (44) Butt, H.-J.; Graf, K.; Kappl, M. Physics and Chemistry of Interfaces, 2nd ed.; Wiley-VCH: Weinheim, Germany, 2006. (45) Guggenheim, E. A. Thermodynamics; North-Holland: Amsterdam, 1949. (46) The silicon substrate increases nc and np by 1 (one supplementary species and one supplementary phase) and can therefore be omitted in Gibbs’ phase rule.

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as that obtained by ATRP is almost constant in the brush when sufficiently far away from the free interface.48 Therefore, it becomes possible to define the reference brush phase as the hypothetical (ideal) brush having the properties of real brushes in their close-to-constant segment density regions (Scheme 1). In real brushes, the region of almost constant segmental density should exhibit uniform properties at all temperatures and again, according to Gibbs’ phase rule, may not separate in two coexisting phases over a range of temperature. In contrast, in the region where the segment density varies more rapidly, it is possible to consider a vertical phase separation to occur over a range of temperatures. This is because Gibbs’ phase rule does not apply where properties are not homogeneous. In this inhomogeneous region that cannot be defined as a phase, the structure of the real brush can be different depending on whether it is placed in liquid water or water vapor. In addition, the brush interfaces are certainly different below liquid water or water vapor; otherwise, complete wetting would ensue.47 Two different interfaces thus have to be considered for real brushes: the brush/liquid and brush/ vapor interfaces. The real brush in liquid water is thus compared to a reference system consisting of a homogeneous phase having the properties of the reference brush and located between the substrate and a reference plane, above which rests pure liquid water. This reference plane, the so-called Gibbs dividing interface, can be selected in different ways; however, depending on its selection, the meanings of some surface thermodynamic parameters change.44,49 Here, we place the dividing interface at a height h* so that50 Z

h/ 0

Z ðφbr0 -φðzÞÞ dz ¼

¥ h/

φðzÞ dz

ð6Þ

where φ(z) is the monomer concentration profile in the real brush and φbr0 is the monomer concentration of the reference brush. This equation means that the dividing interface is placed in such a way as to have the number of monomer units in liquid water above the dividing plane equal to the number of missing monomer units in the brush below the dividing plane (compared to the reference brush). A graphical interpretation of this equation is shown in Scheme 1; note that the location of the Gibbs dividing interface varies with temperature. With this location of the dividing interface, the adsorption of monomer units at the interface (i.e., the excess concentration of monomer units at the interface compared to that in the reference system) is zero. Then, the Gibbs adsorption equation simply reads49 liq liq dγliq br=w ¼ -sbr dT -Γw dμw

ð7Þ

where γliq br/w is the interfacial tension of the swollen brush against liquid water, sliq br is the excess surface entropy (per unit area) of the real brush in liquid water compared to its reference system, Γliq w is the adsorption of water at the liquid interface (i.e., the molar excess of water compared to the reference system, per unit area), and μw is the chemical potential of water (which is constant over the whole system). The chemical potential of the monomer units does not appear in eq 7 by virtue of eq 6, which is precisely the reason that we selected the dividing interface in that way. (47) The reasons that finite contact angles are obtained on solvophilic brushes in contact with good solvents is discussed in the following paper: Cohen Stuart, M. A.; de Vos, W. M.; Leermakers, F. A. M. Langmuir 2006, 22, 1722–1728. (48) He, G.-L.; Merlitz, H.; Sommer, J.-U.; Wu, C.-X. Macromolecules 2007, 40, 6721–6730. (49) Rowlinson, J. S.; Widom, B. Molecular Theory of Capillarity; Clarendon Press: Oxford, U.K., 1982. (50) Note that this selection differs from the one made in our previous report.12

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Similar considerations can be made for the brush in contact with water vapor, and the equivalent of eq 7 reads vap vap dγvap br=w ¼ -sbr dT -Γw dμw

Scheme 2. General Chemical Formula of the Random Copolymer Brushes Used in This Study, P((MEO2MA)x-(OEGMAz)y), with z = 4-5(OEGMA300) or 8-9(OEGMA475)

ð8Þ

with similar meanings as before attributed to the parameters appearing in this equation. We stress that, for hydrophilic responsive systems such as our brushes, the liquid and vapor interfaces might be of quite different structure and may adapt differently depending on temperature. Therefore, the location of the Gibbs dividing interface for the brush in liquid water may not be identical to that for the brush in water vapor and will fluctuate with temperature. In some respect, the location of the Gibbs dividing interface hides most of our ignorance about the structural details of the system. The variation of the chemical potential of water can be expressed using the Gibbs-Duhem equation written for liquid water45 liq liq dμw ¼ -Sw dT þ V w dp

ð9Þ

liq  where Sliq w is the molar entropy of liquid water and V w is its molar volume. Because we work under constant atmospheric pressure,  dp = 0 and dμw = -Sliq w dT. The same equation also holds true for the vapor phase because the chemical potential of water is constant throughout the system under our equilibrium conditions. Therefore, eqs 7 and 8 become liq

liq liq dγliq br=w ¼ ð -sbr þ Γw S w Þ dT ðconstant pressureÞ

liq

vap vap dγvap br=w ¼ ð -sbr þ Γw S w Þ dT ðconstant pressureÞ

ð10Þ

We now introduce the Young-Dupr
e equation51 liq γw cos θ ¼ γvap br=w -γbr=w

ð11Þ

where θ is the contact angle of water and γw is its surface tension. Taking the temperature derivative of eq 11 at constant pressure and injecting eq 10, one obtains  Dðγw cos θÞ  liq liq vap vap liq  ¼ ðsbr -Γliq ð12Þ w S w Þ -ðsbr -Γw S w Þ  DT p

Each term in parentheses on the right-hand side of eq 12 is the excess surface entropy of the brush sbr (in liquid water and water vapor, respectively), from which the entropy arising from the contribution  of adsorbed water molecules (ΓwSliq w ) is subtracted. Hence, these terms represent the excess surface entropy arising from everything except the excess amount of condensed water at the interface, such as the variations of conformational entropy of the chains, variations in the packing of water molecules compared to pure water, and so forth. One can thus globally consider these terms to be an excess configurational surface entropy and can write eq 12 as  Dðγw cos θÞ  conf , liq , vap Þ ¼ Δsconf , liq=vap -sconf  ¼ ðsbr ð13Þ br br  DT p

Equation 13 is central to the interpretation of the equilibrium contact angles. It shows that by multiplying the cosine of the (51) de Gennes, P.-G.; Brochard-Wyart, F.; Qu
er
e, D. Capillarity and Wetting Phenomena; Springer: New York, 2004.

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contact angle by the surface tension of water and taking its temperature derivative one obtains a well-defined thermodynamic function that, broadly speaking, represents a difference in excess surface configurational entropy between the brush in contact with liquid water and the brush in contact with water vapor. Significantly, this function is an entropy, thus a first derivative of (excess) free energy, and provides information on the way all of the other first derivatives of the surface free energy vary. In particular, if the brush surface undergoes a first-order phase transition then this function should exhibit a discontinuity at some temperature. However, we stress that this parameter combines the excess surface configurational entropies of two different interfaces: brush/liquid and brush/vapor. It is, however, possible to extract from this equation thermodynamic information about the brush/liquid interface only, as will be discussed shortly. In practice, the contact angles were measured at different temperatures, and cos θ(T) was fitted by a combination of polynomial segments. The surface tension of water was taken from the literature,52,53 and the derivative was taken numerically . after multiplication to obtain Δsconf,liq/vap br

Results and Discussion Brush Growth. The polymer brushes were synthesized by surface-initiated ATRP, following a previously described procedure,12 in the presence of mixtures of methacrylate monomers bearing methyl-terminated oligo(ethylene oxide) (EO) side chains of varying length. Here, three monomers were used (Scheme 2): MEO2MA with dimeric EO side chains, OEGMA300 bearing side chains containing about four to five EO units (monomer of 300 g/mol average molar mass), and OEGMA475 bearing side chains containing about eight to nine EO units (monomer of 475 g/mol average molar mass). From previous work, it is known that the polymer based on MEO2MA units only, PMEO2MA, displays an LCST in water at 27 ( 1
C31,54,55 and shows a surface collapse transition at a slightly higher temperature (34
C) when grafted in a brush.12 Upon copolymerization with OEGMA units, the LCST and collapse transition increase toward higher temperatures, with a linear dependence on molar content in OEGMA.12,55 (52) (53) (54) (55)

Cini, R.; Loglio, G.; Ficalbi, A. J. Colloid Interface Sci. 1972, 41, 287–298. Kayser, W. V. J. Colloid Interface Sci. 1976, 56, 622–627. Han, S.; Hagiwara, M.; Ishizone, T. Macromolecules 2003, 36, 8312–8319. Lutz, J.-F.; Hoth, A. Macromolecules 2006, 39, 893–896.

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Figure 1. Temperature dependence in water of the third overtone of the frequency shift (Δf ) and of the dissipation shift (ΔD) for thermoresponsive brushes of PMEO2MA (left) and P((MEO2MA)90-(OEGMA475)10) (right). The lines are drawn to guide the eye.

The brushes grew identically to what was reported before.12 For instance, the polymerization rate slightly decreased with polymerization time and also decreased with the addition of larger amounts of the bulkier OEGMA comonomers. Brushes approximately 100 nm in thickness could be grown in a few hours and were selected for the sequel. A brush denoted P((MEO2MA)x(OEGMAz)y) indicates that polymerization was performed in the presence of x mol % MOE2MA and y mol % OEGMA with a molar mass of z g/mol. Bulk Collapse of Thermoresponsive Brushes Probed by QCM-D. Heuristically Defined Bulk Collapse Transition Temperatures. Figure 1 presents typical QCM-D data obtained on a stepwise-heated PMEO2MA brush (left) and a P((MEO2MA)90(OEGMA475)10) brush (right). The data were collected after a long equilibration time at each temperature (Experimental Section). Similar data were obtained for other brush compositions, provided the content in OEGMA units was not too high (∼30%). The frequency shift Δf increases continuously with temperature but exhibits different slopes in the probed temperature range (Figure 1). This is due to the collapse of the brush, with its associated decrease in brush height, loss of water, and change in viscoelastic properties. In contrast, for OEGMA-rich polymer brushes whose collapse occurs well above the highest temperature probed by the QCM, Δf was found to vary strictly linearly with temperature (data not shown). For such OEGMA-rich brushes, a simple linear increase in Δf is predicted from eq 2 as a result of the decrease in water viscosity and density with temperature. The variation of the slope of Δf(T) for collapsing brushes allows us to define heuristically a collapse transition temperature TΔf tr corresponding to the inflection point of this curve (i.e., the temperature corresponding to the largest slope, computed numerically after polynomial smoothing to remove noise). Furthermore, the dissipation shift ΔD(T) presents a change in slope at a temperature close to the inflection point of Δf(T) (Figure 1) because the brush becomes less viscous and collapses to a more rigid layer. Similar behavior for Δf(T) and ΔD(T) was reported for PNIPAM brushes.23,24 Interestingly, the inflection point of ∂ΔD/∂T, which corresponds to the change in slope of ΔD, occurs at Δf a temperature TΔD tr that always happens to be equal to Ttr within 0.5
C, thereby allowing us to define a second heuristic transition temperature. For instance, for the PMEO2MA brush shown in Δf Figure 1 (left), TΔD tr ≈ Ttr = 22.2
C, which is slightly lower than the reported LCST of PMEO2MA in water (∼27 C).31,54,55 Similar results were generally obtained when analyzing other overtones, except for minor temperature shifts of a few tenths of a degree. Kinetic Effects on the Bulk Collapse Transition Temperature. Dynamic QCM-D measurements were also performed on the PMEO2MA brushes, wherein the temperature was increased or decreased continuously while simultaneously acquiring data. 844 DOI: 10.1021/la902285t

Figure 2. Influence of the heating and cooling rate on the bulk collapse transition temperature TΔf tr determined from the third overtone of the QCM-D of a PMEO2MA brush. The data points at zero heating rate correspond to data acquired in stepwise heating or cooling experiments.

Hysteresis between the heating and the cooling ramps was observed, increasing with the heating or cooling rate. The heuristic transition temperature was extracted from Δf(T); it is plotted versus the rate of heating or cooling in Figure 2, with the values obtained for the stepwise experiments plotted at zero rate. The collapse transition shifts linearly to higher temperatures with increasing heating rate, whereas it decreases linearly toward lower temperatures with increasing cooling rate. The two lines extrapolate to a single value at zero heating rate, which corresponds to the experimentally determined values of the collapse transition measured under static conditions (stepwise heating/ cooling). This behavior indicates that the equilibrium time constants of the system are large. This might be due to either extrinsic time constants associated with the experimental setup or the intrinsic time constants associated with the polymer brush itself. However, temperature jump experiments performed on brushes lacking a collapse transition indicated that the time required to reach equilibrium is similar to that observed on brushes displaying a collapse transition. This indicates that the kinetic effects reported in Figure 2 are dominated by extrinsic time constants associated with the QCM-D setup. In the sequel, to avoid this experimental problem, we use either static measurements or measurements acquired at a 0.2
C/min heating rate, which we shift downward by 1
C to correct for kinetic effects. Dependence of the Bulk Collapse Temperature on Brush Composition. The heuristic collapse transition temperature TΔf tr was measured for a series of P(MEO2MA-OEGMA300) brushes of varying OEGMA content (Figure 3). A linear relationship is found between the transition temperature of the bulk of the brush and the OEGMA300 concentration in the feed solution. This is Langmuir 2010, 26(2), 838–847

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Figure 3. Bulk collapse transition temperatures TΔf (open tr symbols) and TΔD (closed symbols) determined from the third tr overtone of the QCM-D for a series of P((MEO2MA)100-y-(OEGMA300)y) brushes, where y is the monomer molar fraction of OEGMA300 in the feed solution.

similar to previous reports for the LCST of closely related polymers measured in solution55 and for P(MEO2MAOEGMA475) brushes,12 although the slopes of the curves differ because of differences in the length of the (EO) side chains. This observation also indicates that the composition of the copolymer is close to the composition of the feed solution, which is expected given the structural similarity of the comonomers. Temperature Dependence of the Collapse of the Bulk of the Brush. Equations 2 and 3 were fit simultaneously to the QCM-D data (third overtone) as described above in order to extract the temperature dependence of the average acoustic height of the brush and its viscoelastic constants. The fits always converged properly; the quality of the fits can be judged directly in Figure 4, where the continuous lines are the best fits for a P((MEO2MA)90(OEGMA475)10) brush measured dynamically at 0.2
C/min (shifted downward by 1
C to compensate for kinetic effects). The resulting temperature variation of the average acoustic brush swelling ratio hbr(T)/hdry br is also presented in Figure 4. Similar good fits were obtained for other brushes as well. The main fit parameters are reported for a series of brushes in Table 1. Despite the number of possible solutions being limited by the constraints imposed by eq 5, it was usually found that a limited set of solutions could be found to reproduce the data. For instance, the jump in shear modulus, |Δμ|, and the jump in shear viscosity, |Δη|, are not fully independent: solutions with |Δμ| of a few MPa and |Δη| of a few tenths of a Pa s or with |Δμ| of a few tens of kPa and |Δη| a few Pa s were often found to reproduce the data equally well. Two examples of such fits can be found in Table 1 (lines 1 and 2). The average acoustic swelling coefficient, however, is much less variable, with values of the swelling in the collapsed state ranging from 1 to 1.4 and the jump in swelling ranging from 1 to 1.5. As for the location of the transition and its width, which are the parameters that we are interested in, these parameters are determined with much more precision: we found that they are essentially identical whatever solution the fit converges to. This is because the temperature dependence of Δf and ΔD is represented by only two parameters. The transition temperature obtained from the fit was always identical to the heuristically determined one within experimental precision. Because the thermal dependence of the collapse is the main information that we are interested in, no further attempt to limit the number of possible solutions was undertaken here. One possibility would be to include more than one overtone in the fit; however, the dependence of the modulus and viscosity on frequency would then be required to avoid introducing new parameters. Another possibility would be to grow brushes in situ and to Langmuir 2010, 26(2), 838–847

Figure 4. Fit of eqs 2 and 3 to the QCM-D data of a P((MEO2MA)90-(OEGMA475)10) brush measured while heating at 0.2
C/min. All curves are shifted downward by 1
C to compensate for kinetic effects. (a) Experimental frequency and dissipation shifts (squares) and fits (lines). (b) Average acoustic swelling ratio hbr(T)/hdry br of the brush as obtained from the fit. The continuous line indicates the experimental range. The dotted line is an extrapolation based on eq 5.

measure them directly after growth, without introducing uncertainties in reference values of f and D as a result of clamping/ unclamping, as was done before for nonresponsive brushes.35,57 The main results we use from the fits are thus the average collapse transition temperature of the bulk of the brush, Ttr, corresponding to 50% collapse, and the width of the transition, which is on the order of 3 to 4 times σtr (i.e., 20-30
C), close to the width reported for PNIPAM brushes (10-40
C).22 This large transition range confirms the absence of a first-order transition in the bulk of the brush as predicted theoretically.16,18,19 Surface versus Bulk Collapse Transitions of Thermoresponsive Brushes. The equilibrium contact angles measured on two brushes, PMEO2MA and P((MEO2MA)90-(OEGMA475)10), are reported in the top panels of Figure 5. The contact angles exhibit a rapid change in slope in the region of the collapse transition; in contrast, they do not exhibit a jump as often reported for out-ofequilibrium contact angles.22,58-60 Indeed, equilibrium (true) (56) Lutz, J.-F.; Weichenhan, K.; Akdemir, O.; Hoth, A. Macromolecules 2007, 40, 2503–2508. (57) Fu, L.; Chen, X.; He, J.; Xiong, C.; Ma, H. Langmuir 2008, 24, 6100–6106. (58) Yakushiji, T.; Sakai, K.; Kikuchi, A.; Aoyagi, T.; Sakurai, Y.; Okano, T. Langmuir 1998, 14, 4657–4662. (59) Liang, L.; Feng, X.; Liu, J.; Rieke, P. C.; Fryxell, G. E. Macromolecules 1998, 31, 7845–7850. (60) Plunkett, K. N.; Zhu, X.; Moore, J. S.; Leckband, D. E. Langmuir 2006, 22, 4259–4266.

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Table 1. Fit Parameters Obtained by Fitting Equations 2, 3, and 5 to the QCM-D Data of a Series of Thermoresponsive Brushes of Varying Comonomer Contenta MEO2MA content (mol %)

OEGMA300 content (mol %)

OEGMA475 content (mol %)

100 0 0 90 0 10 90 10 0 82.5 17.5 0 75 25 0 a The data were corrected for kinetic effects, if any.

hdry br (nm)

Ttr (
C)

σtr (
C)

hcoll/hdry br

|Δh|/hdry br

μcoll (Mpa)

|Δμ| (Mpa)

ηcoll (Pa.s)

|Δη| (Pa.s)

92 135 87 130 128

22.1 35.3 27.7 31.8 34.2

7.1 7.4 6.15 7.6 8.1

1.34 1.04 1.4 1.24 1.19

1.09 1.18 0.98 1.27 1.45

2.3 0.3 2.2 0.4 0.3

1.6 0.01 0.01 0.01 0.01

4.1 9.3 7.2 11.8 7.2

0.1 8.1 3 10 5.2

Figure 5. Comparison between the bulk and surface collapse transition of (left) PMEO2MA and (right) P((MEO2MA)90-(OEGMA475)10) brushes. The bottom panels are the average acoustic swelling ratios of the brushes as determined by QCM-D, which is sensitive to the bulk of the brush. Because P((MEO2MA)90-(OEGMA475)10) was measured at 0.2
C/min, its swelling is shifted downward by 1
C to compensate for kinetic effects. The top panels are, from top to bottom, the water equilibrium contact angle θ, γw(T) cos θ, and its temperature derivative [∂(γw cos θ)/∂T]P, which is the difference in excess surface configurational entropy between the brush in contact with liquid water and the brush in contact with water vapor (Δsconf,liq/vap ). These three parameters provide information on the collapse of the surface of the brush. br

contact angles cannot exhibit jumps versus temperature in the absence of a chemical transformation because the total derivative of γw cos θ depends only on the total derivatives of T and the chemical potential (eqs 7 and 8), which are continuous functions of T. Therefore, the equilibrium contact angle is by necessity also a continuous function of temperature, except when the surface area of the sample varies abruptly with temperature, as for unconstrained gels. The temperature derivatives of γw cos θ are shown in the third panels of Figure 5. These are equal to the difference in excess surface configurational entropy between the brush in contact with liquid ), as water and the brush in contact with water vapor (Δsconf,liq/vap br explained above, and provide relevant thermodynamic information on the behavior of the brush surface. Although the absolute values 846 DOI: 10.1021/la902285t

are not significant, because of large errors resulting of Δsconf,liq/vap br from differentiation and from refraction errors when determining θ, its relative variations are meaningful. As can be seen in Figure 5, the rapid change in slope of θ(T) (T), which inditranslates into a downward jump of Δsconf,liq/vap br cates that the surface of the brush transitions from one surface state to another one over a few
C, either at the liquid interface or at the vapor interface (or both). In the present study, we are essentially interested in the brush/liquid interface because our QCM measurements were performed in liquid water and more importantly because brushes are usually used in liquids, not in saturated vapors. It is thus important to elucidate which interface contributes to the (T) = sconf,liq - sconf,vap . Let us sudden decrease in Δsconf,liq/vap br br br suppose that the downward jump arises solely from changes arising Langmuir 2010, 26(2), 838–847

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Table 2. Comparison of the Transition Temperatures of PMEO2MA and P((MEO2MA)90-(OEGMA475)10) Chains in Solution or in a Dense Brusha sample

free chains in solution LCST (
C)

26,55 2854 PMEO2MA 39,55 4056 P((MEO2MA)90-(OEGMA475)10) a The precision of the brush surface transition temperature is ∼3
C.

at the brush/vapor interface. This requires sconf,vap to increase br suddenly; hence we assume that the surface configurational entropy (i.e., disorder, degrees of freedom, etc.) of the brush/vapor interface increases suddenly during the collapse. This does not make sense for obvious reasons. Therefore, at least part of the (T ) arises from a sudden decrease in entropy at jump in Δsconf,liq/vap br ), which is in agreement with the brush/liquid interface (sconf,liq br expectations regarding the collapse of a brush. Thus, this testifies to the existence of a first-order surface transition occurring at the brush/liquid interface, which implies that all surface properties of the brush in contact with liquid water (including the out-ofequilibrium contact angle measured by most researchers) vary abruptly at some temperature Ttrsurf. Crucially, the surface collapse occurs at the very end of the bulk collapse, as can be realized by comparing the average acoustic swelling ratio of the brush determined by QCM-D, shown in the bottom panels of Figure 5, with the behavior of the excess surface (T). This means configurational entropy difference Δsconf,liq/vap br that the bulk of the brush collapses in liquid water at a lower than its surface, the difference between the two temperature Tbulk tr transitions being on the order of 9 ( 3
C, with the relatively low precision on this value resulting from the fact that we measured the surface properties every 5
C and that the transition is determined after differentiation. The surface collapse transition is also much narrower than the bulk collapse, corresponding to the notion that the bulk transition is not a first-order transition: the bulk of the brush progressively collapses upon heating until the collapse reaches the brush surface, which transitions abruptly and signals the end of the process. Note that the brush surface is nevertheless affected by the collapse of the (T ), bulk of the brush well before the jump occurs in Δsconf,liq/vap br (T ) observed as can be deduced from the curvature of Δsconf,liq/vap br before the jump (especially for the P((MEO2MA)90-(OEGMA475)10) brush): apparently, the surface “feels” that the brush is collapsing below and finally collapses itself when the temperature rises further. These observations are compatible with the theoretical model of a vertical phase separation occurring in the brush, as detailed in the Introduction and shown schematically in Scheme 1. However, alternate models would be acceptable as well, provided that they predict that the surface collapses abruptly at the very end of the broad transition of the bulk of the brush. Finally, it is also instructive to compare the collapse transition temperatures of the brushes with the reported LCST of free polymer chains in solution. These are collected in Table 2. One should be aware that the reported LCST values are dependent on the heating rate and polymer concentration and do not have an absolute thermodynamic meaning. The average transition temperature of the bulk of the brush happens about 5
C below the LCST of the free chains in solution. In contrast, the collapse of the brush surface happens at a higher temperature than the LCST, on the order of 2-6
C. However, one should resist the temptation to provide absolute numbers for these values, first because of the

Langmuir 2010, 26(2), 838–847

brush, bulk Tbulk (
C) tr

brush, surface Tsurf tr (
C)

22 35

34 41.5

limited precision of the transition temperature of the surface of the brush measured in this study and second because collapse transition temperatures are modulated by a series of parameters such as grafting density and chain length61 or even nanopatterning.30

Conclusions By combining for the first time QCM-D, which is sensitive to the collapse of the bulk of a thermoresponsive brush, with equilibrium contact angle measurements, which are sensitive to the collapse of the brush surface, we have provided new detailed information on the collapse process. The bulk of the brush collapses over a large range of temperature (∼25
C), and the end of the process is signaled by a sharp first-order transition of the surface of the brush. These observations support theoretical predictions regarding the occurrence of a vertical phase separation during collapse propagating from the bottom to the top of the brush and indicate that all surface properties of thermoresponsive brushes will exhibit a sharp variation at a temperature of surf ; in contrast, the bulk properties of the brush vary smoothly, Tbr bulk occurring on average ∼8
C below with a bulk transition of Tbr surf and ∼5
C below the LCST of free chains in solution. These Tbr observations are consistent with the current knowledge about PNIPAM brushes, suggesting that this behavior is general to planar brushes of neutral water-soluble polymers. These are important results when trying to harness thermoresponsive brushes for real-world applications because the transition temperature and sharpness of the collapse will depend on whether the surface or the bulk of the brush is the key factor controlling the envisioned application. In addition to this important result, our study also provides a practical way to analyze quantitatively the temperature dependence of the QCM-D response of thermoresponsive brushes and delivers a simple thermodynamic interpretation of equilibrium contact angles. It is hoped that these tools will be of interest in other fields as well and will find widespread use in other temperature-responsive solvophilic systems requiring convenient, fast analysis. Acknowledgment. We are grateful to Karine Glinel (Rouen, France), Wilhelm Huck (Cambridge, U.K.), and Pierre Labb
e (Grenoble, France) for their critical input at various stages of this work, to Christine Dupont (UC Louvain) for access to the QCM-D apparatus, and to Peter Hensenne and Olivier Riant (UCLouvain) for helping to synthesize the silane initiator. B.N. is a senior research associate of the F.R.S.-FNRS. Financial support was provided by the Communaut
e Franc-aise de Belgique (ARC 06-11/339), the Belgian Federal Science Policy (IAP-PAI P6/27), the F.R.S.-FNRS, and the Wallonia Region (NanoticFeeling). (61) Yim, H.; Kent, M. S.; Mendez, S.; Lopez, G. P.; Satija, S.; Seo, Y. Macromolecules 2006, 39, 3420–3426.

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