Letter pubs.acs.org/JPCL
Reduced Water Density in a Poly(ethylene oxide) Brush Hoyoung Lee,† Dae Hwan Kim,† Hae-Woong Park,† Nathan A. Mahynski,† Kyungil Kim,‡ Mati Meron,‡ Binhua Lin,‡ and You-Yeon Won*,† †
School of Chemical Engineering, Purdue University, West Lafayette, Indiana 47907, United States Advanced Photon Source, University of Chicago, Argonne, Illinois 60439, United States
‡
S Supporting Information *
ABSTRACT: A model poly(ethylene oxide) (PEO) brush system, prepared by spreading a poly(ethylene oxide)−poly(n-butyl acrylate) (PEO−PnBA) amphiphilic diblock copolymer onto an air−water interface, was investigated under various grafting density conditions by using the X-ray reflectivity (XR) technique. The overall electron density profiles of the PEO−PnBA monolayer in the direction normal to the air−water interface were determined from the XR data. From this analysis, it was found that inside of the PEO brush, the water density is significantly lower than that of bulk water, in particular, in the region close to the PnBA−water interface. Separate XR measurements with a PnBA homopolymer monolayer confirm that the reduced water density within the PEO−PnBA monolayer is not due to unfavorable contacts between the PnBA surface and water. The above result, therefore, lends support to the notion that PEO chains provide a hydrophobic environment for the surrounding water molecules when they exist as polymer brush chains. SECTION: Glasses, Colloids, Polymers, and Soft Matter
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the notion is not new that the PEO chains are hydrophobic when they exist as polymer brush chains because of the manybody attractive interactions that are forced to be effective in the brush situation. The hydration of PEO involves a configurational rearrangement of the polymer segments in coordination with the surrounding water molecules,12,13 and therefore, at high concentrations of PEO, the specific configuration of the polymer that enables hydrophilic interaction with water may become disrupted, rendering the polymer less (or in)soluble in water. This many-body effect is well supported by experimental evidence of, for instance, an increase in the measured value of the effective Flory−Huggins interaction parameter (χPEO−water)14,15 and the formation of aggregates of PEO chains16 in bulk solution at elevated concentrations of PEO. De Gennes and co-workers have incorporated this notion into a theoretical description of a polymer brush system (often referred to as the n-cluster theory) and predicted that a PEO brush can form a partially collapsed structure.17 In an attempt to find an answer to the question whether the PEO brush chains in water indeed experience an unfavorable (“poor”) solvent environment due to the n-cluster effect, we investigated a model PEO brush system, prepared by spreading a poly(ethylene oxide)−poly(n-butyl acrylate) (PEO−PnBA) amphiphilic diblock copolymer onto an air−water interface, by using the X-ray reflectivity (XR) technique. It needs to be pointed out that when compared with other previously studied PEO-based block copolymers that form insoluble domains at
olymer brushes have been a subject of research in polymer science for more than 30 years.1−3 Most of these studies have focused on examining the structural and thermodynamic behaviors of the end-grafted polymer chains with the surrounding fluids being treated as inert continua whose properties are not affected by the presence of the polymers and are thus no different from their properties in the bulk limit. This assumption of a bulk-like local solvent environment for a polymer segment might become only an approximation (a poor one) when one has to deal with so-called “nonclassical” polymer brush systems in which the interaction between the brush and the solvent involves significant configurational rearrangements of both the polymer segments and the solvent molecules, as is the case for most water-soluble polymer brushes. Water, in fact, is known to be very prone to density variation under the influence of added compounds. The density of water can be significantly increased by dissolving a small amount of, for example, poly(ethylene oxide) (PEO),4 salt,5 or sugar6 in it. When water is in contact with a hydrophobic object, the opposite happens; the density decreases. Several recent studies7−10 suggest that near a hydrophobic surface, the water forms a low-density layer of thickness of the same order as the correlation length of bulk water (∼4 Å11), and the actual thickness of this low-density layer correlates with the degree of hydrophobicity of the surface. These previous findings raise an important question, How would water molecules then behave inside of a brush layer formed by a water-soluble polymer (such as PEO) where the hydrophilicity of the polymer becomes significantly compromised due to the high spatial confinement of the chains? In fact, © 2012 American Chemical Society
Received: March 7, 2012 Accepted: May 29, 2012 Published: May 29, 2012 1589
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the air−water interface (such as PEO−polystyrene,18−20 PEO− poly(ethyl ethylene),21 and PEO−polybutadiene22), the PEO− PnBA material has a unique combination of interfacial properties that makes this copolymer best suited for preparation of a model planar nonadsorbing PEO brush system; the insoluble PnBA block completely wets the air− water interface and forms a flat continuous water-free singlemonomer-thick interfacial film at high surface polymer concentrations,23,24 while the grafted PEO chains do not have any tendency to adsorb to the PnBA−water interface.25 The high-flux synchrotron X-ray source used allowed us to probe the fine details of the electron density distribution inside of the PEO brush layer of the PEO−PnBA film. The XR data were analyzed using the standard Parratt multilayer formalism. From this analysis, we discovered, for the first time, that the water density inside of the PEO brush is significantly lower than that of bulk water. In the present study, a model PEO brush system was prepared by spreading a PEO−PnBA amphiphilic diblock copolymer onto an air−water interface. This PEO−PnBA material was synthesized and characterized as described in our previous publications.24,26−28 The molecular characteristics of this copolymer are DPn,PEO = 113 (determined by 1H NMR), DPn,PnBA = 100 (determined by 1H NMR), and PDI (for the overall molecular weight distribution) = 1.28 (determined by GPC). Figure 1 displays the surface pressure−area (Π−α) isotherm of the PEO−PnBA diblock copolymer monolayer at the air− water interface. Through comparison with the isotherm curve of a PnBA homopolymer (DPn = 111 and PDI = 1.12) (also shown in the figure), the various features (i.e., plateaus and kinks) observed in the PEO−PnBA isotherm curve could be understood. First, it should be noted that the isotherm curve of the diblock monolayer shows a distinct transition upon compression from a fluid phase to a plateau of surface pressure (at an area per chain value of αo = 2200 Å2) that is almost identical (in shape and lateral position) to that observed in the homopolymer data. In the PnBA homopolymer case (DPn = 111), this plateau transition occurs at αo = 2400 Å2, which gives a value of 21.6 Å2 for the area occupied by a PnBA monomer at the transition point. In the diblock situation (DPn,PnBA = 100), the same calculation gives an essentially indistinguishable value of 22.0 Å2 per PnBA monomer for the same parameter. This result indicates that the nature of the plateau transition in the PEO−PnBA curve is identical to the nature of the plateau transition observed with the PnBA homopolymer; the transition point is the point where the water surface becomes fully covered with a flat (i.e., laterally uniform), singlemonomer-thick, water-free monolayer of PnBA.24 We would also like to note that in a previous publication,23,29 we have also shown that the surface pressure−area behavior of a different PnBA-based diblock copolymer, poly(2-(dimethylamino)ethyl methacrylate)−poly(n-butyl acrylate) (PDMAEMA−PnBA, DPn,PDMAEMA = 80 and DPn,PnBA = 94), undergoes the plateau transition at a monolayer area of αo = 2000 Å2 per chain, which again gives essentially the same value of 21.6 Å2 for the area of a PnBA monomer at the transition point (further supporting the above explanation). As discussed in our previous publications,23,24,29 when the PnBA homopolymer monolayer is compressed beyond the transition point (i.e., at α < αo), the surface pressure stays at a constant level because the additional compressional stress is fully relaxed via collapse of the PnBA chains into a three-
Figure 1. Surface pressure (Π) versus area per chain (α) compression isotherms for the air−water interfacial monolayers of the PEO−PnBA diblock copolymer (DPn,PEO = 113, DPn,PnBA = 100, and PDI = 1.28) and the PnBA homopolymer (DPn,PnBA = 111 and PDI = 1.12); the dark solid line represents the Π−α isotherm of the diblock copolymer, and the gray solid line represents the homopolymer isotherm. Also shown for explanation of the method for calculation of the lateral pressure of the grafted PEO chains are the Π−α isotherm curve (gray dashed line) obtained from a different PnBA material (DPn = 102 and PDI = 1.12) that covers a much wider α range (down to a value of α = 200 Å2/chain) and a rescaled plot of this homopolymer isotherm (gray broken-dotted line) produced by first adding a constant (=72 Å2/ chain) to the area/chain values of the original homopolymer isotherm to make the critical area equal to that observed for the PEO−PnBA (this procedure is to correct for the difference in the PnBA molecular weight) and then multiplying the surface pressure values of this shifted homopolymer isotherm further by a constant factor (=1.06) to make its plateau pressure at the full-coverage transition identical to that of the diblock isotherm (in order to account for the difference in γPnBA−water).29 All isotherms were reproducible in the x-direction within 2% among (at least) three independent measurements with almost negligible errors in the pressure values. The black vertical dashed line marks the value of α at which the ratio α/RG,PEO(3D)2 becomes unity (see the main text for discussion). The arrows denote the α conditions at which the XR data presented in Figures 2A and 3A were obtained.
dimensional conformation.24 Therefore, the plateau pressure of the PnBA monolayer in this collapsed full coverage regime is equal to the surface energy change per area associated with removal of the PnBA monolayer from the air−water interface (i.e., Πo = γair−water − γPnBA−air − γPnBA−water).23,29 As has also been demonstrated with the PDMAEMA−PnBA monolayer,29 the slightly higher plateau pressure observed for the PEO− PnBA diblock monolayer (than that observed for the PnBA monolayer, that is, Πo,PEO−PnBA > Πo,PnBA) can be understood as a result of a decrease in γPnBA−water, in the PEO−PnBA situation, caused by the presence of the chemically grafted PEO chains at the PnBA−water interface. Further compression beyond the onset of full surface coverage (i.e., to an area per chain of α < αo) causes the PEO−PnBA monolayer to become more resistant to compression than the simple PnBA film (that is, ΠPEO−PnBA > ΠPnBA). In this area per chain region, the lateral overlap between the grafted PEO chains produces a nonzero lateral pressure of the PEO chains, that is, ΠPEO(α)(≡ΠPEO−PnBA(α) − ΠPnBA(rescaled)(α)) > 0; here, ΠPnBA(rescaled)(α) represents the rescaled surface pressure of the PnBA homopolymer (shown with a gray broken-dotted line in Figure 1), and its values were calculated using the procedure described in the figure caption for Figure 1. This result is also consistent with the fact that in this regime, the normalized area per chain value, α/ 1590
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Figure 2. (A) XR profiles from the PEO−PnBA monolayer at seven different α conditions denoted using arrows in Figure 1. The data are presented in the normalized form, R(qz)/[RF(qz)·Δ(qz)], where RF(qz) and Δ(qz) denote, respectively, the Fresnel reflectivity and the Debye−Waller factor for a fictitious reference air−subphase interface; see the main text for detailed information. Plots of the original reflectivity (R(qz)) as a function of qz are provided in Figure S1 of the SI. (B) The overall electron density profiles (ρe(z)) obtained from the box model analysis of the data in (A) (plotted in a normalized form where the ρe(z) quantities are referenced to the electron density of bulk water ρe,water,∞). The corresponding best-fit XR profiles are shown as solid lines in (A). Note that the z = 0 position is defined as the point where the air-side portion of the ρe(z) function is at its maximum.
πRG,PEO(3D)2, is less than unity (as shown on the second x-axis of Figure 1); here, RG,PEO(3D) is the radius of gyration of the PEO block in the three-dimensional self-avoiding random-walk configuration, and its value (∼25.7 Å) was estimated using parameter values reported in ref 30. It should be noted that the PEO layer becomes significantly more resistant to lateral compression when α is less than RG,PEO(3D)2; in Figure 1, this α/ RG,PEO(3D)2 = 1 condition is marked with a vertical dashed line. This result is consistent with the previous report that transitions in the vertical force profiles31,32 and the segment density distributions33 of the end-grafted PEO chains both occur at an α value equal to RG,PEO(3D)2 (not πRG,PEO(3D)2), and only when α < RG,PEO(3D)2, the end-grafted PEO chains are truly in the “brush” configuration. However, in our opinion, when α takes a value intermediate between the RG,PEO(3D)2 and πRG,PEO(3D)2 values, it becomes a debatable issue whether the grafted PEO layer should be described as a PEO brush or as containing “weakly overlapping mushrooms”.31−33 In the present Letter, we opted to use the term brush (instead of mushroom) in describing this intermediate situation because in this region, already ΠPEO(α) > 0, and also (as will be shown later), the thickness of the PEO layer varies with chain-grafting density. This choice is also consistent with the common practice in the polymer physics literature of defining the mushroom-to-brush transition as a change in the dependence of the height of the grafted chains (H) on the grafting density (1/α) from H ≈ (1/α)0 in the mushroom regime to H ≈ (1/ α)1/3 in the brush regime.34,35 In the range α > αo where there exist open areas of water surface uncovered by the polymer, the PEO−PnBA isotherm becomes significantly different from that of PnBA. The higher surface pressures exhibited by the PEO−PnBA monolayer throughout this partial coverage regime are believed to be a
consequence of strong adsorption of the PEO segments to the air−water interface.36,37 We also note that a small hump-like feature (or “pseudo-plateau”) was seen in the PEO−PnBA isotherm in the α ≈ 3000−6000 Å2 per chain range. This behavior is also believed to be due to the strong adsorption of the PEO segments to the air−water interface. Assuming, for simplicity, that the spread PEO−PnBA diblock chains at sufficiently low surface concentrations assume a 2D Gaussian coil structure and using the literature values for the statistical segment lengths of PEO and PnBA (i.e., bPEO = 5.9 Å,30 and bPnBA = 7.0 Å (based on parameters for poly(ethyl acrylate))38), the 2D chain-overlap condition (at which the pervasive areas of the isolated diblock chains begin to interpenetrate) is estimated to be α*(=πRG,PEO−PnBA2) ≈ 4600 Å2. This estimated α* value closely agrees with the value of α at the onset of the pseudoplateau (≈4500 Å2), which suggests that the plateau-like behavior of surface pressure is an indication of a conformational transition of the PEO segment from a surface-bound state to a water-submerged structure. The conformation of the PEO brush formed by the PEO− PnBA diblock copolymer at the air−water interface was investigated by using the XR technique. Experiments were conducted using the liquid surface spectrometer at the ChemMatCARS synchrotron facility (Sector 15) at the Advanced Photon Source of Argonne National Laboratory.39 The specular reflectivities were measured using an in-plane polarized incident X-ray beam at a wavelength (λ) of 1.24 Å. The reflected intensities were measured in the range of the outof-plane momentum transfer vector (qz) from 0.016 to 0.69 Å−1 (the momentum transfer vector is related to the angle of reflection (θ) by qz = (4π/λ) sin θ), which gives rise to a spatial resolution (≈π/qz,max)10 of about 4.6 Å. During measurements, the monolayers were kept in a humidified helium atmosphere. 1591
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box model equation used); all ten ρe, d, and σ variables listed above were used as fitting parameters. The values of the fit parameters that gave the least errors in simulating the experimental data and the ranges of the parameter values over which the search was conducted are presented in Table S2 (SI); the objective function of the fitting procedure, defined as the sum of absolute error values (eq S4, SI), was minimized using a Matlab constrained nonlinear regression routine (“fmincon”). As shown in Figure 2A, the model’s fit quality under the best-fitting parameter estimates was almost impeccable at all α conditions examined, which fully supports the reasonableness of the estimated parameters. Results from unsuccessful fitting trials conducted using a two-box model (which requires seven fitting parameters (ρe,1, ρe,2, d1, d2, σ1, σ2, σ3)) are demonstrated in Figure S2 of the SI; it should be noted that although this two-box model fails to reproduce the complicated shapes of the R(qz)/[RF(qz)·Δ(qz)] curves (Figure S2B, SI), it provides reasonable quality fits to the XR data presented in the R(qz)/RF(qz) format (Figure S2A, SI), which may lead to a false acceptance of the model and thus supports the necessity of the double-normalization procedure. The overall electron density profiles (ρe(z)) obtained from this fitting analysis are presented (in a normalized form where the ρe(z) quantities are referenced to the electron density of bulk water ρe,water,∞) in Figure 2B. Although these ρe(z) profiles only represent the weighted superpositions of the density profiles of the individual species, a few solid conclusions could be drawn regarding the density distributions of the individual components. First, we note that the peak in ρe(z) near z = 0 corresponds to the PnBA film formed on the air side of the PEO−PnBA monolayer. At α = 1100 (or 900) Å2 per chain, the value of ρe(z) at its maximum (centered at z = 0) is essentially identical to the value of the electron density of pure PnBA (i.e., ρe,PnBA = 0.367 e−/Å3), indicating that the PnBA blocks form a water-free monolayer at the air−water interface. The peaks appearing in the distance (z) range between about 20 and 60 Å are due to the presence of the PEO (brush) segments; note that ρe,PEO(=0.406 e−/Å3) > ρe,water,∞(=0.333 e−/Å3), which gives rise to a reasonable X-ray scattering contrast. Strikingly, the ρe(z) curves obtained at α values between 1100 and 2400 Å2 per chain show an unexpected feature; we observe valleys between the PnBA and PEO peaks (i.e., ρe(z)/ ρe,water,∞ drops below 1 at intermediate z). The full widths of these minima at half heights were found to range between 3.9 and 5.4 Å; these width values are at least of the same order as the minimum spatial resolution of the XR technique (∼π/qz,max = 4.6 Å) and are therefore considered reliable. Given that both the PnBA and PEO electron densities are greater than that of bulk water, the existence of the minimum in the ρe(z) curve can only be interpreted as being caused by a reduction in the density of the water incorporated in the PEO (brush) layer (i.e., ρe,water(z) < ρe,water,∞). The exact thickness of this low-waterdensity zone within the PEO (brush) layer is actually expected to be greater than the width of the minimum in the ρe(z) profile because even at higher z where ρe(z)/ρe,water,∞ > 1, the ρe,water(z) value can still be smaller than the bulk water electron density ρe,water,∞ (note that within the PEO brush layer, ρe(z) ≈ ρe,PEO·ϕPEO(z) + ρe,water(z)·ϕwater(z), where ϕi(z) denotes the volume fraction of species i at position z, and ρe,PEO > ρe,water,∞). This point is also supported by the fact that the value of the integral ∫ ∞ zo [ρe(z) − ρe,water,∞] dz (where zo denotes the point within the PEO (brush) layer where ρe(z)/ρe,water,∞ becomes
All measurements were conducted at room temperature. All results were highly reproducible between independent duplicate experiments. The exposure of an area of the monolayer sample to the X-ray radiation was, in all experiments, kept below a level of total 1.5 × 1013 photons per mm2 (see Table S1 of the Supporting Information (SI) for more detailed information), which is well within the range that is safe against X-ray damage for an organic monolayer at the air−water interface.8 High-qz scans (0.260−0.690 Å−1) were typically repeated 2−3 times at a fixed sample position, and the XR data from these repeated runs were identical to one another, which also confirmed the absence of radiation damage. XR profiles were obtained from the PEO−PnBA monolayer at seven different α conditions (marked with arrows in Figure 1) during compression of the monolayer. As shown in Figure S1 of the SI, the semilogarithmic plots of the reflectivity (R(qz)) as a function of qz show monotonically decaying profiles. However, when plotted in the normalized form, R(qz)/ [RF(qz)·Δ(qz)] (where the terms in the denominator denote, respectively, the Fresnel reflectivity and the Debye−Waller factor for a fictitious reference (air−subphase) interface), the reflectivity data reveal interesting oscillatory features (Figure 2A); here, the normalization factor, RF(qz)·Δ(qz), was calculated by fitting of each R(qz) curve to the formula given in eq S1 (SI) with two adjustable parameters, the refractive index of the fictitious subphase (denoted as nref in eq S1, SI) and the roughness of the reference air−subphase interface (σref in eq S1, SI). As explained in detail in section S2 of the SI, the best-fit value of the reference refractive index was found to be slightly different from that of pure water (probably due to the X-ray absorbance of the sample). As also discussed in that section, when compared with a more conventional way of presenting reflectivity data in the R(qz)/RF(qz) form, the division by the Debye−Waller roughness factor allowed better visualization of the subtle oscillatory features of the XR data originating from the detailed structure of the grafted PEO/ water layer; the conventional R(qz)/RF(qz) presentation visualizes how the measured reflectivity profile deviates from that for an infinitely sharp reference interface, whereas the presentation in the R(qz)/[RF(qz)·Δ(qz)] format visualizes how the data deviates relative to a reference interface with a finite roughness. To our knowledge, this normalization procedure has not previously been demonstrated. As will be demonstrated later, this normalization method does not produce any artifact, while it provides an obvious advantage that the more complicated shapes of the R(qz)/[RF(qz)·Δ(qz)] curves impose more stringent requirements for model fitting. These double-normalized reflectivity data for qz > 0.05 Å−1 were least-squares-analyzed with respect to the so-called multiple-box model (in which the scattering volume is divided into a finite number of horizontal sublayers of distinct electron densities with smeared interfaces between adjacent sublayers);40 the electron density profiles (ρe(z)) calculated based on this multiple-box model were converted through the first Born approximation41 (eq S2, SI) to the expected reflectivity profiles, and the resulting predicted reflectivities were compared with the experimental results. It was observed that at least three sublayers of variable electron density (ρe,1, ρe,2, ρe,3) and thickness (d1, d2, d3), each bounded by error function-shaped interfacial regions of variable width (σ1, σ2, σ3, σ4), should be included in the box model in order to satisfactorily reproduce the complicated shapes of the normalized reflectivity curves (see eq S3 (SI) for the actual 1592
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Figure 3. (A) Normalized XR profiles (R(qz)/[RF(qz)·Δ(qz)]) from the PnBA homopolymer monolayer at six different α conditions denoted with arrows in Figure 1. The data were reproduced from ref 24. Plots of the original reflectivity (R(qz)) as a function of qz are provided in Figure S8 of the SI. (B) The ρe(z)/ρe,water,∞ profiles obtained from the box model analysis of the data in (A). The corresponding best-fit XR profiles are shown as solid lines in (A).
thickness estimated from the measured ρe(z) profiles increases monotonically with a decrease in α. Second, the maximum distance to which the grafted PEO chains stretch also increases monotonically with decreasing α (Figure S6, SI). Lastly, the degree of water density reduction was also found to be a monotonically increasing function of the PEO grafting density; see Figure S7 (SI). To examine this trend, we calculated the spatially varying water density (ρe,water(z)) values from the experimentally determined ρe(z) profiles at five different α conditions (in the α range of 900−2400 Å2/chain) using the overall material balance equation for the water side of the PEO−PnBA monolayer (i.e., for z > 0), ρe,water(z) = [ρe(z) − ρe,PnBA·ϕPnBA(z) − ρe,PEO·ϕPEO(z)]/[1 − ϕPnBA(z) − ϕPEO(z)], where the PnBA volume fraction function ϕPnBA(z) is estimated from the air-side electron density profile (ρe(z < 0)) and the PnBA mass balance constraint, and the PEO segment density distribution ϕPEO(z) is computed using a continuum selfconsistent field (SCF) polymer brush model under the assumption that the water solvent is incompressible, as explained in detail in a separate publication;25 note that, strictly speaking, the assumption of water incompressibility is in contradiction with the concept that the water density is reduced inside of the PEO brush, and this SCF calculation is, therefore, only an approximation, valid for small changes in water density (for this reason, in Figure S7 (SI), the estimated values of ρe,water(z) are shown only for the z > 10 Å region, and the results presented in the figure should only be taken as a demonstration of a qualitative trend). It is well documented that the density of water is reduced near a hydrophobic surface.8−10,42,43 Therefore, one might question whether the low water density observed in the vicinity of the PnBA−water interface is due to the unfavorable contacts between the hydrophobic PnBA surface and water. However,
equal to unity) is always significantly less than the total excess number of electrons on the PEO chains (relative to bulk water) per area (≡MPEO·(ρe,PEO − ρe,water,∞)/(α·NAV·ρPEO), where MPEO and ρPEO denote, respectively, the molar mass and mass density of PEO and NAV is Avogadro’s number); for instance, at α = 1300 Å2 per chain, it is estimated that ∫ ∞ zo [ρe(z) − ρe,water,∞] dz = 0.134 e−/Å2, whereas the value of the MPEO·(ρe,PEO − ρe,water,∞)/(α·NAV·ρPEO) quantity is estimated to be 0.374 e−/Å2. In order to confirm that this unexpected finding is not due to a mathematical artifact associated with the normalization process, we have conducted the same analysis on differently normalized XR data (i.e., the roughness-unsubtracted R(qz)/ RF(qz) data) using the three-box model formalism. As shown in Figure S3 of the SI, the best-fit results were found to be unaffected by the nature of the normalization procedure. We have also tested fitting the XR data after normalizing it with the Fresnel reflectivity of pure water RF,water(qz) (rather than using the Fresnel reflectivity of a fictitious reference subphase RF(qz)). The fit results were again essentially identical to those obtained using the other normalization methods (Figure S4, SI). It should be noted that the overall electron density profiles obtained from the fitting analysis vary nonsystematically with α, which might look counterintuitive at first sight. However, careful analysis revealed that all individual, measurable characteristics of the PEO−PnBA monolayer, in fact, change very systematically with changes of the monolayer area; the seemingly nonmonotonic overall behavior of the ρe(z) profile is simply due to the superposition of these individually monotonic trends. This point was examined in three aspects. First, as can be seen from Figure S5 of the SI, the PnBA layer 1593
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Letter
are relatively negligible, this free energy change can be approximately calculated as ΔF ≈ Δ[∫ χ P E O− water ϕ PEO (r)ρ P EO ϕ w at e r (r)ρ w at e r (r)v dr]k B T ≈ ΔχPEO−waterϕ̅ PEOρPEO(1 − ϕ̅ PEO)ρwater,∞vVkBT, where v represents a characteristic interaction volume for the PEO−water pair and ϕ̅ PEO denotes the mean PEO volume fraction within the brush layer (assumed to be about 0.1 in the calculation below). Combining the above equations leads to a simple relation for the χPEO−water change ΔχPEO−water ≈ ((ΔV/V)2/ [2κϕ̅ PEOρPEO(1 − ϕ̅ PEO)ρwater,∞vkBT]). Using the ρe(z) profile obtained at α = 1300 Å2 per chain, for instance, the fractional volume change and the corresponding pressure variation are computed, respectively, to be ΔV/V ≈ 2.7% and ΔP ≈ −5.9 × 107 N/m2 (which confirms a posteriori the above assumption that |ΔP| ≫ 1 atm =1.013 × 105 N/m2), and the value of χPEO−water for the PEO brush system is estimated to be greater than that corresponding to a good solvent condition by ΔχPEO−water ≈ 0.1, which appears to be a very reasonable estimate considering the known range of concentrationdependent variation of the χPEO−water parameter;45 study is currently in progress toward more rigorously determining the χPEO−water parameter for the PEO brush chains. The molecular structure of the monolayer formed by a PEO−PnBA diblock copolymer at the air−water interface was investigated under various area per chain conditions by using the XR technique. The out-of-plane electron density profiles of the monolayer derived from the least-squares fitting analysis of the XR data unambiguously indicate that there exists a region close to the PnBA−water interface where the water density becomes significantly lower than that of bulk water. We believe that this phenomenon is clear evidence that contrary to what is known for PEO in normal situations, PEO chains are indeed hydrophobic when they are arranged in the polymer brush configuration. We suspect that this effect might play a key role in the mechanism by which a PEO brush system, a coating structure commonly used in biomedical materials for protein resistance and biocompatibilization, is able to resist, so effectively, the adsorption of proteins in physiological conditions. Further study is required to fully understand the exact mechanism by which the water becomes rarefied inside of a PEO brush. However, the finding of the present study appears to be in line with the prediction that in a PEO/water mixture, both the PEO−water and water−water hydrogen bonds are increasingly broken as the PEO concentration increases46 (such as in a PEO brush situation47).
we would like to point out that although the bulk PnBA material is completely insoluble in water, the static contact angle of a water droplet placed on a spin-coated PnBA surface has been measured to be 84.2 ± 3.8°24 (less than 90°), which suggests that the exposed surface of a bulk PnBA material is actually not that hydrophobic possibly due to the rearrangement of the side-chain conformation. Recent studies10,43 have shown that surfaces of comparable contact angle characteristics are not capable of perturbing the structure of water in the contact region to any measurable degree. Therefore, PnBA hydrophobicity is unlikely to be the cause of the dedensification of the water in the PEO brush layer. In order to further test this point, we analyzed the XR profiles obtained from the air−water interfacial monolayer of a PnBA homopolymer (DPn = 111 and PDI = 1.12) at six different area per chain conditions (denoted using arrows in Figure 1). As shown in Figure 3A, the normalized reflectivity curves of this homopolymer sample are characterized by a lack of any oscillatory features. These data were modeled again using the box model. A simple one-box model (eq S5, SI) containing four adjustable parameters (ρe,1, d1, σ1, σ2) was sufficient to quantitatively simulate the PnBA XR profiles; the best-fit values of the parameters and the search ranges for these parameters used are presented in Table S3 (SI). The best-fit curves perfectly coincide with the experimental points (Figure 3A). Figure 3B shows the resulting ρe(z) profiles obtained from this analysis. As can be seen from the figure, at all z > 0, the total electron density remains greater than the bulk water level (ρe,water,∞). This result supports the argument that the PnBA domain does not play any role in the formation of the lowdensity water layer within the PEO-rich region of the PEO− PnBA monolayer. Therefore, the only possible explanation is that the water becomes less dense because of the hydrophobicity of the PEO brush chains. At the present time, it remains an unanswered question whether the water density is reduced solely due to rearrangements of the water molecules or the process also involves an increased amount of gas (e.g., air or helium) dissolved in the water region adjacent to the PnBA surface. However, in the literature, it has been reported by several groups that the gas environment does not influence the behavior of water in contact with a surface,8,9 making the latter explanation less likely. Below, assuming a uniform expansion of the molecular volume of water in the PEO brush layer, we have attempted to make an approximate estimation as to how hydrophobic the PEO brush chains would need to become in order to produce, at equilibrium, the observed amount of water density decrease. As an approximation, the fractional increase in volume accompanying the isothermal expansion of water (ΔV/ V) caused by the hydrophobicity of PEO is equated with the integral quantity, (ρe,water,∞·Δz/∫ zzoo−Δz ρe(z) dz) − 1, where Δz denotes the base width of the minimum in the ρe(z) profile. From this, it is possible to estimate the amount of work done by the system during this fictitious water expansion process, W = −∫ P dV ≈ (ΔPΔV/2q) − ((ΔV/V)2V/(2κ)), where |ΔP| is assumed to be much greater than the final state pressure (i.e., the standard atmospheric pressure) and κ is the isothermal compressibility of water (=4.524 × 10−10 m2/N at 25 °C44). This work compensates for the free energy increase (ΔF) associated with changing the solvency of the water from a good solvent to a poor solvent; that is, W = −ΔF. Assuming that the changes in the chain conformational and translational entropies
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ASSOCIATED CONTENT
S Supporting Information *
Equations used in the XR analysis (section S1); the procedure for the XR data normalization (section S2); radiation doses for the XR experiments (Table S1); three-box model analysis results for the PEO−PnBA XR data (Table S2); one-box model analysis results for the PnBA XR data (Table S3); unnormalized PEO−PnBA XR profiles (Figure S1); unsuccessful fitting trials of the PEO−PnBA XR data using a two-box model (Figure S2); three-box analysis on differently normalized PEO−PnBA XR data (Figures S3 and S4); estimated PnBA and PEO layer thicknesses and water density values (Figures S5−S7, respectively); and unnormalized PnBA XR profiles (Figure S8). This material is available free of charge via the Internet at http://pubs.acs.org. 1594
dx.doi.org/10.1021/jz3002772 | J. Phys. Chem. Lett. 2012, 3, 1589−1595
The Journal of Physical Chemistry Letters
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AUTHOR INFORMATION
Corresponding Author
*E-mail:
[email protected]. Notes
The authors declare no competing financial interest.
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ACKNOWLEDGMENTS The authors are grateful for financial support of this research from the National Science Foundation (DMR-0906567). ChemMatCARS Sector 15 at the Advanced Photon Source of Argonne National Laboratory (where the XR measurements reported in this paper were made) is principally supported by the National Science Foundation/Department of Energy under Grant Number NSF/CHE-0822838. Use of the Advanced Photon Source was supported by the U.S. Department of Energy, Office of Science, Office of Basic Energy Sciences, under Contract No. DE-AC02-06CH11357.
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