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Scaling Behavior and Segment Concentration Profile of Densely Grafted Polymer Brushes Swollen in Vapor Liang Sun, Bulent Akgun, Renfeng Hu, James F. Browning, David T. Wu, and Mark David Foster Langmuir, Just Accepted Manuscript • DOI: 10.1021/acs.langmuir.6b00845 • Publication Date (Web): 12 May 2016 Downloaded from http://pubs.acs.org on May 14, 2016

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Scaling Behavior and Segment Concentration Profile of Densely Grafted Polymer Brushes Swollen in Vapor Liang Sun,† Bulent Akgun,‡,#,∇ Renfeng Hu,°,+ James F. Browning,§ David T. Wu,° and Mark D. Foster*,† †

Department of Polymer Science, The University of Akron, Akron, Ohio, USA NIST Center for Neutron Research, National Institute of Standards and Technology, Gaithersburg, Maryland, USA # Department of Materials Science and Engineering, University of Maryland, College Park, Maryland, USA ∇ Department of Chemistry, Bogazici University, Bebek, Istanbul, Turkey °Department of Chemistry and Department of Chemical and Biological Engineering, Colorado School of Mines, Golden, Colorado, USA + Advanced Research Center for Nanolithography (ARCNL), Amsterdam, The Netherlands § Chemical and Engineering Materials Division, Spallation Neutron Source, Oak Ridge National Laboratory, Oak Ridge, Tennessee, USA ‡

ABSTRACT: The scaling of the thickness, hs, of a densely grafted polymer brush of chain length, N, and grafting density, σ, swollen in vapor, agrees quantitatively with the scaling reported by Kuhl et al. for densely grafted brushes swollen in liquid. Deep in the brush, next to the substrate, the shape of the segment concentration profile is the same whether the brush is swollen by liquid or by vapor. Differences in the segment concentration profile are manifested primarily in the swollen brush interface with the surrounding fluid. The interface of the polymer brush swollen in vapor is much more abrupt than that of the same brush swollen in liquid. This

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has implications for the compressibility of the swollen brush surface and for fluctuations at that surface.

Introduction Polymer brushes have attracted tremendous attention from the standpoints of both basic science and technology1 due to their potential use in a variety of applications including biotechnology,2 responsive surfaces,3 lubrication,4 flow control,5 and flocculation control.6 A polymer brush is a monomolecular film in which each macromolecule is attached at one end to a surface or interface. This tethering can impart remarkable properties to the film, particularly when the polymers are tethered or "grafted" sufficiently densely so that the chains must stretch appreciably along the direction normal to the grafting surface. This stretching of the chains from their most probable configuration in the bulk melt is further exacerbated if the brush is swollen in a good solvent. A balance between the entropic cost of stretching and favorable interactions between chains and solvent dictates the degree to which the brush swells. In applications the brush might be swollen due to contact with liquid solvent or due to contact with solvent vapor, as in solvent annealing.7,8 Alexander9 and de Gennes10 provided the first theoretical description of a brush swollen in solvent using a scaling approach. They predicted that in the “brush regime” the thickness, hs, of the brush in good solvent should scale as Nσ1/3, where σ (chains/Å2) is the grafting density and N is the chain length in number of segments. The Alexander – de Gennes brush model assumes that the polymer chains are uniformly stretched, with a step-function segment concentration profile for the film and all chain ends located at the brush surface. Later, Milner et al.11 published a selfconsistent field (SCF) treatment of the swollen brush. There the segment concentration profile is


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seen to approach a “parabolic” shape, with chain ends distributed throughout the entire brush. Nevertheless, the same scaling of the swollen brush thickness with Nσ1/3 is seen with the SCF model. This scaling relationship proposed by theory has been seen in experiments12,13 and simulations.14 It was first demonstrated experimentally using Small Angle Neutron Scattering (SANS) of polydimethylsiloxane (PDMS) brushes grafted onto porous silica swollen in dichloromethane and acetone.12 Neutron reflectivity (NR) of brushes on planar substrates subsequently proved to be an uniquely powerful method of probing brushes swollen in solvents.13 The wavelength of cold neutrons is well suited to the length scales of interest, deuteration of the solvent provides outstanding contrast, and NR is able to probe the brush structure while the brush is in contact with the liquid. In published experimental NR work the shape of the segment concentration profile has been progressively refined with experiments of increasing resolution and it has been shown that in addition to the parabolic segment concentration profile shape, a depletion zone is found next to the substrate for sufficiently low grafting densities and a "tail" found at the interface between the brush and the liquid.15-17 This tail has also been seen in simulations.14 The development of controlled radical polymerization (CRP) provided a convenient method to prepare covalently bonded polymer brushes with high grafting densities and low polydispersity18 which served to increase the accuracy of the segment concentration profiles. Thus, the most recent explorations of the swollen brush scaling behavior have used NR measurements of polystyrene (PS) brushes prepared by CRP16,17 swollen in good solvent liquid. There have been fewer studies19-23 of brushes swollen in vapor. Beilsalski and Rühe19 demonstrated the swelling of polyelectrolyte brushes at various relative humidities and studied


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the kinetics of swelling. Armes et al.20 demonstrated that a polyelectrolyte brush could swell in response to the presence of acidic vapor. Rabin et al.21 analyzed a mean field lattice model of swelling of brushes in water vapor to explain how a DNA brush could contract for low degrees of water uptake. Genzer et al.22 studied how the swelling of polyelectrolyte and polyzwitterion brushes in water vapor varies with relative humidity levels using NR, X-ray reflectivity (XR) and spectroscopic ellipsometry. Beers et al.23 reported measurements of swelling of two poly(methylmethacrylate) brushes in a variety of organic solvent vapors using XR, providing values of the swelling ratio and how it varies with solvent quality. They also reported X-ray scattering length density (XSLD) profiles for samples and on the basis of those XSLD profiles argued that the swelling with vapor yielded a step-like polymer segment density proﬁle, not a parabolic proﬁle like that observed in liquid swollen brushes in the strong stretching regime. However, XR is not very sensitive to the polymer segment density depth profile as compared to NR, since greater contrast can be achieved with NR using deuterium labeling of the solvent. Those authors went on to note that they expected brush swelling with saturated vapor and liquid to be identical, in so far as the solvent chemical potential in the two systems is the same. They remarked, however, that in the membrane community24 it is known that the swelling of membranes in liquid is, in general, not the same as swelling in saturated vapor and they argued that differences between brush swelling by vapor and liquid require further study. Here we show using NR measurements that, while the same scaling of swollen brush thickness with Nσ1/3 is found for organic vapor swollen brushes as for organic liquid swollen brushes, and the shape of the concentration profile inside the brush is quite similar for the two cases, the interface between the brush and surroundings is, indeed, more abrupt for the vapor case.


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Experimental Section Polymer Brushes Preparation. PS brushes were made using the atom transfer radical polymerization (ATRP) grafting-from method according to literature precedent.25 (11-(2-bromo2-methyl)propionyloxy)undecyltrichlorosilane was deposited onto silicon wafers to make surface macroinitiators, which initiated subsequent ATRP polymerization of styrene to produce PS brushes. The brushes were annealed in high vacuum for 18 h at 120 °C to remove residual solvent. Values of N, dry thickness, ho, and hs for all samples are summarized in Table S1 of the supporting information. Neutron Reflectivity. NR measurements were performed at the Liquids Reflectometer (BL4B) at the Spallation Neutron Source (SNS) in Oak Ridge National Laboratory. The reflectivity data were fitted using MOTOFIT, a fitting analysis package running in IGOR PRO. NR data for the dry brushes (Figure S1) were collected and fit for values of scattering vector, q, up to 0.09 Å1

. PS brushes with dry thicknesses, ho, from 200 Å to 1017 Å were swollen by exposure to

perdeuterated toluene vapor in a closed chamber that contains a trough for liquid solvent. Enough liquid perdeuterated toluene was placed in the trough to ensure that once the atmosphere within the chamber was saturated it remained so. Due to the volatility of the toluene the atmosphere saturated quickly. The kinetics of vapor penetration into the brush were observed by consecutive NR measurements after exposure to vapor (Figures 1 and S2). Typically measurements over a q range of 0.011 – 0.047 Å-1 were run about every ten minutes. This small range of q was required to allow quick measurements. The values of χ2 for the fits are shown in Table S2. The NR curves plotted as Rq4 vs. q are shown in Figure S3 to make more evident the quality of the fits. In addition, data were also collected at NIST for an equilibrated swollen brush (Figure S4) over a larger q range of 0.008 – 0.12 Å-1. In the following, the nominal measurement


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time in the kinetic measurements is taken as the mean of measurement start and finish times. We keep in mind the fact that the sample structure was changing over the time for one measurement. The largest error due to this time resolution was present in the earliest measurements.

(a)

(b) Figure 1. NR curves and SLD profiles of PS brushes, (a) Mn = 43100, σ = 0.0060 chains/Å2, ho = 406 Å and (b) Mn = 53700, σ = 0.0067 chains/Å2, ho = 573 Å, swollen in perdeuterated toluene vapor.


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Results and Discussion The NR fitting results and corresponding scattering length density (SLD) profiles for the dry brushes are shown in Figures 1, S1 and S2 and those for the swollen brushes in Figures 1 and S2. The data from each “dry” brush can be fitted well with a structure model that envisions three primary layers, the silicon oxide, the initiator layer, and the brush itself. Additionally, a finite interface width is associated with each interface. The data for the dry brush is fitted well using the SLD of bulk PS, 1.42×10-6 Å-2. The thickness of the dry brush scales with Nσ (Figure S5) as seen previously.12,16 The change in brush thickness with swelling was apparent from movement to the left of the Kiessig minima in the reflectivity curves. The rate of increase in thickness due to swelling was highest in the beginning and decreased with time. The first two curves in the collections for various times, measured over a smaller range of q, clearly demonstrated increases in sample thickness already at those times, but the change in sample structure was so rapid and the q range so limited that it was of limited utility to suggest a full SLD profile from a fit. For later times the SLD profile had to reflect variation in the concentration of PS segments with depth due to the penetration into the brush of perdeuterated toluene, which has a SLD of 5.66×10-6 Å-2. The SLD profiles for fitting the reflectivity curves from the swollen brushes were created using the simplest possible model. By subdividing the SLD profile for the polymer containing part of the sample into additional layers and using convolution of the interfaces between pairs of those fictitious layers with error functions, smooth curves of SLD variation through the brush and into the vapor were created. The parameters of the error functions used for this smoothing to remove box-like steps in the SLD profile within the swollen brush have no physical meaning. They are simply part of a protocol to generate an SLD profile able to provide a fit to the data. The number of layers was kept as small as possible to provide a good fit with a


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simple modeling approach. In some cases subdividing the swollen brush portion of the SLD profile into three layers was sufficient, while in other cases that portion had to be subdivided into four or five layers. Generally more layers were required to properly capture the shape of the SLD profile for the thicker brushes. The one interface for which the standard deviation of the convoluting function, s, had the most significance was that between the last layer of the swollen brush region and the vapor region. The width of that convoluting function is related to the microroughness of the swollen brush/vapor interface as well as the interface diffuseness characterized by the gradual variation of the ratio of air : toluene molecules : polymer that occurs across that interface. For the dry brush, s is a clear measure of interface microroughness. For the swollen brushes s is a quantity that captures the effective interface width averaged over the beam footprint and which contains contributions from both microroughness and "diffuseness" in a way that cannot be further detailed using specular reflection measurements alone. Nonetheless, consideration of this parameter is sufficient to extract the central result that the interface between brush and surroundings is sharper for the case of vapor swelling than for the case of liquid swelling. Within 25 minutes, toluene penetrated into the brush all the way to the base of the chains. With the mobility increased by the presence of the toluene, the chains then rearranged to accommodate the toluene molecules primarily in the outermost region of the brush, while the volume fraction of solvent in the lower region of the brush stayed close to 0.1. After 90 minutes the SLD profile changed little with time, meaning the swelling had attained nearly its equilibrium character. At the brush interface with the saturated vapor, the SLD value drops over a short depth to nearly zero. This drop in SLD is much more abrupt than that associated with the interface between swollen brush and liquid solvent. The reflectivity measurement is very


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sensitive to the effective "width" of this drop, which manifests the projection of the 3dimensional variation of segment concentration depth profile onto the surface normal.26 As noted above, the width of the SLD drop is quantified as the standard deviation, s, of the error function used to create that part of the SLD profile,27 with the full width of the convoluting function at half maximum being 2.35s. These widths of the interface for the swollen brushes as characterized approximately with s increase with the thickness of the corresponding dry brush. However, the systematic increase in width of the swollen interface with brush thickness does not correlate to variations among the microroughnesses of the dry brush surfaces, since those are scattered about an average value of 18 ± 4 Å (Table S1). The key point is that these swollen interface widths are all much smaller than the distance over which the "tail" of the segment concentration profile for a brush swollen in liquid can extend, which is greater than 100 Å for a brush chains of 20,000 g/mol molecular weight.17 For the equilibrium swollen brush measured with higher resolution (to higher q) fitting the data required an even smaller interface width than used to fit the data from the more limited q range (Figure S4), so there is no question that the interface width is smaller for brushes swollen with vapor than for brushes swollen with liquid. For comparison with theoretical treatments of the scaling relationship between brush thickness and molecular parameters it is necessary to define operationally the "equilibrium thickness", hs, for the vapor swollen brush. Since the interface with vapor is reasonably abrupt, hs may simply be taken as the height from the initiator layer to the middle of the interface with vapor. The scaling of thickness for the brush swollen in toluene vapor is shown in Figure 2, where our data are compared with those of J. P. Chapel et al.16 and T. L. Kuhl et al.17 for brushes swollen in liquid toluene. For the dry brush plot we report one result from J. P. Chapel et al. for


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which numerical data for both N and σ are reported and for which the grafting density (0.0055 chains/Å2) is most similar to ours. (They present additional data in a plot of ho vs. Nσ). From Kuhl et al. we include four data points for which both N and σ are reported, with σ varying between 0.0040 and 0.0049 chains/Å2. The scaling for our dry brushes is consistent with that for these published examples and also with theoretical expectations for brushes in the dense grafting regime. For the swollen brushes we compare to the one result from Chapel et al. (for a grafting density of 0.0055 chains/Å2), and to several data points from Kuhl et al. for which σ varies between 0.0040 and 0.0049 chains/Å2 and the relationship between hs and Nσ1/3 is reported in a plot. Despite the fact that the detailed interface shapes for the brushes swollen in vapor are different from those for brushes swollen in liquid, the scaling behavior of the thicknesses is the same. Not only the exponents, but even the prefactors are the same. We note, however, that Kuhl et al. define the brush "thickness" as the intercept with the abscissa of a power law fit to their experimental volume fraction profile.


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1500 hs (Å)

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1000

500

0

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50

100 -2/3 (Å )

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Figure 2. Thicknesses of PS brushes swollen in perdeuterated toluene vapor scale with Nσ1/3. Data from this work are shown with filled squares. Data from the work of J. P. Chapel et al.16 (open triangles) and T. L. Kuhl et al.17 (open circles) for brushes swollen in toluene liquid are shown for comparison.

In Figure 3 we compare the segment concentration profile measured for our brush of 20,000 g/mol chain molecular weight swollen in vapor and that for a brush, also of 20,000 g/mol chain molecular weight, of 24% lower grafting density (0.0048 vs. 0.0063 chains/Å2), swollen in liquid, from the work of Kuhl et al.17 Our dry brush has a thickness of 200 Å, while the thickness reported for theirs is 152 Å (24% lower). When comparing the segment concentration profiles we must consider this difference in the overall mass of polymer in the brush as well as the difference in grafting density and means of swelling. The area under the segment concentration profile, which is proportional to the mass of polymer in the brush, should agree between the profiles for the "dry" brush and swollen brush to within some uncertainty. Kuhl et al.17 report that the mass of brush polymer determined from their segment concentration profiles agreed to within ± 5%. In our brush of similar thickness we found a discrepancy of 6% between the integrals under segment concentration profiles for the dry and swollen brushes, with the apparent


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mass of polymer in the swollen brush higher than the mass of polymer in the dry brush (Figure S6(a)). The discrepancies for the other brushes were somewhat larger. The fact that the area under the profile for the lower grafting density brush in the work of Kuhl et al. is 25% below that under the profile for brush in this work is fully consistent with the 24% lower initial mass in the brush that was swollen in liquid. For the brush swollen in liquid only two components, PS and toluene, need be considered as contributing to the SLD over the whole depth of interest. In the case of swelling with vapor, at the brush/vapor interface three components are present: PS, toluene, and air. Thus, in order to reduce the SLD profile to a profile of PS segment concentration we have identified a depth at which the interface region begins and then assumed that in the brush/vapor interface region the polymer segment concentration falls to zero over the same length that the SLD falls to zero and with the same shape that the SLD profile falls to zero. Part of the error in matching the mass of polymer for dry samples and swollen samples may be attributed to our simplifying assumption for converting the SLD profile to the segment concentration profile with three components present (air, polymer, toluene) rather than just two. It becomes more difficult to match the mass of polymer for the fit to the NR curve as the brush thickness increases. Further examples of agreement between the integral under the concentration profile for the dry brush and that for the swollen brush are shown in Figures S6(b) – (d).


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Figure 3. Experimental PS segment concentration profiles for (from left to right) a brush in liquid solvent from Kuhl et al.17 (Mn = 20,000 g/mol, ho = 152 Å, σ = 0.0048 chains/Å2), a similar brush (Mn = 20,000 g/mol, ho = 200 Å, σ = 0.0063 chains/Å2) swollen in vapor, and the remaining brushes swollen in vapor in order of increasing thickness.

The shapes of the two profiles are similar for roughly the bottom half of the brush that is closer to the substrate. In that part of the brush, for which crowding due to tethering at the surface is the predominant feature, the brushes behave similarly upon swelling. We note that the segment concentration at the substrate surface is 5% lower for the brush swollen in liquid, but this is due to its having a lower grafting density. The difference is consistent with previous experimental15 and numerical SCF results28 for brushes swollen in liquid showing that the segment concentration at the substrate surface decreases as grafting density decreases. Our value of segment volume fraction at the substrate, or maximum segment volume fraction, ϕm, of 0.83 falls between the value of 0.79 from Kuhl's work for σ = 0.0048 chains/ Å2 and the value of 0.85 from Chapel's work, which claims a value of σ of order 0.01 chains/Å2. The key differences in the segment concentration profiles are found in that part adjacent to the surroundings. The segment concentration drops off more slowly for the brush next to good solvent liquid, which provides a hospitable environment for the chains. The portions of the chains of the wet brush present a sharper interface when next to good solvent vapor. This sharper


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interface reflects the preference for the density of the solvent to be either that of liquid or that of vapor at two-phase coexistence. Since the solvent quality is good for the polymer, we likewise expect a preference for the density of the polymer solution to be either that of a liquid or vapor, leading to confinement of the chains by a sharper interface of the wet brush with vapor. We illustrate this effect by comparison with the result from a simple SCF calculation shown in Figure 4. For the case of the brush in solvent, we use a standard harmonic free energy F(ρ)/kT = (1/2)v(ρ0-ρ)2 in the segment density normalized to its bulk value, ρ, to capture the free energy penalty for density fluctuations to quadratic order. kT is the Boltzmann constant multiplied by the temperature and the parameter v can be considered to be an excluded volume parameter. For the case shown here the values of the statistical segment length b = 7.6 Å and v = 33 Å3 for the brush in liquid are those used by Kuhl et al.17 For the case of contact with solvent vapor, we extend this quadratic free energy to the next order cubic term, F(ρ)/kT = (1/2)v(ρ0-ρ)2-c(ρ0-ρ)3, which allows modeling of two minima corresponding to liquid and vapor densities. This functional preserves the form of the quadratic penalty for density deviations when densities are near that of the bulk liquid. The parameter c controls the magnitude of the free energy barrier between vapor and liquid densities as well as the depth of the vapor phase free energy. The values of c = 3000 Å6 and v = 90 Å3 are selected to give the same brush height as in experiment. Even with the simple functional used here the fact that the interface at the surface of the swollen brush is much sharper for the vapor case is readily apparent, in good qualitative agreement with the experimental finding.


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Figure 4. PS segment concentration profiles calculated from SCF theory for the brushes shown in Figure 3.

A more complete analysis would involve incorporating modeling of the solvent/polymer interaction and its influence on the effective free energy functional of the solvent and polymer concentrations. One might make the assumption that there is a relatively sharp interface between a region consisting of the brush and solvent at near liquid volume fraction, and a region of solvent vapor. The interfacial width between these two regions would be comparable to the width of the pure solvent/vapor interface. For polymers that are not too short, it would also be much narrower than the scale over which the polymer concentration profile varies, i.e., the brush height. In this scenario, one might imagine this liquid/vapor interface plays the role of a confining wall that is semi-permeable to solvent. As solvent is removed from the brush in a bulk liquid, this interface moves towards the grafting wall. At vapor-liquid coexistence, there is no free energy penalty for this motion due to the equal chemical potentials of the solvent in the two phases. However, as the interface contacts the brush, additional removal of solvent invokes the free energy cost of desolvating the polymer (assumed positive for a good solvent) as well as the cost of compressing the brush, also positive. Thus, in the absence of other forces, the equilibrium profile of a brush in contact with solvent vapor would be essentially the same parabolic profile as


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when the brush is in contact with solvent liquid. That the observed profile corresponds to a compressed brush could be explained by two hypotheses. First, the system may not be at thermodynamic equilibrium. This might be the case if, for instance, the temperature of the brush were a little higher than that of the solvent vapor, driving the system towards drying. Moreover, the free energy cost of compressing the outermost portion of the brush is relatively low; compressing the exponential tail of the parabolic profile corresponds to an energy scale of only kT for the outermost "blob", and could easily occur under even mildly drying conditions. Second, there may be effective attractive interactions with the grafting surface, for example by van der Waals attractions for thin enough films.

Conclusions The scaling of densely grafted brushes in solvent vapor is found to be consistent with that for the same brushes swollen in liquid. The key difference between the structure of brushes swollen in liquid and those swollen in vapor is in the width of the interface. The brush/vapor interface is much sharper than the brush/liquid interface, a finding in agreement with a simple SCF calculation. This smaller interface width should have important implications for fluctuations at the surface of the brush and the compressibility of the brush surface in the swollen state. Specifically, the behavior of the brush surface during solvent annealing7,8 and the microroughness and interface width after solvent removal would be impacted by any fluctuations and the form of the interface next to vapor.


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ASSOCIATED CONTENT SUPPORTING INFORMATION PS brushes information, additional NR curves and SLD profiles, values of χ2 from NR fitting, scaling behavior of dry brushes, and segment concentration profiles. This information is available free of charge via the Internet at http://pubs.acs.org. AUTHOR INFORMATION Corresponding Author * E-mail: [email protected].

ACKNOWLEDGMENT Hyungjin Lee assisted with NR measurements. Research performed at the Spallation Neutron Source was sponsored by the U.S. Department of Energy, Office of Basic Energy Sciences.

REFERENCES (1) Brittain, W. J.; Minko, S. A Structural Definition of Polymer Brushes. J. Polym. Sci., Part A: Polym. Chem. 2007, 45, 3505-3512. (2) Senaratne, W.; Andruzzi, L.; Ober, C. K. Self-Assembled Monolayers and Polymer Brushes in Biotechnology: Current Applications and Future Perspectives. Biomacromolecules 2005, 6, 2427-2448. (3) Minko, S. Responsive Polymer Brushes. J. Macromol. Sci., Part C: Polymer Reviews 2006, 46, 397-420. (4) Raviv, U.; Giasson, S.; Kampf, N.; Gohy, J. F.; Jerome, R.; Klein, J. Lubrication by Charged Polymers. Nature 2003, 425, 163-165. (5) Yu, C.; Mutlu, S.; Selvaganapathy, P.; Mastrangelo, C. H.; Svec, F.; Frechet, J. M. J. Flow Control Valves for Analytical Microfluidic Chips without Mechanical Parts Based on Thermally Responsive Monolithic Polymers. Anal. Chem. 2003, 75, 1958-1961. (6) Kutsevol, N.; Soushko, R.; Shyichuk, A.; Melnyk, N. Flocculation Behaviour of Polymer Brushes of Various Nanostructure. Mol. Cryst. Liq. Cryst. 2008, 483, 71-77. (7) Park, K.; Park, S. H.; Kim, E.; Kim, J. D.; An, S. Y.; Lim, H. S.; Lee, H. H.; Kim, D. H.; Ryu, D. Y.; Lee, D. R.; Cho, J. H. Polymer Brush As a Facile Dielectric Surface Treatment for HighPerformance, Stable, Soluble Acene-Based Transistors. Chem. Mater. 2010, 22, 5377-5382. (8) Oren, R.; Liang, Z. Q.; Barnard, J. S.; Warren, S. C.; Wiesner, U.; Huck, W. T. S. Organization of Nanoparticles in Polymer Brushes. JACS 2009, 131, 1670-1671. (9) Alexander, S. Adsorption of Chain Molecules with a Polar Head: A Scaling Description. J. Phys (Paris) 1977, 38, 983-987. (10) de Gennes, P. G. Conformations of Polymers Attached to an Interface. Macromolecules 1980, 13, 1069-1075. (11) Milner, S. T.; Witten, T. A.; Cates, M. E. Theory of the Grafted Polymer Brush. Macromolecules 1988, 21, 2610-2619.


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(12) Auroy, P.; Auvray, L.; Leger, L. Characterization of the Brush Regime for Grafted Polymer Layers at the Solid-Liquid Interface. Phys. Rev. Lett. 1991, 66, 719-722. (13) Field, J. B.; Toprakcioglu, C.; Ball, R. C.; Stanley, H. B.; Dai, L.; Barford, W.; Penfold, J.; Smith, G.; Hamilton, W. Determination of End-Adsorbed Polymer Density Profiles by Neutron Reflectometry. Macromolecules 1992, 25, 434-439. (14) Grest, G. S.; Murat, M. Computer Simulations of Tethered Chains. In Monte Carlo and Molecular Dynamics Simulations in Polymer Science Binder, K., Ed.; Oxford University Press: New York, 1995; p. 476-578. (15) Kent, M. S.; Lee, L. T.; Factor, B. J.; Rondelez, F.; Smith, G. S. Tethered Chains in Good Solvent Conditions: An Experimental Study involving Langmuir Diblock Copolymer Monolayers. J. Chem. Phys. 1995, 103, 2320–2342. (16) Devaux, C.; Cousin, F.; Beyou, E.; Chapel, J. P. Low Swelling Capacity of Highly Stretched Polystyrene Brushes. Macromolecules 2005, 38, 4296-4300. (17) Ell, J. R.; Mulder, D. E.; Faller, R.; Patten, T. E.; Kuhl, T. L. Structural Determination of High Density, ATRP Grown Polystyrene Brushes by Neutron Reflectivity. Macromolecules 2009, 42, 9523-9527. (18) Matyjaszewski, K.; Miller, P. J.; Shukla, N.; Immaraporn, B.; Gelman, A.; Luokala, B. B.; Siclovan, T. M.; Kickelbick, G.; Vallant, T.; Hoffmann, H.; Pakula, T. Polymers at Interfaces: Using Atom Transfer Radical Polymerization in the Controlled Growth of Homopolymers and Block Copolymers from Silicon Surfaces in the Absence of Untethered Sacrificial Initiator. Macromolecules 1999, 32, 8716-8724. (19) Biesalski, M.; Rühe, J. Swelling of a Polyelectrolyte Brush in Humid Air. Langmuir 2000, 16, 1943-1950 (20) Fielding, L. A.; Edmondson, S.; Armes, S. P. Synthesis of pH-Responsive Tertiary Amine Methacrylate Polymer Brushes and Their Response to Acidic Vapour. J. Mater. Chem. 2011, 21, 11773-11780. (21) Wagman, M.; Medalion, S.; Rabin, Y. Anomalous Swelling of Polymer Monolayers by Water Vapor. Macromolecules 2012, 45, 9517−9521. (22) Galvin, C. J.; Dimitriou, M. D.; Satija, S. K.; Genzer, J. Swelling of Polyelectrolyte and Polyzwitterion Brushes by Humid Vapors. J. Am. Chem. Soc. 2014, 136, 12737−12745. (23) Orski, S. V.; Sheridan, R. J.; Chan, E. P.; Beers, K. L. Utilizing Vapor Swelling of Surfaceinitiated Polymer Brushes to Develop Quantitative Measurements of Brush Thermodynamics and Grafting Density. Polymer 2015, 72, 471-478. (24) Vallieres, C.; Winkelmann, D.; Roizard, D.; Favre, E.; Scharfer, P.; Kind, M. On Schroeder’s Paradox. J. Memb. Sci. 2006, 278, 357-364. (25) Akgun, B.; Uğur, G.; Jiang, Z.; Narayanan, S.; Song, S.; Lee, H.; Brittain, W. J.; Kim, H.; Sinha, S. K.; Foster, M. D. Surface Dynamics of “Dry” Homopolymer Brushes. Macromolecules 2009, 42, 737-741. (26) Foster, M. D. X-Ray Scattering Methods for the Study of Polymer Interfaces. Crit. Rev. Anal. Chem. 1993, 24, 179-241. (27) Névot, L.; Croce, P. Caractérisation des surfaces par réflexion rasante de rayons X. Application àl'étude du polissage de quelques verres silicates. Rev. Phys. Appl. (Paris) 1980, 15, 761-779. (28) Baranowski, R.; Whitmore, M. D. Theory of the Structure of Adsorbed Block Copolymers: Detailed Comparison with Experiment. J. Chem. Phys. 1995, 103, 2343-2353.


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TOC Graphic


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(a)

(b) Figure 1. NR curves and SLD profiles of PS brushes, (a) Mn = 43100, σ = 0.0060 chains/Å2, ho = 406 Å and (b) Mn = 53700, σ = 0.0067 chains/Å2, ho = 573 Å, swollen in perdeuterated toluene vapor.


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2000

1500 hs (Å)

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1000

500

0

0

50

100 -2/3 (Å )

1/3

Nσ

150

200

Figure 2. Thicknesses of PS brushes swollen in perdeuterated toluene vapor scale with Nσ1/3. Data from this work are shown with filled squares. Data from the work of J. P. Chapel et al.16 (open triangles) and T. L. Kuhl et al.17 (open circles) for brushes swollen in toluene liquid are shown for comparison.


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Figure 3. Experimental PS segment concentration profiles for (from left to right) a brush in liquid solvent from Kuhl et al.17 (Mn = 20,000 g/mol, ho = 152 Å, σ = 0.0048 chains/Å2), a similar brush (Mn = 20,000 g/mol, ho = 200 Å, σ = 0.0063 chains/Å2) swollen in vapor, and the remaining brushes swollen in vapor in order of increasing thickness.


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Figure 4. PS segment concentration profiles calculated from SCF theory for the brushes shown in Figure 3.


Scaling Behavior and Segment Concentration ... - ACS Publications

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