Letter pubs.acs.org/NanoLett
Nanophase Separation in Monomolecularly Thin Water−Ethanol Films Controlled by Graphene N. Severin,* J. Gienger, V. Scenev, P. Lange, I. M. Sokolov, and J. P. Rabe Department of Physics and IRIS Adlershof, Humboldt-Universität zu Berlin, Newtonstrasse 15, 12489 Berlin, Germany S Supporting Information *
ABSTRACT: Control over nanoscale patterning of ultrathin molecular films plays an important role both in natural as well as artificial nanosystems. Here we report on nanophase separated patterns of water and ethanol within monomolecularly thin films confined between the cleavage plane of mica and single or a few layers of graphene. Employing scanning force microscopy of the graphene layers conforming to the molecular films we quantify the patterns using the ethanol−water cross correlation and the autocorrelation of domain wall directions. They reveal that lateral pattern dimensions grow and the domain walls stiffen upon increasing the thickness of the graphene multilayers. We attribute the control of the patterns through the graphene layers to the competition between the mechanical deformation energy of the graphene sheets and the electrostatic repulsion of dipoles normal to the interface. The latter results from charge transfer between graphene and the molecules confined between mica and graphene. KEYWORDS: Thin liquid film, molecular monolayer, nanopore, graphene deformation, pattern formation, competing interactions
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surfaces in a broad range of ambient humidities.9,10 Upon reducing the ambient humidity below a threshold, fractal depressions occurred, which were attributed to the dewetting of a mica-graphene slit pore, which was initially filled with a monolayer of water.9 The sample preparation we used here provides us with a fluid monolayer of water molecules confined at the interface between graphene and mica.9,10 Exposure of such samples to ethanol vapor causes the exchange of water molecules by ethanol.4 The ethanol molecules diffuse from the edge of the slit pore into the interfacial water layer and phase-separate, forming clusters that eventually grow into a network of irregular patterns. The dynamics of the cluster growth has been followed by imaging of the graphene topography replicating the thickness difference of layers of water and the larger ethanol molecules. After an initial fast growth, the ethanol cluster growth slows down and eventually saturates, resulting in irregular patterns of ethanoland water-rich (EW) domains, which coarsen with the thickness of graphene multilayers conforming to the molecular film. In the following, we will investigate the dependence of the shape of the EW patterns on the graphenes’ thickness. Results and Discussion. Figure 1a−c displays SFM height images recorded on three distinct samples with increasing thickness of graphene multilayers conforming to a heterogeneous ethanol−water film. The EW patterns become noticeably
he formation of regular patterns in molecularly thin heterogeneous films at interfaces is a well-established phenomenon occurring due to the competition between different interactions.1 On the other hand, also irregularly shaped patterns are often observed. A prominent example are the “rafts” in biological cell membranes, which are irregular domains, recognized to be important in a number of cellular processes.2 Their origin is still under debate,2,3 because their understanding is hampered by the system complexity comprising molecular complexity, exchange with the environment, and difficulty to experimentally access their microscopic structure and dynamics. A simpler experimental system would be advantageous, and we demonstrate in the following that this applies to the recently reported heterogeneous monomolecular films of water and ethanol confined between mica and graphene.4 Muscovite mica is a layered crystal, which exhibits macroscopically large atomically flat hydrophilic cleavage planes. Graphene is the thinnest available membrane today, highly flexible to conform to the topography of a substrate with a precision down to single molecules such as ds-DNA5 and impermeable even for atoms and small molecules such as helium and water.6,7 Graphene has been mechanically exfoliated onto mica at ambient humidity conditions.8−10 For samples prepared with the aid of adhesive tape, scanning force microscopy revealed islands between mica and the graphene, which were attributed to a bilayer of Ih ice.8,11 On the other hand, mechanical exfoliation of graphene onto mica surfaces without any adhesive tape, revealed extremely flat graphene © 2015 American Chemical Society
Received: November 5, 2014 Revised: January 16, 2015 Published: January 23, 2015 1171
DOI: 10.1021/nl5042484 Nano Lett. 2015, 15, 1171−1176
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Figure 1. (a−c) SFM height images recorded on three distinct samples of single (a), double (b), and triple (c) layer graphenes conforming to a heterogeneous monomolecularly thick ethanol−water film. (d) The control of the pattern dimensions through the graphene layers is explained by the competition between the mechanical deformation energy of the graphene sheets at the grain boundaries and the electrostatic repulsion of dipoles normal to the interface (see Discussion). (e) Cross sections along the dashed, dotted, and dashed-dotted lines in (a−c), respectively. The height difference between ethanol and water rich domains is roughly 1 Å. Lateral dimensions of patterns in (a) are at the limit of the SFM resolution; therefore the depth of the depressions appears to be somewhat smaller than 1 Å. The faint periodic stripes in (b,c) are due to instrumental noise.
⎧1, σi ≠ σj C EW(r ) = ⟨Iij⟩(i , j) ∈ B(r) , where Iij = ⎨ ⎩ 0 else
coarser for thicker graphenes. Imaging of the same area over longer times reveals that the ethanol−water patterns are dynamic, that is, clusters migrate, some clusters may disappear, and new clusters appear (Supporting Information movie). Yet, despite being dynamic the patterns do not show any noticeable coarsening over time. The above implies that we deal with equilibrium EW patterns with typical dimensions governed by the graphene thickness and we will proceed in the following with the quantification of the pattern dimensions. Note that the layer effective temperature and the observed pattern dynamics correspondingly may to some extent be affected by the SFM tip, but still this would not affect the conclusion that we deal with equlilibrium patterns. We introduce the cross correlation function CEW to quantify the pattern dimensions
⎪
⎪
and B(r ) = {(i , j)|rij = r }
and where σi is the binary value of pixel i with ethanol or water. Thus, CEW corresponds to taking the arithmetic mean of Iij over all pairs (i,j) lying within the image and being separated by a distance r. CEW gives the joint probability to find ethanol and water at a distance r from each other. The position of the main maximum Pm of CEW can be interpreted as the characteristic lateral dimension of the pattern. The positions of the maxima of CEW grow indeed with the thickness of graphene conforming to the EW patterns (Figure 2). The ethanol- and water-filled areas were recognized by setting a certain height threshold with 1172
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property of mica or graphene. The impermeability of graphene and mica to small molecules6,7 excludes furthermore models accounting for suppression of macro-phase separation by direct exchange with the vapor phase.15 The small size of the liquid molecules also excludes microphase separation scenarios similar to those in diblock copolymers.16 A mechanism relying on the equilibrium thermal fluctuations is particularly appealing: while below the transition temperature the macrophase separation takes place, above it the phases mix and only finite clusters of the phases are present. However, thermal fluctuations alone do not lead to the patterns with properties similar to those observed in our experiment. The formation of heterogeneous patterns under graphenes of different thickness and correspondingly different line tensions implies that the heterogeneity is present also quite far from the critical point, that is, it is not due to critical point fluctuations.17 However, for a model with only short-range interactions, which can be mapped onto the 2D Ising model, correlation functions both at18 and well above19 critical temperatures do not exhibit oscillations as clearly observed in our experiment. Therefore, some additional mechanism responsible for the stabilization of the pattern dimensions must be present. In analogy with thin ferromagnetic20,21 and Langmuir22 films, we assume that the additional mechanism sought for the stabilization of the heterogeneous patterns is connected with long-range repulsive interactions associated with the molecules of similar type within the clusters. In both cases, these interactions are dipole−dipole ones. Magnetic and electrostatic dipole interactions have the same power law dependence on the interdipole distance. The ground state of the magnetic model corresponds to domains in form of parallel stripes of finite width. Similar states were found in densely packed planar domains of electrostatic dipoles oriented normally to the plane, mixed with nonpolar domains.1 Irregular shapes of magnetic domains have been reproduced in the simulations of thin ferromagnetic films within a simplified model (taking into account the local ferromagnetic Ising and the long-range dipole−dipole interactions) and attributed to temperature driven fluctuations of the domain walls breaking up the ground state of periodic stripes.23 We infer that our situation is quite close to the one in thin magnetic films as discussed above. Water and ethanol molecules have been reported to p- and n-dope graphenes, respectively.24 Charge transfer between molecules and graphene gives rise to electrostatic dipoles aligned normally to the interface, and therefore our model is very close to the scenario of magnetic dipole domains with a given line tension at the domain walls. This allows us to adopt the following description of the situation: the system consists of clusters of electrostatic dipoles oriented normally to the mica surface but pointing in opposite directions in clusters of different molecules. The domain boundaries are penalized by the additional line tension produced by graphene deformation. Thus, we attribute the patterns we observe to equilibrium thermal fluctuations above the periodic stripe phase melting point.23 The pattern dimensions of the high-temperature phase have not been addressed, but we do this here. The simplified theoretical description of the situation leads to a two-dimensional Ising-like model with spins representing two possible dipole orientations: up and down and with additional long-range dipole−dipole interactions between all spins. The line tension between ethanol and water domains is analogous to the local exchange interaction energy at the magnetic domain
Figure 2. Cross correlation functions CEW in red, blue, and green calculated for Figure 1a single, Figure 1b double, and Figure 1c triple layer graphene images, respectively, with vertical dotted lines indicating the positions of the maxima of the functions.
ethanol being above and water below the threshold. A CEW analysis of ethanol cluster growth confined under a few layer graphene flake (sample described in details previously4) reveals that the correlation functions and thereby the characteristic pattern dimensions saturate fast and hardly vary upon further growth of ethanol clusters (Supporting Information). To quantify the dependence of CEW on the graphene thickness conforming to the EW patterns we averaged the positions of the first (from r=0) CEW maxima from different experiments for a given graphene thickness (Figure 4). The positions of the maxima scatter, yet there is a clear dependence of pattern dimensions defined by the maxima on the thickness of the graphene cover. In the following we will discuss the reasons for the reproducibility of the pattern dimensions and will give next a complementary quantification of their dimensions. The deformation energy of the graphene sheet12 at the domain boundaries (Figure 1) will be one of the driving mechanisms of the EW phase separation, possibly contributed by short-range, e.g. van der Waals interactions. This assumption is supported by the strong influence of the graphene thickness on the properties of the ensuing patterns. Since the graphene deformation is concentrated in the vicinity of the EW boundaries within the patterns, this mechanism essentially contributes to the effective contact energy (line tension) of the patterns. Minimizing the contact line energy of the domain walls would however lead to a full separation of ethanol-rich and ethanol-poor domains, i.e. to continuous growth of the characteristic size of the domains and eventually to macroscopic phase separation,13,14 which we however do not observe. Therefore, there must be mechanisms opposing the indefinite growth of the clusters and bringing it to a halt. We proceed with discussing some of them as known for thin fluid films. A variety of mechanisms were proposed to cause stabilization of heterogeneous patterns observed in thin fluid films, like direct coupling to the bulk phases, patterning of the pore walls, long-range repulsive interactions, and equilibrium thermal fluctuations.1,3 It is often difficult to favor one or another mechanism in experimentally complex systems.3 Our system is however less intricate. Atomic smoothness and homogeneity of the substrate and graphene suggest that the heterogeneity observed is not due to the pore walls’ patterning. The dependence of the patterns on the number of graphene layers supports the conclusion that patterning is also not an inherent 1173
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Figure 3. (a) Analysis of the ethanol−water domain wall undulations is exemplified with the analyses of a topography image of a few layer graphene conforming to heterogeneous ethanol−water layer. (1) Software zoom from a larger image. The ethanol cluster edges are enhanced (2) by plotting the gradients of the image (1) smoothed with Gaussian filter. The path of the highest gradient (3) is manually sketched and then refined with home written software, which calculates furthermore the dependence of the average tangential cosine Ct(l) = ⟨cos(Θ(l))⟩ on the edge length. (b) Ct for different thicknesses of a few layer graphene flakes averaged over a number of samples. The solid lines are fits with A exp(−l/γ) + B, where l is the domain edge length and A, B, and γn are fit parameters depending on the thickness of the few layer graphene flakes. The offset B accounts for the fact that Ct(l) may get negative for large l, which is to be expected if, e.g., the film is dominated by small clusters.
that is, cosine of the angle Θ between the tangents to the ethanol clusters’ edge taken at two points at distance l along the edge (i.e., separated by the contour length l). Then we plotted Ct(l) = ⟨cos(Θ(l))⟩ as a function of the contour length l (Figure 3). To quantify the dependence of Ct on the graphene thickness conforming to the EW patterns we averaged Ct from different experiments for a given graphene thickness (Figure 3b). The small dimensions of EW patterns under graphene monolayers (exemplified in Figure 1a) did not allow following the edges of the smallest domains, thereby possibly underestimating the curvature of domain walls for a graphene monolayer; still we provide the data. Averaging of Ct for equilibrium patterns gives exponential like dependences becoming steeper for thinner graphenes. Exponential decays of tangent correlation functions imply thermally activated fluctuations of domain walls having a certain elasticity, depending on the thickness of graphene multilayer. This can be rationalized assuming the graphene deformation at the ethanol−water domain boundary to be laterally localized and thus the line tension to be independent of the curvature of the domain walls. In this case, the exponential decay constant γn can be interpreted as the persistence length of the domain walls, that is, a measure of their stiffness.12,28 In Figure 4, we show the two characteristic lengths of the system, γn and the position of the maximum Pm of the CEW correlation function at longer times as functions of the number of graphene layers. One readily infers the strong correlation of both lengths with the thickness of the graphene multilayer: both are (approximately) linear functions of this thickness. Moreover, γn is approximately one-half of the typical cluster size as given by the position of the maximum of CEW. This implies that our patterns possess a single characteristic length scale mirrored by both characteristic lengths. The linear extrapolation of the data to zero thickness of graphene shows that the characteristic domain size vanishes, and the phase separation disappears: the free water−ethanol monolayer without graphene sheet would not demix. The mechanism of the cluster formation and development in the course of time can therefore be described by the following model. After the initial nucleation (which may depend on the
walls. Possible differences in the magnitude of charge transfer between ethanol−graphene and water−graphene pairs, and exchange of molecules with the gas phase at the borders of the graphene flakes (both contributing to the chemical potential) correspond to a weak external magnetic field applied to a ferromagnetic film. Exchange of the molecules with ambient and their interdiffusion in the monomolecular layer correspond to the Kawasaki dynamics with free boundaries. The exact type of the dynamics is however irrelevant for equilibrium quantities like the correlation functions. Our own preliminary simulations (using the faster Glauber dynamics) show that the corresponding patterns are visually similar to the EW-patterns as observed experimentally, and indeed give rise to the oscillating correlation functions for dipoles of different orientations. Thus, our model seems to capture the qualitative properties of the patterns. On the other hand, for “isolated” domains in Langmuir films electrostatic repulsion within the domain favors undulation of the domain walls when the domain size exceeds a critical radius given by the counteraction of electrostatic repulsion and the effect of line tension with a specific characteristic wavelength of such undulations.25,26 Motivated by the above we proceeded with the analyses of ethanol−water domain wall undulations (now irregular) in dependence on graphene layer thickness. Here we have to state that although the structure of phase boundaries in systems with “short-range” interactions is a topic of current interest among the mathematical community, initiated by Dobrushin,27 we are not aware of any theoretical works on the phase boundary properties in models with longrange interactions. From the experimental point of view the investigation of the clusters’ boundaries is advantageous compared to the correlation functions: the identification of the boundary does not depend much on artifacts caused by image line flattening necessary to compensate for, e.g., thermal drifts and sample inclinations. As we proceed to show, identification of the boundaries’ correlation lengths provide results very much compatible with those obtained via correlation functions. To quantify the undulations of the domain walls we followed the dependences of tangent correlation along the domain walls, 1174
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transfer from the graphene to the substrate on the one hand, and the line tension contributed by the deformation energy of the graphene layers on the other hand. We anticipate a possible contribution of interfacial dipoles onto the uptake of liquids and their flows in nanoscale confinements. For example, accounting for charge transfer between water molecules and carbon nanotubes could facilitate understanding of water transport through carbon nanotubes.29 Furthermore, monomolecular films with controlled heterogeneity can be of interest for advanced nanofluidic devices and nanoscopic chemistry.30,31 Experimental Section. Graphenes were applied onto a freshly cleaved muscovite mica surface (Ratan mica Exports, V1 (optical quality)) in a glovebox (LABmaster, M. Braun Inertgas-Systeme GmbH) at less than 200 ppm of H2O and O2, each. The graphenes were applied by gently pressing thin graphite flakes onto the mica with the graphite flakes being peeled off a piece of freshly cleaved highly oriented pyrolytic graphite (HOPG, grade ZYB, Advanced Ceramics). Thereafter loose HOPG flakes were carefully removed from the mica surface with a pair of tweezers, and samples prepared in the glovebox were then transferred to ambient. The ambient relative humidities (RHs) were in the range from 25 to 60% and temperatures in the range from 21 to 28 °C. Graphenes were localized optically, and the number of graphene layers was derived from optical and scanning force microscopy (SFM) measurements.32 The typical time between sample preparation and SFM imaging was half an hour. The head of the employed SFM instrument was operated inside a home-built bell-jar chamber, purged either directly with dry nitrogen, or with dry nitrogen bubbled through ethanol. The SFM (Bruker Corporation, Multimode, Nanoscope IV) was operated with a J-scanner in tapping mode at a typical rate of 3 min per image. Silicon cantilevers were used with typical resonance frequencies of 300 kHz and spring constants of 42 N/m. The tips exhibited a typical apex radius of 7 nm with an upper limit of 10 nm, as specified by the manufacturer (Olympus Corporation). The SFM chamber was purged with nitrogen flow directed through a gas washing bottle filled with ethanol (Berkel AHK, 1511U) to increase the ethanol vapor pressure. The resulting ethanol vapor concentrations varied in the range between 50 and 100 mg/L. The vapor concentrations were estimated from the measurements of nitrogen flow rates and associated ethanol weight losses. The nitrogen flow rate was measured with a gas flow meter (TSI instruments, model 4143). Images of 1 or 2 μm scan size were made on double, triple, four, and five graphene layers and between 0.5 and 1.0 μm scan size on single layer graphenes. The SFM images were processed and analyzed with SPIP (Image Metrology A/S) image processing software. First to third order polynomial plane subtractions were applied to SFM height images followed by first or second order line subtractions with either ethanol or water domains manually excluded from the line fits33 to compensate for drifts, image bow, and sample inclinations. The noise in the images was reduced by a Gaussian convolution filter. We verified that positions of the first maxima of correlations functions we were interested in are largely independent of image processing details (Supporting Information). Parts of the images with different graphene thicknesses or graphene folds were removed before analysis and not taken into the statistics (Supporting Information). The images were then reduced to 1 bit color depth and the cross correlation was computed with home written software that explicitly sums over
Figure 4. Positions of CEW function maxima (blue squares, averaged over a number of samples) and domain wall stiffness γn (red circles, from the exponential fits in Figure 3b) plotted versus thickness of a few layer graphene flakes. The error bars are the standard deviations of CEW maxima positions. The dotted line is the linear fit to CEW dependence and is a guide to the eyes.
presence of pre-existing nucleation kernels, for example, contaminants), the dynamics of further cluster growth is governed by the diffusion of ethanol molecules into the water layer.4 The shape of the growing clusters is at first compact, until they reach a certain critical radius, when electrostatic repulsion within the growing domain overweights the line tension, and domain walls start to undulate similarly to domains of amphiphile molecules confined at liquid−air interfaces.25 At a later stage of the growth, the patterns become stabilized by the counteraction of electrostatic dipole repulsion and the line tension depending on the graphene thickness. After considerable time the equilibrium situation is attained. Because the experiments are performed at relatively high (room) temperature, which is presumably higher than the critical temperature of the transition to the periodic phase (as seen, e.g., in thin ferromagnetic films), the ensuing patterns are disordered but still show a typical length scale, which is seen both in the cluster sizes as represented by the correlation function, and in the undulation of domain boundaries. This scale is controlled by the graphene thickness. The separation of the molecules of different type is thus induced by the elastic deformation of graphene conforming to the height relief of molecules of different size and opposed by the electrostatic interaction due to charge transfer and corresponding attraction of electrostatic dipoles of different types (water and ethanol) and electrostatic repulsion within the domains of molecules of the same type. Conclusions. We have investigated pattern shapes of nanophase separated ethanol and water molecules within a monomolecular film confined between single or a few layers of graphene and mica. We demonstrate that graphene does not only allow visualizing the structure of ethanol and water domains conforming to their topography but also causes and controls the nanophase separation. Domains of ethanol and water molecules confined between atomically flat mica and graphenes and imaged by SFM exhibit irregular and dynamic patterns. Still, we quantified their lateral dimensions and the undulations of the domain walls. We show that it is the number of graphene layers, which are deformed at the domain walls, that controls both dimensions. We attribute the stabilization and reproducibility of the pattern dimensions to the competition of electrostatic repulsion of dipoles due to charge 1175
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all possible pairs of pixels and returns a histogram over radial distance (Supporting Information). The analyses of the EW pattern edges were performed with home written software. The SFM height images were line flattened with a first order polynomial. The noise in the images was reduced by a Gaussian convolution filter. The shortest distance of the edge contour analyses was determined by the pixel resolution of the images. The first point, that is, pixel to pixel distance, was disregarded for the Ct functions.
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ASSOCIATED CONTENT
S Supporting Information *
Image manipulation for correlation functions; implementation of correlation functions; influence of image manipulation on correlation functions; and fast saturation of pattern dimensions upon cluster growth. This material is available free of charge via the Internet at http://pubs.acs.org.
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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 would like to thank Jörg Barner (JPK instruments, formerly Humboldt-Universität zu Berlin) for providing the software used to analyze domain boundaries.
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REFERENCES
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DOI: 10.1021/nl5042484 Nano Lett. 2015, 15, 1171−1176
