Article pubs.acs.org/JPCC
Tunable Wetting of Surfaces with Ionic Functionalities Davide Vanzo, Dusan Bratko,* and Alenka Luzar* Department of Chemistry, Virginia Commonwealth University, Richmond, Virginia 23284-2006, United States S Supporting Information *
ABSTRACT: Surface charges can dramatically improve the wettability of solid surfaces by water and aqueous solutions. This effect is common in nature, as in ion channel proteins, and can be used to facilitate fluid transport in microfluidic applications. While it is often possible to make reliable predictions of contact angle reduction due to a uniform electrode charge, we address the effect of discrete charge distribution on a surface carrying a pattern of ionic functionalities. We perform atomistic molecular dynamics simulations to investigate the wetting regimes at the nanoscale on molecular-brush-coated graphane surfaces. We tune hydrophilicity by covering the surface with a mixture of covalently bonded butyl and potassium butyrate (or propylammonium chloride) chains at different densities of ionizing groups. We use thermodynamic integration to determine the relation between wetting free energy and the amount of discrete charges on the substrate. We show that nanopores with oppositely charged walls in neat water feature a Lippmann-like quadratic dependence of the cosine of contact angle on the surface charge density while discretely charged surfaces surrounded by neutralizing counterions exhibit a linear dependence reminiscent of the Cassie−Baxter relation. Nonuniform surfaces show a strong dependence on the distribution pattern, with charge effects on maximally segregated surfaces about 4 times weaker than for the uniform distribution. The findings provide guidance for the design of nanopatterned materials with tailored wettability.
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the relation Δγ = −γlv cos θe (where θe is the equilibrium contact angle and γlv is the liquid/vapor surface tension), the reduction in the wetting free energy Δγ under electric field E can be described by the Lippmann equation14−17 Δγ(E) = Δγ(0) − ε0⟨εr|E|2⟩D/2, where εr is the relative permittivity, ε0 the permittivity of vacuum, and D the thickness of the slab with nonzero E. The unscreened field next to an electrode of uniform surface charge density qs is |E| ∝ qs while the reduction in the interfacial free energy Δ(Δγ)(qs) = Δγ(qs) − Δγ(0) ∝ − qs2. To our knowledge, there exists no systematic study addressing the question whether, and at what conditions, the reduction in the wetting free energy due to discrete charges obeys the quadratic scaling with respect to qs, in analogy with the Lippmann14 equation for uniformly distributed (electrode) charges, or a linear Cassie-like dependence,18 where the screened charges contribute independently of each other. Because of superior control of surface composition and interactions, molecular modeling is ideally suited to address this important question. In this work, we investigate the relationship between the wetting free energy and the amount and distribution of ionic groups on a prototypical hydrophobic surface using molecular dynamics (MD) simulations. The choice of graphane,19−22 i.e., the fully hydrogenated form of graphene, as our model hydrophobic substrate allows us to simulate a realistic
INTRODUCTION Interaction of surfaces with aqueous media is ubiquitous in both nature and technological applications. The design of novel functional materials and devices in the submicrometric range, where capillary forces control the fluid behavior, often requires a precise increase of the hydrophilicity of natively hydrophobic solid surfaces. Enhancing and spatially controlling the wettability of electrodes1 and membranes2 has also been shown to be a powerful strategy to increase the efficiency of energy storage devices. Recent approaches to tuning the interfacial wetting free energy, Δγ = γwet − γdry, span from the application of external stimuli like temperature,3,4 electric fields,5,6 light,7−11 or mechanical deformations12 to the chemical modification of the surface with the addition of polar moieties. The strong influence of electrostatic interactions on wetting suggests the use of ionic groups, instead of polar but neutral moieties, as a particularly effective form of surface functionalization. Recent work by Hanly and co-workers13 illustrates the application of pH titration as a powerful tool to manipulate the wettability of a partially coated metal oxide surface reversibly and with precise control. A quantitative interpretation of the results in this work would, however, require a precise characterization of surface composition and particularly the amount and dissociation of ionizing groups. In experiment, this information is accessible only indirectly and is subject to considerable uncertainties. These uncertainties, compounded by the limitations of conventional mean-field theories, have so far precluded reliable quantitative analyses of the effect. Using © 2012 American Chemical Society
Received: May 7, 2012 Revised: June 21, 2012 Published: June 22, 2012 15467
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to 0.51 elementary charge per nm 2, is approximately commensurate with the strength of uniform electric fields employed in previous simulation works.23,27−31 These charge densities are well within the range of charge densities considered in tensiometric measurements.13 In addition to a regular distribution of charged functionalities, we also considered patterns with varied degrees of segregation to examine the role of charge distribution on the additivity of the contributions of individual ionic groups on the wetting free energy, as could be anticipated from the Cassie equation.18 Since the underlying graphane geometry does not allow for a perfectly uniform distribution, the regular patterns employed in the first part of this work are obtained by arranging the ionic moieties in a way maximizing the nearestneighbor distances. The five regular patterns employed are shown in Figure S1 of the Supporting Information. In the second set of runs, we considered nonuniform patterns characterized in terms of the radius of gyration of ionic groups on the substrate in the simulation box. Three different patch sizes corresponding to constant overall charge density qs = 0.51 e0 nm−2 were obtained by starting from a highly packed configuration with Rg = 181 Å2 and scaling the ionic group positions according to a diffusive model. For comparison, the radius of gyration of the corresponding regular pattern is Rg2 = 800 Å2. The resulting distributions are shown in Figure S2. In the third set of surface patterns, the distributions are obtained by starting with a tightly packed patch of ionic groups and then gradually reducing the number of moieties in the patch while preserving the radius of gyration at Rg2 = 181 Å2, as shown in Figure S3. Wetted sample surfaces were submerged under a 15 000 water molecules slab of thickness D ≈ 4.7 nm and counterion concentration Cc = qs/D. Because of finite thickness of the aqueous slab, we can neglect any acid−base reactions involving surface groups since the protonation of tiny fraction of −COO− would decrease the pH significantly above the pK of the ionic group and analogous argument applies to deprotonation of −NH3+ groups. Additional details on the sample preparations are reported in the Methods section.
functionalized planar surface, whose geometry does not get distorted as a result of added substitutions. To examine possible wetting asymmetries due to different signs of surface charge,23 we compared surfaces functionalized by −COOK and −NH3Cl ionic moieties. In agreement with presumed dominance of nonspecific Coulombic interactions, our results for the wetting free energy Δγ prove essentially independent of specific functionality choice. This observation indicates that our findings concern general features of investigated interfacial behavior, primarily determined by the absolute charge density rather than the sign and identity of ionized surface groups. We show Δγ in a capacitor-like setting, with oppositely charged surfaces and pure intervening water to follow the quadratic dependence on surface charge, known from electrowetting measurements.14 However, in a typical experimental situation where surface charges are surrounded by neutralizing counterions, regularly distributed ionic groups contribute to the wetting free energy in a near-additive manner. Clustering of ionic groups enhances counterion screening, leading to significantly weaker wetting enhancement due to surface charges. An optimal increase in surface wettability is therefore reached at a regular, maximally spaced distribution of ionic functionalities on the surface.
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MODELS Hydrophobic Surface. Although graphene is widely used to model perfectly flat surfaces, its functionalization requires a change in carbon hybridization that implies the formation of wrinkles. To simulate a realistic model for ionic flat surfaces, our system consists of a single graphane sheet that, due to the sp3 hybridization of the carbon atoms, can be functionalized without any loss of planarity. We employ the chairlike conformer in which the hydrogen atoms alternate on both sides of the plane. Graphane geometry is obtained from previous ab initio calculations20,21 that have been shown to be in good agreement with subsequent experimental results.19 Graphane is known to be an insulator with a calculated bandgap of 5.4 eV24 and is not expected to be visibly polarized by the presence of ions. As shown in our previous contact angle calculations on graphane,22 alkyl surface functionalization is required in order to render its surface hydrophobic. We refer to surfaces as hydrophobic if Δγ > 0, corresponding to an equilibrium contact angle θe > 90°. According to our results,22 flexible butyl chains of number density per surface area qs ≈ 4.0 nm−2 give an average contact angle θe = 114 ± 4°. Nanoscale droplets showed no detectable difference between advancing and receding contact angles on this hydrophobic surface. Ionic Functionalized Surfaces. We prepare our functionalized surfaces by adding cationic or anionic headgroups on a fraction of chains of butyl-functionalized graphane. We consider ionic groups of both signs in order to examine any possible role of the known hydration asymmetry between oppositely charged ions.25,26 Moreover, our results for a uniform electric field applied perpendicularly to the surface show the coupled effects of water hydrogen bonding and molecular orientations in the field to lead to a bigger hydrophilicity of positively charged surfaces compared to the negative ones.23 To check if similar effects can be observed in the presence of discrete surface charges, we use surfaces obtained by substituting a selected number of butyl chains with propylammonium chloride or potassium butyrate residues. The size of the surfaces is 99 Å × 95 Å. The selected range of surface charge densities, from 0.04
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METHODS Molecular Dynamics. All the simulations are performed by using the Large-Scale Atomic/Molecular Massively Parallel Simulator (LAMMPS) MD code32 in NVT ensemble. The temperature is kept constant at T = 300 K by means of the implemented Nose-Hoover thermostat33 with a relaxation time step of 0.1 ps. Verlet integrator is used for time integration with a time step size of 1 fs. Nonbonded interactions are calculated by means of a standard 12−6 Lennard-Jones (LJ) potential truncated and shifted using a 20 Å cutoff. Since the slab geometry is adopted, we use no tail correction terms. Graphane atoms positions are held fixed during the simulations by zeroing their velocity and forces acting on them. Computation speed is optimized further by excluding the calculation of graphane atoms self-interactions. Long-range electrostatic interactions are computed by means of the particle−particle−particle−mesh (PPPM) solver with 10−5 accuracy and a 20 Å real space cutoff. A correction term of Yeh and Berkowitz34 is added to the Ewald sum calculation to account for the reduced periodicity in slab systems, with a volume expansion factor along z of 3. Substrate interactions are obtained from the OPLS-AA force field,35 while water is simulated according to the SPC/E 15468
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model.36 Heteroatomic pairwise interaction parameters follow from geometrical mixing rules, as required for OPLS-AA force field. OPLS-AA parametrization of potassium and chloride counterions secures complete dissociation of the ionizing groups. Comparisons between various force fields shows OPLSAA parametrization to yield the highest degree of ion pair dissociation. Force field parameters are collected in Tables S1− S4. Wetting Free Energy Calculations. In previous simulations, wettability of polar functionalized surfaces has been characterized in terms of the microscopic analogue of the macroscopic contact angle.37−41 Nanoscale wetting on a surface with discrete charges due to ionic functionalities, at separation comparable to the size of the spreading droplet, involves strong deformations of the triple line from its circular or linear shape. These deformations impede an accurate determination of the equilibrium contact angle θe and the wetting free energy by means of the Young equation Δγ = −γlv cos θe. We calculate Δγ by thermodynamic integration (TI). This strategy also enables studies of wetting free energies below the value Δγ = γwet − γdry = −γlv, which can no longer be quantified in terms of contact angle θe. Our calculation relies on the thermodynamic cycle represented in Figure 1. According to this scheme, Δγ
described in the Supporting Information. The remaining term, i.e., the wetting free energy of the uncharged surface ΔFWU, can be straightforwardly obtained from the Young equation and the equilibrium contact angle for the butyl-functionalized graphane θe = 114 ± 4°.22 Because of our choice of partial charges on neutral functionalizing groups to match the weak dipoles of the butyl chains, our tests confirm that the presence of these uncharged groups has no visible effect on the contact angle. Using SPC/E surface tension of γlv = 63.6 ± 1.5 mN/m,44 the resulting uncharged surface wetting free energy is ΔFWU = 25.8 ± 2.5 mN/m. Our approach focuses on the influence of the ionic groups on the wetting ability of the natively hydrophobic surface. As mentioned above, the atomic charges of the underlying graphane surface and alkyl chains are invariant during the TI integration. Only interactions between ionic species and water are therefore explicitly taken into account when calculating ΔFWC and ΔFDC, which explains why we can expect at most marginal effects of specific nature of the chosen surface model. Since the thermodynamic cycle starts from a totally dry surface, we expect the free energy change for the reverse process, i.e., the drying of a wet surface like e.g. in captive bubble tensiometry, to be smaller since residual hydration water molecules are likely to remain near the hydrophilic groups on the prewetted surface. We will address this issue in a separate study.
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RESULTS AND DISCUSSION Capacitor-like Configuration. A direct comparison with the capacitor setup used for studying the electrowetting effect under homogeneous electric field23 is enabled by simulating pure water between a pair of parallel graphane sheets carrying oppositely charged ionic groups. The surfaces are held at separation d = 4.7 nm. The snapshots of the two systems are shown in Figure 2. The net charge of −COO− on one wall is exactly compensated by −NH3+ groups on the opposite one, and no counterions are present in the intervening water. Ionic groups are uniformly distributed on the two surfaces at four values of charge densities from qs = 0.13 e0 nm−2 to qs = 0.51 e0 nm−2 to include typical densities on biomembranes45,46 and association colloids at varied pH.13,47 To compare the effect of discrete charges, introduced through surface functionalization, and that of homogeneously charged capacitor electrodes, we also calculated the change in Δγ for homogeneous electric fields associated with identical electrode charge densities on smooth surfaces at the same 4.7
Figure 1. Thermodynamic cycle for the determination of wetting free energy Δγ by thermodynamic integration. Each corner represents the dry (D) or wet (W) and charged (C) or uncharged (U) state of the surface. In agreement with this notation, the Helmoltz free energies, ΔF, refer to the charging process of a dry surface (ΔFDC) or wet surface (ΔFWC) and to the wetting of the uncharged surface (ΔFWU).
represents the sum of the excess free energies associated with the charging of the completely wet ionic functionalized surface (ΔFWC) reduced by the corresponding value calculated for the completely dry surface (ΔFDC), plus the wetting free energy of an identical surface from which we removed all charges of ionizing groups and their counterions. The use of the cycle avoids the technically demanding calculation of the free energy change of the entire wetting process.42,43 The two charging free energies are calculated by means of the TI algorithm as fully
Figure 2. Wetting free energies calculated for a capacitor-like system with two facing butyl-functionalized graphane surfaces of increasing and oppositely equal charge densities (A) and for a uniform electric field capacitor (B). The dashed lines represent the best quadratic fits to the data sets. 15469
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water is primarily polarized by local fields around individual charges. The calculation of the water radial distribution on the upper hemispherical volume centered on the carbon atom of the carboxylic group shows that the outermost hydration shell within which we can expect significant polarization effects has a radius of about r = 6−7 Å. This distance determines the separation between neighboring groups, beyond which there is no significant overlap of hydration shells and hence no notable cooperativity in polarization effects. For surface charge densities on our regularly patterned surfaces, the groups are sufficiently separated to hydrate independently of each other; hence, hydration free energies of individual surface groups and simple ions contribute to the overall interfacial free energy in an additive manner. This picture conforms to our earlier observation for the wetting free energy of an ionic colloid to be dominated by the additive contribution of the counterion hydration.48 Subtracting the wetting free energy at zero charge density, Δγ(qs = 0), from the Δγ value at each charge density and dividing the result by the number of ion pairs in each sample, independently from qs, the average single contribution is −3.5 ± 0.1 mN m−1. This value corresponds to the combined effect of headgroup dissociation and hydration of ≈−2 × 102 kJ mol−1. The small standard deviation between the values at different charge densities reflects the additivity of the effect. It is interesting to compare the trend revealed by our calculation with that observed in recent measurements. The inset in Figure 3 shows measured wetting free energies Δγ = −γlv cos θ on prewetted TiO2 at different degrees of ionization.13 We use contact angles of 0.1 M KNO3 solution at different values of pH, collected in Figure 6 of ref 13, and experimental charge densities at identical pH values,47 taken from Figure 4 in ref 13. These data, obtained within the range 2 ≤ pH ≤ 8, reveal an essentially linear dependence of Δγ over a wide range until saturation sets in at extreme qs. The same holds true if we plot Δγ vs renormalized charge densities from the theoretical model of ref 13. The high symmetry between the Δγ values measured for both positively and negatively charged surfaces suggests that the charge sign of the functionalizing groups does not significantly affect the water−substrate interface. At first glance this seems to be at variance with the well-known hydration asymmetry of oppositely charged ions.25,26 However, our results take into account not only the hydration of polar groups attached to the surface but also that of their counterions in solution. Therefore, the symmetry reflects the similar hydration free energies for the chosen cation and anion pair. We also note that the mean field normal to the surfaces is comparatively weak in the presence of counterions. This differs from the situation of wetted electrodes in neat water where we observe distinctly different effects of incoming and outgoing fields as the field competes with hydrogen bond preferences of interfacial water molecules.23,31 Despite the qualitative differences between the curves Δγ vs qs for uniform and discrete charge distributions, the threshold charge density needed to render Δγ negative and switch the initially hydrophobic surface (Δγ = 25.8 mN/m) to a hydrophilic one is quite similar for both cases, about qs = 0.07 e0 nm−2, for the discrete and qs = 0.11 e0 nm−2 for the uniform distribution at the specified slab thickness d. To separate possible effects of charge reversal23,25,26,29,31,49 from any other change in system constituents, we also calculate the wetting free energy after the charge swap between the surface group/counterion pairs. For a given force field, only the −COO+K− pair is suitable for the test because, due to the
nm interplate separation. Except for the addition of the slabcorrected Ewald sums,34 these calculations were performed following our previous work.23 Figure 2 compares calculated Δγ at different charge densities for discrete and homogeneous charge distributions. To focus on pure electrostatic effects, calculated values are presented as the reduction in Δγ due to surface charge, Δ(Δγ)(qs) = Δγ(qs) − Δγ(0). The quadratic dependence of Δγ with respect to the amount of discrete charges on both types of surfaces conforms to the prediction of the Lippmann equation14 for the uniform electric field, Δ(Δγ) ∝ −qs2D. Although both sets yield the same trend, a quantitative comparison shows that, for the same overall charge density, discrete charges introduced through ionic functionalization also contribute a (weaker) linear term due to individual hydration, resulting in a larger increase on the hydrophilicity of the pore. Isolated Surface. Regular Charge Distribution. While the capacitor-like geometry closely mimics pore electrowetting, a natural model system for ionic functionalized surfaces should include compensating counterions to capture the effects of counterions hydration on the final wetting free energy. To investigate the effect, we carry out simulations to calculate Δγ for a graphane surface with positively or negatively charged functionalities in the presence of counterions. Here, a single graphane surface is functionalized with −COOK or −NH3Cl ionic groups with regular patterns shown in Figure S1. Charge densities span from qs = 0.04 e0 nm−2 to qs = 0.51 e0 nm−2. In the case of discrete surface charges surrounded by screening counterions, the reduction in the wetting free energy no longer follows the Lippmann’s quadratic dependence14 on surface charge. The data for both positively and negatively charged surfaces presented in Figure 3 show a linear relation
Figure 3. Wetting free energies calculated for surfaces with positive (right) or negative (left) discrete charges on butyl-functionalized graphane surfaces. The dashed lines represent the best linear fit for the two branches. The point at qs = 0 is obtained from the water contact angle on the pure butyl-functionalized surface. The symbol size does not relate to standard deviation whose magnitude is invisible on the graph. Inset: wetting free energies on partially charged TiO2 deduced from measured13 contact angles and surface charges.47
over a broad range of surface charge densities. The observed behavior can be rationalized by the absence of any cooperative effects of ionic groups on water polarization. This differs from the case of uniformly distributed charge in the absence of counterions, where the entire water slab is permeated by an essentially uniform electric field. When discrete charges are surrounded by freely mobile ions of opposite charge, these ions effectively screen the mean field normal to the surface, hence 15470
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point-charge nature of the −NH3+ hydrogen atoms with no repulsive potential term, the charges on those atoms cannot be inverted without the risk of divergent interactions with hydrogen atoms of water. To maximize any possible effect of charge swapping, we considered the highest charge density qs = −0.51 e0 nm−2. The computed wetting free energy for the resulting surface with inverted charges is Δγinv 0.51 = −138 ± 2.5 mN m−1. The comparison with the value calculated for correct charges, Δγ0.51 = −139 ± 2.5 mN m−1, reveals no significant sign dependence of thermodynamic observables at conditions adopted in our work. Patch-like Charge Distribution. To examine possible deviations from linear additivity due to irregular surface charge distribution, we first run a set of simulations using three different patch-like charge distributions of potassium carboxylate chains at constant overall charge density qs = −0.51 e0 nm−2. The degree of segregation of charged groups is quantified in terms of the radius of gyration Rg of all charged groups on the area of the simulation box. The values of Rg2 varied from Rg2 = 181 Å2 for the highly packed configuration to Rg2 = 800 Å2, for the regular pattern (see Figure 4 and Figure S2), which
patch reduces the overall hydrophilicity although the overall surface density of −COO− groups remains constant. At these conditions and ignoring finite patch-size effects, the binding concept of ref 50 predicts the fraction of dissociated groups to scale as 1/(1 + b/Rg2), where b is a constant proportional to the overall charge density. This relation can explain the linear dependence of Δγ on Rg2 only at charge densities well above those considered in our work. A possible rationale for the nearlinear dependence we observe (note that the symbol size in Figure 4 does not relate to standard deviation whose magnitude is invisible on the graph) can come from the different contributions of the charges in the center of the patch (high local charge density) compared to the ones placed near the border with the hydrophobic area. This boundary effect can offset the deviation from linearity expected for a uniformly covered surface with charge density corresponding to the central local charge density of the patch. To decouple the two effects, we also considered a set of charge distributions with fixed radius of gyration (Rg = 181 Å2) but different charge densities. This way, any boundary effect remains approximately equal in all the samples. Figure 5
Figure 4. Wetting free energies calculated for butyl-functionalized graphane surfaces with charge density qs = −0.51 e0 nm−2 with patchlike charge distributions at different radii of gyration. The dashed line is a guide to the eye.
Figure 5. Wetting free energies calculated for a patch-like system at different charge densities but constant radius of gyration Rg2 = 181 Å2. The dashed line is a guide to the eye.
presents the resulting values of Δγ as a function of the overall charge density qs. An upward curvature indicative of counterion binding is associated with high patch densities, which notably exceed the overall densities considered in Figures 2 and 3. Note that the density inside the patch, where it ranges from ≈0.55− 2.3 e0 nm−2, is about 4.4 times higher than the overall density qs .
maximizes separations between ionic groups. Clustering of carboxylate groups, resulting in significantly increased local charge density, promotes potassium ion condensation on the high local charge density areas, in qualitative agreement with predictions of Engström and Wennerström for high charge density on electrified plates.50 Note the theory50 is approximate due to the omission of the image ion−surface interaction51 and noncoulombic, van der Waals, attraction.52 Since the ion association from solution is quite slow, an extended simulation time of 2 ns is needed to allow the degree of association to converge. By monitoring the position of counterions in solution during the simulations, we determine the dependence of the degree of association of potassium ions to be inversely proportional to the radius of gyration of the distribution. This observation, consistent with the predictions from ref 50, reflects enhanced binding of counterions attracted by multiple surface groups concentrated within the area of a smaller patch. Figure 4 shows the calculated Δγ values for the three sizes of the patch. The fourth point corresponds to the regular distribution. The observed trend is analogous to that observed with polar but neutral functionalities: effect of a polar group is weakened by the proximity of other polar moieties.53−56 In the case of ionic functionalities, packing of the counterions above a
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CONCLUSIONS Two possible scenarios have been considered to describe the reduction of the wetting free energy Δγ tuned by the addition of ionic surface functionalities. Insights from electrowetting suggest a quadratic dependence on the surface charge density in analogy with the well-known Lippmann equation14 describing the effect of uniform electrode charge. Noncooperative hydration of discrete surface charges and their counterions, on the other hand, will produce a linear dependence of the wetting free energy on the total surface charge. In view of uncertain characterization of surface charge in experiments, we examine the effect by molecular simulations. We consider a set of molecularly smooth surfaces comprised of butyl-functionalized graphane22 with varied densities and distribution patterns of ionizing groups. In planar nanopores with unscreened, oppositely charged walls wetted by neat water we observe an 15471
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approximately quadratic dependence of Δγ on the overall charge density of ionic groups. In the practically relevant case of an isolated charged surface surrounded by compensating counterions, on the other hand, the net effect is significantly weaker and shows a linear dependence on the overall density of ionizing groups, reflecting additive contributions of individual charges. Recent contact angle measurements on hydrophobized Ti oxide at varied pH appear to confirm the linear dependence.13 In analogy with functionalization by neutral polar groups, ionic functionalization is most effective with regular surface patterns that maximize the separation between adjacent ionic sites. Up to 4-fold amount of ionized groups may be required to match the effect of regularly distributed charges when using a maximally segregated, patchy surface. The difference is attributed to counterion binding reminiscent of ion condensation on planar surfaces, which takes place when clustering of ionic groups results in a significant increase in local charge density on the patches.
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(11) Feng, X.; Feng, L.; Jin, M.; Jiang, L.; Zhu, D. J. Am. Chem. Soc. 2004, 126, 62−63. (12) Zhang, J.; Lu, X.; Huang, W.; Han, Y. Macromol. Rapid Commun. 2005, 26, 477−480. (13) Hanly, G.; Fornasiero, D.; Ralston, J.; Sedev, R. J. Phys. Chem. C 2011, 115, 14914−14921. (14) Lippmann, G. Ann. Chim. Phys. 1875, 5, 494. (15) Shapiro, B.; Moon, H.; Garrell, R. L.; Kim, C.-J. J. Appl. Phys. 2003, 93, 5794−5811. (16) Mugele, F.; Baret, J.-C. J. Phys.: Condens. Matter 2005, 17, R705−R774. (17) Daub, C. D.; Bratko, D.; Luzar, A. Top. Curr. Chem. 2012, 307, 155−180. (18) Cassie, A. B. D. Discuss. Faraday Soc. 1948, 3, 11−16. (19) Elias, D. C.; Nair, R. R.; Mohiuddin, T. M. G.; Morozov, S. V.; Blake, P.; Halsall, M. P.; Ferrari, A. C.; Boukhvalov, D. W.; Katsnelson, M. I.; Geim, A. K.; Novoselov, K. S. Science 2009, 323, 610−613. (20) Boukhvalov, D. W.; Katsnelson, M. I.; Lichtenstein, A. I. Phys. Rev. B 2008, 77, 035427. (21) Sofo, J. O.; Chaudhari, A. S.; Barber, G. D. Phys. Rev. B 2007, 75, 153401. (22) Vanzo, D.; Bratko, D.; Luzar, A. J. Chem. Phys. 2012, in press; DOI: http://dx.doi.org/10.1063/1.4732520. (23) Bratko, D.; Daub, C. D.; Leung, K.; Luzar, A. J. Am. Chem. Soc. 2007, 129, 2504−2510. (24) Lebégue, S.; Klintenberg, M.; Eriksson, O.; Katsnelson, M. I. Phys. Rev. B 2009, 79, 245117. (25) Lynden-Bell, R. M.; Rasaiah, J. C. J. Chem. Phys. 1997, 107, 1981−1991. (26) Rajamani, S.; Gosh, T.; Garde, S. J. Chem. Phys. 2004, 120, 4457−4466. (27) Dzubiella, J.; Allen, R. J.; Hansen, J.-P. J. Chem. Phys. 2004, 120, 5001−5004. (28) Dzubiella, J.; Hansen, J.-P. J. Chem. Phys. 2005, 122, 234706. (29) Vaitheeswaran, S.; Yin, H.; Rasaiah, J. C. J. Phys. Chem. B 2005, 109, 6629−6635. (30) Bratko, D.; Daub, C. D.; Luzar, A. Phys. Chem. Chem. Phys. 2008, 10, 6807−6813. (31) Bratko, D.; Daub, C. D.; Luzar, A. Faraday Discuss. 2009, 141, 55−66. (32) Plimpton, S. J. Comput. Phys. 1995, 117, 1−19. (33) Evans, D. J.; Holian, B. L. J. Chem. Phys. 1985, 83, 4069−4075. (34) Yeh, I.-C.; Berkowitz, M. L. J. Chem. Phys. 1999, 111, 3155− 3163. (35) Jorgensen, W. L.; Maxwell, D. S.; Tirado-Rives, J. J. Am. Chem. Soc. 1996, 118, 11225−11236. (36) Berendsen, H. J. C.; Grigera, J. R.; Straatsma, T. P. J. Phys. Chem. 1987, 91, 6269−6271. (37) Godawat, R.; Jamadagni, S. N.; Garde, S. Proc. Natl. Acad. Sci. U. S. A. 2009, 106, 15119−15124. (38) Giovambattista, N.; Debenedetti, P. G.; Rossky, P. J. Proc. Natl. Acad. Sci. U. S. A. 2009, 106, 15181−15185. (39) Hua, L.; Zangi, R.; Berne, B. J. J. Phys. Chem. C 2009, 113, 5244−5253. (40) Halverson, J. D.; Maldarelli, C.; Couzis, A.; Koplik, J. Soft Matter 2010, 6, 1297−1307. (41) Wang, J. H.; Bratko, D.; Luzar, A. Proc. Natl. Acad. Sci. U. S. A. 2011, 108, 6374−6379. (42) Leroy, F.; dos Santos, D. J. V. A.; Müller-Plathe, F. Macromol. Rapid Commun. 2009, 30, 864−870. (43) Grzelak, E. M.; Errington, J. R. Langmuir 2010, 26, 13297− 13304. (44) Vega, C.; de Miguel, E. J. Chem. Phys. 2007, 126, 154707. (45) Vácha, R.; Jurkiewicz, P.; Petrov, M.; Berkowitz, M. L.; Böckmann, R. A.; Barucha- Kraszewska, J.; Hof, M.; Jungwirth, P. J. Phys. Chem. B 2010, 114, 9504−9509. (46) Jurkiewicz, P.; Cwiklik, L.; Vojtí.ková, A.; Jungwirth, P.; Hof, M. Biochim. Biophys. Acta, Biomembr. 2012, 1818, 609−616.
ASSOCIATED CONTENT
S Supporting Information *
Functionalization patterns; force field parameters; charging free energy (Figures S1−S3, Tables S1−S4). 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] (D.B.);
[email protected] (A.L.). Notes
The authors declare no competing financial interest.
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ACKNOWLEDGMENTS We gratefully acknowledge the support of the Office of Basic Energy Sciences, Chemical Science, Geosciences, and Biosciences Division of the U.S. Department of Energy (DE-SC0004406). This research used resources of the National Energy Research Scientific Computing Center (NERSC), which is supported by the Office of Science of the U.S. Department of Energy under Contract DE-AC02-05CH11231, and the Extreme Science and Engineering Discovery Environment (XSEDE), which is supported by National Science Foundation Grant OCI-1053575.
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REFERENCES
(1) Shen, J.; Liu, A.; Tu, Y.; Foo, G.; Yeo, C.; Chan-Park, M. B.; Jang, R.; Chen, Y. Energy Environ. Sci. 2011, 4, 4220−4229. (2) Alyousef, Y.; Yao, S. C. Microfluid. Nanofluid. 2006, 2, 337−344. (3) Huber, D. L.; Manginell, R. P.; Samara, M. A.; Kim, B.-I.; Bunker, B. C. Science 2003, 301, 352−354. (4) Sun, T.; Wang, G.; Feng, L.; Liu, B.; Ma, Y.; Jiang, L.; Zhu, D. Angew. Chem., Int. Ed. 2004, 43, 357−360. (5) Welters, W. J. J.; Fokkink, L. G. J. Langmuir 1998, 14, 1535− 1538. (6) Verheijen, H. J. J.; Prins, M. W. J. Langmuir 1999, 15, 6616− 6620. (7) Abbott, S.; Ralston, J.; Reynolds, G.; Hayes, R. Langmuir 1999, 15, 8923−8928. (8) Ichimura, K.; Oh, S.-K.; Nakagawa, M. Science 2000, 288, 1624− 1626. (9) Rosario, R.; Gust, D.; Hayes, M.; Jahnke, F.; Springer, J.; Garcia, A. A. Langmuir 2002, 18, 8062−8069. (10) Balzani, V.; Credi, A.; Venturi, M. Pure Appl. Chem. 2003, 75, 541−547. 15472
dx.doi.org/10.1021/jp3044384 | J. Phys. Chem. C 2012, 116, 15467−15473
The Journal of Physical Chemistry C
Article
(47) Yates, D. E.; Healy, T. W. J. Chem. Soc., Faraday Trans. 1 1980, 76, 9−18. (48) Wang, J. H.; Bratko, D.; Luzar, A. J. Stat. Phys. 2011, 145, 253− 264. (49) Dzubiella, J.; Hansen, J.-P. J. Chem. Phys. 2004, 121, 5514−5530. (50) Engström, S.; Wennerström, H. J. Phys. Chem. 1978, 82, 2711− 2714. (51) Bratko, D.; Jönsson, B.; Wennerström, H. Chem. Phys. Lett. 1986, 128, 449−454. (52) Tavares, F. W.; Bratko, D.; Blanch, H. W.; Prausnitz, J. M. J. Phys. Chem. B 2004, 108, 9228−9235. (53) Cheng, Y.-K.; Rossky, P. J. Biopolymers 1999, 50, 742−750. (54) Giovambattista, N.; Debenedetti, P. G.; Rossky, P. J. J. Phys. Chem. C 2006, 111, 1323−1332. (55) Acharya, H.; Vembanur, S.; Jamadagni, S. N.; Garde, S. Faraday Discuss. 2010, 146, 353−365. (56) Luzar, A.; Leung, K. J. Chem. Phys. 2000, 113, 5836−5844.
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dx.doi.org/10.1021/jp3044384 | J. Phys. Chem. C 2012, 116, 15467−15473
