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Metastable Vapor in a Janus Nanoconfinement B. Shadrack Jabes, Joshua Driskill, Davide Vanzo, Dusan Bratko, and Alenka Luzar J. Phys. Chem. C, Just Accepted Manuscript • Publication Date (Web): 22 May 2017 Downloaded from http://pubs.acs.org on May 28, 2017
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Metastable Vapor in a Janus Nanoconfinement B. Shadrack Jabes, Joshua Driskill, Davide Vanzo, Dusan Bratko*, and Alenka Luzar* Department of Chemistry, Virginia Commonwealth University, Richmond, VA 23284, United States May 18, 2017 ABSTRACT: We study the competition between liquid and vapor states of water confined between diametrically different surfaces, one hydrophilic and the other strongly hydrophobic (Janus interface). Using atomistic simulations and a generalization of the capillarity approximation, we demonstrate that vapor bubbles can persist in the confinement in long-lived metastable states. In contrast to the well-known metastability of confined liquid with respect to capillary evaporation, a strongly metastable vapor phase has so far not been anticipated, as infiltration does not involve the formation of new liquid-vapor interfaces. In the case of a Janus interface, however, we show that the interfacial free energy passes through a pronounced maximum during infiltration. This counterintuitive phenomenon provides a new mechanism for water-mediated attraction (capillary force) between polar and nonpolar surfaces present in biophysical systems and in dispersions of heterogeneous nanoparticles.
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I. INTRODUCTION Capillary evaporation supports a known mechanism of attraction between strongly hydrophobic surfaces in water1-3. In experimentally relevant situations, however, the expulsion of water is often prevented by kinetic barriers4-6, evidenced by the hysteresis of surface forces measured upon approach and separation of hydrophobic surfaces7-8. The existence of the barrier to the transition from the hydrated to cavitated states has been attributed to the creation of new liquid/vapor interface during vapor nucleation9. This picture is in a qualitative agreement with molecular simulations of metastable liquid phases10-11 or impeded liquid-to-vapor transitions in hydrophobic confinements5-6. In the present work we address the occurence of similarly persistent vapor phase in systems where the liquid phase represents the thermodynamically stable state. We show the phenomenon to be especially prominent at asymmetric (Janus) interfaces12-13 where the opposing walls are characterized by drastically different wettabilities. The thermodynamic condition for spontaneous solvent intrusion in a pore can be approximated using the continuum relation9, 14-15 PVw Aij ij 0
(1)
i, j
where Ω is the grand potential and P the difference between the bulk (reservoir) pressure, Pb, and the vapor pressure at the same chemical potential, Pv. Vw is the volume of confined liquid, and Δ Aij are the changes of the interfacial areas between the three phases (solid/vapor, solid/liquid, and liquid/vapor) with interfacial free energies γij during the process. Avoiding the intricacies of solute curvature effects16-20, we focus on planar particles. In case of parallel planar objects with finite area A at separation d, eq 1 can be rewritten in the familiar form21-22
d dc =
2 cos C P A
A 2 cos C
(2)
dc is the threshold separation above which the liquid-filled pore represents the thermodynamic equilibrium state. γ is the liquid surface tension. C is the circumference, Ad the approximate water-accessible volume of the pore, and Cd the liquid/vapor interface Alv of an evacuated pore. For nanosized aqueous confinements at ambient conditions (T ~ 300 K, Pb=1 atm >> Pv), the pressure term is overwhelmed by the surface one (P -R(cosθ1 + cosθ2)/2, where θ1 and θ2 are the contact angles of the bottom and top plates respectively. In our system, (R=42 Å and d≈12 Å), spontaneous infiltration is predicted for all values of θ2 below 73°. Molecular simulations, however, show that a metastable cavity persists in the pore for all θ2 > 63°. The snapshots shown in Figure 1 (left) illustrate the filling transition in the Janus system with the hydrophilic plate contact angle θ2=62.5°. When θ2 exceeded this value, the cavitated state (resembling the second snapshot in Figure 1) consistently stalled over arbitrarily long simulation times, a behavior indicative of a kinetic barrier to complete pore filling by water. To get an insight into the energetics of water infiltration, we choose the filling fraction
as a progress variable and predict the grand potential profile ΔΩ(Φ)=Ω(Φ)−Ω(0) for the Janus nanopore variationally, applying a generalization of the continuum model (capillarity approximation)15,
21-22
, eq 1, for the varying cavity geometry. For every cavity volume
V V pore VH 2O V pore (1 ) , we determine interfacial areas Ai by presuming an infiltration pathway suggested from the simulated trajectories. As illustrated in Figure 1, the infiltration of water into an initially empty pore proceeds in two stages. As long as vapor spans the entire width of the pore, the cavity shape fluctuates around that of truncated cone, which is wider at the hydrophobic wall and narrower at the hydrophilic one (Figure 1). As the cavity gets smaller, it eventually detaches from the hydrophilic wall. The contact angle of the remaining sessile bubble (measured across the vapor phase) is π-θ1. For a conical cavity of volume V, the top and bottom base radii of the cone, r1 and r2, are interdependent. We determine r1 and corresponding r2(V, r1) variationally by minimizing Ω with respect to r1. The base radius rb of the sessile bubble, on the other hand, is directly determined by the cavity volume V and contact angle (π-θ1). At large bubble volume V (Figure 1 bottom) the bubble contact angle should be increased above π-θ1 to restrict rb according to the condition rb≤R. These situations were, however, thermodynamically inferior to the truncatedconical shape in systems we considered. When both the truncated cone and bubble shapes are sterically allowed, our algorithm chooses the shape with smaller Ω. Notably, the cavity does not detach from the hydrophilic wall and transform from the truncated cone to the bubble shape
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until after the maximum in Ω has been reached. The bubble segment of the infiltration pathway is therefore not relevant to the barrier calculation. The details of the variational procedure are given in the Supporting Information (SI). The top two plots in Figure 2 illustrate the predictions based on the capillarity approximation (CA) for the grand potential Ω(Φ) as a function of water filling fraction Φ in the nanopores with a fixed contact angle on the strongly hydrophobic (bottom) plate with θ1=150o±3o and different values of the contact angle of the upper wall in the interval 45o≤ θ2 ≤75o. The reference point of Ω is chosen in the evacuated state, Φ=0. For all contact angles θ2 except for θ2 =75o, Ω(1) is negative, signifying spontaneous water infiltration. However, for contact angles θ1 above 50o, the variation of Ω(Φ) is nonmonotonic, with a fast initial decrease toward a local minimum with partially wetted hydrophilic wall. The subsequent increase in Ω
Figure 1. Left: Molecular Dynamics snapshots of the Janus nano-pore (from top to bottom) at filling states Φ=0, 50, 75, and 100%. The hydrophilic (yellow) plate has contact angle θ2= 62.5°; hydrophobic (magenta) θ1≈150°. Right: Idealized cavity geometries used in the variational continuum model (CA): cylinder of radius R and height d, truncated cone with radii r1 and r2, or sessile bubble with radius rb≤R and contact angle π - θ1.
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is associated with gradual wetting of the hydrophobic wall. The maximum Ω(Φ) is reached at Φ between 75-85% where the upper portion of the conical cavity is narrowed to ~1 nm. Soon thereafter the cavity detaches from the upper wall, causing a slight discontinuity of the slope of Ω vs Φ. The shrinking of the remaining bubble results in a steep decrease in Ω as Φ approaches 1. As seen from the results for θ1 =75o, this decrease is observed even when complete filling does not coincide with the global minimum of Ω. The bottom plot in Figure 2 illustrates rapid increases in the depth of the local minimum of Ω at low Φ and the barrier to complete filling with increasing asymmetry between the walls at unchanged =(cosθ1+cosθ2)/2. The capillarity approximation estimates of the barriers to infiltration, ~ 28 and 59 kBT in systems with θ1=150o and θ2= 60o and 65o, respectively, suggest that vapor cavities in Janus nanopores can persist in metastable states over experimentally relevant times. The behavior we observe in molecular simulations confirms this prediction. Solid lines in Figure 3 show the MD simulation results for the time dependence of the number of confined water molecules in initially empty Janus nanopores with θ1≈150o±3o and θ2 varied between 55 and 75o. At 15Å separation, all the pores spontaneously fill to Φ of at least ~40±10%. When θ2 is below 63o, the infiltration eventually proceeds to complete filling. For higher θ2, vapor survives over all practically accessible simulation times in numerous trials, including systems in which the fully filled states correspond to the global free energy minima. The longevity of vapor states between asymmetric walls gives rise to a novel, potentially important mechanism enabling adhesion between polar and non-polar particles in biophysical systems and heterogeneous nanomaterials. Computational costs of free energy calculations in simulated systems of given size (~1.6.105 atoms) preclude direct MD validation5-6,
33
of the free energy profiles from the
capillarity approximation (Figure 2). Indirect evidence of the activation barrier and its position is, however, provided by the MD simulation results shown in Figure 3. Here we use trajectory points from the simulation of infiltration by water at θ2=62.5o, the highest value of θ2 allowing spontaneous pore filling. A set of MD simulations runs were initiated from preselected, partially filled states Φ reached with θ2=62.5o after changing the Lennard-Jones
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Figure 2 Top: The capilarity approximation predictions for the grand potential Ω as a function of the filling fraction Φ in a Janus nanopore between a par of plates with radii R=42 Å at separation d=15 Å and plate contact angles θ1=150o and θ2=62.5o (solid line). The slope discontinuity at high Φ denotes the detachment of the cavity from the upper plate. The arrows show the positions of the minimum and maximum of Ω in atomistic MD simulation. Middle: Grand potential profiles for systems with the lower plate contact angle θ1=150o and varying upper-plate θ2=45o-75o. Bottom: Profiles Ω(Φ) for increasingly asymmetric combinations of θ1 and θ2 at constant cosθ1+cosθ2. The black curve corresponds to the symmetric system, θ1=θ2=101.3o where only a modest barrier to infiltration can be expected2,24. While the free energy reduction due to complete pore filling, Ω(1), is identical in all six systems, the depth of the minima at partial wetting, and the height of the barrier to complete infiltration increase with the asymmetry between the walls. ACS Paragon Plus Environment
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parameters of the upper wall, effectively increasing its contact angle to 65o or 70o. According to the simulations discussed with Figure 3, these contact angles do not lead to complete pore wetting if starting from an empty nanopore. If θ2 is increased after the pores had been partially filled using θ2=62.5o, the outcome depends of the filling degree at the time of change in θ2. If we increased the contact angle θ2 to 65o or 70o at Φ ≤ 75%, in all trial runs, the change prevented further filling and the system gradually returned to Φ near 40%. If θ2 was increased after reaching Φ of 85% or higher, however, the filling continued until completion. This behavior indicates a prohibitive barrier in the vicinity of Φ ≈ 80%. In Table 1 we collect calculated free energies of pore filling, barrier heights and positions of the continuum (CA) model systems shown in Figure 3, and barrier positions suggested by the MD simulations for the hydrophilic plate contact angle θ2 of 65° and 70°. The atomistic simulations agree with the CA predictions in confirming the existence and positions of the barriers to water expulsion. The positions of the local free energy minima generally correspond to higher infiltration extents Φ than predicted in the continuum model.
A
possible
explanation
is
provided by the partial filling of the grooves on the flanks of the corrugated superhydrophobic plates (see snapshots in Figure 1). For simplicity, an ideal Cassie state34 on the bottom wall was presumed
in
the
continuum-model
calculations. The MD approach could not be used to locate surmountable barriers at lower θ2. When a pair of asymmetric surfaces are pulled out of contact, a transient cavitation can be expected as illustrated in Figure 4. Analogous
Figure 3 Top: Time dependence of the amount of water in an initially cavitated Janus nanopore CA prediction for systems with the lower plate contact angle θ1=150o and varying upper-plate hydrophilicity, θ2=55o-75o. Bottom: Comparison between the uninterrupted trajectories at θ2=62.5o, 65o and 70o (solid curves) and trajectories obtained by continuing from selected states on the trajectory for θ2=62.5o after switching θ2 to 62.5o or 70o (open symbols).
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cavitation has been detected upon separation of macroscopic surfaces in the Surface Force Apparatus (SFA) experiments7. When one of the surfaces is sufficiently hydrophilic, eq 2 foresees spontaneous water
infiltration between
the
objects. Contrary to this conventional expectation, our model calculations predict the possibility of long-lived metastable vapor states even at separations of a few nm. In these cases, attractive (Laplace
pressure)
force
opposes
particle
Figure 4. Because of the barrier to water infiltration, a long-lived vapor cavity between a hydrophilic solute and a hydrophobic adsorbing surface may give rise to capillary forces delaying the solute desorption.
separation, adding additional stability to the contact configuration already favored by the direct van der Waals interaction between the two surfaces. This behavior can delay or prevent desorption of a moderately hydrophilic protein molecule adhering to a superhydrophobic surface (Figure 4). In Figure 5 we plot the MD-umbrella sampling results for the solvent-induced contribution to the work against the adhesion force between a pair of disk-like plates in
Table 3: Positions of the minima and maxima of the grand potential Ω(Φ) from the capillarity approximation (CA) and Molecular Dynamics (MD) approaches, and barrier heights CA CA and filling free energies CA (1) CA (0) from the CA max min calculations. Φ is the filling fraction of the nanopore by water. θ1=150o. No extrema are detected for θ2
