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Hierarchical Condensation Xiao Yan,† Feng Chen,*,‡ Soumyadip Sett,† Shreyas Chavan,† Hang Li,† Lezhou Feng,† Longnan Li,† Fulong Zhao,‡ Chongyan Zhao,‡ Zhiyong Huang,‡ and Nenad Miljkovic*,†,§,∥,⊥

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†

Department of Mechanical Science and Engineering, University of Illinois at Urbana−Champaign, Urbana, Illinois 61801, United States ‡ Institute of Nuclear and New Energy Technology, Tsinghua University, Beijing 100084, China § Department of Electrical and Computer Engineering, University of Illinois at Urbana−Champaign, Urbana, Illinois 61801, United States ∥ Frederick Seitz Materials Research Laboratory, University of Illinois at Urbana−Champaign, Urbana, Illinois 61801, United States ⊥ International Institute for Carbon Neutral Energy Research (WPI-I2CNER), Kyushu University, 744 Moto-oka, Nishi-ku, Fukuoka 819-0395, Japan S Supporting Information *

ABSTRACT: With the recent advances in surface fabrication technologies, condensation heat transfer has seen a renaissance. Hydrophobic and superhydrophobic surfaces have all been employed as a means to enhance condensate shedding, enabling micrometric droplet departure length scales. One of the main bottlenecks for achieving higher condensation efficiencies is the difficulty of shedding sub-10 μm droplets due to the increasing role played by surface adhesion and viscous limitations at nanometric length scales. To enable ultraefficient droplet shedding, we demonstrate hierarchical condensation on rationally designed copper oxide microhill structures covered with nanoscale features that enable large (∼100 μm) condensate droplets on top of the microstructures to coexist with smaller ( 0.2 (Figure S2; see Section S4, Supporting Information), resulting in a critical contact angle θc < 116° that is lower than the “intrinsic” contact angle (θa = θaapp ≈ 170°) determined by the superhydrophobic nanostructures.57 Indeed, evidence for the CB state of the sink droplet was obtained from the observation of a large number of small droplets growing and disappearing underneath it (Figure 2b−f). The growth of small droplets ensued in spite of the shading provided by the sink droplet that blocks downward vapor diffusion toward the condensing surface. By shifting the focal plane toward the surface, we observed the underlying droplets at differing depths in the valleys of the microhills. At higher elevations closer to the sink droplet and microhill peaks, the underlying droplets grew rapidly and vanished frequently upon touching the sink droplet, followed by renucleation at the same locations (Figure 2c and e; see Video S3). Droplets nucleating in lower elevations further from the sink droplet had more space to grow prior to undergoing shaded coalescence. Due to the high nucleation density in the valleys, a series of coalescence events between multiple droplets was observed (Figure 2f). As the coalesced droplet continued to grow in the valley, it encountered confinement from the diverging hill cavities (Figure 2e), which directed the droplet to navigate toward the sink droplet by virtue of the upward capillary force and the kinetic energy released from droplet coalescence.58−61 As a result, the bottom regions were periodically refreshed by the passive upward transport of the condensate droplets. To verify the mechanism of passive upward transport in the divergent microcavities, we conducted additional experiments on diverging superhydrophobic walls (Figure 2g and h; see Methods). Driven by the Laplace pressure difference arising from the curvature difference,61 droplets confined in the Vshaped groove spontaneously moved in the direction of the channel divergence as the droplet volume increased (Figure 2g; see Video S4). Alternatively, the upward displacement of droplets could be induced by coalescence, which resulted in a

droplets in past and present droplet growth rate studies on hydrophobic and superhydrophobic samples, but also presents an alternative to coalescence-induced droplet jumping to passively shed microscale droplets efficiently with greater surface durability.

RESULTS AND DISCUSSION Sink Droplets and Shaded Coalescence. To study the condensation process in view of satellite droplet condensation and coalescence,50 we began by performing atmospheric water vapor condensation on a single-tier superhydrophobic CuO nanoblade surface (Figure 1a). The surface was fabricated via chemical oxidation and functionalized with a fluorinated selfassembled monolayer chemistry to achieve superhydrophobicity, resulting in apparent advancing/receding contact angles of θaapp/θrapp = 170.3 ± 3°/167.7 ± 3°, respectively (see Methods). Droplet growth dynamics were studied using a custom-built top-view optical light microscopy setup described elsewhere,40,51,52 and the surface was horizontally mounted on a cooling stage (see Methods). Due to the superhydrophobicity of the CuO nanoblade surface as well as the negligible gravitational force on microscale droplets as characterized by a droplet Bond number, Bo ≤ 0.01, droplets remained spherical, acting as a lens or “window”, allowing us to investigate details close to the liquid−solid interface through the droplets. By shifting the focal plane of the microscope,41 small satellite droplets (diameter: ∼1 μm) surrounding and beneath the base of the larger microscale droplet (diameter: ∼630 μm) were observed (Figure 1b). As expected, the satellite droplets grew until they reached the liquid−vapor interface of the top shading droplet into which they were finally absorbed via coalescence. Thus, the surface surrounding the large droplet base was refreshed and the nucleation−growth−absorption cycle repeated (Figure 1c; see Video S1). Interestingly, high-resolution imaging revealed that nanoscale droplets grew and disappeared in the base area of the large droplet (Figure 1c; see Video S1). However, the size and number of these underlying nanoscale droplets were small compared with the aforementioned satellite droplets surrounding the contact line. The observation of underlying droplets indicated that the large droplet was in the stable CB state.53 The preference for the CB wetting state was verified utilizing an energy analysis. The intrinsic advancing contact angle θa ≈ 110° corresponding to the smooth functionalized CuO surface was greater than the critical contact angle54 θc = cos−1(( f n − 1)/(rn − f n)) ≈ 96°, where f n ≈ 0.023 and rn ≈ 10 are the solid fraction and roughness of the CuO nanoblade surface,26 respectively. Thus, the CB state was energetically preferred to ensure minimized system interfacial energy.54 To further elucidate the coalescence dynamics of droplets having large mismatch in radii, we manually grew a large droplet (R ≈ 200 μm) adjacent to a small droplet (R ≈ 50 μm) by dispensing monodisperse droplets with the piezoelectric dispenser until they merged (Figure 1d) (see Methods). Although the final coalesced droplet was unable to jump due to the large droplet size mismatch,39,55 the small droplet was pulled from the surface due to the Laplace pressure difference stemming from the droplet radii mismatch.56 During the coalescence process, the larger primary droplet remained almost unchanged in both volume and position, resembling a sink that could constantly adsorb small droplets in contact with it. The outline of the spherical primary droplet sets a spatial D

DOI: 10.1021/acsnano.9b03275 ACS Nano XXXX, XXX, XXX−XXX

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Figure 3. (a) Droplet diameter (2R) as a function of time (t) for droplets growing underneath (symbols in red) and outside (symbols in blue) CB sink droplets. (b) Droplet diameter as a function of time for droplets growing underneath CB sink droplets at different cavity depth locations. In order to demonstrate the variability of the droplet growth trends, the data in (a) and (b) include droplets at ridges, hilltops, and valleys. The droplets analyzed were small enough so that droplet growth was primarily driven by direct vapor condensation. Droplet size distribution of the underlying droplets at the (c) upper focal plane near the hilltop regions and (d) lower focal plane near the bottom, with respect to the projected area. For comparison, the size distributions of unshaded droplets and droplets growing on the flat nanostructured superhydrophobic CuO surface (flat) are presented. Error bars in (a) and (b) represent one standard deviation of three independent measurements of the droplet diameters. Error bars in (c) and (d) represent one standard deviation of droplet number counts in three consecutive frames spanning 10 min of condensation. Data collection was performed 10 min after condensation initiated to ensure quasi-steady-state conditions. Note, due to optical microscopy limitations in spatial resolution, droplets having 2R < 1.5 μm are not shown in (c) and (d). For experimental details and conditions, see Methods.

nanostructured surfaces have been shown to inhibit droplet formation in structures such as slender nanowires due to the reduced molecular permeability of water vapor in the long aspect-ratio channels.62 To study whether nucleation and growth rate suppression occurred, we examined the growth rates of the shaded droplets (Figure 3a and b) and compared them with the growth rates of similarly sized, unshaded droplets on the same surface having identical condensation conditions. Surprisingly, shaded droplets grew at a faster rate compared to their unshaded counterparts. For shaded droplets, it took an average of ∼10 s to grow from 2R ≈ 2 μm to 2R ≈ 8 μm, while for unshaded droplets, it took an average of 20 to 30 s (Figure 3a). Correspondingly, the average droplet growth exponent63 for

sudden increase of the droplet volume and release in excess surface energy, promoting directional movement (Figure 2h; see Video S5). Enhanced Droplet Growth and Nucleation Rate of Shaded Droplets. The observation of droplet condensation beneath CB sink droplets on rationally designed superhydrophobic hierarchical CuO nanoblade surfaces highlights the role of lateral penetration of water vapor into the cavities between the substrate and CB sink droplets. Due to the increase in mass transfer resistance caused by the tortuous vapor diffusion pathway into the cavities, droplets growing beneath CB sink droplets should theoretically have slower growth and nucleation rates than those exposed to quiescent vapor. Indeed, the effects of spatial confinement using E


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Figure 4. (a) Schematic showing the temperature drop through the CB sink droplet and identifying the vapor velocity entering the cavities beneath the droplet. Vapor depletion due to condensation beneath the sink droplet introduces a net vapor flow with velocity vc entering the microcavities. (b) Droplet base temperature, Tb, as a function of sink droplet radius Rs. (c) Top-view schematic showing vc entering the underlying cavities. (d) Vapor velocity, vc, as a function of Rs. As a comparison, we also plot the velocity toward the condensing surface without sink droplets (v0). Note that vc is parallel to the substrate, while v0 is perpendicular. Model parameters: vapor saturation temperature Tv = 25 °C, substrate temperature Tc = 5 °C, q0″ = 0.1 W/cm2, θapp a = 150°, flat-topped square micropyramid spacing/top width/height sm/ dm/hm = 50/10/40 μm, nanostructure sn/dn/hn = 0.5/0.12/1 μm. See Section S2, Supporting Information, for more model details.

∼30% and ∼29%, respectively. Note, for the same condensation conditions, the proportion of shaded droplets having 2R < 10 μm was greater than that observed on single-tier CuO nanoblade surfaces where coalescence-induced droplet jumping condensation ensued (∼52%). The larger proportion of smaller droplets underneath the sink droplets may have arisen due to the effective and frequent shaded coalescence droplet removal and directional self-transport. Analogous to the case where an increased number of sub-10-μm droplets was observed due to the three-dimensional coalescence,50 the ceiling imposed by the sink droplet and the frequent pull-off of the shaded droplets results in a larger population of small droplets near the hilltop regions (Figure 3c). Meanwhile, directional sweeping of condensate was experimentally

shaded droplets was ∼0.29, 21% greater than that for unshaded droplets. Droplets originating in the valley areas also experienced faster growth rates during initial stages of condensation mainly driven via coalescence with neighboring droplets (Figure 3b). In addition to faster growth, the size distribution of shaded droplets, both near the hilltop regions (Figure 3c) and in the valleys close to the bottom of the cavities (Figure 3d), shifted toward smaller sizes compared with unshaded droplets on the same hierarchical CuO nanoblade surface and on the singletier CuO nanoblade surface. Of the total population, 81% and 67% of the shaded droplets (2R ≥ 1.5 μm) in the hilltop and valley regions had 2R < 10 μm, respectively. For unshaded droplets in the hilltop and valley regions, the percentages were F


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ACS Nano confirmed to generate smaller droplets,64 consistent with what was observed in the bottom regions (Figure 3d) where selfnavigating droplet sweeping occurs. Although the self-transport mechanism observed here drives unshaded droplet motion between microhills, the absence of shaded coalescence coupled with structure-mediated barriers for droplet jumping35 leads to the accumulation of large droplets. On the single-tier nanostructured superhydrophobic surface, coalescence-induced droplet jumping breaks down for coalescing droplets smaller than ∼10 μm in diameter26 and for droplet pairs with appreciable size mismatch due to the minimal kinetic energy conversion efficiency.39 As a result, the proportion of sub-10μm droplets in both cases is smaller than that for shaded droplets underneath sink droplets. When taking into account the total number of microscale droplets residing on the surface normalized by the projected surface area, the ratio of droplet number density in the hilltop and valley regions to the flat superhydrophobic surface was 1.9 and 1.3, respectively. Considering the possible coexistence of droplets in the hilltop and valley regions, the total projectedsurface-area-normalized droplet number density on the hierarchical surface was 1.9−3.2 times that of its flat superhydrophobic counterpart. The number density scaled with the surface roughness of the microstructures (rm ≈ 2−2.5; see Figure S2, Section S4, Supporting Information) indicates the crucial role of total microscale surface area on nucleation density when considering droplet length scales smaller than the microstructure length scale. We hypothesize that the maintenance of elevated shaded droplet nucleation density in the presence of large CB sink droplets resulted from the decreased local surface temperature owing to the presence of thermally inactive sink droplets. The CB sink droplet acts as a thermal barrier to condensation heat transfer, having a conduction temperature drop from the vapor (Tv) to the droplet base (Tb) (Figure 4a) estimated by52,65 Tb = Tv − −

(Figure 4b), showing that Tb is depressed when a CB sink droplet is present. For Rs ≥ 100 μm, Tb ≈ Tc, given a finite vapor−substrate temperature difference (Tv − Tc) stemming from the assumption of negligible noncondensable gas (NCG) effects. Assuming the far-field vapor temperature is equivalent to the cavity vapor temperature, the local temperature difference (Tv − Tb) increases due to decreased Tb, resulting in the a higher driving potential for nucleation of shaded droplets. Note, the incorporation of NCG effects will act to dilute the temperature difference contrast between the hierarchical and flat superhydrophobic surfaces, in effect resulting in equal total-surface-area-normalized nucleation density, in agreement with our experimental observations. In terms of droplet growth rate in steady conditions, one must consider the vapor flow dynamics underneath the CB sink droplet inside the cavities. Due to the presence of NCGs, the governing limitation to droplet growth is vapor diffusion to the liquid−vapor interface from the bulk. Although eqs 1 and 2 are valid in pure vapor conditions, they fail to capture the effect of the 3D diffusive field surrounding the droplet and governing its growth. The condensation and removal of water vapor beneath sink droplets acts to create a partial vacuum, resulting in vapor flow acceleration in the microchannels bounded by the CB sink droplet base and the structured surface. Considering a microchannel geometry depicted in Figure 4a, the vapor enters the microgrids from the inlets at the periphery of the shadowed surface (Figure 4c). The vapor entering velocity vc can be determined by applying an energy balance in the microgrid channel and expressed as vc = f (G , θaapp , R s) v0(q0′′)

where f(G, θapp a , Rs) is a function of the microstructure geometry G and v0 is the vapor velocity toward the condensing surface without a CB sink droplet present, which is a function of average surface heat flux q′0′ (a detailed derivation of eq 3 can be found in Section S2, Supporting Information). Equation 3 assumes that the overall surface heat flux will be identical for both hierarchical condensation and classical condensation without a CB sink droplet. For realistic estimates of water vapor condensation in the presence of NCGs, q0′′ ≈ 0.1 W/ cm2, θapp ≈ 150°, and Rs = 300 μm, vc = 6.5 cm/s, ∼300% a higher than v0 = 1.6 cm/s (Figure 4d). Figure 4d shows that larger sink droplets with optimal microstructures can lead to a higher vapor velocity entering the microchannels stemming from the increased condensation area beneath the base. The enhanced vapor velocity underneath the sink droplet has significant implications for heat and mass transfer. The increased vapor velocity leads to higher mass transfer coefficients and greater disturbance of the local mass transfer boundary layer,66,67 resulting in higher heat transfer and droplet growth rate. Overall Surface Condensation Heat Transfer. To quantify the surface heat transfer in pure vapor conditions, we first considered the case of a micro/nanostructured surface where a single CB sink droplet covers a finite number of shaded droplets that grow in the suspended state with a constant apparent contact angle.65,68 An upper limit of the underlying droplet radius Rc was set to the largest radius that the microcavities can accommodate: É ÄÅ ÅÅ hm sm − (dm + 2hn) ÑÑÑ ÑÑ Å R c = minÅÅ , ÑÑ ÅÅÅ 2 2 ÑÑÖ (4) Ç

Q sk 2Tvσ − 2 R shfg ρ 2πhiR s (1 − cos θaapp) Q skθaapp

4πR sk w sin θaapp

(1)

where Qsk is the individual sink droplet heat transfer rate: ÅÄÅ πR s2ÅÅÅÅ(Tv − Tc) − ÅÅÇ

Q sk =

1 2hi(1 − cos θaapp)

+

R sθaapp 4k w sin θaapp

ÑÉ

2Tvσ Ñ ÑÑ Ñ R sh fgρ Ñ Ñ

ÑÖ ÅÄÅ k pφ Å m ÅÅ + + k n sin 2 θaapp Å ÅÇÅ δnk p + hmk n 1

ÑÉÑ−1 ÑÑ Ñ ÑÖ

δnk v + h mk n Ñ Ñ k v(1 − φm)

(3)

(2)

and σ, ρ, hfg, and kw are the condensate liquid−vapor surface tension, density, latent heat of vaporization, and thermal conductivity, respectively, hi is the liquid−vapor interfacial heat transfer coefficient, Tc is the substrate temperature, Rs is the CB sink droplet radius, θapp a is the droplet apparent advancing contact angle, kv is the vapor thermal conductivity, δn is the nanostructure thickness, kp is the microscale feature thermal conductivity, hm is the microscale feature height, and φm is the volume fraction for the microstructures. Note, kn is the equivalent thermal conductivity of the nanostructure layer (Section S3, Supporting Information). By solving eqs 1 and 2, we obtain the surface temperature at the droplet base Tb as a function of the sink droplet radius Rs G


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ACS Nano where hm, sm, and hn are the height, interval of the square lattice distributed microstructures, and the height of nanostructures, respectively. Droplets having R > Rc are transported upward and merge with the CB sink droplet (Figure 2e). By integrating the individual droplet heat transfer from the critical nucleation radius Rmin to Rc, we obtained the total heat transfer Qun underneath a single CB sink droplet having a radius Rs (see Section S3, Supporting Information): i Q un = a un(R s)jjjj k

∫R

Re min

qun(R ) n un(R ) dR +

∫R

Rc e

y qun(R ) Nun(R ) dR zzzz {

(5)

where aun(Rs), R, Re, and qun(R) are the total microscale surface area underneath the sink droplet, radius of the shaded droplet, merging radius related to the nucleation density,65 and individual droplet heat transfer (Section S3, Supporting Information), respectively. The terms nun(R) and Nun(R) are the size distributions of the noninteracting and interacting droplets normalized by the total surface area, respectively (see eqs S10 and S11, Section S3, Supporting Information).65,69,70 We assume that the hierarchical surface allows all shaded droplets to be eventually collected by the sink droplet, promoting the growth of the sink droplet. Correspondingly, the heat transfer of the shaded condensation should be incorporated into the sink droplet. Therefore, the total heat transfer through the single sink droplet with shaded condensation (Qsu) is the sum of the heat transfer contributed by the direct condensation of the sink droplet (Qsk) and the shaded condensation (Qun): Q su = Q sk + Q un

(6)

Figure 5a shows the heat transfer rate of differing sink droplet wetting states with the same radius Rs = 300 μm. A CB sink droplet with small droplets condensing underneath it (hierarchical condensation) showed the highest heat transfer, ∼270% higher than underlying-condensation-free cases (sink droplet in CB or Wenzel state). Correspondingly, the growth of the sink droplet (see eqs S17 and S18, Section S3, Supporting Information) is significantly faster when considering condensation underlying the sink droplet (Figure 5b). We note that even if the large sink droplet penetrates the microcavities (i.e., Wenzel, or partially wetting state), the heat transfer through the sink droplet (without underlying condensation) remains almost identical to that of the CB state sink droplet (Figure 5a). The identical heat transfer is due to the thermal resistance of the air cushion sandwiched between the sink droplet and the underlying substrate being relatively small compared to the thermal conduction resistance of the sink droplet. Hence, elimination of the air cushion underneath large sink droplets does not contribute to an appreciable enhancement of heat transfer. Enabling condensation underneath sink droplets is a promising method to activate the surface area underneath large droplets to further enhance heat transfer. To evaluate the overall heat transfer flux on the hierarchical surface in the presence of hierarchical condensation, we extended the case of the single sink droplet to the multiple sink droplet scenario. We classified the droplets on the hierarchical surface into three categories based on the droplet spatial position with respect to the microstructures, the growth mechanism, and size distribution: (I) CB state sink droplets sitting on top of microstructures, (II) droplets underneath sink droplets, and (III) droplets in-between microstructures that are

Figure 5. (a) Heat transfer (Q) through an individual droplet in differing configurations: CB state, Wenzel state, and hierarchical mode (CB sink droplet with shaded droplets). (b) Droplet radius (Rs) of an individual sink droplet with and without shaded droplets as a function of time (t). (c) Heat fluxes (q′′) of hierarchical condensation (q′hr′), condensation devoid of shaded droplets (q′cf′), and jumping-droplet condensation (qj′′) as a function of surface = 150°, subcooling (ΔT). Model parameters: Tv = 25 °C, θapp a nucleation site density Ns = 2.5 × 109 m−2, sm/hm/dm = 50/40/10 μm, sn/dn/hn = 0.5/0.12/1 μm. In (a) and (b), ΔT = 5 °C, Rs = 300 μm; in (c), ΔT was varied with Tv = 25 °C, and maximum sink droplet radius Rg = 500 μm. See Section S3, Supporting Information, for more model details. H


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app Figure 6. Apparent advancing (θapp a ) and receding (θr ) contact angles as a function of abrasive wear test cycles for the (a) single-tier CuO nanoblade surface and (b) hierarchical CuO nanoblade surface. Error bars represent one standard deviation of measurements conducted on five distinct spatial locations on each sample for each wear condition. Insets: Images of droplets residing in the advancing state on the abraded surfaces. Droplet radius is ∼200 μm. (c−e) Hierarchical condensation on the hierarchical CuO nanoblade surfaces with increasing extents of abrasive damage. The extent of microstructure damage is schematically shown in (c-I), (d-I), and (e-I), with microstructures in (c) being slightly damaged, while in (e) drastically abraded. Sink droplets on the abraded surfaces are shown in (c-II), (d-II), and (e-II), respectively. By shifting the microscope focal plane downward, (c-III, d-III, and e-III) the solid−droplet interface showing the flattened hilltops and (c-IV, d-IV, and e-IV) shaded droplets are observed. White arrows indicate downward (toward the sample base) focal plane shifting. See Methods for experimental details.

surface area occupied by each droplet group (see Section S3, Supporting Information). When shaded droplets are nonexistent, the overall heat flux is the sum of heat fluxes arising from sink droplets (category I) and unshaded droplets (category III), qcf′′ = qsk ′′ + qus ′′. As a comparison, the heat flux during jumping-droplet condensation on a flat single-tier nanostructured surface having identical nanostructures to the

not shaded by a sink droplet (see Figure S1 and Section S3, Supporting Information). The total heat flux q′hr′ is the sum of the heat fluxes corresponding to each droplet group: ′′ ′′ qhr′′ = qsk′′ + qun + qus

(7)

where q′sk′, q′un′ , and q′us′ are the heat fluxes contributed by the sink droplets in categories I, II, and III, respectively. The heat transfer is solved by analyzing the size distribution and the I


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ACS Nano hierarchical surface without the microstructures, q′j ′, was also calculated.26 The analytical model shows that with an identical departure size of jumping droplets and shaded droplets (Rj = Rc), hierarchical condensation has an 80% higher heat flux when compared to the jumping-droplet condensation (Figure 5c). It should be noted that the ratio of heat fluxes of hierarchical condensation to that of jumping-droplet condensation (qhr ′′/qj′′ = 2.55) is slightly larger than the microscale roughness (rm = 2.19), signifying that the enhancement of heat transfer of hierarchical condensation results from not only the increased surface area underneath sink droplets but also the condensation of sink droplets. Furthermore, the calculation shows that the heat flux of condensation devoid of shaded condensation is 30% lower than hierarchical condensation (qhr ′′/qcf′′ = 1.43), further demonstrating the significance of condensation underneath sink droplets. Our analysis demonstrates that hierarchical condensation has three main heat transfer advantages when compared to jumping-droplet condensation on a plain single-tier nanostructured surface. The passive transport and removal of droplets toward the sink droplet due to divergent microscale roughness eliminates progressive flooding, which exists on the plain single-tier nanostructured surface (Figure 1c and Video S1). The ability of hierarchical condensation to overcome progressive flooding enables utilization of all of the microscale surface area for condensation, hence increasing the heat transfer rate from an equivalent projected area perspective, as revealed by the higher calculated heat fluxes for hierarchical condensation (Figure 5c). A second and key advantage of hierarchical condensation is the ability to limit the maximum coalescing droplet size without the need for biphilic surfaces having precise spatial control of heterogeneous nucleation.34,71,72 By tailoring the surface micro/nanostructure length scales, the minimum droplet departure size, defined by coalescence with the CB sink droplet, can be controlled precisely, promising a means to further increase heat transfer via surface structure optimization. Furthermore, the elimination of progressive flooding on the surface via the presence of classical gravitational shedding of CB sink droplets ensures the long-term stability of hierarchical condensation when compared to droplet jumping.43,44 Lastly, in the presence of NCGs, the enhanced individual droplet growth rate beneath sink droplets allows further performance enhancement when compared to droplet jumping stemming from the minimization of mass transfer limitations. Durability to Abrasive Wear. The laser-ablated microstructures of the hierarchical surfaces studied here not only enable self-transport of the condensate droplets and increase the overall condensation area but also protect the nanotextures from mechanical abrasion by acting as sacrificial areas during degradation.73,74 In order to test the surface durability, we performed abrasive wear tests of the hierarchical CuO nanoblade surface. To elucidate the role of microstructures, a silane-coated single-tier CuO nanoblade surface was used as a reference. The abrasion wear tests were conducted by exerting a finite pressure (∼550 Pa) onto the test samples and moving the samples facedown back and forth on sandpaper (see Methods). For the single-tier CuO nanoblade surface, both the water droplet apparent advancing contact angle θapp and a decreased as the number of receding contact angle θapp r abrasion test cycles increased (Figure 6a). Specifically, θapp a / θapp r reduced from ∼170°/168° to ∼150°/0° after one abrasion

test cycle. However, the hierarchical surface maintained good app hydrophobicity after four abrasion cycles, with θapp ≈ a /θr 159°/98° (Figure 6b). To investigate the effect of abrasion and its effect on hierarchical condensation, we subsequently reperformed atmospheric vapor condensation experiments on the abraded hierarchical CuO nanoblade surface (see Methods). After abrasive wear, the hilltops of the microstructures were flattened (Figure 6c-I, d-I, and e-I), and the damaged areas exhibited hydrophilicity with condensate droplets wetting the local surface during early stages of condensation (Figure S4; see Section S5, Supporting Information). As condensation proceeded, large droplets formed on the abraded surface (Figure 6c-II, d-II, and e-II) via direct condensation and condensate coalescence. The extent of surface damage was characterized by the shape and area of the microhills at the liquid−solid interface (Figure 6c-III, d-III, and e-III). An irregular outline and large surface area indicated microstructures with severe abrasive wear. The condensation tests revealed that even after three cycles of abrasion wear condensation underneath the large sink droplets still ensued (Figure 6c−e). Although few shaded droplets existed in the flattened hilltop plane for all cases with varying abrasive wear cycles (Figure 6c-III, d-III, and e-III), a considerable number of shaded droplets were observed in the valley areas that were free from mechanical damage (Figure 6c-IV, d-IV, and e-IV), especially for the case of lightly abraded samples (Figure 6cIV). On highly abraded surfaces (Figure 6e), even though sink droplets formed nonspherical morphologies due to contact line pinning, tiny droplets were observed in the narrow valleys (Figure 6e-IV), demonstrating the potential of hierarchical condensation to withstand multiple wear cycles. Surface Structure Design Guidelines. From the results presented thus far, we can identify two key criteria governing sustained hierarchical condensation (Figure 7). The first criterion is that the CB sink droplets residing on the surface should provide enough room underneath it to allow for growth of shaded droplets. To meet this requirement, the surface should have larger-scale microstructures to support the sink droplets, as well as smaller-scale micro/nanostructures to make the CB state preferable.75 The second criterion outlines the need for an efficient removal mechanism to exist for the collection of shaded droplets. If shaded droplets are not collected, the accumulation of condensate will fill the cavities underneath CB sink droplets, as previously observed on square-pillar-patterned silicon substrates where the large CB sink droplet transitioned to the Wenzel state due to coalescence.63,76 The removal of shaded droplets can be partially achieved by shaded coalescence (Figure 7b and e). However, a long-range mechanism is required to remove droplets from the bottom regions that may be far from the sink droplet. Long-range removal can be realized by introducing divergent microcavities, which provide capillary forces for passively driving growing droplets upward along the channels (Figure 7c−e).58,59,61,77,78 Although not observed on our surfaces, shaded droplet pinning and flooding are possible if the local surface has significant adhesion to the shaded droplets. Indeed, microstructured surfaces have shown the possibility of nucleationmediated flooding during condensation. Specifically, on the superhydrophobic surfaces with square micropillars, shaded droplets inside the cavities were shown to coalesce with large sink droplets and were unable to depin from the cavities due to J


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self-transport occurs. Furthermore, the diverging microstructures play an important role in promoting the directional transport and removal of the shaded droplets. As shown in Figure S7, larger diverging angles (or taper angles) of the microstructure will delay droplet self-transport. Microstructures with a small solid fraction are desirable to ensure a large area of shaded condensation, as demonstrated in Figure S5 of the Supporting Information. Furthermore, in terms of the local geometric features of microstructures, bumpshaped hilltops are preferable because the curved hilltops allow for a larger number of small shaded droplets near the hilltops (Figure 2e) when compared to flattened microhill surfaces (Figure 6c−e). Lastly, suitably designed nanoscale features are necessary to ensure excellent mobility of the droplets in the cavities.79 In addition to the nanoblade structures presented here, our previous results showed that CuO nanowires with high aspect ratio also enabled good mobility of shaded droplets due to the preferential nucleation on nanowire tips.74 Given the significant role of sink droplets in hierarchical condensation performance, we note that our previous experimental observations were done on horizontally oriented surfaces, where the condensate droplets accumulated on the surface due to the lack of droplet shedding mechanisms, thus facilitating the efficient formation of shaded droplets. However, to promote hierarchical condensation in practical applications, an ideal condensing surface would not only allow for condensation and droplet self-transport within the microstructures but also enable the prevention of sink droplet removal by coalescence-induced droplet jumping and instead favor gravity-assisted droplet shedding. To test the effectiveness of the hierarchical condensation in a vertical setting with the design guidelines in mind, we fabricated a large-scale (40 × 40 mm) flat plate hierarchical CuO nanoblade surface and studied the coalescence and shedding behavior of sink droplets on the vertically oriented hierarchical surface during condensation of atmospheric water vapor. As a comparison, a flat plate single-tier CuO nanoblade surface having the same macroscale face area was fabricated and used in the condensation experiments. The experimental setup is described elsewhere.80 Briefly, the samples were attached to a Peltier cold stage (TP104SC-mk2000A, Instec) set at 1 ± 0.5 °C, and condensation experiments were done in

Figure 7. Schematic of stable hierarchical condensation. During condensation, small shaded droplets near the hilltop regions (a) nucleate and grow beneath CB sink droplets until they (b) touch the liquid−vapor interface at the base of the sink droplet and are sucked into the sink droplet, after which (c) renucleation and growth of new generations of droplets at the same sites occur. Meanwhile, (d) the growing droplets at the bottom of the microscale valleys climb upward spontaneously along the divergent microcavities with the aid of droplet coalescence and capillary forces, until they (e) reach the sink droplet and coalesce with it, enabling (a) surface clearing and renucleation. Once large enough to be removed by gravity, the sink droplet is removed from the surface and the cycle initiates again. On a rationally designed micro/nanostructured surface, the hierarchical condensation cycle can proceed sustainably.

strong adhesion of the shaded droplets to the cavities and a weak upward capillary force.76 To provide guidelines for the ideal balance between droplet accumulation and removal, we conducted a further force analysis of the droplet during selftransport (see Section S7 of the Supporting Information for modeling details). Our model shows that for cone-shaped cavities with a finite contact angle hysteresis (θa − θr) the droplet will be retained in the cavities until it grows large enough (Figure S7a and b of the Supporting Information). Hence, the contact angle hysteresis of the nanostructures conformally covering the microscale structures should be minimized to ensure a small droplet size above which droplet

Figure 8. Optical images of condensation, coalescence, and shedding of droplets on a vertically oriented (a) hierarchical CuO nanoblade surface and (b) single-tier CuO nanoblade surface. Coalescence-induced jumping of millimeter-scale droplets is identified by the whitedotted circles, and the track of gravitation-induced droplet shedding is identified by the white arrow. Scale bars: 1 mm. For all experimental details and conditions, see Methods. K


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ACS Nano ambient conditions (∼23 ± 1 °C air temperature, 50 ± 5% relative humidity). During early stages of condensation, coalescence-induced droplet jumping was clearly observed on both the hierarchical (t = 0 min, Figure 8a) and single-tier CuO nanoblade surfaces (t = 0 min, Figure 8b), showing no significant difference in average jumping-droplet sizes (∼10 μm). As condensation proceeded, large (2R ≈ 100 μm) droplets accumulated on both surfaces, with a greater number residing on the hierarchical surface (t = 15 min, Figure 8a) compared to that on the single-tier surface (t = 15 min, Figure 8b). All of the large droplets on the vertical hierarchical CuO nanoblade surface remained spherical, with an observable and clear presence of microscale droplets beneath larger sink droplets (Figure S3, see Section S5, Supporting Information). The population of large droplets and the maximum droplet size on the two surfaces continued to grow until condensation reached a steady state (t > 60 min), with the average surface coverage by droplets having 2R > 200 μm being ∼44% on the hierarchical surface (t = 145 min, Figure 8a) and ∼10% for the single-tier surface (t = 145 min, Figure 8b). Interestingly, we observed the coexistence of coalescence-induced jumping and gravity-assisted shedding of millimeter-scale droplets on the hierarchical surface (t = 160 min, Figure 8a), with coalescenceinduced droplet jumping remaining as the dominant condensate removal mechanism on the single-tier surface (t = 160 min, Figure 8b). The observed larger shedding size and greater number density of large droplets on the hierarchical surface resulted from the microstructure-governed increased droplet−surface adhesion compared to the single-tier nanostructures.35 The ability to retain sink droplets along with the large-area fractions of shaded condensation make the asfabricated hierarchical CuO nanoblade surface a desirable surface for hierarchical condensation.

and instead attribute droplet growth results to classical heat and mass transfer physics originating at the top-side liquid− vapor interface of the droplet. In the future, significant attention is needed on the potential and presence of shaded coalescence beneath condensing micro and macroscale droplets, especially on highly nonwetting surfaces, where the potential for micro/nanoscale droplets to reside beneath the contact line exists. In addition, the enhanced growth of the shaded droplets within the microroughness highlights the positive effects of vapor-depletion- and microstructure-confinement-induced local vapor flow on the growth dynamics of shaded droplets. We anticipate that accelerated growth of shaded droplets may not always hold true, as varying microscale geometries defining the space for shaded droplet growth significantly affect growth via vapor transport. In the future, it would be interesting to further examine the specific regimes in terms of surface structure geometry, condensation conditions, and sink droplet size, where shaded condensation is preferable. The design and optimization of the microstructures must take into account the three roles that microstructures play on hierarchical condensation: ensuring CB state formation for sink droplets, facilitating self-transport of droplets nucleating in the cavities, and promoting vapor flow entering the shaded cavities. As a tertiary objective, the microstructures also need to protect the surface in the presence of abrasion, which adds a fourth optimization parameter to be weighed with heat transfer considerations. Although the model developed here articulates the heat transfer advantages of hierarchical condensation in pure vapor conditions, it does not take into account vapor flow physics or the presence of NCGs, a significant hurdle to predicting high-fidelity performance in any atmospheric condensation process. Although the current study demonstrated the benefit of hierarchical condensation for atmospheric water vapor condensation, it would be interesting to apply the knowledge gained here to test the performance of hierarchical surfaces in applications such as dehumidification and atmospheric water capture. Indeed, a plethora of studies exist benchmarking an even larger set of functional surfaces for dew collection. Furthermore, it would be interesting to test hierarchical condensation in pure vapor conditions representative of condensation applications where elevated heat fluxes are present (i.e., heat pipes, vapor chambers, industrial condensers). Although our analytical model captures the key physics of condensation in pure vapor conditions and predicts enhanced condensation rate, nucleation-meditated flooding is still an issue that needs to be addressed.

DISCUSSION Our study casts doubt on previous intuition that large “thermally inactive” condensate droplets are never beneficial and must be avoided at all costs in order to enable enhanced condensation. Indeed, we show here that large droplets, coupled with suitably designed hierarchical surfaces, can in fact enhance condensation heat transfer via shaded coalescence. The hierarchical mode of condensation has the potential to prevent heat transfer degeneration due to the accumulation of large droplets (progressive flooding), which has been observed during jumping-droplet condensation on the superhydrophobic single-tier surfaces.44,76 Furthermore, hierarchical condensation is not as dependent on capillary-inertial hydrodynamics,27,81 which governs droplet jumping and requires extremely low contact angle hysteresis to be maintained on the surface in order to achieve desirable performance.32,40 The observation of shaded droplets has broad implications for the experimental determination of droplet growth dynamics. Unlike droplets on a smooth surface, which contact the surface “seamlessly” and whose growth ensues from the direct condensation and coalescence with neighboring droplets,82 droplets on micro/nanostructured surfaces undergo growth from condensation of shaded droplets located underneath them. Our analytical model shows that shaded condensation may contribute significantly to the heat transfer through a single CB droplet sitting on a micro/nanostructured surface (Figure 5). These results call into question many recent studies of droplet growth dynamics on superhydrophobic surfaces, which do not take into account shaded coalescence

CONCLUSIONS In summary, inspired by the interaction between multiscale droplets on the superhydrophobic surfaces, we propose hierarchical condensation consisting of a synergistic combination of micro/nanostructured roughness with divergent microcavities and large CB state droplets acting as sinks on tops of microstructures. Experimental observation on a superhydrophobic hierarchical CuO nanoblade surface revealed that the growth of the underlying droplets is faster than unshaded droplets, with an elevated droplet growth exponent that is 21% higher. Meanwhile, due to the frequent removal of the shaded droplets in the hilltop regions and the dynamic sweeping by the spontaneous upward transport of the droplets confined in the divergent microcavities, the size distribution of L


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ACS Nano

nL, potential droplet resonance due to the addition of small dispensed droplets, which may introduce a water hammer-type pressure and cause droplet wetting transition, was not present, thus allowing for accurate measurements of contact angle during droplet dispensing. The receding contact angle was measured by stopping dispensing droplets and letting the droplet shrink via evaporation. The advancing and receding contact angles were extracted by a commercial software (FAMAS, Interface Measurements & Analysis System, Kyowa) via the ellipse fit method. Measurements were repeated on 3−5 different locations on the surface to obtain the averaged advancing or receding contact angles. Scanning electron microscopy was performed on a SEM (FEI Quanta 200 FEG) at an imaging voltage of 15 kV. Observation of Condensation Phenomena. Condensation behavior on the fabricated surfaces was observed using a customized top-view microscopy setup consisting of an upright optical microscope (Eclipse LV100, Nikon) coupled to a high-resolution camera (Nikon) for top-view analysis.51 Samples were mounted horizontally on a cold stage (TP104SC-mk2000A, Instec) that was cooled to 5.0 ± 0.5 °C to condense water vapor from the laboratory ambient air having a temperature of 23 ± 1 °C and relative humidity of 50 ± 5% (Roscid Technologies, RO120). Condensation behavior was recorded at 4 frames/s with 10−50× (TU Plan Fluor EPI, Nikon) objectives. Illumination was supplied by an LED light source (SOLA SM II Light Engine, Lumencor). The LED light source was specifically chosen for its high intensity and low power consumption (2.5 W) to minimize heat generation at the surface due to light absorption. Furthermore, by manually reducing the condenser aperture diaphragm opening size and increasing the camera exposure time, we were able to minimize the amount of light energy needed for illumination and hence minimize local heating effects during condensation experiments.40 Side-View Imaging of Droplet Coalescence and SelfTransport. To study the coalescence of the primary droplet with the satellite droplets and to eliminate interference from multiple droplets, we interfaced a high-speed camera (Phantom v711, Vision Research) with the frequency-controlled piezoelectric microgoniometer (MCA-3, Kyowa Interface Science).39 The sample was horizontally placed on a three-axis stage, and the primary and satellite droplets were generated through the piezoelectric dispenser. To simulate droplet self-transport in the microscale cone-like cavities on the hierarchical CuO nanoblade surface, we constructed a V-shaped groove composed of two CuO nanoblade superhydrophobic sidewalls and grew droplets in the groove with the piezoelectric dispenser. The V-groove was vertically aligned on a three-axis stage. The upward transport of the droplets induced by the growing droplet size and droplet coalescence in the V-groove was captured with the high-speed camera. To grow droplets, the piezoelectric dispenser was placed above the CuO superhydrophobic surface or V-groove with a spacing of 5−10 mm and turned on to dispense monodisperse microscale droplets having diameters of ∼30 μm. Droplet dispensing was carried out at 6−7 V, 10−500 Hz, depending on the required growth rate of the droplets. Imaging was performed with a ∼25× magnification lens with a capture rate up to 13 001 fps. Illumination was supplied by an LED source (TSPA22x8, AITECSYSTEM). All experiments were performed in ambient conditions with a temperature of 23 ± 1 °C and relative humidity of 50 ± 5%. Observation of Condensate Shedding Behavior on a Vertical Wall. To study the shedding behavior of sink droplets, a hierarchical CuO nanoblade surface and a single-tier CuO nanoblade surface were mounted on the vertically oriented Peltier cold stage (TP104SC-mk2000A, Instec) with a fixed temperature of 1 ± 0.5 °C. Condensation experiments were performed in ambient conditions with an air temperature of 23 ± 1 °C and relative humidity of 50 ± 5%. The coalescence and shedding dynamics were captured with a camera (AMZT61BASIC, Canon) at ∼10× magnification and 1 fps capture rate. Abrasive Wear Tests. The abrasion wear tests were conducted by exerting a finite pressure onto the test samples and pushing the samples back and forth on sandpaper (2/0 grid Emery polishing paper, 3M) with the testing surface facing the sandpaper. One abrasion cycle consisted of a forward motion followed by a backward

the underlying droplets is biased toward smaller droplet sizes, with ∼70% of the observable droplets having sub-10 μm diameters. The enhanced condensation of shaded droplets is attributed to the lower surface temperature beneath sink droplets, as well as the accelerated vapor flow penetrating into the underlying microcavities. Due to the ability to prevent progressive flooding, hierarchical condensation can fully exploit the microscale roughened surface area for condensation, enabling higher overall heat flux than an equivalent jumpingdroplet-condensation surface with single-tier roughness nanostructures. Furthermore, abrasive wear tests showed that hierarchical condensation has good durability against mechanical damage due to the self-protecting action of the microprotrusions. Our study not only provides insights into a “hidden” aspect of condensation on nonwetting surfaces but also demonstrates a platform for enhancing the efficiency of a plethora of condensation applications, in addition to overcoming the limits of jumping-droplet condensation.

METHODS Surface Fabrication. The single-tier CuO nanoblade surface (Figures 1, 6a, and 8b) was fabricated with the chemical-oxidation method.26 Mirror-finish Cu plates (99.9% purity, McMaster) were first ultrasonically cleaned with acetone for 5 min, rinsed with ethanol, isopropanol, and deionized (DI) water, and dried with nitrogen. To remove the native oxide, the samples were then immersed in a hydrochloric acid solution (HCl, 2M) for 30 s and then rinsed with DI water and dried with a clean nitrogen stream. To synthesize the CuO nanoblade structures, the cleaned samples were then immersed into a hot (96 ± 3 °C) alkaline solution composed of NaClO2, NaOH, Na3PO4·12H2O, and DI water (3.75:5:10:100 wt %). The oxidation process lasted ∼10 min, after which the samples were removed from the solution, rinsed immediately with DI water, and dried with a clean nitrogen stream. To functionalize the surface, heptadecafluorodecyltrimethoxysilane (HTMS) (TCI America, CAS no. 83048-65-1) was deposited using vapor phase deposition. The surface sample was placed in a beaker with a vial of 1 mL of HTMS toluene solution (5% v/v). A lid was placed on top to seal the container, followed by heating in an atmospheric pressure oven (Thermo Scientific, Lindberg Blue M) at 90 ± 5 °C for 3 h. The hierarchical CuO nanoblade surfaces (Figures 2a, 6b−e, and 8a) were fabricated with laser-ablation74,83 and chemical-oxidation. Finely polished Cu plates (99.9% purity, McMaster) were first ultrasonically cleaned with acetone for 5 min, rinsed with ethanol, isopropanol, and DI water, and dried with a clean nitrogen stream. To fabricate microstructures on the Cu substrates, a picosecond laser system (PX100 intelliSCANSe14, Edgewave) was used to ablate the surfaces. The central wavelength, repetition rate, and maximum (100%) power of the laser pulse were 1064 nm, 597.44 kHz, and 65.4 W, respectively. The scanning trajectory of the laser beam was programmable, and scanning was repeated 30 times at a velocity of 3 m/s. A 100 mm field lens was used to focus the laser beam with a laser spot diameter of ∼30 μm. To synthesize CuO nanoblade-like structures on the laser-ablated surface, the chemical-oxidation processes detailed above was employed. Finally, the same functionalization method implemented on the CuO nanoblade surfaces was used to achieve superhydrophobicity of the hierarchical CuO nanoblade surfaces. Surface Characterization. Water contact angles of the surfaces were measured using a piezoelectric microgoniometer (MCA-3, Kyowa Interface Science) with voltage and frequency control. To measure the advancing contact angle, monodisperse water droplets with diameters of 30−40 μm were dispensed by the piezoelectric nozzle operating at 7 V and 30−60 Hz. The droplet on the surface was grown to ∼100 nL by accumulating the dispensed droplets, and the advancing of the droplet contact line was recorded at 1 fps by an integrated camera and custom optics. For droplets smaller than 100 M


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ACS Nano motion with the surface rotating 90° to ensure uniform abrasion. The distance of the one-way abrasion was 10 cm. The pressure exerted by the weight was ∼550 Pa. The sandpaper was placed on a smooth, flat, and horizontal desk, and a ruler with a similar thickness to the samples was used to ensure that the surfaces were only subject to a pushing force parallel to the moving direction. After each abrasion cycle and before contact angle measurements, the samples was cleaned with a nitrogen gas stream for ∼30 s to remove any residue from the surface. The contact angles were averaged among five different spots on the surface.

F.C., and Z.H. also gratefully acknowledge funding support from the National Natural Science Foundation of China (Grant No. 51206092) and National Science and Technology Major Project (ZX06901). X.Y. gratefully acknowledges funding support from China Scholarship Council (Grant No. 201606210181). Laser etching was conducted in the School of Mechanical Engineering, Tsinghua University, with help from Xueqian Zhang, Lei Liu, and Guisheng Zou. Thermal oxidation was done with the help of Gengyu Zhang and Mingfen Wen in the Institute of Nuclear and New Energy Technology, Tsinghua University. Scanning electron microscopy was carried out in the Frederick Seitz Materials Research Laboratory Central Facilities, University of Illinois. N.M. gratefully acknowledges funding support from the International Institute for Carbon Neutral Energy Research (WPI-I2CNER), sponsored by the Japanese Ministry of Education, Culture, Sports, Science, and Technology.

ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acsnano.9b03275. Further details on Videos S1 to S5 (Section S1); calculation of the vapor entering velocity underneath the sink droplet (Section S2); modeling of the heat transfer of hierarchical condensation (Section S3); characterization of the hierarchical surface with microhills (Section S4); condensation on the vertically oriented hierarchical surface and on the abraded surface (Section S5); hierarchical condensation on surfaces with varying microstructures (Section S6); force analysis of the droplets in a diverging cavity (Section S7) (PDF) Video S1: Condensation beneath the sink droplets on the superhydrophobic single-tier CuO nanoblade surface (MP4) Video S2: Coalescence dynamics of a small satellite droplet with a sink droplet (MP4) Video S3: Condensation underneath a sink droplet on the superhydrophobic hierarchical CuO nanoblade surface (MP4) Video S4: Self-transport of a growing droplet in the Vshaped groove (MP4) Video S5: Self-transport and coalescence-induced jumping of droplets in the V-shaped groove (MP4)

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AUTHOR INFORMATION Corresponding Authors

*E-mail: [email protected]. *E-mail: [email protected]. ORCID

Xiao Yan: 0000-0001-9948-3468 Shreyas Chavan: 0000-0001-7338-9393 Nenad Miljkovic: 0000-0002-0866-3680 Author Contributions

X.Y., F.C., and N.M. conceived the initial idea for this research. N.M. guided the work. X.Y., H.L., S.S., L.F., F.C., C.Z., and Z.H. fabricated and characterized the experimental samples. X.Y., H.L., F.Z., and L.F. carried out the condensation experiments. L.L. and S.S. did the surface characterization. X.Y., H.L., F.Z., C.Z., and L.F. analyzed the data. X.Y. and N.M. carried out the theoretical analysis. All the authors were responsible for writing the paper and have given approval to the final version of the manuscript. Notes

The authors declare no competing financial interest.

ACKNOWLEDGMENTS The authors gratefully acknowledge funding support from the National Science Foundation under Award No. 1554249. X.Y., N


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Hierarchical Condensation - ACS Publications - American Chemical

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