Wetting Transition at a Threshold Surfactant Concentration of

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Wetting Transition at a Threshold Surfactant Concentration of Evaporating Sessile Droplets on a Patterned Surface Xin Zhong, Junheng Ren, Karen Siew-Ling Chong, Kian Soo Ong, and Fei Duan Langmuir, Just Accepted Manuscript • DOI: 10.1021/acs.langmuir.9b00170 • Publication Date (Web): 13 Mar 2019 Downloaded from http://pubs.acs.org on March 17, 2019

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Wetting Transition at a Threshold Surfactant Concentration of Evaporating Sessile Droplets on a Patterned Surface Xin Zhong,†,‡ Junheng Ren,† Karen Siew-Ling Chong,¶ Kian-Soo Ong,¶ and Fei Duan∗,† †School of Mechanical and Aerospace Engineering, Nanyang Technological University, 50 Nanyang Avenue, Singapore 639798, Singapore ‡State Key Laboratory of Multiphase Flow in Power Engineering, Xi’an Jiaotong University, Xi’an 710049, PR China ¶Institute of Materials Research and Engineering, A∗Star, 2 Fusionopolis Way, Innovis, Level 9, Singapore 138634, Singapore E-mail: [email protected]

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Abstract Wetting transitions induced by varying the components in solution of a drying droplet can lead to its evolving shape on a textured surface. It can provide new insights in liquid pattern control through manipulating droplet solutions. We show the pronounced transitions of wetting for surfactant solution droplets drying on a micropyramid-patterned surface. At low initial surfactant concentrations, the droplet maintains an octagonal shape to the end of drying. At intermediate initial surfactant concentrations, the early octagon spreads to a square, which later evolves to a stretched rectangle.

At high initial surfactant concentrations, the droplet mainly exhibits

the “octagon-to-square” transition, and the square shape is kept to the end. The “octagon-to-square” transition occurs at similar temporal volume-averaged surfactant concentrations for the various initial surfactant concentrations. It results from the dependence of the surface energy change of spread over the micropyramid structure on the temporal volume-averaged surfactant concentration. At high initial surfactant concentrations, the accumulation of surfactant near the contact line driven by outward flows could raise the local viscosity and enhance the pinning effect, leading to the great suppression of the “square-to-rectangle” transition.

Keywords: Wetting transition, evaporation, surfactant, sessile droplet, patterned surface.

Introduction In the liquid-based fabrications of smart and functional materials, the wetting shape of a solution can serve as a template in which insoluble solutes deposit to a replicate layered morphology, hierarchical structures, or line-shaped contours. 1–4 Substantial progress has been achieved in controlling circular depositions from drying sessile droplets on smooth and homogeneous surfaces. 5–9 Non-circular depositions, such as polygons, have received much less attention because such droplet shapes have to be produced on surfaces with topographic and/or chemical heterogeneities. Difficulties exist in the designing of a proper 2


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surface structure for producing a predetermined wetting shape, while the surface fabrication further complicates the process. Recent attempts have been made to address the issues, prompted by the importance of attaining desired wetting areas particularly for droplet-based printing/coating techniques. Great efforts have been devoted to improving the understanding of wetting dynamics and to regulating the liquid profiles on the patterned surfaces. 10–13 Raj et al. probed the contact line dynamics during the advancing and receding of a droplet on a chemically heterogeneous surface. It was found that the advancing contact angle was insensitive to the chemical defects, whereas the relative portion of the distorted three-phase line to the contact area determined the receding contact angle. 14 Kumar and Raj modeled the dynamics of an advancing contact line on a surface with topographic pillar arrays. By adding liquid to the droplet, the contact line zipping enabled the droplet to evolve from a polygon to a square. 15 On the other hand, by allowing the droplet to evolve freely, Courbin et al. obtained various final wetting shapes, namely circle, square, hexagon and octagon by using different liquids on a topographical surface. 16,17 Similarly, Raj et al. indicated that the droplet shapes could be tuned to display square, rectangle, hexagon, octagon, and dodecagon in a high resolution manner by designing topographic or chemical heterogeneity on the substrate. 18 Apart from the polygonal wetting shapes, Jokinen et al. demonstrated that olive oil, a non-volatile liquid, precisely displayed a predetermined text fashion by integrating geometric pinning with the lithographic chemistry patterning. 19 It is worth noticing that, since most liquids adopted to investigate the wetting shapes were mono-component, the evaporation or dissolution of the solution could induce the contact line depinning and the loss of an early wetting profile. The recent study of Peng et al. demonstrated that the droplet morphology kept evolving along with the dissolution of the droplet on an immersed surface with the chemical patterns. 20 Furthermore, it is costly and time-consuming to modulate the wetting conditions through tailoring the substrate surface structure one by one. In addition, the spontaneous wetting transitions have been found in the droplets of

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complex solutions evaporating on the smooth and homogeneous surfaces.

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In a multi-

component droplet, for instance, each component evaporates with a particular rate due to the difference on volatility, so the solution composition will keep changing with evaporation. Meanwhile, each component can distribute non-uniformly along the droplet interface and give rise to solutal Marangoni flows. These phenomena could lead to an imbalance of the droplet and a possible change in the wetting condition. Wetting transitions were reported to occur in the alcoholic droplets, 21 saline droplets, 22 surfactant solution droplets, 23,24 etc. Tan et al. showed that in an evaporating Ouzo droplet (water-ethanol-anise oil), as the ethanol concentration declined rapidly and an oil ring formed at the droplet perimeter, the droplet depinned and lost its spherical profile. 21 In a sodium chloride solution droplet, the saline solution was concentrating with the water drying, and the increases in both liquid-vapor and solid-liquid surface tensions made the droplet recede till the precipitation emerged. 22 Besides, in a surfactant solution droplet containing microspheres, the non-uniform distribution of surfactant along the liquid-vapor interface resulted in multiple Marangoni eddies which prevented most microspheres from reaching the contact line, and thus leading to the contact line depinning at the late stage. 23 The transport of surfactant to the bare solidvapor interface across the contact line can also lead to droplet retraction. 24 The Marangoni flows of complex solution droplets can even enable the migration of them, in addition to the wetting transitions. 25,26 The wetting transition generated in the solution droplet by varying the components normally leads to isotropic contraction or expansion of the circular wetting area on a homogenous substrate. On an ordered patterning surface, such a wetting transition could be anisotropically directed or confined to become a new profile. We therefore are enlightened to integrate the evaporation of a complex solution droplet with an ordered topographic surface to explore if the wetting transition could be induced to make the former wetting shape different. Of the same importance, we aim at revealing how the spontaneous wetting transition is initiated on a structured surface by the varying solution. In this study, we

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investigate the evolution of surfactant solution droplets drying on a micropyramid-patterned surface, and disclose two types of wetting transition which respectively makes the early octagonal profile develop to a square and a rough rectangle. Interestingly, the octagonto-square transition emerges at similar temporal volume-averaged surfactant concentrations for the various initial surfactant concentrations. The understanding of the polygonal shape transition at a threshold can be a universal mechanism for exploring the wetting dynamics of other diverse systems of complex liquids on patterned surfaces, particularly as the surface structure is not strictly vertically-uniform. The enriched knowledge could open a new approach to develop various liquid patterns on a same surface structure by exploiting the evaporation-induced change in the multi-component liquids.

Experimental Methods The surfactant solutions were prepared by dissolving cetyltrimethylammonium bromide (CTAB) powders (Sigma-Aldrich, ≥99%, CMC=0.92 mM (20∼25 ◦ C)) in the nano-filtered water (Milli-Q, resistivity: 18.2 MΩ-cm). The initial surfactant concentration, C0 , was set at 0.00 mM, 0.04 mM, 0.08 mM, 0.4 mM, 0.8 mM, or 1.0 mM. The droplets with a volume at 0.3±0.04 μL were generated by a micropipette (Thermo Fisher Scientific). The drying processes of the droplets were simultaneously captured by a microscope (Nikon Eclipse LV100ND) at 1 fps from a top view and two HiSpec-2 high-speed cameras at 1 fps from side views. The directions of the two side views are in parallel with the side and the diagonal lines of a micropyramid bottom area, and are indicated as line-of-sight “” and line-of-sight “ ”, respectively. The droplet side profile captured along line-of-sight “ ” was non-spherical but exhibited a “bell” shape whose contact angle could be hardly determined. 27 Therefore we used the contact angle captured along line-of-sight “” in this study unless otherwise indicated. The contact angle was measured by the program ImageJ. 28 The droplet lifetime varied from around 6.5 min to 10.2 min in the current experiments with the different values of

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C0 , affected by the evolutions of the wetting areas and the temporal solution concentration. To probe the internal flow of the surfactant solution droplet, the fluorescent function of the microscope with Particle Image Velocimetry (PIV) technique was applied. The droplet with C0 at 0.8 mM was seeded with 1 μm fluorescent microspheres (Life Technologies) such that the concentration of fluorescent microspheres was 0.01 vol %. The droplet was visualized by the microscope with the focal plane 30 μm above the micropyramid bottom. The flow field of the fluorescent droplet was then analyzed by Davis 8.0 with the time interval at 0.25 s for every image pair. The droplets were evaporating in a static atmosphere with the surrounding temperature and humidity maintained at 22±1 ◦ C and 55±2%. After the evaporation was completed, the height of surfactant residuals in the vicinity of the contact line was measured by a confocal microscope (DCM8, Leica Microsystems). To ensure experimental reliability, we repeated the experiment for at least five times for each C0 with the repeated tests indicated with the experiment number (E.N.). The poly(methyl methacrylate) (PMMA) substrates were patterned with micropyramid islands using the nanoimprint lithography. The PMMA was imprinted with a nickel shim mold at a temperature of 140 ◦ C and a pressure of 20 bar for 10 min using an Eitre 6 nanoimprinter (Obducat) so that the polymer could fill up the cavities of the nickel shim mold. The demolding was done at 50 ◦ C. The micropyramid geometries were characterized by the central height h = 13 μm, side length d = 30 μm and edge length l = 23.9 μm. Each substrate was cleaned prior to tests to remove contaminants by rinsing under deionized water (Milli-Q), and blowing to dry with the compressed nitrogen gas.

Results and Discussion Effect of Initial Surfactant Concentrations on Droplet Evolutions The droplets with the different initial surfactant concentration values for C0 all exhibit an octagonal profile once they are placed on the patterned substrate surface (see Figure 1). The 6


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initial octagonal profile is more inequilateral at a higher C0 , such that it is almost a square with the four corners cut at high values of C0 (0.8 mM and 1.0 mM). 27 The liquid-vapor surface tension γLV and the solid-liquid surface tension γSL are lower at a higher surfactant concentration, they consequently enable the droplet to wet a larger area. The spreading, occurring until the droplet reaches the initial equilibrium state, is balanced with the viscous force, ηU x/h, for unit length of contact line, in which η is the liquid viscosity, U as the wetting velocity, and x is the quantity of lateral wetting displacement. 29 Along line-of-sight “”, the viscous force for one row wetting, namely from the current apex to the next apex of a micropyramid, is expressed as ηU d/h. Along line-of-sight “ ”, the viscous force for one row wetting, namely from the current apex to the corner of a micropyramid, is scaled as √ 2ηU d/2h. This smaller viscous force allows the droplet to spread more along line-of-sight “ ”. The enhancement in spreading at a higher C0 therefore promotes the inequilateral degree of the droplet profile. The droplet evolution throughout the evaporation varies greatly against C0 , as shown in Figure 1 and Supplementary Video SI. As 0 mM< C0 ≤ 0.08 mM, the droplet maintains an early octagonal shape to the end of drying, and it is indicated as the “octagon-remained” mode. As 0.08 mM < C0 < 0.8 mM, the initial octagonal droplet spreads along line-of-sight “ ” until it becomes a square. Figure 1 (c, d) demonstrates that the transition toward a square is finished at around 0.52tf and 0.18tf for the droplets with C0 at 0.40 mM and 0.80 mM respectively. Such a process is characterized as the “octagon-to-square” transition. Later the completed square advances solely along line-of-sight “”. It makes the square droplet elongate to an irregular rectangle, which is indicated as the “square-to-rectangle” transition. As C0 ≥ 0.8 mM, the “octagon-to-square” transition also occurs from the beginning of evaporation. The upcoming “square-to-rectangle” transition, however, emerges for only the limited rows of posts, allowing the square wetting profile to be preserved to the very end. The repeated tests with C0 at 0.08 mM reveal that the droplets mainly exhibit the “octagon-remained” mode, but the spread along line-of-sight “ ” also occurs occasionally

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so that the droplet follows the “octagon-to-square” transition and evolves to an incomplete square. Such the inconsistent evolution results suggest that C0 at 0.08 mM might be a critical concentration beyond which the drying schema altered from “octagon-remained” to “octagon-to-square”. Similarly, C0 at 0.8 mM is the other critical concentration beyond which the “square-to-rectangle” transition is greatly suppressed. The repeated experiments show that, after the “octagon-to-square” transition is completed, both limited (for most cases) and unlimited “square-to-rectangle” takes place as C0 was 0.8 mM. It makes the droplet develop to either a square or an irregular rectangle. (a) 0.00 mM 0.05tf

(b) 0.08 mM 0.05tf

(c) 0.40 mM 0.00tf

0.50tf

0.50tf

0.52tf

0.90tf

0.90tf

=

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(d) 0.80 mM 0.01tf

(e) 1.00 mM 0.01tf

< octagon-to-square

0.18tf

0.13tf

0.98tf

0.98tf

squrare-to-rectangle

0.98tf

Figure 1: Drying sequences of the droplets as the initial surfactant concentration C0 is (a) 0.00 mM, (b) 0.08 mM, (c) 0.40 mM, (d) 0.80 mM and (e) 1.00 mM (see Supplementary Video SI). The symbols shown in the first snapshot of (a) 0.00 mM indicate the two line-ofsight directions respectively. tf is defined as the droplet lifetime. The scale bar indicates 200 μm. The distinctly different droplet evolutions at the different values of C0 , as presented in Figure 1, are resulting from the different combinations of the three drying schemas: “octagonremained” mode, “octagon-to-square” transition and “square-to-rectangle” transition. In other words, whether and when the two latter transitions occur determine the way that the wetting profile of the surfactant solution droplet advances. Therefore, we aim at uncovering the mechanism for the emergence of the two transitions by focusing on the droplet dynamics in conjunction with the surfactant effects at the onsets of both transitions. 8


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Initiation of “octagon-to-square” and “square-to-rectangle” transitions The droplet evolutions shown in Figure 1 demonstrate that once the spread along line-ofsight “ ” begins, the “octagon-to-square” transition is initiated. Similarly, the beginning of spread along line-of-sight “” indicates the onset of “square-to-rectangle” transition. The moments when “octagon-to-square” and “square-to-rectangle” transitions begin are denoted as tO−S and tS−R respectively, which are normalized to droplet lifetime tf and plotted in Figure 2 (a). It is shown that the “octagon-to-square” transition occurs always prior to the “square-to-rectangle” transition at different C0 , suggesting that the spread along line-of-sight “ ” takes place before that along line-of-sight “”. Moreover, both transitions occur earlier at a higher C0 . The “octagon-to-square” transition begins at nearly 90% of the droplet lifetime as C0 is 0.08 mM. As C0 is ten times higher (0.8 mM), such transition appears at the very beginning. The “square-to-rectangle” transition exhibits a similar trend that it is shifted from 0.8tf to 0.2tf upon raising C0 from 0.2 mM to 0.8 mM. As a result, the dynamic contact angles, θO−S and θS−R respectively measured at tO−S and tS−R , are larger at a higher C0 , as presented in Figure 2 (b). The large difference on the contact angles at the transitionary moments implies that both transitions are insensitive to the dynamic contact angle. On the other hand, the two transitions are brought in advance upon increasing the initial surfactant concentration, suggesting that they can be more relevant to the surfactant effects. To verify the supposition, we plot the dynamic surfactant concentration, Ct , at the onsets of the “octagon-to-square” and the “square-to-rectangle” transitions for the different values of C0 , which are respectively indicated as CO−S and CS−R shown in Figure 2 (c). It is notably herein that CO−S is obtained for C0 ranging from 0.08 mM to 0.4 mM in which the “octagon-to-square” transition is induced by the condensing solution. The cases for C0 at 0.8 mM and 1.0 mM are not included since the “octagon-to-square” transition takes place at the beginning of drying and thus these two concentrations might have exceeded the 9


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tO-S tS-R

t/tf

0.8

0.4

1.2

C0 0.08 mM C0 0.8 mM

C0 0.2 mM C0 0.2 mM

C0 0.4 mM C0 0.4 mM

(c)

“CS-R”

Ct (mM)

1.0

0.0 (a) 100 (b) ș (deg)

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0.8 “CO-S”

60

0.6 șO-S șS-R

20

0.2

0.4 0.6 0.8 C0 (mM)

1.0

1

3

5

E.N.

7

9

11

Figure 2: (a) The time for tO−S and tS−R at the beginning of the “octagon-to-square” and the “square-to-rectangle” transitions, normalized to the droplet lifetime tf , as a function of the initial surfactant concentration, C0 . (b) The dynamic contact angle for θO−S and θS−R versus the initial surfactant concentration C0 measured at tO−S and tS−R respectively. (c) The temporal volume-averaged surfactant concentration for CO−S and CS−R , at the beginning of the “octagon-to-square” and “square-to-rectangle” transitions respectively at various initial surfactant concentrations from the repeated experiments numbered with E.N.. real CO−S . Likewise, CS−R is obtained for C0 ranging from 0.2 mM to 0.8 mM, in which the “square-to-rectangle” transition appears during the evaporation. Interestingly, both the transitions occur within a relatively narrow range of the temporal volume-averaged surfactant concentration for different C0 . Figure 2 (c) shows that the “octagon-to-square” transition is initiated at CO−S of 0.62±0.065 mM, and that the “square-to-rectangle” begins at CS−R of 0.94±0.061 mM, where the errors are the standard deviations from repeated tests. The droplet with a lower C0 therefore has to undergo a longer time for the solution to concentrate to the threshold of the transition. Herein, Ct indicates the temporal concentration which is averaged throughout the droplet volume at each moment. Ct is obtained from Ct =

C0 V 0 , Vt

where V0 is the initial volume and Vt is the droplet volume at time t. The time-dependent droplet volume is integrated on the basis of either an octagonal or a rectangular wetting area for the sessile droplets. Please refer to Supplementary SII for the details. The similar threshold surfactant concentrations for the different values of C0 and the 10


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emerging sequence of “octagon-to-square” prior to “square-to-rectangle” are resulting from the different surface energy changes along lines-of-sight “ ” and “” during the spread over the micropyramid structure. The surface energy changes are analyzed by extending the theory used for hemiwicking in the rectangular grooves. 29 Herein we consider the spreading along both line-of-sight directions from the current row to the next row of micropyramids, and the surface energy change indicates the difference between the surface energies at the two quasi-steady states. In respect to the spread along line-of-sight “ ”, Figure 3 (a1) presents the liquid invasion of one row of micropyramids from t to t + 35 s, while Figure 3 (b1, c1) schematically shows the intersection manner of the contact line, 2l in length, with a micropyramid prior to and after the spontaneous invasion. As the contact line, confined in the two dashed lines (see Figure 3 (b1, c1)), moves forward to the next row of posts, the solid-liquid interfacial energy is increased by 4SΔ γSL , and the solid-vapor interfacial energy is reduced by 4SΔ γSV , where SΔ is the area of a triangular side of a micropyramid, and γSV is the solid-vapor surface tension. Before the spreading, the liquid-vapor interface is approximately half the micropyramid bottom area as denoted by the triangular area “ABC”. It is increased to roughly the area “ABDEC” once the one row wetting is finished. So the liquid-vapor interfacial energy is increased by d2 γLV . As a result, the amount of change ΔE of the surface energy, E , for unit length of contact line is written as

ΔE =

4SΔ γSL − 4SΔ γSV + d2 γLV 2l

To reach the next row of micropyramids, the contact line has to proceed

(1) √

2 d, 2

thus the

surface energy change Δe for unit distance of liquid propagation along line-of-sight “ ” can be expressed as

√ Δe =

2 (4SΔ γSL − 4SΔ γSV + d2 γLV ) 2 dl

(2)

In respect to the spreading along line-of-sight “”, Figure 3 (a2) shows the liquid invasion of one row of micropyramids from t to t + 5 s. Here we consider the same long contact line 11


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ts

t+27 s

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t+35 s

(a1) C

A

C

A S¨ȖSV

S¨ȖSL

E B

B

D d ¥2

/2

(b1) ts

(c1) t+5 s

t+3 s

(a2) S¨ȖSL

S¨ȖSV

d

(b2)

(c2)

Figure 3: (a1) Snapshots taken at t, t + 27, and t + 35 s indicating an actual spread to the next row of micropyramids along the diagonal line-of-sight. (b1, c1) Schematic illustration √ of a part of the contact line to proceed 2d/2 to the next row of micropyramids along the diagonal line-of-sight to indicate the status before and after the spread. (a2) Snapshots taken at t, t + 3, and t + 5 s indicating an actual spread to the next row of micropyramids along the parallel line-of-sight. (b2, c2) Schematic illustration of a part of the contact line to proceed d to the next row of micropyramids along parallel line-of-sight to indicate the status before and after the spread.

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(2l) intersecting one micropyramid, shown by the contact line confined in the two dashed lines in Figure 3 (b2, c2). The surface energy change, ΔE , for unit length contact line to reach the next row of posts can be expressed as

ΔE =

4SΔ γSL − 4SΔ γSV + d2 γLV 2l

(3)

As seen from Figure 3 (b2, c2), the contact line has to proceed d to the next micropyramid row, thus the surface energy change, Δe , for unit distance of the spread along line-of-sight “” is Δe =

1 (4SΔ γSL − 4SΔ γSV + d2 γLV ) 2 dl

(4)

ΔE is equivalent to ΔE , indicating that the surface energy change after one row wetting is the same from lines-of-sight “ ” and “”. However, due to the different distance for the contact line to reach the next row of posts along the two line-of-sight directions, the respective surface energy change for unit length of spreading is non-identical, and their relation is written as Δe =

√

2Δe

(5)

The expressions of Δe and Δe indicate that they decrease upon decreasing γLV and γSL , or alternatively, upon increasing the surfactant concentration, as shown in Figure 4. It is suggested that both Δe and Δe keep decreasing along with the evaporation of the surfactant solution droplets. The data for γLV , γSL and γSV employed to calculate Δe and Δe are extracted from Ref. 31 for the CTAB solution droplets on the PMMA surface. Most importantly, from the inset of Figure 4, we can see Δe and Δe decrease to be negative as the surfactant concentration increases to 0.76 mM. It is suggested that the spread could be √ triggered along both line-of-sight directions. Since Δe decreases 2 times as fast as Δe , the spread is more likely to occur along line-of-sight “ ”. It is consistent with the fact that the “octagon-to-square” transition takes place ahead of the “square-to-rectangle” transition. On the one hand, the predicted threshold surfactant concentration of 0.76 mM is higher 13


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Wetting Transition at a Threshold Surfactant Concentration of

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