Ultrafast water harvesting and transport in hierarchical microchannels

SUPPLEMENTARY INFORMATION Articles https://doi.org/10.1038/s41563-018-0171-9 In the format provided by the authors and unedited. Ultrafast water harvesting and transport in hierarchical microchannels Huawei Chen 1 *, Tong Ran 1, Yang Gan 1, Jiajia Zhou 2, Yi Zhang 1, Liwen Zhang 1, Deyuan Zhang 1 and Lei Jiang 3 * 1 School of Mechanical Engineering and Automation, Beijing Advanced Innovation Center for Biomedical Engineering, Beihang University, Beijing, China. 2 School of Chemistry, Beijing Advanced Innovation Center for Biomedical Engineering, Beihang University, Beijing, China. 3 Laboratory of Bio-inspired Smart Interface Science, Technical Institute of Physics and Chemistry, Chinese Academy of Sciences, Beijing, China. *e-mail: chenhw75@buaa.edu.cn; jianglei@iccas.ac.cn Nature Materials www.nature.com/naturematerials

Supplementary Information For Ultrafast water harvesting and transport in hierarchical micro-channels Huawei CHEN 1 *, Tong RAN 1, Yang GAN 1, Jiajia ZHOU 2, Yi ZHANG 1, Liwen ZHANG 1, Deyuan ZHANG 1, Lei JIANG 3 * 1 School of Mechanical Engineering and Automation, Beijing Advanced Innovation Center for Biomedical Engineering, Beihang University, Beijing 100191, China 2 School of Chemistry, Beihang University, Beijing 100191, China 3 Laboratory of Bio-inspired Smart Interface Science, Technical Institute of Physics and Chemistry, Chinese Academy of Sciences, Beijing100190, China 1

CONTENT Supplementary Video Legends 3 Supplementary Notes - 6 Supplementary Figures 13 Supplementary Tables 28 2

Supplementary Video Legends Supplementary Video 1. Water transport of real trichome in Mode-I. This video shows the water transport process of real trichome in Mode-I. Fine water droplets are originally condensed on the trichome surface and collect together to form several big droplets, i.e. droplet 1~6. The enlarged droplet 4 transports directionally to coalesce with droplet 3 to form a bigger droplet 3+4, and then transports to collect together with droplet 2 and droplet 1 in successive order. The droplet 6 also transports to coalesce with droplet 5, and then transports to coalesce with droplet 1+2+3+4. As the water droplet grows larger to a certain extent (α~48, β~65 ), the harvested water droplet is quickly transported onto the surface of operculum and disappears immediately. Supplementary Video 2. Water transport of real trichome in Mode-II. This video shows the water transport process of real trichome in Mode-II. As the surface of trichome getting thoroughly wet, the succeeding harvested water droplets transport more rapidly and no big droplets appear any more. Supplementary Video 3. Partial enlarged water transport of real trichome in Mode-II. This video is the partial enlarged water transport process of real trichome in Mode-II, for better observing the water transport process in Mode-II. Supplementary Video 4. Water transport of SBS replica. This video shows the water transport process of SBS replica. The SBS (Styreneic Block Copolymers) replicas are fabricated by direct use of real 3

Sarracenia trichome. Being similar to the real trichome, the SBS replicas still possess the superior capability of ultrafast water transport. Supplementary Video 5. Water transport of Smooth SBS trichome replica. This video shows the water transport process of Smooth SBS trichome replica. After the hierarchical surface structure of trichome is smoothened by excessive SBS polymer, the smooth SBS trichome replicas completely lose the ultrafast water transport capability, demonstrating that the ultrafast water transport capability is greatly dependent on the hierarchical structure of trichome. Supplementary Video 6. Fluorescent video of water transport Mode-I in hierarchical micro-channels. This video shows the water transport Mode-I in hierarchical micro-channels under the fluorescent light microscope. Transport velocity gradient appears during the water droplets filling the dry hierarchical micro-channels, and in general the water transport along the step minor base micro-channel (base front filling) is much faster than that along the normal minor base micro-channel (base following filling). After that, the water begins to spread along the major micro-channel (top major filling) and flow upon the low ribs, which is always behind the base front filling and the base following filling. It is noted that the advancing meniscus of filling appears concave shape in all these processes of filling. Supplementary Video 7. Top major filling in Mode-I and succeeding transport in Mode-II. video shows the comparison of top major filling in Mode-I and succeeding transport in Mode-II. The It is obvious that, after the hierarchical micro-channels are totally wet, water will slide upon the water thin film (succeeding transport) even without any solid-liquid contact, leading to much faster water transport than 4

top major filling in Mode-I. Furthermore, the shape of advancing meniscus changes from concave in Mode-I to convex in Mode-II. Supplementary Video 8. Water transport Mode-II in hierarchical micro-channels and smooth microchannels. The video shows the comparison of water transport Mode-II in hierarchical micro-channels and smooth micro-channels. It can be observed that the velocity of water transport in hierarchical microchannels is faster than that in smooth micro-channels. Furthermore, by the influence of low ribs, the advancing meniscus of water transport in hierarchical micro-channels appears two frontiers. Supplementary Video 9. Dimethyl silicone oil transport in hierarchical micro-channels. The video shows the transport process of dimethyl silicone oil in hierarchical micro-channels, and the play speed of the video is accelerated by 4 times. It can be seen that, apart from water, this unique hierarchical structure can also transport other liquids. 5

Supplementary Notes Supplementary Note 1. Further analysis for Mode-I The number of low ribs between two neighboring high ribs is denoted by n. Supplementary Figure 8a is a brief model for the experiments with n = 3 shown in Fig. 4a. The structural parameters are set to h = 0.4a, H = a and θ = 10. It is noted that for simplify the calculation, the curve lines shown in section images in Supplementary Figure 8 is regarded as straight lines. According to Lucas-Washburn and Onsager principle, the free energy of the system is written as A = 2(d 1 d 3 ) [ (a + h + H)γcosθ + a 2 + (H h) 2 γ] +(d 2 d 3 )[ (a + 2h)γcosθ + aγ] +d 3 [ (5a + 4h + 2H)γcosθ + 5aγ] = (2A 1 d 1 + A 2 d 2 + A 3 d 3 )γ (S1) With A 1 = (a + h + H)cosθ a 2 + (H h) 2 A 2 = (a + 2h)cosθ a A 3 = [2H + (2n + 1)a + 2nh]cosθ (2n + 1)a (S2) (S3) (S4) The total dissipation is Φ = 1 η 2 a 2 [2β 1S 1 (d 1 d 3 )d 1 2 + β 2 S 2 (d 2 d 3 )d 2 2 d 3 + β 3 (2S S 1 d 1 + S 2 d 2 + S d 3) 2 ] (S5) 1 With S 1 = 1 2 a(h + H), S 2 = ah (S6) S 3 = (2n + 1)aH nah, S = S 3 2S 1 (n 1)S 2 (S7) 6

β 1 = 20.682, β 2 = 36.396 (S8) here S i is the cross-section area of each channel, and β i is the dimensionless flow resistance. β 3 depends on n. The dimensionless flow resistance β i is calculated following the method in Ref. [29]. We briefly explain the calculation in the following. Assuming that the flow velocity is almost onedimensional, the z-component (flow direction) is much larger than those in the other two directions: v = (0,0, u(x, y)). The flow velocity satisfies the Stokes equation η 2 v = p η ( d2 u dx 2 + d2 u dp dy2) = dz (S9) Defining a dimensionless velocity with a characteristic length a, u = ηu a 2 ( dp dz ) (S10) Then the Stokes equation becomes a Poisson equation d 2 u dx 2 + d2 u dy 2 = 1 with the boundary condition u = 0 at the no-slip surfaces, and n u = 0 at the free surfaces. (S11) The dimensionless flow resistance is given by β i = u 1 (S12) The evolution equations are coupled first-order differential equations δr δd 1 δr δd 2 = 2A 1 γ + 2η a 2 [β 1S 1 (d 1 d 3 )d 1 + β 3 d 3 S 1 S 3 (2S 1 d 1 + (n 1)S 2 d 2 + S d 3)] = 0 = 1(n 1)A 2 γ + (n 1) η a 2 [β 2S 2 (d 2 d 3 )d 2 + β 3 d 3 S 2 S 3 (2S 1 d 1 + (n 1)S 2 d 2 + S d 3)] = 0 δr = 2A γ + η δd 3 a 2 [β S 3d 3 (2S S 1 d 1 + (n 1)S 2 d 2 + S d 3)] = 0 3 The solutions have a general form of 7

d 1 = D 1 aγ η t, d 2 = D 2 aγ η t, d 3 = D 3 aγ η t (S13) These results are in a set of algebra equations β 1 S 1(D 1 D 3 )D 1 = A 1 S 1 S A (S14) β 2 S 2(D 2 D 3 )D 2 = A 2 S 2 S A (S15) S β 3 D 3 [2S 1D 1 + (n 1)S 2D 2 + S D 3 ] = A (S16) S 3 Using the experimental values, we can calculate the imbibition dynamics. The numerical results are shown in Supplementary Table 1. On basis of Eq. S13, the water transport velocity of base front filling d 1, base following filling d 2 and top major filling d 3 can be presented as d 1 = 1 2 D 1 aγ ηt, d 2 = 1 2 D 2 aγ ηt, d 3 = 1 2 D 3 aγ ηt (S17) where D 1, D 2, D 3 are constants with calculated values shown in Supplementary Table 1. The numerical results clearly demonstrate that the base front filling is the fastest, followed by the base following filling, and the top major filling is the slowest. Supplementary Note 2. Further analysis for Mode-II (1) Time scales of liquid coalescence and liquid propagation in Mode-II The liquid coalescence generally includes two continuous processes. One is the air layer draining after the liquid droplets contacts, and the other is the coalescence of two water layers. Then the time scale of 8

liquid coalescence is the sum of the time scales of both two processes. When tiny water droplets contact with water thin film, coalescence will not happen immediately due to the existence of thin air layer between two water layers 31. The time scale of air layer draining τ γ can be given as τ γ = ρ(h h) 3 /γ 1.92 10 5 s (S18) where ρ is the density of water, H is the height of high ribs, h is the height of low ribs, and γ is the interfacial tension between vapor and liquid. Only after the air layer between two water layers is drained off, these two water layers begin to coalesce 32. Then, the time scale of the coalescence of the two water layers τ D can be given as τ D = h 2 /D water 1.74 10 1 s (S19) where D water is diffusion coefficient of water. On basis of the experiments of water transport shown in Fig. 4d, the time scale of liquid propagation τ can be provided by τ = H/v 4.55 10 3 s (S20) where v is the average velocity of succeeding transport. By comparing the time scale of liquid propagation with that of liquid coalescence, we can get τ 4.55 10 3 s < τ γ + τ D 1.74 10 1 s (S21) It is clear that the time scale of liquid coalescence is longer than that of liquid propagation in Mode-II, which means that the succeeding tiny water droplets prefer to slip upon the water thin film kept inside the hierarchical micro-channels rather than coalesce with it at the very beginning. 9

(2) Analysis for succeeding transport in Mode-II Supplementary Figure 8b is a brief model for the experiments shown in Fig. 4d. The free energy is written as A = d 3 a[ 2ε H/h γcosθ nγ(cosθ 1)] (S22) where ε H/h = (H h)/a. The dissipation can be written as Φ = 1 η 2 a 2 β (s) 3 S (s) 3 d 3 d 3 (S23) where β 3 (s) (taken into consideration of slippage) is shown in Supplementary Table 2, and S 3 (s) = ε H/h 2na 2. The evolution equation is given by δr = 2aε H/h γcosθ naγ(cosθ 1) + 1 η δd 3 2 a 2 β (s) (s) 3 S3 d3 d 3 = 0 (S24) The solution is d (s) (s) aγ 3 = D 3 η t, D (s) 3 = 2ε H/hcosθ + n(cosθ 1) (s) (S25) nε H/h β 3 The numerical results for D 3 (s) are shown in Supplementary Table 2, which is larger than D 3. 10

(3) Analysis for viscous force of succeeding transport With slippage happening, the viscous force which is resistance to succeeding transport is related to the slip length b s. For the model shown in Supplementary Figure 8b, b s indicates the thickness of water thin film from slippage line along normal direction. According to Navier slip law, the viscous force at a specific thickness b s can be presented by F v = 8πη (1 + 4b 2 d (s) (s) 3 d 3 s a ) (S26) We can see that F v declines with increase of b s. For experiments shown in Fig. 4d, the water thin film kept inside the minor base micro-channel is thicker than that covered the edge of major micro-channel. Then the viscous force near the edge of major micro-channel must be larger than other places, resulting in the shape of advancing meniscus change from concave in Mode-I to convex in Mode-II. Supplementary Note 3. Analysis for the flux of hierarchical micro-channels shown in Fig. 3d For Mode-I, the base front filling and base following filling are dominantly to wet the micro-channels in advance. The water transport is mainly attributed by top major filling and the flux can be given by Q = d 3 S = 1 2 D 3S aγ ηt (S27) where S is summation of the cross-section area of total flux. For Mode-II, the flux can be presented by Q (s) (s) = d 3 S = 1 2 D (s) 3 S aγ ηt (S28) We use D 3 S and D (s) 3 S as flux ratio coefficient to compare two parts of flux. To investigate the effect of high-low ribs on flux, the flux of hierarchical micro-channels shown in Fig. 3d is obtained as shown in Supplementary Figure 10a on basis of Eq. S27-S28. It can be seen that the flux 11

in Mode-II is larger than that in Mode-I. Supplementary Note 4. Principle of design the hierarchical micro-channels In case the width of ribs and channels are same respectively, according to Eq. S25 and Eq. S28, the effect of height of high ribs on flux in Mode-II is shown in Supplementary Figure 10b. We can see when θ is fixed, the increase of ε H/h leads to the increase of flux in Mode-II. It means that increasing the height of high ribs is an effective way to enhance flux in Mode-II. Of course, low ribs should have a certain height to remain liquid thin film for slippage happening. The flux along the hierarchical micro-channels with n = 2~3 is maximal. Then 2 or 3 low ribs between two neighboring high ribs are another choice for creative design. In case the width of ribs and channels are same respectively, on basis of Eq. S25 and Eq. S28, the effect of Young equilibrium contact angle θ on flux with n = 2 is shown in Supplementary Figure 10c. The decline of θ leads to the increase of flux in Mode-II, which means that increasing the hydrophilicity can also enhance the flux. 12

Supplementary Figures Supplementary Figure 1. Water transport process on real trichome. Here, white arrows stand for direction of water droplet transport along the dry trichome, blue arrows stand for wet trichome surface after these water droplets sliding through, green arrows stand for specific transport of a single droplet. (a) -(f) are process of water transport Mode-I, and (g) is process of water transport Mode-II. (a) Transport process of harvested droplet 4. (b) Transport process of droplet 3+4. (c) Transport process of droplet 2+3+4. 13

(d) Transport process of droplet 6. (e) Transport process of droplet 5+6. (f) Transport process of droplet 1+2+3+4+5+6. As this droplet becomes larger to a maximum extent (α~48, β~65 ), it is quickly transported and disappears immediately. (g) Ultrafast transport process of tiny droplet 1 in Mode-II. Sometimes, the tiny droplets appear along the wet trichome in the duration of ultrafast water transport. 14

Supplementary Figure 2. Water transport process on real trichome in Mode-II. (a-c) The enlarged images show the screenshot of a tiny water droplet sliding through the trichome. The solid red line marks the initial position of the droplet, and the dotted red lines mark the positions of the droplet after sliding at certain time. (d) The tiny droplet in (a-c) is taken out to piece together, and the yellow dotted lines mark the slicing position of the images. These images show positions of the tiny droplet at certain time interval, 0.01 s and 0.02 s respectively. 15

Supplementary Figure 3. Water transport process and surface appearance of SBS replicas and smoothen SBS replicas. The white arrows in (a)-(b) stand for direction of droplets transport along dry SBS replicas, the blue arrows in (a)-(b) stand for wet trichome surface after these water droplets sliding through, the green arrows in (c) mark three specific droplets on surface of the smoothen SBS replicas. (a) Water transport process of SBS replicas in Mode-I. The process is just the same as that of the real trichome, but the velocity of water transport is slightly slower. The water droplet grows to a certain extent with α = ~78, β = ~89 and disappears quickly. (b) Water transport process of SBS replicas in Mode-II. 16

The yellow arrows mark the dynamic process of tiny droplets near bottom. After the trichome surface becomes thoroughly wet, only a tiny droplet near the bottom with periodical changing can be observed. The tiny droplet grows to certain extent (α is less than ~25, β is less than ~20 ), then disappears quickly. Although the water transport process is not completely as same as the real trichome, the water transport of SBS replicas in Mode-II (~6000 μm/s) is much faster than in Mode-I (~300 μm/s). (a) and (b) can be seen in Supplementary Video 4. (c) Water transport process of SBS replicas smoothen by excessive SBS polymer. The water harvested process is totally changed, lots of big droplets condense on surface without ultrafast directional transport. This process can be seen in Supplementary Video 5. (d) SEM image of SBS replicas. The structure is generally as same as the real one. (e) SEM image of SBS replicas smoothen by excessive SBS polymer. The hierarchical micro-channels are covered, and its surface becomes smooth. 17

Supplementary Figure 4. Statistics of trichome through images of frozen section. (a) SEM image of a whole Sarracenia trichome. (b) SEM images of frozen section of trichome and partial enlarged details. (c) Statistics chart of trichome structure. The diameter of the trichome gradually increases from the tip to 18

the bottom. Ribs near tip are uniform with the height from ~0.6 μm to ~0.8 μm, and the width from ~0.4 μm to ~0.6 μm. At the diameter of ~40 μm, about 1/3 length of the trichome from tip, the ribs become nonuniform, then high-low ribs appear. The height of high ribs gradually increases from ~0.8 μm to ~1.1 μm, and the width increases from ~0.6 μm to ~1.0 μm. With the diameter of the trichome increasing, the width of low ribs has a slight increasing, and the height of low ribs gradually declines from ~0.4 μm to ~0.3 μm. More importantly, the width of minor micro-channels which are formed by two neighboring ribs gradually declines from the tip to the bottom of trichome. 19

Supplementary Figure 5. Water transport velocity variation depending on different parameters. (a) Water transport velocity variation obtained from Fig. 3b-c. (b) Water transport velocity variation obtained from Fig. 3d. It is noted that the velocity of major filling in (b) is faster than that calculated by Fig. 4a. The velocities of major filling in (b) are the average velocity of water transport along the whole microchannels. According to Eq. 1, the velocity of water transport can be presented by d i = 1 D 2 i aγ, which ηt means that with the time t increasing, the velocity of water transport gradually decreases. And with the time t increasing, the distance of water transport increases, so it can also be considered that the farther away from the water reservoir, the lower the velocity of water transport is. The fluorescence images in Fig. 4a can only be recorded at 25fps by normal digital camera. In order to obtain high-quality images, the enlarged part of micro-channels shown in Fig. 4a is far away from the water reservoir, making the velocity of water transport lower than that in (b). (c) Contact angle variation of water on the flat PDMS 20

surface with time after oxygen plasma treatment. When the oxygen plasma treated sample is put in the air, the contact angle of the surface gradually increases over time. (d) Water transport velocity variation over time after oxygen plasma treatment for micro-channels with n = 3. It is noted that with the increase of contact angle, the transport velocities of base front filling, base following filling and top major filling generally decline. Especially at about 15 minutes after the oxygen plasma treatment, the top major filling of water almost stops if no more water droplets are continuously poured. It should be noted that because the water droplets are poured at the center of the cubic water reservoirs, the water droplets tend to contact the middle micro-channels and then the water spreading appear distinct in Fig. 3b-c. 21

Supplementary Figure 6. Water transport in hierarchical micro-channels in Mode-I. (a) The water transport along the step minor micro-channel (base front filling, marked by red dotted line) is much faster than that along the normal minor micro-channel (base following filling, marked by white dotted line). It is noted that the concave shape of liquid advancing meniscus in base following filling is larger than that in base front filling. (b) After the minor base micro-channels are full wet by base front filling and base following filling, the water spreads along the major micro-channel (top major filling). The shape of advancing meniscus is also concave in top major filling. Here, the yellow dotted lines are used to mark the advancing meniscus. 22

Supplementary Figure 7. Water transport models of real trichome. (a) Stage-I: Fine droplets are dispersedly harvested on the trichome surface and their sizes gradually grow in the moisture air. Stage-II: With the continuous progress of harvesting, many condensed droplets collect together to form larger ones and then transport directionally from tip to bottom of the needle-shaped trichome to form water thin film (Mode-I). Stage-III: After water thin film forms upon the hierarchical micro-channels, succeeding water slides upon the thin film (Mode-II). Then the water transport becomes faster and no more big droplets appear. (b-c) Partial enlarged process of water transport in Stage-II. In this stage, the hierarchical microchannels are dry, and the water transport mode is same with Mode-I. During water harvesting and transport on the dry hierarchical micro-channels, water filling the minor base micro-channel (marked by 23

Base Front Filling and Base Following Filling) is always ahead of filling major micro-channel (Marked by Top Major Filling), and transport velocity gradient distinctly appears. (d) Water transport on the thin film in Stage-III. With the hierarchical micro-channels becoming thoroughly wet, a water thin film forms upon the hierarchical micro-channels which is marked by Succeeding Transport, and then the water transport mode turns to Mode-II, i.e. sliding on liquid thin film. The Succeeding Transport sliding upon the water thin film becomes ultrafast without appearance of any big droplets. Furthermore, the shape of advancing meniscus changes from concave in Mode-I (dry) to convex in Mode-II (wet). Indeed, sometimes tiny water droplets appear due to Rayleigh instability during the ultrafast transport along the wet trichome. In order to make clear the transport mechanism, blue color is used to mark the liquid of Mode-I, light green is used to mark the liquid of Mode-II, and red arrows are used to mark the transport direction of harvested droplets. And the yellow dotted lines are used to mark the advancing meniscus. 24

Supplementary Figure 8. Schematic models of water transport in two different modes. (a) Model of water transport Mode-I. Transport velocity gradient is defined by transport distance where d 1, d 2 and d 3 refer to that along the step minor base micro-channel, the normal minor base micro-channel and major micro-channel respectively. (b) Model of water transport Mode-II. d 3 (s) indicates the transport distance along the major micro-channel in Mode-II. 25

Supplementary Figure 9. Long-distance succeeding transport of Mode-II in PMMA hierarchical micro-channels. (a) Optical images of PMMA hierarchical micro-channels. The PMMA hierarchical micro-channels which has only one major micro-channel with 3 low ribs inside is fabricated by micromilling method. A-A is the cross-section image of the PMMA hierarchical micro-channels. The width of the water reservoir w is 700 μm, the height of the water reservoir H is 58 μm, the height of the low ribs h is 24 μm, and the width of low ribs a is set to 100 μm due to the diameter limit of milling tool. (b) Long-distance succeeding transport of Mode-II in PMMA hierarchical micro-channels and partial enlarged details of the convex shaped advancing meniscus with two liquid frontiers. It can be seen that the advancing meniscus with two liquid frontiers of succeeding transport keeps identical along the longdistance micro-channels, demonstrating that the succeeding transport indeed slips upon the water thin film. 26

Supplementary Figure 10. Flux of hierarchical micro-channels with different parameters. (a) Flux in Mode-I and Mode-II of hierarchical micro-channels. On basis of calculated flux of hierarchical microchannels with ε H/h = 0.6 in both two modes, it is clear that the flux on wet hierarchical micro-channels (Mode-II) also becomes larger than the flux on dry micro-channels (Mode-I). Especially the maximum flux appears as n = 2 where n is the number of low ribs between two neighboring high ribs. The number of low ribs n = 2 perfectly lies among low ribs characteristics of trichome n = 1~5 which is marked by Character of trichome. (b) The effect of ε H/h on flux in Mode-II with θ = 10. The increase of ε H/h leads to the increase of flux in Mode-II, and for n = 2~3, the flux is maximal. (c) The effect of Young equilibrium contact angle θ on flux in Mode-II with n = 2. The increase of θ leads to the increase of flux in Mode-II. 27

Supplementary Tables Supplementary Table 1 Numerical results for Mode-I of hierarchical channels n β 3 D 1 D 2 D 3 1 9.446 0.331-0.120 2 8.185 0.322 0.269 0.085 3 7.727 0.316 0.262 0.067 4 7.472 0.312 0.256 0.055 5 7.328 0.308 0.253 0.047 6 7.230 0.306 0.249 0.040 7 7.162 0.303 0.247 0.034 8 7.105 0.301 0.245 0.030 9 7.066 0.299 0.243 0.027 10 7.027 0.298 0.241 0.023 28

Supplementary Table 2 Numerical results for Mode-II of hierarchical channels n β 3 D 3 β 3 (s) D 3 (s) D 3 (s) : D 3 1 9.446 0.120 7.565 0.414 3.455 2 8.185 0.085 6.641 0.340 4.014 3 7.727 0.067 6.307 0.293 4.374 4 7.472 0.055 6.132 0.260 4.693 5 7.328 0.047 6.031 0.236 5.020 6 7.230 0.040 5.962 0.217 5.367 7 7.162 0.034 5.914 0.201 5.750 8 7.105 0.030 5.873 0.188 6.174 9 7.066 0.027 5.848 0.177 6.659 10 7.027 0.023 5.820 0.168 7.210 29