Efficient Collection of Oil Microdroplets by Hyperbranched, Space‐Filling Open Microfluidic Channels

Open microfluidic channels, which capture and transport liquid on flat substrate surfaces through wettability contrast, offer a promising platform for the analysis, mixing, separation, etc. of small‐volume liquid samples. This study focuses on the development of open microfluidic channels featuring oleophilic/oleophobic micropatterning in a hyperbranched, space‐filling structure, thereby creating high‐density channels. These newly designed channels allow for the swift collection of microdroplets with low surface tension within less than 10 s through hierarchical transport and merging of the microdroplets within the channel. The collection efficiency reaches 66% in the channel with the optimized channel geometry. These results underscore the effectiveness of this method for the collection of low surface tension microdroplets, paving the way for the advancement in the domain of open microfluidics of oil, a field that has yet to be fully explored.


Introduction
[3] These devices, termed "open microfluidic channels," offer benefits like ease of fabrication and the flexibility to introduce analytical samples at any desired point.In addition to continuous liquid, individual small droplets in the order of tens of micrometers to millimeters can also be transported on open microfluidic channels.Various mechanisms have been used to drive droplet transport, such as electrowetting, [4] Marangoni effect, [5] and alternating current electric field. [6]A common method to realize open microfluidic channels that capture and transport aqueous droplets is to pattern DOI: 10.1002/admi.202300340 the surface with wettability contrast between hydrophilic and hydrophobic areas.On a narrow hydrophilic strip surrounded by the hydrophobic surface, an aqueous droplet is confined in the hydrophilic strip.When the hydrophilic strip has a width gradient, the width of the droplet at the front is larger than that of the tail, resulting in to larger radius of curvature at the front than the tail of the droplet.This results in a gradient in Laplace pressure along the direction of the channel.Consequently, this pressure imbalance propels the droplet unidirectionally from the channel's narrower side to its wider side. [7]hile open microfluidics for high surface tension solutions, such as aqueous ones, is extensively researched, creating similar systems for low surface tension liquids like oils poses more challenges.These systems, albeit less explored, can prove invaluable for analyses and synthesis in low surface tension liquid, recovery of oil mist from air for environmental monitoring and air purification, etc.To create wettability contrast for low surface tension liquids, oleophobic (i.e., oil repelling) and oleophilic (i.e., wetting with oil) areas need to be patterned on the same substrate.The wettability of a solid surface by liquid is determined by two factors: surface tension and surface roughness. [8,9]Wettability of liquid on a flat solid surface is modeled by Young's equation, cos  = where  is a contact angle,  S is the surface tension of solid,  L is the surface tension of liquid, and  SL is the interfacial tension of liquid and solid.The surface tensions of solid and liquid are largely determined by their chemical compositions, and the surface tension of solid can be lowered by surface modification with oleophobic molecules such as fluorinated compounds.However, low surface tension liquid with small  L leads to a small contact angle, and flat surfaces can only achieve moderate oleophobicity.14] Seeger's research group developed a silicone nanofilament (SNF) coating on a glass surface through the hydrolysis of trichloromethylsilane (TCMS).This process forms a microscopically rough structure. [15]On the surface of this rough structure, 1H,1H,2H,2H-perfluorooctyltrichlorosilane (PFOTS), an oleophobic fluorinated compound, was reacted to make a superoleophobic surface. [16]Furthermore, the group demonstrated a patterning method to differentiate superoleophobic and superoleophilic areas by utilizing silicon grease to mask portions of the substrate. [17][20][21][22] Megaridis' group, for instance, employed laser engraving on a superoleophobic surface to create superoleophilic channels for the transport of low surface tension liquids. [18,19]egarding the mode of transport, besides linear transport of aqueous droplets on a single tapered channel, studies have reported the collection of aqueous microdroplets or fog by merging multiple microdroplets at one location on a wettabilitypatterned surface featuring branching patterns. [23,24]In our previous work, we developed "space-filling open microfluidic channels", composed of hierarchically branching patterns. [25,26] superhydrophobic surface was prepared by a mixed coating of titanium oxide nanoparticles and fluoroacrylate polymer.Irradiation with ultraviolet light on this coating transforms it to be superhydrophilic, and therefore, wettability patterning is easily done by photolithography.The fractal-like branching design enabled efficient water microdroplet collection.When water microdroplets were sprayed, the collection efficiency of water from 1.7 cm 2 area reached 74% within a single second.
Despite these advancements, efficient collection of low surface tension liquids by open microfluidics from a wide area of surface beyond simple linear transport has not been reported.The ability to achieve this could dramatically broaden microfluidics applications for such liquids.Microdroplet mixing in open microfluidic channels holds potential for enhancing microdroplet reactions, many of which can be conducted in organic solvents of low surface tension.These reactions are gaining interest because they are reported to proceed differently than bulk reactions.Past research on microdroplets primarily involved the mixing of aerosols in the gas phase to facilitate these reactions. [27]he design of space-filling open microfluidic channels could offer improved efficiency and more precise control over microdroplet mixing.In the present study, we introduce the spacefilling open microfluidic channels designed to capture, transport directionally, and collect microdroplets of low surface tension liquid (Figure 1).Utilizing finely patterned surfaces with SNFs and PFOTS-modified SNFs, we constructed these channels on a glass substrate.We demonstrate the capture and transport of hexadecane, a low surface tension liquid, by spraying it in microdroplet form.This demonstrates the effectiveness of the spacefilling structures in collecting microdroplets of low surface tension liquids.

Fabrication of Wettability Patterned Surfaces
To fabricate open microfluidic channels suited for low surface tension liquids, we first prepared the oleophilic surface by SNFs with a microscopic roughness according to the literature method. [16]Furthermore, oleophobic patterning of the substrate by selective treatment of SNFs with PFOTS was conducted by a photolithography process to impart wettability contrast to form open microfluidic channels (Figure 2a).In the optical microscopy image of the fabricated substrate, the slight image contrast showed that a regular pattern of the space-filling channel was formed with high fidelity (Figure 2b).Scanning electron microscopy (SEM) images of the fabricated substrates revealed that the resulting surface had rough surface structures for both the intact SNFs and the PFOTS-modified SNFs, although the area with PFOTS-modified SNFs was discernible by the difference of brightness in the image (Figure 2c).The wettability of the surface before and after the coating with PFOTS was evaluated by contact angle measurement using droplets of water, diiodomethane, and hexadecane (Table 1; Figure S1, Supporting Information).Hexadecane spread on the area coated with intact SNFs, which made a contact angle too low to measure (<5°), while the contact angle of hexadecane on the area with PFOTS-modified SNFs was 107 ± 4°.Contact angles of the substrate surfaces with the photolithographic patterning were comparable to those without the photolithographic patterning.This result indicated that the pho-Table 1. Contact angles for droplets of various liquids on an SNF-coated oleophilic surface and an SNF/PFOTS-coated oleophobic surface, both with and without lithographic patterning.For each condition, five measurements using 10 μL droplets were taken.Presented are the mean values and their 95% confidence intervals.tolithographic process did not significantly affect the wettability of SNFs and PFOTS treatment of SNFs.
The fabricated substrate was transparent, and reusable after washing with organic solvent and air drying because the silicone nanofilaments are chemically bound to the glass surface.The contact angles were stable after repeated applications and cleaning of the substates.The transparency and reusability are desirable properties for applications of the wettability patterned substrates.

Transport of Oil Droplets on Single Open Microfluidic Channels with a Width Gradient
To assess the transport efficiency of the channels patterned by wettability, single tapered open microfluidic channels without branches were fabricated with various taper angles, , and their droplet transport behaviors were investigated.When a droplet of hexadecane of 3, 5, or 7 μL was introduced on the channel, the liquid rapidly spread toward the wider end of the channel (Figure 3a,b).The coordinate of the front of the liquid was plotted against time after the deposition of the droplet.We observed that channels with larger taper angles exhibited faster transport speeds, and the difference between  = 3°and 5°was significant (Figure 3c).This trend can possibly be attributed to the fact that channels with larger  have larger Laplace pressure imbalance along the channel. [7]In contrast, the effect of the droplet volume on the transport speed was not significant (Figure 3d).These results suggested that, for this range of droplet volumes, the deposited droplet works as a reservoir to supply liquid to the channel, while keeping the bulge of the droplet at the initially deposited position.Therefore, the transport velocity of the liquid front on the channel is not affected by the volume of the deposited droplet.

Geometric Design of Space-Filling Channel Structures
To collect microdroplets efficiently, we designed space-filling structures with hierarchical branching.A space-filling tree can be systematically generated by recursively dividing a triangle or rectangle and connecting centroids by line segments. [28]In this study, we adopted a regular hexagon as the shape to fill that was modified from triangles used in our previous study. [25]The hexagon was split into six regular triangles, and space-filling trees were drawn in each of these six triangles.The centroids of the hexagon and each triangle were connected by line segments.Each line segment was then given a tapered shape to create a channel for droplet transport.Note that this algorithm to construct a spacefilling channel is applicable to an arbitrary convex polygon by dividing it into triangles and filling each triangle (Figure S2, Supporting Information). [29]To examine the effect of channel geometry on droplet collection efficiency, two geometric parameters for the channels were varied: the generation number, G, which determines the number of repeated branching, and the taper angle, , which determines the shape of each channel segment (Figure 4a,b).To understand how these parameters affect the density of the channel, distances were calculated for all points in the oleophobic region and their respective nearest oleophilic channel segments (Figure 4c).The increase of the generation number leads to dramatic decrease of the distances between points on the oleophobic surface and their nearest oleophilic channel segments (Figure 4d, left).The mean and maximum distances decrease exponentially with respect to the generation number (Figure 4e, left).In contrast, the taper angle has little effect on the distance (Figure 4d,e, right).The shorter mean distance of the channel with higher generation number is expected to be advantageous for efficient capture of microdroplets that are sprayed on the substrate surface.The oleophilic channel area on the substrate surface and its ratio to the substrate surface (bounding hexagon) were calculated from the geometry (Figure 4f).The oleophilic channel area increases linearly with respect to the generation number and taper angle.For the channel with (G, ) = (7, 7°), the mean distance from the channel is 0.256 mm and area ratio of the channel is 27.8%.
Overall, these fractal space-filling tree structures have desirable properties for enabling the efficient capture and transport of microdroplets while keeping small fraction of the oleophilic area.

Collection of Oil Droplets on the Space-Filling Open Microfluidic Channels
Microdroplets of hexadecane were sprayed on the channels, and the distribution of droplets after spraying was recorded by a digital microscope.Upon spraying oil droplets on the surface of the substrate, the large blob of hexadecane was observed at the center of the channel (Figure 5a,c), which indicated transport and accumulation of microdroplets of hexadecane.In stark contrast to hexadecane, when microdroplets of water were sprayed on the channel, only a slight degree of capture of droplets on the channel was observed, and no transport of droplets occurred (Figure 5b).Both the channel and surroundings are similarly hydrophobic and there is little wettability contrast for water, which gives virtually no capillary force that drives water droplets on the surface.
The volume of collected hexadecane was quantitatively evaluated by measuring the geometric shape of the blob of collected liquid on the center of the channels.Although there are some variations between measurements probably due to the variation of sizes and spatial distribution of microdroplets that are inher-ent in spraying, monotonical increase in the collected volume for increased sprayed volume after repeated spraying intervals was consistently observed (Figure 5d,e).Numerical simulations were performed to calculate the equilibrium shapes of liquids of various volumes on the channel with a simple branching channel pattern (G, ) = (2, 7°) using the hybrid energy minimization method (Figure S3, Supporting Information). [30]As a result, regardless of the volume of the liquid, the liquid remained in the center and did not spread to the periphery, which suggested that the branching channels can concentrate droplets at the center efficiently.
Upon closer examination of the profiles, there was a noticeable delay in the onset of the collected volume.This delay was equivalent to a few microliters of sprayed volume.Following this delay, the collected volume showed a linear increase corresponding to the increase in the sprayed volume.Based on this observation, the plots of the sprayed volume, v S , over the collected volume, v C , were fitted to the equation, v c = 0 (for 0 < v s < v 0 ), m(v s − v 0 ) (for v 0 < v s ) to determine the parameters v 0 and m (Figure 5f,g).v 0 decreased from 6.3 ± 1.0 μL (95% confidence interval) to 3.7 ± 0.7 μL with the increase of G from 4 to 7 (Figure 5f, left), whereas v 0 remained largely unchanged with the change of  (Figure 5f, right).In contrast, m showed a different trend with respect to G and .The change of m for the increasing G was not significant (Figure 5g, left).In contrast, when  was increased, m increased significantly from 0.40 ± 0.08 for (G, ) = (7, 3°) to 0.83 ± 0.08 for (G, ) = (7, 5°) and plateaued then (Figure 5g, right).
The collection efficiency, which is defined as the collected volume divided by the sprayed volume, reached 66% ± 9% (95% confidence interval) at the sprayed volume of 20 μL for the channel with (G, ) = (7, 7°).This collection efficiency was significantly higher than the area fraction of the channel (28%, Figure 4f), which suggests that microdroplets can be efficiently captured into the oleophilic channel even if the contact area of microdroplets on the substrate surface only have a partial overlap with the channel.

Transport Dynamics on the Channels
Although the variation in collected volume is large, observed general trends for various channel geometries give insight into the transport dynamics and collection mechanism of hexadecane in the channel.When a dry channel is initially sprayed with microdroplets of hexadecane, the microdroplets are randomly distributed on the substrate surface and some of the microdroplets merge into larger ones.When the microdroplets become large enough, the microdroplets are captured at the oleophobic channel, and they begin to be transported on the channel.This threshold of sprayed volume, which determines v 0 , is smaller for denser channels having shorter mean distances with higher G. Regarding m, the channel with  = 3°showed significantly lower value of m, which means the channel of  = 3°did not transport microdroplets of hexadecane with sufficient efficiency.The coalescence of microdroplets into larger droplets before transport suggests that the channel's collection efficiency might be robust to variations in the initial sizes of the sprayed microdroplets.
To further understand the transport dynamics of oil droplets on the channels, video microscopy was conducted during repeated 100 ms pulses of microdroplet spraying (Figure 6;Supplemental Movie 1-3, Supporting Information).When microdroplets were sprayed, some of them were immediately (<25 ms, video frame interval) incorporated into the oleophilic channel to wet the channel (Figure 6a, red dashed arrow), and others adhered to the oleophobic substrate (white arrow).After accumulation of microdroplets on the oleophobic surface, they merged into stationary blobs, and within ten seconds, they were absorbed into the oleophilic channel (Figure 6b).
The sizes of blobs observed on the substrate were dependent on channel geometries.Relatively small blobs with ≈30-60 μm in diameter were observed in the channel with (G, ) = (4, 5°), while larger blobs with more than 100 μm in diameter were observed in the channel with (G, ) = (7, 3°) (Figure 6c).In highdensity channels of (G, ) = (7, 3°), sprayed oil microdroplets were easily captured by the oleophilic channels and quickly merged into larger blobs during transport in the branching channels.
When channels with the same G value but different  values were compared, many blobs larger than 100 μm in diameter adhered to the substrate with the channel with (G, ) = (7, 3°), while the blobs were effectively transported away toward the center with the channel with (G, ) = (7, 7°), leaving less significant residue on the substrate.These results suggested the narrower segments of the branching channel with (G, ) = (7, 3°) cannot efficiently transport oil droplets above ≈100 μm in diameter, while the channel with (G, ) = (7, 7°) did not impede such transport.As shown in the results for the single tapered channels (Figure 3), the droplet transport at  = 3°is slower than at  = 5°and 7°, and the accumulation of microdroplets occurs too fast at the branching points near the periphery.As a result, large blobs were formed near the periphery before they were transported toward the center, and they were too large to be transported on the channel.This led to significant increase in droplet collection efficiency of (G, ) = (7, 7°) compared to (G, ) = (7, 3°).
When one considers practical application of the present work, saturation in droplet collection can be an important problem.It should be noted that upon repeated spraying on the channel with a time interval, even after droplets were collected at the center of the channel, subsequent spraying led to further accumulation (Figure 6d).This result, along with collection volume measurement in Figure 5d,e, suggested that the efficiency of oil microdroplet transport and collection in our system remains largely unhindered by previous accumulation at the center of the channel up to a certain volume.In addition, there is the possibility of incorporating a drainage mechanism by capillary action into the open microfluidic channel to address concerns about saturation and achieve continuous operation of the system, which is a topic for future study.

Conclusion
In the present study, we successfully demonstrated the effectiveness of using fractal, space-filling designs of open microfluidic channels with oleophobic/oleophilic patterning for the lateral transport and collection of microdroplets of low surface tension liquid.By varying the geometric parameters of the spacefilling patterns, we were able to optimize the droplet collection efficiency to reach 66 ± 9%.This result highlights the effectiveness of fractal, hyperbranched space-filling designs of the channels for oil microdroplet collection.Our study will open new possibilities for low surface tension liquids as media for open microfluidics, a research area that has not been extensively explored.The space-filling open microfluidic channels in the present work could benefit practical applications to the recovery of oil microdroplets from air for environmental monitoring and air purification as well as a unique platform for microdroplet reactions in low surface tension organic solvent.
Preparation of the Oleophobic Surface: Glass slides (26 mm × 76 mm, 1.0-1.2mm thickness, Matsunami Glass Ind., Ltd., S1127) were cleaned by sonication in ethanol for 5 min and the surface was activated by lowpressure air plasma (Yamato Scientific Co., Ltd., PR200, 150 mL min −1 air, 200 W) for 5 min.The glass slides were immersed in toluene solution (80 mL) of TCMS (62.5 μL) for 6 h at room temperature.The fabricated substrate was rinsed with toluene and ethanol followed by drying with a stream of nitrogen to obtain the glass substrate coated with SNFs.The resulting substrate was again activated by air plasma for 5 min and placed at room temperature under reduced pressure for 24 h in the presence of PFOTS (174.4 μL) and powder of calcium chloride as a desiccant.As a result, the oleophobic coating was obtained.
Fabrication of the Open Microfluidic Channels: The SNF-coated glass slide was heated at 110 °C for 10 min to dry the surface.Positive photoresist (AZ 5214E) was coated on the SNF-coated glass slide by spin coating (500 rpm for 5 s followed by 2,000 rpm for 20 s).The coated substrate was pre-baked at 110 °C for 2 min.The substrate was then exposed with UV light (12 mW cm −2 , 20 s) through a photomask with space-filling , or single taper patterns.The exposed substrate was developed by 2.38% aqueous solution of tetramethylammonium hydroxide for 50 s, followed by rinsing with water for 30 s, and dried by a stream of nitrogen.The developed substrate was further activated by low-pressure air plasma for 5 min and treated with PFOTS as above.Finally, the photoresist was lifted off using N-methyl-2-pyrrolidone for 30-60 min at 80 °C, rinsed with acetone and ethanol, and dried to obtain the wettability-patterned substrate.The fabricated substrates were observed by scanning electron microscopy.
Contact Angle Measurement: Contact angles of droplets on the substrate surface were measured by dropping 10 μL of liquid on the substrate.The side view images of a droplets were captured by an upright digital microscope (Leica DMS-1000) with a right-angle prism mirror placed on the side of the substrate and droplet.The digital images were then analyzed using ImageJ software.The contact angles were calculated by the /2 method [31] where the droplet shape was assumed to be a part of a sphere (Figure S1, Supporting Information).The contact diameter of the three-phase contact circle, R, and the height of the droplet, h, were measured on the ImageJ software.The contact angle, , was calculated by the equation,  = 2 arctan 2h R .Five measurements for each condition were conducted to obtain mean values and confidence intervals.
Transport of a Droplet on the Single Tapered Channel: Single tapered channels were fabricated by photolithography as above.3, 5, or 7 μL of droplets were deposited on the fabricated channel by a micropipette, and the motion of the droplet was recorded by a CMOS digital camera (STC-MCS241U3V, OMRON SENTECH CO., LTD.) equipped with a magnification lens (VSZ-0745, VS Technology Corporation).The coordinate of the front of the liquid bulge was then tracked.
Collection of Droplets on the Space-Filling Open Microfluidic Channels: Microdroplets of hexadecane were sprayed on the open microfluidic channels using a spray nozzle (Everoy, MMA 50) with 0.025 MPa air pressure for 100 ms from ≈25 cm above.The sprayed volume was calculated by the increase in weight after spraying.After spraying, the side view image of a liquid blob at the center of the channel (the root of branching) was captured by a CMOS digital camera (STC-MCS241U3V) equipped with a magnification lens (VSZ-0745).The blob shape observed from the side was then fitted to a Bezier curve and approximated as a solid of revolution to calculate the volume.Spraying was repeated multiple times and the sprayed volume and collected volume were measured each time.A total of six repeat measurements of two samples were conducted for each channel design.The profile of the collected volume, v C , against the sprayed volume, v S , was fitted to the equation, v c = 0 (for 0 < v s < v 0 ), m(v s − v 0 ) (for v 0 < v s ), with v 0 and m as parameters using the SciPy package in Python.Video microscopy was performed using the same camera and lens as above at a frame rate of 40.2 s −1 under adequate illumination by LED lights.Oil microdroplets were sprayed on the channel using a spray nozzle (Everoy, MMA 50) with 0.025 MPa air pressure for 100 ms, and spraying was repeated five times with a 5 s or 30 s interval.
Numerical Simulation of Equilibrium Droplet Shape on the Space-Filling Open Microfluidic Channels: A numerical simulation was conducted using the HyDro Droplet Simulator Software. [30]A hemispherical droplet of hexadecane (density: 0.77 g cm −3 , surface tension: 27 mN m −1 ) was placed at the center of the channel with (G, ) = (2, 7°) and a mesh size of 10 μm, and the droplet shape was iteratively optimized until the system reached energy minimum.The volume of the droplet was varied and simulations were performed for each.

Figure 1 .
Figure 1.a) A schematic of space-filling open microfluidic channels designed for low surface tension liquid collection.b) An enlarged diagram showing the capture and transport of microdroplets via the oleophilic channel on the oleophobic surface.c) Surface modification of silicone nanofilaments (SNFs) using 1H,1H,2H,2H-perfluorooctyltrichlorosilane (PFOTS) to form surfaces with oleophilic/oleophobic wettability patterns.

Figure 2 .
Figure 2. a) The fabrication process for the wettability-patterned open microfluidic channels.b) An optical microscopy image of the fabricated substrate.c) The scanning electron microscopy (SEM) images of the fabricated substrates.

Figure 3 .
Figure 3. Directional transport of hexadecane on single tapered open microfluidic channels.a,b) The top and side views of the movement of a 5 μL hexadecane droplet on channels with different taper angles:  = 3°, 5°, and 7°.c) The trajectory of the liquid front for a 5 μL hexadecane droplet on channels with  = 3°(blue), 5°(orange), and 7°(green) plotted over time.d) The trajectory of the liquid front for hexadecane droplets of 3 μL (blue), 5 μL (orange), and 7 μL (green) on channels with  = 5°.The line plots denote the mean value at each time point, with the filled bands indicating the standard error based on six repeated measurements across two samples.

Figure 4 .
Figure 4. Designs of space-filling channel structures and their geometric properties.a,b) Structures with different G values and  values .The blue areas indicate oleophilic channels, while the white background represents an oleophobic surface.c,d) Distribution maps showing the distance between a point on the substrate surface and the nearest channel segment for different G values with  = 5°, and for different  values with G = 7 .e) Graphs indicating the maximum (blue) and mean (orange) distances for different G values with  = 5°(left) and various  values with G = 7 (right).f) The areas of the oleophilic channels and their respective ratios to the area of the bounding hexagon for different G values with  = 5°(left) and different  values with G = 7 (right).

Figure 5 .
Figure 5. Collection of hexadecane microdroplets by the space-filling open microfluidic channels.a,b) Photographs of the open microfluidic channel after spraying microdroplets of a) hexadecane and b) water stained with methylene blue .c) Photographs of the accumulated hexadecane for different G and  values.The sprayed volume was 12 μL.Scale bar: 5 mm.d,e) Plots showing the relationship between sprayed and collected volumes for different d) G and e)  values.Six repeat measurements were taken from two samples for each condition.f,g) Estimated parameters of the fitted lines for different G and  values: f) v 0 and g) m.Error bars represent a 95% confidence interval.

Figure 6 .
Figure 6.Dynamics of oil droplet transport on the channels observed by video microscopy.a) Snapshot images of the surface of the channel with (G, ) = (7, 7°) immediately after microdroplet spraying.Red dashed arrows and white arrows indicate droplets incorporated in the oleophilic channel and those adhering to the oleophobic substrate, respectively.The geometry in the top left indicates the arrangement of the channel segments in the imaged region.b) Intake and transport of droplets on the channel with (G, ) = (7, 7°).Blue dashed arrows indicate droplets being incorporated into the oleophilic channel.c) Droplets on the channels with different geometries after the 4th spraying.d) Droplets on the channels after repeated spraying on the channel with (G, ) = (7, 7°).