Eutectic Gallium-Indium (EGaIn): A Liquid Metal Alloy for the Formation of Stable Structures in Microchannels at Room Temperature

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1 Advanced Functional Material Supporting Information for: Eutectic Gallium-Indium (EGaIn): A Liquid Metal Alloy for the Formation of Stable Structure in Microchannel at Room Temperature Michael D. Dickey, Ryan C. Chiechi, Ryan Laren, Emily A. Wei, David A. Weitz *, and George M. Whiteide * Department of Chemitry and Chemical Biology, Harvard Univerity, 12 Oxford St., Cambridge, Maachuett 02138, USA School of Engineering and Applied Science, Harvard Univerity, 29 Oxford St., Cambridge, Maachuett 02138, USA Department of Phyic, Harvard Univerity, Cambridge, MA 02138, USA. *Correponding Author George M. Whiteide Telephone Number: (617) Fax Number: (617) Addre: gwhiteide@gmwgroup.harvard.edu David A. Weitz Telephone Number: (617) Fax Number: (617) Addre: weitz@dea.harvard.edu 1

2 Experimental Detail Parallel Plate Meaurement. We meaured the linear vico-elatic repone of the EGaIn uing a tre-controlled rheometer (Bohlin Gemini HR Nano from Malvern) in a parallel plate configuration. We dipened ~0.4 ml of EGaIn onto the tainle teel bae plate of the rheometer and lowered a rotating, tainle teel plate (20 and 40 mm diameter) onto the EGaIn drop, depreing it until the material filled the gap between the two parallel plate; thi occurred at a gap of mm. We performed four train weep on each ample. Immediately prior to each train weep, the ample were pre-heared at apparent hear rate of +/- 1 and +/ for 5 minute. Thee are only apparent hear rate becaue in thi flow regime the ample doe not train uniformly acro the gap; a lip layer near the upper plate wa oberved. Thi mean that mot of the flow i limited to a thin layer near the upper plate, while the bottom portion of the ample doe not flow. We meaured the vico-elatic and yielding propertie of EGaIn by impoing a inuoidal deformation at frequency, ω (rad/), to the top plate and meauring the urface ample tre that oppoed the deformation. The ample tre, σ (N/m), i related to the torque, τ (N m), impoed 2 by the rheometer on the EGaIn: τ = 2πσ R, where R i the radiu of the top plate. The urface train, γ, of the ample i given by γ = γ in( ωt) 0. The correponding urface tre, σ, i related to the train according to the relationhip = γ ( G' in( ωt) + G co ( ωt) ) σ 0. G i known a the elatic or torage modulu becaue it i give the component of the tre that i in phae with the impoed train. G i known a the vicou or lo modulu becaue it give the component of the tre that i in phae with the rate of train. 2

3 To meaure the vico-elatic repone and yielding propertie of EGaIn, we performed ocillatory tet at a fixed frequency of 1 rad/ and varied the train amplitude from 10-3 to 10. Oberved value of G and G were independent of train for train amplitude le than Since G >> G, the linear repone of EGaIn i primarily elatic. At train higher than 0.01 there i a gradual decreae in G and an increae in G, indicating the onet of yielding or flow. At the onet of yielding the peak tre value begin to level off, eventually reaching a plateau at about 0.5 N/m (Figure 3b). Thi plateau in the tre how that the material i approaching a flow regime, in which the tre required to flow a material i independent of the train or train rate of deformation. Thee trend are hown in Figure 3a, which how G, G and the peak tre a function of train for EGaIn. Although thi plot qualitatively capture the elatic and flow behavior of EGaIn, the meaured elatic modulu in the linear regime hown in Figure 3a i highly variable from ample to ample (Figure S1). Neverthele, our reult how that for all ample, EGaIn i elatic below ~0.5 N/m of urface tre, and yield beyond ~0.5 N/m. Variability in the Parallel Plate Meaurement Figure S1 i a plot of urface tre, elatic modulu, and vicou modulu a a function of train amplitude for four meaurement for each of two different plate diameter. A expected, the value of and trend in the moduli in Figure S1 are imilar for the 20-mm and 40-mm top plate. Although the general trend for all the data are the ame, the abolute moduli value vary amongt the meaurement. Poible ource of ample-to-ample variability include: i) imperfect filling between the plate, ii) ample-to-ample material variability (poibly ariing from the quality of the oxide), and iii) lip. The variability within four conecutive 3

4 meaurement wa a large a ample-to-ample variation, but neither increaed nor decreaed monotonically over time. Figure S1. Vico-elatic rheological plot of EGaIn for multiple meaurement. A plot of the urface elatic modulu ( G,N/m) and the urface vicou modulu ( G, N/m) v. urface hear tre (σ, N/m), for EGaIn. The general trend of all the meaurement i the ame, but the ample to ample variation i large. The filled and void data point repreent meaurement made uing a 40 mm (red) and 20 mm (blue) diameter top plate, repectively. A expected, thee data how that the urface moduli are independent of plate ize. 4

5 Figure S2. Digital photograph of EGaIn on a plama oxidized PDMS ubtrate. (a) After dipening a mall droplet of EGaIn onto the PDMS, the EGaIn aume a non-pherical hape due to the kin on it urface. (b) The non-pherical hape can be meared into a different, table configuration. (c) Placing a drop of 10 wt% HCl in water on the urface of the EGaIn pictured in (b) caue the EGaIn to contract into a pherical tructure due to the high urface energy of the EGaIn and the lack of kin that would otherwie oppoe movement of the drop. 5

6 Ga Count/ In O C Ga Sputtered Sputtered + Expoed to Air From the Bottle %In:%Ga:%O 5 : 6 : 1 1 : 15 : 17 1 : 10 : Auger Kinetic Energy (ev) Figure S3. Auger pectra (recorded at a preure of ~ torr) of ample of EGaIn i) from the bottle (black line), puttered with argon within the high vacuum chamber of the pectrometer to remove the outer crut (blue line), and iii) puttered within the vacuum chamber, and then expoed to ambient air for one minute before being tranferred back into the vacuum chamber (red line). The relative atomic concentration of In, Ga, and O within each ample are lited at the bottom right of the figure. The pectra i) and iii) the two ample whoe urface wa expoed to air are nearly inditinguihable (both indicate the preence of an oxide of gallium at the urface of EGaIn), and pectrum ii) how a urface enriched with In that i, the oberved ratio of (5:6, In:Ga) i greater than that preent in the bulk of the eutectic (~1:5, In:Ga). 6

7 Figure S4. Top-down, optical micrograph of EGaIn injected into a PDMS channel with an inlet preure of 38 kpa. The EGaIn doe not wet the ide wall of the channel a uggeted by the convex hape (i.e., >90 contact angle) of the EGaIn-air interface; we etimate the contact angle to be ~150. 7

8 Gloary of Term ued in the Rheology Section Surface Elatic (or Storage) Modulu ( G, N/m) A meaure of how elatic-like an interface behave. Thi i the urface analog of the bulk elatic or torage modulu. A perfectly elatic material behave like a pring; the force required to diplace it i proportional to the ditance it i diplaced. It i therefore the amplitude of the component of the tre that i in phae with the impoed train (i.e., the degree to which the material experience maximum tre when maximum train i applied and vice-vera becaue no energy i lot due to vicou diipation). Surface Vicou (or Lo) Modulu ( G, N/m) A meaure of how liquid-like an interface behave. Thi i the urface analog of the bulk vicou or lo modulu. A perfectly vicou material behave like a dahpot; the force required to diplace it i proportional to how fat it i diplaced. For a inuoidally rotating plate, the rate of diplacement of the top plate (i.e. the train rate) i a coine function; the vicou repone therefore i 90 degree out of phae with the plate rotation. The vicou (or lo) modulu, therefore, give the amplitude of the component of the tre that i in phae with the train rate (i.e., the degree to which the material experience maximum tre at maximum train rate). Surface Shear Stre A tre applied parallel (i.e. tangential) to the face of a material. The parallel plate apply a hear tre to the EGaIn. Surface Strain (γ, unitle) The ratio of the radial diplacement of the top plate (with repect to the bottom plate) to the thickne of the material between the plate; the radial diplacement of the top plate i equal to the angular rotation, θ, time the radiu of the plate, R. 8

9 Strain Amplitude (γ 0, unitle) The maximum train (i.e. diplacement) for a given inuoidal ocillation of the plate (the train function i γ = γ in( ωt) given frequency), the rotational velocity correpondingly increae. 0 ). A thi value increae (for a γ Strain Rate ( t, -1 ) The derivative of the train function, = γ in( ωt) γ give the train 0 γ rate, = γ ωco( ωt) t 0. Obviouly, for a contant frequency (a in the reported experiment), thi value i directly proportional to the train amplitude Surface Stre (σ, N/m) The force (required to rotate the top plate for a given train) acting on the perimeter of the plate which i imply the applied torque, τ (N m), divided by the radiu, R, of the top plate normalized by the circumference of the plate (to account for the amount of material it ha to move). σ = τ R 2πR 9