ULPAPER FULL

DOI: 10.1002/adfm.200701216 Eutectic Gallium-Indium (EGaIn): A Liquid Metal Alloy for the Formation of Stable Structures in Microchannels at Room Temperature**

By Michael D. Dickey, Ryan C. Chiechi, Ryan J. Larsen, Emily A. Weiss, David A. Weitz,* and George M. Whitesides*

This paper describes the rheological behavior of the liquid metal eutectic gallium-indium (EGaIn) as it is injected into microfluidic channels to form stable microstructures of liquid metal. EGaIn is well-suited for this application because of its rheological properties at room temperature: it behaves like an elastic material until it experiences a critical surface stress, at which point it yields and flows readily. These properties allow EGaIn to fill microchannels rapidly when sufficient pressure is applied to the inlet of the channels, yet maintain structural stability within the channels once ambient pressure is restored. Experiments conducted in microfluidic channels, and in a parallel-plate rheometer, suggest that EGaIn’s behavior is dictated by the properties of its surface (predominantly gallium oxide, as determined by Auger measurements); these two experiments both yield approximately the same number for the critical surface stress required to induce EGaIn to flow (0.5 N/m). This analysis–which shows that the pressure that must be exceeded for EGaIn to flow through a microchannel is inversely proportional to the critical (i.e., smallest) dimension of the channel–is useful to guide future fabrication of microfluidic channels to mold EGaIn into functional microstructures.

1. Introduction The ability to inject metal into microchannels is important for the co-fabrication[1] of low-cost, flexible electronic components This paper describes a study of the behavior of the electri- such as microscale wires, circuit elements, electrodes, and cally conductive fluid metal eutectic, gallium-indium (EGaIn, electromagnets.[2] We show here that EGaIn i) rapidly flows 75% Ga 25% In by weight, 15.5 8C melting point) when into and fills microchannels at RT when a critical pressure— injected into microfluidic channels at room temperature (RT). the value of which depends on the geometry of the channel—is applied to the inlet of the channel, and ii) maintains structural stability (i.e., does not spontaneously retract from the channel) [*] Prof. G. M. Whitesides, Dr. M. D. Dickey, Dr. R. C. Chiechi, when this pressure is relieved. In some applications, EGaIn Dr. E. A. Weiss may have an advantage over molten solders (used in a set of Department of Chemistry and Chemical Biology, Harvard University methodologies called ‘‘microsolidics’’[2,3]), which require heat- 12 Oxford St., Cambridge, MA 02138 (USA) E-mail: [email protected] ing and cooling steps that increase the time needed for the fabrication process, and make it incompatible with heat- Prof. D. A. Weitz, Dr. R. J. Larsen School of Engineering and Applied Sciences, Harvard University sensitive materials such as organics. For most applications 29 Oxford St., Cambridge, MA 02138 (USA) requiring a liquid metal, EGaIn is superior to Hg, which readily E-mail: [email protected] fills microchannels at RT, but is toxic and forms unstable Prof. D. A. Weitz structures that spontaneously retract from the channels to Department of Physics, Harvard University minimize interfacial free energy. In this work, quantitative Cambridge, MA 02138 (USA) analysis of the behavior of EGaIn i) injected into a channel [**] We acknowledge funding from NSF CHE-0518055 and DMR-0602684. whose width varied along its length, and ii) in a parallel plate This work made use of the shared experimental facilities supported by rheometer, allowed us to determine both the critical stress the MRSEC Program of the National Science Foundation under award required to induce EGaIn to fill a channel of known cross- numbers DMR-0213805 (Harvard) and DMR 02-13282 (MIT), and the shared facilities supported by the National Science Foundation under sectional dimensions, and the primary origin of EGaIn’s NSEC (PHY-0117795) (Harvard). We thank Elizabeth Shaw for the rheological properties: a thin skin (mostly comprised of oxides assistance with the Auger measurements. EAW thanks the Petroleum of Ga, as determined by Auger spectroscopy) on its surface. Research Fund of the American Chemical Society for a fellowship (PRF # 43083-AEF). Supporting Information is available online from Wiley This analysis provides guidelines for the design of microfluidic InterScience or from the author. channels as molds for EGaIn.

Adv. Funct. Mater. 2008, 18, 1097–1104 ß 2008 WILEY-VCH Verlag GmbH & Co. KGaA,Weinheim 1097 08www.afm-journal.de 1098 FULL PAPER iv) iii) ii) commercially attributes: a following is the with EGaIn alloy solders. metal as liquid available such alloys higher-melting and conventional, metals of limitations microsolidics the in addresses used that techniques the of extension temperature or fails, never either EGaIn 1.1.2. metal—that preferable. fluid is self-heals, a and continually cracking example, material— reheating a to (i.e., applications, for microfluidic self-healing for susceptible The but, are cracks), are mends iii) Solders that the device. fatigue. structures that mechanical increase the stresses in mechanical steps form produces result in solder cooling to the interest of and necessary materials solidification potential heating organic time or The many processing real with ii) of compatible devices. biopolymers) be to (especially micro- The high are i) metallic solders ‘‘low-melting’’ too limitations: even creates melt three to cooling, required have temperatures by however, solidify Solders, structures. to it 157 point allowing (melting In as such Electronics for Microchannels in (Solders) Metal 1.1.1. Background 1.1. i) h s fEani ircanl s oetal,aroom- a potentially, is, microchannels in EGaIn of use The solder low-melting a solder—typically, molten Injecting h ufc fEani oee ihati ‘kn’ h knis skin The ‘‘skin’’. thin a with covered is EGaIn of surface The sacnateetoefrteeetia hrceiainof characterization electrical devices. the semiconductor and for organic electrode thin-film contact a as sda neetial odcie hral tbelubricant, stable thermally conductive, electrically an as used rae hnta fwater). of that than greater iino h kni h eut n icsinsection. Discussion and compo- Results the the in analyze skin We the skin. of the sition flow) of (i.e. confines the redistribute the in to underneath EGaIn M1 the behavior); movie cause this (see forces of gravitational tilted demonstration a is for substrate Information Supporting on the placed and is EGaIn substrate of drop a a when eye un-aided the to apparent knwe rpi lcdo itdsbtae(e movie (see substrate tilted Information). a Supporting its on in of placed M1 confines is the drop a readily—within flows skin—when it why explains and The skin. 1.99 the is of EGaIn absence of the viscosity in bulk fluid low-viscosity skin. a its is EGaIn of properties therefore the is and to decreases), attributable structure which the ratio of (a volume size to the the area as surface increases of on ratio the moldability of EGaIn function its a that is mold suggests observation This to moldable). not able is been only m have we Notably, a efre ybfraigado fEanudrtension. under EGaIn of drop a bifurcating by 1 formed as be small, small can example, as For tips minimized. (with cones not stable which is energy in free structures surface stable the free-standing, into material a shape GI seetial odcie h eitvt fEanis EGaIn of resistivity The conductive. electrically is EGaIn GI smlal.W en ‘odblt’ steaiiyto ability the as ‘‘moldability’’ define We moldable. is EGaIn -om iesae(.. ntemcocpcsae EGaIn scale, macroscopic the on (i.e., scale size m-to-mm 29.4 10 6 V -cm; [4,5] hspoet losEant eused be to EGaIn allows property this [8] 8 )it ircanl and microchannel, a C)—into hslwvsoiyalw tt be to it allows viscosity low This 10 m -3 ß ndaee)o EGaIn of diameter) in m Pa 08WLYVHVra mH&C.KGaA,Weinheim Co. & GmbH Verlag WILEY-VCH 2008 s( [6,7] atro two of factor a [9] [7] .D ikye l / al. et Dickey D. M. r-le ih1 t qeu C,wihrmvsteskin. the removes which HCl, aqueous were wt% that 10 channels with behavior into pre-filled EGaIn its injected on also EGaIn we of channels, the skin in the of channel. influence the the filled it highlight once To metal liquid the to stability structural photolithography). by readily achieved be can that ratio ieso sdpeiul ihsolders were with channels previously easily used The therefore these dimension (and others). because used by widely PDMS techniques adaptable and of simple lithography out are channels soft techniques exceeded the be standard made the must We using that deduce flows). stress relationship EGaIn the before (i.e., this stress from surface this critical and and flow dimension, induce to critical required pressure relationship critical the the channel study between the narrowing to of us width but the continuously—allowed height which decreased design—in constant simple with This width. channel cross-sectional designed the microfluidic we hypothesis, on a this test depend To channel. should the of turn, dimensions in channel; pressure, the a in EGaIn channel this to of micron-scale applied pressure a the out into on depend EGaIn readily would inject to pours ability the EGaIn bottle, although that, hypothesized the of stability the determine structures. and resulting microchannels, fill would in Channels Microstructures Fluidic Metallic Stable Forming 1.2.2. sample). sample as a a into probes nm of which 15 layers as spectroscopy, deep atomic photoelectron few that X-ray first technique (unlike the a only with Spectroscopy, bombardment X-rays—from to electrons—due Electron of emission the Auger monitors used we Characterization Surface 1.2.1. Design Experimental 1.2. hne was channel ie,de o omasi)udrabetconditions. ambient readily under oxidize skin) not a does form and not does properties), (i.e., elastic no is, or with water Mercury like oil, fluid, temperature. (a fluid room Newtonian at low-viscosity, a metal however, liquid a EGaIn, like n hrb rvd nih notebhvo fEGaIn of behavior the into insight provide thereby and Characterization Rheological 1.2.3. v) ehpteie httesi nEanwudprovide would EGaIn on skin the that hypothesized We GI sol odbeo h irsae etherefore We microscale. the on moldable only is EGaIn EGaIn which under conditions the study to sought We EGaIn, of surface the (chemically) characterize to order In ecmae h eairo GI ihH eas gis, Hg because Hg with EGaIn of behavior the compared We esuh oqatf h epneo GI ostress— to EGaIn of response the quantify to sought We codn oteCCHnbo,tecmoet fEGaIn of components the Handbook, CRC the to According etlfilnsadG sataentin.Idu salso is Indium nutrient. industry. trace semiconductor the a in solder) is a Ga (as ubiquitous and fillings dental ae‘lwodr ftoxicity’’. of orders ‘‘low have 20 m uetcGlimIdu iudMtlAlloy Metal Liquid Gallium-Indium Eutectic A ie(iie ytehih:it aspect height:width the by (limited wide m d.Fnt Mater. Funct. Adv. [10] nimhsbe sdin used been has Indium [2] ,adtenarrowest the and ), 40 2008, m ep(a deep m 18 , 1097–1104 [10] [4] FULL PAPER 435 mN/m. 500 mtorr), but www.afm-journal.de 1099 ¼ 3 mm. 1 mm long) that connected 0.1 mL) of the metal from a T whereas the surface tension of [4] The EGaIn (which is opaque and [18] m deep m 40 624 mN/m, T m deep) over a length of measurements of the surface tension of a pendant m [4] A top-down schematic of the channel is included at the 40 m wide T [17] m Our conclusion that a surface oxide (in particular, gallium We fabricated microchannels from PDMS, which is highly Figure 1a is a back-lit, top-down optical micrograph of a We filled individual microfluidic channels with EGaIn and 1 s), but stopped at the entrance to the narrow channels. At was permeable to oxygen,oxidized such and that then gallium near displacedreacted the In with surface the at small theoxidized amount surface, gallium, of and or gallium gallium ii)surface. oxide in oxygen Regardless then the of displaced monolayer, that the In in at mechanism, the the presence these ofEGaIn results air will (i.e., suggest be in predominately the covered ambient) with the oxides surface of of gallium. oxide) is responsible forreported the rigid skin agrees with previously drop of EGaIn:conditions The is surface tension of EGaIn at ambient top of Figure 1.(20 The channel consisted of a narrow portion therefore dark in this image) filled< the inlet channel rapidly (in pressures below 85entrance to kPa, the narrow the channels.behaved EGaIn similarly Hg to (right EGaIn, stopped side but only ofthe short required Figure narrow 54 1a) portion of kPa to of reach the thepressure channel. to Despite the the inlet, applicationcenter both of of mass images of the in metal Figure wastaken not 1a moving because when the are the pressure image static: was at the the metal-air interface balanced symmetric inlet and outlet, bothwide of which widened (to 1 mm EGaIn during exposure tocauses acid-promoted aqueous dissolution HCl of the (whichThe oxide) is presumably high surface tensionconditions of may EGaIn therefore measured under besurface oxide ambient explained that by is capable the ofpendant supporting presence drop. more weight of from a a 2.2. Behavior of EGaInComparison in Microchannels, with and Hg permeable to oxygen, byques. established soft-lithographic techni- those channels that sat inbehavior. air for one week exhibited the same 2.2.1. Behavior of EGaIn and Hg Under Applied Pressure channel partially filledpressure was with 85 EGaIn kPa. in which the applied Hg by dispensing asyringe into droplet the ( inlet ofthe the inlet channel, using and regulated, applying pressurizedthe pressure outlet nitrogen, to to while remain at allowing atmospheric pressure.gauge, A digital placed pressure upstreampressure. of We the did inlet, not(with measured silanes, have the for to example) nitrogen to pre-treatused fill the them the PDMS channels with PDMS immediately EGaIn after or channels exposingplasma Hg. them to We of a air for one minute (pressure [12] We [16] 1:15:17) ¼ 2008 WILEY-VCH Verlag GmbH & Co. KGaA,Weinheim ß We performed Auger [14] the majority component of 30%). [12] Torr s), and that the oxide skin 6 —a eutectic alloy of 68.5% Ga, 21.5% When the indium does oxidize, it does 10 [13] , 1097–1104 ¼ A Eutectic Gallium-Indium Liquid Metal Alloy [16] 1:10:14). The observation that gallium oxide 18 , ¼ 2008 to analyze samples of EGaIn i) as purchased but, unlike Ga, In is slow to oxidize when it is ) [11] torr —found within the chamber of the spectro- 5:6:1). Indium has been shown to cover as much as 9 ¼ [15] 10 A prior X-ray study of EGaIn—done under ultra-high To determine the chemical composition of the skin of The ‘‘as purchased’’ EGaIn showed an enhanced amount Ga 5 vacuum—showed that theEGaIn outermost became layer enriched of with thesputtered surface In off of after (this thesurface result ambient energy is skin than reasonable was Ga since by In has a lower Adv. Funct. Mater. 2.1. The Nature of the Surface of EGaIn EGaIn under differentscopy conditions, we (Physical usedMicroscope Electronics Auger spectro- Model 660 Scanning Auger 2. Results and Discussion (straight from the bottle, purchased fromsitu’’ Aldrich), ii) sputtering after with ‘‘in argonwithout (that is, removing we it sputtered the from EGaIn the high vacuum conditions— injected into microchannels—byrheometry. performing parallel-plate M. D. Dickey et al. / exposed to oxygen. 94% of thevacuum, surface of EGaIn after sputtering in ultra-high spectroscopy on EGaIn after in-situthat sputtering and also the found skinIn:Ga:O became enriched with In (atomic % ratio meter), and iii) afterminute after exposure sputtering. We to compared the air measuredratios elemental on for the approximately surface one versusof those in In:Ga). the The bulk (1:5 Supportingthe atomic Information Auger ratio (Figure spectra S3) fromrelative contains atomic these percentages three of samples, In, along Ga, with and O the and in each O sample. at the surface (atomic % ratio In:Ga:O compared to theconsists of bulk, oxides of suggestingfact gallium; this that that result Ga the is isperature. consistent highly skin This with reactive finding the primarily is towards alsoX-ray oxygen consistent at studies with room previous on tem- studies: pure Ga, formed a highly uniformbulk passivating material from layer further oxidation that (much like protected aluminum). the dominated the surface ofwas exposed EGaIn to after air the implies sputtered that surface either i) the monolayer of In sought to test ifinitial the surface state of (i.e., theas-sputtered enriched EGaIn EGaIn reverts with to back Ga ambient to air.EGaIn—after and the Indeed, O) the exposure surface by ofreturned exposing to the to the a ambient state air enriched% ratio with In:Ga:O for gallium and one oxygen (atomic minute— EGaIn, and galinstan not form a passivating layer on the surface of EGaIn. In, and 10%temperature Sn —showed that bygallium both weight materials oxide formed that after aoxygen, is even skin where a of also 1 brief a L exposure liquid to at air room (180 L of 10www.afm-journal.de 1100 FULL PAPER rmtecanl l rsue r ag pressures. gauge are pressures All channel. the from epciey ftecanla h ea-i nefc,and interface, metal-air the at channel the of respectively, P outlet the toward rapidly channel narrow channel the filled ( Hg narrow The side). left the 1b, (Figure through to inlet pressure rapidly the the from Increasing at metal channel. the applied the stopped through and further inlet, the moving at applied pressure the ( instantaneously Hg both the exceeded, whereas they was stable, until pressure was channels critical structure the a EGaIn When filled the ii) metals pressure, channel. Both (in the i) rapidly of dark. metals portion appear narrow metals The consequently the the figure. whereas and reached Hg transparent, the and is light of column) PDMS the The (left top channels. block EGaIn the microfluidic of PDMS at photographs in labeled optical column) are (right top-down PDMS back-lit, are from images fabricated remaining channels the of dimensions 1. Figure esrdtewdh()o h hne ttepita which and at inlet, point the the at to channel (P) the of pressures (W) of width the series measured a applied We film. EGaIn), the of tension. of surface system- the surface value at is the the that as is origin (such film parameter solid-like physical a this For its liquid, unit a but per For interface, force specific. interfacial the of the of measure of length a walls sense, the general and most liquid parameter phenomenological the The between channel. angle contact the nti qain n r h it n egt(m) height and width the are H and W equation, this 1). In (eq. equation Young’s-LaPlace the using interface metal-air side). right 1b, (Figure < ¼ ecnepestepesr rp(,P)ars the across Pa) (P, drop pressure the express can We e)we h ple rsueexceeded pressure applied the when sec) 1 2 g cos xmlso iudmtl nmcohnesadterdpnec npesr.The pressure. on dependence their and microchannels in metals liquid of Examples ð u Þð g 1 < eed ntemcaia rpriso the of properties mechanical the on depends = e)fildtecanl.ii hntesse a eundt ambient to returned was system the When iii) channels. the filled sec) 1 W þ 1 = H 9kacue h GI oflow to EGaIn the caused kPa 89 Þ ß 08WLYVHVra mH&C.KGaA,Weinheim Co. & GmbH Verlag WILEY-VCH 2008 g Nm s nthe in is, (N/m) 7kPa 57 u (1) is .D ikye l / al. et Dickey D. M. < 91ka h lp ftebs tln otedt o gi . / n the between and relationship N/m inverse dimension. 0.7 is the critical Hg illustrates and for plot data pressure This is the intercept kPa. to the line 28.3 and fit is The N/m best 1.1 intercept channel. the is of EGaIn wide slope for The data infinitely the kPa. an to 29.1 line into fit the best metal to the equal the of is slope inject intercept the to and N/m) required to interface, pressure proportional by the is filled of fit length channel linear unit the the per of force of (1/W) slope width The Hg. smallest and the EGaIn of inverse the of function iue2. Figure )withdrew s) 1 lto rsue(P pressure of plot A iue2sosPv.1/W. vs. P pressure; shows given 2 a Figure for flowing stopped EGaIn nlsspromdfrH (2 Hg for performed analysis nwihteol ieso fcneuneis consequence of dimension one only (i.e., the fluid channel which the in wide infinitely inject an to into required metal Hg) pressures for the kPa 18.3 are EGaIn, for kPa (29.1 2 Figure Hg. pure of a that observe than to energy us surface cause lower would that possible thiols) is (e.g., contaminants adsorbed had mN/m—it surface Hg the 480 that of tension surface otc nl siaini cuaet within to accurate þ is estimation other—the angle each contact of error experimental within min odtos(2 mN/m). (624 inter- in EGaIn conditions was of ambient tension’’ what ‘‘surface so the for be to reported preted S4), value the from Figure g Information (see channel the Supporting in EGaIn the of image optical ewe h GI n h iewl fthe of be side-wall the to and channel EGaIn these to the fit between linear 2 the is of N/m) data 1.1 be to found h au eotdi h ieaue(8 mN/ (480 literature the m). in reported value the of tension angle contact m, ¼ / h necpso h ierfist h aain data the to fits linear the of intercepts The codn oE.1 h lp wihwe (which slope the 1, Eq. to According uetcGlimIdu iudMtlAlloy Metal Liquid Gallium-Indium Eutectic A [10] 5 3 Nm hsvlei indistinguishable is value this mN/m; 630 8 n otc nl f136 of angle contact a and , lhuhteetovle o gare Hg for values two these Although g in ple oteilto h hnesa a as channels the of inlet the to applied ) 5 Nm nysihl esthan less slightly only mN/m, 450 cos( 150 u d.Fnt Mater. Funct. Adv. .W siae h angle the estimated We ). 8 140 ae natpdown, top a on based , 8 ile surface a yielded ) g 2008, cos( 8 g [4] ol iea give would amaueof measure (a 18 u similar A ) , ¼ 1097–1104 . N/ 0.7 FULL PAPER (3) (4) (5) ), as s m), is s (N t )—which is a s , N/m) and the s 0 g G www.afm-journal.de 1101 (m) of the top plate. 1.2 mm. The top plate , N/m) applied to the 0) or perfectly viscous l s s s 0.4 mL) of EGaIn between 00 G ÞÞ t v , N/m)—by relating the strain s ð 00 G cos s 00 2 G R s Þ t Þþ v are non-zero. t ps ð s 2 v , of the top plate. We monitored the torque 00 ð u ). ) to the corresponding surface stress ( sin ¼ G 0 0 0 (1 rad/s), as shown in Eq. 3, where R is the radius sin g g g dl s v 0 R and ¼ G s ð s s 0 u 0 0) behavior. The skin of EGaIn has both elastic and d g R G Z s ¼ ¼ We dispensed a small volume ( 0 We recorded the torque required to maintain the constant We thus determined the viscoelastic properties of surface of A perfectly elastic material, such as a highly cross-linked gel, ¼ s s G measure ofamplitude deformation ( of the EGaIn—and the strain Nano from Malvern Instruments, seefor Supporting additional Information experimental details).precisely measures The the rheometer—which deformationapplied response of stress EGaIn to undermeasure an controlled the visco-elastic conditions—allowedthe properties critical us of stress to required thethe to skin, yield properties the determine of skin,Information and its characterize contains flowequations once a for it all glossary of yielded. the The quantities of discussed Supporting here. rheologythe two terms parallel plates and separated by was attached to awide range low-friction of torques bearing (about the capable axisplate, normal of while to the the applying bottom plane plate of a remained the stationary)equipped and was also withdisplacement, an opticalrequired encoder to oscillate that the topfrequency tracks plate sinusoidally with the aof constant radial the plate (10-mm) d is the gapEquation between 3 the also plates defines (1.2 the mm), surface and strain t ( (s) is time. t s g proportional to the surface stress ( oscillatory frequency (described by Eq. 3)strain while amplitude. increasing the The torquerequired is to deform a the measure sample;of of here, the sample we the is assume total a that low stress viscosity thesolid-like liquid, bulk while the properties. surface exhibits In this case, the torque, the EGaIn—the surface elastic modulus ( behaves like a spring, while a perfectlywater viscous material, or such as Hg, behavesalso like a occur dampener. for Similarpossess an behavior either will interface; perfectly in elastic ( that case, the interface can amplitude ( viscous characteristics over a large rangeboth of values of strain, so EGaIn, as shownintegrated around in the Eq. circumference, 4, in which the surface stress is shown in Equation 5. surface viscous modulus ( ( m for Hg. m . EGaIn does 2008 WILEY-VCH Verlag GmbH & Co. KGaA,Weinheim Large surface ß m, as measured 37.5 444 mN/m (based m Non-wetting [4] (Pa) c m for EGaIn and m , 1097–1104 A Eutectic Gallium-Indium Liquid Metal Alloy 18 38.1 , 2008 1 (2) : 1 / 600 mN/m, based on the measurements in this study). . Similar to Hg, the interfacial free energy of EGaIn is > CD The stability of microstructures of EGaIn in channels, and Based on this analysis, we can develop an expression (Eq. 2) When we relieved the pressure at the inlet, the EGaIn did Why then are structures of EGaIn stable while Hg c Adv. Funct. Mater. 2.3. The Rheological Characterization of EGaIn the loss ofsuggests this that stabilitybehavior. EGaIn’s when Little is oxide EGaIn knownoxide is about skin skins the exposed on dictates mechanical liquid to propertiescharacterized its of substrates. HCl, We the rheological sought mechanical torheometer properties quantitatively equipped with of parallel-plates EGaIn (Bohlin Gemini using HR a by profilometry). for the critical pressure, P These values—aspre-determined height expected—are of the roughly channel (38 equal to the 2.2.2. Behavior of EGaInSystem and Hg to upon Ambient Returning Pressure the not reflow ormained reorganize in the within shape pictured the inmoldability Figure channel, 1c indefinitely. (which but EGaIn’s allows ratherstable for re- microstructures the formationdistinguishes in of it channels from structurally our Hg, at returning which the room system reflowed toside). ambient immediately temperature) pressure EGaIn upon (Figure 1c, does right characteristics not that destabilize reflow Hg: i) despite having the same two P required todimension force CD (m). EGaIn In through eq. 2, a the units channel of 1.1 of are N/m. critical the depth ofgeometry the of channel). the Thisaccording to channels eq. pressure 1, should used is equalof the specific in slope the divided by to these channels the height (H). the value experiments The for and, intercepts H from of Figure 2 yielded a M. D. Dickey et al. / on Eq. 1), similar topresence that previously of reported HCl for (432 EGaIn in mN/m). the instantaneously reflows? We suspectdue that EGaIn’s to stability the is skinhypothesis, we of injected gallium EGaIn oxide10 into wt% on a aqueous HCl, channel its which removes pre-filled surface. theoxide with skin To (see by dissolving Figure test the S2 this inin Supporting the Information). The presence EGaIn, withdrew of from HCl, the channel behaved when thepressure. similarly inlet returned Furthermore, to to we ambient Hg: foundEGaIn it in that rapidly the the presence surface of HCl tension dropped of to large ( not wet the wallsSupporting Information, of the the metal-air channel: interfaceof in As the the channel shown middle protrudes in towardsenergy Figure the outlet. S3 ii) in 12www.afm-journal.de 1102 FULL PAPER ucino h mltd ftesraesri ( strain surface the of amplitude the of function tes( flow). stress (or yield to began and elastic, less became o auso tanapiue( amplitude strain ( of values low EGaIn. fteEanwspiaiyeatc( elastic primarily was interface EGaIn the regime, the ‘‘low-strain’’ by this of material In (a the thickness). deformed 0.01 its plate of than upper 1% the less means amplitudes 0.01 strain of strain for strain of independent tano .;ti eutsget htteEanflw edl nei yields. it once readily flows EGaIn the that b) suggests result this 0.1; of strain rae hn00,tedces in decrease the 0.01, than greater ufc icu ouu ( modulus viscous surface ufc lsi n icu ouifrEanpotda a as plotted of values EGaIn The strain. for the surface shows moduli the 3a of viscous Figure function and EGaIn). for elastic i) zero surface through to plates close is this the (although component dissipation of viscous ii) movement and forces restoring the elastic resisted EGaIn the osraiybyn rtclsraesrs ( stress surface critical a beyond readily flows eodti au,i)ol ml muto diinlstress additional of amount small a only ii) value, support this beyond only could skin the ha tes( stress shear 3. Figure ...Rslso h aallPaeMeasurements Plate Parallel the of Results 2.3.1. G ltof plot A 0 tteosto ilig(tanamplitude (strain yielding of onset the At iue3 nldsapo ftesraesrs ( stress surface the of plot a includes 3a Figure s G s [19] 00 s s eee f at off leveled ) ic-lsi hooia lt fEGaIn. of plots rheological Visco-elastic .Ntby h tesddntices infiatybyn a beyond significantly increase not did stress the Notably, ). G 0 sepce,srs nrae ihsri,because strain, with increased stress expected, As s s and s /) h ufc lsi ouu ( modulus elastic surface the N/m), , G 00 s s tesfrEan h aasosta h EGaIn the that shows data The EGaIn. for stress vs. G 00 s /)v.sri mltd ( amplitude strain vs. N/m) , . /.Ti lta ugssta i) that suggests plateau This N/m. 0.5 < .1,Eanhseatclk behavior like elastic has EGaIn 0.01), . / fsraesrs,and stress, surface of N/m 0.5 G 0 s ß G niae htEGaIn that indicates . N/m). 0.5 08WLYVHVra mH&C.KGaA,Weinheim Co. & GmbH Verlag WILEY-VCH 2008 0 s a) > G lto h surface the of plot A .1,tesurface the 0.01), G G 0 s 00 0 s s g and Nm,adthe and ,N/m), .A strains At ). 0 o GI.At EGaIn. for ) G s g 00 s )asa s 0 for ) were .D ikye l / al. et Dickey D. M. ( h ukcnrbto sisgicn) ebleeta this that evidence: phenomenological quantitative believe following and the We on based insignificant). justified is is approach contribution (i.e. the dominate bulk properties (i.e. the surface but the bulk, deformation that the and assumes skin analysis to the our both resistance from arise top can the the torque) required oscillate principle, to In required plate. torque the recorded rheometer EGaIn of Behavior Surface Rheological the its of Dictates Properties the that Evidence 2.4. Supporting The variation. this same. of the discussion a were contains yielded) at Information strain EGaIn the of value the the (and which plots the of shapes the but varied, infiatyoe h iesae foreprmns and experiments, passivating. our is the layer that of show oxide that scales measurements X-ray time previous corroborates the change not over provides does skin result significantly the this of ambient; thickness the the that to hours evidence indirect 24 EGaIn after the 3 of Figure in exposure moduli, shown stress, of plots yield the the with of in shape change general change a and detect properties not could rheological We time. the whether determine GI ewe h w aallpae for plates parallel two the between EGaIn EGaIn the makes simply applied faster. is flow that than stress larger additional surface stresses any critical support the cannot surface as skin of value The this value stress. define this therefore at we yielded and EGaIn stress that implies trend this paeti ltof plot a in apparent exceeded. so was 1b) occur. pressure (Figure EGaIn critical to microchannel the a the appears why once of rapidly explains flow portion stress narrow the the the of filled of within all behavior is plateau that it The interface; regions EGaIn-air the small at these open cracks rheometer it the from or detaches plate region, either it plateau yields, to is, this required ‘‘slips’’—that skin In skin stress the plateaus. that the the amplitude and strain once than flow the to Thus, increase lower resistance EGaIn). minimal is magnitude the there yield of is to torque an orders required applied imparts the six that to which viscosity estimate approximately bulk (we viscosity, the of oscillations low contribution the the a to has resistance to begun insignificant EGaIn and yielded Bulk has which to skin, flow. resistance the the from because arises only further flow EGaIn strain to needed was s i) s nteaoeetoe hooia esrmns the measurements, rheological aforementioned the In moduli the of values absolute the sample, to sample From erpae h hooia esrmnsatrlaigthe leaving after measurements rheological the repeated We h au ftesrs twihEanyed sreadily is yields EGaIn which at stress the of value The ,Fgr b ohmdl erae ail at rapidly decreased moduli Both 3b. Figure ), h xetdcnrbto fbl GI—hc salow a is EGaIn—which bulk of contribution expected The mns hsrsl ugssta h eitneo GI to primarily EGaIn arises of response, resistance elastic the its that including suggests deformation, exper- these result in this recorded those iments; than lower magnitude of orders icst fluid viscosity [8] uetcGlimIdu iudMtlAlloy Metal Liquid Gallium-Indium Eutectic A t h esrdtru sapoiaeysix approximately is torque measured the —to G 0 s and [12] G 00 s safnto fsraestress surface of function a as d.Fnt Mater. Funct. Adv. 2008, 4husto hours 24 18 , . N/m; 0.5 . N/m; 0.5 1097–1104 FULL PAPER and the [4] www.afm-journal.de 1103 0.6 N/m, the product of the pressure 0.5 N/m) is exceeded, at which point it flows 0.5 N/m) to i) estimate the pressure required to air (0.63 N/m) measured by the pendant drop method critical surface stress required tomicrofluidic force channels the ( EGaIn throughapplied the at the inletchannel, and Eq. 2). half of the critical dimension of the The rheological measurements demonstrated that EGaIn The ability of the EGaIn to fill the channels rapidly once it The elastic nature of EGaIn under low-strain (or, equiva- The agreement between the values of critical surface yield 0.5 N/m. We obtained this critical stress value both by 3. Summary and Conclusions 3.1. The Connection between theof Rheological EGaIn and Properties its Behavior in Microchannels has the properties of an elastic materialsurface until stress an applied ( critical readily; this resultEGaIn can is be consistent forcedpressure is with to exceeded fill for the a channelsother given observation rapidly channel words, critical when that EGaIn dimension. a In can critical only support surfacerheological stresses below measurements (Figurecritical pressure 3) required to and injectof EGaIn known by into geometry (Figures a 1 studying microchannel and 2).required The the to critical surface inject stress EGaIn into channels,EGaIn and in the the stability channels after of injection, the surface arises from of a skin the on the EGaIn.skin is Auger composed spectroscopy of showed oxides that of gallium this (Figureyields S3). is consistentnegligible with amount the of rheologicalEGaIn additional to observation stress flow faster that is once‘‘plateau’’ the required a in material the to plot yields of (specifically, stress induce vs. the strain amplitude in Figure 3a). lently, low-stress) conditionsEGaIn explains structures thethe within pressure stability the through ofThe the stability microfluidic the is channels due channelsEGaIn to is in the channels pre-filled relieved skin, once with as HCl. (Figure Formicrofluidic shown the by systems design 1c). of the to future instability moldsurface of stress EGaIn, ( we can use the critical yield EGaIn from an elastic material to a flowing fluid in a stress obtained fromrheological the measurements behavior support inobserved the our rheological properties channels hypothesis ofthe and that EGaIn species the are at the the dominatedmaterial. surface, by and A are Newtonian not fluid,behave a such property elastically, as of nor the Hgstress. do bulk or These fluids they water, do have require does ainto a not critical pressure channels, critical to inject surface the them tension yield and value contact angle of (Eq. 1).is which EGaIn’s behavior, due however, depends to on itsallows skin, the EGaIn which to surface iswhereas maintain Hg elastic. post-injection continually The reorganizes structural to elasticityfree minimize stability, of energy. its interfacial the skin 0.5 N/m) is 2008 WILEY-VCH Verlag GmbH & Co. KGaA,Weinheim ß [12] 0.5 N/m (Figure 3). We , 1097–1104 A Eutectic Gallium-Indium Liquid Metal Alloy 18 , (Figure 4a), centered at its starting position 2008 [20] A series of side-view snapshots of EGaIn between the two Moduli are physical properties of a material that should be independent of the size of the platenormalized since the by surface the moduli are perimeterlength). As of expected, the the surface moduli plate were20 the same (units and for both of 40 force mmmoduli per diameter (which are plates normalized by (see thechanged Figure surface area by S1), of a but the plate), factor themoduli of are bulk the two. relevant parameters, This and that resultis the elastic suggests behavior due that to surface thesurface rheological of properties EGaIn (and of not species in present the at bulk). the and air during the parallel-platein measurements Supporting (see Information). movie M2 Figure 4this contains three interface frames of clockwise taken with the top plate rotating counter- remarkably similar to both the ‘‘surface tension’’ of EGaIn in obtained the same criticalplate surface (40 mm) stress for when the using measurement. a This value larger ( The critical surface stressparallel required plate for EGaIn configuration to was yield in the from the skin. Thesolid-like, elastic which is properties consistent with of previous observations thegallium of skin the oxide suggest skin on it liquid is gallium. (Figure 4b), anddeformed rotating in synchrony clockwise withand (Figure the appeared oscillations 4c). crumpled (Figures after The(Figure 4a, returning 4b), 4c) skin to probably the because of center buckling position and cracking. This skin is visually apparent at the interface between the EGaIn Adv. Funct. Mater. Figure 4. parallel plates of the rheometer. The imagesEGaIn illustrate how surface the ‘‘skin’’ deformed on the Information) (the during the full oscillation of movie, thethe top M2, plane plate of about is the the plate axis available (the normal bottomto to in plate the was Supporting stationary). right a) The of plateconcert rotated the with the center rotation. position, b) Theand and plate the the returned relaxed to creases its skin initial in appearedextended). center crumpled the position, c) after skin The being slanted stretched platecreases (rotationally in rotated of to the the skin left slanted of accordingly. the center position, and the iv) iii) ii) M. D. Dickey et al. / 14www.afm-journal.de 1104 FULL PAPER )Tefraino ofra lcrdsfrmetal- for electrodes conformal of formation The i) applica- several enable to harnessed tions: be exceeded. could is property stress critical This a once tem- rapidly flow Al). room but to temperature, at (similar skin liquid oxide a passivating a is has it and because perature from however, different therefore is metals, EGaIn are many applications. certain can and skin for the beneficial that nuisance showed be we a here, rheometry; to considered These prior stress. removed often critical a are which below oxides for behavior metals dictate liquid oxides and surface solders other of characterization Outlook 3.2. 1). (Eq. stress surface critical the by dictated as channel, to the dimension pressure smallest of required the to The proportional inversely drop. is pressure EGaIn yield given a passage for the block EGaIn the to of required estimate channel ii) the of alternatively dimension or critical dimensions, given of channel v h wthn ftebhvo fEani hnesfrom channels in EGaIn of behavior the of switching The iv) a into distance predetermined a EGaIn of injection The iii) injecting by microstructures metal of formation The ii) h lsi kno GI losi ob odda room at molded be to it allows EGaIn of skin elastic The the to relevant be may paper this in analysis The ooaeso te hnogncfilms. organic thin other or self-assembled monolayers incorporating junctions molecule-metal hto iudt hto neatcsldthrough solid elastic an of that to liquid a of that be may that electrodes. channels or sensors in as formed useful be cross-sectional metal- can technique, the junctions this fluid Using designing channel. the of rationally dimensions by channel transistors. field-effect or sensors interconnects organic or for contacts metal-organic as they used temperature, be room could at Because fabricated channels. are the structures components— –within these etc functional coils, heaters, of as such formation the structures the facilitates of stability The microchannels. into EGaIn the subject metal. evaporated not hot, with does bombardment to junctions film organic EGaIn of fabrication temperature, room so at are deposited be and can film. EGaIn organic Hg, addition, the of In in defects drop contact to a likely less using therefore formed those than with 1 tips smaller with as cones small small as form to diameters it allows EGaIn of ity m :teeeetoe r much are electrodes these m: ß 08WLYVHVra mH&C.KGaA,Weinheim Co. & GmbH Verlag WILEY-VCH 2008 [7] h moldabil- The .D ikye l / al. et Dickey D. M. 1]D .Lide, R. D. [10] 1]Tesri sdrcl rprinlt tanrt (s rate strain to proportional directly is the strain is The pressure total [19] The pressures. gauge are pressures reported All [18] 1]Y i,G .Whitesides, M. G. Xia, Y. [17] 1]H otan .DMs,P .Prhn .M co .G hyk,M. Shpyrko, G. O. Ocko, M. B. Pershan, S. P. DiMasi, E. Tostmann, H. [16] 1]M .Dme .A obel,R .Wle,R .Housley, M. R. Weller, A. R. Tombrello, A. T. Dumke, F. M. [15] 1]M .Rgn .S esa,O .Mgusn .M co .Deutsch, M. Ocko, M. B. Magnussen, M. O. Pershan, S. Har- P. Regan, G. J. M. Knedlik, C. [14] Breternitz, E. V. Cherkashinin, Magnussen, G. M. Scharmann, O. F. Pershan, [13] S. P. Tostmann, H. Regan, J. M. [12] 1]C .Macosko, W. C. [11] 2]Teoinaino oaini endrltv oatpdw iwof view top-down a to relative defined is rotation of orientation The [20] 9 .Lws .F Murray, F. S. Lewis, P. [9] Koster, Whitesides, N. M. J. G. Dickey, [8] D. M. Weiss, A. E. Chiechi, C. R. [7] 6 .A es,V .Pre,R .Cici .M ee,D .Bl,M G. M. Bell, C. D. Geyer, M. S. Chiechi, C. R. Porter, J. V. Weiss, A. E. [6] 2 .C igl .S hvola,D .Wie,D .Bueiz .W. A. Bruzewicz, A. D. Weibel, B. D. Shevkoplyas, S. S. Siegel, C. A. [2] complex of fabrication the simplifying for strategy a is Co-fabrication [1] 5 sabssfrcmaio,terssiiyo opris copper of resistivity the comparison, for basis a Swatik, As S. [5] D. Zrnic, D. [4] 3 .C igl .A rzwc,D .Wie,G .Whitesides, M. G. Weibel, B. D. Bruzewicz, A. D. Siegel, C. A. [3] rni,Bc ao,FL Raton, Boca Francis, o h eeomn fsl-eln materials. self-healing of development implications the has for technique This pressure. of modulation u fteguepesr n h topei pressure. atmospheric the and pressure gauge the of sum Deutsch, .H Cirlin, H. E. .E Berman, E. L. Schaefer, A. J. Weber, T. tung, Deutsch, M. Ocko, 1997 M. B. DiMasi, hm n.Ed. Int. Chem. cations Y16 .98. p. 1961 NY Environments Spatial aed,G .Whitesides, M. G. Bawendi, FL Raton, Boca Francis, and Lide, Taylor R. (D. ohm-cm atnz .M Whitesides, M. G. Martinez, lithography. of layer one using microfabrication of step chan- single microfluidic a in nels etc.—and waveguides, optical components— electrodes, functional heaters, multiple combining by devices microfluidic h plates. the constant. is rotation of frequency Mat. , 2007 55 C,NwYork New VCH, , 0786. 10 , hs e.B odn.Mte ae.Phys. Mater. Matter Condens. B: Rev. Phys. , 19 R adoko hmsr n Physics and Chemistry of Handbook CRC uf Sci. Surf. 727. , rs.Rs Technol. Res. Cryst. hs e.B odn.Matter Condens. B: Rev. Phys. 2008 uetcGlimIdu iudMtlAlloy Metal Liquid Gallium-Indium Eutectic A hooy rnils esrmns n Appli- and Measurements, Principles, Rheology: , 47 1L0 eea lcrcC. Schenectady, Co., Electric General 61GL50, , 1983 R adoko hmsr n Physics and Chemistry of Handbook CRC 142. , .Ls-omnMetals Less-Common J. vlaino ern ytm o s in Use for Systems Bearing of Evaluation 2007 1994 ne.Ce. n.Ed. Int. Chem., Angew. , 124 .A.Ce.Soc. Chem. Am. J. ne.Ce,It Ed. Int. Chem, Angew. . . uf nefc Anal. Interface Surf. 407. , ulse nie ac 0 2008 20, March online: Published 1999 d.Fnt Mater. Funct. Adv. hs e.B odn.Matter Condens. B: Rev. Phys. 2007 eie:Dcme 1 2007 11, December Revised: , eevd coe 2 2007 22, October Received: 34 ). 1129. , 1997 2008 1969 2008, , 1998 55 , 2006 2004 , 1999 130 18 15874. , , 18 alrand Taylor , 1 67. , ic the since ) 37 , ,83. , , , 45 1097–1104 36 550. , 59 17 6877. , Angew. ,981. 783. , Adv. 0 7 ,