Single-layer MoS 2 nanopores as nanopower generators

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1 Letter oi:1.138/nture1893 Single-lyer MoS nnopores s nnopower genertors Jinong Feng 1, Mihel Grf 1, Ke Liu 1, Dmitry Ovhinnikov, Dumitru Dumeno, Mohmm Heirnin 3, Vishl Nnign 3, Nryn R. Aluru 3, Anrs Kis & Aleksnr Renovi 1 Mking use of the osmoti pressure ifferene etween fresh wter n sewter is n ttrtive, renewle n len wy to generte power n is known s lue energy 1 3. Another eletrokineti phenomenon, lle the streming potentil, ours when n eletrolyte is riven through nrrow pores either y pressure grient or y n osmoti potentil resulting from slt onentrtion grient. For this tsk, memrnes me of two-imensionl mterils re expete to e the most effiient, euse wter trnsport through memrne sles inversely with memrne thikness 7. Here we emonstrte the use of single-lyer molyenum isulfie (MoS ) nnopores s osmoti nnopower genertors. We oserve lrge, osmotilly inue urrent proue from slt grient with n estimte power ensity of up to 1 wtts per squre metre urrent tht n e ttriute minly to the tomilly thin memrne of MoS. Low power requirements for nnoeletroni n optoeletri evies n e provie y neighouring nnogenertor tht hrvests energy from the lol environment 8 11 for exmple, piezoeletri zin oxie nnowire rry 8 or single-lyer MoS (ref. 1). We use our MoS nnopore genertor to power MoS trnsistor, thus emonstrting self-powere nnosystem. MoS nnopores hve lrey emonstrte etter wter-trnsport ehviour thn grphene 13,1 owing to the enrihe hyrophili surfe sites (provie y the molyenum) tht re proue following either irrition with trnsmission eletron mirosopy (TEM) 1 or eletrohemil oxition 1. The osmoti power is generte y seprting two reservoirs ontining potssium hlorie (KCl) solutions of ifferent onentrtions with freestning MoS memrne, into whih single nnopore hs een introue 13. A hemil potentil grient rises t the interfe of these two liquis t nnopore in.-nm-thik, single-lyer MoS memrne, n rives ions spontneously ross the nnopore, forming n osmoti ion flux towrs the equilirium stte (Fig. 1). The presene of surfe hrges on the pore sreens the pssing ions oring to their hrge polrity, n thus results in net mesurle osmoti urrent, known s reverse eletroilysis 1. This tion seletivity n e etter unerstoo y nlysing the onentrtion of eh ion type (potssium n hlorie) s funtion of the ril istne from the entre of the pore, s we show here through moleulr-ynmis simultions (Fig. 1). We frite MoS nnopores either y TEM 13 (Fig. 1) or y the reently emonstrte eletrohemil retion (ECR) tehnique 1. With typil nnopore imeter in the rnge nm, stle Motion of ions Conentrtion is MoS trns Ag/AgCl eletroe + + A 7 Conentrtion (M) 3 Cl Cl Cl C mx = 1 C mx = 1 C mx = 1 C mx = 1 C mx = C mx = C mx = 1, Cl C mx = 1, Figure 1 Hrvesting osmoti energy with MoS nnopores., The experimentl set-up. Slt solutions with ifferent onentrtions re seprte y.-nm-thik MoS nnopore memrne. An ion flux riven y hemil potentil through the pore is sreene y the negtively hrge pore, forming iffusion urrent ompose of mostly positively hrge ions., Top pnel, typil simultion ox use in moleulr-ynmis simultions, showing the nnopore memrne (in lue n yellow) n the slt (green n re) in solution. Bottom pnel, moleulr-ynmis-simulte potssium-ion n hlorie-ion onentrtions s funtion of the ril istne from the entre of the pore. The region ner the hrge wll of the pore is representtive of the eletril oule lyer. C mx, mximum onentrtion; C min, minimum onentrtion., Exmple of TEM-rille MoS nnopore of imeter nm. 1 nm Distne from the entre of the pore (Å) 1 Lortory of Nnosle Biology, Institute of Bioengineering, Shool of Engineering, EPFL, 11 Lusnne, Switzerln. Lortory of Nnosle Eletronis n Strutures, Institute of Eletril Engineering n Institute of Mterils Siene n Engineering, Shool of Engineering, EPFL, 11 Lusnne, Switzerln. 3 Deprtment of Mehnil Siene n Engineering, Bekmn Institute for Avne Siene n Tehnology, University of Illinois t Urn-Chmpign, Urn, Illinois 181, USA. 11 ugust 1 VOL 3 NATURE Mmilln Pulishers Limite, prt of Springer Nture. All rights reserve.

2 RESEARCH Letter 1 1, Current (na) 1 Voltge (mv) Figure Eletril onutne n hemil retivity of the MoS nnopore., Current voltge response of MoS nnopores with ifferent pore sizes (lk, nm; re, nm; lue, nm) in 1 M KCl t ph., Conutne s funtion of slt onentrtion t ph. By fitting the Conutne (ns) Slt onentrtion (M) Conutne (ns) ph results to eqution (1), we fin the extrte surfe hrge vlues to e. C m,.3 C m n.88 C m for -nm, -nm n -nm pore, respetively., Conutne s funtion of ph for KCl onentrtion of 1 mm, for -nm, -nm n -nm pore. 1 1 osmoti urrent n e expete, owing to the long time require for the system to reh equilirium. We mesure the osmoti urrent n voltge ross the pore y using pir of Ag/AgCl eletroes to hrterize the urrent voltge (I V) response of the nnopore. To gin etter insight into the performne of the MoS nnopore power genertor, we first hrterize the ioni trnsport properties of MoS nnopores uner vrious ioni onentrtions n ph onitions, whih n provie informtion on the surfe hrge of the MoS nnopore. Figure shows the I V hrteristis of MoS nnopores of vrious imeters. A lrge pore onutne origintes from the ultrthin nture of the memrne. The onutne lso epens on the slt onentrtion (Fig. ) n shows sturtion t low slt onentrtions signture of the presene of surfe hrge on the nnopore 17,18. The preite pore onutne (G), tking into ount the ontriution of the surfe hrge (Σ), is given y 19 : L 1 G = κ + π ldu 1+ α+ βl Du 1 () 1 where κ is the ulk onutivity, L is the pore length, is the pore imeter, l Du is the Dukhin length (whih n e pproximte y Σ /e, where e is the elementry hrge n s is the slt onentrtion), s α is geometril preftor tht epens on the moel use (here, α = ) 19, n β n lso e pproximte to e to otin the est fitting greement 19. From the fitting results shown in Fig., we fin surfe hrge vlue of. C m,.3 C m n.88 C m for pores of size nm, nm n nm, respetively, t ph. These vlues re omprle to those reporte reently for grphene nno pores (.39 C m ) n nnotues (. C m to.1 C m ) t ph. The surfe hrge ensity n e further moulte y justing the ph to hnge the pore surfe hemistry (Fig. ). The onutne inreses with n inrese in ph, suggesting the umultion of more negtive surfe hrges in MoS nnopores. The simulte onutne from eqution (1) t 1 mm KCl is linerly proportionl to the surfe hrge vlues; thus, ph hnges oul sustntilly improve the surfe hrge up to.3.8 C m. The hemil retivity of MoS to ph is lso supporte y mesurements of zet potentil on MoS (ref. 1). However we lso notie tht, s with other nnofluii systems,, the surfe hrge ensity vries from pore to pore, whih mens tht ifferent pores n hve isprte vlues of the equilirium onstnt, owing to the vrious omintions of Mo n S toms 1 t the ege of the pores (s illuminte y moleulr-ynmis simultions 7 ). Next, we introue hemil potentil grient y using the KCl onentrtion grient system. The onentrtion grient rtio is efine s C is /C trns, where C is is the KCl onentrtion in the is hmer n C trns is tht in the trns hmer; the onentrtion rnges from 1 mm to 1 M. The highly negtively hrge surfe seletively psses the ions (in this se potssium ions) oring to their polrity, resulting in net positive urrent. By mesuring the I V response of the pore in the onentrtion grient system (Fig. 3), we n mesure the short-iruit (I s ) urrent orresponing to zero externl is, while the osmoti potentil n e otine from the open-iruit voltge (V o ). The pure osmoti potentil, V os, n urrent, I os, n then e otine y sutrting the ontriution from the eletroe solution interfe t ifferent onentrtions; this ontriution follows the Nernst eqution, (Extene Dt Fig. 1). The osmoti potentil is proportionl to the onentrtion grient rtio (Fig. 3) n shres similr tren with the osmoti urrent (Fig. 3). Current (na) Osmoti urrent, I os (na) I s I os C mx = 1 3 V os 1 1 Voltge (mv) I os , Slt onentrtion grient, C mx Osmoti potentil, V os (mv) Osmoti potentil, V os (mv) , Slt onentrtion grient, C mx Pore size (nm) Figure 3 Osmoti power genertion., Current voltge hrteristis for 1-nm nnopore in 1 M/1 mm KCl grient. The ontriution from the reox retion on the eletroes is sutrte from the mesure totl urrent (grey line) (Extene Dt Fig. 1), prouing the re she line, whih represents the pure osmoti ontriution. I s n V o re the short-iruit urrent n open-iruit voltge, respetively; I os n V os re the osmoti urrent n potentil., The generte osmoti potentil s funtion of the slt grient. C is is set to e 1 M KCl; C trns is tunle from 1 mm to 1 M KCl. The soli line represents liner fitting to eqution ()., Osmoti urrent s funtion of slt grient. The soli line fits proportionlly to the liner prt of eqution ()., Osmoti potentil n urrent s funtion of pore size. The she lines re guie to the eye n show the tren s the pore size is hnge. The error rs ome from the orresponing error estimtions n represent the s.e.m. (Methos). Osmoti urrent, I os (na) 198 NATURE VOL 3 11 August 1 1 Mmilln Pulishers Limite, prt of Springer Nture. All rights reserve.

3 Letter RESEARCH Single-lyer MoS nnopore Monolyer MoS Soure Gtes V+ Rp Is Drin D Vtg 1 μm G Soure S 3. Conutivity (μs). Vtg =.78 V Vtg = V Vtg =.78 V Single-lyer MoS nnopore Current, Is (na) 3. Single-lyer MoS trnsistor Figure Demonstrtion of self-powere nnosystem., Optil imge of the frite MoS trnsistor, with esigne gte, n rin n soure eletroes., Ciruit igrm for the self-powere nnosystem: the rin soure supply for the MoS trnsistor is provie y MoS nnopore, while seon nnopore evie opertes s the gte voltge soure. D, rin; G, gte; S, soure; Rp, pore resistne; Vtg, gte voltge; V+, nnopore output voltge. Rp onnete in series with Vtg hs een omitte., Powering ll the terminls of the trnsistor with nnopore genertors. The grph shows the moulte onutivity of the MoS trnsistor s funtion of the top gte voltge (Vtg). Inset, urrent voltge hrteristis t vrious gte voltges (.78 V, V n.78 V)..1. Vs (V) Vtg (V)... The mesure osmoti energy onversion is lso ph epenent (Extene Dt Fig., ). The inrese in ph les to higher gene rte voltge n urrent, suggesting the importne of surfe hrge to the ion-seletive proess. The extrte osmoti potentil is the iffusion potentil n it rises from ifferenes in the iffusive fluxes of positive n negtive ions, euse the pore is ion seletive: tions iffuse more rpily thn nions (Fig. 1). The iffusion potentil, Viff, n e esrie s: Viff = S(Σ )is is RT KCl ln trns F KCl () Here, S(Σ )is is the ion seletivity3 for the MoS nnopore (n equls 1 for the iel tion-seletive se, n for the non-seletive se); it is efine s S(Σ )is = t + t, where t+ n t re the trnsferene numers for positively n negtively hrge ions respetively. F, R n T re the Fry onstnt, the universl gs onstnt, n the trns temperture, respetively, while is KCl n KCl re the tivities of potssium ions in is n trns solutions. By fitting the experimentl t presente in Fig. 3 to eqution (), we fin the ion-seletivity oeffiient S(Σ )is to e., suggesting effiient tion seletivity. This is euse the size of our nnopores lies in the rnge in whih the eletril oule-lyer overlp n our insie the pore18, euse the Deye length, λb, is 1 nm for 1 mm KCl. As shown in Extene Dt Fig. 3, with onentrtion grient of 1 mm/1 mm in -nm pore, the ion seletivity pprohes nerly 1, presenting the onitions for iel tion seletivity3. To test the tion-seletive ehviour of the pore further, we investigte the reltionship etween power genertion n pore size. As shown in Fig. 3, smll pores isply etter voltge ehviour, refleting etter performne in terms of ion seletivity. The ion seletivity, S(Σ )is, ereses from. to.3 s the pore size inreses. We lulte the istriution of surfe potentil for ifferent pore sizes ( nm, nm n nm) in orer to ompre the seletivity ifferene (Extene Dt Fig. 3 ). It hs een proven tht the net iffusion urrent stems only from the hrge seprtion n onentrtion istriution within the eletril oule lyer, n therefore the totl urrent n e expete to inrese more rpily within smll pores in the oule-lyer overlp rnge ompre with lrger pore sizes (Fig. 3). This slight erese in urrent in lrger pores might e ttriute to reue lol onentrtion grient, n lso to prole overestimtion of the reox potentil sutrtion. The urrent n e lulte using either ontinuum-se Poisson Nernst Plnk (PNP) moel or moleulr-ynmis simultions. The mesure epenene of the osmoti potentil n osmoti urrent s funtion of the onentrtion rtio (Fig. 3, ) is well pture y oth omputtionl methos (moleulr ynmis, Extene Dt Fig., n ontinuum nlysis, Extene Dt Fig. ). The non-monotoni response to pore size (Fig. 3 n Extene Dt Fig., ) might not only e expline y possile epletion of the lol onentrtion grient in lrge pores, ut is lso preite y the ontinuum-se PNP moel (Extene Dt Fig. ) euse of the erese in ion seletivity. In orer to gin further insight into the thikness sling, we first verifie the pore-onutne reltion propose in eqution (1) y using moleulr ynmis (Extene Dt Fig. ). We foun tht ion moility lso sles inversely with memrne thikness (Extene Dt Fig. 7, ), whih my onform to previous oservtions. We then performe moleulr-ynmis simultions of multilyer memrnes of MoS to investigte the power generte y those memrnes. We oserve strong ey in the generte power s the numer of lyers inreses (Extene Dt Fig. 7, ), initing tht the est osmoti power genertion ours in two-imensionl memrnes. The onsisteny etween experiments n theoretil moels highlights two importnt ftors in hieving effiient power genertion from single-lyer MoS nnopore: tomi-sle pore thikness n surfe hrge. If we hve single-lyer MoS memrne with homogeneous pore size of 1 nm n porosity of 3%, then, y exploiting prlleliztion, the estimte power ensity woul reh 1 W m with KCl slt grient. These vlues exee y two to three orers of mgnitue the results otine with oron nitrie nnotues, n re million times higher thn the power ensity otine y reverse eletroilysis with lssil exhnge memrnes1 (Extene Dt Tle 1). As well s using KCl onentrtion grients, the nnopore power genertor onept oul lso e pplie to liqui liqui juntion 1 1 u g u s t 1 V O L 3 N ATU R E Mmilln Pulishers Limite, prt of Springer Nture. All rights reserve.

4 RESEARCH Letter systems with hemil potentil grient, euse the iffusion voltge origintes from the Gis mixing energy of the two liquis (Supplementry Informtion). Thus, high-performne, nnoporese genertors se on lrge numer of ville liqui omintions oul e explore. For exmple, we hve shown sustntil power genertion se on hemil potentil grient tht uses two types of liqui (Extene Dt Fig. 8). Consierle energy oul lso e generte y exploiting prlleliztion, with multiple smll pores or even ontinuous porous struture within lrge re of single-lyer MoS memrne, whih oul e sle up for mss proution using the ECR pore-frition tehnique 1 or plsm-se efet retion 7. The use of iniviul nnopores s miro/nno power soure hs long een expete. We fin here tht n iniviul osmoti genertor n lso serve s nnopower soure for self-powere nnosystem, owing to its high effiieny n power ensity. For this self-powere nnosystem, we hose the high-performne single-lyer MoS trnsistor (Fig. ) euse of its exellent opertion t low power 8. We hrterize this trnsistor in the onfigurtion shown in Fig., using two nnopores to pply voltges to the trnsistor s rin n gte terminls. As shown in Fig., y vrying the top gte voltge in the reltively nrrow winow of ±.78 V, we oul moulte the hnnel onutivity y ftor of to 8. Furthermore, when we fixe the gte voltge n vrie the rin soure voltge V s, (Fig. inset), we otine liner I s V s urve, emonstrting effiient injetion of eletrons into the trnsistor hnnel. Further lirtion with stnr power soure n e foun in Extene Dt Fig. 8. This system is n iel self-powere nnosystem in whih ll the evies re se on single-lyer MoS. We hve shown tht MoS nnopores re promising nites for investigting osmoti power genertion s renewle energy soure. The sustntil power generte in our experiments n e ttriute minly to the tomi-sle thikness of the MoS memrne. Our results lso provie new venues for stuying other memrne-se proesses, suh s wter eslintion 7 or proton trnsport 9. Furthermore, the nnopore genertor my see pplition in other ultrlow-power evies, suh s in eletronis. Online Content Methos, long with ny itionl Extene Dt isply items n Soure Dt, re ville in the online version of the pper; referenes unique to these setions pper only in the online pper. reeive Deemer 1; epte 13 My 1. Pulishe online 13 July Logn, B. E. & Elimeleh, M. Memrne-se proesses for sustinle power genertion using wter. Nture 88, (1).. Pttle, R. Proution of eletri power y mixing fresh n slt wter in the hyroeletri pile. Nture 17, (19). 3. Loe, S. Osmoti power-plnts. Siene 189, (197).. vn er Heyen, F. H., Stein, D. & Dekker, C. Streming urrents in single nnofluii hnnel. Phys. Rev. Lett. 9, 111 ().. Siri, A. et l. Gint osmoti energy onversion mesure in single trnsmemrne oron nitrie nnotue. Nture 9, 8 (13).. Suk, M. E. & Aluru, N. Wter trnsport through ultrthin grphene. J. Phys. Chem. Lett. 1, (1). 7. Heirnin, M., Frimni, A. B. & Aluru, N. R. Wter eslintion with single-lyer MoS nnopore. Nture Commun., 81 (1). 8. Wng, Z. L. & Song, J. Piezoeletri nnogenertors se on zin oxie nnowire rrys. Siene 31, (). 9. Wng, Z. L. Self-powere nnosensors n nnosystems. Av. Mter., 8 8 (1). 1. Tin, B. et l. Coxil silion nnowires s solr ells n nnoeletroni power soures. Nture 9, (7). 11. Xu, S. et l. Self-powere nnowire evies. Nture Nnotehnol., (1). 1. Wu, W. et l. Piezoeletriity of single-tomi-lyer MoS for energy onversion n piezotronis. Nture 1, 7 7 (1). 13. Liu, K., Feng, J., Kis, A. & Renovi, A. Atomilly thin molyenum isulfie nnopores with high sensitivity for DNA trnslotion. ACS Nno 8, 11 (1). 1. Frimni, A. B., Min, K. & Aluru, N. R. DNA se etetion using single-lyer MoS. ACS Nno 8, (1). 1. Liu, X. et l. Top own frition of su-nnometre semionuting nnorions erive from molyenum isulfie sheets. Nture Commun., 177 (13). 1. Feng, J. et l. Eletrohemil retion in single lyer MoS : nnopores opene tom y tom. Nno Lett. 1, 331 (1). 17. Stein, D., Kruithof, M. & Dekker, C. Surfe-hrge-governe ion trnsport in nnofluii hnnels. Phys. Rev. Lett. 93, 391 (). 18. Boquet, L. & Chrlix, E. Nnofluiis, from ulk to interfes. Chem. So. Rev. 39, (1). 19. Lee, C. et l. Lrge pprent eletri size of soli-stte nnopores ue to sptilly extene surfe onution. Nno Lett. 1, 37 (1).. Shn, Y. et l. Surfe moifition of grphene nnopores for protein trnslotion. Nnotehnology, 91 (13). 1. Ge, P. et l. Hyrogen evolution ross nno-shottky juntions t ron supporte MoS tlysts in iphsi liqui systems. Chem. Commun. 8, 8 8 (1).. Kim, D.-K., Dun, C., Chen, Y.-F. & Mjumr, A. Power genertion from onentrtion grient y reverse eletroilysis in ion-seletive nnohnnels. Miroflui. Nnofluiis 9, 11 1 (1). 3. Vlssiouk, I., Smirnov, S. & Siwy, Z. Ioni seletivity of single nnohnnels. Nno Lett. 8, (8).. Co, L. et l. Towrs unerstning the nnofluii reverse eletroilysis system: well mthe hrge seletivity n ioni omposition. Energy Environ. Si., 9 (11).. Wu, J., Gerstnt, K., Zhng, H., Liu, J. & Hins, B. J. Eletrophoretilly inue queous flow through single-wlle ron nnotue memrnes. Nture Nnotehnol. 7, (1).. Wuge, P. et l. Diret n slle eposition of tomilly thin low-noise MoS memrnes on pertures. ACS Nno 9, (1). 7. Surwe, S. P. et l. Wter eslintion using nnoporous single-lyer grphene. Nture Nnotehnol. 1, 9 (1). 8. Risvljevi, B., Renovi, A., Brivio, J., Giometti, V. & Kis, A. Single-lyer MoS trnsistors. Nture Nnotehnol., 17 1 (11). 9. Wlker, M. I., Breuninger-Weimer, P., Wetherup, R. S., Hofmnn, S. & Keyser, U. F. Mesuring the proton seletivity of grphene memrnes. Appl. Phys. Lett. 17, 131 (1). Supplementry Informtion is ville in the online version of the pper. Aknowlegements This work ws finnilly supporte y the Europen Reserh Counil (grnt 9398, PorABEL), y Swiss Ntionl Siene Fountion (SNSF) Consolitor grnt (BIONIC BSCGI_178), y SNSF Sinergi grnt 177, n y funing from the Europen Union s Seventh Frmework Progrmme FP7/7-13 uner Grnt Agreement 3188 (for single-nnometre lithogrphy). We thnk the Centre Interisiplinire e Mirosopie Eletronique (CIME) t the Éole Polytehnique féérle e Lusnne (EPFL) for ess to eletron mirosopes. Devie frition ws prtilly rrie out t the EPFL Center for Miro/Nnotehnology (CMi). N.R.A. is supporte y the Air Fore Offie of Sientifi Reserh uner grnt FA9-1-1-, n y the Ntionl Siene Fountion uner grnts 18, 188, 119 n197. We knowlege the use of the prllel omputing resoure Blue Wters, provie y the University of Illinois n the Ntionl Center for Superomputing Applitions. Author Contriutions J.F. n A.R. oneive the ie, esigne ll experiments, n wrote the mnusript. J.F. n M.G. performe mesurements n t nlysis. J.F. n K.L. frite the nnopore evie. D.O. frite the MoS trnsistor n D.D. performe hemil-vpour-eposition MoS growth uner A.K. s supervision. J.F. n D.O. emonstrte the self-powering of the nnosystem. M.H., V.N., n N.R.A. uilt the omputtionl nnofluiis moel n interprete the simultion results. All uthors provie onstrutive omments on the mnusript. Author Informtion Reprints n permissions informtion is ville t The uthors elre no ompeting finnil interests. Reers re welome to omment on the online version of the pper. Corresponene n requests for mterils shoul e resse to J.F. (jinong.feng@epfl.h) or A.R. (leksnr.renovi@epfl.h). Reviewer Informtion Nture thnks Z. Siwy n the other nonymous reviewer(s) for their ontriution to the peer review of this work. NATURE VOL 3 11 August 1 1 Mmilln Pulishers Limite, prt of Springer Nture. All rights reserve.

5 Letter RESEARCH Methos Nnopore frition. We frite MoS nnopores either y using the tomisle ECR tehnique 1 or y eletron irrition uner TEM 13. Prior to nnopore frition, we rete freestning MoS memrne 3. Briefly, we use KOH wet ething to prepre SiN x memrnes (of size 1 μm 1 μm to μm μm; nm thik). We then use fouse ion em (FIB) or eem lithogrphy (followe y retive ion ething) to rill n opening of 3 nm in the memrne. Next we suspen single-lyer MoS memrnes, grown y hemil-vpour eposition, on the opening y trnsferring them from spphire growth sustrtes 3. TEM irrition n e pplie to rill single pore n imge the pore. ECR is one y pplying step-like trnsmemrne potentil to the memrne n monitoring the trnsmemrne ioni urrent with Femto DLPCA- mplifier (Femto Messtehnik GmH), with ustom-me feek ontrol on trnsmemrne onutne. Nnopores re forme when rehing the ritil voltge of MoS oxition (>.8 V). We then lirte the pore size using I V hrteristis. Nnofluii mesurements. Nnofluii trnsport experiments re performe s esrie 1. The nnopore hips re mounte in ustom-me polymethylmethrylte hmer, n then wette with n H O:ethnol (1:1) solution. Nnofluii mesurements re rrie out y tking the I V hrteristis of the nnopore in ifferent KCl solutions (Sigm Alrih; the ioni onentrtion or ph of the solution vries), using n Axopth B pth-lmp mplifier (Moleulr Devies In.). A pir of hlorinte Ag/AgCl eletroes (whih hve een rehlorinte regulrly) is use to pply voltge n to mesure the urrent. In ition, the eletroe potentil ifferenes in solutions of ifferent onentrtions re lirte with sturte Ag/AgCl referene eletroe (Sigm Alrih). To mesure osmoti power genertion, we fille the reservoirs with solutions of ifferent onentrtions, rnging from 1 mm to 1 M. Mesurements re performe t vrious ph onitions. We foun tht power genertion ws optiml t ph 11. First, we mesure the I V response; we otine the short-iruit urrent from the intereption of the urve t zero voltge, n the open-iruit voltge from the intereption of the urve t zero urrent. Next, to get the purely osmotilly riven ontriution, we sutrte the ontriution me y the eletroe potentil ifferene tht results from the reox potentil in ifferent onentrtions (Extene Dt Fig. 1). For ll experiments, we performe ross-heking mesurements, inluing hnging the iretion of ph n onentrtion to mke sure tht the nno pores were not sustntilly enlrge uring the experiments. Most MoS pores were generlly stle uring hours of experiments owing to their high mehnil strength n stility within the ± mv is rnge. Thus, we strongly reommen the use of smll supporting FIB/eem-rille opening winows (of imeter 3 nm) for suspene memrnes. Chrteriztion of single-lyer MoS trnsistors. We frite single-lyer MoS trnsistors using proeure similr to tht in ref. 8. For eletril mesurements we use n Agilent 7B soure-meter unit (SMU), n SR-7 low-noise urrent premplifier n Keithley igitl multimeter (DMM; input impene >1 1 Ω). All mesurements were performe in mient onitions in the rk. An improve effiieny of power onversion in nnopores is otine y using omintion of pure room-temperture ioni liquis: 1-utyl--methylimizolium hexfluorophosphte (Bmim PF ) n zin hlorie solution. We ompre the performne of the single-lyer MoS trnsistor in two ses. First, we use two nnopores to pply V tg n V s, while using urrent mplifier n voltmeter to ontrol the urrent n voltge rop ross the evie (see Extene Dt Fig. 8). In this se, we use voltge iviers to hnge the soure n gte voltge on the evie (not shown in Fig. n Extene Dt Fig. 8). Seon, we use the SMU to perform stnr two-ontt mesurements. Although the hrteristis of our trnsistor re similr in oth set-ups, we omment here on the ifferene etete in the onutivity of the ON stte. We ttriute it to the slow response of the evie in the first se. The hnge in trnsistor resistne tht ours when pplying gte voltge les to hnge in the impene of the evie n thus hnge in the pplie effetive voltge, V ev (mesure with voltmeter onnete in prllel). The nnopore rets to the hnge in impene with ertin stiliztion time (from 1 s to 1 s). This ppers to e hystereti effet n influenes the onutivity versus gte-voltge mesurements. In the seon se, on the other hn, V ev = V s is onstnt. There re severl seonry effets, whih might in turn influene the mesure vlues of two-proe onutivity. In reltively short hnnel evies, pplie V s might prtilly ontriute to gting of the hnnel n furthermore to moifition of ontt resistne. This oul e unerstoo y ompring the vlues of V s (roun 1 mv) n V tg (78 mv). We lso o not exlue the possiility of slight oping vritions n hystereti effets tht our euse of the filling of trp sttes insie the trnsistor hnnel. However, y riving evie to the ON stte n stilizing the urrent for resonle mount of time, we otine very goo mth in rin soure I s V s hrteristis (Extene Dt Fig. 8). We thus onlue tht, lthough there re ifferenes in performne in the two ses, these ifferenes originte minly from the slow response time of the nnopore. We extrte the resistne n power of the nnopore y using the ioni liqui Bmim PF. By onsiering the simple resistor network (Extene Dt Fig. 8, inset), we oul extrt the output power s funtion of the lo resistne, R lo. We fit our epenene oring to the following moel, whih ssumes onstnt V out n R pore : VoutRlo Power = ( R + R ) p lo n foun goo fit with V out =.83 V, whih is lose to the mesure V out of.78 V, n with nnopore impene, R p, of 9. ±.1 MΩ (Extene Dt Fig. 8). Dt nlysis. All t nlysis hs een one using ustom-me Mtl (R1) oe. First, we reore I V hrteristis with n Axopth B mplifier, y using either n utomti or mnul voltge swith. We then segmente the urrent tre into piees of onstnt voltge, V. We extrte the men, μ(v), n stnr evition, σ(v), of the stle prt of eh segment n generte n I V plot. The error rs re the stnr evitions (see Fig. 3 n Extene Dt Fig. ). All I V hrteristis were liner. In orer to propgte the error orretly, we use liner fitting metho 31. Using this metho, we n extrt the,, σ n σ vlues of the first-orer polynomil I(V) = V +. The onutne is the slope,, of the I V urve, n esries the offset. The height of the error rs reporte for onutne mesurements is σ. We report the osmoti power genertion using the osmoti urrent, I os, n osmoti voltge, V os. Strting from the liner-fit vlues of the I V plot, we n lulte the mesure urrent n voltge: I mes = n V mes = /. These mesure vlues hve to e juste for the eletroe potentil: V os =V mes V reox n I os = (V os /V mes ) I mes. Assuming n unertinty in our estimtion of reox potentil, σ reox, of %, we n propgte the errors using the following formuls 3 : σ = σ σ σ 1 + V + os σ = σ +( V σ ) + σ reox Ios reox reox We use these reltions to lulte the error rs shown in plots of osmoti voltge n urrent (Fig. 3 n Extene Dt Fig. ). Computtionl simultions. Moleulr-ynmis simultions. These simultions were performe using the LAMMPS pkge 33. A MoS memrne ws ple etween two KCl solutions s shown in Extene Dt Fig.. A fixe grphene wll ws ple t the en of eh solution reservoir. A nnopore ws rille in MoS y removing the esire toms. The essile pore imeter onsiere in ll of the moleulr-ynmis simultions is. nm with surfe hrge ensity of.9 C m. The system imensions were nm nm 3 nm in the x, y n z iretions, respetively. We use the extene simple point hrge (SPC/E) wter moel, n pplie the SHAKE lgorithm to mintin the rigiity of eh wter moleule. The Lennr Jones (LJ) prmeters re tulte in Supplementry Tle 1. The LJ ut-off istne ws 1 Å. The long-rnge intertions were ompute y the prtile prtile prtile mesh (PPPM) metho 3. Perioi ounry onitions were pplie in the x n y iretions. The system is non-perioi in the z iretion. For eh simultion, first the energy of the system ws minimize for 1, steps. Next, the system ws equilirte in the isothermi isori (otherwise known s NPT) ensemle for ns t pressure of 1 tm n temperture of 3 K to reh the equilirium ensity of wter. Grphene n MoS toms were hel fixe in spe uring the simultions. Then, nonil (NVT) simultions were performe, uring whih the temperture ws mintine t 3 K y using the Nosè Hoover thermostt with time onstnt of.1 ps (refs 3, 3). Trjetories of toms were ollete every pioseon to otin the results. For urte moility lultions, however, the trjetories were store every ten femtoseons. Continuum moel. We lso use the ontinuum se two-imensionl Poisson Nernst Plnk (PNP) moel. We neglete the ontriution of H + n OH ions in this lultion, s their onentrtions re muh lower ompre with the ulk onentrtion of the other ioni speies ( n Cl ). Hene, wter-issoition effets re not onsiere in the numeril moel. Further, we ssume tht the ions re immoile insie the steri lyer n o not ontriute to the ioni urrent. We lso i not moel the Fri retions ourring ner the eletroe. Finlly, we ssume tht the onvetive omponent of urrent originting from the flui flow is negligile n oes not ontriute to the non-monotoni osmoti urrent oserve in our experiments. We vlite this ssumption y performing etile 1 Mmilln Pulishers Limite, prt of Springer Nture. All rights reserve.

6 RESEARCH Letter ll-tom moleulr-ynmis simultions n preite the ontriution of eletroosmoti veloity in omprison with the rift veloity of the ions. Uner these ssumptions, the totl flux of eh ioni speies (Γ i ) is ontriute y iffusive omponent resulting from the onentrtion grient, n n eletrophoreti omponent rising from the potentil grient, s given y: Γ = D ΩzF φ i i i i i i where F is Fry s onstnt, z i is the vlene of the ith speies, D i is the iffusion oeffiient, Ω i is the ioni moility, i is the onentrtion n φ is the eletril potentil. Note tht the ioni moility is relte to the iffusion oeffiient y Einstein s reltion 37 D, Ω i = i, where R is the iel gs onstnt n T is the RT thermoynmi temperture. The mss trnsport of eh ioni speies is: i = Γi t The iniviul ioni urrent (I i ) ross the reservoir n the pore is lulte y integrting their respetive fluxes over the ross-setionl re, tht is: Ii = zf i Γi S The totl ioni urrent t ny xil lotion is lulte s I = i zf = 1 i Γi S, where S is the ross-setionl re orresponing to the xil lotion n m is the numer of ioni speies. In orer to etermine the eletri potentil long the system, we solve the Poisson eqution: ρe ( εr φ)= ε where ε is the permittivity of free spe, ε r is the reltive permittivity of the meium n ρ e is the net spe hrge ensity of the ions, efine s: m e 1 ρ = F i= z i i We provie the neessry ounry onitions for the losure of the prolem. The norml flux of eh ion is ssume to e zero on ll the wlls so tht there is no lekge of urrent. To onserve hrge on the wlls of the pore, the eletrostti ounry onition is given y: σ n φ = εε where n enotes the unit norml vetor (pointing outwrs) to the wll surfe n σ is the surfe hrge ensity of the wlls. The ulk onentrtion of the is reservoir is mintine t C mx n the ulk onentrtion on the trns reservoir is mintine t C min. As we re intereste in unerstning the osmoti shortiruit urrent, I s, we o not pply ny voltge ifferene ross the reservoirs. Thus, the ounry onitions t the ens of the is n trns reservoirs re speifie s: r = C, φ = i mx = C, φ = i min m The ouple PNP equtions re numerilly solve using the finite volume metho in OpenFOAM ( The etils of solver implementtion re isusse in refs 38. The simulte omin onsiste of MoS nnopore of length, L n,. nm n imeter, n, vrying from. nm to nm. The simulte length of the reservoir ws L is = L trns = 11 nm; the imeter of the reservoir ws nm. KCl uffer solution ws use in the simultion. The ulk onentrtion of the is reservoir ws fixe t 1 M n the onentrtion in the trns reservoir ws vrie systemtilly vrie from 1 mm to 1 M. The simultion temperture ws 3 K. The ulk iffusivities of n Cl were m s 1 n m s 1. The ieletri onstnt of the queous solution ws ssume to e 8. We lso ssume zero surfe hrge ensity on the wlls of the reservoir, s the reservoir is too fr wy from the nnopore to hve n influene on the trnsport. Unless otherwise stte, the hrge on the wlls of the MoS nnopore is ssume to e σ n =.9 C m, onsistent with the surfe hrge lulte from our moleulr-ynmis simultions. 3. Dumeno, D. et l. Lrge-re epitxil monolyer MoS. ACS Nno 9, 11 (1). 31. York, D., Evensen, N. M., Mrtınez, M. L. & Delgo, J. D. B. Unifie equtions for the slope, interept, n stnr errors of the est stright line. Am. J. Phys. 7, (). 3. Ku, H. Notes on the use of propgtion of error formuls. J. Res. Ntionl Bureu Stnrs 7C, 3 73 (19). 33. Plimpton, S. Fst prllel lgorithms for short-rnge moleulr ynmis. J. Comput. Phys. 117, 1 19 (199). 3. Hokney, R. W. & Estwoo, J. W. Computer Simultion Using Prtiles (CRC Press, 1988). 3. Nosé, S. A unifie formultion of the onstnt temperture moleulr ynmis methos. J. Chem. Phys. 81, (198). 3. Hoover, W. G. Cnonil ynmis: equilirium phse-spe istriutions. Phys. Rev. A 31, (198). 37. Prostein, R. F. Physiohemil Hyroynmis: An Introution. (John Wiley & Sons, ). 38. Nnign, V. V. & Aluru, N. Unerstning nomlous urrent voltge hrteristis in mirohnnel nnohnnel interonnet evies. J. Colloi Interfe Si. 38, (1). 39. Nnign, V. V. & Aluru, N. Nonliner eletrokineti trnsport uner omine n fiels in miro/nnofluii interfe evies. J. Fluis Eng. 13, 11 (13).. Nnign, V. V. & Aluru, N. Chrteriztion of eletrohemil properties of miro nnohnnel integrte system using omputtionl impene spetrosopy (is). Eletrohim. At 1, 1 3 (13). 1. Weinstein, J. N. & Leitz, F. B. Eletri power from ifferenes in slinity: the ilyti ttery. Siene 191, 7 9 (197).. Auinos, R. Reverse eletroilysis. Stuy of the eletri energy otine y mixing two solutions of ifferent slinity. J. Power Soures 1, 3 17 (1983). 3. Turek, M. & Bnur, B. Renewle energy y reverse eletroilysis. Deslintion, 7 7 (7).. Su, F., Mtsuo, T. & Ushio, D. Trnsient hnges in the power output from the onentrtion ifferene ell (ilyti ttery) etween sewter n river wter. Energy 3, (7).. Veermn, J., De Jong, R., Skes, M., Metz, S. & Hrmsen, G. Reverse eletroilysis: omprison of six ommeril memrne pirs on the thermoynmi effiieny n power ensity. J. Memr. Si. 33, 7 1 (9). 1 Mmilln Pulishers Limite, prt of Springer Nture. All rights reserve.

7 Letter RESEARCH I mesure V mesure E reox Eletrometer V os = V mesure -Ereox I os = I mesure - I reox R P V os E letroe potentil ( mv ) Nernst eqution Referene eletroe Eletroes Slt onentrtion grient C mx LogC mx I mesure,na V mesure,mv E reox,mv V os,mv I os, na Setto Current (na) Extene Dt Figure 1 Sutrtion of the ontriution me y eletroes, n stility of the nnopore genertor., Digrm showing the ontriutions of ifferent prts of the system to the overll mesure urrent. The osmoti ontriution is otine y sutrting the ontriution of the potentil ifferene t the eletroes from the mesure voltge or urrent. V mesure is the mesure voltge; E reox is the Time (s) reox potentil ifferene., Eletroe ontriution s funtion of the slt onentrtion grient: vlues otine from the Nernst eqution, n mesure eletroe reox potentil ifferenes t the referene eletroe., The t use for the sutrtion. E reox, the reox potentil t the eletroes., A 1-hour tre of ioni urrent, showing the stility of 1-nm pore in 1 M KCl/1 mm KCl. Inset, the esign of the fluii ell. 1 Mmilln Pulishers Limite, prt of Springer Nture. All rights reserve.

8 RESEARCH Letter Osmoti potentil V OS (mv) ph = 3 ph = ph = 11 Osmoti urrent I OS (na) ph = 3 ph = ph = , , Osmoti potentil V OS (mv) Slt onentrtion grient C mx 1 nm, ph = 11 3 nm, ph = 11 Osmoti urrent I OS (na) Slt onentrtion grient C mx , , nm, ph = 11 3 nm, ph = 11 Slt onentrtion grient C mx Extene Dt Figure Depenene of osmoti power genertion on ph n pore size.,, Osmoti potentil () n osmoti urrent () generte using 3-nm pore uner ifferent ph onitions (ph 3, or 11) n in ifferent onentrtion grients. Power genertion (oth osmoti potentil n osmoti urrent) t ph 3 is very low n sometimes Slt onentrtion grient C mx flututes to negtive, initing tht the pore hrge is reltively low. One possile explntion for the negtive voltge point is tht the surfe hrge on the pore hs flutute to positive.,, Osmoti potentil () n osmoti urrent () generte using two ifferent pores (3-nm n 1-nm) t ph 11 in ifferent onentrtion grients. 1 Mmilln Pulishers Limite, prt of Springer Nture. All rights reserve.

9 Letter RESEARCH y istne to pore opening (nm) nm nm nm y istne to pore opening (nm) x istne to pore opening (nm) x istne to pore opening (nm) x istne to pore opening (nm) C min /C mx V mesure, mv E reox, mv V os, mv Ion seletivity y istne to pore opening (nm) Potentil (V) 1mM/1mM mM/1mM mM/1M mM/1mM mM/1M Extene Dt Figure 3 Iel tion seletivity of the pore., Clulte surfe potentil istriution of MoS nnopores of imeter nm (), nm (), n nm () uner fixe surfe hrge ensity., Ion seletivity in ifferent slt grients. The ion seletivity lso epens on the Deye length when the onentrtion grient is fixe; with grient of 1 mm/1 mm n -nm pore, the ion seletivity pprohes nerly 1, initing the iel tion seletivity. 1 Mmilln Pulishers Limite, prt of Springer Nture. All rights reserve.

10 RESEARCH Letter Current (na) - - C mx C mx =1 C mx =1 = C mx = Applie eletri fiel (V Å -1 ) Conentrtion (M) Cl - Cl - Cl - C mx =1 C mx =1 C mx =1 C mx =1 C mx = C mx = C mx =1 Cl - C mx = Distne from the enter of the pore (Å) e Short iruit urrent (na) C mx Open iruit eletri fiel (mv Å -1 ) Extene Dt Figure Moleulr-ynmis simultions of power genertion for vrious rtios of onentrtion grients., A typil simultion ox., Current s funtion of the pplie eletri fiel for single-lyer MoS, t ifferent onentrtion rtios., n Cl C mx onentrtions s funtion of the ril istne from the entre of the pore, for ifferent onentrtion rtios., Short-iruit urrent s funtion of the onentrtion rtio. e, Open-iruit eletri fiel s funtion of the onentrtion rtio. 1 Mmilln Pulishers Limite, prt of Springer Nture. All rights reserve.

11 Letter RESEARCH.3.3 Short iruit urrent I s (na) Short iruit urrent I s (na) Slt onentrtion grient C mx 1 1 Pore size (nm) Extene Dt Figure Continuum-se PNP moelling of power genertion., Short-iruit urrent, I s, s funtion of the onentrtion grient rtio. The imeter of the nnopore here is. nm., I s s funtion of the nnopore imeter. The slinity onentrtion rtio is fixe t 1,. The surfe hrge of the nnopore, σ n, is.9 C m. 1 Mmilln Pulishers Limite, prt of Springer Nture. All rights reserve.

12 RESEARCH Letter 3 3 Current (na) Lyer-MoS Lyer-MoS 3 Lyer-MoS Lyer-MoS Lyer-MoS Applie voltge (V) 1 Lyer-MoS Conutne (ns) Reiprol thikness, t -1 (Å -1 ) 1 8 x1 11 Cl - Moility (s kg -1 ) Numer of MoS lyers Extene Dt Figure Moleulr-ynmis-moelle onutne s funtion of memrne thikness., I V urves for six memrnes with ifferent numer of MoS lyers, ross symmetril 1 M KCl solution. The inset illustrtes simulte multilyer memrnes., Conutne of the nnopore s funtion of the reiprol thikness of the memrne (t 1 )., Averge moility of eh ion for ifferent numers of lyers of MoS memrnes. 1 Mmilln Pulishers Limite, prt of Springer Nture. All rights reserve.

13 Letter RESEARCH Conentrtion (M) lyer Cl - 1 lyer lyers Cl - lyers 3 lyers Cl - 3 lyers lyers Cl - lyers lyers Cl - lyers 1 lyers Cl - 1 lyers λ region Moility (s kg ) within λ Cl - within λ outsie λ Cl - outsie λ Distne from the enter of the pore ( Å) Numer of MoS lyers Open iruit eletri fiel (mv Å -1 ) mx )-1 P n mx (P Numer of MoS lyers Extene Dt Figure 7 Simulte power genertion s funtion of memrne thikness., n Cl onentrtions s funtion of the ril istne from the entre of the pore for single-lyer n multilyer memrnes. The λ region, ner the hrge wll of the pore, is representtive of the eletril oule lyer., The moility of eh Numer of MoS lyers ion type within n outsie the λ region for ifferent lyers of memrnes., The open-iruit eletri fiel ross the memrne for ifferent numers of MoS lyers., Rtio of the mximum power (P) generte y multilyer memrnes to the mximum power generte y single-lyer memrne, for ifferent numers of lyers. 1 Mmilln Pulishers Limite, prt of Springer Nture. All rights reserve.

14 RESEARCH Letter Single-lyer MoS nnopore Single-lyer MoS trnsistor V tg Single-lyer MoS nnopore G R P V + A D S V Conutivity (µs) Nnopore Externl soure V tg (V) V tg =.78V Single-lyer MoS nnopore V out R P 1 1 Current I s (na) -1 - Nnopore Externl soure Power (nw) 1 A R lo V V s (V) Extene Dt Figure 8 Chrteriztion of single-lyer MoS trnsistor with nnopores n SMU., Eletril mesurements with two nnopores (V +, nnopore output voltge; V s, rin soure voltge; V tg, top gte voltge). The voltge rop ross the trnsistor hnnel is monitore with the voltmeter (V); urrent is mesure with urrent mplifier (A)., Comprison of nnopore mesurements with 8 1 R lo (MOhm) 1 1 stnr two-proe mesurements me with n externl soure., I V hrteristis t V tg =.78 V fter urrent stiliztion, mesure in oth set-ups., Output power of nnopore in Bmim PF /zin hlorie s funtion of lo resistne, R lo. Inset, iruit igrm for these mesurements. 1 1 Mmilln Pulishers Limite, prt of Springer Nture. All rights reserve.

15 Letter RESEARCH Extene Dt Tle 1 Power genertion oring to memrne thikness Reverse eletroilysis ells Power ensity(w/m ) Memrne thikness Ref. 1 Ref. Ref. 3 Ref. Ref. Ref. Ref. This work.17 1 mm. 3 mm..19 mm. 1 mm.9. mm mm 1 µm 1. nm Multilyer MoS (Simultions) 3 7. nm The tle shows the power generte y memrnes of ifferent thikness; t from refs,, 1. 1 Mmilln Pulishers Limite, prt of Springer Nture. All rights reserve.