Energy (kcal mol -1 ) Force (kcal mol -1 Å -1 ) Pore axis (Å) Mixed Mo-only S-only Graphene

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1 Force (kcl mol -1 Å -1 ) Energy (kcl mol -1 ) Mixed Mo-only S-only Grphene Mixed Mo-only S-only Grphene Pore xis (Å) -1 1 Pore xis (Å) Supplementry Figure 1 Energy Brriers. () Averge force on wter molecule computed long the pore xis for the Mixed, Mo-only, S-only nd grphene memrnes with similr pore res. () Potentil of men force computed long the pore xis for the Mixed, Mo-only, S-only nd grphene memrnes with similr pore res. To clculte the energy rrier experienced y wter molecule when moving cross pore, the simultion ox is first divided into ins of equl length long the xis of the pore (z). Next, in ech in, the force on ech wter molecule is verged over oth the simultion time nd ll the wter molecules of the in when the system is in equilirium (no externl pressure). Using the resulting verge force (F) long the pore xis (z) (Supplementry Fig. 1), the energy required to move wter molecule from reference point (z o ) in the ulk wter to ny other point (z) cn e otined y z F( z) dz. z

2 Velocity (m s -1 ) Velocity (m s -1 ) Mo-only Geometry S-only Geometry Mo (S site) Mo site Mo (S site) Mo site Distnce from the center of the pore (Å) Distnce from the center of the pore (Å) Supplementry Figure Velocities. Axil velocity profile of wter molecules in the rdil direction t the loction of S nd Mo tom lyers where S toms re replced y Mo toms (ll Mo toms). () For the Mo-only nnopore of Fig. in the mnuscript. () For the S-only nnopore of Fig. in the mnuscript. As discussed in the mnuscript, the higher flux oserved in the Mo-only pores is result of the nozzle-like structure of the pore compred to the S-only pores. To further confirm the importnce of the pore geometry in chieving the higher wter velocities, the role of the tom type (Mo or S) is excluded y replcing ll S toms y Mo toms (leding to fictitious three-lyer molydenum memrne) s shown in Supplementry Fig.. The xil velocities of wter in the rdil direction t the loction of ech tom lyer (the middle lyer of Mo, nd outer lyers of Mo (S lyers in rel MoS )) re plotted in Supplementry Fig. nd Supplementry Fig. for oth Mo-only nd S-only pore structures, respectively. Compring these velocity profiles with those of the rel MoS, in Fig. of the mnuscript, we notice tht the generl shpe of the velocity profiles re identicl mening tht the wter flux is enhnced due to the nozzle-like geometry (hourglss shpe) of the Mo-only pore nd remins lmost independent of the tom types.

3 Filtered wter molecules (#) Filtered wter molecules (#) Filtered wter molecules (#) Filtered wter molecules (#) MoX -Vrying of X MoX -Vrying of X MoX =.1 kcl mol -1 MoX =. MoS =3.13 Å MoX =.3 MoS =.61 MoX =.5 MoX =.6 MoX =3.3 MoX =3.6 MoX =3.9 c MoX -Vrying oth nd of X d YS -Vrying of Y MoX =.3 kcl mol -1 =3.3 Å MoS =.13 kcl mol -1 MoX =.5 MoS =.61 =3.3 =3.13 YS YS =.1 =.1 MoX =.3 MoX =.5 =3.6 =3.6 YS YS =.15 = Supplementry Figure 3 Other Trnsition Metl Dichlcogenide Memrnes. Wter permetion cross Mo-only geometry pore t 5 MP for () MoX y vrying of X () MoX y vrying of X c MoX y vrying oth nd of X (d) YS y vrying of Y. The moleculr dynmics forcefield prmeters re not ville for the other trnsition metl dichlcogenide mterils (TMD). Therefore, we swept over the Lennrd-Jones prmeters (, ) of MoS to investigte the potentil performnce of other TMD mterils. Two different types of mterils (MoX nd YS ) were considered. For the MoX, only the prmeters of the chlcogen tom (X) were vried to resemle the possile properties of memrnes like MoSe nd MoTe. The Mo-only pore geometry ws used nd pressure of 5 MP ws pplied. As shown in Supplementry Fig. 3 (prt, nd c), the wter permetion rte does not chnge significntly with vrying nd of X. Since tomic size of sulfur is smller thn those of the other chlcogen toms

4 (Se, Te, etc.), only higher vlues of were considered. For the other type, YS, the of the trnsition metl (Y) tom ws vried to study the efficiency of YS memrnes (Supplementry Fig. 3d). We did not chnge, since the pore re chnges for Mo-only pore geometry. As shown in Supplementry Fig. 3d, chnging the prmeter of Y effects the permetion rte of wter which decreses with incresing. The ion rejection percentges of MoX nd YS do not chnge significntly nd lie within 3% of ion rejection of MoS (9%). Bsed on the nlysis, we conclude tht the trnsition metl tom plys more importnt role thn the chlcogen tom when it comes to choosing the est TMD mteril for deslintion.

5 Supplementry Figure Clcultion of pore re. () Terminting toms of pore represented y their size. () Extruded re of the pore. The pore re, which is ccessile to wter molecules, is computed y considering the size of the toms on the edge of ech pore. First, the coordintes of ll terminting toms centers s well s the vn der Wls rdii of sulfur nd molydenum re input into the SolidWorks progrm s shown in Supplementry Fig.. Then the ccessile re is extruded through the toms (Supplementry Fig. ) nd the pore re is clculted.

6 Supplementry Tle 1 The Lennrd-Jones prmeters employed in the simultions re tulted elow. Interction [ ] [ ] C-C Mo-Mo..135 S-S O-O H-H 1.. N-N Cl-Cl C-O C-H Rest Otined y Lorentz-Berthelot rules. Supplementry References 1 Frimni, A. B. & Aluru, N. R. Sptil diffusion of wter in cron nnotues: from fickin to llistic motion. J. Phys. Chem. B 115, (11). Ling, T., Phillpot, S. R. & Sinnott, S. B. Prmetriztion of rective mny-ody potentil for Mo-S systems. Phys. Rev. B 79, 511 (9). 3 Joung, I. S. & Chethm, T. E. Determintion of lkli nd hlide monovlent ion prmeters for use in explicitly solvted iomoleculr simultions. J. Phys. Chem. B 11, 9-91 (8). Wu, Y. B. & Aluru, N. R. Grphitic cron-wter nononded interction prmeters. J. Phys. Chem. B 117, (13).

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