Title of proton-exchanged layered sodium. Citation PHYSICAL REVIEW B (2009), 79(14)

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1 Title First-priniples investigtion of of proton-exhnged lyered sodium uthor(s) Mori, Mshiro; Kumgi, Yu; Mtsun Iso Cittion PHYSICL REVIEW B (2009), 79(14) Issue Dte URL Right 2009 The merin Physil Soiet Type Journl rtile Textversion pulisher Kyoto University

2 First-priniples investigtion of tomi strutures nd stility of proton-exhnged lyered sodium titnte Mshiro Mori, 1 Yu Kumgi, 1 Ktsuyuki Mtsung, 1,2, * nd Iso Tnk 1,2 1 Deprtment of Mterils Siene nd Engineering, Kyoto University, Kyoto , Jpn 2 Nnostrutures Reserh Lortory, Jpn Fine Cermis Center, Ngoy , Jpn Reeived 30 Jnury 2009; revised mnusript reeived 1 pril 2009; pulished 24 pril 2009 tomi strutures nd ioni sustitutions in sodium titnte N 2 x H x Ti 3 O 7, hving Ti 3 O 7 sheetlike lyers with N + nd H + in etween, were investigted y first-priniples lultions. The formtion energies vi ion exhnge of N + nd H + were nlyzed y using the superell totl energies nd ioni hemil potentils determined with the id of experimentl thermodynmi dt. It ws found tht ioni sustitutions of N + y H + tke ple even in lkline solution onditions s found in previous experiments. In ddition, the onding strength etween the Ti 3 O 7 lyers tends to derese with more N + sustitutions y H +, whih is relted to ph effets on exfolition events of Ti 3 O 7 sheetlike lyers from lyered titnte prior to the nnotue formtion. DOI: /PhysRevB PCS numers: y, Dy I. INTRODUCTION Reently, titnte nnotues hve drwn gret sientifi nd industril ttention, sine Ksug et l. reported preprtion of TiO 2 -derived titnte nnotues y n lkline hydrotherml method. 1 The nnotue frition y the lkline hydrotherml method n e esily performed y treting TiO 2 powder in superoiled C solution of onentrted NOH 5 15 M without ny srifiil templtes. The titnte nnotues re multiwlled sroll-type open-ended ones with dimeter of out 80 Å nd lyered sping of out 7 8 Å. These titnte nnotues re expeted tht their unique struture derives numerous pplitions not only to phototlysis 2 5 nd tlysis, 6 9 ut lso to ion exhnge, Li ttery, hydrogen storge, 16,17 nd even nnosle onfinement tool 18,19 or retion environment. 20 Mny groups hve ttempted to revel formtion mehnism of the TiO 2 -derived titnte nnotues. pprently, there is onsensus tht, fter reking of hemil onds in the strting three-dimensionl TiO 2 struture y high onentrted NOH queous solution, lyered titntes re formed s intermedite, nd then they onverted into nnotues through Ti-O sheet folding mehnism. Sodium titnte N 2 Ti 3 O 7 is regrded s one of ndidtes for the intermedite phse the rystl struture shown in Fig. 1. This is euse this mteril hs rystl struture ontining Ti-O lyers nd the hemil omposition of the individul Ti-O lyer Ti 3 O 7 is lose to typil Ti/O molr rtio of the TiO 2 -derived titnte nnotues suh s H 2 Ti 3 O 7. However, the nnotue formtion ours in onentrted NOH solutions, nd it is expeted tht N + ions in this phse my e prtilly sustituted y other ions, typilly H +, vi ion exhnge. Conentrtions nd sptil distriution of suh ioni sustitutions in the lyered titnte will strongly ffet exfolition events of Ti 3 O 7 sheets from the lyered titnte prior to the sheet folding. In this regrd, Zhng et l. nd their o-workers theoretilly investigted properties nd the levge mehnism of Ti 3 O 7 sheets from H 2 Ti 3 O 7 y first-priniples lultions, nd disussed tht the symmetri tthment of protons on two surfes of Ti 3 O 7 sheets indues levge nd folding of the sheets. However, they did not tke into ount the effet of NOH solution for the exfolition mehnism nd the sequentil nnotue formtion. The NOH-solution effet will e essentil euse highly onentrted NOH solutions were ommonly used for the nnotue frition. Moreover, ording to Morgdo Jr. et l., 25 N ontent nd the degree of ion exhnge y protons in titnte nnotues re onsidered to ply n importnt role for the tomi strutures nd therml stility. In this study, eletroni nd tomi strutures of the lyered titntes N 2 x H x Ti 3 O 7, x=0 2 re lulted y firstpriniples lultions, in order to investigte the stle omposition in onentrted NOH queous solution. N 2 Ti 3 O 7 nd H 2 Ti 3 O 7 re used s strting struturl models, nd sustitutions of H + or N + ions in their strutures re onsidered. Formtion energies of the sustituted lyered-titnte strutures re evluted from totl energies of superells, together with hemil potentils determined under hemil equilirium with NOH queous solution. From the ph-dependent stility of the lyered titntes nd levge energies of Ti 3 O 7 sheets, the NOH queous solution effet on exfolition of the Ti 3 O 7 sheets from the lyered titnte, whih ours prior to the nnotue formtion, will e disussed. II. COMPUTTIONL METHOD. Eletroni struture lultion nd superell First-priniples eletroni struture lultions re performed y the projetor ugmented wve PW method, implemented in VSP The generlized grdient pproximtion GG is used for the exhnge-orreltion potentil, nd the GG funtionl proposed y Perdew et l. 29 is employed. Wve funtions re expnded up to plne-wve utoff energy of 500 ev nd the Brillouin-zone integrtion is performed y the 222 Monkhorst-Pk sheme for superell lultions desried elow. The k-point smpling ondition ensures good ury of totl energies for lyered titnte within out 1 mev/f.u. Bsed on fores on toms lulted, ll tomi positions, ell prmeters nd /2009/7914/ The merin Physil Soiety

3 MORI et l. () () () () H2 H4 H1 H3 Ti O H () (d) FIG. 2. Color online Optimized tomi struture of the H 2 Ti 3 O 7 superell. Smll lk spheres indite sustitutionl sites of N + see detils in text. N Ti O FIG. 1. Color online Crystl strutures of N 2 Ti 3 O 7 nd nd H 2 Ti 3 O 7 nd d. nd re viewed long the xis. nd d re drwn in prtiulr diretion, nd TiO 6 othedr re olored in lue, in order to highlight the stking sequene of the Ti 3 O 7 lyers. It is noted tht Feist et l. Ref. 31 did not expliitly determine hydrogen lotions in H 2 Ti 3 O 7 nd thus no hydrogen toms re drwn in nd d. ell shpes of unit ells nd superells re llowed to relx until their fores onverge to less thn 2 ev/å. In the PW potentils, eletrons of 1s 1 for H, 3s 1 for N, 4s 1 3d 3 for Ti nd 2s 2 2p 4 for O re treted s vlene. In this study, rystl strutures of N 2 Ti 3 O 7 nd H 2 Ti 3 O 7 re used s struturl models for N 2 x H x Ti 3 O 7. These ompounds n e onsidered s end memers of the solid solution N 2 x H x Ti 3 O 7, ut they hve different stking sequenes of Ti 3 O 7 lyers, s will e disussed elow. Figure 1 displys tomi strutures of N 2 Ti 3 O 7 nd H 2 Ti 3 O 7. ording to ndersson et l. 30 nd Feist et l., 31 N 2 Ti 3 O 7 hs monolini struture spe group P2 1 /m nd the lttie prmeters of =8.571 Å, =3.804 Å, =9.135 Å, nd =101.57, while the monolini phse of H 2 Ti 3 O 7 spe group C2/m hs lttie prmeters = Å, =3.747 Å, =9.188 Å, = In oth ses, TiO 6 othedr re linked to one nother long the plne y orner nd edge shering, forming the sheetlike titnium oxide Ti-O lyers. The resultnt hemil omposition of the individul Ti-O lyer is Ti 3 O 7, whih is quite similr to the Ti/O molr rtio in typil titnte nnotues previously frited. It is lso noted here tht there is differene in stking sequenes of the Ti 3 O 7 lyers long the xis etween the two rystl strutures: one Ti 3 O 7 lyer in H 2 Ti 3 O 7 is reltively displed y /2 with respet to nother. Therefore, the stking sequenes of the Ti 3 O 7 lyers n e desried s... nd..bb.. in N 2 Ti 3 O 7 nd H 2 Ti 3 O 7, respetively. First, struturl optimiztion of N 2 Ti 3 O 7 nd H 2 Ti 3 O 7 is onduted using superells ontining 48 toms. In the se B of N 2 Ti 3 O 7, the superell is otined y douling the unit ell shown in Figs. 1 nd 1 long the xis. On the other hnd, the H 2 Ti 3 O 7 superell is generted y using different ell shpe from the unit ell nd douling this ell long the xis see Fig. 2, so s to mke the superell size nd shpe similr to the N 2 Ti 3 O 7 se. Sine, in the experiment of Feist et l., 31 H + positions in H 2 Ti 3 O 7 were not unmiguously determined, H + ions re introdued in the middle of nerest neighoring O 2 ions in the two djent Ti 3 O 7 lyers in the present study. s n e seen in Fig. 2, however, H + ions in the optimized struture re no longer loted in the middle of O 2 ions in the Ti 3 O 7 lyers. One H + is tthed to O 2 ions ridging two TiO 6 othedr H4, nd nonridging O 2 ions tend to e onded to one or two H + ions H1 3. The O-H ond lengths re out 1.0 Å, nd their onding diretions re oriented to O 2 ions in the djent Ti 3 O 7 lyer, whih is similr to hydrogen onding linkges s found in ie nd wter. It is noted here tht stti struture optimiztion in the first-priniples lultions my find metstle onfigurtions of Ti-O-H ngles O-H onding diretions; see Fig. 2. In order to exmine this, test lultions of the H + ions hving slightly different Ti-O-H ngles from those optimized in the ove mnner were performed, nd it ws onfirmed tht Fig. 2 indites the H + positions energetilly most stle. The ell lengths nd ngles thus lulted re listed in Tle I, whih re in resonle greement with experiment. Regrding the tomi struture of H 2 Ti 3 O 7, Zhng et l. 22 lso performed the similr first-priniples lultion of the titnte. They used the rystl struture of N 2 Ti 3 O 7 y ndersson et l. 30 s model, nd lulted severl tomi onfigurtions of protons introdued insted of N +, in different wy from the present study. Therefore, test lultions with respet to the H 2 Ti 3 O 7 model y Zhng et l. the energetilly most fvorle struture of H1,3 in Ref. 22 TBLE I. Clulted lttie prmeters of N 2 Ti 3 O 7 nd H 2 Ti 3 O 7. For H 2 Ti 3 O 7, the vlues listed here re sed on the originl spe group C2/m. Å Å Å deg. N 2 Ti 3 O H 2 Ti 3 O

4 FIRST-PRINCIPLES INVESTIGTION OF TOMIC were lso rried out, nd it ws found, however, tht the formtion energy of the Zhng s model is lrger y out ev/f.u. thn the present H 2 Ti 3 O 7 model sed on Feist et l. 31 In NOH queous solutions, s often enountered in the previous experiments for titnte nnotues, it is expeted tht some of N + ions in N 2 Ti 3 O 7 re repled y H +, depending on the solution ph ondition, whih is onsidered to ffet tomi strutures nd therml stility of titnte nnotues. 25 In order to lulte suh ion-exhnged strutures of N 2 x H x Ti 3 O 7,H + ions re sustituted for N + ions in the N 2 Ti 3 O 7 superell eight N + ions involved in the superell, vrying the x vlue from 0 to 2, nd the tomi positions nd the ell prmeters of the superells re optimized in the mnner desried ove. It should e noted tht there re numer of possiilities for sustitutionl onfigurtions of H + in the N 2 Ti 3 O 7 superell, depending on the vlue of x. In order to thoroughly investigte vrious ionexhnged onfigurtions, ll of the possile sustitutionl onfigurtions for N + nd H + in the N 2 x H x Ti 3 O 7 superells re tken into ount over the entire rnge of x. The similr proedure is lso pplied to H 2 Ti 3 O 7 hving the different stking sequene of the Ti 3 O 7 lyers from N 2 Ti 3 O 7, nd H + ions in the H 2 Ti 3 O 7 superell re exhnged y N + ions for the N 2 x H x Ti 3 O 7 lultions with different x vlues. It is worth noting, however, tht sustituting N + for H + in the originl H 2 Ti 3 O 7 superell results in the lose proximity etween the sustituted N + nd the djent O 2 ions: the distne etween oxygen in the O-H O linkge in H 2 Ti 3 O 7 is out Å, wheres the dimeter of N + ion is out 2 Å. 32 In order to void suh sitution, the sustituted N + ions re loted t djent open spes y eing shifted y /4 from the originl H + sites see Fig. 2. In this se, the sustituted N + ion hs fourfold oordintion with oxygen nd the verge ond length of N-O is out Å, whih is lose to the lol tomi oordintion environment in ulk N 2 O. It n e thought, therefore, tht suh lotion of sustituting N + is resonle for the N 2 x H x Ti 3 O 7 lultions sed on the H 2 Ti 3 O 7 superells. It is lso noted tht ll sustitutionl onfigurtions of N + ions re onsidered, ording to the symmetry of the lulted H 2 Ti 3 O 7 superell 2 1 helil xis long xis nd plne of mirror symmetry perpendiulr to the xis. s finl note, the totl numer of the onfigurtions of N + nd H + prtilly treted in the present lultions is 193. B. Formtion energies of N 2 x H x Ti 3 O 7 In order to serh the stle omposition nd tomi struture of the N 2 x H x Ti 3 O 7 system in NOH queous solutions, we lulted formtion energies of N 2 x H x Ti 3 O 7 with different x nd N + or H + onfigurtions, sed on the totl energies of the superells. For this purpose, it is ssumed tht N 2 x H x Ti 3 O 7 is formed from N 2 Ti 3 O 7 or H 2 Ti 3 O 7 in NOH queous solution. Then the following ionexhnge retion for formtion of N 2 x H x Ti 3 O 7 is onsidered: N 2 Ti 3 O 7 s + xh + q =N 2 x H x Ti 3 O 7 s + xn + q. 1 By using the totl energies of the N 2 x H x Ti 3 O 7 superells E t, the formtion energy of N 2 x H x Ti 3 O 7 E form, ording to Eq. 1, n e given y E form = E t N 2 x H x Ti 3 O 7 + x N +,q E t N 2 Ti 3 O 7 x H +,q, where N +,q nd H +,q indite hemil potentils of N + nd H + in the NOH queous solution. These ioni hemil potentils n e written in terms of the stndrd hemil potentil M +,q nd the ioni tivity M +,q s M +,q = M +,q + k B T ln M +,q. 3 In this eqution, k B is the Boltzmnn onstnt, nd T is the temperture T=298 K throughout the present study. Then Eq. 1 n e rewritten s E form = E t N 2 x H x Ti 3 O 7 E t N 2 Ti 3 O 7 + x N +,q H +,q xk B T log N +,q + ph. In order to lulte E form, it is neessry to evlute the third nd forth terms of the right-hnd side of Eq. 4. s desried in our previous pper, the third term of the stndrd hemil-potentil differene n e otined in terms of the stndrd Gis formtion energy of N + in queous solution G f s follows: N +,q H +,q = G f N +,q + N,s H 2,g. 5 For G f N +,q, the experimentl thermodynmi dt t T=298 K is used in this study. The solid phse of N nd the isolted H 2 moleule re seprtely lulted in the first-priniples mnner, nd the totl energies per tom or moleule re used to evlute N,s nd H2,g. It is noted tht temperture-dependent entropy nd enthlpy terms were lso onsidered for H2,g, whih ws desried in detil elsewhere C. tivities of ioni speies in onentrted NOH queous solution In order to lulte E form, the remining forth term in Eq. 4 hs to e prepred. In NOH queous solutions, the tivity of N + N +,q nd the solution ph re orrelted with eh other. In this study, NOH onentrtion of the queous solution is ssumed, nd then the solution ph is evluted in the following mnner. t given onentrtion of NOH in the solution, mollities of N + m N +,q nd OH m OH,q n e onsidered to e equl to eh other. lso, the tivity oeffiients of the respetive ions nnot e independently determined, nd thus re generlly pproximted y the men tivity oeffiient N +,q= OH,q whih is defined s

5 MORI et l H2 O E form (ev/f.u.) m NOH (mol/kg) x (N 2-x H x Ti 3 O 7 ) 2 FIG. 3. Vrition in wter tivity s funtion of mollity of NOH, ording to Ref. 37. = N +,q OH,q. Sine it is not strightforwrd to lulte the tivity oeffiient theoretilly, the experimentl vlue s funtion of mollity of NOH is used here. 36 Then the tivity of N + nd OH in the solution n e determined s follows: N +,q = m N +,q N +,q, nd OH,q = m OH,q OH,q. 7 In terms of the ioni produt of wter K w nd the wter tivity H2 O, the following eqution is lso otined, K w = H +,q OH,q. 8 H2 O From this eqution, the solution ph= log H +,q n e given s ph = log OH,q log K w log H2 O. In norml queous solution, the wter tivity H2 O is onsidered to e unity. However, it ws experimentlly reported tht H2 O tends to derese with inresing NOH onentrtion. 37 The highly onentrted NOH solutions the ph rnge of more thn 10, s found in the ommon Ti-O nnotue frition re minly onsidered in the present study, hene the experimentl H2 O vlue ginst the NOH ontent Fig. 3 is used to evlute the solution ph. From the vlues of N +,q nd ph thus evluted, the formtion energies of N 2 x H x Ti 3 O 7 n e lulted y using Eq. 4. III. RESULTS ND DISCUSSION. tomi strutures of N 2 x H x Ti 3 O FIG. 4. Clulted formtion energies of ll possile tomi onfigurtions for N 2 x H x Ti 3 O 7 s funtion of x. In this se, the ondition of ph=16 is ssumed. Figure 4 displys lulted formtion energies of ll possile onfigurtions s funtion of x, ording to the ionexhnge retion of Eq. 1. In this se, the solution ph is ssumed to e 16, whih orresponds to the NOH onentrtion in solution of 10.9 mol/kg, s estimted from Fig. 3 nd Eq. 9. In the ompositions of 0x0.75, the most stle tomi strutures hve the sme Ti 3 O 7 -lyer stking sequene s found in N 2 Ti 3 O 7 given y ndersson et l. 30, while those in the rnge of 1x2 is omposed of the BB Ti 3 O 7 -lyer stking sequene with the one of the H 2 Ti 3 O 7 struture given y Feist et l. 31 For instne, Fig. 5 shows most stle lulted tomi strutures for x=1nhti 3 O 7 nd x=1.5n 0.5 H 1.5 Ti 3 O 7. The O-H onds etween the Ti 3 O 7 lyers re oriented towrd O 2 ions in the neighoring Ti 3 O 7 lyer. Pálinkás et l. 38 defined the presene of hydrogen onds etween two H 2 O moleules from the O O distne of less thn 3.28 Å nd the ngle etween the O-H ond vetor nd the O O vetor H-O O of less thn 20. ording to this definition, the lol tomi strutures of the proton in N 2 x H x Ti 3 O 7 re nlyzed. Tle II shows O-H ond lengths, O O distnes, nd H-O O ngles round the protons. Sine the lol onding onfigurtions of H + in N 2 x H x Ti 3 O 7 1x stisfy the ove definition, they re onsidered to ply n importnt role for mking hydrogen onding linkges etween the Ti 3 O 7 lyers. B. Formtion energies s funtion of ph For the most stle tomi onfigurtions for the respetive x vlues Figs. 4 nd 5, the dependene of their stility () () H1 H1 H3 H3 H4 N Ti O H FIG. 5. Color online Optimized tomi strutures of nd NHTi 3 O 7 nd nd d N 0.5 H 1.5 Ti 3 O 7. () (d)

6 FIRST-PRINCIPLES INVESTIGTION OF TOMIC TBLE II. Intertomi distnes nd ond ngles round protons. The proton sites re displyed in Figs. 2 nd 5. x Proton site O-H length Å O O distne Å H-O O ngle deg. 1 H H H H H H H H H on the solution ph is investigted. Figure 6 shows formtion energies of N 2 x H x Ti 3 O 7 s funtion of ph. s n e understood from Eq. 4, the formtion energies tend to inrese with rising ph, exept for x=0. s more N + ions re sustituted y H + ions inresing x, the grdients of the formtion energy vritions tend to eome steeper. s result, it n e seen tht the most energetilly fvorle ompositions re found to e x=1nhti 3 O 7 for ph 14.9, x=1.5n 0.5 H 1.5 Ti 3 O 7 for 14.4 ph14.9, nd x =2H 2 Ti 3 O 7 for ph14.4. Sine typil titnte-nnotue frition experiments used out 10 M NOH solutions, whih orresponds to the ph ondition of round 16 s estimted from Eq. 9 nd Fig. 3, it n e sid tht more thn hlf of N + ions in N 2 Ti 3 O 7 re repled y H + ions, even in the rther strong lkline solution onditions. It is expeted tht the sustitutions of H + for N + in N 2 Ti 3 O 7 my ffet interlyer onding etween the Ti 3 O 7 lyers, whih is losely relted to exfolition of Ti 3 O 7 lyers from the intermedite phse prior to the Ti 3 O 7 -sheet folding. In order to investigte the interlyer onding strength, therefore, works of seprtion W sep etween the Ti 3 O 7 lyers in N 2 x H x Ti 3 O 7 re lulted from totl-energy differenes per ross setion etween the N 2 x H x Ti 3 O 7 superell nd the one ontining n isolted Ti 3 O 7 -lyer sl. n isolted Ti 3 O 7 -lyer sl is generted y simply elongting the edge length perpendiulr to the Ti 3 O 7 lyer in the N 2 x H x Ti 3 O 7 E form (ev/f.u.) 0.5 x = x = 1.75 x = 0.5 x =0 x = 0.25 x =2 x = 1.25 x = 1.5 x = ph FIG. 6. Formtion energies of N 2 x H x Ti 3 O 7 s funtion of ph. The thik solid lines indite the energetilly most stle ompositions in the respetive ph rnges. W sep (J/m 2 ) x (N 2-x H x Ti 3 O 7 ) FIG. 7. Clulted works of seprtion of N 2 x H x Ti 3 O 7 ginst the omposition x. superell nd mking the two surfes of the Ti 3 O 7 lyer with vuum lyer of out 10 Å. Sine N + ions re present etween the Ti 3 O 7 lyers in the N 2 x H x Ti 3 O 7 superells, unlike H + strongly tthed to O 2, it is neessry to onsider detiled tthment sites nd onfigurtions of N + ions onto the surfes of the isolted Ti 3 O 7 lyers, when the isolted sl superells re generted. In this study, it is ssumed tht oth ends of isolted Ti 3 O 7 lyers ontin n equl numer of N + ions, nd ll possile onfigurtions of N + surfe tthment re lulted. By doing this, the most stle tomi strutures of the Ti 3 O 7 -lyer sls for the ompositions x = 0, 1, 1.5, nd 2, whih re oserved s stle ompositions, re otined in the first-priniples mnner, nd their totl energies re used to evlute the W sep vlues. Figure 7 shows lulted works of seprtion ginst the omposition x. It n e seen tht the W sep vlues tend to derese with inresing x nd those for x1 re smller y more thn 20%, s ompred to the N 2 Ti 3 O 7 se. Therefore, the inlusion of H + ions etween the Ti 3 O 7 lyers, depending on ph, ontriutes to wekening the interlyer onding strength, lthough H + ions tend to form hydrogen onding linkges etween the lyers. It n e sid tht ioni onding etween Ti 3 O 7 lyers vi N + ions is stronger thn the hydrogen onding due to the H + sustitutions. Tsi et l. 6,39 rgued the formtion mehnism of titnte nnotues from TiO 2 in the NOH tretment of the hydrotherml proess. In the proposed mehnism, the lyered titnte formed s intermedite would undergo N + exhnge with H + during post-tretment of id wshing. The smller ph in the post-tretment promotes the nnotue formtion from the lyered titnte, nd the mteril is eventully trnsformed into ntse in further idi onditions. In this regrd, the present lultions lso showed the similr tendeny tht N + ontent in N 2 x H x Ti 3 O 7 dereses y the H + sustitution in smller ph onditions. Even in the rther lkline solution onditions of ph15 16 ommonly used in previous experiments, it ws found tht more thn hlf of N + ions re repled y H + ions etween the Ti 3 O 7 lyers. t the sme time, the Ti 3 O 7 sheets n e more esily peeled off from the lyered titnte, due to the wekened interlyer strength. In other words, the N + ontent is responsile for the hemil stility of the lyered-titnte struture N 2 x H x Ti 3 O 7, whih is onsistent with the rgument y Morgdo Jr. et l

7 MORI et l. IV. SUMMRY First-priniples lultions were performed for N 2 x H x Ti 3 O 7, to investigte the stle tomi strutures when the ompounds equilirte with onentrted NOH queous solutions. The formtion energies vi ion exhnge with N + nd H + were nlyzed y using the superell totl energies nd the ioni hemil potentils determined from omintion of first-priniples results nd experimentl thermodynmi dt. It ws found tht N + ontent in N 2 x H x Ti 3 O 7 dereses with deresing ph, nd yet ioni sustitutions y protons tke ple even in rther lkline onditions employed in previous experiments. In ddition, the interlyer onding strength etween the Ti 3 O 7 lyers tends to derese with more sustitutions of N + ions y H + ions, whih is relted to ph effets on exfolition events of Ti 3 O 7 sheetlike lyers from lyered titnte prior to the nnotue formtion. CKNOWLEDGMENTS This study ws supported y Grnt-in-id for Sientifi Reserh on Priority res Nno Mterils Siene for tomi Sle Modifition 474 from the Ministry of Edution, Culture, Sports, Siene nd Tehnology MEXT of Jpn, nd ws lso prtly supported y reserh grnt from The Murt Siene Foundtion. *uthor to whom orrespondene should e ddressed; k.mtsung@mterils.mox.medi.kyoto-u..jp 1 T. Ksug, M. Hirmtsu,. Hosono, T. Sekino, nd K. Niihr, Lngmuir 14, M. dhi, Y. Murt, M. Hrd, nd S. Yoshikw, Chem. Lett. 29, Nkhir, W. Kto, M. Tmi, T. Isshiki, K. Nishio, nd H. ritni, J. Mter. Si. 39, M. Zhng, Z. Jin, J. Zhng, X. Guo, J. Yng, W. Li, X. Wng, nd Z. Zhng, J. Mol. Ctl. : Chem 217, H. Y. Zhu, Y. Ln, X. P. Go, S. P. Ringer, Z. F. Zheng, D. Y. Song, nd J. C. Zho, J. m. Chem. So. 127, C.-C. Tsi nd H. Teng, Chem. Mter. 16, T. kit, M. Okumur, K. Tnk, K. Ohkum, M. Kohym, T. Koyngi, M. Dte, S. Tsuot, nd M. Hrut, Surf. Interfe nl. 37, D. V. Bvykin,.. Lpkin, P. K. Pluinski, J. M. Friedrih, nd F. C. Wlsh, J. Ctl. 235, P. Umek, P. Cev,. Jesih,. Gloter, C. P. Ewels, nd D. rčon, Chem. Mter. 17, X. Sun nd Y. Li, Chem.-Eur. J. 9, R. M, T. Sski, nd Y. Bndo, Chem. Commun. Cmridge 7, D. V. Bvykin nd F. C. Wlsh, J. Phys. Chem. C 111, Y.-K. Zhou, L. Co, F.-B. Zhng, B.-L. He, nd H.-L. Li, J. Eletrohem. So. 150, L. Kvn, M. Kláč, M. Zuklová, I. Exnr, V. Lorenzen, R. Nesper, nd M. Gretzel, Chem. Mter. 16, J. Li, Z. Tng, nd Z. Zhng, Eletrohem. Commun. 7, S. H. Lim, J. Luo, Z. Zhong, W. Ji, nd J. Lin, Inorg. Chem. 44, D. V. Bvykin,.. Lpkin, P. K. Pluinski, J. M. Friedrih, nd F. C. Wlsh, J. Phys. Chem. B 109, M. Volel, M. rmnd, W. Goreki, nd M.-L. Soungi, Chem. Mter. 17, X.-P. Tng, J.-C. Wng, L. W. Cry,. Kleinhmmes, nd Y. Wu, J. m. Chem. So. 127, Kleinhmmes, G. W. Wgner, H. Kulkrni, Y. Ji, Q. Zhng, L.-C. Qin, nd Y. Wu, Chem. Phys. Lett. 411, S. Zhng, L.-M. Peng, Q. Chen, G. H. Du, G. Dwson, nd W. Z. Zhou, Phys. Rev. Lett. 91, S. Zhng, Q. Chen, nd L.-M. Peng, Phys. Rev. B 71, X. G. Xu, X. Ding, Q. Chen, nd L.-M. Peng, Phys. Rev. B 73, X. G. Xu, X. Ding, Q. Chen, nd L.-M. Peng, Phys. Rev. B 75, E. Morgdo, Jr., M.. S. de reu, O. R. C. Prvi, B.. Mrinkovi, P. M. Jrdim, F. C. Rizzo, nd. S. rújo, Solid Stte Si. 8, P. E. Blohl, Phys. Rev. B 50, G. Kresse nd J. Furthmüller, Phys. Rev. B 54, G. Kresse nd D. Jouert, Phys. Rev. B 59, J. P. Perdew, K. Burke, nd M. Ernzerhof, Phys. Rev. Lett. 77, S. ndersson nd. D. Wdsley, t Crystllogr. 14, T. P. Feist nd P. K. Dvies, J. Solid Stte Chem. 101, R. D. Shnnon, t Crystllogr. 32, K. Mtsung, Phys. Rev. B 77, K. Mtsung, J. Chem. Phys. 128, K. Mtsung, H. Inmori, nd H. Murt, Phys. Rev. B 78, W. J. Hmer nd Y.-C. Wu, J. Phys. Chem. Ref. Dt 1, R.. Roinson nd R. M. Stokes, Eletrolyte Solutions, 2nd ed. Butterworths, London, G. Pálinkás, P. Bopp, G. Jnsó, nd K. Heinzinger, Z. Nturforsh. C 39, C.-C. Tsi nd H. Teng, Chem. Mter. 18,