Insights into ammonia synthesis from first-principles

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Surfce Science xxx (26) xxx xxx www.elsevier.com/locte/susc Insights into mmoni synthesis from first-principles A. ellmn,, K. onkl b, I.N. Remedikis b,á. Logdóttir b, A. Crlsson, S. Dhl, C.

Nørskov b ldor Topsøe A/S, Nymøllevej 55, DK-28 Lyngby, Denmrk b Center for Atomic-scle Mterils Physics, Deprtment of Physics, Technicl University of Denmrk, DK-28 Lyngby, Denmrk c Center for

model for the mmoni (N 3 ) synthesis on n unpromoted Ru-bsed ctlyst. A direct comprison shows n overll good greement in N 3 productivity between the model nd the experiment.

1 Surfce Science xxx (26) xxx xxx Insights into mmoni synthesis from first-principles A. ellmn,, K. onkl b, I.N. Remedikis b,á. Logdóttir b, A. Crlsson, S. Dhl, C.. Christensen c, J.K. Nørskov b ldor Topsøe A/S, Nymøllevej 55, DK-28 Lyngby, Denmrk b Center for Atomic-scle Mterils Physics, Deprtment of Physics, Technicl University of Denmrk, DK-28 Lyngby, Denmrk c Center for Sustinble nd Green Chemistry, Deprtment of Chemistry, Technicl University of Denmrk, DK-28 Lyngby, Denmrk Abstrct A new set of mesurements is used to further test recently published first-principles model for the mmoni (N 3 ) synthesis on n unpromoted Ru-bsed ctlyst. A direct comprison shows n overll good greement in N 3 productivity between the model nd the experiment. In ddition, mcro-properties, such s pprent ctivtion energies nd rection orders, re clculted from the first-principles model. Our nlysis shows tht the rection order of N 2 is unity under ll considered conditions, wheres the rection orders of 2 nd N 3 depend on rection conditions. Ó 26 Elsevier B.V. All rights reserved. Keywords: Density functionl theory; Monte Crlo simultions; Ctlysis; Surfce chemicl rection; Ruthenium; N 3 synthesis. Introduction The ber Bosch method for nitrogen fixtion is considered to be one of the most significnt scientific discoveries in the 2th century []. N 3 is used in vrious pplictions, such s textile processing, wter purifiction, nd mnufcturing explosives. The min prt, however, is used s fertilizer. As consequence of the incresing world popultion there is no reson to suspect tht the significnce of N 3 will become less in the future. On the best elementry metl ctlyst (Ru, Fe) the brnchless N 3 synthesis proceeds long well-defined Lngmuir inshelwood rection pth. ence, the stepwise ddition of dsorbed to the N-compounds cn be written s N 2 þ 2 2N; ðþ N þ N þ; ð2þ N þ N 2 þ; ð3þ Corresponding uthor. E-mil ddress: hell@fysik.dtu.dk (A. ellmn). N 2 þ N 3 þ; N 3 N 3 þ; 2 þ 2 2; where nd X correspond to n empty site nd n dsorbed X chemicl compound, respectively. N 3 synthesis is considered to be the bellwether rection [2] in heterogeneous ctlysis, nd there exists n enormous mount of reserch studies in the literture where some centrl works re collected in series of monogrphs [3 5]. owever, there re three lter contributions tht constitute the bckground to this work. (i) The rection mechnism given in Eqs. () (6) hs been quntittively outlined [6], both on flt nd stepped surfce, using density-functionl theory (DFT) [7,8]. (ii) Under industril conditions the N 2 dissocition is the rte-determining step (RDS) for N 3 synthesis on Ru [9,]. (iii) The dissocition tkes plce t defects nd steps, preferentilly t sites with B 5 configurtion [,2], rendering the N 3 synthesis extremely structure sensitive [9,]. Recently, we published first-principles model for the N 3 synthesis on unpromoted Ru-bsed ctlyst [3]. The integrted model consists of energetics clculted with- ð4þ ð5þ ð6þ /$ - see front mtter Ó 26 Elsevier B.V. All rights reserved. doi:.6/j.susc.25..7

2 2 A. ellmn et l. / Surfce Science xxx (26) xxx xxx in the DFT frmework, coverges nd conditionl probbilities obtined from Monte Crlo (MC) simultions, nd mcroscopic properties, such s, prtil pressures nd flows were chnged within kinetic model. The bsic shpe nd the number of ctive sites for the nno-sized Ru prticles were determined using DFT nd n tomistic Wulff construction. The ctlyst ws chrcterized by highresolution trnsmission electron microscopy (RTEM). Using the size distribution of the Ru prticles s the only link between the ctlyst mteril nd the model, ll trends in ctivity were cptured nd the bsolute vlue of the N 3 productivity ws predicted within fctor of 3 2 depending on the conditions. In this pper, we pply the first-principles model to new set of mesurements. We lso clculte mcro-properties, such s, pprent ctivtion energies nd rection orders t different rection conditions. 2. The first-principles model A complete chrcteriztion of ctlytic rection, bsed only on first-principles, hs been long-desired gol in the surfce science nd ctlysis communities. Recently this ws chieved for N 3 synthesis [3] nd here we give only short review of the model. Fig. shows the potentil energy lndscpe, including N 2 dissocition, step-wise ddition of, nd formtion of two N 3 molecules. Both the energetics for the flt surfce (dshed line)- nd the stepped surfce (solid line)-contining B 5 sites [,2] re shown. The results given in Fig. re for low coverge of dsorbtes. In relity there re toms nd molecules dsorbed in the vicinity of recting molecule nd therefore trnsition stte (TS) energies re coverge-dependent. To include the locl environments into our model we clculte TS energies for N 2 dissocition for severl different cses, see Fig. (b). The use of Monte Crlo techniques ensures tht we clculte the probbility of different locl environments correctly [4,5]. This pproch is well suited for the N 3 synthesis, s the RDS ensures tht the rest of the ctlytic rection, Eqs. (2) (6), cn be considered to be in qusiequilibrium. ere, the equilibrium of the Grnd Cnonicl ensemble is found by MC techniques bsed on the Metropolis lgorithm [6]. The rection rte per ctive site is clculted ccording to rðt ; p N2 ; p 2 ; p N3 Þ¼ð cþ X P i k i p N2 h ; ð7þ i where T is the temperture, p N2 ; p 2 ; p N3 re the pressures of N 2, 2, nd N 3, respectively, P i is the probbility for certin locl environment i, k i is the corresponding rte constnt, h is the probbility to hve two empty sites, one on the upper step () nd one on the lower step (LS), c ¼ p2 N 3 p N2 p 3 K g ensures correct pproch to equilibrium, nd K g is the gs-phse equilibrium 2 constnt. The ctive site density, q, in Eq. (8) is estimted in the following mnner. First we clculte the surfce energy of ll low Miller index (h + k + l < 4) Ru surfces. Using these energies we mke n tomistic Wulff construction for severl Ru prticles with different dimeters. None of the dominnt fces in the Wulff construction contins B 5 sites. After including edge effects the B 5 sites pper long the ðþ= intersection. ence, we know the number of ctive sites per prticle size. The mcroscopic sizedistribution of the Ru-prticles is obtined by the use of RTEM nd is the only link between the rel ctlyst nd our model. q is the integrted result of the number of ctive sites per prticle size nd the mcroscopic sizedistribution. We model plug-flow rector by dividing the ctlyst into N slices nd ssume n equl distribution of the ctlyst mss. Folding Eq. (7), verge number of ctive sites nd the rector model, we get the following expression for the overll rection rte through the rector: X N x¼ r x ðt ; p N2 ðxþ; p 2 ðxþ; p N3 ðxþþqm=n; where m is the ctlyst mss, N the number of slices, p N2 ðxþ, p 2 ðxþ, p N3 ðxþ, re the prtil pressures in slice x, respectively. The N 3 productivity is simply the prtil pressure of N 3 t the outlet. The preprtion of Ru ctlyst nd N 3 productivity mesurements hve been described erlier [7]. In short, the ctlyst consists of g of. wt.% Ru supported on mgnesium luminum spinel crrier with surfce re of 52 m 2 /g. The N 3 productivity ws determined using plug-flow rector with vrition of temperture between 32 nd 44 C, flow rtes between 4 nd 24 ml/min (STP); N 2 : 2 rtios between 4: nd :5; conversions between nd 5% of equilibrium, ll t totl pressure of 5 br. 3. Results nd discussion Fig. 2 shows the comprison between the clculted nd mesured N 3 productivities. Considering the whole rnge of rection conditions, our clculted productivities re fctor of 2 5 too smll, in verge, by fctor of 4. The devitions re not sensitive to different flows nd N 2 : 2 rtios. Insted it is the low temperture conditions tht give rise to the higher bound. Considering tht we use previously published model [3] on completely new set of mesurements without ny further modifictions, the greement is remrkble. This is cler evidence of the predicting power crried by first-principles model. Except N 3 productivities there re number of interesting quntities within the model tht deserve ttention, such s, the surfce composition, pprent ctivtion energies nd rection orders t different rection conditions. Fig. 3 shows the surfce composition in the plug-flow rector for four different N 2 : 2 rtios, :5, :3, :, nd ð8þ

3 A. ellmn et l. / Surfce Science xxx (26) xxx xxx 3 () (b) Fig.. () The rection pthwy for N 3 synthesis on the flt (dshed line) nd stepped (solid line) Ru surfces. The TS configurtions of the N 2 dissocition over the terrce nd step sites re shown in the inserts. (b) The vrition in TS energy due to the presence of different intermedites. As mcroscopic conditions chnge, i.e. the prtil pressures of 2 nd N 3, in the ctlytic rector the N 2 dissocition will be dominted by different chnnels. From A to D, B5 site with (A) no dsorbtes in the neighboring sites, (B) dsorbed N on the, (C) dsorbed N on the LS, nd (D) dsorbed on the LS. From E to, (E) dsorbed, (F) dsorbed N, (G) dsorbed N 2 on the, nd () dsorbed both on the nd LS. 4:, t temperture 36 C nd flow 4 ml/min (STP). Under these conditions the surfce is mostly covered by rection intermedites. At the inlet, the dominting rection intermedite is dsorbed, but s the prtil pressure of N 3 increses, see Fig. 3(c) nd (d), the much more stble N 2 intermedite ppers on the surfce. The increse in coverge of N-compounds results in poisoning effect s the low-brrier configurtions become scrcer, see Fig.. ence, the ctivity of the ctlyst is considerbly lrger t the inlet thn t the outlet. The N 3 productivity is strongly enhnced by the use of high N 2 : 2 rtio. There re two resons for this, (i) high prtil N 2 pressure directly increses the rte (Eq. (7)), nd (ii) the probbility to find empty sites, h increses s the coverge of decreses due to low prtil pressure of 2. Apprent ctivtion energy together with rection order re often used to chrcterize the overll kinetics of ctlytic rection. Apprent ctivtion energy, E pp, is defined s E pp ¼ RT 2 dlnðrþ ; ð9þ dt where R is the gs constnt.

4 4 A. ellmn et l. / Surfce Science xxx (26) xxx xxx Model mmoni output (N 3 -%) The different contributions to E pp come from TS energy for the RDS, nd pprent energy required to crete free sites [8]. FromEq.(7) nd Fig. it is cler tht TS energy for the N 2 dissocition depends on the types of rection intermedites tht re dsorbed on the nerest neighbor sites. ence, the contribution from the RDS to pprent ctivtion energy will be weighted verge of severl N 2 dissocition chnnels. Since the surfce composition chnges during the N 3 synthesis, see Fig. 2, it is cler tht E pp Experimentl mmoni output (N 3 -%) Fig. 2. The clculted N 3 productivity (filled circles) compred with the mesured one. A complete greement would men tht the filled circles should follow the digonl line. The detils of the rection conditions re given in the text. () (c) is not constnt. Insted it depends rther sensitively on the coverges of nd N x, x =,,2,3. The rection orders show how the rte depends on the prtil pressures of rectnts nd product. ence, the rection orders, (N 2 ), ( 2 ), nd (N 3 ) re defined s r ¼ kp ðn 2Þ N 2 (b) (d) p ð 2Þ 2 p ðn 3Þ N 3 : ðþ Fig. 3. The coverge of different rection intermedites on the s function of rector length. ere the synthesis conditions re 4 ml/min (STP), 36 C, wheres the N 2 : 2 rtio chnges s () :5, (b) :3, (c) : nd (d) 4:. Tble The pprent ctivtion energies nd rection orders clculted from the first-principles model, t the inlet of the plug-flow rector, for vrious tempertures nd N 2 : 2 rtios Temp. ( C) Rtio E pp (kj/mol) (N 2 ) ( 2 ) (N 3 ) 32 :3 57 (77)..3 (.9) (.4) 36 :5 54 (82)..2 (.8) (.5) 36 :3 54 (88)..2 (.7) (.6) 36 : 5 (99)..2 (.5) (.8) 36 4: 47 (26).. (.3) (.) 4 :3 5 (95).. (.5) (.8) 44 :3 47 (98).. (.4) (.9) 4 [9] : In the prenthesis the sme quntity is given but t the outlet. The flow is 4 ml/min (STP). As seen in Tble, there is first-order dependence in the N 2 pressure under ll considered conditions, which is in good greement with N 2 dissocition being the RDS. The negtive vlue of ( 2 ) indictes tht the synthesis of N 3 is hindered by dsorbed, nturl consequence of the high coverge of. As shown erlier [3] smll chnge in the dsorption energy of cn correct the underestimte of N 3 productivity within the first-principles model, nd the negtive vlue of ( 2 ) essentilly shows the sme thing. The zero order of N 3 in the inlet of the plug-flow rector is expected s there re no N x, x =,, 2, 3 intermedites present. owever, s the N 3 synthesis proceeds the rection orders of both 2 nd N 3 chnge: ( 2 ) becomes less negtive s dsorbed N 2 replces the dsorbed nd (N 3 ) turns negtive for the sme reson. The clculted pprent ctivtion energies nd rection orders given in Tble re in greement with mesurements of Bécue et l. [9], lthough, it should be noted tht the mesurements re performed under different conditions. 4. Conclusion Using previously published model for N 3 synthesis, we clculted N 3 productivity for totlly new set of mesurements performed t different tempertures, flows nd rtios. We obtin qulittive greement between the clculted nd mesured productivity. The nlysis of mcroscopic properties, such s rection order nd pprent ctivtion energy indictes tht the synthesis is hindered by dsorbed, resulting in n underestimte of the N 3 productivity. Acknowledgements We thnk Dnish Center for Scientific Computing for computer resources nd finncil support by EU-Project No. PRN-CT References [] V. Smil, Nture 4 (999) 45. [2] M. Boudrt, Top. Ctl. (994) 45.

5 A. ellmn et l. / Surfce Science xxx (26) xxx xxx 5 [3] J.R. Jennings (Ed.), Ctlytic Ammoni Synthesis: Fundmentls nd Prctice, Fundmentl nd Applied Ctlysis, Plenum Press, New York, 994. [4] M. Gunze, in: D.A. King, D.P. Wooddrft (Eds.), The Chemistry nd Physics of Solid Surfces nd etrogeneous Ctlysis, vol 4, Elsevier, Amsterdm, 982. [5] A. Nielsen, Ammoni Synthesis, Springer, New York, 995. [6] A. Logdottir, J.K. Nørskov, J. Ctl. 22 (23) 273. [7] P. ohenberg, W. Kohn, Phys. Rev. 36 (964) B864. [8] W. Kohn, L.J. Shm, Phys. Rev. 4 (965) A33. [9] S. Dhl, A. Logdottir, R.C. Egeberg, J.. Lrsen, E. Törnqvist, I. Chorkendorff, J.K. Nørskov, Phys. Rev. Lett. 83 (999) 84. [] S. Dhl, E. Törnqvist, I. Chorkendorff, J. Ctl. 92 (2) 38. [] R. Vn rdeveld, A. Vn Montfoort, Surf. Sci. 4 (966) 396. [2] C.J.. Jcobsen, S. Dhl, P.L. nsen, E. Törnqvist, L. Jensen,. Topsøe, D.V. Prip, P.B. Møenshug, I. Chorkendorff, J. Mol. Ctl. A 63 (2) 9. [3] K. onkl, A. ellmn, I.N. Remedikis, Á. Logdottir, A. Crlsson, S. Dhl, C.. Christensen, J.K. Nørskov, Science 37 (25) 555. [4] K. Reuter, M. Scheffler, Phys. Rev. Lett. 9 (23) 463. [5] K. Reuter, M. Scheffler, Phys. Rev. B 68 (23) [6] D.P. Lndu, K. Binder, A Guide to Monte Crlo Simultions in Sttisticl Physics, Cmbridge University Press, Cmbridge, 2. [7] S. Dhl, J. Sehested, C.J.. Jcobsen, E. Törnqvist, I. Chorkendorff, J. Ctl. 92 (2) 39. [8] P. Stoltze, J.K. Nørskov, Phys. Rev. Lett. 55 (985) 252. [9] T. Bécue, R.J. Dvis, J.M. Grces, J. Ctl. 79 (998) 29.

CHEMICAL KINETICS

CHEMICAL KINETICS Long Answer Questions: 1. Explin the following terms with suitble exmples ) Averge rte of Rection b) Slow nd Fst Rections c) Order of Rection d) Moleculrity of Rection e) Activtion Energy