On the use of standard DRK isotherms in Dubinin s t/f method

Transcription

1 Publihd in Carbon 38, iu 9, , 000 which hould b ud for any rfrnc to thi work 1 On th u of tard DRK iothrm in Dubinin t/f mthod D. Hugi-Clary, F. Stockli* Chmitry Dpartmnt of th Univrity, Avnu d Bllvaux 51, CH-000 uchatl, ˆ Switzrl Abtract It i hown that th adorption of bnzn, carbon ttrachlorid, dichloromthan nitrogn by a typical non-porou carbon black follow th Dubinin Raduhkvich Kaganr quation. Th rquirmnt for tmpratur invarianc i fulfilld, with an avrag charactritic nrgy Eo510.8 kj mol. Thi xprion i compard with th tard iothrm for bnzn carbon ttrachlorid at 93 K propod by Dubinin ud a a rfrnc in th o-calld t/f mthod, which lad to th non-porou urfac ara of activ carbon. It appar that Dubinin iothrm contain inconitnci, which ar compnatd for intrnally. Altrnativ DRK xprion, applicabl to diffrnt vapour, ar thrfor propod. Th prnt tudy alo how th limit of Dubinin mthod with rpct to comparion plot at highr rlativ prur. Kyword: A. Activatd carbon; C. Adorption; D. Microporoity, Surfac ara 3 1. Introduction g (mmol m ) xp[(a/6.35 kj mol )] (1) Activ carbon ar charactrid by thir micropor volum by an xtrnal urfac ara S, which can b a whr A 5 RT ln ( p /p). Thi rlation i purly high a m / g, dpnding on th prcuror th mpirical. typ of activation. Thi ara can b ad by a varity of In th ca of adorption by activ carbon, th xtchniqu uch a comparion plot [1 8], th pr-ad- primntal iothrm i th um of two contribution, th orption of n-nonan followd by nitrogn adorption at 77 claical Dubinin Raduhkvich (DR) or Dubinin A- K [1,3,8,9], th dcompoition of th xprimntal io- takhov (DA) quation [,8] a contribution from th thrm [3,9 11], immrion calorimtry [8]. xtrnal urfac ara S. For bnzn at 93 K, on may Th comparion of th tchniqu lad to a rlativly writ good amnt of S, oftn within 10 to 15% [3,8]. An intrting approach i th comparion of th adorption a (mmol g ) 5 ao xp[(a/e o)] 1 Sg. () iothrm with a rfrnc iothrm, for xampl Sing as-plot [1,5,6], or Dubinin t/f mthod [ 7]. For p/p. A dcribd by Dubinin Kadlc [,], S i 0.05, th micropor ar practically filld adorption obtaind from th linar ction of th plot of a /F v. occur ntially on th xtrnal (non-microporou) ur- g/f, whr F 5 xp[(a/e o) ]. Th charactritic nrgy fac. Undr th circumtanc, th adorption mcha- Eo itlf i obtaind from th low-prur rgion of th nim i th am on th activ carbon a on th non-porou logarithmic plot of Eq. (), whr g i ngligibl. rfrnc th xtrnal urfac S i obtaind from th Dubinin iothrm (1) appli to low rlativ prur linar ction of th plot. (typically 0.001,p/p,0.1). It follow that for a numbr In th mthod propod by Dubinin, on conidr a of activ carbon th proc of micropor filling may till rfrnc iothrm for bnzn at 93 K, givn by contribut ignificantly to th ovrall iothrm lad to an inaccurat comparion plot. In pit of thi hortcoming, rlativly good rult hav *Corrponding author. bn obtaind with th mthod of Dubinin Kadlc, in

2 paralll with othr tchniqu [3,8], but it appar that Eq. trm of packing or molcular orintation at low prur. (1) till contain inconitnci. A hown blow, it can Thi uggt that th ucc of Eq. (1) (3) probably b rplacd by a Dubinin Raduhkvich Kaganr (DRK) rt on an intrnal compnation ffct. It wa thrfor quation [1,1] inc, a pointd out rcntly [13,1], th dcidd to xamin cloly th adorption of bnzn, adorption of a varity of vapour by carbon black m dichloromthan carbon ttrachlorid on a typical to follow thi quation. Morovr, it appar that th non-porou carbon black (Hocht, SBET55 m / g bad rquirmnt for tmpratur invarianc of E o, implid by on th adorption of C6H6 at 93 K). Th low-prur Dubinin thory, i fulfilld. adorption of nitrogn itlf wa alo r-xamind. Th modifid vrion of Eq. (1), propod hr, ha th Following rcnt tudi on adorption by a-mno advantag that it lift inconitnci that it corrlat prliminary work on carbon black [13,1], th adorption adorption in micropor on th xtrnal urfac data wr xamind within th framwork of th DRK Eq. within th framwork of Dubinin thory. () for rlativ prur p/p, On th othr Gravimtric adorption maurmnt wr carrid out h, th BET mthod wa applid to th adorption data following tard tchniqu dcribd in dtail l- for 0.05,p/p, whr [8]. In th modrn formulation of Dubinin thory [,8], th DRK quation tak th form. Rult dicuion a5 am(drk) xp[(a/be o)] () Inpction of Eq. (1) how that th propod monolayr whr am(drk) rprnt th limiting amount adorbd 3 dnity of bnzn on carbon black, mmol in th monolayr. Obviouly Eq. () do not includ 0 m, corrpond to a molcular urfac ara of multilayr adorption, a oppod to th BET modl. 0 m, intad of th claical valu of 310 m am(drk) i thrfor an xtrapolatd valu. obtaind from adorption by graphitizd carbon black in All ytm rvald a linar ction in th plot of ln th BET rang bad on th tard A ( ; 77 ( a) v. A, bfor multilayr adorption t in. Th m 0 K) m [1,1]. At firt, thi diffrnc may ction lad to th monolayr capaciti am(drk) givn b acribd to th packing of bnzn at low prur, in Tabl 1. Th tabl alo giv th valu of th inc th molcul may aum diffrnt poition. How- quivalnt BET monolayr am(bet) obtaind from th vr, at a latr tag Dryagv t al. [7] propod an am iothrm, but at highr prur. quation imilar to Eq. (1), to dcrib th adorption of A illutratd by Fig. 1, in th ca of bnzn adorbd CCl on carbon black at 93 K, at 8, 93, K th plot of ln ( a/ am(drk)) v. A can b fittd to a ingl lin in th rang 5, A, 5 g (mmol/m ) kj mol (for T 5 93 K, thi corrpond to th domain xp[(a/b kj mol )]. 10,p/p,0.05). Th principl of tmpratur-in- (3) varianc i thrfor fulfilld by bnzn ovr a tmpratur rang of at lat 0 K, which indicat a tru DRK b i th affinity cofficint of carbon ttrachlorid, a ud bhaviour for thi adorptiv. Curv fitting lad to an in Dubinin thory for th volum filling of micropor. avrag charactritic nrgy Eo of 10.8 kj mol. It i In th ca of Eq. (3), b(ccl ) Th urfac dnity clo to th valu of 11. kj mol obtaind for bnzn 3 of mmol m corrpond to a molcular adorbd by anothr carbon black, -30, xamind in our 0 urfac ara of 0310 m, which i much mallr than laboratory. Thi uggt that for thi typ of urfac th 0 th valu of m obtaind for adorption by limiting valu of Eo b around 11 kj mol. carbon black in th BET rang [15]. Th lattr i alo in For bnzn at 93 K, th limiting amount am(drk) i agrmnt with th valu calculatd [1] from th liquid 0.5 mmol g, againt 0. mmol g from th BET dnity. rang of th am iothrm. Th valu ar rlativly Thi diffrnc i conidrabl, inc CCl i a clo, a thy lad to pcific urfac ara of 65 5 phrical molcul, th dicrpancy cannot b xplaind in m g, auming a molcular urfac ara A of 33 m Tabl 1 Monolayr capaciti obtaind from th DRK BET rang for adorption on carbon black Hocht. S alo Fig. 1 Vapour C H CCl CH Cl 6 6 Tmpratur (K) 8 K 93 K 311 K 33 K 9 K 305 K 93 K 77 K am (DRK) mmol g am (BET) mmol g

3 3 3 than to th valu of mmol m ud in Dubinin tard iothrm (1). A hown in Fig. 1 in Tabl 1, a imilar pattrn i obrvd for th adorption of dichloromthan at 93 K of carbon ttrachlorid at K. Both vapour follow th DRK quation a good ovrlap with th bnzn data i obtaind with th affinity cofficint b(chcl )50.66 b(ccl ) Th lattr i omwhat mallr than th uual valu of 1.05 rportd in Wood urvy [16]. In th ca of dichloromthan at 93 K, th limiting adorption capacity am(drk) i 0.30 mmol g, th am a that for th BET rang of th am iothrm, which uggt urfac ara of 61 9 m g auming 0 A m(chcl )59310 m, a calculatd [1] from th liquid tat. For carbon ttrachlorid at 93 K, am(drk) am(bet) ar, rpctivly, mmol g, l which corrpond to 65 5 m g, auming 0 A m(ccl ) m [1,15]. With rpct to th urfac ara of 5 m g bad on bnzn, th urfac 3 dnity of CCl in th DRK rang i 0.9/ Fig. 1. Logarithmic DRK plot for th adorption of diffrnt 3 mmol m a oppod to mmol m ud by vapour on carbon black Hocht: C6H6 at 8 K (n), 93 K (m), Dubinin in Eq. (3). Th lattr valu i much too high 311 K (h) 33 K (j); CCl at 9 K (d) 305 K (); CH Cl at 93 K (1) at 77 K (3). unralitic, owing to th fact that th liquid tat alrady 3 uggt a dnity of.5310 mmol m for thi phrical molcul m for bnzn. With rpct to th urfac ara of For nitrogn at 77 K, on obrv a linar DRK rang, 5 m g bad on C H, th urfac dnity of C H in but it i limitd by th rlativly mall valu of T. Th th DRK rang i 0.5/ mmol m which claical valu b( )50.33 yild a charactritic nrgy 3 i clor to th thortical valu of mmol m, Eo of 1.1 kj mol (a imilar analyi of th tard nitrogn iothrm propod by Carrott t al. [6], lad to Eo511.8 kj mol in th rang 0.005,p/p,0.1). A hown in Tabl 1, th monolayr capaciti am(drk) ar ytmatically highr than am(bet) by 0%, xcptd. It i intrting to not that in th ca of at 77 K CHCl at 78 K, 93 K 31 K adorbd on non-porou a-mno [13], th valu of am(drk) ar alo highr than am(bet). o xplanation can b offrd at thi tag. Howvr, it appar that th urfac dniti (mmol m ) ud by Dubinin in Eq. (1) (3) ar dfinitly too high vn unralitic. Thi i tru in particular for phrical or narly phrical molcul uch a carbon ttrachlorid dichloromthan, whr no incra of th urfac dnity can b potulatd on th bai of a chang in molcular orintation, a oppod to bnzn. In viw of th good fit claimd for Eq. (1) (3), th atifactory valu of S obtaind with Eq. (3), it i likly that th unralitic urfac dniti ar compnatd by th cond part of th quation. It contain A th charactritic nrgy of 6.35 kj mol raid to th powr n51, a oppod to th DRK Eq. (), whr Eo510.8 kj mol n5. Thi compnating ffct i confirmd by Fig.. Comparion of th tard iothrm g * g(dubinin) for C H ( ) CCl (- - -) at 93 K, givn by Eq. (5), th comparion of th DRK Eq. (5) (6) for C6H6 6 6 (1) (6), (3). Th p/p cal hown corrpond to bnzn. CCl at 93 K, rpctivly

4 xtrnal urfac ara S ar oftn in good agrmnt with th avrag valu obtaind for th carbon from a varity of tchniqu. Howvr, a illutratd by carbon CAF 1-B, diffrnc may occur. Thi i du to th fact that in th rang of validity of th DRK quation g *or g(dubinin), th proc of micropor filling may not b complt for carbon with wid por. Thi i an intrinic hortcoming of Dubinin mthod, a oppod to traditional comparion plot, whr S i drivd from adorption at highr rlativ prur. Th rult hown in Tabl ar clo to tho obtaind with Dubinin tchniqu, but from a formal point of viw, it would b bttr to rplac Eq. (1) (3) by th DRK tard iothrm (5) (6). Thi approach alo ha vral advantag: firtly, a illutratd by Fig. 1, th rquirmnt for tmpratur invarianc i fulfilld. Thi man that rfrnc iothrm (5) (6) can b combind with Eq. () to a th xtrnal urfac ara S of a carbon at tmpratur othr than 93 K. By uing th appropriat urfac dniti (mmol m ) affinity cofficint b, th procdur can b adaptd to othr Fig. 3. Plot of a/f( p/p ) v. g */F( p/p ), whr F 5 xp[(a/ vapour. From a thortical point of viw, th prnt E o) ], of th bnzn iothrm at 93 K for carbon U-0 (h), approach i alo an intrting xtnion of Dubinin CECA (m), CAF-1B (n) XC-7 (j). Th lop of th thory to opn urfac. linar ction lad to S, givn in Tabl. Scondly, it appar that th charactritic nrgi E o kj mol obtaind for th adorption of 3 g *(C6H 6) (mmol m ) xp[(a/10.8) ] bnzn on carbon Hocht -35 ar clo to th limiting valu of 11. kj mol found in th mpirical corrlation btwn th avrag width L of lit-hapd micropor th charactritic nrgy of th corr- ponding Dubinin Atakhov quation [3,17], g *(CCl ) (mmol m ) xp[(a/b ) ] o (5) (b ) (6) with Eq. (1) (3), propod by Dubinin. A hown in Fig., thr xit a rlativly good corrlation btwn th two t of quation ovr th DRK rang of 0.005, p/p, , at 93 K. Thi uggt that th two t of quation can b ud with a imilar dgr of confidnc for th dtrmination of xtrnal urfac ara. Thi i illutratd in Fig. 3, for a ri of wll charactrid microporou carbon (XC-7, U-0, CECA, CAF 1-B) [8,17 19]. Th xtrnal urfac ara wr dtrmind from th bnzn iothrm at 93 K, from th plot of a/f( p/p ) v. g */F( p/p ), whr F 5 xp[(a/e o) ]. A hown in Tabl, rportd arlir [,8], th L(nm) /(E 11.). (7) A charactritic nrgy Eo of kj mol rpr- nt thrfor th limiting valu whn micropor bcom vry larg. Thi obrvation uggt again that th DRK dcription for adorption by opn carbonacou urfac i a logical xtnion of Dubinin thory. Acknowldgmnt Th author wih to thank th Swi ational Scinc Foundation for th award of a Mari Him-Vogtlin grant ( ) to D.H-C., which upportd part of th prnt tudy. Tabl Extrnal urfac ara S obtaind from th bnzn iothrm at 93 K ( Fig. 3) arlir dtrmination by diffrnt tchniqu, whr th uncrtainti ar 10 15% Carbon U-0 CECA CAF-1B XC-7 S (m / g) thi work S (m / g) arlir dtrmination

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