Growth Deceleration of Vertically Aligned Carbon Nanotube Arrays: Catalyst Deactivation or Feedstock Diffusion Controlled?

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1 Growh clrion of Vriclly Alignd Crbon Nnoub Arry: Cly civion or Fdoc iffuion Conrolld? Rong Xing,b, Zhou Yng b, Qing Zhng b, Guohu Luo b, Wizhong Qin b, Fi Wi b *, Myui Kdowi, Eri Einron, Shigo Mruym prmn of Mchnicl Enginring, Th Univriy of Toyo, Hongo, Bunyo-u, Toyo , Jpn b Bijing Ky Lborory of Grn Chmicl Rcion Enginring nd Tchnology, prmn of Chmicl Enginring, Tinghu Univriy, Bijing 184, Chin ABSTRACT Fdoc nd byproduc diffuion in h roo growh of lignd crbon nnoub rry i dicud. A non-dimnionl modulu i propod o diffrni cly-poioning conrolld growh dclrion from on which i diffuion conrolld. I i found h, currn g, lignd muli-wlld crbon nnoub rry r uully fr of fdoc diffuion rinc whil ingl-wlld crbon nnoub rry r lrdy uffring from rong diffuion rinc. Th mhod prnd hr i lo bl o prdic h criicl lngh in diffrn CV proc from which crbon nnoub rry bgin o m rong diffuion rinc, wll h poibl oluion o hi diffuion cud growh dclrion. To whom corrpondnc hould b ddrd. Fi Wi, wifi@flou.org, prmn of Chmicl Enginring, Tinghu Univriy, Bijing 184, Chin; l, ; fx, Shigo Mruym, mruym@phoon..u-oyo.c.jp, prmn of Mchnicl Enginring, Th Univriy of Toyo, Hongo, Bunyo-u, Toyo , Jpn; l, ; fx,

2 Vriclly lignd crbon nnoub (CNT) rry grown on fl ubr 1-7, in which ll h nnoub r of imilr orinion nd lngh, offr n idl plform o udy CNT growh mchnim nd inic. Sinc , vriou chmicl vpor dpoiion (CV) mhod, including floing clyic CV, plm nhncd CV 3 nd hrml CV 4 hv bn propod o ynhiz lignd muli-wlld crbon nnoub (MWNT) rry. Lly, lcohol clyic CV 5 (ACCV), wr id CV 6, microwv plm CV 7, c. r ud o produc vriclly lignd ingl-wlld crbon nnoub (SWNT) rry. Th proc uully involv diffrn cly, crbon ourc nd oprion prmr, ruling in produc wih diffrn morphologi nd qulii. Howvr, non of h CNT growh proc cn ovrcom h grdul dclrion nd vnul rminion of growh. Th biliy o undrnd nd hrby o ovrcom h undrlying dcivion mchnim bcom on of h mo criicl p o dvlop nno-cl ub ino rl mcrocopic mril. Rcnly, mny group hv ffirmd h roo growh mod of hir vriclly lignd CNT, indicing h h fdoc molcul hv o diffu hrough h hic CNT rry, rch h ubr whr cly r locd, nd hn conribu o h CNT growh In hi boom-up growh proc, h diffuion rinc of h fdoc from h op o h roo ri n obrucion, nd cn c uniqu dclring growh mchnim. Exinc of fdoc diffuion rinc mn h concnrion of h crbon ourc h CNT roo hould b lowr hn h bul concnrion. Prviouly, Zhu l. 14 fid xprimnlly-obind film hicn wih h qur roo of growh im, nd d h h growh dclrion i ribud o h rong diffuion limi of fdoc o h CNT roo. Howvr, Hr l. 15 climd lr h hir growh curv cn b ccurly dcribd by ihr diffuion limi or cly dcivion, ugging h only fiing i no ufficin o clrify diffuion conrolld proc from cly dcivion conrolld (cly dcy) on. Furhrmor, if h proc i in h rniion rgion, i.. no complly diffuion conrolld, roo qur fiing i no longr vilbl. Hr, w propo mhod of uing non-dimnionl modulu o quniivly vlu h dgr of fdoc diffuion rinc (no diffuion rinc rgim, rnin rgim, nd rong diffuion limi rgim). ACCV 16 grown ingl-wlld crbon nnoub (SWNT) 5,17- wr ud ypicl xmpl of hi mhod, nd wr found o b nilly fr of fdoc diffuion rinc. Th byproduc bc diffuion 19, which h nvr bn n ino ccoun prviouly, cn lo b imd by h prn mhod. Conidring h imilr diffuion bhvior in diffrn CV proc, fiv of h mo frqunly ud ym r lo dicud. Th rul gr wll wih h currnly vilbl xprimnl rul. Vriclly lignd SWNT wr ynhizd on Co/Mo dip-cod 1 qurz ubr 8 C from hnol crbon ourc. MWNT rry wr grown on qurz ubr 8 C wih imulnou fding of cyclohxn nd frrocn. il of h growh

3 () 3 μm 5 mm 5 μm (b) C dx xdx x L CNT Fdoc Byproduc Cly C * x Subr Figur 1. () SEM microgrph of vriclly lignd SWNT rry from ACCV, in op-righ i chmic of CNT film on ubr, ugging h diffrn dimnion of film iz nd hicn; (b) chmic prnion dcribing h diffuion of fdoc wll g produc during h roo growh of CNT rry. proc cn b found in our prviou wor. 17, Th lngh of -grown CNT rry wr murd by SEM (JSM-7 nd JSM-741), nd vrg dimr wr drmind by TEM (JOEL 1). Fir, i i worh clrifying h concp of diffuion limi h i o b dicud blow. Figur 1 prn h roo growh proc of lignd CNT rry. A crbon ourc i bing dcompod nd xrudd ino olid CNT on cly. Th concnrion of fdoc molcul (.g. hnol in ACCV) h CNT roo, which chmiclly drmind h rcion r, will b much lowr hn op (bul concnrion) if fdoc molcul r no diffuing f nough from op o 3

4 roo. Similrly, if h byproduc molcul gnrd by CNT growh cn no diffu f, hir concnrion will lo b highr CNT roo hn nr h op. Thi concnrion diffrnc h roo nd op of CNT rry i h origin of diffuion limi. Ohr fc, uch cly oxidion, ggrgion, rcion wih ubr, formion of morphou oo or grphiic rucur covrd on cly pricl, r ribud o h cly poioning (cuing mllr o b dicud lr), lhough om of hm,.g. oo formion, lo prohibi crbon ourc from rching cly. Alo, w only conidr on-dimnionl diffuion (long h ub xi) inid CNT rry. Th diffuion from h id of h for i nglcd bcu of h following wo ron. Fir, h id diffuion dinc, i.. h widh of h vriclly lignd CNT film (~5 mm) i uully much lrgr hn h op diffuion dinc, i.. h film hicn (uully vrl millimr mo). Scond, id diffuion i probbly mor difficul du o h highr colliion frquncy in h nioropic rucur of h vriclly lignd CNT rry. Thrfor, in mll licd CNT rry rgion dx ( indicd by dhd lin in Fig.1b), h diffrnc in h moun of fdoc diffuing in from h op nd diffuing ou from h boom hould b wh i conumd inid hi dx rgion. A CNT-ubr inrfc, lhough microcopiclly ( molculr lvl) no ll colliion bwn fdoc molcul nd cly cn rul in CNT growh, h mcrocopic n diffuion flux qul o h CNT formion r (ihr xprd by h rcion r SC *m or h mcrocopic growh r SdL/d) whn in quilibrium. Following bic diffuion hory, Fic Lw (diffuion flux i proporionl o concnrion grdin), nd rcion hory 3, hi proc cn b xprd by dc dc S S = (inid of CNT for), (1) dx x dx dx x nd dc * m dl S = SC = S (roo of CNT for), () dx x= d whr i h ffciv diffuion cofficin, S film r, x norml coordin from ubr, L lngh of CNT rry, urfc rcion conn of crbon ourc o CNT, C * ffciv fdoc concnrion h CNT roo, m rcion ordr, nd rucur-dpndn conn of CNT rry. Hr, w mphiz h, lhough CNT growh cn b dividd ino dild p, i.. fir fdoc dcompoiion, hn crbon diffuion inid ml nd finl crbon prcipiion, ll h p r rd oghr hr nd i h rcion conn of h ovrll proc from crbon ourc o CNT. In ohr word, rprn h dpndnc of ovrll CNT growh r on crbon ourc concnrion. Thi i lo h only growh conn h w cn d C obin dircly from xprimn. Equion (1) i olvd = or dc = con nd dx dx mn h h fdoc concnrion i linrly dcring from op o roo, hu, quion () cn b modifid o 4

5 * C C * m dl S = SC = S. (3) L d Thrfor, oon w now h rcion ordr m nd h rcion cofficin, h ffciv concnrion C * cn b found from quion (3), nd hn h im-dpndn growh curv cn b drmind from n ingrion of quion (3). Exprimn wr crrid ou undr diffrn hnol prur o invig h growh ordr in h ACCV mhod. I i found h h iniil growh r i lmo proporionl o h hnol concnrion ( upporing informion), ugging m = 1, which i lo found o b pproximly vlid in ohr proc (.g. for wr id upr growh 4 ). If cn b conn, h ffciv concnrion C * i clculd bcom C C L * = dl * C = C = d L By ingring quion (4), im-dpndn growh curv i dducd. Thn, quion (3) C L =. (5) Thi quion cn b proporionl o ihr (no diffuion limi) or 1/ (rong diffuion limi), dpnding on h vlu of C nd ( upporing informion). I i imilr o wh i widly ud in ilicon oxidion, h o-clld l-grov rlionhip 5, dicud prviouly. 14, 6 On cn, in principl, lo prdic h growh curv of CNT rry providd h ll h prmr lid bov r nown. Howvr, big diffrnc bwn growh of CNT rry nd ilicon oxid i h, in mo c, h cly for CNT growh undrgo cly poioning. Thrfor, in CNT growh i lo im-dpndn prmr, unli in ilicon oxidion, whr i conn. Thi mn h quion (5) only prdic h idl growh curv whr cly civiy do no dcy. To nbl impl im on h xinc of diffuion limi for crin ym nd CNT lngh, w cn dfin non-dimnionl numbr φ by (4) ϕ =. (6) Thi numbr rprn phyiclly h rio of clyic cpbiliy o diffuiv cpbiliy. Thn, h rio of ffciv concnrion o bul concnrion, η (uully clld h ffciv fcor) cn b corrld wih φ vi impl funcion from quion (3) L 5

6 * C 1 η = = =. (7) C L ϕ 1 Thi fcor llow u o quniivly chrcriz h dgr of h diffuion limi. Whn φ i mll (.g. <.1), i i much ir o diffu hn o rc, hu h ffciv fcor will b nrly 1 (η >.9), indicing hr i lil diffuion rinc. In conr, whn φ i lrg (.g. >9), i i mor difficul o diffu hn o rc, hu h ffciv fcor η will b nrly zro (<.1) nd h ovrll rcion will b domind by h diffuion r. Th in-bwn iuion i wh w mniond bfor h rniion rgim, whr h growh curv will b proporionl o nihr nor 1/. In ACCV ynhi, h crbon fdoc op of h SWNT rry i connly rfrhd, nd hrfor h byproduc concnrion cn b rd zro du o h high hnol flow r. Thu if w um h on C H 5 OH molcul produc on byproduc molcul,.g. H O or H, fr dcompoiion ( A CNT B...), h byproduc concnrion h CNT roo cn b lo rvld ingl funcion of φ, * M B ϕ C B = C. (8) M A ϕ 1 According o h bov dicuion, long w now nd, h influnc of diffuion cn b concludd imply from h vlu of φ for crin CNT lngh L. W now h h vrg dimr of SWNT producd by ACCV i bou nm, nd h dniy of h -grown film i bou.4 g/cm 3. Thrfor, h vrg dinc bwn djcn SWNT cn b ily clculd o b 8.8 nm. A h mn fr ph of hnol in hi proc i bou 16 nm, much lrgr hn h dinc bwn SWNT, i cn b concludd h h hnol diffuion rinc i minly du o h hnol-cnt colliion, i.. in h rng of Knudn diffuion. Thrby, h diffuion cofficin cn b imd from colliion hory if uming CNT oruoiy diffuion chnnl oruoiy 7. A for, w cn u h iniil vlu = whn h CNT growh i fr of diffuion rinc. Wih h imd nd xprimn-drivd, φ i clculd o b.54 (<<1) for 3 μm SWNT rry in ACCV. Thi mn h hnol concnrion h CNT roo, whr h cly i locd, i lmo h m h concnrion h CNT op (95% from quion (7)). Th vricl diribuion of hnol concnrion in h rry i plod in Fig. A-SWNT. Thu, hi proc i cly dcivion conrolld rhr hn diffuion conrolld. Afr w pl h -grown film off h ubr, mo of h cly rmin on h ubr, bu h ubr i no civ for cond growh. Thi confirmd h h cly poioning conribud o h growh dclrion, which gr wih bov clculion of φ. W now H O i byproduc of hnol dcompoiion, iming hrough quion (8) rvl h concnrion of wr h CNT roo i vrl hundrd ppm. Conidring h prviou rpor on h criicl rol of H O or O on 6

7 h growh of SWNT 6, 16, 8, w plo h concnrion diribuion of H O in Fig.. Thi rul i inring, bu currnly w r no ur if hi wr concnrion i criicl for uccful SWNT nuclion, or i rlion o cly dcivion in ACCV. Furhr wor i ndd in hi r. On my noic h bov dicuion on h fdoc diffuion i vril nd vlid for ll h fir-ordr growh mhod of lignd CNT, pplying o boh SWNT nd MWNT. Thrfor, wih h vilbl d in h lirur, w r bl o im h dgr of diffuion rinc in ohr CV proc ud o grow lignd CNT for. Th only diffrnc hr i whn iming h ffciv diffuion cofficin for MWNT rry, h molculr diffuion hould lo b n ino ccoun bcu h mn fr ph i comprbl o h inr-ub dinc for MWNT rry, lid in Tb. 1., 9-31 W nlyzd four ohr CV proc: mm MWNT rry by floing CV (F-MWNT),.5mm SWNT rry by upr growh by H l. 6, 4, 3 (S-SWNT),.5 mm SWNT rry by microwv plm CV by Zhong l. 7, 6, 33 (P-SWNT), nd 4 μm MWNT by hrml CV by Zhu l. 11, 14, 34 (T-MWNT). Th rul r comprd wih our 3 μm SWNT rry producd by ACCV (A-SWNT) in Tbl 1. I cn b n h, nd, h wo y prmr o drmin φ, nd hu h dgr of diffuion difficuly, hv qui lrg diffrnc mong vriou CV proc, pcilly bwn SWNT nd MWNT rry. in SWNT i uully on ordr of mgniud lowr hn h in MWNT bcu SWNT r much mor dnly pcd hn MWNT (h inr-ub dinc i mllr). Rcion conn r obind xprimnlly from quion r= SC. Lrgr for SWNT growh i du o h lowr crbon ourc concnrion (C) bu imilr CNT growh r (r). On poibl phyicl ron for hi diffrnc in growh conn migh b h highr clyic civiy for mllr ml pricl in borbing nd dcompoing hydrocrbon molcul. Bcu of h diffrnc, i i uggd h, for mm-cl SWNT, φ i uully much lrgr hn 1 nd, vn if hr i no cly poioning, h growh r of mm-cl SWNT rry will ill drop o only 1% du o h rong fdoc diffuion rinc. Howvr, h concnrion h roo of rry i of lil diffrnc from h bul concnrion, bov 9%, vn whn hr i no cly dcivion (if conidring dcr of in rl ym, h concnrion would b highr), h diffuion rinc m o no b h dominn ron for h dcring growh in MWNT rry. Th fdoc concnrion diribuion in h CNT rry i prnd in Fig.. A h φ i imply L dpndn, w cn lo prdic h criicl lngh, hown in Fig. b, bov which diffuion problm bgin o n ffc. I m w migh no nd o worry bou diffuion rinc for MWNT bfor w cn grow lmo 1 cm o 1 m high CNT rry, unl h diffuion phnomnon inid CNT rry i much diffrn from clic Knudn hory. 7

8 Tbl 1. Sym prmr nd -clculd φ nd η. Prmr Abb. Uni A-SWNT S-SWNT P-SWNT T-MWNT F-MWNT Tmprur T (K) Molculr wigh M (-) niy - (g/cm CNT imr - (nm) Numbr dniy - (m - ) 8.5E15 5.E15 1.4E16 3E14.1E13 Poroiy ρ (-) Inr-ub dinc - (nm) Mn fr ph λ (nm) Growh r - (m/) E E-6 5E-8 1.E-6 5E-7 Rcion conn (m/).4e-3 9.E-3 5.7E-3 1.E-4 3.5E-4 iffuion cofficin (cm / Lngh L (mm) Propod numbr φ (-) Effciv fcor η (-) From quion (6), h influnc of diffrn prmr on h diffuion bhvior cn b invigd, nd rgi o ovrcom h diffuion limi for h SWNT growh cn lo b rvld. Incring nd dcring or L r ll poibl wy o dcrϕ. Howvr, h influnc of h prmr r vry limid bcu o bring diffuion limid proc o h rcion conrolld rgion on uully nd o dcr φ by wo ordr of mgniud, xprd in Equion (7). On promiing pproch i o prn h coninuou CNT film ino pillr-li or h-li micron rucur o llow y id diffuion, dmonrd by Zhong l. 6 Howvr, w found hi rgy didn wor for our F-MWNT in yilding longr CNT rry. 3 Thi mn hr xi rong diffuion rinc in P-SWNT bu no in F-MWNT, which gr wll wih h bov clculd rul on h wo iuion. On my lo noic h dg of h CNT rry producd by h upr growh mhod i uully highr hn h cnr pr of h rry. Thi migh lo b n vidnc for h diffuion limi in hi proc. Bid Zhong rgy, grdully incring h fdoc pril prur during h growh o o p h ffciv concnrion h CNT roo conn migh b nohr wy o ovrcom hi diffuion limi cud growh dcy. 8

9 Normlizd fdoc concnrion () A-SWNT S-SWNT P-SWNT T-MWNT F-MWNT Wr Nr CNT ip Nr CNT roo ph in CNT rry (μm) 1 mm Wr concnrion (ppm) Effciv fdoc concnrion (b) A-SWNT S-SWNT P-SWNT T-MWNT F-MWNT Srong diffuion limi mm cm dm 1 6 High of CNT rry (μm) Figur. () Crbon ourc nd by-produc concnrion diribuion in vriou vriclly lignd CNT rry. A-SWNT: 3 μm SWNT from ACCV; S-SWNT:.5 mm SWNT from wr-id upr growh; P-SWNT:.5 mm SWNT from microwv plm CV; T-MWNT: 4 μm MWNT from hrml CV; F-MWNT: mm MWNT from floing CV; Wr: wr concnrion inid 3 μm SWNT from ACCV. (b) Rlionhip of h CNT rry high nd h ffciv fdoc concnrion h rry roo, prdicing h criicl high bov which h vriou CNT rry will m h rong diffuion rinc. 1 m A o h rror in hi clculion, i i unvoidbl inc h influnc of om fcor,.g. h bundl rucur of SWNT, h convrion r of fdoc o CNT, oruoiy of diffuion chnnl (w um i o b 1.5 in ll c) r implifid or xcludd in h bov dicuion. Howvr, mniond bov, rror wihin on ordr of mgniud in im of φ will no ld o ignificn diffrnc in concluding h xn of h diffuion limi. A h lrg rror li on h clculion of, furhr wor on dirc murmn of i undrgoing. Nvrhl, φ i hlpful in undrnding h rol of growh prmr on h diffuion limi nd h diffrn diffuion bhvior inid SWNT nd MWNT rry. To conclud, hr w prn vril modl for on-dimnionl diffuion during h roo growh of lignd CNT rry. Th propod non-dimnionl modulu cn b ud o quniivly vlu h dgr of h diffuion limi of fdoc, wll byproduc molcul. Th rul how h, for mm-cl SWNT rry, h fdoc concnrion h roo of h rry i much lowr hn h bul concnrion, whil for mm-cl MWNT h dcring growh cn no b ribud o diffuion limi. Th rul gnrd from h modl 9

10 gr wll wih xprimn d. Poibl rgi o grow longr CNT in ho diffuion limid proc cn b rvld. Acnowldgmn. Thi wor w prilly uppord by Chin Nionl 863 Progrm (No. 3AA363), Chin Nionl Progrm (No. 6CBN7), NSFC Ky Progrm (No. 36), FANE (No. 548), Ky Projc of Chin Miniry of Educion (No. 1611), THSJZ, h Nionl cnr for nnoicnc nd chnology of Chin (Nnocr), nd Grn-in-Aid for Scinific Rrch from Jpn Sociy for h Promoion of Scinc (No nd No ). Supporing Informion Avilbl: Growh curv of lignd SWNT rry from lcohol CV nd lignd MWNT rry from floing CV (Figur S1), vidnc for h fir-ordr rcion from hnol o CNT in lcohol CV (Figur S), furhr xplnion of quion (5), dil of h clculion, nd om ddiionl dicuion. Thi mril i vilbl fr of chrg vi h Inrn hp://pub.c.org. Rfrnc 1. Li, W. Z.; Xi, S. S.; Qin, L. X.; Chng, B. H.; Zou, B. S.; Zhou, W. Y.; Zho, R. A.; Wng, G. Scinc 1996, 74, Ro, C. N. R.; Sn, R.; Sihumr, B. C.; Govindrj, A. Chm. Comm. 1998, Rn, Z. F.; Hung, Z. P.; Xu, J. W.; Wng, J. H.; Buh, P.; Sigl, M. P.; Provncio, P. N. Scinc 1998, 8, Fn, S. S.; Chplin, M. G.; Frnlin, N. R.; Tomblr, T. W.; Cll, A. M.; i, H. J. Scinc 1999, 83, Murmi, Y.; Chihi, S.; Miyuchi, Y.; Hu, M. H.; Ogur, M.; Oubo, T.; Mruym, S. Chm. Phy. L. 4, 385, H, K.; Fub,. N.; Mizuno, K.; Nmi, T.; Yumur, M.; Iijim, S. Scinc 4, 36, Zhong, G. F.; Iwi, T.; Hond, K.: Furuw, Y.; Ohdomri, I.; Kwrd, H. Chm. Vpor po. 5, 11, Liu, K.; Jing, K. L.; Fng, C.; Chn, Z.; Fn, S. S. Crbon 5, 43, Li, X. S.; Co, A. Y.; Jung, Y. J.; Vji, R.; Ajyn, P. M. Nno L. 5, 5, Pinul, M.; Picho, V.; Khodj, H.; Lunoi, P.; Rynud, C.; Myn-L'Hrmi, M. Nno L. 5, 5, Zhu, L. B.; Xiu, Y. H.; H,. W.; Wong, C.P. Nno L. 5, 5,

11 1. Iwi, T.; Zhong, G. F.; Aiw, T.; Yohid, T.; Kwrd, H. J. Phy. Chm. B 5, 19, Xing, R.; Zhng, Z. Y.; Ogur, K.; Ow, J.; Einron, E.; Miyuchi, Y.; Shiomi, J.; Mruym, S. Jpn. J. Appl. Phy. 8, ubmid. 14. Zhu, L. B.; H,. W.; Wong, C. P.; J. Phy. Chm. B 6, 11, Hr, A. J.; L, L. V.; Slocum, A. H. Smll 7, 3, Mruym, S.; Kojim, R.; Miyuchi, Y.; Chihi, S.; Kohno, M. Chm. Phy. L., 36, Mruym, S.; Einron, E.; Murmi, Y.; Edmur, T. Chm. Phy. L. 5, 43, Murmi, Y.; Mruym, S. Chm. Phy. L. 6, 4, Einron, E.; Murmi, Y.; Kdowi, M.; Mruym, S. Crbon 7, ubmid.. Einron, E.; Kdowi, M.; Ogur, K.; Ow, J.; Xing, R.; Zhng, Z. Y.; Ymmoo, T.; Iuhr, Y.; Mruym, S. J. Nnoci. Nnochno. 7, ubmid. 1. Murmi, Y.; Miyuchi, Y.; Chihi S.; Mruym, S. Chm. Phy. L. 3, 377, 49.. Xing, R.; Luo, G. H.; Qin, W. Z.; Zhng, Q.; Wng, Y.; Wi, F.; Li, Q.; Co, A. Y. Adv. Mr. 7, 19, Lvnpil, O. Chmicl Rcion Enginring, Scond Ediion, WILEY-VCH, Winhim, Grmny Fub,. N.; H, K.; Ymd, T.; Mizuno, K.; Yumur, M.; Iijim, S. Phy. Rv. L. 5, l, B. E.; Grov, A. S. J. Appl. Phy. 1965, 36, Zhong, G. F.; Iwi, T.; Robron, J.; Kwrd, H. J. Phy. Chm. B 7, 111, Zhou, W. P.; Wu, Y. L.; Wi, F.; Luo, G. H.; Qin, W. Z. Polymr 5, 46, Zhng, G. Y.; Mnn,.; Zhng, L.; Jvy, A.; Li, Y. M.; Ynilmz, E.; Wng, Q.; McVii, J. P.; Nihi, Y.; Gibbon, J.; i, H. J. Proc. Nl. Acd. Sci. U. S. A. 5, 1, Xing, R.; Luo, G. H.; Qin, W. Z.; Wng, Y.; Wi, F.; Li, Q. Chm. Vpor po. 7, 13, Xing, R.; Luo, G. H.; Yng, Z.; Zhng, Q.; Qin, W. Z.; Wi, F. Nnochnology 7, 18, Zhng, Q.; Zhou, W. P.; Qin, W. Z.; Xing, R.; Hung, J. Q.; Wng,. Z.; Wi, F. J. Phy. Chm. C 7,111, Fub,. N.; H, K.; Nmi, T.; Ymd, T.; Mizuno, K.; Hymizu, Y.; Yumur, M.; Iijim, S. J. Phy. Chm. B 6, 11, Zhong, G. F.; Iwi, T.; Kwrd, H. Crbon 6, 44, Zhu, L. B.; Xiu, Y. H.; H,. W.; Wong, C. P. Nno L. 5, 5,

12 Supporing informion () 3 5 CNT Lngh (μm) (b) Rcion Tim (min). CNT Lngh (mm) Rcion Tim (hour) Figur S1. Tim dpndn growh of vriclly lignd () SWNT rry from ACCV nd (b) MWNT rry from floing CV, boh of which how dclring growh bhvior ovr im. 1

13 Iniil growh r, γ [nm 1 ] o C 775 o C 8 o C 85 o C 1 3 Prur [P] Figur S. Rlionhip of iniil growh r of lignd SWNT rry in ACCV nd h fdoc (hnol) prur, confirming h pproxim fir-ordr growh undr diffrn mprur. 13

14 14 Furhr xplnion of quion (5) pnding on h vlu of nd C, C L = cn b ihr proporionl o or 1/. Whn C <<, 1/ C C L = = ; Whn C >> C C C C L = =

15 il of om clculion Mn fr ph of molcul: λ = RT πd N p, A whr R i h rl g conn, T i mprur, d h molcul dimr, N A i Avogdro numbr, nd p i prur. Knudn diffuion cofficin: K ρ T = 97r τ M 1/ whr r i h chnnl dimr, ρ i h poroiy of h CNT mmbrn, τ i h oruoiy of diffuion chnnl, T i mprur, nd M i molculr wigh. Toruoiy τ in our imion w pproximd o 1.5 in ll c, bcu i i h ypicl vlu for lignd MWNT (rf 6). A dicud in h min x, rror hr will no ignificnly ffc in h ovrll concluion, i.. judging h xinc (or no) of diffuion limi from φ. Molculr diffuion cofficin: AB ( 1/ M 1 M ) 3 / A / Pσ AB 1/ B T =.1858T Ω M AB 1/ whr T i mprur, M molculr wigh, P prur, σ mn molculr dimr, nd Ω colliion ingrion. A nd B nd for wo componn of h g mixur in our clculion, which r h crbon ourc (.g. C H 4 or C 6 H 1 ) nd crrir g (.g. Ar). Effciv diffuion cofficin: 1 = K 1 AB 1 whr i h Knudn diffuion cofficin nd AB h molculr diffuion cofficin. 15

16 Furhr dicuion on In quion (5) L = C, conn (no cly dcivion) i rquird o fi/prdic h im-dpndn growh curv. Howvr, in mo c, cly civiy i lwy diminihing, which mn hi quion i oo idl o b pplid o rl ym. In h prn mhod, h iniil rcion conn = (whn hr i no diffuion problm involvd), w ufficin o xclud h diffuion limi for MWNT rry nd prdic h CNT lngh for SWNT rry. No compl informion of cly dcy i ndd. For h growh of mm-cl MWNT rry, vn whn conn w ud, φ i mll nd η i nr uniy. If hr i om cly dcivion ( will dcr), φ will b vn mllr. Thrfor, vn whn h diffuion i mximizd, hr i no limi for h lignd MWNT rry. For h growh of mm-cl SWNT rry, vn if hr i no cly dcivion (uing ), h growh will b lowd down by h fdoc diffuion limiion. Thrfor, in rl c wih cly dcivion, SWNT rry migh no b bl o grow ovr vrl mm if ping h bul concnrion conn. 16