Relationship of Five Plate Numbers in Chromatography

Transcription

1 Availabl onlin a Procdia Environmnal Scincs 8 ( ICESB 11: 5-6 Novmbr 11, Maldivs Rlaionship of Fiv Pla Numbrs in Chromaograph ZHANG Dali a, KE Jiajun b, LU Lizhu b a Biochmical Enginring Collg, Bijing Union Univrsi, Bijing, 13, China b Insiu of Procss Enginring, Chins Acadm of Scinc, Bijing, 18, China Absrac Slip mchanism and pla hor wr uilizd o h invsigaion of compuing formulas of fiv pla numbrs. Column pla numbr and pak pla numbr wr wo diffrn concps. Pak pla numbr was a nw concp which cam from slip mchanism. A good rlaion xisd bwn h pak pla numbr and h asmmr of pracical pak of chromaogram. Pak pla numbr could b rgardd as an asmmr indx of chromaogram pak, as column pla numbr is rgardd as an fficinc indx of column. Th pla in slip mchanism was mobil, which was diffrn from h fixd pla in pla hor. Th fiv pla numbrs wr four kinds of column pla numbrs and on kind of pak pla numbr (q ; h four column pla numbrs wr horical pla numbr (n, ral pla numbr (n, pla-modl pla numbr (q and slip-mchanism pla numbr (q. 11 Publishd b Elsvir Ld. Slcion and/or pr-rviw undr rsponsibili of h Asia-Pacific 11 Publishd b Elsvir Ld. Slcion and/or pr-rviw undr rsponsibili of [nam organizr] Chmical, Biological & Environmnal Enginring Soci (APCBEES Opn accss undr CC BY-NC-ND licns. Kwords:chromaographic mchanism; pla hor; slip mchanism; column pla numbr; pak pla numbr 1. Inroducion Modrn chromaograph is h vr imporan mhod of analsis and sparaion in h rsarch of biomdicin c. and h rsarchrs can obain a gra dal of scinific informaion b using chromaograph. Among all sors of chromaograph horis, Marin-Sng s pla hor is h mos famous and wll known, so ha pla hor is inroducd and discussd as basic hor of chromaograph in man schoolbooks and monographs. In using pla hor, howvr, rsarchrs ofn m wih wo problms difficul o xplain in hor. Firs, pracical pak of chromaogram dos no ak on normal disribuion (Gaussian disribuion dscribd b h luion curv quaion of classical pla hor. Scond, wih on srious ailing pak, Corrsponding auhor. Tl.: addrss: dali@buu.du.cn Publishd b Elsvir Ld. Slcion and/or pr-rviw undr rsponsibili of h Asia-Pacific Chmical, Biological & Environmnal Enginring Soci (APCBEES Opn accss undr CC BY-NC-ND licns. doi:1.116/j.pronv

2 688 ZHANG Dali al. / Procdia Environmnal Scincs 8 ( h pla numbr can b calculad o rach housands or n housands. According o pla hor, howvr, vn if pla numbr is hundrd, h chromaogram pak should b normal disribuion narl. For h firs difficul problm, if h luion curv quaion of slip mchanism subsius for h Gaussian quaion of luion curv in pla hor, h problm is radil solvd [1]. This papr discusss and rsolvs h scond problm. Fiv pla numbrs, hir rlaionship and hir calculaing formulas ar discussd firs. Ths pla numbrs ar horical pla numbr (n, ral pla numbr (n, pla-modl pla numbr (q, slip-mchanism pla numbr (q and pak pla numbr (q. Thn, h diffrnc bwn column pla numbr and pak pla numbr is xplaind. Th scond problm abov is rsolvd b us of h concp of pak pla numbr. Abou slip-mchanism pla numbr and pak pla numbr, w hav discussd hm [1] ; b uilizing hir phsical imag, w connc hm o h usual pla numbr, i.. horical pla numbr and ral pla numbr, in his papr. This rsarch aims a promoing h prfcion of pla hor ssm, and making h horical xplanaion of pla modl bcom mor rasonabl.. Slip mchanism Slip mchanism modl of chromaograph: proplld b mobil phas, solu moion in chromaographic column compriss a las h wo procsss of slip moion and Marin-Sng pariion moion. Th slip moion is h mchanical migraion of solu adsorbd a saionar phas surfac undr mobil phas proplling. Anohr procss is h caslss pariion moion of solu bwn h firs adsorpion lar and h scond adsorpion lar, Marin-Sng pariion moion [], which causs solu disribuion in column o conform o h rul of binomial xpansion. Suppos h mass fracion of solu in h firs adsorpion lar is x, h mass fracion of solu in h scond adsorpion lar is, and h pariion raio is k. k x/. Th mobil phas flow hrough h inrsic among granuls of saionar phas should b similar o h liquid flow hrough capillaris, and h should hav vloci gradin in h prpndicular dircion of flow. So, hr is h vloci gradin bwn h firs absorpion lar and h scond adsorpion lar in slip moion. Th pariion moion in vloci gradin should chang h original aggrgaion sa of solu which is on nring column. Th rsul of h moion should conform o Marin-Sng pariion procss, naml, h solu disribuion in column should conform o h binominal disribuion rul. n p n p p Binomial xprssion: Ap Cn x (1 Whn n is larg, binomial disribuion approximal obs h normal disribuion ha μ n and σ nx (D Moivr-Laplac horm. ( pμ ( pn 1 1 σ nx f ( p ( π σ π nx In quaion (1 and (, n is h numbr of ims of Marin-Sng pariion which has happnd ill crain im in chromaographic procss, p is h som posiion in h normal disribuion or binomial disribuion. Equaion ( could xprss h luion curv afr is propr of variabl is changd proprl. Suppos h column oul is a h qh pla, and h column pla numbr is q, lik h mans of pla hor. q is subsiud for p in quaion (. Bcaus n incrass coninuall in chromaographic procss, n should bcom h variabl in quaion. L c b h dcras in pla numbr owing o h ffc of slip moion. Suppos h solu a column oul is dsorbd from h scond adsorpion lar and manwhil flows ou wih mobil phas. Finall, whn quaion ( is usd for h luion curv, quaion ( should b xprssd as quaion (3. (( qc ( nc ( nc x f ( n π ( n c x

3 ZHANG Dali al. / Procdia Environmnal Scincs 8 ( f ( n π ( n c x ( qn ( nc x In quaion (3, c c/. In rms of propr of binomial disribuion, h rlaionship of q and is as follows: q n R, Equaion (4. n R is h numbr of ims for Marin-Sng pariion which happn unil h im whn solu disribuion pak (h maximum concnraion of solu arrivs a oul of column. Equaion (4 is subsiud in quaion (3, and hn quaion (5 is obaind. (( n n R x( nc f ( n (5 π x( n c Equaion (5 can b calld pla quaion of luion curv, bcaus h variabl in h quaion is n, i.. h numbr of ims of Marin-Sng pariion in pla for solu. In usual chromaogram, abscissa is, h luion im, and h ordina is dcor rspons. So, quaion (5 nd b changd ino im quaion of luion curv, which is mor as o us. Givn: a is h uni convrsion facor, i.. a facor o chang ims numbr of pariion (n ino luion im (. a mans h numbr of ims of Marin-Sng pariion pr uni im. Th rms rlad o pariion in quaion (5 ar muliplid b a and simulanousl dividd b a. Equaion (5 is invarian acuall. (( a / aan / a x( an / aac / a f ( an / a π x( an / a ac / a Givn: n R /a, Equaion (6. According o quaion (6, mans h im whn solu disribuion pak (h maximum concnraion of solu movs o column oul. is diffrn from rnion im R, and gnrall largr han R slighl(h rsul of ffc of column oul. Givn: n/a. Obviousl, is luion im, bcaus n is h numbr of ims for Marin-Sng pariion. Givn: c /a c, Equaion (7. c sands for apparn slip facor (gnrall, < c <. Th largr is valu is, h grar h loss of pla numbr is, in chromaographic procss. x( c f ( an / a π ax( c Funcion f(n is normalizd quaion. If h im quaion f( also nd b normalizd, h quaion is as o prov: f(af(an/a and normalizd quaion f( is as follows. a a( x( c f ( af ( n (8 π x( c Givn: B a/x, Equaion (9. Th ara of chromaogram pak A, and bas lin is a Y. Equaion (8 can b changd ino quaion (1. B( A B ( c f ( Y + π ( c 3. Pla numbr of slip mchanism and pla numbr of pla hor a( Equaion (1 is h luion curv quaion of slip mchanism. If c, ha is o sa, h solu slip moion is no considrd or is nglcd, slip mchanism modl is changd ino pla hor modl and quaion (1 is changd ino quaion (11, i.. luion curv quaion of pla hor [3,4]. ( B (11 A B f ( π (3 (1

4 69 ZHANG Dali al. / Procdia Environmnal Scincs 8 ( B in quaion (1 is changd o B in quaion (11, o show modl variaions. Equaion (11, in fac, xprsss a sligh ailing pak, and is ailing dgr is usuall xcdd b ral paks. Whn quaion (1 and quaion (11 ar usd o fi on sam luion curv, hir f(, which ar h xprimn daa usd for fi, ar sam corrspondingl, and hnc h wo quaions can b mad o b quad. B A B B ( c A B (1 π c π L. B h characr of xponnial funcion, 1, h xponnial funcion in quaion (1 can b liminad. B using Ba/x (quaion (9, a n R (quaion (6 and n R q (quaion (4, w can obain quaion (13. q q(1 c / (13 In quaion (13, q is h column pla numbr of slip mchanism from quaion (1, q is h column pla numbr of pla hor form quaion (11. Th calculaing formula of ral pla numbr (n [4], n 5.54(, is obaind hrough h R / W1 / ( k' /(1 + k' ramn o simplif luion curv ino Gaussian curv. Th luion curv of quaion (11 is no Gaussian, bu is ailing pak. Bcaus is ailing dgr is vr low, suppos q n. q (14 n 5.54( R / W1/ ( k'/(1 + k' Rfrnc [4] provs ha h pla numbr of pla hor (q is vr clos o ral pla numbr (n in valu. Equaion (14 is subsiud in quaion (13, o produc quaion (15. q 5.54( / ( '/(1 '(1 / (15 n R W1/ k + k c Equaion (15 is h calculaing formula for pla numbr of slip mchanism. 4. Pak pla numbr Owing o h ffc of solu slip moion, column pla numbr is diffrn from h pla numbr which is rflcd b acual pak form (i will b calld pak pla numbr, blow. Th slip moion could mak acuall conribuing pla numbr bcom smallr. Suppos q is pak pla numbr. q should b column pla numbr (q minus h dcras in pla numbr which is du o solu slip moion (c. q' q c (16 Uilizing quaion (3, quaion (7 and quaion (4, w ar abl o obain [5] : cqc /. So, quaion (16 can b changd ino quaion (17. q' q(1 c / (17 Equaion (15 is subsiud in quaion (17. q' 5.54( ( (18 R / W1 / k' /(1 + k' (1 c / Equaion (18 is h calculaing formula of pak pla numbr (q. 5. Discussion ( 5.1. Pla numbr of slip mchanism (q ( As vron knows, h pla in pla hor is fixd and immobil, for pla hor acuall supposs h solu on h saionar phas (or in saionar phas dos no mov ahad wih mobil phas. Th pla in slip mchanism is movabl, bcaus slip mchanism supposs h solu a boh h firs and h scond adsorpion lars all could slip forward undr mobil phas proplling. Th firs adsorpion lar corrsponds o h pla of pla hor in posiion, and h scond adsorpion lar corrsponds o h mobil phas of pla hor in posiion.

5 ZHANG Dali al. / Procdia Environmnal Scincs 8 ( As shown in Fig.1, h column has 1 plas, which ar fixd and immobil according o pla hor. Solu has o pass h 1 plas o flow ou off h column. According o slip mchanism, h firs adsorpion lar can b pushd forward b mobil phas. Owing o pla movmn, solu (h maximum concnraion of solu movs o h pla ha corrsponds o h 5h of immobil plas, whn h solu has com o h las pla of column (s B in Fig. 1. So h pla numbr is 5, and c.5, (1- c /.5. Th rm (1 - c /, hrfor, could b calld apparn ffciv cofficin of pla numbr. (Th pla ssm of slip mchanism, in a sns, is lik h vr long rain running hrough h unnl in mulipl rangs of mounains (h column and saionar phas, h carriag lik h pla. Figur.1 Diagrammaic skch of pla numbr 5.. Pak pla numbr (q q is h pla numbr rflcd dircl b pak form. I can b usd o xplain h characr of pak asmmr. Thr is h rlaiv slip moion bwn h scond adsorpion lar and h firs adsorpion lar, according o slip mchanism. Th inrsics bwn grains of saionar phas form h srucurs which ar analogous o capillar. Flowing fluid in capillar has flow vloci gradin in h prpndicular dircion of flow. This propr can rsuls in h rlaiv slip moion. As B shown in Fig. 1, column pla numbr q 5. Whn h pak pla numbr q rachs 5, h pak has rachd h oul of column (s C in Fig. 1 owing o h rlaiv slip. This cas corrsponds o ha ohr 5 plas ar passd hrough b wa of slip. Equaion (17 indicas ha pak pla numbr would b qual o column pla numbr whn hr is no h slip moion, c. In our xprimn, h apparn ffciv cofficin of pla numbr could rach downwards.1 or lss for concr ailing pak of chromaogram, and hr pak pla numbr was on prcn or on in a housand of ral pla numbr. If ral pla numbr is ns of housands, h pak pla numbr is dozn or dozns. Th rsul confirms prcisl h rlaion of pla numbr and chromaogram pak form, which is characrisic of pla hor. Rfrnc [1] ZHANG Da-Li, LU Li-Zhu, KE Jia-Jun. Discussing Chromaographic Pla Numbr wih Slip Mchanism. China scinc and chnolog informaion, 7, (, pp (in Chins

6 69 ZHANG Dali al. / Procdia Environmnal Scincs 8 ( [] Marin A J P and Sng R L M. A nw form of chromaogram mploing wo liquid phass, Biochm. J., 1941, vol. 35, pp [3] Han Zhnwi, H Zhimin, Yu Guocong. Taild normal chromaographic pak xprssd b pla modl. Chins J. Chromaograph, 1997,15, pp (in Chins [4] DAI Chaozhng, XIANG Zaijun. Rsarch ino characr of chromaographic luing curv b pla hor. Aca Chimica Sinica, 1994, 5: 64-7 (in Chins [5] ZHANG Dali, KE Jiajun, LU Lizhu. Rlaionship of fiv pla numbrs in chromaograph[ol]. [Spmbr 9, 1] hpp:// (in Chins