Monolayer and multilayer adsorption isotherm models for sorption from aqueous media

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1 Kora J. Chm. Eg., 32(5), (2015) DOI: /s REVIEW PAPER INVITED REVIEW PAPER pissn: ISSN: Moolayr ad multilayr adsorptio isothrm modls for sorptio from auous mdia Ryhah Saadi*,, Zahra Saadi*,, Rza Fazali*,, ad Nargs Elmi Fard** *Dpartmt of Chmical Egirig, Faculty of Egirig, South Thra Brach, Islamic Azad Uivrsity, Thra, Ira **Dpartmt of Chmistry, Faculty of Scic, East Thra Brach, Islamic Azad Uivrsity, Thra, Ira (Rcivd 21 Jauary 2015 accptd 10 March 2015) Abstract Idustrial wastwatr pollutd with various cotamiats, icludig havy mtals, dys, tc., dagrs huma halth ad th viromt. Various sparatio tchius hav b dvlopd for th rmoval of pollutats from auous solutios. Adsorptio procss has draw cosidrabl atttio du to its simplicity of dsig, high rmoval fficicy, v at dilut coctratio, ad coomical aspct. W rviwd th most commo two, thr, four, ad fiv paramtr adsorptio isothrm modls corrspodig to moolayr ad multilayr adsorptio o th basis of paramtrs that ca b usd for xplorig ovl adsorbts. Thrmodyamic assumptios of th modls giv iformatio about th surfac proprtis, capacity of th adsorbt ad adsorptio mchaism. Sv rror fuctios wr ivstigatd to valuat th fitss uality of isothrm modls with th xprimtal uilibrium data. Kywords: Adsorptio, Isothrm, Moolayr, Multilayr, Error INTRODUCTION Th rapid progrss of diffrt idustris ad tchologis has rsultd i a hug amout of wastwatr big producd from idustrial procsss that ds to b rmovd bfor discharg ito th viromt [1]. Iorgaic ad orgaic pollutats dissolvd i auous solutios ar cosidrd to b hazardous bcaus of thir toxicity, v at low coctratios [2]. Th global icras of pollutd watrs sriously thrats huma halth ad th viromt. Various rgulatory agcis hav dtrmid maximum allowabl coctratio of th cotamiats i drikig watr to ovrcom th problm [3]. Various covtioal mthods for th rmoval of wastwatr pollutats hav b dvlopd cotaiig io xchag, rvrs osmosis, mmbra, filtratio, solvt xtractio, floatatio, lctrodialysis, lctrochmical opratios, biological tratmt, coagulatio, oxidatio, ad chmical prcipitatio. Amog ths, adsorptio is cosidrd to b rlativly suprior bcaus it is vrsatil ad widly usd, vry fficit bcaus of its high rmoval capacity, ixpsiv, simpl for dsig, ad applicabl at vry low coctratios [4-13]. Diffrt matrials such as activatd carbo, silica, titaium dioxid, alumia, ad various aomatrials such as aomtal oxids, carbo aotubs ad aozolit composits ar applid as adsorbt for rmoval of cotamiats from auous solutios [14-18]. Ths adsorbts hav larg porous surfac ara, good adsorptio capacity, high thrmal stability, good mchaical strgth, fast kitics ad vrsatility for rmoval of a broad typ To whom corrspodc should b addrssd. r_fazali@azad.ac.ir Th first ad scod authors hav idtical collaboratio i this rviw papr. Copyright by Th Kora Istitut of Chmical Egirs. of iorgaic ad orgaic pollutats dissolvd i auous mdia [19-21]. Howvr, th matrials hav rstrictios i th cas of thir applicatios o a larg idustrial scal bcaus of thir high cost ad difficultis rlatd to rgratio [22]. Cost-ffctiv, atural ad rwabl matrials ar dd such as chitosa, ta lavs, ligit, wast activatd sludg, agricultural wast ad biomass [23-26]. Th adsorptio isothrm is a fudamtal sourc of iformatio o th adsorptio procss. Th aalytical forms of adsorptio isothrm uatios dpd o th typ of th surfac phas that ca b cosidrd as a moolayr or multilayr, ad as localizd, mobil. Ths modls ar complx du to structural ad rgtic htrogity of th adsorbt surfacs, which is charactristic of a grat umbr of adsorbts usd at idustrial or xprimtal scal [27-29]. Most adsorptio isothrms ar applid i both gas-solid ad liuid-solid uilibrium systms. Svral isothrm uatios for adsorptio at th solid-liuid itrfac, spcially uatios rlatd to adsorptio of dilutd solutios, ar drivd from th thortical dscriptio of sigl gass ad thir mixturs o solid surfacs. Isothrm uatios that dal with physical adsorptio of gass giv th most importat proprtis of adsorbts, icludig por volum, por siz or rgy distributio, spcific surfac ara ad capacitis of adsorbts [30]. Th spcific curvs of isothrms ca b itrprtd to obtai iformatio associatd with itractios btw adsorbt matrials ad pollutats, optimizatio of th adsorptio mchaism, ad ffctiv dsig of th adsorptio systms [31,32]. Hossai t al. [33] studid th rmoval of coppr from watr ad wastwatr usig palm oil fruit shlls as a biosorbt. Noliar rgrssio aalyss for isothrm modls rvald that thr-paramtr isothrms (Sips, Kobl-Corriga, Radk-Prausitz, Rdlich- Ptrso, Toth, Hill) had a bttr fit to th xprimtal data tha two-paramtr isothrms (Lagmuir, Tmki, Jovaovich, Flory - Huggis). Subramayam ad Das [34] ivstigatd th adsorptio of ph- 787

2 788 R. Saadi t al. ol oto atural soil. Th xprimtal data wr aalyzd usig thr uilibrium isothrm corrlatios, amly, Lagmuir, Frudlich ad Rdlich-Ptrso uatios, ad rsults showd that th Lagmuir ad Rdlich-Ptrso isothrms providd bttr fit tha th Frudlich isothrm modl. I additio, rror fuctios such as sum suar rror (ERRSQ), avrag rlativ rror (ARE), hybrid fractioal rror (HYBRID), Maruardt s prct stadard dviatio rror (MPSD), ad sum of th absolut rror (EABS) wr discussd to valuat th fitss uality of isothrm modls with th xprimtal uilibrium data. Mor prvious rsarch studis rgardig th studis of adsorptio isothrm modls for various adsorbat-adsorbt systms ar prstd i Tabl 1. Th objctiv of this rviw was dscriptio of th distict proprtis ad applicatio of moolayr ad multilayr adsorptio isothrm systms. Th optimizatio procdur of oliar isothrm ruirs th slctio of a rror fuctio i ordr to valuat th agrmt of th isothrm with th xprimtal uilibrium data. Th choic of rror fuctio ca affct th paramtrs drivd. So that, i this study, valuatio of accuracy of th paramtr valus was ivstigatd basd o sv o-liar rror fuctios. ADSORPTION ISOTHERM Diffrt adsorptio isothrm modls ca b drivd by assumig a thrmodyamic uilibrium rlatioship btw th uatity of th adsorbd molcul by a uit mass of adsorbt ad th amout of adsorbat rmaiig i th bulk fluid phas at a costat tmpratur ad ph [30]. It givs iformatio about th distributio of adsorbabl solut btw th liuid ad solid phass at diffrt uilibrium coctratios. Th paramtrs obtaid from adsorptio isothrm modls ar spcific for ach systm [35]. Th two, thr, four ad fiv paramtr uilibrium adsorptio isothrm modls rlatd to moo ad multi-layr adsorptio (Lagmuir, Frudlich, Tmki, Flory-Huggis, Volmr, Dubii-Radushkvich (DR), Jovaovich, Elovich, Hill, Rdlich-Ptrso, Sips, Toth, Kobl-Corriga, kha, Radk-Prausitz, Kislv, Josss, Hill-d Bor, Uila, Frumki, Fowlr-Gugghim, Fritz-Schludr (III), Fritz-Schludr (IV), Dubii-Astakhov (DA), Baudu, Wbr-va Vlit, Fritz-Schludr (V), Halsy, Bruaur-Emmtt-Tllr (BET), Fig. 1. Moolayr ad multilayr adsorptio isothrm modls. May, 2015

3 Moolayr ad multilayr adsorptio isothrm modls for sorptio from auous mdia 789 McMilla-Tllr (MET), Frkl-Halsy-Hill (FHH), Araovich, Harkis-Jura, Rd Had, -layr BET, Gugghim Adrso d- Bor (GAB), Adrso (IV), Dubii-Srpisky (DS), Adrso (V)) wr discussd. Th diagram of all th studid adsorptio isothrm modls i this rviw is i Fig. 1. Th amout of molcul adsorbd pr uit mass of adsorbt, that is, th uilibrium adsorptio capacity of adsorptio is calculatd as E. (1) [36]: VC ( = o C ) W 1. Moolayr Adsorptio Isothrm Modls 1-1. Two Paramtr Isothrm Modls Lagmuir Th simplst ad still th most usful isothrm, for both physical ad chmical adsorptio, is th Lagmuir isothrm. This modl assums that adsorptio is limitd to a moolayr: oly a sigl layr of molculs o th adsorbt surfac ar absorbd, adsorbt surfac is homogous ad adsorptio rgy is uiform for all sits ad thr is o trasmigratio of adsorbat i th pla of th surfac. Oc a pollutat occupis a sit, o furthr adsorptio ca tak plac i that sit; th itrmolcular attractiv forcs rapidly dcras as distac riss. Thr is o itractio btw molculs adsorbd o ighborig sits, adsorptio o surfac is localizd, which mas that adsorbd atoms or molculs ar adsorbd at dfiit ad localizd sits [37]. Basd upo ths assumptios, th Lagmuir isothrm is writt as E. (2) [37,38]: = ml bc (2) 1+ bc b is th uilibrium costat (L/mg), which is a critrio of th tdcy of th adsorbat to adsorb oto th activ sits of th adsorbt surfac. A largr b valu rprsts highr adsorptio rgy. Th dimsiolss costat of th sparatio factor or uilibrium paramtr to prdict th adsorptio fficicy ad usability of th Lagmuir uatio is dtrmid as E. (3) [39]: R L = (3) 1+ bc 0 R L valus btw 0 ad 1 idicat favorabl adsorptio, whil R L >1, R L =1, ad R L =0 idicat ufavorabl, liar, ad irrvrsibl adsorptio procsss, rspctivly. Basd o prvious rsarch studis [34,40-46], th Lagmuir modl has th bst fitss uality with xprimtal data amog two paramtr moolayr adsorptio isothrm modls Frudlich Th Frudlich isothrm modl is a mpirical uatio ad aothr form of Lagmuir that ca b applid to multilayr adsorptio. This modl assums that th surfac of th adsorbt is htrogous ad activ sits ad thir rgis distribut xpotially [47]. Th strogr bidig sits ar occupid first, util adsorptio rgy is xpotially dcrasd upo th compltio of adsorptio procss [48]. Th Frudlich isothrm is xprssd as E. (4) [47]: 1/ = k f C F whr k f is th adsorptio cofficit ad rprsts th adhsio (1) (4) ability of th adsorbat oto th adsorbt (rlativ adsorptio capacity of th adsorbt). 1/ F idicats th adsorptio itsity of adsorbat oto th adsorbt or surfac htrogity. Th slop (1/ F ) btw 0 ad 1 idicats favorabl adsorptio isothrm. Wh this valu gts closr to zro, th surfac of th adsorbt bcoms mor htrogous ad th adsorptio isothrm bcoms mor oliar, whil, 1/ F abov o is idicativ of ufavorabl adsorptio isothrms [49,50]. As 1/ F gts smallr tha about 0.1 th adsorptio isothrm approachs irrvrsibl isothrm [51]. Bcaus such a uatio dos ot approach Hry s law at low coctratios, it is ot abl to provid a good fit for adsorptio data [52]. Accordig to prvious rsarch [36,43,45,53-56], for two paramtr moolayr adsorptio isothrm modls, th Frudlich modl was foud to b th most appropriat to dscrib th adsorptio of diffrt adsorbats from auous solutios Tmki Aothr mpirical uatio, th Tmki uatio, dscribs th adsorptio of hydrog oto platium lctrods withi th acidic solutios [51].Th modl is giv by E. (5) [57]: =B T l(a T C ) (5) RT B T = (6) b T Th Tmki isothrm uatio assums that th hat of adsorptio of all th molculs i th layr dcrass liarly rathr tha logarithmically as uilibrium adsorptio capacity icrass bcaus th b T factor is rlatd to adsorbt-adsorbat itractios [58] Th adsorptio is charactrizd by a uiform distributio of th bidig rgis, up to som maximum bidig rgy. Th Tmki uatio is bttr for prdictig th gas phas uilibrium rathr tha liuid-phas uilibrium [59] Flory - Huggis Flory-Huggis isothrm modl, which occasioally drivs th dgr of surfac covrag charactristics of adsorbat oto adsorbt, ca xprss th fasibility ad spotaous atur of th adsorptio procss. Th uatio of Flory-Huggis isothrm is prstd as E. (7) [60]: θ = K C FH ( 1 θ) FH 0 C C o θ = Th FH paramtr is th umbr of adsorbat ios occupyig sorptio sits. Th uilibrium costat, K FH usd for th calculatio of spotaity fr Gibbs rgy is rlatd to th E. (9) [61]: ΔG 0 = RTl(K FH ) (9) Volmr Th Volmr isothrm modl assums that adsorbd molculs ar allowd to b mobil o th surfac of adsorbt but adsorbd molculs ar ot allowd to hav itractio with ach othr. Th Volmr uatio is dfid as E. (10) [51]: θ V θ V C = d1 ( θ V ) xp θ V (7) (8) (10) Kora J. Chm. Eg.(Vol. 32, No. 5)

4 790 R. Saadi t al. I which θ V (θ V = / m ) is fractioal covrag lid btw zro ad uity. d is th Volmr affiity costat which dpds o tmpratur. Th factor xp(θ V /1 θ V ) i abov uatio accouts for th mobility of th adsorbat molculs Dubii-Radushkvich Th Dubii-Radushkvich modl was chos to stimat th charactristic porosity ad th appart fr rgy of adsorptio. Th Dubii-Radushkvich isothrm modl ca b computd by E. (11) [60]: = SD xp( K ad ε 2 ) (11) It is grally usd to xprss th adsorptio mchaism with a Gaussia rgy distributio oto a htrogous surfac [30]. Th itrmdiat rag of coctratios data ca b succssfully fittd with this modl; howvr, th modl is ot abl to prdict Hry s law at low coctratio [62]. This isothrm modl is usually applid to distiguish th physical ad chmical adsorptio of adsorbat ios. Th Polayi pottial, ε, ca b corrlatd as E. (12) [60]: Bs = ms a s C (18) Bs 1+ a S C At low adsorbat coctratios th Sips isothrm modl ffctivly rducs to th Frudlich isothrm. Thrfor, it dos ot follow Hry s law. At th high adsorbat coctratios, this modl prdicts a moolayr sorptio capacity charactristic of th Lagmuir isothrm [70]. Th costat Bs is oft rgardd as th htrogity factor ad th systm htrogity could stm from th solid or th adsorbat or a combiatio of both. Th Bs paramtr is usually gratr tha uity, ad thrfor th largr is this paramtr th mor htrogous is th systm Valus clos to (or xactly) 1 idicat a solid with rlativly homogous bidig sits. If Bs is uity, th Lagmuir uatio applicabl for idal surfacs is rcovrd [51]. Prvious studis [33,67,71,72] idicat that sips modl ca b usd as th most applicabl isothrm modl amog th thr paramtr moolayr adsorptio isothrm modls Toth Th Toth isothrm modl is aothr mpirical uatio dvlε = RT l C (12) Th Dubii-Radushkvich isothrm modl is tmpratur dpdt; wh th adsorptio data at various tmpraturs ar plottd as a fuctio of logarithm of amout adsorbd vrsus th suar of pottial rgy, all suitabl data will li o th sam curv, kow as th charactristic curv [63]. Th costat, K ad, is associatd with th ma fr rgy of sorptio pr mol of th sorbat as it is trasfrrd to th surfac of th solid from ifiit distac i th solutio ad this rgy ca b calculatd as E. (13) [60]: 1 E = K ad (13) Jovaovich Th modl of a adsorptio surfac cosidrd by Jovaovich is sstially th sam as that cosidrd by Lagmuir. Th Jovaovich modl ca b show as E. (14) [64]: = mj 1 K jc ( ) (14) Th Jovaovich uatio ca b usd lss i physical adsorptio. It is applicabl to mobil ad moolayr localizd adsorptio without latral itractios. This uatio rducs to Hry s law at low coctratio. At high coctratio, it rachs th saturatio limit. Th Jovaovich uatio has a slowr approach toward th saturatio tha that of th Lagmuir uatio [51] Elovich Th Elovich is modl basd o a kitic pricipl with th assumptio of adsorptio sits icrasig xpotially with adsorptio, which rprsts multilayr adsorptio. Th Elovich isothrm modl is xprssd as E. (15) [65]: C = me K xp E me (15) 1-2. Thr Paramtr Isothrm Modls Hill Th Hill uatio was postulatd to dscrib th bidig of diffrt spcis oto homogous substrats. Th Hill isothrm modl is calculatd as E. (16) [36]: = SH C H (16) K D + C H This modl assums that adsorptio is a cooprativ phomo, with th ligad bidig ability at o sit o th macromolcul, which may ifluc diffrt bidig sits o th sam macromolcul. I this modl thr possibilitis ca occur: H >1, positiv cooprativity i bidig, H =1, o-cooprativ or hyprbolic bidig, H <1, gativ cooprativity i bidig Rdlich-Ptrso Th Rdlich-Ptrso isothrm cotais thr paramtrs ad icorporats th faturs of th Lagmuir ad th Frudlich isothrms, ad th mchaism of adsorptio is a hybrid ad dos ot follow idal moolayr adsorptio. This modl ca b applid ithr i homogous or htrogous systms. Th Rdlich-Ptrso isothrm modl ca b dscribd as E. (17) [66]: K = R C (17) g 1+ a R C Th xpot, g lis btw 0 ad 1. At high liuid-phas coctratios of th adsorbat, th Frudlich uatio ca b cocludd, i.., it rducs to th Lagmuir uatio for g=1 ad it approachs Hry s uatio for g=0. Rgardig rctly publishd paprs [33,34,67,68], Rdlich-Ptrso modl provids th bst agrmt with xprimtal data btw thr paramtr moolayr adsorptio isothrm modls Sips By idtifyig th problm of cotiuig icras i th adsorbd amout with a icras i coctratio i th Frudlich uatio, Sips proposd a uatio that combis th Frudlich ad Lagmuir isothrms. This producs a xprssio that xhibits a fiit limit at sufficitly high coctratio. This modl is valid for prdictig th htrogous adsorptio systms ad localizd adsorptio without adsorbat-adsorbat itractios. Th Sips isothrm modl is giv by E. (18) [69]: May, 2015

5 Moolayr ad multilayr adsorptio isothrm modls for sorptio from auous mdia 791 opd to improv Lagmuir isothrm fittigs with xprimtal data wh applid to Typ I isothrms for porous adsorbts [73]. Th Toth corrlatio is prstd as E. (19) [36]: = mt C z ( a T + C ) 1/z (19) Th sigificac of th uatio is usful i dscribig htrogous adsorptio systms ad multilayr adsorptio, which is a spcial typ of Lagmuir isothrm ad has vry rstrictiv validity. Th Toth uatio also has a advatag ovr th Sips uatio i that it dscribs th bhavior of th data at low ad high coctratios [61]. Paramtr z is said to charactriz th systm htrogity. Th mor th paramtr z dviats from uity, th mor htrogous is th systm [51]. Th paramtr z is idpdt of tmpratur, whras a T icrass rapidly with icrasig tmpratur [73] Kobl-Corriga Similar to th Sips isothrm modl, th Kobl-Corriga isothrm is a thr-paramtr uatio which icorporats both Lagmuir ad Frudlich isothrms for rprstig th uilibrium adsorptio data. Th Kobl-Corriga uatio is computd as E. (20) [74]: AC K = BC K (20) Th modl is grally applid for htrogous sorbt surfac [75]. This modl is valid oly wh K >1. This mas th modl is abl to dscrib th xprimtal data [74] Kha Th Kha isothrm is a gralizd modl suggstd for pur solutios, which ca rprst both xtrms, Lagmuir ad Frudlich typ. It was dvlopd for both multicompot ad sigl compot adsorptio systms. Th gralizd uatio for pur compot adsorptio isothrms is xprssd as E. (21) [76]: = SK b K C ( 1+ b K C ) a K (21) wh a K is ual to uity, E. (21) rducs to th Lagmuir isothrm. This uatio at larg valu of C rducs to th Frudlich isothrm [77] Radk-Prausitz Radk ad Prausitz [78] proposd a slight modificatio to th Lagmuir uatio, itroducig aothr cofficit which improvd th fit to thir xprimtal data. Th thr isothrms of this modl ca b calculatd as Es. (22)-(24): = mrpi K RPI C ( 1+ K RPI C ) m RPI = mrpii K RPII C m 1+ K RPII C RPII = mrpiii K RPIII C m 1+ K RPIII C RPIII (22) (23) (24) Kislv Th Kislv adsorptio isothrm applid i localizd moomolcular layr is itroducd by E. (25) [79]: θ K C = K K ( 1 θ K ) ( 1+ K θ K ) (25) Josss Th Josss isothrm modl is basd o a distributio of th rgy of itractios adsorbat-adsorbt o adsorptio sits. Rgardig th itractios btw adsorbat ad adsorbt, th modl assums that th adsorbt surfac is htrogous. Th Josss modl is writt as E. (26) [80]: u C = --- xp( F H ) (26) F ad H ar oly tmpratur dpdt. This uatio ca b rducd to Hry s law at low capacitis Hill-d Bor Hill ad D Bor [81,82] rprstd a uatio of th isothrm that taks accout of latral itractios amog adsorbd molculs ad th mobility of th adsorbd phas. Th Hill-d Bor uatio ca b xprssd as E. (27): θ C = H (27) K 1H ( 1 θ H ) xp θ H K θ 2H H 1 θ H RT whr K 1H ad K 2H rprst, rspctivly, th adsorbat-adsorbt ad th adsorbat-adsorbat itractios. A positiv K 2H valu idicats attractio btw adsorbd spcis ad a gativ valu mas rpulsio. Th appart affiity riss with loadig wh thr is attractio btw adsorbd spcis, ad it is rducd with loadig wh thr is rpulsio amog th adsorbd spcis. Wh thr is o itractio btw adsorbd molculs (i.., K 2H =0), th Hill-d Bor uatio rducs to th Volmr uatio [51] Uila Th Uila isothrm modl is aothr mpirical uatio obtaid by assumig uiform distributio of rgy. Th trm Uila coms from uiform distributio ad Lagmuir local isothrm. Th Uila uatio has good fit with xprimtal data at low ad high coctratios. Th Uila isothrm modl is dpictd i E. (28) [51]: = 1+ r s C mu l (28) 2s 1+ r s C Th paramtr s charactrizs th htrogity of th systm. Th largr this paramtr is, th mor htrogous is th systm. If th valu of s rachs to aroud 10, th isothrm closs to irrvrsibl bhavior. If s=0, th Uila uatio rducs to th classical Lagmuir uatio as i this limit th rag of rgy distributio is zro Frumki Th Frumki isothrm uatio was dvlopd to dscrib th itractio btw th adsorbd spcis. Th Frumki corrlatio is prstd i E. (29) [83] θ C = xp( K F ( 1 θ) fθ ) (29) If f=0, i.., thr is o itractio btw adsorbat spcis, abov uatio rducs to th Lagmuir isothrm. Kora J. Chm. Eg.(Vol. 32, No. 5)

6 792 R. Saadi t al Fowlr-Gugghim Th Fowlr-Gugghim isothrm is th simplst uatio dvlopd by cosidrig latral itractio of th adsorbd molculs. Th Fowlr-Gugghim modl is dfid by E. (30) [84]: θ C = FG (30) K FG ( 1 θ FG ) xp 2θ FG w RT Th hat of adsorptio varis liarly with loadig. If th itractio btw th adsorbd molculs is attractiv (i.., w is positiv), th hat of adsorptio will icras with loadig. That is why thr is icrasd itractio btw adsorbd molculs as th loadig riss. This mas that if th masurd hat of adsorptio shows a upward trd with rspct to loadig, it idicats th positiv latral itractio btw adsorbd molculs. Cotrarily, if th itractio amog adsorbd molculs is rpulsiv (i.., w is gativ), th hat of adsorptio shows a dcli with loadig. Wh thr is o itractio btw adsorbd molculs (w=0), th Fowlr- Gugghim uatio will rduc to th Lagmuir uatio Fritz-Schludr (III) Fritz ad Schludr [85] proposd a mpirical rlatio with thr paramtr isothrm modls to dscrib th uilibrium data. Fritz-Schludr modl is prstd as E. (31): = mfs K FS C (31) m 1+ mfs C FS 1-3. Four Paramtr Isothrm Modl Fritz-Schludr (IV) Four-paramtr isothrm modl of aothr form of Lagmuir- Frudlich typ was xtdd mpirically by Fritz ad Schludr. Th uatio of this modl is calculatd as E. (32) [85]: CC α = (32) β 1+ DC This uatio is valid wh α ad β 1. At high liuid-phas coctratios of th adsorbat, this modl rducs to th Frudlich uatio. For α=β =1, th modl rducs to th Lagmuir uatio Dubii-Astakhov Th Dubii-Astakhov isothrm modl dscribs surfac htrogity of adsorbt. Howvr, som mpirical data cofirm that this modl ca dscrib adsorptio i a almost homogous microporous systm. Dubii-Astakhov uatio is giv by E. (33) [51]: A θ DA = xp D D E A C A D = RT l ---- (33) (34) whr D dscribs th surfac htrogity Baudu Th calculatio of th Lagmuir cofficits, ml ad b, carrid out by th masurmt of tagts at th diffrt uilibrium coctratios idicats that thy ar ot costats i a wid coctratio rag. Thir variatios with coctratio ar writt as Es. (35, 36). b = b 0 C x (35) ml = mb C y (36) Drawig plots of l ( ml ) ad l (b) vrsus l C givs th paramtrs of modl, b 0, mb, x, ad y. Th Lagmuir uatio has b trasformd to E. (37), which is kow as Baudu isothrm modl [86]: ( 1+x+y) = mb b 0 C ( 1+x) 1+ b 0 C (37) This uatio is valid wh (1+x+y) ad (1+x) 1. For lowr surfac covrag, th modl rducs to th Frudlich uatio. From prvious studis [87-89], Baudu provids th bst agrmt with xprimtal data rgardig four paramtr moolayr isothrm modls Wbr-va Vlit Wbr-va Vlit uatio was proposd as a four paramtr isothrm modl to prdict th bhavior of this modl with th uilibrium data. This uatio is E. (38) [90]: C = P 1 P 2 P 3 +P 4 ( ) (38) 1-4. Fiv Paramtr Isothrm Modl Fritz-Schludr (V) A broad fild of xprimtal uilibrium data ca b aalyzd by usig a fiv-paramtr modl, amd Fritz-Schludr isothrm modl. This modl ruirs oliar rgrssio tchius with highr complxitis for its solutio. Th Fritz-Schludr uatio is xprssd as E. (39) [85]: m = mfs5 K 1 C m 1+ K 2 C 2 (39) Th isothrm modl is valid wh m 1 ad m Multilayr Adsorptio Isothrm Modls 2-1. Two Paramtr Isothrm Modl Halsy This uatio is suitabl for valuatio of th multilayr adsorptio systm for adsorbat ios adsorptio at a rlativly larg distac from th surfac. Th Halsy adsorptio isothrm ca b giv as E. (40) [91]: K = xp l H lc m H (40) Th agrmt of th xprimtal data with this uatio spcially at high coctratios cofirms th atur of htrogous por distributio of th adsorbt. This uatio is a good rprstatio of adsorptio data rgardig isothrms similar to typ II which appar i htroporous solids [92]. With rspct to th litratur [46,54,56], th Halsy modl has th bst fit with xprimtal data compard to multilayr adsorptio isothrm modls Thr Paramtr Isothrm Modls BET Th Bruaur-Emmtt-Tllr (BET) isothrm is a thortical modl, most xtsivly usd i gas-solid uilibrium systms. BET is a spcial form of Lagmuir isothrm xtdd to driv multilayr adsorptio systms. BET modl is commoly applid to dtr- May, 2015

7 Moolayr ad multilayr adsorptio isothrm modls for sorptio from auous mdia 793 mi th surfac ara of a adsorbt from itrog adsorptio data [51]. Th xtsio of this modl to liuid-solid itrfac is dscribd by E. (41) [51,93]: = mbet C BET C ( C ) 1+ ( C BET 1) C ---- (41) Th C BET paramtr is rlatd to th rgy of itractio with th surfac. Validity of this thory is i th rlativ coctratio rag of 0.02 to 0.4. This isothrm uss th sam assumptios applid i Lagmuir isothrm: surfac ad distributio of sits is uiform ad surfac is rgtically homogous) adsorptio rgy dos ot chag with th progrss of adsorptio i th sam layr), ad thr is o itractio amog adsorbd molculs. Bsids, th rat of adsorptio o ay layr is ual to th rat of dsorptio from that layr. Accordig to multilayr adsorptio of th BET modl, othr simplifyig assumptios wr addd to this modl: th scod, third, ad highr layrs hav th sam rgy of adsorptio which uals hat of fusio, ad ar ot iflucd dirctly by adsorbt-adsorbat itractios. Howvr, th rgy for th first layr is diffrt from that for th scod or othr layrs. Furthrmor, th umbr of layrs as th coctratio approachs th saturatio coctratio tds to ifiity [51,94] McMilla-Tllr (MET) Th MacMilla-Tllr (MET) isothrm modl xtdd basd o cosidratio of surfac tsio ffcts i th BET isothrm. Th MET uatio is dfid by E. (42) [95]: 1/3 k = SM l C ---- s C (42) Wh /C is approachig uity, th logarithmic trm ca b approximatd as: = kc SM /3 C (43) This mpirical isothrm ca b fittd with xprimtal data at rlativ coctratios highr tha 0.8. Howvr, th BET isothrm is valid for rlativ coctratios lowr tha FHH Th Frkl-Halsy-Hill (FHH) adsorptio isothrm dscribs multilayr adsorptio, assumig variatio of adsorptio pottial basd o distac from th adsorbd molcul layr from th surfac of th adsorbt [96]. Th BET modl for th cas of htrogous surfacs glcts th ffcts of surfac htrogity o th adsorptio of th molculs i th scod ad th highr adsorbd layrs. Th FHH modl, howvr, assums that surfac htrogity affcts th adsorptio i all th adsorbd layrs [73]. Th FHH adsorptio isothrm is giv by E. (44): = l ---- A FHH C B FHH (44) A FHH spcifis log-rag va dr Waals itractios btw th surfac ad first adsorbd molcul layr ad itractios btw ighborig adsorbat molculs cotaiig iformatio about th capacity of th surfac for adsorptio. (i.., highr A FHH valus idicat that mor adsorbat may b adsorbd). B FHH dscribs th itractios btw th surfac ad subsut adsorbat layrs [97]. This paramtr icrass from th valu 2.55 for th most htrogous sampl, through 2.69 for th lss htrogous sampl, up to 2.95 for th most homogous sampl [73]. For va dr Waals forcs, B FHH is ual to 3. A valu of about 2.7 is commoly obsrvd i adsorbt [51]. Smallr B FHH valus or largr dgr of surfac htrogity idicat that th adsorbt xtds its ifluc o adsorbd molculs at furthr ad furthr distacs from th surfac [73,97] Araovich Th Araovich isothrm is a modifid vrsio of th BET isothrm which has similarity to this uatio. Th Araovich uatio is calculatd as E. (45) [51]: C mar C Ar ---- C = s C /2 C 1+ C Ar ---- (45) Th diffrc btw ths two uatios is th xpot of th trm (1 C / ). I th BET isothrm modl, th xpot is o whil i th Araovich isothrm modl th xpot is o-half. This isothrm dscribs a broad coctratio rag; howvr, th rag of validity of th BET uatio is arrow (rlativ coctratio of 0.02 to 0.4). Th Araovich modl is basd o th followig hypothss: (1) Th adsorbt surfac is flat ad uiform. (2) Th phas i cotact with th adsorbt is a vacacy solutio to which a lattic modl ca b applid. (3) Th rgy chag accompayig th vaporatio of a molcul dpds o th umbr of layrs. (4) Oly th cofiguratioal compots of th fr rgy ar cosidrd Harkis-Jura Th Harkis-Jura isothrm uatio accouts for multilayr adsorptio ad ca dscrib isothrm of typ II that ca appar i htroporous solids. Th Harkis-Jura adsorptio isothrm is prstd as E. (46) [51,98]: = B HJ C A HJ l 1/2 (46) At high coctratios, th high fit of adsorptio data with Harkis-Jura similar to Halsy uatio ca b xplaid with th xistc of a htrogous por distributio [92]. Although th BET thory is applid for valuatio of th surfac ara of a adsorbt as a covit mthod, th Harkis-Jura isothrm ca also b usd to dtrmi th surfac ara [51]. With rgard to prvious studis [46,99], Harkis-Jura givs th bst agrmt with uilibrium data i cas of thr paramtr multilayr adsorptio isothrm modls Rd Had Th Rdhad isothrm covrs th multilayr adsorptio rgio. Th purpos of th Rdhad isothrm is to xpad th rag of validity of this modl to highr coctratio rag. Th Rdhad Kora J. Chm. Eg.(Vol. 32, No. 5)

8 794 R. Saadi t al. isothrm uatio is writt as E. (47) [51]: = mr (47) whr R is th mpirical paramtr ad it was foud to b i th rag of 2.5 ad 4.5 for most cass. Similar to th Araovich uatio, th Rdhad uatio lis blow th BET uatio i th high rag of th rducd coctratio Four Paramtr Isothrm Modls Layr BET Isothrm Modl Th -layr BET isothrm assums thr ar a maximum layrs that ca b adsorbd oto th itral surfac. Wh th adsorptio spac is fiit i th cas of th fiit siz of pors that is wh th adsorptio layr is limitd by layrs. Th -layr BET modl is tak as E. (48) [51,100] (48) whr C BET is BET adsorptio costat rlatig to th rgy of itractio with th surfac. Wh approachs ifiity, E. (48) rducs to th stadard BET uatio. Wh BET =1, th uatio is trasformd to th Lagmuir uatio. Th paramtr C BET is commoly gratr tha 1 bcaus th hat of adsorptio of th first layr is gratr tha th hat of fusio, i.., th attractiv forcs btw th adsorbd molcul ad th adsorbt ar gratr tha th attractiv forcs btw molculs i th liuid stat [51] GAB Th Gugghim Adrso d-bor (GAB) isothrm is a modificatio of th Lagmuir ad BET physical adsorptio isothrms. This isothrm cssarily icluds a additioal paramtr, K G, which is th critrio for th diffrc of th stadard chmical pottial btw th molculs of th scod ad subsut adsorptio layrs ad thos of molculs i liuid stat. Th GAB uatio is dtrmid as E. (49) [101,102]: (49) whr C GAB ad K G ar th GAB costats, which ar rlatd to th rgis of itractio btw th first ad th furthr sorbd molculs at th idividual sorptio sits [101]. A K G paramtr of ormally lss tha uity mas that th hat of adsorptio of th scod layr is idtical to th highr layrs, but hat of adsorptio of th scod layr ad subsut layrs is lss tha th hat of fusio [51,101]. Followig uatio is valid wh: mbet < mg C BET >C GAB Howvr, if K G =1, E. (49) is trasformd ito th BET uatio; thrfor: mbet = mg ( 2 R 1) C / R C 1 ( = m, BET C BET C BET +1) C C BET C 1+ ( C BET 1) C ---- C c BET ---- BET+1 = mg C GAB K G C C ( K G C ) 1+ ( C GAB 1)K G ---- C BET =C GAB BET+1 Basd o BET isothrm, th hat of adsorptio of th scod ad highr layrs uals th hat of fusio [102] Adrso (IV) Adrso (IV) adsorptio isothrm is aothr modificatio of th BET uatio that assums th structur of adsorbt is such that oly fiit umbr of layrs is allowd to adsorb adsorbat, so th surfac ara availabl for adsorptio is smallr i ach subsut layr. Th isothrm ca b xprssd as E. (50) [51]: ma, 4 C A, 4 C = ( jc ) 1+ ( C A, 4 1) C ---- (50) whr j is th fractio availabl i th subsut layr. This fractio is assumd costat i ach layr. Wh j=0, this uatio rducs to th Lagmuir uatio, ad wh j=1, th famous BET uatio is obtaid Dubii-Srpisky A uatio dscribig th adsorptio of watr by activ carbos was proposd by Dubii ad Srpisky [103,104]. It assums that adsorptio iitially occurs at so-calld primary sits ad that furthr adsorptio taks plac at ths hydratd sits by th formatio of hydrog bods. This uatio is th improvd vrsio of a arlir dscriptio [105], ad it ca b prstd as E. (51): C C = s C DS ( 0 + )( 1 k DS ) (51) Th trm (1 k DS ) taks ito accout th dcras i actig adsorptio ctrs with icrasig micropor fillig. Th valu of th paramtr k DS is dtrmid by th coditio that, at th saturatd coctratio, th uatity adsorbd will b ual to th maximum adsorptio capacity [106] Fiv Paramtr Isothrm Modl Adrso (V) Th Adrso (V) uatio is a fiv paramtr isothrm modl that is aothr modifid vrsio of th BET adsorptio isothrm. It xtds th rlativ coctratio rag of th BET modl by combiatio of th GAB ad th Adrso (IV) isothrm modls, which is wh th hat of adsorptio of scod layr ad abov is lss tha th hat of fusio ad th surfac ara of a layr availabl for adsorptio is smallr tha th prcdig layr. By combiatio of Es. (49, 50) th followig is obtaid [51]: ma 5 =, C A, 5 K A C C ( jk A C ) 1+ ( C A, 5 1)K A ---- ERROR FUNCTIONS (52) Isothrm paramtrs ca b dtrmid by o-liar rgrssio mthod ivolvig th origial form of th isothrm uatios. Noliar rgrssio of isothrm modls usually cotais rror btw th xprimtal data ad th prdictd isothrm. Thrfor, svral mathmatically rigorous rror fuctios, icludig sum suar rror (ERRSQ), hybrid fractioal rror fuctio (HYBRID), sum of absolut rror (EABS), avrag rlativ rror (ARE), Maruardt s prct stadard dviatio (MPSD), oliar chi suar rror ad rsidual root ma suar rror (RMSE) wr ivstigatd. If data from a modl ar similar to th xprimtal data, May, 2015

9 Moolayr ad multilayr adsorptio isothrm modls for sorptio from auous mdia 795 th rror valu will b a small umbr, ad if thy diffr, it will b a larg umbr. Th rror valus ca b miimizd by various mthods lik shuffld complx volutio (SCE) i ordr to dtrmi th optimum valus of isothrm paramtrs. 1. Sum Suar Error (ERRSQ) Th sum suar rror fuctio ca b rprstd as E. (53) [107]: This approach is aalogous to ERRSQ rror fuctio. Isothrm paramtrs drivd from th EABS rror fuctio provid a bt- cal i=1 2 (, xp, ) i (53) Dspit xtsiv applicatio of ERRSQ rror fuctio, it has a sigificat imprfctio: isothrm paramtrs calculatd from such rror fuctio provid a bttr fit at highr adsorbat coctratio rag. Th mai raso for this is that as coctratio icrass, th magitud of th rror ad thrfor suar of th rror also icrass. 2. Sum of th Absolut Error (EABS) Th sum of th absolut rror uatio is giv by E. (54) [108]: i=1 cal, xp, i (54) Tabl 1. Applicabl isothrm modls i prvious rsarch studis Adsorbt Adsorbat Bst fittd isothrm Error Rfrc Coppr aowirs loadd Malachit gr Lagmuir - [41] o activatd carbo Naostructurd γ-alumia Ni (II) Lagmuir - [42] Activatd carbo Pb(II), Ni(II) ad Cd(II) Lagmuir, Frudlich, - [43] Dubii-Radushkvich Natural soil Phol Lagmuir, Rdlich Ptrso ARE, MPSD, [34] HYBRID, ERRSQ, EABS Activatd carbo ad bio-polymr Palladium ad platium Lagmuir, Frudlich ERRSQ [45] modifid activatd carbo Magtic viylphyl boroic acid Cr(VI) Lagmuir, Dubii-Radushkvich - [40] microparticls Clay Mthyl blu Lagmuir, Halsy, Harkis-Jura - [46] Novl Silica Basd Hybrid Pb(II) Frudlich, Halsy, - [56] Dubii-Radushkvich Nm lavs, hyacith roots, cocout Cu(II) Halsy, Frudlich - [54] shll, ric bra, ric husk, ric straw Activatd charcoal from tolu ad Aili Harkis-Jura - [99] titaium dioxid from tolu Natural zolit modifid with Ractiv rd 239 ad Frudlich - [55] hxamthyldiami Ractiv blu 250 Acacia ilotica laf carbo Co (II) Frudlich - [53] Yast biomass Ochratoxi A Frudlich, Hill, BET ERRSQ, ARE, [36] HYBRID, MPSD, EABS H 2 SO 4 activatd immatur Gossypium hirsutum sds Basic Magta II Sips, Hill ERRSQ, ARE, HYBRID, MPSD, EABS, RMSE [71] Palm oil fruit shlls Cu(II) Sips, Rdlich-Ptrso, Hill, Radk-Prausitz, Toth, Kobl Corriga Cashw ut shll Cogo rd Sips, Rdlich-Ptrso, Kobl Corriga, Toth ARE, Chi-suar, RMSE, NSD [33] - [67] TiO 2 aoparticls Natural pigmt Sips - [72] Clioptilolit Ammoium Dubii-Radushkvich, ARE, HYBRID [68] Rdlich-Ptrso Aioic xchag rsi α-lactalbumi Jovaovich, Lagmuir Chi-suar [44] Graular activatd carbo Phol ad chlorophols Baudu, Fowlr-Gugghim ARE [87,88] Kalathur soil ad adhaur soil Phol Baudu ARE [89] Dithyltriami cotto fibrs Psticid Josss - [113] Kora J. Chm. Eg.(Vol. 32, No. 5)

10 796 R. Saadi t al. tr fit as xtt of th rror icrass, biasig th fit towards th highr coctratio data. 3. Hybrid Fractioal Error Fuctio (HYBRID) Th hybrid fractioal rror fuctio is calculatd as E. (55) [109]: 100 ( xp, cal, ) p i=1 xp, (55) Th HYBRID rror fuctio was dvlopd to improv sum suars rror at low coctratios by dividig it to th xprimtal solidphas coctratio. It also icluds th umbr of dgrs of frdom rlatd to th systm (th umbr of data poits) ad umbr of paramtrs of th isothrm uatio as a divisor. 4. Avrag Rlativ Error Fuctio (ARE) Avrag rlativ rror uatio ca b dtrmid as E. (56) [110]: cal 100 ( , xp, ) i=1 xp, i (56) Th ARE rror fuctio attmpts to dcras th fractioal rror distributio across th ovrall coctratio rag. 5. Maruardt s Prct Stadard Dviatio Error Fuctio (MPSD) Maruardt s prct stadard dviatio rror fuctio is dfid by E. (57) [111]: 100 xp i= , cal, p xp, 2 i (57) This rror fuctio is similar i som rspct to gomtric ma rror distributio ad has b modifid accordig to umbr of dgrs of frdom of th systm. 6. Noliar Chi-suar Error Fuctio (X 2 ) Th chi-suar rror fuctio is xprssd as E. (58) [112]: xp, i=1 cal, (, cal ) (58) Noliar chi-suar rror is a statistical tool cssary for th bst fit of a adsorptio systm, drivd by judgig th sum suars diffrcs btw th xprimtal ad th calculatd data, with ach suard diffrc is dividd by its corrspodig valu (calculatd from th modls). 7. Rsidual Root Ma Suar Error (RMSE) RMSE is aothr rror fuctio calculatd for validat th fitss of isothrm modls to xprimtal data for udrstadig th adsorptio procss, which is dfid as E. (59) [33]: ( xp, cal, ) i i=1 (59) Th various adsorbts ad th bst fittd adsorptio isothrm modls studid i prvious rsarchs ar prstd i Tabl 1. Basd o th followig tabl, i cas of moolayr isothrm modls, Lagmuir ad Frudlich modls wr foud to b th most appropriat to dscrib th adsorptio of diffrt adsorbats from auous solutios, ad i cas of multilayr isothrm modls, Halsy ad Harkis-Jura modls had th bst agrmt with th xprimtal data. CONCLUSION Diffrt adsorptio isothrm modls hav b discussd ad catgorizd basd o typ of adsorptio (moolayr ad multilayr) ad umbr of adjustabl paramtrs (two, thr, four, ad fiv paramtr isothrm modls). Som isothrms wr obtaid to modify formr isothrms. For istac, th GAB isothrm uatio was dvlopd to modify th Lagmuir ad BET modls by addig othr paramtr. Furthrmor, th Araovich ad MET multilayr isothrms xpadd widr coctratio rag rathr tha th BET thory. Bttr fit of isothrm modls with xprimtal data is commoly cocludd as th umbr of paramtrs of adsorptio isothrms icrasd. Th optimum isothrm paramtrs ca b dtrmid by miimizig th rror fuctio across th cosidrd coctratio rag. For this purpos, sv o-liar rror fuctios wr valuatd. Paramtrs of som isothrm modls icludig Frudlich, Toth, Uila, ad Dubii-Astakhov dtrmi surfac htrogity. Som isothrm modls giv iformatio about adsorbt proprtis. For xampl, BET ad Harkis-Jura isothrms ar applid for valuatio of th surfac ara of a adsorbt. Th majority of publishd paprs ivstigatd two ad thr paramtr isothrm modls. Accordig to prvious rsarch studis, Lagmuir ad Frudlich modls hav th bst fitss uality with xprimtal data i cas of two paramtr isothrm modls. Rgardig thr paramtr isothrm modls, Rdlich-Ptrso ad Sips modls provid th bst agrmt with xprimtal data. With rspct to four paramtr isothrm modls, th Baudu modl is foud to b th most appropriat to dscrib uilibrium data. a K a R a S a T NOMENCLATURE : Kha modl xpot : Rdlich-Ptrso isothrm costat [L/mg] : sips uilibrium costat [L/mg] :toth uilibrium costat A :Kobl-Corriga costat (L mg 1 g 1 ] A D : adsorptio pottial A FHH : FHH costat A HJ : Harkis-Jura costat A T : Tmki uilibrium bidig costat [L/mg] b : Lagmuir uilibrium costat [L/mg] b K :Kha costat b 0 :Baudu uilibrium costat b T : th costat rlatd to hat of sorptio [J/mol] B :Kobl-Corriga costat (L/mg) B FHH : FHH costat B HJ : Harkis-Jura costat B S :sips modl xpot B T :Tmki costat C :Fritz-Schludr(IV) costat C A,4 : adrso (IV) costat C A,5 : adrso (V) costat CAr : araovich costat C BET :BET costat : ratio btw th kitic costats of adsorptio ad dsorp- C DS May, 2015

11 Moolayr ad multilayr adsorptio isothrm modls for sorptio from auous mdia 797 tio ractios C : uilibrium coctratio of adsorbat [mg/l] C GAB :GAB costat C BET :-layr BET costat C 0 : adsorbat iitial coctratio [mg/l] : adsorbat moolayr saturatio coctratio [mg/l] d : volmr affiity costat D :Fritz-Schludr(IV) costat E : ma fr rgy [J/mol] E A : charactristic rgy of adsorptio f : itractio cofficit of th Frumki modl F :Josss costat g : Rdlich-Ptrso isothrm xpot H :Josss costat j : fractio availabl i th subsut layr r :uila cotat R :uivrsal gas costat [8.314J/mol K] R L : dimsiolss costat of sparatio factor D :Fritz-Schludr(IV) costat E : ma fr rgy [J/mol] E A : charactristic rgy of adsorptio f : itractio cofficit of th Frumki modl F :Josss costat g : Rdlich-Ptrso isothrm xpot H :Josss costat j : fractio availabl i th subsut layr k DS : loss of scodary sits i th cours of adsorptio k f :Frudlich costat [mg 1 L g 1 ] K 1 :Fritz-Schludr (V) costat K 2 :Fritz-Schludr (V) costat K 1H : rgtic costat of th itractio btw adsorbat ad adsorbt [J/mol] K 2H : rgtic costat of th itractio btw adsorbats [J/ mol] K ad : Dubii-Radushkvich isothrm costat rlatd to adsorptio rgy [mol 2 /J 2 ] K A : adrso (V) costat K D : hill costat K E :Elovich uilibrium costat [L/mg] K F :Frumki uilibrium costat K FG : Fowlr-Gugghim uilibrium costat [L/mg] K FH : Flory-Huggis uilibrium costats [L/mg] K FS : Fritz-Schludr(IIII) uilibrium costat [L/mg] K G :GAB costat K H :Halsy costat K j : Jovaovich costat [L/mg] K K : Kislv uilibrium costat [L/mg] K : costat of complx formatio btw adsorbd molculs K R : Rdlich-Ptrso isothrm costat [L/g] KRPI KRPII: Radk- Prausitz uilibrium costats KRPIII m 1 : Fritz-Schludr (V) modl xpot m 2 : Fritz-Schludr (V) modl xpot m FS : Fritz-Schludr (III) modl xpot :Halsy uatio xpot m H mrpi mrpii : Radk-Prausitz modls xpots mrpiii : dgr of frdom BET : maximum umbr of adsorptio layrs D : Dubii-Astakhov modl xpot F :Frudlich costat FH : Flory-Huggis xpot H : Hill cooprativity cofficit of th bidig itractio K : Kobl-Corriga modl xpot R :rd had costat p : umbr of isothrm paramtrs P 1 : Wbr-va Vlit costat P 2 : Wbr-va Vlit modl xpot P 3 : Wbr-va Vlit modl xpot P 4 : Wbr-va Vlit modl xpot 0 : surfac coctratio of primary hydrophilic activ ctrs : uilibrium adsorptio capacity of adsorbt [mg/g], cal : thortical uilibrium adsorptio capacity of adsorbt [mg/g], xp : xprimtal uilibrium adsorptio capacity of adsorbt [mg/g] ma,4 : adrso (IV) maximum adsorptio capacity of adsorbt corrspodig to moolayr saturatio [mg/g] ma,5 : adrso (V) maximum adsorptio capacity of adsorbt corrspodig to moolayr saturatio [mg/g] mar : araovich maximum adsorptio capacity of adsorbt corrspodig to saturatio [mg/g] mb : Baudu maximum adsorptio capacity [mg/g] mbet : BET maximum adsorptio capacity of adsorbt corrspodig to moolayr saturatio [mg/g] me : lovich maximum adsorptio capacity [mg/g] mfs : Fritz-Schludr (III) maximum adsorptio capacity [mg/g] mfs5 : Fritz-Schludr (V) maximum adsorptio capacity [mg/g] mg : GAB maximum adsorptio capacity of adsorbt corrspodig to moolayr saturatio [mg/g] mj ml : Jovaovich maximum adsorptio capacity [mg/g] : Lagmuir maximum adsorptio capacity of adsorbt [mg/ g] m, BET : -layr BET maximum adsorptio capacity of adsorbt corrspodig to moolayr saturatio [mg/g] mr mrpi mrpii mrpiii ms mt mu SD SH SK SM s T : rd had maximum adsorptio capacity of adsorbt corrspodig to saturatio [mg/g] : Radk-Prausitz maximum adsorptio capacitis [mg/g] : sips maximum adsorptio capacity [mg/g] : toth maximum adsorptio capacity [mg/g] : uila maximum adsorptio capacitis [mg/g] : Dubii-Radushkvich thortical isothrm saturatio capacity [mg/g] : hill thortical isothrm saturatio capacity [mg/g] : Kha thortical isothrm saturatio capacity [mg/g] : MET thortical isothrm saturatio capacity [mg/g] :uila modl xpot : absolut tmpratur [K] Kora J. Chm. Eg.(Vol. 32, No. 5)

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