+Modelling the Sorption of Zn 2+ Ions onto Luffa cylindrica

Transcription

1 Amrican Journal of Scinc and Tchnology 218; 5(1): 1-13 hp:// ISSN: Modlling h Sorpion of Zn 2+ Ions ono Luffa cylindrica Oboh Innocn O. 1, Aluyor Emmanul O. 2 1 Dparmn of Chmical and Prolum Enginring, Univrsiy of Uyo, Uyo, Nigria 2 Dparmn of Chmical Enginring, Univrsiy of Bnin, Bnin Ciy, Nigria addrss innocnoboh@uniuyo.du.ng (Oboh I. O.) Ciaion Oboh Innocn O., Aluyor Emmanul O. +Modlling h Sorpion of Zn 2+ Ions ono Luffa cylindrical. Amrican Journal of Scinc and Tchnology. Vol. 5, No. 1, 218, pp Rcivd: April 3, 217; Accpd: January 8, 218; Publishd: Fbruary 27, 218 Absrac: Biosorpion xprimn for Zn (II) was invsigad in his sudy using h plan marial Luffa cylindrica. Th applicabiliy of som slcd kinic modls was sd. Characrizaion lik h surfac ara, chmical bonds, bulk dnsiy, Por siz disribuion, microsrucurs, composiion, morphology and lmnal composiion wr drmind. Th cofficin of drminaion (R 2 ) of all h modls sudid wr mosly grar han.9. In mos cass hs cofficins wr found o b clos o on. This indicas ha all h kinic modls adualy dscrib h xprimnal daa of h biosorpion of Zn (II) ions. Kincic modls wr dvlopd mahmaically, and also, Arificial Nural Nwork (ANN) was applid o dvlop a Mulipl Inpu Singl Oupu (MISO) back propagaion nural nwork modl which was validad. Th RMSE valu was found o b.5912 and for MISO Zn-1 and MISO Zn-2 rspcivly. Arificial nural nwork was abl o prdic h sorpion capaciy ui rasonably for h modl. Kywords: Arificial Nural Nwork, Kincic Modl, Luffa cylindrica, Biosorpion, Was War 1. Inroducion Environmnal polluion du o h discharg of havy mals from various indusris, including mal plaing, mining, paining and agriculural sourcs such as frilizrs and fungicidal sprays ar causing significan concrn bcaus of hir oxiciy and hra o human lif, spcially whn olranc lvls ar xcdd [1]. War conaminad wih mal ions can caus svral halh problms. Havy mal ions such as cadmium, zinc, nickl, chromium, coppr and lad can bio-accumula o b oxic comounds hrough h food chain [2]. Zinc is ofn found in ffluns dischargd from indusris involvd in acid min drainag, galvanizing plans, naural ors and municipal was war ramn plans and is no biodgradabl and ravls hrough h food chain via bioaccumulaion. Thrfor, hr is significan inrs rgarding zinc rmoval from was wars sinc is oxiciy for humans is 1-5 mg/day. World halh organizaion (WHO) rcommndd h maximum accpabl concnraion of zinc in drinking war as 5 mg/l [3]. Acivad carbon is h mos mployd adsorbn for havy mal rmoval from auous soluion and hav bn wll documnd in h liraur [4-5]. Howvr, h xnsiv us of acivad carbon for mal rmoval from indusrial ffluns is xpnsiv [6], limiing is larg applicaion for waswar ramn. Thrfor, hr is a growing inrs in finding nw alrnaiv low-cos adsorbns for mal rmoval from auous soluion, such as: h rsiduals of agriculural producs [7-8]. Biosorpion is an araciv chnology which involvs sorpion of dissolvd subsancs by a biomarial [9]. Vry low cos and nvironmnally frindly plan marials ar now usd as biosorbns for h rmoval of divaln caions from auous soluions as h cllulos, hmiclluloss, pcin and lignin prsn in h cll wall ar h mos imporan sorpion sis [1]. Th srucur of Luffa cylindrica for xampl, is cllulos basd [11-12], and h surfac of cllulos in conac wih war is ngaivly chargd. Mal compounds usd in his sudy will dissolv o giv h caionic mal and his will undrgo aracion on approaching h anionic Luffa cylindrica srucur [13]. Howvr, fw rsarchrs hav addrssd h mahmaical modlling of h sorpion of mal ions ono

2 2 Oboh Innocn O. and Aluyor Emmanul O.: +Modlling h Sorpion of Zn 2+ Ions ono Luffa cylindrical hs biosorbns. Earlir rpord mahmaical modls for h sorpion of havy mal ions includd: surfaccomplxaion, caion-xchang and ripl-layr modls [1]. Arificial Nural Nwork (ANN) modlling is a nonlinar saisical chniu usd o solv problms ha convnional saisical mhods canno solv. Apar from ha, applicaion of ANN in modlling is abou 2 ims fasr han numrical ingraion of a diffrnial uaions sysm [14]. Thrfor h applicaion of ANN in various branchs of scinc and procss chnology by rsarchrs is bcoming popular and hnc is usag in his sudy. Th purpos of his work is o dvlop mpirical modls for h ffc of Luffa cylindrica dosag and h iniial ion concnraion on h upak of Zinc (II) ions from auous soluion. 2. Marials and Mhods 2.1. Prparaion of Luffa cylindrica Th sds and spongs of L. cylindrica wr gahrd ino a clan plasic bag. Thy wr drid in h ovn a 15 C for 24 hours and afrwards ground wih a grinding mill. Th ground sds and spongs wr sivd and wr of paricl siz.3 o.6mm. This was o allow for shorr diffusion pah, rsuling in a highr ra of biosorpion [15]. Th ground sd and spong wr mixd a a raio of 1: Prparaion of Auous Soluions Sock soluion of Zinc was prpard wih disilld war and Zinc (II) raoxosulpha (VI). All working soluions wr obaind by diluing h sock soluions wih disilld war. Th ph of h soluions was adjusd o hir rspciv opimum ph. Th concnraion of mal ions in soluions was analyzd by Aomic Absorpion Spcrophoomr. A duplica was analyzd for vry sampl o rack xprimnal rror and show capabiliy of rproducing rsuls [16] Drminaion of Opimum ph A gramm of L. cylindrica sds and spong mixur wr pu ino 25ml conical flasks conaining 5 ml of h auous soluions ach adjusd o ph 2, 3, 4, 5, 6, 7, 7, 8, 9 and 1 for ach mal ions sudid. Thy wr agiad for 2h a 25 C. Th biosorbns wr rmovd from h auous soluions afr biosorpion using h cnrifug a 24 ra pr minu (rpm) for 1 minus. Th final concnraions of h mal ions rmaining wr drmind using Aomic Absorpion Spcrophoomr (AAS) Biosorpion Exprimn Th biosorpion sudis for valuaion of h Luffa cylindrica mixur for rmoval of Zinc (II) ions from auous soluions was carrid-ou in riplica using h bach biosorpion procdur [7-8]. Th mhod of las suars was usd o prdic h kinic modl by linar rgrssion mhod. A rial and rror was usd for nonlinar rgrssion o minimiz or maximiz h objciv funcion using h solvr add-in funcion, Microsof Excl, Microsof Corporaion Drminaion of Surfac Ara Th Auosorb-1c was usd for h drminaion of h surfac ara of h ground Luffa cylindrica mixur undr sudy Drminaion of Por Siz Disribuion Th PorMasr PM-6 was usd o s h ground Luffa cylindrica mixur sampl. Th insrumn drmins boh Por volum and Por diamr of a solid or powdr by forcd inrusion of a non-wing liuid (mrcury) [17] Drminaion of h Microsrucurs, Composiion, Morphology and Elmnal Composiion of h Luffa cylindrica Mixur Th microsrucurs, composiion, and morphology of h Luffa cylindrica mixur wr analysd by mans of scanning lcron microscopy (SEM). A Philips scanning lcron microscop (ESEM XL3) uippd wih nrgy disprsiv X-ray spcromr (EDX) was usd o analys h various lmnal composiion found in h Luffa cylindrica mixur Drminaion of Chmical Bonds in Luffa cylindrica Mixur Fourir ransform infrard spcroscopy (FTIR) of h adsorbn was don by using an FTIR spcromr (Modl FTIR 2, Shimadzu, Kyoo, Japan) [18] Drminaion of Bulk Dnsiy of Luffa cylindrica Mixur Th mhod of Okaka and Por [19] was usd in drmining h bulk dnsiy. 3. Rsuls and Discussion Tabl 1. Physical propris of h Luffa cylindrica biosorbn. Spcific surfac ara - BET (m²/g).28 Toal Surfac ara (m²/g) Por Diamr Rang (µm) o.3577 Bulk dnsiy (g/cm 3 ).34 Tabl 1 show h bulk dnsiy, surfac ara and por diamr rang for h biosorbn usd for his sudy. Th Spcific surfac ara using h BET mhod was.28m²/g and h Por diamr rang was bwn o.3577µm. Th bulk dnsiy was.34g/cm 3. As obsrvd, h surfac ara for h sd and spong mixur of L. cylindrica is rlaivly low, wih por diamr valus in agrmn wih hos found for ypical msoporous marials [2].

3 Amrican Journal of Scinc and Tchnology 218; 5(1): Figur 1. SEM Scan and plo showing lmnal composiion of Luffa cylindrica. Figur 1 gav h lmnal composiion of Luffa cylindrica ha was analysd by mans of scanning lcron microscopy (SEM). Th Luffa cylindrica showd i conaind a vry high prcnag of carbon a 79.33% followd by oxygn, poassium, calcium, chlorin, phosphorus and sulphur wih wigh % valus of 12.25, 3.86, 1.58, 1.29,.95 and.75 rspcivly. Figur 2. Scanning lcron microscopy of Luffa cylindrica biosorbn: A ransvrsal viw of h mixur of sd and spong 1. Scanning lcron microscopy (SEM) of h Luffa cylindrica biosorbn was akn in ordr o vrify h prsnc of macropors in h srucur of h fibr. In h micrographs prsnd, Figur 2 whn obsrvd show h fibrous srucur of Luffa cylindrica, wih som fissurs and hols, which indica h prsnc macroporous srucur. Ths, should conribu a lil bi o h diffusion of h Zn (II) ions o h Luffa cylindrica biosorbn surfac [21-24]. Th small numbr of macroporous srucur is confirmd by h low spcific surfac ara of h biosorbn (s Tabl 1). As h biosorbn marial prsns fw numbrs of macroporous srucur, i adsorbd low amoun of nirogn, which ld o a low BET surfac ara [21-24]. Thrfor h major conribuion of h Zn (II) ions upak can b aribud o micro- and msoporous srucurs (s Figur 2).

4 4 Oboh Innocn O. and Aluyor Emmanul O.: +Modlling h Sorpion of Zn 2+ Ions ono Luffa cylindrical Figur 3a. FTIR spcrum of h mixur of sd and spong of L. cylindrica biosorbn bfor biosorpion. Figur 3b. FTIR spcrum of h mixur of sd and spong of L. cylindrica biosorbn afr biosorpion of Zn 2+ ions.

5 Amrican Journal of Scinc and Tchnology 218; 5(1): Figurs 3 a - b show h FTIR spcral. Th funcional groups on h binding sis wr idnifid by FTIR spcral comparison of h fr biomass wih a viw o undrsanding h surfac binding mchanisms. Th significan bands obaind ar shown in Figur 3 a - b. Funcional groups found in h srucur includ carboxylic, alkyns or nirils and amin groups [25]. Th srching vibraions of C-H srch of -CHO group shifd from o , , and cm -1 afr Zn 2+ ions biosorpion. Th assignd bands of h carboxylic, amin groups and alkyns or nirils vibraions also shifd on biosorpion. Th shif in h fruncy showd ha hr was biosorpion of Zn 2+ ions on h L. cylindrica biosorbn and h carboxylic and amin groups wr involvd in h sorpion of h Zn 2+ ions [1]. Figur 4. A plo showing h por siz disribuion of h biosorbn - L. cylindrical. Th por siz disribuion of h Luffa cylindrica sampl was obaind by Mrcury inrusion mhod, and i is shown in Figur 4. Th disribuion of avrag por diamr curv prsns a maximum wih an avrag por diamr of abou 3 µm. Th amoun of pors sn in h Luffa cylindrica biosorbn; dcrass for avrag por diamrs ranging from 3 o 1 µm. On h ohr hand, h amoun of avrag pors ranging from 3. x 1-3 o 3 µm is prdominan. Thrfor, his biosorbn can b considrd mixurs of micro- and msoporous marials [21-24]. Tabl 2a. Kinic modls and paramrs of iniial ion concnraion for Zn (II) ions using L. cylindrica as biosorbn. Kinic paramrs Concnraion (mol/dm 3 ) Psudo-firs ordr (mg/g) k f (min -1 ) R Psudo-Scond ordr (mg/g) k s(g/mg/min) R Kinic paramrs Concnraion (mol/dm 3 ) Elovich α(mg/g/min) 2x1 2 3x1 15 1x1 2 1x1 2 β(g/mg) R Inra-paricl diffusion K i(mg/g min -.5 ) C R Avrami (mg/g) K a(min -1 ) n a R Tabl 2b. Kinic modls and paramrs of Dosag for Zn (II) ions using L. cylindrica as biosorbn. Kinic paramrs Dosag (g) Psudo-firs ordr (mg/g) k f(min -1 ) R Psudo-Scond ordr

6 6 Oboh Innocn O. and Aluyor Emmanul O.: +Modlling h Sorpion of Zn 2+ Ions ono Luffa cylindrical Kinic paramrs Dosag (g) (mg/g) k s(g/mg/min) R Elovich α(mg/g/min) 2x1 21 2x1 41 2x1 61 3x1 61 4x1 61 β(g/mg) R Inra-paricl diffusion K i(mg/g min -.5 ) C R Avrami (mg/g) K a(min -1 ) n a R A slcd s of kinic racion modls [26-3] wr usd o fi h xprimnal daa and h corrlaion cofficins wr as high as h ra law for a psudo-scond ordr (Tabl 2a and 2b). Th sorpion of mal ion ono Luffa cylindrica could b a psudo-scond ordr procss. Ths rsuls rinforc h nd of using a saisical rror funcion o br valua h adsorpion modls, as prviously rpord [24], [31]. Addiionally, i was vrifid ha h valus found in h psudo-scond-ordr for boh Tabl 2a and 2b wr in good agrmn wih h xprimnal valus. Ths rsuls indica ha h psudo-scond- ordr kinic modl should b akn ino accoun for xplaining h biosorpion procss of Zn (II) rmoval by h L. cylindrica biosorbn. Whn analyzing h valus of h kinic paramrs dpicd on Tabls 2a and 2b, i should b mniond ha h k s valus srongly dpnd on h iniial concnraion, sinc is unis is gmg 1 min 1. Tabl 2a show ha h kinic rsuls fid vry wll o all h kinic modls sudid. Tabl 2b show ha h kinic rsuls fid vry wll o all h kinic modls sudid wih R 2 valus of.999 xcp for.2g Luffa cylindrica dos which had.997 for h Elovich kinic modl Drivaion of Empirical Modl for Zn 2+ Ions Sorbd by Luffa cylindrica Luffa cylindrica conains polar funcional groups such as aldhyds, kons, and acids. Ths groups can b involvd in chmical bonding and ar rsponsibl for h caion xchang capaciy of h Luffa cylindrica [32]. I appars rasonabl ha in many cass ion xchang rahr han sorpion o fr sis is h rlvan ovrall-mchanism for h binding of mal ions in biosorpion. Sinc h ovrall charg of h biomass paricl has o b nural, any binding of on caion mus b accompanid by ihr a soichiomric rlas of ohr caions or by h binding of anions [33]. Thus, h Luffa cylindrica-mal racion may b rprsnd in wo ways: and 2L - + Zn 2+ ZnL 2 (1a) 2HL + Zn 2+ ZnL 2 + 2H + (1b) whr L and HL ar polar sis on h Luffa cylindrica surfac. In dvloping h mahmaical dscripion of his sorpion procss, crain assumpions wr mad: a. Th procss may b psudo-scond ordr and h ra limiing sp may b chmical sorpion or chmisorpion; b. hr is a monolayr of mal ion on h surfac of Luffa cylindrica; c. h nrgy of sorpion for ach ion is h sam and indpndn of surfac covrag; d. h sorpion occurs only on localisd sis and involvs no inracions bwn sorbd ions;. h ra of sorpion is almos ngligibl in comparison wih h iniial ra of sorpion. Th ra of psudo-scond ordr racion may b dpndn on h amoun of divaln mal ion on h surfac of Luffa cylindrica and h amoun of divaln mal ion sorbd a uilibrium. Th sorpion uilibrium,, is a funcion of, for xampl, h iniial mal ion concnraion, h Luffa cylindrica dos and h naur of solu-sorbn inracion [32]. Th ra xprssion for h sorpion dscribd by Es (1a) and (1b) is: or d( L) d d( HL) d k k [( L) ( L) ] 2 whr (L) and (HL) ar h numbr of aciv sis occupid on h Luffa cylindrica a im, (L) and (HL) ar h numbr of uilibrium sis availabl on h Luffa cylindrica [32]. Th kinic ra uaions can b rwrin as follows: d d whr k is h ra consan of sorpion, (g/mg min), is h amoun of divaln mal ion sorbd a uilibrium, (mg/g), is amoun of divaln mal ion on h surfac of h sorbn a anyim,, (mg/g). Sparaing h variabls in E. (2) givs: ingraing his for h boundary condiions o and o, givs: [( HL) ( HL) ] 2 k ( ) d 2 ( ) 1 ( ) 2 kd 1 + k (2) (3)

7 Amrican Journal of Scinc and Tchnology 218; 5(1): his is h ingrad ra law for a psudo-scond ordr racion. E. (3) can b rarrangd o obain: ( 1/ k 2 + / ) (4) 2 h k (5) Subsiuing E. (5) ino E. (4), givs: ( 1 / h + / ) Alhough hr ar many facors which will influnc sorpion, conac im, ph, mpraur, sorbn concnraion, naur of h solu and is concnraion, a kinic modl is concrnd only wih h ffc of obsrvabl paramrs on h ovrall ra. Ths includ iniial mal ion concnraion, mpraur, Luffa cylindrica dos and naur of solu [32] Effc of Iniial Mal Ions Concnraion and Naur of Solu Th sorpion capaciy daa obaind whn Zn 2+ and hir iniial concnraions wr varid a mpraur of 25 C and Luffa cylindrica dos of 2g/l ar as shown in Figurs 5a and 5b. Figur 5a shows ypical daa for h zinc (II) ions plod so ha h consans iniial sorpion ra and uilibrium sorpion capaciy in E. (6) can b drivd. Ths consans ar givn in Tabl 3. Th agrmn bwn h ss of daa rflcs h xrmly high corrlaion cofficins obaind and shown in Tabl 3. Figur 5b shows ypical sorpion curvs for ffc of iniial mal ion concnraions on h sorpion kinics of of zinc ions ono Luffa cylindrica. In ohr words, h daa showd good complianc wih h proposd psudo-scond ordr uaion. I was shown in h daa ha h iniial mal ion concnraions influncd h conac im ncssary o rach uilibrium and ha h sorpion capaciy incrasd for h highr iniial mal ion concnraions (Tabl 3). (6) Figur 5b. Th sorbd capaciy agains im for h ffc of varid iniial ion concnraion on h sorpion kinics of Zinc ion ono Luffa cylindrica a ph 5.. Tabl 3. Th ffc of iniial ion concnraion on mal ions biosorpion daa. M 2+ C o (mg/l) r 2 (mg/g) k (g/mgmin) h (mg/gmin) Zn Th valu of h iniial sorpion ras, h, was drmind by using h valus of h inrcp of h sraigh lins plod in Figur 5a. Th iniial sorpion ra incrass wih an incras in h iniial mal concnraions for h zinc (II) ions sudid. Whil h varis from o mg/g min, h C varis from 1 o 1 mg/l for zinc(ii) ions, h valus of ra consan, k, was found o incras from o g/ mg min, for an incras in h iniial zinc concnraion from 25 o 2 mg/l. Th corrsponding linar plos of h valus of, k and h agains C wr rgrssd o obain xprssions for hs valus in rms of h iniial mal ion concnraion wih high corrlaion cofficins (Tabl 4). Thrfor i is furhr considrd ha, k and h can b xprssd as a funcion of C for zinc as follows: C AC + B C k AC + k B k (7) (8) h C AC + h B h (9) Subsiuing h Es (7), (8) and (9) ino E. (6), h ra law for a psudo-scond ordr and h rlaionship of, C and can b rprsnd as follows: Figur 5a. Th sorbd capaciy agains im for h ffc of varid iniial ion concnraion on h sorpion kinics of Zinc ion ono Luffa cylindrica a ph C AC + B h h + C AC + B (1)

8 8 Oboh Innocn O. and Aluyor Emmanul O.: +Modlling h Sorpion of Zn 2+ Ions ono Luffa cylindrical whn E. (1) is rarrangd i bcoms AC h C + B + ( AC + B ) h (11) Subsiuing h valus of h mpirical paramrs A h, B h, A and B from Tabl 4 ino E. (11), h ra law for a psudo-scond ordr and h rlaionship of, C and can b rprsnd as follows: Tabl 4. Empirical paramrs for prdicd, k and h from C o. C. 766C (. 414C ) (12) Th Euaion (12) rprsns h gnralisd prdiciv modl for h zinc ion sorbd a any conac im and iniial mal ion concnraion wihin h givn rang. Ths uaions can hn b usd o driv h amoun of mal sorbd a any givn ion concnraion and h racion im. M 2+ A B r 2 A k B k r 2 A h B h r 2 Zn Sorpion capaciy, (mg/g) Iniial ion concnraion, Co (mg/l) Tim, (min) 1 12 Figur 6. Effc of iniial concnraion on zinc sorpion a various racion ims. Figurs 6 shows h hr-dimnsional plo of Euaion (12) i indica ha h Zn (II) ions sorbd a any conac im is highr for a grar iniial mal ion concnraion. This is obvious for highr C valus, as a mor fficin uilisaion of h sorpiv capaciis of h sorbn is xpcd du o a highr concnraion gradin prssur [32] Effc of Luffa cylindrica Dos and Naur of Solu Tabl 5. Th ffc of dosag on mal ions biosorpion daa. M 2+ m (g) r 2 (mg/g) k (g/mgmin) h (mg/gmin) Zn Figurs 7a and 7b show ypical sorpion curvs for ffc of Luffa cylindrica dos on h sorpion kinics of zinc, nickl, coppr and lad ions ono Luffa cylindrica a mpraur of 25 C and iniial ion concnraion of 1 mg/l. Th plod xprimnal daa (Figur 7a) also gav a good fi wih h psudo-scond ordr uaion and h rgrssion cofficins for h linar plos wr vry clos o 1. as can b sn in Tabl 5. Figur 7b show ha for all h various doss, h amoun of zinc (II) ions sorbd incrass rapidly wih im in h bginning and vry slowly owards h nd of h racion. Furhrmor, a larg fracion of h oal amoun of mal was rmovd wihin a shor im ha is bfor 2 minus. Th plos as sn in Figur 7a also showd ha sorpion capaciy incrasd for lowr Luffa cylindrica dosags a any spcific im. Thr wr ffcs on h conac im ruird o rach sauraion du o h variaion in Luffa cylindrica doss. I was found ha h uilibrium sorpion of mal ions sudid was a funcion of Luffa cylindrica doss. Th ra consan, k, h uilibrium sorpion, and h iniial sorpion ra, h, of sorpion a diffrn Luffa cylindrica doss wr calculad from h inrcp and slop of h sraigh lin plos of / vrsus. Th iniial sorpion ra dcrasd wih an incras in h Luffa cylindrica dos from.2-1. g.

9 Amrican Journal of Scinc and Tchnology 218; 5(1): Th corrsponding linar plos of h valus of, k and h agains m (dosag) wr rgrssd o obain xprssions wih xponns for hs valus in rms of h m paramrs for all h mal ions sudid. Figur 7b. Th sorbd capaciy agains im for h ffc of varid doss on h sorpion kinics of Zinc ion ono Luffa cylindrica a ph 5.. Th xprssion Figur 7a. Th sorbd capaciy agains im for h ffc of varid doss on h sorpion kinics of Zinc ion ono Luffa cylindrica a ph 5.. Whr x, k or h x Am b (13) Tabl 6. Empirical paramrs for prdicd, k and h. M 2+ A b r 2 A k b k r 2 A h b h r 2 Zn Tabl 6 shows h mpirical paramrs for prdicd, k and h and hir corrsponding corrlaion cofficins. Subsiuing h valus of A, B, A h and B h from Tabl 6 in E. (13), h ra law for a psudo-scond ordr racion and h rlaionship bwn, m and can b rprsnd as: Sorpion capaciy, (mg/g) m 6 Tim, (min) m 1. Figur 8. Effc of L. cylindrica dos on zinc sorpion a various ims. (14) L. cylindrica dos, m (g) This uaion can hn b usd o driv h sorpion amoun zinc (II) ions a any givn dosag and h racion im. Th hr-dimnsional plo of h Euaion (14) is shown in Figur 8. Th Euaion rprsn a gnralisd prdiciv modl for h amoun of zinc (II) ions sorbd a any conac im and involvd L. cylindrica dos. I indicas ha h zinc (II) ions sorbd a any conac im is highr as h L. cylindrica dos is dcrasd. This is du o h fac ha incrasing h L. cylindrica dos incrass h surfac ara for sorpion and hnc h ra of mal sorpion is incrasd whn h iniial mal ion concnraion is consan. Kinic modls hav bn drivd for h sorpion of zinc (II) ions ono L. cylindrica. Th paramr which has h gras influnc on h kinics of h sorpion racion was sorpion uilibrium; is a funcion of iniial mal ion concnraion, L. cylindrica dos and naur of solu and his is in agrmn wih prvious rsarch [32] Arificial Nural Nwork Modl Dvlopmn Diffrn cagoris of sofwar can b usd o do mahmaical modling [34]. Pyhia is a program for h dvlopmn and dsign of Nural Nworks. Pyhia faurs Backpropagaion Nworks and rain nural nworks on any Windows machin [35]. In his sudy, 2 modls of back-propagaion fd forward nwork wr dvlopd in Pyhia nvironmn. Th modls ar MISO Zn-1 and MISO Zn Slcion of Inpu and Oupu Variabls Th mos imporan ask in dvloping a Nural Nwork modl is o slc h mos significan variabls as simaor inpus. In his procss of biosorpion of Zinc (II) ions ono L. cylindrica, hr ar a lo of variabls ha can affc h fficincy of sysm. Thrfor, in ordr o simplify h modl srucur, inpu variabls ha gav dominan impac o h procss oupus wr slcd whil h ohrs wr nglcd. Th indpndn xprimnal variabls slcd ar Conac im, iniial mal ion concnraion and biosorbn dosag. Th

10 1 Oboh Innocn O. and Aluyor Emmanul O.: +Modlling h Sorpion of Zn 2+ Ions ono Luffa cylindrical oupu was sorpion capaciy. Th signal movs from h inpu layr owards h oupu layr as shown in Figurs 9a and b, and in his procss ach nuron uploads all h nurons of h succssiv layrs, ransfrring a porion of h signal ha has bn accumulad. Th porion of signal ransfrrd is rgulad by a ransfr funcion [36]. A fd-forward back-propagaing ANN srucur as illusrad in Figurs 9a and b was usd o dvlop yild prdicion modls. Daa mov hrough h layrs in on dircion, from h inpu hrough h hiddn o h oupu layrs, wihou loops as opposd o fdback nworks. Figur 9a. Layrs and conncions of a fd-forward back propagaing arificial nural nwork (MISO-1). Figur 9b. Layrs and conncions of a fd-forward back propagaing arificial nural nwork (MISO-2) Dvloping Yild Prdicion Modls wih BPNN In h prsn work, h inpu variabls o h fd forward back propagaion nural nwork (BPNN) wr as follows: h amoun of L. cylindrica (g) and iniial ion concnraion of Zn (II) ions (mg/l). Th sorpion capaciy was chosn as h xprimnal rspons or oupu variabl. Th sigmoidal ransfr funcion was usd as a ransfr funcion in h hiddn and oupu layrs. This is h mos widly usd ransfr funcion. Th raining funcion was Frmi (Min., Max1., Thld., Inc1.) and h larning ra was.5. Th svral daa poins gnrad wr usd o dvlop h ANN modl [37]. BPNN modlling for iniial ion concnraion and naur of solu Figur 1a. MISO Zn-1 (2,3,3,1) 7 nurons, 3 lvls, 2 inpus, 1 oupu. Transfr funcion: Frmi (Min., Max1., Thld., Inc1.) Larning ra.5.

11 Amrican Journal of Scinc and Tchnology 218; 5(1): (II) ions usd for his sudy. For h MISO Zn-2 modl h maximum numbr of nurons was 12. Figur 1b. Accuracy of prdicion of Sorpion capaciy (mg/g) of Zn (II) ions ono L. cylindrica for MISO Zn-1 nural nwork modl. Figur 11a. MISO Zn-2 (2,3,2,4,2,1) 12 nurons, 5 lvls, 2 inpus, 1 oupu. Transfr funcion: Frmi (Min., Max1., Thld., Inc1.) Larning ra.5. Figur 1c. Scar plo of h masurd sorpion capaciy and of h prdicd sorpion capaciy drivd from a 7-nuron MISO Zn-1 nural nwork modl. Figur 1a show h Arificial Nural Nwork archicur dvlopd for h iniial ion concnraion. For MISO Zn-1 modl h numbr of nurons was 7. A Fd forward back propagaion Arificial Nural Nwork (ANN) was raind using h raining daa from h xprimnal rsuls. Figur 1b show h xprimnal and ANN prdicd Sorpion capaciy for MISO Zn-1 nural nwork modl dvlopd for h ffc of Iniial ion concnraion on h biosorpion of Zn(II) ions ono Luffa cylindrica as biosorbn.. Th accuracy of h prdicion of h raind ANN was hn compard wih h acual masurd valus. I was obsrvd ha ANN gav nar accura prdicion for Sorpion capaciy valus. To hav a mor prcis invsigaion ino h various modls, a rgrssion analysis of oupus and dsird args was prformd as shown in Figur 1c. Thr was a high corrlaion bwn h prdicd valus by h ANN modl and h masurd valus rsuld from xprimnal daa. Th corrlaion cofficin was.973 for MISO Zn-1 modl, which implid ha his modl succdd in h prdicion of h sorpion capaciy BPNN Modlling for Luffa cylindrica Dos and Naur of Solu Figur 11a show h Arificial Nural Nwork archicur dvlopd for h Luffa cylindrica dos and Zn Figur 11b. Accuracy of prdicion of Sorpion capaciy (mg/g) of Zn (II) ions ono L. cylindrica for MISO Zn-2 nural nwork modl. Figur 11c. Scar plo of h masurd sorpion capaciy and of h prdicd sorpion capaciy drivd from a 12-nuron MISO Zn-2 nural nwork modl. A Fd forward back propagaion Arificial Nural Nwork (ANN) was raind using h raining daa from h xprimnal rsuls. Figur 11c shows h xprimnal and ANN prdicd Sorpion capaciy for MISO Zn-2 modl dvlopd for h ffc of Luffa cylindrica dos on h biosorpion of Zn(II) ions. Th accuracy of h prdicion of h raind ANN was hn compard wih h acual masurd valus. I was obsrvd ha ANN gav nar

12 12 Oboh Innocn O. and Aluyor Emmanul O.: +Modlling h Sorpion of Zn 2+ Ions ono Luffa cylindrical accura prdicion for Sorpion capaciy valus. To hav a mor prcis invsigaion ino h various modls, a rgrssion analysis of oupus and dsird args was prformd as shown in Figur 11c. Thr was a high corrlaion bwn h prdicd valus by h ANN modl and h masurd valus rsuld from xprimnal daa. Th corrlaion cofficin was.95 for MISO Zn-2, which implis ha h modls succdd in prdicion of h sorpion capaciy. Tabl 7. Th RMSE valus for MISO nural nwork modls. Nural Nwork modl RMSE MISO Zn MISO Zn Th roo man suar rror (RMSE) is chosn as indicaor of prformanc of h nworks. Th Roo Man Suard rror (RMSE) is calculad using h following formula [38-39]: RMSE (15) Gnrally, h arificial nural nwork offrs h advanag of bing fas, accura and rliabl in h prdicion or approximaion affairs, spcially whn numrical and mahmaical mhods fail. Thr is also a significan simpliciy in using ANN du o is powr o dal wih mulivaria and complicad problms [4]. Th roo man suar rror (RMSE) of h prformanc of ANN MISO modl on h xprimnal daa for prdicing Sorpion capaciy is.5912 and for MISO Zn-1 and MISO Zn-2 modls rspcivly as can b sn in Tabl 7. ANN was abl o prdic h sorpion capaciy ui rasonably for all modls. 4. Conclusion Obsrvdnumbr ofdaa ( Prdicd) A kinic sudy was carrid ou and h xprimnal daa fid ino Psudo-firs ordr, Psudo-scond ordr, Inraparicl diffusion and Avrami modls. This was don using h nonlinar rgrssion mhod o obain h kinic paramrs. Kinic modls hav bn dvlopd and fid for h sorpion of h divaln mal ions ono L. cylindrica on h ffc of Luffa cylindrica dos and h iniial ion concnraion. Th rsuls showd sorpion for Zn (II) ions ono L. cylindrica during agiaion by suspndd shaking; h procss can b dscribd by all kinic modls bu psudoscond ordr modl basd on h assumpion ha h ra limiing sp may b chmical sorpion involving ion xchang bwn sorbn and sorba. Th paramr which has h influnc on h kinics of h sorpion racion was h sorpion uilibrium capaciy,, a funcion of iniial mal ion concnraion, Luffa cylindrica dos and h naur of solu ion. In his sudy wo ANN modls wr dvlopd, which wr all MISO nworks. BPNN modls wr abl o prdic 2 h sorpion capaciy ui rasonably for h ffc of iniial ion concnraion and Luffa cylindrica dos for h biosorpion procss. Rfrncs [1] Gupa, N., Prasad, M., Singhal, N. and Kumar, V. (29). Modling h Adsorpion Kinics of Divaln Mal Ions ono Pyrophylli Using h Ingral Mhod. Ind. Eng. Chm. Rs., 48 (4), [2] Abdlnaim, M. Y., El Shrif, I. Y., Aia, A. A., Fahy, N. A., El-Shaha. (216). Impac of chmical acivaion on h adsorpion prformanc of common rd owards Cu(II) and Cd(II). Inrnaional Journal of Minral Procssing. 157: [3] Raksh N., Kalpana P., Naidu T. V. R and Vnkaswara Rao M. (21). Rmoval of Zinc Ions from Auous Soluion by Ficus Bnghalnsis L.: Euilibrium and Kinic Sudis. Inrnaional Journal of Enginring Sudis. Volum 2, Numbr 1, pp [4] Luman, C. A., Muhammad, Saidaul S. J. and Thomas S. Y. C. (21). Modlling of Singl and Binary Adsorpions of Havy mals ono Acivad carbon- Euilibrium sudis. Pranika Journal of Scinc and Tchnology 18 (1): [5] Mohan, D., Singh, K. P. and Singh, V. K. (25). Rmoval of hxavaln chromium from auous soluion using low-cos acivad carbons drivd from agriculural was marials and acivad carbon fabric cloh, Ind. Eng. Chm. Rs. 44, [6] Babl, S. and Kurniawan, T. A. (23). Low-cos adsorbns for havy mals upak from conaminad war: a rviw, J. Hazard. Mar. 97, [7] Basil J. L., Ev R. R., Milchark C. D., Marins L. C., Pavan F. A., dos Sanos, Jr. A. A., Dias S. L. P., Dupon J., Norña C. P. Z., and Lima E. C. (26). Saisical Dsign of Exprimns as a ool for opimizing h bach condiions o Cr(VI) biosorpion on Araucaria angusifolia wass. J Hazard Mar; 133: [8] Lima, E. C., Royr, B., Vaghi, J. C. P., Brasil, J. L., Simon, N. M., dos Sanos Jr., A. A., Pavan, F. A., Dias, S. L. P., Bnvnui, E. V. and da Silva, E. A. (27). Adsorpion of Cu(II) on Araucaria angusifoliawass: drminaion of h opimal condiions by saisic dsignof xprimns, J. Hazard. Mar. 14, [9] Vglio, F. and Bolchini, F. (1997). Rmoval of mals by biosorpion: a rviw. Hydromallurgy, 44, [1] Volsky, B. (23) Sorpion and Biosorpion. Monral-S. Lambr, Qubc, Canada, BV Sorbx Inc., 316 p. ISBN [11] Rowll R. M., Jams S. H. and Jffry S. R. (22). Characrizaion and facors ffcing fibr propris, In Frollini E, Lao, AL, Maoso LHC, (d.), Naural polymrs and agrofibrs basd composis. Embrapa Insrumnacao Agropcuaria, san Carlos, Brazil pp [12] Mazali I. O. and Alvs O. L. (25). Morphosynhsis: high fidliy inorganic rplica of h fibrous nwork of loofa spong (Luffa cylindrica). Anais da Acadmia Brasilira d Ciências, Vol. 77, No. 1, p

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