A Simplified Perturbation Model for Prediction of Mean Ionic Activity Coefficient in Aqueous Electrolyte Solution

Transcription

1 Ianan Jounal of Chemcal Engneeng Vol. 10, No. 3 (Summe), 013, IAChE A Smplfed Petubaton Model fo Pedcton of Mean Ionc Actvty Coeffcent n Aqueous Electolyte Soluton E. Saleh 1,, M.R. Dehghan 1, A.R. Fazlal 1- School of Chemcal Engneeng, Ian Unvesty of Scence and Technology Tehan, Ian - Faculty of Chemcal Engneeng, Aak Unvesty, Aak, Ian Abstact In ths wok a smplfed model based on petubaton theoy s pesented fo pedcton of actvty coeffcent of amno acds and electolytes n aqueous electolyte soluton. In compason wth pevous woks, n ths model a new had sphee equaton of state has been utlzed as a efeence tem whle othe nteactons such as chage-chage, chage-dpole, dpole-dpole and dpole-nduced dpole have been consdeed as petubaton tems. Fo smplfcaton, solvent has been consdeed as delectc contnuum. Fnally, aqueous electolyte solutons contanng amno acds have been modeled just usng two adjustable paametes. The esults have been compaed wth smla models and t s shown that new had sphees equaton of state shows an mpovement n accuacy of the model. Keywods: Actvty Coeffcent, Petubaton Model, Amno acd, Peptde, Had Sphee 1. Intoducton Poducton of synthetc potens have eceved moe attenton n ecent yeas due to global food defcency. In ths egad sepaaton of amno acds s helpful because of the applcaton n poducton of synthetc potens. A consdeable numbe of expemental as well as theoetcal eseaches have been focused on studyng amno acds behavo [1-13]. Usually sepaaton and pufcaton of bo-molecules fom dlute aqueous solutons can be as hgh as 90% of the total manufactung cost. Pufcaton costs as well as hgh demands fo bomolecules, especally amno acds have encouaged eseaches to fnd new methods fo pufcaton. Factonal pecptaton and cystallzaton methods ae appled extensvely [13]. The physcal popetes of amno acds such as the actvty coeffcents ae necessay n desgn and scale-up steps. Unfotunately complex stuctue of bomolecules has caused the conventonal themodynamcs models to fal n detemnaton of amno acd physcal popetes. A numbe of attempts have been Coespondng autho: m_dehghan@ust.ac. 14

2 Saleh, Dehghan, Fazlal pesented n the lteatue to calculate the actvty coeffcents of amno acd and potens. Excess Gbbs enegy models ncludng empcal local composton and goup contbuton methods, such as Wlson [6], electolyte NRTL [5], UNIQUAC [7], and UNIFAC [9-11] equatons have seldom been successful n applcaton due to the lage numbe of adjustable paametes whch wee dependent on expemental data. Khoshkbach and Vea [1] poposed a new model based on the petubaton theoy, the wok has been extended and modfed to coelate and pedct actvty coeffcents of amno acds n aqueous bnay and tenay systems [14-16]. Although t has been clamed that the pesented models can satsfactoly coelate the expemental data, most of them ae complcated and some unnecessay complexty has been ntoduced n the models, makng them napplcable. In ths wok, n contnuaton of ou pevous woks [,3,17], we pesent a pmtve and smplfed model based on petubaton theoy fo pedcton of mean onc actvty coeffcents of electolytes n aqueous soluton contanng amno acds. In ou model, a new had sphee equaton of state s used as efeence state. Ths had sphee equaton of state was poposed by Dehghan and Modaess [17] and has shown sgnfcant ablty compaed to othe had sphee equaton of states. In compason wth pevous models, n ths wok the vaaton of delectc constant as well as solvent effects has been consdeed. Howeve, some modfcatons have been mplemented to ncease the abltes and smplcty of the petubaton model.. Theoy of model Dffeent theoes have been utlzed fo coelaton and pedcton of themo-physcal popetes n aqueous electolyte soluton contanng amno acds. In ecent yeas petubaton theoy has attacted moe attenton among dffeent theoes. Petubaton theoy was ntally developed by Zwanzg [18] fo gases and was extended to lquds by Bake and Hendeson [19]. The petubaton theoy has the advantage of ncopoatng vaous types of nteactons easly. Howeve, consdeng all types of nteactons can make them qute complex and unsutable n engneeng applcatons. In ths wok, a smplfed model s pesented based on petubaton theoy fo pedcton of mean onc actvty coeffcent n amno acd and peptde aqueous soluton. In ths theoy, esdual chemcal potental, μ, s defned as a summay of efeence, petubaton, long ange and bon contbutons as shown below: HS L J D D μ μ μ μ = + + kt kt kt kt μ μ μ kt kt kt BORN μ + kt D ID C D ELEC (1) Whee supescpt HS, L-J, D-D, D-ID, C-D, ELEC and BORN efes to had sphee, Lenad-Jones as dspeson tem, dpoledpole, dpole-nduced dpole, chage-dpole, electostatc and Bon contbutons on esdual chemcal potental espectvely. k efes to Boltzmann constant ( J.K -1 ) and T s absolute tempeatue. The Ianan Jounal of Chemcal Engneeng, Vol.10, No. 3 15

3 A Smplfed Petubaton Model fo Pedcton of Mean Ionc Actvty Coeffcent n Aqueous Electolyte Soluton electostatc nteactons ae consdeed usng Ptze-Debye-Huckle model. In petubaton based models, usually had sphee equatons ae used as efeence tem. The accuacy of the had sphee tem s hghly effectve n accuacy of model. In ths wok we have utlzed a new had sphee equaton of state whch has ecently been developed and has shown good pefomance n mean sphecal appoxmaton theoy as efeence tem. Ths had sphee equaton of state was bult based on new hghly optmzed molecula dynamcs smulaton data and s able to meet low densty and closed packed lmts of compessblty facto [17]. We efe the nteested eade to the mentoned efeence fo moe detals. In ths pat and n the appendx just the equed themodynamc popetes have been pesented. Accodng to new had sphee EOS, the esdual Helmholtz fee enegy A, and chemcal potental μ ae defned as Eq. (): μ kt A ( A NkT = + ρ( ) TV,, ρ j NkT ρ Y + Y C ( 1 Y Y ) ln(1 η ) C4+ C3 Y1+ Y + C1+ R3, ( Z p 1) ( 1+ Y -Y ) η R ( C3 C4) ln( 1 η3) + 1 η HS, HS, HS, 1 = , 3 () The paametes have been defned n the appendx secton. The Lenad-Jones, dpole-dpole, dpolenduced dpole, chage-dpole have been calculated based on Bake-Hendeson theoy [19]. Accodng to Tepel-Gubbns [0] the chemcal potental fo these tems can be calculated though substtuton of elevant ntemolecula potental n equaton (3): n n HS μ = π ρjρ u jl( ) g jl ( ) d ρ j= 1 l= 1 σ jl (3) In whch, u(), and g HS () ae ntemolecula dstance, ntemolecula potental and adal dstbuton functon, espectvely. Lenad-Jones (L-J), dpole-dpole (D-D), dpole-nduced dpole (D-ID) and dpolechaged dpole (D-CD) potentals ae defned as shown below []: 1 6 σ j σ L J j uj () = 4ε 1 6 u u u D D j j 6 0 kt (4) DD () = (5) 3(4 πε ε ) α D j 6 0 kt α jd ( ) = (6) (4 πε ε ) D ID j D CD j zed () = (7) 6(4 πε ε ) j 4 0 kt Whee ε, D, ε 0, ε, α, Z and e ae depth of potental well, dpole moment, pemttvty of vacuum, elatve delectc constant, polazablty, chage of on and unt of chage, espectvely. The step functon poposed by Reed and Gubbns [1] has been consdeed as adal 16 Ianan Jounal of Chemcal Engneeng, Vol. 10, No. 3

4 Saleh, Dehghan, Fazlal dstbuton functon as follows: g HS jl 0 ( ) = 1 < σ > σ j j (8) 1 σ j = ( σ + σ j ) (9) Afte substtuton of equatons (4) to (8) n equaton (3), the followng equaton wll be deved as contbuton of Lenad-Jones (L- J), dpole-dpole (D-D), dpole-nduced dpole (D-ID) and chaged- dpole (C-D) nteactons n esdual chemcal potental: L J D D D ID C D μ μ μ μ = kt kt kt kt 4π ρσε S S S + ρσ A S. A εε A S kt 9 9 ρaαs D A kt ρaz Se D A (4 πε 0 ε ) σ S. A 6(4 πε 0 ε ) kt σ S. A (10) Whee subscpt A and S denote Amno acd and ons espectvely. Ths equaton must be expanded fo ons and amno acd sepaately. The Bon tem s also used fo calculatng the effects of ons on solvent as contnuum meda. The esdual chemcal potental fo BORN tem s defned as [3]: coeffcent of salt, γ ±, s defned based on Eq. (1): ν ν ( ν + ν ) = ( + ) + ± + γ γ γ 1 (1) Whee ν s stochometc numbe of ons. In all pevous models, delectc constant has been consdeed as a constant value, but t s clea that wth changng the electolyte and amno acd concentatons, delectc constant wll change. The concentatons of ons as well as amno acds have sgnfcant effect on delectc constant. In ths model Eq. (13) s appled fo consdeng the vaaton of delectc constant vesus electolyte molalty. ε = ε + AI + 0 I 1+ I 1/ 1/ 1 A 1/ (13) In the above equaton ε 0 s delectc constant fo pue wate and I s the onc stength of soluton (Eq (14)). A 1 and A ae the only adjustable paametes n tenay systems. n 1 I = mz (14) = 1 Whee m s the molalty. μ 1 Z e N Z e N = kt kt 8πε ε 8πε BORN, A A Z e N A 1 = 1 kt 8πε 0 ε (11) Whee R s bon adus. Meanwhle the mean onc actvty 3. Model paametes The equed paametes fo calculaton of mean onc actvty coeffcents ae sze paamete, amno acd s dpole moment, caton and anon s polazablty, and depth of potental well fo all components such as amno acd, peptde, catons and anons. Dpole moment of amno acd and peptdes Ianan Jounal of Chemcal Engneeng, Vol.10, No. 3 17

5 A Smplfed Petubaton Model fo Pedcton of Mean Ionc Actvty Coeffcent n Aqueous Electolyte Soluton has been calculated though quantum mechancal appoach usng the Hypechem molecula modelng softwae. Bnay expemental data [6] fo aqueous amno acd soluton n the absence of electolyte has been utlzed fo detemnaton of amno acd sze paametes and depth of potental well. In Table 1, the obtaned paametes have been pesented. Ion paametes such as polazablty, cystallne sze and depth of Potental well have been extacted fom publshed papes [17,7-8]. Table 1. Calculated σ, ε/k fom Coelaton of Amno Acds and Peptde Expemental Actvty Coeffcents [6]. Amno Acd ε/k(k) σ (m) 0(1) 0() 0(3) 0(4) 0(5) Alanne α-amno n-butyc acd Glycne Hydoxypolne Polne Sene Theonne Aveaged RMSD Peptd ε/k(k) σ (m) 0(1) 0() 0(3) 0(4) 0(5) Alanylalanne Alanylglycne Glycylalanne Glycylglycne T-glycne Aveaged RMSD (1) Ths Model; () [15]; (3) [40]; (4) [39]; (5) [10] 18 Ianan Jounal of Chemcal Engneeng, Vol. 10, No. 3

6 Saleh, Dehghan, Fazlal 4. Coelaton The pesented model fo calculaton of mean onc actvty coeffcents n tenay solutons needs two adjustable paametes. In ou model, delectc constant wth two adjustable paametes must be detemned though coelaton of electolyte actvty coeffcents. The paamete estmaton method s effectve n evaluaton of the esults. In ode to avod the local optmzaton nstead of global optmzaton, Davdon-Fletche-Powell (DFP) [9-31] algothm was used. DFP s a well known pocedue, whch appoxmates the nvese Hessan matx, to detemne the global mnmum. Objectve functon (OF) s defned as follows: n = 1 exp cal ( ln ln ) OF = γ γ (15) Whee supescpt exp and cal ae expemental values and calculated values, espectvely. Snce calculated actvty coeffcents ae based on mole facton and expemental data ae based on molalty, Eq. (16) s used to change expemental actvty coeffcent fom molalty base to mole facton base. ( x ) ( m) ln γ lnγ ln( M s m ) = + + (16) In whch M s s molecula weght of solvent. The supescpts x and m show molalty and mole facton base actvty coeffcents, espectvely. The devaton of ou model fom expemental data was calculated based on oot mean squae devaton (RMSD): RMSD = n = 1 ( γ γ ) exp cal Whee n s numbe of data. n (17) 5. Results and dscusson In Table, calculated values fo adjustable paametes (A 1 and A ) have been pesented. The expemental data at K and at atmosphee pessue have been compaed wth coelated data. In Fg. 1 coelaton of mean onc actvty coeffcent of NaNO 3 n DL-Alalne aqueous soluton at dffeent molaltes of electolyte s pesented vesus molalty of amno acd. In the same way, Fg. shows the esults of modelng of mean onc actvty coeffcent of NaCl n wate- NaCl-Glycne system. Also, esults of calculated mean onc actvty coeffcent of KCl n DL-Valne aqueous soluton have been depcted n Fg. 3. The most mpotant advantage of ths model s ts ablty to model the actvty coeffcents n moe complcated systems such as those contanng peptde and electolytes. In Fg. 4 the esults of modelng of mean onc actvty coeffcent of KCl n wate-kcl-glycylglycne as a peptd aqueous soluton has been shown. As t s pesented n Table, the adjustable paametes and RMSD follow a good tend n a elable ange. We checked the model fo othe peptdes and the calculatons showed that ths model wth 1-4% eo can coelate and pedct the mean onc actvty coeffcents of electolyte n the system contanng peptdes. Ianan Jounal of Chemcal Engneeng, Vol.10, No. 3 19

7 A Smplfed Petubaton Model fo Pedcton of Mean Ionc Actvty Coeffcent n Aqueous Electolyte Soluton Table. Adjustable paametes and RMSD of Actvty Coeffcents of Amno Acds and peptde n wate- Electolyte-amno acd and peptde system. A 1 A RMSD Ref. DL-Alanne+NaN [3] Glycne+NaCl [33] Alanne+NaCl [33] Glycne+KCl [34] Glycylglycne+NaCl [35] Glycylglycne+KCl [35] DL-Valne+KCl [36] Alanne+NaCl [36] Glycne+NaCl [] Glycne+NaB [37] L-Valne+NaB [37] Glycne+NaCl [38] Expemental Fgue 1. Mean onc actvty coeffcent of NaNO 3 n wate- NaNO3-DL-Alanne system n dffeent molaltes of electolyte vesus amno acd molaltes. 0 Ianan Jounal of Chemcal Engneeng, Vol. 10, No. 3

8 Saleh, Dehghan, Fazlal Expemental Fgue. Mean onc actvty coeffcent of NaCl n wate- NaCl-Glycne system n dffeent molaltes of electolyte vesus amno acd molaltes. Expemental Fgue 3. Mean onc actvty coeffcent of KCl n wate- KCl-DL-Valne system n dffeent molaltes of electolyte vesus amno acd molaltes. Ianan Jounal of Chemcal Engneeng, Vol.10, No. 3 1

9 A Smplfed Petubaton Model fo Pedcton of Mean Ionc Actvty Coeffcent n Aqueous Electolyte Soluton Fgue 4. Mean onc actvty coeffcent of KCl n wate- KCl-DL-Valne system n dffeent molaltes of electolyte vesus amno acd molaltes. :m NaCl =0.3, :m NaCl =0.5, :m NaCl =0.7, :m NaCl =1.0, : coelated esult. The esults show that adjusted values of delectc constant ae easonable. To the best of ou knowledge, thee ae not any expemental data on delectc constant of electolyte soluton contanng amno acd and peptdes, so we cannot judge the physcal meanng of the obtaned delectc constants. If we could substtute the expemental data of delectc constants n the model, t would be possble to make a pedctve model, othewse the calculated data fo delectc constant must be consdeed just as an adjustable paamete. It s ou opnon that the avalable expemental data on these systems could lead us to geat achevement n modelng of amno acd-electolyte and moe complcated systems. It s shown that the oveall fttng s qute good. Obtaned RMSD usng pesented model ndcates that ths model has vey good accuacy fo coelaton of expemental data. The ablty of the pesented model ponts to the applcaton of the followng tems. Fstly, utlzng new had sphee equaton of state wth hgh accuacy. Secondly, consdeaton of delectc constant changes vesus molalty of electolyte. In the pevous woks delectc constants have been kept constant and equal to delectc constant of pue wate whle t s well known that n the pesence of electolyte and amno acds ths assumpton s not tue. 6. Conclusons In ths wok a smplfed model based on petubaton theoy wth two adjustable paametes was developed fo coelaton of actvty coeffcents n aqueous systems contanng amno acd, peptde and electolytes. A new had sphee equaton of Ianan Jounal of Chemcal Engneeng, Vol. 10, No. 3

10 Saleh, Dehghan, Fazlal state has been utlzed as a efeence system. Dpole-dpole and Lennad-Jones nteactons have been consdeed n petubaton tem. The actvty coeffcents of moe than 40 data ponts fo aqueous amno acd- electolyte soluton have been modeled by the mnmum numbe of adjustable paametes whch had been set on delectc constants. Results of the model denote that the effect of efeence tem n chemcal potental of amno acds s sgnfcant. Compaed to smla models, the modfcatons caused an mpovement n the esults of the petubaton model. The esults of ths wok show that wth the smplfed petubaton model, the mean onc actvty coeffcent of electolyte n aqueous soluton of amno acds can be calculated n a vey smple way, especally fo tenay systems C = 0.186ξ 0.866ξ.16ξ ξ 9.45ξ ξ 53.93ξ ( 1 ξ3 ) ( 1 ξ3 ) ( 1 ξ3 ) ln ( 1 ξ3 ) C = 0.16ξ 0.74ξ 1.846ξ 3.667ξ ξ 13.3ξ 6.963ξ ξ 3 ( 1 ξ3 ) ( 1 ξ3 ) ( 1 ξ3 ) ln ( 1 ξ3 ) (5) ( ) (6) C = Y R + R R R (7) ( ) C4 = Y 3R R0 R3 (8) Appendx Defned paametes n the model: R, k σ = (9) k x jσ j π η = ρjσ j = 0,1,,3 (1) 6 j Whee ρ and σ ae numbe denstes and sze paamete. Y Y ξξ 1 1 = () ξξ 0 3 ξ = (3) 3 ξ0ξ3 ξ s defned as follows: 1 ξ = ρjσ j = 0,1,,3 (4) j s defned as follows: Nomenclatue Boltzmann constant ( k 3 J.K-1) T Absolute tempeatue N Avogado numbe Intemolecula dstance u() Intemolecula potental g HS () Radal dstbuton functon D Dpole moment Z chage of on e unt of chage R Bon adus I onc stength of soluton A 1 and A adjustable paametes m molalty of amno acd d densty of solute densty of pue wate d 0 Ianan Jounal of Chemcal Engneeng, Vol.10, No. 3 3

11 A Smplfed Petubaton Model fo Pedcton of Mean Ionc Actvty Coeffcent n Aqueous Electolyte Soluton M M S OF RMSD μ ρ γ ν σ ε ε 0 ε Molecula weght of amno acd molecula weght of solvent Objectve functon oot mean squae devaton Resdual chemcal potental Numbe densty Actvty coeffcent stochometc numbe of ons Sze paamete Depth of potental well Pemttvty of vacuum Relatve delectc constant α polazablty ε 0 delectc constant fo pue wate LR Long Range (contbuton) SR shot Range (contbuton) BORN Bon tem HS had sphee tem PER Petubaton tem d deal soluton PDH PDH tem L-J Lenad-Jones (nteacton) D-D dpole-dpole D-ID dpole-nduced dpole D-CD dpole-chaged dpole exp expemental value cal calculated value x molalty base actvty coeffcents m mole facton base actvty coeffcents ± mean onc A Amno acd S electolyte + Caton anon Refeences [1] Khavannzadeh, A., Modaess, H., Taghkhan, V. and Khoshkbach, M.K., "Measuement of actvty coeffcents of amno acds n aqueous electolyte solutons: Expemental data fo the systems (H O+ NaB + glycne) and H O+NaB+L-valne at T=98.15 K", J. Chem. Themodynamcs, 35, 1553, (003). [] Dehghan, M.R., Modaess, H. and Bakhsh, A., "Modelng and pedcton of actvty coeffcent ato of electolytes n aqueous electolyte soluton contanng amno acds usng atfcal neual netwok", Flud Phase Equlb., 44, 153, (006). [3] Dehghan, M.R., Modaess, H. and Monfa, M., "Measuement and modelng of mean actvty coeffcents of NaB and amno acd n sodum bomde+potassum phosphate +glycne+wate at and K", J. Chem. Themodynamcs, 37, 1305, (005). [4] Dehghan, M.R., Modaess, H. and Monfa, M., "Measuement and modellng of mean actvty coeffcents of aqueous mxed electolyte soluton contanng glycne", J. Chem. Themodynamcs, 38, 1049, (006). [5] Chen., C.C., Zhu., Y. and Evans., L.B., "Phase pattonng of bomolecules, Solubltes of amno acds", Botechnol. Pog., 5, 111, (1989). [6] Nass, K.K., "Repesentaton of the solublty behavo of amno acds n wate", AIChE J., 34, 157, (1988). [7] Pees, A.M. and Macedo, E., "Repesentaton of solubltes of amno acds usng the unquac model fo electolytes", Chem. Eng. Sc., 49, 3803, (1994). [8] Lu, J.C., Lu, J.F. and L, Y.G., "Study on the actvty coeffcents and the solubltes of amno acds n wate by 4 Ianan Jounal of Chemcal Engneeng, Vol. 10, No. 3

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