Retention modeling and resolution optimization for a group of N-phenylpyrazole derivatives in micellar electrokinetic chromatography using empirical and physicochemical models

Ca men Ga cía-Ruiz Olga Jiménez Ma ia L. Ma ina Depa amen o de Química Analí ica, Facul ad de Química, Uni e sidad de Alcalá, Alcalá de Hena es (Mad id), Spain Re en ion modeling and esolu ion op imiza ion o a g oup o N-phenylpy azole de i a i es in micella elec okine ic ch oma og aphy using empi ical and physicochemical models The op imiza ion o he sepa a ion esolu ion o a g oup o N-phenylpy azole de i a- i es in micella elec okine ic ch oma og aphy (MEKC) as a unc ion o he sepa a ion bu e composi ion (su ac an and o ganic modi ie concen a ion) has been pe - o med. In o de o achie e ou pu pose, he i s s ep has been he p edic ion o he mig a ion imes o he elec oosmo ic low ( 0) and micelles ( m), and he e en ion ac o s o solu es (k), as a unc ion o su ac an (sodium dodecyl sul a e) and alcohol (n-p opanol o n-bu anol) concen a ions, by means o empi ical equa ions. Also, some physicochemical models ha e been applied o ela e he e en ion ac o s o he su - ac an and he o ganic modi ie concen a ions in o de o op imize he sepa a ion esolu ion and o inc ease ou knowledge o he sepa a ion p ocess. Finally, a com- pa ison o he esolu ion op imiza ion h ough he use o he physicochemical and empi ical models selec ed has been made in o de o ob ain he op imum sepa a ion bu e composi ion o he sepa a ion o a g oup o 17 N-phenylpy azole de i a i es as es solu es. Keywo ds: Empi ical equa ions / Micella elec okine ic ch oma og aphy / Physicochemical model / Py azole de i a i es / Resolu ion op imiza ion / Re en ion p edic ion EL 5262 1 In oduc ion The op imiza ion o he sepa a ions pe o med by micella elec okine ic ch oma og aphy (MEKC) is a complex ask due o he g ea numbe o a iables a ec ing he p o- cess: pH, ype and concen a ion o bu e , su ac an , and o ganic modi ie s. In ecen yea s, in o de o p edic he op imal sepa a ion condi ions wi h he minimum num- be o expe imen s, se e al s a egies in MEKC ha e been epo ed [1, 2]. As an example, i can be ci ed he o e - lapping esolu ion mapping (ORM) [3–9], i e a i e eg es- sion s a egies [10], physicochemical app oaches [11– 14], empi ical equa ions [15–18], and a i icial neu al ne - wo ks (ANNs) [19]. In o de o ca y ou hese s udies, se e al designs can be used, e.g., he Placke -Bu man design [20, 21] and he o hogonal a ay design (OAD) [22] which a e ac o ial designs sui able o sc eening he in luence o many pa ame e s and o moni o possible in e ac ions among a la ge numbe o ac o s, o he cen- al composi e design [23, 24] ha can p o ide a esponse su ace o he p edic ion o a eas o op imum pe o - mance. F om he di e en s a egies ci ed, he ORM has been one o he mos used [3–9] because i allows he deduc ion o he op imal sepa a ion condi ions om an o e lay o all he g aphs ob ained plo ing he esolu ion e sus di e en sepa a ion condi ions. Howe e , mig a- ion o solu es is no ollowed. Also, a g ea numbe o expe imen s is equi ed o ca y ou he op imiza ion p ocess. Physicochemical models desc ibing he mig a ion be- ha io o indi idual solu es ha e been epo ed. Thus, Khaledi e al. [11–14] in oduced physicochemical models desc ibing he mig a ion beha io o bo h acidic and basic solu es as a unc ion o he sepa a ion bu e com- posi ion and physicochemical cons an s. Fi s , a desc ip- ion o mig a ion in e ms o pKa, micelle-wa e binding cons an , and mobili y o he anionic solu es in he ab- sence o micelles has been pe o med [11]. A desc ip ion o he solu e mobili y in e ms o physical and chemical cons an s o each solu e, he pH o he bu e , and he micelle concen a ion in he bu e has also been epo ed [12]. Finally, a model desc ibing he mig a ion o ionizable (acidic and basic) solu es as a unc ion o he simul a- neous a ia ion o he pH and micelles concen a ion has Co espondence: D . Ma ia Luisa Ma ina, Depa amen o de Química Analí ica, Facul ad de Química, Uni e sidad de Alcalá, E-28871 Alcalá de Hena es (Mad id), Spain E-mail: [email p o ec ed] Fax: 34-91-8854971 Abb e ia ions: MPRE, mean p edic ion ela i e e o s; PC, p in- cipal componen Elec opho esis 2003, 24, 325–335 325 2003 WILEY-VCH Ve lag GmbH & Co. KGaA, Weinheim 0173-0835/03/0302–325 $17.501.50/0 CE and CEC 326 C. Ga cía-Ruiz e al. Elec opho esis 2003, 24, 325–335 been p oposed [13]. Recen ly, ou esea ch eam has de eloped a physicochemical model o p edic he e en- ion o neu al compounds as a unc ion o micellized su ac an and he o ganic modi ie concen a ion [14]. Al hough hese models usually equi e he use o non- linea i ing so wa e du ing he p ocess o op imiza ion, physicochemical mig a ion cha ac e is ics o compounds a e ob ained. Insigh is gained in he mechanism o mig a- ion in MEKC. On he o he hand, empi ical equa ions ha e been con- side ed e y aluable ools o p edic he e en ion be- ha io o solu es as a unc ion o di e en a iables in MEKC. Pyell and Bü eho n [15] ha e p oposed linea i s -deg ee models o he mig a ion ime o he elec o- osmo ic low ma ke , he loga i hm o he mig a ion imes o he micelles and he loga i hm o he e en ion ac o s o he solu es. They used hese models o p edic he esolu ion be ween peaks, which we e calcula ed assum- ing a cons an pla e numbe . In p ac ice, he p edic ed op imum di e ges om he eal op imum, indica ing ha he unde lying linea unc ion is no able o desc ibe he e en ion beha io accu a ely. La e , Bü eho n and Pyell [16] in oduced he in e ac ion be ween he a iables con- side ed (su ac an and modi ie concen a ions) o model he mig a ion ime o he elec oosmo ic low ma ke , he loga i hm o he mig a ion imes o he micelles and he e en ion ac o s o he solu es, howe e , he numbe o pa ame e s in hei empi ical equa ions was equal o he numbe o expe imen s achie ed, so hei models appea ed o ha e be e desc ip i e han p edic i e qual- i y. Recen ly, Zome en e al. [18] s udied which esponse should be modeled p e e en ly o enable esolu ion op i- miza ion in MEKC ( esolu ion, sepa a ion ac o , appa en and e ec i e mobili y). Al hough hei esul s a e e y p omising oo much da a we e equi ed (14 da a o ob- ain he model pa ame e s). ANNs can be conside ed as so models because hey do no need ma hema ical equa ions [19, 25] and ha e been usually applied o classi ica ion, modeling, associa ion, and mapping [19, 26]. Ha el e al. [19] ha e examined he modeling capabili ies o he ANN app oach in MEKC, wi h compa ison o ha d models and he use o ANNs in combina ion wi h sui able designs o acili a e he op i- miza ion and/o p edic ion o elec opho e ic mobili ies in MEKC. Jalali-He a i and Ga kani-Nejad [27] ha e com- pa ed he p edic ion powe o ANNs and mul iple linea eg ession in capilla y elec opho esis, poin ing ou ha hei esul s we e supe io wi h he ANN. Fa ko á e al. [28] ha e shown ha ANNs can be used o es ima e peak pa ame e s and which expe imen al design can be applied o e icien p edic ion o op imal sepa a ion con- di ions. S ecnik e al. [29] ha e de eloped an ANN model, which can be gene alized and used in a a ie y o applica- ions o e en ion modeling in ion ch oma og aphy. Aga- ono ic-K us in e al. [30] ha e compa ed he use ulness o ANNs o esponse su ace modeling in HPLC op imi- za ion wi h mul iple eg ession me hods. Gao e al. [25] ha e ca ied ou he op imiza ion o gas ch oma og aph- ic expe imen al pa ame e s and compa ed hei esul s wi h ha ob ained by he o hogonal me hod. Loukas [31] has examined he beha io o a se ies o aining algo i hms in he beha io o ANNs and he esul s we e compa ed om he pa ial leas squa e (PLS) me hod. Zhao e al. [32] ha e applied an ANN o model he e en- ion beha io o se e al solu es in e na y sys ems in HPLC and o p edic wo g oups o di e en li e and bile diseases. Madden e al. [33] ha e used ANNs o p e- dic he e en ion imes o anions when elu ed wi h linea hyd oxide g adien s o a ying slope. Jiménez e al. [34] ha e examined he use ulness o ANNs o model he e en ion beha io o o ganic solu es in micella liquid ch oma og aphy. F om he esul s compa ison wi h o he empi ical and heo e ical models i seems ha ANNs a e he bes choice bu some d awbacks mus be clea . The use o ANNs is no a simple ask. P e iously, he ANN a chi ec u e mus be op imized and i means o op imize he numbe o hidden laye s, he numbe o neu ons in he hidden laye (s), he no maliza ion o ans o ma ion o he expe i- men al da a, he da a used o ain he ne wo k (no only he ep esen a i i y bu also he numbe o hem), he momen um and he lea ning a e, he aining algo i hm, he ans e unc ions o he hidden laye (s) and he ou - pu laye , e c. The e a e no ules o humb and “ ial and e o ” mus be adop ed. Mo eo e , al hough he ne wo k s uc u e could be ca e ully op imized some o he p ob- lems mus be aken in mind, ha is, he e ec o o e i - ing and, wha i is mo e impo an , he e is no gua an ee o ind he global minimum. So, ecen ly, Siou i and Phan- Tan-Lun [2] in a e y in e es ing e iew abou op imiza ion me hods in ch oma og aphy and capilla y elec opho esis ha e poin ed ou ha he end is owa ds he use o ANNs bu hey a e s ill in in ancy when applied in sepa- a ions. Mo eo e , i a ha d model (empi ical o heo e - ical model) is a ailable and i can p edic accu a ely he magni ude we a e in e es ed in, he use o ANNs is no jus i ied. So, ou aim in his wo k has been o pe o m a global esolu ion op imiza ion by using empi ical and physicochemical models o p edic he e en ion ac o s o 17 N-phenylpy azole de i a i es as a unc ion o he su ac an and modi ie concen a ions in he bu e com- posi ion. Also, i has been conside ed o g ea impo - ance o p edic he mig a ion ime o he elec oosmo ic low and micelles due o he sca ce da a ound in he li e a u e. Elec opho esis 2003, 24, 325–335 Resolu ion op imiza ion in MEKC 327 2 Ma e ials and me hods 2.1 Ch oma og aphic da a Re en ion da a o he g oup o 17 N-phenylpy azole de i a i es conside ed as model solu es (Table 1 shows hei s uc u es and names) when sepa a ion bu e con ains 0.08 Mo 2-(N-cyclohexylamino)e hanesul onic acid (CHES) in alkaline medium (pH 10) wi h SDS as su ac an and n-p opanol o n-bu anol as he o ganic modi ie ha e been used in his wo k [35]. Al hough he expe imen al condi ions employed o pe o m he sepa a ion o hese compounds a e widely explained in [35], hey a e summa ized below: an Applied Bio- sys ems capilla y elec opho esis ins umen 279A-HT model (No walk, CT, USA), wi h UV de ec ion a 238 mn and empe a u e con olled a 307C was used o ob ain he elec ophe og ams o he compounds unde s udy. The dimensions o he used-silica capilla y (Polymic o Technologies, Phoenix, AZ, USA) used we e 75 cm o o al leng h and 50 cm o e ec i e leng h wi h 25 mm o inne diame e and 375 mm o ou e diame e . The applied ol age was 15 kV. Table 1. Iden i ica ion numbe s, names and s uc u es o N-phenylpy azole de i a i es s udied No. Name R3R4R5R2’ 1DNPP HHHNO 2 2 3-Me hyl DNPP Me H H NO2 3 4-Me hyl DNPP H Me H NO2 4 4,5-Dime hyl DNPP H Me Me NO2 5 3-E hyl DNPP E H H NO2 6 4,5-Dime hyl pNPP H Me Me H 7 3,4,5-T ime hyl DNPP Me Me Me NO2 8 4-Me hyl pNPP H Me H H 9 3-Me hyl-4-ni o-5- clo o DNPP Me NO2Cl NO2 10 3,5-Dime hyl pNPP Me H Me H 11 4-B omo pNPP H B H H 12 3-B omo-4-me hyl DNPP B Me H NO2 13 3,5-Dime hyl-4-b omo DNPP Me B Me NO2 14 5-Me hyl-4-b omo pNPP H B Me H 15 3- e -Bu yl pNPP -BuHHH 16 3,4-Dib omo DNPP B B H NO2 17 3-E hyl-4-b omo DNPP E B H NO2 DNPP, dini ophenylpy azole; pNPP, pa ani ophenylpy azole 2.2 Da a ea men Da a ha e been di ided in o wo se s, he model and he p edic ion da a se s ollowing he ac o ial design plo ed in Fig. 1. Model da a se (c osses) pe mi s he calcula ion o he pa ame e s o he di e en equa ions and he es da a se (ci cles) ha e been used o e alua e he p edic- ion capabili y o he empi ical and physicochemical equa ions used in his wo k. I should be men ioned ha when he bu e consis ed o 0.03 MSDS and 0.03 as he olume ac ion o n-bu anol, esul s ob ained ha e p o ed o be ou lie s and we e no used o build any o Figu e 1. Composi ion o he MEKC sys ems using a 0.08 MCHES (pH 10) bu e . Ci cle da a means he p e- dic ion da a se and c osses he model da a se . 328 C. Ga cía-Ruiz e al. Elec opho esis 2003, 24, 325–335 he models. The e alua ion o empi ical equa ions has been made using box plo s pe o med by he Sigma Plo so wa e [36]. Da a ea men was made using Mic o- so Excel [37]. Mul iple eg ession analysis and es s pe o med in his wo k o compa e he e o a e ages ob ained in di e en expe imen al condi ions we e ca ied ou using he S a g aphics Plus so wa e [38]. Nonlinea eg essions we e pe o med by using he Sigma Plo so - wa e [36]. The pe o mance o equa ions conside ed in his wo k has been e alua ed compa ing he ela i e e o s de ined as ollows: PRE %kcal kexp  kexp 100 (1) MPRE % X iN i1 PREi N(2) whe e kcal is he calcula ed e en ion ac o by he equa- ion ha is being es ing, kexp is he expe imen al e en- ion ac o , Nis he numbe o di e en sepa a ion bu e s (wi h di e en concen a ions o su ac an and alcohol). 3 Resul s and discussion As men ioned, he op imiza ion o sepa a ions pe o med by MEKC is complex and di icul due o he high numbe o pa ame e s a ec ing he sepa a ion p ocess. Thus, esolu ion o wo closely adjacen peaks (Rs), in MEKC, is dependen on he selec i i y ac o , he mean e en ion ac o and he a io o he mig a ion ime o he elec o- osmo ic low o he mig a ion ime o he micelles acco d- ing o he ollowing equa ion p oposed by Te abe and Cheng [39]: RS N p 4 a1 a k k1 1 0 m 1 0 m k (3) whe e Nis he heo e ical pla e numbe ; kis he mean e en ion ac o o he wo peaks conside ed; ais he selec i i y ac o (kj/kibeing kj.ki), and 0and ma e he mig a ion imes o he elec oosmo ic low and micelles, espec i ely. Acco ding o Eq. (3), esolu ion op imiza- ion equi es he knowledge o 0, m,k, and N alues. In he ollowing calcula ions, he e iciency o he ch oma- og aphic sys em (N) has been conside ed independen o he elec oly e composi ion [15, 16]. Howe e , he alues o 0, m,k, and aa e dependen on he elec oly e composi ion. In his s udy, he p edic ion o hese pa am- e e s has been pe o med by means o empi ical and physicochemical equa ions in o de o op imize he eso- lu ion. 3.1 Use o empi ical equa ions o he p edic ion o elec oosmo ic low and micelles mig a ion imes Pyell and Bü eho n [15] i s s a ed he impo ance o p e- dic ing he mig a ion imes o he elec oosmo ic low ( 0) and micelles ( m) as a unc ion o he bu e composi ion. Howe e , al hough hey ha e p oposed he use o di e - en equa ions [15, 16] no alidi y s udies ha e been pe - o med. So, in his wo k a sys ema ic s udy on equa ions ela ing mig a ion imes o he elec oosmo ic low and micelles wi h he su ac an concen a ion and he olume ac ion o he o ganic modi ie (mand , espec i ely) has been pe o med (Table 2). I mus be men ioned ha wo o hem ha e been used p e iously by Pyell and Bü eho n [15], Eq. (22), and by Bü eho n and Pyell [16], Eq. (4). In o de o e alua e he empi ical equa ions (Eqs. 4–33) ha bes p edic he mig a ion imes o he elec oosmo ic low and micelles, mul iple eg ession analysis has been pe o med by using he model da a se shown in Fig. 1. Once he pa ame e s ha e been calcula ed, he p edic- ion has been pe o med in he condi ions shown o he es da a se (Fig. 1). Table 2. Empi ical equa ions used o he p edic ion o elec oosmo ic low ( 0) and micelles ( m) mig a- ion imes Basic equa ion z alue Equa- ion No. z alue Equa- ion No. z=A1Bm1C 1Dm 0 1/ 0 lg 0 4 6 8 m 1/ m lg m 5 7 9 z=A1Bm 010 m11 1/ 012 1/ m13 lg 014 lg m15 z=A1B 1Cm 016 m17 1/ 018 1/ m19 lg 020 lg m21 z=A1Bm1C 022 m23 1/ 024 1/ m25 lg 026 lg m27 z=A1Bm1Cm 028 m29 1/ 030 1/ m31 lg 032 lg m33 In o de o es ablish he alidi y o he es ed equa ions, di e en c i e ia ha e been aken in o accoun . Tha is, he mos simple equa ion o which he lowes mean p e- dic ion ela i e e o s a e ob ained is ou objec i e. Ne e - heless, we mus ake in mind ha all he e ms mus be s a is ically signi ican . In his espec , o he p edic ion o 0when n-p opanol is used, he lowes mean p edic ion Elec opho esis 2003, 24, 325–335 Resolu ion op imiza ion in MEKC 329 ela i e e o s a e ob ained o Eqs. 4, 6, 8, 16, 22, 24, and 26 (no s a is ically signi ican di e ences, P.0.05) as can be obse ed in Fig. 2a. F om hese equa ions, we ha e chosen Eq. (4) because all he e ms a e s a is ically sig- ni ican (indica ing ha i is no possible o simpli y i o Figu e 2. MPRE o elec oosmo ic low ( 0) and micelle ( m) mig a ion imes by using empi ical equa ion in a MEKC sys em wi h (a) n-p opanol o (b) n-bu anol as he o ganic modi ie . These plo s a e de ined in e ms o pe cen iles and ake a quick look a he median and sp ead o he da a, as well as he mean, minimun, and he maximum alues o he a iable s udied. Ou lie s o pe cen iles a e also ep esen ed by ci cles. The leng hs o he uppe and lowe lines associa ed o each box show how s e ches he ails o he dis ibu ion a e. ob ain Eqs. 16, 22, 24, o 26) and due o i is he simples one compa ed wi h Eqs. (6) and (8). Following he same easoning exposed p e iously, we ha e chosen Eq. (4) o p edic 0(Fig. 2b) when n-bu anol is conside ed as he o ganic modi ie and Eqs. (23) and (7) (Figs. 2a and b) o p edic mwhen n-p opanol and n-bu anol a e conside ed as he o ganic modi ie , espec i ely. I can be no ed ha he equa ion ha bes p edic s he mig a ion ime o he sepa a ion bu e is he same when he o ganic modi ie used is n-p opanol and n-bu anol (Eq. 4), bu ha he equa ions di e when he p edic ion o he mig a ion ime o he micelle is achie ed. This ac is in ag eemen wi h Van Ho e e al. [40] ha conside s hese wo alcohols belonging o di e en ca ego ies. 3.2 Use o empi ical equa ions o e en ion p edic ion In o de o p edic he e en ion o he compounds unde s udy, ou empi ical equa ions (Eqs. 34–37) p oposed by Jiménez e al. [17] and ano he one empi ical equa ion (Eq. 38) p oposed by Pyell and Bü eho n [15] ela ing e en ion ac o s wi h he o al su ac an concen a ion and he olume ac ion o he alcohol (mand , espec- i ely) ha e been employed: 1 kAB mC (34) 1 kAB mC m(35) 1 kAB mC 2 m(36) 1 kAB mC mD 2(37) lnkABln mC (38) Mul iple eg ession analysis has been pe o med o ob ain he equa ion pa ame e s (Eqs. 34–38) by using he model da a se shown in Fig. 1. Then, e en ion ac o s o he p edic ion da a se (Fig. 1) we e calcula ed. F om he compa ison o he mean p edic ion ela i e e o s i can be obse ed (Figs. 3a and b) ha when n-p opanol was used, he lowes e o s we e ob ained by means o Eqs. (35–38) (no s a is ically signi ican di e ences obse ed, P.0.05). When n-bu anol is conside ed, he lowes e o s we e ob ained by means o Eq. (37) and (38) (no s a is ically signi ican di e ences obse ed, P.0.05). Howe e , he mul iple eg ession analysis shows ha Eq. (37) con ains a nonsigni ican e m, eason o which Eq. (38) was selec ed as he mos app o- 330 C. Ga cía-Ruiz e al. Elec opho esis 2003, 24, 325–335 Figu e 3. MPRE o he e en ion ac o s by using empi i- cal equa ions in a MEKC sys em wi h (a) n-p opanol o (b) n-bu anol as he o ganic modi ie . p ia e o p edic he e en ion o he solu es conside ed (p edic ion e o s 3.9–11.5% o n-p opanol and 5.4– 15.1% o n-bu anol). Ne e heless, Jiménez e al. [17] ound ha Eq. (35) was he mos app op ia e o p edic he e en ion beha io o a g oup o dihyd opy idines in simila MEKC sys ems using he same i e empi ical equa ions employed in his wo k. These esul s could be explained by he di e en cha ac- e is ics o each g oup o compounds. As an example, he li e a u e shows ha he g oup o he N-phenylpy azole de i a i es s udied in his wo k a e less hyd ophobic (wi h alues o he loga i hm o he oc anol-wa e dis ibu- ion coe icien , log Pow, anging om 2.08 o 2.60 [41]) han he g oup o dihyd opy idines (wi h alues o he log Pow anging om 2.43 o 4.31 [42]). 3.3 Use o physicochemical models o e en ion p edic ion The e en ion p edic ion h ough he use o a physico- chemical model ela ing he e en ion ac o wi h he micellized su ac an (SDS) and he o ganic modi ie (n- p opanol and n-bu anol) concen a ions has been pe - o med. The physicochemical model [14] conside s di e - en in e ac ions among he species p esen in he sys em acco ding o se e al equilib ia. Rela ing hese equilib ia wi h he solu e e en ion ob ained by MEKC he ollowing equa ion can be ob ained: k K11K3Aaq  Mm  1K2Aaq  K2K4Aaq  2(39) whe e, kis he e en ion ac o , is he phase a io, [Aaq] and [Mm] a e he alcohol and he micellized su ac an concen a ions (mola concen a ions), espec i ely, and K1,K2,K3, and K4a e equilib ium cons an s. These con- s an s ake in o accoun he associa ion o he solu e wi h he micelle o o m a complex in he micella pseudo- phase (K1), he enhancemen o solubili y o solu e in he sepa a ion bu e modi ied by alcohols (K2), he o ma ion o complexes among he solu e, he alcohol and he micelle in he micella pseudophase (K3), and he complex o ma ion be ween he solu e-alcohol complex and o he molecules o alcohol (K4), as i is shown in he ol- lowing equilib ia: Saq Mm ! K1SMm Saq Aaq ! K2SAaq SMmAaq ! K3SAMm SAaq Aaq ! K4SA2;aq Ne e heless, some simpli ica ions o his equa ion can be done, acco ding o he ollowing app oxima ions [14]: (i) I 1 .. K3[Aaq] he simpli ied exp ession is: k K1Mm  1K2Aaq  K2K4Aaq  2(40) (ii) I 1 ,, K3[Aaq] he simpli ied exp ession is: k K1K3Aaq  Mm  1K2Aaq  K2K4Aaq  2(41) Elec opho esis 2003, 24, 325–335 Resolu ion op imiza ion in MEKC 331 (iii) I 1 .. K4[Aaq] he simpli ied exp ession is: k K11K3Aaq  Mm  1K2Aaq  (42) In o de o check he alidi y o his model, he e en ion da a o a g oup o es solu es (17 N-phenylpy azole de i- a i es) ha e been used. Fi s o all, nonlinea eg essions we e achie ed o ob ain he equilib ium cons an alues om Eqs. (39)–(42) in o de o p edic he e en ion ac- o s. These alues we e used o calcula e he mean p e- dic ion ela i e e o s acco ding o he ou physicochem- ical equa ions desc ibed. Mean ela i e e o s o he ou equa ions conside ed in MEKC sys ems wi h n-p opanol (5.7, 20.2, 31.4, 5.8 o Eqs. 39, 40, 41, and 42, espec- i ely) and n-bu anol (4.8, 5.4, 30.1, and 6.9 o Eqs. 39, 40, 41, and 42, espec i ely) ha e been compa ed wi h a mul iple compa ison p ocedu e [38] o es ablish he equa- ion ha bes model he expe imen al e en ion beha io . The esul s om he compa ison indica e ha Eqs. (39) and (42) a e no s a is ically di e en when n-p opanol is used as he o ganic modi ie and Eqs. (39), (40) and (42) a e no s a is ically di e en when n-bu anol is employed as he o ganic modi ie . Al hough o he wo sys ems conside ed (n-p opanol and n-bu anol), Eqs. (39) and (42) do no di e signi ican ly, he mean e o alues a e lowe when Eq. (39) is used, so i can be conside ed ha Eq. (39) is he bes equa ion, al hough he use o non- linea eg ession is necessa y. F om he esul s exposed in he wo p eceding sec ions we can conclude ha Eqs. (38) and (39) a e, espec i ely, he bes equa ions o p edic e en ion ac o s by means o empi ical and physicochemical models. Mo eo e , om he compa ison o mean p edic ion e o s ob ained, he s a is ical es indica es ha he physicochemical model is he bes o explain he e en ion beha io o he solu es unde s udy (con idence le el o 95%). 3.4 Resolu ion op imiza ion h ough he use o physicochemical and empi ical models The e alua ion o all hese equa ions has pe mi ed o choose he bes equa ions o he p edic ion o k, 0, and mwi h he aim o op imizing he esolu ion (Rs) be ween wo consecu i e peaks using Eq. (3). In his equa ion i has been conside ed an N alue cons an and equal o 150 000 [43]. The mean e en ion ac o o he wo peaks conside ed has been calcula ed acco ding o he empi i- cal Eq. (38) o he physicochemical Eq. (39); and 0and m ha e been ob ained, espec i ely, om empi ical Eqs. (4) and (23) o n-p opanol, and om Eqs. (4) and (7) o n-bu anol. The esolu ion has been op imized acco ding o he c i e ion o global esolu ion gi en in [44]. This op i- mizing c i e ion is based on he no malized p oduc , , o di e en p ope ies, Xi, i11, associa ed o pai s o con- secu i e peaks. Y n1 i1 Xi;i1 P n1 i1 Xi;i1n1  n1(43) In his wo k, Xis he esolu ion p edic ed wi h he abo e- men ioned equa ions and nis he numbe o solu es. Figu e 4 shows he esponse su aces ob ained o sys- ems con aining SDS as he su ac an and n-p opanol o n-bu anol as he o ganic modi ie . The equa ions used o he p edic ion o e en ion ac o s a e Eqs. (38) (Figs. 4a and b) and (39) (Figs. 4c and d), espec i ely. In bo h cases, he p edic ion o 0and mwas achie ed by empi ical Eqs. (4) and (23) when n-p opanol was used and Eqs. (4) and (7) when n-bu anol was employed. I can be obse ed ha he maximum esolu ion o sepa a e he g oup o N-phenylpy azole de i a i es s udied using empi ical equa ions co esponds o a 0.08 MCHES bu e (pH 10) wi h 0.02 Min SDS and 0.03 olume ac ion o n-p opanol (Fig. 4a). On he o he hand, he maximum esolu ion ob ained o he model solu es s udied using he empi ical equa ions selec ed co espond o 0.08 M CHES bu e (pH 10) wi h 0.05 MSDS and 0.03 olume ac ion o n-bu anol (1), o wi h 0.01 MSDS wi hou n-bu anol (2) (Fig. 4b). When he physicochemical model (Eq. 39) has been used, he esponse su ace o n-p opa- nol shows wo maxima which co espond o 0.08 MCHES bu e (pH 10) wi h 0.05 MSDS and a 0.05 olume ac ion o n-p opanol (1) o wi h 0.02 MSDS and a 0.01 olume ac ion o n-p opanol (2) (Fig. 4c). The bes esolu ion is ob ained o maximum 2. On he o he hand, when n-bu anol is used as o ganic modi ie only a maximum is ob ained, co esponding o 0.08 MCHES bu e (pH 10) wi h 0.02 MSDS and a 0.03 olume ac ion o n-bu anol (Fig. 4d). Figu e 5 shows he expe imen al elec ophe og ams o a selec ed mix u e o solu es and o he bes condi- ions chosen om he esponse su aces shown in Fig. 4. F om he expe imen al elec ophe og ams shown in Fig. 5 some conclusions can be d awn: (i) As expec ed, Eq. (39) leads o he bes op imal condi ions o he sepa a ion o he solu es conside ed in his s udy i we compa e wi h he esul s ob ained by means o Eq. (38). Fo example, i n-p opanol is conside ed (Figs. 5a and c) solu es 5 and 6 a e esol ed (al hough no comple ely) bu when Eq. (38) is used in he e en ion p edic ion hese peaks coelu e. Mo eo e , when bu anol is used as he o ganic modi ie (Figs. 5b and d), and Eq. (39) is used, solu es 15 and 16 a e esol ed (al hough no comple ely) bu when Eq. (38) is used hese wo solu es coelu e. (ii) I is in e es ing o 332 C. Ga cía-Ruiz e al. Elec opho esis 2003, 24, 325–335 Figu e 4. Response su aces ob ained o he g oup o N-phenylpy azole de i a i es s udied in he MEKC sys em wi h SDS as su ac an and n-p opanol o n-bu anol as he o ganic modi ie using he p e- dic ed e en ion ac o s wi h (a, b) he empi ical Eq. (38) o (c, d) he physicochemical Eq. (39). Condi ions o maximum esolu ion: (a) 0.08 MCHES bu e (pH 10) wi h 0.02 MSDS and 3% n-p opanol; (b) 0.08 M CHES bu e (pH 10) wi h 0.05 M SDS and 3% n-bu anol (1) o wi h 0.01 MSDS wi hou n-bu anol (2); (c) 0.08 MCHES bu e (pH 10) wi h 0.05 MSDS and 5% n-p opanol (1) o wi h 0.02 MSDS and 1% n-p opanol (2); (d) 0.08 MCHES bu e (pH 10) wi h 0.02 MSDS and 3% n-bu anol. Figu e 5. Elec ophe og ams co esponding o he injec- ion o a mix u e o 15 N-phenylpy azole de i a i es in he op imal esolu ion condi ions ob ained in Fig. 4. DMF: dime hyl o mamide; BaP, benzo[a]py ene. no e ha n-p opanol (Fig. 5c) be e sepa a es he i s - mig a ing compounds in he elec ophe og ams while n-bu anol be e sepa a es he las -mig a ing compounds as has been epo ed p e iously in [35]. So, hese wo alcohols wo k complemen a ily and he mos adequa e one would depend on he solu es we a e in e es ed in. 3.5 Mechanis ical app oaches h ough he physicochemical model The alues o he physicochemical cons an s ob ained om Eq. (39) a e shown in Table 3. These esul s clea ly show ha he cons an alues depend no only on he solu e na u e bu also on he alcohol na u e. F om he K1 alues ob ained, we can conclude ha al hough he hyd ophobici y is he main d i ing o ce a ec ing he ch oma og ahic beha io , i is no he only one. Thus, a plo o he K1 alues e sus log Pow shows a mode a ely s ong ela ionship be ween he a iables (co ela ion coe icien , , 0.8297). A be e co ela ion is ob ained when he loga i hm alues o K1a e plo ed e sus he log Pow ( = 0.9564), bu solu es wi h he same hyd o- phobici y di e in K1 alues, p obably due o elec os a ic in e ac ions (i.e., solu es 2 and 4, bo h wi h log Pow 2.16, solu es 11 and 16, bo h wi h log Pow 2.43, and solu es 8 and 12, bo h wi h log Pow 2.41). Elec opho esis 2003, 24, 325–335 Resolu ion op imiza ion in MEKC 333 Table 3. Equilib ium cons an s ob ained om physicochemical model conside ed (Eq. 39) Solu e No. n-P opanol n-Bu anol K1K2K3K4 K1K2K3K4 1 38 2.52 0.89 38 3.06 0.27 2 67 2.67 0.87 67 3.43 0.19 3 96 5.15 2.11 67 3.06 0.03 4 109 3.46 0.94 109 4.18 5 162 2.16 0.36 161 3.43 0.44 6 188 6.11 1.98 188 4.04 2.83 2.49 7 196 4.75 1.71 196 4.29 0.05 8 233 4.35 1.70 232 3.81 0.09 9 236 17.50 8.28 236 3.53 10 268 4.85 1.46 267 5.63 0.06 11 363 2.13 0.48 357 2.75 0.70 12 470 1.61 0.45 403 1.78 1.22 13 493 4.19 1.48 757 4.41 14 757 6.15 2.69 753 3.86 0.41 15 795 1.12 0.38 784 7.95 7.71 3.91 16 740 1.59 0.99 1.18 736 2.28 24.70 17 1550 5.01 5.50 1550 0.44 18.70 The alues o K2and K3 o he solu e numbe nine a e signi ican ly highe han hose o he o he solu es when n-p opanol is conside ed, indica ing ha a o able in e - ac ions be ween he alcohol and he ni ogen a om in he py azole ing o his compound a e possible, bo h in he micella phase and in he elec opho e ic bu e . This ac leads o con a y e ec s o he e en ion, i s he o ma- ion o complexes in he micella pseudophase inc eases he e en ion in his phase and, second, he o ma ion o complexes in he elec opho e ic bu e d i s he e en- ion owa ds he hyd o-o ganic phase. When n-bu anol is conside ed, he complex o ma ion be ween he alcohol, he solu e and he micelle is negligible. This alcohol is mo e hyd ophobic han n-p opanol, so he aqueous phase pola i y and he micelle su ace cha ge densi y o he micelle diminish [45]. As a consequence, he elec os a ic in e ac ions a e diminished, ac ha can be iewed by he lowe alue o K2and he negligible alue o K3con- s an s. Gene ally, K3 alues a e lowe o n-bu anol han o n-p opanol wi h wo excep ions (solu es 6 and 15). These solu es ha e a e y oluminous subs i uen in he R3posi ion (see Table 1), so pe haps s e ic impedi- men s can be expec ed. n-Bu anol could enhance he e en ion o his compound (K3 alue highe in n-bu anol han in n-p opanol) due o he expansion o he micelle o o he be e solubiliza ion powe o his sol en in- side he co e o he micelle. The highes alues o K4(solu e 16 o sys ems con aining n-p opanol and solu es 16 and 17 o sys ems con aining n-bu anol) can be a ibu ed o in e ac ions be ween he alcohol head g oup and he posi- i e cha ge densi y o he wo ni ogen a oms (in he py a- zole ing). Fo he o he compounds, he K4 alues a e low o negligible, so in hese cases he e en ion could be explained by means o a mo e simplis ic model (Eq. 42). In o de o cla i y he ela ionship among he e en ion beha io and he s uc u al p ope ies o he solu es, p in- cipal componen (PC) and clus e analysis ha e been achie ed. Massa e al. [46] highly ecommended ha a clus e ing me hod is combined wi h a PC ou pu . So, in his wo k he ou cons an alues ha e been educed o a lowe numbe o a iables by means o he PC analysis ( wo and h ee componen s ha e been ex ac ed when n-p opanol and n-bu anol a e conside ed, espec i ely). The PCs ex ac ed we e: (i) o n-p opanol: PC1 = 0.999998 K120.000781284K210.00159507K3 10.000170362K4; PC2=20.0000369037 K110.888103K210.459474K3 20.0125016K4. (ii) Fo n-bu anol: PC1 = 0.999924 K120.000893064K210.000838577K3 10.0122405K4; PC2=20.0121667 K120.127968K220.0691081K3 10.989293K4; PC3=20.00177059 K110.563511K210.815836K3 10.129861K4. Then, he clus e analysis has been applied o he compo- nen s ex ac ed in e e y case. In his way, we can classi y he compounds wi h he same e en ion beha io . In Fig. 6, he clus e sca e plo s o sys ems con aining n-p opa- nol and n-bu anol a e shown (PC 2 s. PC 1).