Research Article Box–Behnken design for the optimization of an enantioselective method for the simultaneous analysis of propranolol and 4-hydroxypropranolol by CE An experimental design optimization (Box–Behnken design, BBD) was used to develop a CE method for the simultaneous resolution of propranolol (Prop) and 4-hydro- xypropranolol enantiomers and acetaminophen (internal standard). The method was optimized using an uncoated fused silica capillary, carboxymethyl-b-cyclodextrin (CM-b-CD) as chiral selector and triethylamine/phosphoric acid buffer in alkaline conditions. A BBD for four factors was selected to observe the effects of buffer electrolyte concentration, pH, CM-b-CD concentration and voltage on separation responses. Each factor was studied at three levels: high, central and low, and three center points were added. The buffer electrolyte concentration ranged from 25 to 75 mM, the pH ranged from 8 to 9, the CM-b-CD concentration ranged from 3.5 to 4.5% w/v, and the applied run voltage ranged from 14 to 20 kV. The responses evaluated were resolution and migration time for the last peak. The obtained responses were processed by Minitab s to evaluate the significance of the effects and to find the optimum analysis conditions. The best results were obtained using 4% w/v CM-b-CD in 25 mM triethylamine/H 3 PO 4 buffer at pH 9 as running electrolyte and 17 kV of voltage. Resolution values of 1.98 and 1.95 were obtained for Prop and 4-hydroxypropranolol enantiomers, respectively. The total analysis time was around of 15 min. The BBD showed to be an adequate design for the development of a CE method, resulting in a rapid and efficient optimization of the pH and concentration of the buffer, cyclodextrin concentration and applied voltage. Keywords: 4-Hydroxypropranolol / Box–Behnken design / CE / Enantioseparation / Propranolol DOI 10.1002/elps.200800821 1 Introduction CE is a powerful separation technique for innumerous compounds with many applications in various analytical fields. This technique has several advantages such as high efficiency, simple instrumentation and low solvent and sample consumption. On the other hand, optimization of a CE method is a critical step because a large number of variables (buffer composition, ionic strength and chiral selector – enantioselective method, applied voltage, temperature, capil- lary length and injection time) can influence the separation efficiency, resolution, migration times, etc. In this context, design of experiments could be used for optimization of the analytical method resulting in lower reagent consumption and considerably less laboratory work due to the reduction in the number of executed experiments. This methodology allows statistical assessment on the effects of the studied factors and the evaluation of the interactions between the factors [1]. When interactions appear, univariate optimization is not suitable to find the best experimental conditions since the influence of any given variable depends on the magnitude of the other variables [2]. The initial step of a multivariate optimization includes the screening of factors to obtain the their effects on the analytical system. This step could be accomplished by using full factorial or fractional factorial designs. After determining the significant factors, the optimum analysis conditions can be obtained using more complex design of experiments such as Doehlert matrix, central composite designs (CCD) or Box–Behnken design (BBD) [3–5]. In special, BBD allows efficient estimation of the first-order, second-order and interaction coefficients. Since BBD presents fewer design points, it may be experimentally more convenient and less expensive to be performed than central composite designs with the same number of factors [6]. BBD does not appear to be widely used in the optimi- zation of CE analytical methods. Hows et al. [7] proposed a Keyller Bastos Borges 1 Mo ˆ nica Tallarico Pupo 2 Luis Alexandre Pedro de Freitas 2 Pierina Sueli Bonato 1 1 Department of Physics and Chemistry, Faculty of Pharmaceutical Sciences of Ribeira ˜ o Preto, University of Sa ˜o Paulo, Ribeira ˜ o Preto, Brazil 2 Department of Pharmaceutical Sciences, Faculty of Pharmaceutical Sciences of Ribeira ˜ o Preto, University of Sa ˜o Paulo, Ribeira ˜ o Preto, Brazil Received December 18, 2008 Revised January 8, 2009 Accepted January 9, 2009 Abbreviations: Acet, acetaminophen; BBD, Box-Behnken Design; CM-b-CD, carboxymethyl-b-cyclodextrin; 4-OH-Prop, 4-hydroxypropranolol; Prop, propranolol; TEA, triethylamine Correspondence: Dr. Pierina Sueli Bonato, Faculty of Pharma- ceutical Sciences of Ribeira ˜ o Preto, University of Sa ˜ o Paulo, Ribeira ˜ o Preto 14040-903, Brazil E-mail: psbonato@fcfrp.usp.br Fax: 155-16-3602–4880 & 2009 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim www.electrophoresis-journal.com Electrophoresis 2009, 30, 2874–2881 2874