Abstract A super-modified simplex (SMS) method has been used to optimize the mobile phase used for separa- tion of seven water-soluble vitamins in multivitamin tablets by gradient micellar liquid chromatography (MLC) with ultraviolet (UV) detection at 254, 295, and 361 nm. Effect of column temperature and addition of organic modifier to the mobile phase on separation efficiency were investi- gated: the appropriate conditions used were a temperature of 35°C and 1-butanol modifier. The sodium dodecyl sul- fate (SDS) concentration, pH, and 1-butanol% in the mo- bile phase were chosen for simultaneous optimization us- ing the SMS method. The optimum mobile phase was found to be 16 mmol L –1 (mM) SDS, 0.02 M phosphate buffer, pH 3.6, and a gradient of 3.5–10% (v/v) butanol. The total analysis time for vitamins was 75 min. The ana- lytical parameters including linearity (r>0.9970), limit of detection (0.12–50 μg mL –1 ), precision of method (rela- tive standard deviation (RSD) <8.90%), and accuracy ob- tained by the recovery assay (88–103%) support the use- fulness of the proposed method for the determination of the water-soluble vitamins. Keywords Micellar liquid chromatography · Water-soluble vitamins · Sodium dodecyl sulfate · Super-modified simplex Introduction It is well known that vitamins are an essential diverse group of compounds that are needed in relatively small amounts to sustain life and good health. High-performance liquid chromatography (HPLC) has been widely used for separa- tion of vitamins [1, 2, 3, 4, 5, 6]. However, only a few meth- ods have been reported in the literature for the simultaneous determination of all water-soluble vitamins. Most of these methods have used octadecylsilane (ODS) columns and hydro- organic mobile phases containing methanol [1, 2], meth- anol with an ion-pairing agent [3, 4], and acetonitrile [5]. Recently, a micellar liquid chromatographic (MLC) method using isocratic mode, UV detection (at 270, 290, and 325 nm), 0.1 M SDS, 4% pentanol, and pH 3 in an ODS column has been reported for determination of four water-soluble vitamins [6]. The MLC offers a number of advantages compared to other chromatographic methods including low cost, low toxicity, low volatility of mobile phase constituents, the possibility of simultaneous separation of ionic and non-ionic compounds, direct injection of biological fluids, and un- common separation selectivity owing to the involvement of a large number of parameters [7]. The primary objective in the development of MLC separations is the optimization of the chromatographic performance through the adjustment of such experimental parameters as temperature, type, and amount of an or- ganic modifier [7]. HPLC separations are mainly affected by varying the composition of the mobile phase. In MLC, the principal parameters are concentration of organic modifier, pH, and concentration of the surfactant [7]. Or- dinarily, only one factor is varied at fixed values of the other parameters. The one factor at a time method requires a very large number of experiments, particularly when there are many parameters. Further, if the factors interact, the obtained optimum depends on the starting conditions used, and the global optimum is not necessarily found. A number of different experimental designs have been de- veloped for a better examination of the experimental do- main. One of the most efficient optimization designs is the simplex method. Simplex optimization was first intro- duced in HPLC separations by Morgan and Deming [8, 9]. The modified simplex procedure was developed to over- come the disadvantages of the original simplex method [10]. The SMS, which was introduced by Routh and co- workers [11], is a modified version of the modified sim- plex method. The optimization process is started by defin- Ali R. Ghorbani · Fariborz Momenbeik · Jafar H. Khorasani · Mohammad K. Amini Simultaneous micellar liquid chromatographic analysis of seven water-soluble vitamins: optimization using super-modified simplex Anal Bioanal Chem (2004) 379 : 439–444 DOI 10.1007/s00216-004-2594-1 Received: 8 November 2003 / Revised: 7 March 2004 / Accepted: 11 March 2004 / Published online: 6 April 2004 ORIGINAL PAPER A. R. Ghorbani · F. Momenbeik · J. H. Khorasani (✉) · M. K. Amini Department of Chemistry, University of Isfahan, 81746–73441 Isfahan, Iran Tel.: +98-311-7932748, Fax: +98-311-6689732, e-mail: j.h.kho@chem.ui.ac.ir © Springer-Verlag 2004