Turk J Chem 30 (2006) , 181 – 192. ©c TÜBİTAK Optimization of the Nonaqueous Capillary Electrophoresis Separation of Metal Ions Using Mixture Design and Response Surface Methods Cevdet DEMİR∗, Yasin YÜCEL University of Uludağ, Faculty of Science and Arts, Department of Chemistry, 16059 Bursa-TURKEY e-mail: cevdet@uludag.edu.tr Received 25.02.2005 Mixture experimental design was used to enhance the separation selectivity of metal ions in nonaque- ous capillary electrophoresis. The separation of cations (Ag, Fe, Cr, Mn, Cd, Co, Pb, Ni, Zn and Cu) was achieved using imidazole as UV co-ion for indirect detection. Acetic acid was chosen as an elec- trolyte because its cathodic electroosmotic flow permits faster separation. The composition of organic solvents is important to achieve the best separation of all metal ions. Simplex lattice design and response surface methods have proved to be an effective tool to optimize the composition of organic solvents in nonaqueous capillary electrophoresis. Full and reduced experimental design models were compared to obtain the optimum composition of solvents. Contour plots were presented to visualize the effect of the selected solvents on electrophoretic mobility. The highest electrophoretic mobilities were obtained with higher percentages of acetonitrile for all metal ions. Root mean square error (RMSE) and F-test were used to evaluate the models. Key Words: Nonaqueous capillary electrophoresis, metal ions, mixture design, response surface meth- ods. Introduction Improvement of separation selectivity is of fundamental importance in capillary electrophoresis (CE). Sig- nificant improvements were obtained in separation selectivity using different mixtures of 2 or more organic solvents. The majority of CE separations have been accomplished using aqueous buffers as background elec- trolytes, but a limited number of studies in nonaqueous media have shown the usefulness of this approach1−4. The potential of nonaqueous CE is of particular interest for higher mobility and faster separation than with aqueous electrolytes. One of the most important features of organic solvents is that their physical and chemical properties differ widely (Table 1)5. Selectivity manipulation in nonaqueous CE can be achieved simply by changing ∗Corresponding author 181 Optimization of the Nonaqueous Capillary Electrophoresis..., C. DEMİR, Y. YÜCEL the organic solvent or varying the proportions of solvents. Methanol and ethanol are amphiprotic solvents that act as proton donors or acceptors if there are other proton donors or acceptors in the separation system6 . However, there are differences in their proton donor or acceptor capabilities. Aprotic solvents, such as acetonitrile, which have very week autoprotolysis constants, can only accept protons. The viscosity of acetonitrile is low when compared to that of methanol, ethanol and water. It has an inverse effect on electrophoretic mobility that allows the separations in a reasonable time. Organic solvents may exhibit strong absorbance of ultraviolet (UV) light, so that indirect UV or other detection methods are required. Imidazole can be used for the UV co-ion, which has a similar electrophoretic mobility as a range of metal ions. If different selectivity for the metal ions is required additives such as small organic acids can be added. Because of the difference in affinity to the selector the mobility of metal ions decreases, resulting in different migration times and selectivities. Table 1. Physical properties of the solvents5. Solvent Boiling point Viscosity Dielectric Autoprotolysis Surface tension (◦C) (mPa s) constant constant (10−2 N m−1) Methanol 64.7 0.545 32.70 17.20 2.212 Ethanol 78.3 1.078 24.55 18.88 2.190 Acetonitrile 81.6 0.341 37.50 ≥ 33.30 2.760 Water 100.0 0.890 78.39 14.00 7.181 The mixture design and response surface methods have been used to optimize the organic solvent selectivity in liquid chromatography7. Coenegracht et al.8 used the mixture design approach for the si- multaneous optimization of analysis time and resolution in reversed-phase ion pair liquid chromatography. This approach has been used in the optimization of formulation of food9, oil spill dispersant10, paint11, polymers12, concrete13 , glass14 and ceramic products15 . There is no literature to our knowledge on the opti- mization of the composition of organic solvents using mixture design in nonaqueous capillary electrophoresis. The separation selectivity can be enhanced with a combination of 2 or more solvents by means of a mixture design approach. In a mixture design, the total amount of organic solvent is held constant and the mobility of the components changes when the proportions of the solvents are changed. The main purpose of this methodology is to verify how the mobilities of metal ions are affected by the variation of the composition of the mixture components. The simplex lattice design method can be used if separation is not achieved using the single solvent system. Ten experiments are performed; 3 are single systems, 6 are binary systems and 1 is a ternary system. The electrophoretic mobility of each metal ion is calculated in each of the 10 experiments. The determination of the best compositions of organic solvents can be accomplished by using response surface diagrams. The simplified model, which defines a so-called response surface, may correlate the mobility to the proportions of organic solvents. This yields the quantitative estimation of mobility of any composition of the solvent system. The aim of this study was to investigate the influence of nonaqueous capillary electrophoresis on the separation selectivity of metal ions using mixture design. The mixture design approach proves its capability to optimize the composition of organic solvents for the best separation of metal ions in nonaqueous capillary electrophoresis. 182 Optimization of the Nonaqueous Capillary Electrophoresis..., C. DEMİR, Y. YÜCEL Experimental Chemicals All metal ion solutions were prepared from nitrate salts (Merck, Darmstadt, Germany) using deionized water. Imidazole was purchased from Merck (Merck, Schuchardt, Hohenbrunn, Germany). Acetic acid, methanol, ethanol and acetonitrile were purchased from Merck (Merck, Darmstadt, Germany). Apparatus All measurements were performed using the CRYSTAL 100 capillary electrophoresis system equipped with an UV detector. Platinum wire electrodes were inserted into the buffer vials for connection to the electrical circuit. The fused silica capillary (53 cm × 50 µm i.d.) was used in all analysis. The electropherograms were recorded and integrated with PC 1000 software, Version 3.5 (Thermo Separation Products, San Jose, CA, USA) equipped with a Spectra SYSTEM SN 4000 interface. Electrophoretic conditions Before measurements the capillary was always flushed for 10 min with 1M NaOH, deionized water and running buffer, consecutively. Metal cations were indirectly detected on-column by UV absorbance at 214 nm. The sample was introduced into the capillary by a 5 s hydrostatic injection. The measurements were performed at room temperature. A positive voltage of 20 kV was applied for separation. Preparation of stock solutions Stock standard solutions containing 1000 µg ml−1 of 10 cations were prepared from their nitrate salts. A mixture of 10 metal ions containing 1 µg ml−1 each was prepared from stock solution. Imidazole (20 mM) and acetic acid (30 mM) were used as the background carrier electrolyte. Before injection to CE the solutions were filtered through a 0.45 µm nylon filter (Millipore, Molsheim, France). Mixture design Experimental design and response surface methods have been used in a wide range of applications in the literature16−20. Optimization of solvent mixtures in capillary electrophoresis plays an important role in obtaining the best separation of metal ions. The mixture design approach can be adopted if separation is not achieved using single or binary solvent systems. In a mixture design, the constituents of a mixture given in portions of volume are confined to the assumption that the amounts of the N constituents sum up to 100% or normalized to 1. If the proportion of one solvent is changed, the relative ratio of other solvents is changed. When a mixture design is used to optimize the solvent mixture, the electrophoretic mobility (response) is assumed to depend on the relative proportions of the solvents in the mixture. The selection of the optimum solvent composition was performed using a (k,m) simplex lattice design , and is shown in Figure 1. The mixture design table for the 3 factors is given in Table 2. For the k factors (solvents) the lattice describes all experimental points having the factor levels 0, 1/m, 2/m, . . . , (d-1)/m or 1. Ten experiments are performed; 3 are single systems, 6 are binary systems and 1 is a ternary system. 183 Optimization of the Nonaqueous Capillary Electrophoresis..., C. DEMİR, Y. YÜCEL X1 (Methanol) X2 (Acetonitrile) X3 (Ethanol) Figure 1. Mixture designs for ternary solvent mixtures (x1: methanol; x2: acetonitrile; x3: ethanol). Table 2. Simplex lattice design for 3 factors at 5 levels. Experiment x1 (Methanol) x2 (Acetonitrile) x3 (Ethanol) 1 1 0 0 2 0 1 0 3 0 0 1 4 1/3 2/3 0 5 2/3 1/3 0 6 1/3 0 2/3 7 2/3 0 1/3 8 0 2/3 1/3 9 0 1/3 2/3 10 1/3 1/3 1/3 In mixture designs, the purpose of the experimental design is to model the mixture surface with a form of polynomial equation so that the response for any mixture of solvents can be predicted. The factors (x1, x2 and x3) are not independent but the sum of all the factors is constant. Scheffé and Cox developed canonical polynomial models with constraints on the coefficients to analyze mixture data10. Scheffé models are widely used because they are simple and calculation of coefficients is easy. The model can be described as follows. y = b1x1 + b2x2 + b3x3 + b12x1x2 + b13x1x3 + b23x2x3 (1) This quadratic model can be used for obtaining the response surfaces in optimization studies. Results and Discussion Experimental design The simplex lattice design was used in this study to optimize solvent mixtures in nonaqueous capillary electrophoresis. Ten experiments were performed as illustrated in Figure 1 and Table 2. There are 3 single factor experiments, 6 experiments where 1 factor is at 2/3 and the other at 1/3 and 1 experiment where all factors are at 1/3, resulting in 10 experiments in total. There are enough experiments for a full Sheffé model, and so some information about the significance of each parameter could be obtained. The electrophoretic mobilities were calculated for all 10 metal ions (Table 3). The electrophoretic mobilities determine the velocity of an ion under a set of given capillary elec- trophoresis conditions. The velocity of the electrophoretic flow (EOF) and the electrophoretic mobilities 184 Optimization of the Nonaqueous Capillary Electrophoresis..., C. DEMİR, Y. YÜCEL provide the apparent mobility in CE. The electrophoretic mobility µeff of an ion can be determined by ( ) LtLd 1 1 µeff = − V tm t0 where Lt is the total length of the capillary, and Ld the length of the capillary from the inlet to the detector. V the applied voltage, tmthe migration time of the ion and to the migration time of the neutral marker. Table 3. Electrophoretic mobilities of Ag, Fe, Cr, Mn, Cd, Co, Pb, Ni, Zn and Cu in organic solvents. Electrophoretic mobilities (µ ) ×1.10−4(cm2V−1s−1a ) Experiment µ Ag µ Fe µ Cr µ Mn µ Cd µ Co µ Ni µ Zn µ Pb µ Cu 1 4.517 4.247 3.852 2.923 2.686 2.522 2.311 2.259 2.389 2.114 2 4.895 4.517 4.106 2.880 2.636 2.509 2.238 2.189 2.333 1.941 3 4.558 4.283 3.779 2.791 2.529 2.383 2.156 2.070 2.218 1.945 4 4.476 4.265 3.722 2.723 2.466 2.327 2.088 2.012 2.165 1.882 5 5.679 5.372 4.755 4.622 4.265 3.975 2.923 2.807 3.206 2.730 6 3.226 3.096 2.940 2.760 2.664 1.900 1.662 1.590 1.813 1.545 7 3.640 3.206 3.058 2.333 2.119 2.053 1.734 1.696 1.771 1.676 8 4.601 4.359 3.601 2.856 2.615 2.478 2.253 2.179 2.333 2.066 9 5.490 5.096 4.755 4.340 3.627 3.475 2.923 2.529 3.206 2.430 10 4.622 4.417 3.681 2.880 2.636 2.509 2.279 2.185 2.349 2.088 Separation of metal ions in organic solvents Separation of Ag, Fe, Cr, Mn, Cd, Co, Pb, Ni, Zn and Cu was achieved using a voltage of 20 kV and detected indirectly at 214 nm in methanol, acetonitrile, ethanol and their mixtures. Table 3 presents the electrophoretic mobilities of cations in different solvents. The mobilities in the organic solvents are lowest in pure methanol for Ag, Fe and Cr and increase with acetonitrile and ethanol content. The metal ions were determined by capillary electrophoresis. The electropherograms in Figures 2- 4 show the separation of metal ions in an imidazole/acetic acid electrolyte in methanol, acetonitrile and ethanol, respectively. The effect of the addition of acetonitrile to methanol on the separation selectivity of metal ions was also studied for the imidazole/acetic acid electrolyte. The electropherogram in Figure 5 shows the separation of metal ions (dissolved in deionized water) in an imidazole/acetic acid electrolyte in ternary solvent mixtures. 185 Optimization of the Nonaqueous Capillary Electrophoresis..., C. DEMİR, Y. YÜCEL -0.0004 Mn -0.0012 Ni -0.002 Ag Cd Zn Co Fe Cu -0.0028 Cr Pb -0.0036 3 4 5 6 7 8 9 10 11 Time (min) Figure 2. Separation of Ag, Fe, Cr, Mn, Cd, Ni, Pb, Zn, Co, and Cu (1 µg/mL) dissolved in deionized water. Experimental conditions: electrolyte, 20 mM imidazole 30 mM acetic acid in methanol; indirect detection at 214 nm; separation voltage, 20 kV; hydrostatic injection from a 10 cm height for 5 s. -0.0034 Mn -0.0042 Ag Fe Cr Cd -0.005 Ni Co Cu PbZn -0.0058 3 4 5 6 7 8 9 10 11 12 13 Time (min) Figure 3. Separation of Ag, Fe, Cr, Mn, Cd, Ni, Pb, Zn, Co, and Cu (1 µg/mL) dissolved in deionized water. Experimental conditions: electrolyte, 20 mM imidazole 30 mM acetic acid in acetonitrile; indirect detection at 214 nm; separation voltage, 20 kV; hydrostatic injection from a 10 cm height for 5 s. 186 mV mV Optimization of the Nonaqueous Capillary Electrophoresis..., C. DEMİR, Y. YÜCEL Mn -0.0038 -0.0048 Co -0.0058 Fe Cd Ag Cr Ni Zn Cu Pb -0.0068 3 4 5 6 7 8 9 10 11 12 Time (min) Figure 4. Separation of Ag, Fe, Cr, Mn, Cd, Ni, Pb, Zn, Co, and Cu (1 µg/g) dissolved in deionized water. Experimental conditions: electrolyte, 20 mM imidazole 30 mM acetic acid in ethanol; indirect detection at 214 nm; separation voltage, 20 kV; hydrostatic injection from a 10 cm height for 5 s. -0,0035 Mn -0,0045 Ni Co Fe -0,0055 Cr Cd Zn Ag Cu Pb -0,0065 3 4 5 6 7 8 9 10 11 Time (min) Figure 5. Separation of Ag, Fe, Cr, Mn, Cd, Ni, Pb, Zn, Co, and Cu (1 µg/g) dissolved in deionized water. Experimental conditions: electrolyte, 20 mM imidazole 30 mM acetic acid in ternary solvent mixtures (1/3 methanol, 1/3 acetonitrile, 1/3 ethanol); indirect detection at 214 nm; separation voltage, 20 kV; hydrostatic injection from a 10 cm height for 5 s. Optimization of the CE separation of metal ions Mixture experimental design and response surface methods are powerful tools in the optimization of the composition of organic solvents for separation of metal ions in capillary electrophoresis. The electrophoretic mobility could be related to the composition of solvents. The mobility is visualized by the height of the response surface for every possible blend of the 3 solvents. 187 mV mV Optimization of the Nonaqueous Capillary Electrophoresis..., C. DEMİR, Y. YÜCEL The results are presented as 2-dimensional contour graphs, which show the level of curves of elec- trophoretic mobility as a function of the composition. The response surfaces for the 10 metal ions are shown in Figures 6-8. The most effective solvent composition can be estimated from the response surface. High electrophoretic mobilities are observed in the high composition of acetonitrile. The highest electrophoretic mobilities are around points 5 (2/3 methanol and 1/3 acetonitrile) and 9 (1/3 acetonitrile and 2/3 ethanol). The results show the importance of utilizing the response surface information to find the regions satisfying the compositions of solvents. %Ethanol %Ethanol ( ) ×1.10-4 (cm2a V -1s-1) ( ) ×1.10-4 (cm2V -1s-1a ) 3.64 3.82 3.403.58 3.99 3.76 4.17 4.35 3.94 4.53 4.11 4.82 4.70 4.29 4.88 5.06 4.47 4.65 5.06 4.82 5.24 4.88 5.00 4.65 4.47 %Methanol %Acetonitrile %Methanol %Acetonitrile (a) (b) %Ethanol %Ethanol ( ) ×1.10-4 (cm2V-1s-1a ) (a) ×1.10 -4 (cm2V-1s-1) 2.52 2.65 3.54 3.25 2.78 3.38 3.52 2.903.03 3.66 3.80 3.163.94 3.28 4.08 3.41 3.41 4.21 3.28 3.54 3.16 4.35 4.21 3.033.68 4.49 2.902.78 2.65 %Methanol %Acetonitrile %Methanol %Acetonitrile (c) (d) Figure 6. Ternary graphs of elements. (a) Ag, (b) Fe, (c) Cr and (d) Mn. 188 Optimization of the Nonaqueous Capillary Electrophoresis..., C. DEMİR, Y. YÜCEL %Ethanol %Ethanol -4 2 -1 -1 (a) ×1.10 -4 (cm2V-1s-1) (a) ×1.10 (cm V s ) 2.51 2.63 2.74 2.052.86 2.19 2.97 2.322.45 2.59 3.13 3.09 2.72 3.09 2.86 2.99 3.20 2.97 2.86 3.133.32 2.99 3.43 2.74 3.55 2.63 3.26 2.86 2.51 2.72 %Methanol %Acetonitrile %Methanol %Acetonitrile (a) (b) %Ethanol %Ethanol ( ) ×1.10-4 a (cm 2V-1s-1) (a) ×1.10-4 (cm2V-1s-1) 1.81 1.90 2.00 1.75 2.09 1.85 2.18 1.94 2.04 2.60 2.28 2.13 2.37 2.23 2.32 2.51 2.42 2.46 2.42 2.32 2.56 2.23 2.65 2.37 2.13 %Methanol %Acetonitrile %Methanol %Acetonitrile (c) (d) Figure 7. Ternary graphs of elements. (a) Cd, (b) Co, (c) Ni and (d) Zn. 189 Optimization of the Nonaqueous Capillary Electrophoresis..., C. DEMİR, Y. YÜCEL %Ethanol %Ethanol ( ) ×1.10-4 (cm2V-1 -1a s ) (a) ×1.10 -4 (cm2V-1s-1) 1.61 1.69 2.19 1.87 1.761.83 1.97 1.90 2.12 2.07 1.97 2.17 2.78 2.05 2.28 2.38 2.052.68 2.48 2.58 2.12 1.97 1.90 2.68 2.19 1.83 2.58 1.76 2.48 2.26 1.691.61 %Methanol %Acetonitrile %Methanol %Acetonitrile (a) (b) Figure 8. Ternary graphs of elements. (a) Pb and (b) Cu. The Scheffé model and its reduced model were tested to define the best experimental model. Mathe- matical models relating electrophoretic mobilities to the factors under study are as follows: y = b1x1 + b2x2 + b3x3 + b12x1x2 + b13x1x3 + b23x2x3 (2) y = a0 + a1x1 + a2x2 + a 2 211x1 + a22x2 + a12x1x2 (3) The relationship between the 2 models can be shown by substituting x3 = 1 − x1 − x2 into the equation for model 1. Tables 4 and 5 illustrate the regression coefficients in the models of electrophoretic mobility of Ag, Fe, Cr, Mn, Cd, Co, Pb, Ni, Zn and Cu cations calculated using multiple linear regression (MLR). The positive coefficients corresponding to the interactions between solvents methanol-acetonitrile and acetonitrile-ethanol represent the synergetic effect of the mixture of solvents on the electrophoretic mobility. The negative coefficient of b13 indicates that methanol and ethanol are antagonistic towards one another. High electrophoretic mobilities were observed at experimental points 5 and 9 (Table 3) with the binary mixtures. The experimental design model was selected based on root mean square error (RMSE) and F-test criteria. The results of RMSE and F-test are shown in Tables 6 and 7 respectively. As a result, the Scheffé and its reduced experimental design models were compared to obtain the optimum composition of solvents. According to the results the lowest RMSE was obtained using model 1. Table 4. The regression coefficients of Ag, Fe, Cr, Mn, Cd, Co, Pb, Ni, Zn and Cu for the Scheffé model. (bx1.10−4) Ag Fe Cr Mn Cd Co Ni Zn Pb Cu b1 4.75 4.41 4.03 3.19 2.91 2.81 2.43 2.37 2.53 2.24 b2 4.55 4.21 3.78 2.47 2.29 2.17 2.03 2.02 2.07 1.78 b3 4.62 4.36 3.95 3.14 2.82 2.55 2.25 2.11 2.38 1.99 b12 2.30 2.72 1.63 3.52 3.23 2.92 1.37 1.14 1.76 1.46 b13 -5.42 -5.28 -4.46 -3.18 -2.44 -3.35 -2.85 -2.59 -3.03 -2.21 b23 2.44 2.42 1.53 3.29 2.31 2.69 2.15 1.47 2.50 1.76 190 Optimization of the Nonaqueous Capillary Electrophoresis..., C. DEMİR, Y. YÜCEL Table 5. The regression coefficients of Ag, Fe, Cr, Mn, Cd, Co, Pb, Ni, Zn and Cu for the reduced model. (bx1.10−4) Ag Fe Cr Mn Cd Co Ni Zn Pb Cu a0 4.62 4.36 3.95 3.14 2.82 2.55 2.25 2.11 2.38 1.99 a1 -5.33 -5.27 -4.42 -3.17 -2.39 -3.10 -2.69 -2.36 -2.89 -1.97 a2 2.09 2.00 1.12 2.36 1.57 2.11 1.76 1.23 2.02 1.42 a11 5.46 5.33 4.50 3.21 2.48 3.35 2.87 2.61 3.05 2.23 a22 -2.16 -2.15 -1.30 -3.04 -2.10 -2.49 -1.99 -1.33 -2.32 -1.63 a12 5.48 5.78 4.74 3.57 3.50 3.69 2.18 2.36 2.40 1.99 Table 6. Root mean square error (RMSE) of Ag, Fe, Cr, Mn, Cd, Co, Pb, Ni, Zn and Cu for the 2 models. Model (1.10−5) Ag Fe Cr Mn Cd Co Ni Zn Pb Cu 1 3.77 3.23 3.70 5.66 4.95 4.35 2.34 1.91 3.02 192 2 3.84 3.30 3.73 5.69 4.97 4.39 2.37 1.94 3.06 1.95 Table 7. F-test of Ag, Fe, Cr, Mn, Cd, Co, Pb, Ni, Zn and Cu for the 2 models. Model DF FTable Ag Fe Cr Mn Cd Co Ni Zn Pb Cu (95 %) F(s1/s2) 9 3.18 1.01 1.01 1.01 1.02 1.02 1.02 1.01 1.01 1.02 1.01 The estimated optimum compositions of the solvents are given in Table 8. The predicted elec- trophoretic mobilities under these optimum compositions of the solvents are given in Table 9. The optimum compositions correspond approximately to the electrophoretic mobility that indicates the better separation of cations. The optimum compositions of organic solvents for Ag, Fe, Cr, Mn, Cd, Co, Pb, Ni, Zn and Cu were determined according to model 1 (Table 8). The predicted electrophoretic mobilities of these ions were calculated under optimum compositions of methanol, acetonitrile and ethanol (Table 9). The predicted electrophoretic mobilities are in the region of the response surface model for all metal ions. Table 8. The optimum composition of organic solvents for Ag, Fe, Cr, Mn, Cd, Co, Pb, Ni, Zn and Cu. Solvent (%) Ag Fe Cr Mn Cd Co Ni Zn Pb Cu x1 (methanol) 11.38 11.06 7.06 18.21 7.44 10.55 28.68 6.93 24.19 24.07 x2 (acetonitrile) 68.14 65.98 71.58 50.95 46.51 62.25 60.77 68.31 64.51 47.03 x3 (ethanol) 20.48 22.96 21.36 30.84 46.04 27.20 10.56 24.76 11.29 28.90 Table 9. The predicted electrophoretic mobilities of Ag, Fe, Cr, Mn, Cd, Co, Pb, Ni, Zn and Cu under optimum composition of methanol, acetonitrile and ethanol. Electrophoretic mobilities Ag Fe Cr Mn Cd Co Ni Zn Pb Cu (cm2V−1s−1) (µ ) ×1.10−4a 5.031 4.784 4.252 3.437 3.097 3.095 2.416 2.440 2.682 2.088 Conclusion Separation of cations (Ag, Fe, Cr, Mn, Cd, Co, Pb, Ni, Zn and Cu) in nonaqueous capillary electrophoresis was achieved using imidazole as the UV co-ion for indirect detection. Simplex lattice design and response 191 Optimization of the Nonaqueous Capillary Electrophoresis..., C. DEMİR, Y. YÜCEL surface methods were employed for the optimization of ternary solvent mixtures (methanol, acetonitrile and ethanol). RMSE and F-test were used to evaluate the models. Two experimental design models were compared to obtain the optimum composition of solvents. The lowest RMSE was obtained using the full model. Acknowledgment The authors thank Uludağ University Research Foundation (Project No. 2000/17) for providing financial support for this project. References 1. L.W. Vicki and M.G. Khaledi, J. Chromatogr. A, 859, 203 (1999). 2. K.D. 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