Quantitative Theory of Electroosmotic Flow in Fused-Silica Capillaries Using an Extended Site-Dissociation-Site-Binding Model Marilyn X. Zhou* ,† and Joe P. Foley ‡ Aveva Drug Delivery Systems, 3250 Commerce Parkway, Miramar, Florida 33025, and Chemistry Department, Drexel University, 3141 Chestnut Street, Philadelphia, Pennsylvania 19104 To optimize separations in capillary electrophoresis, it is important to control the electroosmotic mobility of the running buffer and the factors that affect it. Through the application of a site-dissociation-site-binding model, we demonstrated that the electroosmotic mobility could be controlled qualitatively and quantitatively by the param- eters related to the physical and chemical properties of the running buffer: pH, cation valence, ionic strength, viscosity, activity, and dissociation constant. Our study illustrated that the logarithm of the number of apparent silanol sites on a fused-silica surface has a linear relation- ship with the pH of a buffer solution. The extension of the chemical kinetics approach allowed us to obtain the thickness of the electrical double layer when multivalent inorganic cations are present with monovalent cations in a buffer solution, and we found that the thickness of the electrical double layer does not depend on the charge of anions. The general equation to predict the electroosmotic mobility suggested here also indicates the increase of electroosmotic mobility with temperature. The general equation was experimentally verified by three buffer scenarios: (i) buffers containing only monovalent cations; (ii) buffers containing multivalent inorganic cations; and (iii) buffers containing cations and neutral additives. The general equation can explain the experimental observa- tions of (i) a maximum electroosmotic mobility for the first scenario as the pH was varied at constant ionic strength and (ii) the inversion and maximum value of the elec- troosmotic mobility for the second scenario when the concentration of divalent cations was varied at constant pH. A good agreement between theory and experiment was obtained for each scenario. Capillary electrophoresis (CE) is a liquid-phase separation technique and has been applied in many fields. Throughout many years since its emergence, researchers have understood that the driving force for conventional capillary zone electrophoresis is the bulk electroosmotic flow (EOF) under the presence of the electric field. However, the drawback of this separation technique is its poorer precision compared with the more mature and popular separation technique, high-performance liquid chromatography, partly due to an imprecise control of EOF. This has significantly limited the acceptance and application of CE by industry, despite its low operating cost. Therefore, the purpose of this paper is to provide practical means for predicting EOF not only qualitatively but also quantitatively, through an established site-dissociation- site-binding model 1 from both a chemical equilibrium and a chemical kinetic point of view. With this insight, we may be able to understand and control EOF better. The origin of EOF is directly related to the material made of the capillary. The most common material made of the capillary for CE is fused silica. Silica itself is silicon dioxide (SiO 2 ). There are many types of silica with varieties of different physical properties. The soluble form of silica is the monomeric acid, or Si(OH) 4 . All other forms of silica are the polymers of SiO 2 containing certain numbers of silanol (SiOH) groups; fused silica, a type of massive dense amorphous silica glass, is one of them. The catalyst of this process is the hydroxyl ion, OH - . Therefore, the hydrolysis process is largely dependent upon the solution pH. As claimed in most publications, 2-4 the pK a for the equilibrium between Si(OH) 4 and (OH) 3 SiO - is in the range of 9-10. Above pH 11, the hydroxyl ions convert Si(OH) 4 to silicate ions and silicate ions leave the solid surface so that the silica continues to dissolve into the solution. Below pH 11, OH - ion is only the catalyst that controls the rate at which silica dissolves until the solution reaches saturation. 5 Smit et al. 6 demonstrated that the characteristics of vitreous silica (or fused silica), after soaking in NaCl solution at pH 10 for up to 28 h, were changed. Its surface charge after the treatment was much lower than it was before. Therefore, the maximum pH of this study was up to pH 9 so that the characteristics of the fused silica were unchanged. We focus on establishing a mathematical formula that predicts the EOF inside the fused-silica capillary with consideration of varying pH, ionic strength, and valence charge of ions. * Corresponding author. E-mail: marilyn.zhou@avevadds.com. Telephone: 954-624-1309. Fax: 954-435-0714. † Aveva Drug Delivery Systems. ‡ Drexel University. (1) Hunter, R. J. Zeta Potential in Colloid Science: Principles and Applications; Academic Press: New York, 1981. (2) March, A. R. I.; Klein, S.; Vermeulen, T. Energy Research and Development Administration, Contract W-7405-ENG-48, Report LBL-4415, University of California, Lawrence-Berkeley Laboratory, October 1975 [files as thesis by A. R. March, III]. (3) Schwarts, R.; Muller, W. D. Zeit. Anorg. Allg. Chem. 1958, 296, 273. (4) Bilinski, H.; Ingri, N. Acta Chem. Scand. 1967, 21, 2503. (5) Iler, R. K. The Chemistry of Silica: Solubility, Polymerization, Colloid and Surface Properties, and Biochemistry; John Wiley and Sons: New York, 1979. (6) Smit, W.; Holten, C. L. M.; Stein, H. N.; de Goeij, J. J. M.; Theelen, H. M. J. J. Colloid Interface Sci. 1978, 397. Anal. Chem. 2006, 78, 1849-1858 10.1021/ac0518708 CCC: $33.50 © 2006 American Chemical Society Analytical Chemistry, Vol. 78, No. 6, March 15, 2006 1849 Published on Web 01/20/2006