Anal. Chem. 1997, 69, 2567-2574
Effect of Acetonitrile/Water Mobile-Phase Composition on Adsorption Characteristics of Reversed-Phase Liquid Chromatography Kanji Miyabe* and Shigeya Takeuchi
Chemistry Section, Faculty of Education, Toyama University, Gofuku, Toyama 930, Japan
The influence of volumetric composition of acetonitrile in a mobile phase on adsorption characteristics of reversedphase liquid chromatography using octadecylsilyl (ODS)modified silica gel was studied by the pulse response method and the moment analysis. The results were compared with those obtained for the reversed-phase system consisting of ODS-silica gel and methanol/water mixtures. In both systems, surface diffusion was dominant for intraparticle diffusion in ODS-silica gel particles. The contributions of three mass transfer steps in a column to peak broadening were of about the same order of magnitude. The activation energy of surface diffusion, Es, was found to be larger than the isosteric heat of adsorption, Qst. Because similar tendencies were observed for these adsorption characteristics, adsorption mechanisms may be analogous in both chromatographic systems. However, absolute values of the adsorption equilibrium constant, K, the decreasing ratio of hydrophobic surface area, ∆A/A, Qst, and Es for acetonitrile/water systems were smaller than the corresponding values for methanol/ water systems. Oppositely, greater values of Ds were obtained for acetonitrile/water systems. It was concluded that the interaction between ODS ligands and adsorbate molecules was weaker compared with that in methanol/ water mobile-phase systems when acetonitrile was used as an organic modifier in a mobile phase of reversedphase liquid chromatography. High-performance liquid chromatography has been frequently employed for both analytical and preparative separations.1-6 The reversed-phase mode is the most popular in the field of liquid chromatography. It was estimated that about 70-80% or more of analytical separations had been carried out by means of reversed-phase techniques, in which mainly octadecylsilyl (ODS)modified silica gel was used as a stationary phase. Mixed solvents of organic modifiers and water are usually employed as a mobile phase. A few organic solvents, such as methanol, acetonitrile, and tetrahydrofuran, are used as organic modifiers. Because the change in mobile-phase conditions significantly influences adsorp(1) Kirkland, J. J. Modern Practice of Liquid Chromatography; John Wiley and Sons: New York, 1971. (2) Done, J. N.; Knox, J. H.; Loheac, J. Applications of High Speed Liquid Chromatography; John Wiley and Sons: London, 1974. (3) Krstulovic, A. M.; Brown, P. R. Reversed-Phase Liquid Chromatography; John Wiley and Sons: New York, 1982. (4) Sander, L. C.; Wise, S. A. CRC Crit. Rev. Anal. Chem. 1987, 18, 299-415. (5) Snyder, L. R.; Glajch, J. L.; Kirkland, J. J. Practical HPLC Method Development; John Wiley and Sons: New York, 1988. (6) Poole, C. F.; Poole, S. K. Chromatography Today; Elsevier: Amsterdam, 1991. S0003-2700(96)01044-X CCC: $14.00
© 1997 American Chemical Society
tion phenomena of adsorbates on stationary phases, the optimization of the mobile-phase conditions is important in order to establish optimum chromatographic separations. Extensive studies have been made on the effect of the type of the organic modifiers and mobile-phase compositions on retention behavior in reversed-phase liquid chromatography. Linear or quadratic relations have been observed between the logarithm of capacity factor, k′, and volumetric fractions of an organic modifier in a mobile phase, φ.7-13 It has also been reported that the linearity of the relation between log k′ and φ is attributed to the value of k′ and the type of the organic modifier.7-9 The effect of solvent composition on retention behaviors in reversed-phase liquid chromatography has also been studied on the basis of the solvophobic theory. Horvath et al.14 investigated the solvent effect on the retention behavior of toluic acid in reversed-phase liqud chromatography using methanol/water and acetonitrile/water mixtures as mobile phases and ODS-silica gel as stationary phase. They quantitatively interpreted the variation of the solvent effect due to the change in the mobile phase composition.14 In previous paper,15-17 the authors compared adsorption properties of ODS-silica gel in both gas- and liquidphase adsorption systems. It was experimentally confirmed that a mobile-phase solvent influenced adsorption equilibrium in reversed-phase liquid chromatography. An attempt was also made to explain the solvent effect by applying the solvophobic theory.17,18 It is essential to study adsorption characteristics in reversedphase liquid chromatography from kinetics and thermodynamic properties as well as adsorption equilibrium in order to elucidate separation mechanisms. From this viewpoint, the authors studied adsorption phenomena in reversed-phase liquid chromatography by using ODS-silica gel and methanol/water mixtures as stationary and mobile phases.16-23 Pulse response experiments were carried out under various conditions with respect to adsorbates and (7) Berendsen, G. E.; de Galan, L. J. Chromatogr. 1980, 196, 21-37. (8) Schoenmakers, P. J.; Billiet, H. A. H.; de Galan, L. J. Chromatogr. 1979, 185, 179-195. (9) Karger, G. L.; Gant, J. R.; Hartkopf, A.; Weiner, P. H. J. Chromatogr. 1976, 128, 65-78. (10) Hennion, M. C.; Picard, C.; Caude, M. J. Chromatogr. 1978, 166, 21-35. (11) Tanaka, N.; Thornton, E. R. J. Am. Chem. Soc. 1977, 99, 7300-7307. (12) Melander, W. R.; Chen, B. K.; Horvath, C. J. Chromatogr. 1979, 185, 99109. (13) Jandera, P.; Colin, H.; Guiochon, G. Anal. Chem. 1982, 54, 435-441. (14) Horvath, C.; Melander, W.; Molnar, I. J. Chromatogr. 1976, 125, 129-156. (15) Miyabe, K.; Suzuki, M. AIChE J. 1993, 39, 1791-1798. (16) Miyabe, K.; Suzuki, M. Proceedings of the Fourth International Conference on Fundamentals of Adsorption; Kodansha: Tokyo, 1993; pp 437-444. (17) Miyabe, K.; Suzuki, M. AIChE J. 1995, 41, 536-547. (18) Miyabe, K.; Suzuki, M. AIChE J. 1992, 38, 901-910. (19) Miyabe, K.; Suzuki, M. AIChE J. 1995, 41, 548-558. (20) Miyabe, K.; Suzuki, M. J. Chem. Eng. Jpn. 1991, 24, 772-777.
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stationary and mobile phases constituting reversed-phase liquid chromatographic systems.16,18,21-23 Their type, composition, and concentration were changed. Chromatographic peaks measured under the various conditions were analyzed by applying the method of moments.24 Some results were obtained for adsorption equilibria, mass transfer rates, and thermodynamics properties in reversed-phase liquid chromatography. For example, surface diffusion had a significant role in the intraparticle mass transfer mechanism in reversed-phase packing materials in both gas- and liquid-phase adsorption systems.15,16,18,21-23 The surface diffusion coefficient, Ds, increased with an increase in the amount adsorbed.16,18 The positive concentration dependence of Ds was interpreted in terms of diffusion by potential chemical driving force.16,18,21 The activation energy of surface diffusion, Es, was found to be larger than the isosteric heat of adsorption, Qst, in liquid-phase adsorption.16-18,22,23 The absolute values of K and Qst in liquid-phase adsorption were found to be smaller than the corresponding values in gaseous systems.16,17 It could be quantitatively interpreted on the basis of the solvophobic theory that the phenomena were attributed to the influence of a solvent on liquid-phase adsorption.17 In reversed-phase liquid chromatography, the changes in mobile-phase composition or alkyl chain length were accompanied by changes in Qst, Ds, and Es as well as K.17,21-23 On the basis of the results concerning the characteristics of mass transfer phenomena, it was elucidated that the enthalpyentropy compensation effect was in place for surface diffusion and that the linear free energy relation held in reversed-phase liquid chromatography.21 This paper is concerned with adsorption characteristics in reversed-phase liquid chromatography. Mixtures of acetonitrile and water of various compositions were used as mobile phase and ODS-silica gel as stationary phase. Adsorption equilibria, mass transfer rates, and thermodynamic properties were determined from the moment analysis of pulse response curves. MOMENT ANALYSIS First and second moment analyses provide information about adsorption equilibria and mass transfer rates in a column. Details of the moment analysis of chromatographic peaks were described in previous papers.15,18,21,23 The adsorption equilibrium constant, K, was determined from the first moment, µ1. The intraparticle diffusivity, De, and the axial dispersion coefficient, Ez, were determined from the second moment, µ2′, by subtracting the contribution of fluid-to-particle mass transfer to peak spreading. The fluid-to-particle mass transfer coefficient, kf, was estimated by the equation of Wilson and Geankoplis.25 The molecular diffusivity, Dm, of adsorbates in acetonitrile/water mixtures of various compositions was calculated from those in acetonitrile and water by applying the Perkins-Geankoplis equation.26 Although the Wilke-Chang equation is the most popular for the estimation of Dm, the association coefficient in the equation has not been proposed for acetonitrile. The values of Dm of the adosrbates in acetonitrile and in water were estimated by the Scheibel equation and the Hayduk-Laudie equation, respectively.26 The contribu(21) Miyabe, K.; Suzuki, M. J. Chem. Eng. Jpn. 1994, 27, 257-259. (22) Miyabe, K.; Suzuki, M. Ind. Eng. Chem. Res. 1994, 33, 1972-1802. (23) Miyabe, K.; Suzuki, M. J. Chem. Eng. Jpn. 1994, 27, 785-789. (24) Suzuki, M. Adsorption Engineering; Kodansha/Elsevier: Tokyo/Amsterdam, 1990. (25) Wilson, E. J.; Geankoplis, C. J. Ind. Eng. Chem. Fundam. 1966, 5, 9-14. (26) Reid, R. C.; Prausnitz, J. M.; Sherwood, T. K. The Properties of Gases and Liquids; McGraw-Hill; New York, 1977.
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tion of adsorption rate at an adsorption site to µ2′ was assumed to be negligibly small. Intraparticle diffusion was assumed to consist of pore and surface diffusions. The value of Ds was calculated by subtracting the contribution of pore diffusion to intraparticle diffusion. Pore diffusivity, Dp, was estimated from Dm, porosity of an adsorbent, p, and the tortuosity factor, k, of the pores. The values of k was determined from chromatographic experiments with inert pulses. The values of µ1 and µ2′ of peaks were calculated by applying the equations proposed by Foley and Dorsey27 for the calculation of chromatographic figures of merit for ideal and skewed peaks. Retention time was obtained by correcting the effect of an extracolumn volume between an injection port and a column and that between the column and a detector. The contribution of the extracolumn volume to µ2′ was measured by the chromatographic method without the column, and it was corrected. The effects of µ1 and µ2′ of pulses introduced at the inlet of a column were neglected because the size of the pulses was extremely small. In this study, some corrections were made in order to estimate some diffusivities from µ2′. The influence of the corrections on the conclusions of this study was considered. Calculation of First and Second Moments from Chromatographic Peaks. First and second moments are usually calculated from the position and the width of peaks by assuming that the peaks can be represented by a normal distribution curve. Chromatographic peaks, however, frequently show somewhat tailing profiles. Accurate estimation of µ1 and µ2′ may be difficult under such conditions. Foley and Dorsey27 proposed some equations for the calculation of chromatographic figures of merit for ideal and skewed peaks. In this study, µ1 and µ2′ of peaks were calculated by applying the equations. The influence of skewed profiles of chromatographic peaks on the results of the moment analyses was eliminated. Estimation of Some Diffusivities and a Mass Transfer Coefficient. The contribution of fluid-to-particle mass transfer to µ2′ was subtracted when De was determined. An uncertainty in the estimation of kf influences the results of the second moment analyses. In this study, kf was estimated by the WilsonGeankoplis equation.25 The value of kf for benzene at 298 K was calculated as 0.034 cm s-1 under the condition that u0 for 70 vol % acetonitrile was 0.12 cm s-1. According to the equation proposed by Kataoka et al.,28 another value for kf was obtained, 0.026 cm s-1, under the same conditions. The resulting value of Ds calculated by taking kf as 0.026 cm s-1 was 7.2 × 10-6 cm2 s-1. Compared with the original value of Ds, i.e., 5.8 × 10-6 cm2 s-1, both values were of the same order of magnitude. It is concluded that the results of this study may not be significantly changed by the variation in the value of kf estimated. The contribution of Dp to De was corrected when Ds was calculated from De. As mentioned above, Dp was calculated from Dm, p, and k. The accuracy of the estimation of Dm influences the determination of Ds. In this study, Dm in acetonitrile/water mixed solvents was estimated by the Perkins-Geankoplis, Scheibel, and Hayduk-Laudie equations because the association coefficient in the Wilke-Chang equation was not reported for acetonitrile. A value of Dm estimated by the above equations was compared with that obtained by the Wilke-Chang equation in order to confirm the accuracy of the estimation of Dm. The value of Dm of (27) Foley, J. P.; Dorsey, J. G. Anal. Chem. 1983, 55, 730-737. (28) Kataoka, T.; Yoshida, H.; Ueyama, K. J. Chem. Eng. Jpn. 1972, 5, 132-136.
Table 1. Properties of ODS Column and Experimental Conditions average particle diameter, dp (µm) 45 0.81 particle density, Fp (g cm-3) 1.36 (80),a 1.29 (70), 1.26 (60), true density, F (g cm-3) 1.24 (40), 1.48 (20), 1.70 (0) 0.50 (80), 0.46 (70), 0.43 (60,40), pore volume (cm3 g-1) 0.56 (20), 0.57 (0) 0.40 (80), 0.37 (70), 0.35 (60,40), porosity, p (-) 0.45 (20), 0.49 (0) carbon content (wt %) 17.1 mass of adsorbent (g) 2.1 column size (mm) 6 i.d. × 150 void fraction, (-) 0.39 5.5 tortuosity factor, k2 (-) column temperature (K) 288-308 mobile phase acetonitrile/water, 80/20-0/100 (v/v) -1 0.06-0.12 superficial velocity, u0 (cm s ) a The number in parentheses is the volumetric fraction of acetonitrile in acetonitrile/water mobile phase.
benzene in 70 vol % methanol was calculated to be 9.1 × 10-6 cm2 s-1 by the above equations. On the other hand, 8.2 × 10-6 cm2 s-1 was obtained by the Wilke-Chang equation. Similar values of Dm were obtained by the two estimation procedures. As will be shown later, the contribution of surface diffusion to overall mass transfer in ODS-silica gel particles was as much as 85-98%. Because surface diffusion is dominant for intraparticle diffusion, the influence of the variation in Dp on the determination of Ds is negligibly small. It is concluded that the uncertainty in the estimation of Dm and Dp has little influence on the results of this study. In conclusion, appropriate results are obtained for the adsorption characteristics in reversed-phase liquid chromatography using ODS-silica gel and acetonitrile/water mixtures. EXPERIMENTAL SECTION Apparatus. A high-performance liquid chromatograph (LC6A, Shimadzu) was employed. A small volume of sample solution was introduced into a fluid flow by use of a sample injector. A thermostated water bath was employed to maintain the column temperature constant. The concentration of the samples was monitored by an ultraviolet detector. Column and Reagents. Properties of an ODS column (YMC) are shown in Table 1. The ODS-silica gel may be synthesized with a monofunctional n-octadecyldimethylsilyl ligand.29 The carbon content is probably close to a maximum amount of carbon, which can be introduced on the surface of silica gel by chemical bonding of n-octadecyldimethylsilyl ligands. To make it easy to quantitatively analyze the influence of mass transfer rates on peak spreading, the ODS column packed with relatively large ODSsilica gel particles was employed. Mobile phases consisted of acetonitrile and water, in which the volumetric composition of acetonitrile was 0-80% (0-80 vol % acetonitrile). Water was distilled from an ion-exchange system. Organic compounds, such as benzene, toluene, ethylbenzene, and naphthalene, were used as adsorbates. Sodium nitrate was used as an inert substance to determine the porosity of ODS particles and the void fraction of the ODS column. Procedure. Experimental conditions are also listed in Table 1. Pulse response experiments were made at zero surface coverage of the adsorbates, varying the temperature of the ODS column and the flow rate of the mobile phases. Small concentra(29) Miyabe, K.; Orita, N. Talanta 1989, 36, 897-902.
Figure 1. Adsorption equilibrium constant as a function of volumetric fraction of organic modifiers. Adsorbate: O,b, benzene; 4,2, toluene; 0,9, ethylbenzene; ],[, naphthalene. Mobile phase: open symbols, acetonitrile/water systems; closed symbols, methanol/water systems.
tion perturbation pulses were introduced into a fluid flow. The volumetric flow rate of the mobile phase was varied from 0.017 to 0.033 cm3 s-1 (1-2 cm3 min-1). The porosity of ODS particles and the void fraction of the ODS column were determined by means of the pulse response method, varying the amount of sodium nitrate injected. RESULTS AND DISCUSSION First Moment Analysis. The value of K was determined by analyzing µ1. In Figure 1, K was plotted against φ. When acetonitrile was used as an organic modifier, the logarithm of K increased with decreasing φ. Though almost linear correlations were observed, the lines were slightly concave upward. Similar results have been reported for ODS-silica gel and acetonitrile/ water systems.4,9 Corresponding results for ODS-silica gel and methanol/water systems are also illustrated in Figure 1. In that case, the slope of the relationship between ln K and φ decreased when φ was 40 vol % or below.17 The relationship showed slight convex profiles. A linear approximation, however, can be made for both of the mobile-phase systems in narrow ranges of φ. The difference in the relationships between ln K and φ in both mobilephase systems has not been interpreted rigorously. The phenomena appear to be related to both the physical nature of alkyl chains on the surface of ODS-silica gel and the interaction between ODS ligands and adsorbate molecules. As shown in Figure 2, the values of K in acetonitrile/water systems were smaller than those in methanol/water systems at same values of φ. These results indicate that the interaction between ODS ligands and adsorbate molecules in acetonitrile/water systems is weaker than that in methanol/water systems. Horvath et al.14 quantitatively explained the effect of a solvent on the retention behavior in reversed-phase liquid chromatography by applying the solvophobic theory. In the theory, it is assumed that the contact area between polar solvents and the hydrophobic Analytical Chemistry, Vol. 69, No. 13, July 1, 1997
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Figure 2. Correlation of adsorption equilibrium constants for both methanol/water and acetonitrile/water mobile phases. For key to symbols, refer to Table 2.
surface, A, of both adsorbate molecules and ODS ligands decreases due to the adsorption of the adsorbate molecules. The magnitude of the decrease in the hydrophobic surface area, ∆A, is assumed to be proportional to A of the adsorbate. Horvath et al.14 confirmed a linear relationship between log k′ and A for three kinds of homologies. From the slope of the linear plots, Horvath et al. indicated that ∆A was about 35% of the hydrocarbonaceous surface area of adsorbates in reversed-phase liquid chromatographic separations. Belfort et al.30 also reported that ∆A was estimated as 20-30% of the solute total cavity surface area. In this study, it was similarly attempted to quantitatively analyze the change in K due to the variation in φ. In Figure 3, K was plotted against A of adsorbates. The values of K plotted in Figure 3 were average values of several (usually six) experimental data. For example, the coefficient of variance was 1.6% for the chromatographic measurements of benzene using 70 vol % acetonitrile at 298 K. Reproducible measurements of K were attained. On the basis of the average values of K, ∆A/A values were determined. The ratio of ∆A/A was estimated from the slope of the linear plots in Figure 3. The slope increased with a decrease in φ. As shown in Figure 4, ∆A/A was calculated for acetonitrile/ water systems as follows: 17% (80 vol %), 18% (70 vol %), 19% (60 vol %), 24% (40 vol %), and 31% (20 vol %). The numbers in parentheses are the volumetric fractions of acetonitrile in the mobile phases. Corresponding results in methanol/water systems are also illustrated in Figure 4. The values of ∆A/A in acetonitrile/water systems are smaller than the corresponding values in methanol/water systems. The results indicate that the magnitude of the interaction between the adsorbate molecules and ODS ligands in acetonitrile/water systems is weaker than that in methanol/water systems. The values of Qst were determined from the temperature dependence of K according to the van’t Hoff equation:
d ln K/d(1/T) ) -Qst/Rg
(1)
Figure 5 illustrates the plot between ln K and 1/T for benzene. (30) Belfort, G.; Altshuler, G. L.; Thallam, K. K.; Feerick, C. P., Jr.; Woodfield, K. L. AIChE J. 1984, 30, 197-207.
2570 Analytical Chemistry, Vol. 69, No. 13, July 1, 1997
Figure 3. Correlation of the logarithm of adsorption equilibrium constant with hydrocarbonaceous surface area of adsorbates. For key to symbols, refer to Table 2.
Figure 4. Plot of ∆A/A against volumetric fraction of organic modifiers in a mobile phase.
Resulting values of Qst in Table 2 were of the same order of magnitude compared with the other results previously reported.31-37 Figure 6 shows the correlation of Qst with φ. With a decrease in φ, the absolute value of Qst increased. The correlations between Qst and φ in ODS-silica gel and methanol/water mixtures systems are also illustrated in Figure 6. The value of -Qst decreased with a decrease in φ in the range of φ lower than 40 vol %. A maximum was observed at φ ) 40 vol %. Colin et al.31 reported similar results in a reversed-phase liquid chromatographic system using methanol/ water mixtures as mobile phases. As shown in Figure 6, a (31) Colin, H.; Diez-Masa, J. C.; Guiochon, G.; Czajkowska, T.; Miedziak, I. J. Chromatogr. 1978, 167, 41-65. (32) Knox, J. H.; Vasvari, G. J. Chromatogr. 1973, 83, 181-194. (33) Colin, H.; Guiochon, G. J. Chromatogr. 1978, 158, 183-205. (34) Colin, H.; Guiochon, G. J. Chromatogr. 1977, 141, 289-312. (35) Horvath, C.; Melander, W. J. Chromatogr. Sci. 1977, 15, 393-404. (36) Unger, K. K. Porous Silica; Elsevier:Amsterdam, 1979; p 122. (37) Issaq, H. J.; Jaroniec, M. J. Liq. Chromatogr. 1989, 12, 2067-2082.
Figure 5. van’t Hoff plot of adsorption equilibrium constants of benzene.
maximum was observed between Qst and φ in acetonitrile/water systems at φ ) 20 vol %. In both of the mobile-phase systems, maxima were observed under the condition that φ was relatively low. Though the phenomena may result from the variation in the physical nature of ODS ligands, a strict explanation has not yet been obtained for the curved profiles. The absolute value of Qst was smaller in acetonitrile/water systems than in methanol/ water systems. These results also indicate that the interaction between ODS ligands and adsorbate molecules is weaker in acetonitrile/water systems than in methanol/water systems. Second Moment Analysis. Second moment analyses provide information about all mass transfer steps involved in chromatographic processes. In this study, the ODS system packed with relatively large ODS-silica gel particles was employed to make it easy to quantitatively analyze the influence of mass transfer rates on peak spreading. The value of Ez consists of two terms,24
Ez ) γDm + u0dp/Pe
(2)
The first term on the right-hand side of eq 2 is attributed to molecular diffusion and the second term to fluid dispersion. The contribution of the first term is negligibly small in liquid-phase adsorption. The Peclet number of the ODS column employed was calculated to be about 1.1-1.3. According to the theory of moment analysis, a second moment is represented as a sum of the contribution of each mass transfer step in a column. The contributions of each step to µ2′ are compared in Table 3. The contributions obtained from the second moment analysis vary with the change in the particle diameter of packing materials. The results in Table 3 were observed when the particle diameter was 45 µm. The contribution of fluid-toparticle mass transfer, δf, and intraparticle diffusion, δd, significantly changed according to the chromatographic conditions and were of same order of magnitude. However, the direction of the change in both contributions was opposite with respect to the variation in K. The contribution of axial dispersion, δax, was found to range from about 30 to 40% and was greater in acetonitrile/
water systems than in methanol/water systems.23 This situation resulted from the decrease in mass transfer resistance at the external film and intraparticle diffusion. It is concluded that the contributions of the three rate processes in the ODS column packed with the relatively large ODS-silica gel particles to peak spreading are of about the same order of magnitude in liquidphase adsorption. The contributions of pore and surface diffusions to intraparticle diffusion were compared with each other. As shown in Table 4, De values were about 5-50 times Dp. The contribution of surface diffusion to overall mass transfer in the ODS-silica gel particles was found to be as much as 85-98%. The values of Ds were of the order of 10-6-10-5 cm2 s-1. It is concluded that surface diffusion is dominant for intraparticle diffusion in the ODS-silica gel particles. Figure 7 shows linear correlations between ln Ds and φ. When acetonitrile was used as an organic modifier, ln Ds linearly increased with an increase in φ irrespective of the type of the adsorbates. Similarly, linear relations were observed between ln Ds and φ in ODS-silica gel and methanol/water systems.23 Larger values of Ds were obtained in acetonitrile/water systems. As indicated above, a decrease in φ was accompanied with an increase in K and -Qst. These results suggest that the intensity of the adsorptive interaction between adsorbate molecules and the surface of the ODS-silica gel increases with a decrease in φ. The restraints for surface diffusion due to the adsorptive interaction probably increase with a decrease in φ. The values of K and -Qst were smaller in acetonitrile/water systems than in methanol/water systems, indicating that the adsorptive interaction and the restraints for surface diffusion were weaker in acetonitrile/water systems than in methanol/water systems. As a result, larger values of Ds were observed in acetonitrile/water systems compared with those in methanol/water systems. According to the Arrhenius equation, Es at zero surface coverage of adsorbates was determined:
d ln Ds/d(1/T) ) -Es/Rg
(3)
Figure 8 illustrates linear plots for benzene at various φ. Resulting values of Es are listed in Table 2. The correlations of Es with φ are illustrated in Figure 9. The value of Es increased as φ decreased in the range from 40 to 80 vol %. The values of Es at various φ were smaller than corresponding values in methanol/ water systems.23 The smaller values of Es in acetonitrile/water systems are consistent with the result in Figure 7. Figure 10 shows a schematic illustration of the correlation between Qst and Es. Adsorbate molecules release a heat of adsorption, i.e., Qst, when the adsorbate molecules are adsorbed onto the surface of an adsorbent. Inversely, the gain of an activation energy corresponding to Qst must be required when the adsorbate molecules adsorbed are desorbed from the surface of the adsorbent. On the other hand, the adsorbate molecules adsorbed can migrate in a potential field of adsorption. This mass transfer mechanism in the adsorbed state is called surface diffusion and is considered an activated process. The gain of an activation energy is necessary for the adsorbate molecules adsorbed to surpass the boundary energy barrier, Es, between two adsorption sites. However, it is not necessary that the activation energy is beyond the absolute value of Qst, because the adsorbate molecules do not need to be completely desorbed from Analytical Chemistry, Vol. 69, No. 13, July 1, 1997
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Table 2. Thermodynamic Properties in Liquid Phase Adsorption mobile phase
key
adsorbate
Qst (kJ mol-1)
K0 (cm3 g-1)
Es (kJ mol-1)
Dso (cm2 s-1)
80 vol % CH3CN
O 4 0 ] O 4 0 ] O 4 0 ] O 4 0 ] O 4
benzene toluene ethylbenzene naphthalene benzene toluene ethylbenzene naphthalene benzene toluene ethylbenzene naphthalene benzene toluene ethylbenzene naphthalene benzene toluene
5.4 6.1 6.5 7.2 5.8 5.8 6.1 7.1 6.4 6.4 6.3 7.4 9.5 9.9 10.1 11.7 11.1 13.6
0.11 0.11 0.13 0.089 0.15 0.21 0.26 0.16 0.19 0.290 0.43 0.26 0.17 0.27 0.43 0.22 0.36 0.35
11.4 11.9 12.6 13.0 14.6 16.2 16.6 16.0 17.4 19.0 20.6 20.4 25.5 26.1 26.8 32.9 nda nd
8.1 × 10-4 7.5 × 10-4 7.2 × 10-4 7.7 × 10-4 2.0 × 10-3 3.1 × 10-3 2.8 × 10-3 2.0 × 10-3 5.0 × 10-3 7.3 × 10-3 1.1 × 10-2 9.2 × 10-3 7.0 × 10-2 7.1 × 10-2 7.0 × 10-2 7.1 × 10-1 nd nd
70 vol % CH3CN
60 vol % CH3CN
40 vol % CH3CN
20 vol % CH3CN a
Not determined.
Table 3. Comparison of the Contributions of Axial Dispersion, Fluid-to-Particle Mass Transfer, and Intraparticle Diffusion to Second Momentsa adsorbate benzene
toluene
ethylbenzene
naphthalene
Figure 6. Relationship between isosteric heat of adsorption and composition of mobile phase. For key to symbols, refer to Figure 1.
the surface of the adsorbent to a bulk phase. In this study, Es was found to be larger than -Qst as shown in Table 2. Similar results have been reported for surface diffusion phenomena in liquid-phase adsorption.16-18,22,23,38-40 These conditions suggest the following unreasonable situation: it is energetically advantageous for the adsorbate molecules adsorbed to be desorbed from the surface to the bulk phase rather than to migrate on the surface. The presence of surface diffusion phenomena should be denied under the given conditions. The correlations between Es and Qst listed in Table 2 are probably connected with thermodynamic properties of surface diffusion mechanisms. A strict explanation, however, has not yet been attained. In a previous paper,17 the authors compared the thermodynamic properties in both gas- and liquid-phase adsorption systems. The absolute values of K and (38) Awum, F.; Narayan, S.; Ruthven, D. Ind. Eng. Chem. Res. 1988, 27, 15101515. (39) Ma, Y. H.; Lin, Y. S.; Fleming, H. L. AIChE Symp. Ser. 1988, 84, 1-12. (40) Ching, C. B.; Hidajat, K.; Uddin, M. S. Sep. Sci. Technol. 1989, 24, 581597.
2572 Analytical Chemistry, Vol. 69, No. 13, July 1, 1997
φb (vol %) 80 70 60 40 80 70 60 40 80 70 60 40 80 70 60 40
µ1/(z/u0) (-) 1.1 1.4 1.8 4.5 1.3 1.7 2.5 7.7 1.5 2.1 3.4 13.3 1.4 2.0 3.1 12.5
µ2′/(2z/u0) (s) 0.094 0.16 0.31 2.0 0.14 0.27 0.60 6.0 0.21 0.45 1.2 18.3 0.20 0.41 1.0 17.0
δax (%) 43.2 39.2 33.8 31.3 38.8 34.9 31.9 31.2 34.6 34.2 31.1 33.4 31.8 30.4 28.3 31.7
δf (%) 18.1 21.7 28.6 40.0 20.6 24.8 32.2 46.5 22.1 27.3 35.5 49.7 21.0 26.0 34.6 48.8
δd (%) 38.7 39.1 37.7 28.7 40.7 40.4 35.9 22.4 43.3 38.5 33.5 16.9 47.3 43.6 38.1 19.5
a Experimental conditions: superficial velocity of mobile phase, 0.12 cm s-1; column temperature, 298 K. b Volumetric fraction of acetonitrile in acetonitrile/water mobile phase.
Qst were smaller in the liquid-phase adsorption than in the gaseous system. It was only interpreted on the basis of the solvophobic theory that the experimental results were attributed to a solvent effect in the liquid-phase adsorption. The analysis of the thermodynamic properties between Es and Qst in liquid-phase adsorption is a subject currently being studied. CONCLUSIONS A chromatographic study was made on the effect of mobile phase composition on adsorption characteristics in ODS-silica gel and acetonitrile/water systems by applying the moment analysis. The effect of φ on several characteristics, such as K, ∆A/A, Qst, Ds and Es, was elucidated. The values of K, ∆A/A, Qst, and Es increased with a decrease in φ. Oppositely, the logarithm of Ds linearly increased as φ increased in the range from 40 to 80 vol %. The tendency of the change in the adsorption characteristics due to the variation in φ was similar to that in methanol/water
Table 4. Comparison of the Contributions of Pore and Surface Diffusions to Intraparticle Diffusiona φb (vol %) benzene 80 70 60 40 toluene 80 70 60 40 ethylbenzene 80 70 60 40 naphthalene 80 70 60 40 adsorbate
De (cm2 s-1) 8.0 × 10-6 8.5 × 10-6 1.0 × 10-5 1.6 × 10-5 8.1 × 10-6 8.9 × 10-6 1.1 × 10-5 2.2 × 10-5 7.8 × 10-5 9.7 × 10-6 1.3 × 10-5 3.0 × 10-5 6.6 × 10-6 8.0 × 10-6 1.1 × 10-5 2.5 × 10-5
Dp De/Dp (cm2 s-1) (-) 1.5 × 10-6 5.2 1.2 × 10-6 7.1 9.4 × 10-7 10.9 7.3 × 10-7 22.1 1.4 × 10-6 5.8 1.1 × 10-6 8.1 8.5 × 10-7 13.3 6.5 × 10-7 34.2 1.3 × 10-6 6.0 1.0 × 10-6 9.6 7.8 × 10-7 16.2 6.0 × 10-7 49.7 1.3 × 10-6 5.3 9.8 × 10-7 8.2 7.5 × 10-7 14.1 5.8 × 10-7 42.6
Ds (cm2 s-1) 8.3 × 10-6 5.9 × 10-6 4.5 × 10-6 2.4 × 10-6 6.2 × 10-6 4.4 × 10-6 3.4 × 10-6 1.9 × 10-6 4.5 × 10-6 3.5 × 10-6 2.6 × 10-6 1.4 × 10-6 4.1 × 10-6 3.1 × 10-6 2.4 × 10-6 1.2 × 10-6
a Column temperature is 298 K. b Volumetric fraction of acetonitrile in acetonitrile/water mobile phase.
Figure 7. Surface diffusion coefficient as a function of volumetric composition of organic modifiers in mobile phase. For key to symbols, refer to Figure 1.
Figure 9. Relationship between activation energy of surface diffusion and composition of mobile phase. For key to symbols, refer to Figure 1.
Figure 10. Schematic illustration of thermodynamic properties relating to adsorption and surface diffusion phenomena.
the interaction between ODS ligands and adsorbate molecules is weaker in acetonitrile/water systems than in methanol/water systems. In the range of φ ) 40-80 vol %, Es was determined to be larger than -Qst. This result appears to be partially attributed to the influence of a solvent on the liquid-phase adsorption. The contributions of the three mass transfer steps in the ODS column to peak spreading were evaluated separately. Mass transfer resistances of the three steps were of about the same order of magnitude. Surface diffusion was dominant for intraparticle diffusion in the ODS-silica gel particles. NOMENCLATURE
Figure 8. Arrhenius plot of surface diffusion coefficient of benzene.
mobile phase systems. Chromatographic mechanisms seem to be similar in both of the reversed-phase liquid chromatographic systems. Absolute values of K, ∆A/A, Qst, and Es, however, were smaller than the corresponding values in ODS-silica gel and methanol/ water systems. To the contrary, greater values of Ds were obtained in acetonitrile/water systems. These results suggest that
A
surface area, cm2 mol-1
De
intraparticle diffusion coefficient, cm2 s-1
Dm
molecular diffusivity, cm2 s-1
dp
particle diameter, cm
Dp
pore diffusivity, cm2 s-1
Ds
surface diffusion coefficient, cm2 s-1
Ds0
frequency factor, cm2 s-1 Analytical Chemistry, Vol. 69, No. 13, July 1, 1997
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Es
activation energy of surface diffusion, kJ mol-1 cm2
s-1
Ez
axial dispersion coefficient,
K
adsorption equilibrium constant, cm3 g-1 cm3
contribution of fluid-to-particle mass transfer to µ2′
δd
contribution of intraparticle diffusion to µ2′
void fraction in bed, -
K0
adsorption equilibrium constant at 1/T ) 0,
p
porosity, -
k′
capacity factor, -
µ1
first absolute moment, s
k
tortuosity factor, -
µ2′
second central moment, s2
kf
fluid-to-particle mass transfer coefficient, cm s-1
Fp
particle density, g cm-3
Pe
Peclet number, -
φ
Qst
isosteric heat of adsorption, kJ mol-1
volumetric fraction of an organic modifier in a mobile phase, vol %
Rg
gas constant, kJ mol-1 K-1
T
temperature, K
u0
superficial velocity, cm s-
Greek Letters γ
obstructive factor, -
δax
contribution of axial dispersion to µ2′
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Analytical Chemistry, Vol. 69, No. 13, July 1, 1997
g-1
δf
Received for review October 9, 1996. Accepted March 27, 1997.X AC961044M X
Abstract published in Advance ACS Abstracts, May 15, 1997.
