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Mendeleev Communications Electronic Version, Issue 1, 2000 (pp. 1–42) Calculation of sorption isotherms from the retention parameters in high-performance liquid chromatography Sergei N. Lanin,* Mariya Yu. Ledenkova and Yuri S. Nikitin Department of chemistry, M. V. Lomonosov Moscow State University, 119899 Moscow, Russian Federation. Fax: +7 095 932 8846; e-mail: SNLanin@phys.chem.msu.ru DOI: 10.1070/MC2000v010n01ABEH001191 A new rapid method for the calculation of sorption isotherms from the dependence of retention volumes on concentrations with the use of an equation in the form of virial expansion was suggested. Recently, studies of sorption from solutions particularly at low concentrations are often carried out by HPLC.HPLC is a unique combination of a directly studied sorption system and a highly sensitive measuring instrument.In chromatography, the calculation of sorption isotherms by the Glueckauf method1,2 is commonly used. The disadvantages of this method are due to the fact that in real chromatography the conditions of ideal equilibrium chromatography with the instantaneous establishment of equilibrium are not always met; i.e., the Glueckauf method does not take into account factors occurring in real chromatography, such as diffusion broadening of chromatographic zones and mass transfer dispersion process of sorbate between the mobile and stationary phases.3–5 Huber6–7 has improved the Glueckauf method; he found that a curve drawn through peak tops approximates the elution curve for the case of ideal equilibrium chromatography. A near-equilibrium sorption isotherm can be calculated by the Glueckauf method.However, the necessity of the determination of chromatographic peak and adsorption areas in the Glueckauf and Huber methods complicates the calculation of sorption isotherms and introduces errors due to an inaccuracy of the determination of these areas. The purpose of this work was to develop a new rapid method for the calculation of sorption isotherms from chromatographic data (retention values and chromatographic peak heights).The normal-phase HPLC measurements were conducted on a Milikhrom-1 microcolumn chromatograph with a syringe pump (the mobile phase flow rate 2–600 ml min–1) and a spectrophotometric UV detector (spectral range 190–360 nm). The sorbates (benzene, nitrobenzene and anisole) were injected into the chromatographic column with a needle by a stopped-flow technique.A steel column (120×2 mm) was packed with Silasorb-300 hydroxylated silica with a specific surface area of 300 m2 g–1 and a particle diameter of ~5 mm (the adsorbent mass in the column m = 0.2±0.005 g). n-Hexane used as a mobile phase was dried with zeolite NaA (heated for 4 h at 450 °C) for 2–3 days.Experimental conditions: mobile phase flow rate w = 100 ml min–1, room temperature, detection at 254 and 300 nm. The injected sample volume was 1–25 ml. The dead volume (V0) was determined by measuring the elution time of a practically unsorbed substance, CCl4. The corrected retention volume V'R,g was determined by the equation V'R,g = (VR – V0)/m.It is known from the theory of equilibrium chromatography4,8 that where V'R,g is the corrected retention volume per gram of adsorbent, a is the Gibbs adsorption, vm is the average mole volume of a binary solution of the mobile phase (i.e., the mixture of a solvent and an adsorbate), c and Xs are the equilibrium concentration and the mole fraction of the sorbate, respectively, as determined from the calibration functions c = f(h) or Xs = f(h), where h is the detector response.Usually, the detector response is directly proportional to the substance concentration c = Kh, where K is constant for a given adsorbate and a given detector sensitivity. The sorption values for any type of isotherms can be calculated from the retention volumes by integrating equation (1).If the virial expansion equation is used for describing the retention volume V'R,g as a function of the adsorbate mole fraction Xs, then sorption can be calculated by the equation on the assumption that Xs ® 0, the sorption a ® 0 and const ® 0 and equation (3) takes the form where bi and ci are the virial expansion coefficients. Equation (4) is identical to an equation of sorption in the form of virial expansion, which is derived strictly by methods of statistical9–11 and classic thermodynamics.4 It can describe both convex and concave isotherms of sorption.Consequently, equation (2) derived easily from equation (4) can be considered theoretically valid, and it can be used for the calculation of isotherms of sorption. da dc V'R,g= =vm , da dXs (1) Table 1 Dependence of the retention volume of sorbate (V'v) on equilibrium concentration (Xs).Sorbate Equation V'v = f(Xs) Correlation coefficient Benzene V'v = 4.518×106Xs 2 – 0.156×106Xs + 6500 V'v = –1756.8×106Xs 3 + 37.782×106Xs 2 – – 0.3514×106Xs + 6900 0.9958 0.9979 Anisole V'v = 740.744×107Xs 2 – 516.166×105Xs + 113128 V'v = –365.708×1010Xs 3 + 294.654×108Xs 2 – – 848.870×105Xs + 122196 0.9686 0.9921 Nitrobenzene V'v = 513.328×107Xs 2 – 470.884×105Xs + 136561 V'v = –171.672×1010Xs 3 + 201.102×108Xs 2 – – 838.488×105Xs + 159140 0.9685 0.9924 V'v = V'R,g / vm = b0 + b1Xs + b2Xs 2 + ... , (2) a = b0Xs + b1Xs 2 /2 + b2Xs 3/3 + ...+ const (3) a = c0Xs + c1Xs 2 + c2Xs 3 + ... , (4) 400 350 300 250 200 150 100 50 0 10 20 30 40 50 c/mmol dm–3 anisole nitrobenzene a/mmol g–1 Figure 1 Adsorption isotherms of anisole and nitrobenzene from n-hexane on Silasorb-300 hydroxylated silica calculated ( ) by virial equation (3) of fourth degree, ( ) by the Glueckauf method, ( ) determined by the static adsorption method for anisole.Mendeleev Communications Electronic Version, Issue 1, 2000 (pp. 1–42) We obtained asymmetric chromatographic peaks of anisole and nitrobenzene with tailing edges, and the retention times significantly shortened with increasing sample volume.This is consistent with the type of sorption isotherm which is convex to the axis of sorption (Figure 1). The dependence of the retention volume on the equilibrium sorbate concentration in the mobile phase (for all sorbates the retention decreased with increasing concentration) was processed by polynomials of second and third degrees [equation (2)].The coefficients of equation (2) were calculated by the regression analysis method; next, the sorption isotherms were calculated using equation (3). The sorption isotherms for anisole, nitrobenzene and benzene calculated by the Glueckauf method and by equation (3) using the coefficients of equation (2) (see Table 1) are presented in Figures 1 and 2.There is a good agreement between the values of sorption calculated by the Glueckauf method and from the retention volumes calculated by virial equation (3) (Table 2) and those obtained by the static sorption method (Figure 1). Note that the sensitivity of the method suggested is higher than that of the Glueckauf method in calculations of slow-adsorbed substances, for example, the sorption isotherm of benzene.Table 2 indicates that the retention volumes decrease with increasing sample volumes; this corresponds to a convex isotherm. However, a linear sorption isotherm calculated by the Glueckauf method and inconsistent with experimental data (with the peak shape and changes in the retention time) was obtained. This can be explained by lower sensitivity of measurements of the chromatographic peak areas in comparison with the retention volumes.Thus, the proposed method allows us to measure rapidly isotherms of sorption from a solution with a sufficient accuracy in the region of low concentrations. In this method of processing of chromatographic data, as well as in the Huber method,7 the influence of diffusion broadening of chromatographic peaks is minimised (unlike the Glueckauf method).This work was supported by the Russian Foundation for Basic Research (grant no. 98-03-32690). References 1 E.Glueckauf, J. Chem. Soc., 1947, 1302. 2 E.Glueckauf, Disc. Faraday Soc., 1949, 7, 199. 3 S. I. Zverev, O. G. Larionov and K. V.Chmutov, Zh. Fiz. Khim., 1974, 48, 1556 (Russ. J. Phys. Chem., 1974, 48, 916). 4 A.V.Kiselev, Molekulyarnye vzaimodeistviya v adsorbtsii i khromatografii (Molecular Interactions in Adsorption and Chromatography), Vysshaya Shkola, Moscow, 1986 (in Russian). 5 A. V. Kiselev and Ya. I. Yashin, Gas-adsorption chromatography, New York, Plenum Press, 1969. 6 J. F. K. Huber and A. I. M.Keulemans, in Gas Chromatography, ed. M. Van Swaay, Butterworth, London, 1962, p. 26. 7 J. F. K. Huber and R. G. Gerritse, J. Chromatogr., 1971, 58, 137. 8 F. Riedo and E. J. Kovats, Chromatographia, 1982, 239, 1. 9 W. A. Steel and G. D. Halsey, Jr, J. Chem. Phys., 1954, 22, 979. 10 W. A. Steel, in The Solid–Gas Interface, ed. E. A. Flood, Dekker, New York, 1967, vol. 1, p. 199. 11 R.A. Pierotti and H. E. Thomas, in Surface and Colloid Science, ed. E. Matijevic, Wiley Interscience, New York, 1971, vol. 4, p. 93. Table 2 Retention and sorption values of sorbates calculated by different methods. Corrected retention volume V'R/ml Equilibrium concentration of sorbate in the column c/mmol dm–3 Calculated sorption a/mmol g–1 the Glueckauf method virial equation (3) of third degree virial equation (3) of fourth degree 3044 0.79 12.64 11.38 12.14 2871 1.37 21.10 19.42 20.54 2582 2.21 31.57 30.10 31.50 2297 3.33 46.64 44.49 45.86 2072 4.56 51.91 58.70 59.64 1857 5.62 69.81 70.06 70.40 1816 6.53 81.44 79.19 78.91 1371 12.32 125.90 125.42 121.45 1039 16.37 146.60 147.95 144.04 824 22.15 179.55 170.97 171.93 555 30.54 217.02 197.19 203.89 3116 4.42 85.41 71.26 79.08 2179 8.72 137.36 127.41 135.95 1795 12.0 168.03 162.69 169.56 1521 17.0 216.01 206.02 209.75 1157 20.6 223.51 230.15 232.59 1047 26.5 269.01 261.38 264.72 863 31.7 283.93 283.03 289.61 826 34.7 317.00 294.39 302.83 669 40.4 351.48 315.73 324.0 159 25.1 23.5 20.58 21.03 152 40.9 36.1 32.83 33.26 149 53.0 47.2 41.90 42.33 145 64.6 57.2 50.37 50.83 143 77.2 69.4 55.83 56.29 Anisole Nitrobenzene Benzene c/mmol dm–3 a/mmol g–1 80 70 60 50 40 30 20 10 0 0.02 0.04 0.06 0.08 0.10 Figure 2 Adsorption isotherms of benzene from n-hexane on Silasorb-300 hydroxylated silica calculated by ( ) virial equation (3) of fourth degree and ( ) the Glueckauf method.Received: 15th July 1999; Com. 99/1519

ISSN:0959-9436     

出版商:RSC    

年代:2000

数据来源: RSC