Environ. Sci. Technol. 1993, 27, 943-948
Determination of Nonlinear Adsorption Isotherms from Column Experiments: An Alternative to Batch Studies Chrlsta S. Burglsser, Mirosiav Cernk, Michal Borkovec,' and Hans Stlcher
Institute of Terrestrial Ecology, Federal Institute of Technology, Grabenstrasse 3, 8952 Schlieren, Switzerland From measured breakthrough curves of sorbing chemicals in local equilibrium, one can obtain the entire nonlinear adsorption isotherm by a simple integration. The feasibility of the procedure is demonstrated by comparing nonlinear adsorption isotherms obtained from column experiments with batch studies for sorption of a heavy metal and an organic cation on sand. The advantages and drawbacks of this technique for the measurement of isotherms on materials of environmental origin are discussed. 1. Introduction Description of sorption processes of chemicals from a fluid phase onto a solid matrix plays a fundamental role in most disciplines of environmental science (1, 2). Particularly in soil science and subsurface hydrology, this type of information is essential to estimate the mobility of pollutants such as heavy metals, radionuclides, and organic compounds in soils, groundwater aquifers, and fractured rocks (3-7). Such results allow one to assess the subsurface water quality risks near contaminated sites. The sorption equilibrium is usually characterized by the adsorption isotherm. A linear isotherm is completely determined by the distribution coefficient while in the case of a nonlinear isotherm the entire functional dependence must be determined (8). Measurements of isotherms are commonly obtained in the laboratory by performing batch experiments. Such experiments in which the adsorbate is added to the sorbent in an aqueous suspension have been used in numerous studies (3, 8-10). Such experiments are routinely performed in many environmental science laboratories, and one can easily study sorption processes with time constants of days to weeks. In spite of the apparent ease of such experiments, many sources of errors are possible (11). For example, the separation of the medium-to-high molecular weight fraction of organic matter from sorbent cannot often be achieved by ordinary centrifugation but is probably only feasible by ultracentrifugation, dialysis, or ultrafiltration techniques (9). Such problems are probably one of the most important reasons for the observation of the particle concentration effect, that is the dependence of the distribution coefficient on the solid-to-solution ratio (10). The common procedure of the concentration measurement in the supernatant leads to large experimental errors in the case of weak adsorption and requires laborious procedures to measure the sorbed amount (12). Finally, particle ruboff and milling during shaking leads to apparently larger sorption capacity and is quite difficult to control. These difficulties inherent to the classical batch experiment have motivated the development of alternative techniques such as the use of flow-through reactors for the determination of sorption parameters (13-1 7). An-
* To whom correspondence 0013-936X/93/0927-0943$04.00/0
should be addressed. 0 1993 American Chemical Society
other alternative to the classical batch experiment which allows simple and rapid measurements of an entire, possibly nonlinear adsorption isotherm relies on column experiments and the use of techniques borrowed from nonlinear chromatography. While such methods have a long history in the field of chemical engineering (18-201, examples of their use in environmental sciences are rare (211. The aim of the present paper is to introduce such a column technique for the measurement of nonlinear isotherms. We shall demonstrate its practical feasibility with a few selected experimental studies and discuss its advantages and disadvantages for environmental applications. The method employsa simple column experiment for the measurement of adsorption isotherms. While the determination of retention factors and the evaluation of the distribution coefficient for linear adsorption isotherms is well-documented in environmental science literature (1, 3), one has to consult textbooks on nonlinear chromatography for discussions on the more complicated behavior of solutes obeying nonlinear adsorption isotherms (22,23). Nonlinear behavior is very common for natural sorbing media such as soils and aquifer materials. As an alternative to batch experiments with these materials, one can often pack a column with the material in question and elute the solution of interest. Results of such experiments can be easily interpreted, and the entire nonlinear adsorption isotherm can be extracted. Column techniques might, therefore, present a welcome alternative to the classical batch studies. The column experiment is carried out near the relevant solid-to-solution ratio, and the percolating solution may be easily adjusted to the composition of interest (e.g., composition of the groundwater or rain). Another nice feature of the column experiment is that from the appearance of the breakthrough response one can unambiguously distinguish the different shapes of the isotherm such as linear, convex, or concave. The procedure gives very accurate quantitative results and can often be automated for the measurement of the entire isotherm in a single experiment. The main disadvantage of the column experiment for the determination of adsorption isotherms is the necessity of local equilibrium in the column which may lead to a prohibitively long duration of experiments. 2. Theoretical Section In this section the mathematical justification for the present method is briefly summarized. Details can be found in classicaltreatments of nonlinear chromatography (22-25). The concentration c ( x , t ) of a sorbing chemical per unit pore volume of the mobile phase is described by the convection-dispersion equation
where D is the dispersion coefficient and v = q/B, the travel velocity, which is related to the porosity 0 and to the Darcy Envlron. Sci. Technol., Vol. 27, No. 5, 1993 943
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Flgure 1. Schematic representation of the response of the chromatographic column for different adsorption isotherms (top). The column breakthrough of a step concentratlonchange without dispersion effects Is shown (below) for dlfferent isotherms: (a) linear, (b) convex, and (c) concave.
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flow q (solvent volume per unit area and time). The latter quantity can be expressed in terms of the overall flow rate through the column F (mL/min) as q = F / A where A represents the total cross-sectional area of the column. In the case of no adsorption, the total concentration of the species ctot is equal to the concentration in solution c (Le., ctot = c ) and eq 2.1 can be solved analytically (24).In this case, the species is called a conservative (or ideal) tracer. The travel time distribution of the tracer at the end of the column of length L can be characterized by an average time t o = L / v and a standard deviation u. The latter quantity can be related to the column Peclet number Pe = LuiD by a2/to2= 2/Pe or to the plate number J by u2/to2 = 1/J(for approximately J > 100) (25). For an adsorbed species, the total concentration is given by the sum of the concentration in solution c and the concentration on the sorbate, namely (2.2) Ctot = c + PCa We have introduced the amount of the sorbed species per unit mass of sorbent ca and the mass of sorbent per unit pore volume p = p,(l - @ / e (psis the density of the sorbent matrix). In the case of rapid adsorption (localequilibrium), the concentration of the adsorbed species ca is a unique function of the concentration of the dissolved species c. In the simplest case of a linear adsorption isotherm (i.e., ca = KDC; K Dbeing the partition coefficient) the shape of the breakthrough curve is the same as the breakthrough of a conservative tracer. The breakthrough is just delayed . type in time by the retention factor R = 1 + ~ K DThis of behavior is illustrated in Figure l a with dispersion effects neglected. (The abscissa t/tois equivalent to the number of pore volumes eluted.) Due to the linearity of the isotherm, the value of the retention factor does not depend on the concentration of the chemical. In the case of anonlinear isotherm, however,the response depends on the concentration. In the case of a step input, one usually observes either a self-sharpening or a diffuse front (22,25-27). (The case of combined fronts will not be considered here.) Suppose the isotherm is convex (i.e., d2cddc2 < 0, see Figure lb), then according to the Golden rule (25,28) a step concentration increase at the column input leads to a self-sharpening front, and in the case of step decrease, a diffuse front will be formed (22,25,26). This behavior is caused by the fact that the retention of the chemical decreases with increasing concentration in solution. In the case of the adsorption front, the retention 044
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The concentration at the outlet of the column c(L,t) is determined by L = (dx/at),t(c)or, using eq 2.3, one finds that (2.4) The concentration dependent retention time t ( c ) can be easily measured at the column outlet and represents essentially the derivative of the adsorption isotherm. An experimental record of the retention time t ( c ) can be integrated to obtain the adsorption isotherm
The overall retention factor R ( c ) , which represents the
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area of the normalized breakthrough curve, depends on the input concentration c and must be equal for the selfshapening and the diffuse front. Its value turns out to be (25)
In order to show that the role of the dispersivity is indeed small we have performed numerical studies using the boxmodel (24) which represents a finite difference approximation to eq 2.1. In Figure 3, results at finite dispersion for the Freundlich isotherm (same parameters as in Figure 2) are presented. As long as the dispersion is small (large Peclet number), the effect of the dispersion on the diffuse part of the isotherm is indeed small. In our experience, column Peclet numbers Pe > 50 can be considered as sufficiently large for the determination of isotherms. 3. Experimental Section
Sorbent Material. Experiments were carried out with a silica sand (Seesand, Siegfried), which was sieved down to size fractions of 125-250 or 250-500 pm and washed repeatedly with dilute nitric acid and distilled water before use. The sand contains 99 % SiOz, with traces of Na, Al, and Ca as determined by X-ray fluorescence spectroscopy and consists mainly of cristobalite, which has been identified by X-ray diffraction. The relatively high BETarea of 0.1 m2/g is probably caused by the presence of several cracks in the surface, which are visible in scanning electron micrographs. The density of the sand has been determined by an air pycnometer and amounts to 2.31 g/cm3which is in good agreement with reported values for cristobalite (30). Sorbing Chemicals. All chemicals unless indicated otherwise were obtained from Merck (p.a. quality). In a first set of experiments, we have employed cadmium nitrate dissolved in a 0.01 M imidazole buffer adjusted to pH = 7.9 with nitric acid and to an ionic strength of 0.01 M with sodium nitrate. In a second set of experiments, we have used methylene blue (Janssen Chimica, high purity) dissolved in an acetate buffer of pH = 4.7 and an ionic strength of 0.05 M. Batch Experiments. The sand was equilibrated for 24 h under gentle shaking in a thermostated container at
25 "C. The supernatant was removed after sedimentation, filtered through a membrane filter (0.45 pm, Schleicher & Schuell), and analyzed by atomic absorption spectroscopy (AAS, Varian 400) or photometry at 665 nm (Philips PU 8620). Column Experiments. The sand suspended in water was packed into glass chromatography columns of 24-mm diameter and 30-40-cm lengths. The feeding solutions were passed through a degasser (Erma). They were pumped using an HPLC pump (Jasco) at flow rates between 0.2 and 3 mL/min through the column past an injector (for pulse experiments) and two-way valve (for step experiments) into the thermostated column. The outflow of the column has been monitored with an UV/ VIS flow-through detector (Linear UVIS 2041, which was connected to a PC for data accumulation. For metal analysis, samples collected by a fraction collector (Pharmacia Redi Frac) have been analyzed by AAS. The flow rate has been determined by a flow meter (Humonics Optiflow 1000). In order to characterize the columns, we first performed pulse experiments with conservative tracers in order to determine the average travel time t G = L/vand the column Peclet number. Potassium bromide, sodium nitrate, sulforhodamine (Aldrich), and sulfaflavine (Aldrich) dissolved in distilled water have been injected from a sample loop of 50-500 p L and measured on-line. Since all these chemically different substances showed the same breakthrough response, we were assured to deal with conservative tracers. The average travel time and the pulse width have been determined by fitting the pulse response data to the analytical solution of the convection dispersion equation, eq 2.1, using a nonlinear least-squares procedure (24, 29). These results were in good agreement with calculations based on the first and second moment of the column output. By comparing the travel velocities with the Darcy flux, we have observed a porosity of 0 = 0.46 f 0.02 from the column experiments. Using the measured density of the sand and the mass of the sand in the known volume of the column, we obtain an independent estimate of the porosity 0 = 0.44 f 0.01, which is in good agreement with the above value. The columns were quite long (3040 cm) and were carefully packed in order to achieve as high Peclet numbers as possible (typically Pe = 500-1000). The observed dispersivities were independent of flow velocity and close to the value for glass beads of the same size as the sand fraction (31). (For velocities v = 0.2-3 x lo-* m/s, the dispersivities are Dlv = 0.3 and 0.6 mm for the 125-250-pm and the 250-500-pm size fraction, respectively.) 4. Results
A first set of step breakthrough experiments has been performed with cadmium in a buffered solution at pH = 7.9. The results are shown in Figures 4 and 5. As can be seen from Figure 4, the breakthrough curves for different flow rates superpose, which proves that the sorption equilibrium is established on the time scale of the column experiment. In Figure 5 one observes the typical sharp adsorption front and diffuse concentration independent desorption front of a sorbate obeying a convex isotherm. Since there is a substantial tailing of desorption front, we can conclude that the isotherm does not attain linearity in the concentration range considered. We have used the Environ. Sci. Technol., Vol. 27, No. 5. 1993
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Flgure 4. Breakthrough curves through a column packed with sand (125-250 pm) of cadmium step input for 0 It/fo< 3.8 (arrow) at a concentratlon of 17.5 pM at two different flow velocities v [(U)0.457 X m/s, (0) 2.38 X m/s]. The superposltion of the data points confirms the absence of kinetic effects. 200
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Flgure 6. Adsorption isotherm of cadmium on sand. Solid line is calculated from the diffuse desorption front of the breakthrough curve shown in Figure 5. Data points represent resultsof Independent batch experiments at a solid-to-solution ratio of 250 g/L (0)and at different values between 50 and 1000 g/L(O). (Inset: double logarithmic plot).
The least-squares spline interpolation scheme represents a consistent procedure which allows us to obtain a correct estimate of the adsorption isotherm essentially down to the lowest concentrations measured in the elution curve. This interpolation scheme yields automatically the necessary extrapolation of the breakthrough curve for c 0 which is needed for the integration. One can employ equally well a simpler integration scheme (e.g., trapezoidal rule) for the integration of the desorption front. The trapezoidal integration technique becomes somewhat more sensitive to experimental errors but gives in the present case reasonably good agreement with batch data (relative root mean square deviation of 102% ). The problem is rather the necessity of performing the extrapolation of the elution curve down to zero “by the eye”. In the above example, the zero point found by the least-squares spline lies at tlto = 6.2. Using the same value in the trapezoidal integration, we obtain good agreement even at the lowest concentrations measured. Doubling this zero point value (tito = 12.4), the agreement in the high concentration regime is still good, but for low concentrations the isotherm calculated from the column overestimates the batch results by 30%. A second, quite differently behaving, sorbate considered was methylene blue, which serves as an example of sorbing organic cation and obeys a concave adsorption isotherm. This fact is quickly uncovered by considering the breakthrough behavior of this chemical shown in Figure 7. In contrast to the previous example, the adsorption front is diffuse while the desorption front is sharp. The shape of the breakthrough curve is independent of the flow rate which reveals chemical equilibrium on the time scale of the column experiment. In this case, the adsorption front contains the relevant information on the shape of the isotherm. The evaluation of eq 2.5 using the least-squares spline integration procedure yields an isotherm which is shown as the solid line in Figure 8. Again, we observe very good agreement with independent batch experiments. Note that the isotherm is concave in the lower concentration range only (up to 15 pmol/L). For higher concentrations (not shown in Figure 7) the isotherm appears S-shaped.
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Flgure 5. Equilibrium breakthroughcurves through a column packed with sand (125-250 pm) of cadmium step input for 0 5 t / f o < 3.8 (arrow) at two different feed concentrations [(U) 175 pM, (0) 17.5 pM]. Note the similarity with Figure 2.
experimental data points of the desorption front (decreasing part), and these data points were interpolated using a least-squares spline fit (32). This interpolating function has been numerically integrated using eq 2.5 to obtain the adsorption isotherm. The calculated isotherm from the column breakthrough is shown as the solid line in Figure 6. In the same figure, results of the batch experiments are also presented. One can observe very good agreement between the isotherms obtained from batch and column experiments. As can be concluded from the doubly logarithmic plot (inset in Figure 6), the procedure is able to catch the proper shape of the isotherm over a few orders of magnitude of the concentration. The relative root mean square deviation of the batch points from the column result is approximately 5 2% over the entire concentration range of the desorption front measured. We have also performed some batch experiments in order to address the question of particle concentration effect in the present experiments. The results obtained by covering a range of solid to liquid ratios between 50 and 1000 g/L at one particular cadmium concentration are also shown in Figure 6. No influence of the particle concentration on the batch results could be observed. 948
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5. Discussion
The aim of this paper was to show that column experiments can be used for accurate measurements of
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Flgure 7. Breakthrough curve through a column packed with sand (250-500 pm) of methylene blue step input for 0 Itho < 8.2 (arrow) at a concentration of 9.91 pM.
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nonlinear adsorption isotherms. The experiment consists in performing step breakthrough experiments with the chemicals of interest through a packed chromatographic column of a high Peclet number (typically Pe = 100-1000) with the sorbent in question. Using a simple numerical integration of the observed diffuse front, one obtains the complete adsorption isotherm. The measured isotherms agree very well with independent batch studies. If one is able to detect the chemical on-line (e.g., by UViVIS, fluorescence, conductometry), the procedure can be entirely automated and allows one to extract the complete isotherm in a single experiment. Particularly, if sorption experiments have to be performed on the same sorbent but under varying conditions (e.g., ionic strength, additives, temperature), the column experiment is very versatile. While we have focused on nonlinear isotherms, the column technique is obviously also applicable in the case of linear isotherms. The linear case is easily recognized from the breakthrough curve since the adsorption and the desorption front have exactly the same shape. The observed retention factor determines the value of the partition coefficient. Let us briefly summarize the main advantages and disadvantages of the method when compared with classical batch experiments. The main advantage of the column method is the ease of performing automated and very accurate measurements of adsorption isotherms under different experimental conditions on the same sorbent
avoiding essentially all problems inherent to batch experiments. A further advantage of the column is that one works at a high solid to solution ratio close to the one encountered in the natural system of interest. This leads to larger sorbed amounts than in traditional batch experiments. If the sorption capacity is very high, one may employ very short columns or the medium can be diluted with inert sand or glass beads. The latter technique may also be used for experimentally with poorly aggregated soils and finely structured materials. Experiments with these materials may be also carried out using HPLC techniques and higher pressures (33). During the initial leaching of the column, suspended organic matter or inorganic colloidal particles will be washed out and the experiment is performed precisely in the percolating solution. In batch studies, vigorous shaking disperses the material, and one has to use advanced analytical techniques such as ultracentrifugation or ultrafiltration in order to achieve the proper separation of the solid and liquid phase. Another serious problem inherent to batch studies is the surface ruboff and particle breakup during shaking. We have observed that in batch experiments these types of effects can often lead to incorrect results which are very difficult to recognize without the availability of independent column data. The main disadvantage of the column method lies probably in the often long duration of the experiment. In the column experiment, one can unambiguously recognize kinetic effects by changingthe flow velocity (29). However, the necessary experimental times may turn out to be prohibitively long. The time needed to reach equilibrium in the column is necessarily much longer than in a batch experiment. In the column experiment, one essentially carries out a succession of batch experiments for each plate. In a well-packed column, the number of plates is larger (proportional to the column Peclet number), and one consequently needs much longer equilibration times. Another disadvantage is that every new sorbent has to be packed into a chromatography column of a high Peclet number (Pe > 100)which must be characterized by a (quite simple) tracer experiment. Packing the material is usually no problem for sandy aquifer materials or aggregated soils. Preliminary experiments on whole soils have been performed in our laboratory, and the results are encouraging.
Acknowledgments We thank Ph. Behra, F. Helfferich, M. Sardin, A. Scheidegger, D. Schweich, and J. C. Westall for essential comments and enjoyable discussions. Note Added in Proof. Very recently, a similar method has been applied to determine ion-exchange isotherms in soils (34).
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Received f o r review August 24, 1992. Revised manuscript received December 22, 1992. Accepted January 14, 1993.
