Kinetics of Ion-Pair Formation on Variable-Charge Minerals Using the Frequency Domain Method

Soil Chemistry Kinetics of Ion-Pair Formation on Variable-Charge Minerals Using the Frequency Domain Method Predicting nutrient behavior is ever more critical to understanding and management of the environment, Xiufu Shuai* particularly in highly weathered and tropical environments. Th e fate of nutrients in the environment seems heavily Water Resources Research Center infl uenced by the kinetics of ion-pair formation on the surfaces of variable-charge minerals coupled with transport Univ. of Hawaii at Manoa processes. Th e objective of this study was to generate the coupled processes in column experiments and estimate the Honolulu, HI 96822 reaction rates using the frequency domain method. Columns were packed with ground natural minerals (gibbsite, goethite, and hematite). Th e input signals were designed as a sinusoidal change in NaNO3 concentration within Russell S. Yost −1 −1 Dep. of Tropical Plant and Soil Sciences 0.1 and 0.2 mmol L and constant pH 4.0, and the highest frequency of the input signals was 0.714 min . − + Univ. of Hawaii at Manoa Th e input and output signals of NO3 and H concentrations were monitored by ultraviolet–visible light and Honolulu, HI 96822 pH detectors, respectively. A mathematical model was derived to describe the diff usion process of a counterion from aqueous solution to β plane, the recombination–dissociation reaction between a charged surface site and the counterion, and the coupled transport process described by the convection–dispersion equation. Results showed that the output signals were dominated by the designed frequency and thus the coupled processes were linear. Th e + − aqueous H concentration changed linearly with that of the aqueous NO3 concentration. Th e mathematical model fi t the measured transfer function of the processes. Th e estimated rates of recombination of ion pairs were 52.0, 30.5, and 8.0 L mol−1 min−1, and the estimated rates of dissociation of the ion pair were 0.189, 0.256, and 0.285 min−1 for the natural gibbsite, goethite, and hematite, respectively. Abbreviations: CDE, convection–dispersion equation; RA, relative amplitude; TLM, triple-layer model; XRD, x-ray diff raction. inerals with variable surface charge such as gibbsite, goethite, and hematite Mare abundant in soils and important in environmental chemistry, especially in highly weathered soils of the tropics (Uehara and Gillman, 1981). Surface complexation models, such as the constant capacitance model (Schindler and Kamber, 1968; Hohl and Stumm, 1976), the diff use layer model (DLM) (Stumm et al., 1970; Huang and Stumm, 1973; Dzombak and Morel, 1990), the triple-layer model (TLM) (Yates et al., 1974; Davis et al., 1978; Hayes et al., 1991), and the charge-distribution multisite complexation (CD-MUSIC) model (Hiemstra et al., 1989a,b, 1996; Hiemstra and Van Riemsdijk, 1996) are being used to describe the surface chemistry of variable-charge colloids. In both the DLM and the TLM, + + − − ions such as Na , K , NO3 , Cl can be nonspecifi cally adsorbed at the electric diff use layer by electrostatic attraction or repulsion. In the TLM, the counterions can be adsorbed at the β plane by ion-pair formation with the charged surface sites. A kinetic study has shown that ion-pair formation on the β plane in the TLM is a physical diff usion process through the electric double layer with a subsequent recombination–dissociation reaction between charged sites on the surface of goethite and the counterion on the β plane (Sasaki et al., 1983). Surface reactions are usually coupled with transport processes in chemically and physically heterogeneous soil systems, and thus modeling and parameter esti- Soil Sci. Soc. Am. J. 74:1568–1576 Published online 3 Aug. 2010 doi:10.2136/sssaj2009.0161 Mention of a specifi c brand of equipment does not imply an endorsement by the University of Hawaii or the authors. Received 28 Apr. 2009. *Corresponding author ([email protected]). © Soil Science Society of America, 5585 Guilford Rd., Madison WI 53711 USA All rights reserved. No part of this periodical may be reproduced or transmitted in any form or by any means, electronic or mechanical, including photocopying, recording, or any information storage and retrieval system, without permission in writing from the publisher. Permission for printing and for reprinting the material contained herein has been obtained by the publisher. 1568 SSSAJ: Volume 74: Number 5 • September–October 2010 mation of the coupled processes are important for more realistic sociation reaction. Th e recombination–dissociation reaction of descriptions of the fate of nutrients and contaminants. Th e ki- counterions with charged surface sites to form an ion pair in the netics of ion-pair formation of ions as counterions at the surface β plane is described as of variable-charge soils is very helpful in predicting their mobil- + ⎯⎯kr→ CIββSS←⎯⎯ -CI [2] ity and transport in the environment. Th e kinetic methods used kd to study surface reactions, however, such as the electric fi eld pulse technique (Sasaki et al., 1983) and the pressure-jump method where S and S–CIβ are the concentrations of charged surface (Astumin et al., 1981), cannot be used to study the coupled pro- sites and the ion pair in the β plane, respectively, and kr and kd cesses because the time range of the pressure jump is on a scale are the rates of the recombination and dissociation reactions, re- −5 of 10 s (Sparks, 1989), which is much faster than transport spectively. Typically, all species, CIβ and S–CIβ, in the β plane processes on a scale from minutes to days. Recently, a frequency are considered adsorbed at the surface of minerals. domain method was developed by Shuai and Yost (2007) to Th e intrinsic equilibrium constant of the diff usion process study the transport of inert tracers in columns using the sinu- through the electric double layer is soidal change in tracer concentrations with time as input. Th e ≡ kf K diffusion [3] advantage of this method is that the spectra of the input were of k the widest passband (the portion of a spectrum between limit- b ing frequencies that is transmitted with minimum relative loss Th e intrinsic equilibrium constant of the recombination–disso- or maximum relative gain in a dynamic system) and the high- ciation process of the counterion is est amplitude, which permitted stimulation of the transport k K int ≡ r process and measurements with a maximum signal/noise ratio counterion [4] kd (Shuai and Yost, 2007). Th is method can also be used to measure Transport Process of the coupled surface reactions and transport processes by applying an Convection–Dispersion Equation active tracer of interest to columns in the infl uent solution. Th e frequency domain approach has not been reported in column Th e transport process of the convection–dispersion equa- experiments for the study of the coupled processes of ion-pair tion (CDE) has been widely used to describe transport in soils formation and transport. (Nielsen and Biggar, 1961; Biggar and Nielsen, 1967): Th e objectives of this study were (i) to measure the kinet- ∂∂ccc2 ∂ ics of ion-pair formation at the surfaces of three variable-charge RD=− V [5] ∂∂tzz2 ∂ minerals (natural gibbsite, goethite, and hematite) coupled with a transport process using the frequency domain method, and (ii) where c is the resident concentration of solute, t and z are the to estimate the reaction rates of ion-pair formation at the sur- time and space coordinates, respectively, D is the dispersion coef- faces of the variable-charge minerals. fi cient, V is the pore-water velocity, and R is the retardation fac- tor, which was 1 in this study. MATHEMATICAL MODELS AND For a fi nite system for which the exit boundary condition ALGORITHM FOR PARAMETER ESTIMATION does not aff ect the solute concentration inside the column, the Process of Ion-pair Formation at the Surfaces initial and boundary conditions are of Minerals cz(),0= 0 Th ere are two processes in the mechanism of ion-pair for- ∞= mation at the surface of goethite (Sasaki et al., 1983). Th e fi rst ct(),0 [6] process is diff usion of a counterion from an aqueous phase to the ctut()()0, = β plane in the TLM; the counterion is bound electrostatically to cLt()(), = yt the particle surface but not to any specifi c site. In this study, the physical diff usion process through electrical layers is described as and the transfer function of the CDE to describe the relationship between the input u(t) and the output y(t) is ⎯⎯kf→ CIaq ←⎯⎯ CIβ [1] kb Ys() Gs()≡ Us() where CIaq and CIβ are the concentrations of counterions in [7] aqueous solution and in the β plane and k and k are the for- ⎡⎤LV⎛⎞4 Ds f b =−+exp⎢⎥⎜⎟ 1 1 ward and backward rate constants, respectively, for adsorption ⎣⎦⎢⎥2DV⎝⎠2 and desorption of the counterion through the electrical double layer (Sasaki et al., 1983). where L is the length of the column, Y(s) and U(s) are the Laplace Th e second process is the movement of the counterion in transform of y(t) and u(t), respectively, and s is the Laplace op- the β plane until it fi nds a charged surface site and becomes a erator (s = jω, where j is an imaginary unit and ω is the angular site-bound counterion, which is termed the recombination–dis- frequency) (Jury and Roth, 1990; Shuai and Yost, 2007). SSSAJ: Volume 74: Number 5 • September–October 2010 1569 Mathematical Model for Ion-Pair Formation at ⎡⎤⎛⎞kS⎣⎦⎡⎤ the Surfaces of Minerals Coupled with Transport Hs()=+ s⎢⎥11 K ⎜⎟ +r diffusion ⎜⎟+ [18] ⎢⎥⎝⎠skd Ion-pair formation at the surface of a variable-charge min- ⎣⎦ eral was coupled with transport (the CDE) along the columns.

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