Environ. Sci. Technol. 2005, 39, 6757-6764
A New Method To Estimate Adsorption Energies between Cations and Soil Particles via Wien Effect Measurements in Dilute Suspensions and an Approximate Conductivity-Activity Analogy LI CHENGBAO,† ZHAO ANZHEN,† AND S H M U L I K P . F R I E D M A N * ,‡ Institute of Soil Science, The Chinese Academy of Sciences, Post Office Box 821, Nanjing 210008, China, and Institute of Soil, Water, and Environmental Sciences, Agricultural Research Organization, The Volcani Center, Bet Dagan 50250, Israel
Measurement of the Wien effect (increased electrical conductivity at strong electrical fields) in soil suspensions is proposed as the basis of a new method to characterize energy relationships between cations and soil particles. The simplified theory behind the method, the working principle of the short high-voltage pulse apparatus, and the measuring procedure are outlined briefly. The new method was used to evaluate the adsorption energies of two monovalent (Na, K) and two divalent (Ca, Cd) cations on yellowbrown soil and black soil particles, assuming an analogy between the activity of the cations and their contribution to the electrical conductivity of the suspension. Both the mean free bonding energies, ∆Gbo, and the adsorption energies, ∆Gad, of the cations for these two soils increased in the order: Na < K < Ca < Cd. Under the conditions of our experiments, estimated ∆Gbo ranged from 4.7 to 6.4 kJ mol-1 and from 7.0 to 8.2 kJ mol-1 for mono- and divalent cations, respectively. The bonding energies obtained with the new method were similar to those determined previously by ionic activity measurement. The determined mean adsorption energies of cations desorbed at a field strength of 100 kV cm-1, for example, ranged from 0.7 to 1.2 kJ mol-1 and from 1.9 to 2.3 kJ mol-1 for mono- and divalent cations, respectively.
Introduction Most soil minerals are negatively charged in ambient conditions, in which the pH is close to neutral, and adsorb cations from the soil solution electrostatically. These cations may act as plant nutrients (e.g., K+, NH4+, Ca2+, Mg2+, Fe2+) or as environmental pollutants (e.g., Al3+, heavy-metal ions, cationic pesticides). The prediction of the transport and retention of these cations in soils necessitates a better understanding of the interactions of the cations with the active, high-surface-area clay minerals and organic matter. Another reason for studying these interactions is the need * Corresponding author phone: +972-3-9683424; fax: +972-39604017; e-mail:
[email protected]. † The Chinese Academy of Sciences. ‡ Institute of Soil, Water, and Environmental Sciences. 10.1021/es050070b CCC: $30.25 Published on Web 07/30/2005
2005 American Chemical Society
for better evaluation of the contribution of the adsorbed cations (surface conductivity) to the bulk electrical conductivity of the soil, when the latter is measured to determine the electrical conductivity (salinity) of the soil solution (1). Traditionally, soil scientists have described the spatial distribution and adsorption energies of counterions on charged surfaces in terms of the classical double-layer models that address the negative charge of the particles and the (excess) positive charge surrounding them (2, 3). Many variants of the classical diffuse double layer (DDL) models were proposed, to account for negative adsorption of anions, specific (nonelectrostatic) adsorption of the cations on localized adsorption sites, the hydration status of the adsorbed counterions, variably charged surfaces, amphoteric (containing positive, negative, and neutral sites) surfaces, competition among different adsorbed cation species, variation of the water properties (dielectric constant) near the solid surfaces, nonflat geometry of the adsorbent surface, and overlapping of the DDLs of adjacent particles (4-11). Nevertheless, we still lack understanding of this complex phenomenon, mostly because of limited ability to directly characterize the relevant features of the electrostatic interactions of the cations with the highly variable clay minerals (12, 13). In the middle of the 20th century, Marshall proposed the concept of the mean free bonding energy to indicate the bonding strength of ions with soil particles; he developed an experimental method for evaluating it by measuring the ionic activity (14, 15) and used this method to study the competitive adsorption of K, Ca, and Mg on several clay minerals. However, Marshall’s proposed method was not generally adopted, because the activity of an ionic species is not thermodynamically well determined, and because the usual method for measuring ionic activities with ion-selective electrodes has two major weaknesses: the limited specificity of the indicating electrode, and interference with the reference electrode by the liquid-junction potential. Subsequently, the concept of adsorption energy was used in studying the adsorption of, for example, herbicides on montmorillonite clays (16) and of cations on the surface sites of kaolinite under mildly acidic and mildly alkaline conditions (17). Blanchet (18), for example, used a simple chemical method to determine the adsorption energy (or desorption work) of potassium ions on clay particles, but this method has not been used in subsequent studies because of the long time needed to measure the adsorption isotherm from which the adsorption energy is calculated, and because this method can only be applied to a few monovalent cations such as K+ and Na+. Agbenin and van Raij (19) examined the process rates in addition to the energy relationships governing the simultaneous release of Ca, K, and Mg from variably charged soils to mixed ion-exchange resins. The trends in the enthalpy change, ∆H, and entropy change, ∆S, for the desorption of Ca, Mg, and K from the soils indicated that the binding energy for K was stronger than those for Ca and Mg. Soil chemists usually explain the interactions between various ions and clay minerals/soil particles in terms of the affinity parameter of a best-fitted Langmuir isotherm, whether the assumptions behind the originally derived Langmuir model are applicable or not (20-25). Recently, Critter and Airoldi (26) experimentally determined the ionexchange equilibrium on cationic latosol soils/aqueous solution interface and calculated the Gibbs free energy, ∆G, by linearization of the Langmuir equation. The negative ∆G values that they determined represent spontaneous ion VOL. 39, NO. 17, 2005 / ENVIRONMENTAL SCIENCE & TECHNOLOGY
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exchange with the hydrogenated soils, indicating high affinities of these soils for calcium and lead. To summarize, the investigation of energy relationship between cations and soil particles in the second half of the 20th century was based on indirect deduction, rather than on direct measurement. Because there is no practical and simple method to determine the bonding energy of cations to soil particles, this attribute was not studied and reported extensively. The electrical conductivity (EC) of an electrolytic solution is expected to be independent of the applied electrical field strength (E) according to Ohm’s law. A deviation from Ohm’s law, characterized by EC increasing with E, was experimentally discovered by Wien (27, 28) and was later named the Wien Effect (29-31). For simple (strong) electrolytes, the EC increase stems from diminishing relaxation and electrophoretic retardation forces when the “center ion” (the ion of reference) is moving sufficiently fast to prevent the formation of an asymmetric ionic atmosphere of counterions moving in the opposite direction. To produce a measurable increase in the solution EC requires electrical fields of the order of 107 V m-1, and the ultimate conductivity approaches that corresponding to the ionic mobility at infinite dilution, when no interaction of the flowing ions is expected. This increase is usually termed the First Wien Effect (30). For weak electrolytes, another reason for an increasing EC(E) relationship is that the strong applied electrical field increases the net dissociation of the uncharged salt (ion pair) into its ionic charge carriers: the strong electrical field increases the ionpair dissociation rate, but not its association rate (32). This is usually termed the Second Wien Effect or the Dissociation Field Effect (30, 33). Again, to achieve full dissociation of the ionic species requires very strong electrical fields, of the order of 107 V m-1. The first and second Wien effects in electrolyte solutions exposed to strong E have been thoroughly studied, they are sufficiently well understood and are predictable (32, 34-39), and they will not be discussed further in this Article. Our proposed method is to measure the EC(E) relationship of dilute aqueous suspensions of charged particles for field strengths up to about 2 × 107 V m-1, which is the dielectric strength of such suspensions. To the best of our knowledge, EC(E) measurements at such strong electrical fields have never been made previously by other research groups. One research group from the University of Hiroshima (Japan) performed experiments with pulsed electrical fields (E-jump method) to study the kinetics of Pb2+ adsorption-desorption on γ-Al2O3 in aqueous solutions at a fixed E of 1.6 × 106 V m-1 (40) and the kinetics of ion-pair formation on the surface of R-FeOOH (goethite) in aqueous solutions at variable E ranging from 0.3 × 106 to 4 × 106 V m-1 (41). However, according to our evaluation of the electrostatic fields surrounding the soil particles, and our preliminary Wien effect measurements (42, 43), these 10-times weaker electrical fields are not sufficient to strip the cations from the soil particles and to activate the Wien effect mechanisms involved in our proposed method. In previous publications, we described a novel apparatus for measuring the Wien effect (39), and Wien effect measurements in suspensions of electrodialyzed soil particles (42-44). In the present paper, we present a new method to determine the bonding energy and the adsorption energy of cations with soil particles, in terms of excess Gibbs free energy, ∆G, on the basis of measurements of the Wien effect in soil suspensions. The new method was used to evaluate the adsorption energies of two monovalent (Na, K) and two divalent (Ca, Cd) cations on yellow-brown soil and on black soil particles. In contrast to our previous studies (42-44), the soil particles in the present study were homoionic, that is, saturated with the investigated cation. 6758
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Theory Bonding Energy Evaluation. In suspensions of negatively charged soil particles saturated with a cationic species in distilled water, the cations adsorbed on the surfaces of the soil particles can partly ionize into the bulk solution and contribute to the electrical conductivity of the suspension. Results of preliminary measurements of the Wien effect in soil suspensions (43) showed that the suspension EC was basically unchanged as the field strength increased from 0 to 15 kV cm-1. Thus, the EC measured at the lowest applied field could be regarded as that corresponding to zero applied field, EC0. The electrophoretic mobility of soil particles is lower as compared to the mobility of dissolved cations. Furthermore, even if the particles are moving fast enough, under conditions of a relatively thin double layer (ratio of Debye screening length to particle diameter less than 0.1), the moving assembly of the negative particle with its surrounding positive countercharges is electrically neutral and does not contribute to the suspension EC (45, 46). Thus, it can be safely assumed that the contribution of the electrophoretic movement of the particles to the suspension EC under weak fields (15 kV cm-1) is negligible as compared to that of the ionized cations. The compliant counterpart to the electrical conduction mechanism in such suspensions must be from anions created by complex reactions occurring in the bulk of the suspension and near the electrodes (and perhaps from other cations as well). These fast reactions and the resulting anionic species are as yet not well known or understood. Therefore, instead of speculating about them, we preferred at this stage of our ongoing study to assume that the metallic cations and the unidentified anions made similar contributions to the overall suspension EC, that is, that the ionized cations accounted for half of the suspension EC at weak fields (EC0). If all of the saturation cations on the surfaces of the soil particles could ionize, the corresponding EC (ECu) (S m-1) should be:
ECu ) 2‚CEC‚cp‚λ
(1)
where CEC is the cation exchange capacity (mol-equiv kg-1), cp is the particle concentration of the suspension (kg L-1), and λ is the equivalent conductivity (S m-1 mol-equiv-1 L) of the ionized cation. Thus, the degree of dissociation or the fraction active of cations can be evaluated by
f0 ) EC0/ECu ) EC0/(2‚CEC‚cp‚λ)
(2)
Marshall’s formula for calculating the mean free bonding energy of a cation, in terms of Gibbs free energy, is (14, 15):
∆Gbo ) RT ln(ci/Ri) ) RT ln(1/f0)
(3)
where R is the universal gas constant (8.315 J mol-1 K-1), T is the thermodynamic temperature, Ri represents the activity of the cation, ci is the total concentration of the cation in a soil suspension, and f0 is the fraction active (equal to the activity coefficient, Ri/ci). The exact terminology of the energy to which we refer to along the manuscript should be “excess Gibbs free energy”, but, for brevity, we omit the “excess” and sometimes also the “free”. Also, for the sake of clarity, all bonding/adsorption energies will be assigned positive signs in this Article, thus, the missing minus sign in eq 3. If we assume an analogy between Marshall’s fraction active, which reacts with a specific electrode, and the fraction of ionized cations that contribute to the suspension EC, we can substitute eq 2 into eq 3, which yields an approximate expression for evaluating the mean Gibbs free bonding energy of cations to soil particles, from measurements of the weak field electrical conductivity, EC0:
∆Gbo ) RT ln(2‚CEC‚cp‚λ/EC0)
(4)
Marshall’s formula (eq 3) and its electrical current conductance analogy ( eq 4) are approximate thermodynamic relationships, because, for example, they disregard possible changes that take place in the adsorbent when the cations are “brought from infinity”. Referring to only two kinds of cations, either fully reactive/fully conductive (of an activity coefficient of one or mobility of free ions) or fully immobilized, provides a sketchy description of the actual DDL cation population that exhibits a varying degree of reactivity/ mobility. Furthermore, the averaging procedures of the reactivity/mobility of the distributed cations differ between Marshall’s and our methods. In the reactivity case, the specific electrode (/chemical potential) is averaged according to the natural logarithm of the activity coefficients; that is, this averaging procedure gives higher weighting to the smaller activity coefficients, which represent the more tightly bound cations, and this results in a geometric averaging of the distributed cation population. In contrast to this, the suspension EC is regarded as a simple summation of the contributions of all kinds of cations; that is, it represents the arithmetic average of the populations of cations of various degrees of ionization and various electrophoretic mobilities. Adsorption Energy Evaluation. Following the above description of a method for evaluating an average bonding energy of the total cation population, that is, the mean Gibbs free bonding energy, we now present a proposed method for evaluating the spectrum of adsorption energies, based on Wien effect, EC(E), measurements. By analogy to eq 3, the change in free chemical energy of a cation in a soil suspension when the suspension system changes from state (1) to state (2) at constant temperature and pressure is given by
∆G ) RT ln(R2/R1)
A scheme of the probability density function of the Gibbs free adsorption energies (PDF(∆Gad)) and the fractions of the adsorption energy spectrum derived from the Wien effect EC(E) measurement are depicted in Figure 1. The weak-field, EC0 measurement characterizes the whole spectrum of adsorption energies (colored area), its weighted mean termed above bonding energy:
(5)
where R2 and R1 are the activities of the suspension’s component, the cations in the present case, in states (2) and (1), respectively. Repeating our use of the approximate analogy between the electrophoretic mobility and the activity of the ionized cations results in
R2/R1 ) EC2i/EC1i
FIGURE 1. A scheme of the probability density function of the Gibbs free adsorption energies. The weak-field EC0 measurement characterizes the whole spectrum of adsorption energies (whole area: colored light and dark gray), with the weighted mean, ∆Gbo. The strong-field EC(E1) measurement determines the mean adsorption energy of the dissociated ions (in the ∆Gad range, colored light gray). The incremental fraction of the cations possessing a given adsorption energy of ∆Gad(E1) (colored medium-tone gray) is determined from two consecutive Wien effect measurements at E1 and E1 + dE.
(6)
where EC2i and EC1i are the contributions of the released cations to the overall suspension EC in states (2) and (1), respectively. Therefore, the mean Gibbs free adsorption energy of the cations can be represented as
∆Gbo )
(7)
If we define the states (1) and (2) of the suspension as those under a weak and a strong electrical field, respectively, eq 7 can be rewritten as
∆Gad ) RT ln(EC/EC0)
(8)
where EC and EC0 represent the electrical conductivity of the suspension under the strong and the weak electrical fields, respectively. This expression enables us to evaluate the mean adsorption energy of the population of cations released from the soil particles as the electrical field was increased from zero to E, and application of the expression to a series of Wien effect measurements, EC(E), may provide a spectrum of the cation adsorption energies. The increase in the mobility of the cations in the suspension stems from the work done by the applied electrical field in overcoming the binding forces between the cations and the soil particles. The positive adsorption energies calculated with eq 8 reflect the work done by the applied electrical field.
∆Gmax ad
0
∆GadPDF(∆Gad) d∆Gad
(9)
Upon increasing the applied electrical field, more cations are being stripped off the charged particles and the spectrum of the remaining adsorbed cations (colored dark gray) is truncated at higher minimal adsorption energies. The incremental fraction of the cations possessing a given adsorption energy of ∆Gad (E1) (colored medium-tone gray) is determined from two consecutive Wien effect measurements at E1 and E1 + dE:
∫
∆Gad(E1+dE)
∆Gad(E1)
∆Gad ) RT ln(EC2i/EC1i)
∫
∆Gad(E)PDF(∆Gad(E)) d∆Gad(E)
(10)
Experimental Section Soil Samples. The tested soils, a yellow-brown soil (Alfisol, Nanjing, Jiangsu) and a black soil (Mollisol, Haerbin, Heilongjiang), expected to carry only negative charge, were collected from a depth of about 1 m. The dominant clay minerals of the yellow-brown soil were hydromuscovite and vermiculite; the principal clay mineral of the black soil was hydromuscovite plus some saponite and chlorite, and this soil also contained some organic matter in its clay fraction. The clay fraction comprising particles less than 2 µm in diameter was separated by sedimentation (the suspended fraction down to a depth of 10 cm after 7 h at 25 °C), dried, and ground. The positive and negative charge densities of the clay fractions of the two soils at different pH values were determined according to Schofield (47). Preparations of Homoionic Soil Samples and Suspensions. The clay fractions of the two soils were saturated with various cations by three sequential equilibrations with 1 M solutions of different chlorides of these cations. The clay samples were then centrifuged and the concentrated chloride VOL. 39, NO. 17, 2005 / ENVIRONMENTAL SCIENCE & TECHNOLOGY
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supernatants were discarded. Distilled water or a mixture of distilled water with ethanol was then added, with thorough stirring, and the suspensions were centrifuged. The supernatants were discarded, and their EC and Cl- concentration had been measured. This procedure was repeated up to 11 times, until the supernatant did not contain any detectable Cl- ions. The chloride-free clay fraction was then dried and ground. Suspensions were prepared by adding distilled water to soil samples in 50-mL flasks to a solid concentrations of 10 or 5 g L-1. The flasks were sealed and shaken for 10 min, and the suspensions were dispersed ultrasonically for 45 min. Measurement of Electrophoretic Mobilities of Soil Particles. The electrophoretic mobilities of the soil particles were measured according to Zhang and Zhang (48) with a DPM-1 double-tube micro-electrophoresis apparatus (Experimental Factory of Shanghai Measurement Bureau, China), immediately after the Wien effect experiments. Short High-Voltage Pulse Apparatus. We developed and built the prototype short-high-voltage pulse apparatus, designated model SHP-1, to measure and investigate the Wien effect in soil suspensions (39). Its main components are a pulse-type variable high-voltage power generator, an RC charger circuit with a parallel set of three high-voltage nylon capacitors (each of 2.2 nF), a spark-gap switch, and a twopath circuit to determine the resistance of the test sample (electrode cell) by comparison with a variable resistor with the aid of an analogue galvanometer. The output voltage ranges from 1 to 25 kV, and the pulse width (when most of its energy is dissipated) ranges from several to tens of microseconds, depending on the total resistance in the return discharge circuit. The conductivity cell resistance ranges from 1 to 20 kΩ. The maximum output voltage of 25 kV is sufficient for measurements with an electrode spacing of, for example, 1 mm, for which the resulting electrical field of 250 kV cm-1 is similar to the dielectric strength of aqueous solutions (or suspensions). Application of stronger electrical fields causes a dielectric breakdown (sparking). The short pulse duration (roughly equal to τ ) RC, R-resistance, C-capacitance) is necessary to minimize undesirable electrode polarization and Joule heating. The pulse shape exhibits a steep rise and a relatively long tail. A more detailed description of the apparatus and of its testing with Wien effect measurements in simple electrolyte solutions was presented previously (39). Two model SHP-1 prototypes were constructed and are currently held in Nanjing and in Bet-Dagan. Electrode Cell. The electrode cell is made of a two-part Plexiglas cylinder, equipped with a pair of circular parallelplate stainless steel electrodes, 10 mm in diameter. One electrode of each pair is fixed, and the other is mounted on a bolt that advances 1 mm per revolution, thus enabling the electrode spacing to be varied continuously. In the present study, the spacing was fixed at 1 mm, enabling the field strength applied to the cell to be as high as about 250 kV cm-1. The electrode cell constant, determined with standard KCl solutions of a range of ionic strengths, was 0.124 cm-1. The electrode cell used in the present study, as well as another, smaller one, were described in more detail previously (39). Wien Effect Measurement Procedure. The prepared homoionic suspensions were allowed to stand for a few days, and, prior to the strong-field measurements, their weakfield EC was determined with a regular conductivity bridge, to ensure that it was well within the 1-20 kΩ measurement range of the SHP-1 apparatus. The suspension of interest was poured into the electrode cell, which was connected to the apparatus via regular copper wires and crocodile clips, and the resistance of the variable resistor was set to about the expected resistance of the test sample. An initial, relatively low voltage of about 1.5 kV was set, and the spark gap button was pushed to initiate a short pulse. The needle of the 6760
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FIGURE 2. Negative and positive charge densities of the clay fractions (
