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V. Transferring the Variable-Charge Models to Soils

V. Transferring the Variable-Charge Models to Soils

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2 1000rn
















Phosphate concentration ( p g P/ml)


FIG.12. Relation between retention of phosphate and concentration over a wide range of

concentrations for three soils of widely differing phosphate retention. The lines drawn are taken

from a model of the effect of pH and concentration on retention. They are a section in the

concentration dimension of Fig. 16.

ions remain in solution, and plots may be prepared of the amount retained

against the concentration remaining in solution (Fig. 12). Such curves are

often called “adsorption isotherms.” However, it is now becoming clear that

the process involved is not simply adsorption, and the term “isotherm”

implies that temperature is the only other variable affecting the curve. I have

therefore argued that this impressive-sounding terminology be avoided

(Barrow, 1978). A better terminology is Q/Z (quantity/intensity) plots or

retention curves.

Much effort has been expended in seeking a mathematical description of

these Q/Z plots. The reasons for this effort have not always been clear. I have

argued that the only good reason is to seek a way of summarizing behavior

by a few numbers (Barrow, 1978). For this purpose, the fewer the numbers the

better. A simple equation that often describes Q/Z plots is the Freundlich



= acb


were S is the amount retained and should include any adsorbate initially

present, c is the concentration remaining in solution, and a and b are

constants. If this equation holds, logarithmic plots of S against c give a

straight line. This is often a convenient approximation over important

concentration ranges, but over larger ranges the nonlinearity becomes more

important (Figs. 12, 13,14, and 15). The Langmuir equation, or versions of it,

have been widely used to describe Q/Z curves on the grounds that they are






v 91









0 3


0 1













Phosphate concentration ( p g Plml)












Phosphate concentration



1 .o



(Hg P/rnl)

FIG. 13. Effect of time and temperature (“C) of incubation on the relationship between

phosphate retention and solution concentration. The data are from Barrow and Shaw (1975a)

and the lines are for the mechanistic model of Barrow (1983b).

more mechanistic. However, the mechanism of ion reaction with soils does

not meet the Langmuir criteria. Furthermore, a truly mechanistic approach

should be capable of also describing the effects of variables other than

concentration. This will be discussed further in Section V,C.

2. Period of Reaction

It is widely observed that when phosphate and several other nutrients react

with soil, the solution concentration continues to decline for a long period.

The problems that this behavior produces are often circumvented by making

measurements after some convenient, but constant, period. Again a semantic

trap arises. Many workers use the verb “equilibrate” to describe the process

of mixing the soil and nutrient solution, and then deal with the results as if

equilibrium had been reached. Rather than avoiding the problems caused by




Fluoride concentration ( p g F/ml)

FIG.14. Effect of the time and temperature (“C)of incubation on the relationship between

fluoride retention and solution concentration. The data are from Barrow and Shaw (1977a) and

the lines were obtained by fitting the mechanistic model of Barrow (1983b). (From Barrow,


the slow rate of reaction, it would be better to measure the rate of reaction. It

is, after all, an important property affecting both the long-term effectiveness

of fertilizers and the long-term retention of pollutants.

As for any other reaction, measuring the rate involves mixing the reactants

and measuring either their rate of decrease or measuring the rate of increase

of the product. In this case, the most practical measurement is the rate of

decrease in nutrient concentration. However, there are difficulties both in

making these measurements and in interpreting them [reviewed by Barrow

(1983a)l. One problem is that, at the commonly used solution/soil ratios,

concentration and retention both vary through time. If the effect of time is to

be defined, we need to be able to see the effect on concentration at constant

retention-or the effect on retention at constant concentration. Approaches

that relate just two of the three important variables can give misleading

results. It was shown (Barrow, 1983a) that the Elovich equation, which

relates retention to time and which was advocated by Chien and Clayton

(1980), could not be used to characterize soils. The rate measured using this

equation varied with both the level of addition of nutrient and the solution/

soil ratio. One way of overcoming these difficulties is to incubate soil and

nutrient solution at moisture contents near those occurring in the field. The

solution/soil ratio is thus low (say, 0.2/1) and the amount of nutrient











ZnOH' concentration ( p g Zn/rnl)

FIG.15. Effect of time and temperature ("C) of incubation on the relationship between zinc

retention by soil and calculated solution concentration of ZnOH+. Lines were obtained by

fitting the mechanistic model of Barrow (1983b). Retention is plotted against ZnOH+. (From

Barrow, 1985b.)

remaining in solution is low relative to the amount reacted with the soil.

Changes in concentration can therefore be measured at near-constant values

for retention. Another approach is to use an apparatus to hold concentration

constant (van Riemsdijk and De Haan, 1981). However, it seems easier to

measure both retention and concentration through time and to mathematically describe the surface which interrelates them. If desired, the changes in

retention at constant concentration, and vice versa, could then be interpolated.

Equations that describe the changes in retention and concentration of

phosphate through time have been summarized and reviewed by Berkheiser

et a!. (1980). They concluded that the most satisfactory equation for

describing phosphate retention was



where b , and b, are constants. They also concluded that such equations may

describe the observations but they do not do so in a mechanistic sense.

Equation (17) also applies to molybdate, fluoride, sulfate (Barrow and Shaw,

1975b, 1977a,b), arsenite (Elkhatib et al. 1984), and zinc retention by soil

(Kuo and Mikkelsen, 1979). When plotted on a logarithmic scale, it gives a

planar surface relating log S to log c and log t. However, when a wide range of

concentrations are used, this is seen to be an approximation, and the

relationship is curved in the log c direction (Kuo and Mikkelsen, 1979; and

Figs. 13, 14, and 15).

Although the rate of change in solution concentration is perhaps the best

way of characterizing the rate of reaction, the rate of change of the

effectiveness of a fertilizer is of such practical importance that it merits further

discussion. The decrease, with time, in the effectiveness of phosphate fertilizer

is well documented [reviewed by Barrow (1980a)l. The rate of change has

been measured over a range of periods and has been shown to be consistent

with Eq. (17) (Barrow, 1974). Furthermore, the coefficients of Eq. (17) have

been shown to be of value in characterizing differences between soils and the

residual effectiveness of phosphate fertilizers (Barrow, 1980b). Rather less

work has been done on other nutrients. There is field evidence that the

effectiveness of molybdenum fertilizer decreases with time (Smith and Leeper,

1969), and it was shown, in pots, that the rate of decrease was also consistent

with Eq. (17) (Barrow and Shaw, 1975b). The effectiveness of copper

fertilizers was found to decrease with increased period of incubation with

moist soil (Brennan et al., 1980, 1984). A similar effect was also observed

when sulfate was incubated with a soil which retained sulfate strongly

(Barrow and Shaw, 1977b).

3. Effects of Temperature

In general, temperature may have two distinct effects on a chemical

reaction: it may affect the rate of approach to equilibrium, and it may affect

the position of the equilibrium. Both these effects occur for the reaction of

nutrients with soil [reviewed by Barrow (1979b)I. High temperatures of

reaction of soil and phosphate decrease the effectiveness of phosphate

fertilizer to plants and usually give rise to decreased concentrations in

solution (Fig. 13). Both of these effects are due to an increased rate of

reaction. Increasing the temperature of incubation also increases the rate of

reaction of copper with soil and decreases the effectiveness of copper

fertilizers (Brennen et al., 1984). Similarly, high temperatures increase the rate

of desorption. Analogous effects occur for molybdate and sulfate (Barrow

and Shaw, 1975b, 1977b) and for fluoride (Fig. 14) and zinc (Fig. 15). In

?neral, effects of temperature on the rate of a reaction occur because the



reaction involves an intermediate, high-energy state. Only those molecules

with sufficient energy can make the transition over this stage, and the higher

the temperature, the higher the proportion of sufficiently energetic molecules.

The effect of temperature is conveniently described by the energy required to

jump over the barrier, the activation energy.

For phosphate, the effect of temperature on the forward (sorption) reaction

is about the same as that on the backward (desorption) reaction, that is, the

activation energy is about the same (Barrow, 1979b). This suggests that the

rate-limiting step in sorption is similar to that in desorption, as it would be

for a diffusion process. Further, the lack of difference indicates that temperature would have little effect on the position of the equilibrium eventually

reached by the rate-limiting steps. Yet, if conditions are chosen such that the

slow step has almost stopped, then high temperatures are found to increase

the concentration of phosphate (Barrow and Shaw, 1975a; Barrow, 1979b)

and of molybdate in solution (Barrow and Shaw, 1975b). This is strong

evidence that there is an initial adsorption step, that the equilibrium for the

step is reached quickly, and that it is exothermic and thus high temperatures

decrease the amount of product.

For agronomists, the effects of temperature in increasing the rate of

reaction between nutrients and soil can provide a valuable experimental tool.

It means that effects that might take years in the field can be produced in a

few days in the laboratory.

4. Efects of pH

Soil pH can be readily measured and fairly readily changed. It has

therefore been widely investigated as a means of controlling the reaction with

nutrients. Most work has been done on phosphate. Nevertheless, it remains a

poorly understood subject. This is because seemingly contrasting effects have

been observed by different workers. This has been noted in recent reviews:

“Reports on the effect of liming on the sorption of phosphate are conflicting”

(Probert, 1980); “Considerable controversy exists in the literature regarding

whether or not liming decreases P fixation” (Sanchez and Uehara, 1980);

“Liming has been reported to increase, decrease, or not affect the phosphate

that can be extracted from soils” (Haynes, 1982). There are several reasons

for these conflicting observations. Haynes (1982) suggested two: that changing the pH may affect mineralization of organic phosphate and that airdrying the soil after applying lime may cause an artifact leading to decreased

retention. Further reasons are that the direction of the effect may differ in

different parts of the pH range (Barrow, 1984; and Fig. 16), that the direction

and magnitude will depend on the electrolyte in which retention is measured

(Barrow, 1984), and that the effect of changing pH on the release of “native”



FIG.16. Effect of pH on retention of phosphate from four widely differing soils. Points are

interpolated values for retention at indicated concentrations and pH values. Lines are modeled

values. (From Barrow, 1984.)

phosphate may differ from that on the retention of new phosphate (Barrow,

1984). Nevertheless, the main reason for inconsistent results is that the effect

of pH on phosphate retention is fairly small. Ancillary effects can therefore

have a relatively large effect and can change the direction of the net effect.

The effect of pH on reactants other than phosphate is much greater.

Retention of sulfate and especially of molybdate decreases as pH increases.

Sulfate, molybdate, and phosphate retention were compared for a group of

soils that ranged in pH (in calcium chloride) from about 4 to just above 6

(Barrow, 1970).The decrease in sulfate retention between pH 4 and pH 6 was

about three times greater than for phosphate. For molybdate, the decrease

was about 20 times greater than for phosphate. Such marked effects tend to

dominate any other effects. Boron retention is also affected by pH, but

increasing the pH increases retention (Hatcher et al., 1967). For most soils,

the maximum pH attainable is usually limited by the equilibrium between

calcium carbonate and carbon dioxide. This seems to be lower than the pH at

which maximum retention of boron occurs. Sims and Bingham (1967,

1968a,b) showed that for soil constituents such as clay minerals and

aluminium and iron oxides, in sodium or potassium systems, maximum

retention was near pH 9. They concluded that retention by clay was mostly

caused by iron and aluminium oxide impurities. A retention maximum near 9



Dekalb B















- 1






= 4.6





4.3 *










Equil. Solution Concentration (Mrnol /ml)



FIG. 17. Effect of pH on retention of lead, copper, zinc, and nickel by two soils. (From

Harter, 1983.)

was also reported for clays by Keren and Mezuman (1981) and Keren et al.


Retention of the hydrolyzable cations increases markedly with increasing

pH. A comprehensive set of results for lead, copper, zinc, and nickel was

provided by Harter (1983) (Fig. 17).



Time (h)





1 .o

Fluoride concentration ( p g F/rnli



FIG.18. Sorption and desorption of fluoride. The fluoride had been incubated with soil for 4

days at 80°C and desorption was then induced by mixing the soil with a range of solution/soil

ratios. The lines indicate the modeled values for sorption and for desorption after 40 h, using the

model fitted to Fig. 14. The inset shows the modeled and observed effects of time of desorption

for two solution/soil ratios and the 700 pg F/g soil level of addition. (From Barrow, 1985a.)

5. Desorption

Suppose that a range of concentrations of a nutrient is mixed with samples

of soil for a specified period and then a plot is prepared of retention against

solution concentration. If the concentration in solution of one of these

samples is then decreased, some desorption will occur but the original

retention curve will not be retraced. Such observations have been made

several times, and an example is illustrated in Fig. 18. Nevertheless, this

description is inadequate inasmuch as desorption, like the forward retention

reaction, is also a slow process. Rather than merely specifying the position of

the desorption curve at one time, it is better to specify the change in position

through time and thus the rate of desorption. This poses some problems

because, in most practical systems, increasing desorption is accompanied by

an increasing solution concentration. It is therefore difficult to measure

desorption at a constant solution concentration and seemingly impossible to

measure it at the ideal of zero solution concentration.

It has been argued (Barrow, 1979a) that desorption can be specified by two



end points. One is at zero concentration in solution. Although this point

cannot be achieved experimentally, it provides a conceptual limit and is the

point at which maximum desorption would occur. Observed desorption can

be described by assuming that desorption at this point is proportional to a

fractional power of time. This was the case for phosphate (Barrow and Shaw,

197%; Barrow 1979a), fluoride (Barrow and Shaw, 1977a), and sulfate

(Barrow and Shaw, 1977b). Sharpley et al. (1981), in a slightly different

approach, also found that desorption was proportional to a fractional power

of time.

The other conceptual end point is the concentration in solution at which

neither sorption nor desorption occurs. Clearly desorption can only occur if

the concentration is lower than this null point. The value of the null point

decreases with increasing period of reaction, that is, as the retention reaction

proceeds. Consequently, the rate of desorption decreases (Barrow and Shaw,

1975~).These are not direct cause-and-effect relations but rather separate

manifestations of the same process-the continuing reaction between the

nutrient and the soil.





The four-layer model is well able to describe qualitatively many of the

observed effects with soils. Consider the contrasting effects of pH on

molybdate, sulfate, and borate (Section V,A,4). The pK, for sulfuric acid is

about 2 and hence, at soil pH values, only SO:- ions are present. Furthermore, there is little change in the proportion of the ions with changes in pH.

The only effect that can occur is due to the change in electrostatic potential

with change in pH. If the sulfate ion does not approach the s plane very

closely, the change in potential will not be large, and hence the effect of pH on

adsorption will not be large. Molybdate is more complex, as both pK, and

pK, are near 4. Hence both H,MoO, and HMoO; are weak acids and both

dissociation products (HMoO,, MOO:-) could be adsorbed (Section 111,A).

The concentration of HMoO; decreases rapidly as the pH increases above 4,

and this could be one reason for the marked effect of pH in retention. A

further reason could be that the mean plane of molybdate adsorption is closer

to the s plane than the mean plane of sulfate adsorption. This mechanism

would also give a steeper effect of pH on retention (Fig. 4). The tendency for

borate retention to increase up to pH 9, and to then decrease, is consistent

with the adsorption of the monovalent B(0H); ion, for which the pK value is

about 9 (Fig. 6). This seems to be a simpler assumption than to assume that

boric acid, borate, and hydroxide all compete for the same adsorption site

(Keren et al., 1981).







1. Description of a Quantitative Model

Although qualitative models can help one understand observations, they

only become convincing and satisfying if they can be rigorously tested against

data, that is, if they become quantitative models. The challenge is to adapt the

detailed quantitative models used for simpler systems to the more complex

problems of soils.

In the development of models for the reaction with variable-charge

surfaces, the pathway was to understand and to describe the charging

process. Adsorption models were then added to the charge models. This does

not seem to be a feasible pathway for soils. It is too daunting a task to

describe the charge for all of the materials that might be present in a soil. If,

however, we emphasize the importance of the electrostatic potential, then the

charge models can be regarded simply as a way of estimating this potential.

They show that the potential decreases as pH increases and that it also

changes as adsorption proceeds. For soils we may not know a priari what

these rates of change are, but we can investigate the rates of change that are

needed to describe the observed behavior. This is the first step in adapting

detailed models to soils.

The second step is to take account of the heterogeneity of soils. This seems

to show itself in the Freundlich equation that often approximately relates

retention and concentration. A Freundlich equation can be generated if it is

assumed that the adsorbing surface is nonuniform and that there is an

appropriate distribution of values of the parameters of the adsorption

equation. It has been shown (Sposito, 1980) that one appropriate distribution

is a normal distribution of the logarithms of the binding constants of a

Langmuir equation. This is similar to assuming a normal distribution of log

ki of Eq. (13) or of assuming a normal distribution of $ a of Eq. (1 3). These two

assumptions are mathematically indistinguishable. I have assumed that $,

varies (Barrow, 1983b).

The third and final step is to accept that the diffusive process that seems to

occur in pure systems also occurs in soils but is even more marked. Many

authors have suggested that diffusion mechanisms may be involved in the

slow reaction between nutrients and soils. Often this has been a qualitative

suggestion and the consequences have not been quantitatively explored.

Further, the suggestion has often been that diffusion in the solution phase,

from the bulk solution to the surface, is the rate-limiting process. It is

important to emphasize that, in the present case, the postulated diffusion is

solid-state diffusion within the adsorbing particle. The source of this diffusion

is the surface concentration of adsorbate, that is, it is postulated that

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V. Transferring the Variable-Charge Models to Soils

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