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IV. Models and Microelectrode Response .

IV. Models and Microelectrode Response .

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control may be modified by electrolyte transport polarization at low pH

and low salt contents (McIntyre, 1967, and above). In both models

resistance polarization has been shown to occur, but its effect may be

removed by measurement of the electrical resistance and correction of

results to constant effective voltage (Kristensen, 1966; McIntyre, 1966b,


Results in the literature are consistent with the “composite model”

and its modifications. The microelectrode response as found by a number of workers under a variety of conditions will therefore be discussed

in relation to the two models. Their meaning and usefulness in soil aeration studies will be treated in conjunction with this discussion.



Current as a function of applied voltage is found by normal use of the

method. The relation is affected by electrical resistance of the soil, whose

effect is to increase (negatively) with increasing resistance the apparent

decomposition voltages of O2 and H + ions as well as that voltage at

which diffusion becomes limiting for two-phase media (the beginning of

the plateau-see Fig. Ib). Resistance affects the parameters in the same

way for three-phase media, but because of the shape of the curves these

critical voltages are not obvious in a current-voltage plot (Fig. 4).

Birkle et al. ( 1964) first showed current-voltage relations for threephase media, and the absence of a plateau in such relations. Their

measurements were made in soil under lawn, presumably at a number of

moisture levels; unfortunately electrical resistance was not recorded, but

approximate calculations indicate that, in their middle ODR range, resistance would be of the order of 30,000 ohms. Current as a function of

applied voltage gave straight lines for a limited range of the applied negative voltages (greater than -0.5 with respect to Ag-AgC1). The slope of

the lines increased with ODR (or decreasing moisture). It was realized

that under such circumstances constancy of voltage was necessary for

comparison of results. From the curves they calculated approximate

corrections for measurements of O2 flux at other voltages to a constant

applied voltage of -0.65 V. Will (1963) and Maget and Rothlein (1965)

show current-voltage relations for a platinum electrode covered by a

water film over part of its area. The relationship is linear over restricted

parts of the voltage range; Rickman (1966) then assumes that this relationship is general in three-phase media and is related to nonuniformity

of current density over the electrode. While nonuniformity undoubtedly

occurs, the apparent linearity is more likely due to a combination of the



limited voltage range and high electrical resistance. The latter obviously

occurs in the measurements of Birkle et al. ( 1 964) as judged by the apparent decomposition potential of H+.

When electrical resistance is comparatively low, current is not linearly

related to applied voltage (Kristensen, 1966; McIntyre, 1966b) as shown

in Fig. Ic. The important relation, however, is that of current as a function

of the efective voltage of the electrode, which has even greater curvature.

It can be determined from the results of these authors, who measured

electrical resistance, using relation ( 15). Resistance values measured in

unsaturated soils of medium to low salt content were shown to affect

significantly the current-voltage relations. Two conclusions can therefore

be made: (a) O2fluxes (ODR) are not comparable between soils, or within

one soil at different moisture contents unless comparison is made at

constant efective voltage; (b) the diffusion model is not applicable to

three-phase media.

The question arises whether diffusion is limiting in near-saturated

media under suction. Letey and Stolzy (1967) have stated, without critical experimental verification, that “under low ODR values, which are

limiting to plant growth, the results observed indicate that the ODR is

diffusion controlled.” The relations of Birkle et al. (1964) show, however,

that even with Or flux given as a function of applied voltage, significant

g cm+ min-’.

slope occurs in the curves for Or flux values near 20 X

Correctly plotted in terms of effective voltage, the curves would show

a greater slope. Gavande ( I 969) found that the range of O2flux 20-40 x

g cm-2 min-’ occurred at air-filled porosities close to and greater

than lo%, while Finn et al. (1 96 I ) obtained an Or flux less than 20 x

g cm-* min-’ at air-filled porosities of 14% and 20%. It is certain that in

these cases current-voltage relations will have been of the type shown

in Fig. (Ic) and not as in Fig. ( I b). Further evidence on this point is provided by Campbell et al. (1969) whose Or flux values near 20 x


cm-* min-’ occurred at high air-filled porosities. I t may be argued that

correction by diffusion theory of those results obtained with large diameter electrodes to the smaller diameter used by Stolzy and Letey

( 1964a,b) would give a somewhat greater value of 0 2 flux. While this is

legitimate for saturated media (McIntyre 1966a), experiment shows

that other influences make it a doubtful procedure for unsaturated media

(see Fig. 9d and McIntyre 1966a) and values of Or flux obtained with

large diameter electrodes can be equal to or greater than those obtained

with the smaller ones.

There is a scarcity of direct evidence for very wet media, but the results of Gradwell ( I 9 6 9 , Kristensen ( I 966), .Martin ( 1 9681, McIntyre


27 I

( I966b), Rickman ( I966), and Sims and Folkes (1964) seem to indicate

that the continuous dependence of current on voltage occurs at very

high moisture contents; Mclntyre’s glass beads contained 5% air-filled

porosity ( 1966b). With the probability of physical changes due to probe

penetration already discussed, the conclusion can be made that currentvoltage relations for many soils with water under suction are of the type

shown in Fig. 4. The shape of these current-voltage curves is not consistent with the diffusion model. When the data are plotted with log i as

a function of VE,a straight line is obtained in accordance with a Tafel

plot for activation polarization (Fig. 7). As previously discussed, concentration polarization occurring simultaneously will not affect the linearity, but only the slope. The results appear to be in accordance with the

proposed composite model .



Few measurements have been made in three-phase media; in suspensions Lemon and Erickson (1955) and Birkle et d.(1 964) found the

expected linear relationship between i and Cox.The former authors measured current at 10 and 20 seconds with an applied voltage of -0.8 V with

respect to SCE, and obtained a residual current. The latter held the applied voltage at -0.65 V with respect to a Ag-AgCI electrode and measured the current at 10 minutes but found no residual current. The residual

current at -0.8 V would undoubtedly be due to H+ ion reduction. In

three-phase media McIntyre (1966b) found a linear relationship for current as a function of 0 2 concentration if the latter did not exceed 21%.

Current values plotted are those found at constant efective voltage (Fig.

8). However, both models predict this relationship. For the alkaline glass

beads the residual current is very nearly zero but still measurable; for the

acid sandy loam (pH of 6.3 in 1:s ratio of soil to electrolyte, which was

0.1 M KCI) residual current was relatively large. The current-voltage

curves (McIntyre, 1966b) and the Tafel plots (presented in Fig. 7)

indicate that some H + ion reduction was occurring at an effective voltage

of -0.5 V with respect to SCE. This is the voltage at which the currentconcentration curves were constructed. Gradwell ( 1965) also examined

these relations but made measurements at constant applied voltage without resistance measurement. His relations would probably be near linear

if comparison was made at constant effective voltage.

In two cases (van Gundy and Stolzy, 1963; McIntyre, 1966b), a curvilinear relation was found between current and O2 concentration. These

have been discussed under Sections 11, E, I , a and b. The curves could



result from electrolyte transport polarization and/or activation polarization. There are insufficient data to decide what process is the cause,

and only the relation shown by McIntyre has been determined at constant

effective voltage. The results of van Gundy and Stolzy were determined

at constant applied voltage without measurement of electrical resistance,

which would undoubtedly be large, so that the relation cannot be accurately tested.



Both models predict an inverse relationship between current and moisture content. The diffusion model is partly based on those current-moisture relationships measured at constant applied voltage (Fig. 9) which

show a maximum in the curve at a critical moisture content (8,)so that

for 8 < 8, diffusion rate of Onlimits current and, from Eq. (4),

i = n FAJ,,.,, =

n F A D Cb

a In ( I


where 6r is proportional to 8. At 8 = 8,,effective area A is said to decrease due to rupture of the film on the electrode surface. Hence at this

moisture content, current begins to decrease as 8 decreases, or it may

remain constant due presumably to a balance between the effects of decreasing A, and decreasing 6 r at other parts of the electrode.

The composite model predicts an increase of current with decreasing

8,the rate of increase becoming less as parts of the electrode come under

the influence of activation polarization, with parts still experiencing concentration polarization. Current should approach a constant value as

most of the electrode becomes activation polarized, and would ultimately

decrease but at very low moisture contents.

The only data obtained at constant effective voltage are those of

Kristensen ( 1 966); all other available data were determined at constant

applied voltage. Kristensen’s results conform to the composite model

predictions, but unfortunately were not continued to high enough matric

suctions to thoroughly test the model, and to differentiate from the

diffusion model. Kristensen also, very fortunately, included his measurements at constant applied voltage, and these may be used to interpret the

data of others. For full interpretation, the soil data needed are electrical

resistance and moisture characteristics, and degree of saturation of the

soil. All data available give either moisture content only or matric suction

only: in some cases degree of saturation may be inferred.





Tension (cm water)

Volumetric water content




A 22 g a q e acid tmottd

A 25gouge

acid treoled

rn 25 gauge untreated

0 22 gauge untreated

- 120-












Suction cb


I .


Volumetric water contenl


FIG. 9. Current or oxygen flux (ODR) as a function of soil moisture content. (a) From

Kristensen ( I 966), showing the relations obtained at constant applied voltage (upper) and

constant effective voltage (lower). (b) From Stolzy and Letey ( I 964a). (c) From Lemon and

Kristensen ( I96 I ) for beds of aggregates. (d) From Birkle et al. ( 1 964) for a sandy loam.

In three-phase media the electrical resistance and through it the

effective electrode voltage appears to have an overwhelming influence on

measured current-moisture relationships. I t is expected that soil resistance characteristics will parallel moisture characteristics. Kristensen

( 1966) has demonstrated the effect of resistance by plotting against

moisture tension the current determined at constant applied voltage

(Fig. 9a, upper), and also the current corrected for ohmic loss in the

medium (Fig. 9a, lower). The latter is equivalent to the use of constant

effective voltage. At constant applied voltage, for significant resistance

(4000 ohms and greater), the current for his sandy soil is constant at



tensions greater than 50 cm, and the clay loam has almost reached a

constant value at 150 cm (points X A 0 ) . In both cases the results are

consistent with the expected moisture characteristic curves. After

correction to constant efective voltage a very different picture arises, as

the current is still increasing at the highest tensions plotted. The supposed rupture of a water film at a certain moisture content, which varies

from soil to soil IBirkle et al., 1964) is therefore an artifact. The shape of

the curve relating the current to the moisture content is most probably a

direct consequence of the increase in electrical resistance as moisture

content decreases. Such behavior is brought about by alteration of the

effective voltage according to the relation V E= V , - iR, and t3e type of

dependence of current on VE in three-phase media (Fig. 4).

Stolzy and Letey (1964a) show relations for a krilium-treated silt

loam and a loamy sand (Fig. 9b) which are similar to those for Kristensen’s sandy soil. In both cases the curves are consistent with the expected

moisture characteristics of such soils. The loss of a large part of the water

from the loamy sand over a small suction range is very probable, and

would give rise to a large ohmic loss over that range. The curves of Lemon

and Kristensen ( 1961) (Fig. 9c) for beds of aggregates, and of Birkle et al.

( 1 964) for Ramona sandy loam (Fig. 9d) are also consistent with the

expected moisture characteristics for beds of aggregates.

The moisture range for useful operation of the microelectrode in various

soils, based on measurement of current at constant applied voltage and

the diffusion model, is therefore also an artifact. The true moisture range

over which the electrode can be used is unknown for any soil; from Kristensen’s measurements the lower moisture limit is obviously much less

than that indicated by other workers. Van Doren (1958) and van Doren

and Erickson ( I 966) measuring in soil cores with constant applied voltage

showed that maximum current occurred at a matric suction of about 300

cm for a sand, 1000 cm for a sandy loam, and had not been reached at

2000 cm for a silt loam and a silty clay. Stolzy and Letey’s data (1964a)

indicate useful operation only to about 100 cm in a loamy sand, and 200

cm in a silt loam, while results of Birkle et al. ( 1 964) for a sandy loam

show a maximum at a volumetric moisture content of 0.2, which would

probably be reached at about 100 cm suction. The maximum of Lemon

and Kristensen ( 1 961) would also probably have occurred at a similar

suction. However, all these values have been obtained at constant applied

voltage and have little meaning. Kristensen’s data (1 966) indicate, on the

basis of a measurement at constant applied voltage, that for his sandy

soil the critical moisture is reached at about 50 cm suction, and for his

clay loam at not much greater than 150 cm. However his results corrected



to constant efective voltage show that current is still increasing in both

cases at the respective tensions, and that the rise is very steep for the

latter soil. Measurement of current as a hnction of moisture content and

degree of moisture saturation, along with moisture and electrical resistance characteristic determinations, is needed to thoroughly test the

operating range of the microelectrode and relate its behavior to the two

proposed models. It should be noted that the current-effective voltage

relations found by Kristensen for the two soils conform to the predictions of the composite model, but not the diffusion model.



Current has generally been found to decrease with time at various

rates, to a quasi-steady state, but it is difficult to deduce a great deal from

the many relations appearing in the literature, because of a lack of

critical information. A true steady state can never be attained, for even in

unsaturated soils there must be some liquid continuity between electrodes

which will allow the concentration gradient to move to infinity. The lower

the moisture content or the fewer the continuous paths, the nearer the

steady state will be attained. However, such conditions will also make the

resistance high so that the effective voltage of the electrode will decrease

according to the relation VE = V , - iR, thus confounding the normal rate

of decrease of current.

The diffusion model predicts current-time relations according to

diffusion theory; the composite model predicts a less rapid drop in

current, for under activation polarization current would remain constant

with time. The best measurements are those of Rickman (1 966) who endeavored to maintain VE constant by continuously adjusting the voltage

on the electrode compared with a second reference electrode, and with

zero current in this reference circuit. He then compared the curve with

ones calculated for various values of other parameters involved. In

general rate of decrease of current was less than expected from a diffusion

model, and in some cases rapidly reached an equilibrium state of near

constant current; the effect was enhanced by the use of 100% 0 2 . His

measurements lend support to the occurrence of activation polarization

over at least part of the electrode.



Chronopotentiometric measurements (Lingane, 1958, 196 1) have

been made only by Rickman (1966), apparently with the idea of measuring 0 2 concentrations in the soil solution as suggested by Lingane ( 196 1).



The method involves measurement of voltage variation with time at constant current. A distinct transition time appears in the curve for pure

solutions (Lingane, 1961) when supply of the reactant by diffusion is not

able to maintain the current. Hence the voltage changes rapidly to that

required for a second reaction, in this case 2 H + + 2e- + HP.Rickman

found no distinct transition time in soil aggregates, although it appeared

in suspensions. As his current density was only of the order of onequarter to one-eighth that used by Lingane (1961), and since possible 0 2

supply rate is much greater in three-phase than in two-phase media or in

solution, a more distinct change may have been obtained at a higher

current density. Rickman found a continuous change of voltage with

time in aggregated soils from the onset of O 2 reduction to that of H +

reduction, and showed that decomposition potentials for O2 and H +

varied with electrode pretreatment, and with type of salt in solution.

Actual values given will be affected by the ohmic loss in the medium,

which, in this case, remains constant at constant current.

Rickman did not attempt to interpret the chronopotentiograms for

aggregated soil, but assuming his current density was too great for

maintenance of current by O 2 diffusion, as it apparently was from the

steady change in voltage, the results could be interpreted in two ways,

particularly at the prereduced electrode. First, because O2 supply rate

only gradually becomes limiting to voltage, activation polarization could

occur over part of the electrode; secondly that H + ion reduction may be

occurring at relatively low negative voltages. He gives no indication of

pH of the medium.



1. There is doubt as to the exact reaction taking place at the microelectrode, and the efficiency of the reaction.

2. The diffusion model probably applies only to saturated porous

media with the water at zero or positive pressure.

3. The composite model -activation and concentration polarization applies to unsaturated porous media and probably to media that are

saturated but in which the water is under tension.

4. The type of behavior of the microelectrode in two-phase media, in

which the OP diffusion rate has an overwhelming influence on current,

cannot be extrapolated to three-phase media.

5 . The electrode environment is probably affected by insertion

differently in different soils and may vary with the shape of the supporting




6. Most results obtained so far with unsaturated soils are not comparable within and between soils mainly because of resistance polarization,

but also because of pH effects on current at the voltages used: in some

cases electrolyte polarization also occurs. Comparison of results is valid

only at constant effective voltage.

7. If the composite model applies, comparison of results is further invalidated, for the current will depend on the relative areas of the electrode

subjected to activation and concentration polarization. These areas will

vary with the structure and the moisture content of the soil. The concept

of “film thickness” has little meaning in quantitative studies of root


8. pH assumes more importance than previously recognized. The

process responsible for the behavior at acid pH probably differs from that

responsible at alkaline pH. In acid soils the possibility of reduction of H +

ions at the often used voltage of-0.65 V is real; a better voltage would be

-0.40 or-0.45 V with respect to SCE, but with near anaerobic conditions

some H reduction may occur even at these voltages.

9. The shape of the curve for current as a function of moisture content

is not due to rupture of a water film on the electrode surface but to ohmic

loss in the medium and its increase with decreasing moisture content.

I t has previously been assumed that the lower moisture limit to which

the method is applicable is denoted by the maximum in the currentmoisture content relations (see Fig. 9). This has been shown above to be

an artifact of the measurement, as correction for resistance polarization

greatly alters the relationship. Moreover activation polarization must

occur well before the lower moisture limit is reached, thus making the

diffusion model inapplicable. A corollary to such conditions is that the

microelectrode as presently used in no way simulates a root. It is not

impossible, however, that the microelectrode can be made to simulate a

root because of the occurrence of activation polarization.

Wiegand and Lemon (1958, 1963) and Lemon and Wiegand (1962)

obtained results which they consider indicate among other things that

“when O2 is plentiful the substrate supply (or other necessary compounds) at the reaction loci determines the reaction rate” and “when 0 2

concentration at the root surface is below the critical level, diffusion

controls the rate of O r uptake.” The latter statement presumably refers

to diffusion through the root. Under these circumstances reaction rate

control of current for the electrode might just possibly be equivalent to

the situation for the root in which rate of O2uptake is controlled by

processes occurring within the root. It is first necessary, however, that a

thorough investigation of electrode behavior be made with careful con+



trol of O2 and moisture, as well as measurement of electrical resistance,

over a range of soil moisture content. This range should be from saturation at zero or positive pressure, to that moisture content corresponding to

say 15% air-filled porosity. There are two basic requirements for determination of meaningful flux values. First the current-voltage relationship should be obtained at constant O2 concentration to find whether

diffusion control occurs over the relevant moisture range. If the current

is not diffusion-controlled the electrical resistance between the electrodes

must be measured so that comparison of results can be made at constant

effective voltage. The effects of pH, electrolyte concentration, and of

penetration of the electrode, and the shape of its support, need checking

also. Such an investigation should decide, once and for all, whether the

platinum microelectrode method can give meaningful measurements of

soil aeration which are universally applicable.

If further investigation shows conclusively that the method cannot

give intrinsic values, it may still be worth using for correlation purposes,

as used by Wengel ( 1966), Kaack and Kristensen (1 967), Erickson and

van Doren (1961), McIntyre (1966a), and Loveday and McIntyre

(1966). It could also serve as a quick method to determine whether O2

concentration in a field soil is near zero, provided one can be certain no

H + ion reduction is occurring. However the current value determined

(and hence O2 flux) should be that at constant effective voltage to overcome the influence of soil electrical resistance, and of its variation with

moisture content.


02 Flux and Plant Response

Because the foregoing treatment shows that many soil and electrode

conditions can influence the value of O 2 flux measured, little is gained

by a detailed discussion of published values in relation to plant growth.

The values measured as being minimal for plant growth cover a wide

range and are confounded by the use of different diameter electrodes,

different applied voltages, measurement at different times in relation to

watering, and the use of fundamentally incorrect procedures, as well as

the various soil and electrode effects discussed above. It is maintained by

Stolzy and Letey (1964a,b) and Letey and Stolzy (1 967) that the critical

range for root growth of most species (including grasses) is 20-40 X

g ern+ min-', with corn (and perhaps barley) having a significantly lower

threshold value. These values are based on a series of experiments in

which, in general, threshold values for root growth varied between 15 and

25 X

g cm-* min-I. It should be noted, however, that in the majority



of their experiments use has been made of the same soil with the same

technique. Where measurements were made using another soil, with

various amendments, for growth of turfgrass, their threshold values

g cm-2 min-I

for root extension broadened to a range of 12 to 33 x

(Letey et af., 1966).

Waddington and Baker ( 1 965) found that root growth of Merion Kentucky bluegrass was not stopped till 0 2 flux was between 5 and 9 X 1Ow8g

cmP2min-l [against 20 X

g cm-2 min-I found by Letey et al. (1964)

for Newport bluegrass] and Penncross creeping bentgrass roots grew well

at an 0 2 flux of 5 X lo-" g cm-2 min-I. Gradwell (1967, 1969) found that

ryegrass roots grew freely in soil for which O2flux was 7.5 x

g cm-*

min-' and that for white clover root growth was not impaired but shoot

g cm-2 min-I; West and

growth was depressed at an O2 flux of 10 X

Black (1969) found that pasture grasses grew at near-zero fluxes and

apparently grew well at a mean O2 flux of 1 1 X lop8g cm-2 min-'. Although they did not examine root growth, they concluded from their

measurements of dry matter from a mixture of ryegrass, bluegrass, and

fescue grown on very wet soils, that "flux minima previously suggested

as limiting for root growth have been overestimated." However, their

relatively uncontrolled (field) experimental conditions, and comparatively

few measurements, do not really justify such a conclusion.

In other work Williamson (1964) found that although corn, sorghum,

and cabbage yields were reduced by a decrease in O2flux from 15 X

to 5 x

g cm-2 min-I, somegrowth took place and yields were obtained

at the lower value. On the other hand, Campbell et al. (1969) found that

seed set and wheat yield were increased when the range of O2flux altered

with altered water regime from that of 20 to 100 X IO-' g cm-' min-' to

that of 28 to 200 X

g cm-' min-'. Even a t the low O2flux end of the

range, calculation from their results indicates that air-filled porosity was

in excess of 20%. Letey et al. (1965), once more using Krilium-treated

Yo10 silt loam, found that corn roots would grow a t an O2 flux greater

than 10 X lo-' g cm-' min-', and Valoras and Letey (l966), again with

the same soil, showed that rice roots extended at 0 2 fluxes down to 7 X

g ern+ min-I. In both cases it could be shown that O2was supplied

by internal diffusion, thus accounting, in their opinion, for a threshold

value less than 20 X 1 0-8 g cm-' min-'.

Wengel ( 1966) obtained a highly significant relation between emergence

of corn and O2 flux; emergence reached a maximum (near 100%)at a flux

of 20 to 25 X 10-8g cm-' min-'. Kaack and Kristensen ( 1967)using a very

similar technique found a similar correlation between wheat emergence

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