22
REPRINT
3s(r)21-26(re7s)
PHPLAT
W. ARMSTRONG and E. J. WRIGHT
RadialOxygenLossfrom Roots:
The TheoreticalBasisfor the Manipulationof Flux Data
Obtainedby the CylindricalPlatinumElectrodeTechnique
P U B L I S H EBDY
SOCIETY
THE SCANDINAVIAN
FORPLANTPHYSIOLOGY
Physiol.Plant. 35: 2l-26.1975
RADIAL
OXYGEN LOSS FROM ROOTS
2l
Radial Oxygen Loss from Roots: The TheoreticalBasisfor the Manipulation
of Flux Data Obtainedby the Cylinrlrical Platinum ElectrodeTechnique
By
W. ARMSTRONG and E. J. WRIGHT
Departmentof Plant Biology, University of Hull, Hull HU6 7RX, U.K.
(Received18 February, 1975;revised 12May,1975)
Abstract
(Armstrong and Read 1972), pea seedlings(Healy and
Armstrong
1,972),andinmaize, mung-bean,and in conifer
A r6sum6is given of the cylindrical platinum electrode
techniquefor measuringthe rate of oxygenreleasefrom the cuttings (unpublished data). There remains little doubt
that some internal oxygen movement from shoot to root
submerged
roots of intact plants.
Methodsare thendescribed
for manipulatingthe oxygenflux is likely in most specieseven under non-wetland soil
datato quantifythefollowingroot characteristics:
total effective conditions (see also Greenwood 1,967a,b,Heide et al.
internal diffusional resistance,non-metabolic(pore-space) 1963,Luxmore et al.1970).
resistance,internal apical oxygen concentration,effective
Since 1967 we have come to realize that the flux data
diffusioncoefficient
ofinternaltransportandfractionalporosity, yielded by quite simple procedures can
be successfully
and the respiratorycontribution to internal transport.The
manipulated to give information on a variety of factors
diffusionalresistance
of theroot wa1lis discussed
andthemethod
connected with the internal oxygen relations of intact
formerlysuggested
for convertinglow temperature
flux datato
the appropriateroom temperaturevalues(Armstrong1971)is roots. Examples of these include the determination of
revised.Finally, suggestionsare made for overcomingthe non-metabolic difusional resistanceto longitudinal diffudifficultiesencountered
in usingflux datafor comparative
work sion, the overall (or effective)porosity of the root system,
and the effect of root respiration on the concentrationof
if therootsdifferin their aoicalradii.
oxygenwithin the root.
This paper is intendedas a guide to the manipulation of
Introduction
flux data obtained using cylindrical Pt electrodes:earlier
The construction of cylindrical Pt electrodesand their theoreticaltreatmentsare brought up to date.
use for the "polarographic" measurementof oxygen flux
from roots in anaerobicmediawerefirst reportedsomeyears
CylindricalPt ElectrodeTechnique- a R6sum6
ago (Armstrong 1964, 1967). At that time interspeciflc
differencesin root oxygen flux were listed, and marked
The polarographic determination of oxygen flux from
basipetalreductionsin root wall oxygenpermeabilitynoted roots is basedon the characteristicsof the current-voltage
in a number of wetland species;there was someindication curve obtainedwhen oxygenin aqueoussolution is electroalso of oxygen storage in aerenchymatoustissues.Theo- lyticallyreducedin a cellin which oneelectrode,the cathode,
retical points discussedincluded the relationship which consists of a sleeve-insulatedthermo-pure platinum
exists betweenroot radius, electroderadius, and oxygen cylinder (Figure 1) while the other is some standard half
flux and it wasconcludedwith experimentalveriflcationthat cell.
someestimateof the oxygenconcentrationinside the root
The reduction of oxygen at a Pt surface is thought to
is possibleby a manipulation of apical flux data.
proceedin two stages(Mclntyre 1970).At pH 3.5 or above
The technique has since provided evidenceof internal the overall reaction follows the equation: Or]-ZHzO+
oxygentransport in the roots of non-wetland plants also; 4e- + 4OH-, and for each molecule of oxygen reduced
woodland plants such as Mercurialis perennis and Des- there is a current transfer of4e-. A current plateauplaced
champsia caespitosus(Martin 1968), conifer seedlings somewherebetween -0.2 V and -0.8 V applied E.M.F.
22
W. ARMSTRONG AND E. J. WRIGHT
Pbysiol.Plant.35.1975
from the Equation (l) by substituting root surface area
within the electrode,in place ofelectrode surfacearea.
Equation (1) simplifiesto the expression
RoL: leJl!
(2>
where
ROL : radial oxygenloss or flux, (Ozng cm-2 root surface
min-1)
1: diffusion current (pA) with the root in the electrode - diffusion current (pA) with a glass rod
through the electrode (residual current)
l1 : surfacearea of root within the electrode (cm2).
(-)
Fig. I
Figure l. Cylindrical platinum electode and inserted root, A:
Celluloid guide (one at each end) to position the root, R, in a
central path through the electrode. B: Perspextube. C: Eponepoxy resin. D: Platinum cylinder. E: Solder joint. F: Copper
wire (sleeved)to polarographic circuit.
Figure 2. Simple circuit analogue of rootlelectrode system,
Rt : plant resistance.Rz : liquid shell resistance. Y : oxygen
concentration difference between the atmosphere and electrode
surface,
(Armstrong 1967a, Black and West 1967) indicates that
the rate of oxygen reduction is independent of voltage
and dependent on the rate of oxygen diffusion to the
electrode surface. When a voltage setting in the plateau
region is sustained, the current equilibrates to a value which
is related to the oxygen flux to the electrode according to
the equation
i7: nFAf,:s,7
Manipulation of Flux Data
Fig.2
Fig,2
(l)
wnere
r'r: the diffusion current in amperes at the time of
equilibration, T
n: number of electronsrequired for the reduction of
one moleculeof Oz:4
F: the Faraday.96,500coulombs
f,:o,r: oxygenflux at zero distance(x) from the platinum
surfaceat equilibrium time, Z(mol cm-2 s-1)
A: Area of electrodesurface(cm2)
Oxygen flux from roots is measuredin de-oxygenated
liquid medium (* supportingelectrolyte,Armstrong 1971).
Roots are inserted through the Pt electrodeas shown in
Figure 1 and a shell ofliquid lies betweenthe root surface
and the inner electrodesurface;the above-groundparts of
the plant remain above the liquid surface. Under the
appropriate polarizing voltage the platinum acts as a
sink for oxygen(substitutingfor a soil sink), and a diffusion
gradient is set up between root and electrode. The rate of
oxygenloss from the root at equilibrium can be calculated
(1) Calculating the diffusional resistance ofered by the
Iiquid shell betweenroot and electrode
Considera root segmentdescribedby a cylinder of radius
r" (cm),lengthZ (cm),and surfaceareaA1 (cm2),longitudinally orientatedthrough the centreofa water-filledelectrode
of radius r", arld length Z.
If the liquid phaseoxygenconcentration(g cm-3) at the
root wall is C(rat toC, andtheconcentrationat the electrode
surfaceis zero, the oxygenflux from the root is given by the
expression:
oxygennu*:ff!gcm-2s-r
r.l log"3 |
r"/
(3)
\
(seeArmstrong 1967)where
Di,: the diffusion coefficient for oxygen in water at
temperature t.
The oxygendifusion rate from the root will be:
gs-'
oxygen diffusionru@:W
r.l log. 3 I
r'-l
\
(4)
and the diffusional resistanceof the liquid path alone
(Rjr) is therefore:-\
/
{ r , r o g . 3|
1q'r_Jscm-3
D'- Ar
(5)
However, acrossan air-water interfacesuch as the rootliquid shell junction the oxygen concentrationwill fall by
an amount which is dependentupon the temperatureof the
system (Hale 1965), and hence the effective resistance
betweenthe root and the electrodesurface(R"t),is
^r:Wxfi,scm-'
(6)
Physiol.Plant.35. 1975
RADIAL OXYGEN LOSSFROM ROOTS
where Cj is the concentration of oxygen in air at temperature t, and Cj-. is the concentrationofair-saturated water
at the sametemperature.
At23"C the oxygenconcentrationin air is 269x 70-6g
cm-3, that of air-saturated water is 8.56 x lQ-o g sm-3,
and D. is 2.267 x 10-5 cm2 s-1 (Millington 1955).Thus
wherer. = 0.05,r.:0.1125 andL:0.5, R, takesthe value
3.285x10sscm-3.
If the concentrationof oxygeninsidetheroot is 269 x 10-o
g cm-3 and the root wall resistanceis zero, then the radial
oxygen flux from the wall at 23"C will be 287.2ng cm-2
min-1.
(3) The ouerall diffusional resistanceof the root
Q) Apical root wall resistance
Estimates of root wall oxygen permeability indicate a
very low resistanceto radial oxygen flow from the apical
regionsat laboratory temperaturesQ0-25'C). A comparison of internal gas concentrations with apical oxygen
flux from roots at 23"C (Armstrong 1967) points to a
negligiblewall resistancein the root apicesof a number of
speciesincluding rice. Greenwood (1967) estimatesthe
maximum wall resistancein mustard seedlingsto be the
equivalent of 12 pm of liquid path diffusion through
the epidermal layers. Luxmore et al. estimate apical root
wall permeabilityin rice and maize to be 11 x 10-acm s-1
and 8 x 10-a cm s-1 respectively, but regard these as
minima, pointing out that the permeability may indeed
be significantly greater than this. Berry and Norris's data
for onion roots yielded slightly lower values. Luxmore's
permeabilityvaluesfor rice andmaizecan be accountedfor
by water paths of 8-10 7zmin the root wall but from what
has been said this may well representan over-estimateof
effectivewall thickness.
The apparentliquid path in rice aiz. the observedthicknessof wall layers which Iie beyond the observableperipheral gas spacesis of the order of 50-60 pm at the root
apex.In maizethe valueis c. 55pm. If root wall permeability
was a function of diffusion through a liquid path of these
dimensions root wall resistance would be substantial.
The apparentconflict betweenthis observedwall thickness
and the root permeabilitiesmentionedaboveis considered
againin section4.
If the mean effective path Iength throueh the wall is wl,
then by analogy with Equation (6) the wall resistanceR*1
will be given by the expression
x
frs cmu (7)
where wl is the effective thickness of the cell layer(s) in
the wall and Az is the surfaceareaofthe cylinder ofradius
r- - wl.
23
The longitudinal oxygen flow down to the apex of a
root, and the radial flux from it to a surroundingelectrode,
may be likened to the flow of electricity in a simple circuit
in which there are two resistancesnr and R, (Figure 2).
J(1 represents the effective resistance of the root and &
is the liquid shell resistancebetweenroot and electrode.If
the difference in oxygen concentration between the top
of the root and the electrodesurfaceis represeotedby Z,
then following Ohm's law we may write:
Ir:#
when Rr :0
(8)
and
Iz:
v
Rr*&
when R'>0
(9)
Combining (8) and (9) with respectto V anldre-arranging
we obtain
Rr: Rz - t)
[i
(10)
If the currents 1' and .I2 are considered to be the radial
oxygenflux from the root surface,then 11is given by Equation (3) and is the flux from an air-filled root having zero
internal and wall resistances(i.e. 287.2 ng cm-2 611-r
where r. : 0.05, r": 0.1125and the temperatureis 23'c).
The resistanceR2 may be calculated from Equation (6),
and the flux 1z is computed from the measuredcurrent by
substitution in Equation (2).
It follows that the diffusional resistanceof the root R1
may be calculatedby fitting values of 11,12 and Rz into
Equation (10).
Rr represents the overall effective internal diffusional
resistancewhich separatesthe outer surface of the root
apex from the atmospheresurrounding the aerial parts of
the plant.
If the effectiveresistanceof the root wall R*, has been
estimated(Equation 7), then Rr - R*r will be an estimate
of the overall efective internal resistance, Rr, which
separatesthe cortical gas spaceof the root apex from the
atmospheresurrounding the aerial parts. Recent experiments on pea and E. angustifulium (unpub.) indicate that
Rr is chieflya property ofthe root and that the contribution
made by the shoot is relatively insignificant.ltr will therefore be a function of the gas-filledporosity and length of
the root, the tortuosity (if any) of the interconnecting
gas-filled channels,the root respiratory activity and the
amount of oxygen leakage occurring through the subapical regionsof the root.
(4) Pore spaceresistance
The following two methodslend themselvesto the determination of pore spaceresistance.
Physiol.Plant.35.1975
W. ARMSTRONG AND E. J. WRIGHT
24
for pearoots by the cooling method (Healy and Armstrong
in preparation),closelyapproachthe estimatesmade by the
method to be described below in which temperature is
maintained at 23"C and the wall resistancecounted as
negligible.
It is tempting to account for the high wall permeability
at normal temperature$as the result of oxygen
detected
( 11 )
Rp: Rr - R*r
transport by cytoplasmicstreamingin the epidermal wall
In practicethe derivation of Rn is not as straightforward layers.At 3"C diffusionwould accountfor the observations.
as the equation suggestsfor the required reduction in
(ii) In this method no attempt is made to curtail respirarespiratoryactivity is most satisfactorilyachievedby cooling
to a low temperature (Armstrong 1971) and account tory activity but, as before, it is necessaryfor the leakage
must be taken of this in subsequentcalculations.However, of oxygenfrom sub-apicalregionsto be minimized. Greenlow temperaturesare also helpful in minimizing oxygen wood (1968) has maintained that the respiratory sites
leakagefrom the sub-apicalregionsofthe root, while even in the root will be oxygen saturatedat very low internal
at more normal temperaturesthe static anaerobicmedium gas-phaseconcentration(c. l)( or evenless).Data we have
bathing the roots will only form a weak oxygen sink obtained using cylindrical electrodes with rice and E.
unless contaminated by micro-organisms. Low tem- angustifoliumplants fully support this view and the followperature, weak-sink activity and the natural reduction in ing procedure is dependent upon the validity of these
root wall permeabilityreducessub-apicalleakagein wetland observations.
If at normal laboratory temperaturesthe concentration
roots to insignificant levels. To be assured of similarly
the
roots
of
oxygenin the atmosphereis Zr k.s.269x 10-6g cm-3)
with
non-wetland
levels
leakage
insignificant
practice of growing and experimentingon roots encased and the oxygenflux from the apex,12,indicatesan internal
in agar (Healy and Armstrone 1972) has proved to be oxygen concentration of ll or greater, then 1z can be
expressed:
satisfactory.
by
subcan
be
determined
3oC
at
R1
resistance
The
3'1rand 3'R2computed
(r4)
stituting 3'-Izinto Equation (10)with
usingthe appropriate3'C valuesfor C*1and D. (13.4 x 10-6
9 cfl-3, and 1.16x 10-s cm2 s-1) in Equations (3) and where Ro is the pore spaceresistanceand the apical wall
(6).
resistanceat room temperatureis consideredas negligible,
and Resp. is the respiratory oxygen component removed
The pore spaceresistanceat 3oCis thereforegivenby
t?*,
t?,
3'lto:
(12) by the plant.
Ifthe concentrationofoxygen around the aerial parts is
where 3'R*, is also calculated from the appropriate 3'C now raisedto a value Vtt (e.g.357g cm-3)we may express
values of C*r and D. The value taken by R, at normal the new apical flux 121as follows:
temperatures(e.g. 23'C) will be given by:
VI
(15)
r]:
23oRp:r"R,
ffiJAt-Resp.
(1
3)
"-*
x'+-r,
(i) If the leakageeffect from sub-apicalregions of the
root is eliminated and respiratory activity curtailed, then
diffusional resistan@in the root becomesa function of
length and efective gas filled porosity only. Under these
circumstances1z will reflect this pore spaceresistanceRn,
and the magnitudeof the resistancewill be given by
I": (Rfu, -Resp.
tr",
wnere
3'Do: diff. coeff of oxygenin air at 3o,0.182cm2s-l
26'Do:diff. coeff.of oxygeninairat 23',0.205cm2s-1
t'C. : conc.of oxygenin air at 3o,294v' 16-eg srn-:
23"
(o: conc.of oxygenin air at 23o, 269x 16-eg srn-:i
It has already been pointed out that at normal working
temperaturesthe resistanceof the wall should be small,
perhapseven insignificant. At 3'C the situation appears
to be altered,and, using observedwall thicknessas effective
thicknessvery good agreementis obtained betweenvalues
of.Rn deducedfrom 3'C flux data, and values calculated
from the known gasspacevolume and distribution in roots
of rice (unpublisheddata). Similarly, valuesof .Roobtained
NB. If respiratory oxygen demand is fully satified by
oxygen concentrationsof c. ll in the gas phase, then
Resp. will not alter at the higher value of Z. Hence,
combiningEquations(14) and (15) with respectto Resp.,
and re-arrangingwe obtain:
V+_V,
Ro:(fffi,-R"
(16)
Results of pore spaceresistanceobtained for pea roots
usingthis procedureapproximateto the lowest of the range
of valuesobtained by the previous method.
(5) Further extrepolationfrom low temperatureflux data
Flux data collected at low temperatue by the cooling
method (section 4i) may be used to predict the flux which
Physiol.Plant.35. 1975
RADIAL
might be expectedwere the root to exhibit a minimal rate
of respiration at more normal temperatures(e.g.23"C).
Proceedingvia Equation (13) we get:
Predictedflux (respiration minimal at 23')
C.
OXYGEN LOSS FROM ROOTS
25
The interpretation of D, will dependupon A*, whether
it be the apical cross-sectionor the mean cross-section.
For example, if the root approximates to a cylinder of
uniform cross-section
then D" will be the effectivediffusion
coefficientof the root. It will be relatedto D6 (the diffusion
coefficientof Oz in air) by the expression
D":
and where R?,ti is very small (see previous section) we
may approximateas follows:
Doe
(22)
wheree is the meaneffectiveporosity of the root.
If the root has linear uniformity of porosity and conPredictedflux (respirationminimal at 23')
tinuity and non-tortuosity of the intercellular spacesthe
C.
:
(18) value of e will be that of the true porosity of the root.
cm-2 s-r
x zre
@\7g:-l
Where the intercellular gas spacesform a tortuous path
A comparison of the predicted flux with the original then
D": DorP (Jensenet al. 1967)
(23)'
room temperaturevalue will indicate the extent to which
root respiration influencesthe apical oxygenregime.
where z is a tortuosity factor and P is the fractional porosity
It must be pointed out that the method previously used of the root.
to arrive at the predictedflux (Armstrong 1971)is in error
becauseofa failure to take accountofthe 3'C wall resistance
(8) Internal oxygen concentration
and the temperature dependentresistancechange within
Internal oxygen concentration and apical flux are related
the root itself.
by the expression:
(6) Respiratory r esist ance
^ A t
fluxx;-a2
Respirationalong the root will be reflectedin the apical
flux data as a further diffusional resistance.Similarly the
leakage of oxygen to the surrounding medium in subapicalregionsreducesthe oxygenflux at the apex.
The combined resistanceeffect of respiration Rn and
IeakageRr will be given at normal temperaturesby:
60D"*Ct
g cm-2min-r
(24)
where11 is the surfacearea of that part of the root within
the electrode(cmz), Az is the correspondingsurfacearea
of the cylinder radius r, - wl (cm2), and Cl is the internal
oxygen concentration(g cm-t).
(1e) Consequentlyif a value can be given for wall
Rn -F Rl: Rr - Rp
thickness
Where the roots are jacketed in agar or have a natural the internal oxygenconcentrationin the root apex C; may
impermeabilityof the walls in the sub-apicalregionswe can be calculated. With wall resistanceapparently very low
at normal temperaturesthe error introduced by ignoring
approximateas follows :
wall resistanceseemsunlikely to exceed 3/o where the
Rt:Ri-&
Q 0 ) apicalroot radius lies above0.02cm.
It must be recognizedthat the internal oxygen concenthe
and
efective resistanceoflered by respirationalonecan
be estimated.This estimatereflectsthe degreeto which sub- tration in a root may be significantly influenced by the
apicalrespiration restrictsoxygentransport to the apex of effective strength of the oxygen sink imposed by the
the root; it is not a simple reflection of root respiration cylindrical electrode, and different apical root radii can
complicatecomparisonsfrom root to root. The useof short
rate.
electrodes(Z:0.5 cm) reducesthe sink effect and where
roots are of low porosity and r,:<0.07 cm its influence
(7) Effectiuedffision cofficient
is negligible.At higher porosities however (e.g. rice from
Under certain circumstancesit may prove informative to waterloggedsoil) the oxygen consumption by the short
manipulatepore spaceresistancedata to estimateeffective electrodecan be shown to lower the apical internal oxygen
gas-filledporosity or effectivediffusion coefficientsof roots concentrationby as much as 7l oxygenat a
root radius
usingan equation of the form
of 0.05 cm. The influencewill tend to be greater at radii
in excessof 0.05cm and lesswherethe roots are narrower.
(21)
o,:#^
Final Comments
wherelisrootlength(cm),D,isaneffectiveoxygendiffusion
coefficient(cm2s-r) and A, is a crosssectionalarea of the
To compare the effectiveness of internal aeration in
root (cm2).
the roots of various specieswe have used in the past the
26
W. ARMSTRONG AND E. J. WRIGHT
flux data per se, before or after adjustments aimed at
eliminating differencesdue to different apical root surface
areas.Whereroots of approximatelythe sameapicalradius
arecompared,the raw flux data can sufficefor a comparison
of the effectiveinternal aeration and indicate the relative
potential for rhizosphere oxygenation. Where roots
differ in apical radius a direct comparisonof raw flux data
must be avoided, for the magnitude of the apical oxygen
flux is a function of electrode:root radius and root surface
area,as well as upon the internal diffusional resistancesof
theroots.
An alternativeto comparingraw flux data is to compare
internal resistancesor calculate flux values basedupon
theseresistances.
Where the apical root radius differsfrom
somechosenstandard(e.g. r:0.05 cm) the new flux value
basedon a standardelectrodesink may be computedusing
the expression:
6o c"
new flux : crrl-' min-r
Q5)
(n +-n*) x '<- I
where R is some value of internal resistance,e.g. Ri ot
Rn; A* is the apical surface area for a root of standard
radius (1.e.r: 0.05 cm), and R"* is the shell resistance
for the root of standardradius.
The new flux value is a function of the root's internal
resistance;root surface area and liquid shell resistance
differenceshave been eliminated, electrode sink activity
standardized.The imposition of a standardshellresistance
and surface area term means that the flux values may
legitimately be used to compare the efective internal
aeration of different roots. The method used earlier to
adjustflux values(Armstrong 1,967)reflectsthe differences
in apical oxygen concentration of the roots but is a less
rigorous treatment than either of the methods suggested
above.
Wewishto thank MissS, Lythefor her assistance
duringthe
experimental
work. Our thanksareduealsoto Mr. R. WheelerOsmanfor preparingthefiguresand MissE. M. Sharpefor her
helpin preparingthemanuscript.
Physiol. Plant. 35. 1975
References
Armstrong, W. 1964.Oxygen diffusion from the roots of some
British bog plants. - Nature 204: 801-802.
- 1967. The useofpolarography in the assayof oxygenditrusing
from roots in anaerobicmedia.- physiol. plant. 20: 540_553.
- 1967a.The relationship between oxidation-reduction
ooten_
tials and oxygen-diffusionlevelsin somewaterloggedorganic
-J.
soils.
Soil Sci. l8:27-34.
- 1971. Oxygen diffusion from the roots of rice grown under
non-waterloggedconditions. - physiol. plant. 24: 242_247.
- & Read, D. J. 1972.Some observationson oxygen transport
- New Phytol.jl:55-62.
in coniferseedlings.
Berry, L. J. & Norris, W. E. Jr. 1949. Studies of onion root
respiration. I. Velocity of oxygen consumption in different
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partial pressuresof oxygen. - Biochim. Biophys. Acta 3:
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Black, J. D. F. & West, D. W. 1969. Solid-statereduction at a
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flux in soil. - Aust. J. Soil Res. 7 : 67-72.
Greenwood, D. J. 1967a. Studies on the transport of oxygen
through the stems and roots of vegetableseedlings._ New
Phytol.66: 337-347.
- 1?97b.Studieson oxygentransport through mustard
seedlings
(Sinapsisalba L.) - Ibid.66:597-606.
- 1968.Root growth and oxygen distribution in soil. _
Trans.
9th Int. CongressSoil Sci. 1:823-832.
Hale, L. J. 1965. Biological Laboratory Data. - Methuens
(London), p. 109.
Healy, M. T. &Armstrong, W.lgT2.Theeffectivenessof internal
oxygentransport in a mesophyte(pisum sativum L.) _ planta
(Berl.). 103: 302-309.
Heide, H. van der, Raalte, M. H. van & Boer-Bolt. B. M. de.
1963.The effectofa low oxygencontent ofthe medium on the
roots of barley seedlings.- Acta Bot. Neerl. 12: 231_247.
Jensen,C. R., Stolzy,L. H. & Letey, J. l967.Tracer studiesof
oxyggn diffusion through roots of barley, corn, and rice. _
Soil Sci. 103:23-29.
Luxmore, R. J., Stolzy, L. H. & Letey, J.1970. Oxygen diffusion
in the soil plant system.- Agron. J. 62: 317-322,
Martin, M. H. 1968. Conditions affecting the distribution of
Mercurialis perennisL. in certain Cambridgeshirewoodlands.
-J. Ecol. 56:777-793.
Mclntyre, D. S. I970. The platinum microelectrodemethod for
soil aeration measurement.- Adv. Agron.22;235-2g3.
Millington, R, J. 1955. Diffusion consAnt and diffusion coefficient.- Science122:109V1091.