Diffusion coefficients of oxygen, hydrogen peroxide and
glucose in a hydrogel
Biezen, S.A.M.; Everaerts, F.M.; Janssen, L.J.J.; Tacken, R.A.
Published in:
Analytica Chimica Acta
DOI:
10.1016/0003-2670(93)80202-V
Published: 01/01/1993
Document Version
Publisher’s PDF, also known as Version of Record (includes final page, issue and volume numbers)
Please check the document version of this publication:
• A submitted manuscript is the author's version of the article upon submission and before peer-review. There can be important differences
between the submitted version and the official published version of record. People interested in the research are advised to contact the
author for the final version of the publication, or visit the DOI to the publisher's website.
• The final author version and the galley proof are versions of the publication after peer review.
• The final published version features the final layout of the paper including the volume, issue and page numbers.
Link to publication
Citation for published version (APA):
Stroe-Biezen, van, S. A. M., Everaerts, F. M., Janssen, L. J. J., & Tacken, R. A. (1993). Diffusion coefficients of
oxygen, hydrogen peroxide and glucose in a hydrogel. Analytica Chimica Acta, 273(1-2), 553-560. DOI:
10.1016/0003-2670(93)80202-V
General rights
Copyright and moral rights for the publications made accessible in the public portal are retained by the authors and/or other copyright owners
and it is a condition of accessing publications that users recognise and abide by the legal requirements associated with these rights.
• Users may download and print one copy of any publication from the public portal for the purpose of private study or research.
• You may not further distribute the material or use it for any profit-making activity or commercial gain
• You may freely distribute the URL identifying the publication in the public portal ?
Take down policy
If you believe that this document breaches copyright please contact us providing details, and we will remove access to the work immediately
and investigate your claim.
Download date: 01. Aug. 2017
553
Analytzca Chmuca Acta, 273 (1993) 553-560
Ekvler Science Publishers B V , Amsterdam
Diffusion coefficients of oxygen, hydrogen peroxide
and glucose in a hydrogel
S A M van Stroe-Blezen,
F M Everaerts, L J J Janssen and R A Tacken
Instrumental Analysts, Chemcal Technology, Eandhoven Unrversity of Technology, P 0 Box 513, 5600 MB Emdhoven (Nethedandd
(Received 27th May 1992)
Abstract
For the design of a new glucose sensor, a knowledge of the diffusion of all partlclpatmg compounds ISneeded A
rotating disc electrode covered unth hydrogel layer was used to determme the effectlve dlftislon coefficients (Den) of
oxygen, hydrogen peronde and hydroqumone m a hydrogel, which ISused m the sensor Measurements were camed
out under steady-state condltlons The three compounds appeared to be slowed by the gel to the same extent A
comparison was made between the Den values of glucose and hydroqumone by simultaneous dlffuslon through a
hydrogel membrane In this case glucose dlffuslon was slowed to a larger extent than hydroqumone diffusion The
effect, however, was independent of the degree of cross-hnkmg of the hydrogel
Keywords Bmsensors, Dlffuslon coefficient, Glucose, Hydrogel, Hydrogen peroxide, Oxygen
It 1s unportant to obtain continuous mformatton about the blood glucose concentration
of
dlabetlcs and an nnplantable sensor 1s a good
altematlve for regularly analysmg blood samples
A number of glucose sensors have already
been developed [l-83 In most of these sensors
glucose reacts with oxygen to yield hydrogen peroxide [l-5] The reaction 1s catalysed by the enzyme glucose oxldase (GOD) Hydrogen peroxide
1s oxldlzed or reduced at a detectlon electrode, its
detectron current 1s proportional to the glucose
conwntratlon
The enzyme 1s unmoblllzed m a
hydrogel by chemical cross&lung with a blfunctlonal reagent As blood 1s low of oxygen, oxygen
should be electrochemlcally produced m the sensor Itself
The disadvantage of extstmg sensors 1s that the
concentration profiles and the dlffuslon patterns
for oxygen, hydrogen peroxide and glucose m the
enzyme-contammg layer are not well defined This
can be the cause of a low detection current, as
only a part of the hydrogen peroxide wdl reach
the detectlon electrode
For a proper design of a glucose sensor, measurement of the dlffuslon coefflcxents of all the
partlclpatmg compounds m the hydrogel seems to
be essential The dlffislon coefficients of oxygen
and hydrogen peroxide have been determmed
electrochermcally, but this method 1s not useful
for glucose The dlffuaon coefficient of glucose
had to be determined with a dlffuslon cell To
correlate the data for oxygen, hydrogen peroxtde
and glucose properly, an addltlonal species, w ,
hydroqumone, IS used, as this compound IS apphcable m both the electrochemical and diffusion
cell methods
THEORY
Correspondence to SAM van Stroe-Biezen, Instrumental
Analysis, Chenucal Technology, Emdhoven Umverslty of
Technology, P 0 Box 513,560O MB Emdhoven (Netherlands)
A rotatmg disc electrode (RDE) covered with
a hydrogel layer appears to be an accurate means
0003~2670/93/S% 00 0 1993 - Elsevler Science Pubhshers B V All rights reserved
554
Pt
S.A M van Stroe-Btezen et al /Anal
disk
where C, 1s the bulk concentration
From Eqn 4, it follows that
f
_ ‘b
udl ddl
c; =
“Dhl
dl
As J = D,,aC$/d,,
that
“Dh,
--
4
-I
-
d,, -I
dastance
J=
FIN 1 Schematic profiles for the concentration of electroactlve species vs the distance from the platinum disc surface
Hydrogel layer thickness IS denoted by d, and Nemst dlffuslon layer by ddl
Ddl
J=Jhl
(1)
=Jdl
From the defimtlon for J and assummg a linear
concentration profile, it follows that
JM=Jd,-Dhl-
4,
dhl
AC,,
=Ddl--d dl
(2)
At the hydrogel layer-Nemst dlffuslon layer mterface a lump m the concentration of the active
component can take place The partition coefficient LY1s defined by
(r = c;/c;
(3)
where the astensk refers to the mterface
The concentration of the electroactlve speaes
at the electrode surface wdl be virtually zero, as a
sufficiently high overpotentlal 1s applied In this
case, from Eqns 2 and 3 the followmg expression
1s derived
ffccii
D,---- = Ddl
dhl
c,-c,*
d dl
(4)
and using Eqn 4, it is found
P
4
dd,bb
aDhl
Ddl
(6)
dh, + d,
The permeablhtles
Phi = “D,,/&
of measurmg dtislon
coefflclents of electrochermcally active compounds [9,10] Figure 1
shows schematically the concentration profile for
active species
Under steady-state condltlons, the flux J (mol
m-2 s-l) m both the hydrogel layer (J,,) and the
Nemst dlffuslon layer (.Zdl)IS the same
(mol mm31
(5)
Ddl
d hl
-+d
-
Chun Acta 273 (1993) 553-560
phi and pdi are defined by
= De&&,
(7)
and
‘dl
= Dd,/dd,
where Deff 1s the effective dfislon
coefficient
(m2 s-l)
Combmmg Eqns 6,7 and 8 and usmg
Z,, = nFA, J
where Z1,, 1s the lmutmg current (A), n the
number of electrons mvolved m the electrode
reaction, F the faraday, 1 e , the charge on one
mole of electrons (Cl, and A, the electrode area
(m2), the followmg equation can be derived
1
1
-Zhm = nFA,C,P,,,
+
1
nFA,CbPd
(10)
The hmltmg current depends on two serial dlffislon resistances The total diffusion resistance
(l/k) is defined by
1
1
ii ---+k=P+P
kh,
1
1
1
(11)
dl
hl
dl
where k IS the total mass transfer coefflclent (m
s-l> The first term (l/k,J 1s mdependent of the
rotation speed The second term (l/kdl), however, 1s proportional to the rec@rocal of the
square root of the angular rotation rate (w) of the
RDE as P,,, is inversely proportional to d,, From
S.A M van Stroe-Btezen et al /Anal
the theory of mass transfer to an RDE [ll], it 1s
known that
(12)
d,, = 1 61( Ddl/~dl)1’3( v~,/w)~‘~
and so
Pcll=
555
Chm. Acta 273 (1993) 553460
Ddl
1 61(D,l/~,,)“3(~dl/~)1’2
(13)
Hence, if the reverse of the hmxtmg current is
plotted against the reverse of the square root of
the angular rotation rate, a lmear plot 1s obtamed, the slope of which and the mtercept gve
mformation about the permeability of the solution (Levlch slope [ 111) and the permeablhty of
the hydrogel layer, respectively
In this way, effective diffusion coefficients of
oxygen and hydrogen peroxide can be determined
electrochemlcally
However, glucose IS electrochemically inactive and its diffusion coefficient
has to be determmed by the diffusion cell method
A comparison between the effective diffusion coefficients of hydroqumone (electrochermcally determined) and glucose can be made by slmultaneous diffusion through a membrane made of the
same hydrogel material as used for the RDE
expernnents, which 1s strengthened by a filterpaper on each side of the membrane The concentration profile 1s shown m Fig 2 In this
c*
method two stirred solutions, A and B, where
C, * C,, were separated
For relatively short tnnes the total flux J
through the various layers 1s constant
J=kAC
(14)
where AC = C, - C, = C, and k IS, similarly to
Eqn 11, the total mass transfer coefficient (m
s-l)
Again, the diffusion resistance 1s built up of
several terms
1
1
2
2
z=k,+k,+k,
2dcM 2d,
=-+-d,
(15)
D eff
Ddl + D,
where the subscripts m, dl and f refer to the
membrane, the Nemst diffusion layer and the
filter-paper, respectively Combmmg Eqns 14 and
15 gives
AC
2d,,
2d,
(16)
-+D+D
Dell
f
eff
The total amount of glucose or hydroqumone
transported from compartment A to compartment B can now be rotten as
C,V= J&t
(17)
I
stirred
\
stirred
C”
A’
solution
;olutlon
A
B
F@ 2 Concentration
compartments,
d,
profiles through a hydrogel membrane (d,)
A and B Nemst dtffuslon layers are denoted by d,
wth
a filter-paper
(dt) on each side, placed between two
SA M van Stme-Bwen
556
and so the rate of Increase of the concentration
m solution B 1s
1
dC,
JA,
-=-c
AC*
dt
v
2d,,
2d,
d,
Ddl
( -+D+D
f
eff
1
(18)
By comparing the slope of the plots of C, vs
tune, the ratlo of the effective diffusion coefflclents of hydroqumone and glucose m the membrane can be determined However, first the dlffusion resistance of the Nemst dlffuslon layers
and the two filter-papers for both hydroqumone
and glucose have to be checked and inserted m
Eqn 18
In this diffusion cell method, lmperfectrons of
the gel do not matter as the two compounds
dffise simultaneously through the same membrane The thickness and area of the membrane
are also of no unportance
EXPERIMENTAL
Reagents
The hydrogel used for these experiments was
made of poly(vmy1 alcohol) (PVA) from Denka
Poval (B24) and cross-lmked mth glutaraldehyde
(25%, w/w, aqueous solution, Merck) and photosensitive DTS-18 (polyazomum salt from PCAS,
LoneJumeau, France)
NaH,PO,
2H,O and Na,HPO,
2H,O, used
for the buffer solution were purchased from
Merck Hydrogen peroxide (30%, w/w, aqueous
solution) was obtained from Chempro Pack, hydroqumone from Merck and D-glucose from
Janssen Chlmlca
Glucose detection was performed with a Sigma
glucose lut (No 6351, based on the reaction of
glucose with o-tolmdme, which yields a bluegreen complex All solutions were prepared with
demmerahzed, distilled water
Instrumentatwn
For the RDE expemnents a Wenkmg POS 73
potentlostat was used, eqmpped with a dlgltal
multimeter (Fluke 8600 A> and a Motomatlc E550-M stn-rmg motor Recordmg was carried out
wrth an x,y recorder (Phllps 8120) A clrculatmg
et al /Anal
Chm Acta 273 (1993) 553460
water-bath (Colora NB-32981) was used for temperature control of the one-compartment cell
Diffusion cell experunents were performed
wth a magnetic stirrer m both compartments,
which were thermostatically controlled with a
Colora NB-32981 clrculatmg water-bath For the
determmatlon of the glucose concentration an
LKB Blochrom Ultrospec II Qpe 4050 spectrophotometer was used for detecting the glucase-o-tolmdme complex at 635 nm The same
spectrophotometer
was used to determme the
hydroqumone concentration at 290 nm
A Talysurf 4 roughness meter from Rank Preclslon Instruments was used to measure the thlckness of the gel layers
Preparatwn of gel layers
A 10-g amount of PVA was slowly added to 90
cm3 of demmerahzed water and stirred The solution was heated for 15 h at 80°C until all the
PVA had dissolved and a homogeneous solution
was obtained The solution was cooled to room
temperature Just before the spmmng procedure,
0 20 g (0 2%, w/w) of DTS-18 and 0 16 or 0 40 g
of 25% (w/w) aqueous glutardlaldehyde were
added With a pipette an ahquot of the resultmg
solutron was placed on the required surface (electrode surface or glass plate) After spmmng for 5
s at 1000 rpm and for 25 s at 3000 rpm, the gel
layer was dried for 30 mm at 40°C The spinning
and drying procedure was repeated until enough
layers had been spun on the surface Thereafter
the gel layer was u-radiated with UV radiation at
room temperature for 90 s The gel layer was
developed m demmerallzed water for 2 mm and
unreacted reactants were washed away Finally,
the gel layer was dried for at least 1 h at 60°C
The thickness of the gel layer on both platmum electrodes and glass plates (control measurement) was measured v&h a roughness meter,
connected mth a thermograph The thickness of
a swollen gel layer (after contact with an aqueous
solution) could also be measured with this technique
Procedures
For all electrochenucal experunents a polished
platmum electrode was used as the workmg elec-
SA M van Stroe-Bwzen et al. /Ad
557
Chm Acta 273 (1993) 553-560
trode (A, = 0 50 x low4 m2) Further, a platmum
counter electrode wrth a surface area of 5 x 10m4
m* s-l and a saturated calomel reference electrode (SCE) with a Luggm capillary were placed
m the one-compartment
cell A circulating
water-bath was used to keep the temperature
constant As supportmg electrolyte 0 1 M sodmm
phosphate buffer (pH 6 7) was used with a kmematlc vlscoslty of 0 9 x 10m6 m2 s-l at 25°C and
0 7 X 10m6 m2 s-l at 37°C [12]
For oxygen measurements the buffer solution
was saturated with oxygen (1 atm) for at least 30
mm This yields an oxygen concentration of 1 1
mol me3 at 25°C and 0 9 mol mm3 at 37°C [13] A
voltamrnogram was recorded from + 600 to - 650
mV (vs SCE) at a rotation speed varymg from 1
to 49 s-l (Pt electrode experunent) or from 0 5 to
16 s-l (Pt-PVA electrode experunent)
For hydrogen peroxide measurements (7-8 mol
mm31 the buffer solution was saturated wth argon before adding hydrogen peroxide and voltammograms were scanned from +300 to -650 mV
(vs SCE) The rotation speed for both the Pt
electrode and Pt-PVA
electrode experiments
varied between 1 and 9 s- ’
Hydroqumone studies (2 mol rnp3) were performed with an argon-saturated buffer solution
wth hydroqumone added before saturation Anodlzatlon from - 550 to + 1200 mV (vs SCE) was
conducted at various rotation rates (Pt electrode
l-36 s-l, Pt-PVA electrode 0 5-9 s-l)
For all three compounds the electrode was
rotated at high speed ( > 50 s- ’ for a Pt electrode
and > 16 s-l for a Pt-PVA electrode) for about
20 s before a new scan was made The scan rate
varied between 25 and 50 mV s- ’ for Pt electrode expenments and between 2 and 10 mV s-l
for Pt-PVA electrode experiments
With a dlffuslon cell contammg two compartments, the ratio of the effectwe diffusion coefflclents of glucose and hydroqumone was determmed Compartment A of the cell contamed 160
cm3 of 0 1 M sodium phosphate buffer with 100
km01 rnv3 glucose and 0 100 km01 mm3 hydroqumone Imtlally compartment B contained only
160 cm3 of phosphate buffer Between the two
compartments
a cross-lmked PVA membrane
(3 46 cm21 was placed with a filter-paper
(Rotband, Schlelcher and Schull) on each side for
solidity purposes Thereafter both compartments
were snnultaneously filled with the solution The
concentration
mcrease m compartment B was
followed for 5 h, v&h UV spectrophotometry for
hydroqumone and Hrlth a glucose lut [14] and
vlslble spectrophotometry
for glucose Although
only samples from compartment B were analysed,
an equal amount of sample was taken from compartment A to keep the solutron levels m both
compartments equal and to prevent forced dlffuslon through the membrane and destruction of
the membrane
The influence of the two filter-papers and the
Nemst diffusion layers was checked by conductmg a comparative expemnent Hrlth only the two
filter-papers placed between the two compartments
The temperature was mamtamed at 25°C with
a clrculatmg water-bath for all diffusion cell experiments and both compartments were stirred
magnetically
RESULTS AND DISCUSSION
Properttes of the gel layer on an RDE
Several PVA gel layers wth different degrees
of cross-hnkmg were used to investigate the dlffuslon behavlour oxygen, hydrogen peroxtde and
hydroqumone
In Table 1 properties of gels A-D are grven,
such as thickness, percentage of glutardlaldehyde
added and swelling factor after saturation with
buffer solution All gels were made on different
days Although gel solutions A, B and C were
TABLE 1
PropertIes of the various hydrogels used for dtislon
surements
mea-
Gel
No of
layers
Glutardlaldehyde
added
0
d,,, (dry)
(pm)
Swellmg
factor
A
B
c
D
4
2
4
4
0 16
0 16
0 16
040
13 5
80
260
13 0
23
23
23
21
SxI M van Stroe-Btezen et al /Anal
558
made wth the same procedure, the thrckness of
one spun layer, vaned substantially
If the same gel solution (1 e , gel A) was spun
on several surfaces (platmum discs or glass plates),
it was found that the spmrung and cross-l+nkmg
procedure provided layers of reproduclbll thickness and degree of cross-hnkmg This means that
the dtierence m the behawour of the gel layers 1s
due to the gel solution preparation
Chtm Acta 273 (1993) 553-560
4
3
sP
2
2
F
L
Detemzznatwn of dzffzuwn coefficzents
Plots of 1;: versus U-~/’ gave straight lines,
as expected, for measurements with both the Pt
electrodes and Pt-PVA electrodes (Figs 3 and
4)
Table 2 shows the diffusion coefflclents m the
buffer solution and the effective diffusion coefficients m the gel layer for various gels and at two
temperatures (25 and 37°C) The ratlo Deff/Dd, IS
also given
For oxygen, hydrogen peroxide and hydroqumone the Deff/Dd, ratios are virtually ldentlcal
and depend on the properties of the gel and
temperature
This means that the ratlo of the
effectwe diffusion coeffrclents for the three compounds m the hydrogel layer is almost ldentlcal
with this ratio m the buffer solution
Snnultaneous diffusion of glucose and hydroqumone through two filter-papers shows a lmear
Increase of C,/C,
for both species (Fig 5) C,
was divided by C, (= AC) to correct for the
different starting concentrations The slopes of
the lines of glucose and hydroqumone have a
2
1
0
000
020
rotation
040
rate
060
(rad/sJyo5
Fig 3 Rotatmg disc electrode data wth a Pt electrode
(T = 25°C) for (A 1 H,O,, ( +) O2 and (01 hydroqumone
ratio of 0 81 Washburn [121 gave a dlffuslon
coefficient of 0 52 X 10m9 m2 s-l for glucose m
pure water at 15°C and of 0 66 X lop9 m2 s-l for
hydroqumone The ratio of the diffusion coefflclents under these condltlons 1s 0 79, which makes
it acceptable to consider the two filter-papers as
a stagnant layer of buffer solution wth a dlffuslon coefficient equal to that m the Nemst drffuslon layer The diffusion resistance of the Nemst
diffusion layer and the filter-paper (Eqn 15) can
TABLE 2
DdYuslon coefficients m the buffer solution and effectlve dlffnslon coefficients m the various gels for O,, H,O, and hydroqumone
(HQ) at two temperatures
T
(“0
25
37
Buffer
Ddl
00-g
m* s-l )
02
Hz%
HQ
02
Hz%
HQ
193
143
089
246
183
1 17
Gel A
D
($9
Gel B
2
m2 s-l)
040
031
020
060
045
027 a
a Unreliable measurement, gel destroyed
$L9
Gel D
Gel C
D
G-9
2
m* s-l)
0 21
021
022
0 25
0 25
023 a
068
050
031
099
0 73
043 a
D
g
mz s-l)
0 35
0 35
0 35
040
040
037 =
055
040
025
082
058
028
028
028
033
031
036
027
0 18
054
037
0 19
0 19
0 20
022
022
-
S.A M van Stroe-Bezen
et al /Ad
559
Chm. Acta 273 (1993) 553-560
12
‘?
9
Lh
i
0’
F
--b
0
E
3
5
-
0’
rotation
rate-O5
0
060
040
020
000
be considered
tion layer
2
2
dl
f
k+k=_=D=D
120
240
180
time
300
(mln)
Fig 6 Data for a dlffuslon cell with a hydrogel membrane and
two filter-papers Ca / C, plotted agamst tune for ( + 1 hydmqumone and (A ) glucose T = 25°C
as one resistance of a buffer solu-
1
dbl
kbl
dbl
bl
(1%
dl
15
i
12
9
Q
0”
‘m
0
60
kad/s)-05
F@ 4 Rotating disc electrode data with a Pt-PVA electrode
(T = 25Q for (A 1 H,O,, (+I 0, and (0) hydroqumone
’
6
where the subscnpt bl refers to the buffer solutlon layer
As the dlffuslon coefficient of hydroqumone m
0 1 M phosphate buffer at 25°C is 0 89 x 10V9 m2
s-l, it can be calculated that the diffusion coefflclent of glucose under the same condltlons IS
0 72 X 10m9 m2 s-l Also, kb, can be calculated
for both compounds using the slopes of Fig 5, as
m this case dC,/dt = kblfiG4f/C/’ with A, =A,
= 3 46 x 10e4 m2 s-l For hydroqumone a value
of k,,= 59X lo-’ m s-l was found and for
glucose k,, = 4 8 x lo-’ m s-l
A gel C membrane, together with a filter-paper
on each side, was placed between the two com-
6
TABLE 3
Dlffuslon coefficients m the buffer solution and effectwe
dlffislon coefficients m two gels mth dtierent degrees of
cross-hnkmg for hydroqumone and glucose at 25°C
Compound
0
40
80
time
120
160
200
m* s-l)
(mln)
Fig 5 Data for a dfiuslon cell wtth two filter-papers Ca /C,
plotted agamst tune for (+I hydroqumone and (A) glucose
T = 25°C
Buffer
Ddl
(1o-9
Hydroqumone
Glucose
089
072
Gel D
Gel C
:;_g
m* s-l 1
025
0062
g
d,
028
0086
Dee g
(lom* s-l)
0,~
z
018
0045
020
0 062
560
SA M van Stroe-Btezen et al /Anal Chm Acta 273 (1993) 553460
partments and also gave straight lmes (Fig 6)
Now the slopes have a ratio of 0 63, which means
that glucose 1s slowed by the membrane to a
greater extent than hydroqumone The ratlo of
0 63 can also be seen as the ratio of the total
mass transfer coefficients of hydroqumone and
glucose, so
1
i k,
l
REFERENCES
1
+ kbl 1hydrcqumone
1
1
k+k
ul
The authors wish to acknowledge M H KUIJpers, M W C M Nleuwesteeg and G Steeghs
from Drager Medical Electromcs, Best, Netherlands, for their contrlbutlon to this work
= o 63
(20)
bl I glucose
InSerting the value of kb, for both ghKose and
hydroqumone, the ratio of the effective diffusion
coefflclents
1s found to be 0 25 CD,,/
= 0 28 whereas
(D&Q,&_
=
Ddl)hydroqunone
0 086 (Table 3) For a second, extra cross-linked
membrane (gel D), the same ratlo of the slopes of
0 63 1s found (Table 3) The ratio of the effective
diffusion
coefflclents
1s 0 24, and (Deff/
= 0 20 whereas
(Deff/Dd,)glu_ =
Ddl)hydroqumone
0062
The conclusion can be drawn that glucose 1s
slowed more than hydroqumone and also than
oxygen and hydrogen peroxide, because of an
mteraction of glucose urlth the gel matrix In both
gels glucose 1s slowed 3 2 tunes more than hydroqumone (0 086 vs 0 28 and 0 062 vs 0 20) A
size-exclusion effect can be excluded because,
although gel D 1s far more cross-hnked than gel
C, this has evidently no mfluence
1 S Gemet, M Koudelka and N F de Rooy, Sensors Actuators, 18 (1989) 59
2 M H Kugpers, US Pat, 4 492622 (1985)
3 K. Mosbach, Methods Enzymol , 44 (1976) 263
4 M Lambrechts, PhD Thesis, Cathohc Umversity of Leuven, Leuven, 1989
5 M Sluclun, R Kawamon, N Hake, N Asakawa, Y
Yamasaltl and H Abe, Blamed Ebochlm Acta, 43 (1984)
561
6 P Janda and J Weber, J Electroanal Chem, 300 (1991)
119
7 D Hale, H L Lan, LI Boguslavsky, HI Karan, Y
Okamoto and T A Skotheim, Anal Chun Acta, 251(1991)
121
8 P Bmnco, J HaladJlan and C Bourddlon, J Electroanal
Chem , 293 (1990) 151
9 DA Gough and J K Leypoldt, Anal Chem , 52 (1980)
1126
10 CA Marrese, 0 Miyawalu and L B Wmgard, Jr, Anal
Chem , 59 (1987) 248
11 V G Levlch, Physxochenucal Hydrodynarmcs, Prentice
Hall, Englewood cliffs, NJ, 1962
12 E W Washburn, International Critical Tables, McGrawHdl, New York, 1st edn , 1929
13 ML Hitchman, Measurement of Dissolved Oxygen
(Chemical Analysis, Vol 491, Wdey, New York, 1978
14 J E Middleton, Clm Glum Acta, 31 (1968) 433