Calibrationless determination of electroactive species

c 2006 Institute of Chemistry, Slovak Academy of Sciences DOI: 10.2478/s11696-006-0032-x

Calibrationless Determination of Electroactive Species Using Chronoamperograms at Collector Segment of Interdigitated Microelectrode Array P. JENČUŠOVÁ, P. TOMČÍK*, D. BUSTIN, M. RIEVAJ, and Z. DOVALOVSKÁ

Institute of Analytical Chemistry, Faculty of Chemical and Food Technology, Slovak University of Technology, SK-812 37 Bratislava, Slovakia e-mail: [email protected] Received 27 July 2005; Revised 24 February 2006; Accepted 6 March 2006

The possibility of calibrationless chronoamperometric determination is described using a pair of individually addressable and diffusion layers interacting segments of interdigitated microelectrode array (IDA). It utilizes dual voltammetric mode where the first segment is polarized with potential corresponding to the limiting current of determined species electrode reaction and the second segment is polarized with potential corresponding to the opposite electrode reaction limiting current. Time at which the current of the collector segment reaches one half of the steady state is hyperbolically dependent on the diffusion coefficient of analyte. The determination of diffusion coefficient allows direct calculation of bulk concentration avoiding calibration with a standard solution. The equipment for measuring of fast response of IDA arrays in dual mode has been developed using a bipotentiostat connected with A/D transducer. It allows less than 1 ms sampling period for ultrafast registration of chronoamperogram. The method was tested and validated with [Fe(CN)6 ]4− , [Ru(NH3 )6 ]Cl3 , and ferrocene model samples using various types of IDA arrays.

INTRODUCTION Interdigitated array (IDA) microelectrodes are geometrically improved kinds of two-dimensional planar microelectrodes which become more and more popular devices in modern electroanalysis [1, 2]. They exhibit unique properties based on coupling them to the arrays with individually addressable segments. The distance between them is very short (for some cases in the under micrometer range), therefore diffusion layers can overlap. If both segments of array are polarized with the same potential, the array operates as a macroelectrode with the area equal to the sum of both segments and insulator gaps. An individual polarization of electrodes with potentials of non-equal value opens new possibilities of electroanalysis. Electrochemically reversible or quasireversible redox species generated on one of the segments (generator) can diffuse to the second segment (collector) and there can undergo the opposite electrochemical reaction producing original (analyzed) species [3]. Due to the concentration gradient they dif-

fuse through the gap and electroreact once more. This redox cycling (self-induced or forced) is a very popular principle of interferences elimination in HPLC-EC analysis of biological samples [4, 5]. Neurotransmitters are transferred in such way and interferents are not recorded because of their electrochemical irreversibility. Chromatogram is then cleaned from e.g. ascorbic acid, homovanillic acid, which are the most common interferents. Another applications of the redox-cycling enhanced current are known in trace analysis of redox species where the detection limit of voltammetry is the decreased signal amplification of redox cycling and time integration of obtained response. Iron(III) can be determined by this method [6]. For electroinactive or irreversible redox species a reaction electroanalysis approach was suggested [7]. Species reacting with added analyte is produced on generator segment in this case. Chemical reaction occurs only in the close vicinity (diffusion layer) of the IDA system, so this procedure can be repeated many times with excellent repeatability. When the flux of electrogenerated titrant becomes higher than the dif-

*The author to whom the correspondence should be addressed.

Chem. Pap. 60 (3) 173—178 (2006)

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P. JENČUŠOVÁ, P. TOMČÍK, D. BUSTIN, M. RIEVAJ, Z. DOVALOVSKÁ

fusion flux of analyte incoming from the bulk phase of solution, titrant diffuses through the gaps and reaches the collector the segment potential of which is fixed at the value corresponding to its reduction. This is a typical example of amperometric detection. Ascorbic acid in pharmaceutical dosage form with electrogenerated iodine has been determined in this way [8]. If iodine is replaced by hypobromite which is a stronger oxidation agent, the possibilities of determination of iodides in edible salt, ammonium in natural water [9], organic compounds such as dithiocarbamates and pesticides [10] are opened. A significant effort is given to another special utilization of electroanalysis leading to the development of chronoamperometric techniques avoiding the necessity of calibration. This approach is well known in application of semimicroelectrodes, e.g. hanging mercury drop electrode. The calibrationless determination is based on the separation of linear and nonlinear components of total diffusion flux, thus their portions should be comparable. The electrode diameter should be in tens of micrometer. The limitation of this method is in special care of handling and maintaining of mercury drop hanging from the thin-walled capillary [11—13]. In this paper we propose a calibrationless determination of chronoamperometric method based on fast registration of chronoamperograms of transient characteristics of IDA segments in dual mode. From time at which the collector current reaches the half value of steady-state collector current the diffusion coefficient can be calculated and consecutively bulk phase concentration of the electroactive species can be determined from the steady-state current. EXPERIMENTAL All chemicals were used as received from commercial sources. Doubly distilled water was used for preparation of solutions. Potassium hexacyanoferrate(II) (Lachema, Czech Republic), hexaammineruthenium(III) chloride (Strem Chemicals, MA, U.S.A.) and ferrocene (Strem Chemicals, MA, U.S.A.) were used as model species in chronoamperometric experiments. The mixture of 0.2 mol dm−3 Na2 HPO4 and NaH2 PO4 (ϕr = 1 : 1) served as the supporting electrolyte. In the case of hexaammineruthenium(III) chloride only NaH2 PO4 (pH was adjusted to 4) was used. Experiments with ferrocene were performed in acetonitrile (99 %, Sigma) and tetrabutylammonium tetrafluoroborate was supporting electrolyte. The stock solutions of all model species (5 × 10−2 mol dm−3 ) were standardized by constant potential coulometric analysis and diluted to desired concentration before each analysis. Chronoamperometric experiments were carried out using a Bipotentiostat Model 366A (EG & G Princeton Applied Research, N.Y.) allowing independent po174

Fig. 1. Fig. 1. The layout of the Au thin-film microsystem with the horizontal IDA electrodes. The strip microsystem was realized on alumina-boron-silica glass, with dimensions 15 mm × 3 mm × 1.25 mm. The widths of both the microelectrodes and the gap between them were 5 µm and 10 µm. The first microelectrode consisted of 65 digits and the second one of 32 digits.

larization of two working electrodes which were connected to the computer PC IBM through an A/D transducer PC-818L. Horizontally separated gold IDA microelectrodes (Fig. 1) prepared microphotolitographically were used. The first one contained two individually addressable segments with 65 digit pairs of 1.25 mm length, 5 µm width and with the gap between them of 5 µm. The second one contained only 32 digit pairs with the width and the gap between them equal to 10 µm. I—t curves of collector segment were registered at constant potential 0.1 V vs. SCE for hexaammineruthenium(III) chloride, 0 V for potassium hexacyanoferrate(II) and 0 V for ferrocene. Generator segment was polarized with a potential step in the range from + 0.1 V vs. SCE to −0.5 V vs. SCE for hexaammineruthenium(III) chloride and from 0 V vs. SCE to + 0.8 V vs. SCE for potassium hexacyanoferrate(II) and ferrocene. RESULTS AND DISCUSSION The method proposed in this paper is based on Aoki’s theory [14] which has been verified in our laboratory and found to be in agreement with experimental results. According to this theory the following postulates should be assumed for the calculation of chronoamperometric curves of generator and collector segments in dual mode: a) Interdigitated array has a large number of single microband microelectrodes with negligible edge effect; b) each microband has the same width We ; c) length of microband b is many times longer than We ; d ) transport of electroactive species is made only by diffusion; e) oxidized and reduced forms have the similar values of the diffusion coefficient. The working potentials are stepped to values at which both processes (cathodic and anodic) start to


Chem. Pap. 60 (3) 173—178 (2006)

CALIBRATIONLESS DETERMINATION USING CHRONOAMPEROGRAMS

-20

a

Icoll [t0.5,Icoll/2]

0

I/µA 20

Igen

40

Fig. 2. Schematic diagram of PC connection through A/D transducer with a bipotentiostat. Gen – generator array, Coll – collector array, R – reference electrode, C – counter electrode.

proceed. Generator and collector should be polarized by the sufficient value of potential to assure electrolysis at 100 % current efficiency. Aoki treated these processes through dimensionless anodic current Ia /nF cDt and cathodic current Ic /nF cDt as a function of dimensionless time Θ = Dt/W 2 where W = We + Wg (We – width of microband, Wg – gap width between two adjacent microbands). The steady-state current Iss (cathodic or anodic) can be expressed as (Ia )ss = (−Ic )ss = zF cbDK(1 − p)/K(p)

(1)

where z is the number of electrons, F Faraday constant, c bulk phase concenration of electroactive species, b length of microband, D diffusion coefficient of electroactive species (all symbols are valid for all equations) where ⎛ ⎞2 πWg ⎜ ⎟ 2W ⎟ p = 4 sin ⎜ (2) ⎝ πWg ⎠ 1 + sin 2W

0

10

20

30

40

50

t/s

-20

Icoll

b [t0.5,Icoll/2]

0

I/µA 20

Igen 40

0.00

0.02

0.04

0.06

0.08

0.10

t/s Fig. 3. Chronoamperometric current—time curves of 3 mmol dm−3 ferrocene in 0.1 mol dm−3 tetrabutylammonium tetrafluoroborate acetonitrile solution at an Au-IDA microelectrode with 5 µm width, 5 µm gap, and 65 digits; the generator potential was stepped from 0 V to + 0.8 V vs. SCE, whereas the collector potential was polarized at 0 V vs. SCE (a). Detailed view (b).

K is total elliptic integral expressed approximately K(1 − p)/K(p) = 0.318 ln[2.55(1 + We /Wg )] − − 0.095(1 + We /Wg )−2 (3) An important characteristic of dual mode chronoamperometric specific transfer from the collector to the generator is the time t0.5 at which half value of steadystate collector current is reached. This time is dependent on the microelectrode geometry according to the equation derived by Aoki and Tanaka [14]. t0.5 = 0.9(Wg + We /6)2 /D

Chem. Pap. 60 (3) 173—178 (2006)

(4)

Knowing this time and electrode geometry as well as steady-state current the diffusion coefficient and the bulk phase concentration can be obtained using eqn (1). Transient times are very short, therefore an ultrafast chronoamperogram recording is needed. For this purpose a bipotentiostat in four-electrode arrangement is used. For registration a home-made PC-818L transducer was used (Fig. 2) which allows polarization of IDA microelectrode and synchronized ultrafast acquisition of current—time values of both electrodes. Bipotentiostat allows to set and control the gen-


175


-25

Icoll

-20

Icoll/µA -15

[log t0.5, Icoll/2] -10

-2

-1

0

1

2

log t Fig. 4. The collector current vs. logarithmic time of simulation plot for 1 mmol dm−3 solution of hexaammineruthenium(III) chloride in 1 mol dm−3 KNO3 at Au-IDA microelectrode with 10 µm width, 0 µm gap, and 32 digits. The generator potential was stepped from +0.1 V to −0.5 V vs. SCE, whereas the collector potential was polarized at +0.1 V vs. SCE.

erator potential Eg as well as the collector potential Ec . From external source a voltage input can be added. In case of [Fe(CN)6 ]4− potentials Eg and Ec are set out values −0.1 V vs. SCE. At this value oxidation of [Fe(CN)6 ]4− does not proceed. In the moment of starting chronoamperogram registration a voltage

+0.5 V vs. SCE is put on the generator through input IN and its actual value becomes +0.4 V vs. SCE. At this value oxidation of [Fe(CN)6 ]4− proceeds with limiting current. Chronoamperometric measurements are carried out in the following order: 1. Registration of chronoamperogram on generator and collector with frequency 20000 Hz (10000 points); 2. registration of background under above-mentioned conditions; 3. subtraction of background current; 4. determination of Iss and t0.5 and calculation of concentration. The utilization of the equation describing the relation of t0.5 and D for diffusion coefficient calculation is determined by its validation. Steady-state current Iss is reached with practically 100 % probability when actual time is one hundred times higher than t0.5 , therefore the total time of experiment was 40 s from the beginning of potential step of generator. Values of t0.5 were obtained directly from I—t dependence (Fig. 3) or from dependence I—log t (Fig. 4). This dependence has a lot of noise for times less than 1 ms (first touch of generator product with collector). Influence of capacity current has not been observed due to constant value of collector potential during the recording of chronoamperogram. Precision and accuracy of the determination of t0.5 are the same for both plots. Validity of eqn (4) was tested on gold IDA microelectrode with a gap and band width equal to 5 µm and the results are summarized in Table 1. It is evident that relative reliability interval for 95 % confidence limit is approx. 5 %. The values of diffusion coefficients of three species do not depend on bulk phase concentration in the range of mmol dm−3 and they are in good agree-

Table 1. Verification of Relationship between Half-Time and Diffusion Coefficient for 3 Testing Redox Systems at Au-IDA Microelectrode with 5 µm Band, 5 µm Gap, and 65 Digits

Species

c

t0.5

Dcalc

Dlit

mmol dm−3

ms

10−10 m2 s−1

10−10 m2 s−1

± ± ± ± ± ±

7.1 7.1 6.4 6.4 24.0 24.0

Hexaammineruthenium(III) chloride

1.00 3.00 1.00 3.00 1.00 3.00

Potassium hexacyanoferrate(II) Ferrocene

43.7 44.4 49.4 47.1 13.4 13.1

± ± ± ± ± ±

3.4 2.0 3.2 2.0 1.0 0.8

7.0 6.9 6.2 6.5 22.8 23.3

0.6 0.5 0.4 0.5 2.0 2.0

Number of analyses was 6. Table 2. Characteristic Values of the IDA Electrodes for the Calculation of Electroactive Species Concentration from Measured t0.5 and Iss Wg

We

0.9(Wg + We /6)2

b

Type of IDA microelectrode array

µm

µm

µm

µm

Au 5 µm IDA Au 10 µm IDA

5 10

5 10

30.6 122.5

162.5 80.0

176


K(1 − p)/K(p)

0.494 0.494

Chem. Pap. 60 (3) 173—178 (2006)

CALIBRATIONLESS DETERMINATION USING CHRONOAMPEROGRAMS

Table 3. Validation of Calibrationless Chronoamperometric Method for the Determination of Hexaammineruthenium(III) Chloride, Potassium Hexacyanoferrate(II), and Ferrocene at Horizontally Arranged Au-IDA Electrode with 5 µm Band, 5 µm Gap, and 65 Digits of Generator and Collector Electrodes

Species

Hexaammineruthenium(III) chloride Potassium hexacyanoferrate(II) Ferrocene

c(given)

c(found)

SD

RSD

∆c

(c ± ∆c)/c · 100

103 mol dm−3

103 mol dm−3

104 mol dm−3

%

105 mol dm−3

%

1.00 3.00 1.00 3.00 1.00 3.00

1.20 2.94 0.96 2.91 1.09 2.93

0.37 1.68 0.65 1.20 0.92 1.32

3.5 5.7 6.8 2.6 8.5 4.5

4.0 19.5 7.2 13.2 11.8 16.9

102.0 98.0 96.0 97.0 109.8 97.6

± ± ± ± ± ±

4.0 6.4 7.1 4.4 11.8 5.6

Number of analyses was 6. Table 4. Validation of Calibrationless Chronoamperometric Method for the Determination of Hexaammineruthenium(III) Chloride, Potassium Hexacyanoferrate(II), and Ferrocene at Horizontally Arranged Au-IDA Electrode with 10 µm Band, 10 µm Gap, and 32 Digits of Generator and Collector Electrodes

Species

Hexaammineruthenium(III) chloride Potassium hexacyanoferrate(II) Ferrocene

c(given)

c(found)

SD

RSD

∆c

(c ± ∆c)/c · 100

103 mol dm−3

103 mol dm−3

104 mol dm−3

%

105 mol dm−3

%

1.00 3.00 1.00 3.00 1.00 3.00

1.05 3.07 0.98 3.07 0.99 3.13

0.42 4.20 0.56 1.10 2.30 12.10

4.0 12.8 5.7 3.5 2.3 3.9

4.6 46.2 6.5 11.9 2.9 15.5

105.0 102.3 98.0 102.4 99.4 102.4

± ± ± ± ± ±

4.6 15.4 6.4 4.0 2.9 5.2

Number of analyses was 6.

ment with the values from literature [15]. The explicit equation for bulk phase concentration of analyte without using an additional species as standard was obtained by a combination of eqns (1) and (4). c=

Iss t0.5 2 We K(1 − p) 0.9 Wg + zF b 6 K(p)

(5)

Two gold IDA electrodes used in validation procedure are then characterized by diffusion length 0.9 (Wg + We /6)2 , total elliptic integral K(1 − p)/K(p) calculated from eqn (3), and b value which represents the length of digit multiplicated by the number of digits. Characteristic values are in Table 2. Reliability of this technique was investigated further with model samples of three species at two concentration levels. The results are summarized in Tables 3 and 4. From these tables it can be deduced that arithmetic means do not differ statistically from given values and reliability interval is sufficiently narrow. Therefore, the calibrationless method based on ultrafast collector chronoamperogram registration can be considered as precise and reliable. Precision and accuracy of this method do not differ significantly for the two tested IDA electrodes differing by the band and gap widths.

Chem. Pap. 60 (3) 173—178 (2006)

CONCLUSION Calibrationless chronoamperometric electroanalytical method on IDA microelectrode was developed. It is based on ultrafast recording of chronoamperogram of the collector segment of IDA array in dual mode detecting the product of generator reaction. Time when current is equal to one half of the steady-state current is hyperbolically dependent on diffusion coefficient of electroactive species. Knowing its value and value of steady-state current allows the direct calculation of bulk phase concentration of analyzed species. The A/D transducer with sampling period in the under millisecond range was developed for this purpose. Acknowledgements. The authors gratefully acknowledge the financial support from the Slovak Scientific Grant Agency VEGA (Project No. 1/2464/05).

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Chem. Pap. 60 (3) 173—178 (2006)