A general approach to the deri v ation of peak area ﬂow dependence inFIA and HPLC amperometric detection

A general approach to the derivation of peak area flow dependence inFIA and HPLC amperometric detection

P. Agrafiotou, C. Maliakas, A. Pappa-Louisi 1, S. Sotiropoulos *

Physical Chemistry Laboratory, Department of Chemistry, Aristotle University of Thessaloniki, Thessaloniki 54124, Greece

Received 18 March 2003; received in revised form 30 March 2003; accepted 30 March 2003

Abstract

The dependence of the peak area, Q , on the analyte volumetric flow rate, U , in flow injection analysis (FIA) and high

performance liquid chromatography (HPLC) with amperometric detection, was studied for typical electroactive species and in a

wide flow rate range. Based on the hydrodynamics of thin channel flow cells (as established by steady state experiments) and simple

dispersion theory considerations, a linear relationship between log Q and log U with a �/2/3 slope has been derived in a general

manner (irrespective to the type of dispersion) for amperometric detectors operated in the limiting current potential region. In the

case of mixed mass transfer and kinetic control the variation of Q with U is more complicated but the peak area is still smoothly

decreasing with the flow rate. These predictions were found to be in reasonable agreement with experiment for a few indicative

systems both in FIA and HPLC experiments. On the contrary, the non-steady state current corresponding to the peak maximum of

FIA and HPLC exhibited local maxima and the former could not be described by any of the equations proposed for the dispersion

in FIA experiments. The practical implications of the form of integrated signal, Q , dependence on flow rate for FIA and HPLC

amperometric detection are also discussed.

# 2003 Elsevier Science Ltd. All rights reserved.

Keywords: Electrochemical detection; HPLC; FIA; Flow rate

1. Introduction

Electrochemical detection has long been established

as a useful detection method in flow injection analysis

(FIA) and high performance liquid chromatography

(HPLC) due to a number of advantages it offers namely,

high sensitivity and selectivity, low cost and detector

miniaturisation [1�/4]. The latter is of great importance

in chromatographic and flowing analysis since mini-

misation of detector dead volume limits additional

sample dispersion and chromatographic peak distortion.

This is particularly useful for the current trend to

employ microbore columns and low dispersion chroma-

tography in order to achieve faster analysis with

minimal sample volumes [5].

Among the various types of amperometric and

coulometric electrochemical sensors for FIA and

HPLC [4�/6], perhaps the most widely used is that of

the thin channel flow cell, made of two blocks and a

spacer. The indicator electrode is usually glassy carbon

(GC), carbon paste electrode (CPE), Au or interdigi-

tated electrodes (IDE), embedded in an insulating block

and separated by the opposite block (which can be the

counter electrode) by an insulating spacer which defines

the channel thickness [7,8].

Analytical expressions for the steady state, mass

transport limited current at rectangular electrodes in

thin channel flow cells have been derived by Weber and

Purdy [9,10], Roosendaal and Poppe [11], Moldoveanu

and Anderson [12] and Compton and Daly [13].

Numerical solutions to the equations describing the

cell hydrodynamics are also due to Anderson and co-

workers both for macro-electrodes [14] and microarray

electrodes [15], to Compton and co-workers [16] for

microband electrodes and to Bond and co-workers for

microdisc electrodes [17]. In these expressions, the

* Corresponding author. Tel.: �/30-2310-99-7742; fax: �/30-2310-

44-3922.

E-mail addresses: [email protected], [email protected]

(S. Sotiropoulos).1 ISE member.

Electrochimica Acta 48 (2003) 2447�/2462

www.elsevier.com/locate/electacta

0013-4686/03/$ - see front matter # 2003 Elsevier Science Ltd. All rights reserved.

doi:10.1016/S0013-4686(03)00271-8

mailto:[email protected]

mailto:[email protected]

steady state current is related to the cell geometric

characteristics, the solute and solvent properties and,

more important, to the solution flow rate. In cases that

radial diffusion to the electrode can be neglected (as it isthe norm except for very small electrodes and wide

channels), the steady state limiting current at an

amperometric detector has been found both theoreti-

cally and experimentally to vary with the cube root of

analyte flow velocity. However, there is little work on

the prediction of the non-steady state peak current in

HPLC (see for example Ref. [18] where a complicated

expression for the peak current as a function of flowrate, based on the van Deemter model for the plate

height, has been fitted to experimental data). At the

same time, we are only aware of a single paper

discussing the effect of flow on peak current in FIA,

based on experiments limited in a narrow flow rate

range [19] and proposing a U�1/6 dependence of the

peak current. There has not either been any attempt to

transform existing theoretical expressions for the flowdependence of dispersion coefficient, D [20�/22] to

corresponding peak current expressions in FIA with

electrochemical detection. Note that the former propose

conflicting dependencies of D on either U1/2 [20] or

U�0.206 [21,22].

Apart from the peak height, a very useful parameter

in quantitative FIA and HPLC analysis is the area under

the peak which, in the case of electrochemical detection,corresponds to the charge passing through the electrode.

The peak area is independent of the type of dispersion

(hence, of system geometric characteristics and arrange-

ment) in FIA and of peak asymmetry (hence of ideal

column behaviour) in HPLC, since it is directly related

to the amount of analyte eluted [23,24]. In the case of

electrochemical detection, the peak area corresponds to

the amount of analyte having reacted as it passesthrough the detector. Despite the usefulness of this

parameter, there is again a single paper discussing the

variation of amperometric detection peak area with flow

rate and testing it in FIA experiments [25]; that

theoretical derivation, based on the analytical solution

of concentration profile equations and predicting a

U�2/3 dependence of Q on U , was limited to the cases

of extended analyte dispersion (Taylor dispersion regime[26,27], i.e. small samples, long reactors, low-to-moder-

ate flow rates [28]). Its validity was experimentally tested

only for a few indicative velocity values and only for

FIA experiments with a single species (not for HPLC

detection or a variety of analytes).

The main aim of this paper is to propose a general

approach to the prediction of the effect of flow rate on

peak area both in FIA and HPLC with amperometricdetection. In more detail, its main objectives in order of

discussion are (i) to test expressions for maximum

current in FIA with electrochemical detection based on

the most popular dispersion equations, (ii) to derive in a

simple and general manner the peak area-flow rate

dependence in FIA and HPLC and test its validity for a

number of systems and experimental conditions and,

(iii) to compare the effect of flow rate on peak area inelectrochemical detection under mass transfer control

with that under mixed or kinetic control (as well as with

that in UV-photometric detection) and discuss the

practical implications for FIA and HPLC analysis.

2. Experimental

2.1. FIA and HPLC system

A Schimatzu model LC-9A pump and a Rheodyne

model 7125 syringe-loading sample injector, fitted with a

20 ml injector loop, have been used in all FIA and HPLC

experiments. The volumetric flow rate range studied was

0.01�/3 ml min�1.

Teflon tubing of 0.01 in. (0.025 cm) ID from Alltech

was employed; its length up to the inlet of the detector inFIA was 24.5 cm (in one set of experiments this length

was 100 cm). This corresponds to a tubing volume

(‘reactor volume’), VR, of 0.012 ml for the 24.5 cm long

tubing and 0.049 ml for the 100 cm one. Since the

sample volume is VS�/0.020 ml, it follows that the ratio

VS/VR is 1.66 and 0.44, respectively, i.e. relatively large

samples and small volume tubing have been used and

hence not very high dispersion is expected in our FIAexperiments, at least at moderate and high flow rates.

Note that Valcarcel et al. (Ref. [28], p. 91) give as an

empirical criterion for limited dispersion in FIA, at flow

rates higher than 2 ml min�1, that of VS/VR�/0.2. Thus,

for the samples and tubing used in this study, the Taylor

dispersion regime (large dispersion, pure diffusional

transport) is only expected for the lowest flow rates

used (for a more quantitative argument see Section 3below).

A 250�/4.6 mm i.d. Kromasil C18 reverse phase

column of 5 mm particle size from MZ-Analyzentechnik

was employed in HPLC experiments with electrochemi-

cal detection, whereas an Alltech 100�/4.6 mm Adsor-

bosphere Catecholamine 3U reverse phase column was

used in the few UV detection experiments carried out.

Again, 24.5 cm long Teflon tubing of 0.01 in. (0.025 cm)ID from Alltech were used both for the column inlet and

outlet.

2.2. Thin layer flow cell and electrochemical

instrumentation

A commercial two-block flow cell was the electro-

chemical detector (Gillson model 141). It consisted of aTeflon† block where a 3 mm diameter GC indicator

electrode is embedded, a stainless steel block serving as

the counter electrode, and 100 mm thick Teflon† spacers

P. Agrafiotou et al. / Electrochimica Acta 48 (2003) 2447�/24622448

(used individually or in stacks of two or three) to

separate the two blocks. The reference electrode (Ag/

AgCl in 3 M NaCl) was screwed into a port drilled

through the stainless steel block; the solution inlet andoutlet ports were on the stainless steel and Teflon†

blocks, respectively. This arrangement was similar to

that of many flow cells that appear in the literature and

first introduced by Poppe and co-workers [29] and

Wightman and co-workers [30]. The opening in the

spacer was such that the channel length was 1.2 cm and

its width 0.5 cm; these, together with the spacer

thickness of 100 mm or 0.01 cm, result in a total detectorvolume of 0.006 ml and a dead volume of 0.00225 ml

from the cell input up to the leading electrode edge (for a

single spacer). In some experiments a modified cell was

used whereby the working electrodes were four carbon

fibres 30 mm thick (WPI Inc.), attached to the Teflon

block and placed perpendicular to the flow.

A laboratory-made potentiostat and a computer-

based data acquisition system were used for electro-chemical detection.

2.3. Chemicals

Ascorbic acid (99.9%) and hydroquinone (99%) from

Aldrich were used in steady state experiments asreversible electrochemical probes. They were also used

together with m -dopa (L-a-methyl-dopa or 2-methyl-3(-

3,4,-dihydroxy-phenyl-L-alanine) from Sigma Chemicals

(99.5%), 5-hydroxy-tryptophan (5-htp; Biochemica, 99%

NT) from Fluka and potassium ferrocyanide from

Aldrich (99.9%) in FIA and HPLC experiments. In

HPLC with UV detection, vanillylmandelic acid (99.5%)

from Sigma Chemicals Co. was used. The supportingelectrolytes in the carrier solution (FIA), the mobile

phase (HPLC) and the sample solutions were phosphate

buffers of required pH and ionic strength values [31].

Potassium phosphate, potassium dihydrogen phosphate,

potassium hydrogen phosphate and phosphoric acid for

buffer preparation were analytical reagent grade. In

HPLC experiments with m -dopa and 5-htp, the mobile

phase included 10% v/v of methanol from Sigma (HPLCgrade).

3. Results and discussion

3.1. Theoretical considerations

3.1.1. Steady state current at a disc electrode in a thin

channel flow cell

The dimensionless number correlation describing theflow in a parallel plate cell with short rectangular

electrodes and for fully developed laminar flow is of

the general form [32]:

Sh�1:85FRe1=3Sc1=3

�de

Lel

�1=3

(1)

where Sh�kmde=D is the Sherwood number,//

/Re�(vde=n)�((U=S)de=n) is the Reynolds number,

Sc�n=D is the Schmidt number, km the electroactivespecies mass transport coefficient, D its diffusion

coefficient, n the solution kinematic viscosity, v the

solution mean linear velocity, U the solution volumetric

flow rate, S the channel cross-section, Lel the electrode

length and de the cell hydraulic diameter. The latter is

equal to four times the area S of the cross-section

divided by its perimeter P and in the case of a

rectangular channel of width wch and thickness dch isgiven by:

de�4S

P�

4(wchdch)

2(wch � dch)�

2(wchdch)

(wch � dch)(2)

F is a parameter in the 0.788�/1 range, depending on cell

geometry (Ref. [32], p. 24). For the equivalent disc

electrode length (Lel)eq�/0.2658 cm (i.e. the length of a

square electrode having the same area as the disc

electrode of del�/0.3 cm diameter; (Lel)eq2 �/pdel

2 /4),

channel width wch�/0.5 cm and thickness dch�/0.01

cm of our cell, F approaches 1 [32]. Eq. (1) (with F�/1)has also been proposed by Picket et al. [33] to hold for

[33,34] ReB/2000, wch�/dch and L /deB/35. Based on the

cell geometric characteristics presented above, it readily

follows that the second condition holds whereas from

Eq. (2) we have de�/0.0196 cm and (Lel)eq/de�/13.5B/

35. Furthermore, for the U�/0.01�/3 ml min�1 range

used, the cell dimensions, and a typical value of 0.011

cm2 s�1 for n , very low Reynolds numbers result (in theRe�/0.059�/17.82 range) and hence laminar flow is

expected in our case. Finally, the distance between the

solution inlet and the electrode is 0.5 cm in the cell used,

i.e. much higher than the entry length of le�/0.01deRe�/

35 mm (calculated for the maximum value of Re)

required according to Ref. [32], p. 18 for fully developed

laminar flow. Summarising, all conditions are met for

Eq. (1) (with F�/1) to describe our steady stateexperiments.

If we take into account that the steady state mass

transport limiting current is given by:

ISS�nFAkmC (3)

where A is the electrode area and km the analyte mass

transfer coefficient, then, substituting the expressions ofthe dimensionless numbers in (1), solving for km and

substituting in (3), it follows:

ISS�1:85nFCAD2=3 1

L1=3

el

1

d1=3e

�U

dchwch

�1=3

(4)

For dch�/wch (as is in our case), the hydraulic diameter

can be approximated according to (2) by de�/2dch. Then

P. Agrafiotou et al. / Electrochimica Acta 48 (2003) 2447�/2462 2449

Eq. (4) becomes:

ISS�1:47nFCAD2=3 1

L1=3el

1

d2=3ch

�U

wch

�1=3

(5)

For rectangular electrodes, where A�/welLel, Eq. (5)

becomes:

ISS�1:47nFCwelD2=3L

2=3el

1

d2=3

ch

�U

wch

�1=3

(6)

which is the equation derived by Weber and Purdy [9,10]

and Roosendaal and Poppe [11] and widely used for

rectangular electrodes in thin channel cells. However,

although there exists an analytical solution for a flow

perpendicular to a disc electrode [6] and a numerical

solution for a flow parallel to microdisc electrodes [17],we are not aware of an analytical solution for the

current at a disc electrode parallel to the flow in a

parallel plate cell. We can attempt an approximation by

modifying Eq. (5) and replacing the electrode length

parallel to the flow, Lel, by an equivalent electrode

length (Lel)eq that corresponds to the length of a square

electrode having the same area as the disc electrode of del

diameter. It then holds by definition (Lel)eq2 �/pdel

2 /4 andsubstituting (Lel)eq from this expression and A�/pdel

2 /4

in (5), we get:

ISS�1:20nFCd5=3el

�D

dch

�2=3� U

wch

�1=3

(7)

It should be noted that if one used as Lel simply the discdiameter del then this would result to a small (ca. 4%)

underestimate of the current. According to Eqs. (5)�/(7),

both for rectangular and disc electrodes, the steady state

current in amperometric detection mode is expected to

be proportional to the cubic root of the flow rate U .

3.1.2. Peak current in FIA experiments with an

amperometric detector

A useful parameter that characterises the extent of

dilution of the injected sample up to the point of

detection (and hence the shape of the FIA peak too) is

the dispersion coefficient D introduced by Ruzicka et al.

[20]. It is defined as the ratio of the injected sample

concentration Cs to the average (in the radial tubing

direction z , see Fig. 1(A) and (B)) concentration

C(xD; t)/of the dispersed analyte over the detector (atan axial coordinate position same as the axial coordi-

nate of the detector, x�/xD, see Fig. 1(B)) at a particular

elution time:

D(t)�CS

C(xD; t)(8)

This means that each point in the concentration

versus time profile (hence in the FIA peak too)

corresponds to a different value of D. At the peak

maximum the concentration of the dispersed analyte

over the detector takes its maximum value and hence the

dispersion coefficient takes its minimum value Dmin (the

subscript is often dropped in the literature):

Dmin�D�CS

Cmax(xD)(9)

When detectors responding to the average radial

analyte concentration are used (such as for example

UV spectrometers) then, introducing the steady state,

non-steady state and maximum signals Sss�/KCs,/S�KC(xD; t); Smax�KCmax(xD) into (8) and (9) is

straightforward (where K is a proportionality constant).

However, in the case of an amperometric detector, as

pointed out by Meschi and Johnson [19], the signal

(mass transport limited current) is proportional to the

analyte concentration at a distance from the electrode in

the radial direction equal to the length of the diffusion

layer d , i.e. at z�/d (see Fig. 1(B)):

I �KelC(xD; d; t) (10)

and for the peak current:

Imax�KelCmax(xD; d) (11)

However, the concentration profile of the dispersed

analyte is not in general homogeneous in the z direction.

This is depicted in Fig. 1 which presents the parabolic,

highly non-homogeneous profile (A) for dispersion in

the convective regime (very short tubing, very highvelocities) and a more homogenised one (B) for disper-

sion in the diffusive or in the mixed convective�/diffusive

regimes [19,28]. It follows that, in general, the average

concentration in the z direction above the detector

C(xD; t)/does not coincide with C (xD, d , t). This

difference is expected to be significant in the case of

purely convective transport (very high flow rates, very

small tubing lengths) but it is expected to graduallydiminish as diffusive transport gets into play at moder-

ate flow rates and tubing lengths (mixed transport,

Taylor dispersion, Taylor�/Aris dispersion) and radial

diffusion tends to homogenise the concentration profile.

Indeed, Meschi and Johnson (Ref. [19], Fig. 2 therein)

have shown that the FIA currents calculated based on

Eq. (10) differ very little from those calculated based on

the average concentration in cases of Taylor-typedispersion. Furthermore, they proved that in these cases

the maximum of the concentration variation with time

at z�/d from the electrode coincides with the maximum

average concentration at the same location, i.e. Cmax(xD,

d )�//Cmax(xD): All these facts point out that, in all cases

but those of pure convective dispersion, Eq. (11) can be

replaced by Imax�KelCmax(xD): On the other hand, the

steady state (limiting) current can be written accordingto (7) as ISS�/KelCS. Hence, for an amperometric

detector in FIA experiments of mixed or diffusion-type

dispersion, Eq. (9) becomes:


D�ISS

Imax

(12)

It follows that, knowledge of the flow rate dependence

of the dispersion coefficient D , in connection with the

cubic root dependence of Iss on the flow rate (Eq. (7),

would provide via (12) the dependence of the peak

current Imax on U . There have been two main equations

suggested in the literature for the dependence of D onU .

The first one is due to Ruzicka et al. ([20] and Ref.

[28], p. 76) and has been derived analytically for Taylor

dispersion conditions:

D�KDU1=2 (13)

where KD is a constant. Given that according to (7) Iss�/

KssU1/3 where Kss a constant, this means that Eq. (12)

results in:

Imax�(KSS=KD)U�1=6�KImaxU�1=6 (14)

where KImax�/KSS/KD.

It should be noted that Meschi and Johnson [19] have

derived the same �/1/6 dependence solving directly the

problem of peak current rather than using FIA theory.

The second equation is empirical and was derived by

Valcarcel and co-workers [22,28] who fitted a large

number of experimental results, in the mixed convectiveand diffusive dispersion regimes, into equations with

adjustable parameters:

D�K ?DU�0:206 (15)

Again, according to (7) Iss�/KssU1/3, and Eq. (12) results

in:

Imax�(KSS=K ?D)U0:54�K ?ImaxU0:54 (16)

At this point, it would be useful to introduce the

parameters whose values define in a quantitative mannerthe type of dispersion in FIA experiments. According to

References [35,28] (pp. 61�/63), a convenient parameter

for dispersion classification is the ratio of reactor

(tubing) length, L , to the flow rate, U . They give the

following indicative limits for a typical analyte diffusion

coefficient of 1�/10�5 cm2 s�1: for L /U B/2.1 cm min

ml�1, the dispersion is governed by pure convection

(very short times, very large sample volumes, very smallreactor volumes, very high flow rates); for 53.1B/L /

U B/159.1 cm min ml�1, mixed convective and diffu-

sional transport prevails (the usual situation under

Fig. 1. (A) Schematic representation of the entire injected analyte dispersion profile in a tubular FIA reactor for convective mass transport

conditions; v denotes the mean linear flow velocity. (B) Schematic representation of injected analyte dispersion in the vicinity of the electrochemical

detector (depicted with its centre positioned at x�/xD) in a tubular FIA reactor for diffusive or mixed mass transport conditions; dVx is the

elementary part of reactor volume above the detector and C(xD)/the mean analyte concentration in that volume; v denotes the mean linear flow

velocity and d the thickness of the electrochemical diffusion layer.


practical FIA conditions); for L /U �/425 cm min ml�1,

diffusional transport prevails (Taylor regime, long

times, small samples, long reactors, very low flow rates).

3.1.3. Peak area in FIA and HPLC experiments with an

amperometric detector

Let Cs and Vs be the concentration and volume of the

injected sample in a FIA or HPLC experiment. If C is

the analyte concentration of an elementary volume dV

in the dispersion zone then, the mass balance require-

ment between the injected sample and the dispersedsample in the total system volume, Vtotal, can be written

in terms of analyte mol at all times as:

CSVS� gVtotal

0

CdV (17)

Let us also consider an elementary volume dVx at an

axial coordinate x in the direction parallel to the flow

and extending over the entire channel diameter in a

direction perpendicular to the flow, as shown in Fig.

1(B). We can then replace in (17) the sum of all

elementary mol quantities CdV within the elementaryvolume dVx by Cx/dVx , where Cx/is the average analyte

concentration in the radial direction within the elemen-

tary volume dVx .

Thus, Eq. (17) can be rewritten as:

CSVS� gVtotal

0

CxdVx (18)

Eqs. (17) and (18) express the mass balance at all times

in the space domain.

In a flowing system the entire quantity of the

dispersed analyte has to pass from any specified point

or elementary region of the system over the period of its

residence in the system, tr, i.e. from the time of injectiont�/0 until the time t�/tr when all the analyte has passed

by this point or elementary region.

We can choose this point or elementary region to be

above the detector (of very small dimensions), i.e. close

to a location of an axial coordinate x�/xD. If we take

into account that the volumetric flow rate in the system

in general, and over the detector specifically, is U �dVxD

=dt then, it follows that the number of analyte molwithin the elementary volume dVxD

at any time is:

C(xD; t)dVxD�UC(xD; t)dt (19)

Then the mass balance of (18) can be expressed in the

time domain as:

Fig. 2. Steady-state current, Iss, recorded at �/0.8 V vs. Ag/AgCl on a GC disc electrode in a thin channel cell as a function of volumetric flow rate,

U , from flowing solutions of 5�/10�6 M ascorbic acid �/0.05 M phosphate buffer (pH 5) and for interelectrode gaps of 100, 200 and 300 mm as

indicated on the graph. Inset; log�/log plots of Iss vs. U .


CSVS�U gtr

0

C(xD; t)dt (20)

As discussed in Section 3.1.2 above, the signal-current

of an amperometric detector is at any time proportionalto the analyte concentration at a radial coordinate

above the electrode equal to the diffusion layer, C (xD,

d , t). Due to the non-homogeneous profile of concen-

tration in general, the latter expression for concentration

does not coincide with the average radial concentration

of Eq. (20) but for the case of purely diffusive mass

transport (Taylor regime), where the concentration in

the radial direction is fully homogenised.However, the left-hand-side of Eq. (20), CsVs, is equal

to the number of injected analyte mol and hence

independent of the type of dispersion and associated

concentration profile. Therefore, the integral of the

right-hand-side of (20) should be independent of these

parameters too. Hence, in calculating this integral for

any type of experimental conditions and dispersion we

can use (with no loss of generality) instead of the realconcentration profile an equivalent profile with a

constant concentration along the radial direction (per-

pendicular to the flow). For this equivalent profile the

above-mentioned concentrations coincide, i.e. C (xD, d ,

t)�//C(xD; t); and hence we can use Eq. (10) to

introduce the current in Eq. (20):

CSVS�U

Kelgtr

0

Idt (21)

The integral in Eq. (21) is the total charge, Q , passing

through the amperometric detector as the eluted analyte

is oxidised or reduced and corresponds to the area under

the FIA or chromatographic peak. Taking also intoaccount (as discussed in Section 3.1.2) that the steady

state current is Iss�/KelCs, and substituting for Kel in

(21), we have:

Q�ISSVS

U(22)

From Eq. (7) we have for the flow rate dependence ofthe current that Iss�/KssU

1/3 (where Kss sums up all

analyte and cell constants of (7)) and, therefore, the

peak area dependence for amperometric detection

becomes:

Q�KQU�2=3 (23)

where KQ�/KssVs, a constant.

The simple form of peak area flow rate dependence

predicted by Eq. (23) is only valid if the potential of

electrochemical detection of the analyte is in the masstransfer control potential range, since it is only then that

the steady state current is given by Eq. (7). However, in

many cases of electrochemical detection the electrode

reaction is under mixed kinetic and mass transfer

control. In that case, the steady state current is made

up of a kinetic current contribution, (Iss)k, which is

independent of flow rate and depends only on reactionkinetics and electrode potential, and a mass transfer

controlled current contribution, (Iss)m, which is given by

Eq. (7). The three currents are related by:

1

ISS

�1

(ISS)k

�1

(ISS)m

(24)

which, if we replace the mass transfer current by

(Iss)m�/KssU1/3 and solve for Iss, gives:

ISS�(ISS)kKSSU1=3

(ISS)k � KSSU1=3(25)

Putting Eq. (25) into (22) we obtain for the peak area of

amperometric detection under mixed kinetic and masstransfer control:

Q�VSKSS(ISS)k

(ISS)kU2=3 � KSSU�

VSKSS

U2=3 �KSS

(ISS)k

U

(26)

It can be seen that the dependence of Q on U is also

affected in this case by the standard rate constant of the

electrochemical reaction of the particular analyte and

the electrode potential, as expressed by the kinetic

current (Iss)k.

In the limit of pure mass transfer control (Iss)k�/Kss

and Eq. (26) is diminished to the form of Eq. (23)

(taking into account that VsKss�/KQ). In the limit ofpure kinetic control (Iss)k�/Kss and (26) becomes:

Q�VS(ISS)kU�1 (27)

At this point we would like to comment briefly on the

very popular technique of pulsed amperometric detec-tion (PAD) which is also being used extensively in the

chromatographic detection of important classes of

organic molecules (see for example Ref. [2], pp. 145�/

148 and Ref. [4], pp. 836�/840). Since the pulse duration

is very short (a few tens of ms) and the diffusion layer is

smaller than the convective shear layer, convection has

no effect on the current and hence the steady state pulse

current, (Iss)p, is at all potentials independent of flowrate. Therefore, by putting (Iss)p in (22) it follows that, in

PAD too, the peak area is given by an equation similar

to (27), i.e. it is proportional to U�1.

It can be seen that in the case of simple amperometric

detection the log Q versus log U plots are only predicted

to be linear in the limits of pure mass transfer or kinetic

control, with a slope of �/2/3 or �/1, respectively. In all

other cases, the dependence of Q on U takes the morecomplicated form of (26) and the slope of the empirical

linear approximation of the log Q versus log U curve is

expected to have values between �/2/3 and �/1.


It is interesting to note that the case of amperometric

detection under pure kinetic control is formally the

same, with respect to peak area flow dependence, to the

case of spectrophotometric (e.g. UV) detection, with adetector signal S independent of flow rate and a peak

area A. Then Eqs. (22) and (23) become:

A�SSSVS

U�KAU�1 (28)

3.2. Steady state experiments for flow cell

characterisation

Fig. 2 shows the variation with volumetric flow rate of

the steady-state limiting current for the two-electron

oxidation of ascorbic acid, recorded at �/0.8 V versus

Ag/AgCl on a GC disc electrode in the thin channel cell

of this work. Flowing solutions of 5�/10�6 M ascorbicacid and phosphate buffer of pH 5 and 0.05 M ionic

strength were used and three inter-electrode distances

were tested (100, 200 and 300 mm depending on whether

a single spacer or a stack of two or three spacers were

employed). The experiments were carried out to check

the validity of the steady state current flow rate

dependence predicted by Eq. (7) for a disc electrode in

a thin channel cell. The Inset in Fig. 2 shows log Iss

versus log U plots exhibiting very good linearity and

slopes close to the theoretically expected slope of 0.33

according to (7).

Furthermore, if we substitute in the same equation

n�/2, D�/6.9�/10�6 cm2 s�1 [7] and C�/5�/10�6

M�/5�/10�9 mol cm�3 for ascorbic acid, del�/3

mm�/0.3 cm, dch�/100 mm�/0.01 cm (one spacer) and

wch�/0.5 cm for our thin channel cell, and U�/1 mlmin�1�/1/60 cm3 s�1 (as an indicative flow rate), we

predict a theoretical current of (Iss)th�/391.2 nA which

is very close to the experimentally observed value of

(Iss)exp�/400 nA. The same tests on the validity of Eq.

(7), were performed using the two-electron oxidation of

hydroquinone (5�/10�6 M in 0.02 M phosphate buffer

of pH 4.68; n�/2, C�/5�/10�6 M, D�/8.5�/10�6 cm2

s�1 [9]) as a model reaction and a ratio of (Iss)exp/(Iss)th�/0.97 was obtained. A summary of results

obtained both for ascorbic acid and hydroquinone

oxidation steady-state experiments is presented in Table

1.

3.3. Variation of peak current with flow rate in FIA

experiments

Fig. 3(A) shows the amperometric responses at twoindicative flow rates, during FIA experiments with a

0.05 M phosphate buffer (pH 5) carrier solution and a

5�/10�6 M ascorbic acid�/0.05 M phosphate buffer

(pH 5) injected sample of 20 ml (reactor length of 24.5

cm). Fig. 3(B) shows similar curves for an experiment

with a 0.05 M phosphate buffer (pH 3) carrier solution

and a 5�/10�6 M m -dopa �/0.05 M phosphate buffer

(pH 3) injected sample of 20 ml (reactor length of 24.5

cm). The potential of the GC electrode was in both cases

�/0.8 V versus Ag/AgCl, i.e. in the limiting current

regime for both compounds (as preliminary variation of

the electrode potential showed) and the current was

measured from the baseline current. It can be seen that

in both cases, as the flow rate increases from 0.5 to 1 ml

min�1 the FIA peak becomes narrower and more

asymmetric, as simple dispersion theory predicts [28]

for the shift from conditions of mixed convective�/

diffusive transport to those of convective transport,

and the peak current increases as well.

A more detailed study of the flow rate effect on FIA

amperometric peak height for the two systems men-

tioned above (reactor length of 24.5 cm), as well as for a

5�/10�6 M hydroquinone �/0.02 M phosphate (pH

4.68) injected sample of 20 ml (reactor length of 100 cm),

is presented in Fig. 4 where the maximum current Imax is

plotted against the flow rate. A maximum is observed in

all three cases and this was also the situation for a

number of other analytes tested (e.g. ferrocyanide and

tryptophan derivatives). The inset shows the variation of

the dispersion coefficient D with flow rate for the

ascorbic acid and hydroquinone systems; D was calcu-

lated from Imax at each flow rate and the steady-state

current Iss for that flow rate, as obtained from the

steady-state experiments described in Section 3.2 above.

It can be seen that the dispersion coefficient shows an

increase for flow rates higher than 1 ml min�1 (the flow

rate range of the maximum in the Imax vs. U curves).

None of Eqs. (14) or (16) could be fitted to an

appreciable range of the results. This is not surprising,

for two reasons. First of all, both equations were

proposed for very limited parts of the dispersion regime,

whereas our results cover a wide range of flow rates. Eq.

(14) strictly holds for Taylor dispersion and when tested

by Meschi and Johnson [19] for a single experimental

system, with L /U values in the 298�/73.5 cm min ml�1

range, it was found that it could only predict the results

obtained at the lowest flow rate. Eq. (16) is based on the

empirical equation for the dispersion derived in Ref. [22]

and tested for L /U values in the 200�/20 cm min ml�1.

It should also be noted that the two equations proposed

by these authors are contradicting each other since Eq.

(14) predicts a decrease of the peak current with

increasing flow rate whereas Eq. (16) predicts the

opposite trend. Secondly, both the theoretical treatment

and the experimental set up of the above two studies

involved a flowing system of a linear and uniform

geometry whereas our system (as well as similar systems

based on electrochemical detection with a thin channel


cell) is characterised by different channel thickness for

the reactor-tubing (internal diameter, dr�/0.025 cm)

and the detector (channel thickness, dch�/100 mm�/0.01

cm) as well as a 908 change in flow direction upon entry

to the detector cell. Hence, flow conditions are expected

to change as the analyte passes from the reactor to the

detector.

Table 2 gives the Reynolds numbers both within the

reactor-tubing of the FIA system, (Re)r, and within the

thin channel detector (Re)d for the flow rates used. The

values of the dispersion type characteristic parameter L /

U and of dispersion coefficient D are also tabulated for

the ascorbic acid and hydroquinone experiments dis-

cussed above. The Reynolds number within the tubing-

reactor was calculated based on:

(Re)r�vdr

n�

(U ?=S)dr

n�

Udr

60Sn�

Udr

60(pd2r =4)n

(29)

where dr�/0.025 cm the tubing diameter, U? and U the

volumetric flow rates per second and minute, respec-

tively, and n�/0.011 cm2 s�1 the typical kinematic

viscosity of aqueous solutions. The Reynolds number

within the thin channel cell-detector was calculated (as

in Section 3.1.1 above) based on:

(Re)r�vde

n�

(U ?=S)de

n�

Udr

60Sn�

Ude

60(dchwch)n(30)

Table 1

Slopes and linear correlation coefficients of log�/log plots of the steady state current Iss vs. flow rate U (for three values of channel thickness dch), for

ascorbic acid and hydroquinone oxidation in a thin channel flow cell

Ascorbic acid Hydroquinone

1 spacer 2 spacers 3 spacers 1 spacer 2 spacers 3 spacers

Slope of log Iss vs. log U

plot

0.3170 (R2�/

0.9995)

0.3123 (R2�/

0.9995)

0.3234 (R2�/

0.9981)

0.342 (R2�/

0.9999)

0.3331 (R2�/

0.9998)

0.3291 (R2�/

0.9994)

Fig. 3. (A) Electrochemical detection FIA peaks recorded at �/0.8 V vs. Ag/AgCl on a GC disc electrode in a thin channel cell for a 20 ml injected

sample of 5�/10�6 M ascorbic acid in a 0.05 M phosphate buffer (pH 5) carrier solution and for flow rates as indicated on the graph. The arrow

indicates the point of injection. (B) Electrochemical detection FIA peaks recorded at �/0.8 V vs. Ag/AgCl on a GC disc electrode in a thin channel

cell for a 20 ml injected sample of 5�/10�6 M m -dopa in a 0.05 M phosphate buffer (pH 3) carrier solution and for flow rates as indicated on the

graph. The arrow indicates the point of injection.


where de�/0.0196 cm the hydraulic cell diameter (as

defined and calculated in Section 3.1.1), whereas dch�/

100 mm�/0.01 cm and wch�/0.5 cm the channel thick-

ness and width, respectively. From the values presented

in this table it can be seen that our results cover an

extended range of the diffusional and mixed transport

dispersion regimes unlike the results of the works of Eqs.

(14) and (16) which cover only parts of them. The

significant change in the Reynolds numbers as the

analyte passes from the reactor to the detector can be

readily seen. Although the volume of the latter is too

small when compared with that of the former (see

Fig. 4. Variation of peak current, Imax, with flow rate, U , in electrochemical FIA experiments under the conditions of Fig. 3 and for the same

ascorbic acid and m -dopa systems, as well as for a 20 ml injected sample of 5�/10�6 M hydroquinone in a 0.02 M phosphate buffer (pH 4.68) carrier

solution. Inset; log�/log plots of dispersion coefficient, D , and volumetric flow rate.

Table 2

L /U (reactor length/flow rate) parameter, reactor and detector Reynolds numbers, (Re)r and (Re)d, and dispersion coefficient, D , for various

volumetric flow rates, U , for ascorbic acid (L�/24.5 cm) and hydroquinone (L�/100 cm) FIA experiments

U (ml min�1) L /U (cm ml min�1) (Re)r (Re)d D

Ascorbic acid

(L�/24.5 cm)

Hydroquinone

(L�/100 cm)

Ascorbic acid

(L�/24.5 cm)

Hydroquinone

(L�/100 cm)

0.01 2450 0.78 0.06 2.9

0.03 817 2.3 0.18 2.2

0.05 490 3.9 0.30 2.4

425 lower limit for purely diffusional transport [28,35]

0.07 350 5.4 0.42 2.5

0.1 245 7.7 0.60 2.5

159.1 upper limit for mixed transport [28,35]

0.3 81.7 333.3 23.2 1.78 3.1 4.45

53.1 lower limit for mixed transport [28,35]

0.5 49 200 38.6 2.97 3.4 4.55

0.7 35 143 54 4.16 3.6 4.7

1 24.5 100 77.2 5.94 3.7 5.2

2 12.25 50 154.4 11.88 5.8 7.25

3 8.2 3.3 231.6 17.82 9.1 9.2

2.1 upper limit for purely convective transport [28,35]


Section 2) to affect to a considerable extent analyte

dispersion, such a drastic change in flow conditions

(combined with the abrupt change in flow direction) is

nevertheless expected to affect to some extend the Imax

versus U curve characteristics. At this point, it should

also be mentioned that the variation of D with U has

often be reported in the experimental literature to pass

through a minimum (see for example Ref. [28], p. 78) in

accordance with our results of the Inset to Fig. 4.

3.4. Variation of peak area with flow rate in FIA and

HPLC experiments

Fig. 5 shows the variation of the peak area-charge, Q ,

of FIA experiments with electrochemical detection for

the m -dopa system for which results have been pre-

sented in Fig. 3(B) and Fig. 4 above. The Inset gives the

log�/log plot of the peak area versus the flow rate and

excellent linearity is observed, with a slope equal to�/0.64, i.e. very close to the expected slope of �/0.66

according to Eq. (23) and our arguments in Section 3.1.3

above. Also, the applicability of (23) extends over a wide

flow rate range (0.03�/3 ml min�1 in this case) in

accordance with our prediction that the peak area-flow

rate relationship is independent of the type of dispersion

in FIA. A test of the validity of Eq. (22) (Q�/IssVs/U , U

in ml s�1 or Q�/IssVs/(U /60), U in ml min�1) was alsoperformed, based on the experimentally found Q values

for various flow rates and the Iss values found from

steady state experiments for the same flow rates, for the

ascorbic acid and hydroquinone systems. The Vs values

thus calculated were 19.59/2 and 21.39/1.7 ml, in

reasonable agreement with the nominal 20 ml of injected

sample.

Fig. 6 presents two typical electrochemical detection

HPLC chromatograms (at two indicative flow rates of

0.5 and 1 ml min�1 flow rates) for a 5�/10�6 M

m -dopa �/0.05 M phosphate buffer (pH 3) injected

sample of 20 ml, through the HPLC column described in

Section 2 and in a mobile phase of a 0.05 M phosphate

buffer (pH 3) aqueous solution �/10% v/v methanol.

Inset (A) shows the variation of the maximum peak

current Imax with the flow rate. Again, similar to our

FIA results, an unclear dependence is observed, not

markedly different to that presented for electrochemical

HPLC experiments in Ref. [18]. Of course, in HPLC

experiments the peak shape and maximum depend

mainly on the thermodynamics and kinetics of analyte

distribution between the mobile and stationary phases

and an attempt to fit the peak current to empirical

equations containing the capacity factor and the height

equivalent of a theoretical plate, based on the Snyder

[36] or van Deemter [37] approximations is also given in

[18]. However, a smooth variation of the peak area, Q ,

with flow rate was observed and, more important, the

log Q versus log U plot given in Inset (B) of the same

figure shows good linearity and a slope of �/0.62 again.

This indicates that our arguments of Section 3.1.3.

regarding the peak area flow dependence hold equally

well both for FIA and HPLC experiments. Table 3

presents the slopes of the log Q versus log U curves for a

number of FIA or HPLC experiments with ampero-

Fig. 5. Variation of peak area, Q , with flow rate, U , in the electrochemical FIA experiment of the m -dopa sample of Fig. 4. Inset; log�/log plot of Q

vs. U .


metric detection, for four different analytes, detected

under conditions of mass transfer control. It can be seen

that, within experimental error, all slopes are close to the

theoretical value of �/0.66.

In order to explore the variation of Q with U in the

case of amperometric detection under mixed control we

have performed experiments for the detection of m -dopa

at different constant potentials so that the electrode

reaction is either at mass transfer or mixed control,

depending on the choice of potential. The Inset in Fig. 7

shows the variation of peak area Q for a similar HPLC

experiment to that of Fig. 6 (at a flow rate of 0.5 ml

min�1) but at different values of electrode potential. In

this curve (also known as hydrodynamic diagram in the

electrochemical HPLC and FIA literature) the mixed

control (ascending part of the curve) and the mass

transfer limiting (constant charge part of the curve)

regions are clearly seen. Fig. 7 itself presents the log Q

versus log U plots for different detection potentials. It is

shown that, as one moves from potentials in the mass

transfer control region (�/0.8 V vs. Ag/AgCl) to

potentials in the mixed control region (�/0.7, �/0.6

and �/0.5 V vs. Ag/AgCl), the linearity of the plots

deteriorates and the slope of the linear approximations

of the curves (its magnitude) increases from 0.6121 to

0.7426, 0.8206 and 0.9034, respectively, i.e. in qualitative

agreement with the prediction of Section 3.1.3 that the

slope for mixed control cases should lie between the

theoretically values of �/0.66 and �/1, predicted for pure

mass transfer or kinetic control, respectively. Fig. 8

presents a similar log Q versus log U plot for the HPLC

amperometric detection of a 20 ml injected sample of 1

mg ml�1 5-htp in a pH 3 phosphate buffer of 0.05 M

ionic strength, on four carbon fibre electrodes at �/1.2 V

Fig. 6. Electrochemical detection reverse phase HPLC peaks recorded at �/0.8 V vs. Ag/AgCl on a GC disc electrode in a thin channel cell, for a 20 ml

injected sample of 5�/10�6 M m -dopa in a 0.05 M phosphate buffer (pH 3) �/10% methanol mobile phase and for flow rates as indicated on the

graph (injection at t�/0). Inset (A); variation of peak current, Imax, with flow rate, U . Inset (B); log�/log plot of peak area, Q , and volumetric flow

rate, U .

Table 3

Values of the slope of log�/log plots of the peak area-charge, Q vs. flow rate U , for ascorbic acid, m -dopa, potassium ferrocyanide and hydroquinone

electrochemical detection FIA and HPLC experiments

Ascorbic acida m -dopab Ferrocyanidec Hydroquinoned

Slope of log Q vs. log U plot 0.669/0.08 0.659/0.05 0.679/0.09 0.639/0.01

a 5 FIA experiments.b 4 FIA and 3 HPLC experiments.c 5 FIA experiments.d 2 FIA and 1 HPLC experiments.


Fig. 7. Log�/log plots of chromatographic peak area, Q , and volumetric flow rate, U , from electrochemical detection reverse phase HPLC

experiments, using a 3 mm diameter GC disc electrode in a thin channel cell, for a 20 ml injected sample of 5�/10�6 M m -dopa in a 0.05 M phosphate

buffer (pH 3) �/10% methanol mobile phase and at various electrode potentials vs. Ag/AgCl, as indicated on the graph. Inset; hydrodynamic (charge)

voltammogram for the m -dopa sample during reverse phase HPLC electrochemical detection experiments under conditions described above, at a 0.5

ml min�1 flow rate.

Fig. 8. Log�/log plot of chromatographic peak area, Q , with volumetric flow rate, U , from electrochemical detection reverse phase HPLC

experiments, using four carbon fibre electrodes of 30 mm diameter at �/1.2 V vs. Ag/AgCl in a thin channel cell, for a 20 ml injected sample of 1 mg

ml�1 5-htp in a pH 3 phosphate buffer of 0.05 M ionic strength; the mobile phase was a 90% v/v pH 5 phosphate buffer of 0.05 M ionic strength �/

10% v/v of methanol. Inset; hydrodynamic (charge) voltammogram for the 5-htp sample during reverse phase HPLC electrochemical detection

experiments under conditions described above, at a 1 ml min�1 flow rate.


versus Ag/AgCl. As it can be seen from the Inset to the

Figure which presents the hydrodynamic voltammo-

gram at 1 ml min�1, this potential is not in the pure

mass transfer control region of the system hence theslope of the linear approximation of the log Q versus

log U plot is �/0.8724.

Finally, Fig. 9 presents a log�/log plot of the HPLC

chromatographic peak area with UV detection (at 254

nm), A, versus the flow rate, U , for the case of 10�3 M

vanillylmandelic acid injected in a mobile phase of a

0.005 M total ionic strength and pH 7. Excellent

linearity is observed and a slope of �/1 is found, incomplete agreement with the theoretical arguments of

Section 3.1.3 and Eq. (28).

4. Conclusions

Steady-state experiments of constant analyte concen-

tration in the flowing solution at various flow rates haveproven that the current at a disc electrode of a thin

channel flow cell is given by an expression similar to that

established for rectangular electrodes. Most important,

the steady state limiting current, Iss, is proportional to

the volumetric flow rate to the power of 1/3, U1/3.

No simple dependence of maximum peak current,

Imax, on flow rate, U , has been found neither in FIA or

HPLC experiments with a common amperometric thinchannel flow cell; instead, Imax versus U curves exhibited

local maxima and, in the case of FIA, none of the main

dispersion equations proposed in the literature could be

fitted to the results over any appreciable flow rate range.

This was attributed to the limited theoretical and

experimental range that these equations have been

derived for or tested in (as opposed to the wide range

of our experiments) and, mainly, to the 908 change in

flow direction of the analyte as it passes from the FIA

tubing-reactor to the detector as well as to the differ-

ences in flow conditions between the reactor and the

detector due to different channel thickness.

On the contrary, in all electrochemical FIA and

HPLC experiments the peak area-charge, Q , varied

smoothly with flow rate, U , being a decreasing function

of the latter. The log Q versus log U curves for analytes

detected under mass transfer control had a slope close to

�/0.66. This value has been derived by simple dispersion

theory and mass balance considerations that hold for

any type of dispersion in FIA (hence irrespective of flow

rate conditions and system geometric characteristics)

and any type of analyte-column-mobile phase interac-

tions in HPLC. Based on similar considerations, the

peak area of FIA and HPLC with amperometric

detection under pure kinetic control as well as with

UV detection have both been found to be proportional

to U�1. In cases of amperometric detection under mixed

kinetic and mass transfer control, Q is a more compli-

cated function of U and the linear approximations of

the log Q versus log U plots have slopes between the �/

0.66 and �/1 values of the mass transfer and kinetic

control limits, respectively.

The use of peak area as the analytical signal instead of

the peak maximum has been known to be advantageous

because the former is independent of the type of

dispersion (hence, of system geometric characteristics

and arrangement) in FIA and of peak asymmetry (hence

of ideal column behaviour) in HPLC [23,24]. Based on

the flow rate dependence of the peak area in electro-

chemical detection FIA and HPLC, we can comment on

Fig. 9. Log�/log plot of peak area, A, vs. flow rate, U , in the UV detection (at 254 nm) reverse phase HPLC experiment of a 20 ml injected sample of

10�3 M vanillylmandelic acid in a mobile phase of a 0.005 M total ionic strength phosphate buffer (pH 7).


a number of special features associated with the choice

of the peak area, Q , as the analytical signal, S , in the

case of amperometric detection.

First of all, the establishment of a universal lineardependence of peak area on U�2/3 in the case of pure

mass transfer control or of a smooth descending Q

versus U working curve in the case of mixed control (as

opposed to the maxima of the Imax versus U curves),

permits for comparisons of results obtained in the same

system but at different flow rates as well as limits the

number of calibrations needed.

Second, if one chooses to work at relatively low flowrates (of course, the lowest practical flow rate will be

determined by elution time, peak broadening and peak

overlapping considerations) then the signal Q for a

given analyte concentration will increase resulting in an

increase in sensitivity. This effect will be enhanced in the

case of analytes with very slow electron transfer kinetics

where an increase in flow rate-mass transport conditions

would shift the voltammetric curve to higher over-potentials and hence decrease the current at a given

potential; on the contrary, working at low flow rates

with such systems and choosing Q as the signal, not only

will the signal increase due to the dependence of Q on U

discussed above but also due to the shift of the

voltammetric wave to lower overpotentials.

Finally, particular attention has to be given on the

definition and assessment of the signal-to-noise ratio (S /N ratio) when using the peak area as the signal. The

baseline of the FIA signal or HPLC chromatogram is

due to the steady-state oxidation (or reduction) of

impurities dissolved in the carrier solution/mobile phase

or of the solvent itself. If at the detection potential the

oxidation (or reduction) of the impurities is under pure

kinetic control (as that of the solvent is), then the

baseline current, Ib, will remain unchanged if the flowrate changes and equal to a kinetic current (Ib)k. If,

however, the reaction of impurities is under mixed or

mass transport limited control, then the steady-state

baseline current will change with flow rate. In the case of

pure mass transport control it will increase linearly with

U1/3 as described in Section 3.1.1, i.e.:

Ib�KbU1=3 (31)

whereas in the case of mixed control and in accordance

with (25) it will hold:

Ib�(Ib)kKbU1=3

(Ib)k � KbU1=3(32)

It can easily follow from (31) and (32) that an increase of

flow rate results in an increase of this type of contribu-

tion to the baseline current.Variations and fluctuations of the background cur-

rent result in signal drifts or peaks that give rise to the

noise, N, of the analytical determination. These current

fluctuations and the corresponding noise can be due

either to voltage fluctuations or changes in the electrode

surface (e.g. by changing adsorption or wetting extent)

or flow fluctuations. The first two sources of noise areindependent of flow rate (dIb is constant). The last

source is only operative when impurities oxidised (or

reduced) under mixed or mass transport control are

present, as discussed above. Therefore, in the latter case,

a fluctuation of flow rate by dU will result, according to

(31) in a baseline current fluctuation-noise of:

dIb

dU�1=3KbU�2=3[dIb�1=3KbU�2=3dU (33)

if the impurities react under pure mass transfer control

and, according to (32) in:

dIb

dU�

1=3[(Ib)k]2KbU�2=3

[(Ib)2k � KbU1=3]2

[

dIb�1=3[(Ib)k]2KbU�2=3

[(Ib)2k � KbU1=3]2

dU (34)

if the impurities are transformed under mixed kinetic

and mass transfer control.

The noise N is defined as the maximum value of the

peak current, dIb (above the baseline current Ib), from a

number of observed noise peaks, when the peak current

is used as the signal. However, when the peak area is thesignal, then the corresponding noise can be defined

either as the area under the maximum noise peak or, as

the product of the maximum noise peak current multi-

plied by the maximum duration-width of the recorded

noise peaks, Dtnoise (i.e. as N�/dIbDtnoise), or (in a

modification of the definition proposed in Ref. [29]) as

the product of the maximum noise peak current multi-

plied by the width of the analyte chromatographic peak,Dtsignal (i.e. as N�/dIb Dtsignal). The dependence of the

S /N ratio (which becomes Q /(dIbDtnoise) or Q /(dIbDt-

signal) in this case) on flow rate, can be predicted by all

possible combinations of Eqs. (23), (26), and (27) with

Equations (34), (35) and that of a flow independent dIb,

for the analyte and the impurities being transformed

under either pure mass transfer, or mixed, or kinetic

control. The situation becomes even more complicated ifone takes into account that Dtsignal and, in general,

Dtnoise too, both depend on flow rate. Regarding the

former, the width of the FIA peak is suggested to be

proportional to U�1 (Ref. [28], p. 90) whereas for the

width of the HPLC peak, empirical expressions based on

the dependence of chromatographic plate height on flow

which describe peak broadening have been proposed

[38]. On the other hand, the width of a noise peak is onlyexpected to depend on flow in cases that the main

contribution to baseline current is from impurities

transformed under mixed or mass transfer control.


A simplification of the situation arises by considering

that the background current is often mainly due to

solvent oxidation (always under kinetic control, hence

associated with a flow independent noise dIb and noisepeak width Dtnoise) and that Q always increases with

decreasing flow rate (Eqs. (23), (26), and (27)). Then, the

S /N ratio (when defined as Q /(dIbDtnoise) is expected to

be higher at low flow rates.

Summarising, it can be seen that the choice of peak

area as the signal in amperometric FIA and HPLC

detection, due to its specific dependence on flow rate,

has a number of implications for electroanalysis inflowing systems.

References

[1] K. Stulik, V. Pacakova, Electroanalytical Measurements in

Flowing Liquids, Ellis Horwood, Chichester, 1987.

[2] H. Parvez, M. Bastart-Malsot, S. Parvez, T. Nagatsu, G.

Carpenter (Eds.), Electrochemical Detection in Medicine and

Chemistry, Progress in HPLC, vol. 2, VNU Science Press,

Ultrecht, 1987.

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