Anal. Chem. 1988, 60, 1751-1758
1751
Spectroelectrochemical Sensor Based on Schlieren Optics Janusz Pawliszyn' Department of Chemistry, University of Waterloo, Waterloo, Ontario, Canada N 2 L 3G1, and Department of Chemistry and Biochemistry, Utah State University, Logan, Utah 84321
A theoretlcal model descrlblng the thermal relaxation process, associated with a Selective concentration gradient technique applied to electrochemlcal Interface studies, has been developed. The method conslders both the effects associated wlth the contrlbutlon of the concentratlon gradients as well as the electrode surface light adsorptlon to the total deflection slgnal. The model clearly lndlcates the required experimental procedures leadlng to optlmum condltlons for measuring quantities or absorption propertles of electrochemlcal species present In an electrolyte or deposited on a surface. Data obtained durlng a slmple two potential step experiment Involving benzoquinone reductlan are In agreement with the theory. A tightly focused He-Ne laser probe beam was used to measure the refractlve Index gradient formed above the electrode after the excltatlon pulse. A pollshed face, platlnum wire was used as a worklng electrode. The excltatlon beam was Introduced by an optical fiber. I n another experimental arrangement, the tip of an optical fiber with a thin metal fllm spattered on Its cut end constituted the electrode. The llmlt of detection of thls method, In relatlon to the electroactlve specles present In the electrolyte, Is close to lod M In the universal mode and 3 X lo-' M In the Selective mode of operation. Its dynamic range extends over 4 orders of magnitude of bulk analyte concentration. Thls method has also been appNed to characterlze concentration profiles above the electrode surface and to measure the analyte concentratlon In a flowing stream.
Schlieren optics techniques (1)were widely applied to study concentration gradients produced by early electrochemical methods (2, 3). In these techniques, the refractive index gradient fields associated with concentration gradients are detected by measuring the local deflections of the probing light beam. Schlieren methods were found to be simple, inexpensive, and able to provide good universal qualitative representation of a diffusion layer. However, more quantitative investigation required lengthly evaluation of the Schlieren images by integrating microdensitometry (4). Therefore, interferometric methods, which one more convenient but less sensitive toward the high gradients (5),are used almost exclusively at the present time to provide universal quantitative information about the concentration profiles above electrode surfaces (6). Recently, laser beam deflection and lensing methods, associated with mirage effects produced after an excitation pulse (Schlieren optics generated by the temperature gradient), were developed to investigate light-absorbing samples (7,8,22). For example, the investigation of absorption properties of molecules present on surfaces has been possible (9,lO) (see Figure lb). This method is very sensitive, since small beam deflections down to lo+ rad (shot noise limit) can be measured by using a lock-in amplifier (11). Present address: Department of Chemistry, University of Waterloo Waterloo, ON, Canada N2L 3G1. 0003-2700/88/0360-1751$01.50/0
This development opened up new possibilities for simple and high-sensitivity concentration gradient measurements. The first observations of this type were reported by Roger and co-workers (12)and Royce et al. (13)in association with their electrode surface studies. However, not until very recently have analytical applications of the concentration gradient method been proposed (14). The initial measurements indicate that the laser deflection method provides information similar to that gained from electrometer detection in cyclic or step voltammetry. The only difference is related to the time delay associated with the diffusion of the electrogenerated species into the probing beam region. This observation should not be a surprise, since electric current magnitude (number of electrons per time) detected by the electrometer is proportional to the mass flux of reactant diffused to the electrode surface. This flux, by the Fick's law relationship M A / S = DA dCA/dx, where MA is a mass flux of reactant A, S is the surface area of the electrode, and DA is the corresponding diffusion coefficient, is also directly proportional to the concentration gradient of the reactant produced in the diffusion layer. Therefore both current and concentration gradient magnitudes are related to the concentration of reactant in the bulk. This will be discussed more clearly in the theory section of this paper. The exact sensitivity of the concentration gradient technique varies, depending on the particular redox system, but is close to the sensitivity achieved by electrometer detection. In addition, other investigators have reported that this method could be used to study zero net electron electrochemical processes (15)and could provide the information about the whole electrochemical interface by moving the probing beam to various locations with respect to the electrode surface (16). This method, similar to the orthodox Schlieren optics schemes, provides only universal information about the electrochemical interface. The most limiting factor of Schlieren optics methods is the fact that the net refractive index gradient above the electrode is produced by opposing concentration gradients related to products and reactants. Investigation of complex electrochemical processes requires the application of selective methods in order to distinguish between various electrochemical species. A direct absorption method was proposed for this application (17). A monochromatic laser beam is passed parallel to the electrode surface and measures the concentration of absorbing species at a given location. This method is able to image the whole diffusion layer by use of a diode array detector (18). However, this direct absorption technique requires a good-quality laser source that is able to produce highly coherent light beams. It also is limited by the availability of sensitive detectors for a given wavelength of interest. These restrictions significantly reduce the flexibility of this method. For example, it would be difficult to obtain an entire absorption spectrum of species present in a diffusion layer. Recently another selective technique based on indirect optical absorption measurement, using the photothermal process, has been proposed and investigated experimentally (19,20). It uses an experimental arrangement similar to that of the laser beam deflection method mentioned above and also measures the refractive index gradient. Electrochemical ex@ 1988 American Chemical Society
1752
ANALYTICAL CHEMISTRY, VOL. 60, NO. 17, SEPTEMBER 1, 1988 EXCITATISN I N T E N S I T Y
t 'L
a'z
X,Y,L
TEI"PERATUI1E REFRACTIVE INCEX
X,Y
!&
_ _+ 5C
500
000
50C
8 *Y
-t
. CO
+--\-+ I 50
2 00
2 50
3 OD
3 50
0
Flgure 2. Concentration profiles of product (a) and reactant (b) above the electrode surface. The distance from the electrode surface is expressed in u = (20,~)"~ units.
X,Y
k
1 OC
understand better the involved processes. These investigations are required to determine an optimum experimental configuration and the most favorable conditions, with respect to the most essential information. The theoretical predictions are compared with experimental data.
THEORY
X,Y,L
X,Y,2
Flgure 1. Probelpump two-beam photothermal schemes.
periments involving absorbing species generate optical density gradients above the electrode surface. Therefore, the various parts of the electrolyte absorb different amounts of excitation energy. After relaxation this condition leads to the temporal temperature profile closely related to the distribution of absorbing species above the electrode (20) (Figure IC). The magnitude of the associated refractive index gradient is detected with the help of the probing beam. Therefore, in this type of measurement, the excitation wavelength is not a limiting factor since its adsorption is not measured directly. The sensitivity of this method can be optimized by the appropriate match between the detector system and the probing beam wavelength. This selective concentration gradient technique is able to provide the whole absorption spectrum of electrogenerated species by using a broad-band light source and a monochromator (19). Simultaneously, with a different phase (delay time), the deflection signal also carries spectroscopic information about the electrode surface. With this method, the spectroscopic identification of the peaks appearing in the cyclic voltammogram is possible (19). This selective concentration gradient method is related to other probe/pump two-beam photothermal techniques (21)(Figure 1). However, there are very important differences between the concentration gradient method and other photothermal schemes, which affect the optimum experimental conditions and scope of their applications. In thermal lensing (22-25), photothermal deflection (7, 26), or cross-beam photothermal refraction (27, 28) (Figure la), the refractive index profile corresponds to the excitation beam intensity profile. Therefore the signal in these techniques is proportional to [dI/dx],,C(xo) while in the concentration gradient method (Figure IC),it corresponds to Z(xo)[dC/dx],,. Surface photothermal deflection (7,9,10,29) measures the concentration of the absorbing species on the surface. The signal in this method is related to the temperature gradient created above the surface after heat is allowed to diffuse from the surface to the portion of the medium through which the probing beam propagates (Figure Ib). In this paper a theoretical model has been developed for this selective concentratrion gradient method in order to
Figure 2 shows the distribution of the electroactive species above the large flat electrode surface placed in a large homogeneous volume of electrolyte during a single-potentialstep experiment. For an uncomplicated electrochemical reaction O+ne=R
(1)
the concentration profiles for the reactant 0 (oxidant) and the product R (reductant) at a distance x from the electrode surface after time 7 following a potential step and diffusioncontrolled region are given as (30) r
and
respectively. Here ?C is the bulk concentration of the reactant 0,Do and DR are diffusion coefficients of the reactant 0 and product R, 62 is the ratio of the concentration of the reactant to that of the product at the electrode surface, and E is expressed as (D0/DR)lJ2.In the diffusion-controlled potential step experiment involving very fast electron-transfer reaction, 02 would approach 0. Assuming DO = DR, eq 3 is reduced to r
.
(4) The concentration profiles of the reactant and product will generate the concentration gradients (Figure 3)
and
ANALYTICAL CHEMISTRY, VOL. 60, NO. 17, SEPTEMBER 1, 1988
de---+
000
500
.-_i
100
1.50
200
0:STPYCE 101
1753
e i --+-+-.300 350 430 450 5CO
25C
T l P E It1
Flgure 3. Concentration gradient profiles of product at different times
Flgure 4. Concentration gradient magnltude of a product at a given
after the potential step: (a) 7,(b) 7(2)'", and (c) 27. The distance from the electrode surface is expressed in u = 2DRr units.
location x o of a probing beam as a function of time after the potential pulse. The time is expressed as T R = x,2/2D, time units; x o corresponds to probe beam position.
respectively. The resulting refractive index gradient formed above the electrode is as follows:
The dn/dC can be approximated to (20)
where M, is the molecular weight of the electrochemicalspecies (solute), n, and nMare the refractive indexes of the solute and the electrolyte, respectively, and m M is the mass of 1 L of electrolyte (medium). It is clear from eq 8 that the difference dn/dCo - dn/dCR is expected to be significantly smaller than the absolute values dn/dCR and dn/dCo, unless dramatic chemical changes affecting the mass and refractive index of the product occurred during the electrochemical process. Therefore, it can be expected that the sensitivity of the method, based on laser beam deflection (14) e = - -d d n n dx (d is electrode dimension; n is the refractive index gradient of the medium) will be highest when the product or reactant is not soluble. In that case the sensitivity can be as high as M of analyte. In practical cases when both the product and reactant are soluble, the detection limit is about 2-3 otders of magnitude larger (14). Figure 3 shows the effect of time length, after the potential step, on magnitude and distribution of a product concentration gradient. For any particular distance x o of the probe beam from the electrode surface, the maximum of the deflection signal can be expected at a time TR = $/mR (Figure 4). This optimum decreases with an increase in xo:
assigned to be transparent at the excitation wavelength and will not be considered in our discussion (see Figure 2). The electrode surface itself can absorb some energy if it is irradiated by the beam. This absorption will depend on the molecular structure of the surface (9-11). Following the energy pulse, excited molecules either in the solution or on the surface relax their energy to the medium (electrolyte or electrode material, respectively) and therefore produce a local rise in the temperature. The resulting temperature profile generates the refractive index gradient fields, which can be detected by the laser beam. After thermal relaxation, the system will again reach equilibrium with the environment, During this time, a transient deflection signal is produced by the laser beam, which is placed at a given distance from the electrode surface. This signal contains important information about the system. The full understanding of the heat relaxation process is important to properly understand and analyze experimental data. The one-dimensional unsteady heat conduction problem with the heat source (heat produced during relaxation) described above can be presented in the form of the differential equation (31)
where T i s a temperature rise above the average value, DT is the heat diffusion coefficient, p is the density, C, is the heat capacity of the medium, and t is time after laser pulse. The heat source Q ( x , t ) describing the excitation relaxation process can be presented as follows:
= 0 for t The discussion above describes the generation of the concentration gradients corresponding to reactants and products. The refractive index gradient measured in the laser beam deflection technique is produced by both species and therefore cannot be used to describe the diffusion layer comprehensively. In the discussion below, a selective method based on the photothermal process is described. Let us assume that a concentration gradient of a product, which absorbs the excitation beam of intensity lo[W/cm2], is generated above the electrode surface. The reactant is
> to
where Io is an energy of the excitation beam in joules per square centimeter and tois its pulse length, a describes the portion of the light energy absorbed by the surface and Ax corresponds to the surface film thickness, 2,and Z2 describe the fraction of the adsorbed energy converted to heat by the surface or the soluble product, respectively, t A is a molar absorption coefficient of the product in liters per mole per centimeter, and C(x, t ) describes the concentration profile of the product given by eq 4. There me several assumptions that can be made to simplify the difficult general case represented by the differential
1754
ANALYTICAL CHEMISTRY, VOL. 60. NO. 17. SEPTEMBER 1, 1988 A
'1
Flgure 6. Axonometric plot illustrating the dynamics of the thermal relaxation process produced for absorbing electrode surface. A
t
B O,Sl"n[~
101
Flgure 5. Temperature profile produced for (5A) nonabsorbing electrode surface and (SB) abswbing electrode surface. Key: (a) just after excitation pulse, (b) after i = 'Irat,,(i. = a2/2D,)and (c) after f = f,. The distance is expressed in a = (20.~)'" units. equation (11). The most accurate information about the system can he obtained by applying a short laser pulse (impluse excitation). In that case, the temperature profile just after the fast excitation relaxation process corresponds exactly to the concentration distribution of absorbing species. Also, the mass diffusion length is very short, due to small mass diffusion coefficients in liquid and solid media during the laser pulse and the relaxation time. Therefore, it can be assumed that no change in the absorbing species concentration profile occurs during excitation and relaxation. In this discussion the solution for a short excitation pulse will be found first (impulse response function). Then the response of the system to an excitation period of a given length can be calculated by convoluting it with the impulse response function. Under the condition of a short excitation pulse, the heat transfer problem can he simplified to an unsteady onedimensional heat conduction case (31):
with the initial condition of
T(x.0) = 0 x < -Ax
-
Cp'Y
and boundary condition
T(x = *m; t ) = 0
i i
I.iIi '
Figure 7. Temperatue gradient profiles produced fm (A) nonabsorbing electrode surface and (E)absorbing electrode surface. Key: (a)just after excitation pulse, (b) after i = '/,of,. and (c)afler t 1,. where C,', p' and C,", 0'' are the specific heat and densities of the electrode material and the electrolyte, respectively. This general problem can be solved by numerical methods frequently used by engineers (32). However, if bomogeneous heat diffusivity is assumed throughout the system, then the solution to the problem can he obtained more easily by using the Fourier transform method. The Fourier transform of the solution to the above differential equation can be calculated as (33)
FT[T(x, t ) ] = exp[-D&]
FT[T(x, O)]
(13)
In other words, the solution to the unsteady heat transfer problem with an initial temperature distribution, T(x,01, can be found essentially by applying a filter to the initial temperature distribution T(x,0) of a frequency response given by exp[-D&t]. This filter describes the thermal relaxation process. These calculations can be very nicely handled by a computer's fast Fourier transform subroutine. The results
ANALYTICAL CHEMISTRY, VOL. 60, NO. 17, SEPTEMBER 1, 1988 A
Table I. Thermal Properties for Various Materials” material
--I
, COC
. 203
. 400
,
600
.BOO T;YE
1. OC
I. 20
1. 40
11.
1755
k, W/ C, J/ p, DT X lo6, d n / d T X lo4, (m deg) (g deg) g/m3 mz/s l/deg
1iqu id s 0.2 water 0.61 CCl4 0.10 nitrobenzene 0.15 solids (non- 2 metallic) glass 0.8 graphite 1.5 metals 20-200 platinum 70
2 4.2 0.86 1.5 1
1 1.0 1.6 1.2 2
0.1 0.15 0.08 0.08 1
5 0.8 5.8 4.6
0.5 0.71 0.2 0.13
3.0 1.8 20 21.5
0.6 1.2 5-50 25
2
“From ref 33. 34.
, 000
,200
,400
.BOO
,800
1.00
1.20
1.40
T I W 11.
Flgure 8. Transient deflection signal produced after the excitation pulse at a distance of (a) x o = ’/,u, (b) x o = ‘ / * u , (c) x o = u, and (d) x o = 2u. A represents nonabsorbing electrode and 6, absorbing electrode surface. Time is in t u units.
Initially, let us consider the situation when no excitation light is adsorbed by the electrode surface. This will occur for the ideally transparent or reflecting electrode, or in the more practical case, when the excitation light is introduced parallel to the electrode surface. The electrochemical interface will be irradiated efficiently, while the light will “miss” the electrode itself. Figure 5A shows the temperature profile distribution for various times t after the excitation pulse, t = 0 (a), t = l/lot, (b), and t = t u (c), where t u = u2/2DT and u is the thickness of the diffusion layer defined as a root-mean-square displacement of electrochemically generated species from the electrode surface after time 7 following the potential change CT = ( ~ D R T ) ~(30). /’ The temperature profile after t = O . l t , undergoes small changes at distances close to or much larger than u. For times t > tu,the temperature distribution closely resembles Gaussian. Therefore, the temperature profile for t > t u can be described as T(x, t )
=
_/--
/----
where x, is the location of the temperature maximum (see ref 20 for details). It can be observed that for t > 0, the maximum temperature is located away from its initial position ( t = 0) at the electrode surface. This is due to the fact that some heat is conducted from the electrolyte into the nonabsorbing electrode surface. For cases where k(e1ectrode) >> k(e1ectrolyte), this effect will be larger. The temperature gradient change with distance illustrates this effect more clearly (Figure 7A). The change in the laser beam deflection signal 61
- l l l E I1.l
Figure 9. Effect of the pulse length on the transient signal: (a) very short pulse, t o = 0;(b) t o = t u / 2 0 ;(c) t o = t J 5 .
of such an analysis are presented in Figures 5-9. As was mentioned earlier, the use of a simple Fourier transform method is limited to the cases where DT is constant throughout this single-dimensional system. This assumption is close to the real situation when the electrode substrate material conducts heat poorly (for example, a thin platinum film on a glass substrate). However, for a solid metal electrode, the heat diffusivities are 2 or even 3 orders of magnitude larger when compared to liquids (see Table I). It is quite straightforward to be able to predict results for any case when the solution to the homogeneous DT problem is found. The ratio of heat conductivities (k = DTpC,,) will reflect the portion of the heat generated at the interface and conducted into the electrode material compared to electrolyte.
= d dn d T ndTdx
where d is a dimension of the flat electrode (path length of the probe beam through the gradient) will not be significant for times 0 C t < O . l t , and distances x > u. Figure 8A shows transient deflection signals for several locations of the probe beam with respect to the electrode surface. When xo = 1/4u (Figure 8A-a), the signal initially has a large magnitude, but it quickly drops to zero and changes its sign due to heat being transported into the electrode material. This effect has been discussed earlier. At ditance x,, = 1/2u (Figure 8A-b) the positive deflection is almost unnoticeable. The deflection transient curve for xo = u (Figure 8A-c) shows an initial plateau for 0 < t < t u / l O , as expected, and then it decays slowly to zero. For larger distances x = 2u (Figure 8D-d), the maximum deflection occurs sometime after the excitation pulse due to the fact that the concentration gradient of the absorbent at this point is small. The heat that is conducted from the area close to the electrode produces a higher temperature gradient compared to the gradient formed just after excitation. The
magnitude of this effect never exceeds a few percent of the maximum gradient reached close to the electrode. In the next step we will consider the situation when the electrode surface absorbs excitation energy. For example, in our experiments reported here, the platinum electrode is expected to absorb 10-5% of the excitation energy during each pulse. Figure 5B illustrates the situation where after the pulse, the temperature rise at the electrode surface is 5 times larger than that in the adjacent electrolyte. Similar to a previously discussed case, the temperature profile at distances xo > does Again, not undergo significant changes at times 0 < t < the distribution resembles Gaussian for t > t,. The dynamics of the relaxation process disscussed above has been shown in a three-dimensional axonometric projection by adding a time axis on Figure 6. An important difference, compared to the situation of the nonabsorbing electrode, is that the maximum temperature is located very close to the electrode surface at all times. The ratio of the heat generated at the interface and conducted into the electrode material to that conducted into the electrolyte can be expressed as a ratio of corresponding heat conductivities. Therefore, for a solid platinum electrode (kpt >> k(electrolyte)), most of the heat is transferred into the metal. However, if a thin layer of platinum is supported on a glass substrate (k(g1ass) k(electrolyte)), a large fraction of heat will be transferred into the electrolyte and a larger signal due to absorption associated with the electrode surface can be expected. Figure 7B shows the temperature gradient distribution (proportional to the laser beam deflection) with the dimension x for t = 0, l/lOtc,and t,. It clearly indicates that for time t < l/lOt,,, there is a significant increase in the signal close to electrode surface, while the profile remains the same for x > U. This effect is due to heat being transmitted into the electrolyte from the surface. The signal associated with this heat describes the absorption properties of the electrode. The transient deflection signals that are expected for distances x = 1/4u(a), (b), u (e), and 2u (d) are shown in Figure 8B. The signal due to electrode absorption is largest when the probing beam is collected to the electrode surface. The signal, associated with the concentration gradient of the electroactive species in the solution, is also largest close to the electrode surface. However, a large deflection corresponding to the surface absorption is superimposed on it. Figure 8B suggests that the optimum probe beam location is at the distance xo = u if information about low concentration gradients is of primary interest. At this point there is a significant time lag of about t,/10 after the pulse, before the signal associated with surface absorption appears at this location. This time allows an accurate measurement of the concentration gradient. It should be remembered that the situation xo = u (for time T R = xo2/2DR) corresponds to the largest concentration gradient for a given distance xo as shown above (Figure 4). If, on the other hand, the most accurate information about the species located on the electrode surface is of primary interest, it appears that the best experimental procedure would be to allow a longer time after the potential step or slower potential scanning in cyclic voltametry experiments (then xo > k(electro1yte)). This will allow most of the heat generated at the electrode surface to be conducted into the electrode. If, on the other hand, characterization of the electrode is a major task, a thin metal film supported on a heat insulator should be used. In this case, a significant portion of the heat will be transferred into the electrolyte where the probing beam is present. A point should be made regarding the type of solvent used as an electrolyte. The higher the medium temperature coefficient of the refractive index dn/dT (see eq 14 and Table I), the higher is the sensitivity of the selective deflection method. Organic solvents have much larger d n / d T values than water. Figure 9 shows the effect of the pulse length on the transient signal produced by the probing beam located a t xo = u from the electrode surface. The pulse duration of to = l / m t u(Figure 9b), or shorter, produces a transient similar in shape to one for to = 0 (a). However, for the pulse length of to = (c), the signal is distorted and the information corresponding purely to the concentration gradient is difficult to measure. This conclusion clearly defines required experimental conditions for a particular geometry. For example, if the concentration gradients are to be probed 1pm from the surface, a pulse length shorter than 0.5 p s (DT= 1.0 X m2/s) is required, followed by a similarly short data acquisition time. This result clearly indicates that fast lasers and electronics are required to investigate the electrochemical species very close to the electrode surface (x, < 1pm). On the other hand, if the probe beam is located far from the surface (xo > 25 pm), even a chopped continuous wave (CW) excitation beam can be used.
EXPERIMENTAL SECTION Figure 10 illustrates two types of working electrode/excitation beam arrangements. In both cases the excitation pulse from the flashlamp pumped dye laser (Model DL-l200V, Phase-R Corp., New Durham, NH) operated at about 460 nm, using Coumarin 460 dye (Exciton, Dayton, OH) coupled into a 300 pm core UV transmitting optical fiber (Spectran Corp., Sturbridge, MA) with the help of a precision fiber coupler (Model F-915T, Newport Corp., Fountain Valley, CA). In one of the arrangements (Figure loa), the optical fiber was fitted into a piece of Teflon tubing.
ANALYTICAL CHEMISTRY, VOL. 60, NO. 17, SEPTEMBER 1, 1988
From the other end of the tubing a 0.3 mm 0.d. platinum wire with a polished end was fitted and sealed. The Teflon tubing had two cut “windows”that allowed the transmission of the probe beam. The distance between the end of its optical fiber and the electrode surface was only 2 mm, which allowed effective irradiation of the electrochemical interface by the excitation beam. This probe was placed in the detector cell described below. In the other experimental arrangement (Figure lob), the surface of the optical fiber itself was a working electrode surface. A thin layer of metal (50-100 i\)was deposited on the tip of a 300 pm core UV transmitting fiber. The light penetrating through such a transparent electrode was efficiently irradiating the electrochemical interface. The electrode was fitted in a flow-through detector cell composed of a short piece of square capillary (Wale Apparatus Co., Hellertown, PA). The cell was equipped with a silver oxide/silver wire pseudoreference electrode and a platinum-wire counter electrode. The cell was mounted on a X-Z-Tilt stage of resolution close to 1 pm in the vertical direction. A probing beam was generated by a He-Ne laser mounted on a precision-adjustablemount (Model M-811, NRC). The beam was focused by a lox microscope objective (NRC) that allowed the probing distance from the electrode surface to be close to 10 pm. The position of the probe beam was measured by using a PINSPOT/2D silicon detector together with a Model 301 DIV signal-conditioning amplifier (United Detector Technology, Hawthorne, CA). The detector was equipped with a 632.8-nm interference filter (Ealing, South Natick, MA). In some experiments, a fast position sensor was used (35). The light source, detector cell, and position sensor were mounted on an optical vibrationisolated table (Micro-g,Technical Manufacturing Corp., Peabody, MA). In most of the experiments, the electrochemistry system (Model 170, Princeton Applied Research Corp., Princeton, NJ) was used to operate the electrochemical experiment. The potential of the working electrode was modulated at a frequency of about 0.25 Hz in a square wave mode. The excitation laser was pulsing at the same frequency as the delay time, which corresponded to the maximum of gradient at the location of the laser beam (7 = xO2/2DT).A box car integrator was used to collect the selective signal in a manner similar to that described in ref 20. In order to collect the transients, the probing beam was located about 30 pm from the electrode surface to allow for slow thermal relaxation times and the collection of data directly by an analog-to-digital converter (20). In nonselective measurements, a lock-in amplifier (Model 5208, PAR) measured the amplitude of the deflection signal. A lock-in reference signal corresponding to the potential modulation frequency was used. The experimental data was acquired with the help of a DT 2800 data acquisition and control board (Data Translation, Marlboro, MA). The theoretical calculations and data processing were performed on an IBM-compatible computer using the scientific software ASYST (Macmillan Software, New York). The electrolyte solutions were prepared by dissolving 1,4benzoquinone (Eastman Organic, Reagent Grade) and tetra-nbutylammonium perchlorate (Southwestern Analytical, Austin, TX, Polarographic grade) in dimethyl sulfoxide (Matheson, Coleman and Bell, Spectrograde). The electrode potential was modulated between -0.30 and -0.52 V versus the Ag wire pseudo reference electrode. In most of the experiments, the linear velocity of the fluid in the detector cell was varied to study its impact on the signal magnitude.
DISCUSSION OF EXPERIMENTAL RESULTS Figure 11 shows examples of transient deflection signals for three different distances of the probe beam from the electrode surface produced after about a 10-mJ excitation pulse. In these experiments, the diffusion layer thickness u was kept a t 30 pm (by proper selection of delay time T) to allow long relaxation times in order to capture the transient by using the A/D converter and the detector. Figure 11 clearly indicates a general agreement between the overall shape of the experimental data and the theoretical predictions. For the distance of the probe beam from the electrode surface zo = 15 pm (Figure l l a ) , the large signal related to the electrode absorption appeared just after the excitation pulse. In the
.5oc
-
. L3C
T
,203
-
1757
--
coo t
+
’C
-
2:
-
A-n
1 I
.e/ 2 00
,
: _t
~
co
3
co
cc 5 T a r : 1m.l
4
(10
2 00
7 c0
_-
B 30
9 00
0
s
Figure 11. Transient deflection signal produced after 10-mJ excitation pulse at (a)x o = 15 pm, (b) x o = 30 pm, and (c)x o = 60 pm. The diffusion layer thickness in this experiment is about 0 = 30 pm. Bulk benzoquinone concentration was 10-5 M.
case of zo = 30 pm (Figure l l b ) , there was a significant time delay before this signal could be seen. The initial deflection, just after the excitation pulse, corresponds exclusively to the concentration gradient of the absorbing species present in the electrolyte probed by the He-Ne laser beam. For a distance xo = 60 pm (Figure llc), the signal associated with surface absorption appears much later compared to those for closer locations. In addition, the initial deflection signal related to the concentration gradient is very small. More quantitative comparison between experimental and theoretical results c o n f i i s the good agreement. For example, the ratio of deflection signals a t distances 1/20, u, and 20 is close to 8 5 1 in Figure 11compared to 7 5 1 in Figure 8B. The discrepancies between experimental and theoretical data for small distances is most likely due to difficulties in accurate positioning of the probing beam close to the electrode surface. Also, it should be remembered that theory assumes a very narrow probe beam, while in reported experiments its width was about 10 pm. The peak corresponding to surface absorption moves toward longer times and becomes shallower when the probe beam is moved away from the surface (Figure 11). Estimated tuvalue of the relaxation process from Figure 11 is about 4.5 ms, somewhat shorter than expected: (zO2/2DT) ( x o = 30 pm) = 5.5 ms. However, it should be remembered that in our model we assume one-dimensional heat conduction, while the temperature profile will relax in all three directions and therefore reduce experimental tu. In the experiments from Figure 11,a solid platinum-wire working electrode (Figure loa) was applied. If the optical fiber with spattered thin layer of the metal (Figure lob) was used instead, the deflection signal corresponding to the surface absorption increased by close to 2 orders of magnitude. This result clearly illustrates the advantages of each system to study the species located either on the electrode surface or in the electrolyte adjacent to the electrode. This topic has already been discussed in the Theoretical Section. Figure 12 shows the concentration gradient profile generated by the benzoquinone radical above the platinum electrode. The shape of the curve follows the theoretical prediction (Figure 3). Figure 12 and formula 9 indicate that the higher concentration gradients are encountered close to the electrode surface. I t should be remembered, however, that the total deflection signal is also proportional to the electrode dimension d (see eq 9). A tightly focused probe beam can access areas of an electrolyte very close to an electrode surface, but it requires a small dimension d due to the short depth of focus. Therefore, as expected, the new geometric arrangement
1758
ANALYTICAL CHEMISTRY, VOL. 60, NO. 17, SEPTEMBER 1, 1988
PISTAIICE 'pml
Flgure 12. Concentration gradient profile of the benzoquinone negative radical above the electrode surface. Bulk benzoquinone Concentration was loF5M.
(shorter d ) did not significantly improve the universal detection limits ( lo4 M) of the concentration gradient method compared to the results reported before (14). It can be expected, however, that small-dimension electrodes can significantly increase the sensitivity of the selective concentration gradient method. This fact is associated with the quadratic increase in the excitation light densities in joules per square centimeter per pulse due to electrode diameter decrease. The calibration curve for the pulsed excitation has about 4 orders of magnitude of linear range. The upper limit of the linear range is associated with the large absorption of the analyte, which generates significant intensity gradients. This effect is discussed in detail in ref 20. The detection limit for the concentration gradient method and simple gated detection is about 3 x M of benzoquinone. In this experiment, the probe laser beam propagated about 10 pm above the surface, and the excitation pulse density was about 10 J/cm2. The sensitivity of this method can be improved even further when the probing beam is placed even closer to the electrode surface. However, for example, a decrease of the distance to 1 km will require an electrode diameter of about 10 pm and very fast data acquisition and electronics (about 10 MHz for DT = IO9 m2/s). The effect of the moving electrolyte on the sensitivity of the method has been investigated. The deflection signal magnitude remains constant for the flow rate range of 0-1.5 mm/s. The higher rate introduced turbulent flow in the detector cell due to its poor hydrodynamic design.
CONCLUSIONS In the experiments reported in this paper, a potential step procedure and the single redox system in the electrolyte were used. In real multicomponent mixtures analysis, a more appropriate type of experiment is cyclic voltammetry. In that method, various species are oxidized or reduced at different times in the cycle. The change of the deflection signal associated with absorption with the time and wavelength is able to spectroscopically characterize the electroactive species present on the surface or in the electrolyte. The feasibility of this approach was partially demonstrated in ref 19 and 15. The Schlieren method is more general than electrometer detection, since any process that generates concentration gradients can be investigated, not only those that involve electron transfer from or to the electrode. Therefore any chemical system that involved mass transport (diffusion) and/or mass conversion (chemical reaction) processes can be studied by similar methods developed for electrochemistry by using the concentration gradient detection scheme described here (36).
A zero-dimension method applied in this paper utilizes a single He-Ne laser beam. However, Schlieren optics techniques are naturally suited for multidimensional sensing of even complex concentration profiles such as parabolic or toroidal shapes (37, 38). Electroactive species form a singledimensional concentration gradient field above the electrode surface, which can be investigated by using a diode array detector. Similarly, as in the parallel absorption method (17, 18), the change in light intensity distribution is measured. This change occurs not because of the absorption of the probing beam but rather due to its local deflections. The total probe beam intensity will remain constant, and only its spatial distribution will undergo changes due to local deflections in the diffusion layer.
ACKNOWLEDGMENT I thank Michael Weber for the sputtered transparent electrode and Michael Dignam for some optical components. LITERATURE CITED Pawliszyn, J. "Spectroelectrochemical Sensor Based on Schlieren Optics". Presented at the 194th National Meeting of the American Chemical Society, New Orleans, LA, Aug. 1987. Wranglen, G. Acta Chem. Scand. 1958, 12, 1543. Schardin. H. Ergeb . Exakten Naturwiss 1942, 2 0 , 303. Muller, R. "Optical Techniques for the Study of Phase Boundaries"; National Bureau of Standards, Clearinghouse, 1965. Howes, W. Appl. Opt. 1985, 2 4 , 816. Muller, R. I n Advances in Electrochemistry and Electrochemical Engineering; Muller, R. Ed; Wiley-Interscience: New York, 1973; Vol. 9, p 281. Jackson, W. ; Amer, N.; Boccara, A.; Fournier, D. Appl. Opt. 1981, 2 0 , 1333. Murphy, J.; Aamodt, L. J. Appl. Phys. 1980, 5 1 , 4580. Low, M.; Morterra, C.; Severdia, A.; Lacroix, M. App. Surf. Sci. 1982, 13, 429. Royce, E.; Sanchez-Sinencio, F.; Goldstein, R.; Muratore, R.; Williams, R.; Yim, W.J. Electrochem. SOC. 1982, 129, 2393. Fournier, D.; Boccara, A.; Badoz, J. Appl. Opt. 1982, 2 1 , 74. Roger, J.; Fournier, D.; Boccara, A. J. Phys. (Les Ulls, Fr.) 1983, 44, C6-313. Royce, E.; Voss, D.: Bocarsly, A., J. Phys. (Les Ulis, F r . ) 1983, 4 4 , C6-325. Pawliszyn, J.; Weber, M.; Dignam. M.; Mandelis, A,; Venter, R.; Park, S.-M. Anal. Chem. 1986, 58, 236. Russo, R.; McLarnon, F.; Spear, J.; Cairns, E. J. Nectrochem. SOC. 1987, 134, 2783. Tamor, M.; Zanini, M. J. Electrochem. SOC. 1986, 133, 1399. Fukunaka, Y.: Dempo, K.; Inata. M.: Maruoka, K.;Kondo, Y. J. Electrochem. Soc. 1983, 130. 2492. Jan, C.-C.; McCreery, R. Anal. Chem. 1986, 58, 2771. Pawliszyn, J.; Weber, M.; Dignam, M.; Mandelis, A,; Venter, R.; Park, S.-M. Anal. Chem. 1988, 5 8 , 239. Pawliszyn, J. Anal. Chem. 1988, 60. 766. Morris, M.; Peck, K. Anal. Chem. 1986, 5 8 , 811A. Gordon, J.; Leite, R.; Moore, R.; Porto, S.; Winnery, J. Appl. Phys. 1965, 3 6 , 3. Whinnery, J. Acc. Chem. Res. 1974, 7 , 225. Harris, J.; Dovichi, N. Anal. Chem. 1980, 5 2 , 695A. Leach, R.; Harris, J. Anal. Chem. 1984, 5 6 , 1481. Rose, A.; Vyas, R.; Gupta, R. Appl. Opt. 1986. 2 5 , 4626. Weimer, W.; Dovichi, N. Appl. Opt. 1985, 2 4 , 2981. Dovichi. N.; Nolan, T.; Weimer, W. Anal. Chem. 1984, 5 6 , 1700- 1701. Aamodt, L.; Murphy, M. J. Appl. Phys. 1983, 5 4 , 581. Bard, A.; Faulkner, L. Electrochemical Methods; Wiley: New York, 1980. Beek, N.; Muttzall, K. Transport Phenomenon; Wiley: New York, 1975; p 144. Patankar, S. Numerical Heat Transfer and Fluid Flow; McGraw-Hill; New York, 1980; p 54. Carslaw, H.; Jaeger, J. Conduction of Heat in Solids; Clarendon: Oxford, England, 1966; p 459. CRC Handbook of Chemistry and Physics, 64th ed.; CRC: Boca Raton, FL, 1985. Pawliszyn, J. Ref. Sci. Instrum. 1987, 58, 245. Pawliszyn. J.. submitted for publication In Anal. Chem. Decker, G.: Deutsch, R.; Kies, W.; Rybach, J. Appl. Opt. 1985, 2 4 , 823. Noll. R.; Haas, C.; Weiki, B.; Herriger, G. Appl. Opt. 1966, 2 5 , 769.
RECEIVED for review June 18, 1987. Resubmitted March 1988. Accepted March 28, 1988.
17,
