14824
J. Phys. Chem. 1995, 99, 14824-14831
Scanning Electrochemical Microscopy as a Probe of Silver Chloride Dissolution Kinetics in Aqueous Solutions Julie V. Macpherson and Patrick R. Unwin* Department of Chemistry, University of Warwick, Coventry, CV4 7AL, UK Received: May 25, 1995; In Final Form: July 28, 1995@
The dissolution kinetics of electrochemically grown films and pressed pellets of silver chloride in aqueous potassium nitrate solutions have been investigated using the well-defined, and high, mass transport properties of the scanning electrochemical microscope (SECM). The reaction was found to be diffusion-controlled under all conditions utilized, suggesting that the heterogeneous rate constant controlling the surface process is in excess of 3 cm s-l. In parallel with the experiments, a theory for SECM-induced dissolution has been developed for the case where dissolution of a binary salt occurs in a solution in which none of the lattice ions are buffered. Under these conditions, theoretical and experimental results demonstrate that when only one of the lattice ions is removed from the tip-substrate gap by electrolysis, the trapping of the electroinactive counterion in the gap between the tip and substrate by hindered diffusion strongly retards the dissolution rate.
Introduction Recent work from this group has shown that scanning electrochemical microscopy (SECM)'.* is a powerful technique for kinetic and mechanistic studies of the dissolution of soluble crystal^.^-^ In particular, the high spatial resolution of SECM has allowed the effect of dislocationdensity on dissolutionrates and mechanisms to be directly addressed, through studies on the (100) face of copper sulfate pentah~drate.~-~ In addition, by use of the scanning facility of SECM, it has been possible to map the dissolution activity of targeted areas of a crystal face, as illustrated by studies of the dissolution of the (010) face of potassium ferrocyanide trihydrate.6 The initiation of dissolution reactions, using SECM, is achieved by an ultramicroelectrode (UME) probe positioned close to the surface of interest. By the stepping of the UME potential from a value where no reaction occurs, and the solution is saturated with respect to the lattice ions, to one where the electrolysis of one of the solute ions occurs at a diffusioncontrolled rate, the concentration of the solute ion in the tipsubstrate gap is depleted. The resulting undersaturation at the crystal-solution interface provides the driving force for the dissolution reaction, and the resulting current which flows at the tip of the UME provides information on the rate and mechanism of the dissolution p r o ~ e s s . ~Hitherto, -~ we have used this approach to tackle dissolution problems which could be reduced to the consideration of only one species by setting the experimental conditions such that the supporting lattice ion concentration remained constant during a measurement. In this paper we significantly develop SECM-induced dissolution by (i) showing that SECM can be used to characterize the dissolution kinetics of a sparingly soluble salt and (ii) developing SECM theory to address the problem where none of the lattice ions are buffered during the course of a measurement. Both developments are achieved through investigations of silver chloride dissolution in aqueous 0.1 mol dm-3 KNO3. For this system, SECM-induced dissolution is effected through the reduction of Ag+ ions at the tip of the UME. Under the defined conditions with no buffer of the C1- ion in the solution, the C1- level increases in the gap between the tip and the substrate, while Ag+ is depleted. This results in a temporally @
Abstract published in Advance ACS Abstracts, September 1, 1995.
0022-3654/95/2099-14824$09.00/0
and spatially dependent nonstoichoimetric dissolution environment during the period of a measurement. A consequence of this for the silver chloride system is that the charge, and hence potential, at the crystal surface will vary, which in principle provides the opportunity to assess the role of surface potential in the dissolution of an ionic crystal under well-defined conditions. The kinetics and mechanisms controlling the dissolution of silver chloride in aqueous solutions are currently unresolved despite a number of ~ t u d i e s . ~ -By ' ~ the monitoring of the change in conductivity as a functioq of time, for the dissolution of a stirred suspension of silver chloride crystals in water, it was suggested that the process followed second- or one- and -a-half-order kinetics, in accordance with the following equati~n:~-* dt
= K(co - c)"
where K is a dissolution rate constant, c is the concentration of silver chloride at time t, n is the order of the reaction, and co is the solubility of silver chloride. By use of a similar experimental procedure, it was later reported that the dissolution of AgCl crystals into a range of undersaturated solutions was diffusion-controlled when the solution was more than 85% ~aturated.~ Later work by Jones'O determined that the dissolution reaction was diffusion-controlled from 0 to 90% of saturation. In these latter studies the temporal change of Ag+ concentration in bulk solution was monitored, using radioactive tracer techniques, during the dissolution of radioactively labelled 'O"AgC1 electrochemically deposited on a rotating platinum rod. Several of the above-mentioned studies considered the dissolution of AgCl into nonstoichoimetric solutions of the lattice ions. In one study, it was found that the dissolution rate was retarded when either Ag+ or C1- ions were present in excess, the effect being more marked with excess Ag+.9 In contrast, later work found no such deviation except with excess C1- above 60% saturation.I0 The discrepancies between the results and conclusions of these early studies may, in part, be due to inherent drawbacks in the experimental methodologies employed. For example, the use of stirred suspensions makes it difficult to quantify the role 0 1995 American Chemical Society
AgCl Dissolution in Aqueous Solutions
J. Phys. Chem., Vol. 99, No. 40,1995 14825
of mass transfer. Secondly, in all of the studies outlined above, kinetic information was inferred from the change in chemical composition of the bulk solution as a function of time. Consequently, the rate was determined in terms of bulk solution, rather than interfacial, undersaturation which is inappropriate. In the studies reported herein, the dissolution kinetics of silver chloride are investigated using similar surfaces to those employed in early work on this reaction but under the well-defined experimental conditions provided by SECM. In particular, since the diffusion of species in the tip-substrate gap in SECM is well defined and calculable, the role of the interfacial undersaturation in the overall kinetics may be quantified. Moreover, by the employment of small electrodes and close tip-substrate distances, very high rates of mass transfer are achievable, enabling fast surface processes to be characterized.
The initial and boundary conditions for the experiment of interest are
t>
G,+ --0,
0, R = 0,O < Z < L:
aR
acc1- -aR
Theory rate laws are considered in which As stated the dissolution kinetics show either a first- or second-order dependence on the interfacial undersaturation. These cases represent the two limits to the Burton, Cabrera, and Frank dissolution model" and can also be derived from other dissolution mechanisms.I2 For the dissolution of AgCl, the rate law is
where j i denotes the flux of species i (Ag+ or C1-) at the sample-solution interface, k,, is a dissolutionrate constant where n has the value 1 or 2, and (5 is the relative undersaturation at the sample-solution interface given by
o=l-s
(3)
where S is the saturation ratio, which for AgCl is defined as =
(
A ' g+;-'
)IR
a**g+a CI-
(4)
In eq 4, a i denotes the activity of species i and the asterisk superscript refers to the bulk saturated solution activity. The UME chronoamperometric response is considered, following a step in the potential to a value where Ag+ is reduced at a diffusion-controlled rate. The UME tip and solid form an axisymmetric geometry, and the general dimensionless SECM diffusion equation for the species of interest is
In eqs 10-12
L = dla
(13)
RG = r i a
(14)
where d is the distance between the tip and the substrate surface and r, is the radius of the probe (electrode plus glass insulator). The boundary conditions at the electrode reflect the following facts. (i) Prior to the potential step, the system is at equilibrium and the solution is saturated with respect to AgCl (eq 8). (ii) The reduction of Ag+ to Ag occurs at a diffusion-controlled rate at the UME surface (eq 9). (iii) Both ions are inert with respect to the glass insulating sheath surrounding the electrode (eq 10). (iv) The geometry of the SECM is axisymmetric (eq 11). (v) Both ions recover their bulk, saturated, values outside the tip-substrate domain (eq 12). The latter assumption is expected to be valid provided that RG 2 10,i3*'4 as in the studies in this paper. At the substrate-solution inferface the boundary condition is t>
O,Z= L, 0 IR
-- acC,-
IRG: acAg+
az
az
The dimensionless dissolution rate constant, K,,, is given by
Kn =
kna C*AgCIDAg+
where C i is the concentration of species i , Ag+ or C1-, normalized with respect to the bulk (saturated) solution concentration of AgCl, cRgc1. R is the radial coordinate of the axisymmetric geometry (starting at the center of the electrode) normalized with respect to the electrode radius, a, and Z is the coordinate normal to the UME surface (starting at its surface) normalized with respect to a. The parameterfi, reflects the fact that, under the conditions of the experiment, Ag+ and C1- have unequal diffusion coefficients: f=-
'
The solution to the SECM dissolution problem yields the UME current, i, normalized with respect to the steady state current at infinite probe-substrate separation, i(-),
whereI5
Di DAg+
Dimensionless time, z, is related to time, t, by
In eq 18, F is Faraday's constant and n (=1) is the number of electrons transferred in the diffusion-limited reduction of Ag+. The problems were solved numerically using the alternating direct implicit (ADI) finite difference method,I6which has been used previously to solve a wide variety of SECM problem^.^^^^^.^^
14826 J. Phys. Chem., Vol. 99, No. 40, I995
Macpherson and Unwin
20
15 cci
-2.=
cci
10
5
0
I
I
I
0
10
20
30
40
50
T-112
Figure 1. Normalized chronoamperometric characteristics for an induced dissolution process defined by the model outlined in the text with Kl = 100 and a tip substrate separation, L, of 0.16. The data relate to the situations where (i) none of the lattice ions are buffered during the period of the measurement (-) and (ii) the electroinactive counterion of the salt is buffered during the measurement (- - -).
CCI'
Modifications required for the present problem are moderately straightforward and will not be discussed further here.
Theoretical Results and Discussion All simulations were carried out for an UME probe characterized by RG = 10, typical of the UME tip employed experimentally. A typical example of the calculated chronoamperometric response for the dissolution problem, defined by log KI = 2 and L = 0.16, is shown in Figure 1. At this tip-substrate separation, the rate constant corresponds to an effectively diffusion-controlled dissolution process. For comparison, the response is also shown for a diffusion-controlled dissolution process under conditions where the lattice counterion is buffered during the course of the chronoamperometricmeasurement. As shown previously, this latter case is equivalent to the chronoamperometric response for SECM positive feedback.'^^ For both cases, the current ratio-time characteristics are the same at short times when the diffusion field thickness is smaller than the tip-substrate distance and the surface does not therefore influence the diffusion field. However, at longer times, when the diffusion field has intercepted the surface, the current response for the case where none of the lattice ions are buffered lies below that for the situation where the electroinactive counterion is buffered. The reason for this behavior is explained by reference to Figures 2 and 3, which shows the C1- and Ag+ concentration profiles, respectively, in the tip-substrate gap at selected times during the chronoamperometric characteristics shown in Figure 1. It is clear that, for the case of interest, the concentration of the electroinactive counterion, C1-, increases in the tip-substrate gap during the period of the chronoamperometric measurement. Consequently, at the substrate-solution interface where, for a diffusion-controlled dissolution process, the solution remains saturated with respect to AgCl, a buildup of C1- promotes a decrease in the concentration of Ag+ with time. This leads to a decrease in the flux of Ag' (and C1-) from the interface which is ultimately reflected in a diminution in the current flowing at the tip electrode toward longer times. As the tip-substrate distance is increased, the deviation of the current response from the behavior found when the electroinactive counterion concentration is buffered becomes less pronounced. This is because C1- can more readily escape from the tip-substrate gap by diffusion, with the result that its concentrationdoes not increase as significantly as at close tipsubstrate separations, as shown in Figure 4 for the case where
Ccr
CCI'
Figure 2. Chloride ion concentration profiles in the tip-substrate gap for various times during the chronoamperometric transient shown in Figure 1, with none of the lattice ions buffered. The data relate to normalized times, t,of (a) 0.1, (b) 1.0, and (c) 10. d/u = 1. As expected, the corresponding Ag+ profiles, shown
in Figure 5, demonstrate that the depletion in concentration of Ag+ at the substrate-solution interface, from the initial saturated value, is now not so severe. Typical working curves for the first-order process, illustrating the dependence of the long time current (specifically, at z = 50) on K I, are shown in Figure 6 for L = 0.16 and 1.OO. From this it can be seen that rate constants can be deduced with the greatest accuracy at the closest tip-substrate distances, as found for SECM kinetic measurements in genera1.3y6*17However, it should be noted that the (long time) current ratio changes over a much narrower range, for the present case, compared to the situation where the concentration of the electroinactive counterion is buffered during the period of the SECM chronoamperometric mea~urement.~.6
Experimental Section Materials. All solutions were prepared with Milli-Q reagent water (Millipore Corp.). The saturated silver chloride solutions (Fluka, puriss p.a.) contained 0.1 mol dmd3 potassium nitrate (Aldrich, 99.99% purity), which served as a background electrolyte. Two types of AgCl substrates were employed: (i) AgCl in the form of a pressed pellet (Crystran, Poole, England) of diameter 12.7 mm and (ii) electrochemically grown AgCl films. The latter substrates were prepared from the oxidation of home-constructedI*Ag disc UMEs, either 50 or 125 pm in diameter, in 0.1 M KCl (Fisons, AR grade). In order to obtain complete coverage of the surface with AgCl, a current density of approximately 0.16 mA cm-2 was maintained at the electrode for a period of 15 min.19 The electrochemicallygrown surfaces were aged by storage of the electrodes in 0.1 M KCl for 24 h in the dark.
J. Phys. Chem., Vol. 99, No. 40, 1995 14827
AgCl Dissolution in Aqueous Solutions
1.7 1.o
-
-1.6
1
1
0.8
Ca-
I
Ca-
O
Figure 3. Silver ion concentration profiles in the tip-substrate gap for various times during the chronoamperometric transient shown in Figure 1, with none of the lattice ions buffered. The data relate to normalized times, z, of (a) 0.1, (b) 1.0, and (c) 10.
Apparatus and Instrumentation. The SECM instrumentation has been described previously.6*20 All electrochemical measurements were made using a two-electrode arrangement. A silver wire served as a quasi-reference electrode (AgQRE), and pt UMEs with diameters of 10 and 25 pm served as working electrodes. The cells were comprised of a fully detachable Teflon base (which contained, where appropriate, a hole in the center which could accommodate securely an UME), a glass cylindrical body, and a plexiglass lid. For experiments with AgCl pressed pellets, the substrate was mounted flat on the teflon base using double-sided adhesive tape, with the exposed face lying parallel with the cell base. For measurements on Ag/AgCl electrodes, the UME was secured perpendicularly through the center of the cell base, such that the surfaces of the substrate and tip electrodes were parallel. Prior to all dissolution experiments, the solution was thoroughly degassed with argon for a period of cu. 30 min, and during all measurements argon was passed over the surface of the solution. Light was kept out of the dissolution cell by covering it with aluminium foil. Procedures. For kinetic measurements involving a silver chloride pressed pellet, the UME tip was placed at selected distances from the substrate surface and the current was recorded as a function of time following the reduction of Ag+ at a diffusion controlled rate in the chronoamperometric mode by stepping the potential from open circuit to -0.3 V. The absolute tip-substrate separation was generally established by carefully contacting the substrate surface with the tip and then retracting the tip a known distance from the surface. The position at which the tip contacted the surface was readily established as the position at which very large currents flowed when Ag+ was reduced (typically i/i(-) > 100). . For kinetic measurements involving the electrochemically grown AgCl film, it was first necessary to locate the position
Figure 4. Chloride ion concentration profiles in the tip-substrate gap for various times during an induced dissolution process (K = loo), with none of the lattice ions buffered, at a tip-substrate separation, L, of 1.0. The data relate to normalized times, z, of (a) 0.1, (b) 1.0, and (c) 10.
of the film with respect to the tip electrode. This was achieved by utilizing SECM in the imaging mode, in which the electrode tip was first carefully placed on the surface of the Ag/AgCl electrode and retracted 10 pm. While held at a potential of -0.3 V, sufficient to reduce Ag+ at a diffusion-controlledrate, the tip was then scanned at a constant height (in a fixed x,y plane) in a series of unidirectional line scans over the surface of the AgCl film and surrounding glass insulator. The scans were usually over an area of 500 pm x 500 pm, with a step size of 25 pm between individual line scans. The tip speed was typically 100pm s-I. By the monitoring of the diffusionlimited electrolysis current for the reduction of aqueous Ag+ as a function of tip position, it was possible to locate the presence of the film from the increase in the current when the tip initiated dissolution over the AgCl surface. The tip was then repositioned so that it sat directly above the center of the AgCl film,and a series of kinetic chronoamperometricmeasurements at different tip-substrate separations were carried out as described above. Higher resolution images, recorded as a function of tipsubstrate separation were measured using scan areas of 200 pm x 200 pm with a step size between line scans of 10 pm. The tip scan speed employed in these experiments was 10 pm s-I. For all of the above experiments, although direct reduction of Ag+ resulted in deposition of Ag on the UME tip, the quantity of material deposited (with typical current densities of 20 pA cm-2 and smaller) was not sufficient to significantly alter the electrode geometry, substrate geometry, or the tip-substrate distance, even over time periods of several minutes.
Macpherson and Unwin
14828 J. Phys. Chem., Vol. 99, No. 40, 1995
Figure 5. Silver ion concentration profiles in the tip-substrate gap for various times during an induced dissolution process (K = 100), with none of the lattice ions buffered, at a tip-substrate separation, L, of 1.0. The data relate to normalized times, t,of (a) 0.1, (b) 1.0, and (c) 10. "O 0.9
1
0.8
F=
k 0.7
0 0
0.6
5
10
15
20
tlt
0.5 0.4
!
1
I
I
1
0.0
0.5
1.o
1.5
2.0
log
KL
Figure 6. Working curves of long time (t= 50) normalized current vs K Ifor (a) L = 1.00 and (b) L = 0.16.
Experimental Results and Discussion Ag+ Reduction: Voltammetry and Chronoamperometry. Initial voltammetric experiments for the reduction of Ag+ were carried out using 25 pm diameter Pt and 50 pm diameter Ag electrodes in solutions containing either 0.001 or O.OOO1 mol dm-3 AgN03, with KNO3 added as a supporting electrolyte at a concentration of 0.1 mol dm-3. The steady state current response was measured by scanning the potential in the range 0.0 to -0.3 V at a scan rate of 10 mV S-I. Application of eq 18 to the measured diffusion-limited current yielded a value for DAg+ of 1.65 x cm2 s-', which was in very good agreement with the values of 1.65 x and 1.55 x cm2 s-I quoted, respectively, by Newman2I and Spiro et ~ 1 for similar experimental conditions.
pigure 7. Dynamic electrochemical characteristics for the reduction of Ag+ at a Pt UME (a = 12.5 pm) from a saturated silver chloride solution (0.1 mol dm-3 KNO3): (a) steady state voltammogram; (b) chronoamperometric behavior. In the latter case the behavior expected for a simple diffusion-controlledelectron transfer process is also shown (.
0).
Voltammetric measurements carried out with 25 and 10 pm diameter Pt electrodes in solutions containing 0.1 mol dm-3 KNO3, and saturated with respect to AgCl, yielded typical diffusion-limited currents of 103 and 45 PA, respectively. A typical voltammogram showing the steady state voltammetric response at a 25 pm diameter Pt UME is shown in Figure 7a. Armed with a knowledge of DAg+ from above, the saturated concentration of AgCl was determined to be 1.35 x mol dm-3 after the application of eq 18. This value compares favorably with the literature value measured under similar
condition^.^^ Chronoamperometric characteristicsfor Ag+ reduction, measured after stepping the electrode potential from open circuit or 0.0 V to -0.3 V, were found to deviate markedly at short . times ~ ~ from the theoretical predictions for a simple diffusioncontrolled electrolysis process, in that much larger currents
J. Phys. Chem., Vol. 99, No. 40, 1995 14829
AgCl Dissolution in Aqueous Solutions
1.m 1.36364 to 1.45 1.27727 to 1.36364 1.19091 to 1.27727 1.10455 to 1.19091 1.01818 to 1.10455 0.931818 to 1.01818 0.845455 to 0.931818 0.759091 to 0.845455 0.672727 to 0.759091 0.5a6364 to 0.672727
-50t
'
'
'
-300
'
'
,
-200
,
'
-100
0
100
300
200
x scan I pm Figure 8. Variation of the normalized diffusion-limited current for Ag+ reduction as a tip (a = 12.5 pm) was scanned over a silver chloride disc (125 pm diameter) embedded in a glass sheath. The position of the disc is identified from the increase in the current response when the tip induces dissolution of the silver chloride substrate. The tip was positioned at a height of 10 pm above the substrate and scanned at 100 pm s-'. The color bar key represents values of i/i(-).
-
7.0 -,
5.0 4.0 -
5.0 -k.-8 4.0 3.0 2.0 1.0 -
7.0
6.0
--8 .>
3.0
-
2.0
-
1.0 0.0
6.0
-
1 !
I
I
I
i
0.0
0.2
0.4
0.6
0.8
0.0
oo " uI
u w
0 1
u
u 0 I
0 I
d/a
Figure 9. Experimental approach curve (0)of normalized long time current for Ag+ reduction vs tip (a = 12.5 pm) to substrate separation with a 125 pm diameter silver chloride disc. Also shown is the theoretical behavior for a diffusion-controlled process predicted by the model outlined in the text (-) together with the behavior for the situation where the electroinactive counterion of the substrate is buffered (- - -).
flowed, as shown in Figure 7b. Crucially, however, at longer times (3 s and greater with the 25 pm diameter tip), measured current values were found to be in good agreement with the steady state voltammetric response. All measurements were thus restricted to this time scale. SECM-InducedDissolution Kinetics. Initial studies focused on electrochemicallygrown films of AgCl, a substrate identical to that employed by Jones in earlier work.l0 For these experiments a 125 pm diameter AgCl film was employed as the substrate, which was located by the tip using SECM in the imaging mode as described above. A typical image, resulting from this procedure with a Pt tip of 25 pm diameter, is shown in Figure 8. The dark areas represent areas of low tip current and correspond to the hindered diffusion of Ag+ to the tip as it passes over the insulating glass sheath surrounding the AgCl film. The light area indicates a higher current, representing the position in which the tip is directly over the AgCl film and initiates dissolution. After identifying the coordinates of the AgCl film, the tip was repositioned so that it sat above the center of the film, and chronoamperometry for Ag+ reduction was carried out in this area as a function of tip-substrate distance. A typical approach curve for a tip of a = 12.5pm, constructed by plotting the normalized long time currents from chronoamperometric measurements as a function of tip-AgC1 film distance, is shown in Figure 9. The best fit of the experimental data to the theory outlined above was obtained for a diffusioncontrolled dissolution process (K1 = 100) under conditions
where none of the lattice ions are buffered. Strictly, the theoretical analysis outlined above applies to substrates which extend over a distance 0 5 R 5 RG &e., an "infinite" substrate); however results obtained with a tip of a = 5 pm were also found to fit a diffusion-controlled model, suggesting that the model is generally valid for the data in Figure 9 on the time scale of the measurements. Also shown in Figure 9 is the theory for a diffusion-controlled dissolution process where the electroinactive lattice counterion is buffered. Comparison of this response, to that described above clearly demonstrates that unbuffered ion concentrations have a dramatic effect on the SECM current response in dissolution systems. We turn next to experiments in which pressed pellets of AgCl were used as a substrate. The approach curves of long time normalized current for the diffusion-controlled reduction of Ag+ vs distance for this case, obtained with 25 and 10 pm diameter Pt tip electrodes, are shown in Figure 10. In both cases, experimental data are again seen to fit well with the theoretical behavior predicted for a diffusion-controlled process, indicating that, under the experimental conditions imposed, the surface kinetics associated with AgCl dissolution are extremely rapid. In principle, one could attempt to probe the surface kinetics by increasing mass transfer still further by employing smaller tips and closer tip-substrate separations. However, this would require the ability to accurately measure very small currents (< 10 PA), which would be difficult to achieve with our present setup.
14830 J. Phys. Chem., Vol. 99, No. 40, I995 12
Macpherson and Unwin
1
h
0
1.2
1.2
I
1
1
I
i
2
4
6
8
10
R = r/a
Figure 11. Concentration profiles of Ag+ and C1- at the AgCl substrate-solution interface as a function of the radial coordinate for a diffusion-controlleddissolution reaction with a tip-substrate separation, L = 0.1, and a measurement time, t = 40.
The above results allow the minimum heterogeneous rate constant for AgCl dissolution to be estimated as follows. We assume that the currents measured in Figure 10 are accurate to ca. f5%. At the closest distance (d = 0.5 pm for a tip of a = 5 pm), it then follows from the working curve of steady state normalized current vs normalized rate constant for dla = 0.1 that the observation of a diffusion-controlled dissolution process means, for a first-order process,
K,=
kla DAg+c*AgCI
'100
(19)
Given the values for DAg+and a cited above, this implies that
This value is several orders of magnitude higher than the value which may be derived from earlier work,Io where the mass transfer coefficient associated with the experiment procedure adopted is estimated to be on the order of 6 x cm S-I. As illustrated in Figures 2-5, SECM-induced dissolution, under the conditions of the experiments described herein, leads to a solution environment in the tip-substrate gap which is highly nonstoichiometric with respect to the lattice ions. In earlier work9,10such conditions were found to influence the dissolution rate and it is therefore useful to identify the range of interfacial concentrationswhich prevail during the conditions of our experiments. It follows from Figures 2-5 that, for a . diffusion-controlled reaction, the degree of nonstoichiometry of the interfacial solution with respect to the lattice ions is greatest at the closest tip-substrate separation. Figure 11 shows the interfacial concentration profiles for Ag+ and C1- within the tip-substrate domain as a function of the radial co-ordinate for dla = 0.1 (equivalent to the data in Figure 10 obtained at d = 0.5 pm with a tip of a = 5 pm) at a measurement time, z = 40. It can be seen that the extent to which the interfacial concentration is nonstoichiometric with respect to the lattice ions varies dramatically with the radial coordinate and that the interfacial ratio of [Cl-]/[Ag+] can be in excess of 130 at the part of the surface directly under the UME. Dissolution Rate Imaging. In addition to locating the surface of interest as described above, the scanning mode of the SECM can be used to provide kinetic information via dissolution rate imaging. In these experiments, the tip is scanned at a series of constant heights above the surface while the diffusion-controlled
Figure 12. Selection of typical dissolution rate images for the diffusioncontrolled reduction of Ag+ at a tip (u = 12.5 pm) scanned at heights of (a) 3.0 pm, (b) 4.0 pm, and (c) 5.0 pm over a silver chloride disc (125 pm diameter) embedded in a glass sheath. current for the reduction of Ag+ is recorded as a function of tip position. To avoid prolonged deposition of Ag at the electrode surface, smaller diameter (50pm) AgIAgC1 electrodes were used as the substrate in these experiments. A series of typical dissolution rate images recorded as a function of tip-substrate distance are presented in Figure 12. The scan area for each image was 200 pm x 200 pm with a step size between line scans of 10 pm. The scan speed of the 25 pm diameter tip was 10 pm s-'. The position of the AgCl film in each image is clearly evident as the peak in the current when the probe passes over the film and initiates dissolution, which provides an additional source of Ag+ for reduction at the tip. By taking the maximum value of the current in each image as a function of d, an approach curve can be produced, as shown in Figure 13. The long time (approaching steady state) theoretical analysis presented above is expected to be applicable to the data in Figure 13 since, at the slow probe scan speed employed, the characteristic residence time of the probe in the vicinity of the AgCl film, ~
dAgCl
tres= *tip
where dAgclis the diameter of the AgCl substrate and Vtip is the tip scan speed, is of the order of 5 s. It is clear from Figure 13 that the experimental data are in good agreement with the diffusion-controlled dissolution model with none of the lattice ions buffered, which provides further support for the deductions from the transient measurements described above.
Conclusion Through studies of AgCl dissolution into aqueous solutions of 0.1 mol dm-3 KNO3, SECM methodology and theory have
AgCl Dissolution in Aqueous Solutions
J. Phys. Chem., Vol. 99, No. 40, 1995 14831 References and Notes
2.0
1
1
'.O 0.0 ! 0.00
0
0
n
v
0
I
!
I
0.15
0.30
0.45
dla
Figure 13. Approach curve (0)of the normalized peak currents for Agt reduction from images such as those in Figure 12 as a function of tip-substrate separation. The theoretical characteristics for a diffusioncontrolled process defined by the model in the text (-) and a diffusioncontrolled process where the electroinactive counterion of the substrate is buffered (- - -) are also shown.
been successfully extended to treat the case of a sparingly soluble, binary symmetric salt dissolving into a solution where none of the lattice ions are buffered. In contrast to most earlier ~ o r k , the ~ - process ~ was found to be diffusion-controlled with a lower limit on the dissolution rate constant of 3 cm s-'. This value is several orders of magnitude greater than the value which can be derived from another study which also found the reaction to be transport-controlled,'O demonstrating the ability of SECM to achieve very high mass transport rates under well-defined conditions. Since it was not possible to determine an absolute value for the surface rate constant or order of the dissolution process, it has not been possible to address the question of surface potential effects on the dissolution rate and mechanism. This point will be addressed in future work on other suitable systems. Additionally, the effect of inhibitors on the dissolution of AgCl will be the subject of a future paper.
Acknowledgment. We thank the EPSRC for equipment grants (GIUH63739 and GR/H61360) and an earmarked studentship for J.V.M.
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