Handbook of Modern Coating Technologies

The scanning vibrating electrode technique

• The principle

The SVET provides the localization of the anodic, cathodic, and inactive areas on electroac­tive surfaces. Fig. 1 —1B shows current lines and the electrical field in solution related to the corrosion at the surface. In a SVET measurement, a vibrating microelectrode is brought close to the surface (typical distances are from 50 to 200 pm) where it measures the potential dif­ference in solution, dV, between the ends of the vibration, dr (10—40 pm are typical values). The local potential gradient in solution, ГФ, in point (x, y, x) is given by,

where i, j, and к are the standard unit vectors in the directions of the x, y, and z coordinates, respectively. The electric field in solution in each point of measurement is

E 5 - УФ                                                                           (1.2)

which multiplied by the solution conductivity, к, gives the local current density,

^E 5 K~                                                                            (1.3)

Most SVET systems only measure the field in a single direction, usually the normal to the surface, thus providing the component of the current density that flows perpendicularly to the sample surface,

For imaging purposes this is the most important current component because the positive and negative currents can be related to the anodes and cathodes, respectively. Naturally quantitative information is limited since the X and Y components are unknown.

The potential difference can also be measured with two microelectrodes placed at dis­tance dr [31,32] in an arrangement called scanning reference electrode technique (SRET) [33]. The advantage of the vibration is that it modulates the signal allowing its amplification and filtering, thus significantly increasing the signal-to-noise ratio. In practice, instead of Eq. (1.4) a calibration routine allows the system to immediately give the current density from the measured potential [26—28,34].

SVET has been used to analyze many corrosion systems, such as galvanic corrosion [35—39], pitting corrosion [40—43], crevice corrosion [44], stress corrosion cracking [45], microbiologically influenced corrosion [46—48], corrosion inhibitors [49—54], and corrosion of weldments [55—57]. Regarding coated systems it was used to characterize metallic coat­ings [36,58,59], inorganic coatings [60,61], organic coatings [62—68], conducting polymers [69—74], and more recently, self-healing properties of protective coatings [75—79]. Revisions of published work can be found in Refs. [80—83].

• Experimental set-up

A few designs of SVET equipment have been described in the literature [26,27,34,84—89]. Fig. 1—2 shows the photographs of the equipment produced by Applicable Electronics [85]. The set-up exists basically to place a vibrating electrode at known positions in space, make it vibrate and record the potential difference between the ends of vibration. A collection of such points gives a SVET line or a SVET map. The oscilloscope (a) is used to check the quality of the probe tip response. The light source (b) and the camera (h) help placing the electrode in the desired position and allow monitoring the corroding sample. The motion control interface (c) controls the motors (f) which govern the position of the vibrating electrode in the three directions in space with micrometer resolution. The camera is also moved with a motor (not shown). Signals from two lock-in amplifiers (d) actuate piezoelectric benders inside a metallic

P)

FIGURE 1-2 Photographs of the SVET model used by the authors: (a) oscilloscope, (b) light source (with infrared filter and optical fiber to lamp), (c) motion control interface, (d) lock-in amplifiers, (e) computer with ASET software, (f) side of Faraday cage on the top of air table, (g) motors, (h) preamplifier, (i) ring lamp around a zoom scope connected to CCD camera, (j) metal box with 2 piezoelectric benders inside, (k) sample holder, (l) vibrating electrode, (m) sample, (n) ground electrode, (o) pseudoreference electrode, (p) vibrating electrode tip with platinum black deposit, and (q) electrode vibrating. SVET, Scanning vibrating electrode technique.

box (i), which are glued to a plastic arm with the vibrating probe connected at the end. Each piezoelectric bender transmits X and Z movement to the electrode, making it vibrate in the two directions with respect to the surface. Usually the vibrating electrode (k) is a 1.5-cm long Pt80Ir20 metal wire of 225 pm diameter, thinned at the end, and insulated with parylene C polymer except the ~5 pm tip [90]. A small cathodic current is applied to produce a 10- to 40- pm platinum black deposit at the electrode tip (o), which increases the surface area and conse­quently decreases the tip impedance [91]. The vibration frequency can be chosen in a range between 40 and 1000 Hz and the vibration amplitude (p) is usually between 5 and 10 pm (resulting in 20 pm between the ends of probe vibration for a 10-pm tip with 5-pm vibration amplitude). During the measurements the probe vibrates at the selected frequencies (triggered by signals from the lock-in amplifiers to the piezoelectric benders). The potential difference between the vibrating probe and a platinum black pseudoreference electrode (n) is measured with a dual n-channel field effect transistor inside a preamplifier (g), and sent back to the lock- in amplifiers. The amplification can be up to 50,000 X . A second Pt black electrode (m) is con­nected to the ground of the equipment.

The typical electrochemical cell comprises the sample (l), glued to a nonconductive holder of 3 cm in diameter with tape around it to make the walls of the solution container. The ASET software (e) developed by Science Wares, Inc. (USA) [92] controls the measure­ment sequence. Best results are obtained using a Faraday cage, an antivibration table, and an uninterruptible power source, to minimize noise, ground loops, and external power peaks. Other SVET systems have only the Z vibration, bigger electrodes, larger volumes of solution, and no camera on the top of the sample [34,88,89].

Eq. (1.4) converts the potential between the ends of the vibration into local current den­sity. In practice, the correlation between the two quantities is done directly by the system after a prior calibration. Different ways have been reported in the literature [26—28,34]. For the system being described, the calibration consists of a routine in which the SVET probe is placed at a certain distance (e.g., 150 pm) from a point source that injects a known current, I (e.g., 60 nA). The current density i at the distance r from the source is given by [26,27,93],

I

4 n r²

A brief explanation is given in the SVET manual from Applicable Electronics [85] and Science Wares [92]. The system acquires two voltage signals for each vibration. As an exam­ple for the X vibration, the two signals are the voltage in phase (X_Ph = V_x sin A) and voltage in quadrature (Xq = V_x cos A), where V_x is the voltage amplitude (potential difference) and A is the phase angle determined from the relative amplitude of the signals in the sin and cos channels, A = arctan Xq/X_p}i. Assuming the phase angle stays constant (true for well-made probes, in a properly operating linkage and a calibration near the depth of the measure­ments), it is possible to determine the proportionality constant K relating the measured vol­tages to the actual current density. In the X vibration (1D) case,

The calibration determines A and K_x, and during scans the computer reads X_Ph and Xq from the lock-in outputs and uses them to calculate i_x. For 2D measurements, the system acquires four voltage signals, X sin A, X cos A, Z sin B, and Z cos B, at two known points (chosen along the coordinate axes of vibration) with known current densities. The 2D case involves a calibration matrix that is designed to take into account the possibility of nonper­pendicular axes of vibration. The mathematical statement is more complex than the 1D case but the principle is the same. The calibration is valid for other solutions provided the system is updated with the new testing conductivity.

No electrochemical reactions take place at the tip of the microelectrode because no elec­trical currents pass through due to the high impedance of the preamplifier (10¹⁵ O). In addi­tion, the vibration mixes the solution around the probe nullifying the concentration gradients that could otherwise be sensed and added to the SVET signal [94,95].

• Common measurements

Fig. 1—3 illustrates the sequence of steps to obtain a SVET map. The sample for this example is presented in Fig. 1—3A. It consists of a zinc foil of 50 pm thickness and a 900-pm thick iron sheet, mounted side by side in nonconductive polymeric matrix, and connected electrically at the back. This simulates the cut edge of galvanized steel with a better perception of the process in each metal due to the spatial separation between them. The area to be mapped by SVET is indicated in Fig. 1—3A. The part of the sample that will not be scanned is insulated with var­nish to insure the active area is entirely scanned. This area is shown in more detail in Fig. 1—3B with the position of the measured points (50 X 50). The probe scans in a plane par­allel to the surface at a height of 200 pm and in each point the probe waits 0.1 s and acquires the signal for 0.1 s. The total scanning time was 25 min for this map. Details about experimen­tal parameters are given in the next section. In each point the probe vibrates in two directions, sensing the potential in the X and Z directions. Each vibration originates an alternating current (AC) potential signal that is amplified and filtered in a lock-in amplifier, as described earlier. Fig. 1—3C shows the maps of potential (difference between the ends of amplitude vibration) that are actually measured by SVET. Some SVET systems only provide this information. More important is the current density flowing in solution in the plane of measurement. This is obtained by the calibration using Eq. (1.6). The X and Z components of the current density are presented in Fig. 1—3D. The most common way of presenting SVET results is the map of the Z component (normal to the surface) because it gives a good picture of the positive (anodic) and negative (cathodic) areas of the corroding surface. Alone the X component (only accessible by one equipment) is not so insightful for corrosion studies but it is certainly helpful for a more complete description of the processes that are taking place. Maps with vectors of each compo­nent of the current density are possible (Fig. 1—3E) and maps of 2D vectors offer a nice visual­ization of the current flowing in solution from anodes to cathodes. Measurements in the three directions are not presently possible but have been reported in the past [84,86].

The SVET results can be presented in many ways. The maps of the current density in Fig. 1—3D can also be presented in a sort of 3D plot as in Fig. 1—4B. A different way is the

superimposition of contour lines or current vectors to an image of the surface, as shown in Fig. 1—4C and D, respectively. Plots with vectors are produced by the ASET program from Science Wares. For other plots, the experimental results can be exported to files easily read­able by any plotting program. Most of the figures in this chapter were made with the Quikgrid program written by John Coulthard (Canada) [96]. SVET maps show the "instant” activity on the sample during the period of measurement, whereas the optical images display the total corrosion accumulated from the beginning of immersion.

Apart from maps parallel to the surface, other measurements are sketched in Fig. 1—5A. A map in the plane normal to the surface (XZ map) (Fig. 1—5B) can be interesting in some studies because it shows the regions inside the solution that are affected by the interfacial

1. E) 150

100

a

50 0

0     300 600 900120015001800210024002700300033003600

Time (min)

FIGURE 1-5 Other SVET measurements: (A) sketch of the sample surface with the position of sampled regions, (B) map in a plane normal to surface, (C) lines normal to the surface, (D) line parallel to the surface, and (E) measurement in a fixed position over time. SVET, Scanning vibrating electrode technique.

processes. Alternatively lines in the Z-axis can provide similar information, with the advan­tage that lines for various times or different conditions can be overlaid in the same plot. The lines in Fig. 1—5C show current density particularly intense close to the surface and a rapid decay until a height of 1—2 mm, where the bulk of the solution is reached. Lines parallel to the surface can be chosen to highlight superficial differences, as in Fig. 1—5D. Several lines can be plotted in the same graph to reveal the effect of time or changes in the system. Another way to continuously monitor changes in the kinetics of the processes at the surface is to place the probe at a point of interest (pit, defect, inclusion, intermetallic, active spot, etc.) and measure the response over time after variations have been introduced in the sys­tem (O₂ concentration, pH, Cl^_ concentration, corrosion inhibitors, etc.).

It is important at this time to refer the type of samples that can be studied and how the electrochemical cells can be assembled. Fig. 1—6 shows various examples. Bulk materials

FIGURE 1-6 Examples of samples preparation for SVET analysis: (A) metal sample embedded in polymeric matrix (the tape around the mount delimits the solution reservoir), (B) sample glued to the polymer mount and isolated with scotch tape except for the area to be measured, (C) sample insulated with beeswax + colophony (3:1 mass ratio), (D) larger painted metal sample glued to a Petri dish and the sides isolated with a varnish, (E) thick metal plate in a larger solution reservoir, and (F) cross section of metal sheet. SVET, Scanning vibrating electrode technique.

can be embedded in polymeric matrix and, after the test, be abraded and polished for reuse in subsequent measurements. Coated samples cannot be processed in the same way and must be glued to the epoxy mount. The samples must be isolated except the area to be mea­sured. This can be done with adhesive tape, beeswax, varnish, etc. If polarization of the sam­ple is desired, an electrical wire through the epoxy mount provides the connection to a potentiostat. In general, tape around the epoxy mount makes the reservoir for the testing solution. A volume around 5 cm³ is usual. The small volume can be a problem for measure­ments prolonged for more than a few hours because solvent evaporation or very active sam­ples can change the solution concentration and pH, leading to alteration in the system kinetics. A variation in solution conductivity by solvent evaporation leads to incorrect current estimation. Different procedures can be applied to overcome this problem. The simplest is to perform experiments for just a few hours, renew the solution from time to time, or add water to the initial level to compensate for the evaporation. More elaborate measures involve elec­trochemical cells of larger volume, communicating vessels, or even solution recirculation between the small cell and a larger pool. Most of the SVET systems use larger solution ves­sels. The reduced size in the Applicable Electronics system comes from the original develop­ment for biological applications where small volumes are sufficient and easier to handle.

• Experimental parameters

When performing SVET measurements it is important to be aware of the most important experimental parameters and how they influence the results.

1. Electrode tip size. In Applicable Electronics equipment the electrode tip ranges typically from 10 to 40 pm in diameter. Other systems have bigger tips, of the order of 100—500 pm.
2. Amplitude of vibration. Values between 5 pm [25] and 30 pm [34] are reported in the literature. Usually this parameter is not changed. If it does recalibration is needed. Higher amplitudes can lead to better sensitivity but may also stir the solution increasing the transport of O₂ to the active surface [97]. The electric field is overestimated when the vibration amplitude is 0.25 times higher than the distance to the surface [98].
3. Frequency of vibration. Any can be used. Recalibration is needed if changed.
4. Acquisition rules. SVET measurements can be performed point by point or continuously while the probe scans the surface. The scan rate, time constant, and gain play a decisive role in the data quality. For the Applicable Electronics system, which measures point by point, the most important parameters are the wait and average times. The first is the time the probe waits in a point before starting measuring, the second is the time given for acquiring signal. Typical values vary from 0.02 + 0.02 to 1 + 1 s in each point. The optimal combination for fast measurements keeping low noise depends on the system under study and should be checked before measurements.
5. Height of measurement. Common values are 50, 100, and 200 pm above the surface. The probe-surface distance is an important parameter in determining the spatial resolution. Isaacs determined the FWHM to be 1.533 times the height of the probe [99]. Therefore the closer the better for spatial resolution. However, close distances increase the risk of collision with the surface or touching corrosion products. Additionally, distances shorter than 4 times the vibration amplitude may lead to an overestimation of the electric field measured by SVET [98].
6. Number of points. SVET systems measure the electric field either continuously or point by point. The Applicable Electronics equipment measures only point by point. Typical maps range from 10 X 10 to 100 X 100 points and the most common are between 20 X 20 and 50 X 50 (for sample areas ranging from 1 X 1 to 10 X 10 mm²). More points usually mean better map definition but there is no advantage for spatial resolution in having points closer than the distance to the surface.

The parameters of the maps presented in this chapter were probes between 10 and 30 pm in tip diameter, frequencies between 70 and 400 Hz, vibration amplitude of 5—10 pm, distances to surface of 100 or 200 pm (sometimes 50 pm), and testing solutions from 0.005 to

1. 1 M NaCl. The conditions used for each SVET map presented in this chapter are given in Annex. The proper selection of the experimental parameters, along with the quality of the equipment, is decisive for two important figures of merit, the sensitivity and the spatial resolution.

• Sensitivity

The sensitivity corresponds to the smallest currents that can be measured above noise. For a discussion about the types of noise and their sources in SVET measurements see Ref. [91]. The noise level in a solution of interest is easily obtained from the measurements in that solution without any current source present. The noise level is dependent on the solution conductivity, decreasing as it increases. Limits of detection in 0.005, 0.05, and 0.5 M NaCl have been found to be, respectively, 0.1, 1, and 7.5 pA/cm² [25]. Using these values in the fol­lowing equation:

Д V 5 - i pAr                                                                          (1.7)

where i is the minimum detectable current density, p is the solution resistivity, and Ar is the peak to peak amplitude (here taken as 10 pm), leads to AV = 165-180 nV, which can be considered the limit of the equipment.

• Spatial resolution

Spatial resolution depends on the distance to surface, tip size, and vibration amplitude. In normal operation, the distance to surface is the most important parameter. The FWHM = 1.533h (h is the distance to the source) [99] means that higher spatial resolution is achieved when the probe is closer to the surface. It also means that there is no advantage for spatial resolution in having a SVET tip much smaller than the scan height. In other words, no improvement in spatial resolution is obtained with points closer than the distance to the surface.

• Quantitative information

The greatest benefit of SVET is the qualitative imaging of the corrosion process, revealing active (anodic and cathodic) and inactive areas. Alone, this capability is already of utmost importance because it is not matched by any other technique. Nevertheless, quantitative information is often reported [34,43,100-109] and the approaches to correlate the current density that is measured in solution by SVET with the current at the surface (current source) include (1) treating local spots as point sources, (2) integrating the currents of the SVET map, and (3) using numerical simulation and modeling [95,106-110].

1. The simplest equation to be used when analyzing the data is

I = 2i_z nh²                                                                           (1.8)

which gives the current I, emerging from a point source at the surface, that originates the current density iz, measured at a height h directly above the source. This may be used in cases of localized activity, if all active sites are well identified and separated and admitting that they can be treated as point sources.

• The most common approach is to integrate the currents of the map. (1.9) gives the total anodic current, I_a, in a map of area A, by integrating the currents of all positive points (i_z > 0) [34,102,104],

Alternatively when the data are discrete (e.g., collection of points in a table), the total anodic current can be determined by summing the small currents that flow in the positive points of the map. This corresponds to the summation of the local current densities of all positive points (above noise level) multiplied by the area related to a single point (obtained dividing the map area A by the number of points in the map N), as shown in Eq. (1.10),

_Aⁿ (⁺)

^Ia N           ⁽ⁱⁿ > ^{14оУ)                                                                                                    (}1.10)

n=1

where N( + ) is the number of positive point in the map, i_n is the current density of the nth positive point, and i_noise is the noise level of the experimental conditions.

It is advisable to have the area of the map A coincident with the area of the sample. In Eqs. (1.9) and (1.10) the calculation is presented for the anodic current (i > 0) but it could be similarly done for the cathodic current (i < 0).

3. In any case, the best approach, leading to more accurate results, is to use modeling and simulation tools to analyze the SVET data. This can overcome most of the limitations inherent to the experimental results, as discussed in the next section.

• Limitations

It is difficult to achieve quantitative and accurate results with Eqs. (1.8)—(1.10). In fact, only underestimations are usually obtained for the following reasons:

1. the probe scans at a certain height above the surface and the current that flows below is missed;
2. the current outside the mapped area is not measured,
3. currents below the noise level will not be detected; and
4. only one (or two at the most) component of the current density is measured by SVET, leading to an underestimation of the total current density.

These reasons explain why calculations from SVET should always be considered with great care. This is also why many times the anodic and cathodic currents in a map do not cancel. Since SVET gives a partial picture of the current flowing in the system, the best approach is to use numerical modeling tools to reconstitute the missing information. Nowadays this is done using the finite elements method with models using the Laplace
equation [106,109,111 — 113] and models analyzing the transport and reaction of chemical species in the system under analysis [95,107,108,110].

• Main sources of artifacts and errors

The difficulties in using SVET as a truly quantitative technique were described. In addition, there are errors and artifacts easy to occur, with strong impact on the results. Fortunately they are easy to detect.

• Electrode platinization

The active area of the SVET microelectrode needs to be substantially increased, to lower the impedance and decrease noise. This is done by plating platinum black (hair-like threads) at the tip. If the tip is not well "platinized,” maps will be noisy and, in the limit, no coherent signals will be detected. A routine exists to check the quality of the tip response [91,114]. SVET systems using large electrodes do not require platinization.

• Bad calibration

The calibration relates the potential difference measured by SVET to the current density flowing in that point in space. It is performed in a medium with a known conductivity and remains valid for other solutions if their conductivities are updated in the software. Moreover, a similar probe size and the same frequency and vibration amplitude must be used. If any of these change, the calibration must be repeated in the new conditions.

• Wrong conductivity

As referred in the last point, wrong conductivity leads to erroneous current values. If the con­ductivity of the new solutions is higher and not updated, the currents will be lower than the true ones. The wrong current densities can be corrected using the following equation:

^Ktrue

^true I wrong

^K wrong

• Unknown distance to source

Since the current density varies with the inverse square of the distance to the source (Eqs. 1.5 and 1.8), measurements performed at different heights will give different current values and cannot be directly compared. If the distance to the surface is unknown, the value of the measurements is very limited.