Some issues in increasing the sensitivity of the APN method using a film electrode
Abstract Generated abstract
This paper examines ways to increase the sensitivity of amalgam polarography with accumulation using a film amalgamated electrode. The authors derive relationships for the minimum determinable impurity content, optimal solution volume, electrode surface, and amount of deposited substance, and use these to specify conditions under which impurities at about 10^-9 to 10^-11 percent may be determined. They describe a rotating microcell for 0.03 to 0.3 ml working volumes that raises the electrolysis constant through intensified mass transfer, and report experimental bismuth measurements down to 2 x 10^-11 g in the cell. A stepwise electrochemical concentration procedure is also proposed, increasing the effective electrolysis constant by a factor of about 20 to 25 and facilitating the use of microvolumes in high-purity material analysis.
Full Text
SOME ISSUES IN INCREASING THE SENSITIVITY OF THE APN METHOD USING A FILM ELECTRODE
A. A. KAPLIN, A. G. STROMBERG
(Presented by the Scientific-Methodological Seminar of the KhTF)
Previously we theoretically considered two variants for increasing the sensitivity of the APN method to \(10^{-9}\)—\(10^{-12}\%\): increasing the electrolysis constant to \(10^5\)—\(10^6\ \text{A}\cdot\text{sec}/\text{g-ion}^{-1}\), or decreasing the volume of the working solution [1—3]. It was shown that, for a hanging mercury drop electrode, reducing the volume to the optimum amounts to creating in the mercury drop a concentration of metal atoms that is constant at all polarograph sensitivities.
The purpose of the present work is to estimate the minimum sensitivity of determination on a film amalgamated electrode at the optimum electrode surface and solution volume, to develop the design of an electrolyzer, and to develop one working technique for experimental verification of the derived relations.
The amount of substance \((Q, \gamma)\) deposited on the electrode during the accumulation process is related to the area under the anodic peak \((q,\ \text{coulomb})\), at complete removal of the metal from the amalgam, by the relation:
\[ Q=\alpha q\cdot 10^{-3}, \tag{1} \]
where \(\alpha\) is the electrochemical equivalent of the element being determined, \(\text{mg}/\text{A}\cdot\text{sec}\). The total content of the element in the solution is determined by the expression
\[ Q=\frac{\alpha\cdot q\cdot 10^{-3}}{\gamma_*}, \tag{2} \]
where \(\gamma_*\) is the optimum degree of depletion of the solution after accumulation. The percentage content of impurity \((a\%)\) for a sample weight \(g,\ \text{g}\):
\[ a=\frac{\alpha\cdot q\cdot 10^{-3}}{\gamma_*\cdot g}\cdot 100 =\frac{0.1\cdot \alpha\cdot q}{\gamma_*\cdot g}. \tag{3} \]
Technique [1—2]
\[ q=I_a\cdot \frac{\delta}{W}\cdot \nu, \tag{4} \]
where \(\delta\) is the half-width of the peak, V; \(W\) is the rate of change of potential, V/sec; \(\nu\) is a coefficient depending on the shape of the mercury electrode, \(\nu=1.1\); \(I_a\) is the height of the anodic peak, A.
At a polarograph sensitivity \(i_*,\ \text{A/mm}\),
\[ I_a=h\cdot i_*. \tag{5} \]
From expressions (3)—(4) and (5) we obtain, for the impurity content minimally determinable at the given sensitivity of the instrument,
\[ a=\frac{0.1\cdot \alpha \cdot \delta \cdot h_{\min}\cdot i_*\cdot v}{W\cdot g\cdot \gamma_*}. \tag{7} \]
The minimum anodic current at the film electrode, with complete exhaustion of the solution, may be expressed as
\[ I_{\min}=h_{\min}\cdot i_* = K_2\cdot Q_{\min}\cdot \frac{s_*}{v_*}\ [8], \tag{8} \]
where \(s\) is the surface area (\(\mathrm{cm}^2\)) and \(v_*\) the volume of the electrode, \(\mathrm{cm}^3\); \(K_2^{1)}\) is the anodic-current constant.
At the same time, the minimum depth of the anodic notch is related to the residual-current density \((j=pc_yW)\) by the relation:
\[ I_m=ms_*pc_yW, \tag{9} \]
where \(m\) is a coefficient whose magnitude is determined by the requirements for measuring the notch depth with a specified accuracy, for example, \(\pm 10\%\); \(p\) is a coefficient indicating how many times the residual-current density exceeds the capacitive-current density \((c_yW)\); \(c_y\) is the mean capacitance of the electrical double layer, \(\mu\mathrm{F}/\mathrm{cm}^2\).
From (8) and (9) it follows that the minimum amount of substance in the electrode required to obtain an anodic notch \(h_{\min}\), recorded with the specified accuracy, is
\[ Q_{\min}^*=\frac{mpc_yW}{K_2}\,v=\frac{mpc_y\cdot W}{K_2'}. \tag{10} \]
Let us estimate the value \(a_*\) by formula (7). We shall take the following values of the quantities: \(\delta=0.04\ \mathrm{V}\); \(w=7\cdot 10^{-3}\ \mathrm{V/sec}\); \(h_{\min}=10\ \mathrm{mm}\); \(g=1\) and \(\alpha=0.7\) (for example, for bismuth). Then
\[ a_*=4\cdot \frac{i_*}{\gamma_*}. \tag{11} \]
The value \(a_*\) does not depend explicitly on the volume of the solution \((v,\ \mathrm{ml})\) or on the electrode surface \((s,\ \mathrm{cm}^2)\). However, the optimal degree of exhaustion \(\gamma_*\), according to [1], is
\[ \gamma=1-e^{-b} \tag{12} \]
and
\[ b=\frac{K_1}{zF}\,s\,\frac{\tau}{v_p}. \tag{13} \]
where \(K_1\) is the electrolysis constant, \(\mathrm{A\cdot cm/g\text{-}ion}\); \(\tau\) is the electrolysis time, sec. Hence the optimal value of the solution volume is
\[ v_*=\frac{K_{1*}s_*\tau_*}{b_*zF}. \tag{14} \]
The optimal value of the electrode surface is determined from expression (9), depending on the residual-current density \((pc_yW)\) and the required accuracy of measuring the notches at the given sensitivity of the polarograph,
\[ s_*=\frac{I_{\min}}{mpc_yW}=\frac{h_{\min}i_*}{mpc_yW}. \tag{15} \]
Then, taking \(c_y=20\ \mu\mathrm{F}/\mathrm{cm}^2\), \(\tau_*=30\ \mathrm{min}=1800\ \mathrm{sec}\); \(z=3\), \(b=3\) (prac—
\(^{1)}\) The sensitivity of determination \(2\cdot 10^{-11}\ \mathrm{g}\) is, for the time being, apparently the maximum attained by the APN method.
practically complete depletion of the solution, \(\gamma = 0.95\)), \(K_{1*}=10^4\ a\cdot\mathrm{cm}/\mathrm{g\text{-}ion}\), \(m=p=1\), we obtain
\[ s_* = 7.1 \cdot i_* \tag{16} \]
and
\[ v_* = 1.4 \cdot 10^{-9} i_* . \tag{17} \]
From relations (11), (16), and (17) we obtain, for the minimum determinable impurity content \((a_*)\) in high-purity material when operating at a specified sensitivity of the polarograph \((i_*)\), and for the corresponding optimal values of the solution volume \((v_*)\) and electrode surface \((s_*)\), the values given in Table 1, \(K_1 = 1\cdot10^4\ a\cdot\mathrm{cm}/\mathrm{g\text{-}ion}\); \(\tau=30\ \mathrm{min}\).
Table 1
\(K_1 = 1\cdot10^{-4}\ a\cdot\mathrm{cm}/\mathrm{g\text{-}ion}^{-1};\ \tau=30\ \mathrm{min}\)
| \(i_*,\ a/\mathrm{mm}\) | \(10^{-9}\) | \(10^{-10}\) | \(10^{-11}\) |
|---|---|---|---|
| \(a_*,\) wt. % | \(4\cdot10^{-9}\) | \(4\cdot10^{-10}\) | \(4\cdot10^{-11}\) |
| \(v_*,\ \mathrm{ml}\) | 1.4 | 0.14 | 0.014 |
| \(s_*,\ \mathrm{cm}^2\) | 0.07 | 0.007 | 0.0007 |
It follows from the data of Table 1 that, in order to achieve higher sensitivities of determination \((a,\%)\), it is necessary to use higher sensitivities of the polarograph. At the same time, the electrode surface and the solution volume must be reduced so that, independently of the sensitivity of the polarograph, an amount of substance \(Q\) [see (10)] required for recording, with a specified accuracy, an anodic peak of height \(h_{\min}\) is deposited on the electrode. The calculations given above and those made in [3] suggest that, in order to increase the sensitivity of determination, working solution volumes of 0.01–0.3 ml should be used. In the APN method up to the present time the volumes of solutions have been 2–3 ml and larger. A cell for 0.3–0.5 ml was described by Underkofler and Shain [4]. Earlier [5], a number of determinations were carried out by us from a volume of 0.1 ml in a reduced model of an electrolyzer with insertable quartz cups [6]. Two designs of microcells for working volumes of 0.03–0.06 ml, in which delivery of the substance to the electrode is accomplished only by diffusion, \(K_1 = 100\ g\ a\cdot\mathrm{cm}/\mathrm{g\text{-}ion}\), are described in [7]. One of the most important requirements imposed on microcells is the possibility of attaining, in small volumes, sufficiently high values of the constant \(K_1\), which indicate intensive delivery of the substance to the electrode. Stirring of the solution by a magnetic stirrer and by passing gaseous nitrogen through it is practically inapplicable when working with volumes below 0.3–0.5 ml. To increase the sensitivity of the APN method, in particular to attain values of the electrolysis constant of (2000–3000) \(g\ a\cdot\mathrm{cm}/\mathrm{g\text{-}ion}\),\(^1\) we propose the design of a rotating microcell (Fig. 1). The advantage of the rotating cell over rotating electrodes is the simpler connection of the contacts. The body of cell 1 is made of fluoroplastic. Inside the body there is a through circular opening 2–3 mm in diameter. From below, a fluoroplastic tube 2 fits tightly into the opening; it is filled with agar-agar and serves for contact with the saturated calomel electrode through transition elbow 3 containing a pure supporting electrolyte. The space above the tube is the working volume of the cell.
\(^1\) When the solution is stirred with gaseous nitrogen or by a magnetic stirrer \((n=600\ \mathrm{rpm})\), in a solution volume of 2 ml the value of the electrolysis constant is (500–800) \(g\ a\cdot\mathrm{cm}/\mathrm{g\text{-}ion}\).
A fluoroplastic cover 5 is fitted onto glass cylinder 4, 12 mm in diameter and 35 mm long; inserted into the cover are a tube for passing gaseous nitrogen and a cathode—a glass tube with a silver wire of the required diameter (from 0.02 mm to 1 mm) and length sealed into it. The value of the optimum electrode surface is calculated on the basis of the residual current, the specified sensitivity of the recording device, and the required accuracy of measuring the anodic current (see 15). A silver wire, sharpened at the end and amalgamated, or a mercury drop built up on such a wire, is also used as the cathode. The electrode is displaced somewhat relative to the center for more effective stirring. A cylindrical channel 6, machined in the fluoroplastic body and filled with water or mercury (at low rotation speeds), serves as a seal after the cylinder is lowered into it. The lower part of the cell is machined for a bearing, which, like the cover with cylinder 4, is fastened to a stand. Rotation of the cell is effected directly by the shaft of motor 8. The number of motor revolutions (up to 4000 rpm) is regulated by a transformer and measured with a stroboscope (type 2371/B, Hungary). The working solution (from 0.03 to 0.3 ml) is introduced into the cell with graduated pipettes.
Fig. 1. Rotating microcell. Designations in the text.
Fig. 2. Dependence of the electrolysis constant on the number of revolutions of the cell. Experimental conditions: Bi (+3); 0.25 N HCl; \(c = 10^{-6}\) g/ml; \(v = 0.05\) ml; \(\tau = 3\) min; \(s = 3 \cdot 10^{-4}\ \text{cm}^2\); \(\varphi_{\mathrm{H}} = -0.58\) (relative to N.C.E.).
A comparison was made of the magnitude of the electrolysis constant on electrodes of various types: a film amalgamated cylindrical electrode; an electrode in the form of an amalgamated disk sharpened at the end; an electrode with its end directed toward the rotating liquid flow; and an electrode with a spiral-shaped end. The greatest value of \(K_1\) was achieved on electrodes with the end directed toward the rotating liquid flow (\(K_1 = 3000\) l·cm/equiv-ion). The dependence of the electrolysis constant \(K_1\) on the number of revolutions \(n\) of the cell in the interval \((10 \div 50)\) rev/sec is linear in character (Fig. 2). In the rotating—
bismuth anodic peaks were obtained in a microcell on a hydrochloric-acid background at a concentration of \(5\cdot 10^{-10}\) mole/liter. Experimental conditions: \(v=0.2\) ml; \(\tau=40\) min; \(s=7\cdot 10^{-3}\ \text{cm}^2\); \(i_*=3.6\cdot 10^{-10}\) A/mm. The use in the microcell of electrode surfaces 10–20 times smaller than those usually employed makes it possible to record anodic peaks at the maximum sensitivities of the instrument, \((3.6\div 7.2)\cdot 10^{-11}\) A/mm, instead of \((1\div 3)\cdot 10^{-9}\) A/mm, owing to the reduction of the interference—the residual current. At the same time, in view of the small volume of solution and the comparatively high values of \(K_1\), practically complete depletion of the solution is achieved \((\varepsilon \cong 3)\). However, the use of microcells is hindered by the difficulty of transferring the sample into the microvolume of the supporting electrolyte.
We propose a procedure of stepwise electrochemical concentration, which makes it possible to eliminate these difficulties to some extent. The essence of the procedure is as follows. The sample is treated in the usual way in quartz beakers in a volume of 1–2 ml [6]. Then, in an electrolyzer with insert beakers, the ions to be determined are accumulated on an electrode with a large surface area \((0.2–0.6)\ \text{cm}^2\), while the solution is stirred with nitrogen or a magnetic stirrer, until practically complete depletion of the solution. The electrode with the concentrated impurities is removed from the cell under the applied accumulation potential and transferred to a microcell, where the metal amalgam is dissolved anodically. Then the electrode is removed from the microcell and an electrode with a small optimal surface area is inserted. The accumulation process is again carried out and the anodic peak is recorded under optimal conditions \((s_*, v_*, i_*)\). Preliminary experiments were performed with bismuth \((+3)\) on a hydrochloric-acid background at a concentration of \(10^{-6}\) g/ml. The possibility was established of determining bismuth after transfer of the electrode with concentrated bismuth in air from an electrolyzer of volume 2 ml into a microcell of volume 0.04 ml. Anodic polarograms of bismuth were recorded after the accumulation process in the electrolyzer without removal into air and after repeated accumulation with removal into air for 15, 60, and 240 sec with the circuit open (Table 2). It follows from Table 2 that during transfer of the electrode (20–30 sec) the height of the bismuth peak remains constant within the experimental error\(^2\). Next, the bismuth concentrated in a volume of 2 ml was transferred into a microcell \((V=0.04\ \text{ml})\), where a bismuth anodic peak had first also been recorded at a concentration of \(10^{-6}\) g/ml on an electrode with a surface area of \(3\cdot 10^{-4}\ \text{cm}^2\). After anodic dissolution of bismuth from the large-surface electrode \((s=0.15\ \text{cm}^2)\), peaks were again recorded on the microelectrode. The effective constant of the elect-
Table 2
Experimental conditions: \(10^{-6}\) g/ml \(\mathrm{Bi}^{+3}\), 0.25 HCl; \(v=2\) ml; \(\varphi_{\mathrm{n}}=-0.45\) V (sat. cal. el.); \(i_*=6\cdot 10^{-7}\) A/mm; \(\tau=3\) min; \(s=0.15\ \text{cm}^2\)
| \(t,\ \text{sec}\) | 0 | 15 | 60 | 240 |
|---|---|---|---|---|
| \(h,\ \text{mm}\) | 48 | 48 | 47 | 48 |
| \(h,\ \text{mm}\) | 50 | 46 | 50 | 50 |
| \(h,\ \text{mm}\) | 54 | 50 | 46 | 48 |
a) \(h\)—height of the anodic peak recorded after holding the electrode with the concentrated metal in air for \(t\) sec with the circuit open.
\(^1\) The determination sensitivity of \(2\cdot 10^{-11}\) g is still, apparently, the maximum achieved by APN methods.
\(^2\) In contrast to the experiments described on p. 8, the metal ions formed through oxidation of the amalgam by air are also transferred into the microvolume, from which they are then completely deposited on the microelectrode.
...lysis in the microcell can be estimated as follows. In the absence of depletion of the solution (only in experiments for estimating the constant \(K_1\)),
\[ K_1=\frac{q_1}{s_1 c_1 \tau_1}. \tag{18} \]
After transfer and repeated accumulation in the electrolyzer, and transfer to the microcell, upon repeated determination of \(K_1\) in the microcell:
\[ K_{1\mathrm{eff}}=\frac{q_2}{s_1 c_1(\tau_1+\tau_2)}, \tag{19} \]
where \(\tau_1\) is the accumulation time in the microcell and \(\tau_2\) in the electrolyzer, sec; \(q_2\) is the area under the anodic tooth in the microcell, increased due to stepwise concentration, coulomb.
From expressions (18) and (19) it follows:
\[ K_{1\mathrm{eff}}=K_1\cdot \frac{q_2}{q_1}\cdot \frac{\tau_1}{\tau_1+\tau_2}. \tag{20} \]
On the basis of the experimental data obtained (a mercury drop in the microcell), the effective electrolysis constant is \((20 \div 25)K_1\) and is equal to \((25 \div 30)\, g\cdot cm/g\text{-ion}\). In expression (19), the surface of the electrode used for accumulation in the electrolyzer is not explicitly taken into account. The magnitude of this surface is limited by the size of the working space in the microcell (Fig. 1–9). The optimal volume of solution in the electrolyzer is calculated from expression (14).
Conclusions
-
Theoretical expressions have been derived for the optimal volume of solution, the electrode surface, and the optimal amount of substance in a film electrode, making it possible to select conditions for achieving higher sensitivities of determination. The possibility has been shown of determining \(10^{-9}\)—\(10^{-11}\%\) impurities by selecting optimal conditions.
-
For experimental verification of the derived relationships, a rotating microcell design has been developed for working volumes of \(0.03\)–\(0.3\) ml with an electrolysis constant of \(3000\, g\cdot cm/g\text{-ion}\).
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Anodic bismuth teeth have been obtained at a content of \(2\cdot 10^{-11}\) g in the cell.
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A procedure of stepwise electrochemical concentration has been proposed, making it possible to increase the effective electrolysis constant by a factor of \(20 \div 25\) and to use microvolumes in the analysis of high-purity materials by the method of amalgam polarography with accumulation.
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