696
JAMES C. NICHOLAND RAYMOND M. Fuoss
VOI.
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A NEW CELL DESIGN FOR PRECISION CONDUCTIMETRY BY JAMESC. NICHOL~ AND RAYMOND M. Fuoss Sterling Chemistru Laboratory, Contribution No. 1880, Yale University, New Haven, Conn. Received March 16, 1964
The design of a conductance cell intended for use with dilute non-aqueous solutions is described. The electrodes (bright platinum) are concentric cylinders with the lead to the outer electrode being a platinum tube which acts as an electrical shield for the lead to the inner electrode. Stray electrical paths are thus eliminated. The electrode assembly 1s mounted on a Tcflon plug which is turned to a standard taper, so that the electrodes are interchangeable. Tests covering the resistance range 1000 5 R 5 50,000 ohms over the frequency range 500 5 f 5 5000 cycles per second show that the frequency variation is significantly less than that obtained with cells of other designs. Resistances up to 50,000 ohms can be measured with a precision of a t least 0.02%. The R-f -'I2 plot is nearly linear a t low resistances but its curvature steadily increases with cell resistance; the curve can be accurately reproduced by a parabola. Consequently, a simple numerical extrapolation to infinite frequency can be made, using data a t three frequencies equally spsced on a f-'h scale (e.g., 5000, 1290 and 556 cycles).
Introduction In order to obtain conductance data on nonaqueous systems which are useful for extrapolation, it is necessary to work a t quite low concentrations, Two experimental consequences follow : resistances well over 10,000 ohms frequentlyknust be measured, and bright platinum electrodes must be used to minimize difficulties due to adsorption2 of solute on the electrodes. These are precisely the conditions under ivhich errors due t o polarization and to parasitic currents are most likely. It has been standard practice since 1935 to extrapolate observed resistance linearly to infinite frequency on a reciprocal root frequency scale, following the recommelldation of Jones and Christian3 although these authors mention that their data show a small systematic deviation from linearity. Their resistanceS \!.ere in the range of 50-2000 ohms; when the resistance is of the order of 104 ohms in organic SOIVentS, the curvature becomes extremely pronounced and linear extrapolation on an R-f --'/e scale becomes impossible. To eliminate the difficulties arising from the Parker effect4 it has been recommended5v6that cells be constructed in such a way that no shunt circuits which contain Capacity in series with the cell contents be present. This goal is readily achieved by spacillg the leads relatively far from the cell when the cell impedance is lojFr~but the necessary becomes awkward when the cell resistance is greater than 5,00010,000 ohms. The erlenmeyer type cell7 offers the of being simu]taneous~ythe conductance cell and the mixing but we have found that it shows a Parker effect a t high resistFurthermore, each such cell obviously has a antes, a ,+,ider range fixed cell one could of concentrations in one run if the cell constant could be changed. Dipping electrodes would permit change of cell COnStallt, but they are bad electrically because the leads to the electrodes necessarily go the and as Shed10vsky6 pointed out, there is then a series capacity-resistance shunt across the unknown resistance. (1) On leave of absence from Willamette University, Salem, Oregon. Grateful acknowledgment ia made to the California Research Corporation for a research fellowship for the academic year 1953-1954. (2) N. L. COX,C.A. Kraus and R. M . Fuoss, Trans. Faraday sot., 31, 749 (1935). (3) G. Jonee and S. 14. Christian, J. Am. Chem. Sot., 67, 272 (1935). (4) H. C. Parker, zbzd., 45, 1336, 2017 (1923). (5) T. Shedlovsky, zbzd., 6 4 , 1411 (1932). (6) G.Jonea and G. M. Bollinger, ibzd., 59, 411 (1931).
(7) 0,A. Kraus and R. M, Fuoss, %bzd., 55, 21 (1933).
The purpose of this paper is to describe a cell design which permits interchange of electrodes in a vessel equipped with a standard taper opening, and which does not involve any stray electrical paths. Briefly described, the electrodes are conCentric cylinders, with the lead to the outer eketrode being a platinum tube which acts as an electrical shield for the lead to the inner electrode. Only one Soft glass-platinum bead seal is necessary; the cell is therefore much easier to construct than the one with Platinum tube seals through hard glass.* We have found that the observed resistance with these electrodes is accurately a quadratic in f-'"; we Present below a numerical method of extrapolating data to infinite frequency in order to eliminate the effects of polarization. It must be emphasized that the method may only be used when one is certain that no parasitic currents are present. Our shielded dipping electrodes satisfy this criterion. AS far as the cell is concerned, we feel that it is ~ I O W possible to measure resistances UP to 50,000 ohms with a Precision of a t least 0.02%. Experimental cell Constmction.-Figure 1 shows a cutaway diagram of the electrode design finally adopted (electrode pair I). The steps in the construction of such a cell are as follows:
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$ ~ ~ & o ~ ~ ~ f ~ drels and then soldering the seams with pure gold (oxygengas flame). For sturdy construction, a t least 10 mils of latinum sheet for A and B and 6 mils for C is recommended. t o the inside wall a t one end of C is gold-so1,dered D short length of B. and S. No. 25 platinum wire, D The other end of C is connected to A by means of four platinum strips, E (10 mils thickness) using gold as solder (two of the strips are indicated in the diagram). The sections of E between A and c are a t an angle of 100-105" to the axis of c in order to increase the rigidity of the connection. Additional rigidity, as well as increased electrical shielding of B, is attained by gold-soldering two circular platinum strips, F, across E. The openings which remain are ample to permit free Passage OT liquid. Inner electrode B is supported by a short section of 1 mm. diameter platinum rod, G, goldsoldered &crow one end of B, the rod itself being welded a t its midpoint to a second section of rod which in turn 1s welded to the platinum wire lead D". A layer of soft glass, H, built up along part of the second section of rod, starting about 5-6 mm. above B, serves to seal the electrode support into the platinum tube C. strips of platinum, J, are gold-soldered across the bottom of A to provide further electrical shielding. The platinum tube is fitted snugly into a Teflon stopper K which has been machined to fit a standard taper joint ( T 29/42 is a convenient size). A piece of glass tubing, L, is inserted into C and around D" to insulate the latter from C. The ends of D' and D" arc:
.
(8)
Y,F, Hnizda and C. A. Kraus, ibid.
71, 1565 (1949).
l
Sept., 1954
A NEw CELLDESIGN FOR PRECISION CONDUCTIMETRT
697
was checked using pure resistances ( 102-106 ohms) with capacitances up to 0.01pf in parallel as “unknowns.” A variation of less than O.Olyo was found in the resistance readings over the range f = 250 to 5000 cycles per second. The oscillator scale readings were checked using a Type 813 A General Radio 1000 cycle oscillator by observing the appropriate Lissajou@ figures on the bridge oscilloscope. All resistance readings involving cell resistance ratios were corrected for bridge lead and cell lead resistances. The latter were calculated from resistance data on platinum wire.’o Solutions.-For the majority of the tests of cell performance, 10-3-10-6 N solutions of tributylammonium picrate in 95% ethyl alcohol were used, mainly because a good supply of the salt was a t hand and because past experience had shown. that stable resistances were readily obtained with this solution. The above concentration range corresponds to a resistance range of 1,000-50,000 ohms for a cell constant of about 0.04. No attempt was made to determine accurately the solution concentrations since only approximate values were needed in comparing the behavior of different cells. It was noted in a few instances when aqueous solutions were measured that ionic impurities appeared to be dissolving from the soft glass plug, as indicated by a downward drift in the resistance reading. This drift was eliminated by boiling the electrode assembly in distilled water for several hours.
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wound around and soft-soldered to t,he copper posts, M, set in the Teflon plug. The cell is completed by constructing an electrode vessel of appropriate size and shape. The electrode dimensions naturally depend on the cell constant desired. The latter is approximately equal to (1/27rL)ln(b/a) where I is the 1engt.h of the cylinders and b and a are the radii of the outer and inner electrodes. As a specific example, in a case where the cell constant is 0.03833, t,he outer and inner electrodes are, respectively, 3 and 2 cm. long and 2 and 1 cm. in diameter. For reasons to be discussed below, the diameter of the inner electrode should iiot be less than 1 cm. The length of the tube C depends on the dimensions of the electrode vessel. The diamet,er of C for reasons of sturdiness should be a t least 5 mm. In Fig. 1 are also shown schematic diagrams of other dipping electrodes (11-V) which were constructed for comparison experiment,s. In I1 a 1 mm. diameter rod replaces cylinder B of I. In IT1 a wire replaces tube C as the lead to the outer electrode. The two electrode leads are enclosed in a soft glass tube and are separated from each other by a second smaller glass tube. In IV the leads are cont,aincd in separate glass tubes which pass through the solution in the cell, and in V the lead arrangement is the same as in IV while the cylindrical electrodes are replaced by flat rect.angular ones. The electrode vessels for the testing experiments are not shown. They consisted simply of large test-tubes fitted with ’$ 29/42 joints and provided with a side-arm for filling. Two such vessels joined by short glass tubes were used to compare the resistances of two electrode pairs in the same solution. We will refer t o the complete assemblies of elect.rodes and vessels as cell I, cell 11, etc. A cell of tbe erlenmeyer type (flat elect,rodes4 mm. apart, cell constant 0.04153) also used in comparison runs is designated as cell VI. Resistance Measurements.-The bridge used has been described by Eisenberg and Fuoss.9 Its R-f performance
Results and Discussion The cells were rated according to three criteria, namely, the magnitude and nature of the frequency dependence of resistance of a given cell over a range of resistances, the variation of the resistance ratios of different cells with changing resistance, and the sensitivity of the resistance to changes in the position of the electrodes in the cells. The better the cell the smaller is the frequency dependence of the resistance, and for a pair of good cells the resistance ratio should be independent of concentration. (If the design of a cell is such that resistance-capacitance shunts are present, then the ratio of its resistance to that of a good cell kvill decrease with increasing resistance of the solutionl6t8 ie., the cell will show a Parker effect.) For a dipping electrode to be satisfactory, of course, there should be no sensitivity to electrode position and depth of immersion. The frequency dependence of resistance for cells I-VI is shown in Fig. 2 where R is plotted as a function of f-‘”. The cell constants are about 0.04 except for cell I1 (constant = 0.15). The curves are displaced vertically for the sake of compact presentation; the absolute resistance for any point is obtained by adding the ordinate from the graph to the number of ohms shown a t the left of each curve. Resistance readings observed a t frequencies of 5000, 2000, 1000 and 500 cycles per second are shown. The absolute ordinate scale is the same for all the curves of Fig. 2, namely, 10 ohms per vertical unit as drawn. At a cell resistance of 1000 ohms, one unit is therefore 1%, while a t 50,000 ohms, one unit corresponds to 0.02(3& It will be observed that the erlenmeyer cell VI is usable up to about 8000 ohms, in the sense that the frequency dependence is small and monotone. Beyond lo4 ohms, however, a minimum appears in the R-f-‘/a curve, which presumably is due to the f 2 terms in the impedance. These terms are the consequence of a high impedance shunt which consists of capacity from the lead wires to the cell
(9) H. Eisenberg and R. M. Fuoss, J . Am. Chem. Soc., ‘76, 2914 (1953).
(10) “Handbook of Chemistry and Physics,” Chemical Rubber Publishing Company, Cleveland, Ohio, 33rd edition, p. 2808.
Y I Fig. 1.-Dipping electrode cells (electrode vessels not shown): I, cutaway diagram of shielded electrodes; 11-V, schematic diagrams of other electrode assemblies.
JAMESC. NICHOL AND RAYMOND M. Fuoss
G98
986
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0 0
n
I -
0.02
0.04
0.02
I-
I
0
0.04
(fi Fig. 2.-R-f112 curves for cells I-VI: 0,tributylammonium picrate-95% EtOH; 0, HOAC-H~O; 0 , KC1-HZO.
(through glass and thermostat oil), in series with the resistance of the cell contents. Cell V contains conventional dipping electrodes; as shown in Fig. 2V, the apparent resistance changes very rapidly with frequency. Incidentally, this design is sensitive to vibration, and the hazard of accidental change of cell constant by inadvertently bending the electrodes is always present. The data for cell IV show the remarkable improvement in the behavior of the dipping electrodes when one electrode shields the other. But solution is still present in the electrical field between the lead wires, and the corresponding Parker effect appears as a downward concavity on the R-f-'/P plot, which makes extrapolation hopelessly uncertain a t high resistances. Only a slight improvement (111) is obtained by putting both leads in the same tube; while there is no solution between the lead wires themselves, there is solution in the field from the outer cylinder to the lead from the inner cylinder. Cell I, in which the lead to the inner cylinder is completely shielded by the lead to the outer electrode gives the highly satisfactory performance shown in Fig. 21. One precaution must be mentioned in connection with this design: The diameter of the inner cylinder may not be too small, or the unsatisfactory pattern of Fig. 211 appears. The per cent. changes in resistance ratio as a function of cell resistance for several cells compared to cell I (cell constant = 0.03833) are shown in Fig. 3. The ratio a t a resistance of about 1000 ohms N solution) is taken as the reference point. For a cell of the type I design and cell constant 0.06097 there is no significant change in the ratio.
Vol. 58
A NEW CELLDESIGNFOR PRECISION CONDUCTIMETRY
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099
calculating the two AR/Ax ratios indicated in Fig. -I, dividing these values by the midpoint values of .u (0.02121 and 0.03535), averaging the two numbers so obtained, and dividing the average by 2 (since d2R/dx2 = 2b). The three bx2 products 1092 are calculated and subtracted from the appropriate R values to give three numbers R' = R , ax. From Fig. 4 it can be seen that the R' values lie 'K.O ' F on a straight8line of very gentle slope which extrapolates to R,. Since the x increments are equal, subtraction of the average AR' value from R (5000) immediately gives R,. The value obtained agrees with that determined by drawing a parabola through the original points. If one fits a straight line to the data by the method of least squares (dotted line, Fig. 4) the I value of R mso determined is 0.G ohm lower, a sig0 0.01414 0.02828 0.04242 xm(f)'". nificant difference in this example where the resistFig. 4.-Extrapolation curves for a typical set of data: ance is of the order of 1000 ohms. For aqueous 0, observed resistances; 0 , R' = R , + ax; dotted line, solutions of not too high a resistance, the R-f-'/l linear extrapolatmionplot calculated using the method of curves are practically linear, and the resistance can least squares. be expressed satisfactorily by the equation
+
R
=
R , +ax
the higher terms in .2: being negligible. Hence the linear extrapolation recommeiided by Jones and Christian does not introduce a very large error for these solutions. In the case of non-aqueous solutions which in general have a much higher resistance, however, the square term in x becomes the major factor and it is necessary to use a quadratic equation in making the extrapolation. DISCUSSION T. SHEDLOVSRY (Rockefeller Institute).--I should like to suggest that you try saturating your solutions with hydrogen. A437 guess is that this may result in less irreversilile electrode polarization and therefore show less frequency dependence of the measurements. It. h'I. Frross.-Even if saturation with hydrogen would reduce polarization, it probably would not eliminate it entirely, and we therefore prefer elimination hy extrapolation to a complication of the experimental technique. H. I. SCHIFF(McGill University).-The direct current method of measuring electrolytic conductances developed
by Dr. A. R. Gordon and his associates is free of the impedance difficulties discussed in the paper of Nichol and Fuoss. Moreover, i t is capable of yielding high precision data \vit>hvery simple apparatus. However, the method as described is restricted to solutions for which suitable reversible electrodes can be found. This is a serious limitation in the case of very dilute and non-aqueous solutions. For example, we found SgC1 to be soluble in nitromethane solutions of quaternary ammonium chlorides. It has been found possible to circumvent this difficulty by immersing the Ag, AgCl probe electrodes in aqueous KCl and forming a liquid junction between this solution and the non-aqueous solution whose conductance is t o he measured. Since the d.c. method involves the measurement of the potentidl difference between two such probe electrodes the junction potentials cancel. The olmrved probe bias potentials were not subutantinlly larger than t>hosereported l ) ~ Gordon. Moreover, when precaution8 are ta,ken to keep the liquid junctions sufficiently distant from the m2in body of the cell the conductance measurements remain constant to 0.01% for more t,lian 4 hours. The conductance is also independent of the curi,ent pnssed through the mitin body of the cell over the same range as is clainied for aqueous solutions. -It therefore appears that this modification may render the d.c. method applicable to the measurement of eonductances of any electrolyte.
