A VACUUM TUBE POTENTIOMETER FOR THE DETERMINATION OF THE TRUE E.M.F. O F A HIGH-RESISTANCE CELL BY RCSSEL J. FOSBINDER
The recent development by MacInnes and Dole’ of a new type of glass electrode has greatly enhanced its value for the determination of the p H of fluids. The universal use of the system is, however, limited by the usual difficulties encountered in measuring the electromotive force of a high resistance cell. Various types of electrometers have been employed as null instruments but they are expensive and difficult to use in a routine fashion. This paper describes a single-tube direct-current amplifier whose chief attributes are simplicity, stability, high sensitivity, and ease of control. A null method is employed and a t balance no current is drawn from the cell, thus permitting the determination of the true E.M.F. of the system. With a galvanometer having a sensitivity of 2 . 5 X IO-^ amperes a, deflection of 15 mm. for a millivolt change of the potential on the grid is obtained. This sensitivity permits the determination of an E.M.F. with an accuracy of = ~ : . O O O Ivolt, providing the resistance of the cell satisfies a condition discussed in a subsequent portion of the paper. Recently several papers2 have appeared in the literature describing vacuum tube potentiometers for use with high resistance cells. The fault, common to all, is that a t balance a current flows in the grid circuit causing an I R drop in the cell and possibly a polarization. This fact, of course, limits their usefulness if one is interested in determining the true E M F . of the cell. A perfect vacuum tube should have no grid current a t a bias of o grid volts but the presence of gas in the tube alters the grid current so that uniformly no grid current flows when the applied biasing voltage is equal to the potential assumed by the grid on open circuit (Le., with an infinite resistance in series with the grid). Mulder and Razek,3 taking advantage of the gas effect, have perfected a high grid resistor amplifier of very high sensitivity. Partridgezbdescribed a circuit in which he chose as his operating point a plate current corresponding to the grid biased to the negative filament lead, stating that ‘(themaximum current taken from the cellisoftheorder of IO@ ampereat ‘balance’ it is zero.’’ I n general, this statement is not valid as it implied the fulfilment of certain demands. Some of these are (I) the electron current to the grid must be equal and opposite to the positive ion current when the grid potential is zero, ( 2 ) with a given tube this will be true for a particular value of plate potential and filament current, (3) any change in either filaInd. Eng. Chem. (Analytical Edition), 1, j 7 (1929);J. Gen. Physiol., 12, B o j (1929);
J. Am. Chem. SOC., 52,29 (1930).
* (a) Elder and Wright: Proc. Nat. Acad. Sci., 14, 936 (1928);(b) Partridge: J. Am. Chem. Soc., 51, I (1929);( c ) Stadie: J. Biol. Chem., 83, 477 (1929);(d) Elder: J. Am. Chem. Soc., 51, 3266 (1929). 8 J. Opt. Soc. America and Rev. Sci. Inut., 18, 466 (1529).
A VACUUM TUBE POTENTIOMETER
I295
ment current or plate potential will cause an excess of electron current or an excess of positive ion current, leaving a net current thru the chemical cell a t ‘balance’ which is not zero and will therefore introduce an error in the measurement equal to the 1R drop of this net grid current thru the cell resistance. Thus it seems that the claim made by Partridge that “it (the amplifier system) is independent of the characteristics of the valves and of their power supply,” should be qualified. Elderzd and Elder and Wrightza operated their circuit with a grid current flowing, consequently the observed E.M.F. of the cell varied with the resistance. This fault was recognized by Elder by a comparison of the observed E.M.F.’s obtained with the electrometer with those obtained with the vacuum tube potentiometer. A subsequent discussion will show that E, may have some value other than o when i, = 0.
The Vacuum Tube Amplifier as a Null Instrument4 The method of operating a practical circuit with no grid current flowing’ a t balance involves a discussion of the plate current-grid voltage and the grid current-grid voltage characteristics of a tube. Since the sensitivity of the circuit is dependent on the grid impedance Z, one must consider the factors which operate to produce a change in the magnitude of this quantity. There are three main causes for decreasing the grid resistance, namely: (a) leakage currents, (b) grid electron current and (c) ion grid current resulting from the ionization of gas in the tube. The components of the grid current characteristics are represented by Figs. Ia, Ib, and I C ; however, ~ in reality all three exist simultaneously and the characteristic takes the form indicated in Fig. 2 . The equation for the flat portion having a positive slope is i, = io m E, where i, = gridcurrent io = constant m = slope E, = grid voltage When i, = 0, m = iO/E, and since m = r/Z, one can easily see that Z, is positive and will be fairly large at this point. Two plate currenbgrid voltage curves are indicated in Fig. 3 . The normal characteristic may be represented by i, = f (Eg). The introduction of a high resistance in the grid circuit alters the slope of the characteristic and the plate current is now represented by i, = f (E). Direct current amplification depends on a relay effect of the electron tube, that is to say, a variation AE, of the grid potential produces a variation
+
4 A more complete discussion of this and other similar vacuum tube circuits can be found in the paper by W. B. Nottingham: J. Franklin Inst., March (1930). It has been the writer’s privilege to read parts of the manuscript before pubhcation. * The value of Eg = Eog,i. e. where ig = o haa been designated aa the floating potential by Nottingham: J. Franklin Inst., 208, 469 (1929). SFigs. ra, rb, IC, 2, and 3 have been taken from a paper by Ebbe Rasmussen: Ann. Physik, 2, 357 (1929).
1296
RUSSEL J. FOSBINDER
Aip in the plate current. The relationship is called the mutual conductance c7 of the tube, and is generally very small, about IO+ amp/volt. For a parai di ticular value of E, and of E respectively we have G = 4 and G' = 4
a h
aE'
G ' being the effective mutual conductance. Again considering the plate current-grid voltage characteristic when Z, is positive, the inclusion of progres-
FIG.I b
FIG.l a
FIG.I C
FIG.3
FIG.2
sively higher resistances in the grid circuit continuously decreases the slope, i.e., the value of G' decreases. Further, the curves will intersect the normal characteristic a t the same point, corresponding to o grid current, Le., when t h e grid current changes sign. Finally, when the grid is on open circuit, that is to say R, = m, a free grid appears a t the same potential corresponding to i, =
0.
Referring- to the circuit sketched in Fig. 4 we have a relationship given by E = E, R'%, E, = E R%, or
+
when E, = E,, = floating potential i, = o
A Y A C l T M TUBE POTESTIONETER
and Z, therefore i, = E, - E,, Ze
Differentiating and considering the last term a constant’ we have
From this relationship it is seen that G’ will be equal to G when =
I
or when Z,
> >R.
z
z,+
If a potentiometer be inserted in the grid circuit to balance the e.m.f. of the cell and if e = amount by which the circuit is unbalanced e’= fraction of e which gets thru to the grid which also shows that Rmust be small compared to Z,if the ae’ Zg than - = de Z, R
+
1298
RUSSEL J. FOSBINDER
sensitivity is t o be retained. The above relationship also indicates that if e is to be determined with an accuracy of *O.I mv E must also be controlled with the same accuracy. Finally, it is seen that a compensation carried out thru the resistance R determines only the potential drop across R independent of Z,-in other words the amplification need not be constant, it need only be sufficient. Considering the plate circuit containing an external resistance in series we have the relationship
where Zp
=
plate impedance and the Sensitivity
-ai,. - dE, aE, aE
=
ai, aE
=
G . - z, 1+RP/Zp Z,+R
(7)
The preceding equations refer only to the unbalanced circuit for when i,
= 0,e’ = 0,e = 0,and
E,
=
Eo,.
The tube which best fulfills the requirements for the amplifier under discussion is the screen grid type “ 2 2 , ” having the additional advantage of a highly isolated control grid.
The Practical Amplifier I n order to locate E, = E,, (Le. when i, does not change on open or closed grid) with the use of a galvanometer as null instrument in the plate circuit it is necessary to employ some form of zero-shunt circuit. The working circuit is shown schematically in Fig. 5 . A zero-shunt is obtained by means of the battery VI and the variable resistance R1. The potentiometer and variable resistances are of the radio type and are conveniently mounted on a
FK 6
cleaning thc glass xurfrtcc with absolute alcohol and gnxtnding tire point at which the glass eornw in contact with t i a basc. All lcads to and from the tobe, swit.cht,n, and ecll art' insoiabcd by iiieans of sulfiw. The wll is provided with high insolation as it is nupportcd by 1wo metal clanips which arc cd to glass rods firinly ioibidded i n a block of sulfur. The switches and Sa arc insiilaied with solfir and to avoid contact potentials all ei)nt.acts me rnadc oi gold. The load wires frmo the hox t o the potentiometer are encloscd in grounded copper tubing and are insulated from the tubes by the use of sulfur. The preceding and many ot,lier details of the apparatus w e revealod in the aeconrpanying pliot,ograph, Yis. 6 . The componcnt parts of the amplifier ape given Iierc~for wffrmw. i---lJX-222 tube V4-r-4 t o 6 V storage battery V3-2-45V Heavy duty "X" battrrirs v-i dry cell
RUSSEL J. FOSBISDER
1300
1‘1-9
dry cells connected in series-parallel to give 4.5 volts
( rl-~o,ooo ohm rheostat R1 { r2-5,ooo ” ( r3-100 )>
1)
Rz-~oo,ooo ohm grid resistor R3-25 ohm rheostat R4-5 ohm rheostat R6-200
”
1J
R~-2000 ohm potentiometer SI,SZ,S3-sulfur insulated switches S4-double pole double throw switch G-NO. 2 4 2 0 (c) Leeds & Iiorthrup galvanometer P-Leeds & Korthrup potentiometer MA-Weston 506 I . 5 ma-milliammeter Operation of the Amplifier
To operate the amplifier the plate and filament battery circuits are closed and the filament rheostat adjusted until the plate milliammeter reads 0.5 ma. The tube is then allowed to reach a steady state which usually requires about twenty minutes. With the grid circuit open, R,is adjusted until the galvanometer shows no deflection. SI is then closed and R4,S,gadjusted until the galvanometer again reads zero. Upon opening SIthe galvanometer should show no deflection as E, = Eo,. If a Leeds & Northrup Laboratory H ion potentiometer be used the galvanometer binding posts must be short circuited and the E+ post should always be connected to the biasing battery. To measure the potential of the cell R, SI and S2 are opened, S3 is closed; the potentiometer key depressed, and the e.m.f. at o galvanometer deflection is read directly. The potentiometer is checked against the standard cell by opening Sg, closing the potentiometer-galvanometer circuit and balancing in the usual manner. Since only one tube is used the characteristics need not be determined. The stability of the circuit is remarkably good, a drift of more than z mm. per minute never occurring on the plate side. The grid bias is also stable for several minutes before an observable drift occurs. S o oscillations of the galvanometer take place and the deflections are well defined. The Determination of the Grid Impedance near Grid Zero Since the sensitivity of the grid circuit is dependent on the value of the ratio
i5
+
(Equation 3 ) one should determine the value of the grid imZ, R pedance very near grid zero. The following method may be employed in determining the value of Z, corresponding to a value of AE, = E, - Eo,. A known resistance R is inserted in the grid circuit in place of the cell. A circuit is adjusted, an e.m.f. of one mv is introduced from the potentiometer P and the galvanometer deflection noted. With the resistance in series an e.m.f. sufficient to give the same galvanometer reading is introduced.
A VACUUM TUBE POTENTIOMETER
1301
If we let eR = e.m.f. with the resistance in series es
=
e.m.f. without the resistance in series
then and Since R, es and eR are known, Z, may be computed. Substituting experimentally determined values in the above equation the following result was obtained zg =
1 ,I O d . 7 . 5 . IO’
i.6.10-~
= 4 7 . 1 0 ~ohms.
If an accuracy of +O.I mv is desired with the use of this tube the resistance of the cell must, therefore, not exceed 2 5 megohms. Results with the Glass Electrode The best test of a circuit is, of course, in its operation in determining the e.m.f. of a high resistance cell. I n order to test the reliability of the circuit, the e.m.f.’s of the following cells were determined.
1 1 0.I N HCl, AgCl I Ag 1 Hg2Cl?,KCl Sat’d 11 o.1N HC1 I Glass I O.IXHCl, AgCl 1 Ag Hg 1 Hg2C12,KC1 Sat’d
Hg
(1) (2)
The potential of cell ( 2 ) should be equal to that of celi ( I ) providing the glass functions as a membrane reversible to hydrogen ions and is the source of no other potential. The O.IN HCl and the silver-silver chloride electrodes were previously checked by the recommended cell combinations and were found to be satisfactory. The e.m.f.’s of cells ( I ) and ( 2 ) were determined with the vacuum tube potentiometer at z 1°C with the following result
E(t) = -.0395 volts E(2) = -.0420 volts The difference between Ez and El (-.oozgV) should be equal to the membrane potential existing in the glass. To test this point the e.m.f. of the combination -4g 1 hgC1, O.IN HCl I Glass I O . I NHCl, AgCl I Ag was determined and found to be .ooz4V. This procedure was carried out with a number of glass electrodes with similar results To further test the behavior of the circuit a number of Sorensen phosphate buffer solutions were prepared and the e.m.f.’s of cells of the type Hg 1 Hg2C12,KCl Sat’d were determined a t z 1°C.
11
Sol’n A 1 Glass 1 O.IN HCl, AgCl I Ag
1302
RUSSEL J. FOSBINDER
For the purpose of obtaining comparative values of the e.m.f. of such a cell the potential of the cell HP I O.INHC1, AgCl [ Ag was assumed to be -0.3524 volts at 21OC. Using the observed value for the e.m.f. of cell (I) the equation relating pH to the observed potential becomes E210 = --.1023 .os83 p H Since the particular glass electrode employed had a membrane potential of -.0024 volts the potential of cell ( 2 ) is given by E210 = --.I047 ,0583 pH The results of a series of measurements on the above cell with varying hydrogen ion concentration of solution A are given in the following table.
+
+
TABLE
Calc. E
,2590 ,2924 ,3256 ,3642
1
Obs. E
PH
pH obs.
,2595 ,2902 ,3249 ,3628
6.23 6.81 7.38 8.04
6.24 6.78 7.38 8.02
The small deviations of the observed from the assumed pH values are to be expected as the exact pH values of the buffer solutions were not determined electrometrically. It is sufficient to show that the observed e.m.f. values are of the correct order of magnitude. Electrodes of the type described by MacInnes and Dole were employed, the glass being of the same composition, and were approximately 7 mm. in diameter. The author is indebted t o Dr. W. B. Nottingham of the Bartol Research Foundation for many valuable suggestions.
summary The theory and construction of a vacuum tube potentiometer for detkrmining the true e.m.f. of a high resistance cell have been described. Operating the amplifier under well defined conditions an accuracy of *.OOOIV is obtainable. The Cancer Research Laboratories of the Graduate School of Medicine of the University of Pennsylvania, Philadelphia, Pennsylvania.
