J
Chemical Instrumentation
.feature
S. 2. LEWIN, New York University, Washington Square, New York 3, N. Y
5. pH Meters The determination cf pH, which in the 1920'8 and 1830's was generally carried out by visual or optical comparison of tho color of an indicator in the unknown with standard colors, has a t present been almost entirely taken over by electronic instruments. This is a oonacquence of the development in the late '30s and early '40s of remsskahly sensitive yet atable circuits and vacuum tubes. The electronic pH meter with glans electrode sensor is now 80 reliable and relatively inexpensive an instmment, that no laboratory can afford to he without a t least one. The electrometrir measurement of pH depends upon thc determination of the voltage existing hetween a hydrogen-ionsensing, and a reference electrode. The accuracy and precision of the detemination depend critically upon the nature and design of the electrodes, as well as on the jnnct,ion between them and the solution. For the present, we shall assume that a suitable electrode pair is available, and shall address ourselves to tho question of the pH meter itself; i.c., tho voltage measuring device.
resistance, generates s. voltage difference across it equal to
amplifier; and the vihrat,ing-reed cond~nser.
I.R,.,
The Potentiometer-Amplifier
= (5 X 10-'0) (1
X 108) = 0.5 volt
The voltage is opposite in polarity to Eo; hence, tho net voltage apparent to the voltmeter, which is that existing between paints 1 and 2, is only 0.5 volt. The measured voltage is thus 50% in error due to the minute current t h a t flowed doring the measurement. I n order to reduce the error to the order of 0.1%, the resistance of the voltmeter would have to bc at least as great as 10" ohms, so that the current being drawn from the electrode is not greater than amperes. This example deals only with the effect of internal resistance; the tendenry of the
rELECTRODE - - - - -PAJR
A simplified diagram of s conventional potentiometer circuit for a pH meter is shown in Figure 2. The battery, Es, sends s constant current through the slidewire ilC, establishing s, voltage difference across it that i~ larger than the largest
1
Requirements of a pH Meter A pH meter is simply a voltmeter. But the special properties of the glass electrode whose potential is to be measured impose several very stringent requirements on thc characteristien of the voltmeter. The glass electrode is a high impedance voltage Booree, and it is suhjcot to polarisation. "High impedance" means that there is a large resistance to the flow of current t,hrough the glass membrane; "polarieatian" means that n small flow of current significantly changes the concentration of ions s t tho electrode surface, and hence the electrode potential. Them properties of the glass electrode require that the voltage-measuring device must not draw appreciable curvent from tho electrode in the process of making the measurement. The importance of this requirement may be appreciated hy a consideration of t,he example shown in Figure 1. Suppose that the truo potential (En) hotween a glass and a refemnce elrrtrode in a given solut,ion is 1.0 volt, and the internal msistsnrt: is 1000 megahms (104 ohms), which is possible for modorn glass electrodes a t room tcmperaturc. If the voltage meamring device also has a resistance of 109 ohms, the current that will flowin the circuit is:
I
=E" -
R
= 1.o - - 5 X 10" 108
amperes
This rurrrnt., flowing t,hrough t,hc int,ernel
0
G R I D - TO--CATHODE VOLTAGE
.
Figure 2. Conventional potentiometer-ampliRer. At balance point, B, grid is at same potential as cathode, and meter shows a standard deflection. Moving sliding contact to left decreaser tube current, to right increase, it.
Figure 1. lllurtrafing the role of electrode resistance in pH measurements. Any current ollowed to Row b y the voltage measuring device treatel an IR-drop o~rossR , . , tnat opposer the pofentiol onRerenre between the electrodes. Volmge m e o w e o an meter :r E, - IR , I .
~.lwtnwlc I., n r ~ m >polnr~ml ~ :In ronw l w n r t , of the 11.,\r of w r n ut s o ild :$lzn It id i ( , :L m ~ ~ s w Y t d ~ 1I1a1 I ~i - ~ milll6.r K ~ than the true value. At present there are several approaches that have been applied with wrying degrees of success to the problem of measuring a n electrode potential without drawing more than lo-" amperes during the measurement. These are: the ootentiometw rirmrit with varuum tube amplifi~r; thc electrometer tuhe; the chopper-
voltage it is desired to measure. The sliding contactor, B, is moved along t,he slidewire until the point is found a t which the output meter, M , gives a standard deflection. At this paint, the voltage drop from A to B is equal to E,; the slidewire may he marked off in voltage or in pH units, and read directly. I f the nlidewire contactor is moved to the left of point B, current would Ron t,hroogh resistor BD, creating a voltage drop across it, and thereby altering the grid potential of the vacuum tuhe. If the rontaetor is moved to the right of B, current flaws through BDin the oppo~itedirection, altering the grid potential oppositely. Thus, the meter needle has a rertsin deflection when the potentiometer is exaotly tralaneed (this is marked 0 on the meter dial, but actually corresponds to a current of the order of 0.5 milliampere), and a greater or lesser deflection on either side
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of this "zero" point. The resistance LID can bc made very large, so that only very small mrrents can flow through the sensing elrct,rodes. The vacuum tohe serves sr an amplifier of this small unbalance potential; n second stage of amplification is aftrn used t o improve the sensitivity of detection. The null indicator for the output of the amplifier may he a n ammeter, galvsnometer, clcrtran-ray ("magir eye") tohe, ar glow tuhe. However, in ~ e c k i n gthc null h d a n c r with the conventionsl potentiometer rirw i t as described above, the current that flows (through BD) is soffirient1.v great to reduce markedly t,hc accuracy of pH drt,ermina.tions with the usnal t y p ~ of s glass elert,rodes. Modification of the potrntiomeiric circuit for use n i t h an electrometer tube. wibh whirh verv small rurrents are caused to flow throuph the glass drrtrodc, is descrihcd hrlav..
The Electrometer Tube The potentid difference of the dertrode pair enn hr rlirwtly measurrd without signifirnnt r u r r m t drnin by using nn elcrtromrtor tnhe. This is a vacuum tobc that has lrren cmstl.ort~d to have an ertrrmely low grid current. To nnderstand the significanre of this design Tea-
L _ _ J ELECTRODE PAIR
A.
Figure 3. A. An electrode poir connected between cathode and grid of o triode ~ontroir the magnitude of the current flawing from cathode to piate. B. Grid current is produced by the capture of electrons from the grid by positive 9.1 ions. The.= electronr come from the cothode, porring through the electrode poir on the way.
The el~ctroururrent Rowing from cnthode t o plate of the tuhe is dependent upon thp potential of t,h? grid, vhii.11 ~xerbss t h n W i n g action nhen nepstive, s mngnifying srtion ~ h positive. ~ n If the elert,t.odc pair is connerted b r t v n n l the grid and cathode as s h o m ~ ,tlie difference in putcntid between grid mid cathode heromps simpl" that cristing l x t w e n the glass and rdrronre dectrotles, and the
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plate current read on the meter is a. measurr of t,his voltage. In the construction of vacuum tubes, it is inevitable that a small residusl gas pressure remains after sealing off. Some of the electrons emitted from the cathode strike such gas molecules, and if the accelerating valtzge is greater than about 8 volts, produce ionization. Positive gas ions striking the grid steal electrons from it, and thereby cause an electron current to flow up to the grid, as shown in Figure 3B. T h i ~is the principal source of grid current. Other sources are leakage paths from grid t,o cathode across the tube envelope or the innulator carrying the socket pins. I n eleet,rompter tubes, the following techniques are employed to keep the grid current low: (1) high quality insulators are used far the tubo base; (2) the tube pins are spared as far apart as is pract,icahIe; (3) the residual gas pressure is made its low ss possible; (4) a positively charged screen grid may be employed in front oi the control grid to shield the latter from positive ions; (5) cathodes of high electron cmissivit,y are used, so t,hat only law voltages need he applied between plate and cathode; (6) the grid may he made positive with respect to the plate so that positive ions are repelled and t,he grid crment is rodured. By these means it is possihle t,o eonst,ruet electrometer tubes in which the grid current is as low as 10-86 amperes. Electrometer tubes me employed in dire~t~readine VH meters. thn besio circuit
Figure 4. Potentiometer circuit for use with el&trometer tube. Electrode pair voltage opposer the voltage picked off the slidewire; when there ore eauol. arid and cathode ore at same potentiol and meter shows standard deflection.
. .-
instrument, the voltage of tho electrode pair is applied to the grid of the electrometer tubc in oooosition to a. voltaee nicked
value, corresponding to the "zero" "null" of the read-out meter.
or
T h e Chopper-Amplifler One of thc principal prohlems in the wmnlifieat,ion of H, dc sienal is the drift in
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1
The nature of this drift ia ilhtstmted hy the diagram in Figure 5 A .
Figure 5. A. In a dc amplifier, drih, of the plote voltage, Ea, produce approximoteiy pro8. If portional drifts in the tube current, I,. on oc signal is being omplifled,the ac component of the tube current is practically independent of the plote voltage, in the iineor region of the tube choracterirtic curve.
I n the amplification of a dc signal, the plate current of the vacuum tube is dependent upon the grid voltage, as well as on the cathode-to-plate electron-aeeelerating voltage. For u given signal impmetl on the grid, the output of the tube drifts up or dawn if the plate voltage drifts, as shown by the arrows in the figure. However, if the signal to be amplified is a n alternating voltage, and the aUernating component of the lube current is the part of the output of interest, then the amplification is much less dependent an the plate voltage. If the tube characteristic curve is a~oroximatelvlinear. the ma=-
asahownin Figure 5B. I n order to arhiove the stability characteristic of ac amplification when meesuring s. dc signal, it is necessary to convert that signal to ac. This is done by means of a "chopper," shown schematically in Figure 6. A vibrating reed (vibrating in
Figure 6. Conversion of o dc rignd to ac b y means of on electromilgnetic "chopper."
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response to the presence of an ac electramagnet, not shorn in the diagram) alternately makes and breaks contact with a pair of eontsctors wrhich are connect,ed to the ends of a. center-tapped primary transformer winding. As shown in t,he figure, the rurrent in the primary coil flows first in one direction, then in the opposite direction, alternating with the frequency of the vibrating reed. The alternating current in tho primary is picked up hy the secondary winding and fed into the amplifier. After amplification, it is then converted back to a dc signal by a. rectifier, and this rectified voltage may he read on a meter, or balanced against a known volt,age in a potentiometer circuit. I t r i l l he noted that some current must flow in the c h o n ~ e rcircuit to ~ r o d u c ethe ac signal, hut this is made small hy keeping the impedance of the circuit high.
..
The Vibmting-Reed Condenser A device for oonverting a dc signal to ac without requiring any significant flow of current is t h r vil,rat,ing reed, or dynamic,
Figure 7. A Vibroting-reed, or dynornk, condenser consilts of o fixed plate, ond a moving which is vibrated by on ac-energized electromagnet. B. The vibration produces o periodic voriotionin thecondenser spacing, hence in the capacitance. This generote. a tlvctvoting voltmge.
condenser, shown ~rhrlnstieallyin Figure 7. If a condenser contains a charge, (2, on its plntcs, t,he voltage difference, V, hptwoen these plates due to that rharge depend8 upon the expacitimre, C, of the eondonser.
Q
=
CV
The capacitance is a function of t,hc shape and area of the plates, and of the separation hetwccn them. I n the dynamic randenser, one plate remains fixed in position while the other is caused to vihrate. Henre, the rapsdtsnre of this condenser fluctuates with the frequency of tho vihmtion. This generates n flnrtuating voltage, which can he amplified and mrasorcd. When the platen of a vihrating-reed condenser are connected to the glass and rcferenec electrode pair, the amplitude of the fluctuating voltage generated hv the condenser is proportional to tho voltage difference between the electrodes. The (Conlimed an page A482?) Volume 36, Number 9, September 1959
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A481
only currcnt that flows is that dur to charging of the condenacr plate- ( ~ h i e his rxeeedingly minute), and lrxkage arrow the insulators. In these instrumpnts, the total current drain from the elwtradtv i? commonly as lorv an 10-'5 amperes.
Feedback Stabilization One of the most important factors rrspanfiihle for the high stability of the amplifier~employed in modern pH meters is their utilization of the principle of negaliir, or inverse, Jeedbnrk. This has the ~ f f e cof t making the nmplification of the rirr~lit practically indrpend~ntof variations in the propert,ies of the vacuum t,ol>es. Thp fundamental prinriple of feedback rireuit,~.? ma? he understood q~rslitativrly hy ronsidwation of Figure 8. An input signal voltagr of magnitude Ri, is fed into a n zmplifie~.having a n nmplification factor n , and appears as an output voltng? of magnitude n .Ei, = E.,,. A fraction, ,f, of this output is then f e d back into thc inpat circuit i n apposition to the originnl signal. Thus, the net input. signal is no>!Ei, - f.E,",, and the net oi~tput is n . E i , - i . n . E , , b . Hmrr:
Figure 8. Iiluttrating the principle of feedbock rtobiiirmion of mpliRcotion. 1. input voltage; 2. net input to amplifier; 3. amplifier; 4. output voiloge; 5. feedback voltage. A. Net output is (I function of input, ampiiflcation foctor, and feedback. B. A decrease in the amplificotion factor is cornpenmted by a corresponding de. crease in the magnitude of th. feedback voltage. leaving net outnut ~Onrtont.
EOub= n.Ei. - f-n.E..t Rearranging this equation:
If n is large, and f is not too small, i.?., ii hoth the amplification factor and the feedback are ronsiderahle, 1 f . n can he
+
(Contintred on page A484)
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reduced merely t,o j.n, and t h equation ~ bcromra:
Em",Ei.
'
.f
= constant
Thrrefore, the output signal is proportional to the input signal, and independent of t h r smplifirstion factor, or variations init. Figure 8 shows the significance of these equat,ionfi in s grnphio farm. Figure 8 A s h o w thc r~lntionbetween input, output, and fecrlbark vokages for a given amplifiration fact,or. If the properties of the amplifier drift during use, so that the amplificntion fartor becomes, e.g., smaller, as depicted in Figure 8 R , the output signal mould trnd t,o be smaller. However, this causes the feedbark voltage to be smaller, which in torn causes the net input (Ei. - f . E ,,,, ), to he larger. This tends to make the output larger, thus campmsating t,he initial e8ect. The feedback ronrtitutes a built-in correction factor that automnt~ir.zllyadjusts for variations in the smplifirr's characteristics, and maintains a n output that is a faithful and constant cnlnrgement of the input function.
Comparison of pH Meter Types Eneh of t,he different types of highimpedance voltage measuring technique has its fiperial area of application. A potentiometer circuit is primarily suitable for a null-balancing inst,rument. That is, the amplifier and currentdetecting device are- used to detect the balsnce point, rather
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than to give a quantitative reading of the extent of unbalance. Tho slidewire rontaetor is adjusted manually until the null is found, and the setting is read. Null balance has the advantage that it is more accurate than direct deflection. I n the balanced condition, no current flaws throueh the oH-sensine elect,rodes. so is timoconsuming, and during this process appreciable current does flow through the sensing electrodes if a conventional pobentiameter-with-vac1111m-tubeamplifier is used. With the potentiometer-sn6eL.ctrameter-tube instruments, the grid current is larger while the balance point is being sought than it is in the balanced condition, for when the ~ y s t e mis out-ofbalance, the grid potential may he negat,ive enough to draw substantial n u m h e r ~of positive ions to it. Consequently, the potent,iometric method is suitable for work in which accuracy ismaro important than convenicnco or speed, and time can be taken to ayproach the null bitlance with approprist,e care. When an apparent null balance has been found, the electrodes should be given time to recover, and then the balance should be rechecked. Since the amplifier is utilized solely an a yes-or-no drvire, rhoppers and feedback stahilisation are not,necessary. Direct-reading pH meters ~mploying electrometer tuhes are relatively simple and inexpensive. They have the advaatage of presenting the output rapidly and in a convenient farm, but are subject t,o
zero-point drift nnd &rtrirnl noise. They are ranvenient,l.v adaptnl,le to operation from the 110-volt, ar line, whereas nullbahnce pH meters are more easily designed for battery operation. Feedback rirruitry is important in stabilizing these inst,ruments. The accuracy of a direct-reading instrument cannot I,? hettpr than the linearity or calibration of the meter employed for the read-out; this is commonly 1% of full-male deflection, although it can be as good as +O.lO/, in high-quality meters. A direct-reading, elertrometer-based pH meter is particularly n s ~ f t dwhere a large number of measurements of limited aerurary is required, as in some clinical and control laboratory work. The inst,ruments based on the use of the chopper-amplifier or the vibrating-reed condenser comhinc speed and convenience of reading with high accuracy. The eircuitry i~ rclntively rornplex, and carreaponrlingly erpcnsive.
Other Design Considerations A number of additional factors are invalved in adapting the high impedance valtmrtrr to convenient USP a8 B laboratory pH mrter. The source of power for thpse in~tumentsmay bp either batteries or the I 10-volt, ac line. Babteries are a very stahle, noise-Rce source of voltage and power, l,ut have- the disadvantage of hnving a limitrd usefd life. As the intrrnal resistanre riser;, and the voltage-
under-load falls, the battery must he replaced. Even batteries delivering very fim;tllcurrents, or no ourrent a t all, have a limited life. The effective lifetime of a battery delivering no current to an external circuit is called the "shelf life," far it is the same as the life it has while sitting in storage, waiting to he used. The shelf life depends upon ambient conditions of temperature and humidity, as well as on the interior construction, which determines the tendency for internal eleetrolynis to ooeur. Although it is occasionally a nuisance to have to change batteries, i t is downright dangerous not to, when deterioration .sets in. Old hatteries may leak and spread corrosive chemicals inside an expensive instrument, leading to extensiveand costly damage. For these reasons, same models of pH
meters have heen designed to operate directly on power derived from the ae line. This works well far direct-reading meters hased on the electrometer tube. However, if a null-balance instrument is desired, a source of stable dc is needed far the slidewire. If this is to he obtained from the 110-volt, ac line, an expensive rectifiervoltage-regulator circuit must he added. Chopper-amplifier and dynamio condenser type pH meters can he completely aeoperated. All line-operated instruments should he stabilized by feedback t a eliminate drifts and fluctuations originating fromsurges of the supply voltage. A pH meter can only give information about voltages, since it is a voltmeter. The reading of pH's in the scale of such a meter can be accurate only if d l ffactors that influence the relationship between
voltage and pH me controlled or corrected for. One of these factors is t,he temperature, for an the Nernst equation ~holvs,a change in pH of one unit corr?rponds to a change in voltage of 2.303RTIF volts. This wries from 54.2 millivolt,s per pH unit a t O°C to 70.0 millivolts/pH a t SOT. hfany pH meters have a. built-in adjusting resistor that is designed to regulate the slidewire or electrometer voltage in proportion to the ambient temperature. Other models of pH meters use x temperature-sensitive resistance, such as e t,hermi~tor, to compensate automatically for the temperature of the sample. Meters that do not have temperature compensation come equipped with charts or nomograph8 from which the pH corresponding to the meter reading at any temperature may he read. Most pH meters are usahle far othcr laboratory applications than the measurement of pH. They are applicable to any voltage measurement, and it is a. convenience to have the scale marked directly in volts, in addition to pH units. Thr instrument should have a built-in strtndwd
measurement of the voltage of a high impedance somce requires s specialized type of instnlmentation. I t will renrlily he appreciated that this measurement can he seriously interfcred mith by the enistenre of leakage paths within the circuitry of the instrument. Henee, a well-designed pH meter has its eireuit laid out with thp maximum spacing between points a t different potentials, partirularly in the input side. High-quality insulators of quartz, ceramic, or lowconductivity plastic me wed, and the input section may be hermetically sealed in s. dry atmosphere, or may be keptdry with a desircabing agent. Minintnrizntion of pH metcrs is difficdt. to arhiove uithout creating serious prohlems from leakage. A high impedance circuit is prom to t h r pickup of stray elertrir signals nhirii are radiated from nearly all ar instnimcnts, electric lights, motors, ete. This is minimized in mpat pH meters hy sumnunding the input section uith a shert metal shirld, and hy appropriate grounding. The pickup prohlem tends to he greater with line-powered than with hsttery-operated in&ruments.
Bibliography
BATES,R. G., "Elcctr~metric pH DPterminations, Theory and Practic~," J. '1Vile.y and Sons, Inc., N. Y., 1954. BECKMN,A . O., "The Development of pH Instrumentation," Reprint No. R-36, Beckman Instruments, Inc., South Pasadena, Calif., 1950. CLARK, W. R., and PERLEY,G . A,, ".Modern Developments in pH Instrumentation," in "Symposium on pH Mea~urement,"ASTM Special Technicsl Publication No. 190, Bmeriean Society far Testing Materials, 191fiRace St., Philadelphia 3, Pa., 1956, pp. 34-54. DOLE, M., "The Glass Electrode," J. Wiley and Sons, Inc., N. Y., 1941.
Nezt: Modern Commercial Laboratory pH Meters.
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