Advisory Panel Jonathan W. Amy Richard A. Durst G. Phillip Hicks
INSTRUMENTATION Donald R. Johnson Charles E. Klopfenstein Marvin Margoshes
Harry L. Pardue Howard J. Sloane Ralph E. Thiers
Instruments for Rate Determinations HOWARD V. MALMSTADT, COLLENE J. DELANEY, and EMIL A. CORDOS School of Chemical Sciences University of Illinois at Urbana-Champaign Urbana, Ill. 61801 Widespread commercial introduction of inexpensive general-purpose minicomputers and hardware interfaces is greatly changing the design concepts of chemical reaction-rate instruments. Circuits, integration systems, variable-time methods, hybrid analog-digital systems, and software systems for reaction-rate determinations are presented imposed on strong background signals (7). quantity with respect to another are Of all the analytical examples where frequently encountered. in analytical rate information is utilized, none has methods. For example, one type of had so much attention focused on the automatic titrator (1) electronically various instrumental methods of en generates a signal proportional to the coding rate data as have the so-called rate of change of transducer output kinetic or reaction-rate methods of (E) vs. volume (V) of titrant and utilizes analysis (8). In these methods the the first derivative signal (dE/dV) to time rate of change of some property control the rate of titrant delivery. Ρ that is proportional to the concentra Another type of automatic titrator tion of one of the reaction products is electronically computes a second de measured, as illustrated in Figures rivative signal (d2E/dV2) during the le and If. For most practical proce course of the titration. This signal is dures the desired rate information is ideally suited for the automatic ter obtained shortly after the start of the mination of a titration at the endpoint, reaction. The rate measurement sys because it crosses the zero reference tem must be sensitive and capable of at the inflection point of the titration determining average initial rate amidst curve independently of the absolute considerable background noise. magnitude of the transducer output After the first automated reaction(2, S). A series of regular and derivative rate methods and instrumentation for titration curves is shown in Figure la. the rapid determination of glucose were developed in our laboratories about a Recently, there has been increased dozen years ago (9-12), many further interest in derivative spectrophotometry investigations were initiated—both of (4, 5), where the rate of change of abspecific chemical reactions and of the sorbance (A) or emission (F) with re instrumentation that would provide spect to wavelength (λ) is determined sensitive and selective quantitative rate and recorded vs. wavelength. The dA/d\ derivative signal (Figure lb) is procedures. I t was apparent from the start of these studies that more in especially useful in locating overlapping strumentation developments were es absorption bands (5, β). The second sential if rate methods were to be widely derivative signal (d2A/d\2), Figure lc, accepted as routine quantitative chem is said to provide improved sensitivity ical methods. Also, of course, reliable in the determination of absorbing gases in the ultraviolet regions (4). The automated instrumentation was im 2 portant for more rapid investigation second derivative emission signal (d F / of chemical reactions that might be d\2), Figure Id, has been used to provide used for quantitative rate procedures. increased sensitivity for trace constit uents that have emission lines super For over a decade there have been DETERMINATION and utilization THEof the rate of change of one physical
many published improvements from several laboratories for all major sec tions of reaction-rate instrumentation for quantitative analyses. Many of these developments, including com puter-controlled instruments with auto mated sample and reagent handling systems, are described in this month's Report for Analytical Chemists, page 26 A (IS). In this report the principles and characteristics of several electronic devices for rate determinations are presented which provide excellent noise immunity. Although the methods pre sented here were specifically developed for chemical reaction-rate procedures, several are generally applicable when ever the direct readout of the rate of change of some parameter with re spect to another is required. Classical Circuits for Rate Determinations
A differentiator circuit that provides an output proportional to the rate of change of an input signal can be easily assembled from a single operational amplifier (OA), an input capacitor, and a feedback resistor (14)· However, relatively small noise components on the input signal can result in a high noise level a t the output that often obscures the desired rate information. Even when the time constant of the differentiator is increased, the noise is usually prohibitive for chemical reac tion-rate procedures (IS). An all-electronic rate comparison technique has been successfully used for some reaction-rate procedures. An
ANALYTICAL CHEMISTRY, VOL. 44, NO. 12, OCTOBER 1972 ·
79 A
Instrumentation Ε
A
dE dT dX
d
ë VOLUME
WAVELENGTH,
TITRANT (a)
X
(b)
A Ba
5536
F
dA dX CoOH
BAND
SYSTEM
MEASURED
~d*
SIGNAL
θα
553$
À
dt' WAVELENGTH
,
λ
WAVELENGTH,
Χ
(d)
Ρ p
SOppm
\eoppm
dP dt
dP dt
60 ρ ρ m
SO ppm
methods can also be considered as general categories for the classification of circuits for rate determinations (8, 17, 18). Pardue (17) and Ingle and Crouch (18) have indicated that the choice of method might be dependent on considerations other than noise, but in any event, it is important to modify the basic techniques to eliminate the noise problems illustrated in Figure 2. In making a fixed-time measurement (Figure 2a), the noise component causes uncertainty in determining the value of Pi andP 2 and, therefore, in the measured value, ΔΡ. The values determined for Pi and Pi can fall anywhere within the dashed lines. The same considerations apply to the variable-time measurement shown in Figure 2b. In addition to the un certainty caused by the noise, an even greater error can be introduced by ran dom spikes that can cause false trig gering of the measurement system. For example, if the spike shown in Figure 2b is interpreted by the measure ment system as an indication that the preselected value of P 2 has been reached, then the t^me interval (W — ii) is erroneously taken as the measured value, At. Greater noise immunity has been obtained for all three general methods by using hardware and software aver aging and smoothing techniques (1923). Because space restrictions prevent a detailed discussion of all three cate gories, it was considered of greater value and interest to show how only one gen eral method, the fixed-time method, can be implemented to provide high noise immunity with analog and digital hardware or with software procedures. The variable-time and derivative meth ods are briefly outlined and referenced. Integration (Fixed-Time) Technique for Reaction-Rate Determinations
TIME
(e)
TIME (f )
Figure 1. Analytical methods by use of rate determinations, (a) Titration curves illustrating first and second derivative curves, (b) Benzene absorption curves recorded by minicomputer-controlled spectrophotometer (6). (c) Atomic absorption line showing first and second derivative curves, (d) Flame emission spectra of barium in presence of calcium (7). (e) and (f) Reaction-rate curves
OA integrator is used to generate a reference rate curve that is continuously compared by an OA comparator and maintained equal to the unknown input rate curve (15, 16). Although the performance of the comparison system is superior to the simple OA differen tiators, it does not give sufficient averaging of noise for many typical chemical reaction-rate measurements, especially where high sensitivity is required. Both the simple OA differ entiator and the rate comparison cir cuits can have fast response to provide output data proportional to the "in 80 A ·
stantaneous" rate. Instruments capa ble of providing more or less instantane ous rate data for reaction-rate methods have been classified as derivative meth ods (8,17,18). An early approach to combat noise on rate signals was to use one of the two-point methods as illustrated in Figure 2. The change in monitored parameter, ΔΡ (fixed-time), is mea sured over a preselected time interval, or the change in time, At, is measured over a preselected change in monitored parameter, ΔΡ (variable time). The so-called fixed-time and variable-time
ANALYTICAL CHEMISTRY, VOL. 44, NO. 12, OCTOBER 1972
Greater noise immunity has been obtained by applying an integration fixed-time technique rather than the two-point fixed-time method (16). The method involves the integration of two segments of the rate curve and sub sequent subtraction of the resultant areas. As shown in Figure 3, the integration is made over two equal time increments, At, which are se quential, and the difference, AA, be tween the resultant areas A\ and AÏ is the parallelogram ABCD. The area of the parallelogram is given by : AA = (At)a
(1)
The slope is defined as: S = tan a = a-
(2)
Substitution of Equation 1 into Equation 2 provides an expression relating
Instrumentation
0.2
t,
t2 te
TIME
(b)
(b)
04
0.6
0.8
1.0
TIME (sec)
(c)
Figure 2. Illustration of noise suscepti bility in (a) fixed-time measurement technique and (b) variable-time measure ment technique
Figure 3. Principle of integration method for reaction-rate determinations, (a) Ex panded section of typical rate curve illustrating integration and subtraction of two sequential areas A\ and Ai. (b) Expanded section of typical rate curve illustrating integration and subtraction of two areas Ai and ΑΪ separated by a mea surement delay interval t2 — tt
Figure 4. (a) Integration and subtrac tion circuit of rate meter, (b) Oscillo scope trace of slope from ramp generator and input voltage of 0A2. (c) Oscillo scope trace of output voltage of 0A2
slope to the difference in area :
be implemented by use of the relatively simple analog circuit shown in Figure 4a. This circuit uses two operational am plifiers (OA's) which are tied to one another and to a signal modifier by a switch network. During the first in tegration period, the signal is directed through switches 1 and 2 to the in tegrator (OA2). If the signal modifier output is as illustrated in Figure 4b, then line BC represents the signal ap plied to the integrator which charges capacitor C, causing the output of OA2 to rise to a voltage Vi as shown in Figure 4c. During the second integration period the signal from the modifier is first directed to the gain-of-one inverter (OA1) by switch 1 and then to the in tegrator by switch 3. The voltage rep resented by line DE is applied to the integrator input which discharges ca pacitor C, and the integrator output decreases in magnitude by the amount
V2. The voltage difference, AV, which is read out at the end of the measure ment period, is proportional to the difference in area, AA, and is therefore proportional to the initial slope accord ing to Equation 3. The switches (S1-S4) are activated with pulses generated by a logic circuit. Thus, upon receipt of a suitable trigger pulse, the logic circuit controls the start of the sequence of delay time, the length of the integration periods, the subtraction, and the readout of the result. The integration period is se lected to be as long as feasible to average the noise most effectively. The shortest practical integration period is governed by the switch times and OA response and at present is about 0.1 msec. During the integration period, the output voltage, e0, of the integrator changes as the square of the time, t, so that e„ = St2/(RSC). Thus, the rising and falling portions of the in-
ΛΑ
(Atr
(3)
Since At is a constant the slope is directly proportional to the measured difference, AA. In Figure 3b the two time increments are not consecutive but are separated by a time interval
