1058
Anal. Chem. 1984, 56, 1058-1065
Pulsed-Accelerated-Flow Spectrometer with Integrating Observation for Measurement of Rapid Rates of Reaction Stephen A. Jacobs, Mark T. Nemeth, Gary W. Kramer, Thomas Y. Ridley, and Dale W. Margerum* Department of Chemistry, Purdue University, West Lafayette, Indiana 47907
A pulsed-flow Instrument based on a hlgh-resolution dlgltalpositlonlng syringe ram has been constructed. Acceleratedflow profiles (velocities in the observation tube of 2-13 m/s with Increments of 0.053 m/s) In conJunctionwlth the method of lntegratlng observatlon for continuous flow are used to measure rapid rates of reactlon In soiutlon. Rates of mlxlng and chemical reaction are treated as sequentlal flrst-order processes. Measurements as a functlon of veloclty permit resolution of the two steps. Flrstorder reaction rate constants In the range of 300 to 12000 s-' may be determined In a single push wlth the use of only 6 mL of each reagent. The capablltlles of the system are demonstrated by measurlng rate constants for electron-transfer reactlons In aqueous solutlon (25.0 " C ) under pseudo-first-order conditions for four callbratlon systems: Ru(bpy)2+ F e a T , Ce( I V ) Fe(CN);-, F e 8 F , and IrClsz- Fe(CN);-. IrCit-
+
design and flow velocity. Several investigators have addressed the problem of reactions in turbulent fluids (2, 7, IO). The mixing operation can be described as a first-order process (11, 121, where complete homogeneity is approached exponentially from the point of mixing. Gerischer and Heim (13) have reported a mathematical description, eq 3, for the constantvelocity-flowwith integrating observation experiment, where mixing and chemical reaction rates are treated as two sequential first-order processes. In eq 3 to 6, 7L is the lifetime
A, - A, -=A0 - A ,
7,
+ 7, + 7, 2 exp(-rL/7,)
7L
A,-A, 1 -e-Y -=A0 - A, Y Y = bk/u
(1) (2)
made down the length of the flow tube. Evaluation of the reaction rate constant, k , requires the initial absorbance, A,, the final absorbance, A,, the observation path length, b , and the absorbance, A , as a function of velocity, u , in the observation cell. The velocity of reagents in the flow tube must be measured accurately since it is the independent variable to which absorbance values are correlated in order to obtain a rate constant. Unfortunately the mixing process, which results in a bias in the measured values of A,, cannot be neglected. Reynolds numbers (9),calculated from flow velocities and the diameter of the observation tube, are much larger than those needed to create turbulence, but the extent of mixing varies with cell
exp(-rL/7,)
-
(3)
7,
Flow methods are used for the characterization of very rapid chemical processes, particularly irreversible reactions. In recent years there has been a renewed interest in continuous-flow methods (1-3), exemplified by the investigation of extremely rapid electron-transfer reactions ( 4 , 5 ) . Work in this laboratory has resulted in the construction (6) and application ( 4 ) of a pulsed-continuous-flow spectrometer. This unit combines the advantages of a "pulsed" constant velocity profile (7),where reagent consumption is minimized, and the "continuous-flow method with integrating observation" (8), which results in enhanced optical sensitivity for fast reactions. In continuous-flow techniques which utilize the method with integrating observation, the complete mixing process and subsequent chemical reaction occur inside the observation tube. Hence, the lifetime of the reactants is the sum of the lifetime of the mixing process and the lifetime of the chemical reaction. The first rigorous treatment of data for the continuous-flow method with integrating observation was undertaken by Gerischer and Heim (8). For an ideal mixer the observed signal change is due solely to the chemical process. For an irreversible first-order reaction under constant velocity conditions, eq 1and 2 describe the response from observations
7:
~ ~ ( 7 7,) r
+
+ +
-
71,
= b/U
(4)
7,
= l/k,
(5)
=
l/kmobsd
(6)
of a volume element in the observation tube, k , is the firstorder rate constant for the chemical reaction, kmobsdis the observed first-order rate constant for the mixing process, and the remaining symbols have the same meaning as eq 1 and 2. The observed mixing rate constant has been reported to be proportional to the mean flow velocity (14, 15), eq 7 , where k , is a proportionality constant. kmobad
= kmv
(7)
In order to resolve the constants, k,, kmobsd,and k,, the absorbance must be measured as a function of velocity. Our first pulsed-flow apparatus (6) was restricted to a constantvelocity operation for each push. This required multiple pushes in order to collect data for one kinetic determination. The procedure was costly in terms of the time needed for data collection and the consumption of reagents. In 1940 Chance (16) demonstrated that both the period of measurement and the reagents consumed could be reduced by using a range of velocities during one push, the accelerated-flow method. The instrument developed by Chance employed observation perpendicular to the flow tube. The point of observation was several millimeters beyond the point of mixing with optical detection path lengths of 1-3 mm. This restricted the technique to the study of reactions with species of high molar absorptivities; a maximum first-order rate constant of 200 was reported (17). To overcome these drawbacks Chance (16) suggested that it would be advantageous to use rectangular observation tubes or to monitor the progress of the reaction parallel to the direction of flow. The latter corresponds to the method of integrating observation. The present work merges the concepts this laboratory has developed for the pulsed-flow instrument with the accelerated-flow technique to allow measurement of very rapid reactions in solution. A high-resolution digital positioning syringe ram is used to generate velocity profiles. Attention has been given to the design of better mixing cells both for continuous-flow methods where the observation does not include the point of mixing (2, 7, 10, 15, 18, 19) and for continuous-flow methods where the actual mixing process is monitored (3, 6, 8, 14). It is critical to minimize the period
0003-2700/84/0356-1058$01.50/00 1984 American Chemical Society
ANALYTICAL CHEMISTRY, VOL. 56, NO. 7, JUNE 1984
I
MASTER I
1
CONTROLLER
l-r----r
SYNC
,
light path
I
+
1059
-
A-
reoctonts
products
E--
+F$FT PLTR
PRNT
Flgure 1. Schematic of the pulsedaccelerated-flow Instrument: DPT, digital positioning translator; MTC, motor controller; E, optical encoder; T, tachometer; MT, motor; SR, syringe ram; DS, drive syringes: MC, mixing chamber; RS, receivlng syringes; LT, linear displacement transducer; PPS, programmable power supply: S, light source; M, monochromator; BS, beam splitter; SD, signal detector; RD, reference detector; EI, electronics interface; LTI, linear displacement transducer interface; SYNC, synchronization line; CPU, computer; TERM, terminal; CRT, digital storage scope; PLTR, digital plotter: PRNT, line printer; DISC, disk drives. The dashed lines show the light path. required for complete mixing in order to measure very rapid reactions with flow methods, especially when the mixing process is observed. Gerischer and Holzwarth (3, 24) developed a multiple jet mixer for flow methods which utilizes the integrating observation technique. The present work describes mixing chambers which are compatible with the pulsed-accelerated-flow spectrometer with integrating observation. Four rapid electron-transfer reactions are used t o evaluate the performance of the pulsed-accelerated-flow spectrometer and the mixing cells. This work shows that a reduced form of eq 3 can be successfully applied t o absorbance vs. velocity data in order to simultaneously measure both mixing and reaction rate constants. Pseudofirst-order rate constants as large as 12 000 s-l (half-life of 60 ks) can be measured with the use of relatively small volumes (6 mL) of each reagent per push.
Flgure 2. Top view and end-on view of MC, cell A (14 jet, radial mixer): W, windows; A and B are reactants.
- ---- -
Oscillotor
ZPosition L I
I
Detector
I I
EXPERIMENTAL SECTION Instrumentation. Figure 1is a block diagram of the instrument. The function of the master controller is to generate the velocity vs. time driving function for the digital positioning system and to synchronize this function to velocity and optical measurements. The digital positioning system consists of the digital positioning translator (DPT), motor controller (MTC), optical encoder (E), tachometer (T),motor (MT), and syringe ram (SR). This system produces a linear displacement of the drive syringes (DS) which inject the reagents into the mixing chamber (MC). Figure 2 gives a blowup of the mixing chamber. A receiving syringe (RS) collects the spent solution and provides a link to the linear displacement transducer (LT). Another section of the master controller monitors the intensity of the light from the source (S) and monochromator (M). A quartz plate beam splitter (BS) deflects a portion of the light to a reference detector (RD) which controls the programmable power supply (PPS) of the lamp in order to maintain a constant light level at the observation cell. The outputs from the reference detector (RD) and signal detector (SD) are conditioned (amplified and digitized) by an electronics interface (EI). The 16-bit position word from the linear displacement transducer interface (LTI), the digitized detector signals, and a synchronization flag (SYNC) are collected by the computer (CPU) which stores, processes, and displays the results. Digital Positioning System. In order to perform successful pulsed-constant-velocity-flow or pulsed-accelerated-flow experiments there must be accurate, adjustable, and reproducible control over the lifetimes of the mixed reagents in the observation
- - - - --
Digital
Analog
Error Detector
Tachometer
Motor
Encoder
D
Flgure 3. Control logic for digital positioning ram system: (A) function generator for velocity profile; (B) digital positioning translator (Indexer); (C) motor controller and power supply: (D), motor, tachometer, and optical encoder. flow cell. Figure 3 is a block diagram of the logic used to generate constant-velocityor accelerated-velocityprofiles. The four major components are (A) function generator (in the master controller), (B)digital positioning translator (indexer), (C) motor controller and power supply, and (D) motor, tachometer, and optical encoder. A specialized digital function generator was constructed to supply a signal which closely approximates a desired velocity profile. The operator defines a pulse function by specifying the
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ANALYTICAL CHEMISTRY, VOL. 56, NO. 7, JUNE 1984
initial ( Vo) and final (Vf) velocity (two 8-bit words) and the rate of conversion between velocities (0-9.00 kHz). The system slews a t maximum acceleration to Vo and then approaches V, at a specified acceleration. For an accelerated-flow experiment a linear velocity vs. time profile is used. Typical parameters for a constant-acceleration experiment are an initial velocity in the observation tube of 2-4 m/s, a final velocity of 13 m/s, and a conversion rate of 470 Hz (0.053 m/s step size). The reaction mixture experiences a constant acceleration of about 25 m s - ~ . For constant-velocity experiments a two-step function is used, because a single step function causes the system to overshoot V , This is a consequence of the positioning nature of the indexer, where an instantaneous position error at the beginning of the run causes a command for too much acceleration. A preferred algorithm is to set Vo to 50% of V, with a velocity conversion rate of 1.2 kHz. This profile gives the system a chance to maintain the desired position and velocity (servo lock) while slewing as rapidly as possible to Vf. The progress of the experiment is monitored in real-time through the master controller. Several analog signals are available for user convenience: system trigger, ram position, position error, velocity, and acceleration. The requested speed at any point during the experiment is sent to the indexer as an 8-bit word. The digital positioning translator (Figure 3B, Model TSIRON-19, Electro-craft Corp., Hopkins, MN) responds to the velocity command and a preset position command (24-bit work, 1bit = 0.00102 cm of linear displacement), follows the progress of the motor (i.e., position feedback) and generates an actuating signal for the motor controller/power supply. The velocity command is converted into an analog voltage by an 8-bit digital-to-analogconverter. This voltage drives a voltage-to-frequency converter which generates a pulse train with a frequency proportional to the command velocity. An up/down counter (position error detector) sums these pulses and generates a positive position error. Pulses from the optical encoder (1pulse per 0.72' of shaft rotation) indicate that a translation has occurred. Each pulse decreases the counter value by one which therefore generates a less positive error. The encoder pulses are also totaled in a second counter (current position), and when the value is equal to the desired distance of travel (position command) the system is halted. The digital position error word is fed into an 8-bit digital-to-analog converter to generate the analog actuating signal which is proportional to angular velocity (ca. 6 rpm/bit). The motor controller and power supply (Model MC6300-R19, Electro-craft Corp.) is a pulsed-width modulator which differentially drives the dc motor. The analog actuating signal is negatively coupled to the velocity signal generated by the tachometer (i.e,,velocity feedback). The resulting voltage difference represents the error between the desired speed and the actual speed. This error voltage is superimposed upon the actuator voltage and generates the actual drive level. The resulting signal is passed to the pulsed-width modulator which controls the current to the motor (Model MT 703/OPT500, Electro-craft Corp.). The two feedback signals (the position from the optical encoder and the velocity from the tachometer) represent the information necessary for a proportional-plus-derivative control action. The overall system operates in a closed-loop servo mode which provides precise angular velocity profiles for reproducible constant-velocity-flow or accelerated-flow experiments. The angular velocities generated by the motor are converted to linear motion by a zero-backlash ball bearing loaded screw (Model RP-1105-12F-O-D-D-W,Warner Electric Brake & Clutch Co., Beloit, WI). The 1 in. diameter screw has a lead of 0.200 in./turn (i.e,, five rotations of the screw are required to generate a 1.000 in. linear displacement). The screw is supported by two pillars with shielded bearings for horizontal support and thrust bearings for radial loads. The screw flange is oriented for a forward load and coupled to four 3/8 in. precision stainless steel rods which travel in brass guide sleeves. The four rods are coupled to a ram plate which drives the two reagent syringes. The motor, screw jack assembly, and syringe block are mounted on a 24 X 54 X 1 in. aluminum tooling plate. The syringe block and associated valves have been described previously (6). The duration of the push is 0.4 s and 6 mL of each reagent is used. Optical and Velocity Measurements. The mixing cell, monochromaticlight source, detectors, receiving syringe, and linear
____-_ Table I. Types of Jet Mixers for Flow Experiments with Integrating Observationa cell A cell B cell C Kel-F and cross-linked cross-linked cross-linked material PVC PVC PVC no. of slits 14 10 14 slit orientation radial tangential radial slit dimensions, cm depth 0,010 0.025 0.025 width 0.036 0.025 0.025 length 0.676 1.666 1.984 a The observation chamber has a cylindrical geometry, 2.00 cm path length, and 0.20 cm diameter. displacement transducer are mounted on a separate 24 X 48 x 1in. aluminum tooling plate, which rests on a granite optical table. The optical and velocity measurements are mechanically isolated from the syringe ram. The light source, receiving syringe, and the basic design for the observation/mixing cell and temperature control have been detailed elsewhere (6). The reference/feedback and reaction mixture optical signals are monitored by two operational amplifier/photovoltaic detectors (HUV-4000B,EG&G Electro Optics, Salem, MA). The features of the mixing cells are listed in Table I. Cell C has been described in detail previously (I,6). Cells A and B are modified designs which differ from cell C in construction material, size, number, and/or orientation of the slits. The reagents from the drive syringes enter a cell by separate paths (see Figure 2). The two solutions flow through alternating feed channels into 10 or 14 slits (5 or 7 per reagent) arranged in either radial (Figure 2) or tangential orientations at the entrance of the observation cell. Mixing occurs as the reagent jets enter the observation tube from the slits. The cells are constructed with materials which are resistant to aqueous acids, bases, and most redox reagents. In dynamic flow experiments, the independent variable is velocity. The velocity in the observation tube is derived from the ratio of the cross-sectional areas of the receiving syringe (1.47 cm diameter) to the flow tube (0.198 cm diameter) times the observed velocity of the receiving syringe plunger. In order to evaluate the velocity and acceleration,the position of the receiving syringe plunger is monitored as a function of time. The position transducer is a high-resolution (0.000254 cm)linear optical encoder (Model SST-E-4-0Dynamics Research Corp., Wilmington, MA). Time values are derived from a 20.000 MHz crystal reference oscillator and the actual sampling frequency is 10 kHz. Electronics. The master controller generates the velocity profile, monitors the position of the linear transducer, coordinates the initiation and execution processes for data acquisition (Figure 4 , monitors the output of the photodiode detectors (Figure 5) and uses a reference detector for a proportional-plus-integral control action to control the lamp intensity (20). Figure 4 indicates the timing logic for synchronization of the velocity ramp generator and data acquisition. There is a 500-ms delay after the start switch is engaged. During this period the initial value of the velocity is loaded into an 8-bit counter. The digital positioning translator must slew from the previous final speed to this initial speed. At the end of the 500-ms delay the velocity counter is enabled. The output velocity increases linearly (constant acceleration) at the rate defined by a programmable acceleration clock. The current velocity is compared to a preset final velocity and when they are equal the counter is disabled which generates a constant velocity command. The linear displacement transducer produces two square waves 90° out of phase, which are decoded into countup and countdown TTL pulse trains ( 4 converter) ~ (21). A 16-bit up/dom counter, which is zeroed during the 500-ms delay, algebraically adds the two signals and sends the result through buffered line drivers to the computer. Signals from the photodiodes are differentially driven to the second computer interface, Figure 5. The two signals from each detector are combined to eliminate common-mode noise (Analog Devices AD522 precision instrumentation amplifier) and are
ANALYTICAL CHEMISTRY, VOL. 56, NO. 7, JUNE 1984 START switch pushed
cxperimd
storls
I
500 msec +DELAY +
ihll I ,Ail i- LPERIMENT
n
Im.3 EN1 TIAL SPEED 7ESET LINEAR TRANSDUCER to 0 on
'CCELERWIDN CLOCK
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2nd Poinl WINDOW 1st MI 2nd Mll
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1061
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START lDELAY
I WINDOW AVERAGER
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I
WINDOW AVERAGER
.'(4,?F CYCLES FRAME DELAY
TIME
,
FRAME DELAY
-
Figure 4. Timing diagram: (A) master controller; (B) data acqulsltion. OPTICAL COUPLERS
REFERENCE AND FEEDBKK ETECTOR
AVERAGE VELOCITY, M/S 3
6
9
12
U
Figure 5. Communication flow for optical detection system. amplified. The heart of the interface is a subsystem which consists of two sample and hold amplifiers (Analog Devices SHA-1A) which feed a multiplexer (Analog Devices MPX-8A) and a 12-bit analog-to-digital converter (Analog Devices ADC-QM). The conversion clock, programmed at 10 kHz, is derived from a 20.000 MHz crystal oscillator (Motorola K1091A). Communication lines with the computer are optically coupled (Hewlett-Packard 6N137) to reduce digital noise in the analog subsystem. Data Analysis. Data acquisition and numerical calculations were performed with a Hewlett-Packard 2100A minicomputer. The mathematical treatment requires the initial absorbance, fiial absorbance, and the absorbance during the reaction as a function of velocity in the flow cell. In order to improve the transmittance signal-to-noise ratio a real-time moving window averaging routine is employed (Figure 4B). Absorbance values are calculated from transmittance measurements and the media transmittance (100% 7') taken for identical velocity profiles. The velocity at each absorbance value is calculated from the linear transducer data as a function of time. Values for the rate constant of reactions are calculated from absorbance and velocity data by using standard regression techniques according to the models presented here. In constant-velocity and accelerated-velocity experiments our preferred method of velocity calculation is to use multiple linear regression techniques (22)to fit the respective law of motion. Use of instantaneous velocities (A position/A time) tends to propagate
DAC SETTING (DECIMAL)
Flgure 6. Llnearity and precision of velocity in the mixing/observation cell: (0)velocity in the mixing chamber vs. digital speed command (DAC settlng); (H)% relative error vs. average velocity in the mixing chamber. additional error into the resolved rate constant. The relative between-run precision at constant velocity was found to be better than 0.1% from 3 to 12 m/s and 0.4% at 13 m/s, Figure 6 (based on 5 pushes per velocity value, 7 velocities, 1to 2 ensembles, total of 55 pushes). Figure 6 also illustrates the overall linearity of the observed final velocity values vs. the DAC setting. In a constant-acceleration experiment the displacement vs. time is a quadratic function. The relative between-run reproducibility is 2.8% for the initial velocity and 1.1%for the acceleration (based on 24 determinations, 1 to 4 ensembles, total of 63 pushes). The two primary sources of noise were electronic and mixing effects. Typically the electronic noise was small compared to the noise from mixing. Noise due to the mixing process can be attributed to two sources. The Schlieren effect (light scattering due to small differences in the refractive index of the reactants) causes an appreciable decrease in transmittance. Second, local depletion of one reagent in regions of inhomogeneity causes the rate of reaction to vary slightly, which results in proportional changes in the observed transmittance. The observed transmittance possesses a noise component due to these effects and
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ANALYTICAL CHEMISTRY, VOL. 58, NO. 7, JUNE 1984
u 135
OI54O
59
78
97
116
VELOCITY, M/S
Figure 8. Absorbance vs. velocity data: (0)accelerated flow.
,/'
(m) constant velocity flow:
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