Anal. Chem. 1980, 52, 130-138
130
Pulsed-Flow Instrument for Measurement of Fast Reactions in Solution Grover D. Owens, Richard W. Taylor,’ Thomas Y. Ridley, and Dale W. Margerum” Department of Chemistry, Purdue University, West Lafayette, Indiana 47907
any desired degree of accuracy by means of a straightforward iterative procedure.
A pulsed-flow instrument is constructed which combines the advantages of small sample volumes with the method of integrating observation of continuous flow. A syringe ram unit provides constant velocity flow (2 to 9 m/s) for short pulses (0.8 to 0.4 s) resulting in the consumption of only 3 to 4 mL of each reagent per determination. The apparatus is used to determine first-order rate constants in excess of 5000 s-’ (excess Fe(CN)6’ 1rCi6*-)and a secondorder rate constant of 1.6(3=0.4) X 10’ M-’ s-’, first half-life N 100 ps (Fe(phen);’ Fe(CN),’). The instrument has been calibrated for half-lives down to 40 ps under second-order equal concentration condltlons. The technique is used to study the oxidation of a Cu(1) complex by a series of Cu(II1)-peptide complexes.
A-A, In ( X + 1) -A0 -
X
+
X
= kCol/U
(1) (2)
In Equation 1,A is the absorbance during the flow at velocity u , A. and A , are the absorbances of the reactants and products, respectively, and X is defined in Equation 2. In Equation 2, k is the second-order rate constant, Co, the initial concentration of the reactants, and 1 is the pathlength of the observation tube. Similar relationships have been derived for first-order reactions, second-order reactions where the reactant concentrations are unequal ( I O ) , consecutive first-order reactions ( I O ) , and reversible second-order reactions (11). Further development of the integrating observation of continuous flow method by Gerischer, Holzwarth, and coworkers (12,13) has extended the capability of the technique to reactions whose half-lives are on the order of 20 ps. This advance has allowed the study of the effects of cations (14) and ionic strength (15)on the rates of extremely rapid electron-transfer reactions. The major disadvantage of the Gerischer-Holzwarth instrument is the consumption of large volumes of reagent (500 mL per determination (16)). This disadvantage is of crucial importance in the characterization of rather expensive copper and nickel peptide complexes and the study of even more costly enzyme preparations. Hence, the goal of this work has been the development of a continuous flow instrument which incorporates the integrating observation technique using short pulses of constant velocity flow. A pulsed-flow instrument has been constructed which utilizes a syringe ram to provide flow velocities between 2 and 9 m / s through a 2-mm diameter and 2-cm long observation tube requiring only 3 to 4 mL of each reagent per determination. The instrument has the added advantage that the flow velocity is easily varied and precisely determined for each push cycle. The above range of flow velocities corresponds to Reynolds numbers of 4500 and 20 000, respectively for water a t 25 “C. The transition from laminar to turbulent flow usually occurs a t Reynolds numbers between 2000 and 2500 (17). Thus the flow velocities provided by the pulsed-flow instrument should produce a turbulent flow. The performance of the pulsed-flow instrument is evaluated using several redox reactions which have been characterized by other techniques. A computer-interfaced Durrum stopped-flow instrument, developed in this laboratory (181,is also examined using one of the same redox systems. The response of the Durrum instrument provides a basis for judging the performance of the pulsed-flow as compared to the most widely used, commercially available apparatus. Pseudofirst-order rate constants in excess of 5000 S? ( t 1 / 2 = 140 p ~ are reliably determined using the pulsed-flow instrument. This represents more than a tenfold increase over the range of rate constants which can be measured on the Durrum stopped-flow and a factor of four over the Berger ( 7 ) and
+
Since the classical investigation by Hartridge and Roughton (I),flow methods have become one of the most, important techniques for the investigation of fast reactions in solution. This topic has been reviewed several times by Chance ( 2 , 3 ) and technical difficulties have been discussed recently by Berger ( 4 ) . Chance (5,6)used a range of velocities (up to 10 m/s) for a given sample (the accelerated flow method) and reduced the volume of reagents that were required for each determination. Half-lives down to 0.5 to 1ms were determined using two 1-mL tuberculin syringes fused to a stopcock and mixing chamber. Berger (7) has designed a stopped-flow instrument which employs driving pressures in excess of 200 psi and a “high speed” stop valve. Flow velocities of 20-30 m/s, before stopping the flow, are attained in resolving half-lives down to 0.5 ms while consuming about 1 mL of each reactant. These techniques are limited in their ability to determine shorter half-lives by the finite distance between the onset of mixing and the point of observation. Both methods also employ observation perpendicular to the direction of flow restricting optical pathlengths to 1-3 mm and thus decreasing the sensitivity of optical measurements. In 1965 Gerischer and Heim (8) proposed a continuous flow method with observation in the direction of flow (integrating observation) using a cell in which mixing begins just as the reactants enter the observation tube. This mode of observation differs from the earlier design of Gibson and Milnes (9)because in the latter the observation tube is separated from the mixer by about 1 cm and observation is commenced after the flow is stopped. The mathematical treatment required by an integrated view of the reaction becomes more complex. Chance first addressed the problem for unimolecular reactions in his “slit length error” analysis for accelerated flow ( 5 ) . Gerischer (8) has derived expressions of the form given in Equations 1 and 2, for second-order-equal concentrations, which do not have an analytical solution. However, solutions can be obtained to
-
Present address: Department of Chemistry, University of Oklahoma, Norman, Okla. 73069. 0003-2700/80/0352-0130$01 .OO/O
Am
C
1979 American Chemical Society
)
52, NO. 1, JANUARY 1980
ANALYTICAL CHEMISTRY, VOL.
w Flgure 1. Schematic of pulsed-flow instrument. Syringe ram unit: C/B, clutch brake; MCU, motion control unit; MTR, motor; SR, syringe ram. Solution handling system: DS, drive syringes; MC, mixing cell; R, reservoir: RS, receiving syringe; V, three-way valve; VT, velocity transducer; W, waste. Optical System: BS, beam splitter; DP, detector photodiode; L, lenses; M, monochromator; OF, optical feedback controller; PP, programmable power supply; RP, reference photodiode; s, source. Analog electronics and computer interface: AA, analog amplification; CPU, minicomputer; HSP, high speed punch; I, computer interface; SS, storage scope; TTY, teletype
Chance (6) instruments. The pulsed-flow is calibrated under second-order conditions for half-lives down to 40 ks allowing the determination of rate constants in excess of lo9 M-' s-l. Results of the study of electron-transfer reactions between and Cu1(dmp),2+(dmp is 2,9-dimethyl-l,lO-phenanthroline) Cu(II1)-peptide complexes are presented which demonstrate the range of rate constants which can be studied using a combination of stopped- and pulsed-flow technqiues.
EXPERIMENTAL Instrumentation. Figure 1 is a block diagram of the major components of the pulsed-flow instrument which are: (1)the syringe ram unit; (2) the solution handling system; (3) the optical system; and (4) the analog electronics and computer interface for data acquisition. Syringe Ram Unit. One objective in the design of this instrument is to minimize the amount of reagents expended during each measurement. Large values of flow velocity must be employed to achieve turbulent flow and to follow fast reactions. Therefore, solution economy can best be realized by minimizing the length of time the solution flows. The syringe drive system must also maintain a constant linear velocity and attain this velocity rapidly. These requirements have been met by a syringe ram assembly similar to that reported by Hansen and Beinert (19) for a rapid-freeze sampling instrument. The principles of operation of the syringe ram are as follows. A 3/,-horsepower variable speed (0-2500 rpm) motor (Model 22846, Dayton Electric Co., Chicago, Ill. 60648) is brought to the desired rate of revolution and maintained a t that value. An electromagnetic clutch/brake (Model EP-400, Warner Electric Co., Beloit, Wis. 53511) is used to transfer power from the motor to the syringe ram. Initially, the electromagnetic clutch is disengaged and the brake is engaged. To start the experiment, the brake is relased and the clutch is energized. The clutch/brake is operated by a "Motion Control Unit'' (Model MCS-109, Warner Electric Co.). The output of the clutch/brake is coupled to a ball-bearing screw jack (Model R-0308-1, Warner Electric Co.). The rotary motion of the jack is converted to linear motion by a traveling ball-bearing threaded nut (Model R-0308-2, Warner Electric Co.). The nut is connected to a plate which pushes the reagent syringes. The push cycle is completed when the traveling nut breaks the light path of an opto-interrupter module (Model H13B1-549, General Electric Co., Syracuse, N.Y. 13201) acting as a limit switch. The time required for the entire push cycle ranges from 0.4 to 0.8 s for constant flow velocities of 9 m/s to 2 m/s, respectively. Figure 2 is a plot of velocity vs. time for one of the larger velocity values. The figure illustrates that constant
6.0
cI
0.01 0.0
131
Y'
i
i:
I
I
0.1
0.2
1
0.3
0.4
0.5
Time, s
Figure 2. Velocity vs. time profile for the pulsed-flow instrument. constant flow velocity of 7.31(f0.03) m / s is attained for 90 ms
A
velocity flow, u = 7.31(&0.03) m/s, is maintained for 90 ms. Percent transmittance data are acquired during this 90-ms time period. Four mL of each reagent are required for push cycles at velocities comparable to that shown in Figure 2. A mechanical limit switch is positioned near the end of the path of the traveling nut to automatically energize the brake in the event of any control unit malfunction. A pneumatic piston (Model 0315 2009040 Aro Corp., Bryan, Ohio 43506) was also evaluated for use as the syringe drive system. This particular piston was not used because the velocity vs. time profiles obtained were not as horizontal in the plateau region and because the drive velocity could not be varied and controlled as precisely as the motor driven ram. Pneumatic drive units similar to the design used by Berger (7) should be suitable for use with the pulsed-flow instrument. Solution Handling System. The drive syringe assembly is constructed from a Kel-F block equipped with plungers made of brass and Teflon to withstand the mechanical stress encountered during the push cycle. The drive syringe unit is encased in an aluminum housing thermostated by a circulating temperature bath (Model K-2/R, Lauda Co., Brinkmann Instruments, Westbury, N.Y. 11590). Three-way slider valves made of Kel-F (Model 201-51, Aspec Co., Ann Arbor, Mich. 48107) connect each syringe to either a reagent reservoir or to the mixing cell. Two experiments were performed to show that the drive syringe and valve assembly deliver equal volumes of each reagent to the mixing cell. In the first experiment the drive syringe and valve assembly were mounted on the traveling table of a milling machine in such a fashion that the syringe plungers could be reproducibly displaced a total distance of 1.000 f 0.0005 in. The syringes were then loaded with water and the valves positioned so that water displaced could be weighed. Using this procedure, each of the drive syringes and its respective valve was found to deliver the same volume of water to within h0.07%. In the second experiment, the drive syringes and valves were reinstalled on the instrument and alternately loaded with water in one syringe and 2 X M Fe(phe&'+ in the other syringe. The absorbance during the flow was monitored a t 510 nm on the pulsed-flow instrument and the effluent was collected and its absorbance was determined at the same wavelength in a 2-cm cell using a Cary 16 spectrophotometer. Flow velocities of 5 and 9 m/s were employed to measure the absorbance during the flow. For these dilution experiments the average difference in absorbance for effluents collected when the Fe(phen)?' was in the right syringe vs. the left syringe was h0.4% as determined by the Cary 16. Absorbance values during the flow at. the different flow velocities agreed to within f0.5% as determined on the pulsed-flow. Hence, it is concluded that the drive syringe and valve assemblies deliver equal volumes k0.570 to the mixing cell for velocities up to 9 m/s. The radial mixer/observation cell is shown in greater detail in Figure 3. Reagents enter the cell separately, via inlet holes
132
ANALYTICAL CHEMISTRY, VOL. 52, NO. 1, JANUARY 1980
* SOURCE
FEC
0
1I1e DETECTOR
0
Flgure 3. (Top)Radial rnixer/observation cell (cut-away side view). C, reagent channel; CB, cell body (Kel-F); FC, front collar (Kel-F); FEC, front end cap (brass and Lucite); FT, feed tube; I, inlet; 0 ,O-ring (Vlton); 0, outlet; OT, observation tube (2-mrndlam., 2-crn long); RC, rear collar (PVC);REC, rear end-cap (brass); S, slit; W, window (quartz). (Bottom) (top view)
in the front and rear collars, and flow into reagent channels around the circumference of the cylindrical cell body. Each of these channels feeds seven slits on the top face of the cell via angular feed tubes bored through the cell body. The slits are arranged in a radial fashion around the observation tube, with the reagents introduced through alternating slits. Upon mixing, the reagents proceed down the 2.0-cm long, 2-mm diameter observation tube. This design is essentially that described by Gerischer and Holzwarth (12) with the following modifications. Fourteen radial slits, each 0.010 in. wide and 0.010 in. deep at the edge of the observation tube, are used instead of ten. O-ring seals are employed on either side of the reagent channels and at the front and rear windows to prevent leakage due to high pressure development during the push cycle. The front and rear end caps are constructed of brass with Lucite or Kel-F pads adjacent to the windows. In addition to an aluminum housing, a 3/4-in.thick stainless steel bar clamp is positioned on the front and rear end caps to hold the quartz windows (T-19, Superasil 1,Amerisil Inc., Sayreville, N.J. 08872) in place. The clamp minimizes movement of the front window away from the face of the mixer. A cylindrical aluminum sleeve and a Lucite water jacket limit expansion of the collars during the push and allow the cell to be thermostated. A three-way valve (Model 3 MMF3, Hamilton Co., Reno, Nev. 89510) connects the outlet of the cell to a 10-cm3glass receiving syringe. This syringe functions as a receptacle for spent reagents and provides a link to the linear velocity transducer. An important variable in the data treatment employed in the integrating observation method is the flow velocity of the reaction solution through the observation tube. A device similar to that described by Holler, Crouch, and Enke (20) is employed to accurately determine the velocity of the solution during each push
cycle. A series of equally spaced slots were cut in an aluminum rule to a tolerance of 0.001 in. The rule is positioned on the plunger of the receiving syringe so that it moves through the slot of an opto-interrupter module during the push. The movement of the rule causes the opto-interrupter to generate a two-state switching pattern. The appropriate amplification is employed so that this two-state signal can be applied directly to the minicomputer. On-line monitoring of this switching pattern allows a precise and accurate calculation of the solution flow velocity since the computer sampling interval, slot spacing, receiving syringe diameter, and observation tube diameter are well known. The sampling interval of 5 kHz is set to a precision of better than 1 part in 1 O l o by the crystal clock in the computer interface. The slot spacing on the aluminum rule, the receiving syringe diameter, and the diameter of the observation tube have been measured to the nearest 0.001 in. This allows an overall precision of < I % to be expected for the velocity measurements. As Figure 2 indicates, the relative uncertainty in the velocity measurement at >7 m/s is on the same order as the expected value of 1%. The simplicity of this approach to flow velocity determination suggests a high degree of accuracy. This type of transducer is preferred over a magnetic induction transducer because it is easily interfaced to the computer and it is immune to vibrational noise. Other velocity transducers such as the chain-potentiometer method of Chance (6)or the “sliding device which gave 200 pulses per 2.54 cm of travel” of Berger (7) should also be suitable for use with the pulsed-flow instrument. Optical System. The second variable utilized by the integrating observation method is the steady-state absorbance of the reaction mixture at a given flow velocity. Rate constants are determined from the measured absorbance values as shown in Equation 1. Hence, the optical system must be able to provide a constant light intensity for a sufficient period of time to measure the absorbance of the reactants and products as well as the steady-state absorbance at several flow velocities (approximately 1h). For this reason, a photometer stabilized by optical feedback, similar to that described by Pardue and Rodriguez (211, has been constructed. The source (Model 7292, Oriel Corp., Stamford, Conn. 06902) is capable of providing radiation from 200-900 nm. Visible radiation is supplied by a 50-W tungsten lamp energized by a programmable power supply (Model 6267A, Hewlett-Packard Co., Palo Alto, Calif. 94304) operating in a remote programming constant voltage mode. The source output is focused on the entrance slit of an f/3.0 grating monochromator (Model 7240, Oriel Corp.). ‘The beam emerging from the monochromator is split by a quartz microscope slide causing a portion of the light intensity to fall on the reference photodiode (Model 935, Hamamatsu Corp., Middlesex, N.J. 08846). The optical feedback control circuit which links the reference photodiode to the programmable power supply consists of a FET operational amplifier (Model CA 3140, RCA, Harrison, N.J. 07029) functioning as an integrator. Using optical feedback stabilization, the combined long term drift in the source and detection system is routinely 230 s-l). Presumably an empirical correction could be applied to faster reactions if the mixer geometry and flow velocity are held constant. Maintaining
Table 11. Kinetic Data from a Stopped-Flow Determination of the Reaction Fe(CN),,+ IrCl,*- under Pseudo-First-Order Conditions with Fe( CN)64-in Excess T = 25.0 'C, h
0.125 0.250 0.500 0.750 0.900 1.00
1.15 1.25 1.40 1.50
=
0.062 0.125 0.125 0.125 0.900 0.500 0.900 0.500 0.900 0.500
490 nm, 0.5 M H,SO., or HCIO,
51(i3) 1 0 6 ( i 10) 203(i7) 300( i 20) 346(+9) 3 9 0 ( i 15) 430 ( t 26) 470(i24) 515( 1 30) 540( i 22)
51.3 103 206 308 369 410 41 2 513 574 615
Calculated from ha,, = 4.1 :il o 5 M-' Calculated from % deviation = [ ( h c d c d 100.
b
+3 -1
-3 --7
-5 -9 -9 - 11 - 14
s-' [Fe(CN,+]. hobd)/hobd] x
the latter quantity a t a constant value is not a trivial matter with a conventional stopped-flow apparatus. The flow velocity with a Durrum instrument (18)using a constant gas pressure of 55 psi on the gas piston, was observed to vary considerably as a function of the amount of material in the drive syringes (i.e., the position of the plunger in the syringe). When the drive syringes were fully loaded 12.3 mL), the flow velocity was 2.5 m/s. When only 0.5 mL remained in the drive syringes, the velocity increased to 3.8 m/s. Thus, in order to ensure a flow velocity constant to 5 5 % requires that the syringes be refilled to a set volume before each determination. Maintenance of a constant flow velocity is of greater importance in the determination of very rapid reactions where the half-life of the chemical process approaches the mixing time. Hence, the time span of the reaction is the determining factor when stopped-flow methods are employed. If the reaction is slow enough that a significant portion of the signal change remains after 8-10 ms, then changes in the solution flow velocity can be disregarded. However, for fiist-order reactions faster than -230 s-l, precautions should be taken to maintain a constant flow velocity from one determination to the next. If sufficient precautions are taken, then an empirical calibration of the instrument for larger rate constants is possible. The upper limit of such a calibration is imposed by the signal-to-noise characteristics of the instrument and data acquisition system. Comparison of the results in Table I1 with those obtained using the pulsed-flow instrument, Table I, suggests that the pulsed-flow extends the range of first-order rate constants that can be reliably determined by more than an order of magnitude over the Durrum instrument. Second-Order Reactions. Campion, Purdie, and Sutin (26) have studied the reaction between Ce(1V) and Fe(CN)tusing a stopped-flow apparatus. They obtained a rate constant
136
ANALYTICAL CHEMISTRY, VOL. 52, NO. 1, JANUARY 1980
Table 111. Kinetic Data for the Reaction Fe(CN),+ Ce(1V) under Various Second-Order Conditions h =
+
2'
380 nm, T = 25.0 "C, 0.5 M H,SO,
Second-Order-Equal M, A ,
C, = 6.0 X
=
0.1974, A,
velocity, mls
absorbance"
3.17 4.04 5.79 6.42 7.33 8.03 8.84 9.34
0.1678 0.1737 0.1806 0.1806 0.1820 0.1829 0.1834 0.1840
=
0.0780 k,
av.
=
1.91 1.79 1.66 1.85 1.89 1.92 2.03 2.04 1.85(+0.05)
Second-Order-Unequal CA = 5.0 X lo-' M (CeIV), CB = 2.5 X A A = 0.1605, AB = O.GO05, A p = 0.0246 velocity, mis 3.02 3.84 4.68 5.55 6.34 7.08 7.92 8.59 9.14
absorbance"
//
M-""
5
2.47 2.02 1.95 2.37 2.08 2.03 2.30 2.58 2.1(+0.1)
M (Fe"), CB= 5.0 X 10'' M (CeTV),A A 0.0016, AB = 0.1605, Ap = 0.164
velocity, mis 3.03 3.95 4.74 5.51 6.42 7.19 1.84 8.68 9.01
absorbance"
av. =
' Corrected for medium
=
1 W 6 k , M - ' s-'
0.1222 0.1272 0.1332 0.1367 0.1375 0.1403 0.1417 0.1432 0.1420
1.98 2.09 1.91 1.86 2.08 1.99 2.00 2.03 2.27 1.99(*0.05)
effects (see text).
of 1.9 X lo6 M-ls-' a t 25.0 "C in 0.5 M H2S04. This reaction was studied on the pulsed-flow under a variety of conditions. Reactions were monitored a t wavelengths between 380 and 485 nm depending on the concentration used. The medium was 0.5 M H2S04a t 25.0 "C. Table I11 summarizes the results obtained when the data were treated using Equations 1 and 2 for the second-orderequal case and Equations 11, 12, 13, and 14 for the secondorder unequal cases (8). CB
=
(11)
qcA
A - AA(1 - 4 ) - A ,
M =
A A +- l / q ( A B - A P )
M = (1- q ) l / R In
.
IO-^
'10-2
B
M (Fe"),
CA = 1.0 X
1 6 ~ +1/2 9
1.94
av. =
.
Figure 6. Dependence of the rate constant, determined usin Equations 1 and 2, on the first half-life of the reaction Ce(1V) 4- Fe(CN), . Velocity = 7.2 mfs
k , M - ' s-'
0.1474 0.1473 0.1511 0.1526 0.1522 0.1539 0.1546 0.1544 0.1541
0l . 5
(12)
(1 - q e-R)
In these expressions CAand CB are the initial concentrations of the reactants, AA and AB are the initial absorbances of the
reactants, Ap is the absorbance of the products of the reaction, and the other terms are defined as stated previously. From Table I11 the average of the rate constants obtained on the pulsed-flow is 2.0 x lo6 M-' which is in excellent agreement with the literature value. Figure 6 summarizes the results of an experiment in which the initial concentrations of the reactants in the Ce(1V) + Fe(CN)64-reaction were increased. The first half-life values, t1,2,were calculated using the rate constant of 2.0 X lo6 M-' s-' determined previously. The initial concentration was increased up to the point that a half-life of 5 X s was expected. The absorbance values at a flow velocity of 7.2 m/s were employed along with Equations 1 and 2 to calculate the rate constant values plotted as k,bsd. As Figure 6 indicates, large deviations from the expected rate constant of 2.0 x lo6 M-' s-l were encountered a t half-lives less than 1 ms. Similar behavior has been noted by Gerischer, Holzwarth, Seifert, and Strohmaier (13) in their detailed study of the influence of the mixing process on the integrating observation flow method. In this investigation, the mixing process also was observed to play an important role in second-order reactions where the first half-life was less than 1 ms. The authors were unable to derive an expression which satisfactorily accounted for the influence of mixing in these cases. However, an empirical correction for mixing based on a linear dependence of (A - A,)/(AO - A , ) (see Equation 1) on the half-life of the reaction was discovered. The same correction was found for three reactions with rate constants differing over three orders of magnitude allowing half-lives down to 0.02 ms to be determined. I t was concluded that for a given flow velocity and mixer construction, the mixing kinetics are always the same. Their influence on a given reaction, however, depends on its rate. T o determine whether or not this empirical correction is applicable to the pulsed-flow instrument, the Ce(1V) Fe(CN),4- reaction was studied a t several velocities under second-order-equal conditions such that the first half-life was in the range from 0.05 to 0.2 ms. Some of the results of these determinations are summarized in Figure 7 where (A A,)/(AO - A,) is plotted vs. the first half-life, calculated from the initial concentration of the reactants and the rate constant of 2.0 X lo6 M-' s-l. This figure is in good agreement with the observations of Gerischer (13)suggesting that a plot similar to Figure I should be used, rather than Equations 1 and 2, to determine the rate constants of second-order reactions where mixing is an important factor. Hence, the calibration plot should be employed with t l l P< 1ms or when the quantity (A - A,)/(AO - A,) is observed to be
