IN8TRUMENTATION
Advisory Panel Jonathah W. Amy Jack W . Frazer G. Phillip Hicks
Donald A. Johnson Charles E. Klopfenstein Marvin Margoshes
Harry L. Pardue Ralph E. Thiers William F. Ulrich
Instrumentation for the Study of Rapid Reactions in Solution RICHARD M. REICH American Instrument Co., Division of Travenol Laboratories, Inc. 8030 Georgia Ave., Silver Spring, Md. 20910
Continuous-flow,accelerated-flow, or stopped-flow apparatus, coupled with equipment for relaxation methods such as temperature jump or pressure jump, comprise much of the instrumentation available today for the study of rapid reactions in solution. With continued development of systems having automatic data reduction, such instrumentation is likely to become a standard tool found in most laboratories B e f o r e the early 1920’s, the term instantaneous was often applied to reacting systems with half-lives of less than a few seconds. Methods for disturbing a chemical system from equilibrium in a time period which was short with respect to its rate of reaction and methods to monitor and record the properties of a rapidly changing system were not yet developed. Visual, comparative determinations of opacity and color, successive titrations, and measurement of temperature were among the methods used to determine a system’s properties, These methods were slow and limited the possible time resolution in the detection of the progress of a reaction. Rapid-mixing techniques were first introduced in 1923 by Hartridge and Roughton ( I ) with the development of the continuous-flow apparatus. This system allowed studies of the kinetics of reactions with half-lives as short as a few milliseconds and bypassed the need for a rapid detection system. The reversion spectroscope, developed by Hartridge ( 2 ) , was used as a visual means of detecting changes in absorbance of the reacting species. As improvements were made in the response time of detection and display devices, new configurations of rapidmixing systems were developed which reduced reactant consumption and provided real-time data presentation. But until the introduction of relaxation methods in 1854 by Eigen ( 3 ) , rate studies were restricted by the limita-
tions of mechanical mixing to millisecond kinetics. Relaxation methods have extended the range of kinetic investigation to sub-nanosecond diffusion-limited reactions ( 4 ) . Some of the more widely used instrumentation for flow and single perturbation relaxation methods will be discussed, and no attempt has been made
to present a comprehensive review of all developments. Continuous-Flow System
The principles of the continuous-flow apparatus, as illustrated in Figure 1, are based on the assumptions that the time required for complete mixing of
Solution A
Solution B
Point of Mixing
Variable Point of Observation
Figure 1. For the continuous-flow apparatus, the age of mixture at the point of observation is proportional to the distance between the point of mixing and the point of observation ANALYTICAL CHEMISTRY, VOL. 43, NO. 12, OCTOBER 1971
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Instrumentation
1 I
i
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solution A and solution B is much smaller than the age of the mixture a t the point of observation and that the solutions flow at a constant' volume flow rate, Q, through an observation tube of uniform geometry. The progress of the reacting mixture can then be monitored by measurement of some property of the system at various points along the length of the observation tube. For the above conditions, the age of the mixture a t the point of observation will be directly proportional to the distance bet,ween the point of mixing and the point of observation. Because the extent of progress of the reaction will remain constant a t any fixed distance from the point of mixing, a method of rapid detection is not essential. The minimum time resolution of the complete apparatus is most often labeled dead time and will be dependent on the efficiency of mixing. Mixing efficiency is a mensure of the percentnges of solution A and solution B which are homogrneously mixed in n given time
number is proportionnl to the flow velocit;, is inversely proportional to the dynamic viscosity, and requires increased flow velocities for an increase in solution viscosity. Various configurations of mixers have been constructed which are capable of mixing two solutions to 99% completion in less than 1 msec. Turbulent flow is desired also along the length of the observation tube to complete the mixing of any unmixed reagents after they leave the mixer. Again, tiirbulent flow can be maintained with sufficient flow velocit,y. A major disadvantage of the continuous-flow system is the large amount of reactants consumed while a set of measurements is being performed. The more time required by the detection procedure, the more reactants are used. Accelerated-Flow System
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p
Driving Block
Mechanical Stop Mixed Solutions Flow Down Tube with
Driving Force
I '
Point of Observation
Point of Mixing
Figure 2. Basic components of stopped-flow apparatus
both syringes are rapidly discharged by a. manual push through the mixing chamber and flow into the observation are:i. The solutions are, therefore, accelerated from zero velocity to some maximum velocity before the syringes are exhausted. Since the detector position is fixed with respect to the mixer, the age of the reaction, t, a t the point of observation, is inversely proportional to the flow velocity down the axis of the tube. Chance obtained flow velocities of 10 m/sec in a 1-mm diam circular tube. The detector was positioned 7 m m from the mixer, thereby allowing measurement of times on the order of 1 msec. The electrical output of a potentiometer, mechnnically coupled to the pushing block, was differentiated to produce a flow velocity output. The extent of the reaction was then displayed as a, function of flow velocity (proportional to l / t ) on an oscillographic recorder or oscilloscope The use of a rapid detection system permitted fluid consumption to be as small as 100 pl,
similar to the accelerated-flow apparatus discussed previously, but incorporates a stopping device which is capable of stopping the flow very quickly. A simple and effective method to accomplish this is the addition of a third stopping syringe connected to the effluent part of the observation tube. A driving block, either manually or pneumatically driven, rapidly accelerates the fluids to a steady maximum flow velocity, V,,,; the stopping syringe begins t o fill, and its plunger extends. The flow stops abruptly when the motion of the plunger of the stopping
syringe is arrested by a mechanical stop. The age of the reacting misturc, to, in the observation area at the time of stopping will be 1/V,,,, where 1 is the distance between the point of mixing and the point of observation, and ,,,Ti is the maximum steady-state flow velocity obtained before stopping. The oscilloscope trace, shown in Figure 3, illustrates the different phases of flow. -4 solntion of NaHCOs with bromphenol blue added as an indicator was mixed with HC1. A rapid-response spcctrophotomctric system was used t o monitor the state of the mixed reagents.
I Constant Flow
Flow Accelerating From Zero to Vmal
'
Reaction Proceeds
Stopped-Flow System
The stopped-flow apparatus is the most widely used rapid-mixing technique because of its simplicity and realtime data presentation. Reactants flow through a mixing chamber into an observation area and the flow is then abruptly stopped. At the time of stopping, the mixture is only a few milliseconds old, and the remaining progress of the reaction is monitored with a rapid-response detection system. The stopped-flow apparatus, diagrammatically shown in Figure 2, is
LFIow
Stops
Figure 3. Detection of flow cycle at point of observation Solution A. NaHC03 w i t h indicator bromDhenol blue Solution 6 . HCI
ANALYTICAL CHEMISTRY, VOL. 43, NO. 12, OCTOBER 1971
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t mire syring..
Micm switch
q
I
-
Figure 4. Stopped~flow apparatus
The acceleration phase c l a r l y illustrates the function of the acceleratedflow apparatus discussed previously. After the solutions reach Vmax, they flow a t constant velocity until stopping occurs. The progress of the resulting reaction (the information of interest) is then monitored. The dead time of the stopped-flow apparatus is affected by three major components: efficiency of mixing, transport item, and stopping time. Mixing efficiency, as explained previously, is dependent on mixer configuration and flow velocity. The transport t,ime is the time required for the mixed solutions to travel from the point of mixing to the observation area and is dependent on flow velocity and the distance between the observation point and the mixer. The stopping time is the t,ime required for the complete closed-fluid system to come to a halt after the stopping syringe makes contact with its mechanical stop. The dead time of the system will be degraded if the fluids do not come to a stop in a time period which is small in comparison to the mixing and transport times. It is desirable for mixing to reach 9S% of completion within the transport time interval. If the minimum time resolution is limited by the 88A
ANALYTICAL CHEMISTRY, VOL. 43. NO. 12. OCTOBER 1971
transport time, the first observation after the flow stops will be free from artifacts due to incomplete mixing. Mixing artifacts will appear if the solution ia transported to the observation area in a time much shorter than that required for complete mixing. The physical arrangement of one of the many instrumental configurations ( 6 ) is shown in Figure 4. To simplify loading of the driving syringes, a valving arrangement is incorporated which seats the tips of a set of loading syringes. The pneumatically actuated driving block is retracted by pressing the reset button, and the reagents contained in the loading syringes are transferred into the drive syringes. To set the apparat,us for an experiment, the remains of spent reactant,s from previous experiments are exhausted from the stopping syringe through a waste valve. A microswitch is mounted on the face of the mechanical stop to signal the detection device when the flow stops. Flow is initiated when the drive button is depressed. The micrometer connected to t,he mechanical stop will set t,he amount of distance the stopping plunger must travel before it makes cont,act. The micrometer will, therefore, allow control of the flow interval. An extended flow interval will increase
Instrumentation
Exhaust
I 4
1 0-mm Light Path
Input
-
I >Length
_I
Inout
Point Where Observation Begins-
\ 2-mm
Point Where Observation Ends
Light Path
Chamber Point Where Mixing Begins
Figure 5. Mixer and observation cell
the consumption of reactants but allows a thorougli flushing of the observation cell before flow stops. For minimum consumption of reactants, the flow interval must be only of sufficient duration for the solutions to travel from the mixer to the observation cell and fill the volume of the cell. Satisfactory results can be obtained with reactant volumes as small as 100 pl. Extendedflow intervals (of any length) will not affect the dead time of the appnratus; the age of the mixture in the observation area will depend on V,,,, and not how long Vmas is maintained. An expanded diagram of the mixer and observation cell is shown in Figure 5 . The efficiency of mixing is greater tliaii 98% in less than 1.5 msec, and the dead time is about 2.5 msec. Figure 6 i.hows the results of a typical stoppedflow experiment.
a function of time If an instantaneous cliange of an external parameter could be nccomplished, the resulting shift to n. new equilibrium state would not be instantaneous, but its rate would be governed by the reaction mechan~smof the chemical sjstem in solution The time course of the concentration changes of the reactants and products can be characterized b l a summation of exponential relaxation terms, each
with a characteristic relaxation time constant The extent of change in concentrations of the reactants and products obeys the thermodynamic la^ d In K p / d T = h H / R T z for a temperature perturbation. and d In K t / d P = - A v o / RT for a pressure perturbation K , and K t are the equilibrium constants at constant iiressure and constant temgerature, respectively
-12
L 0.02 volts 3-
-,1
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Relaxation Methods
,4 different approach to rate studies, which eliminated the necessity for mixing and extended time resolution into the microsecond range, was taken by Eigen. il solution containing components which are already in an equilibrium state is perturbed by a rapid change of an external parameter such as temperature or pressure. The shift to a new equilibrium state at the new temperature or pressure is observed as 90A
Percent Transmittance
4 ~~
0.02 Seconds
~
Figure 6. Reaction between aged Ce(lV) and HI02; X = 420 nm Equal amounts of reagents A and B were mixed Ce(NO:,)c; in 0.03M " 0 3 Reagent A: 0.01M ceric a m m o n i u m nitrate: ("1)s Reagent 6 : 4 x 10-'M H,O, in 0.03M HNO, , Solution A is aged to promote the formatlon of a polynuclear Ce(lV) species X = 420 n m Path Length = 10 m m
ANALYTICAL CHEMISTRY, VOL. 43, NO. 12, OCTOBER 1971
Instrumentation
Instrumentation
T o determine the rate-law parameters, a mechanism first must be assumed, the rate-law parameters must be derived in terms of relaxation times, and the proposed mechanism must be verified by experimentation. This may seem like a formidable task, but for small perturbations, where the changes in reactant and product concentrations are less than IO%, second-order concentration effects in the differential rate equations can usually be neglected. Relaxation methods can be applied to all systems which are reversible and have a nonzero enthalpy change of reaction ( A H # 0 ) . Mathemnticnl derivations for many one-step, two-step: and multi-step mechanisms can be found in various references (7-9). Temperature-Jump Apparatus
The function of the temperaturejump apparatus is to produce a small perturbation in a solution which contains a reversible chemical system in equilibrium, by elevating the temperature 5-10OC within a few microseconds. The most common method for producing rapid heating is the Joule heating resulting from the discharge of a capacitor through a resistive solution
(Figure 7 ) . The magnitude of the temperature rise, A T , will be given by
AT = W k J Q k ,
(1)
where W = energy transferred from the capacitor, J ; Q = cell volume, cm3; k t = 0.239 cal/J; and k , = specific heat' of the solution, cal deg-1 cm". The energy, W , stored on the capacitor of capacitance, C (farads), is
w = cv2/2
(2)
where V is the voltage across the capacitor. The simplest way to control AT, therefore, will be to adjust V to the required value. For example, a 10,000-V charge on a 0.25-pF capacitor is equivalent to 12.5 J of energy. This would produce approximately a 6°C rise in temperature in a 500-pl cell. An inert electrolyte is added to the solution to control the resistivity. The resistance between the electrodes is then dictated by the ionic strength of the solution and the geometry of the cell. If stray inductance in the discharge circuit, is negligible, the discharge voltage across the electrodes will decrease exponentially with the time constant,, RC, where R is the solution resistance in ohms. This results in a n exponential
L
temperature rise with a heating-time constant of RC/2. Shock waves of considerable intensity are propagated through the solution when the heating-time constant is reduced below a few microseconds. Behind the high-pressure wavefront exists a low-pressure region which will cause cavitation in the solution. Shock waves of excessive amplitude will cause optical aberrations, if not damage to the cell. The formation of cavitation will cause random artifacts which can degrade the quality of the signal to the point where no useful information can be obtained. To minimize these effects, a number of conditions must be maintained. The maximum ionic strength of the solution must be limited to prevent heating-time constants of much less than 1 p e c . The cell must be ruggedly constructed to withstand the intense shocks produced when the high-voltage capacitor is discharged through a solution containing an air bubble. The shock waves and resulting cavitation will be minimized if an aqueous sample solution is thermostated to 4°C. This is the point of maximum density of water. The electrodes are usually plated with a thin layer of platinum to prevent attack by acidic or oxidizing solutions. They must be arranged in the sample cell so that thermal gradients, due to nonuniformities in heating, will be minimized in the optical path. Since the refractive index of a solution will be temperature dependent, thermal gradients in the optical path will cause optical distortions. As mentioned before, the heating-time constant of a temperature-jump apparatus generally will be limited to values greater than 1 psec. The fastest relaxation process that can be studied, then, will be reactions with relaxationtime constants a t least a few times the heating-time constant of the apparatus. The slowest processes that can be observed will depend on the heat-transfer properties of the cell. All measurements should be taken in a time period in which the solution temperature remains relatively constant a t the new elevated temperature. The majority of temperature-jump cells will reequilibrate at a rate slow enough to allow measurements to be extended to hundreds of milliseconds. Combination of Stopped-Flow and Temperature-Jump Methods
Figure 7. Schematic representation of temperature-jump apparatus W K Temperature rise AT = - - A Q K,
Energy stored
cv 2
= -= 2
W
RC
H e a t i n g t i m e constant T~ = 2 R = solution resistance, ohms; W = energy, J; Q = volume of cell, cms: K , = 0.239 cal/J: K , = specific heat, cal deg-1 ~ m - ~
Stopped-flow methods are limited to the study of reactions with half-lives greater than a few milliseconds by the time required to mix two solutions completely. The temperature-jump method can be used for reactions as short as a few microseconds but is limited to re-
w
P.tm
I
I Figure 8. Pressure-jump apparatus
versible systems in equilibrium. It is possible to combine these two methods ( I O ) to study reactions in which a short-lived steady state appears. The reaction is initiated by rapid mixing and then perturbed during the appearance of this pseudosteady state. The time range of the stopped-flow apparatus is then effectively expanded to microsecond kinetics. I n some enzymatic systems, a steady state may be maintained for a few tens of milliseconds. These systems can be quite complex, however, making data reduction very difficult. Pressure-Jump Apparatus
The pressure-jump apparatus applies a rapid increase or decrease in pressure to a chemical system in equilibrium. The pressure perturbation causes a shift t o a new equilibrium state a t the new pressure. The relaxation to the new equilibrium is monitored by conductometric or spectrophotometric methods.
The extent of change in equilibrium consdant for a change in pressure will be proportional to AVO, the standard volume change for the reaction. The pressure-jump technique, therefore, will be applicable to chemical systems in solution which exhibit reasonable volume changes and are not suitable for temperature-jump studies because of the small enthalpy changes. Although the equilibrium constant is usually more sensitive to a change in temperature rather than pressure, pressure-jump studies can be used for systems which are susceptible to thermal decomposition from a temperature perturbation. The first pressure-jump apparatus was constructed in 1958 by Ljunggren and Lann ( 1 1 ) . The pressure in a sealed vessel was raised from 1 atm to 150 atm in 50 msec by opening the valve on a nitrogen tank. Because they were working with ionic species, the relaxation process was monitored by measuring conductance changes. The sample mas contained in a conductance cell which formed one arm of an alternating-current Wheatstone bridge. .An improved system \vas introduced by Strehlow and Becker ( 1 2 ) which caused a pressure drop in a dual conductivity cell, from about 60 atm to 1 atm in 60 psec. The addition of the reference cell allowed compensation for errors due to temperature and viscosity changes resulting from the pressure drop. The cell compartment, sealed by a metallic disk, was pressurized to 60 atm. -4solenoid-controlled steel needle rnptured the disk, causing a rapid drop to atmospheric pressure. A pressure transducer contained wit,hin the cell signaled the initiation of the pressure transition. rl similar apparatus is illustrated in Figure 8.
Characteristics of a Rapid Photodetection System
The components of a rapid photodetection system, shown in Figure 9, are similar to those found in a standard spectrophotometer but differ greatly in their response characteristics. Noise which is normally filtered out by a slowresponse amplifier and recording device can now cause significant degradation in the signal-to-noise rat,io of the system. The signal-to-noise ratio, or limit of detection, will improve in direct proportion to the square root of the luminous flux impinging on the photocathode of the photomultiplier tube, and in inverse proportion t o the square root of the bandwidth of the detection system. Because there are no universal sources of radiant energy presently available which will provide both sufficient energy and acceptable stability over the complete ultraviolet, visible, and infrared spectrum, it is necessary to examine the most commonly used sources and evaluate their merits and limitations. For work in the visible and infrared region, n tungsten lamp powered by a low-ripple, highly regulated dc power supply forms a very stable. lorn-noise source : however, below approximately 300 nm, the energy output is significantly reduced, lowering the signal-tonoise ratio of the system to an unacceptable level. LTltraviolet energy sources include the mercury and xenon high-pressure arc lamps and the hydrogen and deuterium low-pressure lamps. The intensity of the high-pressure arc lamps is considerably greater than that of the lowpressure lamps. The xenon and mercury lamps, hoivever, suffer from instabilities due to arc wander and fluctuations. In R single-beam spectrophoto-
Figure 9. Basic components of rapid photodetection system
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ANALYTICAL CHEMISTRY, VOL. 43, NO. 12, OCTOBER 1971
Instrumentation
Figure 10. Current to voltage converter Eoat = I,R, 0.16 r = R,C, = 7
Curnnt Input- I,
>
___T
A
Eout
R,, ohms; C,, F; I , , A; E,,, V;
HZ
T.
sac,
metric system, the deuterium or hydrogen lamp is, therefore, the best source of ultraviolet energy. The monochromator must have the largest possible aperture to avoid unnecessary reduction of the luminous flux entering into the observation cell. The slits should be opened as wide as permitted by the specific requirements for spectral bandwidth for the species under study. I n an optimized detection system, the signal-to-noise ratio should be limited by the statistical shot noise inherently produced in the photocathode of a photomultiplier tube and not by the effects of lamp instabilities, power supply ripple, and amplifier noise. The rms noise current produced in the photocathode, I,, is described by the relationship Tn = ( 2 eZ,B)s, where e is the charge on an electron, C ; Z, is the photocathode current, A ; and B is the bandwidth of the detection system, Hz. The signal-tonoise ratio, Zp/Zn, is, therefore, ( Z p / 2 e B ) % . Both I , and 7, are now equally amplified by the n dynodes, producing an anode signal current of magnitude 1, = (Tn Z,)An, where A is the average amplification per dynode stage. The amplification provided by the dynodes is almost ideal because their noise contribution is considerably less than the shot noise produced by the photocathode. There is a limitation to the amount of radiant energy that may be imposed on the photocathode because of the heat produced by the resulting photocurrent. The maximum amplification of I , by the dynodes is limited by the maximum anode current rating of the tube. T o ensure stable operation of the photomultiplier tube, the power supply, which supplies the high voltage bias to the dynodes, should be about 10 times more stable than the desired stability of the signal current. The amplifier serves the function of transducing the signal current into a proportional voltage and tailoring the system response characteristics to pro-
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ANALYTICAL CHEMISTRY, VOL. 43, NO. 12, OCTOBER 1971
duce a suitable signal level and the best possible signal-to-noise ratio. The expression for shot noise indicates that a decrease in system bandwidth will decrease the proportion of noise in the signal. But an excessive decrease in the bandwidth will affect the response to an event of typically exponential nature containing the information of interest. The current-to-voltage converter, shown in Figure 10, is a simple and effective circuit which is commonly used, as its name implies, to convert a current to a proportional voltage and to limit the response of the detection system. The anode of the photomultiplier tube is connected directly into the inverting input of the operational amplifier, thereby eliminating a load resistor. This circuit presents a low impedance to the source (the photomultiplier) and, therefore, is much less susceptible to the response-limiting effects of the capacitance of the interconnecting cable. The low frequency gain of the circuit, expressed in V/pA, A,, is equal to the resistance of the feedback resistor in megohms. A 1-pA input will produce a 1-V output for a 1-Ma feedback resistor. The response to a step input is exponential, with a time constant, T , of RC seconds, where R is in ohms and C is in farads, and is related to the bandwidth B by B = 0.16/~. To pass the signal of interest with minimum error, the time constant of the circuit should be at least five times greater than the time constant of the signal. A storage oscilloscope, used as a display device, will display for periods in exces of 1 hr, an image of a rapid transient event, occurring in microseconds. The time base of the horizontal axis is triggered from an external source, such as a microswitch on a stopped-flow apparatus, signaling the stopping of flow, or a pulse transformer on a temperature-jump apparatus which is initiating the breakdown of a triggered spark gap that causes the en-
Instrumentation
ergy of the storage capacitor to be transferred to the cell. When the kinetic experiment is complete, the signal trace is stored. The trace may then be examined before making a permanent photographic record for subsequent evaluation and can afford a considerable savings in film usage. Future Developments
Stopped-flow and temperature-jump instrumentation are the most widely wed methods of those discussed. Their level of tlevelopment is sufficiently mature to produce reliable and repeatable information. The data generated by these techniques can contain a great amount of information of considerable complexity. The optical detection system discussed in the previous section reqiiirev manual data reduction from the information presented in a photograph. Enough information can be obt:iined in a day t o require a week of analysis, Analog manipulation, such as logarithmic conversion, will eliminate home of the Pteps required in analysis but will not improve the limited resolution of a photograph. Digital data acquisition systems can
considerably improve resolution and reduce the time and effort required to perform analysis of rate data. I n the past two years, dedicated computer systems have been introduced which digitize the analog rate data, smooth the data by a least squares procedure, and compute various kinetic parameters ( I S , 1 4 ) . Future developments in the software for data reduction will significantly increase the efficiency and versatility of these techniques. Indications are t,hat with the continlied development of systems with automatic data reduction, instrumentation for the study of rapid reactions in solutions will become n standard tool found in most laboratories.
(7) G. W. Castellan, Ber. Bunsenges. Phys. Chem., 67,898 (1963). (8) G. Schwarz, R e v . Mod. Phys., 40 ( I ) , 206 (1968). (9) A. F. Yapel, Jr. and R. Lumry, “Methods of Biochemical Analysis,” Vol 19, Interscience, New York, N.Y. 1970. (10) J. E: Erman and G. G. Hammes, R e v . Sct. Instrum., 37 (6), 746 (1966). (11) S. Ljuggren and 0. Lamn, Acta C h e m . Scand., 12, 1834 (1958). (12) H. Strehlow and M . Becker, 2. Electrochem , 63,457 (1959). (13) P. J. De Sa and Q. H. Gibson, C o m p u t . Bzomed. Res., 2,494 (1969). (14) B. G. Willis, J. A . Bittikofer, H. L. Pardue, and D. W. Margerum, ANAL. CHEM.,42, 12 (1970). Bibliography
Literature Cited ( 1 ) H . Hartridge and F. J. W. Roughton, Proc. l i o y . SOC. (London), A104, 376 (1923). ( 2 ) H. Hartridge, ibid., A102,575 (1923). (3) M. Eigen, Discuss. Faraday SOC.,17, 194 (1954). ( 4 ) R . G. Penrson, ibid., p 187. (5) B. Chance, J . Fmnklin Inst., 229, 455 (1940). ( 6 ) J. I. Morrow, Chem. Instrum., 2 (4), 375 (1970).
( 1 ) E . F. Caldin, “Fast Reactions in So-
lution,” Blackwell Scientific, Oxford, England, 1964. (2) G . H. Czerlinski, “Clinical Relaxation,” Marcel Dekker, New York, N.Y., 1966. (3) K. Kytin, Ed., “Methods in Enzy-
mology, Vol XVI, Academic Press, New York, N.Y., 1969. (4) A . Schechter, Science, 1970, 273 (1970). ( 5 ) J. E. Finholt, J . Chem. Educ., 45, 394 (1968). (6) L. Faller, Sci. Amer., p 30, May 1969.
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