Topics in.. . Chemical Instrumentation I

Edited by GALEN W. EWING, Seton Hall University, So. Orange, N. J. 07079

These ariicles are intended to serve the readers O ~ T K I S JOURNAL by calling aUention to new deuelopments in the theory, design, or availability of chemical laboralorg instrumentation, or by presenting useful insights and ez- plana/ions o j topics that are o j practical importance to those who use, or leach /he use oj, modern inslrumentation and instrumental techniques. The editor invites correspondence from prospective conlributors.

LX. Step Perturbation Relaxation Techniques Z. A. Schelly, Deporfmenf of Chemisfry, The Universify of Georgia, Athens. Georaia 30607. nnd " -. , - - E. M. Eyring, Department of Chemistry, University of Utah, Salt Loke City, Ufoh 84 1 12

Introduction

Chemicd relaxat.ion spectroscopy was introduced b y h1. Eigen and cowo~.kers in the 1950's for studying the rates and mechnnisms of fast, reactions in soh- tions (1, 3). The term "isst reaction" is of course relative, hu t in general usage i t means a reaction that is fast compared to the Qrne required for mixing and observabion by conventional methods. Thus, a reaction with a. half-time of a second or less wo~tld he fast according to our criterion, if t,he reaction is con- ducted a t ordinarv temoeratures and eon- centrations. he" restriction "ordinary" is necesswy since reactions that are fast a t room t,emperat,nre may become accos- sible to conventional techniques if the temperature is lowered, or a fast, second- order reaction may take place slowly if the concentrations are small enough. With increasing rates of reactions, effec- tive, rapid mixing becomes impracti- cable even if carefully designed high flow velociby jet,s are used. The basic idea of relaxation speot,roscopy is t o circum- vent mixing b y starting with a. pre- mixed equilihriom system. Perturba- tion of the eqoilibrium b y varying a parameter (such as temperature, pres- sure, or electric field intensity) causes n. shift to new eqrdibrium concentrstions. Measurement of t,he rate of this shift per- mits the kinetics and eventually the mechanism of t,he reaction to be deter- mined. Aside from therelavation methods many other techniques have been de- veloped for measuring rapid reaction rates. On this general subject. the reader may refer to some excellent treatises (.9-6).

Principles of Chemical Relaxation

To begin with, let us consider the single

step reaction

with t,he forward and reverse rate con- stants kt and k,, respectively. The activities of the species xt equilibrium are fixed, and their relation is expressed b y the thermodynamic eqrdlibrim~ constant K. The equilibrium ronsbant is a fone- tion of external as well as internal param- eters such as temper~t.ure T, pressure P, elect.rio field intensity E, total concent,rsi tion CT, ionic strength p, et,c. Suppose t,hst. one or more of these parameters is suddenly changed. The pert,orhation mo- mentarily will result in a deviation of the activities from those required by the new conditions. The deviation, however, will tend to vanish. The ~yst ,em will ndjrmt it- self and will approach its stable eq~dihr inm in a mannor described b y the rstc equn- tions. As long as t,hese deviat,ions from the new eqttilihriom are small, a linear- ioation of the rnle equations with respect, tn the t,ime dependent concentration variable is possihle. This moms, that. tho rate of disrrppearanoe of thc difference between the actual and equilibriwn eon- cerrtrntions is proportionnl to i.his dif- ference itself. The reciprocal of the proportionslit,y fact,or k has the dimen- sion of bime and is cdled the relaxation time 7.

At the inst,ant of a perturbation the concent,ration Ci of any of the reacting species i will-differ from the find equilib- rium value Ci b y Xi, i.e., Ci = Ci + Xi. If Xi << Ci t,he rnleof disappearance of Xi can be written as

Dr. Zoltan A. Schelly rereived his n.Sc. n pliysic:il r11emist1.s- in Viennn Technical Unirorsity. Austria in 1967. Ire spent a ienr ns n postdortorll fellow a t the Cni- iersity of \Iriseonsin (Nilmnukee) work- ng on mass spectrometric measurements ,f diffusion and isotope errhnnge reaction 'ntes in solids. Subsequently, he spent w~ years with Dr. E. 11. &ring at the hiversity of Utnb working on chemical .elnxntion problems, and on the applicn- ion of giant laser pulses in studying fast 'enctions. He is presently nn Assistant ?rofessor of Chemistry a t the University ,f Georgia. His mnin research interest s the dynamics of fast rhemienl-physical .ate ~ " O C ~ S S ~ S .

ipectrom&ir kinetic 8tudies of the de- :omposition of gaseous prop;tne ions. He was a Nnt,ionnl Science Foundation rostdootoral fellow in the Goettingen, >ennnny lahor;~tory of Professor Man- 'red Kipen in 1960-61. Re hnr since been m the chemistry fnoulty a t Utah koom- np a full professor in 1968. His present .erearch involves kinetic st~fdies of ionio liffusion controlled renotions as well as rinetie studies of aqueous suspensions of mlloidnl ~nrtieles (detergent, micelles. rythrocytes, lipid vesirles, vimaes, ete.) w relaxation techniques.

(Continued on pa(p A840)

Volume 48, Number 7 0, Ocfober 1971 / A 6 3 9

Chemical Instrumentation

Applying this resolt to eq. (1) and ns- suming that the equilibrium will he dis- placed in favor of C , we obtain

krC*Ce - k,Cc ( 3 )

By substituting Ci = ci + Xi into eq. ( 3 ) we obtain

dXo/d t = kt ( Z A + X A ) ( C B + X B ) -

k. (?c + X C ) (4)

= kr (cA h + X A ~ B + X B ~ A + X A X S ) - kr co - krXo ( 5 )

This differential equation can be lin- earized since X A = XB = - X O , nnd Xi1 is negligible second-order-small term. S_ub_stituting the equilibrium condi- tion ~ ~ C A C B = k,& into eq. ( 5 ) we obtain

-dXo/d t = [kf (?B + ?A) + k, lXc

Obviously, r-I = kr (CB + CA) + k. (6) follows from eq. ( 2 ) . The solution of the homogeneous relaxation equation ( 2 ) is

X = X O exp(-11.) (7)

Thos, the relaxation time is the time interval during which t,he initial "dis- tance" from the final eqnilihriam concen- t.vation decreases t,o i/e of its init,ial value. As can be seen from the analytical ex- pression for r-', the relaxation time r is s. frmction of the forward as well as the reverse rate constant,^. Close to equilibrium both processes compete in the equilibration.

Ileaetionn involving more than one step osunlly cannot be represented by a single relaxation time (2, 4, 7). I n the general case the t,rentment of R. system of rate equations is required resulting in a spect,rnm of relaxation times. Since the individt~al equilibria are coupled, similar to vibrations in a multiple oscillator system, each r is in general a function of all the equilibrium eoneentr&ms and rate con- stant,.;, and cmnot be idenMed with any single step. Thos in a mnlt,iple step sequence c,f reactions the change in con- centrabion of component. i is given by the general eqrmtion

wheve the aij me fwletions of the rate constants and the equilibrium concen- trations. This follows directly from the convent,ianal rate equations in the neigh- borhood of equilibrium. In order to obtain the conenponding relaxation times, the Xi has to he transformed into a new system of concentration coordinates Yi far which

Here Yi = ZbiiXi (i.e., linear cambina- tions of the true coneentrrttian variables

(Calimced a page A846)

A640 / Journal of Chemical Education

Chemical Instrumentation

Figure 1 Photograph of a typical orcilla- graphic single-re!axotian troce. Verticol oxir I20 mv/divl i s lineorly proportion01 to the con- centration of the chemical species abrerved. Horizontal axis is the time (20 mrec/divl lcourtery Amincol.

Xi), w d the recipwr.nl re lnsnt im l inics ri-I are eigenvnlnes of the rh;rlsrterisl ic eqnatinn. In ionic i i l i a ~ ~ n l e s s the ionic

strong111 is kep l constarl! d w i n g tho re- sotion, the t ime dependence of the nc- t i v i t y coellicients m ~ r l lheir ell'eef r m tho ~&xat iou l imes also m l s l h e rotmidered (2, 8).

Experimental Approach

The expc~.irnental nsprcis of wlnml ion c t ~ t ~ l i r s i l ivnlve ( i ) I he pertnrhal ion of the e t g d i h ~ . i t ~ m swlern in a known m:inner, ; t n r l ( i i ) 1he rhswv :~ t i on mil r o r d i u g r,f n rmrcnll.;ilinn vnl.i:hlc 0 1 . ~.elnled pl.c,p- c1.1.v n; n i \ l n r l i on of l ime. The ~ l l l l w l t of :,I> ozpe~.imenl i s the irl;/unlii,n i.tll.vr (I<'ig, I ) cjr wlam! i<m s ~ w d m n of lhc fwrn ( ! I )

will, however, reslr i r t our diw,w&ln 11, lhosr l lansienl mr lhods where the c r j ~ i l i h -

A642 / Journal o f Chemical Education

The Concentration-Jump Technique

A perlmhntion of the tot,al cmicetl- t,ration of n sohttr can he achieved hy sudden dilniion. Similnrly, the pl l , the ionic slrength r r , or the cumpoiition of n solvent mixture cnn he nbixpt,ly chnnged by rapid miring of two sohllions. If the oqnilihl.iiun is sensitive t,o theso changes, i t will relax lo i:oncentl~ntiow consislent, with the new condit.ions. This tvpe of . . experiment was fit.st snggest,ed by Ljung- gren nnd J,:trnm (11) and has been soc- cessfully nppliod to slow (12) as well ns to fast renet,ions ( 1 1 ) . Ilowever, t,he experiment is feasible only if the relnm- tion time is, say, 8 1 , lens1 iwiee or ihree limes longel. 1h:ut (Ire lime of mixing. In the followiup we will deswihe thc stopped-flow nppn~hlos with w h i d ~ one e m mix two scnlnticm* within 2 lo (1.2 rnsee, depending on design, :u~d viseosily of the solulions. This, of cowre, sets n limitntiun :IS lo wh:~t, reactions can he rtndied by this terhuique.

There is ;I verv exteltsive li1ernt.ul.e

enlly used in most st,opped flow machinos. We may refer to Pig. 2 for nn explnnntion uf how n. stopped-fhw nppnrnl,os operates. The solutions 1.1, he mixed are hken from the reservoirs and filled inlo the driving syringes. When the expcrimont st,mts, n flow net.iv:~tor, naually operated prren- mst,ienlly, pushes !.he pistons of the driv- ing syringes nnd ihe 1.wo liquids are iorccd into the mixing jet. The design

cnnsl~~i~ctions we show the details of one in Fig. 8. The mixed solution then enters the photome1,ric nhservnt,ion cuvet, nnd from there the stopping syringe. The stopping syringe piston is pushed along by the renctiorr mixtwe, and is aud- denly haltcd by corning np ngninst an ex- t,erna.l slop. Sim~~ltsneously, x trigger switch is closed .and a signnl triggers the osd~ ,seope that displays the output, of

LIGHT OUTPUT TO PHOTOMULTIPLIER TUBE

applicaliot~s. Thc cc~ncenlmtiol l - j~l~~l~ re- ~i~~~~ 2 schematic diagram of ~ t o ~ ~ e d - f l o x .,pporat~~ ( c o Y ~ ~ ~ s ~ DYTTYRI). Inxnt,iou technique is jnrt n snblaading in lhis very b~x,nd field. (Catinwd on page A646)

A644 / Journol of Chemical Education

Chemical Instrumentation photomultiplier deterliug thc ~.e:tr:tion iu Ihe euvel. Monacht~ornntic lighl for t l ~ c photometric detection is provided by the light somee that consists of a DC power supply, lamp, and monochromator. I t is very convenient to use a ~ t o m g e oscil- loscope, possibly in combination with x logarithmic converter thnt increases ae- curacy and enables one to photograph tho output of only the best nus. Iliroct interfacing with a computer through analog to digital converters has also been used (#I), eliminating (,he necessity of taking photographs of the oscilloscope traces, and permitting direct computer analysis of the da1.a.

Depending on the system under in- vestigation, emf-glass electrode (SZ), fluo- rescence (85), or conductanre (24) de-

tection can he used in place of sped,rill photometry.

In desiming nrd using n stopped flow appnratns far t.daxntiou oxperinm~t,s the fallowing aspects iihould bo kept. in mind: 1) mixing nrd slopping of t,he flow should be inst and dfoient (say !XI$<. mixing and stopping in 2 msec); 2) t,he method of detection s h o ~ ~ l d he fast and quantitative; 3) (,he rhange of tho eon- eent,ration vnrinble shrndd he kept in n range where tho rate eqttaliorts cart he linearized; 4) in the case of photometvic dotcction tho ehmge in liahl intensity during rearlion sllrnlld bc small enough in order to ohlain n linew relationship between light intensity and aoncent,r:~- tion; 5 ) all pmls of the flow system should be t,hermostaled m d the so l~ l l , io~~s de- gassed in ol.der 10 avoid lens eflect, and eavit,at,ion, respectively; 6) all parts of the machinc in cuntnd n i th the solulions

nhould he chemicrtlly inert. Two eom- mo~~eirtlly R V R ~ ~ R I ~ O insttvments that have proved relinhle are shown in Figs. 4, 5, and 6. The 1)urrnrn insO.ument, pat- terned niter Gibson's nppnmt,us, has a minimum mixing dead time of 2 msee. The Amina,-Mr,mlw stopped-flow appa- ra1.11~ has a deatl-t,ime of 1.5 nrsec. The Aminco rompnny has mothel. ~.apid mir- ing system im the market with n dead tirno of 0.2 maw. The prototype of this lst,ter mrnme~~ri:rl iastrwnent wxv de- veloped hy R. Bergel. 12.5). The instrn- ments of Imth companies have provisions for flno~esrence obxervntion, as well as for variable palh lengths of the photnmetric cell. Bath mnchines oat) he operaled r i t h adcqnntc 1nbolxtot.y light sources and fast recolding devices. Tho inrtl.nmont- packages offored hy the conlpa~lies as electronic console and light source include the fallowing units (see hloek diagl.am in Fic. 7): .. .

Aminco light source: tongstm-iodine amp, lamp horuing and reflector as- jemhly, aondcnsing lens nssemhly, Aminco :rating monochtmnafor (wavelength range 200-800 nnr, w;~velength arrwncy 1.5 nm, slits stepwise adjustnhle, aperture 4 encapsulated %stage type 11-136 (Hamamatsu TV) side-an fused-silica wiw dnw photomultiplier.

Durrum light source: tmgsterl-iodine and optiorml dertteriorn lamps, lamp hoos- ing with reflector, l ) ~ l ~ r u m monochromator (wavelength range IN-1000 nm, wave- length accuracy 2 nm, slits corrtinoously adjnstahle, aperture f/10, order-overlap filters), 11-stage type It-375 (Raman~atru TV) end-on fused-dies u k d o a photo- multiplier.

I lu t~n~ra elecbronic co~~sole: Ilewlebt- Pscknrd stumge oseillosmpc 1207-A, kinetic photomete? (djoslnhle time con- stant, I)C zevo offset, and buffw am- plifier), 1 ) w n m 1)-121 deuteri~m-lamp power supply, Power \late PS-100 tung- 'iten lamp power supply, I)un.nm 1I.V. photumultiplie~~ pone^. supply, aud lug converter Rccessory.

Aminao eleetronia conscde: Tektronix Il-.5MII storage mscilloscope, kinetic pho- tometer (adjustable gain and response time, and 1)C zero offset), Kepco ABC 1I.V. power supply, and IIa1.1.isotl-1I.P. 627A I)C power s ~ ~ p p l y . The power supplies listed are all adeqwbely regcllnted, and have low rms and peak-to-peak voltage i . Tho optical components are of high quality and satisfy the requirements of mosl. npplications.

The Temperature-Jump Method

The temperature dependence of the equilihrinm constant, K,, i.e., alnK,/A?' = A H 0 / R T 2 , is utilized in temperature- jmlp relaxst,iou method studies. Clearly, for reaction mechanisms where any one step i r l t,lx rsacliur seqtlertce has AH" # 0, a tempet.nttlre distwhance cause.; a change in the ~:onoentvstions of renetants. The tempernl.oro-jump is generally brought. about hy discharging a previously charged high voltage capacitor through the suitably eondudhig reaction mixture. Jlr,weve~; other m c t h d s of mpid stepwise heating have also been used (26-29).

(Continued on page A648)

A646 / Journal of Chemical Education

breaks down, or is triggered externally.

discharges to ground through the sample The first Jade-heating (or ohmic heating) cell S, containing the conducting reaction T-jump apparatus, perhaps the most mixture. The sample cell (Fig. 9) is versatile of the relaxation techniques, was usually made of Plexiglas or Teflon con- constructed hy Cserlinski and Eigen taining two platinum (alternatively non- ('30). The simplified diagram of this in- magnetic type stainless steel or brass strument is shown in Fig. 8. The typi- plated with platinum or gold) electrodes cally 30-kV voltage generator charges the spaced ca. 1 cm apart and immersed in the 0.1 &F low inductance pulse oondenser C solution. The sudden surge of current to R. voltage a t which the spark gap G raises the temperature of the ca. 1 ml

1

Figure 4 Durrvm Stopped-Flow Spectropho- tometer, Model D-110 lcourfery Durruml.

Section 0-8 1 I

I cm Figure 3 Mixing jet of Gibson and Milnes (201. End view (01, longitudinal section (b), ond crorr Figure 5 Aminco-Morrow Stopped-Flow Ap.

rection (c). The reagents enter the mixing chamber, or in the center drawing (c), from the ,ight- povatu$ (courtesy Amincol.

hand ride and ore then driven into the central tube through 8 jets, which open tongentidly into it. The ietr are ro that the two series attempt to spiral the liquid in opposite directions. (Continued on page A660)

A648 / Journal of Chemical Education

Chemical Instrumentation volume of solution, between the elec- trodes. If we make the assumption that all of the energy is dissipated in the cell, tht: temperature rise AT can be estimated by AT = E/CppV where C,, p, and V are the heat capacity, density, and volume of the solution, respectively. The energy E stored in the condenser is given by E =

CUP, where C is its capacitance, and U is the voltage to which i t is charged. Typical temperature jumps are 3-10°C.

Figwe 7 Block diagram of a ,topped-tlow experimental set-up (courtesy Durrum).

Figure 6 Electronic c o n d e for Aminco Stopped-Flow Spectrophotometric System b u r - tesy Aminco).

The time constant ro of the heating is de- lamp L (Fig. 8) enters amonochromator M fined as ro = RC and can he easily that is set to the wavelength of a major calculated from the resistance R of the absorption band of one of the components sample cell, and the capacitance C of the of the reaction. The monochromatic condenser. Usually, heating time con- light is split into two beams. The stmts are on the order of 0.1-10 rrsec. sample heam SB traverses the sample cell, The course of reaction is followed spec- trophotometrieally. The white light of (Coniimicrl m page A652)

A650 / Journol o f Chemical Educotion

Chemical Instrumentation

Figure 8 Simplifled schematic of 0 temperoture- jump apparatus, from Eyring and Eyring ( 54 ) .

arid its intensily is omqmred with the referenee beam N l 3 by the phr,l,,multiplier bridge P. The diffetwtee signal is applicd tu the vertiral plates {lf osrillwcops, 0, that is triggered by n trigge~irrg circuit T, usually simultnueously with, o r romc micruseewds lalet. thiul thc qmrk gap. In mnny 11~lel. designs (.il) Ihe refwcnae beam has been elia~i~mletl, since most light'sonrees are sufficiently stzhle during the short time required by the reaction, and only tlre c h w ~ e of inleusity of 8 1 3 is registered versus time. While current, i s f lowi~g thwugh the cell, uniform hest,ing occurs only in the hmwgezmms regiw,

.of tho electvir field hetween tlre eler:trades, xrrd eledrrrly6is is localized a t the eIeetl.de surfaces. T h ~ s the path rlf the mmdor- ing light besm shc,uld nut i,e closet. t h m 1 mm t , ~ the e ler l l rde . I~tterdiRwiori and convectim pwcesses ill the sample liquid become impoltsnt <,I> x 0.1 ser bime scale t,hnt sets limitatirms as to haw slow rewtkms car be that are studied by this method.

Besides speetn,photomelril: deteetim, flunrimetrv, pd:wimetry ( and, in ease of heterowneous systems, the mex- surements of scattered light intensity, (33) have also been used.

Though malty iuvestigi~twr build theil. own instl.urnent,s, usually adapting them to specific problems, thew w e several manofaeturet.~ mwket,ing T-jump inst,ru- rnents 01. ~:umponent.s. The unit built, b y Messnnlagen Studiengesellschnft m.b.lT., (:iitli~lge-ell, West-Germany (Fig. 10) was developed by I.. IkMaeyer. The inst,tutnent's high time ~.esolntion ( T , = 0.2.; wscc nt 5011 aamplo resistance) is obtained 1,y tile use of h i ~ h (up to 50 kV) discharge volt,ages. Three different capacitors (0.05, 0.02, and 0.01 pF) can he used for wwk in difi'erent solvents and with different cell sizes. The disch:%w is initiated b y pneom;~tirally driven s111~l.k gaps. High sensitivity is ublnitxd by the use of higlr-aperture r,pticsl design aud in- tense light fluxes f m n the ditkrent light sources (i~talrdiug qnnrto-iodine t,tu~gsl,e~i arid hi$ pressure am: l:mps), driven from a tandem regulated constant current power supply (0-10 A, 0-150 W), that contains au arc I tmp stnl.lel. ns well. The detector sysl,em is based on t,wu two 1P2X RCA photr,mnlt~iplie~~r. The number. of active dynodes can be selected independently fur the reference and the measuring photornnltiplior. The ratio- amplifier compensates for light source f luc tus t io~~s and allows for a calibri~led output, which aat Imlnneed crmditims, corresponds to 10 mV f c r x change of 0.001

A652 / lournol of Chemical Education

Figure 9 T-jump sample cells with conical windows for rpectrophotornetric detection lcourj lesy Messanlogen Studiengerellschoffl.

in optical densit,y. Amplifier rise time is variable between 1 rsec to 3 msec. The ratio-detector may be used in s manual or automatic balanuiug mode. I n the man- ual mode, calihrnled sensit,ivit,y is obtained when the amplifier outpnt is s t zero volts. I n the automatic mode, s. fast feedback loop nmintnins the untput a t zero volts even if the light intensities on the multi- pliers are chalging. The feedback loop may he illterrupted by s. gating signal. If the gating signal is obtained from x delayed sweep oscilloscope, rapid and large initial perturbations or relaxiltion~ call be suppressed and slower changes of smaller amplitude can b e displayed on the oscilloscope without the use of an offset voltage.

Removable sample cells (available in direrent mwterials and provided with solid platinum or gold eleat,rodes) are plugged in s thermostatable sample eell holder. Standard eella with a sample volorne of 5 ml and 10 mm light path, and micro-cells with a vnlomo of 1 ml and 7 mm light path can be provided. Special cells for presswe-jump and stopped- Row experiments, comhined stopped- flow-tompe~.atore-jttrnp experiments, fluo- reseenee ohse~.vxtions, as well as sample cell compnrtments f or wwk under extreme conditions (e.g., high pressure) can he de- signed and may easily be incorporated in the instrument..

Figure 11 shows an Amiucu T-jump apparatus, that has a heatil~g time eon- stant of 6.25 pser a t 50 ohm re.;istsnce nf the snmple eell. It is peculiarly well stlited tu the investigation of enzyme y s - iems because of the small volume (0.5 ml) of the sample eell. I t has n sillgle- beam photometric detection system with an RCA 2020 phutomultiplier (S-11 spec- tral respo~~se). I t uses interference filtors, hn t :L high inteonit,y monochromalor can he added optionally. Suitnhle delay aud grounding circuit,^ are employed for display of the relnx:rtiou curve. The elec- tronic aolmle includes a H.V. power sup- ply (0-10 kV), solid state timing logic and phatometer, a Harrison-T1.P. 6274 A lamp power sopply, a modified Kepeo ABC 1.500 phot,onudtiplier powel. supply, and a Tek- tsonix 1<M ,704 storage oscilloscnpe with Type 3AB vertical and 3U3 (modified) hori;..outsl nrnplifiel. plug-ills. Thenno- stntine of the snmmle is achieved b v direct ~ ~ ., temperature contml of the electrodes from an external thermastst,.

The T-jump instrument of the Durrnm Iustrnment Carp. will he discnssed in the next section.

Figure 10 T-jump Transient Spectrometer with- out orcillorcope lcourfesy Merronlagen Sfudienge- rellrchaftl.

The Combined Stopped-Flow- T-Jump Method

Itelaxation methods are limited b y the fnrt that t,lley are usually applicable only to systems a t equilibrium. However, in principle they can also he applied to any system where the overall net chmge of concentrations is zero. Thnr, systems in a steady st,atc can he perturbed and the relaxation to a new steady state can be ohserved, provided the new steady state persists for a time that is long compnred to t,he relaxation.

Nevertheless, certain theoretical eon- siderations are involved here ($, 34). As a consequence of the principle of micro- scopic reverilihility, the rate equntions cart have only real (i.e. non-periodic) sol~t- tions for systems a t or close to equilibrium. This is not true for the steady state, un- less the reaction system is void of any type

Figure 1 1 T-jump A p p a r a t u s (courlery AmiocoJ.

of (notucntnlytia) feedback, that leads to chemical "resonance" processes.

The possible experimental procedures are the following: (i) one ran use n con- tinuous Row of rapidly mixed reactants and apply n temperature jump to the solution ns i t flows by an ohservntion rell, or (ii) one can suddenly stop the flow and set up a pseudo-steady state, where the concentration of some intermediate is e~sentinlly constant for a few nlilli- seconds, and apply the '/'-jump during this period of time. Thus, the nppli- cabilit,y of the T-jnmp meihod can he extended to essentially irreversible reae- tions, which approach rompletion in times nf millisecotds 01. lonyer, hut w11ir.h have intrrmcdii~tr faster s l q w .

References (1) EIDEN. M . , Disc. Fniadoy Soc.. 17, 194

(1994). (Continued on p a y e ' ~ 6 ~ 5 4 )

- ~ ~

I

! You get better results I when you see things our way I

I I I I 1 The new Luminon spectrophotometer cells I I feature fully fused quartz or glass seams. . . I no low melting intermediate cements

I

to cause problems. This also insures that I the cells are impervious to cleaning I

1 solutions and other deteriorating media. i I - - I

Luminon produces a complete line of cells I I for U.V., far U.V., near U.V., I 1 visible light and near I.R. I 1 And, i f needed, we can produce I customized cells to your specifications.

I I

I For information on our complete line I I of low priced cells, write today. I I I I @JUMINON, ,,,. I

I 1 126 Coil Street. Irvington, N. J. 07111 . 201 - 373-4242

Assoeititednuith International Cwstal La6oratoGs I

I I I , , , - ,,,,,,,,,,,,,,,,,, 1

Circle Ma. 104 In Readers' Snice Card

Volume 48, Number 10, October 1971 / A653

Chemical Instrumentation

STUEXR, J . and Yrnar.n, E., Phvr. Acouatier. ?A a* , ,,OR., ~... " ..,.

S o n n . ~ r . Z. h.. T~ARINA, R. D., and R m l N a , E. M.. Monnlrh. Chem.. 101,498 (1970).

S ~ n s n r o w . 11. and JEI, ,I., C h e m . I n ~ t t . , 3, 47 (1971).

For s revie," see CZ.RLI"SX,. G. A,. "Chem- ical Rebration." Marcel Dekker, Inc., Nev York. 1966.

Lmmonrx. S. and L n u ~ . 0.. Acla Chem. scnnd.. li.1834 (1968).

m ~ n n r . . ~ ~ n n , D.. E N ~ E G , .I.. and G.wsnn, V.. Biopolpmerr. 10,721 (1971).

S W I N E R A ~ T . J. TI. and CAPTELLAN, G. W.. Inorg. Chem., 3.278 (1964).

PCHW.GY, Z. %., TIAWN*. R . D. ~ n d EYBTNQ. E. M.. . I . Plzyr. Chem., 74, 617 (1070).

For a review see Rovoxrorr. T. J. W. and CHANCE, n.. ref. 6, chapter 14.

~ d . 5, 3. CHANOE, n . . G ~ ~ O N . Q. H.. EIS&NHAIIDT.R.

?I. nnri 1 . 0 ~ n r ; n c - l T o ~ ~ . T<. I<.. ads.. "Rapid Mixing and Shmpline Techniques in niochemistry," Academic Press, Nem York. 1064.

Ref. 10. ohapiers 15-18. Gmaort. Q. H.. J . Plirraiol.. 117, 49P (1952). Grnaov. Q. H. a n d n l ~ ~ x e a . L.. Biorhrat. J . .

91, 161 (1964). Gmaori. Q. H. in ref. 5, pp. 227.228: D ~ S A .

R. J. and G r e a o ~ . Q. H.. Cornp?'t. Biomed. Res..2,494 (1969).

Slns. J. A.. T~ana. Fnrndnv Sor., 54, 207 (1958).

CHEN, R. F., ECIECATER, A.N., ~ ~ R E R O E R . R. I,.. And. Bioehem.. 29. 68 (1969).

(24) Sms. J. A., Tmns. Farndny Soc., 54, 201 (1958): P ~ w m R. H.. Trons. Fnroday Sor.,54,838(1958).

(251 B ~ n c ~ n . R. L.. BALKO, B.. Boncaznor,W. and Fnr*ur, W.. Rm. Sci., Inatrum.. 39, 486 (1068): Be~aen, R. L.. I 3 ~ ~ x o . R.. CXAPMAN. H. F., ibid.. 493.

(26) On heating by eleotronio eroitatton see: N=l . ao~ . L. 8. and I.uwon*no, J. L.. No- lure, 179, 367 (1957); J . Phys. Chem., 63, 483 (1959): S~nenbow. H. and KALA- mcu*L, S., S. J . , Boy. Bunsenges., 70, 139 (1966).

(27) om beating by vibrational exoitstion (laser- T-jump) see: INSKEEP. W. TI., JONES. D. L., SILFYABT. W . T. and E m m a , E. M.. Proe. Not. Acad. Sci. (USA), 59, 1027 (1968): H o ~ ~ x n s a , H. Y E ~ ~ E R , E., and S ~ o m n , J.. Rev. Sci. Instrum.. 39, 649 (1968); CALDIN. E. F.. el el.. J. Phus. E: Sci. Inst?.. 4, 165 (1971).

(28) On T-jump achieved by s~itohinp: the eir- oolating fluids of two thermostats around the cell, see: PO,,,., r. M., ~~-uIoPL",, J . Biochem.. 4,373 (1868).

(29) On T-jump obtained by s miorowave pulae, see: E R T ~ , G. m d G E R I ~ ~ H E R . H., Ber. Bumengar. phyiilc. Chem. 65.629 (1961).

(301 C z ~ n ~ , h r r ~ , G . H . * ~ d E . a e . , M.. Z . E l e l t o - chem., 63,652 (1959).

(31) HAM ME^, G. G. snd STEINPELD. J . I. J . Am. Chem. Soc.. 84,4639 (1962).

(32) Fnmon. T. C. and HAMMES, G. G.. Chapter 1 of rei. 5.

(33) l l ~ ~ m o w . B. C.. T a w , L. K. J., Ho'r~s , L. P. and Emm~o, E. M.. J . Phus. Chem., 73, 3288 (1960).

(Concluded in the November issue.)

Erratum In the August 1971 issue of the JOURNAL OF C H I ~ M ~ C A L EDUCATION part of Figure

20 of the article by Peter F. Lott and Itobert J. Hurtubise mas inadvertently omitted. The complete figure and caption are printed here.

Figure 20. Optical Diogrom for h e Zeirs Chromatogram Scanner. 11) light source, 121 mmo- chromator, (3) intermediate system, rimplifled, (4) deviating mirror. (51 chromotogrom, (61 intermediate optical system, (71 flltor, (81 detector.

A654 / Journol of Chemical Educafion