Revista Latinoamericana de Metalurgia y Materiales, Vol. 18, 1998, 12-20

SWITCHING CHEMICAL REACTION DYNAMICS AND KINETICVS. THERMODYNAMIC CONTROL IN REFERENCE TOPOLYMORPHIC PRECIPITATION OF HgI2 CRYSTALS

Seung-Am Cho

Department of Materials Science, Scientific Research /nstitute of Venezuela (IV/C)PO Box 21827, Caracas 1020-A, Venezuela

andSchool of Metallurgical Engineering and Materials Science, Central University ofVenezuela (UCV)

PO Box 50361, Caracas 10S0-A,' Venezuela

ResumenLas características experimentales observadas en la precipitación polimórfica de ioduro de mercurio

en una solución acuosa indicaron una biestabilidad del sistema de la reacción con vías bimodalesdependientes de la concentración inicial nRo del reactante y la temperatura del baño T. Cada víafunciona cuando el estado del sistema es cinéticamente favorable lo cual es determinado por nRo y Tdespués de los respectivos límites críticos neo y Te para que la reacción cambie de un lado a otrodinárnicamente entre las regiones bistables siempre que el estado cruce por encima de los límitescríticos. Este fenómeno es interpretado en términos de una dinámica de reacción hipotética llamadaMecanismo de Histerésis de Reacción Química (MHRQ). Una unión entre la biestabilidad y el modelode formación bicolor espacial periódico de Liesegang en gel del sistema se discute y se sugiere laposibilidad de una oscilación química no-periódica sostenida de este sistema en un flujo contínuo poragitación en un reactor.

Palabras Clave: Precipitación Polimárfica de Hgl-, Sistema de reacción biestable, Mecanismo deHistéresis de Reacción Química, Banda de Liesegang

AbstraetExperimental characteristics observed in the polymorphic precipitation of mercuric iodide in

aqueous solution implyed a bistability of the reaction system with bimodal pathways contingent uponinitial concentration of reactant nRo and bath temperature T. Each pathway functions when the stateof the system is in the kinetically favorable region that is determined by the nRo and T beyond therespective criticallimits neo and Te so that the reaction switches back and forth dynamically betweenthe bistable regions whenever the state crosses over the criticallimits. This phenomenon is interpretedin terms of a hypothetical reaction dynamics called Switching Chemical Reaction Mechanism(SCRM). A linkage between the bistability and the periodic bicolor spatial Liesegang pattemformation in gel of the system is discussed and possibility of a sustained aperiodic chemical oscillationof this system in a continuos-flow stirred tank reactor is suggested.

Keywords: Polymorphic precipitation of Hgl-, Bistable reaction system, Chemical switchingmechanism, Liesegang band

i~~r.:a Lazinoamericana de Metalureia Y. 'ateriales. \ 01. 18. 1998 13

".;-."'-¡

llave been publishéd onkinetic vs.:::a:==crl~~-~ control of products formatión in ~'both

inorganic reactions [l-7].In discussingz r- ..""."." yield of two different products A and ·B.from

r R by a parallel reaction under rather restrictivecoodition that for the specific reaction rate :coefficientskl>k2 and for the equilibrium 'constants K¡(=k¡/k:¡) ..<K2(=k2lk2), more rapid1y formed product A is called thekinetically controlled product andjhe stable produ~t'Bformed : aft~¡'a.' oertaintlíne" -is "designated ; _thethermodynamically controlled product[1].' .

In spite of recent criticisms on tbis title phrase andconcept [6,7], the precipitation of polymorphic mercuriciodide crystals, red tetragonal (X-HgI2 and yelloworthorhombic ~-HgI2, in aqueous solution at roomtemperature

HgC12(aq) + 2KI(aq) = HgI2(s) + 2KCI(aq) (2)

has incorrectly been interpreted [5] as

. ~Orangel tetragonal H9I2 .. ..' ~ (thenodinacal1y controlled product)

~k.2·. '1(¡¡if+ +2q . . . .(3)

.~.,

: .. ~YellOVl rhOlbic Hg12. (kinetically controlled produd)

The detailed tudies on the precipitation reactioncharacteristics based on complete reaction field exploredin terms of a ser of reaction system variables; initialconcentrations of reactants [8] and teperature (presentwork) inclucling reaetion time, showed a bistability naturein the chemical reactioo system. The operative reactionmechanism con i of two independent competingparallel chemical p or pathways across the criticalconditions, namely the critical ioitial concentration ofreactants [Reo] and the crirical remperature Te of thereaction system: a one-step parh-Il proces, i operativeabove the critical condition and a rwo-srep consecutivepath-l process is operative below the critical condition as

>

HgClz(aq)+2KI(aq)=( ~-¿(X)Hglz(s)+_ e

These two reaction processes switch or flop overbetween them across the critica1 condition as the systemcondition changes. This reaction dymnamics is proposedas the Switching Chemica1 Reaction Mechanism (SCRM).The proposed mechanism is ana1yzed in detail in thepresent paper and suggested a possib1e chemicaloscillation process, i.e. [9-11], based on our mechanism.

2. Experimental

Experimental details and materials used are presented inour previous paper [8], in which we demonstrated aprecipitation reaction scheme of po1ymorphic (X and ~mercuric iodide crystals represented by their color as afunction of starting or initial molar concentration [R0]

or ne° of reactant R(Hg2++21") in terms of HgClz and ofreaction time (RO_tscheme) at room temperature as shownin Fig. 1.

0.20

0.18

0.16

~QO.12O'IO.lO

'---'

Reda-HgI2

ore .

Yellow

,B-Hg I2

° 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20t(min)

Fig. l.Crystalline phase field in the auqeous precipitation reactionof a-HgI2 and ~-Hgh polymorphs in terms of initial molarconcentration of reactant [HgCl2l as a function of time at roomtemperature. The hatched field represents two phase region inwhich solid state transformation~ -7 a takes place in the solution[8].

The initial 1emon yellow suspension of metastab1e~-HgI2 crystallites was only observed for [Ro] below aboutO.06M HgC12. lts color rapidly changed to rose which inturn gradually con verted into the bright red color ofthermodinamically stable (X-HgI2 crystallites. At [Ro]above about O.17M HgC12 the red crystallites formedimmediately. This limit O.l7M HgClz is termed thecritical inital reactant concentration [Reo] or neo. As themetastable yellow precipitate transforms so rapidly into

14 S-A. Cho/Revista Latinoamericana de Metalurgia y Materiales

the stable red crystallite, the X-ray powder diffractogramof the final crystallite obtained fram 0.01M Hgz

+ startingsolution after a reaction period of 30 min. revealed theonly red modification of tetragonal n-Hgl- crystal (SG N°137, file W 21-1157 [12] as hown in Fig. 2. We thus, forthe first time, identified the initial yellow suspensionformed in the ionic aqueou Hg2

+ +2H' solution bypowder XRD meIhod [ ] as me metastable yelloworthorhombic ~HgI~ crysral (SG °36) by employingthe colloidal protection technique [13].

Fig. 2. The powder XRD pattem of red a-Hglz precipitates.

The color photo (Fig. 3) represents our gelatinized X-ray powder sample plate of the yellow suspensioncaptured by the colloidal protection method. The pressureexerted by the scribbling steel pencil on the gelatinizedyellow spread caused irnmediate color change (the redchinese character in Fig.3) due to the solid state phasetransforrnation, p(yellow)-HgIz ~ o.(redj-Hgl-, and thecolors remained as they were for weeks after the photowas taken[8]. In fact, because of its rapid conversion toa fonn in the solution in addition to its physicochemicalvulnerability [8] the powder XRD work on the yellow p-HgI2 formed in the aqueous solution has been left formore than a century.

We extended experiment to prove if the rosy transientzone in between the initial yellow and the final red inFig. 1 were represented suppostedly by a mixture of aand P crystallites resulted fram the phase transformationp~a in the solution thraugh the reaction processs (4b).The two sediments obtained after five days resulted framthe reactions of a set of starting solutions, (O.02M HgCh +O.04M KI) and (0.04M HgCh + 0.08M KI) of 50 mleach, in the lightly magnetically stirred 200ml of 1%gel atine solutions, were yellow for the fonner as before[8] and rase for the latter. The powder XRD spectra takennext day on the dried sample plates exhibited ~-HgI2 forthe yellow and mixture of a and p phases for the rasyplate as shown in Fig. 4.

Fig. 3. Color photo of the X-ray powder diffractionsample plate ofthe transient initial metastable yellow ~-HgI2precipitates that werecaptured by protective colloid technique.The red chinese characteron me dry gelatinized spread was substantiated by the phasetransformarion, f3(yellow)-Hglz --¿ a(red)-HgIl, caused by thepressure exertedby the scribblingsteel pencil [8].

'f'ELLOW (ORTHORHOMBIC {3- HqI2)

10

AOSY (0+,8)

RED (TETRtoGONAL a-HQI2)

Fig. 4. The powder XRD spectra of red a-Hglz and yellow B.HgI2,and their rosy mixmre «(1 + (3).The outcome proves that themetastable initial yellow (}fOlID transformsinto the stable final reda form through the f3--¿ a pbase transformationin the solution.Fordetails see the text,

The outcome proves that the metastable initialyellow p indeed rransforrns into the stable final red athrougb the f} ~ a pbase transfonnation in the solution,which in faet represeats tbe transient rosy zone in Fig. l.Tbe characreristi of rapid and transient nature of initialyellow preeipitation pracess manifests that the yellow ~-HgI~ - tbe true intermediate reaction praduct and isindeed Ihe metastable phase.The previonsly observed temperature effect on the bahviorof tbe same precipitation reaction [8] is fully extendedhere and obtained a new reaction phase field as afuocrion of reaction bath temperature versus reaction

Revista Latinoamericana de Metalurgia y ateriales 01. 18, 1998 15

time (T-t sebeme) as demonstrated in Fig. 5, whichappears similar to RO-t scheme of Fig. l.

Red a-HgI2

Yellow,8- Hg I2

192021 22

Fig. 5.. Phase field of polymorphic o-Hgl, and ~-HgI2crystallites in the aqueous precipitation reaction in terms oftemperature of the reaction system as a function of time for thefixed initial molar concentrationof reactant at O.OIM Hg+2Thehatched field represents two phase region in which solid statetransformation ~ -7 ex takes place in the solution.

Both reactant solutions, HgClz and 2KI, weremaintained at the same temperature before startingreaction; below room temperature an ice bath aroundreaction beaker containing Hg2

+ solution was placed on amagnetic stirrer and above room temperature Hg2

+

solution was simultaneously heated and stirred on atemperature controlled hot plate magnetic stirrer. Themaximum temperature at which yellow suspension wasdetectable for RO of O.OIM HgCl2 was about 338.15K(65°C).

Above about 363.15K (90°C) the red precipitationappeared immediately. This temperature, lattertemperature, limit is termed the critical temperature Te.These two temperatures should, in theory, convergeinto the phase transformation, ex ". ". ~, temperature T, assuch Te=T,=400.15K (l27°C) [18] provided that theexperiment is carried out accurately enough.

3. Dynamic Reaction Process

The two reacrion fields, RO-t scheme (Fig. 1) and T-tscheme (Fig. 5). implies an existence of two independentreaction pathway thar are operati ve across the criticalconditions, [Re] or /leo and Te, in accordance withEqs.(4a) and (4b). which indeed manifest a parallelreaction but is different from fashion (1) and fashion (3)as such.

__(5)

The reaction phenomenon (5) suggests a chemicaldynamics with bistability nature; an existence of bistablereaction regimes, having the relevant reaction pathways 1and Il, separated by a limit of instability at a criticalcondition of the reaction system defined either by the[ReO] or neo at a given temperature or by the Te at a fixedinitial concentration.

The two chernical processes, path-I and path-Il, withdistinctive overall forward velocities, VI and VII, bothleading to the thermodynamically stable ultimate sameproduct o.-phase, can be independent but are competitiveacross the critical conditions, [ReO] and Te. Above thecritical conditiones, [Ro] > [Reo] and T> Te, the path-II isactive and red rx-phase directly precipitates out fromsolution while below the critical conditions, [Ro] < [Reo]and T<Te, the two-step series path-I reaction becomesactive. The first RO ~ ~ step must be faster asprecipitation of yellow metastable ~-phase involvesnucleation through liquid-Iiquid reaction as in the case ofpath-II reaction compared to the second step at wherea sluggish phase transition, ~ ~ a, reaction takes placein the solid state within the solution bath. The operativemechanism flips or switches when the conditions changeinto either region of the reaction fields the state of thesystem resides. The two paths can dynamically flip-flapor switch back and forth between them whenever the stateof the system changes across the instability point either[RoL,,""" [ReO] at a fixed T or T.J"··Te at a fixed [Ro]. Themechanism responsible for the proposed reactiondynamics is termed here the Switching Chemical ReactionMechanism (SCRM).

To substantiate the pro posed SCRM in terms of thefamiliar transition state activated-complex -theory (ACT),the required thermophysical quantities of the polymorphicphases are presented in Table l.

16 S-A. Cho/Revista Latinoamericana de I. alureia Materiales

Table 1. Structure and Thermophysical Quantities of the a-HgI2 and ~-Hgl, el)

Structure Color P cp LUioz98 óS °298 ~ Tr(K) LUir(kg.m') (J.mole·' X') (kl.mole') (kl.rnole'l.K") (kJ.mole·') (kl.rnole')

~-HgI2 yellow 6094.4' 84.52+ -102.72# (178.2/ 532.15' 18.S+orthorhombic$

Cmc21

a-HgIz red 6364' 77.4+ -105.4# (178.2/ -100. 1" _7_+tetrazonal''b

PLh/nrnc

(*)Ref.14, (+)Ref.l5, (#)Ref.16, ($) Ref.l7, (a)Ref.1S

G

G~ G'R

6G;(¡3)

----'-----g: ="[L:::::¿r~L -__aFig. 6. The proposed representative free energy potential profile ofthe polymorphic precipitation reaction of c-Hgl- and ~-HgI2 phasesfrom ionic aqueous solution. For details see the text.

The thermodynamic stability of a over ~ is wellreflected by the densities, especially by the standard freeenergy of formation by the relation

ÓG298([J.)o=-100.71 kJ/mole < ÓG298(P)0= -96.7 kJ/mole

with a relatively small difference between them as

ÓG298(~-7[J.)0=ÓG298([J.)0-ÓG298(P)0=- 4.06 kJ/mole (6)

An appropriate and plausible free energy potential profileis deviced in Fig.6 in relation to thermodynamic stabilitiesof the phases. The profile is depicted based approximatelyon the data of free energies of formation, ÓGIO(~) and6Gt(a) and of transition ÓGIO'(a)=ÓG20(a)-ÓGIO(~).The respective activation free energies, ÓGI * (~), ÓG2*(a) and ÓGI '*(a) = GB*(a) - Gp, are reasonably scaledfor favorable explanation of the chemical dynamics byalso taking into account the interrelations among k, K andG*. Application of the sequences, ÓGI*(~) < ÓG2* (a) <

ÓGI*'(a), ÓGI* (~) « ..lG1*' a and IÓG2° (a) 1>I!lGlo (~) 1» IÓGIO'(a) 1, ro equatioos (7) and (8) [19]

k T G*k = vrK"= vK* =_B_ exp(---)

h RT(7)

k !:J.GoK= _f == exp(- --)

kr RT(S)

for equilibrium between normal and activated complex, nand n*, in our particular experimental ranges inconcentration and temperature.

ÓG*= (G*-G) = -RT In K* (9)

K*=* *n !lG

-=exp(---)n RT

results in the following relevant relations among k and K

ki> ka> k/ or k] > kz, k] » k/ and kz> k/ (lO)

(11)

The single energy profile of Fig. 6 is remodeled into adouble energy profile in Fig. 7 to facilitate argument of theauthor's concept on the chernical switch as flip-flap betweentwo independent pathways, path-I (left) and path-I1 (right),across the instability limit, neo or Te, of our proposedbistable reaction system. The fact kl>k2 manifests path-IkineticalIy prevails over path-I1 when the state is belowcritical condition, where the formation of ~ predominatesover a both kineticalIy and thermodynamically even thoughthe a is the thermodynacally stable ultimate phase becausesimultaneously kj» k/ and K¡ » K/ since ÓGI* (~) «ÓGI*'(a) and I!lGlo (~) 1» I!lGIO'(a) l.

.•.~Iis;¡r.aLminoamericana de Metalurgia y Materiales, Vol. 18, 1998 17

G

1 Q

----Poth-I----j

Fig. 7.Remodeled double free energy potential profile from thesingle energy profile of Fig. 6 as representativeof dynamic natureof chemical switching as flip-flap between two independentreaction pathways, path-I (left) and path-II (right), across theinstability lirnit of the our proposed bistable reaction system. Formoredetails see the text.

Whenever the state crosses over into the region abovecritical condition, a new situation, k2 > k¡' and K2 > K¡ ,arises, which makes it now possible to trigger path-IIreaction so that the path-I switches into path-II since notonIy the kinetics favors path-II over path-I by the fact k2 >k¡' but also the equilibrium constant K2 for direct aformation predorninates over the rest, K¡ and K¡' at thesame time.

The above phenomenological interpretation of theSCRM can be much elegantly explained in terms of n' andV in conjunction with Fig. 7 and Fig. 8 since the both ofthem are simultaneous functions of n and T as well as ofactivation free energies as

*( TJ K' ( I1G *n: n, = "'n=nexp ---) (12)RT

dn .. kBT I1G*V(n,T}= -- =/01=v*n*-'" vK*n=n( -- )exp(---) (13)

dt h RT

Equation 13) leads to the following two overall velocitiesif one pay anenrion only to the same ultimate product a

V ¡(R--7f3--+m= k T[ *']/ B I1G a

~= n~(--)exp _ 1 ( )h RT

(14)

r.T)e [ I1G~(a)]-- xp -h RT

(15)

'hen the state of is in the regime below thecritica! condition, the - reacrion is effective becauseme nR' (f3J in the free euergy e 1Gs' (f3J for P formation

n: 1m = n,exp [- "ri;fll1 (16)

is already reached to trigger this reaction R --7 ~(kl)since I1G¡*(~)<I1G2*(a). Once it starts, it produces ~ eryrapidly by

V,cR ->m = k,n, = n, ( knexp [ - "'i;P)1 (17)

which makes the P accumulates fast enough to decomposeslowly into the product a by sluggishly passing over thefollowing second high energy barrier I1G¡*' (a) for phasetransformation ~ --7 a as the thermodynarnic stability ofa, I1G/ '(~--7a) < O, favors the a over p. The overall rateof this reaction path, V¡ (R --7 P --7 a) of (14), is slowbecause this second step for p--7 o( k, ') acts as the rate-lirniting-step since I1G¡*'(a) »I1G¡*(P) and kl'« k..When the state is above the critical condition the. 'ns (a) beyond the level GR*( a) required for direct passover activation peak I1G2*(a) of path-II reactionR--7a(k2)

[ '" 1• I1G~(a)ns (a) = ns exp - RT (18)

becomes sufficient enough that the reactants directlyform the end product a with velocity vll(R --7 a) of (15)without having recourse to path-I since k2>k/ and K2>KIfavor path-II in this state so that, by now, the existence ofthe first small barrier I1G1 *(P) of path-I is irrelevant.

G

Palh - 1 I Palh - IIa -----/3----R----- a

a

Fig. 8.. An overall view of dynamic switching mode of ourbimodal reaction system contingent upon nRo and T, whichfunction as the control elements (regulators) and the activatedcomplex nR* acts as a control agent inducing switch between thebistable pathways. When the condition nRo or T crosses over therespective instability threshold, neoor Te> the reaction switchesover. See the text for moredetails.

18 S-A. Cho/Revista Latinoamericana de Metalurgia y Materiales

4. Discussion

An overall view of the dynamic swirchíngreaction system with bimodal patb" ...,.....-,.T-"~••.....•.nRo and T in a closed stirred

graphically in Fig. 9. The n T fun tion as tbecontrol elements ( ) nR* acts as a controlagent inducing switch berween the bistable patyhwayswhen the nRo or T crosses over the respective criticalpoint or threshold of instability, neoor Te' Thisphenomenon is analogous to tilting process of a beam bycrossing a person over a fulcrum point so that the n/orTe corresponds to the fulcrum of the beam, The argu¡nentsfavor the kinetics view on the dominant factor becausethe nR* (n,T) in relation to ~GR* plays the deterrninantagent in our reaction system,

R

a

Fig.9. The proposed chemical reaction switching dynamicscheme operative between two independent reaction pathways,path-I and path-II, having respective overall reaction velocities, VI

and VII, in the polymorphic precitation reactions of HgI2 crystalsleading to the stable ultimate o-Hgl, form in the aqueou solution.See the text for more details,

The proposed physical cause on bistability quitepredicts a chernical oscillation in our system when thereaction is carried out in a contínuous-flow stirred tankreactor (CSTR) [9,10] even our system is not a transientand self-oscillating type of Belousov-Zhabotinskii (B-Z)reaction observed either in a closed reactor (CR; a beaker)or in a CSR [20]. Our oscillation mechanism is expectedto be simpler than those numerous variety of oscillationbehaviors [9-11,21-23] as discussed in the following.

It is, in principle, possible to imagine that the twoindependent reaction paths could result in a genuineconcurrent or parallel reaction provided that the CSTRwas designed to maintain the state of the system exactlyat the critical condition as purely idealized situation,nRo = neo and T =Te, at where the two overall rates interms of nRo

(19)

(20)•must VFVIl, so that the two reactionsbecome n' :m::ro.::peOOdll and will interfare each other in thefashion

e -(21)•-k. t ~-,

(e I -e ,..)

This ideal situation is represented by the horizontaldotted arrows in Fig. ID, In practice, however, it isexpected to be impossible experimentally to maintain theideal operational condition of a CSTR. The resulting

external variation of either nRo or T or both aroundinstability point, n," or Te, shall trigger a fluctuationbetween the bistable pathways. Even if the operation ofthe CSTR were in the ideal condition, an additionalfluctuation may be inevitable because of perturbation ofstate variables, p, V, T and n, of reaction system caused bytheir internal natural fluctuations. Wave form of theresulting sustained chernical oscillation shoud be dictatedby the dominant one between the external and internalfluctuations. A mixed fluctuation of the two may give rise toa complex aperiodic behaviors or chernical chaos. Ahypothetical oscillation is also presented in Fig. 10. Theproposed chemical oscillation may be observed if oneemploys a sophisticated experimental setup attached withappropriate rapid and sensitive opto-chernical sensorscoupled with detectors.

a Poth - Il

Porallel Reaetion(Ideal)

<:a Poth - 1

Fig, 10. Two additional imaginary reaction modes over thepathways 1 and II; a purely idealized genuine parallel reactionrepresented by the horizontal dotted arrows and a probableaperiodic chemical oscillationwhen the reaction is carried out in acontinuous-flow stirred tank reactor.See the iext for more details.

Our chernical switching mechanis:m is phenomeno-logically equivalent to that of recent molecular switch [24]and of those popular electrical tb:resbold switching of gas

Revista Latinoamericana de Metalurgia y Materiales, Vol. 18, 1998 19

(i.e. neon-lamp) [25] and solid (i.e, V02 [26] provided thatOUT switching regulator tn«° or T) and control agent (nR*)are properly identified with regulators and agents in odIcrsystems. In case of molecular switch an acidity (functions as a regulator and a hydronium ion (lI30)an agent in the translocation between the two ligatioaIn case of electrical switches of the mentioned gasa voltage (V) functions as a regulator and elagent in the transition between the two states - differentregistances; normal and ionized in gas and OFF (msulatoror semiconductor) and ON (meta1lic) in solid in thelanguage of Mott [27]. The molecular switch may alsooscillate in accord with our hypothesis as those gas and soliddemonstrate experimental evidence that a bistable systemactuates either switching or oscillation depending onimposed condition on the system [25, 26, 28, 29]. We haveextensively studied this phenomenon on many inorganicsand semiconductors inc1uding V02 [29].

Figures 11 and 12 demonstrate our previousexperimental results on the precipitation of HgI2 crystallitesfrom HgClz and 2KI in two different sets of concentrations[8], that were obtained by gel technique [30]. Tbe test tubecontaining a low concentration solutions, 0.02M HgCl2 insilica gel and 0.04M KI as supernatant, formed a spatial andrhythmic two color Liesegang pattern or bands (Fig. 11)while the other tube containing a high concentrationsolutions, 0.24M HgClz in gel with 0,48M KIsupernatant, produced a mass of red crystallites (Fig. 12).

Hg. 11. Forrnation of in yellow (~)/red(a),periodic bands in silica gel srep path-1 reaction

es place below the criticalCOIJCe[~:m 110< fle°. See the textordetails.

periodicctXX:eD1aDoo (O_02M;x::mcric:m of mass of red crystals

-00 (0.24M > n-" = 0.17 M HgCl1),

think of a probable linkage between thebehavior in gel and the proposed chemica1mechanism of Eq. (5), whiéh may in tum shed light on thosehitherto controversial theory of the Liesegang phenomenon[9, 31-34]. In accord with our switching mechanism, thesingle step path-I1 reaction must be active at the conditionnRo > n." so that the precipitation of red a-HgI2 shouldcontinue until the opposing gradients can not maintain therequired level of concentration for the nuc1eation of redphase at the reaction front, at where metastable yellow ~-HgI2 starts to precipitate. Figure 12 indicates that thereaction system is probably reached in this stage of process.However, when the starting condition of the reactionsystem is at nRo < n.", the two step path-I reactionprevails so that a repetitive precipitation process of twodifferent color phases, R ~ ~(yellow) .....')a(red), continuesuntil the reservoir reactants become depleted, Figure 11explicitly demonstrates the proposed process; the mixedbicolor yellow/red bands reside near the reaction front andthose red bands consist of ultimate n-phase are accumulatedbehind them.

Fig. 12. Precipitation of a mass of red a-HgI2 crystallites whenthe single step path-II reaction takes place above the critica!concentrationnRo > neo. See the text for details.

20 S-A. Cho/Revista Latinoamericana

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