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J. phys. Chem. 1983, 87 , 1449-1453 1449A Kinetic Study of Ion-Pair Formation on the Surface of a-FeOOH in AqueousSuspensions Using the Electric Fleld Pulse Technique

Mlnoru Sasakl, Mlklhlko Morlya, Tatsuya Yasunaga;Department of Chemlstty, Faculty of Sclence, Hlroshlma Unlverslty, Hlroshlme 730, Japanand R. D. Asiumlan'Department of Chemistry, The Unlverslty of Texas at Arllngton, Arllngton. Texas 780 19 (Recelved: June 10, 1982;In Final Form: November 23, 1982)

Two relaxations on the order of microseconds were observed in acidified aqueous suspensions of a-FeOOH,by using the electric field jump technique with conductivity detection. The faster relaxation was observedas a decrease in the conductivity of the solution in the electric field, and the relaxation time is dependent onthe applied electric field intensity. Consequently, this relaxation was attributed to physical phenomena. Theslower relaxation, however, is observed as an increase in the conductivity of the electric field and is independentof the applied electric field intensity. Therefore, this relaxation was attributed to the dissociation field effectand was interpreted in terms of the association-dissociation eaction of counterions with the protonated surfacehydroxyl groups. A t a particle concentrationC, = 20 g dm+ and at I at 25 OC, the intrinsic anionassociation and dissociation rate constants were determined to be kEiOn,* 6.0 X lo5mol-' dm3s-l and kgi,,n,d= 1.0X lo4s-l for C1-, and kEi0, ,= 1.4 X lo5mol-' dm3 s-l and k%on,d= 2.0 X lo4s-l for Clod-, respectively.1x

IntroductionThe acid-base properties of metal oxides are of greatimportance in many fields, such as soil chemistry, geo-chemistry, civil engineering, materials science, and colloidThis is perhaps because most of these oxidesare amphoteric, able to act as either proton donor or ac-ceptor, depending on the environment. In general, theseoxides may be thought to have hydroxyl groups existingon the particle surface, characterized by two acidity con-stants, K,, and K,, which depend on the surface poten-tial.*1 I t has been shown that H+ and OH- are thepotential determining ions for these system^."'^ In ad-dition, both specific absorption of ions in the outer Sternlayer and physical adsorption, involving only electrostaticinteraction, of noninteracting electrolytes, in the outerStern layer, have been well studiedgJ0J3J4 nd shown tobe of great importance in determining the properties ofdispersed metal oxide systems.Recently, kinetic studies of the adsorption-desorptionof H+ and OH- on various metal oxide surfaces have re-vealed that the mechanism of this reaction is simplechemisorption of the potential determining pre-(1) Muljadi, D.; Posner, A. M.; Quirk, J. P.J. Soil Sci. 1966,17,212.(2) Allen, L. H.; MatijeviE, E.; Meites, L. J. Inorg . Nucl. Chem. 1971,(3) Huang, C. P.; St u" , W. J.Colloid Interface Sci. 1973,43,409.(4) Hohl, H.; S tu ", W. J.Colloid Interface Sci. 1976,5 5, 281.(5) Schindler, P. W.; Fiirat, B.; Rick, R.; Wolf,P. U. J. Colloid In -(6)Davis, J. A.; Leckie J. 0. J. Colloid Interface Sci. 1978, 67, 90.(7) Elliott, H. A.; H uang , C. P. J. Colloid Interface Sci. 1979, 70, 29.(8) Schindler, P. W.; GamsjHger, H. Kolloid-2. 2.Polym. 1972,250,(9) James, R. 0.; avis, J. A,; Leckie, J. 0. J. Colloid Interface Sci.(10) Davis, J. A,; Jame s, R. 0.;eckie, J. 0.J. Colloid Interface Sci.(11) Li , H. C.; De Bruyn, P. L. Surf. Sci. 1966,5,203.(12) Atkinson, R. T.;Posner A. M.; Quirk, J. P. J.Phys. Chem. 1967,(13) Ahmed, S. M.; Maksimov, D. Can. J. Chem. 1968,46, 3841.(14) Breeuwsma, A.; Lyklema, J. Discuss. Far ada y SOC.971,52,324.(15) Ashida, M.; Sasaki, M.; Kan, .; Yasunaga, T.;Hachiya, K.; In -(16) Ashida, M.; Sasaki, M.; Hachiya, K.; Yasunaga, T. J. Colloid(17) Astumian, R. D.; Sasaki, M.; Yasunaga,T.; Schelly,2.A. J.Phys.

33, 1293.

terface Sci. 1976,55, 469.

17.1978, 65, 31.1978, 63, 480.71, 550.

oue, T. J. Colloid Interface Sci. 1978, 67, 219.Interface Sci. 1980, 74, 572.Chem. 1981,85, 3832.

ceded by a very rapid reequilibration of the ionic atmo-sphere surrounding the particles." This reequilibrationis too rapid to be observed by the pressure jump techniquewhich was utilized in these studies. Therefore, the muchfaster technique of electric field jump was used in thepresent investigation to study the detailed mechanisminvolved in the formation of the ionic atmosphere aroundthe colloidal particles of goethite in acidified aqueoussuspensions.It is shown that the mechanism of ion-pair formationat the surface must consist of a very rapid diffusion ofcounterions to the surface, with subsequent ion-pair for-mation. The numerical values of the rate constants aregiven, and the mechanism is discussed in terms of thecurrent literature.Experimental Section

The electric field pulse apparatus used has been pre-viously described" The a-FeOOH was supplied by TodaKogyo Corp. and details of the purification and prepara-tion have been published previou~ly.'~he specific surfacearea, the intrinsic value of the acidity constant, and thetotal site concentration of the a-FeOOH particles were 44m2 g-', Pnt 1.0X lo4 mol dm-3, and 2.02 X lo4 mol g-l,respecti:hy. The HC1, HC104, NaC1, and NaC10, wereall reagent grade and were used without further purifica-tion.Goethite forms very stable suspensions under our ex-perimental conditions, with no appreciable sedimentationover a period of 1h. All samples were allowed to equili-brate for 1 2 h after the addition of the acid and the salt.The ionic strengths of all samples were adjusted to I =(1-1.3) X with NaC10, or NaC1, where I was correctedon the basis of the adsorption isotherm of proton. The [A-]concentrations were varied by changing the amount of acidadded.The electric field pulse measurements were performedon samples of C, = 20 g dm-3 except for the experiments

(18) Ikeda, T.; Sasaki, M.; Astumian, R. D.; Yasunaga,T.Bull. Chem.(19) Ikeda, T.;Saaaki, M.; Yasunaga,T.J.Phys. Chem. 1981,86,1678.(20) Hachiya, K.; Ashida, M.; Sasaki, M.; Kan,H.; Inoue, T.; Yasu-

SOC.p n . 1981,54, 1885.naga, T. J. Phys. Chem. 1979,83, 1866.

0022-385418312087-1449$0 1.5010 0 1983 American Chemical Soclety

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1450 The Journal of Physical Chemistry, Vol. 87, No. 8,1983 Sasaki et al.

Figure 1. Typical double relaxation curve in the acidic a-FeOOHsuspension observed by the electric field pulse technique with con-ductivity detection. Particle concentration of a-Fe OO H, C,, = 20 gdm-3, [HCIO,] = 1.0 X N, [NaCIO,] = 5 X lo-, mol dm-3, andelectric field intensity of 41 kV cm- at 25 OC; sweep, 50 ps/division.where optical detection was used to determine if physicalrelaxations were present. In these experiments, C , = 1-5g dm-3 was used. A step functional electric field (rise time< 0.1 ps) of 41 kV cm-l was applied in all cases except forthe experiments where the dependency of the relaxationamplitude and relaxation time on the amplitude of theelectric field were being investigated.The potential was determined by ultramicroelectro-phoresis.Result and Discussion

Two relaxations were observed over the range of pH3.2-5.5 in acidic suspensions of a-FeOOH containing hy-drochloric acid and perchloric acid by using the electricfield pulse technique with conductivity detection. A typ-ical relaxation curve obtained is shown in Figure 1, wherethe more rapid relaxation is in the direction of decreasingconductivity. No relaxations were observed in either thesuspension a t pH,, or in supernatant solutions. We willdiscuss first the fast relaxation, and then the slow one.Fast Relaxation. The rapid, conductivity decreasingrelaxation could be observed only in the range of [A-] 52 X lo4 mol d~n-~ ,here [A-] represents the concentrationof the anion. The reciprocal relaxation times, 7-l, areproportional to the electric field strength, as shown inFigure 2. These data were taken only for the FeOOH-HC104 system. The relaxation amplitudes, AK / , whereK is the conductivity, were about ten times larger thanthose for the slow relaxation, as may be seen from Figure3. It is alsonoted that a small, polarization independent,turbity change was detected on the same time scale as thisrapid relaxation. Considering these facts, it would seemmost likely that the fast relaxation may be attributed toeither a physical phenomenon or a chemical reactioncoupled to a rapid physical change. Clearly, the directionof the conductivity shift cannotbe explained by Onsagers%theory of the dissociation field effect for weak electrolytes.It should benoted here that this is not the only observationof a conductivity decrease under the application of a highelectric field. Spinnler and Patterson2 have observed aconductivity decrease in homogeneous solutions of uranylnitrate and uranyl perchlorate with a stat ic field method

(21) Spinnler, J. F.; Patterson, Jr., A. J . Phys. Chem. 1965,69, 500.

6cfn0ct-. 4en0- 21-)

0 01 2 3 4 5E , 104 V C ~

Flgure 2. Electric field intensity dependences of the reciprocal fastand slow relaxation times in the acidic a-FeOOH suspension at 25 OC.The reciprocal fast relaxation time in a-Fe00H-HCIO , system (9):C,= 29 .1 g dm3, [HCIO,] = 1.0 X l o 4 N, and salt free. The reciprocalslow relaxation times in a-Fe 00H -HCI O, (0 ) nd a-Fe00H-HCI (0 )systems: C, = 20 g dm-, [acid] = 1.75 X lo 3 N, and [satt] = 1.25X mol dm-3.

4

I 1-20 2 4

E , lo4 v c m Flgure 3. Electric field intensity dependences of the relaxation am-plitude at 25 OC, where the values are expressed as the relativechange of conductivity,A K / K . he dashed line shows the theoreticalstraight line evaluated by Onsagers theory for dissociation field effect.utilizing a differential pulse transformer bridge. This resultwas verified by Cole et al.,n who used an electric field pulsetechnique similar to that used in the present study.A possible explanation of this effect, which is currentlyunder study in our laboratories, may be the rapid polar-ization of the electrical double layer, followed by inducedadsorption of ions. The experimental data to this point,however, do not warrant further speculation, and so we willpublish later the results of the experiments currently underway.Slow Relaxation. As can be seen from Figure 2, thereciprocal relaxation time of the slow relaxation is inde-pendent of the electric field intensity. This fact, coupledwith the observation that the faster relaxation shows amarked dependence on the electric field intensity, leadsus to the assumption tha t this slower relaxation is inde-pendent of any.physical phenomena involved with the fastrelaxation. The direction of the slow relaxation indicatesan increase in the conductivity with the electric field, whichis in agreement with the direction predicted by Onsagerst h e ~ r y . ~ ~ - ~ ~ccording to this theory, the electric field

(22) Cole, D. L.; Eyring E. M.; Rampton,D.T.;Silzars,A.; Jensen, R.(23) Eigen, M.; Schwarz, G. J . Colloid Sci. 1957, 12, 181.(24) Onsager, L. J . Chem. Phys. 1934,2, 599.(25) Eigen, M.; Schoen, J. 2. Electrochem. 1955,59,483.

P. J. Phys. Chem. 1967, 71, 2771.

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Ion-Pair Formation on the S urface of a-FeOOH

6 -

4 -v)*-?J 2 -

The Journal of Physical Chemistry, Vol. 87 , No. 8, 1983 1451

L1 2 3IKI , m ~ l d m - ~Flgure 4. Plots of the reciprocal relaxation time vs. the initial con-centration of anion in a-Fe00H-HCIO, (0 ) nd a-Fe00H-HCI (0)systems at I = (1.0-1.3) X and 25 OC.dependence of the relaxation amplitude for a 1:l electrolyteis expressed by the following equations:(1 )(2 )

where a is the degree of dissociation, u1 and uz are themobilities of ions 1 and 2, respectively, e = 1.60 XC is the charge on the electron, eo = 8.85 X F/cm isthe permittivity of free space, t is the dielectric constant( E - 80 in water at the experimental frequency), k isBoltzmann's constant, and T is the temperature in K.Thus, if we consider the relaxation to be due to the reaction

AK 1 - a IEe(ui - U z ) l e2- -K 2 - f f u1 + u2 8 ~ t o t ( k T ) ~a ( A K / K ) 1 - lU1 - U z l e3-=--aE 2 - a u1 + u2 8 ~ t o t ( kT) '

SOHz++ A- SOH2+-A- Kanionand assume that the actual Kanions not toodifferent fromPdon70 for A- = C1- and Rgi0,= 5 for A- = C104-, hea's are cycl-= 0.014 and aC1o,-= 0.167. Further if uparticleis negligible, the theoretical values of a ( A K / K ) d E in eq 2are calculated to be 6.8 XFe00H-HC1 and a-FeOOH-HClO., systems, respectively.These values are in good agreement with the experimentalvalues obtained from the slopes of the straight lines inFigure 3 (5.2 X lo-' and 9.6 X for the a-Fe00H-HC1and a-Fe00H-HC104 systems, respectively). Thisagreement, along with the linear dependence of 7-l on [A-]shown in Figure 4, eads us to the conclusion that theobserved slower relaxation may be attributed to the dis-sociation field effect on the adsorption-desorption reactionof the anions on the surface, and since the 7-l was seen tobe independent of E, we can consider that the relaxationtime obtained is equal to that in the absence of an electricfield.In considering mechanisms for the adsorption-desorp-tion of an anion consistent with both static and kineticdata, a natural choice is the simple mechanism proposedby Davis, James, and Leckie'O for metal oxide dispersionsbelow the pH,,:

and 6.2 X 10- for the a-

SOH2++ SOH + H+ K,, (1)

(26) Persoons, A. P. J.Phys . Chem. 1974, 78,1210.

I- 2'ETIk- 1I0m.N

Y

I0 2 4 6[H'] , 10'3moldm-3

Flgure 5. Proton adsorption Isotherms In a-Fe00H-HCIO, (0) nda-FeOOH-HCI (0 ) ystems.

5 t1 I0.5 1 1.5 2 2.5[SOH:] , 1O "mo l dm-3

Figure 6. {-potential as a function of the conc entra tlon of protonatedsurfac e hydroxyl group, [SOH,], in a-Fe00H-HCIO, (0 )and a-Fe00H-HCI (0 ) ystems.where SOHz+and SOH are the charged and unchargedsurface groups, respectively,kf nd kb are the forward andbackward rate constants, respectively, and K,, and Kanionare the acidity constant and ion-pair equilibrium constant,respectively. It has previously been reported that therelaxation time for surface protonation reaction I of variousmetal oxide suspensions is on the order of mi llise~onds, '~J~and thus itmay be assumed that reaction I cannot possiblycontribute to the microsecond order relaxation of thepresent study. In reaction 11, it is noted tha t the inter-action between the protonated surface hydroxyl group andthe counterion results in a decrease of electrostatic po-tential in the vicinity of surface and an increase of amountof proton adsorbed. In order to obtain the stat ic infor-mation for reaction 11, the amount of proton adsorbed,[SOHz+],was measured and the results are shown in Figure5. As can be seen from this figure, the amount of protonadsorbed in the a-Fe00H-HC1 system is larger than thatin the a-Fe00H-HC104 system. This fact indicates thatthe interaction between C1- and SOH2+ s stronger thanthat between C104- and SOHz+.Meanwhile, the intrinsic equilibrium constant for reac-tion I1 is expressed as a function of the potential createdby the adsorption of counterion, +b :

K&:o, = Kmion xp --( ; (3 )Here, the +@ was calculated from the {-potential shown inFigure 6 by using eq A-12 and A-13 (see Appendix), whereC1 = 140 and Cz= 20 reported by Davis et a1.I0 were used

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1452 The Journal of Physical Chemistry, Vol. 87, No. 8,1983 Sasaki et at.

0 0.5 1.0 3.0 3.5exp(%){lSOH;] + [A*] (K~,~f 'exp(-e$)} , 10-Zmoldm'3

Flgure 7. Plots of the reciprocal relaxation times vs. the concentrationterm in eq A-7 using various values ofem 10 (0), 0' (O), ndlo3 (0 )n the a-Fe00 H-HCi systems.and the value of q0 in eq A-13 was estimated from theacidity constant. The agreement between the values of $@calculated from both equations was within f6%, whichindicates the applicability of these equations to the presentsystems.The relaxation time based on reaction I1 is expressedin eq A-7 (see Appendix). When the experimental T-% areplotted against the concentration term as shown in Figure7 , he result does not even remotely resemble a straightline through the origin, and thus the simple reaction I1 maybe eliminated from consideration.Considering the possibilities for somewhat more com-plicated explanations of the surface reaction, two similartwo-step mechanisms come to mind. One mechanism isthe initial formation of a solvent-separated ion pair, withsubsequent exclusion of water, which may be expressedas

SOH2++ A- + SOH2+(SoljA-* OH2+-A- (111)It can be easily predicted that the relaxation time for thefirst step is given by the same equation as (A-7) in theAppendix and the one for the second step is independentof any species concentrations. These predictions contradictthe experimental facts. The other mechanism can bethought of as the diffusion of an anion, with three degreesof trmslational freedom,to /3-plane near the surface of theparticle, which was introduced by Davis et al.1 Afterdiffusion, the ion is bound electrostatically to the particlesurface but not to any specific site. It can move aroundon this surface (with only two degrees of translationalfreedom) until it finds a positively charged surface site withwhich to react, becoming then a site-bound counterion.This mechanism may be written as

A- + surface* [ (diffusion process, Kd)A,- + SOH2++ SOHZ+-A-

(recombination-dissociation process, Kk\onj (IV)with

where @$ion and Kd are the intrinsic equilibrium constantsof the recombination-dissociation process of the counterionand the diffusion process through the electric double layer,respectively.According to the rate theory for a diffusion-controlledprocess into an electric double layer surrounding particle

-[SOH;] [A], , lO-'mol dm-31 + Kd'0 2 4 6 8 1 06 -

0 1 2 37 [ S O H ; ] [A-1, , lo-' mo l dm-3l * K ,

F w e . Plots of the reciprocal relaxatb n times vs. the concentrationterms in eq A-1 1: (0 ) -Fe00H-HCIO, system: (0 ) -Fe00H-HCisystem.

P "0.201

u'ud1 5 10 50 100( K G 0 " ) S

Figure 9. Standard deviations of the plots calculated from the ad-justable parameter (@-)s: (0 ) -Fe00H-HCIO, system; (0 )a-Fe0 0H- HCi system. The arrows show the minima of the standarddeviations.TABLE I: Thermodynam ic and Kinet ic Parameters ofIon-Pair Formation Reaction on the a-FeOOHSurface at 2 5 " C

11-1-5 x

a - F e 0 0 H - H C 1 70 ( 5 0 y 6 0 6.0 1. 0a - F e 0 0 H - H C 1 0 , 5 6 1.4 2.0a This value has been rep orted by Davis and Leck ie."

surface,15 he relaxation time for the f irs t step in mecha-nism IV is expected to be at least shorter than 0.1 ps.Expression for T - ~or the second step coupled with the fiiststep is given by eq A-11 in the Appendix. A plot is shownin Figure 8, and can be seen to show a reasonably linearrelation between the experimental 7 - l ' ~ nd the concen-tration term of eq A-11. Rgions'sere treated as variableparameters, and the values used for the plots in Figure 8were determined as the value at minimum standard de-viation (see Figure 9). It should be noted that, as seenin Table I, the determined by this static methodare in very good agreement with those determined kinet-ically from the rate constants obtained. Furthermore, inthe case of the a-Fe00H-HC1 system, the value of R'io,

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Ion-Pair Formation on the Surface of a-FeOOHis in good agreement with that reported by Davis, James,and Leckie.lo The value ofF2i?nn the a-Fe00H-HC104system was one order of magnitude smaller than that inthe a-Fe00H-HC1 system; the ion-pair formation reactionin the latter system is much stable compared with that inthe former system. This result is supported by the factthat the stability constant of the ion pair of C1- and metalions is 1-2 orders of magnitude larger than tha t of Clod-and metal ions.27All of these results argue for the validity of mechanismIV . This mechanism also fits in well with the theory ofsurface conductivity, where the anions on the surface, Af,are able to move freely on the surface when a potential isapplied, but must overcome an activation barrier in orderto leave the surface.The values for the intrinsic association reaction rateconstants, ItZion,*,as calculated from the slopes of theplots, and those for the dissociation reaction, kgion,d ,romthe intercepts, and are also listed in Table I. A noticeabledifference exists between the rate constants for the twosystems, especially the association rate constants, andfurther work is being performed to clarify these differences.

Acknowledgment. The authors express their apprecia-tion to Professor A. P. Persoons of the University of Le-uven, Belgium for many helpful discussions and sugges-tions, and to Dr. Z. A. Schelly of the University of Texas,Arlington for critically reading the manuscript.Appendix

In reaction 11, the forward and backward rate constantsof the adsorption-desorption of ion through the electricaldouble layer are givenkf = kfint x.( -..>\k+ (A-1)

(A-2)where \kft and \kb*are the electrostatic activation energies,and k and T ar e the Boltzmann constant and the absolutetemperature, respectively. An equilibrium constant isexpressed from these equations:

From eq A-3 and 2, the following relation is obtained:(A-4)

Under the assumption that the magnitude of \k$ is equalto tha t of \kbt, eq A-1 and A-2 are rewritten as\k+ + \kbt = - \ k P

k, = kfintex.( 2) (A-5)(27) S i l lh , L . G. "Sta bility Constanta of Metal-Ion Complexes",No .25; The Chemical Socie ty Burlington House: London, 1971; pp 163-87,

19-199.

The Journal of Physical Chemistry, Vol. 87, No . 8, 1983 1453

(A-6)Thus, the relaxation time for reaction I1 is derived as

For reaction IV , equilibrium constants are defined as

with(A-8)

A-1, = [A-] exp( 2) 64-91(A-10)

Under the assumption that the diffusion process is ex-tremely fa& compared with the recombination-dissociationprocess, the reciprocal relaxation time, T - ~ ,or reaction IVis given by

where kZion,,and kEion,d re the intrinsic recombinationand dissociation rate constants, respectively.According to the theoretical treatment of the electro-chemical potential by Davis and Leckie,'O \k, is expressedasad\ k ,={ - - CZ (A-12)

(A-13)with

ud = -11.74P5 sinh (5%)106F6 0 = -([SOH,+] + [SOH,+-A-])CPS

where \ko is the surface potential, ud and uoare the chargedensities in the diffuse layer and on the surface, respec-tively, C1 and C2 are the integral capacitances, F is theFaraday constant, s is the specific surface area of theoxide, and I is the ionic strength.

Registry No. FeOOH, 20344-49-4; C1-, 16887-00-6; ClO;,14797-73-0.