J. Chem. SOC., Faraday Trans, I, 1982, 78, 3341-3356 Radiation Chemistry of Dilute Aqueous Solutions of Thallous Ion Formation of Colloidal Thallium and its Catalysis of the Reduction of Water by (CH,),cOH and CH$HOH Radicals BY GEORGE V. BUXTON* A N D TREVOR RHODES University of Leeds, Cookridge Radiation Research Centre, Cookridge Hospital, Leeds LS16 6QB A N D ROBIN M. SELLERS Central Electricity Generating Board, Berkeley Nuclear Laboratories, Berkeley, Gloucestershire GL 1 3 9PB Received 26th February, 1982 In the absence of 0, relatively stable (several hours to several days) thallium metal colloids are formed when dilute aqueous solutions of thallous ion ([Tl+l0 z 1.2 x lop4 mol drn-,) are irradiated (dose rate z 10 Gy min-I) under reducing conditions (lo-' mol dm-3 propan-2-01 or ethanol) in the pH range 6-12 in the presence of mol dm-, surfactant (sodium dodecyl sulphate or Triton-X-100).The colloid is also stable at pH 3, but it cannot be formed at this pH because H,O+ competes with TI+ for e&. Once nucleation has occurred, T1+ is reduced by (CH,)$OH and CH,cHOH at the particle surface. Electrophoresis measurements showed that the particles are negatively charged, and kinetic analysis indicated that their mean diameter ranges from 30 nm at pH 3.4 to 24 nm at pH 11.8 under the experimental conditions specified above. Increasing the dose rate or [Tl+] resulted in smaller particles being formed. Colloidal thallium catalyses the reduction of water by (CH,),cOH and (CH,)cHOH, and also catalyses the disproportionation of these radicals.A mechanism is proposed for these processes in which the rate-determining step for hydrogen production is the discharge of H,O+ (low pH) or H,O (pH 2 7) at the metal surface, and radical disproportionation involving electron transfer to and from the particle. The rate constant for the discharge of H,O is estimated to be 820 s-I. The radiation chemistry of aqueous colloidal systems naturally involves the reactions of free radicals at phase interfaces and is a topic of burgeoning interest from several standpoints. These range from the effects of a radiation field on physical properties, the subject of much of the early work,l and the radiation-induced dissolution of metal oxides,, which are of importance in water-cooled nuclear reactor^,^ to catalysis of the cleavage of water into hydrogen and oxygen by free radicals4 and the kinetics of electrode processes.It has been shown recently that ~ i l v e r , ~ ~ 6gold 7 , and cadmium9 metal sols catalyse the reduction of water by reducing radicals such as (CH,),cOH, CH$HOH and CO; -, and that silver sols catalyse multielectron reductions of inorganiclo and organic species.ll The noble metals behave as microelectrodes, accumulating electrons from the reducing radicals until they acquire a negative potential sufficient to cause evolution of hydrogen from water. In this paper we report a study of the preparation and properties of colloidal thallium which, like cadmium, is an electronegative base metal ( E e = -0.336 V). 33413342 RADIATION CHEMISTRY OF AQUEOUS TI+ EXPERIMENTAL All chemicals were AnalaR grade and were used as received.Solutions to be irradiated were made up in triply distilled water. 0, was removed by evacuation. Irradiations were carried out in conventional Pyrex cells fitted with an optical cell on a sidearm. A 6oCo pray source providing a maximum dose rate of 10 Gy min-' was used in the majority of the experiments; in a few cases higher dose rates were achieved using a d.c. beam of electrons from a 3 MV Van de Graaff accelerator. Gaseous products were collected by Toepler pump and analysed by gas chromatography. Solution products were determined by conventional g.1.c. methods. Electrophoresis measurements were made with a Rank Bros. mark I1 instrument using a cylindrical cell configuration. Changes of light transmittance by the colloidal solutions were measured as absorbance using a Pye Unicam SP 8-100 u.v.-visible spectrophotometer.The observed absorbance is due to light absorption and light scattering, but the relative contributions of these two processes to the observed absorbance spectrum have not been established in the present work. RESULTS FORMATION A N D SPECTRA OF THALLIUM SOLS Fig. 1 shows the development of the spectrum due to colloidal thallium formed by the radiolysis of oxygen-free 1.25 x lop4 mol dm-3 T1+ (as Tl,SO,) solution buffered at pH 7 with 4 x mol dm-3 phosphate and containing 10-1 mol dm-3 propan-2-01 and mol dm-3 sodium dodecyl sulphate (SDS). The surfactant is necessary to prevent coagulation and precipitation of the colloid.Similar results were obtained when SDS was replaced by Triton-X-100. No colloid was formed when the solution initially contained N 2 0 or acetone. The developing spectrum shows a gradual red shift with dose up to a dose of ca. 350 Gy followed by a sharper blue shift between 350 and 400 Gy, and no appreciable further change at larger doses. Fig. 2 summarises the spectral changes observed at various pH including neutral unbuffered solution. The colour of these sols was generally purple and the particles were too large to pass through a 25 nm millipore filter. The intensity of the weak absorption band at ca. 300 nm (fig. 1) was roughly proportional to dose at all pH, but the proportionality constant increased abruptly between pH 10 and 11. This is shown in the inset to fig.1. The sharp absorption peak at 216 nm in fig. 1 is due to T1+ and was used to measure the change in concentration of the ion during colloid formation. Different results were obtained depending on whether the absorbance at 216 nm was measured in the presence of the colloid or after precipitating it by repeatedly freezing and thawing the solutions. These are shown in fig. 3, where it is seen that there was a residual [Tl+] of ca. mol dmP3 after colloid formation. The smaller residual concentration observed in the presence of the colloid suggests that most of the ions are on or near the surface of the particles. Electrophoretic measurements showed that the particles were negatively charged whether the surfactant was SDS or Triton-X-100 when the anion was sulphate o r chloride.Electrophoretic mobilities were measured for the thallous chloride/Triton- X-100 system at natural pH and pH 1 1.8, and were 1.8 x lops and 8 x m2 s-l V-l, respectively. The < potential was calculated for these mobilities using the method of Wiersema et a1.12 was found to be 33 mV at natural pH and 83 mV at pH 11.8, corresponding toG . V. BUXTON, T. RHODES AND R. M. SELLERS 3 343 2.c 1 . 8 1.6 1 . 4 1 . 2 aJ K -e 1.0 s: D m 0.8 0.6 0 . 4 0.2 0 wavelength/nm FIG. 1 .-Development of the absorption spectrum of colloidal thallium with radiation dose. Initial conditions: 1.25 x lop4 mol dmp3 T1+, lo-' mol dmF3 propan-2-01, mol dm-3 C,,H,5S0,Na, buffered at pH 7 with 4 x mol dm-3 phosphate. Dose rate 10 Gy min-*. The dose is shown for each spectrum.Inset: Dependence on pH of the rate of increase of absorbance at 300 nm with dose. one negative charge per 70 and 7 nm2, respectively. These results are consistent with T1+ being incorporated into the metal lattice at the particle surface, any excess of anions being held at the surface by electrostatic and chemisorptive effects, and cations being concentrated in the diffuse region of the double layer. The effects of dose rate and the concentrations of TI+ and SDS on colloid formation were examined briefly. The effect of dose rate is shown in fig. 4 and, since smaller particles scatter light of shorter wavelengths, the blue shift in the absorption spectrum with increasing dose rate indicated the formation of smaller particles. The effect of [T1+] is shown in fig.5. By decreasing [SDS] in 1.25 x mol dm-3 T1+ solution it was found that as little as mol dm-3 SDS was sufficient to stablise the colloid. Because of these variations in colloid properties with experimental conditions, the standard conditions, except for pH, chosen for colloid preparation were as detailed for fig. 1 . Colloidal solutions at pH > 7 were obtained by adding NaOH to unbuffered solutions before irradiation, and at pH < 7 by adding HC10, to unbuffered solutions after irradiation.3344 RADIATION CHEMISTRY OF AQUEOUS T1+ FIG. 2.-Dependence on dose of A,,, of the absorption spectrum of colloidal thallium at natural pH (A), pH 7 (O), pH 10.8 (O), pH 11.8 (+) and pH 10.8 with ethanol instead of propan-2-01 (---). 1.25 1.00 m E 5 0.75 E P 0, +, k, 0.5 U --.- 0.25 I I I I I I I '0 d ose/G y FIG. 3.-Decrease in thallous-ion concentration with dose at pH 7 (A) and pH 10.8 (x), and at pH 7 after precipitation of the colloid by freezing and thawing (0). The solid circles represent [TI+], - 2[N,] (see text).G. V. BUXTON, T. RHODES AND R. M. SELLERS 3345 1 .o 0.9 0.8 0.7 0.6 0.5 0 . 4 0.3 0.2 0.1 0 a, E s1 D m I I I I I I I 2 09 400 600 8 00 1000 X/nm Fic. 4.-Effect of dose rate on the spectrum of colloidal thallium at natural pH. [Tl+], = 1.25 x lop4 mol dm--3, dose = 700 Gy. The dose rate (Gy s-') is shown for each spectrum. STABILITY O F COLLOIDAL THALLIUM In air-free solution the colloid was stable for several days at pH 7- 12, and for several hours at pH 3; in more acidic solution the metal dissolved more rapidly.The colloid could be formed at pH 13 but it precipitated as soon as the dose exceeded the formation dose. The colloid dissolved immediately when exposed to air and over a period of hours in the presence of N,O. In the latter case N, and T1+ were produced in the ratio of 1 :2 and the N, yield provided an accurate measure of the amount of T1+ that had been reduced to the metal. mol dm-3 H,O, was added to a sol containing 7 x lop5 mol dmU3 T1 under air-free conditions, the colloid dissolved completely at pH 7 but not at pH 1 1.8 where the colour of the sol changed from purple to yellow. These results indicate that H,O, reacts by different mechanisms in neutral and alkaline solutions and it seems likely that this is the cause of the higher rate of colloid formation at pH > 10 (see fig.1 inset). When 5 x FORMATION OF H, AND ORGANIC PRODUCTS Fig. 6 shows the dependence of the formation of H, and acetone on dose under the same conditions as for fig. 1. The data are characterised by an abrupt increase in G(H,) at the dose where colloid formation is complete from 1.0 to 2.5, indicating catalytic production of H,. Table 1 summarises data for propan-2-01 and ethanol solutions at various pH ; table 2 shows the effect of dose rate on G(HJ for propan-2-01 solutions. Both sets of data relate to yields obtained from linear yield against dose plots after colloid formation (see fig. 6).3346 RADIATION CHEMISTRY OF AQUEOUS TI+ 1 .c 0.9 0.8 0.7 0.6 2 0.5 B % 0.4 0.3 0.2 0.1 0 a, c L I I I I I I 1 1 0 LOO 600 800 1000 X/nm FIG.5.-Effect of thallous ion concentration on the spectrum of colloidal thallium at natural pH for a dose of 200Gy at a dose rate of 10Gymin-'. The concentration of T1+ (moldm-3) is shown for each spectrum. H, was generally measured within 15 min after irradiation, but an experiment at pH 1 1.8 showed that a small amount of the gas (cu. 2.5 x lop6 mol dm-3) was formed at longer times in a thermal reaction (see fig. 6 inset.) SILVER COLLOID For comparison purposes the yield of H, was measured for a colloidal silver solution at natural pH which initially contained 2 x mol dm-3 Ag+, lop3 mol dm-3 SDS, 3 x lo-, mol dm-3 acetone and 10-l mol dmP3 propan-2-01. For a dose rate of 9.7 Gy min-l, G(H,) = 3.38 0.08 after colloid formation was complete and is in good agreement with data from previous SILVER COLLOID COATED WITH THALLIUM It has been shown" that when a solution containing Ag+ and Tl+ is irradiated under conditions similar to the standard conditions described above, silver particles are formed first and subsequently become coated with thallium.Since silver particles under these conditions are much smaller than thallium particles, this experiment provides a method of generating effectively small thallium particles for the purpose of obtaining a relationship between Amax of the absorption spectrum and particle size. Fig. 7 summarises the results obtained on irradiating a solution containing 1.25 x mol dmP3 TI+, 1.6 x lop4 mol dm-3 Ag+, 10-l mol dmP3 propan-2-01, lo-, mol dmP3 acetone and The results show clearly the formation of the silver sol first with Amax at 390 nm, mol dm-3 SDS at natural pH.G .V. BUXTON, T. RHODES AND R. M. SELLERS 3347 250 200 m E E i -0 150 c OJ U 2 100 0 N 50 1 I I I I I I P / / Y. y I 2 '2; 6;. 110 1; time/min / 0 400 800 1200 1 dose/Gy 00 FIG. 6.-Yields of H, (a) and acetone (0) from colloidal thallium solution at pH 7 containing lo-' mol dm-3 propan-2-01. Dose rate = 10 Gy min-l. The broken line represents the theoretical yield of acetone (see text). Inset: Post-irradiation formation of H,. TABLE YIELDS OF PRODUCTS FROM THE RADIOLYSIS OF COLLOIDAL SOLUTIONS OF THALLIUM CONTAINING 0.1 mol dm-3 PROPAN-~-OL OR ETHANOL (DOSE RATE = 10 Gy min-l) colloid PH G(H2) G(organic product) propan-2-01 absenta presentb presentb presentb presentb ethanol absenta presentb acetone natural 1 .OO f 0.05 3.5 f 0.1 natural 4.99 & 0.02 4.90 + 0.02 7 2.50 & 0.04 2.5 + 0.1 10.7 2.1 fO.l 2.06 f 0.03 11.8 1.20 & 0.05 1.24& 0.10 10.8 1 .OO f 0.05 1.5 f 0.2 1.9 +O.1 10.8 1.39f0.05 0.25k0.05 1.10+0.05 butane-2,3-diol acetaldehyde a Solution saturated with N,O. Yields obtained from the slopes of linear yield against dose plots after formation of colloid was complete. followed by the coating with T1 which shifted Amax progressively to the blue until it reached 350 nm and remained constant when no further reduction of Tl+ occurred. When N,O was added to the colloidal system, the thallium metal dissolved as before and the silver sol remained with almost the same spectrum as the initial one.3348 RADIATION CHEMISTRY OF AQUEOUS TI+ TABLE 2.-EFFECT OF DOSE RATE ON G(H,) FROM COLLOIDAL SOLUTIONS OF THALLIUM CONTAINING 0.1 mOl dm-3 PROPAN-2-OL pH dose rate/Gy min-la G(H,) 3.4b7C 10 naturalb 10 7 10 2.0 2.0 1.9 0.7 10.8 9.7 2.0 2.9 & 0.1 3.25 f 0.03 2.28 & 0.02 2.76 0.02 2.50 L 0.04 3.15 & 0.05 3.28 & 0.02 2.1 kO.1 2.85 & 0.05 a Dose rate was varied after the formation of colloid was complete; 0.03-0.05 mol dm-3 acetone added after colloid formation (see Discussion section); pH adjusted with HClO, after 2 .o 0.5 a, 5 -E s: -2 1.0 0.5 0 I I I I I 1 1 200 300 400 500 600 h/nm FIG.7.--Spectrum of thallium-coated silver colloid (-), silver colloid (. . .), and silver colloid after dissolution of the thallium coating by N,O (---). [Ag+], = 1.6 x mol dm-3, [TI+],, = 1.25 x loe4 mol dm-3, natural pH, dose rate = 10 Gy min-I.G.V. BUXTON, T. RHODES A N D R. M. SELLERS 3 349 DISCUSSION MECHANISM OF THALLIUM COLLOID FORMATION The radiolysis of water is described by reaction (1) H20*ecq, H, OH, H,, H20,, H+ ( 1 ) and Geiq = Go, = GH+ = 2.7, G, = 0.6, GH2 = 0.4 and GH2O2 = 0.6 are the yields (molecules per 100 eV) of the primary species appropriate to our experimental ~0nditions.l~ The radicals formed in reaction (1) can react as follows ecq + T1+ -+ T1° (2) eiq + H+ -+ H (3) (4) ( 5 ) H+RHOH -+ROH+H2 (6) (7) (8) H2O ecq+RO-+RO- -+ ROH+OH- H,O eLq + N20 + N, + 6- -+ OH + OH- OH + RHOH + ROH + H 2 0 ROH + ROH + RO + RHOH ROH + ROH -+ HORROH (9) where RHOH represents propan-2-01 or ethanol, ROH is (CH),),oH or CH$HOH etc.Although OH is known not to abstract a hydrogen atom exclusively from the carbon atom carrying the hydroxy group,14 the product yields from N,O-saturated solutions of ethanol and propan-2-01 (table 1) are consistent with all other radicals being transformed into (CH,),eOH or CH,cHOH, through a radical transfer reaction with the parent alcoho1,15 before disproportionation or combination can occur. - E* for Tlo/T1+ is estimated to be - I .9 V,16 so that eGq ( E e = - 2.7 V) is the only species capable of reducing T1+ since E* for (CH,),cOH and CH$HOH are - 1.5 and - 1.1 V, respectively.li This is confirmed by our observation that T1+ was not reduced when the solution initially contained acetone or N,O, i.e. when reaction (2) was suppressed by reactions (4) or (5).However, fig. 3 shows that G( - TI+) increased after some colloid had formed, and this may be explained by a lowering of the reduction potential of T1+ on or near the metal surface so that reaction (10) can occur ROH + TI&rface -+ T1:urface + RO + H+. (10) The larger initial G( - T1+) at pH 10.8 (fig. 3) is probably due to ionisation of a fraction (ca. 4%) of the (CH,),COH radicals (pK = 12.29 since ES for (CH,),cO- is estimated to be - 2 . 2 V.17 CATALYTIC ACTION OF COLLOIDAL THALLIUM Once the colloid has been formed, all the radicals produced in reaction (1) form ROH through reactions (4), (6) and (7). The data in table 1 show that at this stage the overall reaction taking place is RHOH + RO+H,3350 RADIATION CHEMISTRY OF AQUEOUS TIS i.e.the thallium colloid catalyses the dehydrogenation of the alcohols. In reality, reactions (8) and (9), which occur in the bulk solution, are replaced to some extent by reaction (I 1) T1 ROH + ROH + 2R0 + H, (1 1) but half of the ROH are generated from the product RO through reaction (4). In unbuffered solution at natural pH, H+ increases through reaction (10) and reaction (3) becomes faster than (4). Thus RO is protected but an equivalent amount of H, is formed via reactions (3) and (6) (see table 1). Nevertheless, the yield of catalytic H, can still be measured in acidic solution by adding sufficient acetone to the colloidal solution to ensure that reaction (3) does not occur (see table 2). The extent of reaction ( I I ) is given by for which the maximum value will be G(H2)excess = .fG(ROH) = 3.0.In practice the largest measured G(H2)excesS for thallium colloid was 2.3 (see table 2) compared with 2.4 for the silver colloid. In the latter case it was proposed5 that the shortfall in G(H,) is due to reoxidation of the metal by H,O, in a two-electron process. Such a reaction would explain the H, yields at pH 7 in the thallium case and also account for the complete dissolution of 7 x mol dm-3 T1 by 5 x mol dm-3 H,O, that was observed. At high pH, however, both the effect of added H,O, and the increased rate of colloid formation are consistent with H,O, acting as a one-electron oxidant above pH 10 (see fig. 1 inset). This change in mechanism with pH might be associated with the ionisation of H,O, (pK = 1 1.75) at the particle surface, since the electrophoresis measurements are consistent with the hydroxide-ion concentration being higher at the surface than in the bulk solution. The overall result of one-electron oxidation by H,O, is its catalytic decomposition through reaction (12) followed by (7) and (10) (12) With increasing pH G(H2)excess becomes quite small, indicating that reaction (1 1) is no longer efficient.Similar observations have been reported for silver5 and gold8 sols, and have been ascribed5* to the catalysed disproportionation of ROH througn one radical donating an electron to, and the second radical accepting an electron from, the metal particle. The data for propan-2-01 in the absence of colloid (see table 1) show that (CH,),COH only disproportionates in the bulk solution [reaction (S)], whereas for ethanol 43% of CH3cHOH combine [reaction (9)]. In the latter case, therefore, catalysed disproportionation will show up as an increase in the yield of acetaldehyde relative to butane-2,3-diol.Thus the data for ethanol (table 1) provide clear evidence for the catalysed disproportionation of ROH at high pH. H,O, + T1+ Tl+ + OH + OH-. SIZE OF THE COLLOID PARTICLES In order to elucidate the reactions of ROH at the colloid surface it is necessary to know what fraction of the radicals actually reach the surface, which in turn requires a knowledge of the size and shape of the particles. Because of the instability of colloidal thallium in air we have been unable to examine the sol by electron microscopy, and attempts to use light-scattering methods were unsuccessful.We believe, however, thatG. V. BUXTON, T. RHODES A N D R. M. SELLERS 3351 meaningful average particle sizes can be obtained using a kinetic method as outlined below. We begin with the propan-2-01 system at pH 3.4 and assume that (i) all (CH,),COH reaching the particle surface form H,; (ii) the radicals donate an electron on the first encounter (i.e. the reaction is diffusion controlled); (iii) the particles are uniform spheres and have the same density as thallium metal (p = 11.85 g cm-,); (iv) the competing reactions involving (CH,),t)OH are 2 (CH,),COH -+ disproportionation in the bulk solution (CH,),t)OH -+ diffusion to the particle surface. (1 3) (14) Then under steady-state conditions for (CH,),COH (R) d[R1 = 0 = G(R) d - 2kl3[RI2 - k14[R] [PI (1) dt where G(R)d is the rate of formation of R [G(R) is the yield of R and d the dose rate in appropriate units], and P represents a thallium particle. When reaction (14) is diffusion controlled 4nrP D, N 1000 N - since rp % rH.and DR % D,, where r and D are radius and diffusion coefficients, respectively, and N is Avogadro's number. The concentration of particles is given by MTlO1 [PI = ~ Nm where A4 is the molecular weight of T1 and rn = g r i p is the mass of a particle. Hence 3M[T1°] DR 1OOOrbp ' k14PI = The fraction,f, of radicals that reach the particle surface is given by and eqn (I) and (11) can be solved for kI4[P], and hence rp. Taking D, = cm2 s-l, 2k1, = 1.5 x lo9 dm3 mol-l s-l,19 GHtO, = 0.6 and G(R) = 6.0 gives rp = 15.4f 1.1 nm and 15.5 kO.9 for dose rates of 10.0 and 2.2 Gy min-l, respectively.The agreement between these two values indicates that the assumptions made in their calculation are valid. The data for the ethanol system can be treated in an analogous way. In this case not all the radicals reaching the surface form H,, but the alternative assumption made is that butane-2,3-diol is only formed in the bulk solution and is therefore a measure of the number of radicals that combine or disproportionate in the bulk solution.3352 RADIATION CHEMISTRY OF AQUEOUS TI+ Taking D, = cm2 s-l and 2k, = 2k, = 2.3 x lo9 dm3 mol-l s-' gives rp = 14.4 0.9 nm, which is in good agreement with the values of rp calculated from the propan-2-01 data. In fact, this slightly smaller value for the ethanol system is consistent with the blue shift in A, (see fig.2). The data for the silver sol coated with thallium (see fig. 7) provide further information on the relationship between A, and particle size for colloidal thallium. Since the exterior of these particles consists of a shell of thallium they are expected to have the optical properties of a small thallium particle. The radius of the silver particles is taken to be 7 nm6 and the thallium coated particles are calculated to have a radius of 8.7 nm. Fig. 8 shows that the limited amount of data available conform to a linear relationship between A, and particle size. 81 I I I I 300 400 500 600 700 ~rnaxlnm FIG. 8.-Dependence of A,,, of the spectrum of colloidal thallium on particle size (see text).OXIDATION A N D REDUCTION OF R o H AT THE PARTICLE SURFACE Knowing the size of the particles, it is possible to calculate the yield of radicals that donate, G(R),,, or accept, G(R)red, electrons at the surface using the following relationships for pH < 10: and the same relationships without the term GHZo2 for higher pH. The results obtained, using the data in fig. 8 to estimate particle size, are listed in table 3. KINETICS OF SURFACE REACTIONS It is clear from the data in tables 2 and 3 that colloidal thallium catalyses both the reduction of water by ROH and their disproportionation, the latter reaction becoming more important in alkaline solution. These features relate to the mechanism of hydrogen evolution on a thallium surface.G . V. BUXTON, T.R H 0 4 E S AND R. M. SELLERS 3353 TABLE 3.-CALCULATED YIELDS OF (CH,),t'OH RADICALS WHICH ARE OXIDISED OH REDUCED AT THE COLLOID SURFACE 3.4 15.5 10.0 2.0 natural 15.5 10.0 2.0 7 13.8 10.0 1.9 0.7 10.8 12.2 10.0 2.0 11.8 11.8 10.0 10.8" 14.4 10.0 0.83 0.95 0.83 0.95 0.88 0.97 0.99 0.92 0.97 0.93 0.8 1 5.0 5.7 4.35 5 . 4 4.75 5.67 5.85 3.91 5.72 3.0 2.82 0 0 0.60 0.35 0.55 0.17 0.09 1.60 1.05 2.58 2.04 " Data for CH,t'HOH. The process of hydrogen disLharge at a cathodically charged metal is generally assumed to be as follows: Volmer or discharge reaction M+H++e- + M-H M + H,O + e- --+ M-H +OH- (16) followed by Heyrovsky or electrochemical reaction M-H+H++e-+M+H, M-H + H,O+e- + M + H, + OH- (18) M-H+M-H +2M+H, (19) where M-H represents a hydrogen atom adsorbed on the surface of the metal.Theories put forward to account for hydrogen overvoltage are based on one of these three reactions being rate limiting. We show below that our data for colloidal thallium are consistent with reaction (1 6) being the slow step in neutral and alkaline solution. If we represent a thallium particle in its equilibrium state as Tl,, having T1+ on or near the surface, then the reactions in which electrons are removed from the particles can be written as or Tafel or catalytic reaction -TI+ kOH + Tl,,, + T1, + RHOH +OH- (20) HzO -,TI+ 2H,O + TI,,, -+ Tl,-l + 20H-+ H, -ZTP H,O, + Tl,,, -, Tl,-l + 20H-3354 RADIATION CHEMISTRY OF AQUEOUS TI+ and reactions in which electrons are donated to the particles as T1+ ROH + Tl,-, + T1, + RO + H+ Tlf ROH +TI, + Tl,,, + RO + Ht.T1, and Tl,-, may be regarded as oxidised, and Tl,,, as reduced, forms of the colloid. Under catalytic conditions where the rates of the charging and discharging reactions are equal, the steady-state approximation may be applied to ROH, Tl,-,, Tl,,, and H,O,. This treatment leads to the following expression for k21: and the same expression without the term 2GHzO1 at high pH when H,O, is a one- electron oxidant. The assumptions made in deriving eqn (111) are that k,, = k,, = k,, (all diffusion controlled) and The mechanism of reaction (21) may be written as follows: Volmer reaction -T1+ H,O + Tl,,, + TI,--H +OH- T1+ OH-+ TI, - H + Tl,,, + H,O Heyrovsky reaction -T1+ H,O + Tl,-H + Tl,-, + H, + OH- Application of the steady-state approximation to TI,-H gives eqn (IV) for k,, k25 k - 21 - 1 +k,,[OH-]/k,,’ Values of k,, can be determinted from experimental quantities using eqn (111) and hence k,, and k,,/k,, can be calculated using eqn (IV).Fig. 9 shows a comparison of the values of k,, determined experimentally with calculated values obtained using eqn (IV) with k,, = 8.2 x 10, s-l and k26/k2, = 8.2 x lo3 dm3 mol-l. The two sets of data agree reasonably well over the pH range 7-1 2 and for dose rates 0.7- 10 Gy min-’, showing that the proposed mechanism of H, evolution is consistent with the experimental data. We conclude, therefore, that the Volmer reaction (16) is the rate-determining step for thallium. This is not unexpected, since thallium has a relatively high hydrogen overvoltage and low adsorption energy for hydrogen atoms.20 In the kinetic analysis outlined above it is implicitly assumed that [T1,-HI 6 [Tl,,,], and therefore that reactions between ROH and TI,-H can be neglected.This assumption seems to be justified by the data in fig. 9, and is easily rationalised if reaction (25) is the rate-determining step.G. V. BUXTON. T. RHODES AND R. M. SELLERS 3355 7 8 9 10 11 12 PH FIG. 9.-Dependence of k,, on pH for dose rates of 10 Gy min-I (O), 2 Gy min-I (A) and 0.7 Gy min-I ( x ). The solid circle represents k,, when propan-2-01 is replaced by ethanol (dose rate 10 Gy min-I). The solid line is calculated with k,, = 820 s-I and k,,/k,, = 8.2 x lo3 dm3 mol-' (see text). In acidic solution it is expected that reactions (28) and (29), equivalent tc reactions (15) and (17), will occur, so that eqn (IV) simplifies to eqn (V) -Tlf H++Tl,+, -, Tl,-H -TI+ H++Tl,-H -P Tl,-,+H, This accounts for the fact that G(H,) is larger at pH 3.4 than at pH 7 (see table 2) since reaction (20) will be less able to compete with reaction (21) under these conditions.In calculating the particle size at pH 3.4 we,assumed that reaction (20) did not occur at all, which implies that the diffusion of ROH to the particle surface is the rate-determining step. The colloidal thallium particles may be treated as microelectrodes by analogy with other colloidal systems.,, 9 9 21 It has been pointed out2, that the microelectrode will acquire a mixed potential under steady-state conditions corresponding to equal anodic and cathodic currents. In the present case the anodic current is generated by reaction (24) and the cathodic current by reactions (20) and (21), which are in competition.Thus the mixed potential attained by the particle will be independent of pH below the pK of the radicals as long as reaction (20) takes place. This differs from the usual electrochemical situation where the hydrogen evolution reaction is the sole cathodic reaction and is pH dependent.22 Henglein23 has discussed redox reactions of free radicals at electrodes in terms of the distributions of their electronic energy levels. Catalytic disproportionation of (CH,),cOH and CH,cHOH and H, formation at a thallium particle requires that the energy distributions of occupied and unoccupied electronic levels in the radicals overlap with one another at a potential where reduction of water can occur.This3356 RADIATION CHEMISTRY OF AQUEOUS TIS potential is -0.7 V at pH 11.8, so the thallium particles must acquire at least this value. As noted earlier, the values of Ee for (CH,),cOH and CH,cHOH are - 1.5 and - 1.1 V, respectively,16 so that the particles will acquire a negative potential which is lower in the ethanol system than in the propan-2-01 system. This explains the observation (see tables 1 and 3) that reaction (21) competes less with reaction (20) at pH 10.8 when ROH is CH,cHOH than when it is (CH,),cOH. An implication of this interpretation of the surface disproportionation of ROH is that these radicals also disproportionate in the bulk solution by an electron-transfer mechanism, as has been suggested before.,, The slow post-irradiation formation of H, (see fig.6 inset) at pH 1 1.8 indicates that the thallium particles store an excess of electrons during irradiation, as has been observed for silver,6 gold8 and cadmium sols. From the amount of H, formed (2.5 x lod6 mol dm-,) the quantity of stored charge, Q,, at the steady state is ca. 0.5 C dmP3 when the charging rate is 0.6 C dmP3 min-l. 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