J. Phys. Chem. 1983, 87,1004-1008
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Medium Effects in Chromium( III)Photochemistry. Dynamic vs. Static Processes in Tris(bipyridine)chromium(II I)and trans-Diammine(tetrathiocyanato)chromium( I I I ) Ions in Acetonitrile-Water Mixtures' Mary A. Jamieson, Cooper H. Langford, Nick Serpone, *' Department of Chemlsfry, Concordk Unlversify9Montreal H3G 1M8, Canada
and Mark W. Hersey Department of Chemisfry, Carleton Unkersify, Ottawa K1S 566, Canada (Received October 20, 1982)
Preferential solvation data of C r ( b p ~ ) (bpy ~ ~ += 2,2'-bipyridine) in acetonitrile-water solvent mixtures and obtained from NMR line width measurements are reported and discussed in relation to those of the Reineckate anion, trans-[Cr(NH3),(NCS),1-, reported earlier. Lifetimes, luminescence intensities, and photosolvolytic reactivity from the lowest-energydoublet states, ,T1/,E, of C r ( b p ~ )are ~ ~reported + for the whole mixed-solvent composition range, 0 IXCH~CN I 1. It is shown that the doublet excited-state properties follow preferential solvation curves for the Reineckate ion but not for the Cr(bpy):+ cation. This has been interpreted in terms of static effects of solvent on such properties for the the former ion, and dynamic effects for the latter complex. The difference between these two effects is illustrated.
Introduction Recently, several groups have reported on the sensitivity of photoprocesses in Cr(II1) complexes to medium changes.*' A basic question in understanding such effects is to distinguish those effects which are static, and depend upon prior encounters with the relevant medium component in a manner analogous to static quenching, from those effeds which are dynamic and involve diffusional processes in solution. To make such distinctions, it is useful to have information on the distribution of solvent molecules around the complex. In the case of chromium(II1) complexes, a nuclear magnetic resonance method for the determination of preferential solvation of the complexes in mixed solvents has been applied to a variety of kinetic problems in mixed solvents.* In this paper, we consider the preferential solvation of trans-[Cr(NH3),(NCs),1- and Cr(bpy)SS+(bpy = 2,2'-bipyridine) ions in CH3CN-HzO mixtures and show that doublet excited-state properties follow preferential solvation curves for the first complex but not for the second. This suggests "static" effects of solvent on the Reineckate ion and "dynamic" effects on the bipyridylchromium(II1) complex. As expected, the dynamic effects follow concentration laws like the Stern-Volmer relation. The new data presented here include the preferential solvation data of C r ( b ~ y ) , ~in+ CH3CN-H20 mixtures, along with a study of the phosphorescence intensities, and the photosolvolysis of the complex in these mixtures. The results are compared to the data on the Reineckate anion, trans-[Cr(NH3),(NCS),1- (henceforth R-) reported by Adamson3 and by Langford and co-w~rkers.~The two complexes are well suited to illustrate the difference between static and dymamic effects since, in water, the (1) Supported by Formation des Chercheurs et Action ConcerMe du Quebec and Natural Sciences and Engineering Research Council, Canada, and by the North Atlantic Treaty Organization (No. 046.81 to NS). (2) To whom correspondence should be addressed. (3) Gutierrez, A. R.; Adamson, A. W. J. Phys. Chem. 1978, 82, 902. (4) Cusumano, M.; Langford, C. H. Inorg. Chem. 1978, 17, 2222. (5) Wong, C. F. C.; Kirk, A. D. Can. J. Chem. 1975,54, 3794. (6) Henry, M. S.; Hoffman, M. Z. Adu. Chem. Ser. 1978, 168, 91. (7) Porter, G. B.; VanHouten, J. Inorg. Chem. 1979,18,2053; 1980,19, 2903. (8) Langford, C. H.; Tong, J. P. K. Acc. Chem. Res. 1977, 10, 258. (9) Sastri, V. S.; Henwocd, R. W.; Behrendt, S.; Langford, C. H. J. Am. Chem. SOC.1972,94, 753.
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doublet lifetime of R- is -6 ns3 and therefore may survive but only for a few successive encounters, whereas the doublet lifetime of C r ( b ~ y ) , ~is+-60 ps, long enough to allow thousands of successive encounters with the solvent components.
Experimental Section Materials. Tris(bipyridine)chromium(III) perchlorate trihydrate was prepared as previously described.'O Spectrograde acetonitrile and distilled, deionized water were used for solution preparation. Common reagents were of commercial analytical grade and were used without additional purification. Phosphorescence Measurements. Luminescence intensities were measured with a Perkin-Elmer MPF-44B spectrofluorimeter at 22 "C; the concentration of Cr(bpy):+ was 1.54 X lo4 M. Excitation wavelength was 400 nm and emission intensity at 727 nm was obtained by recording the emission spectrum from 680 to 750 nm; slits were 10 nm. Lifetime measurements were made with a pulsed N2 laser system of local design and previously described.1° Quantum Yield Measurements. Quantum yield determinations for the disappearance of Cr(bpy):+ were carried out in a manner similar to that described earlier for Cr("):+.lo Exactly 3.00 mL of a solution of Cr(bpy)QS+in the appropriate, air-equilibrated CH3CN-H20 solvent medium ([Cr3+]= 1.3 X M) was irradiated (for successive periods of time at 313 nm) in a 1-cm quartz cell thermostated to 22 "C; the absorption spectrum (PerkinElmer Model 552 UV-vis spectrophotometer) of the solution was recorded after each irradiation time up to -10% absorbance change at the 400-nm monitoring wavelength. Stirring during irradiation was accomplished by bubbling compressed air through the solution. A sample of unirradiated solution was kept in the dark at 22 "C and analyzed in the same way to account for the thermal component. The loss of C r ( b p ~ ) due ~ ~ +to successive irradiations was determined from the decrease in absorbance at 400 nm, and a plot of [ C r ( b ~ y ) ~vs. ~ +irradiation ] time was con(10) Serpone, N.; Jamieson, M. A.; Sriram, R.; Hoffman, M. Z. Inorg. Chem. 1981,20, 3983.
0 1983 American Chemical Society
Medium Effects in Chromium(II1) Photochemistry
structed. Where there were deviations from linearity, the initial slope was utilized to determine the rate of loss of Cr(bpy),3+,RrX.The quantum yield, a,, was obtained as the ratio of the slope R,, to the absorbed light intensity, I,. Wn (=0.11) for C r ( b ~ y ) , ~at+22 "C in air-equilibrated solutions and pH 9.5 (0,008 M Britton-Robinson buffer" and 1.0 M NaC1) was determined by ferrioxalate actinometry (-2 X 10" einstein min-l). A comparison of the rate of loss of the complex in various CH3CN-H20 media (R,) with that at pH 9.5 (R:x) leads to arX = ~'nR,x/R',x. All experiments were performed in dim, red light. Continuous photolyses were performed with an Oriel 1-kW Hg-Xe lamp fitted with a 0.25-m Bausch and Lomb grating monochromator (22-nm bandwidth). The light beam was previously passed through an 8-cm path of cooled, distilled water to avoid IR heating of the sample. Preferential Solvation Studies. In McConnell's fast exchange regime,12the paramagnetic solute contribution to the relaxation of the solvent NMR signals can be expressed as TAU = 1/T2 = P A / T ~+AP B / T 2 B (1) where Av is the width at half-height of the solvent NMR line, T2is the observed average relaxation time, Tu is the relaxation time in the bulk diagmagnetic environment, and PAis the probability that the proton is in the bulk environment (PA 1.00 in dilute solution). T2Bis the relaxation time in the paramagnetic solvation shell environment and PBis the probability of finding the observed nucleus in that environment. The ratio of P B / T 2 B can be determined from excess line width measurements as P B / T 2 B = 1/T2- l/Tu where l/TMis measured from the intercept of plots of line widths vs. concentration of the paramagnetic substance, and/or measurement in solvent without paramagnetic solute. (The two agree in the present cases.) TB cannot be determined in absolute terms with sufficient precision to allow calculation of accurate absolute solvation numbers from PB.However, comparison of a neat solvent to a mixed solvent can be done either with the assumption that T2B= TZB0 (where the superscript zero denotes neat solvent and no superscript refers to the same proton signal in the mixed solvent) or with correction of 1/T2 for changes in T2Bdue to changing v i s ~ o s i t y . ~Hence, ~~~~ PB/PBo can be estimated reasonably accurately. This easily gives13J4the ratio in n/no,which represents the number of solvent molecules solvating the paramagnetic complex in the mixed solvent medium compared to the number solvating that complex in the neat solvent. A check on the correctness of handling of T2Barises from the agreement of n/nodata obtained from nuclei on the two components of the mixture. The NMR spectra were recorded on a Varian T-60 spectrometer at 35 "C with careful attention to phasing. Line widths were measured from absorption spectral records.
The Journal of Physical Chemistry, Val. 87, No.
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xcnJCN Flgure 1. Preferential solvation data of Cr(bpy)2+ at 25 OC plotted as n l n vs. mole fraction of CH,CN for CH,CN-H,O mixtures. Solid circles show values of nln, derived from NMR line widths of H,O protons; open circles refer to data derived from the methyl protons of CH,CN. For meaning of n and no, see text.
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Results and Discussion Preferential Solvation Curves. The preferential solvation data for both C r ( b p ~ )and ~~+ trans-[Cr(NH3),(NCS),1(R-) in CH3CN-H20 mixtures are presented in Figures 1 and 2, respectively. Note that both complexes in the ground state are preferentially solvated by acetonitrile at XCHICN > 0.1. The extent to which preferential solvation (11) Mongay, C.; Cerda, V. Ann. Chim. (Paris) 1974,64, 409. (12)McConnell, H.M.; J. Chem. Phys. 1958,28, 430. (13) Frankel, L. S.; Langford, C. H.; Stengle, T. R. J. Phys. Chem. 1970,74, 1376. (14) Langford, C. H.; Stengle, T. R. In LaMar, G. N., Harrocks, W., Holm,R. H., Ma.;"NMR of Paramagnetic Molecules";Academic Press: New York, 1973; Chapter 9.
0
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XCH~CN Flgure 2. Preferential solvation data of Wans-[Cr(NH,),(NCS),]- at 25 O C . Circles denote data from the NMR line widths of CH,CN proton; squares show values of nln, derlved from the NMR line widths of water protons. Reprinted from ref 9.
tends to be expressed in CH3CN-H20 is a function of the nonideality of the mixture of these two solvents.* The solvent pair is especially favorable for demonstrating the preferential solvation phenomenon because of the large positive deviation from Raoult's law behavior of both components. To put the matter informally, "a little bit of either constituent goes a long way". In consequence, we see that the equisolvation point (the point at which the composition of the solvation shell contains equal numbers of moles of each) occurs at about XCHSCN = 0.1. This is the point at which the thermodynamic activity of acetonitrile in mixtures reaches about 90% of the activity of acetonitrile in neat CH3CN. This situation affords an interesting opportunity to probe the different static and dynamic processes involving excited states in view of the strong similarities evident in the solvation curves of the two complexes. Static processes will show a simple relation to n/no curves inasmuch as these define the encounter situation of the excited state at the time of its formation. However, when preferential solvation by either component is strong, the immediate solvation environment about the ion can be very different from the bulk solvent composition. In this case, dynamic processes will show a dependence on solvent composition which is very different from n/no. That is, the probability
The Journal of Physical Chemistry, Vol. 87, No.
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Flgure 4. Effect of added acetonitrile on the relative luminescence intensity and emission lifetime of (?1/2E)Cr(bpy),3+ species expressed as a function of mole fraction of acetonitrile. Temperature is 22 OC; air-equilibrated solutions; [Cr(b~y),~+] 1.5 X lo-' M.
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Flgure 3. Dependence of emission lifetime of (*T#'E)Cr(bpy)2+ species on solvent composition expressed as mole fraction of acetonltrlle. Closed circles denote data obtained in air-equillbrated solutions; open circles refer to data for argon-purged solutions.
of dynamic collision is more nearly related to bulk composition and not overwhelmed by preferential local solvation. The remainder of this report is devoted to a discussion of static and dynamic quenching of the phosphorescence of the lowest doublet excited state of chromium(II1) species, and the effect of solvent on photochemical ligand substitution. The two cases, R- and C r ( b p ~ ) ~differ ~ + , in an important respect which rather "stacks the deck". The doublet lifetime of R- is in the (ns)time domain and, consequently, the excited state is rather short-lived for any but static processes. By contrast, the doublet lifetime of Cr(bpy)gB+is in the 104-s (ps) domain, and therefore quite favorable for dynamic processes. Emission Lifetimes. Previously, Henry and Hoffmans noted that, in nitrogen-purged aqueous solution at 22 "C, the transient absorption spectrum of the 2Tl/2Estate of C r ( b p ~ )decays ~ ~ + via first-order kinetics with k = 1.6 X lo4 s-l ( T 63 ps). Within one standard deviation (0.3 X lo4 s-l), the decay rate was unchanged in the solvent systems CH3CN-H20 (0 IXCGcNI1)and DMF-H20 (0 I XDMF I 0.1). Henry15 concluded that solvent polarity changes do not effect sufficient perturbation to alter the rate of nonradiative decay, within experimental uncertainty. Recently, VanHouten and Porter' reported that the lifetime of the 2Tl/2Estate of C r ( b p ~ ) in ~ ~oxygen+ free, neat DMF (XDW = 1.0) is 3 f 1ys. Throughout the I1, the doublet lifetime decreases exrange 0 I XDMF ponentially with increasing ratio of DMF/H20 in parallel with the emission intensity, suggesting that quenching by DMF must involve an increase in the nonradiative rate constant of 2T1/2E,while the radiative rate constant remains unchanged. Clearly, the decrease in luminescence intensity is not the result of decreased efficiency in populating 2T,/2Efrom the precursor state "T2(note that the solvent composition range for DMF-H20 was very small, 0 . 1 mole fraction in DMF in the work of Henry15). As noted above, to the extent that T ( ~ T , / ~ is E )very long compared to solvent exchange, the doublet species encounters many nonaqueous solvent molecules during its lifetime. This implies6that the presence of the nonaqueom solvent component in the first solvation sphere of the 2T1/2Ecomplex is not sufficient for reaction; thus, the nonaqueous solvent appears not to introduce any static
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(15) Henry, M. S.
J. Am. Chem. SOC.1978.99, 6138.
0 0
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Flgure 5. Dependence of the photosolvoiysis quantum yield, @,x, on the solvent composition for Cr(bpy):+ in CH3CN-H 0 mixtures. Tem= 1 X 104-2 X 10'M; air-equiiibrated perature, 22OC; [Cr(bpy):+] solutions.
quenching process for deactivating the doublet state. Figure 3 demonstrates that 7 of the doublet states varies as a function of solvent composition in both air-equilibrated and argon-purged solutions. It is worth noting also that T in argon-purged pure water (XcH3CN= 0) is -62 ps and is -50 ps in argon-purged neat acetonitrile solutions. We now understand the discrepancies in the values of the lifetimes reported earlier. Previously, the above values in water and acetonitrile were takens to be identical within experimental uncertainty (standard deviation 10-15 ys) in studies of transient absorption decay. The parallelism between relative emission lifetimes and phosphorescence intensities (Figure 4) in CH3CN-H20 negates a decrease in the intersystem crossing efficiency (see below); rather, the variations arise from an increase in the nonradiative decay mode, 2kN, in the relaxation of the doublet species, at least in the range 0 IXCH3cN I0.7 where the species appear to be diffusionally quenched by the nonaqueous solvent. At XCH3CN > 0.7 there is a significant increase in the lifetimes in oxygen-free CH3CN-H20 solutions, which probably reflects a decreased chemical quenching by the water molecules (compare, for example, Figures 3 and 5 in this range). Phosphorescence Quenching. The phosphorescence lifetime of R- varies from 6 ns in H20 to 106 ns in CH3CN? , T~ is the lifetime in Figure 6 shows a plot of T ~ / . T where neat acetonitrile and T the lifetime in the mixed solvent, vs. mole fraction of water and n/no (H20). It is seen that T o / r is linear in n / h but has no simple dependence on bulk solvent composition. This is as expected for a static quenching process. Water quenching is proportional to the number of 1:l encounters. Water molecules are equally effective in all solvation positions. In the case of thermal substitution reaction kinetics, linearity in n/nowas shown
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The Journal of Physical Chemistry, Vol. 87,No. 6, 1983
Medium Effects in Chromium(I1I) Photochemistry
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Figure 6. Effect of water on the relative emission lifetimes of IX"[Cr(NH,),(NCS),]in acetonitrile-water solvent mixtures. Open ckcles denote T , / T vs. mole fraction of water; solid circles denote T,/T against nln, of water. Reprinted from ref 3.
TABLE I : Solvent Dependence of the Doublet Emission Lifetimes and Luminescence Intensity for C r ( b ~ y ) ,in ~+ Acetonitrile-Water Mixture
0.944 0.892 0.843 0.798 0.716 0.659 0.494 0.400 0.340 0.256 0.186 0.128 0.079 0.037 0 a
22 23 20 19 19 22 23 26 26 29 30 35 37 37 37
0.97 0.95 0.93 0.90 0.85 0.82 0.76 0.70 0.62 0.56 0.48 0.40 0.23 0.13 0
22 "C; air-equilibratedsolutions.
0.45 0.46 0.44 0.4 2 0.42 0.4 5 0.52 0.60 0.59 0.62 0.66 0.70 0.81 0.79 0.8
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W,Ol, n Figure 7. Stern-Volmer plots for the water quenching of the phosphoresence intensity and emission lifetimes for Cr(bpy):+ in acetonitrile-water solvent mixtures range, 0.8-1.0): (a) S o l i circles denote I,data while open circles denote lifetime data. Temperature, 22 OC; air-equilibrated solutions; [Cr(bpy):+] 1.5 X IO4 M. (b) Same conditions but argon-purged solutions; note that the slope here gives k, directly (see text).
(b
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diative decay rate constant, qisc is the intersystem crossing efficiency, and T refers to the lifetime of the 2Tl/2Estates. The estimation of the solvent dependence of kmd is a little uncertain but the only obvious factor is the refractive index. Inasmuch as the refractive indices of the solvents are close (water = 1.333; acetonitrile = 1.342), it is reasonable to assume that & ItEd. It is also well established16that vCc 1.0. Thus
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@/IF = o L ( T ~ / T ~ )
Arbitrary units,
to reflect one-to-one reaction of the solvolytically reactive solvent with the complex without significant involvement of the other solvating molecule^.^*^ That is, each solvent molecule is an independent nucleophile. This would be consistent with the suggestions of Gutierrez and Adamson3 that quenching of R- is by substitution reaction. However, the example of linear n/no dependence in thermal nucleophilic substitution is Cr(NCS)63- and not R-. The solvent dependence of solvent substitution at R- is somewhat more complex and reflects both nucleophilicity and a role of H-bond acceptance from the ammine ligand? Table I and Figure 4 present results on the solvent dependence of the relative lifetime and phosphorescence T ~ $/IF, reintensity of C r ( b ~ y )expressed ~~+ as T ~ / and spectively. The first point to note is that the situation is more complex, as is immediately indicated by the fact that a plot of relative T'S as a function of solvent composition in Figure 4 is not monotonic. We begin the analysis by comparing the data from lifetimes to those from phosphorescence intensity. Using superscripts H and S to designate H 2 0 and a solvent mixture, respectively, we write
(@/I/? = (@:hos/@%~)
1.0
(kSad/kfI,d)(O~//~c;fc)(TS/TH)
(3)
To the extent that I and T map the same solvent dependence, we conclude that & remains approximately 1.0 throughout the whole solvent mixture domain. The test of the parallelism of this mapping between I and T is best carried out while examing the mechanism of quenching of Cr(bpy):+ by water. In the water-poor region of the solvent composition range, an ideal circumstance for testing for dynamic quenching arises. In this region, water is not a significant component of the ground-state equilibrium solvation shell population. Consequently, it is not a part of the initial excited-state solvation shell, available for static quenching. And the n/nocurve, with all its uncertainties, shows clearly that any water occupancy that does occur depends nonlinearly on bulk solvent composition. However, collision probability will depend on bulk composition in simple form as long as water is dilute. In other words, dynamic quenching predicts a conventional Stern-Volmer plot in contrast to what was observed for the Reineckate anion. This Stern-Volmer plot is shown in Figure 7. Luminescence intensity data and lifetime data are in satisfactory agreement. On the basis of luminescence data, the Stern-Volmer slope is Ksv = 0.056 M-l. The quenching constant It is related to Ksv by the lifetime in pure acetonitrile by k s v = k T. If T is taken as 25 ps, k,(H20) is 2.3 X lo3 M-' s-l. I n argonpurged acetonitrile solutions, k,(H20) = 1.3 X lo3 M-'s-l and T~ = 43 ps from a plot of 1 / against ~ [H20]bee upper plot of Figure 7). These results are taken as evidence for
(2)
where
is the phosphorescence yield,
krad
is the ra-
(16) Bolletta, F.; Maestri, M.; Balzani, V. 2499.
J. Phys. Chem. 1976, 80,
J. Phys. Chem. 1983, 87,1008-1013
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dynamic quenching. Also, since the 1-7 parallelism is supported, it can be concluded that vic remains close to unity. This will be a significant point in the discussion of solvolytic reactions. Solvolytic Reactivity. Neither of the complexes in this study shows solvent dependence of quantum yields for photosolvolytic reaction which relate closely to the solvent quenching of doublet phosphorescence. This does not at all deny the importance of the luminescent doublet species on the reactive pathway. Cr(bpy),,+ is one of the few chromium(II1) complexes for which there is definite evidence for doublet origin of reactivity.“ About 50% of the reaction of trans-[Cr(NH&,(NCS),]- can occur through the doublet even though reaction from the quartet via back intersystem crossing has been suggested.18 Reactions of the Reineckate anion in mixed solvents have been discussed exten~ively.~-~ The present results do not add measurably to the factors considered before. There is only one important point to emphasize. The role of the solvent in the reaction must be “static”. In this context, the dependence of the total quantum yield on solvent is different from the dependence of doublet lifetime and different from the solvent dependence of thermal substitution in Cr(NCS)63-,a solvent dependence which parallels R- doublet quenching. This calls attention to the component of this reaction pathway dependent upon the (17) Jamieson, M. A,; Serpone, N.; Hoffman, M. Z. Coord. Chem. Reu. 1981, 39, 121. (18) Chen, S.;Porter, G. B. Chem. Phys. Lett. 1970, 6, 41.
quartet. Gutierrez and Adamson3suggest that the quartet is the main precursor to reaction. Considering C r ( b ~ y ) , ~we + can begin with the region (Figure 5) of solvent where the Stern-Volmer relation holds. Here we see an increase in quantum yield with increasing water concentration, which reaches a limit well before water has become an important constituent of the solvation shell of the complex. This suggests a saturable equilibrium leading to a primary intermediate which might, for example, be the seven-coordinate derivative of the doublet excited state, Cr(bpy)3(H20)3+.17 The saturation at low water suggests that additional water molecules do not affect the reaction as the seven-coordinate hypothesis would seem to suggest. The only problem is to rationalize the modes and decrease in yield between water mole fractions of 0.9 and 1.0. This is the region where the preferential solvation data indicate that the majority of solvation sites are becoming occupied by H20 rather than by CH3CN. A simple explanation (which is consistent but not unique) would suggest that the saturable equilibrium is one in which water solvation stabilizes sixrather than seven-coordination when the immediate solvation environment is aqueous. Consistent with the findings by Henry and Hoffman,6 the quantum yield of photosolvolysis of C ~ ( b p y ) ~in~ + air-equilibrated, neat acetonitrile solutions is 0.03 are inferred. Data are compared with previously published results.
Introduction The Ti-0 system is a complex chemical system with many condensed phases and the gaseous molecules T i 0 a d TiOz. m e condensed phases consist of a solid solution of oxygen in Ti, Ti20, TiO, Tiz03,Ti,O5, and the homologous series of phases with the chemical formula Ti,02n-1 beginning with n = 4. The phase behavior of the system was summarized bv Wahlbeck and Gilled in 1966. The region of the diagram unclear at that time was the region of the homologous series. Originally the purpose of the present research was to examine the oxygen chemical potential between Ti305and (1) P. G. Wahlbeck and P. W. Gilles, J . Am. Cerum. Soc., 49, 180 (1966). 0022-3654/83/2087-1008$01.50/0
Ti02, the region of the homologous series. An excellent study of the oxygen pressures Over this range has been performed by Merritt and Hyde.’ The data of Mer& and Hyde are in good agreement with measurements on Ti%, by F d a n d 3 and Kofshd,4 and electrochemical cell measurements near TiOz by Zador5v6and Blumenthal and W h i t m ~ r e . ~Merritt and Hyde2 have provided data for (2) R. R. Merritt, B. G. Hyde, L. A. Bursill, and D. K. Philp, Phil. Trans. R. SOC.(London),274, 627 (1973). (3) K. S.Forland, Acta Chem. Scand., 18, 1267 (1964). (4) P. Kofstad, J.Phys. Chem. Solids, 23, 1579 (1962). (5) S. Zador in “Electromotive Force Measurements in High Temperature Systems”, C. B. Alcock, Ed., London Institute of Mining and Metallurgy, 1967. (6) S.Zador, Thesis, University of London, 1969.
0 1983 American Chemical Society
