J. Phys. Chem. 1987, 91, 2342-2347
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inhibiting effect on hydrogenolysis activity than has been observed for actual Ru-Cu catalysts by other workers?-3,29-30If the required site for hydrogenolysis comprises an array of ruthenium atoms rather than a single atom,4 it would appear that differences in the manner in which the copper is distributed on the ruthenium surface could be an important factor in accounting for the different magnitudes of the effects. One might also consider this matter from the point of view that defect sites on a ruthenium surface could be more active than normal sites, whether or not the reaction requires a large array (29)R u m , A . J.; Haller, G. L.; Oliver, J. A,; Kemball, C. J. Catal. 1983, 84,297. ( 3 0 ) Haller, G. L.; Resasco, D. E.; Wang, J. J . Catal. 1983,84, 477.
of ruthenium atoms in a site. If there is preferential interaction of copper with the defects, as can be inferred from the results of the present work, it would be reasonable for copper to have a different effect on the catalytic activity of ruthenium when defects are present. Consequently, the effect of copper on catalytic activity could well be different for a ruthenium powder than it is for a smooth (001) plane of ruthenium. The results of the present investigation clearly demonstrate the value of ultraviolet photoemission spectroscopy of physisorbed xenon as a probe of surfaces of interest in catalysis. Since it is sensitive to localized properties of the surface, it is a powerful probe. for the detection of surface heterogeneity. It can therefore make a useful contribution in studies of the structure sensitivity of surface-catalyzed reactions.
Sensitlzation of TiO, in the Visible Light Region Using Zinc Porphyrins K. Kalyanasundaram, N. Vlachopoulos, V. Krishnan,+A. Monnier,t and M. Gratzel* Institut de Chimie Physique, Ecole Polytechnique Federale, CH- 101 5 Lausanne, Switzerland (Received: November 13, 1986)
Efficient charge injection from the excited state of a zinc porphyrin to the conduction band of Ti02 has been observed during the visible light irradiation of Ti02 electrodescoated with a film of [tetrakis(4-~arboxyphenyl)prphyrinato]zinc(II)(ZnTPPC). The mechanism of the charge injection process has been studied in dye-adsorbed Ti02dispersions and colloids, using steady-state and time-resolved photolysis techniques. The process is extremely sensitive to the pH. The charge injection occurs primarily from the singlet excited state of the porphyrin, that too only from the dyes that are adsorbed on the electrode.
Introduction Sensitization of stable, large bandgap semiconductors in the visible light using dyes has been a long sought, continuing goal in the area of photochemical solar energy conversion in many laboratories.lS2 The reported overall quantum efficiencies span almost 2 orders of magnitude. Progress in this area has been hampered by the limited knowledge available on the mechanism of the charge injection processes and on the factors that control them. Electrochemical techniques such as potential modulation3 and use of rotating ring disk electrodes (RRDE)4 have been of immense help in deciphering some of the mechanistic details. Sensitization processes investigated on TiOz electrodes and dispersions include dyes such as phthalocyanines,5 R ~ ( b p y ) , ~and + derivatives,6 ~hlorophyllin,~ and 8-hydroxyquinoline complexes.* With the availability of small (colloidal) semiconductor particles amenable to fast kinetic studies, we9 and others1° recently have been investigating the mechanism of such dye-sensitization processes using steady-state and laser photolysis techniques. Resonance raman spectroscopy1 and microwave absorption techniques'* have also been recently demonstrated to be useful. The present study involves the use of a water-soluble anionic porphyrin, [tetrakis(4-carboxyphenyl)porphyrinato]zinc(II) (abbreviated hereafter as ZnTPPC) as a sensitizer to study electron injection from the dye excited state(s) to the conduction band of the semiconductor Ti02. Precise information is availableI3 on the ground- and excited-state properties of the dye as well as the absorption spectra of its monoreduced and monooxidized radical forms, facilitating identification of the transient species formed during the photoreaction. Photocurrent measurements under visible light illumination on the porphyrin-coated polycrystalline TiOl electrodes revealed very efficient charge injection from an 'Visiting Professor from the Department of Inorganic and Physical Chemistry, Indian Institute of Science, Bangalore 560 012,India. *Institut de Chimie Mintrale, Analytique et AppliquC, Universitt de GenEve, CH-1211, Switzerland.
0022-3654/87/2091-2342$01.50/0 , I
,
excited state of the dye (incident photon to current conversion efficiencies exceeding 40% at the Soret absorption maximum of the porphyrin). By a combined use of steady-state and time-resolved photolysis techniques on dye-coated colloidal T i 0 2 dispersions, the mechanism of the process is shown to involve the singlet excited state of the dye, that too only from the dyes that are adsorbed onto the electrode.
Experimental Section Materials. Preparation of the Polycrystalline Ti02Electrode. Ti02 (anatase) electrodes were prepared by thermal decomposition of titanium ethanolate solutions, deposited on the cross section (1)Gerischer, H.; Willig, F. Top Curr. Chem. 1976,61,31. (2)Watanabe, T.;Fujishima, A,; Honda, K. In Energy Resources Through Photochemistry and Catalysts;Gritzel, M., Ed.;Academic: New York, 1983; Chapter 11. (3)Matsumura, M.; Mitsuda, K.; Tsubomura, H. J . Phys. Chem. 1983, 87, 5248. (4)Watanabe, T.;Fujishima, A.; Honda, K. Chem. Lett. 1978,735. ( 5 ) (a) Fan, F. R. F.; Bard, A. J. J . Am. Chem. SOC.1979,101,6139.(b) Giraudeau, A.; Fan, F. R. F.; Bard, A. J. J. Am. Chem. Soc. 1980,102,5137. (6) (a) Borgarello, E.;Kiwi, J.; Pelizetti, E.; Visca, M.; Gratzel, M. J . Am. Chem. Soc. 1983,103,6423.(b) Hashnoto, K.; Kawai, T.; Sakata, T.Nouv. J . Chim. 1983,7, 249. (c) Furlong, D. N.; Wells, D.; Sasse, W. H. F. J . Phys. Chem. 1986,90, 1107. (d) Kiwi, J. Chem. Phys. Lett. 1981,83,594. (7)Kamat, P. V.; Fox, M. A. Chem. Phys. Lett. 1983,102,379. (8)Houlding, V.; Gritzel, M. J . Am. Chem. SOC.1983,105, 6595. (9)(a) Moser, J.; Gratzel, M. J . Am. Chem. SOC.1984,106, 6557. (b) Moser, J.; Gratzel, M.; Sharma, D. K.; Serpone, N. Helu. Chim. Acta 1985, 68,168. (10)Kamat, P. V.; Chauvet, J.-P.; Fessenden, R. W. J. Phys. Chem. 1986, 90, 1389. (11)Rossetti, R.; Brus, L. E. J . Am. Chem. SOC.1984,106,4336. (12) Fessenden, R. W.; Kamat, P. V. Chem. Phys. Lett. 1986,106,4336. (13)(a) Kalyanasundaram, K.; Neumann-Spallart, M. J . Phys. Chem. 1982,86,5163. (b) Neumann-Spallart, M.; Kalyanasundaram, K. Z . Naturforsch. 1981,36B,596. (c) Neta, P. J . Phys. Chem. 1981.85,3678. (d) Richoux, M.-C.; Harriman, A. J . Chem. SOC.,Faraday Trans. 1 1982,78, 1873. (e) Harriman, A.; Porter, G.; Walters, P. Zbid. 1983,79, 1335.
0 1987 American Chemical Society
Sensitization of TiOz Using Zn Porphyrins of Ti rods (KobeSteel, Japan, 99.5% purity, Fe content < 0.2596, 6 mm in diameter and 6 cm in length). The tip of the titanium rod on which the oxide layer was deposited was subjected to a pretreatment consisting of polishing with emery paper of decreasing coarseness (Stryers, Denmark, Type Minor 220,320,500, and 1OOO) and 0.5 h boiling in 18% HCl. The titanium ethanolate solution was prepared by dissolving 21.1 mM of freshly distilled TiCI4 (Fluka, puriss) in 10 mL of ethanol. The solution was then diluted with absolute methanol to give a titanium concentration of 25 or 50 mg/mL. The oxide layer was deposited according to a procedure developed by Stalder and Augustynski.16 The tip of the Ti rod was dipped in the titanium ethanolate solution containing 25 mg of Ti/mL. Excess solution was removed by tapping the electrode against the wall of the glass container. In this way, a thin coating was produced which was dried in air for 30 min. The electrode was subsequently heated in air in a tubular oven kept at 450 OC. Preheating it in the entrance of the oven for 5 min was followed by 15 min heating in the interior. Three more layers were produced in the same way. Subsequently 10 thick layers were deposited, each by dipping the electrode in the titanium ethanolate solution containing 50 mg/mL and subsequent heating. The same procedure as for the first layers was applied except that the heating of the final layer lasted for 30 min. Total thickness of the oxide layer was about 20 pm. The doping of the TiOz layer was carried out by heating it in highly purified Ar. A horizontal tubular oven composed of a quartz tube with suitable joints was employed. After insertion of the electrodes, the tube was twice evacuated and purged with the high-purity Ar (Air Liquide, Belgium, 99.997%). Subsequently, the electrodes were heated under Ar flux (2.5 L/h) at a rate of 500 OC/h upto 550 OC, which temperature was maintained for 35 min. The electrodes were removed from the oven after cooling. The [tetrakis(4-~arboxyphenyl)porphyrinato] zinc (ZnTPPC) was available from previous work.13 The polycrystalline TiO, electrodes were coated with the Zn porphyrin by keeping the electrodes immersed in a stirred aqueous solution (ca. M of ZnTPPC) for ca. 1 h and subsequent air-drying of the electrode. Adsorption of the dye to the electrode appears to be very efficient and strong, as evidenced by the ease of uptake and the absence of any release of the dye upon immersion of the dye-coated electodes in moderately acidic or neutral aqueous solutions. (Slow desorption of the dye occurs in 1 M NaOH). Steady-state photolysis of the dye-coated TiOz electrodes employed the output of a 150-W tungsten-halogen lamp, used in conjunction with a water filter. Photocurrent action spectrum was recorded by sending the lamp output through a Kratos monochromator and intensities were measured with a Yellow Springs Institute-Kettering (YSI-K) radiometer. The illuminated dye-coated electrode area was 0.28 cm2. Colloidal T i 0 2 particles were prepared by hydrolysis of freshly distilled TiCl, (Fluka, puriss.) at 0 OC according to earlier published procedure^.^ The mean particle radius obtained by quasi-elastic light scattering is 120 A. At pH < 4 and pH > 9, the TiOZ sol is stable over several days. In the intermediate pH domain, the colloids require a protective agent such as poly(viny1 alcohol) (PVA) to prevent the flocculation. Commercial PVA (Mowiol40-88, Hoechst, W. Germany) was treated with UV light to remove impurities before use. Methods. Photoelectrochemical experiments were carried out in a three-compartment cell equipped with a quartz window, with the auxiliary and reference electrode compartments separated from the working electrode compartments by glass frits. The measurements were made using a Pine Instruments potentiostat and the currents were recorded with a Watanabe X-Y recorder (Model WX442 1). Laser photolysis experiments employed a Q-switched frequency-doubled Nd:YAG laser (JK Lasers 2000) (A = 532 nm) combined with fast kinetic spectroscopy to detect transient species. Fluorescence spectra were obtained with a Perkin-Elmer M P F 44 instrument. Diffuse reflectance spectra of dye-coated TiO,
The Journal of Physical Chemistry, Vol. 91, No. 9, 1987 2343
T
Scnsltizatiw of TiO, by Znippc
E
PH 31-1
.
I~z~PIIz~PO- 1.211
pH 71-.-1
Figure 1. Schematic representation of the energy levels of the Zn porphyrin in the ground and excited states in relation to the valence, conduction band energy levels of Ti02.
powders were recorded on a Perkin-Elmer absorption spectrophotometer equipped with an integrating sphere accessory. All solutions were thoroughly degassed by passing Ar from at least 15 min prior to use.
Results and Discussion Among different classes of visible light absorbing dyes that one can choose to study the sensitization processes on large bandgap semiconductors, porphyrins stand unique. Extensive information that has accumulated over the years on various porphyrin derivatives and their photochemistry allow choice of a porphyrin with appropriate charge, hydrophobicity, and ground- and excited-state redox properties. Anionic zinc porphyrins such as [tetrakis(4-~arboxyphenyl)porphyrinato] zinc (ZnTPPC) are attractive candidates to scrutiny in this context. Figure 1 presents the relative location of the redox levels of this zinc porphyrin (in the ground and excited states) in relation to the valence, conduction band edges of Ti0,. Photoelectrochemical Studies on Dye-Coated Electrodes. In order to examine the feasibility of the charge injection process from the excited state(s) of the zinc porphyrin, we coated polycrystalline TiO, electrodes with ZnTPPC from an aqueous (neutral) solution of the dye and examined their photoelectrochemical response for visible light irradiation in 0.1 M NaCIO, M ) as the solutions containing hydroquinone ( “supersensitizer” ZnP*
-
ZnP+ + eCb-(TiO2)
In acidic aqueous solutions (pH -3) significant photocurrent was obtained. For example, at 430 nm incident light (intensity 1.53 W/m2) the current density was 23 hA/cm2 at an electrode potential of 0. l V vs. SCE. Figure 2 presents the action spectrum for the photocurrent observed during visible light irradiation of dye-coated TiOz electrode. The action spectrum is characterized by maxima characteristic of the Soret (or B band) and Q-band absorptions of the porphyrin. The incident photon-to-current conversion efficiency, q, defined as electrons divided by the number of incident photons, was calculated by using eq 2 and is in the [(1.24 lo3) photocurrent density (pA/cm2)] ‘(%I = [wavelength (nm) photon flux (W/m2)] X
X
X
(2)
range of 8-10% for the Q band and ca. 42% for the Soret band. Since the absorbance ratio of Soret band to the Q band is over
-
50
-
2
vs.
SCE.
ZnTPPC/Ti02/PVA
pH 3 0.4
30 -
Y
0.lV
A
I1
L,
0.5
ZnTPPC/TiO2/H2Q a c t i o n s p e c t r u m
40
Y
Kalyanasundaram et al.
The Journal of Physical Chemistry, Vol. 91, No. 9, 1987
2344
A
! I
E
I
I A I
2olj I
m
n
L 0
g
0.5 g/L), the fluorescence quenching exhibited in the sigmoidal curve is fully reversible; Le., increase of the solution pH from 2.9 to pH 10.0 leads to a recovery of the fluorescence intensity and vice versa. One can consider two possible mechanisms for the quenching of fluorescence by colloidal Ti02: concentration quenching among the adsorbed dye molecules or electron transfer (reaction 1). To evaluate the former pathway, the dependence of fluorescence quenching efficiency on the extent of dye loading (vary the T i 0 2 sol concentration at a fixed dye concentration) was examined in acidic aqueous solutions at p H 3.0. At a fixed Zn porphyrin concentration of lo-' M, the fluorescence intensity decreases initially rather sharply upon addition of very low concentrations of Ti02 (C20 mg/L). Upon further increase in TiOZconcentration to 50 mg/L, the fluorescence intensity recovers partially to reach a plateau value, in a manner very similar to that reported earlier9 for eosin. Analysis on lines similar to eosin presented earlier showed that, at Zn porphyrin occupancy at below 32 molecules per TiOl particle, the fluorescence intensity remains constant, but at much reduced level (low by a factor of 4) than in Ti02-free
I
Inm)
Figure 6. Transient absorption (difference) spectra recorded at the end of 532-nm Nd laser pulse excitation of ZnTPPC in aqueous solution containing colloidal TiOl (0.5 g/L) and poly(viny1alcohol) (0.25 g/L) at pH 9.40 and 5.35. .03 E
ZnTPPC/TiO,/PVA
0 P
m
vi
+,
0
r(
.Ol.
a .r(
L
? r(
0
a 0
2
6
4
8
18
PH
Figure 7. Variation in the triplet excited-state yield of ZnTPPC as a function of pH during laser pulse photolysis of ZnTPPC in aqueous
TiO,/PVA solutions. (Plotted are transient absorbances at 840 nm measured at 50 ps after laser pulse excitation.) solutions. Hence it is deduced that a t the low loading levels examined (conditions used for Figure 5) concentration quenching plays a very minor role. In a subsequent section, the occurrence of electron-transfer quenching is demonstrated in a more direct manner by laser photolysis studies. Laser Photolysis Studies on the Triplet State and Photoredox Products. Colloidal T i 0 2 solutions are readily amenable to detailed flash photolysis investigations. The concomitant quenching, if any, of the triplet excited state of the porphyrin and formation of redox products upon excitation of Zn porphyrin adsorbed onto colloidal Ti02 sols were examined by using 532 nm, 10-ns Nd-laser pulses. The features of the triplet-triplet absorption as well as that of porphyrin cations have been well characterized earlier. In the red-near-IR region, ZnTPPC triplet states are characterized by absorptions with maxima at 840 and 760 nm, respectively, with a triplet lifetime of 1.6 ms in degassed aqueous solutions.*3 Pulse radiolysis and spectroelectrochemical studies of water-soluble Zn porphyrins have shown porphyrin cation radicals to have a red absorption maximum located around 700 nm.13 Detailed laser photolysis studies of ZnTPPC/Ti02/PVA solutions showed that the transient absorbances at very early times after laser pulse excitation and their time evolution vary significantly with pH. Figure 6 presents transient absorption spectra recorded at the end of laser pulse excitation of ZnTPPC/ Ti02/PVA solutions at two different pH values 9.40 and 5.35. In alkaline solutions (pH > 9) one observes essentially a single transient, which by its absorption spectral features (curve a, Figure 6 ) , long lifetime (1.6 ms), and extreme sensitivity to the presence of oxygen has been identified as that of the triplet excited state.
2346
The Journal of Physical Chemistry, Vol. 91, No. 9, 1987 ZnTPPC/TiO,/PVA/
840nm
Kalyanasundaram et al. very favorably with the intersystem crossing rate of the singlets to form the triplet excited state. Precedent to this type of occurrence can be found in the sensitization of TiOz by eosin.9 If the early fast component is indeed due to the formation of Zn porphyrin cation radicals derived from the singlet excited state, then the rate for the reverse pathway of reaction 1 differs from the forward rate by at least 3 orders of magnitude: ZnP
1 Figure 8. Decay traces monitored at 840 nm illustrating the time course of transient absorbances during laser pulse photolysis of ZnTPPC in
aqueous Ti02/PVA solutions. Upon lowering of pH, the transient absorbance curves show a biphasic character, with an initial fast component decaying over 5-50 @ (depending on the pH). The slow component is deduced to be the unquenched triplet excited state from the similarity of its spectrum to that of the triplet state and long lifetime. At pH 5.35, for example, the transient spectra at the end of the laser pulse excitation (curve b, Figure 6) consist of absorptions due to the triplet state (maxima at 850 and 750 nm) and a new absorption maximum at ca. 690 nm. The contribution of this early product with a maximum around 690 nm becomes major in acidic solutions, pH 3.0. Based on the known absorption maximum of ZnP cation radicals around 700 nm, the early fast component has been assigned to the porphyrin cation radicals, formed during charge injection from the singlet excited state of the porphyrin. Figure 7 presents data on the variation of the triplet excited-state yield (monitored at 840 nm, plotted as transient absorbances at t = 50 q after laser pulse excitation) as a function of pH. As with the fluorescence quenching (Figure 5), the triplet-state yield drops in a sigmoidal manner with decreasing pH. Pronounced decrease in the triplet-state yields occurs in the narrow pH range of 5-7. The triplet yield decreases nearly by a factor of 7 upon change of solution pH from 9.5to 2.95.As with the fluorescence quenching, the p H dependence curve of the triplet yield can be followed in either direction (from low pH to high pH or vice versa). Figure 8 presents a series of transient absorbance decay curves monitored at 840 nm at different p H values. The increasingly dominant biphasic form of the decay curves with decreasing pH is very clear. Lifetimes in the range of 1.2-1.5ms (difficult to measure precisely due to very low absorbances) for the long-lived second component suggests that the triplet state is not quenched in any significant manner during the variation of the pH. If so then, the decreasing triplet-state yields depicted in Figures 5 and 6 should have their origin elsewhere. The singlet excited-state quenching among the adsorbed ZnP molecules should be an extremely rapid, efficient pathway, occurring in subnanosecond time scales. It is likely that, in these fast time scales, the singlet-state quenching via the charge injection process (reaction 1) competes
ZnP’
+ eCb-(TiO2)
(3)
Analysis of the fast component decay showed that the reverse reaction 3 does not follow simple first- or second-order laws. It is reasonable to suppose that the back electron transfer between surface-bound (adsorbed) ZnP’ radicals and conduction band electrons is likely to be complex (the role of PVA as an electron donor can be ruled out, as similar results are obtained in acidic solutions devoid of PVA). Returning to Figure 1, it was pointed out that both the singlet and the triplet excited state of the porphyrin can participate in the charge injection process. Experimentally it has been found that only the singlet excited state injects charges, that too in neutral or acidic solutions. The very short lifetime of the singlet excited state (7” = 1.8 ns) precludes diffusional type quenching of free (unbound) excited dye molecules by the Ti02sols. As adsorbed species the excited dye molecules do inject from the singlet state in acidic solutions. Desorption from the surface at alkaline pH drastically reduces the efficiency of singlet processes. As regards the triplet excited state, long lifetime (1.6ms) should allow diffusional quenching of unbound excited dye molecules. Lack of quenching at alkaline pH presumably reflects insufficient driving force (ca. 0.30V). In acidic conditions (dyes adsorbed into TiOz sols), efficient fluorescence quenching (a subnanosecond process) occurs in competition with the intersystem crossing, with the result that the triplet-state yield is considerably reduced in the adsorbed dye molecules (cf. eq 4). It may be recalled that,
(4) except for the primary photosynthetic reactions that occur in vivo, practically all the known photoredox reactions of metalloporphyrins (reactions in vitro) involve the triplet excited state. The present system thus represents a “novel” in vitro case involving the singlet excited state of the porphyrin. Efficient charge injection from adsorbed dyes to the conduction band of TiOz has been hitherto observed with dyes that have -COOH group as a substituent, e.g., eosin,9 tris(4,4’-dicarboxy2,2‘-bipyridine)r~thenium,’~ and the present case of ZnTPPC. It is tempting to propose that dyes with carboxyl group on the periphery have a special affinity to adsorb onto the surface of TiOz. In order to test whether electrostatic interactions dominate in the dye-association process, we examined the efficiency of an anionic Zn porphyrin, structurally very similar to ZnTPPC, viz., [tetrakis(4-sulfonatophenyl)porphyrinato]zinc (ZnTPPSe) under similar conditions. In support of the earlier hypothesis, the charge injection efficiency was found to be very inefficient in comparison to ZnTPPC. In the discussions so far, the absence of any quenching (charge injection) of the Zn porphyrin excited state in alkaline solutions has been attributed to the lack of adsorption of the anionic dye on the negatively charged surfaces of TiOz. Though this deduction is based on electrostatic grounds, it has been difficult to verify it to be the case. Persistent red shifts of ca. 6 nm in the Soret adsorption suggest that some weak interactions still persist in alkaline solutions, though they are not strong enough to affect either ground-state or excited-state absorption properties significantly. In an alternate scenario the dye can remain adsorbed (14) DeSilvestro, J.; Grstzel, M.; Kavan, L.; Moser, J.; Augustynski, J. J . Am. Chem. Soc. 1985, 107, 2988.
(15) (a) Mochida, I.; Tsuji, K.; Suetsugu, K.; Fujitsu, H.; Takeshita, K. J . Phys. Chem. 1980, 84, 3159. (b) Mochida, I.; Suetsugu, K.; Fijitsu, H.;
Takeshita, K. J . Phys. Chem. 1982, 87, 1524. (16) (a) Stalder, C.; Augustynski, J. J . Electrochem. SOC. 1979,126,2007. (b) Stalder, C. Thbse de doctorat, UniversitC de Gentve, 1981.
J. Phys. Chem. 1987, 91, 2347-2350
2347
on the T i 0 2 surface at all pH due to dominant hydrophobic/
process inefficient a t alkaline pH.
hydrophilic interactions. It is well-known that, in TiOz with increasing pH, the valence and conduction band edges move to more cathodic potentials. This then would reduce considerably the driving force for the reaction 1, rendering the charge injection
Acknowledgment. It is a pleasure to acknowledge support of this work by the Swiss Federal Office for Energy (OFEN) and the Gas Research Institute.
Ion-Neutral Carrier Transport in Open and Closed Systems Richard P.Buck Department of Chemistry, University of North Carolina, Chapel Hill, North Carolina 2751 4 (Received: August 1 1 , 1986; In Final Form: December 29, 1986)
Equations describing spontaneous, one-dimensional transport of univalent ions across asymmetrically bathed membranes and films can be solved to give simple, closed-form, steady-state fluxes. The equations have explicit dependences on carrier loading, ion-carrier complex formation constants, salt extraction and diffusion coefficients, and membrane thickness. Conditions for nearly exact solutions are practical, and the analysis is based on reversible ion exchange and electroneutral diffusion-migration transport. Conditions for linear concentration profiles of species and for coupling of fluxes are clearly shown. For generality and perspective, open and closed thermodynamic systems are considered, with varying degrees of ion and carrier trapping in the membranes. Some progress on transport selectivity theory is disclosed.
Introduction The role of neutral carrier-induced, spontaneous, one-dimensional transport across asymmetrically bathed, electroneutral, site-free (and site-containing) membranes has been troublesome, conceptually and mathematically for many years.' With the advent of synthetic neutral carriers after 1965, especially crown ethers (1967) and a ready supply of natural carriers, e.g., valinomycin, many new devices and experiments have been explored.'" but the cases The theoretical background has not been investigated have been limited to systems simplified by approximations and assumptions, e.g., all carriers confined to the membrane as in some ion-selective electrodes, or all charged sites confined to a membrane as in liquid ion exchanger films, or both confined to membranes as in certain counterflow ion separation schemes including transport against an ion's own concentration gradient. Descriptions of Transport. Transient species fluxes, concentration profiles, potential profiles, and electric fields are particularly difficult to obtain because the equations of motion and extraction boundary conditions are nonlinear. Descriptions of the same properties in the steady state are less difficult, and progress has been made for both zero current, chemical potential driven transport,' and finite current, applied voltage driven t r a n ~ p o r t . ~ , ~ Nearly exact solutions of steady-state flux equations showing dependences on extraction and complex formation parameters are
'
(1) Buck, R. P. Anal. Chem. 1978,50,17R; 1976,48,23R; 1974,46,28R; 1972,44, 270R. (2) Dobler, M. Ionophores and Their Structures; Wiley: New York, 1981. (3) Burgermeister, W.; Winkler-Oswatitsch, R. Top. Curr. Chem. 69; Znorg. Biochem. 1977, 2, 91. (4) Kolthoff, I. M. Anal. Chem. 1979, 51, 1R. ( 5 ) Membranes-A Series of Advances; Eisenman, G., Ed.; Marcel Dekker: New York, 1973; Vol. 2. (6) Morf, W. E. In Studies in Analytical Chemistry; Elsevier: Amsterdam, 1981; Vol. 2. ( 7 ) Reusch, C. F; Cussler, E. L. AZChE J . 1973, 19, 736-741. '(8) Lamb, J. D.; Christensen, J. J.; Oscarson, J. L.; Nielsen, B. L.; Asay, B. W.; Izatt, R. M. J. Am. Chem. Soc. 1980, 102, 6820-6824. (9) Choy, E. M.; Evans, D. F.; Cussler, E. L. J . Am. Chem. Soc. 1974,96, 7085-7090. ... .. .. (10) Caracciolo, F.; Cussler, E. L.; Evans, D. F. AIChE J . 1975, 21, 160-167.
0022-365418712091-2347$01.50/0
possible and will be given below. Recently, the number and kinds of neutral carriers have increased prodigiously. The questions that naturally arise in transport process analysis are the following: (1) What is the role of carrier partition equilibrium magnitudes? (2) What is the role of ion-carrier complex formation constant magnitude? (3) What is the role of complex formation kinetics in each phase? Is extraction rate important in the outcome of transport experiments? These questions can be answered and arguments settled on the basis of thermodynamics (electrochemical potential concepts), and transport can be described by diffusion-migration using the Nernst-Planck equations (based on derivatives of the electrochemical potentials). The latter are ideally suited to analysis of transport in these homogeneous-phase problems.
Reversible Interfacial Equilibria and Mass Transport Generally, thick membranes and U-tube experiments use asymmetric, stirred, immiscible bathing electrolytes M+,X- conThe membrane contains M+, taining a neutral carrier MS+, X-, and S, depending on the formation of complex species, described by S.798311-'3
Kf = (MS+)/(M+)(S) The important reversible phase equilibria are
(1)
(M+)(X-)/(M+)(F) = KMx
(2a)
( N + ) ( X - ) / ( g ) ( F ) = KNx
(2b)
or
(3) Hypothetical extraction of MS+X- is secondary and derived from eq 1-3. (11) Behr, J.-R.; Kirch, M.; Lehn, J.-M. J. Am. Chem. SOC.1985, 107, 241-246. (12) Wong, K. H.; Yagi, K.; Smid, J. J . Membr. Bioi. 1974,6, 379-397. (13) Moore, J. H.; Schechter, R. S . AIChE J . 1973, 19, 741-747. (14) Buck, R. P. J. Membr. Sci. 1984, 17, 1-62.
0 1987 American Chemical Society
