Applied Surface Science 254 (2008) 5408–5412

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Applied Surface Science

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Hydrolysis–condensation reactions of titanium alkoxides in thin films: A study ofthe steric hindrance effect by X-ray photoelectron spectroscopy

Vincent Barlier a, Veronique Bounor-Legare a, Gisele Boiteux a, Joel Davenas a,Didier Leonard b,*a Universite de Lyon, Ingenierie des Materiaux Polymeres, Laboratoire des Materiaux Polymeres et Biomateriaux,

UMR CNRS 5223, CNRS-Universite Claude Bernard Lyon 1, F-69622 Villeurbanne, Franceb Universite de Lyon, Laboratoire des Sciences Analytiques, UMR CNRS 5180, CNRS-Universite Claude Bernard Lyon 1, F-69622 Villeurbanne, France

A R T I C L E I N F O

Article history:

Received 4 December 2007

Received in revised form 19 February 2008

Accepted 21 February 2008

Available online 4 March 2008

Keywords:

Titanium alkoxide

Hydrolysis–condensation

Thin films

X-ray photoelectron spectroscopy

A B S T R A C T

An original approach based on X-ray photoelectron spectroscopy (XPS) is proposed to study the influence

of the surrounding humidity on the hydrolysis–condensation reactions of five titanium alkoxides in thin

films. More precisely, the influence of the nature of the ligands (propoxide, butoxide, isopropoxide,

phenoxide, and 9H-carbazole-9-yl-ethyl-oxy) on the reaction rate was evidenced. The reaction

advancement was evaluated by comparing XPS chemical compositions to theoretical compositions

calculated for all the possible rates. XPS chemical environment information allowed validating the

reliability of this approach through the evaluation of the condensation state. In both approaches, the

influence of the steric hindrance on the reactivity of titanium alkoxides was highlighted to be similar to

what has been previously observed in solution. Theses results corroborate the validity of our XPS

approach to determine titanium alkoxide hydrolysis–condensation reactions in the specific application of

thin films.

� 2008 Elsevier B.V. All rights reserved.

1. Introduction

TiO2 thin films are currently used in electric and optic fieldssuch as for solar cells [1], electrochromic devices [2] or lithiumbatteries [3] applications. Sol–gel processing, based on hydrolysis–condensation reactions in solution, is one of the most commontechniques to elaborate TiO2 thin films with controlled morpho-logy [4]. As starting materials, titanium alkoxides are widely used[5–7] even if their use involves specific operating conditions.Indeed, titanium alkoxides vigorously react with water producingill-defined metal-oxo/hydroxo precipitates [8].

Several reaction parameters in solution, such as pH, H2O/Ti ratio[9,10], size of ligands [11,12] or chemical modifications tointroduce less hydrolysable groups (Cathenol [13], b-diketonate[14,15] or carboxylate [16–18]) are then used to control thealkoxide hydrolysis–condensation reactions and therefore, theTiO2 thin film morphology. The parameters in solution arenowadays well defined and the tools to monitor in situ these

* Corresponding author at: CNRS, UMR5180, Laboratoire des Sciences Analy-

tiques, F-69622 Villeurbanne, France. Tel.: +33 4 72 43 11 82; fax: +33 4 72 43 12 06.

E-mail address: didier.leonard@univ-lyon1.fr (D. Leonard).

0169-4332/$ – see front matter � 2008 Elsevier B.V. All rights reserved.

doi:10.1016/j.apsusc.2008.02.076

chemical reactions deeply developed. Classical 1H and 13C nuclearmagnetic resonance spectroscopy (NMR) have allowed followingthe change in the alkoxide group chemical environment [19]. Morerecently, 17O NMR [20] has appeared to be a straightforwardcharacterization tool for probing the different oxo bridges.Hydrolysis–condensation reactions in solution have been alsostudied by Fourier transform infrared spectroscopy (FTIR) [21],calorimetry [22], rheology [23], electron microscopy and SAXS[21,22,24].

However, some studies [25,26] have revealed specific modi-fications of the hydrolysis–condensation rates of titaniumalkoxides at the surface level. Jang et al. [25] evidenced the roleof the relative humidity (RH) on the organization of mesoporoustitanium thin films using X-ray diffraction and TEM. They werethen able to synthesize highly organized TiO2 films by controllingthe moisture exposure. Pucceti and Leblanc [26] studied by FTIRand pulsed photoacoustic spectroscopy the hydrolysis–condensa-tion reactions of pure titanium tetrabutoxide when exposed tosurrounding humidity. Results showed that sol to gel evolutionoccurs differently at the surface and in the bulk.

X-ray photoelectron spectroscopy (XPS) characterization of themetal alkoxides has already been proposed. For example, thehydrolysis step during the sol–gel preparation of sulphated

Scheme 1.

Scheme 2.

Scheme 3.

V. Barlier et al. / Applied Surface Science 254 (2008) 5408–5412 5409

zirconia catalysts was estimated through the S/Zr ratio [27]. XPSwas also reported to allow determining the oxidation state of Siand the nature of substituted group for a silicone elastomerconsisting of alkoxysilane and poly(dimethyl siloxane) (PDMS)[28], an acrylic film containing PDMS [29] and a silicone rubbercontaining PDMS [30,31] and polyurethane film containingpolyalkoxysiloxane [32]. Nevertheless, to the authors’ knowledge,the XPS characterization of the hydrolysis–condensation oftitanium alkoxides reactivity has not been described yet.

In this study, we propose an original approach based on XPS toevaluate the titanium alkoxide hydrolysis–condensation reactionsin thin films. Five alkoxides were compared: titanium propoxide[Ti(OPr)4], titanium butoxide [Ti(OBu)4], titanium isopropoxide[Ti(iOPr)4], titanium phenoxide [Ti(OPh)4] and tetrakis [9H-carbazole-9-yl-ethyl-oxy] titanium [Ti(OeCarb)4]. The influenceof steric hindrance on the reactivity of these alkoxides in thin filmswas highlighted through XPS experimental elemental composi-tions and binding energies values. TiO2 (anatase) was used as areference.

2. Experimental details

TiO2 nanopowder (25 nm, anatase) was purchased from Aldrich(99.7%). Titanium propoxide (Aldrich, 98%), titanium isopropoxide(Fluka, Purum), and titanium butoxide (Aldrich, 97%) were storedunder argon and used without any further purification.

Titanium phenoxide was synthesized by the method describedby Cayuela et al. [33]. The reaction was carried out according toScheme 1. The manipulations were carried out using Schlenktechniques. Briefly, titanium n-propoxide and phenol (99%, 1:4molar ratio, Aldrich) were mixed in dry toluene (Aldrich, 99.8%).After 1 h 30 heating with reflux, a dark red-orange solution wasobtained. After propanol elimination by fractional distillation atreduced pressure to complete the reaction, washing with dry n-hexane (Aldrich, >95%) and drying under vacuum at 40 8C, anorange powder was obtained and identified as titanium phenoxideby 1H and 13C NMR spectroscopy (Bruker DRX-400 MHz NMRspectrometer). It was stored under argon.

Tetrakis [9H-carbazole-9-yl-ethyl-oxy] titanium was synthe-sized following a similar route to Ti(OPh)4. The reaction was carriedout according to Scheme 2. The manipulations were carried out usingSchlenk techniques. Briefly, 9H-carbazole-9-ethanol (Aldrich, 95%)was purified by crystallization in ethanol and dried under vacuumduring 3 days at room temperature. A homogeneous yellow solutionwas obtained by dissolving the 9H-carbazole-9-ethanol (1.7 g,8 mmol) in toluene (10 mL, Aldrich, extra dry <30 ppm in water)under argon. Titanium isopropoxide (0.57 g, 2 mmol, Aldrich) wasadded drop by drop to the solution and an olive coloration was clearlyobserved. After 2 h vigorous stirring, the solution became orange. Thesolution was then heated 2 h with reflux. To complete the reaction, afractional distillation at 90 8C during 4 h under argon flow was

carried out to remove isopropanol (iPrOH). Toluene was removedunder reduced pressure to obtain a yellow powder. Anhydrousdiethyl ether (10 mL, Aldrich, 99.7%) was added to wash the powderand then removed with canula. Finally, the powder was dried during15 h under reduced pressure. It was stored under argon. Ti(OeCarb)4

was identified by 1H and 13C NMR spectroscopy (Bruker DRX-400 MHz NMR spectrometer). NMR shifts are described in Scheme 3.

To prepare the solution for thin film elaboration, the alkoxideswere solubilized in organic solvents. Isopropanol (Acros Organics)was used for Ti(OPr)4, Ti(iOPr)4 and Ti(OBu)4 and toluene (Aldrich,extra dry <30 ppm in water) for Ti(OPh)4 and Ti(OeCarb)4. Themolar concentration was kept identical for all the solutions. Thinfilms were elaborated by spin coating (2000 rpm, 60 s) (Specialitycoating system, P6700 series) on Si wafer under argon with arelative humidity reduced to about 0 to avoid any hydrolysis–condensation reaction during the coating process. To convert thetitanium precursor into TiO2, thin films were stored in a controlledenvironment (20 8C, RH = 50% and obscurity) for 24 h. The sampleswere further kept in vacuum for 2 h to remove residual alcohol.

X-ray photoelectron spectroscopy measurements were carriedout using a Riber SIA 200 spectrometer (Riber, Reuil Malmaison,France). A nonmonochromatized AlKa source generated at 10 kV,20 mA was used to irradiate the samples and the XPS spectra werecollected at 658 take-off angle between the sample and theanalyzer. The pressure in the instrumental chamber was less than1.0 � 10�4 Pa. No radiation damage was observed during the datacollection. All spectra were referenced to the C1s peak (C–C and C–H bonds) whose binding energy was fixed at 285.0 eV. Thestandard deviation of binding energy measurements was esti-mated to be about �0.15 eV. Atomic concentrations as determinedfrom XPS peak areas are considered to be accurate within around 10%.

3. Results and discussion

3.1. Hydrolysis–condensation advancement derived from XPS

chemical compositions

Titanium alkoxide structures are displayed in Scheme 4 as afunction of the steric hindrance.

Scheme 6.

Scheme 4.

Scheme 5.

V. Barlier et al. / Applied Surface Science 254 (2008) 5408–54125410

The reactions involved in the hydrolysis–condensation oftitanium alkoxides are reported in Scheme 5. The competitivemechanism between hydrolysis (1), oxolation (2) and alcolation(3) (Scheme 5) should lead to titanium oxide provided that thehydrolysis step (1) is complete. The hydrolysis–condensationprocess is characterized by the removal of alcohols derived fromalkoxide ligands (reactions (1) and (3)).

For the sake of a relevant analysis of XPS experimental data,theoretical atomic concentration calculations were considered toevaluate the hydrolysis–condensation advancement (x) of tita-nium alkoxides. C/Ti/O theoretical ratio was calculated for all thepossible compositions between the no reactivity case (x = 0) andthe full reactivity case (x = 1) (see Scheme 6). In the case ofTi(OeCarb)4, C/Ti/O theoretical ratio was calculated excluding thepresence of N in the structure. Assuming that alcolationcontributes also to the creation of residual alcohol, this approachcompares theoretical calculations based only on hydrolysis processto experimental hydrolysis–condensation process. Hence, reactionadvancement (x) cannot be assimilated to the actual hydrolysisadvancement but it allows meaningful comparison.

Table 1 displays the XPS surface elemental compositions of thevarious titanium alkoxide thin films after their conversion in thecontrolled environment (20 8C, RH = 50% and obscurity) for 24 h.On the basis of the theoretical atomic concentration C/O/Ticalculations, a specific reaction advancement (x) could bedetermined for each alkoxide. Indeed, when displaying elementalcompositions as a function of x on a ternary graph, a curve of thecomposition variation was obtained (Fig. 1) and experimentalresults (cross) could then satisfactorily be compared to thetheoretical composition variation law (squares).

The maximum reaction advancements were obtained forTi(OPr)4 and Ti(OBu)4 (x = 0.88 and x = 0.92, respectively)(Table 1). Ti(iOPr)4 and Ti(OPh)4 displayed a slightly lowerhydrolysis–condensation rate (x = 0.75 for both precursors). Therelative amount of N and C revealed a lower hydrolysis–condensation rate (x = 0.65) for Ti(OeCarb)4. These results showan influence of the nature of ligands onto the hydrolysis–

Table 1Experimental (XPS) versus theoretical (calculation) atomic compositions of titanium al

Ti(OPr)4 Ti(OBu)4 Ti(iOPr)4

Experimental Theoretical Experimental Theoretical Experimenta

% C 22 23.1 20 19.3 37

% O 58 61.5 64 64.5 48

% Ti 20 15.4 16 16.2 15

% N – – – – –

x 0.88 0.92 0.75

condensation rate. This difference highlights more precisely thatthe hydrolysis–condensation rate decreases with steric hindrance.Propoxide and butoxide precursors led to a strong reactivity withhumidity whereas phenoxide or isopropoxide showed a lowerreactivity. Very bulky ligands, like carbazole groups, exhibited abetter stability to hydrolysis–condensation. In solution, thechemical reactivity of metal alkoxides towards hydrolysis andcondensation mainly depends on the steric hindrance of alkoxidegroups. Transition metal alkoxides are usually too reactive and areusually stabilized by complexation to prevent fast condensation[11,12]. XPS results displayed here highlight the influence of thesteric hindrance in thin films through the possible identification ofthe reaction advancement at the surface by comparison totheoretical calculations. However, even if XPS analysis appearsreliable to evidence the variation in reaction advancement as afunction of the steric hindrance, it was not possible in ourconditions to exhibit a difference between, on one hand, butoxideand propoxide and on the other hand, isopropoxide and phenoxidewhile such a difference was expected from theoretical calculations.This highlights that the XPS chemical composition variations arenot sufficiently precise to conclude for relatively similar chemicalenvironments. The variation in the binding energy values observedby XPS was then studied.

3.2. Condensation state derived from the variation in XPS elemental

chemical environment

The variation of the binding energy values extracted from theXPS measurements is an accurate indication of the chemicalenvironment modification.

Table 2 shows the XPS binding energy for the Ti and O corelevels of the various titanium alkoxides after their conversion inthe controlled environment (20 8C, RH = 50% and obscurity) for24 h as well as for the reference TiO2 powder (anatase). The Ti2pdata showed the Ti2p contributions at around 465 eV (Ti2p1/2

peak) and around 459 eV (Ti2p3/2 peak). The literature [34–37]indicates that the Ti2p3/2 binding energy around 461 eV corre-sponds to Ti in a tetrahedral environment and that around 459 eV

koxides hydrolyzed in thin films (x is reaction advancement)

Ti(OPh)4 Ti(OeCarb)4

l Theoretical Experimental Theoretical Experimental Theoretical

37.5 54 54.5 76 75.4

50 36 36.4 16 15.4

12.5 10 9.1 3 3.8

– – – 5 5.4

0.75 0.65

Fig. 2. XPS O1s spectra of the titanium alkoxides hydrolyzed in thin films for

propoxide (a), butoxide (b), isopropoxide (c), phenoxide, (d) 9H-carbazole-9-yl-

ethyl-oxy, (e) precursors.

Fig. 1. XPS elemental compositions of titanium alkoxide hydrolyzed in thin films as a function of the hydrolysis–condensation advancement process for propoxide (a),

butoxide (b), isopropoxide (c), phenoxide (d), 9H-carbazole-9-yl-ethyl-oxy (e), precursors. The cross stands for the elemental composition derived from XPS analysis.

V. Barlier et al. / Applied Surface Science 254 (2008) 5408–5412 5411

corresponds to Ti in an octahedral environment. Tetrahedral andoctahedral environments can be assigned to noncondensed andfully condensed titanium alkoxides, respectively. In this study,Ti2p3/2 binding energy values indicate rather octahedral environ-ments (Table 2). It means that saturation of the Ti ion coordinationsites may occur due to Ti–O–Ti bond formation. The Ti2p3/2 valuesare still exhibiting some slight shift differences as a function of thesteric hindrance. More precisely, values slightly shifted towardshigher binding energy, meaning that an increasing number ofreaction intermediates (characterized by an incomplete condensa-tion) are probably observed, which is consistent with the trendexhibited by above XPS chemical composition data.

The O1s binding energy peaks were observed between 530 and532 eV (Fig. 2). Peaks were broad, indicating possible multiplecontributions. Here, three different contributions are possible: Ti–O–Ti (529.5–530.5 eV) [34–40], Ti–O–H or Ti–O–C (531–532.5 eV)[34–36,39–43] and Ti–O–O (532–533.6 eV) [34–36,39,40,41].However in our case, the deconvolution of these spectra appearedrelatively adventurous.

TiO2 anatase O1s binding energy value (530.65 eV) wasassigned to a complete condensation rate. For titanium alkoxides,when considering a unique O1s peak, O1s binding energy appearsto regularly increase with the Ti site steric hindrance from530.70 eV for Ti(OPr)4 to 531.80 eV for Ti(OeCarb)4). Consideringthe possible contributions, this shift can then be related to acondensation rate less significant (less Ti–O–Ti) for more hinderedTi sites.

Table 2XPS Ti2p and O1s core levels of the various titanium alkoxides hydrolyzed in thin

films and of the TiO2 anatase reference

Precursors Binding energies of hydrolyzed precursors (eV)

O Ti

O1s Ti2p1/2 Ti2p3/2

TiO2 530.65 464.53 459.07

Ti(OPr)4 530.71 464.87 459.12

Ti(OBu)4 530.94 464.87 459.18

Ti(iOPr)4 531.12 465.05 459.24

Ti(OPh)4 531.35 465.17 459.24

Ti(OeCarb)4 531.77 465.17 459.36

4. Conclusion

This study focused on the use of X-ray photoelectron spectro-scopy (XPS) to determine the hydrolysis–condensation state oftitanium alkoxides in thin films. For that purpose, commerciallyavailable titanium alkoxides were used [Ti(OPr)4,Ti(OBu)4 andTi(iOPr)4] and bulky precursors were synthesized [Ti(OPh)4 andTi(OeCarb)4]. All precursors were deposited on Si wafer, hydro-lyzed by contact with controlled environment (20 8C, RH = 50 andobscurity) for 24 h and kept in vacuum to remove residual alcohols.The elemental composition allowed determining the reactionadvancement by comparison with a theoretical elemental compo-sition law. By matching data, an excellent agreement with theinfluence of steric hindrance on the reactivity appeared. Thisanalysis was corroborated by the study of Ti2p and O1s core levelbinding energy values allowing evaluating the condensation stateof titanium alkoxides. Ti2p binding energies showed the Ti atomwas in octahedral environment but also that reaction intermedi-ates (incomplete condensation) were observed more significantlyas a function of steric hindrance. Furthermore, the O1s bindingenergy shift was related to a condensation rate less significant formore hindered Ti sites. In summary, the influence of steric

V. Barlier et al. / Applied Surface Science 254 (2008) 5408–54125412

hindrance on the reactivity of titanium alkoxides was highlightedthrough consistent XPS experimental elemental composition andbinding energy values. These results corroborate the validity of aXPS approach to determine the hydrolysis–condensation extent inthin films.

Acknowledgements

This study was supported by REGION RHONES ALPES (pro-spective program).

We thank Dr. E. Drockenmuller (Laboratoire Materiaux Poly-meres et Biomateriaux, UCBL) for fruitful discussions and Dr. F.Boisson (NMR department of the federation des polymeristesLyonnais, FR 2151, CNRS) for NMR characterization of newsynthesized precursors.

References

[1] A. Hagfeldt, M. Gratzel, Acc. Chem. Res. 33 (2000) 269–277.[2] M. Wagemaker, A. Kentgens, F. Mulder, Nature 418 (2002) 397–399.[3] A. Manthiram, J. Kim, Chem. Mater. 10 (1998) 2895–2909.[4] S. Burnside, V. Shklover, C. Barbe, Chem. Mater. 10 (1998) 2419–2425.[5] M. Ritala, M. Leskela, L. Niinisto, Chem. Mater. 5 (1993) 1174–1181.[6] M. Gopal, W. Chan, L. DeJonghe, J. Mater. Sci. 32 (1997) 6001–6008.[7] M. Nakamura, L. Sirghi, T. Aoki, Surf. Sci. 507 (2002) 778–782.[8] A. Soloviev, R. Tufeu, C. Sanchez, J. Phys. Chem. B 105 (2001) 4175–4180.[9] J. Blanchard, S. Barboux-Doeuff, J. Marquet, C. Sanchez, New J. Chem. 19 (1995)

929–941.[10] K. Terabe, K. Kato, H. Miyazaki, J. Mater. Sci. 29 (1994) 1617–1622.[11] M. Crisan, A. Braileanu, M. Raileanu, D. Crisan, V. Teodorescu, R.V. Marinescu, J.

Madarasz, G. Pokol, J. Therm. Anal. Cal. 88 (2007) 171–176.

[12] J. Livage, C. Sanchez, J. Non-Cryst. Solids 145 (1992) 11–19.[13] K. Egawa, K. Suzaki, Y. Sugahara, J. Sol–Gel Sci. Technol. 30 (2004) 83–88.[14] A. Leaustic, F. Babonneau, J. Livage, Chem. Mater. 1 (1989) 240–247.[15] A. Leaustic, F. Babonneau, J. Livage, Chem. Mater. 1 (1989) 248–252.[16] S. Doeuff, M. Henry, C. Sanchez, Mater. Res. Bull. 25 (1990) 1519–1529.[17] S. Barboux-Doeuff, C. Sanchez, Mater. Res. Bull. 29 (1994) 1–13.[18] D.D. Dunuwila, D. Gagliardi, K.A. Berglund, Chem. Mater. 6 (1994) 1556–1562.[19] D.P. Birnie, N.J. Bendzko, Mater. Chem. Phys. 59 (1999) 26–35.[20] C. Bonhomme, C. Coehlo, F. Babonneau, Acc. Chem. Res. 40 (2007) 738–746.[21] M. Harris, A. Singhal, L. Toth, J. Sol–Gel Sci. Technol. 8 (1997) 41–47.[22] J. Blanchard, M. In, B. Schaudel, C. Sanchez, Eur. J. Inorg. Chem. (1998) 1115–1227.[23] E. Rude Payro, J. Llorens Llacuna, J. Non Cryst. Sol. 352 (2006) 220–2225.[24] N.V. Golubko, M.I. Yanovskaya, I.P. Romm, A.N. Ozerin, J. Sol–Gel Sci. Technol. 20

(2001) 245–262.[25] K. Jang, M. Song, S. Cho, J. Kim, Chem. Commun. 13 (2004) 1514–1515.[26] G. Puccetti, R. Leblanc, J. Phys. Chem. B 102 (1998) 9002–9005.[27] L.B. Hamouda, A. Ghorbel, J. Sol–Gel Sci. Technol. 39 (2006) 123–130.[28] S. Bullock, E. Johnston, K.J. Wynne, J. Colloid Interface Sci. 210 (1999) 18–36.[29] B.D. Ratner, P.K. Weathersby, J. Appl. Polym. Sci. 22 (1978) 643–664.[30] D.W. Dwight, J.E. MacGrath, J.S. Riffle, Polym. Prep. 20 (1979) 528–530.[31] D.T. Clark, J. Peeling, J. Polym. Sci. 14 (1976) 543–551.[32] R. Tomita, S. Urano, S. Kohiki, J. Polym. Sci. 40 (2002) 2917–2926.[33] J. Cayuela, V. Bounor-Legare, P. Cassagneau, A. Michel, Macromolecules 39 (2006)

1338–1346.[34] Y. Gao, Y. Masuda, K. Koumoto, J. Korean Ceram. 40 (2003) 213–218.[35] Y. Gao, Y. Masuda, K. Koumoto, Langmuir 20 (2004) 3188–3194.[36] Y. Gao, Y. Masuda, K. Koumoto, Chem. Mater. 16 (2004) 1062–1067.[37] L. Ge, M. Xu, H. Fang, M. Sun, Appl. Surf. Sci. 253 (2006) 720–725.[38] Y. Masuda, Y. Jinbo, T. Yonezawa, K. Koumoto, Chem. Mater. 14 (2002) 1236–

1241.[39] D. Huang, Z. Xiao, J. Gu, N. Huang, C. Yuan, Thin Solid Films 305 (1997) 110–

115.[40] F. Zhang, S. Jin, Y. Mao, Z. Zheng, Y. Chen, X. Liu, Thin Solid Films 310 (1997) 29–33.[41] L.D. da Silva, Y. Gushikem, S. de Castro, J. Appl. Polym. Sci. 58 (1995) 1669–

1673.[42] J.C. Yu, L.Z. Zhang, Z. Zhang, J.C. Zhao, Chem. Mater. 15 (2003) 2280–2286.[43] N.R. Rao, P. Ganguly, M.S. Hegde, D.D. Sarma, J. Am. Chem. Soc. 109 (1987) 6893.