摘要:

Theoretical study of the structure and torsional potential of pyrrole oligomers Salvatore Mille–ori* and Andrea Alparone Dipartimento di Scienze Chimiche, di Catania V iale A. Doria 8, 95125 Catania, Italy Universita` The molecular structure and conformational behaviour of 2,2@-bipyrrole (a-BPy), 2,2@ : 5@,2A-terpyrrole (a-TPy) and 2,2@ : 5@,2A : 5A, 2”-quaterpyrrole (a-QPy) have been determined by ab initio HF, MP2 and density functional theory methods, using the 6-31G* basis set.The syn%anti interconversion process through internal rotation about the CwC inter-ring bond generates in all calculations a three-barrier, four-fold potential. Minima are found in the anti-gauche and syn-gauche regions, maxima for the planar and perpendicular conformations, the anti-gauche structure being the global minimum. The energetics and the location of these critical points signi–cantly depend on the theoretical method, the electron correlation and zero-point vibrational energies beng important factors.The relaxed rotor approximation must be used to obtain quantitative results, especially in the syn region where strong NH»NH dipole interactions are present which induce some loss of planarity of the pyrrole ring and tilting of the NH bond with respect to the ring plane. HF and B3LYP potential-energy curves are rather —at, particularly around the planar anti conformation, suggesting conformational —exibility. By contrast MP2 calculations strongly favour the anti-gauche form, indicating hindered rotation.The energetics and conformational behaviour of a-oligopyrroles are closely related to the torsional potential of the parent a-BPy. The minimum-energy conformations of a-TPy and a-QPy were all found to be anti-gauche (helixlike) structures. There is evidence that the p-electron system strengthens, the geometrical parameters of the pyrrole ring rapidly converge and the torsional potential around the planar anti conformation decreases as the a-oligomerization increases, suggesting that in the polymer limit planar, very conformationally —exible structures are highly probable, in agreement with the X-ray results in the solid.The potential-energy curves were analyzed in terms of conjugative and nonbonding interactions through a Fourier decomposition procedure. This highlights the predominant role of nonbonding interactions over conjugative ones and the peculiar behaviour of the MP2 method which favours hyperconjugative and probably NH»p hydrogen-bonding interactions which stabilize the perpendicular conformation.Five-membered heterocyclic p-conjugated polymers such as polypyrrole and polythiophene have attracted wide interest as materials with interesting optical, nonlinear optical and electrical conduction properties.1h5 Obtaining the desired physical properties strongly depends on structure modulation as de–ned by internal forces, such as the torsional barriers between adjacent rotamers and/or packing forces in the solid.Useful information on the optimal structural arrangement and properties of the polymer can be derived from experimental and/or theoretical data on small oligomers. In the absence of strong steric eÜects even small conjugative forces can stabilize planar structures, maximizing anisotropic properties, such as electrical conduction and polarizability, which depend on the one-dimensional delocalization of the electronic charge.Structurally relevant information can be derived from the ìeÜective conjugation lengthœ of the polymer.6 Similarly, vectorial properties such as the –rst hyperpolarizability and dipole moment, and the orientability of the poled polymer in an electric –eld, are in—uenced by the conformational —exibility or free rotation of adjacent rotamers. Thus, it is of interest to acquire reliable theoretical predictions on the evolution of the molecular structural parameters and energetics along the series of computationally accessible oligomers.Polypyrrole is one of the most intensively studied polymers. It exhibits high conductivity when it is doped7,8 and large third-order nonlinear optical response.9 Interest has also focused on applications as cathode materials for rechargeable batteries,10 gas sensors,11 selective biosensors,12 electromagnetic shielding materials,13 ion-exchange chromatography resins14 and membranes15 and as electrorheological materials.16 Experimental structural information on oligopyrroles is scarce.X-Ray data on bipyrrole and terpyrrole crystals4 indicate a planar con–guration. N-substitution or 3,3@-substitution causes important twisting around the essentially single C2wC2, bond4,17 (Fig. 1), producing relevant changes in the spectroscopic behaviour.18 Polypyrrole itself is planar in the solid.4 Gas-phase data are restricted to the microwave results of the pyrrole monomer.19 The electronic properties,20 conformational disorder,21 vibrational spectra6,22 and polarizabilities20d,23,24c of oligopyrroles, including pyrrole, have been extensively studied in order to understand the electronic and structural properties of the polymer.As for theoretical studies, the correlated ab initio equilibrium structure of pyrrole has been reported24 using MP2 theory. Density functional theory (DFT) has also been applied.22a,24d The equilibrium geometry of 2,2@-bipyrrole has been obtained at the HF level only using 3-21G20d and MIDI- 422a basis sets, while the torsional potential has been investigated at the HF ab initio level using minimal20c,25 and double-zeta basis sets under the rigid rotor22a,25 and the relaxed rotor26 approximations.The results diÜer signi–- cantly. The minimal basis set calculations predict the coplanar anti structure to be the most stable conformation followed by the syn one; by contrast split bases predict a global antigauche minimum near 150° and a second local syn-gauche Fig. 1 Atom numbering of 2,2@-bipyrrole. / is the torsion angle formed by the planes of the pyrrole rings. /\180° denotes the anti form, f\0° denotes the syn form. J. Chem. Soc., Faraday T rans., 1998, 94(1), 25»32 25minimum at ca. 45°, the syn conformation being the least stable one. This strong basis set dependence suggests the use of higher-level calculations which also should include electron correlation eÜects. The HF/MIDI-4 equilibrium structures of terpyrrole and quaterpyrrole have been reported.22a However, the torsional potentials in these molecules and the relative stability of the planar versus twisted conformation have never been investigated.The remaining theoretical investigations on these subjects have used semiempirical methods.27 The purpose of this work is a theoretical study of the conformational behaviour and torsional potentials of small pyrrole oligomers up to quaterpyrrole as models of the polypyrrole chain, using conventional ab initio and DFT calculations.The latter approach has been applied successfully to many chemical problems.28 It explicitly includes approximate electron correlation eÜects at a lower computational cost and has been proved to give results competitive with the most sophisticated post-HF methods, particularly when gradientcorrected functionals that also include some exact HF exchange are used (the so-called hybrid functionals).28,29 DFT is here applied for the –rst time to the present topics.It has been applied previously to predict the coupling positions in the electropolymerization reactions of pyrrole through calculations of p-spin density distribution in the radical cations.30 Theoretical methods The calculations were performed on IBM RS/6000 and JEPSSEN computers using the GAUSSIAN 94 program31 with the 6-31G* basis set. Electron correlation was introduced at second-order (MP2) perturbation theory M‘ller»Plesset level in calculations on pyrrole and 2,2@-bipyrrole, and by DFT in all cases.The Becke three-parameter exchangefunctional32 with non-local correction provided by the Lee» Yang»Parr method,33 denoted B3LYP, was used. The molecular geometries were fully optimized. The potentialenergy curve for the anti%syn isomerization was computed by a potential surface scan using redundant internal coordinates at –xed dihedral angle, starting from N1wC2wC2{wN1{ the planar anti conformation (/\180°).To evaluate the eÜect of the geometry both the rigid and relaxed rotor approximations were used. The relative energies of the rotamers with respect to the planar anti form were –tted to a six-term truncated Fourier expansion:34 V (/)\ ; n/1 6 1 2 Vn[1[cos n(180[/)] where V is the relative energy at torsional angle /. Critical points in the potential-energy curve were precisely located by direct optimization and tested by vibrational analysis. Zero-point vibrational energies (ZPVE) were obtained at both HF and B3LYP levels.Results and Discussion Pyrrole and 2,2º-bipyrrole : geometries and energetics The HF/6-31G*, MP2/6-31G* and B3LYP/6-31G* geometries of pyrrole are reported in Table 1 along with the experimental microwave data.19 Our results agree with the previous estimates at a comparable level of theory,22a,24 so we note only a few points here : (i) HF calculations overestimate the CwC distance and underestimate CxC and CwN distances, thus they overestimate bond length alternation (*r\0.069 ” vs.an experimental value of 0.035 Correlated calculations ”). correct this de–ciency, particularly MP2 (*r\0.035 by ”), providing a greater p-electron stabilization of the ring. (ii) MP2/6-31G* and B3LYP/6-31G* geometrical parameters are in overall good agreement, both displaying the same bond length *r rms value of 0.007 Bond angles are more accu- ”. Table 1 Equilibrium geometries of pyrrolea HF MP2 B3LYP /6-31G* /6-31G* /6-31G* exp.b N1wC2 1.363 1.373 1.375 1.370 C2xC3 1.358 1.383 1.378 1.382 C3wC4 1.427 1.418 1.425 1.417 N1wH 0.992 1.011 1.008 0.996 C2wH 1.070 1.081 1.080 1.076 C3wH 1.071 1.082 1.082 1.077 rmsc 0.012 0.007 0.007 C2wN1wC5 109.5 110.1 109.8 109.8 N1wC2wC3 108.1 107.4 107.7 107.7 C2wC3wC4 107.1 107.5 107.4 107.4 HwC2wC3 130.8 131.4 131.2 130.8 HwC3wC2 126.0 125.6 125.7 125.5 rmsc 0.3 0.3 0.2 l/D 1.90 1.98 1.91 1.74 a Bond lengths in bond angles in degrees.b Gas phase microwave ”, values from ref. 19. c Root mean square deviation rms\A;i n (xi, exp.[xi.calc.)2NnB1@2. rately predicted by the B3LYP calculations. (iii) electron correlation is necessary for an accurate description of the molecular geometry. Pyrrole is a molecule of medium polarity with an experimental gas-phase dipole moment of 1.74 D.19§ HF/6-31G* and B3LYP/6-31G* calculations overestimate k by 9»10%, while MP2/6-31G* calculations overestimate it by a somewhat greater amount (14%), principally owing to a greater pelectron contribution from the N atom. The theoretical data probably suÜer from the lack of diÜuse functions in the basis set.For 2,2@-bipyrrole we started our conformational analysis by optimizing the two planar anti and syn structures. The geometrical parameters of the anti form are reported in Table 2 together with the experimental planar anti structure in the solid4 for comparison. No signi–cant diÜerences were found between the geometrical parameters of the two computed planar forms.Both MP2/6-31G* and B3LYP/6-31G* data for the anti structure are in good agreement with experiment, the latter giving a somewhat better rms *r value. The largest discrepancy is encountered in the CxC double bond which is overestimated by 0.01»0.015 although the bond-length dif- ”, ference r(C2xC3)[r(C4wC5)\0.012 is perfectly repro- ” duced. The two pyrrole rings are connected through a CwC bond 1.448 long both in the experiment and in the corre- ” lated calculations.This is somewhat shorter than a normal single CwC bond (1.51»1.52 which implies partial ”35), double bond character and some delocalization between the rings. Indeed the bond length alternation in the dimer is reduced relative to the monomer, particularly when the ì internal œ C2xC3 and C3wC4 bonds are considered, while the ìexternalœ C4xC5 bond length remains unchanged. The coplanar anti and syn structures are transition states in the potential energy curve of 2,2@-bipyrrole, one imaginary frequency being found in both cases in all the calculations, suggesting rotation of the pyrrole ring around the bond: C2wC2{ 70 and 54 cm~1 in the anti conformer in the HF/6-31G* and B3LYP/6-31G* calculations, respectively. The corresponding values for the syn conformer are 123 and 114 cm~1. Loss of planarity is generated by CH»NH interactions in the anti form, while both H»H interactions and Coulombic repulsions between the two nearly parallel N»H dipoles operate in the syn form.The syn conformation is less stable than the anti one by 2.86 and 2.83 kcal mol~1 at the HF/6-31G* and B3LYP/6- 31G* levels, respectively, in good agreement with the 2.72 kcal § 1DB3.335 64]10~30 C m. 26 J. Chem. Soc., Faraday T rans., 1998, V ol. 94Table 2 Equilibrium geometries of anti forms of 2,2@-bipyrrole and 2,2@ : 5@,2A-terpyrrole ; basis set 6-31G* bond length bond angle /” HF MP2 B3LYP exp.a /degrees HF MP2 B3LYP 2,2@-bipyrrole N1wC2 1.365 1.376 1.380 1.374 C2wN1wC5 110.0 110.7 110.4 N1wC5 1.363 1.373 1.375 1.369 N1wC5wC4 108.1 107.3 107.7 C2xC3 1.365 1.394 1.390 1.380 C3wC4wC5 107.1 107.6 107.4 C3wC4 1.423 1.415 1.421 1.418 C2wC3wC4 107.6 107.9 108.0 C4xC5 1.356 1.383 1.378 1.368 N1wC2wC3 107.3 106.5 106.6 C2wC2{ 1.458 1.447 1.448 1.448 C3wC2wC2{ 131.2 132.2 131.7 N1wH1 0.992 1.012 1.008 2,2@ : 5@,2A-terpyrrole N1wC2 1.365 1.381 1.368 C2wN1wC5 109.9 110.4 N1{wC2{ 1.365 1.380 1.391 C2{wN1{wC5{ 110.5 111.0 N1wC5 1.363 1.375 1.369 N1wC5wC4 108.1 107.7 C2xC3 1.366 1.390 1.359 C3wC4wC5 107.1 107.4 C2{xC3{ 1.365 1.390 1.350 C2wC3wC4 107.6 108.0 C3wC4 1.423 1.421 1.412 C2{wC3{wC4{ 107.5 108.0 C3{wC4{ 1.420 1.416 1.412 N1wC2wC3 107.3 106.6 C4xC5 1.357 1.378 1.364 N1{wC2{wC3{ 107.2 106.5 C2wC2{ 1.457 1.445 1.449 C3wC2wC2{ 131.1 131.6 N1wH1 0.992 1.008 C3{wC2{wC2 131.3 131.7 k/D 1.80 1.81 a Solid-state X-ray values from ref. 4. mol~1 HF/MIDI-4 –gure reported by Kofranek et al.22a These values are reduced to 2.69 and 2.63 kcal mol~1, respectively, when the ZPVE is taken into account.The corresponding MP2/6-31G* value, uncorrected for ZPVE, is 2.64 kcal mol~1. Thus both correlation eÜects and ZPVE corrections appear to have a modest role on the syn»anti energy diÜerence. This is at some variance with respect to the results on 2,2@-bithiophene36,37 and 2,2@-bifuran,37 where the MP2/6- 31G* correlation energy decreases by ca. 37 and *Esynhanti 30%, respectively. The results also evidence signi–cant eÜects of dipole»dipole interactions in the syn form. In comparison, the related 2,2@-bithiophene and 2,2@-bifuran systems show an MP2/6-31G* syn»anti energy diÜerence of 0.9836,37 and 1.6237 kcal mol~1, respectively, the corresponding B3LYP/6-31G* values being 1.00 and 1.78 kcal mol~1.37 The above results suggest that the minimum-energy conformations in the free molecule have nonplanar structures.Thus the most interesting conformational parameter is the rotation angle / around the bond together with the concomi- C2wC2{ tant bond-length variation, this being an indicator of C2wC2{ p-electron interactions between the rings. The variation of as a function of / is shown in Fig. 2. The curves r(C2wC2{) obey a cos / law, but around the 90° region, indicating that in the perpendicular conformation besides orbital Cpz»Cpz overlap other factors in—uence the distance. On C2wC2{ passing from the planar to the 90° conformation r(C2wC2{) increases by 0.014, 0.011 and 0.018 at HF/6-31G*, MP2/6- ” 31G* and B3LYP/6-31G* levels, respectively.These are modest changes, suggesting reduced p delocalization between the rings. Anyway they indicate opposite behaviour of the MP2 and B3LYP methods, the latter providing a greater pelectron contribution to the bond, the –rst a smaller one, relative to the HF calculations. This behaviour was already evidenced in bipyrrole and bithiophene by STO-3G calculations, 20c which predicted a bond elongation of C2wC2{ 0.014 and 0.013 respectively.It was suggested20c that this ”, short CwC bond is a ìgenuine feature of an sp2»sp2 single bondœ in these compounds, the p-electron contribution to the bond being 6.1 and 6.4%, respectively. Indeed the inter-ring distance in bipyrrole (1.448 in the solid4) is comparable to ” that found in bithiophene from X-ray (1.447 and electron ”38) diÜraction (1.456 studies. Following these results the ”39) barrier through the perpendicular conformation in 2,2@-bipyrrole is expected to be rather small and it should increase in the order MP2\HF\B3LYP.This was indeed the case. The HF/6-31G*, MP2/6-31G* and B3LYP/6-31G* relative energies of 2,2@-bipyrrole rotamers in the 0»180° relaxedrotation scan around the bond in steps of 30° under C2wC2{ symmetry constraint are plotted in Fig. 3 as a function of C2 the rotation angle. The corresponding rigid torsional potentials are also reported to highlight the eÜect of the molecular geometry relaxation.In the rigid rotor approximation the geometry of the planar anti (/\180°) conformation was C2v used as a reference. All calculations predict a three-barrier, four-fold type potential for the anti%syn interconversion process. The geometrical parameters appear to be little in—uenced by the conformation. However in the syn-gauche form the pyrrole ring losses some planarity (up to ca. 1.5°) and the NwH bond displays a wagging angle u with respect to the NwC2wC5 plane of 5.0, 8.3 and 4.7° at HF/6-31G*, MP2/6- 31G* and B3LYP/6-31G*, respectively. Reoptimization of the syn form under symmetry gives corresponding u values of C2 5.7, 4.8 and 6.3°. This loss of full coplanarity induces very Fig. 2 Dependence of the CwC inter-ring bond length on the torsion angle of 2,2@-bipyrrole J. Chem. Soc., Faraday T rans., 1998, V ol. 94 27Fig. 3 Torsion potential of 2,2@-bipyrrole.The curves were obtained by –tting the relative energies of the rotamers to a six-term Fourier expansion. Open marks and dashed lines refer to rigid-rotor approximation results. slight energetic changes (ca. 0.02»0.03 kcal mol~1) except for the MP2 calculations where the syn form is 0.44 kcal C2 mol~1 more stable than the one. All the calculations indi- C2v cate a twisted anti-gauche structure as the global minimum with relative energies with respect to the planar form of ER [0.71, [1.48 and [0.40 kcal mol~1 at the HF, MP2 and B3LYP levels, respectively, at corresponding dihedral angles of 147.5, 138.0 and 152.1°.Another local minimum is located in the syn-gauche region (/\42.1, 51.2 and 37.1° at HF, MP2 and B3LYP levels, respectively, with corresponding values ER of 0.60, [0.10 and 1.23 kcal mol~1). The two minima are separated by a relatively small 90° barrier (HF), [ER\1.43 [0.01 (MP2), 2.39 (B3LYP) kcal mol~1]. These results are in qualitative agreement with previous HF/DZ calculations, 22a,25 but not with STO-3G20c,25 and semiempirical calculations,27 which fail to predict two stable gauche conformations and overestimate the perpendicular barrier.The correlation eÜect on the rotational barriers is remarkable. The HF 0.71 kcal mol~1 –gure of the 0° barrier falls to 0.40 kcal mol~1 ([44%) in the B3LYP calculations, while it is doubled in the MP2 calculations. However, the energy diÜerence between the anti-gauche and syn-gauche conformers (and thus their relative populations) has little dependence on the correlation.The MP2 correlation eÜect on the perpendicular barrier is signi–cant : the 2.26 kcal mol~1 HF value in the anti-gauche]syn-gauche conversion falls to 1.64 kcal mol~1 (ca. [30%), while for the inverse process the barrier is half that for the HF one. As a result the MP2 calculations predict a transition-state conformation that is almost isoenergetic with the planar anti structure.ZPVE corrections are equally important. They destabilize the anti-gauche form by 50% (HF) and 70% (B3LYP), the syngauche form by 32% (HF) and 12% (B3LYP), and the perpendicular form by 13% (HF) and 4% (B3LYP). Therefore ZPVE consistently —attens the potential-energy surface, especially in the anti region. The rigid-rotor approximation produces potential-energy curves where the relative energies of the critical points are signi –cantly overestimated and the torsion angles of the gauche forms are biased towards the twisted conformation.The importance of a full molecular optimization along the interconversion process is particularly evident in the MP2 calculations, where the rigid-rotor approximation does not evidence a stable syn-gauche conformer as well as a precise location of the perpendicular transition state, producing in this region a metastable plateau. Thus the rigid-rotor approximation can give only a qualitative description of the torsional potential of 2,2@-bipyrrole.The above results suggest the following observations : (i) the potential-energy surface of 2,2@- bipyrrole in a wide torsional potential range is rather —at, the energy diÜerence among critical points being within 3 kcal mol~1, suggesting a high degree of conformational —exibility, particularly in solution where twisted and syn forms are favoured owing to their higher dipole moment. The potentialenergy curve in the anti region is particularly —at. B3LYP calculations predict essentially free rotation in the 180^50° range. Planar structures in the solid4 are therefore conceivable.(ii) B3LYP and MP2 calculations give opposite results with respect to HF calculations. The –rst favour p-electron contributions stabilizing planar forms consistently with the noted dependence of the distance on /, the latter evi- C2wC2{ dence nonbonding interactions, thus favouring twisted conformers. Experimental data are not available to assess the most correct prediction.However, note that in 2,2@-bithiophene, which shows conformational behaviour similar to that of 2,2@-bipyrrole, B3LYP/6-31G* calculations provide better agreement with the experimental 0° and perpendicular barriers than MP2 calculations.37 Torsional potentials The solid curves in Fig. 3 represent the Fourier-–tted relative energies of the rotamers. The Fourier analysis appears to be of good accuracy, with the relative energies and torsion angles of the critical points (Table 3) being reproduced to within 1° and 0.04 kcal mol~1, respectively, with respect to those obtained by direct optimization, but with syn-gauche minimum energies and torsion angles in error by up to 0.2 kcal mol~1 and 5°, Table 3 Dihedral angles //degrees, total, and relative energies, (kcal mol~1), of pyrrole oligomers; basis set ET (Eh) ER 6-31G*{ anti anti-gauche syn-gauche syn perpendicular [ET ER / ER / ER ER / ER bipyrrole HF 416.47073 0.0 145.8 [0.73 42.5 0.36 2.84 81.1 1.53 MP2 417.81649 0.0 138.2 [1.48 45.7 [0.38 2.64 73.8 0.16 B3LYP 419.14006 0.0 150.0 [0.37 40.3 1.05 2.80 82.3 2.48 terpyrrole (double rot.) HF 624.13378 0.0 148.4 [1.21 43.7 1.09 5.96 82.6 3.25 B3LYP 628.13065 0.0 158.0 [0.51 39.7 2.58 5.68 82.7 5.41 quaterpyrrole (rigid rot.) HF (single internal rot.) 831.79689 0.0 149.2 [0.37 46.4 1.14 3.16 85.2 1.99 HF (single external rot.) 831.79689 0.0 149.1 [0.35 47.1 1.22 3.11 84.5 1.95 28 J.Chem. Soc., Faraday T rans., 1998, V ol. 94respectively. Strong electrostatic and steric interactions which, as previously noted, cause loss of coplanarity of the NH bond, are responsible for this behaviour. This is particularly evident in the MP2 calculations where, in the syn-gauche region, a 30° step in the potential-energy curve building was no longer sufficient to achieve the reported accuracy. The V (/) term values of the Fourier expansion are reported in Table 4.They allow us to analyze the potential-energy curve in terms of conjugative, steric and electrostatic interactions. It is known that conjugative interactions contribute only to the term, while nonbonding interactions contribute V2 to all terms. Fig. 4 shows the Fourier decomposition of the MP2/6-31G* potential-energy function taken as a model for discussion. As expected for a four-fold potential, the shape of the curve is de–ned by the term. The term dominates V4 V1 and accounts for the destabilization, owing to steric interactions, of the planar forms and for the syn»anti energy diÜerence.The term is negative in the MP2 calculations but V2 positive in the HF and B3LYP ones. Since p-conjugation cannot be stabilizing in the perpendicular conformation, the peculiar behaviour of the MP2 approach in this system has to be ascribed to contributions of r»p hyperconjugative interactions and/or to NH»p hydrogen-bonding interactions. Hyperconjugation was previously invoked by Hernandez and Lopez-Navarrete to explain the low barrier height at the perpendicular conformation in 2,2@-bithiophene.40 It is also supported by the short bond length (1.457 Indeed C2wC2{ ”).MP2 and B3LYP results diÜer just in for the term, the V2 V1 and terms being very similar in both cases and the other V4 terms of negligible importance. The comparison with torsional potentials of the analogue 2,2@-bithiophene obtained at the same MP2/6-31G* level of theory,36 is of interest giving evi- Fig. 4 Fourier decomposition of the MP2/6-31G* V (/) torsional potential of 2,2@-bipyrrole dence of smaller nonbonding interactions kcal (V1\0.8 mol~1) and higher conjugative interactions kcal (V2\0.34 mol~1) in the sulfur derivative. In this case, on introducing MP2 correlation, the term is much less reduced and does V2 not become negative, being likely due only to hyperconjugative eÜects. In conclusion correlation eÜects modify the contribution of nonbonding interactions to the torsional potential of 2,2@- bipyrrole.DiÜerences between the theoretical methods in describing the conformational behaviour essentially rely on the treatment of conjugative interactions : MP2/6-31G* theory appears to disfavour conjugative contributions and to favour hyperconjugative ones with respect to both HF/6-31G* and B3LYP/6-31G* calculations. Terpyrrole and quaterpyrrole Several rotational isomers are possible for 2,2@ : 5@,2A-terpyrrole (a-TPy) and 2,2@ : 5A,2A : 5A,2”-quaterpyrrole (a-QPy) by rotation around the inter-ring CwC bonds.Equilibrium geometries of the planar all-anti structures of a-TPy and a-QPy were previously obtained by HF/MIDI-4 calculations. 22a Ab initio studies on the potential-energy surface of these compounds are lacking, while semiempirical calculations on a-TPy gave discordant results. MNDO calculations27c showed only one minimum around 120°. By contrast AM1 calculations27h localized the minimum energy in the anti»anti (AA) (180°, [180°) conformation.Relative minima were also found for the 180^30° and 30^30° con–gurations with relative energies of 0.79 and 2.05 kcal mol~1, respectively. Energy maxima were located around ca. 3.4 kcal mol~1 high in the 90^90° region. From CNDO calculations a-TPy was expected to be a rigid molecule in the coplanar anti con–guration, showing a 90° barrier of 8.74 kcal mol~1.27g We started our conformational analysis for a-TPy by optimizing the planar AA structure at the HF/6-31G* and B3LYP/6-31G* levels, then generating potential-energy curves by rigid rotation of a single external ring as well as by rotating the two external rings in both conrotatory and disrotatory ways.The –rst mode generates eclipsed structures, the second one gauche structures. In the latter case relaxed potentialenergy curves were also obtained. In perfect analogy with the conformational behaviour of the 2,2@ : 5@,2A-terthiophene (a- TTh)41 we found gauche anti, anti (gAA), eclipsed anti, anti (eAA), gauche syn, syn (gSS) and eclipsed syn, syn (eSS) con- –gurations, (Fig. 5). Possible gauche syn, anti (gSA) and eclipsed syn, anti (eSA) forms were not located since the present results and the analogy with the HF/6-31G* conformational behaviour of a-TTh41 indicate that their relative energies can be obtained to a good approximation by additive contributions from the two bipyrrole moieties.Corresponding eclipsed and gauche forms were found to be practically isoenergetic as in a-TTh.41 The HF/6-31G* and B3LYP/6-31G* equilibrium geometries of the AA structures of a-TPy are reported in Table 2. The gAA form, which is the minimum- Table 4 Torsional potentials (kcal mol~1) of pyrrole oligomers (kcal mol~1) method V1 V2 V3 V4 V5 V6 bipyrrole HF/6-31G* 2.082 0.319 0.432 [1.517 0.350 [0.324 MP2/6-31G* 2.236 [1.009 0.161 [1.435 0.207 [0.357 B3LYP/6-31G* 2.238 1.178 0.294 [1.380 0.294 [0.205 terpyrrole HF/6-31G* (/1]/2) 4.329 0.657 1.017 [2.907 0.609 [0.524 B3LYP/6-31G* (/1]/2) 4.531 2.793 0.643 [2.539 0.508 [0.387 quaterpyrrole (rigid rot.) HF/6-31G* (/1) 2.456 0.518 0.553 [1.248 0.130 [0.126 HF/6-31G* (/2) 2.493 0.481 0.494 [1.173 0.112 [0.113 J.Chem. Soc., Faraday T rans., 1998, V ol. 94 29Fig. 5 Calculated minimum energy structure of a-terpyrrole. g\gauche, e\eclipsed, AA\anti, anti, SS\syn, syn. energy structure (HF) and [0.53 (B3LYP) kcal [ER\[1.20 mol~1; (HF) and 155.1° (B3LYP)], shows /1\/2\148.4° practically identical geometrical parameters. For a-QPy, rigid potential-energy curves were generated as a function of the dihedral angle of one outer N1»C2»C2{»N1{ ring or as function of the internal dihe- (/1) N1»C5{»C2_»N1_ dral angle starting from the optimized all-anti planar (/2), conformation.As in the dimer, anti-gauche and syn-gauche minimum-energy conformers were found. The planar all-anti structure of a-QPy is shown in Fig. 6. The torsional potentials of a-TPy and a-QPy –tted in the six-term Fourier analysis are shown in Fig. 7 and 8 and Table 4, while relative energies and torsion angles are reported in Table 3. Geometrical parameters and energetics of the syn%anti interconversion in a-TPy and a-QPy, as compared with the corresponding values in the dimer, provide insight into the evolution of the balance between nonbonding and conjugation eÜects on increasing the degree of polymerization.The CxC (CwC) bond length decreases (increases) slightly along the dienic framework in the trimer relative to the dimer. A smaller variation is observed on passing from a-TPy to a-QPy, so the inner rings in these compounds have practically the same structure. This behaviour is somewhat more obvious following B3LYP/6-31G* calculations and indicates an Fig. 6 Equilibrium geometries of planar all-anti conformation of aquaterpyrrole. (HF/6-31G*) and [837.113485 Etotal\[831.796894 (B3LYP/6-31G*) Eh .evident strengthening of the resonant p-electron system as well as rapid convergence of the geometrical parameters of the pyrrole ring in the oligomerization process. The potential-energy curves of a-TPy and a-QPy are similar to those in the dimer. In the comparison some trends can be noted, once the qualitative nature of the rigid-rotor approximation is taken into consideration : (i) consistent with an increased extension of the p-electron system following oligomerization, the torsion angle of the outer ring and the relative energy of the anti-gauche form increases and decreases, respectively, so the —atness of the potential-energy surface around the planar structure increases, allowing a large libration angle of the end-rings. Concomitantly the perpendicular barrier increases slightly.Similar behaviour is shown by the syn-gauche structure. (ii) Consistent with point (i), the relaxed double rotation of the outer pyrrole rings in a-TPy produces somewhat less than additive values for the relative energies of the gAA and gSS forms. (iii) In a-QPy both single rotations around the external CwC inter-ring bond and around the middle CwC bond generate almost identical torsional- Fig. 7 Relative energies vs.torsion angle for disrotatory /1\/2 rotation of the two external rings of a-terpyrrole. Open marks and dashed lines refer to rigid-rotor approximation results. The curves were obtained by –tting the relative energies of the rotamers to a six-term Fourier expansion. 30 J. Chem. Soc., Faraday T rans., 1998, V ol. 94Fig. 8 Rigid torsional potential for the rotation around the external CwC inter-ring bond and internal CwC inter-ring bond in (/1) (/2) a-quaterpyrrole. The curves were obtained by –tting the relative energies of the rotamers to a six-term Fourier expansion. potential-energy curves (Fig. 8), indicating a uniform conformational —exibility along the polymer. The Fourier-–tted torsional potentials of a-TPy and a-QPy (Table 4) lend support to the above results.The term, by considering the V2 rigid rotation of the external ring, increases markedly on passing from the dimer to the trimer, while the increment is much less from the trimer to the tetramer ; in agreement, both the rigid and relaxed rotation approximations give terms in V2 a-TPy which are somewhat more than doubled relative to the dimer (note that B3LYP calculations give very similar V2 values in both approximations).Nonbonding interactions (the term) remain almost constant. V1We also fully optimized at HF/6-31G* and B3LYP/6-31G* levels the all-anti-gauche (helix-like) structure of a-QPy under symmetry restrictions. The relative geometrical parameters C2 are not reported as they are practically equal to those of the planar all-anti structure within the obtainable uncertainty. The helical structure is more stable than the planar one by 1.64 and 0.60 kcal mol~1 at HF/6-31G* and B3LYP/6-31G* levels, respectively.Relevant parameters are : HF/6-31G*: B3LYP/6- ET\[831.799512Eh , /1\148.5°, /2\149.9° ; 31G*: These ET\[837.114440 Eh , /1\155.6°, /2\158.5°. data, in comparison with the results on small oligomers, indicate a slight tendency towards coplanarization of the inner rings together with an evident decrease of the relative energy per rotating couple in the planar form with respect to the twisted one: 0.71 kcal mol~1 in the dimer, 1.20/2\0.60 kcal mol~1 in a-TPy and 1.64/3\0.55 kcal mol~1 in a-QPy, at the HF/6-31G* level, the corresponding B3LYP/6-31G* –gures being 0.40, 0.27 and 0.20 kcal mol~1, respectively. The torsional potential around the planar anti conformation of adjacent pyrrole rings decreases smoothly as aoligomerization proceeds.Note that Raman spectroscopic studies6e,22e showed that in unsubstituted oligopyrroles the largest eÜective delocalization length is ca. 7»9 rings. In such systems anti and coplanar (or near coplanar) structures are very probable.4 In conclusion, in the polymer limit planar very conformationally —exible structures may be expected, in agreement with the experimental X-ray results in the solid.4 partially supported by CNR and MURST, Work Rome. References 1 A. O. Patil, A. J. Heeger and F. Wudl, Chem. Rev., 1988, 88, 183. 2 A. J. Heeger, S. Kivelson, J. R. SchrieÜer and W-P. Su, Rev. Mod. Phys., 1988, 60, 781. 3 Nonlinear Optical Properties of Polymers, ed. A. J. Heeger, J. Orenstein and D. R. Ulrich, MRS Symposia Proceedings N.109, Materials Research Society, Pittsburgh, 1988. 4 Handbook of Conducting Polymers, ed. T. A. Skotheim, Marcel Dekker, New York, 1986, vol. 1 and 2. 5 Conjugated Polymeric Materials : Opportunities in Electronics, Optoelectronics and Molecular Electronics, ed. J. L. Breç das and R. R. Chance, NATO ASI Ser. E, Vol. 182, Kluwer, Dordrecht, 1990. 6 (a) V. Hernandez, C. Castiglioni, M.Del Zoppo and G. Zerbi, Phys Rev. B, 1994, 50, 9815, and references therein ; (b) R. H. Baughman and R. R. Chance, J. Poym. Sci. Polym. Phys. Ed., 1976, 14, 2037; (c) G. N. Patel, R. R. Chance and J. D. Witt, J. Chem. Phys., 1979, 70, 4387; (d) G. Wenz, M. A. Muller, M. Schmidt and G. Wegner, Macromolecules, 1984, 17, 837; (e) G. Zerbi, M. Veronelli, S. Martina, A-D. Schlué ter and G. Wegner, Adv. Mater., 1994, 6, 385. 7 (a) A. F. Diaz, K. K. Kanazawa and G.P. Gardini, J. Chem. Soc., Chem. Commun., 1988, 183; (b) K. K. Kanazawa, A. F. Diaz, R. H. Geiss, W. D. Gill, J. F. Kwak, J. A. Logan, J. F. Rabolt and G. B. Street, J. Chem. Soc., Chem. Commun., 1979, 635; (c) K. K. Kanazawa, A. F. Diaz, W. D. 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Bargon, T etrahedron, 1984, 40, 3963; (h) E. Yurtsever and B. Erman, Polymer, 1993, 34, 3887. 28 K. Burke, J. P. Perdew and M. Levy, Modern Density Functional T heory: A T ool for Chemistry, ed. J. M. Seminario and P. Politzer, Elsevier, Amsterdam, 1994. 29 (a) Density Functional Methods in Chemistry, ed. J. Lobanowski and J. W. Andzelm, Springer-Verlag, New York, 1991; (b) N. Oliphant and R. J. Bartlett, J. Chem. Phys., 1994, 100, 6550. 30 J. R. Smith, P. A. Cox, S. A. Campbell and N. M. RatcliÜe, J. Chem. Soc., Faraday T rans., 1995, 91, 2331. 31 GAUSSIAN 94, Revision B.1, M. J. Frisch, G. W. Trucks, H. B. Schlegel, P. M. W. Gill, B. G. Johnson, M. A. Robb, J. R. Cheeseman, T. A. Keith, G. A. Petersson, J. A. Montgomery, K. Raghavachari, M. A. Al-Laham, V. G. Zakrzewski, J. V. Ortiz, J. B. Foresman, J. Cioslowski, B. B. Stefanov, A. Nanayakkara, M Challacombe, C. Y. Peng, P. Y. Ayala, W. Chen, M. W. Wong, J. L. Andres, E. S. Replogle, R. Gomperts, R. L. Martin, D. J. Fox, J. S. Binkley, D. J. Defrees, J. Baker, J. P. Stewart M. Head- Gordon C. Gonzales and J. A. Pople, Gaussian, Inc., Pittsburg PA, 1995. 32 A. D. Becke, J. Chem. Phys., 1993, 98, 5648. 33 C. Lee, W. Yang and R. G. Parr, Phys. Rev. B, 1988, 37, 785. 34 (a) Internal Rotation in Molecules, ed. W. J. Orville-Thomas, J. Wiley, London, 1974; (b) L. Radom and J. A. Pople, J. Am. Chem. Soc., 1970, 92, 4786. 35 L. Salem, T he Molecular Orbital T heory of Conjugated Systems, Benjamin, New York, 1966. 36 E. Ortïç , P. M. Viruela, J. Saç nchez-Marïç n and F. Tomaç s, J. Phys. Chem., 1995, 99, 4955. 37 S. Mille–ori and A. Alparone, in preparation. 38 G. J. Pyrka and Q. Fernando, Acta Crystallogr., Sect. C, 1988, 44, 562. 39 S. Samdal, E. J. Samuelsen and H. V. Volden, Synth. Met., 1993, 59, 259. 40 V. Hernandez and J. T. Lopez-Navarrete, J. Chem. Phys., 1994, 101, 1369. 41 M. Ciofalo and G. La Manna, Chem. Phys. L ett., 1996, 263, 73. Paper 7/05780F; Received 7th August, 1997 32 J. Chem. Soc., Faraday T rans., 1998, V ol. 94

ISSN:0956-5000    

DOI:10.1039/a705780f

出版商:RSC    

年代:1998

数据来源: RSC

摘要:

EÜect of basis set on the calculated geometry of the CH4 Æ HCl complex Edmond P. F. Lee*§ and Timothy G. Wright*î Department of Chemistry, University of Southampton, High–eld, Southampton, UK SO17 1BJ The complex is studied using a variety of basis sets at the MP2 level of theory. It is found that the calculated CH4 … HCl geometry depends critically on the precise nature of the basis set used, with a particularly important ro� le played by polarization and diÜuse functions. It is established, that the ìbestœ basis sets lead to a geometry, in agreement with the conclusions reached C3v by microwave spectroscopy.The geometry is then recalculated at the MP4(SDQ) and QCISD level of theory, and the binding energy of the complex is calculated at the CCSD(T) level of theory. Introduction The complex has been studied using microwave CH4 … HCl spectroscopy by Legon et al.1 and Ohshima and Endo.2 It was found that the complex has an eÜective geometry, but that C3v it exhibits wide-amplitude motion.Craw et al.3 performed an ab initio calculation of the complex at the MP2 level of theory. It was found that the structure, obtained by standard ana- C3v lytical gradient techniques, had two imaginary frequencies, indicating that it was a saddle-point. This geometry consisted of the HCl molecule bonding along a axis, with the hydro- C3 gen atom pointing towards the centre of a face. They CH3 then allowed the H atom to move oÜ axis, and found that a new structure was obtained with an energy lower than that Cs of the stationary point ; however, this new structure was C3v not characterized, with respect to the number of real or imaginary vibrational frequencies.Other structures were also investigated, but they had energies higher than the abovementioned geometries. It was noted3 that the zero-point vibrational energy (ZPVE) (of the intermolecular librational mode) was greater than the barrier corresponding to the C3v geometry, and so the geometry was eÜectively of sym- C3v metry, in accordance with the microwave studies.Of interest, however, is that the authors3 then went on to correct the potential energy surface for basis set superposition error (BSSE) along the librational angle coordinate (this corresponds to the H atom moving oÜ the axis), by using the C3v counterpoise (CP) correction. The new surface obtained had a minimum at the geometry. The CP corrected dissociation C3v energy of the complex was 3.4 kJ mol~1 (0.8 kcal mol~1), (De) compared to a value of 4.5 kJ mol~1 (1.1 kcal mol~1) for De the structure, calculated before the CP correction was Cs applied.It is also noted that Nguyen et al.4 used the 6-311G** basis [alternatively written as 6-311G(d,p)] at the MP2 level to calculate the equilibrium geometry; however, vibrational frequencies were only calculated at the HF level. Single point calculations at the MP2/6-311G** geometry were performed at the MP4 level, using the 6-311]]G** basis set.The conclusion was that the complex had a geometry, and C3v although the calculations indicated that the complex was bound, inclusion of the CP correction led to an unbound complex (although it was noted therein that the full CP cor- § E-mail: epl=soton.ac.uk î E-mail: tgw=soton.ac.uk rection is considered by some workers as being an overcorrection to the BSSE). It has been noted5 that diÜuse polarization functions are necessary in order to describe the bonding (and hence geometry and vibrational frequencies) of weakly-bound van der Waals species, and also that at least two polarization functions per atom are required (one for the description of the dipolar eÜects, and the other for the quadrupole polarizability eÜects6), especially where dispersion eÜects are important (as they are expected to be here).Consequently, it was decided to reinvestigate the geometry of the complex in order CH4 … HCl to characterize further the and structures obtained pre- C3v Cs viously and to determine whether particular portions of the basis set might be more important than others in determining the minimum energy geometry accurately.In addition, the eÜect of higher levels of theory ought to lead to a more reliable value for the binding energy. Calculational details The calculations were performed using CADPAC7 and GAUSSIAN94.8 The majority of the basis set variation calculations were performed using the MP2 method, with the frozen core (FC) approximation being used, as well as the full method.The basis sets used were mostly standard, including the diÜuse and polarization functions. The variations, and the labels for the resulting basis set, are given in Table 1. Calculations were also performed using the TZ2P basis set,3 with variations systematically carried out, to try to ascertain which parts of the basis set were important in the determination of the minimum energy geometry. These variations and the labels for the resulting basis set are given in Table 2.All optimizations were performed using analytical gradient techniques, with the gradient tolerance made tight enough in each case, such that there were six unprojected frequencies very close to zero. The frequencies were calculated using analytic second derivative methods. The eÜect of including higher correlation methods was investigated by: (i) re-optimizing the geometry at the MP4(SDQ) and QCISD levels, with three basis sets being used for the MP4(SDQ) calculations. In each case, the optimization was started with a structure of symmetry; and (ii) Cs calculating the interaction energy using the CCSD(T)/aug-ccpVTZ method at the MP2/aug-cc-pVTZ geometry.The eÜect of BSSE was accounted for by the application of the full CP J. Chem. Soc., Faraday T rans., 1998, 94(1), 33»38 33Table 1 Various ìstandardœ basis sets useda basis set label notation Cl C H n-basisb (d, f)c 1 6-31G** [6631/631] [631/31]] d [31]] p 59 (6) 2 6-311]]G(2d, 2p) [631111/52111]]MspN]2d [6311/311]]MspN]2d [311]] MsN] 2p 116 (6) 3 6-311]]G(2df, 2p) [631111/52111]]MspN]2df [6311/311]]MspN]2df [311]]MsN]2p 130 (5, 7) 4 6-311]]G(3d, 2p) [631111/52111]]MspN]3d [6311/311]]MspN]3d [311]]MsN]2p 126 (5) 5 6-311]]G(3df, 2p) [631111/52111]]MspN]3df [6311/311]]MspN]3df [311]]MsN]2p 140 (5, 7) 6 Sadlej10 [63111M1N/611M1N/2M2N] [41M1N/2M2N] [41M1N/2M2N] 105 (6) 7 aug-cc-pVTZd [5s4p2d1f]] MspdfN [4s3p2d1f]]MspdfN [3s2p1d]]MspdN 211 (5, 7) 8 TZ2P3 [411111111/41111]]MspN]2d [62111/3111]]MspN]2d [311]]MsN]p 111 a Where MN indicates diÜuse functions ; [ ] indicates contracted functions, in the usual manner.b Number of basis functions for the complex. c 5 (for d) and 7 (for f) implies the use of spherical harmonics for the d and f functions. 6 implies the Cartesian d functions were used. d The uncontracted basis set which leads to the cc-pVTZ basis set has 15 and 9 primitives for the lowest three s and two p contractions, respectively, for Cl; and 8 and 3 primitives for the lowest two s and one p contractions, respectively, for C.The exponents of the diÜuse and polarization functions used in the standard basis sets are as follows. 6-311]]G**: Cl 0.75 (d), 0.0483 (sp) ; C 0.626 (d), 0.0438 (sp) ; H 0.75 (p), 0.036 (s). 6-311]]G(2d, 2p) : diÜuse functions as for 6-311]]G**, polarization functions : Cl 1.5, 0.375 (d) ; C 1.252, 0.313 (d) ; H 1.5, 0.375 (p). 6-311]]G(2df, 2p) : as for 6-311]]G(2d, 2p), except f functions are added to Cl and C, with exponents: 0.7 (Cl) and 0.8 (C). 6-311]]G(3d, 2p) : as for 6-311]]G(2d, 2p), except the two d polarization functions on Cl and C are replaced with three, with exponents: 3.0, 0.75, 0.1875 (Cl) ; 2.504, 0.626, 0.1565 (C). 6-311]]G(3df, 2p) : as for 6-311]]G(3d, 2p), but with the addition of f functions as in the 6-311]]G(2df, 2p) basis set ; aug-cc-pVTZ: Cl polarization 1.046, 0.344 (d), 0.706 (f) diÜuse 0.0591 (s), 0.0419 (p), 0.135 (d), 0.312 (f) ; C polarization 1.097, 0.318 (d), 0.761 (f) diÜuse 0.04402 (s), 0.03569 (p), 0.1 (d), 0.268 (f) ; H polarization 1.407, 0.388 (p), 1.057 (d) diÜuse 0.02526 (s), 0.102 (p), 0.247 (d).Sadlej : Cl polarization0.9528, 0.3580], [0.1250, 0.0436] (d) diÜuse 0.0696 (s), 0.0436 (p) ; C polarization [1.2067, 0.3855], [0.12194, 0.03865] (d) diÜuse 0.047 (s), 0.038 (p) ; H polarization [1.1588, 0.3258], [0.1027, 0.0324] (p) diÜuse 0.0324 (s).TZ2P]diÜ: Cl 1.2, 0.4 (d), 0.0645 (s), 0.0417 (p) ; C 0.7, 0.2 (d), 0.0450 (s), 0.0303 (p) ; H 0.8 (p), 0.0526 (s). correction of Boys and Bernardi.9 In the CP calculations, the geometry of the monomer was –xed at that obtained with the monomer basis set. Results and Discussion The results of the calculations are summarized in Tables 3 and 4. Table 3 gives the symmetry of the geometry at which the optimization was started, together with the symmetry of the resulting optimized geometry.In addition, each optimized structure was characterized via its vibrational frequencies, to see whether it was a minimum or a transition state. Basis sets 1»7 are standard basis sets, with variations in the diÜuse and polarization space; basis set 8 is that used previously3 (the exponents of the polarization and diÜuse functions for these basis sets are given in the footnotes to Table 1) ; and basis sets 9»17 are variants on the basis set used previously.3 The results obtained using exactly the same basis set as that of Craw et al.3 will –rst be described.The geometry was initially optimized under symmetry, and the results were in C3v excellent agreement with those previously obtained,3 in particular that the structure was a transition state, with two C3v imaginary frequencies, see Table 3. The symmetry was then relaxed to but the Cl atom was –xed on the axis, as Cs , C3 was the case previously ;3 this yielded a minimum energy geometry that had all real vibrational frequencies, as would be expected for a minimum.It is interesting to note, however, that subsequently allowing the Cl also to move oÜ axis yielded a geometry of lower energy, but the energy diÜerence was very slight (3.4]10~6 This new geometry was also a Eh). minimum, and demonstrates that the potential energy surface is extremely —at around this region. The question arises, however, as to whether the true calculated minimum energy geometry is or remembering –rstly, that Nguyen et Cs C3v , al.4 obtained a structure of symmetry, and secondly a CP C3v correction along the librational angular coordinate of the potential energy surface yielded a minimum.3 C3v The results in Table 3 demonstrate that very few standard basis sets actually yielded a calculated minimum energy geometry of symmetry [most yielded a structure, which Cs C3v was the case whether the optimizations were started at a Cs symmetry or a symmetry (upper part of Table 3)].This is C3v in contrast to the result using the basis set of ref. 3, where a Cs structure was obtained with the basis set therein (see also Table 3). The question thus arises : what features of the basis set used previously3 can lead to the optimized geometry being rather than To this end, a systematic variation in the Cs , C3v ? basis set was also performed, with the variations used summarized in Table 2, and the results obtained summarized in the lower part of Table 3.Basis set variation at the MP2 level The TZ2P basis set3 (basis set 8), augmented with diÜuse functions, gave a optimized geometry. The underlying basis sets Cs Table 2 Variations in the TZ2P basis set of Craw et al.3 basis set label underlying basis set diÜuse region polarization regiona n-basisb 9 6-31G as ref. 3 as ref. 3 84 10 cc-pVDZ as ref. 3 but MspN on H standard 87 11 cc-pVTZ as ref. 3 but MspN on H standard 177 12 as ref. 3 except [7s5p] for Cl as ref. 3 as ref. 3 106 13 as ref. 3 except [7s5p] for Cl as ref. 3 as ref. 3 but two p for H 121 14 6-311G, but [9s5p] for Cl as ref. 3 as ref. 3 107 15 as ref. 3 as ref. 3 as ref. 3 but two p for H 126 16 as ref. 3 as ref. 3 as ref. 3 but diÜerent exponent 111 for the two C d functions 17 as ref. 3 as ref. 3 two p on H, and diÜerent exponent 141 for the two C d functions a Where the additional non-standard polarization functions mentioned in the table are as follows : H 0.388, 1.407 (p) ; C 0.318, 1.097 (d).b Number of basis functions. 34 J. Chem. Soc., Faraday T rans., 1998, V ol. 94Table 3 Summary of the optimized geometries obtained for the Complex CH4 Æ HCl no. of starting optimized imaginary [total energy/ basis set MP2 (full)a geometry geometry frequencies Eh]500 1 N Cs C3v 0 0.571476 1 Y C3v C3v 0 0.586916 2 Y Cs C3v 0 0.748205 3 N C3v C3v 0 0.701297 4 Y C3v C3v 0 0.782489 5 N C3v C3v 0 0.707112 6 Y Cs C3v 0 0.682987 7 Y Cs C3v 0 0.787839 8 Y Cs b Cs b 0 0.835647 8 Y C3v C3v 2 0.835538 9 Y Cs C3v 0 0.636938 10 Y Cs C3v c 0 0.622507 11 Y Cs C3v 0 0.789393 12 Y Cs Cs 0 0.569773 13 Y Cs Cs 0 0.576043 14 Y Cs C3v 0 0.828518 15 Y C3v C3v 0 0.841283 16 Y C3v C3v 2 0.840241 17 Y Cs C3v 0 0.847310 a N indicates the frozen core approximation was employed; Y indicates no orbitals were frozen.b Two diÜerent structures were found, one Cs with the Cl axis –xed on the axis and one where both the H and Cl atoms moved oÜ of the axis.Neither of these had imaginary C3 C3 frequencies. The energy quoted in the table is for the one with the both H and Cl oÜ-axis. c A geometry that was very slightly oÜ of was C3v obtained here, but the surface was extremely —at. used were the contracted basis sets of Dunning: [9s5p] for Cl; [5s,4p] for C; and [3s] for H. These are not strictly triple-zeta quality for all the atoms concerned: for Cl the p region is slightly less than triple-zeta quality and for C the p region is slightly more than triple zeta, with the s region slightly less.Thus there is an imbalance in the underlying basis set, in particular it is noted that going from 5s to 9s between C and Cl seems to emphasize the s region of Cl unduly, compared to C. In addition, as the footnotes in Table 1 show, the hydrogens really only have diÜuse s character, and one p polarization function. As noted in the Introduction, dispersion eÜects need two polarization functions, at least one of which should be diÜuse.Since the main bonding here is through the hydrogens (whether in or orientation), then it would appear that C3v Cs they ought to be described adequately (and equally with the C and Cl atoms) in order to obtain a reliable geometry. It is clear that the interactions in this complex are extremely weak, and so the balance of the basis set will be crucial to a reliable calculated geometry.In summary, there not only could be an imbalance in the underlying basis set in ref. 3, but the polarization and diÜuse regions appear better described for Cl and C than for H. Variations of the basis set used by Craw et al. were then carried out to test the above ideas. The results of Table 3 shows that it is a mixture of the polarization functions and the underlying basis set that determines the calculated geometry here. In particular, two sets of p functions are necessary in order to obtain the geometry in the main.It is clear from C3v the results using the basis sets of Table 1 (standard basis sets), and the larger of the basis sets derived from that used in ref. 3 [in particular, basis sets 11, 15 and 17 (Table 2)] that the C3v geometry is the more reliable. It may be concluded that a balanced basis set with ì sufficient œ diÜuse and polarization functions appears to lead to the ìcorrectœ description of the intermolecular interactions and, consequently a structure here.For the other basis C3v sets, it would appear that there is a delicate balance of both the underlying basis set and the added polarization and diÜuse functions, and that changing the characteristics of the basis set slightly can lead to a change in the calculated Table 4 The calculated intermolecular bond length and intermolecular harmonic vibrational frequencies for the complex CH4 Æ HCl (C3v minima only) vibrational frequencies/cm~1 basis MP2 set (full)a r(CwCl)/” a1 symmetry e symmetry 1 N 3.9121 73.8 79.4, 124.1 1 Y 3.9017 75.1 79.9, 127.0 2 Y 3.7746 80.8 81.8, 110.1 3 N 3.7731 83.4 88.5, 110.8 4 Y 3.7638 89.1 111.3, 161.4 5 N 3.7749 87.1 105.7, 182.5 6 Y 3.6667 109.6 167.0, 294.4 7 Y 3.6603 105.2 124.0, 181.7 9 Y 3.8252 85.4 112.2, 174.6 10 Y 3.8719 75.8 81.0, (82.3/89.5)b 11 Y 3.7494 88.0 114.1, 187.5 14 Y 3.8511 75.4 29.3, 124.4 15 Y 3.8030 83.7 49.4, 104.8 17 Y 3.7924 79.2 75.1, 129.8 a N indicates that the frozen-core approximation was used; Y indicates that no orbitals were frozen.b A geometry very slightly oÜ of was C3v obtained here. J. Chem. Soc., Faraday T rans., 1998, V ol. 94 35geometry. A more sensitive test of the intermolecular bonding is the intermolecular bond length and the vibrational frequencies, and these are now considered. Intermolecular bond length and vibrational frequencies. The general trend for the intermolecular bond length (Table 4) is that the more polarization and diÜuse functions added, the shorter the bond length.In particular, the shortest bond lengths are obtained with the aug-cc-pVTZ and Sadlej basis sets (ca. 3.667 and 3.660 respectively), where the aug-cc- Aé , pVTZ basis set is the largest one used here with a signi–cant quantity of diÜuse and polarization functions (in particular, diÜuse polarization functions), and the Sadlej basis set is also rich in diÜuse polarization functions, and is designed for the study of molecular electrical properties.10 The increase in the size of the basis set between these two is considerable (105» 211 basis functions) and when compared to the modest decrease in the bond length, it might be assumed that the basis set eÜect is saturated.The intermolecular vibrational frequencies (Table 4) suggest that this is not quite so clear cut, however, as one of the degenerate e vibrational modes changes from 181.7 to 294.4 cm~1 between these two basis sets : note, however that the 6-311]]G(3df, 2p) basis set (140 basis functions) yields similar results to the aug-cc-pVTZ basis set.In fact these, together with the results of the MP2/6- 311G(3d, 2p) calculation indicates that it is the three d functions that are giving the higher values of the frequency for this mode (and do not change the intermolecular bond length signi–cantly). An analysis of the normal coordinates for this vibration show that it is in fact the librational motion, corresponding to a movement of the HCl moiety oÜ-axis»the description of the potential energy in this direction is therefore very sensitive to the d orbital space.Looking at these results, and that obtained with the Sadlej basis set, it appears clear that it is the most diÜuse d function that is critical. It seems that at the MP2 level, the aug-cc-pVTZ basis set gives the best picture of the bonding in this complex, where there is a large underlying basis set, and also diÜuse s, p, d and f functions. The TZ2P basis set used previously3 does not have a and so is not included in Table 4; however, the C3v minimum, variants on the basis set, which led to a minimum, are.It C3v may be seen that the intermolecular bond lengths are ca. 0.2 Aé longer than the aug-cc-pVTZ basis set, not that unreasonable, but the intermolecular vibrational frequencies show a very large scatter. In line with some of the observations made above, it is felt that this is due to imbalances present in this basis set, and even very modest changes in the basis set are leading to large changes in the calculated frequencies.A point about the MP2 energies ought to be mentioned at this juncture : it can be seen (Table 3) that the basis set used previously gives a very low MP2 total energy compared to some of the large basis sets (even lower than the aug-cc-pVTZ basis set) ; however, this is not the case at the HF level, where the calculated energies follow the expected ordering as indicated by the size of the basis set.Some attempt to shed light on this oddity was made, in particular, the energy of the isolated HCl moiety was calculated and it was found that the same sudden lowering occurred at the MP2 level, and not at the HF level. In addition, even when the underlying basis is changed to 6-311G for C and H, but is left as [9s5p] for Cl (basis set 14), the dramatic lowering in energy is still present. Thus, there is some peculiarity here, caused by the use of the Cl [9s5p] basis set in the MP2 procedure, but no further attempts were made to isolate the problem further. Calculated geometry at higher levels of theory Higher level calculations were performed in order to ascertain the eÜects of higher-order electron correlation eÜects on the calculated geometry.This proved to be more problematical than anticipated : at both the MP4(SDQ) and QCISD levels, the surface is so —at that although the energy gradient converged fairly straightforwardly, the displacement criterion did not (this implies that the energy changes are very small for relatively signi–cant changes of the geometry around the minimum).Table 5 shows the angle of the HCl to the axis C3 at the last geometry obtained when the very —at potential energy region was encountered, i.e. where the energy changes between successive points near the minimum were \10~6 Eh . The MP4(SDQ) calculations were carried out with three basis sets : 6-311]]G**, 6-311]]G(2d, 2p) and 6-311]]G(3df, 2p).The smallest basis set led to an unconverged geometry, when after 28 optimization steps, the energy gradient was still rather large and so the optimization was halted. For the second basis set, the initial optimization led to a geometry with the HCl oÜ-axis by B3.5° [both for the MP4(SDQ) and QCISD methods]. For the MP4(SDQ) method, the convergence criteria for the wavefunction and the gradient were then tightened and this led to an angle of only 0.7°.Similarly, with the largest of the basis sets the tight criterion led to an angle of only 0.2°, with the energy changing by \10~6 at Eh this point. At the point that the QCISD/6-311]]G(2d, 2p) calculation was halted, it had started to change symmetry from to the calculation was then restarted under Cs C1; C1 symmetry, but again the gradient converged, while the geometry was still changing signi–cantly. Nontheless, the energy diÜerence between the structure (Table 5) and the Cs structure was \10~6 indicating the surface is —at in C1 Eh , more than one direction at this level of theory.Despite this slightly diÜerent behaviour between the MP4(SDQ) and QCISD methods using the 6-311]]G(2d, 2p) basis set, they lead to broadly similar results. Dissociation energy. The calculated dissociation energy at the MP2 level employing the two largest basis sets is shown in Table 6. It may be seen that the CP correction is of the order of 1 kcal mol~1, indicating that the basis sets are close to saturation ; however, the dissociation energy is so small that the BSSE is a signi–cant percentage of the dissociation energy.It is a philosophical point as to whether an in–nite basis set would lead to a zero BSSE as calculated by the full CP approach, especially at the correlated level. From the experience of a large number of calculations, a BSSE of ca. 0»1 kcal mol~1 appears to indicate merely that the basis set is very close to saturation.The higher level CCSD(T) single point calculation indicates that the MP2 result, as far as the CP-corrected energy is concerned, is fairly reliable. The ZPVE correction destabilizes the complex slightly. These calculations suggest that at the low temperatures in a molecular beam the complex is stable, as is seen experimentally, but that at even moderate temperatures the complex will be unstable. It is noted that Craw et al.3 calculated the complex to be stable at the MP2 level (both with and without CP correction, yielding values of 0.81 and Table 5 Calculated geometry at higher levels of theory [total energy] level of theory 500/Eh r/” last ha/degrees MP4(SDQ)/ 0.699979 3.8576 0.73 6-311]]G(2d, 2p) MP4(SDQ)/ 0.704967 3.8498 0.21 6-311]]G(3df, 2p) QCISD/ 0.700371 3.8813 3.48 6-311]]G(2d, 2p) a This was the last angle in the optimization before the energy changes were insigni–cant (\10~6 The MP4(SDQ) calculation Eh).had a tighter convergence criterion than the QCISD: the MP4(SDQ)/ 6-311]]G(2d, 2p) optimization was also performed with this less stringent criterion, and gave, then, an angle of 3.5° (see text). 36 J. Chem. Soc., Faraday T rans., 1998, V ol. 94Table 6 Calculated dissociation energies MP2(full)/6-311]]G(3df, 2p) MP2(full)/aug-cc-pVTZ CCSD(T) (FC)/aug-cc-pVTZ//MP2(full)/aug-cc-pVTZ *Ee/kcal nol~1 [1.500 [2.374 » *Ee(CP)/kcal mol~1 [0.970 [0.153 [0.985 *Ee(CP)] [0.067 [0.163 ]0.005 ZPVE/kcal mol~1 *H298(CP)/kcal mol~1 [0.017 [0.177 [0.009 *S/ cal mol~1 K~1 [15.477 [16.56 » 1.1 kcal mol~1, respectively ; but the ZPVE was not included), as do Nguyen et al.4 (best value is 1.0 kcal mol~1).The latter authors also calculated the dissociation energy at the MP4 level, and obtained a value of 1.0 kcal mol~1. It was noted, however, that the complex was unbound when the CP correction was employed.4 The CCSD(T) calculations in the present work (including CP and ZPVE corrections) are the highest level to date, and do seem to imply that the complex is stable at very low temperatures, in agreement with the observation of the complex in molecular beams.Isotopic substitution and comparison with the experimental values The vibrational frequencies and the rotational constants were calculated for some isotopically substituted complexes, and the results are shown in Table 7. The two microwave spectroscopy experiments1,2 derived rotational constants for the ground vibrational level giving results in fairly good agreement with those obtained here, which are equilibrium values. Similar trends between the variations of these constants are observed in the experiment and calculations.As an example, for the isotopomer the vibrational ground state CH4 Æ H35Cl value was observed to be B2.9 GHz (0.097 cm~1), compared with a calculated value of 3.36 GHz (0.112 cm~1) obtained here. This agreement might not be as close as it could be as the complex is extremely —oppy, even with only the ZPVE present,2 and so it is probable that the geometry diÜers sig- re ni–cantly from the structure.r0 There is only a limited amount of information on the intermolecular vibrational frequencies of this complex. Ohshima and Endo2 estimated the intermolecular stretch frequencies for various isotopomers, from the values of the centrifugal distortion constants for each of the methane internal rota- (DJ), tional levels.Values of 57»58 cm~1 were obtained, in general, which compared rather poorly with the calculated stretch vibrational frequency values here (Table 4, under a1 symmetry). Given that the experimental value is obtained using a pseudodiatomic picture, and that the complex is very —oppy, perhaps this poor agreement is not entirely unexpected. Internal rotational states were also calculated elsewhere, 2 but a de–nitive value for the parameter was not V3 able to be obtained, thus also not allowing an accurate picture of the internal rotor levels to be deduced.Two internal rotational axes, which were assumed in ref. 2, were labelled s and h: [s corresponded to motion around a axis, whilst h cor- C3v responded to movement away from the intermolecular axis (see Fig. 2 of ref. 2)]. Analysis of the normal modes calculated in this work indicate that this is a simplistic picture : although both the stretch and the h internal rotation are relatively clear from the normal modes calculated here, the other internal rotation (s) is not so clear. There does not appear to be any more experimental information on the intermolecular vibrational modes of this complex.Of note is that the higher of the two intermolecular e modes, second lowest vibrational frequency of e symmetry overall, (assigned to the librational motion of the HCl moiety), is particularly sensitive to deuteration of the HCl, as would be expected.Other modes also show strong isotopic dependences. Of note here, however, is that the intermolecular stretch (lowest vibrational frequency of symmetry) is only weakly isotope dependent. a1 Finally, the microwave studies derived values for the CwCl distance of B3.94 (and these compare quite favourably with ” the calculated values ofB3.66 at the MP2 level, using large re ” basis sets remembering that these will be values). r0 Conclusions The eÜect of the basis set on the calculated equilibrium geometry of the complex has been studied at the CH4 Æ HCl MP2 level of theory.It is found that the resulting geometry can depend on some quite subtle eÜects of the basis set. The most important feature for this complex appeared to be the provision of two sets of p polarization functions on the hydrogen atoms. The intermolecular vibrational frequencies Table 7 Calculated rotational constants and vibrational frequencies for some isotopomers of the complex (values obtained at the CH4 Æ HCl MP2(full)/aug-cc-pVTZ level of theory) CH4 Æ H35Cl CD4 Æ H35Cl CD4 Æ D35Cl CD4 Æ H37Cl CH4 Æ H37Cl CH4 Æ D37Cl equilibrium 158.7418 79.4319 79.4319 79.4319 158.7418 158.7418 rotational 3.3565 2.8366 2.8366 2.7961 3.3004 3.2999 constants/GHz 3.3565 2.8366 2.8366 2.7961 3.3004 3.2999 vibrational a1 symmetry 105.2 91.5 97.1 96.8 104.4 104.0 frequencies/cm~1 1367.4 1033.1 1033.1 1033.1 1367.4 1367.3 3040.4 2175.2 2172.5 2175.2 3038.2 2178.1 3076.2 2368.7 2183.1 2368.7 3076.1 3074.9 3201.2 3041.1 2368.7 3039.4 3201.2 3021.1 e symmetry 124.1 88.5 88.5 88.4 124.0 123.8 181.7 181.5 129.6 181.5 181.6 129.9 1365.7 1031.7 1031.6 1031.7 1365.7 1365.7 1601.2 1132.9 1132.6 1132.9 1601.2 1601.0 3193.8 2364.7 2364.7 2364.7 3193.8 3193.7 J.Chem. Soc., Faraday T rans., 1998, V ol. 94 37appeared to be sensitive to the basis set as well, with the librational mode (bending of HCl oÜ the axis) being particu- C3 larly so. A good description of the potential energy surface along this coordinate appeared to need three d functions on the non-hydrogen atoms, and it was concluded that the most diÜuse d function was having the greatest eÜect.The complex was computed to be bound at the levels of theory used here, even when BSSE and ZPVE had been accounted for. Finally, it is noted that at higher levels of theory [MP4(SDQ), QCISD], the surface appears to become even —atter than at the MP2 level. This complex is clearly a challenge to ab initio methods.authors are grateful to the EPSRC for the award of com- The puting time at the Rutherford Appleton Laboratories, and to Dr J. Altmann for technical support. E.P.E.L. is grateful to the Hong Kong Polytechnic University for support during this work. T.G.W. is grateful to the EPSRC for the award of an Advanced Fellowship. References 1 A. C. Legon, B. P. Roberts and A. L. Wallwork, Chem. Phys. L ett., 1990, 173, 107. 2 Y. Oshima and Y. Endo, J. Chem. Phys., 1990, 93, 6256. 3 J. S. Craw, R. G. A. Bone and G. B. Bacskay, J. Chem. Soc., Faraday T rans., 1993, 89, 2363. 4 M. T. Nguyen, B. Coussens, L. G. Vanquickenborne and P. W. Fowler, Chem. Phys. L ett., 1990, 175, 593. 5 P. Hobza and R. Zahradnïç k, Stud. Phys. T heor. Chem., 1988, vol. 52, ch. 2, p. 45. 6 F. Mulder, M. Hemert, P. E. S. Wormer and A. van der Avoird, T heor. Chim. Acta, 1977, 46, 39. 7. CADPAC, The Cambridge Analytic Derivatives Package, Issue 6, Cambridge, 1995. A suite of programs developed by R. D. Amos with contributions from I. L. Alberts, J. S. Andrews, S. M. Colwell, N. C. Handy, D. Jayatilaka, P. J. Knowles, R. Kobayashi, K. E. Laidig, K. E. Laming, A. M. Lee, D. E. Maslen, C. W. Murray, J. E. Rice, E. D. Simandiras, A. J. Stone, M.-D. Su and D. J. Tozer. 8 GAUSSIAN 94 (Revision C.3), M. J. Frisch, G. W. Trucks, H. B. Schlegel, P. M. W. Gill, B. G. Johnson. M. A. Robb, J. R. Cheesemans, T. A. Keith, G. A. Petersson, J. A. Montgomery, K. Raghavachari, M. A. Al-Laham, V. G. Zakrzewski, J. V. Ortiz, J. B. Foresman, J. Cioslowski, B. B. Stefanov, A. Nanayakkara, M. Challacombe, C. Y. Peng, P. Y. Ayala, W. Chen, M. W. Wong, J. L. Andres, E. S. Replogle, R. Gomperts, R. L. Martin, D. J. Fox, J. S. Binkley, D. J. Defrees, J. Baker, J. P. Stewart, M. Head- Gordon, C. Gonzalez and J. A. Pople, Gaussian, Inc., Pittsburgh, PA, 1995. 9 S. F. Boys and F. Bernardi, Mol. Phys., 1970, 19, 553. 10 A. J. Sadlej, Collect. Czech. Chem. Commun., 1988, 53, 1995. Paper 7/05362B; Received 24th July, 1997 38 J. Chem. Soc., Faraday T rans., 1998, V ol. 94

ISSN:0956-5000    

DOI:10.1039/a705362b

出版商:RSC    

年代:1998

数据来源: RSC

摘要:

Competitive autocatalysis in reaction-diÜusion systems Exclusive product selectivity J. H. Merkin,a A. J. Poole,a,b S. K. Scott,b J. Maserec and K. Showalterc a Department of Applied Mathematics, University of L eeds, L eeds, UK L S2 9JT b School of Chemistry, University of L eeds, L eeds, UK L S2 9JT c Department of Chemistry, W est V irginia University, Morgantown, W V 26506, USA The behaviour of a system comprising two competitive autocatalytic processes, A]B]2B, and A]C]2C, rate\k1a6 b 6 where and represent the concentrations of the various species, is considered.In a well-stirred batch reactor, the rate\k2 a6 c6 , a6 , b 6 c6 –nal equilibrium composition always corresponds to a mixture of the two product species B and C, with their respective equilibrium concentrations depending on the ratio of the rate coefficients and the initial concentrations and If the i\k2/k1 b0 c0 . same reactions are carried out in a reaction-diÜusion system, with local initiation of the reaction at one end of the reactor, travelling waves of reaction develop.This system can show exclusive product selectivity, with only one of the products being formed in the reactor, provided either the rate coefficient ratio i or the diÜusion coefficient ratio diÜers from unity. If d\DB/DC both diÜer from unity the system will select pure production of B if d[i and pure production of C otherwise. Some interesting complex transient behaviour close to the marginal condition d\i is reported.Introduction In this paper we present a study of the dynamical behaviour in a system in which two autocatalytic processes proceed in competition with each other for a common sustaining resource such as fuel or food. The model scheme employed can be written as A]B]2B rate\k1a6 b 6 (1) A]C]2C rate\k2 a6 c6 (2) where B and C are the autocatalytic species and and a6 , b 6 c6 represent the concentration of the three species involved. The are the reaction rate coefficients, and we allow these to have ki diÜerent values from each other.We will be particularly interested in the evolution of this system from some local initial seeding under conditions where reaction is coupled with diÜusion of the autocatalytic species. The motivation for this study is two-fold. First, in thermodynamically closed, well-stirred systems the –nal equilibrium mixture composition will comprise a mixture of both species B and C in a proportion dependent on the relative values of the rate coefficients and the initial concentrations of the two ki autocatalytic species.In many real-life chemical syntheses, only one of a pair of possible products is actually the desired chemical species, so the other represents a reduction of potential yield and also requires an additional extraction or puri–- cation stage. (In the special case where B and C are enantiomers of biologically active molecules, one product may be a bene–cial drug and the other a substantial hazard to life.) We seek to demonstrate here that if the two product species have diÜerent diÜusivities in the reaction-diÜusion system, an increase in the selectivity may be obtained in terms of the overall yield of one of the products at the expense of the other.Second, the above scheme is a ìminimal caricatureœ of a chemical system, itself proposed as a model for competitive DNA replication. The autocatalytic nature of enzyme-free replication involving relatively short, six nucleotide-long DNA oligomers has been demonstrated.1,2 This autocatalysis, which is an essential feature of biological DNA replication, arises when an existing molecule acts as a template to direct the formation of the next from a mixture containing the appropriate nucleotide base building-blocks.Bauer et al.3 showed that short RNA chains also have this property and that such a system supports reaction-diÜusion wave propagation in narrow capillary tubes.In these experiments, a solution of the bases was con–ned in a polythene tube and seeded at one end with a single species of RNA of a known base sequence. The reaction wave was monitored through UV-—uorescence in the presence of ethidium bromide as an indicator and was observed to propagate with a constant velocity and wave form. On completion of the reaction, the tube was separated into sections and the composition of the RNA determined by gel electrophoresis.Early sections showed a single electrophoresis band, corresponding to RNA of the same type as the seeded material. Later sections, however, show a decrease in this band and the appearance of additional bands corresponding to mutations from the original RNA. A simpler, nonbiological system with the same essential underlying mechanism has been devised by Rebek and co-workers,4h6 again involving the formation of a template molecule that directs the formation of further molecules of the same type.Masere7 produced an 11-variable, 8-step model of two coupled Rebek systems, in which two conformational isomers compete for the component bases, and has shown numerically that this displays reaction-diÜusion wave behaviour. The competitive autocatalysis leads to an exclusive selection of one product over the other, depending on the relative values of the rate constants and diÜusion coefficients of the competing subsystems. Here, we reduce this model to the two-step scheme [eqn.(1) and (2) above], which preserves the essential features of autocatalytic competition. Governing equations We imagine a 1D reaction domain in which the reactant species A is loaded with some spatially uniform initial concentration and at one end of which the system will be seeded a6 0 locally with the autocatalytic species. The reaction-diÜusion equations for the above system can be written in the following J. Chem. Soc., Faraday T rans., 1998, 94(1), 53»57 53dimensionless forms at\Daxx[ab[iac (3a) bt\dbxx]ab (3b) ct\cxx]iac (3c) Here, the concentrations are scaled by so a\1 uniformly a6 0 , for all x at t\0.Time has been scaled with respect to the pseudo-–rst-order rate coefficient for step (1), i.e. tref\1/k1a6 0 and length has been scaled with the diÜusion coefficient of species C and the reference timescale, The lref\(Dc tref)1@2. parameters and represent the diÜusi- D\DA/DC d\DB/DC vities of reactant A and autocatalyst B relative to C, and i\ is the ratio of the rate coefficients. For convenience, we k2/k1 take D\1 throughout but allow arbitrary values for d and i.For i\1 and d\1, we have a competition, with the kinetics favouring process (1) and diÜusion favouring process (2). Well-stirred, closed system In the absence of the diÜusion terms, eqn. (3) describes the evolution of a well-stirred batch system. The relative rate of production of B to C is given, for by iD0, db dc \ b ic (4) Assuming a\1, and at t\0, this integrates to b\b0 c\c0 give c c0 \Ab b0Bi (5) Also, adding eqn.(3a)»(3c) and integrating, we have a]b]c\1]b0]c0 (6) The equilibrium state approached as t]O has a\aeq\0. The equilibrium concentration of species C is then given by the positive root of the equation ceq]b0Aceq c0 B1@i [(1]b0]c0)\0 (7a) with then, from the mass conservation condition beq\1]b0]c0[ceq (7b) The variation of the equilibrium solution with 0OiO1 for a system with is shown in Fig. 1. For i\0, no b0\c0\0.5 additional C is produced and so all the A reacts to B. Otherwise, the equilibrium state is a mixture of both products. For i\1, equal amounts of B and C are produced. Fig. 1 Variation with rate coefficient ratio of the equilibrium mixture composition for competitive autocatalytic reactions in a wellstirred batch reactor : and indicate the net production (b[b0) (c[c0) of species B and C by reaction above the initial concentrations Reaction-diÜusion system Several predictions can be established analytically following the methods developed by Billingham and Needham:8 (a) a constant velocity reaction-diÜusion front will be established from localised inputs of the autocatalytic species, in which there will be complete consumption of the reactant A; (b) if d[i, then the wave will correspond to a front in which A is converted entirely to B and the wave speed will be given by l\2d1@2; (c) if d\i, then the wave will correspond to a front in which A is converted entirely to C and the wave speed will be given by l\2i1@2.This theory predicts, therefore, a critical condition given by d\i (8) at which the system switches from step (1) to step (2) as the dominant (in fact, the exclusive) autocatalytic channel. The derivation of this condition is sketched in the Appendix. To check these predictions, eqn. (3a)»(3c) were integrated numerically with the following initial conditions : a\1 for all x b\(1[x)b0 for 0OxO1 and b\0 for x[1 (9) c\(1[x)c0 for 0OxO1 and c\0 for x[1 with in all computations reported here.(It was b0\c0\0.5 also established that the results below are robust to the precise initial conditions.) Two numerical methods were employed: an explicit scheme and a standard implicit scheme for solving parabolic equations.9 Evolution of the concentrations of species B and C for a system with d\1 and i\0.5 is shown in Plate 1. For these parameter values a wave in species B develops from the initial seeding and propagates with a constant velocity given by the gradient of the space»time plot, Plate 1(a), has l\2, in accordance with the above predictions.The initial input of C disperses mainly by diÜusion into the reacted B on a substantially slower timescale, Plate 1(b). The ìoppositeœ case, in which a wave in C develops, is shown in Plate 2, for d\0.1 and i\0.5. The wave speed obtained from the long-time gradient of the space»time plot, Plate 2(b), agrees well with the predicted value of 21@2.The early evolution in this system is slightly diÜerent from the previous case. Locally at the origin there is an initial production of B, as step (1) has the higher rate coefficient, so the local concentration b increases more rapidly than the local concentration of C. The associated increasing concentration gradient allows B to diÜuse into the surrounding reactant, and initiate further production of B, even though it has a substantially lower diÜusion coefficient.This allows a slightly greater extent of ìspreadingœ of B than was possible for C in the previous case. Eventually, however, the higher mobility of C causes step (2) to become the dominant process. The initial development of a transient wave in B is more evident in Plate 3, for a system closer to the marginal conditions with d\0.45 and i\0.5. The ì kinetic advantageœ of step (1) allows a wave of B to develop more quickly from the seeding and this wave propagates, almost reaching a constant wave speed, up to xB100, before the higher mobility of the species C causes the system to switch to the other channel at longer times and distances.In this system, then, we have a high concentration of B at low x and a high concentration of C, with virtually no B, at larger x. The –nal example, shown in Plate 4 (a) and (b), corresponds to a system with d\0.079 and i\0.1. The theoretical analysis predicts that a wave of species C should –nally become established in this case.As before, the initial development is of a wave in B that persists up to xB150 after which the system makes a transition to a wave in C. This is not, however, stable and the system switches back to channel (1) 54 J. Chem. Soc., Faraday T rans., 1998, V ol. 94Plate 1 Space»time plots showing the evolution of the concentrations of (a) species B and (b) species C as functions of position x and time t for a system with d\1 and i\0.5.The key indicates the concentration ranges corresponding to each colour. The –gure shows the establishment of a wave in which A is converted entirely to B propagating with constant velocity, indicated by the constant slope in (a), and only diÜusive spreading of the initial C added locally over 0\x\1 in (b). and yields a propagation front in B. There is thus a narrow region of C formed surrounded on either side by regions of almost pure B. The development of the concentration pro–les in this example are also shown, Plate 4(c)»(e).At early times, a sharp front in the a and b pro–les can be seen emerging from the initiation region. In the –fth pro–le shown, the front becomes notably less sharp and the c pro–le develops into a sharp pulse. The transition back to a wave in species B is accomplished by what is eÜectively a second initiation event, producing another sharp front in A and B. The b pro–le now has a maximum and a minimum, the latter corresponding to the location at which c is high.With d\0.078, a similar overall evolution results, but the region of C is wider: as d is decreased further, the wave in C is eventually established as the long-term structure. Numerical integration for other parameter combinations have been performed to map out the d»i plane as indicated in Fig. 2, where crosses denote systems in which a wave of B is established and the dots indicate a wave of C. The theoretical prediction, eqn.(8), gives a relatively good estimate of the boundary between the two regions, although the computed boundary appears to lie slightly below this simple condition at low values of both d and i. One other point of interest is that for systems in which a wave of species B is achieved, the development of the constant-velocity front is generally rapid and direct, even for Plate 2 As for Plate 1 but for a system with d\0.1 and i\0.5. The long-term behaviour corresponds to a constant velocity wave in which A is converted entirely to C although some B is produced locally to the origin at short times.Plate 3 As for Plate 1 but for a system with d\0.45 and i\0.5. The long-term behaviour corresponds to a constant velocity wave in which A is converted entirely to C but initially there is the transient initiation of a wave in B for x\ca. 100. J. Chem. Soc., Faraday T rans., 1998, V ol. 94 55Plate 4 (a), (b) As for Plate 1 but for a system with d\0.079 and i\0.1.The theoretical prediction is for a wave in which A is converted entirely to C. In fact, there is an initial transient wave in B followed by a small region in which C is produced, but ultimately the system re-establishes a wave in B. The concentration pro–les a(x), b(x) and c(x) at selected times are shown in (c), (d) and (e) respectively. parameter values close to the boundary in Fig. 2. In systems for which a wave of species C results, the wave development is a more extended process, indeed, as shown above, the system may spend some time deciding which type of wave to support, and there may be a damped oscillatory evolution of the front velocity as it approaches its asymptotic value.The parameter D, representing the scaled diÜusion coefficient of the reactant A, has little eÜect on the behaviour of the system. We have computed the evolution of systems over a range of small and large values and found that the long-time wave selection is not dependent on this quantity, although there is some in—uence on the timescale of the initial wave development.This observation is entirely consistent with the Fig. 2 The d»i parameter plane indicating the asymptotic solution determined numerically (], wave in B; …, wave in C) compared to the theoretically predicted transition boundary given by eqn. (8) analytical prediction and with previous knowledge based on the single, quadratic autocatalytic step, for which it is –rmly established that the wave speed is determined by the diÜusivity of the autocatalytic species (and the reaction rate coefficient) and is independent of that for the reactant.Discussion Perhaps the most signi–cant point of this study is that reaction-diÜusion systems can oÜer important advantages over traditional well-stirred batch reactors. In the latter, competing reactions all make some contribution to the –nal equilibrium state, producing a mixture of product species.The same chemistry occurring through reaction-diÜusion waves in an unstirred system under otherwise identical conditions can, however, be substantially more selective. Either by tuning the kinetic parameters (rate coefficients) or by selectively altering the diÜusion parameters, eÜectively complete selectivity can be achieved in autocatalytic systems. Only relatively small diÜerences in the rate constant or diÜusion coefficients need to be arranged. For instance, computations indicate that even with equal kinetic coefficients (i\1), a 5% diÜerence in diÜusivity (i.e. d\1.05 or 0.95) rapidly leads to the development of waves in either B or C, respectively.A general method for the selective control of individual species diÜusion coefficients has been devised by Lengyel and Epstein,10 who suggested the incorporation into a gelled reaction matrix of bulky molecules, which are eÜectively immobilised, with which one species in the reacting mixture can form a complex.This partitioning reduces the eÜective diÜusion coefficient of the binding species in much the same way as occurs in chromatography. The development of appropriate stationary phases for chiral chromatographic separation suggests that a straightforward extension of the Lengyel»Epstein technique would allow selective chiral synthesis. The role of template molecules in directing the production of one of a pair of enantiomers has 56 J. Chem. Soc., Faraday T rans., 1998, V ol. 94already been demonstrated11 in another type of system involving a stirred crystallisation process. Close to the critical conditions, the present system shows some evidence of complex dynamics, at least in terms of the transient oscillatory evolution to the –nal asymptotic structure. The development of a travelling front involves both diffusion and kinetics and is determined primarily by the balance between these at the leading edge of the front. In this region, the reactant is eÜectively in large excess and so the kinetics are psuedo-–rst-order, and the reaction and diÜusion are both linear processes.This is the origin of the simple form of the condition given by eqn. (8) for the change from the ì kinetically favouredœ channel (1) involving B to the ìdiÜusivity favouredœ channel (2) involving C as d decreased or i increased. The complex behaviour and the persistence of the wave involving B slightly below this transition line, observed for small values of the parameters, is unexpected and not easily explained.It may represent very long transients, although we have performed very long runs over very large spatial domains in which the expected asymptotic wave entirely in C has not been established. This behaviour is qualitatively robust to changes in the numerical methods, step size, error control, etc., and so appears not to be a simple numerical artefact. are grateful to the following for –nancial support: NATO We (K.S.and S.K.S.) ; EPSRC (A.J.P.) ; NSF (K.S., grant CHE- 9531515); The Office of Naval Research (K.S.) and The Petroleum Research Fund (K.S.). Appendix: Mathematical analysis To derive condition (8) we consider the travelling wave equations corresponding to eqn. (3). These are expressed in terms of a single travelling coordinate y\x[lt, where l is the (positive) wave speed, giving *aA]la@[ab[iac\0 (A1) dbA]lb@]ab\0 (A2) cA]lc@]iac\0 (A3) (where primes denote diÜerentiation with respect to y) subject to the boundary conditions that a]1, b]0, c]0 as y]O (A4) and that the concentrations are uniform as y][O.This latter condition, together with eqn. (A1)»(A3), requires that we must have a]0 as y][O with reactant A then being fully consumed in the wave. It has already been established,8,9 for quadratic autocatalytic kinetics, that the wave speed is determined by the behaviour of the solution at the front of the wave, where aB1 and b and c are small.Applying this in eqn. (A2) and (A3), we obtain the linear equations dbA]lb@]b\0 (A5) cA]lc@]ic\0 (A6) valid near the front of the wave. For non-negative solutions (nodal behaviour as y]O), eqn. (A5) and (A6) require lPlB\2)d, and lPlC\2)i (A7) For localized initial data, as in (9), we can establish,12 following very closely the analysis of Billingham and Needham,8 that any waves that form will ultimately travel with their minimum possible speed, i.e. l\max (2)d, 2)i) (A8) Conditions (A7) and (A8) suggest that, if d[i, a wave only in species B will ultimately form, with a wave only in C if this condition is reversed.This is con–rmed if we continue the analysis of Billingham and Needham. This shows that, if d[i, c is exponentially small in the wave, being of OMexp[[(d[i)t]N as t]O. Similarly we –nd that, if i[d, then b is exponentially small in the wave, of OMexp[[(d[i)t]N as t]O. This analysis is performed under the assumption that o d[i o is not small. It suggests that a wave only in species B or only in species C will form rapidly depending on whether d[i or d\i respectively. If then further o d[i o@1, detailed considerations are necessary, as is borne out by the numerical results. References 1 K. J. Luebke and P. B. Dervan, J. Am. Chem. Soc., 1989, 111, 873. 2 G. von Kiedrowski, B. Wlotzka, J. Helbing, M. Matzen and S. Jordan, Angew. Chem., Int. Ed. Engl., 1991, 30, 423. 3 G. J. Bauer, J. S. Caskill and H. Otten, Proc. Natl. Acad. Sci. USA, 1989, 86, 7937. 4 T. Tjivikua, P. Ballester and J. Rebek, J. Am. Chem. Soc., 1990, 112, 1249. 5 J. S. Nowick, Q. Feng, T. Tjivikua, P. Ballester and J. Rebek, J. Am. Chem. Soc., 1991, 113, 8831. 6 V. Rotello, J. Hong and J. Rebek, J. Am. Chem. Soc., 1991, 113, 9422. 7 J. Masere, PhD Dissertation, West Virginia University, 1996, 51»86. 8 J. Billingham and D. J. Needham, Quart. J. Appl. Math., 1992, L, 343. 9 J. H. Merkin and D. J. Needham, J. Eng. Math., 1989, 23, 343. 10 I. Lengyel and I. R. Epstein, Science, 1991, 251, 650. 11 D. Kondepudi, R. J. Kaufman and N. Singh, Science, 1990, 250, 975. 12 A. J. Poole, PhD Thesis, University of Leeds, 1997. Paper 7/05384C; Received 25th July, 1997 J. Chem. Soc., Faraday T rans., 1998, V ol. 94 57

ISSN:0956-5000    

DOI:10.1039/a705384c

出版商:RSC    

年代:1998

数据来源: RSC

摘要:

Temperature and pH-dependent inversion of photoelectric response in bacteriorhodopsin Tao Lu,a,b Bao Fang Li,a Long Jiang,a Ulrich Rotheb and Udo Bakowskyb a Institute of Photographic Chemistry, Academia, Sinica, 100101, Beijing, China b Institut Physiologische Chemie, Martin-L uther- Holly Str 1. D-06097 Halle, f ué r Universtaé t, Germany The temperature and pH-related polarity inversions of transient photocurrents developed from randomly deposited bacteriorhodopsin (bR) –lms (on transparent conductive ITO glass) were investigated.It was observed that the photocurrent reversed its polarity when the bulk pH was changed from alkaline (pH\8) to acid (pH\3), but under extreme acidic conditions (pH\1), in combination with high salt (saturated KCl), the reversed photocurrent regained the same polarity as that obtained in alkaline solution, which supports the notion that at extremely low pH, a high Cl~ concentration can catalyze the rate of the retinal photoisomerization.Moreover, heating the –lm (from 20 to 60 °C) will also trigger a current inversion which diÜers from the pH-induced reversal. It evolves from a peak splitting process rather than through a cancellation step of the photocurrent. The splitting and the –nal inversion, which are pH-dependent, occur symmetrically on both the positive and negative stroke of the diÜerential photocurrent. Comparative studies have been carried out and an explanation is discussed in terms of the inversion of the proton pump sequence.Bacteriorhodopsin (bR), the only protein in the purple membrane (PM), is part of the cellular membrane of Halobacterium salinarium. Upon illumination, it undergoes a photocycle (K, L, M, N, O) during which protons are unidirectionally translocated across the cell membrane, thus forming detectable photoelectric signals. DiÜerent photoelectric signals can be extracted from various measurement conditions and time resolutions.1 Under rectangular light excitation, a transient photocurrent could be observed from bR coated tin oxide glass,2h4 the attractive properties and possible applications2 of which warrant comprehensive study.Recently, a chargedisplacement model for the origin of this transient current was proposed.3 More recently, an alternative explanation was given which attributed the origin exclusively to the rapid pH change due to proton release and uptake from bR.4 However, ambiguities still remain and require elucidation.Studying the course of photocurrent inversion, which re—ects both the qualitative and quantative changes in PM, is informative and will lead towards a better understanding of how bR functions. It is generally accepted that the photoelectric response in the ls scale, which corresponds to the proton pump, is pHdependent. 5 At high pH values, proton release precedes uptake concomitantly with an accumulation of N intermediates ; whereas, at low pH values, proton uptake is followed by release, together with the accumulation of O,6 as shown in Fig. 1. When the pH is reduced to 2»3 a purple-to-blue transition occurs. The blue membrane has an altered photocycle and does not pump protons.7 Successive reduction of the pH (\1) in the presence of KCl regenerates the purple membrane which is thought to function as a halide ion (bRacid purple) pump.8,9 Heating the PM solution, especially when it is above the lipid phase transition temperature (30 °C),10 will usually irreversibly disturb its surface charge distribution as a result of the release of divalent cations into the bulk solution,11 it appears to raise the amount of O intermediates at pH\8.0.12 In this report, we present evidence that the photocurrent will change its polarity either upon heating or reduction in pH.These processes, though diÜerent, indicate a similiar sequence inversion mechanism of the proton pump which occurs as a result of the accumulation of O intermediates.This agrees with the previously reported spectroscopic results.6,11,12 We also demonstrate that the acid purple membrane under extremely low pH and high KCl conditions, functions as a proton pump or, most likely, a chloride pump in the opposite direction. Materials and methods The PM was prepared and isolated from Halobacterium halobium strain S-9 cells according to the traditional method.13 Before use, the PM was centrifuged twice at 20 000 rpm for 20 min to exclude basic salts. 50 ll PM (A567 nm\1.5) resuspended in triply distilled water was evenly distributed on an indium tin oxide (ITO)-modi–ed optically transparent glass plate (1.2]3.5 cm) to a –nal absorption of ca. 0.4 and dried in a clean chamber without any external orientations. The light source was a 300 W continuous halogen lamp –ltered with a yellow –lter ([500 nm, I\30 mW cm~2). The liquidjunction photocell was constructed as ITO oPMo 0.5 M Fig. 1 A simpli–ed model for the bR photocycle at diÜerent pH (at room temperature: for details, see ref. 6. The proton pump sequence is changed by the pH which is triggered by an unknown group with a At high pH, proton release (through L]M reaction) pKa\5.8.16 precedes uptake (through M]N reaction), whereas, at low pH 5»3, this sequence is reversed and the O intermediate rather than N or M is involved. J. Chem. Soc., Faraday T rans., 1998, 94(1), 79»81 79KCl o Pt. Photoelectric measurements were carried out with a home-made current ampli–er (minimum time resolution is ca. 10 ms) and recorded by an oscilloscope (Pm 3375 100 MHz). The system impedance, due mainly to the electrodes (bRmodi –ed ITO and a platinum bar), was below 10 k), which determined the time resolution of the system to be ca. 50 ms (the capacitance of the deposited –lm is ca. 5.0 lF). The temperature was changed stepwise from 20 to 60 °C by draining out and heating the electrolyte to the temperature a little above the desired value and then injecting the electrolyte into the measurement chamber mounted with a temperature meter.(This procedure was used because it was believed harmful for bR to be exposed for long periods to high temperatures.) The electrolyte was 0.5 M KCl (analytical purity) and the pH was adjusted with 0.1 M HCl and 0.1 M NaOH of the same purity. Results Fig. 2 demonstrates the transient photocurrent at various pH values. At high pH values, the cathodic on-current, as well as the anionic oÜ-one, reach their maximum value at a pH around 8.4, Fig. 3. Reducing the pH causes a constant decline in the magnitude of both on and oÜ currents, and they are totally eliminated at pH ca. 5 [see Fig. 2(b)]. Successive reduction of the pH regenerates the photocurrent response but with an opposite polarity, which reaches its maximum at pH ca. 3 [Fig. 2(c)]. Decreasing the pH further to 0.8 in the presence of saturated KCl, however, reverses the polarity of the photocurrent back to that found in an alkaline medium but exhibits a remarkably suppressed magnitude (300 nA at pH\9 compared to 30 nA at pH\0.8), see Fig. 2(d). No photocurrent is detectable when using saturated or Na2SO4 other salts than KCl (data not shown). This is comparable to previous results from PM immobilized in oriented gels.9 The pH dependency of the diÜerential photocurrents was studied over a wide range, from 0 to 10, as shown in Fig. 3. Fig. 4. shows the eÜect of temperature on reversal of the photocurrent.It is evident that the temperature reversal is developed from a signal-splitting process, whereby the newly arising opposite current symmetrically modi–es both the proton release and uptake over a delayed timescale [Fig 4(b), (c)]. A complete inversion was obtained when the temperature Fig. 2 The pH-induced polarity inversion of the diÜerential photocurrent measured under yellow light ([500 nm, I\30 mW cm~2) in 0.5 M KCl at room temperature (T \20 °C): (a) typical waveform of the photocurrent at higher pH (\9) ; (b) transient state without photoresponse at pH around 5; (c) inversion of photocurrent at low pH (2»4) ; (d) polarity regeneration at extreme acid (pH\0.8) in the presence of saturated KCl Fig. 3 EÜect of pH (0»10) on the light-induced diÜerential photocurrent. Only the positive stroke (on-current) is shown, the oÜ-current behaves similiarly but with an opposite polarity. The pH is adjusted by 0.1 M HCl or NaOH, other conditions are the same as in Fig. 2. The photocurrent reverses its direction at pH ca. 5. The regeneration of photoresponse at pH below 1 is detectable only in the presence of saturated KCl. Three maximums of peak current are evidenced with a suppression in magnitude at pH\8.4, 3.0 and 0.5, respectively. reached about 50 °C, as shown in Fig. 4(d). In most cases, cooling the –lm restored the original response. Repeated heating of this restored –lm will raise the critical temperature for splitting, thus causing a further reversal much more severe than that of the freshly deposited –lm.Moreover, pH values higher than 9 or PM with basal salt make the photocurrent less susceptible to reversal (data not shown). Discussion In normal PM, the release of protons from the extracellular side into the bulk solution is faster and occurs earlier than the uptake from the opposite side (400 ls compared with 15 ms)14 through the L]M]N reaction. As a result of the diÜerence in the extent of proton release and uptake, a slight acidi–cation of the PM suspension under continuous light is usually observable.15 But when the pH is reduced below 5.0, a signi–- cant change occurs in the photocycle of bR, which is triggered by an unknown group with whereby a quick pKa\5.8,16 proton uptake is followed by a lagged and slow release.6 In Fig. 4 The temperature-dependent inversion of diÜerential photocurrent measured under yellow light ([500 nm, I\30 mW cm~2) in 0.5 M KCl at pH\7.1 : (a) the capacitive photocurrent at room temperature (T \20 °C); (b), (c) when the temperature is elevated from T \30 to 40 °C a signal splitting is caused by an increase of an opposite component; (d) a total inversion of the photocurrent with only a trace of the original signal is observed at T \50 °C 80 J.Chem. Soc., Faraday T rans., 1998, V ol. 94this case, a net alkalization instead of acidi–cation was observed15 and the O state rather than the N state was involved, Fig. 1. Unlike the —ash light induced photoelectric response (ls range),5 which corresponds directly to the proton release, the diÜerential photocurrent which occurs in a delayed timescale (100 ms) is probably the net result of the equilibration of proton release and uptake. Indeed, it has been proposed that a cathodic photocurrent is related to a net proton release, and an anodic photocurrent to a net proton uptake.4 These pH induced inversions are indicative of the involvement of diÜerent forms of bR, referred to as purple membrane, blue membrane and acid purple membrane.Here, we diÜerentiate the purple membrane into the N-PM in alkaline and O-PM in moderate acidic conditions, as they undergo diÜerent photocyles. The photocurrent increases steadily from pH 5.0 to 8.4. This can be explained as the result of a constant increase in the amount of N-PM at the expense of O-PM, whereby the dominant N-PM contributes mainly to the observed photocurrent. In addition, the optimum pH of 8.4 is in agreement with the (8.2) of a proton-pump-related unknown group XH pKa (possibly Arg-82 or Tyr-57).17 Moreover, the decline in the photocurrent at pH[8.4 is caused by a decrease in the amount of the protonated XH needed for pumping protons.On the other hand, under acidic pH condition (5»3), the photocurrent increases but in the opposite direction to that observed in alkaline solution. This can be explained as an increase in the number of the O-PM.The suppression of the photocurrent, when further reducing the pH (below 3), can be explained when we take into account the transformation of purple to blue membranes with an intrinsic of Asp- pKa\2.6 85.18 In this case, together with the formation of the blue membrane (603 nm), Asp-85, the proton acceptor of the SchiÜ base, has been protonated before illumination and is incapable of proton pumping. Therefore, as a result of the transformation of the O-PM into blue membrane, the photocurrent decreases in magnitude upon reduction of the pH from 3 to 1.Furthermore, the restoration of the current polarity in the presence of saturated KCl at pH values below 1.0 agreed with recent spectra observations19 whereby at high Cl~ concentrations and extremely low pH values the perturbed chromophore environment could be rebuilt leading to the formation of When compared to the physiological form, bRacid purple . reveals an almost identical spectrum and may bRacid purple probably function as a chloride pump in the opposite direction. 8,9 At room temperature and pH around 5, a non-response region exists where no proton pump or photocurrent was detectable. However it has been documented15 that heating a PM suspension causes a pH shift such that the non-response region is observed at more alkaline values. In fact, this equilibrium point has been increased to pH 7.5 at a temperature of ca. 40 °C.15 This notion is also supported by the spectroscopic evidence of a striking increase in the O state upon an increase in temperature.12 Therefore, the temperature-induced reversal of the photocurrent could be the result of the partial formation of O-PM which contributes to an opposite photocurrent such as that observed at moderately acidic pH.As both the proton uptake and release in O-PM occur later than that in the normal purple membrane,6 the opposite component should split the peak behind, rather than before, the original signal, as shown in Fig. 3(b) and (c). Furthermore, it is known that the temperature-provoked accumulation of the O state is pH-dependent12 but its occurrence is clearly evident only when the pH is below 9. This is consistent with our observation of the in—uence of pH on the temperature reversal of the photocurrent, whereby neither inversion nor splitting was oberved when the pH reaches 9.0 (data not shown as no splitting was reached).The temperature-triggered inversion is not fully reversible in the same –lm. This may stem from some only partially reversible events, such as the temperature-dependent release of divalent cations from the PM surface to the bulk,11 or the passage through the lipid phase transition at a temperature around 30 °C.10 Even though the O-PM mechanism for the temperature reversal explains most of the observations, there are still some aspects of the nature of transient photocurrents which are equivocal.For instance, signal splitting is absent in the pHinduced inversion, which is most likely an indication that the kinetics of the photocycle is in—uenced by pH and temperature in a diÜerent way. Therefore, further investigations to remove these ambiguities are necessary, and other models such as counter-ion current20 should also be taken into consideration. Conclusion Even though the diÜerential photocurrent occurs far later than the proton pump process in a single photocycle, the relationship between them could be established by analyzing the striking changes in the photocurrent under appropriate conditions.The temperature and pH-induced signal inversions have been investigated and explained as the result of net changes in the proton transfer process (net uptake or net release). Acidi–cation and temperature elevation favour the accumulation of the O-PM state at the expense of the M-PM state which macroscopically reveals as inversion and splitting of the photocurrent signal.authors would like to acknowledge the excellent technical The help from Mr. P. D. Tao, X. C. Li and J. S. Yuan. This work was supported by the Academia Sinica and the National Sciences Foundation of China (NSFC). References 1 H. W. Trissl, Photochem. Photobiol., 1990, 51, 793. 2 T. Miyasaka, K. Koyama and I. Itoh, Science, 1992, 255, 342. 3 K. Koyama, N. Yamaguchi and T. Miyasaka, Science, 1994, 265, 762. 4 B. Roberton and E.P. Lukashev, Biophys. J., 1995, 68, 1507. 5 T. L. Okajima and F. T. Hong, Biophys. J., 1986, 50, 901. 6 Y. Cao., L. S. Brown., R. Needleman and J. K. Lanyi, Biochemistry, 1993, 32, 10239. 7 P. Dupuis, T. C. Corcoran and M. A. El-Sayed, Proc. Natl. Acad. Sci. USA, 1985, 82, 3662. 8 L. Keszthelyi, S. Szaraz, A. Der and W. Stoeckenius, Biochim. Biophys. Acta, 1990, 1018, 260. 9 A. Der, S. Szaraz, R. Toth-Boconadi, Z. Tokaji, L. Keszthely and W. Stoeckenius Proc. Natl. Acad. Sci. USA, 1991, 88, 4751. 10 R. Korenstein, W. V. Sherman and S. R. Caplan, Biophys. Struct. Mech., 1976, 2, 267. 11 C. H. Chang, R. Jonas, S. Melchiore, R. Govindjee and T. G. Ebrey, Biophys. J., 1986, 49, 731. 12 I. Chizhov, M. Engelhard, D. S. Chernavskii, S. Zubov and B. Hess, Biophys. J., 1992, 61, 1001. 13 D. Oesterhelt and W. Stoeckenius, Methods Enzymol., 1974, 31, 667. 14 L. Zimanyi, Y. Cao, R. Needlman, M. Ottolenghi and J. K. Lanyi, Biochemstry, 1992, 32, 7669. 15 H. Garty, G. Klemperer, M. Eisenbach and S. R. Caplan, FEBS L ett., 1977, 81, 238. 16 L. Zimanyi, G. Varo, M. Chang, B. Ni, R. Needleman, and J. K. Lanyi, Biochemistry, 1992, 31, 8535. 17 M. Kono, S. Misra and T. G. Ebrey, FEBS L ett., 1993, 331, 31. 18 S. P. Balashov, E. S. Imasheva, R. Govindjee and T. G. Ebrey, Biophys. J., 1996, 70, 473. 19 S. L. Logunov, M. A. El-Sayed and J. K. Lanyi, Biophys. J., 1996, 71, 1545. 20 S. Y. Liu, M. Kono and T. G. Ebrey, Biophys. J., 1991, 60, 204. Paper 7/01858D; Received 17th June, 1997 J. Chem. Soc., Faraday T rans., 1998, V ol. 94 81

ISSN:0956-5000    

DOI:10.1039/a701858d

出版商:RSC    

年代:1998

数据来源: RSC

摘要:

Sensitized photoisomerization of cis-stilbazolium ions intercalated in saponite clay layers Hisanao Usami,* Takashi Nakamura, Tetsuya Makino, Hitoshi Fujimatsu and Shinji Ogasawara Faculty of T extile Science and T echnology, Shinshu University, T okida 3-15-1, Ueda, Nagano 386, Japan Sensitized photoisomerization of the cis-stilbazolium ion 1 by ruthenium tris-2,2@-bipyridine was studied in sapon- [Ru(bpy)32`] ite clay layers. The reaction yield was 100 times higher than the reaction yield in a homogeneous solution.The Stern»Volmer constant of the luminescence of by 1 was 3.4]105 dm3 mol~1, which made the quenching rate constant faster than Ru(bpy)32` the diÜusion limiting rate. The fast quenching rate implies a static quenching by 1 in the vicinity of The reaction Ru(bpy)32`. efficiency showed a maximum when 70 mol% of 1 was intercalated on the basis of the cation exchange capacity (CEC), where the ruthenium complex and 1 are suitably arranged in the saponite layer for eÜective photoelectron transfer and subsequent electron relay.Photochemistry at interfaces has been investigated as an active research area of substantial interest due to the large molecular aggregates and their speci–c orientations applicable for control of photochemical reactions.1 Molecular aggregates of surfactants, such as micelles, vesicles and LB –lms have been investigated to date. Their potential ability to organize molecular arrangements have been reported as being eÜective for controlling molecular arrangements to improve chemical reactions, as seen in photosynthetic centers in biomembranes.2 They are —exible for application to many types of photoreactions ; however, more stable and larger aggregates will be required in some cases, especially in multimolecular reactions.Layered minerals are excellent materials for arranging molecules in two-dimensional symmetry to make the molecules interact more eÜectively side by side with their neighbors. The interlayer space is accessible to many types of molecules regardless of their bulkiness, in contrast to the onedimensional pores of zeolites with rigid selectivity by molecular size.1,2 For example, smectite clay minerals can act as layered hosts for largescale molecular aggregates.3 The clay layers are composed of anionic aluminosilicates and the equivalent amount of counter-cations in the interlayer space.The cations are easily exchanged with organic ammonium and pyridinium ions as well as metal cations.4 The amount of exchangeable ions is given in terms of the cation exchange capacity (CEC) for 100 g of dried clay mineral.The exchange reaction, known as intercalation, causes a systematic arrangement of the intercalated molecules depending on the allocation of anionic sites on the clay layers. The area occupied by the anionic charge can be estimated as ca. 1 nm2 on the clay layers, according to the crystal structure. The particle size of clay minerals is on average, several micrometers for typical samples.Considering the particle size and the anionic charge density on clay minerals, the aggregation number of the intercalated molecules can be evaluated as tens of millions in the clay layer. Some molecules intercalated in clay layers show diÜerent absorption or —uorescence spectra than those in homogeneous solutions owing to strong interaction with the layers.5 The spectral change in absorption or —uorescence depends on the molecular arrangement, which is modi–ed by the surface charge density of the clay and the addition of photoinactive alkylammonium ions.Spectral changes are also useful for studying the chemistry and physics of the clay interlayers.6 Ruthenium tris-(2,2@-bipyridine) derivatives [Ru(bpy)32`] intercalated in clay minerals have been intensively reported with respect to luminescence spectra and decay pro–les.7 In clay layers they can aggregate and exclude smaller molecules, such as methyl viologen, due to the diÜerence in shape and bulkiness.8 The chirality of is also recognized by Ru(bpy)32` clay layers.Oxygen atoms in the surface of the clay layer show periodic defects with threefold symmetry, causing optically selective intercalation of the complex.9 Ru(bpy)32` Spectral changes are mainly caused by the molecular arrangement in clay minerals and can be applied to control photochemical reactions to obtain high reaction efficiency and good yields. However, only a limited number of papers utilizing clay minerals as reaction media to control photoreactions have been reported, despite their potential applicability.For a unimolecular reaction, photochromism of spiropyran is controlled according to the polarity in montmorillonite clay interlayers.10 The interlayer space of this natural clay is sufficiently polar to stabilize the polar merocyanine isomer. Modi- –cation of the interlayers with alkylammonium ions changes the hydrophobicity of the interlayer space to stabilize the spiropyran isomer.Photocyclodimerization of trans-stilbazolium ions in saponite clay minerals is an example of a bimolecular reaction, in which a syn head-to-tail type cyclobutane is obtained in accord with the antiparallel molecular arrangement in the interlayers.11 Anionic alkenes can also dimerize to syn head-to-tail and head-to-head type cyclobutanes in layered double hydroxides (LDH).The higher charge density of the LDH layers enables a dense packing of alkenes to give both head-to-tail and head-to-head type dimerization.12 However, multimolecular photoreaction is not known in clay interlayers, where the large scale of molecular aggregation should be strongly re—ected by the reactivity. Photosensitized isomerization of the cis-stilbazolium ion 1 by is a multimolecular reaction and the reaction Ru(bpy)32` mechanism has been reported by Takagi et al., considering the redox potentials and excitation energy of the stilbazolium ions and the ruthenium complex in addition to a sensitizing experiment. 13 It has been reported that the quantum yield is correlated with the aggregation number of 1 in an anionic micellar system. Because the quantum yield was comparable to the aggregation number of 1 on the micelles, an electron relay mechanism was proposed among the aggregates. This implies that the more the molecules are aggregated, the higher is the J.Chem. Soc., Faraday T rans., 1998, 94(1), 83»87 83obtainable quantum yield. Polystyrenesulfonate was studied as a reaction medium with a high aggregation number; however, it could not improve the reactivity as molecules of 1 —occulated into small globular aggregates in which the aggregation number is as high as that in the ordinary micellar system.14 Therefore, a host for larger and more stable aggregation of 1 is required to improve the reactivity of the photoisomerization.Here, the photoisomerization of 1 is studied as an example of a multimolecular reaction in saponite clay minerals. Saponite clay allows 1 to aggregate on a large scale so that the reaction yield was improved to a level comparable to that observed in micellar systems, even on dilute solution. The mechanism is also discussed based on steady state —uorescence quenching. Experimental Materials trans-Stilbazole was synthesized following a reported procedure. 15 The trans-stilbazole was isomerized to cis-stilbazole by irradiation with a 300 W mercury lamp through a chemical –lter of a naphthalene solution in methanol (0.1 M) to excite the trans-isomer selectively.An aqueous solution of cisstilbazolium ions was prepared by dissolving the cis-stilbazole in 1.2 equivalents of hydrochloric acid solution. Tris-(2,2@- bipyridine)ruthenium(II) dichloride was synthesized by mixing ruthenium chloride with 2,2@-bipyridine at 250 °C after Burstallœs method.16 Synthetic saponite clay, a standard sample JCSS-3501, was obtained from the Clay Science Society of Japan and was used without further puri–cation.17 The size of the clay particles, composed of stacks of layers, was ca. 20 lm in diameter. The CEC of the clay was 99.86 mequiv./100 g for a dried clay sample. Concentrations of saponite clay are expressed on the basis of the CEC for convenience because stilbazolium ions were almost quantitatively intercalated through the ion exchange process.Sodium dodecyl sulfate (SDS, Wako Chemical Co., chemical grade) was puri–ed by recrystallization from ethanol. Intercalation and reaction procedure cis-Stilbazolium ions 1 were intercalated in saponite clay by mixing an aqueous solution of 1 and a colloidal solution of saponite clay. An intercalation equilibrium was attained within a few minutes at room temperature. Amounts of intercalated molecules were estimated from the absorption spectra of –ltrates through a membrane –lter (Toyo Advantec, pore size 0.45 lm).UV»VIS spectra were recorded on a Shimadzu UV-2200 or UV-2400PC spectrometer. The colloidal mixture was treated with bubbling nitrogen gas for 5 min, then irradiated with a 150 W xenon lamp equipped with a Hamamatsu photonics C-4263 power supply under vigorous stirring. The wavelength of irradiating light was adjusted to 420»500 nm, using HOYA L-42 and B-390 color –lters so that the sensitizer could be excited selectively.For measuring the quantum yield, a Shimadzu SP-100 monochromator was used to select 450 nm light. After decomposing the clay structure by the addition of conc. HCl, the reaction yield was measured from the absorption of the solution at 323 and 338 nm, which correspond to the absorption maxima for cis- and trans-stilbazolium ions, respectively. Emission spectra Emission spectra were observed with a Shimadzu RF-5000 spectrometer. and 1 were carefully intercalated to Ru(bpy)32` avoid precipitation since emission spectra are more sensitive to the light scattering eÜect of the colloid than absorption spectra.Saponite clay is a two-dimensional aluminosilicate, which is intrinsically stable even in dilute solution. Therefore, the concentration of saponite for —uorescence measurements was set at O100 lM to retain transparency of the solution, except during investigations of the eÜect of adsorption. The sample cell (1 cm) was —ushed with nitrogen gas for 5 min before the measurements.X-Ray diÜraction analysis A wet precipitate cake was –ltered from a colloidal mixture of aqueous 1» or 2»intercalated saponite through a 0.45 lm membrane –lter. The cake was ground mechanically, then painted on a glass plate and dried in air for 3 h at room temperature. Untreated sodium saponite was ground and mounted on the plate as dry powder. Wide angle X-ray diffraction measurements were made using a Rigaku RAD-X system with a rotating copper target. Currents were limited at 40 kV, 30 mA so as not to damage samples.Results and Discussion Intercalation of cis-stilbazolium ion cis-Stilbazolium ions 1 were easily intercalated in saponite clay layers by mixing the solutions of 1 and saponite clay. Sodium ions between the interlayer space of saponite clay were easily exchanged for 1 through an ion exchange process as expressed in eqn. (1).18 (Na`/clay~)]StzHfree ` E8F Kad Na`](StzH`/clay~) (1) where (Na`/clay~) and (StzH`/clay~) represent unintercalated and 1»intercalated saponite clay, respectively.The concentration of 1 in the bulk solution, at equi- [StzHfree ` ], librium was estimated from a UV»VIS absorption spectrum of the –ltrate of the mixed solution passed through a membrane –lter. The equilibrium constant for the intercalation was (Kad) calculated and values are listed in Table 1. A value of of 5 Kad corresponds to ca. 80% net intercalation of 1 in the saponite clay on mixing in equivalent amounts.This value shows that 1 can migrate easily in the interlayer space though the clay layers and —occulate with each other. It is notable that the equilibrium constant for 1 is only 0.01 that of trans-stilbazolium ions 2, which intercalated quantitatively in saponite. The basicity of 1 and 2 are almost equal,19 thus the diÜerence in their intercalation equilibrium constant must be explained by their diÜerent molecular bulkiness. The average distance between adjacent adsorption sites in the saponite, calculated as 1 nm based on the crystal structure, is suitable for a crowded packing of 2 of ca. 0.5 nm molecular width. Such an arrangement makes molecules of 2 photocyclize eÜectively to a head-to-tail type dimer.11 On the contrary, the bent molecular structure of 1 of ca. 0.8 nm in width inhibits close molecular packing to give the lower amount of intercalation in the saponite clay. Table 1 Intercalation equilibrium constants and basal spacings of saponite clay intercalated basal spacing molecular lengthc ions Kad a pKa b /nm /nm Na` » » 1.32 » cis-StzH` 5.0 5.46 1.53 0.97 trans-StzH` 400 5.73 1.58 1.04 a Intercalation equilibrium constant, calculated for [StzH`]\[saponite]\1 mM.b Ref. 18. c Calculated for a molecular model. 84 J. Chem. Soc., Faraday T rans., 1998, V ol. 94Fig. 1 X-Ray diÜraction pattern for saponite clays ; (a) trans-Stzsaponite, (b) cis-Stz-saponite, (c) Na`-saponite Interlayer distance was measured by wide angle X-ray diffraction of the intercalated saponites.Considerable expansion of the layers was observed in 1» or 2»intercalated saponite clay, compared with the spacing of untreated saponite clay. Fig. 1 shows X-ray diÜraction patterns of the intercalated saponites of cis- and trans-stilbazolium ions. The 001 diÜraction peak at 2h ca. 3° shifts to smaller angles, re—ecting the expansion of the clay layer on intercalation of 1 and 2. Table 1 summarizes basal spacings of the intercalated saponites evaluated from 001 diÜraction peaks. The untreated saponite clay has a spacing of 1.32 nm owing to the presence of hydrated sodium ions in the interlayer.Intercalation of 1 expanded the spacing to 1.53 nm. The net distance between the adjacent layers (clearance space) was evaluated by subtracting the thickness of the aluminosilicate layer from the basal spacing. The clearance space of 1»intercalated saponite was estimated to be 0.87 nm, which is slightly shorter than the molecular length of 1 along the long axis.The correlation between the clearance space and molecular length was observed for 2, suggesting that 2 was also arranged mostly perpendicular to the clay layer, such as that reported for alkylammonium ions4 and trans-stilbazolium ions.11 Furthermore it is noted that the spacings of 1» and 2»intercalated saponite are almost the same distance. An analogous arrangement of 1 and 2 in the saponite clay layers as well as their similar layer distance suggest that 1 can isomerize smoothly to 2 with least movement of the aggregate structure.Photosensitized isomerization of cis-stilbazolium ions The colloidal mixture of 1 and the saponite clay gave gelatinous precipitates owing to —occulation of clay sheets. An solution was then added as a sensitizer in the clay Ru(bpy)32` layer. According to the equilibrium constant of intercalation, 80% of 1 can be intercalated, with 20% of sodium ions remaining after a typical reaction.Since clay interlayers can recognize molecular structures,8 a sequential intercalation of 1 followed by that of will result in a segregation as Ru(bpy)32` shown in Scheme 1. The integrated system in the layers can be expected to promote both the –rst electron transfer from the to 1 and the following electron relay process. Ru(bpy)32` Vigorously stirred mixtures were irradiated using a xenon lamp with color –lters selecting wavelengths between 420 and 500 nm after treatment with bubbling nitrogen.Irradiation of the mixture for 2 min gave 60% of trans isomer, 2, with no observable by-product. Fig. 2(a) shows the time»yield curve for the photoisomerization of 1 in saponite, compared with those in micellar and in aqueous homogeneous systems. The initial reaction rate in saponite was 100 times as fast as that in the homogeneous solution. The reaction rate in clay layers is slightly faster than that in a micellar solution of sodium dodecyl sulfate (SDS).Because 1 Scheme 1 Schematic mechanism for sensitized isomerization of cisstilbazolium ion in clay layers has a cationic charge only in the protonated form, the electron relay process was not as eÜective as that reported for the Nmethylstilbazolium »SDS system.13 The quantum yield in the 1»SDS system was 1.1, while an apparent quantum yield was also estimated to be ca. 3 for the 1»saponite system. A 1 mM solution of aqueous 1»saponite is so turbid that [90% of the irradiating light was scattered by the colloidal particles as estimated by an actinometer set behind the cell ; this results in reduction of the quantum yield.A reaction yield of 60% is comparable with the net amount of intercalated 1. Though the value is rather low, most of the 1 intercalated in saponite clay was isomerized readily after 2 min of irradiation. The half-life for exchanging transstilbazoliums by free ions in the bulk solution is about 30 min.20 The intercalation equilibrium constant of 2 is 100 times higher than that of 1 (Table 1).Therefore, it is unlikely that photoisomerized 2 was exchanged over a few min by 1 in the bulk solution and then isomerized eÜectively. Fig. 2(b) shows the time»yield curve for photoisomerization promoted in a 100 lM solution of 1»saponite 1 : 1 mixture. The reaction rate is comparable to that in the 1 mM solution, which con–rms that saponite clay aggregates 1 in the layers even in dilute solution.Unfortunately the transparency of the Fig. 2 Photoisomerization of cis-StzH`, eÜect of concentration of supports of aggregates ; (a) [saponite]\1 mM; [SDS]\1 mM; =, Ö, homogeneous solution ; [cis-Stz]\1 mM, lM. >, [Ru(bpy)32`]\50 (b) [saponite]\100 lM; [SDS]\100 lM; homogeneous =, Ö, >, solution ; [cis-Stz]\100 lM, lM. [Ru(bpy)32`]\5 J. Chem. Soc., Faraday T rans., 1998, V ol. 94 85solution was not sufficient to give a higher apparent quantum yield.This contrasts with the 1»SDS system diluted to 100 lM which did not give a photoisomerization product within 2 min of irradiation. The critical micelle concentration (c.m.c.) of 1»SDS was evaluated as 0.6 mM from the surface tension decrease, depending on the concentration of 1»SDS.21 When the micellar solution was diluted to 100 lM, the micelle structure should collapse and eÜective electron relay can no longer operate. These results mean that saponite clay is a preferable host for stable molecular aggregates regardless of the concentration.EÜect of hydrochloric acid Neutral stilbazole has a reduction potential of ca. 1 V more negative than the cationic stilbazolium ion in acetonitrile ; therefore, excited can reduce only the cationic stil- Ru(bpy)32` bazolium ion. The UV»VIS absorption spectrum of 1 in clay interlayers was almost comparable to that of completely protonated 1, while it was slightly blue shifted.This spectrum reveals that most of 1 is protonated, however, a small amount of neutral stilbazoles are present in the interlayers. Because the neutral stilbazole is hardly reduced by the excited ruthenium complex, the electron relay process could be enclosed in a smaller area of the aggregates. Such a limitation will cause a decrease of quantum yield as reported for a polystyrenesulfonate system.14 Additional HCl can protonate the neutral stilbazoles and combine them to give a larger aggregate of 1.Table 2 shows the eÜect of hydrochloric acid on the reactivity and the concentration of 1 in the bulk phase, and little eÜect of HCl concentration was noted. However, the absorption spectra of the bulk solution revealed that 1 was excluded from the saponite layers up to 52% in the presence of 120 equivalents of HCl. Hydrochloric acid does not destroy the layered structure of the saponite clay in this concentration range as seen from the XRD pattern which was almost the same as for the untreated clay.The net amount of intercalated 1, therefore, decreased by ion exchange with the protons from HCl. The results mean that most of the intercalated 1 isomerized quantitatively when 13 equivalents of HCl were added in the 1»clay system. The eÜect of HCl was speci–c for the clay system because no eÜect was observed in the reactivity in the homogeneous system. Considering the trade-oÜ between intercalation and protonation in the eÜect of HCl, 1.2 equivalents of HCl were added in the following experiments. Quenching of the excited state of by Ru(bpy)3 2ë cis-stilbazolium ion For the quenching process of the excited an elec- Ru(bpy)32` tron transfer mechanism had been proposed according to the excitation energy and the redox potentials of 1 and and the results of ineÜective sensitization by Ru(bpy)32` triplet sensitizers with sufficient energy.13 The quantum yield for the SDS micellar system is comparable to the aggregation number of the SDS and stilbazolium ions.These results support the following reaction mechanism composed of three Table 2 EÜect of hydrochloric acid on reaction yield and replacement of stilbazolium ion [HCl]/[cis-Stz] yielda (%) 1 remaining in solutionb (%) 1.2 41 22 13 45 43 61 45 51 120 46 52 a [cis-Stz]\[saponite]\1 mM, lM; irradiation [Ru(bpy)32`]\50 time; 40 s. b [cis-Stz]\[saponite]\1 mM; evaluated from absorption spectra of –ltrates through membrane –lters.sequences as shown in Scheme 1: (i) initial electron transfer from excited to 1, (ii) an electron relay among 1, Ru(bpy)32` and (iii) back electron transfer from a stilbazole radical to Here, the efficiency of sequence (i) was estimated Ru(bpy)33`. from the emission quenching of excited by 1. The Ru(bpy)32` linear correlation in the Stern»Volmer plot on Ru(bpy)32` emission, as shown in Fig. 3, reveals that a conventional quenching process is operating. The apparent slope increased in the higher concentration region, suggesting a complex quenching.A Stern»Volmer analysis only at relatively low concentrations will be focused upon for simplicity. The slope of the plot, represents a relative quenching kq q, efficiency and was evaluated as 3.4]105 dm3 mol~1. A comparable quenching efficiency, 2.3]105 dm3 mol~1 in was kq q, also observed for the trans-isomer, 2, as shown in Fig. 3. These results suggest that a common quenching process is operative for the –rst electron transfer from excited The Ru(bpy)32`.comparable quenching efficiency also suggests a smooth electron relay in mixed aggregates containing both 1 and 2. Considering the emission lifetime, q, of of about Ru(bpy)32` 1 ls,7 the quenching rate is evaluated to be about 3]1011 dm3 mol~1 s~1, exceeding the diÜusion limiting rate of electron transfer in an aqueous homogeneous solution ; 7.5]109 dm3 mol~1 s~1 at 25 °C.22 If the quenching was dynamically operated on the basis of a diÜusion of intercalated molecules, the quenching rate could not exceed the diÜusion limit but would be much lower than in a homogeneous solution due to a tight coulombic attraction between the intercalants and anionic charges of the clay layer.Therefore, the quenching is concluded to be static between and 1, which hap- Ru(bpy)32` pened to adsorb in the vicinity of each other in the clay layers. was reported to be segregated from viologen mol- Ru(bpy)32` ecules owing to the diÜerence in their size and shape.8 A sequential intercalation of 1 followed by that of Ru(bpy)32` will result in segregation as shown in Scheme 1, where both the –rst electron transfer and the following electron relay will be promoted.EÜect of intercalation degree on reaction yield and emission intensity The relative concentrations of 1 and in the sapon- Ru(bpy)32` ite clay can control the average distance among them, which correlates closely to the reactivity as the electron relay process is included in the mechanism.In this context, the eÜect of the Fig. 3 Quenching of emission from excited by cis- or Ru(bpy)32` trans-stilbazolium ions : lM, [saponite]\50 lM; [Ru(bpy)32`]\1 quenching by cis-stilbazolium ; quenching by trans- L, Ö, stilbazolium. Excitation\450 nm, emission\610 nm 86 J. Chem. Soc., Faraday T rans., 1998, V ol. 94Fig. 4 EÜects of intercalation degree of cis-StzH` on isomerization yield and emission intensity of Reaction yield after 2 Ru(bpy)32`: Ö, min irradiation of 450 nm light ; [cis-Stz]\1 mM, [Ru(bpy)32`]\ 5 lM; relative intensity of —uorescence from L, Ru(bpy)32`.[cis-Stz]\25 lM, lM. [Ru(bpy)32`]\0.5 ratio of 1/saponite on the reactivity and the emission intensity of was examined. Here, we tentatively de–ne the Ru(bpy)32` ratio of 1/saponite as being equal to the degree of intercalation. Concentrations of 1 and were kept con- Ru(bpy)32` stant for each degree of intercalation so that the apparent condition was identical in each equivalent intercalation, except for the concentration of saponite clay.Fig. 4 shows the eÜects of degree of intercalation on the reaction yield and the emission intensity of Ru(bpy)32`. Maximum yield was obtained at ca. 70% intercalation, which is explicable on the basis of the relative concentration of intercalants in the clay layers : at low intercalation, molecules of 1 are dispersed and isolated from each other in the saponite layers, so that electron relay will not operate.A higher intercalation degree is necessary for the formation of close aggregates of 1 and an efficient electron relay process. These results are contrasted with the photocyclodimerization of 2 where the syn head-to-tail cyclobutane of 2 was obtained in 80% yield, even at a low degree of intercalation. The quenching efficiency of the reaction decreased with the degree of intercalation of 1 at \50% and slightly decreased at higher intercalation values.Judging from the equilibrium constant of intercalation, it is notable that most of 1 should be intercalated in the saponite layer at 50% intercalation. Therefore, the increase of the —uorescence intensity can be explained by noting that 1 and are dispersed in the inter- Ru(bpy)32` layer space. When so separated, the –rst electron transfer from excited was restricted and promoted the emission Ru(bpy)32` process. The intermolecular distance between 1 and was Ru(bpy)32` close enough to allow them to interact with each other even at 40% intercalation ; however, it was not sufficient for an eÜective subsequent electron relay process among the aggregates of 1.At a higher intercalation degree the aggregates of 1 become —occulated with each other, and the electron relay process is efficient leading to a considerable increase in reaction yield. The photoisomerization of 1 requires a relatively large molecular aggregate as it has an electron relay process.authors would like to express their appreciation to Pro- The fessor Yasuhiko Sawaki and Professor Katsuhiko Takagi for their active discussions and for their involvement in the synthesis of the sensitizer. We are also grateful for the support of the Grant-in-aid for Encouragement of Young Scientist no. 05750732 from the Ministry of Science, Education, Sports and Culture of Japan. This work was partly supported by the Research foundation for the Electrotechnology of Chubu no.R-07258. References 1 J. H. Fendler and E. J. Fendler, Catalysis in the Micellar and Macromolecular Systems, Academic Press, New York, 1975; J. K. Thomas, T he Chemistry of Excitation at the Interfaces, ACS monogr. 181, American Chemical Society, 1984; Kinetics and Catalysis in Microheterogeneous Systems, ed. M. Graé tzel and K. Kalyanasundaram, Marcel Decker, 1991. 2 K. Kalyanasundaram, Photochemistry in Microheterogeneous Systems, Academic Press, New York, 1987; I. Yamazaki, N.Tamai and T. Yamazaki, J. Phys. Chem., 1990, 94, 516. 3 R. E. Grim, Clay Mineralogy, McGraw-Hill, New York, 1953; G. Lagary, Angew. Chem., Int. Ed. Engl., 1976, 15, 575; B. K. G. Theng, T he Chemistry of Clay-organic Reaction, Adam Hilger, London, 1974. 4 A. Weiss, Chem. Ber., 1958, 91, 487; A. Weiss, Angew. Chem., 1963, 75, 113. 5 Z. Grauer, G. L. Grauer, D. Avnir and S. Yariv, J. Chem. Soc., Faraday T rans. 1, 1983, 83, 1685; S. Yariv and A.Nasser, J. Chem. Soc., Faraday T rans., 1990, 86, 1593; C. S. Sunwar and H. Bose, Clays Clay Miner., 1990, 136, 54; F. Gessner, C. C. Schmitt and M. G. Neumann, L angmuir, 1994, 10, 3749. 6 M. Ogawa and K. Kuroda, Chem. Rev., 1995, 95, 399. 7 R. A. DellaGuardia and J. K. Thomas, J. Phys. Chem., 1983, 87, 990; A. Habti, D. Keravis, P. Levitz and H. van Damme, J. Chem. Soc., Faraday T rans. 2, 1984, 80, 67; N. J. Turro, C. V. Kumar, Z. Grauer and J. K. Barton, L angmuir, 1987, 3, 1056. 8 P. K. Ghosh and A. J. Bard, J. Phys. Chem., 1984, 88, 5519. 9 A. Yamagishi and M. Soma, J. Am. Chem. Soc., 1981, 103, 4640; A. Yamagishi, J. Phys. Chem., 1982, 86, 2472; M. Taniguchi, M. Kaneyoshi, Y. Nakamura, A. Yamagishi and T. Iwamoto, J. Phys. Chem., 1990, 94, 5856. 10 K. Takagi, T. Kuramatsu and Y. Sawaki, J. Chem. Soc., Perkin T rans. 2, 1991, 1517; H. Tomioka and T. Itoh, J. Chem. Soc., Chem. Commun., 1991, 532. 11 K. Takagi, H. Usami, H. Fukaya and Y. Sawaki, J. Chem. Soc., Chem. Commun., 1989, 1174; K. Takagi and Y. Sawaki, J. Chem. Soc., Perkin T rans. 2, 1990, 1723; H. Usami, K. Takagi and Y. Sawaki, Bull. Chem. Soc. Jpn., 1991, 64, 3395. 12 K. Takagi, T. Shichi, H. Usami and Y. Sawaki, J. Am. Chem. Soc., 1993, 115, 4339. 13 K. Takagi, K. Aoshima, Y. Sawaki and H. Iwamura, J. Am. Chem. Soc., 1985, 107, 49; K. Takagi and Y. Ogata, J. Org. Chem., 1982, 47, 1409. 14 K. Takagi, H. Fukaya and Y. Sawaki, J. Am. Chem. Soc., 1988, 110, 7469. 15 D. G. Whitten, P. D. Wides and C. A. DeRosier, J. Am. Chem. Soc., 1972, 94, 7811. 16 F. H. Burstall, J. Chem. Soc., 1936, 173. 17 JCSS-3501 is prepared from Kunimine Ind. Co. For the comparable sample, Sumecton SA, some chemical properties are available in Sumecton SA T echnical Report, Kunimine Ind. Co. 18 C. T. Cowan and D. White, T rans. Faraday Soc., 1958, 54, 691. 19 J. C. Doty, J. L. R. Williams and P. J. Grisdale, Can. J. Chem., 1969, 47, 2355. 20 H. Usami, K. Takagi and Y. Sawaki, J. Chem. Soc., Faraday T rans., 1992, 88, 77. 21 The c.m.c. of a 1»SDS equimolar mixture was estimated as a bending point in the concentration»surface tension plot obtained by the Wilhelmy slide method. The slightly lower c.m.c. for 1»SDS than for pure SDS could be explained that the electrostatic repulsion among dodecyl sulfate ions was cancelled by the cationic charge of 1, which stays in the vicinity of paired SDS due to the hydrophobicity. 22 Handbook of Photochemistry, ed. S. L. Murov, I. Carmichael and G. L. Hug, 2nd. edn., revised and expanded, Marcel Dekker, New York, 1993, Section 7. Paper 7/04446A; Received 24th June, 1997 J. Chem. Soc., Faraday T rans., 1998, V ol. 94 87

ISSN:0956-5000    

DOI:10.1039/a704446a

出版商:RSC    

年代:1998

数据来源: RSC

摘要:

Dispersion of ruthenium oxide on barium titanates (Ba6Ti17O40 , and and photocatalytic activity Ba4Ti13O30, BaTi4O9 Ba2Ti9O20) for water decomposition Mitsuru Kohno, Takatoshi Kaneko, Shuji Ogura, Kazunori Sato and Yasunobu Inoue* Department of Chemistry, Nagaoka University of T echnology, Nagaoka, Niigata 940-21, Japan Ruthenium oxide supported on barium titanates and was employed as a photo- (Ba6Ti17O40, Ba4Ti13O30 , BaTi4O9 Ba2Ti9O20) catalyst for water decomposition. The titanates were subjected to either reduction or reduction»oxidation. RuCl3-impregnated High-resolution electron microscopic images demonstrated that ruthenium metal and ruthenium oxides were uniformly dispersed on with an average particle size of 2.6 nm.Similar uniform ruthenium oxide dispersions were observed for the other BaTi4O9 barium titanates ; the average particle sizes were 4.7 nm for 2.3 nm for and 4.4 nm for Ba6Ti17O40, Ba4 Ti13O30, Ba2 Ti9O20 . Particle size distributions were narrower for and and slightly larger for and BaTi4O9 Ba4Ti13O30, Ba6 Ti17O40 Ba2Ti9O20 .Stoichiometric production of oxygen and hydrogen occurred for a photocatalyst. A small amount of hydrogen RuO2/BaTi4O9 and no oxygen were produced from the other barium titanates and combined with ruthe- (Ba6Ti17O40, Ba4Ti13O30 Ba2Ti9O20) nium oxides. EPR spectra at 77 K in He or with UV irradiation demonstrated that a strong signal, assigned to a surface O~ O2 radical, appeared for but not for the other barium titanates. These produced small complicated signals, indicating that BaTi4O9 only has a high efficiency for photoexcited charge formation.Raman spectra showed that a strong single peak at a high BaTi4O9 wavenumber of 860 cm~1, characteristic of was absent in the rest of the barium titanates. The diÜerent photocatalytic BaTi4O9 , properties among these titanates are discussed on the basis of structure diÜerences of the barium titanates, and the presence of internal –elds ; a long TiwO bond in the distorted octahedra is proposed to be important in photocatalysis.TiO6 Introduction We have recently shown that the combination of ruthenium oxide and makes a good photocatalyst which is BaTi4O9 able to decompose water to oxygen and hydrogen in stoichiometric ratio.1,2 Barium titanates are represented by where n\2»4.3h6 In view of the corre- Ba2(n~1)Ti4n`1O10n , lation between the photocatalytic activity and oxide structure, it is desirable to extend research to photocatalysts using a series of barium titanates combined with ruthenium oxide which works as a promoter.In particular, it is of importance to see whether is the only barium titanate that BaTi4O9 becomes a good photocatalyst by combination with ruthenium oxide and, if so, to clarify why RuO2-deposited BaTi4O9 is speci–c as a photocatalytic titanate. In this work, in addition to and BaTi4O9, Ba6 Ti17O40, Ba4 Ti13O30 Ba2Ti9O20 were chosen as representative barium titanates.has BaTi4O9 orthorombic symmetry with a unit cell of a\14.53, b\3.79, c\6.29 has monoclinic symmetry with a Aé 3.7 Ba6Ti17O40 unit cell of a\9.88, b\17.08, c\18.92 b\98.7°.3 Aé 3, has orthorombic symmetry (a\17.06, b\9.86, Ba4Ti13O30 c\14.05 and triclinic symmetry (a\14.36, Aé 3),4 Ba2Ti9O20 b\14.10, c\7.48 a\95.53, b\98.7, c\89.95°).5 Aé 3, has a pentagonal prism tunnel structure, and BaTi4O9 a hollandite-like tunnel structure, whereas Ba2Ti9O20 and have close-packed arrays of Ba6Ti17O40 Ba4Ti13O30 oxygen and barium atoms in which some of the octahedral voids are –lled by titanium atoms.3h8 In this study, the photocatalytic properties for water decomposition of these barium titanates with supported ruthenium oxides were examined. The photocatalytic activity is controlled by two factors regarding the efficiency of photoexcited charge formation and of charge transfer to the surface reactants.In the development of efficient photocatalysts, both factors have to be taken into account.In a photocatalytic system of ruthenium oxidesupporting barium titanates, the titanates absorb light and produce photoexcited electrons and holes, thus it is essential to compare the ability of photoexcited charge formation among the titanates. In a previous study on the photocatalyst, we demonstrated that the EPR RuO2/BaTi4O9 signals of under UV-irradiation in diÜerent gas BaTi4O9 atmospheres were a good measure of the photoexcitation ability.9h12 Thus, this method was employed here.For the establishment of correlations between the photoexcitation ability and titanate structures, the structural features of the titanates were investigated by laser Raman spectroscopy. As for the charge transfer, no photocatalytic activity was observed in the absence of ruthenium oxide in the photocatalytic system using Ruthenium oxide thus plays BaTi4O9 .1 an important role in the transfer of the photoexcited charges to the surface reactants.Thus, in comparison of photocatalytic activities among the titanates, it is desirable to prepare photocatalysts with similar ruthenium oxide distributions. In the previous study, direct oxidation after impregnation was RuCl3 employed to prepare ruthenium oxide.1,2 This study involves reduction and reduction»oxidation of RuCl3-impregnated barium titanates in an attempt to obtain well dispersed states of ruthenium. The dispersion was investigated by highresolution transmission electron microscopy (HRTEM) combined with elemental analysis by EDS.From comparison with the photocatalytic activity for water decomposition, the ability to produce photoexcited charges, the extent of ruthenium oxide dispersion, and the structural features, a model for photocatalysis by RuO2-deposited barium titanates is proposed. Experimental The barium titanates were prepared by calcining a stoichiometric mixture of (high-purity grade, Soekawa Chemical TiO2 Co.) and (high-purity grade, Soekawa Chemical Co.) BaCO3 in air at 1323 K and 20 h for 1523 K and 10 h for BaTi4O9 , 1423 K and 10 h for and 1523 K Ba6Ti17O40, Ba4 Ti13O30 , J.Chem. Soc., Faraday T rans., 1998, 94(1), 89»94 89and 10 h for The structures of the titanates were Ba2Ti9O20 . investigated by powder X-ray diÜraction using a Rigaku Denki RAD III diÜractometer. Their morphology was examined by observations with a JEOL JXA-733 scanning electron microscope.The surface area of titanates was measured by the BET method using nitrogen at 77 K. Photocatalysts were prepared by impregnation of the barium titanates with aqueous solutions at 353 K to RuCl3 incipient wetness and then dried in air at 353 K. The loading of ruthenium was 0.5 wt.% metal content. The RuCl3- barium titanates were subjected to either impregnated reduction in an —ow at 723 K for 2 h or reduction fol- H2 lowed by oxidation in air. The reduction temperature was maintained at 723 K, whereas the oxidation temperature was changed from 373 to 773 K.For simplicity, reduction and oxidation are denoted by R and O and only the oxidation temperature (in K) is given : e.g. a photocatalyst prepared by reduction and subsequent 573 K oxidation of impregnated is represented by The dis- BaTi4O9 RuO2(R,O573)/BaTi4O9 . persion of ruthenium oxides and the photocatalytic activity were compared to those prepared by direct oxidation of impregnated at 773 K; this is denoted as BaTi4O9 RuO2(O773)/BaTi4O9 .The photocatalytic water decomposition was carried out in a gas-circulation system described elsewhere.1,7 Brie—y, 0.2 g of powder photocatalysts were dispersed in 20 cm3 of pure water in a quartz cell, stirred by bubbling with Ar gas circulation, and irradiated with a 400 W Xe lamp through a water –lter. The UV —ux (330»390 nm) was ca. 12 mW cm~2. Hydrogen and oxygen produced were analyzed by a gas chromatograph connected to the reaction system.High-resolution electron microscopic images of barium titanate-supported ruthenium and ruthenium oxides were obtained with a JEOL 2010 transmission electron microscope (TEM) operated at an accelerating voltage of 200 kV. The sample preparation for TEM observation was made by dispersing the powder sample ultrasonically in methanol and putting the resultant suspension onto a holey carbon coated –lm supported by a Cu grid. The energy-dispersive X-ray (EDS) spectra were collected for nanometre-size areas of the samples with a Voyager energy dispersive analyzer (Noran Instruments) installed on the microscope.The beam diameters for the microanalysis of the samples were varied in the range 2»5 nm. EPR spectra were recorded on a JEOL JES-RE2X spectrometer at a microwave power of 0.1 mW, a microwave frequency of ca. 9.1 GHz and a modulation width of 1 G. In a typical run, 350^1 mg of sample was placed in an X-band quartz cell and degassed at 573 K.For adsorption experiments, 30 Torr of He or were introduced at room tem- O2 perature. EPR measurements were performed at 77 K, unless otherwise speci–ed, without or with UV irradiation of the samples with a 500 W high-pressure mercury lamp. The g values were calibrated by Mn2` in MgO, the error of which was within ^0.001. Results All of the XRD patterns of the barium titanates were in good agreement with those reported in the XRD data –les.13 The particle sizes of these titanates ranged from 1 to 5 lm, and there were no signi–cant diÜerences.The speci–c surface area of the barium titanates was 1 m2 g~1 for both Ba6Ti17O40 and 2.3 for and 1.2 for BaTi4O9, Ba4 Ti13O30 Ba2Ti9O20 . Fig. 1 shows the laser Raman spectra of the barium titanates. As reported previously, had clearly distin- BaTi4O9 guishable three main bands at 430»450, 590»650 and 860 cm~1. The characteristic peak was a strong single peak appearing at a higher wavenumber than 860 cm~1 since it re—ects a short TiwO bond.9,10 In contrast, Ba6Ti17O40 , Fig. 1 Raman spectra of (a) (b) (c) Ba6Ti17O40, Ba4 Ti13O30 , and (d) BaTi4O9 Ba2Ti9O20 and exhibited complicated spectra Ba4Ti13O30 Ba2Ti9O20 consisting of many small peaks. Although they also showed peaks at 875, 858 and 846 cm~1 , respectively, the relative intensities of these peaks were considerably lower. Fig. 2 shows the UV diÜuse re—ectance spectra of these titanates.The absorption had a threshold wavelength at around 420 nm for and and shifted to around BaTi4O9 Ba2Ti9O20 , 400 nm for and The maximum Ba6Ti17O40 Ba4Ti13O30 . absorption shifted to shorter wavelength in the order of (340 (335 Ba6Ti17O40 nm)[Ba2Ti9O20 nm)[Ba4Ti13O30 (330 (320 nm). A shoulder was observed at nm)[BaTi4O9 around 380 nm for and BaTi4O9 Ba2Ti9O20 . Fig. 2 UV diÜuse re—ectance spectra of (-------), Ba6Ti17O40 (» » » »), (»»») and Ba4Ti13O30 BaTi4O9 Ba2Ti9O20(»-»-) 90 J.Chem. Soc., Faraday T rans., 1998, V ol. 94Fig. 3 shows an HRTEM image of an photocatalyst. Spherical dark spots, RuO2(R,O573)/BaTi4O9 2»5 nm in diameter, were uniformly dispersed on the regular lattice image. These dark spheres were observed over BaTi4O9 the entire surface. EDS analysis was performed for BaTi4O9 the two regions represented by circles (a) and (b) on the TEM image (Fig. 4). For region (a), two peaks observed at 4.5 and 4.9 keV were assigned to Ba(Ka and Lb) and Ti(Ka and Kb), respectively.For region (b), in which a dark spherical spot was present, an additional peak appeared at 2.6 keV which was due to Ru La. Thus it was obvious that the dark spherical spots were composed of ruthenium. Fig. 5 compares the HRTEM images of Ru/BaTi4O9 , RuO2(R,O773)/BaTi4O9 and For black spots RuO2(O773)/BaTi4O9 . Ru/BaTi4O9 , ranging from 0.8 to 3.0 nm were observed, which were due to metallic Ru. For and RuO2(R,O773)/BaTi4O9 spots with similar particle sizes and RuO2(O773)/BaTi4O9 , distributions were observed. Note that these particle sizes and distributions are analogous to those of (cf.Fig. 3). RuO2(R,O573)/BaTi4O9 Fig. 6»8 show the HRTEM images of sup- RuO2(R,O573) ported on and respec- Ba6Ti17O40, Ba4Ti13O30 Ba2Ti9O20 , tively. In each image, spherical dark spots due to ruthenium were clearly seen on the regular lattice images of the barium titanates. Fig. 9 shows particle size distributions. Ba6Ti17O40 and had symmetrical distributions having centred Ba2Ti9O20 around 4»5 nm in which the distribution was broader for than for For and Ba2Ti9O20 Ba6Ti17O40.Ba4 Ti13O30 smaller particles were present with a higher density, BaTi4O9 , and the maximum of distributions shifted to particle sizes as small as 2»3 nm. The average diameter of the particles increased in the order of (2.3 (2.6 Ba4Ti13O30 nm)\BaTi4O9 (4.4 (4.7 nm). nm)\Ba2Ti9O20 nm)\Ba6Ti17O40 Fig. 10 compares the photocatalytic activities for water decomposition of as-impregnated BaTi4O9 , Ru/BaTi4O9 , Fig. 3 HRTEM image of Circles (a) and RuO2(R,O573)/BaTi4O9 . (b) correspond to areas used for EDS analysis. Fig. 4 EDS spectra of regions (a) and (b) on BaTi4O9 Fig. 5 HRTEM images of (a) (b) Ru/BaTi4O9 , and (c) RuO2(R,O773)/BaTi4O9 RuO2(O773)/BaTi4O9 and in which RuO2(O773)/BaTi4O9 RuO2(R,O)/BaTi4O9 , oxidation was performed at 373, 573 or 773 K. The production of was extremely small for as-impregnated H2 and slightly increased with For BaTi4O9 , Ru/BaTi4O9 .a considerable increase in the activ- RuO2(R,O373)/BaTi4O9 , ity of hydrogen production was observed, but oxygen was poorly produced. A remarkable enhancement of photocatalytic activity occurred for and RuO2(R,O573)/BaTi4O9 the activities of both hydrogen and oxygen production were Fig. 6 HRTEM image of RuO2(R,O573)/Ba6Ti17O40 J. Chem. Soc., Faraday T rans., 1998, V ol. 94 91Fig. 7 HRTEM image of RuO2(R,O573)/Ba4Ti13O30 Fig. 8 HRTEM image of RuO2(R,O573)/Ba2Ti9O20 Fig. 9 Distributions of particles deposited on (a) RuO2 Ba6Ti17O40 , (b) (c) and (d) Ba4Ti13O30 , BaTi4O9 Ba2Ti9O20 Fig. 10 Photocatalytic activity for water decomposition of BaTi4O9- (a), Ru(R723) (b), (c), supported RuCl3 RuO2(R,O373) RuO2(R,O573) (d), (e) and ( f ). 4, RuO2(R,O773) RuO2(O773) 34, H2, O2 . Fig. 11 Photocatalytic activity for water decomposition on titanates of (a) (b) RuO2(R,O573)/barium Ba6Ti17O40, Ba4 Ti13O30 , (c) and (d) 4, BaTi4O9 Ba2Ti9O20 . 34: H2; O2 . 167 and 78 lmol g~1 h~1, respectively, in which the stoichiometric hydrogen-to-oxygen ratio was nearly achieved. For the activity was lowered by a factor RuO2(R,O773)/BaTi4O9 , of ca. 30%, but was ca. twice as large as that of Note that the activity of RuO2(O773)/BaTi4O9 . was similar to that of 0.5 wt.% RuO2(O773)/BaTi4O9 which was obtained in the previous RuO2(O848)/BaTi4O9 study.1 These results indicate that reduction»oxidation is useful for catalyst activation, compared to direct oxidation.Fig. 11 shows the activities of a photocatalyst system of and RuO2(R,O573)/ (Ba6Ti17O40, Ba4 Ti13O30 Ba2Ti9O20), together with the activity of for a RuO2(R,O573)/BaTi4O9 comparison. There was no evolution of oxygen, and the rate of production was extremely small : 1.0 lmol g~1 h~1 for H2 7.0 lmol g~1 h~1 for RuO2(R,O573)/Ba6Ti17O40 , and 1.5 lmol g~1 h~1 for RuO2(R,O573)/Ba4Ti13O30 Note that there were quite large RuO2(R,O573)/Ba2Ti9O20 .diÜerences in activity between photocatalysts using BaTi4O9 and the other titanates. Fig. 12 shows the EPR spectra of the barium titanates at 77 K in 30 Torr of He with UV irradiation. Two signals (g\2.034 and 1.981) observed at both ends of each spectrum are due to Mn2` in MgO which is used for the calibration of g values. provided a strong signal with g\2.018 BaTi4O9 and 2.004, in agreement with previously reported values.9h12 On the other hand, and Ba6Ti17O40, Ba4Ti13O30 Ba2Ti9O20 showed no such characteristic strong signals with irradiation.Instead, produced small signals at g\2.021 and Ba6Ti17O40 2.002. Complicated small signals appeared at g\2.022 , 2.018 and 2.003 for and broad signals for Ba4Ti13O30 Ba2Ti9O20 . In order to observe the reactivity of the EPR-active species, signal changes with heat treatment in an oxygen atmosphere were examined. The barium titanates were irradiated at 77 K in 30 Torr of instead of He, and the sample temperature O2 was raised to room temperature in the presence of gaseous oxygen.EPR spectra were measured at 77 K without UV irradiation. showed characteristic large signals at BaTi4O9 g\2.010 and 2.003 and a very small signal at g\2.018, consistent with those reported previously.11 However, the small signals observed in disappeared completely, and Ba6Ti17O40 the signals in and diminished, as Ba4Ti13O30 Ba2Ti9O20 shown in Fig. 13. Discussion The HRTEM observations demonstrated that ruthenium metal and ruthenium oxides were uniformly dispersed as small particles on the surface.The interesting feature is BaTi4O9 that Ru metal and Ru oxides had similar particle sizes and distributions, as shown in Fig. 5; furthermore, nearly the same particle sizes of were obtained in the oxidation of RuO2 at temperatures ranging from 373 to 773 K, and Ru/BaTi4O9 92 J. Chem. Soc., Faraday T rans., 1998, V ol. 94Fig. 12 EPR spectra of (a) (b) (c) Ba6Ti17O40, Ba4 Ti13O30 , and (d) BaTi4O9 Ba2Ti9O20 Fig. 13 EPR spectra of (a) (b) (c) Ba6Ti17O40, Ba4 Ti13O30 , and (d) These titanates were UV irradiated at 77 BaTi4O9 Ba2Ti9O20 . K in heated to room temperature without evacuation, and then O2 , cooled to 77 K. All the spectra were measured at 77 K without UV irradiation. even in the direct oxidation at 773 K. A comparison with the results on and RuO2(O773)/BaTi4O9 RuO2(O848)/BaTi4O9 which was obtained by direct oxidation of the impregnated at 848 K,1 also showed that there were no signi–cant BaTi4O9 diÜerences in particle sizes and distributions of between RuO2 reduction»oxidation and direct oxidation.On the other hand, the photocatalytic activity for water decomposition was strongly dependent on the oxidation temperature of ruthenium and on the presence or absence of reduction prior to oxidation. Similar dispersion but diÜerent photo- RuO2 catalytic activity indicates that the density of RuO2-based active sites is nearly the same, but their efficiency is higher for produced by reduction»oxidation than by direct oxida- RuO2 tion without reduction.One of the reasons for this is possibly that reduction»oxidation permits strong interfacial contact of small particles with surfaces, which facilitates RuO2 BaTi4O9 the transfer of the photoexcited charges to particles. It RuO2 is plausible that the transformation of metallic to oxide phases brings about strong interfacial interactions between RuO2 particles and the oxide surfaces.The appearance of a maximum in the activity dependence on oxidation temperatures (Fig. 10) means that there are optimum states in for charge transfer. The possibility is not ruled out that RuO2 reduction produces ruthenium metal particles and then, the following oxidation leads to the formation of a ruthenium oxide shell covering the metal particles. Domen et al. proposed a structure of NiO-covered Ni as a promoter in a photocatalytic system for water decomposition of NiO deposited on SrTiO3 .14 The photocatalysts except for had very RuO2/BaTi4O9 poor performance with respect to photocatalytic activity for water decomposition, i.e.no oxygen evolution and a very small amount of hydrogen production. As for the lack of oxygen in the gas phase, it is likely that the oxygen is retained on the surface or interior of the barium titanates, as observed in Since the SEM observation and the measure- Pt/TiO2 .15 ments of surface area showed that there were no signi–cant diÜerences in macromorphology and in speci–c surface area of the titanates, it follows that large diÜerences in photocatalytic activity between and the rest of the titanates are BaTi4O9 explained in terms of diÜerences in either particle sizes and distributions of or microstructure-related photo- RuO2 chemical properties of the titanates.TEM observations showed that the particles were RuO2 composed of analogous spherical shapes, irrespective of the type of barium titanates, although showed nar- Ba4Ti13O30 rower distributions, similar to that of whereas BaTi4O9 , and exhibited broader distributions : Ba6Ti17O40 Ba2Ti9O20 the average particle size varied in the order (2.3 Ba4Ti13O30 (2.6 (4.4 nm)\BaTi4O9 nm)\Ba2Ti9O20 nm)\Ba6Ti17O40 (4.7 nm).The surface area of was calculated from the RuO2 size by assuming round shapes: the ratio was 1.1 : 1 : 0.6 : 0.5, respectively. This ratio was too small to explain the diÜerence of photocatalytic activity shown in Fig. 11. Moreover, the abovementioned order of the particle sizes was not in agreement with the order of photocatalytic activity. Thus, these results indicate that the particle sizes and dispersions of RuO2 are not a key factor in distinguishing the photocatalytic activity between and the three other barium titanate- BaTi4O9 based photocatalysts. As shown in Fig. 12 and 13, a strong EPR signal with g\2.018 and 2.004 appeared only for whereas the BaTi4O9 , signal was not observed for the other barium titanates and except for very Ba6Ti17O40, Ba4 Ti13O30 Ba2Ti9O20 small complicated signals. Furthermore, the characteristic signal was transformed to a new signal with g\2.018, 2.010 and 2.003 upon exposure to an atmosphere at room tem- O2 perature. On the other hand, the very small complicated peaks for the other barium titanates disappeared under similar conditions.These EPR experiments clearly showed that the radical production with UV irradiation was quite diÜerent between and the other titanates.As shown in the BaTi4O9 previous study, the signal with g\2.018 and 2.004 was assigned to a surface radical, O~,11,12,16,17 derived from lattice oxygen O2~,18 and the new signal with g\2.018, 2.010 and 2.003 was associated with the radical.11,19 Note that O3~ the formation of the O~ radical was not due to bulk phenomena, but occurred only at the surface region of as BaTi4O9 , is evident from the fact that the radical completely changed to J.Chem. Soc., Faraday T rans., 1998, V ol. 94 93Table 1 Percentage of TiwO bonds in the unit cell bond length \1.8 ” P2.3 ” barium titanate (%) (%) Ba6Ti17O40 2.0 2.0 Ba4Ti13O30 5.1 0.0 BaTi4O9 8.3 8.3 Ba2Ti9920 4.6 0.9 a new radical species by the reaction with gaseous These O2 . radicals undoubtedly appeared as a consequence of the photoexcited electron and hole formation, which is indicative of the high ability of to produce photoexcited charges.BaTi4O9 Thus the high photocatalytic activity of is RuO2/BaTi4O9 strongly associated with the higher efficiency of the surface radical production of which is intrinsically diÜerent BaTi4O9 , from the other barium titanates employed here. possesses a pentagonal prism tunnel structure BaTi4O9 consisting of two kinds of strongly distorted octahedra. TiO6 One octahedron has displacement of a Ti ion by 0.030 TiO6 nm from the center of gravity of six surrounding oxygen ions and the other by 0.021 nm.7 The displacement leads to the presence of large dipole moments (5.7 and 4.1 D§).It has been previously proposed that the internal –elds due to the dipole moments were responsible for the higher efficiency of separation of the photoexcited charges.12 Furthermore, from the fact that the surface O~ radical was very stable in the presence of gas molecules, it has been suggested that TiwO bond breaking occurred by charge transfer with UV irradiation.11 This breaking is considered to be strongly related to the presence of the long TiwO bond in the distorted octahedra.TiO6 Crystallographic data are available for the barium titanates, 3h5,7 and Table 1 compares the proportion of TiwO bonds with short (O0.18 nm) and long (P0.23 nm) bonds in the unit cell of the titanates. In the Raman spectra of barium titanates, the sharp peak observed at 860 cm~1 re—ects the presence of short TiwO bonds.The most interesting point is that has percentages of as large as 8.3% for the pres- BaTi4O9 ence of both short (O0.18 nm) and long (P0.23 nm) TiwO bonds, whereas the other barium titanates have low percentages, especially for long TiwO bonds. Since the O~ radical is con–ned to the surface region,11 its production requires higher percentages of long TiwO bonds. This accounts for the absence of the surface O~ radical in barium titanates apart from BaTi4O9 .From these considerations, it is con–rmed that the internal –elds due to the dipole moments of promote the BaTi4O9 charge transfer, and TiwO bond breaking stabilizes the § 1DB3.335 64]10~30 C m. surface O~ radical produced. Therefore, in comparison with the other barium titanates, the unique photocatalytic properties of are that it is composed of distorted with BaTi4O9 TiO6 short and long TiwO bonds. In relation to photocatalysis, the stable surface O~ radical works as a hole center to oxidize OH~, whereas the transferred electrons, which could be delocalized at the surface, move to ruthenium oxides and then reduce H` to hydrogen.In the present work, it has been revealed that in a photocatalytic system of ruthenium oxide-deposited barium titanates and (Ba6Ti17O40, Ba4 Ti13O30 , BaTi4O9 Ba2Ti9O20), only is active for water decomposition. The RuO2/BaTi4O9 particle sizes and distributions of are similar among the RuO2 titanates, and the photocatalytic diÜerences are attributed to the diÜerent structures of the titanates, in which important factors are the presence of internal –elds due to dipole moments for promoting photoexcited charge transfer, and long TiwO bonds leading to the formation of stable surface O~ radicals.work was supported by a Grant-in-Aid for Scienti–c This Research (B)(07555249) from The Ministry of Education, Science, Sports, and Culture of Japan. References 1 Y. Inoue, Y. Asai and K. Sato, J. Chem. Soc., Faraday T rans., 1994, 90, 797. 2 Y. Inoue, T. Niiyama, Y. Asai and K. Sato, J. Chem. Soc., Chem. Commun., 1992, 579. 3 E. Tillmanns and W. H. Baur, Acta Crystallogr., Sect. B, 1970, 26, 1645. 4 E. Tillmanns, Inorg. Nucl. Chem. L ett., 1971, 7, 1169. 5 G. D. Fallon and B. M. Gatehouse, J. Solid State Chem., 1983, 49, 59. 6 E. Tillmanns, W. Hofmeister and W. H. Baur, J. Solid State Chem., 1985, 58, 14. 7 D. H. Templeton and C. H. Dauben, J. Chem. Phys., 1960, 32, 1515. 8 W. Hofmeister, E. Tillmanns and W. H. Baur, Acta Crystallogr., Sect. C, 1984, 40, 1510. 9 M. Kohno, S. Ogura, K. Sato and Y. Inoue, Stud. Surf. Sci. Catal. A, 1996, 101, 143. 10 M. Kohno, S. Ogura and Y. Inoue, J. Mater. Chem., 1996, 6, 1921. 11 M. Kohno, S. Ogura, K. Sato and Y. Inoue, Chem. Phys. L ett., 1997, 267, 72. 12 M. Kohno, S. Ogura, K. Sato and Y. Inoue, J. Chem. Soc., Faraday T rans., 1997, 93, 2433. 13 JCPDS, No. 34-70, No. 35-51, No. 35-750 and No. 35-817. 14 K. Domen, A. Kudo, T. Onishi, N. Kosugi and H. Kuroda, J. Phys. Chem., 1986, 90, 292. 15 K. Yamaguti and S. Sato, J. Phys. Chem., 1985, 89, 5510. 16 N. B. Wong, T. B. Taarit and J. H. Lunsford, J. Chem. Phys., 1974, 60, 2148. 17 V. A. Shvets and V. B. Kazansky, J. Catal., 1972, 25, 123. 18 M. Kohno, S. Ogura, K. Sato and Y. Inoue, in preparation. 19 N. B. Wong and J. H. Lunsford, J. Chem. Phys., 1972, 56, 2664. Paper 7/04947A; Received 10th July, 1997 94 J. Chem. Soc., Faraday T rans., 1998, V ol. 94

ISSN:0956-5000    

DOI:10.1039/a704947a

出版商:RSC    

年代:1998

数据来源: RSC

摘要:

Thermal expansion behavior of a shock-synthesized BñCñN heterodiamond Tamikuni Komatsu§ Analytical Research Center, Asahi Chemical Industry Co., L td. 2-1 Samejima, Fuji, Sizuoka 416, Japan The thermal expansion coefficient of heterodiamond determined by means of high-temperature X-ray diÜraction, is BC2.5N negligible up to 800 °C, it changes abruptly in the range 900»1100 °C and increases steadily above 1100 °C. The thermal expansion coefficient is ca. 5.5]10~6 K~1 in the range 1100»1300 °C.This expansion coefficient is in fairly good agreement with that of cubic BN at high temperatures. The rapid expansion preceding the steady expansion is unknown for diamond and cubic BN. The thermal expansion behavior is discussed from a structural viewpoint. Diamond is a non-metallic material, having the highest hardness, the highest thermal conductivity and a wide band-gap semiconductivity. Cubic BN has half the hardness of diamond and excellent abrasive resistance to steel.When these hard materials are used as a hard coating for cutting tools and semiconductors, matching the thermal expansions of the hard materials with those of the substrates is very important for preventing the hard coating from cracking due to thermal shock. In addition, the thermal expansion is directly related to the diÜerence between the speci–c heats at constant pressure and constant volume as described by the Gruneisen relation, so the measurement of this parameter is useful for studying an equilibrium diagram of the hard material.Slack and Bartram have reviewed the thermal expansion of diamond, cubic BN, Mo, W and other cubic semiconductive crystals such as Ge, Si and SiC.1 Recently, we have developed a new diamond-structure material composed of B, C and N atoms, a so-called heterodiamond, and have con–rmed that the material has several desirable properties for use as a hard coating : it has the highest bulk modulus next to diamond and a good hightemperature oxidation resistance superior to diamond.2,3 In this paper, the thermal expansion of the heterodiamond was investigated by means of high-temperature X-ray diÜraction.Experimental Sample preparation The heterodiamond of composition was prepared by BC2.5N shock-compression of a hexagonal compound (h- BC2.5N according to a method described previously.2 h- BC2.5N) was obtained by chemical vapor deposition of BC2.5N according to ref. 4. The powder was MeCN»BCl3 h-BC2.5N mixed with small copper balls in a h-BC2.5N : copper\6 : 94 mass ratio, pressed to form a disk, and shock-compressed using a cylindrical shock-compression apparatus.The incident shock pressure on the sample was estimated to be 35 GPa. The recovered sample was machined, immersed in aqua regia to remove the copper matrix, heated in concentrated HClO4 to remove unchanged treated with molten NaOH h-BC2.5N, to remove trace amounts of metallic contaminants, washed with distilled water and dried under vacuum at 200 °C.The material obtained had the approximate chemical composition § Correspondence should be addressed to the author at Tukuba Ninomiya Daini-Apartment Rm. 1-201, Ninomiya 4-13-1, Tukubacity, Ibaraki 305, Japan. B : C :N\1.0 : 2.5 : 1.0, and included negligible amounts of hydrogen and metallic elements. Thermal expansion measurements The thermal expansion of the heterodiamond was measured using a high-temperature X-ray diÜraction technique.A mixture of the heterodiamond (95 wt.%) and a-Al2O3 (Kojundo Kagaku, 99.999% purity and 2»3 lm size) (5 wt.%) was used for the XRD measurements, where was a-Al2O3 5 used as the internal standard to make 2h readings more accurate. The mixture was placed in the depression in a Pt(80)» Rh(20) specimen holder which was also a heater (the depression size was 6 mm long]4 mm wide]0.5 mm deep) and was mounted in a high-temperature X-ray diÜractometer (Mac Science MXP18VA), held at 10~3 Pa with an ion pump and heated with a DC current.The XRD measurements were carried out with nickel-–ltered Cu-Ka radiation (j\0.154 178 nm) generated at 40 kV and 40 mA. The diÜraction data were recorded on an imaging plate detector and retrieved using a personal computer. The step width of 2h was 0.01°. The 2h range measured was 0»140° and the scanning time was 20 min. The XRD pattern of the sample was measured in the range 25»1300 °C at a pressure of 10~3 Pa.In the range 25» 1000 °C, the XRD measurements were carried out 25 °C intervals with a heating rate of 25 °C min~1, with a 1 min hold time at each temperature; in the range 1000»1300 °C, XRD measurements were made at 100 °C intervals with a heating rate of 65 °C min~1, and a 1 min hold time. The temperatures in each range were measured to within ^5 K by a Pt(95)» Rh(5) vs. Pt(80)»Rh(20) thermocouple that was welded at the bottom of the sample holder. The linear thermal expansion coefficient, a, of the sample was obtained by a\ 1 a0 da dT where was taken as the lattice constant at room tem- a0 perature, and da/dT was given as the slope of the plot of the lattice constant vs.temperature. The thermal expansion experiments required more than 10 h, so there was some concern that the sample might be degraded by long heating. To investigate this in—uence, the X-ray powder pattern of the sample annealed at high temperatures was measured accurately.The sample was prepared as follows : the heterodiamond powder was placed in an crucible, heated in an electric furnace to 1300 °C at a Al2O3 heating rate of 10 °C min~1 at 1]10~4 Pa, maintained for 3 h at this temperature, left to cool to room temperature under J. Chem. Soc., Faraday T rans., 1998, 94(1), 101»104 101vacuum. The XRD measurements were made at room temperature with Cu-Ka radiation generated at 40 kV and 40 mA using a Philips PW-1800 X-ray powder diÜractometer. The step width was 0.01°, the 2h range measured was 10»150° and the sampling time was 5 s.The XRD pattern obtained was compared with that of the original sample. Results and Discussion Fig. 1 shows a collection of the XRD patterns of the sample measured at diÜerent temperatures. The XRD pattern consists of peaks due to the heterodiamond, added as BC2.5N a-Al2O3 the internal standard and the Pt specimen holder. Fig. 2 shows a magni–cation of the peak at 2h\43.4° due to the (111) plane of the heterodiamond.It is noticeable that the peak scarcely shifts up to 800 °C but shifts apparently to lower angles above 900 °C. In order to determine an accurate lattice constant of the heterodiamond, the measurements of other peaks in addition to the (111) peak are desirable, but the peaks other than the (111) peak were so weak and broad that accurate peak positions could not be read. Therefore, a provisional lattice constant, a, was calculated from the equation based on the cubic lattice geometry: where a\)3 d111 , d111 is the d value of the (111) plane.Fig. 3 shows a plot of the provisional lattice constant vs. temperature. The lattice constant scarcely changes up to 800 °C, increases markedly in the Fig. 1 XRD patterns of the heterodiamond at diÜerent temperatures : heterodiamond; as the internal standard; Ö, >, a-Al2O3 Pt»Rh specimen holder = Fig. 2 Magni–cation of the (111) peak of the heterodiamond at different temperatures Fig. 3 Plots of the provisional lattice constant vs. temperature. The provisional lattice constant, a, was calculated from the equation: a\ where is the d value of the (111) plane. )3 d111 , d111 range 900»1100 °C and increases linearly above 1100 °C. The slope in the range 1100»1300 °C is ca. 2]10~6 nm K~1, the thermal expansion coefficient is therefore ca. 5.5]10~6 K~1. For comparison, the reported data1 for diamond and cubic BN are plotted in the same –gure. The following diÜerences are clearly noticeable : (1) the initiation temperature for appreciable thermal expansion is ca. 400 °C for both diamond and cubic BN, but is ca. 900 °C for the heterodiamond: (2) the heterodiamond undergoes a steep thermal expansion in the range 900»1100 °C that has not been observed for either diamond or cubic BN. The steep thermal expansion behavior suggests the possibility of phase separation into cubic BN plus structural defects. The former is impossible because the sample after the experiment showed the same XRD pattern as the original. The latter is related to the processing of the materials.Diamond and cubic BN consist of well ordered single crystals of gem quality or industrial grade in which negligible amounts of structural defects are present. On the other hand, the shock-synthesized heterodiamond is a polycrystal aggregated with nano-crystallites and the grain boundaries are –lled with poorly ordered crystalline phases containing considerable amounts of free radicals.Such grain boundaries and lattice vacancies may accelerate the softening of the crystal lattice by thermal vibration. Similar enhanced thermal expansion has been observed for Mo and W, and this is believed to be caused by Schottky vacancy generation.1 However, for the heterodiamond it is unlikely that vacancies and Schottky vacancy generation would have any eÜect, because these ideas are insufficient to explain the steady increase following the steep expansion.Other factors such as inclusions, partially ionic bonding, polycrystallinity and residual stress of the heterodiamond are very unlikely because these factors are known to cause only minor eÜects on the thermal expansion of many cubic crystals.1 The XRD pattern shown in Fig. 1 also shows that the peak at 2h\46.1° arising from the Pt specimen holder decreases markedly at 825 °C and disappears completely at 1000 °C. Also, when the sample was heated at temperatures [1000 °C during the thermal expansion measurements, the pressure increased from 1]10~3 Pa to 3]10~3 Pa.This suggests that the sample is slightly decomposed over 1000 °C. In order 102 J. Chem. Soc., Faraday T rans., 1998, V ol. 94to investigate whether some structural changes or reactions are induced by long heating during thermal expansion experiments, an XRD powder pattern of the sample annealed at 1300 °C under vacuum was measured at room temperature.Fig. 4 shows the XRD patterns of the samples before and after annealing. Both patterns were identical, implying that the original crystalline structure does not change at 1300 °C in a vacuum and no oxidation compounds, such as are pro- B2O3 , duced under these conditions. Fig. 5 shows the magni–cation of the (111) peaks of the samples before and after annealing. There was no change in the peak position or the FWHM for both samples. This means that neither crystalline growth nor thermal decomposition of the crystallites of the heterodiamond is induced under these conditions. Therefore, the slight decomposition observed during the thermal expansion experiment over 1000 °C is possibly due to elemental diÜusion or thermal decomposition arising from the grain boundaries of the sample.The behavior of this decomposition seems to be related to the disappearance of the XRD peak of the Pt specimen holder. To investigate whether the disappearance of the Pt peak is characteristic of the heterodiamond, the hightemperature XRD measurements of shock-synthesized diamond and cubic BN were made in the same way as that for the thermal expansion experiment.On noting the behavior of two peaks at 2h\40 and 46° of the Pt specimen holder, in the case of diamond the peak at 2h\40° disappeared at 1200 °C, whereas for cubic BN the two peaks remained unchanged even at 1200 °C. Therefore the disappearance of the Pt peak is caused by the diÜusion of carbon gas into the surface of the Pt specimen holder rather than a chemical reaction between Pt and carbon.This is because a carbon source at the grain boundaries can diÜuse near 1000 °C under Fig. 4 XRD patterns of the heterodiamond before and after annealing : (a) before annealing ; (b) after annealing. The sample was annealed at 1300 °C for 3 h under vacuum. Fig. 5 Magni–cation of the (111) peaks in Fig. 1: (a) before annealing ; (b) after annealing vacuum but the chemical reaction to produce Pt carbides does not occur at these low temperatures.6 The probability of elemental diÜusion from the grain boundaries also suggests the possibility of atomic rearrangement within crystallites. As the heterodiamond is a metastable compound, the original lattice atoms can possibly be rearranged to a thermodynamically more stable position in an intermediate stage preceding the phase transformation.The rearrangement temperature would be below 1800 °C which induces the cubic-to-graphitic phase transformation at normal pressures.3 This process, which is performed by atomic diÜusion within the crystalline lattice without a change in the crystalline structure, seems most likely to explain the abrupt thermal expansion behavior. However, it was impossible to detect this atomic rearrangement by the usual XRD measurement because of the close similarity of the atomic scattering factors of the neighbouring light elements of the heterodiamond.In conclusion, elemental diÜusion from the grain boundaries may be partly related to the characteristic thermal expansion behavior, but this eÜect would not be essential. Atomic rearrangement seems probable but remains unresolved at present. The thermal expansion of solids originates from softening of the crystal lattice by its thermal vibration, as described by the following Gruneisen relation : a\ ciCv 3V ; Cv\ALE LT B where a is the thermal expansion coefficient, c is the Gruneisen parameter, i is the volume compressibility, V is the volume and is the molar speci–c heat capacity at constant Cv volume, which is de–ned as a temperature diÜerential of the lattice vibration energy E.These parameters of the heterodiamond are expected to lie between those of diamond and cubic BN because the lattice constant and bulk modulus (401 GPa, unpublished data) of the heterodiamond are between those of diamond (442 GPa)7 and cubic BN (369 GPa).8 Therefore, the thermal expansion coefficient of the heterodiamond is also expected to lie between those of the two crystals.This explains the agreement of the thermal expansion coefficient of the heterodiamond with those of cubic BN at high temperatures, but cannot explain the abrupt expansion followed by the steady expansion at higher temperatures. Conclusions The thermal expansion of the heterodiamond material BC2.5N was investigated in the range 25»1300 °C by high-temperature XRD and showed a behavior diÜerent from either that of diamond or cubic BN.The thermal expansion is negligible up to 800 °C, increases abruptly in the range 900»1100 °C, and increases steadily above 1100 °C. The thermal expansion coef- –cient above 1100 °C is ca. 5.5]10~6 K~1, which is in fair agreement with that of cubic BN at high temperatures. This result is presumed from the lattice structure of the heterodiamond lying between those of diamond and cubic BN, but the abrupt expansion preceding the steady expansion cannot be explained by the lattice structure.Such thermal expansion behavior has not been observed for diamond and cubic BN, although high thermal expansion has been observed for Mo and W in which Schottky vacancies are generated at high temperatures. The heterodiamond is a metastable material and has many structural defects such as grain boundaries and lattice vacancies peculiar to the shock-compression process. This suggests the eÜects of atomic rearrangement within the lattice and elemental diÜusion from the defects to be possible as the reason for the characteristic thermal expansion behavior. J. Chem. Soc., Faraday T rans., 1998, V ol. 94 103References 1 G. A. Slack and S. F. Bartram, J. Appl. Phys., 1975, 46, 89. 2 T. Komatsu, M. Nomura, Y. Kakudate and S. Fujiwara, J. Mater. Chem., 1996, 6, 1799. 3 T. Komatsu, Y. Kakudate and S. Fujiwara, J. Chem. Soc., Faraday T rans., 1996, 92, 5067. 4 T. Sasaki and N. Bartlett, Proc. 197th ACS National Meeting (Inorganic), ACS, Washington, DC, 1990, p. 46. 5 J. B. Wachtman Jr, T. G. Scuderi and G. W. Cleek, J. Am. Ceram. Soc., 1962, 45, 319. 6 K. A. Gingerich, J. Chem. Soc., Chem. Commun., 1974, 00, 199. 7 H. J. McSkimin and P. J. Andreatch, J. Appl. Phys., 1972, 43, 2944. 8 E. Knittle, R. M. Wentzcovitch, R. Jeanloz and M. L. Cohen, Nature (L ondon), 1989, 337, 349. Paper 7/05944B; Received 13th August, 1997 104 J. Chem. Soc., Faraday T rans., 1998, V ol. 94

ISSN:0956-5000    

DOI:10.1039/a705944b

出版商:RSC    

年代:1998

数据来源: RSC

摘要:

Effect of cationic polyelectrolytes on the dissolution of magnetite in thioglycolic acid solutions Erwin Baumgartner, Marta I. Litter, Joseç Romagnolo and Miguel A. Blesa* Unidad de Actividad Nacional de Av. del L ibertador 8250, Quïç mica, Comisioç n Energïç a Atoç mica, 1429 Buenos Aires, Argentina The in—uence of cationic polyelectrolytes, polyethyleneimine (PEI) and polyvinylbenzyltrimethylammonium chloride (PVBTA-Cl), on the kinetics of dissolution of an iron oxide (magnetite, by thioglycolic acid (HTG), is presented.It was found that both Fe3O4) polyelectrolytes accelerate the dissolution reaction at pH values below ca. 4, whereas an inhibition is observed at higher pH values. These –ndings are at variance with the results obtained in the case of anionic polyelectrolytes, in which the reaction is inhibited over the whole pH range. The eÜects of PEI concentration, of the addition of inert salt to the system PEI»HTG»Fe3O4 and of temperature on both systems were also studied.The main eÜects of PEI are the enhancement of the acidity of the oxide surface, and the decrease of the available surface sites for HTG complexation; the eÜect of PBVTA-Cl is more modest, due to the higher rigidity of the polyelectrolyte. Modeling of the experimental results in PEI media leads to a kinetic scheme similar to that describing the reaction in the absence of PEI, with a shifted by [2; this shift alters the pH dependence of the surface pKa s speciation, thus modifying the rate»pH pro–les.For PVBTA-Cl, the shift derived from the data is [1. Polyelectrolytes are extensively used in technical applications in various –elds such as waste-water treatment,1 food industry, paint production, soil stabilization, pharmacy and medical sciences, paper and board production, and boiler water treatment.2h4 Their role as colloid stabilizers and —occulants is described in several reviews, where these phenomena are related mainly to the ability of polyelectrolytes to adsorb on colloids.To be precise, the interactions between colloidal systems and polyelectrolytes have been widely studied because of the interest in controlling the stability of dispersed systems.5 Also, the role of polyelectrolytes in inhibiting corrosion was reported.6 In homogeneous solutions, the in—uence of the so-called polyelectrolyte eÜect in accelerating or retarding reactions of charged species is well documented;7,8 in heterogeneous reactions, and especially in the dissolution of metal oxide particles, the in—uence of polyelectrolytes has been less studied.In a previous paper,9 we studied the eÜect of some anionic polyelectrolytes such as polyacrylic acid (HPA), polymethacrylic acid (HPMA) and sodium polystyrenesulfonate (NaPSS), on the reductive dissolution of magnetite by thioglycolic acid (HTG). The main –ndings of this study were the inhibition of the dissolution reaction by the —exible polymeric chain of HPA, and the lack of eÜect of the other more rigid polyelectrolytes. Additional studies related to pH, HTG concentration or molecular weight variations, addition of NaCl and temperature changes, lead to support for the hypothesis of a blocking eÜect caused by a strong competitive polyelectrolyte adsorption in the case of HPA, the basic dissolution mechanism described previously10h14 remaining essentially unaltered.In the present case, we have studied the in—uence of two cationic polyelectrolytes, polyethylenimine (PEI) and polyvinylbenzyltrimethylammonium chloride (PVBTA-Cl), on the same reaction. In principle, in acid or neutral solutions, where dissolution occurs, and considering only electrostatic arguments, cationic polyelectrolytes should not adsorb onto the oxide surface, that is positively charged at acid or neutral pH.9 As a matter of fact, the point of zero charge of our sample of magnetite, measured by electrophoretic techniques is ca. 7. However, strong surface eÜects are observed, which can be explained only if polyelectrolyte segments are held on the surface by forces that outweigh those of electrostatic origin.2,15,16 The interaction of the cationic polyion and the anionic ligand in bulk solution must also be considered. Experimental Magnetite was the same used in the previous work.9 Its average particle diameter was 0.17 lm, and its speci–c surface area was 10 m2 g~1. Samples of PEI and PVBTA-Cl were obtained through the courtesy of Dow Chemical Co.; according to the manufacturersœ speci–cations, their molecular weights are 50 000»100 000 and ca. 300 000, respectively. The structural formulas of the repeating units are given in Fig. 1. All the other reagents were of analytical purity or better, and used as provided. Water was bidistilled in a quartz apparatus. Kinetic experiments were performed as previously described,9 suspending magnetite in water (0.267 g dm~3) in a thermostatted cylindrical reactor, adding the required amounts of HTG and polyelectrolyte, adjusting pH with dilute NaOH when necessary, and magnetically stirring.No additives have been added for ionic strength control. Samples of the suspension were periodically taken from the reactor, Fig. 1 Structural formulas of the repeating units of the polyelectrolytes used in the present study J. Chem. Soc., Faraday T rans., 1998, 94(1), 115»119 115and –ltered through a 0.45 lm membrane.Total iron concentration in solution was measured by the HTG spectrophotometric technique.9,17,18 Absorbances were measured in a Shimadzu UV-210 A spectrophotometer. Results The dissolution of magnetite in HTG proceeds according to the contracting volume rate,19 eqn. (1) 1[(1[f )1@3\kt (1) where f is the extent of dissolution de–ned as f\(w0[w)/w0 (w being the mass of undissolved solid, and the initial w0 mass), and k is related to the initial rate, through the (df/dt)0 expression : k\ 1 3 Adf dtB0 (2) The qualitative features of the dissolution mechanism remain unchanged upon addition of PEI and PVBTA-Cl, and the time evolution of the reaction rate still follows the contracting volume expression, at least up to 65% dissolution.Fig. 2 shows the applicability of eqn. (2) to the dissolution in both 1]10~2 mol (monomer) dm~3 PEI and PEI-free media at pH ca. 1.95 and [HTG]\0.147 mol dm~3. As discussed previously,11 the shape of the f»t plots for the dissolution of magnetite in mercaptoacetic acid is deceivingly simple, and hides the acceleration in the rate brought about by dissolved FeII; this eÜect, barely observable in Fig. 2, is much more evident in the course of dissolution by other mercaptocarboxylic acids and results in sigmoidal f»t pro–les. For our purposes however, we do not need to deal with these aspects. The deceleratory pro–les observed in HTG are due to high dissolution rates of surface complexes formed by species and Ü åFeIII adsorbed thioglycolate anions.This dissolution rate, mediated or followed by internal electron transfer is then given by R\k0MÜ åFewLN (3) where is a rate constant (in m2 dm~3 s~1 when R is the k0 rate of increase of the concentration of dissolved iron), represents the active surface thioglycolate complex, Ü åFewL and the brackets MN are used to denote surface concentrations (mol m~2). When surface coverage by HTG is total is related to k [eqn. (2)] through (MÜ åFewLN\Ns), k0 k\ 3k0NsMV w0 (4) where is the number of active sites per unit area (6 nm~2, Ns or 10 lmol m~2 for magnetite10), V is the solution volume and M the formula mass of magnetite The results (FeO1.33).Fig. 2 1[(1[f )1@3 vs. t for the dissolution of (0.267 g Fe3O4 dm~3) in 0.147 mol dm~3 HTG, initial pH ca. 1.95, T \303 K. (a) [PEI]\0; (b) [PEI]\1]10~2 mol (monomer) dm~3 shown in Fig. 2 demonstrate that eqn. (1) still applies, the in—uence of added PEI showing itself on either or k0 or on both.MÜ å FewLN, Depending on solution pH, addition of PEI may either accelerate or inhibit dissolution. Solution pH is known to in—uence drastically owing to the changes in MÜ å FewLN; a maximum is observed at a pH value related to MÜ å FewLN, the surface acidity, eqn. (5) and to the acidity of mercaptoacetic acid, eqn. (6) : Ü åFeIIIwOH2 `¢Ü åFeIII[OH]H` pKa1 S (5) HL¢H`]L~ pkaL (6) In the absence of PEI,11 pHmaxB12 (pKa1 S ]pKaL) (7) Fig. 3 and Fig. 4 show the in—uence of 1]10~2 mol (monomer) dm~3 PEI on the rate»pH pro–les in 0.147 mol dm~3 and 0.735 mol dm~3 ligand, respectively ; the points are the experimental values and the lines are the –ttings of the data according to the further discussion (see below). The main eÜect is a shift of the maximum towards lower pH values ; also the rate values at the maximum are changed, the maximum rate being increased by PEI in 0.147 mol dm~3 ligand, and decreased in 0.735 mol dm~3 HTG.Important changes in the width at half height are also apparent. The shift in the maximum, and the changes in the width at half height in the plot of k vs. pH at constant ligand concen- Fig. 3 Speci–c rate constants for the dissolution of (0.267 g Fe3O4 dm~3) in 0.147 mol dm~3 HTG at 303 K vs. pH in water and (L) (=) in the presence of 1]10~2 mol (monomer) dm~3 PEI. (»»») Fitting of data in water; (» » » ») –tting of data with PEI. Fig. 4 Speci–c rate constants for the dissolution of (0.267 g Fe3O4 dm~3) in 0.735 mol dm~3 HTG at 303 K vs.pH in water and (L) (=) in the presence of 1]10~2 mol (monomer) dm~3 PEI. (»»») Fitting of data in water; (» » » ») –tting of data with PEI. 116 J. Chem. Soc., Faraday T rans., 1998, V ol. 94Fig. 5 In—uence of PEI concentration on the speci–c rate constant k for the dissolution of (0.267 g dm~3) in 0.147 mol dm~3 HTG, Fe3O4 initial pH ca. 2, T \303 K tration may be readily related to shifts in and/or as pKa1 S pKaL, discussed below.The decrease in the maximum attainable rate, observed at high ligand concentration, may also be related to a decrease in due to a decrease in the MÜ å FewLN, number of sites available for surface complexation (see Discussion section). On the other hand, the changes in pKa1 S and/or an increase in surface complexation affinity, or an pKaL, increase in the value of may all contribute to the enhance- k0 ment of the maximum rate observed at the lower ligand concentration.The in—uence of PEI concentration on the dissolution rate re—ects a rather strong interaction (adsorption) of PEI and Although the adsorption isotherms were not mea- Fe3O4 . sured directly, they may sometimes be derived from the kinetic results. Fig. 5 shows the values of k for various experiments performed at diÜerent PEI concentrations, [HTG]\0.147 mol dm~3 and pH ca. 2. We shall show later that this dependence should be interpreted in terms of an adsorption equilibrium.Increasing ionic strength is known to accelerate the rate of metal oxides dissolution because surface complexation is favored by the presence of counter-ions to suppress double layer eÜects ; in more complex systems, like ours, opposite eÜects may also operate. For example, high ionic strengths suppress the in—uence of polyions on the rate of ionic reactions (the kinetic polyelectrolyte eÜect). Experiments were performed to determine the in—uence of ionic strength in the acid range, in which the rate is enhanced by PEI.Salt addition up Fig. 6 Speci–c rate constant for the dissolution of (0.267 g Fe3O4 dm~3) in 0.147 mol dm~3 HTG at 303 K vs. pH in water and (L) (=) in the presence of 1]10~2 mol (monomer) dm~3 PVBTA-Cl. (»»») Fitting of data in water; (» » » ») –tting of data with PVBTA-Cl. to an ionic strength of 0.1 mol dm~3, decreases slightly the observed rate ;9 at higher salt concentrations, an essentially constant rate value is obtained.For our purposes, and in our reaction media, the in—uence of ionic strength may be safely ignored. The in—uence of temperature was also explored. Dissolution rate constants in the presence of PEI [1]10~2 mol (monomer) dm~3] were determined at temperatures varying between 283 and 313 K and initial pH 2.3^0.2. From them, a value of 70^6 kJ mol~1 for the apparent Arrhenius Ea , activation energy, was calculated. This value should be compared to 50^5 kJ mol~1, the Arrhenius activation energy for the same reaction in the absence of polyelectrolyte.9 A more limited set of experiments was performed in the presence of PVBTA-Cl, a rigid polycation with –xed charges.Fig. 6 shows that its presence produces a similar but much smaller eÜect on the dissolution reaction than PEI. Again, the k vs pH curve is displaced to the left, but the displacement here is smaller. The in—uence of temperature is similar to that observed for PEI, with an apparent activation energy of 72^7 kJ mol~1.Discussion As stated, the main experimental facts that must be accounted for are the shifts in the maximum in the k»pH pro–les, the changes in the half-height width, and the increase or decrease in the maximum rate in the same plots. The whole rate»pH pro–les, both in water and in PEI or PVBTA-Cl media can be described by eqn. (3), by assuming that pH de–nes MÜ å FewLN, and that the polyelectrolyte in—uences the pH dependence of and eventually the value of The surface con- MÜ å FewLN, k0 .centration of the reactive complex can be described by the stoichiometric eqn. (8) :§ Ü åFeIIIwOH2 `]L~¢FeIIIwL]H2O Kads (8) From eqn. (3) and (8), at constant HL concentration, and expressing and [L~] in terms of the number MÜ åFeIIIwOH2 `N of active sites, the proton concentration, the total Ns , (analytical) ligand concentration, and the fraction of [LT], active sites covered by the ligand (h), the following expression results for the rate of dissolution : R\A3w0 MV Bk\k0MÜ å FeIIIwLN\ k0KadsNs L TA~1B~1 C (9) where A\1][H`](KaL)~1 B\1][H`]~1Ka1 S C\1]Kads[LT]A~1B~1 Thus, the values and de–ne both the position KaL, Ka1 S Kads of the maximum and the width of the curve.The height of the maximum is also in—uenced by In water, reasonable k0Ns . –ttings of the experimental points can be obtained using values slightly diÜerent from those reported in the § Eqn. (8) is equivalent to the dissociative chemisorption of neutral HL.In fact, thioglycolic acid loses two protons upon surface complexation. The stoichiometric reaction is practically indistinguishable from eqn. (8) ; only the value of is Ns changed (see ref. 11). The use of the more cumbersome notation is therefore not necessary. J. Chem. Soc., Faraday T rans., 1998, V ol. 94 117literature11,12,19 and (pKaL\3.47, pKa1 S \5.0 Kads\6.6 mol~1 dm3), and setting mol dm~3 s~1. k0Ns\1.87]10~2 As it is shown in Table 1, the best –tting is obtained if is KaL allowed to change slightly as the HTG concentration changes.The results are depicted in Fig. 3 and 4. It is possible to improve the –tting by using higher values, but we felt this pKaL procedure to be unwarranted in view of the high inherent error in the measured rates. In the presence of PEI, –tting of the data may be achieved if lower and values are used. The values do not pKa1 S k0Ns pKaL change much, being essentially identical to those used in water.For the value 6.6 dm3 mol~1 was maintained Kads , unchanged. In the case of PVBTA-Cl media, the decreases in and were smaller. Table 1 summarizes the param- pKa1 S k0Ns eters used in –tting the data. We shall discuss these results by examining –rst the interactions between polyelectrolyte and thioglycolic acid in bulk solution, and later, the surface interactions PEI (or PVBTACl)/ Fe3O4 . Bulk interactions The –rst eÜect to be considered is the change in the acidity of mercaptoacetic acid in solutions containing polycations.Dye molecules, such as acid»base indicators, change their pK when dissolved in polyelectrolyte solutions,20 the cause being the polyelectrolyte eÜect. By this eÜect, dyes of opposite charge are attracted by the macro-ion, and simultaneously protons are also attracted or rejected, depending on the sign of the charge, thus changing local pH. Bromothymol Blue in PEI solutions exhibits a maximum change in pK of [1.4. Similar results were obtained by Arcelli and Concilio, when studying the eÜect exerted by PEI on the ionization constant of substituted phenols,21 and Morishima et al.in their work on pK shifts of pH sensitive chromophores attached to the chain of anionic and cationic polyelectrolytes.22 The degree of enhancement of the acidity of a weak acid in homogeneous solution is determined by the electrostatic W0 , potential on the polyelectrolyte surface, which is in turn related to the degree of ionization of PEI, and thus also to pH.Very modest shifts in are expected in neutral media pKaL (where the degree of ionization of PEI is low), with increasing shifts as the pH decreases, until the limiting, saturation, W0 value is reached. The operative values never approach W0 high values, and modest values result, especially in the *pKaL region pH[3.5, the of HTG in water. This shift in pKaL pKaL may contribute to the observed shift in the maximum of the rate»pH pro–les, but it is not the main cause for the overall shift ; heterogeneous eÜects, discussed next, are substantive.Indeed, modeling of the data leads to identical or slightly modi–ed values ; furthermore, the smaller shift in the pKa maximum in PVBTA-Cl media (see Fig. 6), in which heterogeneous eÜects are expectedly smaller, also agrees with a modest solution eÜect. Heterogeneous eÜects As opposed to the previously reported case of anionic polyelectrolytes, 9 the electrostatic contribution to the PEI and PVBTA-Cl adsorption affinity onto is negative.In fact, Fe3O4 the data obtained in PVBTA-Cl media demonstrate that this rigid and strong polycation in—uences the rate much less than the weak and —exible PEI. However, in both cases, the data also demonstrate the occurrence of the interaction polycation/ oxide particle. Several examples in the literature show that nonelectrostatic forces often override electrostatic factors, especially in the case of polymeric adsorbates.2,15,16 In the case of PEI, which contains primary, secondary and tertiary amine groups, the possibility of hydrogen bonding with OH groups and/or complexation with Fe3` or Fe2` at the interface, can be invoked as short range interactions. Furthermore, the adsorption of macromolecules on charged surfaces is determined by a complicated interplay of energetic (adsorption energy, electrostatic repulsion/attraction, solvent quality) and entropic factors (conformational entropy, crowding eÜects).23 These latter factors become especially important in the case of —exible macromolecules, as it is the case of PEI.3,23,24 Surface eÜects could manifest themselves in changes in pKa S , and/or as stated, experimental results indicate that Kads Ns; does not change (see Table 1).This latter result agrees Kads with the fact that the stoichiometry of adsorption is essentially neutral11 (see footnote on previous page.§). In principle, modeling of adsorption in Fe3O4»PEI»TGA would involve a previous description of the affinity of PEI for the oxide surface as a function of [PEI] and pH, that would lead to surface charge density values de–ned by the degree of ionization of the polymer on the surface.Alternatively, the experimental determination of the electrophoretic mobilities, coupled with an adequate double layer model could yield the surface charge density. This value could then be used to calculate again using an adequate double layer model (e.g.the W0 , constant capacitance model). The shift in apparent surface acidity constant could be calculated through the usual expression Kaint\Kaapp exp([eW0/kT ) (10) We have chosen a more direct, albeit more empirical approach, that involves the calculation of the values that Kaapp best –t the dissolution data. All values discussed below are Ka therefore values, the app superscript having been Kaapp dropped for notation simplicity.In the absence of PEI, the rate follows a Langmuir» Hinshelwood dependence on [HTG], with a saturation value k\1.13]10~3 s~1 at [HTG]\0.735 mol dm~3 (see Fig. 4). In the presence of PEI, the rate also increases monotonously, but the maximum rate is lower, k\7.0]10~4 s~1. This result indicates that and/or decrease in the presence of k0 Ns PEI [see eqn. (4)]. Although it is possible to envisage a possible in—uence on (e.g., changes in surface acidity due to the k0 adsorption of PEI), the most direct eÜect is the blocking of surface sites for ligand adsorption.The coverage of the surface by PEI does not lead to total passivity, a fact that may imply only partial coverage or, more probably, dynamic interchange at the surface, with a decrease of the number of bound thioglycolate ions. In our –tting of the rate»pH pro–les, the result is a decrease of (see Table 1) by ca. three orders of k0Ns magnitude, as expected in the case of high degree of coverage by PEI.The available data does not justify a more detailed Table 1 Parameters used in the –tting of the dissolution data at 303 K in water with PE with PVBTA-Cl low HTG high HTG low HTG high HTG low HTG Ka S 5.0]10~6 5.0]10~6 4.0]10~4 4.0]10~4 1.8]10~5 KaL 2.5]10~4 3.8]10~4 4.0]10~4 4.0]10~4 3.2]10~4 k0Ns/mol dm~3 s~1 1.87]10~2 1.87]10~2 3.68]10~5 3.68]10~5 2.28]10~3 Kads/dm3 mol~1 6.6 6.6 6.6 6.6 6.6 118 J. Chem. Soc., Faraday T rans., 1998, V ol. 94analysis of the various possibilities (competitive, noncompetitive adsorption, etc.).The eÜect brought about by increased [PEI], shown in Fig. 5, agrees with a high degree of coverage at 1]10~2 mol (monomer) dm~3 PEI; further increases do not in—uence the rate much, although a slight decrease may be inferred. In fact, the shape of the k»[PEI] plot agrees with a high initial affinity of the surface, followed by a further, less strong adsorption. As stated, the adsorption of PEI decreases the number of available sites, but increases substantially the apparent affinity of the residual sites for HTG.The surface acidity constant increases by a factor of 80 (see Table 1). This enhanced acidity re—ects the in—uence of the increased positive surface charge brought about by PEI adsorption, and is the main cause of the shift in the maximum in the rate»pH pro–les towards higher acidities (see Fig. 6). The interaction of the surface with the rigid and highly charged PVBTA-Cl polycation is weaker; accordingly, smaller decreases in and are indicated by the –tting of the pKa1 S k0Ns experimental data.The in—uence of temperature From eqn. (9), the changes in rate due to increases in temperature may be in—uenced by the behavior of k0 , Ns , Kads , and Thus, the activation energies in solutions contain- KaL Ka1 S . ing polyelectrolyte may diÜer appreciably from those in water. In the case of the anionic polyelectrolyte HPA, the activation energy does not change appreciably.In PEI or PVBTA-Cl containing media, the important changes in and are Ns Ka1 S accompanied by an increase in the activation energy; it is tempting to conclude that more surface sites become available for attack as the temperature increases, and the increase in the activation energy is related to a positive value of (dNs/dT ), whereas the increase in the rate observed at 303 K under some pH conditions is due to the shift in However, it should be Ka1 S .noted that the activation energy in PBVTA-Cl media is increased from the aqueous value by the same factor ; we do not have a good explanation for this result. Conclusions The in—uence of additives on the rate of dissolution of metal oxides is usually discussed in terms of competitive or cooperative adsorption of the dissolution reagent and the additive. Competitive adsorption results in rates that increase upon ligand addition and decrease upon increasing additive concentration ; in the simplest case in which the adsorption of both solutes may be described by a Langmuir isotherm, the ratio [L]/[A], where A is the additive, determines the rate at high [L] and [A] concentrations.Documented cases are those of adsorption of EDTA and oxalate on iron oxides in the presence of phosphate25 and EDTA»EDTA»Fe.26 This simple behavior is expected when there are no important interactions between L and A, either in bulk solution or on the surface. The cooperative eÜect, on the other hand, results when A alters the surface characteristics in such a way that the eÜective affinity for L increases.The dissolution of magnetite in mixtures of thioglycolic acid and polyethyleneimine (or PVBTA-Cl) is in—uenced by both types of interactions. In addition to a modest solute»solute interaction in bulk solution, a strong eÜect results from the in—uence of the surface charge, produced by PEI adsorption, on the acidity of the surface ; depending on pH and HTG concentration, the eÜect may result in increasing or decreasing extent of L-adsorption.The blocking of a large fraction of surface sites by A is also evident from the rate data. and M.I.L. are members of M.A.B. CONICET. References 1 Polyelectrolytes for W ater and W astewater T reatment, ed. W. L. K. Schwayer, CRC Press, Boca Raton, FL, 1981. 2 J. E. Gebhardt and D. W. Fuerstenau, in Interfacial Phenomena in Mineral Processing, ed. B. Yarar and D. J. Spottiswood, The Engineering Foundation, New York, 1982, p. 175. 3 D. Horn, in Polymeric Amines and Ammonium Salts, ed. E. J. Goethals, Pergamon Press, Oxford and New York, 1980, p. 333. 4 S. D. Strauss, Power, 1993, 137, 17. 5 B. Vincent, Adv. Colloid Interface Sci., 1974, 4, 193. 6 T. Hirai, J. Yamaki, T. Okada and A. Yamaji, Electrochim. Acta, 1985, 30, 61. 7 J. Rabani, in Photoinduced Electron T ransfer, Part B, ed. M. A. Fox and M. Chanon, Elsevier, Amsterdam, 1988, p. 642. 8 E. Baumgartner and R. Fernaç ndez Prini, in Polyelectrolytes, ed. K. C. Frisch, D. Klempner and A. V. Patsis, Technomic, New York, 1976, p. 1. 9 E. Baumgartner, J. Romagnolo and M. I. Litter, J. Chem. Soc., Faraday T rans., 1993, 89, 1049. 10 M. A. Blesa, P. J. Morando and A. E. Regazzoni, Chemical Dissolution of Metal Oxides, CRC Press, Boca Raton FL, 1994, p. 293. 11 E. B. Borghi, P. J. Morando and M. A. Blesa, L angmuir, 1991, 7, 1652. 12 E. Baumgartner, M. A. Blesa, H. Marinovich and A. J. G. Maroto, Inorg. Chem., 1983, 22, 2224. 13 M. A. Blesa, H. A. Marinovich, E. C. Baumgartner and A. J. G. Maroto, Inorg. Chem., 1987, 26, 3713. 14 E. Matijevic, J. Colloid Interface Sci., 1990, 134, 475. 15 D. L. Sussmann and W. Stumm, Koloid-Z., Z. Polym., 1968, 275, 147. 16 L. Jaé rnstrom and P. Stenius, Colloids Surf., 1990, 50, 47. 17 D. L. Leussing and I. M. KolthoÜ, J. Am. Chem. Soc., 1953, 75, 390. 18 D. L. Leussing and L. Newman, J. Am. Chem. Soc., 1956, 78, 552. 19 E. Baumgartner, M. A. Blesa and A. J. G. Maroto, J. Chem. Soc., Dalton T rans., 1982, 1649. 20 E. Baumgartner, R. Fernaç ndez Prini and D. Turyn, J. Chem. Soc., Faraday T rans. 1, 1973, 69, 1518. 21 A. Arcelli and C. Concilio, J. Chem. Soc., Perkin T rans. 2, 1989, 887. 22 Y. Morishima, T. Kobayashi and S. Nozakura, Macromolecules, 1988, 21, 101. 23 J. Lyklema, Colloids Surf., 1984, 10, 33. 24 O. A. Evers, G. J. Fleer, J. M. H. Scheutjens and J. Lyklema, J. Colloid Interface Sci., 1986, 111, 446. 25 O. K. Borggaard, Clays Clay Miner., 1991, 39, 324. 26 M. A. Blesa, E. B. Borghi, A. J. G. Maroto and A. E. Regazzoni, J. Colloid Interface Sci., 1984, 98, 295. Paper 7/05500E; Received 29th July, 1997 J. Chem. Soc., Faraday T rans., 1998, V ol. 94 119

ISSN:0956-5000    

DOI:10.1039/a705500e

出版商:RSC    

年代:1998

数据来源: RSC

摘要:

Brownian dynamics simulations of –lled particle gels Christopher M. Wijmans* and Eric Dickinson Procter Department of Food Science, University of L eeds, L eeds, UK L S2 9JT The structure and small-deformation shear rheology of mixed particle gels is investigated by means of Brownian dynamics simulation. The simulation model accounts for gelation through the formation of —exible, irreversible bonds between the particles. Larger particles are added to a solution of smaller particles which themselves form a network.If the larger ì –ller œ particles are incorporated into that network, they increase the gel strength. If equal volumes of –ller particles are added, smaller particles have a bigger eÜect than larger ones. These –ndings agree qualitatively with experimental results reported in the literature. Filler particles that do not interact with the network have very little eÜect on the gelation process or the rheology of the network. Only very large particles show a small eÜect on the shear modulus. Introduction Particle gels can be de–ned as space-–lling networks of aggregated particles.Silica gel is the classic example of an inorganic particle gel. Many food colloids are protein particle gels. The constituent components of these gels are protein particles which can be single globular protein molecules, oligomeric globular proteins, complex proteinaceous colloidal particles (e.g. casein micelles) or protein-coated emulsion droplets.Experimentally, gelation of these particles may be induced by heating, enzyme treatment, lowering the pH, or by addition of divalent counter-ions.1 Strong attractive interactions (covalent linkages, ion bridges, hydrophobic bonds, etc.) are formed between the particles, leading to a coherent network structure. During the past 15 years a signi–cant number of computer simulations have been published of particle aggregation and gelation.2 In particular, Dickinson3 introduced a simulation model which can be used to describe the protein gels which occur in food systems. The original model by Dickinson is a two-dimensional simulation of hard-sphere particle gelation incorporating —exible irreversible bond formation with longer range attractive or repulsive interactions.3 The reactivity of the particles is set by a bonding probability.Starting from a random distribution of particles, a network structure can be produced with all particles in one single aggregate.It was shown how in this model the network and pore structures depend on the particle reactivity and strength of the interparticle interactions. Using repulsive interparticle interactions particle gels were produced with small average pore sizes. Many experimental structural features in particle gels could be reproduced by this model. An extension of this work considered mixed particle gels consisting of two diÜerent kinds of particles.4 DiÜering attractive or repulsive interactions between like and unlike as well as diÜering rates of bond formation were investigated.In systems with a sufficiently repulsive net interaction between unlike particles, phase separation can occur. This process is inhibited by bond formation between the particles. The resulting network depends sensitively on the relative rates of cross-linking and phase separation. Complex structures can be formed in binary systems containing a self-aggregating component which does not form irreversible bonds with itself, and a bonding component which forms cross-links.The gel network is then held together by both permanent —exible bonds and weaker reversible interactions, which may give rise to a complicated rheological behaviour. In systems containing a mixture of a gelling component and a non-gelling component, the non-bonded interactions may in—uence the rate of cross-linking and the –nal gel structure. The non-gelling particles can act as a steric barrier inhibiting the gelation of the other component.Eventually, regions of the non-gelling component can become entrapped within a closed aggregate of the other gelling component. The two-dimensional simulations of mixed systems are thought to be especially relevant to mixed proteins –lms at interfaces.5 Whittle and Dickinson6 developed a three-dimensional Brownian dynamics simulation model analogous to the twodimensional simulation. They used soft-sphere particles rather than hard spheres, so that all potentials are continuous.As a consequence, it is possible to extract rheological properties from the simulations in addition to structural information. Whittle and Dickinson showed that the long-range interaction also has an important eÜect on the structure of the threedimensional gels. As the interaction becomes more attractive, more coarse structure are developed and the fractal dimension of the gels decreases. These diÜerences in structure are most clearly re—ected in the small-deformation rheological behaviour by the stress correlation function, which starts to display a signi–cant long-time tail as the repulsive interaction between the particles changes to an attraction.This eÜect is thought to be the result of slower stress relaxation processes in the dense close-packed regions and is suggestive of a relatively rigid solid. The magnitude of the high-frequency shear modulus was shown to scale linearly with the total number of bonds in the system.This indicates that the stress in the whole system is localized in the particle bonds rather than in any interactions between the particles. In the present paper we introduce a second type of particle into the Whittle»Dickinson model. The diÜerent particle types may be characterized by diÜerent interaction parameters for the long-range interaction and/or the bonding interaction. Alternatively, they may have diÜerent sizes. The aim of this study is twofold.First, we want to extend the two-dimensional investigation of mixed systems in ref. 4 to three dimensions, studying both the structure and viscoelastic behaviour of the gels. However, owing to the far larger number of parameters in a two-component system compared to a one-component one it will not be feasible to explore the whole range of the available parameter space. We will not discuss here processes involving phase separation due to a repulsion between the two types of particles which is counteracted by the irreversible bonding that takes place between these particles.4 In a future J.Chem. Soc., Faraday T rans., 1998, 94(1), 129»137 129publication we will explore the rheology of such systems. In this paper we limit ourselves to binary systems with two particle types which may or may not diÜer in size and which can have diÜerent bonding probabilities. We consider a system with a particle type which on its own can form a gel and another (larger) particle which is either compatible or incompatible with the gel network; this forms a good model for a gel to which ì –ller œ particles have been added.An important aim of this paper is to study the rheological eÜect of such –ller particles. This is a subject that has received a lot of attention, mainly from experimentalists. We will –rst give a brief overview of the literature on this topic. Filled particle gels»experimental position Over the past half-century an extensive literature has appeared on the eÜect of particulate –llers in materials made from synthetic macromolecules; reviews can be found in ref. 7 and 8. Van der Poel9 proposed a useful method for calculating the shear modulus of a particulate composite in which the matrix material is incompressible. Smith10,11 corrected the derivation and generalized this method to apply to any matrix material. Assuming the validity of Hookeœs law, the shear modulus of the composite can be expressed as a function of the Poisson ratios of the matrix and the –ller particles and their respective moduli.It was not until the 1980s that serious work was done on biopolymer systems. Since then a variety of groups have investigated protein networks with –ller particles. Richardson et al.12 measured the shear storage and loss moduli of glass-–lled gelatin gels. Size and size distribution of the glass particles were not very signi–cant as compared to particle shape.The loss tangent of the gel was found to increase with increasing volume fraction of the –ller particles, the eÜect being smallest for spheres. In an extension of this work Ross-Murphy and Todd13 studied the ultimate tensile properties of –lled gelatin gels. They could collapse all their fracture data onto a master curve, using an empirical relationship which was within experimental error identical to the van der Poel»Smith relation between small deformation modulus and –ller volume fraction.Ring and Stainsby14 considered a number of rigid and deformable –llers which were added to a gelatin gel and which increased the shear modulus of the gel. The reinforcement of the gel by the rigid particles did not depend on the strength of the un–lled gel. When deformable –llers were used, this increase was more pronounced for weaker un–lled gels. Instead of using solid –ller particles, Dickinson et al.15 measured the shear modulus of a gelatin gel mixed with a gelatinstabilized oil-in-water emulsion.Depending on the gelatin concentration, the shear modulus increased or decreased with oil volume fraction. However, the decrease can be explained by a lowering of the gelatin concentration due to adsorption at the oil/water interface. If one compensates for this eÜect, a linear increase of the shear modulus is found as a function of oil volume fraction. Such an increase of the gel modulus is generally found when the –ller particles interact favourably with the gel matrix.Van Vliet16 studied the interaction between casein micelles and emulsion droplets stabilized by diÜerent macromolecules. By choosing diÜerent macromolecules the droplets could be made to have either no interaction or to interact strongly with the casein gel. When the –ller particles did not interact with the gel, the storage modulus decreased monotonically with particle concentration. Interacting particles gave a strong increase of the storage modulus. Similar measurements on a –lled rubber gel could be –tted to the van der Poel»Smith theory for the shear modulus of a composite material consisting of small spheres with a larger shear modulus imbedded in a matrix with a lower shear modulus.However, the experimental results for the casein gel showed a far stronger dependence of the shear modulus on the –ller particle concentration than predicted by this theory. It was suggested that this was due to aggregation of the oil droplets during gelation.The importance of the interaction between –ller and gel particles is further demonstrated by the work of Aguilera and co-workers17h20 on the eÜect of fat globules on properties of mixed dairy gels obtained from skim-milk powder and whey proteins. Fat globules were added to gels prepared from whey protein concentrate.17 Milk-fat globules with modi–ed membranes increased the gel –rmness, whereas washed globules had a weakening eÜect.A similar reinforcement was found for mixed gels.18,19 The mixing of skim-milk powder and whey protein concentrate can have a synergistic eÜect on the resulting gel strength as compared to the single-component gels. Scanning and transmission electron microscopy (SEM and TEM) indicated the compatibility between the two protein sources and between the fat globules and the protein matrix. Micrographs showed linking of casein chains by whey protein strands and fat globules integrated into the mixed gel network.In the case of fat globules without membranes, which weaken the mixed gels, TEM demonstrated that these –ller particles were individually dispersed.20 SEM and TEM of whey protein gels containing fat globules was also performed by Jost et al.21 and by Yost and Kinsella,22 demonstrating that the droplets were intimately associated with the gel protein matrix rather than simply ì –lling in gel matrix poresœ. McClements et al.23 measured the compressive stress of whey protein gels with emulsion droplets stabilized either by whey protein or by surfactant (Tween 20). The protein» stabilized droplets increased the gel strength, whereas the droplets stabilized by small-molecule surfactants decreased the gel strength.These –ndings again indicate that the rheological eÜect of –ller particles depends on whether the –ller particles are incorporated into the gel network. In this paper the eÜect of the droplet size was also investigated.The proteinstabilized droplets had a greater eÜect on the gel strength as the average droplet size decreased. Little eÜect was found of the droplet size in the case of the surfactant-stabilized emulsion droplets. A qualitatively similar particle size eÜect was found by Matsumura et al.,24 who studied the eÜect of oil droplets on emulsion gels. The storage and loss moduli of the gels increased due to the oil droplet, this eÜect being greater for the more –ne emulsions.The eÜect of particles other than emulsion droplets on whey protein gels has also been considered. Brownsey et al.25 added Sephadex beads as –ller particles. The degree of cross-linking of this polysaccharide, dextran, determines the particle rigidity. This rigidity (together with the –ller volume fraction and the shear modulus of the matrix) determines the smalldeformation behaviour of the –lled gel. At high deformations the affinity of –ller particle and matrix profoundly aÜect the strength and failure properties of the material.Langley and Green26 added coated glass particles as well as oil droplets to whey protein gels. Particles with a hydrophilic surface were shown to be an integral part of the composite. Composites containing these particles were much stronger in compression than those containing hydrophobic particles. Gels containing particles with a hydrophobic surface fractured adjacent to the particle surface, indicating little or no interaction between particle and matrix.In contrast, in gels with hydrophilic particles failure occurred within the protein matrix. The work of Dickinson and Hong27 further demonstrates how in slightly more complicated systems, the gel properties can be determined by a subtle balance of interfacial forces. They studied the in—uence of a non-ionic emulsi–er (Tween 20) on the small-deformation shear rheology of blactoglobulin emulsion gels. The storage modulus increased at 130 J.Chem. Soc., Faraday T rans., 1998, V ol. 94low emulsi–er contents, probably due to strong interfacial protein»emulsi–er complexation. At intermediate emulsi–er contents the storage modulus decreased due to competitive displacement of protein from the oil/water interface. At high concentrations of emulsi–er and protein the storage modulus was found again to increase. This increase was attributed to a combination of hydrophobic complexation and excluded volume eÜects, and possibly also depletion —occulation of the emulsion droplets due to the high surfactant micelle concentration.However, at high emulsi–er but low protein content, gel formation was inhibited and the storage modulus decreased further. Using our simulation model, we will attempt to explore the rheological properties of –lled gels as described above. Despite the relatively simple nature of the model, we believe it will add to our understanding of these sorts of systems.Simulation method Brownian dynamics algorithm The Brownian dynamics algorithm is a straightforward extension of that described by Whittle and Dickinson.6 We consider a cubic box of volume V \L3, with periodic boundary conditions in all three dimensions, containing rigid, spher- N1 ical particles of type 1 with diameter and particles of p1, N2 type 2 with diameter is taken as the basic unit p2 (p2Pp1). p1 of length. Two (non-bonded) particles i and j (i, jON1]N2) of type p and q, respectively (p, q\1, 2), at an interparticle distance (i.e.the distance between their particle centres) rij\ experience a spherical potential which is the sum of a o ri[rj o, hard-core and a long-range term: /(rij)\/C(rij)]/LR(rij) with /C(rij)\eA12 pp]12pq rij B36 and /LR(rij)\7eLR p, q 0 A rc p, q[rij rc p, q[12pp[12pqB 0 for rij\rc p, q for rij[rc p, q (1) where we have introduced the parameters e [determining the magnitude of the (quasi-)hard-core potential] and the longrange interaction constant between particles of type p eLR p, q and q, and the cut-oÜ limit for the p, q interaction.The rc p, q hard-core interaction has been chosen in such a way that the normalized interaction between two particles of the same size does not depend on their radius. The long-range interaction can be seen as an interaction between two particle surfaces. We de–ne the basic unit of time as with the p1(m1/e)1@2, m1 mass of particle type 1. We also de–ne the characteristic time as the time taken for a type 1 particle to diÜuse (at in–nite qr dilution) over a distance equal to its particle radius : qr\ where is the viscosity of the suspending —uid. 3np1 3gs/4kBT , gs When the distance between a p and a q particle is less than (i.e. their surface separation is less than bint]12pp]12pq bint), there is a probability that a bond is formed between these PB p , q two particles. Only one bond may be formed per particle pair. A bond is de–ned by an interaction between bonding nodes on the surface of each particle (at r\p/2).These nodes are initially formed on a line joining the particle centres, but the alignment is destroyed by subsequent motion of the particles. The bond potential depends on the distance between the bij nodes on the bonded particles and is taken to be independent of the particle types : /B(bij)\ebAbij[bint b0 B2 for bmax[bij[b1 /B(bij)\0 for bij\b1 (2) or bij[bmax The parameters and determine the range bint , bmax , b0 , b1 eb and magnitude of this potential.We use bint\0.1 ; bmax\1.0 ; The interaction distance is b0\0.1 ; b1\0.1 ; eb\1.0. bint chosen to be equivalent to so that particles do not suddenly b1 experience an extra force when they become bonded. For bond lengths larger than the bonding potential has a b1 Hookean response. In all the simulation runs presented in this paper the bond length never reaches its maximum value bmax so that the bonding is completely irreversible.The maximum bond length typically remains smaller than during a 0.5]bmax simulation run. The total potential U, which is the sum of the potentials in eqn. (1) and (2), can be diÜerentiated to –nd the total interparticle force which is used to update the simulation and Fij , calculate the interparticle stress, U(rij , bij)\/C(rij)]/LR(rij)]/B(bij) Fij\[+U(rij , bij) (3) When a bond does not remain collinear with the particle centres it generates a torque on those particles.If is the Fik force on particle i due to bond k, then the total torque on that particle can be written as Ti\;k ak]Fik (4) where is the position of bond node k relative to the particle ak centre. The translational update algorithm can now be written as a function of the interparticle forces ri(t]*t)[ri(t)\Fi(t) *t fp ]Ri(t, *t)]zi(t)c5 xz(t)*t (5) where the Stokes friction coefficient of particle p is mp\3ngspp and *t) is the familiar Gaussian random displacement.Ri(t, The last term on the right-hand side of eqn. (5) is the displacement due to an added linear shear —ow –eld with strain rate When this shear —ow –eld is applied, the periodic c5 xz(t). images are also moved to ensure a continuous pro–le over the whole simulation.28 The rotational part of the Brownian dynamics algorithm is based on the assumption that the contributions from the interparticle torques and the random motion can be treated as being commutative.The total angular displacement of particle i about the axis in the *Ui n� direction of the torque during a time step *t can Tib]TiG then be written as *Ui\ T ib]T iG fp *t (6) where the rotational friction coefficient of particle type p is is the total interparticle torque acting on par- fp\npp3 gs , Tib ticle i due to its bonds, and is a torque with a random TiG direction whose magnitude has a Gaussian distribution with mean zero and variance equal to 6fp/*t. Rheology We calculate the interparticle stress tensor s from29,30 s\ 1 V ; j;i N1`N2 ; i/1 N1`N2~1 rij Fij (7) J.Chem. Soc., Faraday T rans., 1998, V ol. 94 131As we neglect the contribution due to the kinetic term, the particle sizes do not explicitly enter in eqn. (7). The stress time correlation function can now be calculated as Cs(t) Cs(t)\V Sp6 ab(0)p6 ab(t)T (8) where a,b\x, y, z and p6 is averaged over all three dimensions. Without applying a shear strain, the complex shear modulus G* can be calculated within the linear response theory approach from the Fourier transform of Cs(t) : G*(u)\G@(u)]iGA(u) \iu P0 =Cs(t)exp([iut) dt (9) The stress time correlation function is calculated after the system has formed a gel network.All bonding probabilities are set to zero and the simulation is run typically for 4]105 timesteps. Alternatively, the system can be subjected to a timedependent strain and the rheological behaviour derived cxz(t) from the resulting stress.We subject the system to an integral number n of shearing oscillations at frequency f\u/2n, cxz(t)\c0 sin(ut) (10) and integrate the stress function to –nd the complex shear modulus: G*(u)\ u nnc0 P0 2nn@u dt(12 pxz]12pzx)sin(ut) ]i u nnc0 P0 2nn@u dt(12 pxz]12pzx)cos(ut) (11) We typically perform 10 shearing cycles. The standard deviations which are reported are based on the —uctuations between these cycles. Fractal analysis For one-component gels the radial distribution function is a power law of power being the fractal dimension of df[3, df the network structure, which turns out to be of a self-similar nature over a limited range.In the mixed systems one can de–ne pair distribution functions and for the 1 and g1(r) g2(r) 2 particles, as well as which de–nes the normal- g12(r)4g21(r) ized probability to –nd a 1 particle at distance r from a 2 particle. In principle one might expect to –nd three diÜerent fractal dimensions associated with the three diÜerent pair distribution functions.These fractal dimensions are found by plotting the logarithm of the average number n(r) of a p particle at a distance r from a q particle against log r, completely analogously to ref. 6. Choice of parameters The parameter values used in the simulations are shown in Table 1. In all cases *t\0.1 (it is necessary to use such a small timestep because of the inclusion of bonding and rotations6). The total simulation time ttot refers to the gelation stage only.When the long-range interaction is turned on (run K, where the cut-oÜ distance for this interaction is eLR 1, 2\[2) set at After a simulation time of ttot all bonding rc1, 2\3.5. probabilities are set to zero and the rheology and structure of the system are studied. This is done using two separate procedures. First, the stress time correlation function and pair distribution functions are calculated from several (typically 4) independent runs of length t\104.Alternatively, the system is subjected to a time-dependent strain in order to (c0\0.05) –nd the storage and loss moduli at a speci–c frequency from eqn. (11). System A is exactly the system as considered by Whittle and Dickinson.6 Compared to system A, system B has half the particle concentration and system C has twice the particle concentration. Systems D and E are basically system B with an added component of the same size which does not interact with the particles of the –rst component.System F is similar to system B with an equal volume of added particles having double the radius of the dash;rst ones. Except for their larger size, these larger particles interact in exactly the same way as the smaller ones. Similarly, systems G, H, and K resemble system A, but with an equal volume of added particles which are two, three and –ve times larger than the small ones, respectively. System J resembles system H, but in system J the larger particles do not form any bonds, although they do have an attractive interaction with the smaller particles.In system I bonding and long-range interactions of the larger particles are both zero. This is also the case in system L, which contains just one, very large particle. Results First we describe the aggregation kinetics for the simulation runs given in Table 1. In Fig. 1(a) the number of aggregates, is shown as a function of time for several of these runs. Nagg , It should be borne in mind that, especially at long times when there are only a few aggregates left in the system, the Brownian motion which leads to aggregation can cause considerable —uctuations in the aggregation rate.Fig. 1(b) shows results for –ve independent runs of system H. The spread of the data amongst these –ve runs is caused by statistical —uctuations in the simulations. Although these —uctuations are clearly not negligible, they are certainly smaller than the diÜerences between pairs of runs with diÜerent parameter values.System A, which is the one-component reference system, has an overall particle volume fraction of 0.05. It is clear from Fig. 1 Table 1 Parameter values used in simulation runs system p2/p1 N1 N2 L PB1, 1 PB1, 2 PB2, 2 eLR 1, 1 eLR 1, 2 eLR 2, 2 ttot/105 A » 1000 0 21.9 10~3 » » 0 » » 1 B » 1000 0 27.6 10~3 » » 0 » » 2 C » 2000 0 21.9 10~3 » » 0 » » 0.4 D 1 1000 1000 27.6 10~3 0 0 0 0 0 1.8 E 1 1000 1000 27.6 10~3 0 10~3 0 0 0 1 F 2 469 63 21.9 10~3 10~3 10~3 0 0 0 2 G 2 1000 125 21.9 10~3 10~3 10~3 0 0 0 0.5 H 3 1000 37 21.9 10~3 10~3 10~3 0 0 0 0.6 I 3 1000 37 21.9 10~3 0 0 0 0 0 2 J 3 1000 37 21.9 10~3 0 0 0 [2 0 1 K 5 1000 8 21.9 10~3 10~3 10~3 0 0 0 1 L 15 1000 1 21.9 10~3 0 0 0 0 0 0.6 is the ratio of the two particle radii ; and are the numbers of type 1 and type 2 particles ; is the bonding probability between a p p2/p1 N1 N2 PB p , q and a q particle ; is the long-range interaction parameter between a p and a q particle ; ttot is the total simulation time.eLR p, q 132 J. Chem. Soc., Faraday T rans., 1998, V ol. 94Fig. 1 (a) Number of aggregates as a function of time in systems Nagg A, B, C, F, G and H. For run C, has been plotted ; for run F, Nagg/2 has been plotted. See Table 1 for details of the diÜerent runs. (b) 2Naggas a function of time for –ve independent simulation runs of Nagg system H. that for a one-component system the aggregation rate increases strongly with concentration.In system C (twice the volume fraction of A) the time it takes for all particles to be incorporated into one large aggregate is less than 30% of that for system A. Conversely, when the particle volume fraction is reduced further by a factor two (to 0.025, run B), the aggregation slows down strongly. It is not possible any more to form a fully gelled system within a reasonable computation time. The simulation run B was stopped at t\2]105 when there were still 20 separate aggregates present, the largest consisting of 158 particles.In Table 2A the largest aggregate size and the number of bonds at t\ttot are given for all nmax systems. For some key systems several independent simulation runs have been made. The results of these runs are given in Table 2B. Latin superscripts have been used to distinguish individual runs (e.g. Ha, Hb, Hc, Hd and He are independent runs of system H). The aggregation kinetics for run D (not shown in Fig. 1) are practically indistinguishable from run B. Clearly, the addition of another 1000 particles that do not interact or form any bonds has no detectable eÜect whatsoever on the aggregation rate. Similarly, in system E, where both types of particles are present at a volume fraction of 0.025 (so that the total volume fraction is 0.05), but where the particles only form bonds with particles of the same type, the kinetics are again indistinguishable (within statistical error) from those of run B.We therefore conclude that the aggregation is only determined by the concentration of the particles that are incorporated in the network, and not by other particles which do not interact with that network. In system E one might perhaps have expected the aggregation of like particles to be slowed down due to steric hindrance by unlike aggregates. In two-dimensional systems it is even possible for clusters of like particles to become completely enclosed by an unlike aggregate.4 However, at least at the volume fraction used in run E, no such eÜect could be detected in the three-dimensional simulation.The aggregation rate in run F is appreciably higher than in run B. In system F the volume fraction of small particles (p\1) is equal to the volume fraction in system B. But, in addition to the small particles, system F also contains an equal volume of double-sized particles. These particles speed up the aggregation as measured by The aggre- [dNagg/dt.gation does, however, still remain slower than in run A, which has the same overall particle volume fraction. Clearly, adding same-size particles to a single-component system is more eÜective than adding an equal volume of larger particles. The same Table 2 Number of bonds of type (1,1), (2,2) and (1,2) and largest aggregate formed in the various systems (A) and individual simulation nmax runs (B) ; the values in section (A) for systems A, G and H are averages of the individual runs in section (B) ; the numbers given in brackets are the values at that point in the simulation when all particles have just formed one aggregate A system (1,1) bonds (2,2) bonds (1,2) bonds total bonds nmax A » » » 2403 969 B » » » 2481 158 C » » » 4608(4411) 1000 D 2316 0 0 2316 169 E 2186 2114 0 (2])2150 153 F (0.5])1836 (0.5])42 (0.5])698 (0.5])2576 322 G 1683(1615) 50(46) 677(629) 2410(2290) 1115 H 1913(1869) 8(6) 339(296) 2259(2170) 1030 I 2584 0 0 2584 968 J 2349(2305) 0 0 2349(2305) 1000 K 2414 0 0 2437 1001 L 2349(2307) 0 0 2349(2307) 1000 B run (1,1) bonds (2,2) bonds (1,2) bonds total bonds nmax Aa » » » 2421(2414) 1000 Ab » » » 2403 959 Ac » » » 2385 948 Ga 1708(1691) 49(48) 635(627) 2392(2366) 1125 Gb 1687(1539) 49(44) 694(631) 2430(2214) 1125 Gc 1653 51 703 2407 1096 Ha 1970(1924) 3(3) 298(281) 2271(2208) 1037 Hb 1865 8 353 2226 1022 Hc 1901(1813) 9(9) 320(310) 2230(2132) 1037 Hd 1900 7 356 2263 1032 He 1927 11 367 2305 1020 J.Chem. Soc., Faraday T rans., 1998, V ol. 94 133conclusion can be drawn from a comparison of runs A, C and H. In all three systems the volume fraction of the small particles is 0.05. Triple-sized particles increase the aggregation rate, but adding the same volume fraction of small particles increases the rate more strongly. Replacing the larger particles of run H by an equal volume of even larger ones (system K) slows down the aggregation even further, giving an aggregation rate lying between those of runs A and H (not shown in Fig. 1). The aggregation kinetics of run J are again very similar to those of run A. The large particles in system J do not form bonds and therefore cannot (according to our de–nition) participate in aggregates. However, the particles do have a (longrange) attractive interaction with the small particles. One might expect that, due to this attraction, the small particles will on average be clustered around the large ones and will therefore more readily bond to each other.However, if this eÜect does exist it is not very important. At small times there is no diÜerence at all in the aggregation rate for runs A and J. At larger times the aggregation is slightly quicker in run J, although even then the aggregation remains slower than in run H. Finally, run I shows exactly the same behaviour Nagg(t) as run A. In system I the large particles do not interact at all with the network-forming small particles.This again con–rms our previous conclusion that non-interacting particles do not in—uence the aggregation process. We now turn our attention to the structure of the mixed systems. In system H the two diÜerent particle types only diÜer in size. Their reactivities are the same. How are the large particles distributed throughout the network? Fig. 2 is a snapshot of system H at t\ttot. The large particles seem to be distributed in a random manner. Fig. 3 shows the radial distributions functions, and as well as g1(r), g12(r)4g21(r) g2(r), the corresponding integrated distribution functions for this system. The integrated functions and all n1(r), n12(r) n21(r) clearly have an intermediate spatial region where the function n(r) is a power-law leading to a fractal dimension of ca. 2.1 df in all three cases. The absence of a clear power-law for is n22(r) probably due to the low concentration of the larger particles in the system. It is pertinent to note that the mixed gel can still be characterized by a single fractal dimension.In system H the average ratio of the number of (1,1) and (1, 2) bonds is 5.7. If the bond formation took place completely randomly between non-interacting point-particles, one would expect the ratios of (1,1), (2,2) and (1,2) bonds to be 750 : 1 : 56, Fig. 2 Snapshot of system H at t\6]105 (\ttot). The system contains large –ller particles The image shows the N2\37 (p2/p1\3). simulation box and one-half of the adjacent image boxes [i.e.a total of particles] to give a better impression of the gel struc- 4(N1]N2) ture. Fig. 3 Structure of binary gel system H. (a) Radial pair distribution functions and as a function of centre»centre g1(r), g2(r) g12(r)4g21(r) separation r. (b) Integrated-pair distribution functions plotted as log[n(r)] vs. log r ; circles : plusses : triangles : crosses : n11, n12 , n21, The lines indicate slopes of 2.1 and 3.0. n22 . that is, a ratio of 13.5 for the number of (1,1) and (1,2) bonds.If one assumes that the particles only form bonds when they are at a surface separation of 0.1, then the probability of a 1-particle to bond to a 2-particle at in–nite dilution increases by a geometric factor 2.62/1.12\5.6, as compared to the probability that it bonds to another 1 particle. This gives a (1, 1) : (1,2) ratio of 2.4 : 1. One only expects to –nd this theoretical ratio at the beginning of the gelation process.If we compare run F with run A, or run G (or H) with run C, we are considering pairs of systems with equal particle volume (mass) fraction. However, in the bidisperse system the number of bonds per unit of volume is far smaller (roughly by a factor of two) than in the monodisperse system, which has important consequences for the rheology as discussed below. This is due to two causes : (i) the larger particles have a smaller relative surface area and (ii) the surface density of bonds is smaller for the larger particles.Fig. 4(a) shows the storage and loss shear moduli of system H as a function of frequency. These values were obtained by Fourier transforming the stress time correlation function Cs(t). The graph is very similar in shape to that of the onecomponent system.6 For the storage modulus G@ is fP10/qr greater than the loss modulus GA, so that from the rheological viewpoint the system can be considered to be a gel. Fig. 4(b) shows the ratios of the shear moduli in systems H and A [G(H)/G(A)] and in systems G and A.Over the whole frequency range we have G@(G)[G@(H)[G@(A). Adding –ller particles increases the storage modulus of the gel. Smaller –ller particles (p\2, system G) have a slightly stronger eÜect than larger ones (p\3, system H). The increase in G@ shows a relatively weak dependence on the frequency, with a larger increase occurring at lower frequencies. At low frequencies the loss modulus GA also increases due to the –ller particles. However, at high frequencies (where the values of GA are small) GA shows a small reduction.There are no systematic diÜerences in GA( f ) for systems G and H. The value of the 134 J. Chem. Soc., Faraday T rans., 1998, V ol. 94Fig. 4 Rheology of binary particle gel systems. (a) Shear storage and loss moduli, G@ and GA, for system H derived from the Fouriertransformed stress correlation function. The reduced modulus Gp3/e is plotted against the reduced frequency (b) Ratios of the storage fqr .(squares) and loss moduli (circles) in systems G and A (open symbols) and systems H and A (–lled symbols). The data points are averages over the sampling intervals. phase angle d\tan~1 [GA( f )/G@( f )] increases owing to the presence of –ller particles in both systems. More accurate values for G@ and G@ at diÜerent frequencies can be found by doing simulated shearing experiments. For two frequencies these values are collected in Table 3A.The moduli given in this table are averages over 10 shearing cycles. The error values are the standard deviations of the individual cycles. For systems A and H all values are averages over the independent simulation runs. Table 3B gives the results for these independent runs themselves. DiÜerences amongst runs of the same system are due to the (slight) structural diÜerences which have arisen at the end of the gelation stage (at t\ttot). These structural diÜerences can be characterized by the diÜerent numbers of bonds amongst the simulation runs (see Table 2B).For system H the shearing experiments show exactly the same trends as were found from the stress-correlation functions. The particles with diameter p\3 which do not bond, but which do have an attractive long-range interaction (system J), have virtually no eÜect on the gel rheology. The diÜerences from the behaviour of system A are smaller than the statistical —uctuations.The long-range attractive interaction is clearly not strong enough to cause an eÜect of similar magnitude to that of the bonding interaction. The shear moduli found for system K are also practically identical to those for system A. In system K the –ller particles have a radius p\5. The smaller moduli values for this system again illustrate that an equal volume of –ller particles has a larger eÜect the smaller they are. The value of the stress time correlation function at t\0 equals the in–nite frequency shear modulus The values G=.31 of for gelled systems A, G and H are given in Table 3.G= Whittle and Dickinson6 showed that for a one-component system, is a linear function of the number of bonds. They G= showed how the origin of this linear relationship lies in the Zwanzig»Mountain formula,32 which gives as a summa- G= tion over all pair-interactions. By comparing the values of G= in systems A and C, we conclude here that this linear relationship remains valid when the particle concentration changes.However, when comparing single component and mixed systems, the linear relationship between and the number G= of bonds breaks down. System H has fewer bonds than system A but a larger The value of per particle or per bond is G=. G= also higher in system G than in system A. This is to be expected, as the summation in the Zwanzig»Mountain formula depends not only on the interaction potentials between the neighbouring particles but also on their distribution of (centre»centre) separations.Larger particles are farther separated from their nearest-neighbours, which make the greatest contribution to G=. So far, we have only considered the rheology of mixed gels containing two diÜerent kinds of particles which interact with Table 3 In–nite-frequency shear modulus and shear moduli G@ and GA at strain for frequencies f\0.1 and f\0.01 ; part A lists a G= c0\0.05 set of system averages and part B gives the results of individual runs for systems A, G and H A system G=\Cs(0) G@( f\0.1) GA( f\0.1) G@( f\0.01) GA( f\0.01) A 12.61^0.25 9.67^0.34 3.01^0.27 4.14^0.32 3.19^0.20 C 24.61^0.70 18.63^0.50 5.34^0.28 8.81^0.37 5.71^0.36 G 15.28^0.48 H 14.71^0.54 11.97^0.36 2.92^0.24 5.80^0.32 3.73^0.34 J 9.63^0.45 2.74^0.36 4.62^0.17 3.11^0.26 K 9.94^0.28 2.95^0.27 4.49^0.22 3.10^0.25 L 12.21^0.38 0.27^0.28 2.77^0.24 4.01^0.35 3.13^0.25 B run G=\Cs(0) G@( f\0.1) GA( f\0.01) G@( f\0.01) GA( f\0.01) Aa 12.82^0.23 9.89^0.36 3.06^0.30 4.06^0.39 3.09^0.24 Ab 12.44^0.09 9.52^0.38 3.00^0.29 4.15^0.39 3.17^0.18 Ac 12.56^0.44 9.60^0.28 2.98^0.23 4.22^0.17 3.31^0.19 Ga 14.86^0.70 Gb 15.06^0.35 Gc 15.91^0.40 Ha 14.09^0.23 11.14^0.30 2.69^0.21 5.51^0.35 3.54^0.35 Hb 14.36^0.50 12.08^0.38 2.79^0.21 5.74^0.29 3.92^0.32 Hc 14.69^0.66 11.85^0.44 2.90^0.29 5.84^0.33 3.71^0.39 Hd 15.19^0.60 12.06^0.28 2.95^0.23 6.14^0.29 3.52^0.20 He 15.21^0.73 12.70^0.40 3.24^0.26 5.77^0.35 3.96^0.42 J.Chem. Soc., Faraday T rans., 1998, V ol. 94 135other. In contrast, the larger particles (p\3) in run I are completely inert, not bonding with either themselves or the smaller particles. We saw already that these inert particles have no signi–cant in—uence on the gelation kinetics of the small particles. There is no eÜect either from these inert particles on the rheology of the small particle gel network. However, we wondered if perhaps far larger inert particles would show some eÜect.This was the motivation for simulation run L, where one very large particle (p\15) is mixed with 1000 small particles. The large particle forms a cavity which is inaccessible to the small particles. The small particles are forced to form a network around this cavity. The resulting gel is slightly weaker than the standard one-component gel (see Table 3). However, the eÜect is hardly any larger than the statistical uncertainty. Discussion Before we make a closer comparison between the simulation results and the experimental data reported in the literature, we must realize that the simulations do have several restricting limitations.A ubiquitous limitation in all computer simulations is formed by the limited availability of computer resources. Therefore, we are forced to restrict the simulations to systems containing on the order of 103 particles. Any phenomena taking place on (far) larger length scales than the box size cannot be studied. There is also a quite strong limitation on the particle size ratio that can be used in the simulation of binary systems.If the larger particles are far bigger than the smaller ones, the number of smaller particles needed to get a roughly equal volume ratio of both particle types increases strongly. Therefore, this size ratio has been set equal to or less than three in the large majority of simulations reported in this paper. Secondly, the spherical and undeformable nature of the particles may restrict the applicability of the model.When these systems are sheared, real food particles may dissipate some of their energy by undergoing shape deformations. In the model all the stress becomes localized in the particle bonds. Thirdly, many-body hydrodynamic interactions are neglected. Previous simulations of the aggregation of DLVOtype particles seem to justify the neglect of multi-body hydrodynamic interactions.33,34 However, although such interactions are unlikely to aÜect greatly the structure of particle gels formed by Brownian aggregation, they could have a profound in—uence on the large-deformation rheology or on the structure of gels formed during aggregation in a —ow –eld.We are at present studying this eÜect in more detail and hope to report on it at a later stage. In addition to these limitations, one must bear in mind that in many practical systems the gel properties are determined by a subtle balance of forces.This is, for example, illustrated by the complex relationship between the gel strength and the concentration of an added nonionic surfactant, which was found by Dickinson and Hong.27 In the simulation model the interactions between particles are simply accounted for by a bonding probability and a long-range interaction. These two parameters may show a complicated dependence on the experimental conditions. Therefore, it is not realistic to expect the simulation model to give a good quantitative prediction of the properties of practical systems.Rather we should expect the simulations to reproduce and explain more general experimental trends. The simulations show a clear eÜect on the gelation due to the addition of ì –ller œ particles. If the total mass (or volume) of the added particles is kept constant, then smaller –ller particles increase the gelation kinetics more strongly than larger ones. As far as we know, no measurements have been reported in the literature of the eÜect of –ller particles on the aggregation kinetics.Most experiments are restricted to studying the properties of gels when the gelation is completed. However, Dickinson and Hong27 did report that the incorporation of emulsion droplets greatly reduced the overall concentration of protein (by at least a factor of two) required to make a self-supporting gel in a b-lactoglobulin system. In other words, by adding the emulsion droplets the time required for gelation decreased from in–nite to a –nite value.This can be compared to our one-component system at /\0.025 (system B), which shows very slow aggregation, not leading to a fully gelled system within the available computation time. However, complete gelation does occur upon addition of –ller particles (run F). The simulations clearly show that the incorporation of –ller particles in a network formed by smaller colloidal particles does increase the storage and loss moduli of such a network.Although the particle size ratio used in the simulations is far smaller than in most experimental systems (e.g. globular protein emulsion gels), the quantitative trend found in the simulations is in good agreement with the wide range of experimental data which show that –ller particles that are ìcompatibleœ with the gel network (as seen, for example, in micrographs) strengthen the gel. We assume that a similar increase of the gel strength will also be found in large deformation shearing simulations, which we have not yet performed.We conclude that small –ller particles lead to a larger increase in the shear moduli than do larger –ller particles. The same trend has been found experimentally, for instance by Matsumura et al.,24 who used three diÜerent size oil droplets as –ller particles, and by McClements et al.23 A further general trend which emerges from the experimental literature is that the presence of –ller particles reduces the gel strength when the particles are not compatible with the gel.However, in the simulations we –nd that the –ller particles with radius p\3 do not have any eÜect on either the gelation kinetics or the rheology of the gels when they do not interact with the gel-forming particles. Such an eÜect will probably only occur if the –ller particles are large enough to signi–cantly disturb the intrinsic network structure of the one-component gel, that is, if the –ller particles are far larger than the voids that exist in the one-component network.For p\15, we do indeed detect a small reduction in the shear modulus. However, for such a large particle radius ratio, it is obviously not possible to simulate a system containing many –ller particles. In run E we do not –nd any synergistic eÜect due to the mixing of two diÜerent types of particles on the gelation process. In this binary system the two diÜerent types of particles only form bonds between like particles, and the gelation of like particles is not in—uenced by the presence of unlike particles. This system resembles the experimental system formed by mixing solutions of skim milk powder and whey protein concentrate.18,19 However, the experimental system does show a synergistic eÜect on the gel –rmness.Microstructural studies revealed the compatibility of both protein sources. The simulations suggest that without this compatibility a mixture of two protein particle networks behaves exactly the same as the parent gel networks.In our model the –ller particles are hard spheres (just as are the primary network-forming particles). Consequently, we cannot study the eÜect of the –ller particle rigidity on the viscoelastic behaviour of the mixed gel in order to model the experiments of, for example, Brownsey et al.25 When –ller particles are used with a low rigidity (a smaller shear modulus than that of the primary gel) a system under stress will be able to relax due to internal rearrangements within the –ller particles rather than due to movement of the particles relative to each other.A possible way to incorporate such an eÜect in the model would be to make the particles deformable spheroids rather than rigid spheres. This would, however, increase the complexity of the Brownian dynamics algorithm a great deal. A simpler alternative is to treat the –ller particles as threedimensional arrays of small particles bonded to each other. 136 J. Chem. Soc., Faraday T rans., 1998, V ol. 94The rigidity of these macroparticles can then be controlled by varying their internal bond density and the stiÜness of their internal bonds (in comparison with the ìnormalœ gel bonds). Thus it is possible to use the present simulation model to study the eÜect of the –ller particle rigidity on the composite network rheology. Finally, we note that our results also have signi–cant implications for systems which, although without added –ller particles, are not perfectly monodisperse.Even if the total particle volume fraction is the same, it can make a big diÜerence for the viscoelastic behaviour of a gel whether all particles are of the same size or whether they diÜer in size. This implies that the characteristics of two gels can diÜer rather strongly if their constituent particles have diÜerent size distributions (even if the average size is the same in both cases). thank Dr. M. Whittle for useful discussions and advice. We This research was supported by Contract FAIR-CT96-1216 of the EU Framework IV Programme. References 1 A. H. Clark and S. B. Ross-Murphy, Adv. Polym. Sci., 1987, 83, 57. 2 T. P. M. Beelen, Curr. Opinion Colloid Interface Sci., 1996, 1, 718. 3 E. Dickinson, J. Chem. Soc., Faraday T rans., 1994, 90, 173. 4 E. Dickinson, J. Chem. Soc., Faraday T rans., 1995, 91, 51. 5 E. Dickinson, in Biopolymer Mixtures, ed. S. E. Harding, S. E. Hill and J. R. Mitchell, Nottingham University Press, Nottingham, 1996, p. 349. 6 M. Whittle and E. Dickinson, Mol. Phys., 1997, 90, 739. 7 T. S. Chow, J. Mater. Sci., 1980, 15, 1873. 8 Y. S. Lipatov, Adv. Polym. Sci., 1977, 22, 1. 9 C. van der Poel, Rheol. Acta, 1958, 1, 198. 10 J. C. Smith, J. Res. Natl. Bur. Stand., 1974, 78A, 355. 11 J. C. Smith, J. Res. Natl. Bur. Stand., 1975, 79A, 419. 12 R. K. Richardson, G. Robinson, S. B. Ross-Murphy and S. Todd, Polym. Bull., 1981, 4, 541. 13 S. B. Ross-Murphy and S. Todd, Polymer, 1983, 24, 481. 14 S. Ring and G. Stainsby, Prog. Food Nutr. Sci., 1982, 6, 323. 15 E. Dickinson, G. Stainsby and L. Wilson, Colloid Polym. Sci., 1985, 253, 933. 16 T. van Vliet, Colloid Polym. Sci., 1988, 266, 518. 17 J. M. Aguilera and H. G. Kessler, Milchwissenschaft, 1988, 43, 411. 18 J. M. Aguilera and H. G. Kessler, J. Food Sci., 1989, 54, 1213. 19 J. M. Aguilera and J. E. Kinsella, J. Food Sci., 1991, 5, 1224. 20 J. M. Aguilera, J. E. Kinsella and M. LiboÜ, Food Struct., 1993, 12, 469. 21 R. Jost, F. Dannenberg and J. Rosset, Food Microstruct., 1989, 8, 23. 22 R. A. Yost and J. E. Kinsella, J. Food Sci., 1992, 57, 892. 23 D. J. McClements, F. J. Monahan and J. E. Kinsella, J. T ext. Stud., 1993, 24, 411. 24 Y. Matsumura, I-J. Kang, H. Sakamoto, M. Motoki and T. Mori, Food Hydrocolloids, 1993, 7, 227. 25 G. J. Brownsey, H. S. Ellis, M. J. Ridout and S. G. Ring, J. Rheol., 1987, 31, 635. 26 K. R. Langley and M. L. Green, J. T ext. Stud., 1989, 20, 191. 27 E. Dickinson and S-T. Hong, J. Agric. Food Chem., 1995, 43, 2560. 28 M. P. Allen and D. J. Tildesley, T he Computer Simulation of L iquids, Oxford University Press, Oxford, 1989. 29 J. H. Irving and J. G. Kirkwood, J. Chem. Phys., 1950, 18, 817. 30 D. M. Heyes and P. J. Mitchell, J. Chem. Soc., Faraday T rans., 1994, 90, 1931. 31 P. N. Visscher, P. J. Mitchell and D. N. Heyes, J. Rheol., 1994, 38, 465. 32 R. Zwanzig and R. W. Mountain, J. Chem. Phys., 1965, 43, 4464. 33 G. C. Ansell and E. Dickinson, J. Chem. Phys., 1986, 85, 4079. 34 G. C. Ansell and E. Dickinson, Faraday Discuss. Chem. Soc., 1987, 83, 167. Paper 7/06632E; Received 12th September, 1997 J. Chem. Soc., Faraday T rans., 1998, V ol. 94 137

ISSN:0956-5000    

DOI:10.1039/a706632e

出版商:RSC    

年代:1998

数据来源: RSC

摘要:

Excited state intramolecular proton transfer of 2-(2º-hydroxyphenyl)benzimidazole in non-ionic micelles : Brijs Someskumar Das and Sneh K. Dogra* Department of Chemistry, Indian Institute of T echnology Kanpur, Kanpur-208016, India Excited state intramolecular proton transfer (ESIPT) of 2-(2@-hydroxyphenyl)benzimidazole (2-HPBI) has been studied in four diÜerent Brijs, i.e. Brij-35, Brij-58, Brij-78 and Brij-99. In comparison to water, —uorescence maxima of the tautomer band is red shifted by B20 nm, whereas that of normal —uorescence is not aÜected much.The —uorescence quantum yield of the tautomer band increases and that of the normal band decreases. The eÜective relative permittivity of the site where neutral 2-HPBI is (eeff) present is 20^2, whereas of the sites where monocation»neutral and neutral»monoanion equilibria are taking place are eeff higher. The critical micelle concentration (c.m.c.) of the Brijs at pHB7 decreases with increase of Brij number.At pH B1.0 (ionic strength 0.3 M), the c.m.c. of the Brijs are larger, by nearly two orders of magnitude than at pH 7. The values of the pKa prototropic reactions are determined in diÜerent Brijs and are discussed. 1 Introduction Among the non-ionic surfactants, Triton X-100 (TX-100) has received the most attention, as it forms micelles in aqueous solution1h6 and –nds wide applications in biochemical studies involving membranes and protein puri–cation7,8 and lipolytic enzymes.9 A number of studies have been carried out to establish its size, shape and hydration.5,6 Based on the molecular weight and viscosity data,6 it is shown that if distinct polar and apolar regions of micelles exist, the micelle structure must be an oblate ellipsoid. However, a Raman spectroscopic study5 has shown the structure of TX-100 micelles to be spherical.In the latter model, the hydrophilic oxyethylene groups penetrate into the hydrophobic core of the micelles and do not exhibit clear distinct polar and apolar zones.The other classes of non-ionic surfactants, known as Tweens and Brijs, are shown in Scheme 1. Both these surfactants, similar to TX-100, contain poly(oxyethylene) groups as the polar part. The main diÜerences between the Tweens and Brijs are that : (i) the poly(oxyethylene) moiety of the Tweens is highly substituted and (ii) the Tweens are the esters of fatty acids of diÜerent chain lengths whereas the Brijs are the corresponding ethers.Unlike TX-100, the characteristics of these surfactants have not been investigated in detail, except for a few studies on the Tweens.10h13 These studies have shown that the hydrophobicity and the aggregation number of Tweens increase and the critical micelle concentration (c.m.c.) of Tweens decreases with an increase in the Tween number. Similar studies are not available for the Brijs except for Brij-35,11 where the prototropic equilibria of the weak acids or bases have been used to –nd the polarity of the site where the above equilibria are established.In the present study, we have tried to use the spectral characteristics of 2-(2@-hydroxyphenyl)benzimidazole (2-HPBI) and prototropic reactions [monocation (MC)»neutral (N) and neutral»monoanion (MA) equilibria] to –nd out the characteristics of four Brijs, viz. Brij-35 [C12H25(OCH2CH2)23OH], Brij-58 Brij-78 [C16H33(OCH2CH2)20OH], and Brij-99 [C18H37(OCH2CH2)20OH] The reasons for using this probe [C18H35(OCH2CH2)20OH].(2-HPBI) are : (i) the molecule exhibits dual —uorescence, the normal and tautomer bands, the former has a small Stokes shift, the band maximum is insensitive but the —uorescence quantum yield is sensitive to the solvent polarity, whereas the latter has a large Stokes shift and the band maximum is sensitive to the solvent polarity ; and (ii) the molecule possesses acidic and basic centres that are close to each other and this may provide better information about the site of these prototropic reactions.Both these aspects of 2-HPBI have previously been investigated thoroughly.14h21 2 Experimental 2-HPBI was synthesized by re—uxing o-phenylenediamine with o-hydroxybenzoic acid in polyphosphoric acid media and was puri–ed as described in the literature.22 AnalaR grade dioxane (E. Merck) was further puri–ed as suggested in the literature.23 All the Brijs (Aldrich Chemical Company) were used as received. AnalaR grade HCl, and NaOH H2SO4 (BDH) were used as received.Triply distilled water was used for making aqueous solutions. The instruments used to measure the absorption, —uorescence intensities and lifetimes of the excited singlet state, the preparation of solutions and adjustment of their pH, the procedure to correct the —uorescence spectra and the calculation of are all the same as described elsewhere.12,24h27 A /fl pH\7 required in the measurement of the apparent pKa values in the state was adjusted by addition of HCl.S0 However, was used for the adjustment in the measure- H2SO4 ment of the —uorescence intensities because halide ions quench the —uorescence intensities.28,29 The values of the MC»N and N»MA pKa (pKaI) (pKaII) equilibria were determined by using the procedure as described by Drummond et al.11 H2PBI`HHPBI]H` (I) HPBIHPBI~]H` (II) The respective equations used are as follows : pKam\B]log(UH 0 )[logA [HPBI] [H2PBI`]B[log cHPBI cH2PBI` (1) pKa1\pKa[logm cB (2) pKa0\pKaobs] eW0 2.303kbT (3) J.Chem. Soc., Faraday T rans., 1998, 94(1), 139»145 139Scheme 1 Structures of the non-ionic surfactants studied where and are the values of the indica- pKam, pKai pKaobs pKa tor (2-HPBI) determined in dioxane»water mixture, the intrinsic values and the values determined in the micellar pKa pKa solutions, respectively. is the mean ionic activity coeffi- mcB cient of HCl in the particular medium, is the apparent pKa0 value if the surface potential of the surfactant is zero.pKa (W0) B is the pH meter reading and is the correction factor log UH0 to be applied to the pH meter reading to depict the actual hydrogen ion concentration in dioxane»water solution, e is the charge on the electron, is the Boltzmann constant and kb T is the temperature in Kelvin. The other implicit assumptions involved in case of the above relations have been discussed by Drummond et al.11 and will not be discussed here.For convenience of discussion, the following relations are de–ned: *pKam\pKam[pKaw (4) *pKai\pKai[pKaw (5) *pKa0\pKa0[pKaw (6) where and are the values of the respective pKaw pKa0 pKa equilibrium in water and in non-ionic micelles. 3 Results 3.1 Spectral characteristics of neutral species Absorption band maxima —uorescence band maxima (jmax, ab), of the normal (norm) and tautomer (taut) bands, —uo- (jmax, fl) rescence quantum yields in diÜerent micelles at 298 K (/fl) and pH 7 are compiled in Table 1.The absorption spectra are shown in Fig. 1 and the —uorescence spectra in Fig. 2. Similar data in dioxane, 55% v/v dioxane»water mixture, water, SDS, CTAB, TX-100 and Tweens from our earlier studies20,30 are also given in Table 1 for comparison purposes. is jmax, ab Fig. 1 Absorption spectra of 2-HPBI in diÜerent micelles at pH 7 and 298 K. Surfactant concentration\0.02 M. [2-HPBI]\1]10~5 M. A, water; B, Brij-35 ; C, Brij-78 ; D, Brij-99. Table 1 Absorption band maxima, —uorescence band maxima, BWHMH, —uorescence quantum yield, (108 s~1), of 2-HPBI (1]10~5 qfl , kr knr M) and relative permittivity (e) of diÜerent micelles at pH 7 (pH 4 for CTAB) and 298 K jmax, fl/nm system jmax, ab/nm norm taut BWHMH/103 cm~1 e /fl qf/ns kr/108 s~1 knr/108 s~1 dioxane 318, 331(sh) » 467 2.83 2.3 0.56 4.20 1.33 1.05 55% dioxane 316, 330(sh) 353 447 2.81 28.0 0.79 4.50 1.76 1.46 water 313, 325(sh) 353 430 4.0 78.0 0.33 3.00 1.10 2.23 SDS (0.05 M) 315, 328(sh) 353 444 2.96 42.0 0.45 3.70 1.20 1.51 CTAB (0.001 M) 320, 334(sh) » 450 2.99 16.5 0.75 4.80 1.56 0.52 Brij-35 (0.02 M) 317, 331(sh) 353 448 3.05 22.5 0.54 4.97 1.09 0.92 Brij-58 (0.02 M) 319, 333(sh) 353 449 2.98 19.5 0.54 5.14 1.05 0.89 Brij-78 (0.02 M) 318, 333(sh) 353 450 3.02 16.5 0.54 5.30 1.03 0.86 Brij-99 (0.02 M) 318, 333(sh) 353 449 3.06 19.5 0.49 5.17 0.95 0.97 Tween-20 (0.001 M) 318, 333(sh) 353 449 3.03 19.5 0.54 5.4 1.00 0.85 Tween-40 (0.001 M) 318, 333(sh) » 450 3.07 16.0 0.59 5.1 1.16 0.80 Tween-60 (0.001 M) 318, 333(sh) » 451 3.05 14.0 0.61 5.3 1.15 0.74 Tween-80 (0.001 M) 318, 333(sh) » 450 3.02 16.0 0.62 5.7 1.09 0.66 TX-100 (0.001 M) 318, 333(sh) 353 450 3.0 16.0 0.63 3.8 1.66 0.97 140 J.Chem. Soc., Faraday T rans., 1998, V ol. 94Fig. 2 Fluorescence spectra of 2-HPBI in diÜerent micelles at pH 7 at 298 K. A, water; B, Brij-35 ; C, Brij-78 ; D, Brij-99. Normal band intensities are enlarged by 10 times. nm.[2-HPBI] jexc\314 \1]10~5 M. Surfactant concentration 0.02 M. nearly 8»9 nm (3 nm in SDS at 0.05 M) red-shifted in all these micelles in comparison to those in water. Whereas of jmax, fl the normal band in all the micelles (except CTAB, Tween-40, Tween-60 and Tween-80, where the intensity is too small to notice) is the same as in water. The band width at half the maximum height (BWHMH) of the tautomer band is less in these surfactants [(2.96»3.0)]103 cm~1] in comparison to that in water (4.0]103 cm~1).As with that for nonionic micelles and unlike that for ionic micelles (SDS and CTAB), the —uorescence intensity of the tautomer band increases continuously with increasing surfactant concentration (Fig. 3) and becomes almost constant at a concentration of 0.001 M. The c.m.c. values obtained from the in—ection points are shown in Table 2. The values obtained using absorption spectra are not very accurate as the changes observed are not very large, but the order of magnitude is the same.The —uorescence intensity of the normal band decreases by a factor of 3»4 with increasing surfactant concentration, but does not tend to zero. This behavior is diÜerent from that observed in CTAB and Tweens but is similar to that in SDS. The relative with respect /fl, taut to water increases upto Brij-78 and decreases slightly for Brij- 99. A similar trend is also observed for the However, /fl, norm . decreases with increasing Brij number./fl, norm//fl, taut 2-HPBI was also excited using excitation wavelengths in the range of 315»340 nm, known as the red-edge eÜect,31 and observed in each case was similar. This indicates that jmax, fl the —uorescence occurs from the completely relaxed excited state and that the environments around the —uorophore in the Brijs are at equilibrium at room temperature. It is also evident that the solvent relaxation time of the medium around the Fig. 3 Plot of —uorescence intensities of the tautomer band vs.the logarithm of surfactant concentration. A, Brij-35 ; B, Brij-58 ; C, Brij- 78; D, Brij-99. nm for all Brijs. Intensities are at 448, 447, jexc\314 450 and 450 nm, respectively. —uorophore in micelles is shorter32,33 than that of the radiative decay time. Similar behavior has been observed earlier.34 A calibration curve (Fig. 4) was constructed for the —uorescence band maxima of the tautomer band and (l6 max, fl/cm~1) the relative permittivity of the medium, obtained by mixing diÜerent amounts of water»dioxane.20 By using this correlation diagram, it was found that the polarity at the binding site of 2-HPBI in each Brij, expressed as decreases from eeff , Brij-35 to Brij-78, and then increases slightly in Brij-99, which has much less water content.The values of so obtained for these micelles are much less than that of SDS20 but are slight- Fig. 4 Plot of —uorescence band maxima vs. relative per- (l6 fl/cm~1) mittivity of dioxane»water mixtures Table 2 Binding constants of 2-HPBI [neutral (N), monocation (MC) and monoanion (MA)] with diÜerent micelles (Brijs) and their c.m.c.(Ks) values at 298 K determined by eqn. (7) (the values given in parentheses indicate the c.m.c. values determined from the surfactant concentration vs. absorbance or —uorescence intensity plots) Ks/dm3 mol~1 c.m.c./M tautomer, normal, tautomer, normal, probe micelle absorbance —uorescence —uorescence absorbance —uorescence —uorescence N, pH 7 Brij-35 500 690 2600 8.4]10~5 8.0]10~5 (10.0]10~5) 8.7]10~5 (9.0]10~5) Brij-58 1800 2750 4200 3.65]10~5 3.3]10~5 (3.0]10~5) 3.0]10~5 Brij-78 2050 1680 4200 1.85]10~5 (0.45]10~5) 1.5]10~5 (1.25]10~5) 1.4]10~5 Brij-99 1770 1370 2700 0.9]10~5 (0.6]10~5) 1.2]10~5 (1.3]10~5) 0.9]10~5 MC, pH 1.2 Brij-35 150 » » 1.75]10~3 » » Brij-78 98 » » 1.50]10~3 » » Brij-99 95 » » 1.40]10~3 » » MA, pH 13.2 Brij-35 138 » » 2.25]10~3 » » Brij-78 128 » » 1.0]10~3 » » Brij-99 147 » » 0.5]10~3 » » J.Chem. Soc., Faraday T rans., 1998, V ol. 94 141ly larger than those of CTAB, TX-100 and Tweens. In other words SDS is more hydrophilic than the Brijs, whereas the Brijs are slightly more polar than the Tweens, of the same hydrocarbon chain, as well as TX-100 and CTAB. 3.2 Spectral characteristics of the ionic species The spectral characteristics of 2-HPBI have been studied over pH 1»13 at diÜerent surfactant concentrations. The relevant data are shown in Table 3.It is clear from the data that the values for the monocation of 2-HPBI (pH 1.2) in Brijs jmax, ab are red-shifted by 6 nm in comparison to that of monocation in water and also by 6 nm with respect to the of the jmax, ab neutral species in Brijs. On the other hand, the values jmax, ab of the monoanion (pH 13) in Brijs are red-shifted by 3»6 nm in comparison to that of the monoanion in water, but it is red-shifted by 15»18 nm with respect to that of the neutral in micelles and by 25 nm when compared to the neutral species in water.The values of the monoanion in micelles are jmax, fl red-shifted by 2»3 nm to that in water at pH 13, but are largely blue-shifted in comparison to that in water at pH 13. It is largely blue-shifted in comparison to the 450 nm and redshifted in comparison to the 350 nm —uorescence bands of neutral 2-HPBI in Brijs. The of the tautomer band is jmax, fl blue-shifted by 7»8 nm as the acid concentration increases. The —uorescence intensity of the 442 nm band reaches its maximum by pHB3 and starts decreasing at pH\3.At the same time, the structured normal Stokes-shifted band is replaced by a broad band with very low —uorescence intensity at pH\3. The assignment of the species in the state, i.e. mono- S0 cation at pHB1 and monoanion at pH[11, are consistent with the spectral changes previously observed for a similar system.35 In the state, assignment of the 413 nm band to S1 monoanion at pHP11 and the 376 nm band to monocation at pHO2 are again consistent with previous spectral changes.35 The assignment of the 442 nm band to the zwitterion band, which is formed by the reorganization of charge transfer leading to structure VI, can be made on two grounds: (i) the band maxima observed for the various species are in the order36 and agree with our jzwitterion[janion[jcation[jneutral observation ; and (ii) the increase in the acidity and basicity of the wOH group and the xNw atom, respectively, in the S1 state is such that the order of prototropic reactions in the S0 state are changed upon excitation. Similar observations have been made for molecules containing both electron donating and electron attracting functional groups.35 The blue-shift observed in the —uorescence spectrum of the tautomer band at pH 6»2 could have been due to the increase in the polarity of the micelles when the acid concentration is increased.A similar behavior is observed when the polarity of the pure solvents increases.14 But this is rejected on the grounds that : (i) an increase in the polarity or in the hydrogen bond formation capacity of the solvents leads to an increase in the —uorescence Table 3 Absorption band maxima and —uorescence (jmax, ab/nm), band maxima of monocation and monoanion (pH 13) of (jmax, fl/nm) 2-HPBI in aqueous and micellar media ([Brijs]\0.02 M) monocation monoanion medium pH jmax, ab jmax, fl a jmax, ab jmax, fl water 2.5 320, 332(sh) 364, 442 345 408 SDS (0.02 M) 4.4 325, 337(sh) 376, 443 345 410 CTAB (0.01 M) » » » 348 418 Brij-35 (0.02 M) 1.6 323, 338(sh) 376, 442 348 412 Brij-58 (0.02 M) 1.2 324, 338(sh) 376, 442 351 418 Brij-78 (0.02 M) 1.1 323, 338(sh) 376, 442 351 413 Brij-99 (0.02 M) 1.2 323, 338(sh) 376, 442 351 413 a Zwitterion. intensity of the normal Stokes-shifted band,14 which is not observed in our case ; and (ii) the values of observed at two Ks diÜerent pH values, i.e. 7 and 1.2, are diÜerent (see later), e.g. ca. 10~4 dm3 mol~1 at pH 7 and ca. 100 dm3 mol~1 at pH 1.2. 3.3 Binding constants The binding constants at pH 7 and 298 K, in all the Brijs (Ks) have been determined using eqn. (7) :37 f 1[f \KsA[D]t[ [S]t f B[Ks[c.m.c.] (7) where and [D]t (\[S]m][D]m]c.m.c.) [S]t (\[S]a][S]m) are the total surfactant and substrate concentrations (a and m stand for aqueous and micellar phase respectively) and f is de–ned as : f\ A[Aa Am[Aa (8) where A, and are the absorbances (or the —uorescence Aa Am intensities) in surfactant, in water and when the —uorophore is completely solubilized in micelles, respectively.The values of f lie in the range from 0.0 to 0.8 to minimize the errors. A plot of f/1[f vs. is a straight line. The slope gives ([D]t[[S]t/f ) the value of and the intercept The absorption Ks Ks/[c.m.c.]. spectra, tautomer and normal —uorescence spectra are used to determine the and c.m.c. The relevant data are given in Ks Table 2.The value of the c.m.c. observed in each of the three cases for each micelle agrees with each other as well as with the literature values.38 The values of obtained using absorbance or —uorescence Ks data of the tautomer band agree with each other whereas those obtained using the normal —uorescence band are higher. The value of increases up to Brij-78, but decreases slightly Ks in Brij-99. One other aspect worth considering is that the values of for the species giving normal —uorescence are dif- Ks ferent from those obtained from the tautomer band.This clearly suggests that the two species have diÜerent structures and thus are interacting diÜerently with the micelles. The above conclusions are consistent with earlier results,17 which suggest that : two ground state conformers are present in the state ; conformer II, which leads to normal —uorescence, is S0 present in the relatively polar region ; and conformer I, which leads to the tautomer band, is present in the less polar region of the micelles.The observation of the tautomer band also suggests that the formation of tautomer (III) is a very fast step even in micellar medium. The values of for the species present at pHB1.2 Ks (monocation) and at pHB13 (monoanion) were determined using absorption data. The relevant data along with the c.m.c. values are also given in Table 2. The values of and c.m.c. Ks for both the species could not be determined with the help of the —uorescence data because the changes in the intensities are not very large. Unlike the eÜect of ionic strength on the ionic micelles, the c.m.c.of the non-ionic micelles increases with increasing ionic strength. Similar behavior has been observed previously for TX-100 and Tweens.39 Furthermore, no de–nite trend is observed in the values of for monocations or Ks monoanions as seen for neutral species. 3.4 Lifetimes in the excited state Lifetimes of neutral 2-HPBI were measured in all Brijs at 0.02 M concentration at pH 7 and 298 K.The excitation wavelength used was 313 nm and the decay emission was recorded at 450 nm. The decay curves followed a single exponential, indicating that the —uorophore is completely solubilised and is present at only one site of the micelles. This is consistent with the large values of the for each Brij. The values of the Ks radiative and non-radiative decay constants can be (kr) (knr) 142 J. Chem.Soc., Faraday T rans., 1998, V ol. 94calculated from the following relations : kr\/fl/q knr\1/qf[kr The values of and the decay constants are given in qf , /fl Table 1, along with the values of similar parameters in water, dioxane, a 55% v/v dioxane»water mixture, 0.05 M SDS, 0.001 M CTAB, 0.001 M TX-100 and diÜerent Tweens for comparison. The agreement between the literature values is very good.14 The data in Table 1 clearly show that the rate of the radiationless process is accelerated by water molecules.The other point worth mentioning is that the values of knr observed in the Tweens and CTAB are less than those determined in the Brijs or TX-100. This clearly indicates that the interior of TX-100 or the Brijs are relatively more hydrated than the Tweens and CTAB. 3.5 Proton transfer reactions of HPBI in the state S0 The 2-HPBI molecule contains an wOH group that can act as an acid and an xNw moiety that can act as a base. Hence both MC»N and N»MA equilibria can be studied with this molecule, as given in Scheme 2.Furthermore, as pointed out earlier, the dioxane»water mixtures adequately represent the interfacial region of the non-ionic micelles composed of poly(oxyethylene) groups.40,41 Therefore, the values of pKa the MC»N and N»MA equilibria of HPBI have been determined in 1, 11, 21, 31, 41, 51, 61, 71 and 81% v/v dioxane» water mixtures. The values of and in these organic pKam pKai solvent»water mixtures were calculated by using eqn.(1) and (2), respectively. The values of and have been log UH0 log mcB taken from the work of Drummond et al.11 as mentioned above. The relative permittivities for the dioxane»water solutions were obtained from the work of Critch–eld et al.42 The other assumption made in these calculations is that in the MC»N and in N»MA log(cHPBI/cH2PBI`) log(cPBI~/cHPBI) equilibria are very small and therefore can be neglected. The values of for the MC»N and N»MA equilibria in 1% v/v pKaw dioxane»water mixture agree with our earlier work.14 The Scheme 2 values of and obtained by using eqn.(4) and (5), *pKam *pKai respectively, for the two equilibria of 2-HPBI vs. relative permittivities of various dioxane»water mixtures are plotted in Fig. 5 and 6, respectively. The apparent values of the MC»N and N»MA equi- pKa libria of 2-HPBI have been determined at various concentrations of Brijs and are given in Table 4. The concentrations of the micelles were selected in such a way that at least 99% of the indicator is solubilized in the micelles and this concentration is found to be less than 0.02 M.The value found for eeff the sites of the micelles, at which the prototropic reactions are occurring, from the correlation diagrams (shown in Fig. 5 and 6) are also given in Table 4. It is evident from the data in Table 4 that the values of the MC»N equilibrium pKa decrease, whereas that of N»MA increase with increasing surfactant concentration.This is consistent with the fact that the polarity in the micelles is much less than that of aqueous phase. In other words, in the micellar phase the equilibrium will shift towards the direction where the neutral species are stable. Hence, high acid concentration is required for the former equilibrium and high base concentration for the latter. It is also clear from the data of Table 4 that the values of at the site at which the prototropic reactions are occurring eeff decrease with increasing surfactant concentration and almost levels oÜ at a surfactant concentration of 0.02 M.This indicates that nearly complete micellization of 2-HPBI is achieved at this concentration and hence the prototropic reactions only Fig. 5 Plot of and of 2-HPBI monocation»neutral *pKam *pKai equilibrium vs. relative permittivity of dioxane»water mixtures. A, B, *pKam; *pKai. Fig. 6 Plot of and of 2-HPBI neutral»monoanion *pKam *pKai equilibrium vs.relative permittivities of dioxane»water mixtures. A, B, *pKam; *pKai. J. Chem. Soc., Faraday T rans., 1998, V ol. 94 143Table 4 Apparent values for the monocation»neutral and neutral»monoanion equilibria of 2-HPBI and the relative permittivities at the pKa binding site of the micelles at diÜerent concentration Brij-35 Brij-58 Brij-78 Brij-99 equilibrium [D]/M pKa e pKa e pKa e pKa e MC»neutral 0.00 5.1 78.0 5.1 78.0 5.1 78.0 5.1 78.0 0.000 05 4.9 70.0 » » » » » » 0.0001 4.8 63.5 5.0 44.0 » » » » 0.0005 4.6 55.0 » » 4.0 42.0 » » 0.001 4.15 45.0 4.02 42.0 3.85 40.0 3.9 40.0 0.01 3.6 35.0 3.4 32.5 3.25 31.0 3.35 32.5 0.02 3.4 33.0 3.15 30.0 3.10 29.5 3.08 29.5 0.05 3.35 32.0 » » » » neutral»MA 0.00 8.9 78.0 8.9 78.0 8.9 78.0 8.9 78.0 0.0005 9.1 67.0 » » 9.05 69.0 » » 0.001 9.45 56.5 9.65 54.5 9.8 40.0 9.7 52.5 0.01 10.45 33.0 10.67 25.0 10.67 25.0 10.6 34.5 0.02 10.5 31.0 10.82 21.0 10.85 20.0 10.8 21.5 occur at one site of the micelles.This is consistent with the high values of and the —uorescence intensity following Ks single exponential decay. The values of observed using the eeff apparent values for the MC»N equilibrium of 2-HPBI pKa are found to be 32^2, with a slight decreasing trend with increasing Brij number, whereas the value of found from eeff the N»MA equilibrium is always less than that obtained from the MC»N equilibrium for the same Brij. The value of eeff\ observed for Brij-35 agrees with the literature11 data; 35 eeff values are not available for the higher Brijs.The values of eeff obtained from the —uorescence band maxima of the tautomer band vs. the relative permittivity plot (Fig. 4) are lower than those obtained from the prototropic reactions. 4 Discussion As stated earlier,5,6 con—icting views are available for the shape, size and geometry of TX-100. If a spherical shape is assumed for TX-100, it is necessary that some of the oxyethylene groups are present in the core of the hydrophobic region of the micelles.This view will allow the outer portion to oÜer more channels for the seepage of water, suggesting the presence of 1.2 Hence for this model a sharp gwater gsurfactant ~1 . boundary does not exist between the hydrophobic interior and the polar oxyethylene chains. On the other hand, if a classical model (the presence of a hydrophobic core, followed by hydrophilic oxyethylene chains) is considered, then the preferred structure of TX-100 micelles ought to be oblate.Based on our results in TX-100,20 diÜerent values of eeff have been predicted, i.e. the —uorescence data for the tautomer band predict the value of to be 16, whereas the values eeff pKa for the MC»N and N»MA equilibria predict to be 35 and eeff 18, respectively. This disagreement between values in eeff TX-100, as determined by diÜerent techniques, can be rationalized as follows. The value determined from the —uores- eeff cence data is obtained from the correlation diagram, drawn between the tautomer —uorescence band maxima and the relative permittivity (Fig. 4). The tautomer species is a neutral molecule and may not have a large dipole moment in the S1 state. In reality the blue-shifts observed in the tautomer —uorescence with the increase of polarity re—ect the decrease in the dipole moment of this species (III) and are supported by theoretical calculations.17 On the other hand, for the N»MA equilibrium, although the monoanion is an ionic species, it has a closed ring structure, V, as shown in Scheme 2.The bond between the O~ and the H of is very strong. This is also Ü åN manifested by the fact that the for the deprotonation pKa reaction of NHwO~ in 2-HPBI is not observed even up to in aqueous medium,14 even though the value H~\16 pKa for the similar deprotonation reaction of in Ü åNH benzimidazole43 is 13.4. Because this charge on the phenoxyphenyl ion might be distributed over the complete molecule, thereby reducing the ionic character, it might resemble the phototautomer and be located inside the non-ionic micelles.On the other hand, in the MC»N equilibrium the ionic species monocation is an open structure IV and hence can not be located inside the micelles but can be present at the interface of the micellar and aqueous phase. In other words, the MC»N equilibrium re—ects the of the interface between the micel- eeff les and water or the more polar region of the micelles, whereas the N»MA equilibrium re—ects the site away from the interface and towards the core of micelle TX-100.Although the Ks values of monocation IV and monoanion V of 2-HPBI have not been determined in TX-100, those determined in the Brijs suggest that the monocation dm3 mol~1) should be (KsB100 more polar than the monoanion (V, dm3 mol~1). KsB150 Two ground state conformers (I and II) are established17 and the values of observed support this. Based on the values of Ks it can be predicted that conformer II, which leads to the Ks formation of monocation IV, is present near the interface, whereas conformer I, which leads to the formation of tautomer III, is located inside the core. The high value of for the knr tautomer band in TX-100 indirectly supports the presence of oxyethylene groups in the core, which can interact with the —uorophore. This is supported by the fact that with the similar hydrocarbon chain-length of CTAB, the value of is much knr less than that in TX-100 because the CTAB micelles do not contain oxyethylene groups.The main diÜerence between TX-100 and the Brijs is the presence of a long hydrocarbon chain, i.e. instead of a p-(1,1,3, 3-tetrabutyl)phenoxy group in TX-100, the minimum chainlength in the Brijs is and that is linear. Thus the length of C12 the hydrophobic core will be much larger (1.67»2.43 nm) than that of TX-100 (1.172 nm).3 Although our results cannot predict the shape, size or geometry of the Brijs, some speculations can be made.Based on the results observed in the Brijs, it can be concluded that the two conformers I and II of 2-HPBI are present in the Brijs. Based on the diÜerent values of observed from the tautomer and normal —uorescence Ks bands, the former is present away from the interface towards the core, as supported by the values for N»MA equi- pKa librium, and the latter is present near the interface, as supported by the value of the MC»N equilibrium.The values pKa of observed for the tautomer band also suggests the pres- knr ence of oxyethylene moieties in the hydrophobic core. The slightly smaller values of in the Brijs, in comparison to knr TX-100, could be due to the presence of oxyethylene groups (not too deep) as might be present in TX-100, because of the longer hydrocarbon chain-length. In other words, the Brijs 144 J. Chem. Soc., Faraday T rans., 1998, V ol. 94might also represent a similar shape and geometry as that observed for TX-100.Lastly, by comparing the results observed in the Brijs and in the Tweens, i.e. Tween-20, -40, -60 and -80, the following diÜerences are observed: (i) for the equal hydrocarbon chainlength in the Brijs and Tweens, the values of predicted for eeff the Tweens, from the —uorescence band maxima of the tautomer and the value of the N»MA equilibrium, are slightly pKa lower than those observed for the Brijs ; (ii) the values of in knr the Tweens are less than those observed in the Brijs ; and (iii) the normal Stokes-shifted —uorescence band is absent in the Tweens.The above points clearly suggest that the interiors of the Tweens are more hydrophobic than those of the Brijs. This suggests that the number of oxyethylene groups present in the core of the Tweens will be less than those present in TX-100 or the Brijs. This could be due to : (i) the highly substituted furan ring in the Tweens, which might oÜer steric hindrance and/or (ii) the presence of an ester group in between the furan and hydrocarbon chain in the Tweens.Conclusion The above study has revealed that : (i) two kinds of conformers are present in 2-HPBI, conformer I is present more towards the core than is conformer II. This is supported by the pKa values of the MC»N and N»MA equilibria, as well as by observance of a normal Stokes-shifted —uorescence band; (ii) for the equal hydrocarbon chain-length the Brijs are more polar than the Tweens or TX-100, (iii) a model similar to that for TX-100 can also be proposed for the Brijs or Tweens but the oxyethylene groups might not be present as deep in the Brijs or Tweens as those present in TX-100; (iv) the hydrophobic character increases with increasing Brij number; and (v) the decrease and increase in the values for the MC»N and pKa N»MA equilibria, respectively, in the Brijs are due to the smaller eeff .authors are thankful to the Department of Science and The Technology, New Delhi for the –nancial support to the project no.SP/S1/H-19/91. References 1 A. A. Ribeiro and E. A. Dennis, in Nonionic Surfactants, ed. M. J. Schick, Marcel Dekker Inc., New York, 1987, p. 971 and references listed therein. 2 T. Nakogawa, in Nonionic Surfactants, ed. M. J. 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ISSN:0956-5000    

DOI:10.1039/a703656f

出版商:RSC    

年代:1998

数据来源: RSC