摘要:

DiÜusion of electrically neutral radicals and anion radicals created by photochemical reactions Koichi Okamoto, Noboru Hirota and Masahide Terazima* Department of Chemistry, Graduate School of Science, Kyoto University, Kyoto, 606 Japan DiÜusion processes of the intermediate radicals created by the photochemical reactions of ketones in alcoholic solvents are investigated by using the transient grating (TG) method. The electrically neutral radicals and the anion radicals of acetophenone, benzaldehyde, xanthone, benzophenone and benzil were created selectively by controlling the concentration of sodium hydroxide (NaOH) in alcoholic solvents.The translational diÜusion constants (D) of the anion radicals, the neutral radicals, and the parent stable molecules can be successfully measured under the same conditions by this method. It is found that both the neutral and anion radicals diÜuse slower than the parent molecules. Values of D of the anion radicals, the neutral radicals and the parent molecules are compared in detail in wide ranges of solvent viscosities, solute sizes and temperatures.Under any conditions, D values of the charged radicals are similar to those of the neutral radicals. A possible origin of such a similarity is discussed in term of the intermolecular charge polarizabilities of the radicals. 1 Introduction DiÜusion constants (D) have been measured by several methods and analyzed based on various theories.1 Values of D are often described by the equation derived from the hydrodynamic theory such as the Stokes»Einstein (SE) equation or many other empirical modi–cations of the SE equation.2 Experimentally determined D values for molecules without any intermolecular interaction can be reproduced reasonably well based on these equations.Interesting cases arise when intermolecular interaction plays an important role in the dynamics. The translational diÜusion process of molecules is sensitive to the environment around the solute molecule, and information of the intermolecular interaction, the solvation structure and the existence of microscopic aggregation, etc., may be extracted from the studies of the diÜusion process.For example, there are three interesting cases for diÜusing species ; ionic molecules (atoms), hydrogen bonded systems, and transient radicals. Mobilities (k) or conductivities (j) of ions have been measured by several methods to elucidate solvation structures and charge eÜects on mobilities.1,3 The mobilities of ions can be transformed to the diÜusion constants by the Nernst relationship.1,3 Generally, D values of ions are smaller than those of neutral molecules of similar sizes in the same solvent and at the same temperature.3 This is due to the strong intermolecular interaction between the charge of ions and solvent molecules by Coulombic forces.With decreasing molecular size, this eÜect becomes stronger and the diÜerence between the D values of ions and stable molecules will increase. Two models are well known to interpret this size dependence of ionic mobilities. One is the excess size model,4 which is based on an increase of the molecular radius by the solvation structure of ions.The other is the dielectric friction model5 which is based on a friction which arises when the polarization of solvents follows the movement of the charges of ions. Both of two models can explain the size dependence of the D of the ion qualitatively.Boyd,6 Zwanzig7 and Hubbard»Onsager8 proposed equations to estimate the contribution of the dielectric friction by the continuous —uid theory. These equations can reproduce the experimental D values qualitatively, but not quantitatively. Recently, Bagchi and co-workers succeeded in reproducing the experimental D values quantitatively by a theory based on the dielectric friction. 9 The in—uence of the solute»solvent interaction through hydrogen bonding was reported recently by Chan and Chan,10 and Tominaga et al.11 They reported that the hydrogen bonding between the OH or group of a solute mol- NH2 ecule and polar solvents makes the diÜusion process very slow.Naturally, this eÜect was not observed in non-polar solvents. Radicals are another interesting system for diÜusion studies as well as for elucidating the mechanism12 and dynamics13 of chemical reactions. Unfortunately, until recently, only a few D values of radicals have been reported14 because of the technical difficulty.However, recently, we succeeded in measuring the D values of many intermediate radicals which appear during photochemical reactions by the transient grating (TG) method.15h18 It was found that the transient neutral radicals created by photoinduced hydrogen abstraction reactions of ketones, quinones and N-heteroaromatic molecules diÜuse much slower than their parent molecules.15h18 We further investigated the viscosity (g) dependence,16 the solute radius (r) dependence17 and the temperature (T ) dependence18 of the D values of such radicals.The diÜerences in D between the radicals and the parent molecules become larger with increasing g, 1/r or 1/T . These tendencies are similar to those of ions.3 We could reproduce such dependences by using the excess size model with a volume increase of 5»8]102 ”3.18 This apparent volume expansion was interpreted in that the radicals interact with surrounding molecules strongly.This model is similar to that used for D of ions. However, since these electrically neutral radicals do not have charges, the source of the radical»solvent interaction is not immediately clear. Considering that not all of the radicals diÜuse more slowly than closed shell molecules [e.g. benzyl radicals,19 2,2, 5,5-tetramethyl-1-piperidinyloxy (TEMPO) or some other stable radicals20], we cannot attribute the origin of the radical»solvent interaction to only the presence of the unpaired electron.Since the slow diÜusion of radicals was observed not only in polar solvents but also in non-polar solvents and in aprotic solvents,16 hydrogen bonding between the OH or NH group of the radical and the solvents cannot be the origin of the slow diÜusion. Therefore, contrary to ions or hydrogen bonding systems, the origin of the slow diÜusion remains unclear. A natural extension of this research is the study of the diÜusion of ion radicals, which have an unpaired electron and a J.Chem. Soc., Faraday T rans., 1998, 94(2), 185»194 185charge. In this case, since the motion of the radicals can be detected as electronic current, experimental measurement is easier. Indeed, the mobilities of the photochemically produced intermediate radical cations and anions probed by the time of —ight (TOF) technique have been reported by Houser and Jarnagin, 21 Freeman and co-workers,22 and Albrecht and coworkers. 23 They found that D of the ion radicals are smaller than those of neutral molecules of similar shapes and sizes. Freeman and co-workers attributed the origin of the slow diffusion to the electrostrictive drag by the charged species and dimerization for some compounds.22 Albrecht and co-workers found that D of the charged radicals can be well reproduced by the SE equation.23 This result, in good agreement with the SE relation, is similar to that found for the neutral radicals we have studied. However, even if one wishes to extract the eÜect of the charge or the unpaired electron by comparison of D of the charged radicals determined by this method with those of closed shell molecules, one has to use D of closed shell molecules measured by other methods under diÜerent conditions.Because D is very sensitive to environment and experimental conditions, accurate comparisons are very difficult. However, if we use the TG method, D values of stable molecules can be measured simultaneously with those of the transient species.For example, Terazima et al. have determined D of a cation radical and its parent molecule, N,N,N@,N@-tetramethyl-pphenylenediamine (TMPD), by the TG method under exactly the same conditions.24 The result showed that the TMPD cation radical diÜuses only half as quickly as the TMPD parent molecule in ethanol. However, the contribution of the charge and the unpaired electron could not be separated from this measurement.It would be very useful, if D values of closed shell molecules, neutral radicals, and ion radicals of similar shapes and sizes can be measured under the same condition. In this work, we performed TG experiments along this line. Values of D of parent molecules, neutral radicals and anion radicals of ketones are determined by the TG method under the same conditions and compared. To create the neutral radicals, we employed hydrogen abstraction reactions. Charged radicals can be created from the neutral radicals by subsequent reactions.For example, the photochemical process of acetophenone (AP) is described in Scheme 1.25 The lowest excited triplet state of AP is created by the (T1) intersystem crossing from the lowest excited singlet state (S1) by UV irradiation within an excitation laser pulse width (ca. 10 ns). The neutral radical is created from the state of AP T1 by hydrogen abstraction (process b). The neutral radical and the anion radical are in equilibrium (process c).Therefore, one can create the anion radical or the neutral radical selectively by controlling the pH (pOH) of the solution. In aqueous solution such selective creation of the AP anion radical has been reported and the was determined to be 9.9.26 Here we pKa create the anion radicals or the neutral radicals of acetophenone, benzaldehyde, xanthone, benzophenone and benzil in Scheme 1 alcoholic solvents by controlling the concentration of sodium hydroxide (NaOH).Values of D of the anion radicals, the neutral ketyl radical and the parent stable molecules are measured under the same conditions and compared. The role of the charge and unpaired electron in diÜusion is discussed on the basis of the obtained results. 2 Experimental The experimental arrangement for the TG technique has been described elsewhere in detail.15h20,24,27 Brie—y, an excitation laser pulse from an excimer laser [XeCl (308 nm); Lumonics Hyper-400] was split into two beams and crossed inside a 10 mm path quartz sample cell.The laser power at the crossing point was measured by a pyroelectric joulemeter (Molectron J3-09) and was typically ca. 0.3 mJ cm~2. Solute molecules in the cell were excited by the interference pattern between these beams (optical grating). The excited molecules release the heat by non-radiative relaxation and the temperature of the sample is modulated (thermal grating). A part of the excited molecules react and the concentrations of the reactant and product was also modulated, giving rise to the species grating.The thermal grating and the species grating disappear by heat conduction and mass diÜusion, respectively. Therefore, these processes can be measured from the time pro–le of the light intensity of the diÜracted probe beam (TG signal). The TG signal was detected by a photomultiplier tube (Hamamatsu R-928) after isolation with a pinhole and a glass –lter (Toshiba R-62) and recorded with a digital oscilloscope (Tektronix 2430A). The time pro–le of the TG signal was analyzed with a microcomputer.The signal was averaged by a digital oscilloscope and a microcomputer to improve the S/N ratio. The fringe spacing K was roughly estimated from the crossing angle h and then calibrated from the decay of the thermal grating signal of a benzene solution containing a trace of Methyl Red.28 The temperature of the sample solution was controlled by —owing temperature-regulated methanol around a cell holder with a temperature control system (Lauda RSD6D).For the transient absorption (TA) measurement, the sample was excited by the excimer laser (ca. 5 mJ cm~2) and probed by a 100 W Xe lamp. The probe light was monochromated with a Spex model 1704 monochromater and detected by the photomultiplier. Spectroscopic grade solvents (methanol, ethanol, propan-2- ol, butan-1-ol and pentan-1-ol) and solute (acetophenone, benzaldehyde, xanthone, benzophenone and benzil) were purchased from Nacalai Tesque and used without further puri–- cation.Typical concentrations of the solutes were ca. 10~2 M. Sample solutions were deoxygenated by the nitrogen bubbling method and —owed by a peristaltic pump (Atto SJ-1211) to avoid the eÜect of reaction products in the signal. The van der Waals volumes of the molecules were Vw obtained from the atomic increments method given by Edward.29 The radii of the molecules, r, were calculated from using the relation Vw r\(3V w/4p)1@3. 3 Results 3.1 Assignment of the TG signal The time pro–le of the TG signal after the photoexcitation of AP in ethanol is shown in Fig. 1(a). The time pro–le of the root square of the TG signal can be –tted well with [ITG(t)1@2] a sum of three exponential functions. ITG(t)1@2\a1 exp([k1t)]a2 exp([k2 t)[a3 exp([k3 t) (1) where, are the decay constants and k1[k2[k3 a1[a3[ are the pre-exponential factors. The solid line in Fig.a2[0 1(a) is the line –tted by using the non-linear least-squares 186 J. Chem. Soc., Faraday T rans., 1998, V ol. 94Fig. 1 (a) Time pro–le of the TG signal after the photoexcitation of AP in ethanol at 20 °C (dotted line) and best –tted curve (solid line) by eqn. (1). (b) Three components for the –tting in (a) are shown separately. The assignments of these components are : 1, thermal grating ; 2 and 3, species grating of AP and that of the neutral ketyl radical of AP, respectively.method with eqn. (1) and the pro–les of the three components are shown in Fig. 1(b). The method for assignment of each exponential component of the TG signal to its origin has been described previously in detail.15,20,24,27 The TG signal intensity is proportional to a sum of the square of the refractive index change and the absorbance change induced by the optical grating.30 In this reaction system, absorption bands of any species are on the far blue side from the probe wavelength (633 nm).26,31 Thus, the TG intensity is proportional to only the square of the refractive index change.The thermal eÜect (thermal grating) and the creation or depletion of chemical species (species grating) can contribute to the refractive index change. The time pro–les of the signals due to the thermal grating and the species grating are given by solving Fourierœs thermal diÜusion equation and Fickœs reaction»diÜusion equation, respectively.15 Since in the observation time range of the TG signal, the creation and termination reaction of the radicals can be neglected as shown later, the time dependence of the TG signal is given by15h20,24 ITG(t)1@2\dnth 0 exp([Dth q2t) [;P dnP0 exp([DP q2t)];R dnR 0 exp([DR q2t) (2) where, q is the grating vector [q\2p/K, (K; fringe length)], the –rst term of eqn.(2) represents the thermal grating and is the initial refractive index change just after the excita- dnth 0 tion.and are the initial refractive index changes by dnP° dnR 0 the species grating of the parent molecules and the radicals, respectively. is the thermal diÜusion coefficient of the Dth solvent and are the diÜusion constants of the parent DP , DR molecules and the radicals, respectively. Generally, as the refractive index decreases with increasing temperature, is negative. Because the heat conduction dnth 0 process is a faster process than the mass diÜusion process, Dth is about 100 times larger than or Therefore, com- DP DR .ponent 1 in the TG signal obtained [Fig. 1(b)] is assigned to thermal grating. Comparing eqn. (2) with eqn. (1), is given Dth by q2. The obtained value is close to the literature k1\Dth values.32 As both the parent molecules and the radicals in this system have absorption bands at shorter wavelengths than that of the probe beam, both and are expected to be positive dnP0 dnR 0 from Kramers»Kronig relationship. Therefore, the sign of the parent molecule component is negative, which is the same as the sign of the thermal grating term.On the basis of this reasoning, component 2 in the TG signal [Fig. 1(b)] is assigned to the signal from the parent molecule. On the other hand, the radicalœs contribution in the TG signal should be positive. Component 3 in Fig. 1(b) should be due to the radical. It has been reported that the electrically neutral radical is created by photoexcitation of AP in a pure alcoholic solvent.17 In this reaction system, four chemical species (AP, AP ketyl radical, ethanol, hydroxyethyl radical) could contribute to the signal.However, since the absorption coefficient of ethanol and hydroxyethyl radical are smaller than those of AP and the ketyl radical, the TG signal due to ethanol and the hydroxyethyl radical could not be detected. Therefore, we assign component 2 to the species grating of AP and component 3 to that of the AP ketyl radical. Then, and are the diÜusion DP DR constants of AP and the AP ketyl radical, respectively.Next, we performed a similar measurement for AP in ethanol which contains sodium hydroxide. Fig. 2(a) shows the time pro–le of the TG signal of AP»ethanol]0.01 M NaOH. The shape of this signal is slightly diÜerent from that given in Fig. 1(a). This time pro–le can also be –tted by eqn. (1) very well [solid line in Fig. 2(a)]. The three exponential components are shown in Fig. 2(b). Comparing Fig. 2(b) with Fig. 1(b), we –nd that the intensity of component 3 is enhanced relative to the other components. The enhancement suggests that the transient in pure ethanol is diÜerent from that in ethanol]NaOH. In an aqueous solution, it was reported that the anion radical is created in an alkaline solution, while the electrically neutral radical is created in pure water.26 In the next section, we use the transient absorption technique to identify the intermediates in ethanol and ethanol]NaOH.Fig. 2 (a) Time pro–le of the TG signal after the photoexcitation of AP in ethanol]0.01 M NaOH (dotted line) and best –tted curve (solid line) by eqn. (1). (b) Three components for the –tting in (a) are shown separately. The assignments of these components are : 1, thermal grating ; 2 and 3, species grating of AP and that of the anion ketyl radical of AP, respectively. J. Chem. Soc., Faraday T rans., 1998, V ol. 94 1873.2 Transient absorption measurements We examine the intermediates created in pure ethanol and ethanol]NaOH by the transient absorption (TA) method.Fig. 3(a) shows the TA spectra with a 10 ls time delay after excitation in pure water and in NaOH]water. The observed TA spectrum in pure water [–lled circles in Fig. 3(a)] is assigned to the AP neutral radical [reported TA spectrum26 is shown by the solid line in Fig. 3(a)]. Upon adding NaOH to that solution, the TA spectrum changes and it becomes similar to the reported spectrum of the AP anion radical [dotted line in Fig. 3(a)].26 Hayon et al. have reported values of AP, pKa benzophenone and benzil as 9.9, 9.25 and 5.5, respectively.26 The TA spectra observed in pure ethanol and NaOH]ethanol are shown in Fig. 3(b). The TA spectrum in pure ethanol [–lled circles in Fig. 3(b)] is close to the reported spectrum of the AP neutral radical in ethanol (solid line).31 The TA spectrum in AP»NaOH]ethanol [open squares in Fig. 3(b)] is similar to the spectrum of the AP anion radical in water26 [dotted line in Fig. 3(a), (b)]. Therefore, we assigned this spectrum to the AP anion radical. Based on these observations, we conclude that the electrically neutral radicals and the anion radicals can be created selectively by controlling the concentration of NaOH in alcoholic solvents. Fig. 4 shows the intensities of the TA signals at 450 nm and the intensities of the TG signals at various concentrations of NaOH in ethanol. Both of the intensities steeply change at pOH4[log [NaOH]\3»4.Under dilute conditions (NaOH\ca. 10~4 M), the neutral radical is created. If the concentration of NaOH is [ca. 10~3 M, the anion radical is dominant in ethanol. Since the spectra do not depend on the monitoring time (10 ls to a few ms), the neutral radical and the anion radical of AP are in equilibrium within 10 ls after the creation (Scheme 1) in water and in ethanol. The value of this equilibrium is in ethanol pKb pKb\3»4 in water26). According to this result, (pKb\14[9.9\4.1 component 3 in the TG signal in pure ethanol [Fig. 1(b)] is assigned to the AP neutral radical and that in ethanol]0.01 M NaOH [Fig. 2(b)] to the AP anion radical. The created radicals are relatively stable and their TA signals are observable for tens of milliseconds after excitation Fig. 3 (a) Transient absorption spectra at a 10 ls time delay after the excitation of AP in water and AP in water]0.01 M NaOH (Ö) (K). (b) Transient absorption spectra of AP in pure ethanol and AP in (Ö) ethanol]0.01 M NaOH Spectra of the neutral radical of AP (K).(solid line) and the anion radical of AP (dotted line) from ref. 26 (in water), 31 (in ethanol) are shown in both –gures for comparison. Fig. 4 Plot of the signal intensity of the transient absorption at 450 nm (top) and that of the transient grating (bottom) at a 100 ls delay after the excitation against the concentration of NaOH in AP» ethanol]NaOH (1»5 mJ cm~2). The TA signals show second-order decay which should be due to the self-termination reaction of the radicals.26,33 Under a weak excitation laser power for the TG measurement (ca. 0.3 mJ cm~2), the intensities of the TA signals are almost constant and the shapes of the TA spectra do not change within the time range for the TG measurement (a few milliseconds). Therefore, it is evident that the created radicals do not react with the solvent or the parent molecules, and the time pro–le of the TG signal (Fig. 1 and 2) can be analyzed simply by the diÜusion process of each species. 3.3 Comparison of values of D for neutral radicals with anion radicals The decay rate constants obtained by the –tting of the k2 , k3 TG signals at various fringe spacings are plotted vs. the square of the grating vector q in Fig. 5. Based on the assignment given above and from eqn. (1) and (2), the following relationships are obtained. k2\DP q2 (3a) k3\DR q2 (3b) The TG signal decays not only by the diÜusion process but also by any reaction processes.In this case, the decay rate of the TG signal is accelerated by the reaction, and more detailed consideration is necessary for the analysis as we have reported for the benzyl radical case.19 However, the linear relationship between the decay rate constants and q2 with small intercepts with the ordinate (Fig. 5) and also the slow radical decays measured by the TA method ensure that D can be determined from the slope of the plot.The values obtained for D of the parent molecule, the neutral radical and the anion radical in ethanol are listed in Table 1. The value of D for AP in ethanol is the same as that in ethanol]NaOH within experimental error. This suggests that the eÜect of addition of 0.01 M NaOH on diÜusion is negligibly small. The main source of the experimental error comes from the –tting error of the double-exponential function and the fact that the D values of the parent molecules have large errors.34 Recently, Donkers and Leaist have reported D of AP by using the Tayler dispersion (TD) method as 1.24]10~9 and 188 J.Chem. Soc., Faraday T rans., 1998, V ol. 94Fig. 5 Relationship between the decay rate constants (k) of each component of the TG signal and q2. denote the parent molecule Ö, L (AP), the neutral radical of AP in ethanol, respectively. denote =, K the parent molecule (AP), and the anion radical of AP in ethanol]0.01 M NaOH, respectively. 0.76]10~9 m2 s~1 in ethanol and propan-2-ol, respectively. 35 Our values from the TG method are close to their values from the TD method with relative errors of 10 and 17% in ethanol and propan-2-ol, respectively. The solvent viscosity depends on the concentration of electrolytes. In diluted solution (\1 M), the Jones»Dole equation describes the concentration dependence of the viscosity well.36 g/g0\1]AC1@2]BC (4) where g and g0 are the viscosities of the electrolytes solution and the pure solvent, respectively.Parameter A expresses the ion»ion interaction and is zero when the solvent is neutral ; C is the concentration (M) of the solute while B is the coefficient of the solvent viscosity, which indicates the ion»solvent interaction. Values of B for Na` and OH~ have been reported as 0.086 and 0.112 dm3 mol~1, respectively, in water.37 Generally, B depends mainly on the ion volume and does not change much with variation of solvent.38 We estimated the viscosity change of the solution by the addition of NaOH from eqn.(4). Using B data in water, we obtained g/g0\1.002 at 0.01 M NaOH. Since, roughly, D is inversely proportional to the viscosity, this small change of the viscosity is within the experimental error of this work. Therefore, the viscosity change upon the addition of NaOH (0.01 M) is negligible and D of the neutral radical and the anion radical can be compared directly. Both D of the neutral radical and anion radical of AP are smaller than that of the parent molecule.Previously, the reduction of D of neutral radicals relative to the parent molecules was explained in terms of intermolecular interactions between the radicals and the solvent molecules. In this case, we suspect that the intermolecular interactions between both the neutral and anion radical and the solvent molecules are similarly strong. Before this study, we expected the values of D of anion radicals to be smaller than those of neutral radicals because the anion radical has both charge and an unpaired electron, both of which can aÜect the diÜusion process.However, this is not the case, although a slight diÜerence between D of neutral radicals and the anion radicals is just detectable beyond experimental error (Table 1). This slight difference may be due to the contribution of the charge to the diÜusion process or possible ion pair formation between the anion and sodium cation. However, previous EPR studies showed that the ion pairs of ketyls tend to dissociate in alcohol.39 Another possibility is that the anion radicals are associatively active and form dimers.40 In this case, D of the anion radical dimer is expected to be ca. 1.25(\21@3) times larger than that of monomer,23a since D is inversely proportional to the radius of the solute. It is interesting that this charge eÜect on D of the anion radical is much smaller compared with the reported charge eÜect on D of the ions of similar sizes.1,3 The charge eÜect on diÜusion in the anion radical may be reduced by some factors.This phenomenon could be related to the origin of the anomalously slow diÜusion of radicals. In later sections, we discuss the solvent viscosity, solute size and temperature dependence of D of neutral and anion radicals to clarify this behavior. 3.4 Solvent viscosity, solute size and temperature dependence of D Contrary to our initial expectation, the diÜusion of the AP anion radical is similar to that of the neutral radical.In order to examine further the cause of the eÜects of the charge and unpaired electron on the diÜusion process, we investigate D under various conditions. According to the SE equation, D is proportional to temperature (T ) and inversely proportional to the viscosity of solvent (g) and radius of solute (r). Dependences of D of these species on solvent viscosity, solute size and temperature are discussed below. In order to monitor the eÜect of viscosity, we measured the TG signal of AP in methanol, propan-2-ol, butan-1-ol and pentan-1-ol.The time pro–les of the TG signals in various solvents are similar to that in ethanol and D can be determined by the same method as before. Values of D of the parent molecules, the neutral radicals and the anion radicals in these solvents are listed in Table 1 and plotted vs. g~1 in Fig. 6. To monitor the eÜect of molecular size, benzaldehyde, xanthone, benzophenone and benzil were studied with their neutral radicals and anion radicals being created by the same method as for AP.The time pro–les of the TG signals of such solutes are quite similar to that of AP in both pure ethanol and ethanol]0.01 M NaOH. The obtained D values of these species are listed in Table 2 and plotted vs. 1/r in Fig. 7. Values of D of the parent molecules are close to the literature values [(1.39, 0.90 and 0.95)]10~9 m2 s~1 for benzaldehyde, xanthone and benzophenone, respectively] within ^15%.35 From Fig. 6 and 7, it is evident that the D values of the anion Table 1 DiÜusion constants (D/10~9 m2 s~1) of acetophenone (AP), the neutral radical of AP in alcoholic solvents and the anion radical of AP in alcohols]0.01 M NaOH obtained by the TG method at 20 °C D in pure solvent D in solvent]0.01 M NaOH solvent AP neutral radical AP anion radical ethanol 1.36^0.11 0.58^0.01 1.37^0.10 0.52^0.03 methanol 1.78^0.05 1.25^0.04 1.91^0.12 1.15^0.02 propan-2-ol 0.89^0.03 0.33^0.01 0.89^0.05 0.28^0.02 butan-1-ol 0.77^0.08 0.26^0.01 0.80^0.20 0.19^0.03 pentan-1-ol 0.66^0.09 0.19^0.01 0.63^0.06 0.14^0.05 J.Chem. Soc., Faraday T rans., 1998, V ol. 94 189Fig. 6 Viscosity dependence of D of AP in alcohols the neutral (Ö), radical of AP in alcohols AP in alcohol]0.01 M NaOH the (L), (=), anion radical of AP in alcohol]0.01 M NaOH Solvents are 1, (K). pentan-1-ol ; 2, tert-butan-1-ol ; 3, propan-2-ol; 4, ethanol and 5, methanol. Solid line and dotted line are D calculated from eqn.(7) and (8), respectively. radicals of all solutes in all solvents in this work are close to those of the neutral radicals. Therefore the reduction of the charge eÜect on D seems to be general for the intermediate ketyl radicals created by the hydrogen abstraction reaction. We compare the experimental D values of these species with theoretical calculations where D is described by the Stokes law1 D\kB T /f (6) where f is the friction of the solute molecules in the solvent.Fig. 7 The solute size dependence of D of parent molecules in ethanol neutral radicals in ethanol AP in alcohol]0.01 M (Ö), (L), NaOH the anion radical of AP in alcohol]0.01 M NaOH (=), (K). Solute ketones are 1, benzil ; 2, benzophenone; 3, xanthone; 4, acetophenone and 5, benzaldehyde. Solid line and dotted line are D calculated from eqn. (7) and (8), respectively. Fig. 8 The temperature dependence of D of AP in ethanol the (Ö), neutral radical in ethanol AP in ethanol]0.01 M NaOH the (L), (=), anion radical in ethanol]0.01 M NaOH Solid line and dotted (K).line are D calculated from eqn. (7) and (8), respectively. Einstein estimated f by assuming the solvent to be a continuous —uid.1 fSE\apgr (7) Eqn. (6) and (7) are well known as the Stokes»Einstein (SE) formula, which gives one of the most fundamental equations for D. Constant a in eqn. (7) indicates the boundary condition of the friction between the solute and solvent.For the stick boundary condition, a\6, and for the slip boundary condition, a\4. The calculated D of the SE equation gener- (DSE) ally reproduce experimental D well when the sizes of solute molecules are sufficiency large. However, if the volume of a solute molecule is small or close to the solvent volume, DSE underestimates the experimentally observed D because the continuous —uid approximation for the solvent is no longer valid. Some modi–cations of the SE equation have been proposed. 2 Evans and co-workers proposed an empirical equation, which is given by41 fEV\ g(c@rA`d) kB exp(a/rA]b) (8) where a, b, c and d are constants, which were determined by Evans and co-workers as a\5.973 b\[7.3401, ”, c\[0.863 65 and d\1.0741.42 In a series of our previous ” studies, we have shown that the calculated D values from this equation agree very well with the D values of the parent (DEV) molecules.18,19 On the other hand, the D values of radicals are closer to under the stick condition.15h18 Fig. 6 and 7 DSE show plots of and (stick boundary). As can be seen, D DEV DSE values of the parent molecules are close to and D of both DEV the neutral and anion radicals are close to It is inter- DSE . esting that the experimental data indicate that the diÜerence in D between the parent molecules and the anion radicals increases with increasing g and/or decreasing r. This tendency is what we observed before in neutral radicals.Table 2 Size dependence of the diÜusion constants (D/10~9 m2 s~1) of the parent molecules, the neutral radicals and the anion radicals in ethanol and ethanol]0.01 M NaOH D in ethanol D in ethanol]0.01 M NaOH solute parent molecule neutral radical parent molecule anion radical benzaldehyde 1.60^0.05 0.58^0.01 1.52^0.02 0.48^0.02 xanthone 0.90^0.05 0.50^0.01 0.87^0.04 0.46^0.01 benzophenone 0.80^0.05 0.49^0.03 0.80^0.10 0.43^0.02 benzil 0.77^0.05 0.50^0.03 0.70^0.10 0.45^0.01 190 J.Chem. Soc., Faraday T rans., 1998, V ol. 94Table 3 Activation energy for diÜusion and the pre-exponential (ED) factor of AP, the neutral radical and (D0) [D\D0 exp ([ED/kBT )] the anion radical obtained by the Arrhenius plot of D (Fig. 8) in ethanol and ethanol]0.01 M NaOH D0/10~7 m2 s~1 ED a/kcal mol~1 parent molecule in ethanol 2.0^0.1 2.97^0.04 in ethanol]0.01 M NaOH 1.7^0.2 2.88^0.05 neutral radical in ethanol 2.3^0.2 3.52^0.06 anion radical in ethanol]0.01 M NaOH 1.9^0.1 3.56^0.03 a 1 cal\4.184 J.The temperature dependence of D in pure ethanol and ethanol]NaOH between 50 and [50 °C is shown in Fig. 8. The temperature dependence of D in various solutions can generally be expressed by the following Arrhenius-type equation. 1 D\D0 exp([ED/kB T ) (9) where is the diÜusion activation energy and is the pre- ED D0 exponential factor. The log D vs. 1/T plots of Fig. 7 indicate that an Arrhenius-type relation holds for this system.Determined and values are listed in Table 3. It is of note that, ED D0 although D of the parent molecules and neutral (or anion) radicals are very diÜerent, of these species are very similar. D0 On the other hand, of both types of radical are larger than ED those of the parent molecules. This behavior can be again reproduced by calculation from eqn. (7) and (8), both qualitatively and quantitatively (Fig. 8). Again this is similar to the case of the neutral radicals reported before.18 In that paper, we explained the temperature dependence by the excess size model.The activation energy of the anion radical is almost the same as that of the neutral radical. The charge in the radical does not change the activation energy of diÜusion. We consider a possible origin of this fact below. 4 Discussion 4.1 Comparison of D between ionic radicals and stable ions In the previous section, we compared D of charged radicals with those of neutral radicals. This comparison will provide information of the charge eÜect on the radicals.In order to discuss the charge eÜect on the radicals and also that on the closed shell molecules, D of stable ions are compared with those of the closed shell molecules. A large number of studies have been made on the diÜusion process of metal ions.1 As the metal ions become small, the eÜect of the Coulombic force becomes remarkably large and values of D of metal ions become much smaller than This eÜect has been explained DSE .by the formation of a complex with a large number of solvent molecules.4 Since the sizes of the metal ions are too small for the hydrodynamic theory based on the continuous —uid model, it would not be appropriate to use such data for comparison with our samples. Values of D of larger non-metallic ions have been measured by the ionic conductance method for some tetraalkylammonium ions and the values are compared with values of D of some tetraalkyltins by the Trylor dispersion technique.3 The results show that the ionic mobility is slower than that of non-ionic molecules and such diÜerences were analyzed by the dielectric friction model.The eÜect of the dielectric friction is given by f\f0]R/r3 (11) where is the hydrodynamic friction and the R/r3 term is the f0 dielectric friction. Generally, is calculated from the Ein- f0 steinœs formula [eqn. (7)]. According to the theory by Zwanzig, R is given by7 RZ\ Ae2(e0[e=)qD e0(2e0]e=) (12) Based on the Hubbard»Onsager (HO) theory, R is written as8 RHO\ Ae2(e0[e=)qD e0 2 (13) where, and are the static and optical dielectric constants, e0 e= respectively, e is the charge of the proton and is Debyeœs qD relaxation time.Constant A has a value of 3/8 for the stick boundary condition and 3/4 for the slip boundary condition of eqn. (12), 17/280 for the stick boundary condition and 1/15 for the slip boundary condition of eqn. (13). Evans and co-workers3 experimentally determined R of some tetraalkylammonium ions in several solvents by comparison of D of non-ionic molecules. The experimentally obtained values of D of the ionic molecules studied by Evans and co-workers3 are plotted vs. 1/r and 1/g in Fig. 9 along with our data. Both and calculated from eqn. (7) and DSE DEV (8) are plotted. It is evident from the –gures that values of D of the ions are close to under the stick condition, similarly to DSE Fig. 9 The reported D of the tetraalkyltins and D calculated (>) from the reported j of the tetraalkylammonium ions from ref. 3 (|) with our data.(a) The solvent viscosity dependence of D of Me4Sn, (radii are 3.06 and 2.84 respectively) in 1, butan-1-ol ; 2, Me4N` ”, propan-2-ol; 3, ethanol; 4, methanol; 5, acetonitrile and 6, acetone. (b) The solute size dependence of D of the stable molecules 1, 2, Bu4Sn; 3, 4, and the ions 5, 6, 7, Et4Sn; Me4Sn; CCl4 Bu4N`; Pr4 N`; 8, in ethanol. The curved solid line, straight solid line, Et4N`; Mt4 N` dotted line, and broken line are D calculated by eqn.(8), the SE equation [eqn. (7)], the excess volume model [eqn. (14)], and the dielectric model corrected by the Hubbard»Onsager equation (ref. 43), respectively. J. Chem. Soc., Faraday T rans., 1998, V ol. 94 191radicals. This agreement indicates that the diÜusion of the stable ions is expressed by the stick boundary condition of the hydrodynamic model rather than the dielectric model.(The agreement of D of the non-ionic molecule with is expected DEV since eqn. (8) was empirically determined from these data.) 4.2 Models for slow diÜusion For a detailed comparison of D values of neutral radicals, anion radicals and stable ions, the size dependence of diÜusion of the three types of species are plotted in Fig. 9(b). Although [straight solid line in Fig. 9(b)] reproduce D of three DSE species, some diÜerences are notable; D decreases in the order: stable ions, neutral radicals, anion radicals.We have explained the diÜusion process of the neutral radicals based on the excess volume model.17,18 In this model, the equation derived by Evans and co-workers41,42 was modi- –ed as if the molecular volume of the radical was expanded. An equation from this model is given by18 fV\kB~1 expC [a (r3]3V0/4p)1@3 [bDg@*c@(r3`3V0@4p)1@3+`d@ (14) where is the apparent excess volume of the radical. In a V0 series of investigations on radical diÜusion, we have succeeded in reproducing the size, viscosity and temperature dependences of D of the radical by this model with V0\5»8]102 Although values of D calculated from this model are ”3.(DV) close to the size dependence of the diÜusion activation DSE , energies of radicals agrees better with the calculation based on this model rather than on the SE equation.18 Values of DSE are proportional to 1/r [straight line in Fig. 9(b)] while the slope of on 1/r is gentler [dotted line in Fig. 9(b)]. Values DV of are close to D of the neutral and anion radicals but DV those of the stable ions are slightly larger than DV . Felderhof showed that the HO theory for ionic mobility needs to be corrected and performed more careful numerical studies based on dielectric friction theory.43 In a similar manner, Ibuki and Nakahara tested the dielectric friction theory for ion mobility in polar solvents. They found that the HO theory is better than the Zwanzig theory to describe D of an ionic species and proposed an approximate HO equation. 44 We calculated values of D from their approximated equation and compared them with the experimental D values. However, the calculated D values are very diÜerent from the experimental values. For example, D for in ethanol is Et4N` 0.72]10~9 m2 s~1, while the calculated D is 0.47]10~9 m2 s~1. A similar result has been reported by Terazima et al. for the TMPD cation radical.24 The disagreement is expected because Ibuki and Nakahara used the Einstein equation [eqn.(6)] for in eqn. (11), yet cannot reproduce the experi- f0 DSE mental D values. In order to improve we used [eqn. (8)] f0 , fEV instead of The calculated values by the corrected HO fSE . equations with the slip boundary constants are plotted (DHO) in Fig. 9 (broken line) and compared with the experimental D values of these species. We –nd that reproduce D of the DHO stable ions well rather than those of the radicals in region of r~1\0.3 From Fig. 9, it is evident that increases ”~1. DHO exponentially with 1/r. This deviation becomes larger with increasing 1/r of ions. In this region, the corrected HO equations can no longer reproduce the experimental D, therefore, in a wide range of 1/r, the experimental D values are better reproduced by rather than DSE DHO . 4.3 Intermolecular interactions of neutral and anion radicals One of main interesting –ndings in this research is that D values of neutral radicals are quite close to those of the anion radicals and ions.This fact indicates that the friction of the neutral radicals (whatever its origin), and the dielectric friction of ions are not additive. It is interesting that D values of ions, neutral radicals and ionic radicals are close to under the DSE stick boundary condition under a variety of conditions of solvent, temperature and molecular size (although slight diÜerences are apparent). This fact may suggest that at the stick DSE boundary condition could be the lowest limit of D.If the boundary condition is already completely stick-like for the neutral radicals and ions, the condition cannot be ìmore sticklike œ even if a charge is attached to the neutral radical or if an unpaired electron is attached to the ion. Another possible explanation for the similar D values of neutral and ionic radicals may be related to the origin of the slow diÜusion of the neutral radicals. We will come back to this point later in this section.What is the origin of the slow diÜusion of the neutral radicals ? To answer this the fact that D of the neutral radicals and that of the stable ions are very similar over wide ranges of viscosities and molecular sizes (Fig. 9) may be a clue. It suggests that the solute»solvent intermolecular interaction of ions and neutral radicals could be similar, more speci–cally, similar to the electrostatic interaction. Of course, neutral radicals have no overall charge, but if the charge densities of the radicals are polarized signi–cantly and/or the radicals have large dipole moments, they can interact with the solvent molecules by electrostatic interaction.This eÜect may be the origin of the slow diÜusion of the radicals. Nee and Zwanzig proposed a theory of the dielectric friction for a dipolar molecule,45 and subsequently, many theories have been proposed to account for the dielectric friction to the rotation of polar solutes in polar solvents46 or reorientation of polar solute molecules interacting with polar solvents.47 No theory to explain the dielectric friction eÜect of a polar solute to the translational diÜusion have been reported.However, by analogy with the rotation process, it is natural to consider that the diÜusion process of the polar solute should be in—uenced by the dielectric friction. In fact from the dynamic Stokes shift measurement, Maroncelli and co-workers concluded that, even in non-polar solvents, the dielectric friction can be notable by the interaction with the quadrupole moment of the solvent.48 Moreover, Okazaki et al.found that a merocyanine form of a benzospiropyran, which has a large dipole moment (ca. 12 D§) diÜuses slower than the noncharge- separated spiro-form not only in ethanol but also in cyclohexane.49 These observations suggest that the dielectric friction is not so small as predicted from eqn. (12), (13), and the corrected HO equations even in non-polar solvents. If electrostatic interaction is the main origin of the slow diffusion of the radicals (such as due to dielectric friction), the radicals should be more polar than the parent molecules.We calculated and compared the polarizabilities and the dipole moments of the radicals and the parent molecules by using a semi-empirical molecular orbital (MO) calculation with modi- –ed neglect of diatomic overlap (MNDO) method.19 However, the calculated dipole moments of the ketyl radicals of AP and benzophenone (1.6, 1.4 D, respectively) are smaller than those of the parent molecules of AP and benzophenone (2.7 and 2.5 D, respectively). Furthermore, the polarizabilities of the radicals and the parent molecules are found to be similar.19 Therefore, we could not –nd any signi–cant diÜerences in the molecular orbital character between the radicals and their parent molecules by simple MO calculations.A possible explanation of the slow diÜusion of radicals was given very recently by Morita and Kato.50 They investigated electric properties of radicals created by the hydrogen abstraction reactions by ab initio MO calculations, and found that the sensitivities of the intramolecular charge polarization induced by an external electrostatic –eld are remarkably enhanced in the some radicals, though this sensitivity does not § 1DB3.335 64]10~30 C m. 192 J. Chem. Soc., Faraday T rans., 1998, V ol. 94appear in the usual polarizability calculated by the MO calculation we used.50 According to their analysis, such an enhancement is due to the r»p mixing that facilitates the deformation of the p-electron orbital of aromatic radicals.They suggested that this particular sensitivity of aromatic radicals could be the origin of the anomalous slow diÜusion of the radicals. Their theoretical suggestion seems to be consistent with our –nding that the friction of neutral radicals is similar to that of ions.Their calculations show that the charge sensitivity depends on the molecular structure. When a charge is attached to the neutral radical, the structure should be changed and the r»p mixing, which is the origin of the enhanced charge sensitivity, could diminish. In that case, only the intermolecular interaction by the electric charge (not the charge sensitivity) causes the slow diÜusion of the ionic radicals like that of stable ions. This exclusive mechanism of the slow diÜusion of neutral and ionic radicals may answer to the question as to why the eÜect of the charge and the unpaired electron is not additive. 5 Conclusion The translational diÜusion constants (D) of electrically neutral ketyl radicals, anion radicals and parent molecules were measured by the transient grating (TG) method in alcoholic solutions. The neutral radicals and the anion radicals could be created selectively by controlling the concentration of sodium hydroxide not only in aqueous solution but also in alcoholic solutions.The presence and the decay kinetics are examined by transient absorption and the time pro–le of the TG signal is interpreted in terms of the mass diÜusion of these species. It was found that both the neutral and anion radicals diÜuse more slowly than the parent molecules. Values of D of the anion radicals are compared to those of the neutral radicals for studying the eÜect of the charge and the unpaired electron on the diÜusion process. We measured the solvent viscosity dependence, the solute size dependence and the temperature dependence of D.These D values are compared with the values calculated based on the Stokes»Einstein equation (DSE) and the equation proposed by Evans and co-workers (DEV). Values of D of the parent molecules are close to while D DEV , of both types of radicals are close to D values of anion DSE , radicals are close to that of the neutral radicals over a wide range of solvent viscosity, solute size and temperatures.Comparing this result with reported D values of stable ions, we found that the diÜusion of neutral radicals, ionic radicals and ions are similar. For a more careful comparison, we calculated D values using the excess volume model based on DEV (DV) and the dielectric friction model, which is corrected by the Hubbard»Onsager equation The D values of the radical (DHO). are close to On the other hand, the D values of ions are DV . closer to than At present, we think that the slow DHO DV .diÜusion of the radicals and ions may be due to a similar origin, which may be solute»solvent electrostatic interaction. Recently, Morita and Kato reported that the sensitivities of the intramolecular charge polarization of the radicals are enhanced remarkably by an external electrostatic –eld. They proposed that such an enhancement is the origin of the anomalously slow diÜusion of radicals. Their proposal is consistent with our explanation.thank Dr A. Morita and Prof. S. Kato (Kyoto University) We for the discussion on the origin of the anomalous slow diÜusion of radicals and showing us the results of ab initio MO calculations before publication. This work is supported by Scienti–c Research Grant-in-Aid (No. 08554021) and on Priority-Area-Research ìPhotoreaction Dynamicsœ (No. 08218230) from the Ministry of Education, Science Sports and Culture of Japan. References 1 (a) E. L. Cussler, DiÜusion, Cambridge University Press, Cambridge, 1984; (b) H.J. V. Tyrrell and K. R. Harris, DiÜusion in L iquid, Butterworths, London, 1984; (c) L andolt-Bornstein T abellen, Springer, Berlin, 1961, 6 Au—., Bd. II. 2 (a) F. Perrin, J. Phys. Radium., 1931, 7, 1; (b) A. Spernol and K. Z. Wirtz, Z Naturforsch., T eil A, 1953, 8a, 352; 522; (c) E. G. Scheibel, Ind. Eng. Chem., 1954, 46, 2007; (d) C. R. Wilke and P. C. Chang, Am. Inst. Chem. Eng. J., 1995, 1, 264; (e) C. J. King, L.Hsueh and K. W. Mao, J. Chem. Eng. Data, 1965, 10, 348. 3 (a) F. D. Evans, C. Chan and B. C. Lamartine, J. Am. Chem. Soc., 1977, 28, 6492; (b) D. F. Evans, T. Tominaga and C. Chan, J. Solution Chem., 1979, 8, 461. 4 (a) H. S. Frank and W. Y. Wen, Discuss. 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ISSN:0956-5000    

DOI:10.1039/a706220f

出版商:RSC    

年代:1998

数据来源: RSC

摘要:

Laser —ash photolysis studies of some rhodamine dyes Characterisation of the lowest excited singlet state of Rhodamine 3B, Sulforhodamine B and Sulforhodamine 101 Paul C. Beaumont,* David G. Johnson and Barry J. Parsons Multidisciplinary Research and Innovation Centre, School of Science and T echnology, North East W ales Institute, Plas Coch, Mold Road, W rexham, W rexham County Borough, W ales, UK L L 11 2AW The UV»VIS absorptive and emissive properties of three laser dyes, viz Rhodamine 3B, Sulforhodamine B and Sulforhodamine 101, have been studied in ethanol.Time-resolved methods were used to study the decay of the –rst excited singlet state of each dye. The absorptive properties of the lowest excited singlet states of the dyes were generated using picosecond laser pulses. Values for the absorption coefficient for the absorption process were measured, for each dye, by both comparative and complete- Sn ^S1 depletion methods. Values for the absorption process, in ethanol, were found to be 4.6]104 (444 nm), 3.4]104 (446 S4 ^S1 nm) and 3.6]104 (458 nm) dm3 mol~1 cm~1 for Rhodamine 3B, Sulforhodamine B and Sulforhodamine 101, respectively, with the corresponding values for the absorption process being measured as 1.0]105 (556 nm), 1.2]105 (556 nm) and S3 ^S1 1.2]105 (578 nm) dm3 mol~1 cm~1.The relevance of such data in predicting lasing characteristics of dyes is discussed. The use of organic molecules as the lasing medium in dye lasers has led to the availability of a wide range of tuneable light sources thereby allowing many spectroscopic applications. 1,2 The mode of operation of a dye laser is based on the absorptive and emissive properties of the dye which is used (see ref. 3 for a comprehensive review). The principal events may be summarised as follows : (i) the dye molecule, present in the lowest vibrational level of its ground state, absorbs a photon from the pump beam thereby promoting a transition to a vibrational of an upper excited singlet state ; (ii) rapid relaxation to the lowest vibrational level of the –rst excited singlet state ; (iii) the molecule returns to the ground state by a mechanism involving the emission of —uorescence; (iv) the photon which is emitted may further stimulate light emission from other molecules.It is clear from the foregoing that a complete understanding of the photophysical properties of the ground state and lowest excited singlet state are of fundamental importance when considering why materials perform as efficient laser dyes.In this regard it is useful to consider the gain coefficient of a dye laser at a given wavelength, g(j), which may be de–ned as : g(j)\pe(j)C1[pg(j)C0[ps(j)C1[pt(j)Ct (1) where is the stimulated emission cross-section at j, pe(j) pg(j) is the ground state absorption cross-section at j, is the ps(j) absorption cross-section of the lowest excited singlet state at j, is the absorption cross-section of the lowest excited pt(j) triplet state at j, and are the molecular population C1, C0 Ct densities (molecules cm~3) of the –rst excited singlet, the ground state and the –rst excited triplet state, respectively. For most laser dyes, the quantum yield of intersystem crossing is small and the –nal term in eqn.(1) may be ignored. Laser gain at any wavelength will be compromised if either the ground state or the lowest excited singlet state absorb the emitted light of that wavelength.The term, is readily pg(j), measured using conventional UV»VIS spectroscopic methods. The emission cross-section, may be calculated by apply- pe(j), ing eqn. (2) and (3) : pe\ j4E(j) 8cn2nq (2) where E(j) is the —uorescence lineshape function normalised such that : P0 = E(j) dj\UF (3) n is the refractive index of the solvent, c is the speed of light in vacuo, and q is the —uorescence lifetime of the dye. In a recent study4 from this group, spectral properties of the lowest excited singlet states of Rhodamine 6G, Rhodamine B and Rhodamine 101 were investigated and values of the molar absorption coefficients for the and transitions S3 ^S1 S4 ^S1 were measured using both comparative and complete depletion methods.In this work, the demonstrated advantages of the experimental approach reported earlier4 are retained to study novel absorption processes for three rhodamine Sn ^S1 dyes viz Rhodamine 3B, Sulforhodamine B and Sulforhodamine 101.Materials and methods All rhodamine dyes (Lambda-Physik), 2,2@-bipyridine ruthenous dichloride hexahydrate [G. F. Smith Chemical Co, absolute alcohol (drawn from laboratory stock) Ru(bpy)3 2 `], and absolute methanol (J. T. Baker) were used as received. ìLaser gradeœ dyes were used throughout this study and the high purity of such samples is evidenced by the low values of reduced s2 observed in time-resolved —uorescence measurements (vide infra). Water was puri–ed by passage through a Millipore –ltration system.Ground state absorption spectra were measured with either a Hewlett-Packard 8450A or a Hewlett-Packard 8451A spectrophotometer. Fluorescence emission spectra were obtained using a Perkin-Elmer MPF-43A spectrophoto—uorimeter and were corrected for instrumental response as described previously.4 An excitation wavelength of 530 nm was used in all —uorescence experiments. Quantum yields of —uorescence were obtained by using J. Chem. Soc., Faraday T rans., 1998, 94(2), 195»199 195dilute solutions (absorbanceO0.05 in a 1 cm cell) optically matched at the excitation wavelength.The areas under the corrected emission curves were compared to the area under the corrected emission curve of Rhodamine 101 in ethanol. Suprasil quartz —uorescence cuvettes (pathlength 1 cm) were used throughout this study for both —uorescence and picosecond absorption experiments. The picosecond absorption apparatus has been described elsewhere.4,5 The excitation source was the second or third harmonic (532 or 355 nm, respectively) from a Quantel YG 402 mode locked Nd:YAG laser (pulse width 30 ps).Pulse and probe beams traverse the cell in a collinear arrangement. For time-resolved studies the following protocol was used. Before each experiment the two diode arrays were balanced. The delay line was set such that excitation occurred 66^5 ps after the analysis pulse had interrogated the sample (this method allowed for the reticon to detect —uorescence produced by the excitation pulse).Typically 500 laser pulses (either 532 or 355 nm as appropriate) were averaged in this position and a series of correction factors, C, were calculated : C(n)\ l1(n) l2(n) (4) where l(n) is the output voltage of the nth diode; 1 and 2 are used to indicate the two arrays. For the measurement of the diÜerence absorption spectrum of the excited singlet state, the sample was excited 66^5 ps before the analysis pulse traversed the sample, this delay being sufficiently short to ensure negligible lowest excited singlet state loss. 500 laser pulses were averaged in each experiment and the absorption computed channel by channel according to : A(n)\logC l0(n) l(n)C(n)D (5) Excitation beam energies were attenuated using metal screen –lters of known transmission at the excitation wavelength. Singlet excited state lifetimes were measured using a timecorrelated, single-photon counting method.The output from a mode-locked, cavity-dumped dye laser (ca 60 mW, 800 kHz) was tuned and frequency doubled to give an excitation wavelength of 300 nm. Instrument response (FWHM) was measured to be ca 100 ps. At least 10 000 counts were accumulated in the maximum channel before data analysis was performed using methods previously outlined.6 The dye concentration for single photon counting experiments was 10~5 mol dm~3 in each solvent. All experiments were performed at ambient temperature (20^2 °C), solutions being in free equilibrium with the atmosphere. Results and Discussion Fluorescence quantum yields and —uorescence lifetimes Ground state absorption spectra for ethanolic solutions of the three dyes were measured (data not shown) and the derived values of ground state absorption coefficient and wavelength maxima were found to be in accord with previous studies for these molecules.7 Fluorescence quantum yields were measured relative to Rhodamine 101 using ethanol as solvent, the —uorescence quantum yield for Rhodamine 101 being taken as unity.8 Results from such measurements are presented in Table 1.The —uorescence lifetimes of the dyes were measured in (qf) both ethanol and data are presented in Table 1. All solvent» dye combinations gave reasonable –ts (as evidenced by values of reduced s2) to single exponential behaviour indicating the presence of one emitting species. Table 1 Fluorescence lifetimes (ns) and emission quantum yields for Rhodamine 3B, Sulforhodamine B and Sulforhodamine 101 (excitation wavelengths of 300 and 530 nm were used for lifetime and quantum yield measurements, respectively) reduced dye solvent lifetime/ns s2 UF Rhodamine 3B ethanol 2.4 1.18 0.51 Sulforhodamine B ethanol 3.8 1.23 0.69 Sulforhodamine 101 ethanol 6.2 1.00 1.00 Picosecond absorption data The transient absorption spectra of the species observed (66^5 ps) after laser excitation (532 nm, ca. 2 mJ per pulse) of an ethanolic solution of Rhodamine 3B (ground state concentration 2.9]10~5 mol dm~3) are shown in Fig. 1. Qualitatively similar spectra were observed in methanolic solutions (data not shown). As can be seen from the data in Fig. 1, a maximum is observed at approximately 440 nm together with a bleaching centred at around 570 nm. Additional data is shown in Fig. 1 for ethanolic solutions of both Sulforhodamine B and Sulforhodamine 101. The excitation conditions used to generate the data in Fig. 1 were such that approximately 10% of ground state molecules were converted to excited states. The assignment of the transitions observed in Fig. 1 to excited singlet states was con–rmed by analysis of the decay of the transient absorbance as a function of time after the laser pulse. Typically, 300 laser pulses (532 nm) were delivered to a solution containing the dye and the transient absorption spectra measured at a given delay setting ; the data thus generated being averaged and stored.The delay setting was then changed so as to alter the time at which the analysis beam interrogated the sample and a further 300 laser pulses were delivered to the sample and a further absorption spectrum recorded. This process was repeated for a number of diÜerent delay settings and the data at a single wavelength plotted as a function of time after excitation. The shape of the spectrum remained the same at all delay settings con–rming that only a single species is responsible for the spectra observed in Fig. 1.Data is presented (Fig. 2) for Rhodamine 3B in methanol although similar experiments have been performed for the other two rhodamines under study. The observed absorbance at 440 nm as a function of time is well –tted (r2\0.98) Fig. 1 Transient absorption spectrum measured (66 ps) after laser —ash photolysis (excitation wavelength 532 nm) of Rhodamine 3B (2.9]10~5 mol dm~3, Sulforhodamine B (5.9]10~6 mol dm~3, =), and Sulforhodamine 101 (8.7]10~6 mol dm~3, in ethanol. K) L) Solutions were contained in quartz cuvettes (pathlength 1 cm) in free equilibrium with the atmosphere at ambient temperature. 196 J. Chem. Soc., Faraday T rans., 1998, V ol. 94Fig. 2 Decay of the absorption observed (wavelength of observation 430 nm) after laser —ash photolysis (excitation wavelength 532 nm) of Rhodamine 3B (5.5]10~6 mol dm~3) in methanol. The solid line yields a lifetime of 1.7 ns. assuming the presence of a single species which decays by a –rst order process (lifetime\1.7 ns).This value of 1.7 ns for the lifetime of the species shown in Fig. 6 is to be compared with the value of 2.0 ns obtained using the (superior) techniques of single photon counting (Table 1). In order to measure the absorption coefficient for the Sn ^ transitions shown in Fig. 3»5 two methods were adopted. S1 In the –rst case a comparative method using as Ru(bpy)3 2 ` actinometer was employed.The charge-transfer excited state of is produced with unit quantum efficiency9 upon Ru(bpy)3 2 ` excitation (355 nm) and the reported value for the molar difference absorption coefficient for the charge transfer state is reported to be [7600 dm3 mol~1 cm~1 at 450 nm.10 Solutions of each dye in either ethanol or methanol and Ru(bpy)3 2 ` Fig. 3 Plots of *e (]) and for Rhodamine 3B in (K), e1?0 enH1 (=) ethanol. See text for further information. Fig. 4 Plots of *e (]) and for Sulforhodamine B (K), e1?0 enH1 (=) in ethanol.See text for further information. Fig. 5 Plots of *e (]) and for Sulforhodamine (=), e1?0 enH1 (=) 101 in ethanol. See text for further information. in water were prepared such that they had identical absorbances (0.6^0.02) at the excitation wavelength (355 nm). Under such conditions, since both and dye excited Ru(bpy)3 2 ` states are produced with unit quantum efficiency, the following may be derived : *e(dye)\ *e(Ru)Adye(j) A(Ruâ 450 nm) (6) where and represent the diÜerence absorption *e(dye) *e(Ru) coefficients for the dye absorption (at wavelength j), Sn ^S1 and the charge-transfer excited state of (450 nm), Ru(bpy)3 2 ` respectively.and are the observed absorb- Adye(j) A(Ruâ 450 nm) ance values for the excited states of the dye and Ru(bpy)3 2 `, respectively, as measured (66^5 ps after the pulse) at wavelengths j and 450 nm after picosecond laser photolysis. The rates of production and decay of the charge-transfer excited state of are such that after 66 ps a full yield is Ru(bpy)3 2 ` obtained.Excitation conditions were arranged such that \10% of the ground state of either dye or were Ru(bpy)3 2 ` converted to excited states. The value of for the peak in *e(dye) the blue region was measured for each of the three dyes. The second approach adopted is the so-called ìcomplete conversionœ method. In such experiments, laser power is increased and consequently increasing proportions of the ground state molecules are converted to the excited singlet state by the laser pulse until the only species present is the –rst excited singlet state At the time of observation little triplet state would have been formed since intersystem crossing would be insigni–cant on the timescale of observation.The laser system used in this study produced insufficient energy at 355 nm to ensure complete conversion. However, excitation at 532 nm, where more excitation energy was available, did show plateaux typical of such experiments.From a knowledge of the limiting value of absorbance and the ground state concentration of the dye, calculation of is relatively straight- *e(dye) forward, although it should be remembered that the maximum concentration of excited singlet state molecules, which can be produced by this method is :3 Cmax , Cmax\ e532 e532]o e1?0(532 nm) o C0 (7) where is the ground state molar absorption coefficient at e532 532 nm, is the absolute value of the molar o e1?0 (532 nm) o stimulated emission coefficient [application of eqn.(2) and (3) allows to be calculated from steady state —uores- e1?0 (532 nm) cence emission data] at 532 nm and is the ground state C0 concentration. The results obtained from both approaches are shown in Table 2 for the ethanol data sets. As can be seen, reasonable agreement exists between the values obtained by the two methods. For subsequent interpretation of our data J.Chem. Soc., Faraday T rans., 1998, V ol. 94 197Table 2 DiÜerence absorption coefficients for the –rst excited singlet state of Rhodamine 3B, Sulforhodamine 101 and Sul- (enH1[eg]e1?0) forhodamine B: data were obtained either (A) by a comparative method using and excitation at 355 nm or (B) by complete conversion Ru(bpy)3 2 ` (excitation wavelength 532 nm) of ground state to excited state (ethanol data only) corrected as per eqn. (8) in the text (estimated errors^20%) dye solvent method wavelength/nm *e(dye)/104 dm3 mol~1 cm~1 Rhodamine 3B ethanol A 444 4.5 Rhodamine 3B ethanol B 444 4.5 Sulforhodamine B ethanol A 444 3.4 Sulforhodamine B ethanol B 446 4.0 Sulforhodamine 101 ethanol A 455 3.5 Sulforhodamine 101 ethanol B 455 3.5 Rhodamine 3B methanol A 441 4.1 Sulforhodamine B methanol A 443 3.7 Sulforhodamine 101 methanol A 457 3.5 those values obtained by the comparative method have been adopted.Having thus obtained values for the absorption coefficients of the transitions observed at the wavelengths listed in Table 2, we can readily convert the data in Fig. 1 to plots of absorption coefficient vs. wavelength. The absorbance changes (*A) shown in Fig. 1, at any wavelength, may be described by: *A\(enH1[eg]e1?0)C1 l (8) where is the absorption coefficient of the ground state, eg e1?0 is the molar stimulated emission coefficient and is the enH1 absolute absorption coefficient for the absorption Sn ^S1 process.Since represents transitions of an emissive e1?0 nature it carries an implicit negative sign. Values of were e1?0 obtained from eqn. (2) given that : pe\3.82]10~21e1?0 (9) can be calculated from a knowledge of at the C1 *e(dye) absorption maximum. We now present (Fig. 3»5) absolute spectra (i.e. for the absorption process for each enH1) Sn ^S1 of the three dyes. Also included in these Figures are plots of and *e. e1?0 Having assigned the spectral transition shown in Fig. 1 to being singlet»singlet in nature, it is interesting to further speculate on the exact nature of the transition which is observed around 450 nm.In previous work such a transition has been assigned, in the related case of Rhodamine 6G, to one arising from an absorption process.11,12 Similar assignments S4 ^S1 have also been made4 in the case of Rhodamine B and Rhodamine 101. On the basis of spectroscopic data, it should be possible to observe the transition close to where the S3 ^S1 —uorescence emission from such samples is at a maximum.It is this transition which, if sufficiently probable, will S3 ^S1 impair dye laser efficiency [eqn. (1)]. Because of the intense —uorescence emission from such samples, published estimations of the absorption cross-section for the transition S3 ^S1 are rare for rhodamine dyes with a few exceptions in the case of Rhodamine 6G and Rhodamine B.2,11h16 The collinear experimental arrangement used in this work reduces the complication which may arise from —uorescence emission.Our recent estimate4 of the molar absorption coefficient (6.4]104 dm3 mol~1 cm~1 at 532 nm) for the transition in the S3 ^S1 case of Rhodamine 6G can be compared with the work of Gazeau et al.16 which yielded a value of at 5.2]104 dm3 mol~1 cm~1 at 530 nm. For the dyes studied in this work, however, our results are the –rst published values. The values obtained in this work and from our previous studies4 are collected and presented in Table 3.Comparison of wavelength maxima for the and the tran- S4 ^S1 S3 ^S1 sitions reveal some correlation with the transitions in Sn ^S0 the ground state. On average the excited state tran- S3 ^S1 sitions are some 2800 cm~1 greater than that which would be calculated from diÜerences in the analogous transitions in the ground state. Similarly for the excited state tran- S4 ^S1 sitions the observed transitions are on average 2100 cm~1 greater than that which would be calculated from ground state spectra.For practical application of these dyes, the eÜective stimulated emission cross-section, is an important parameter peff , and is calculated as follows : peff\([e1?0[enH1)]3.82]10~21 cm2 (10) The values of for the three dyes studied in this work are peff shown in Fig. 6. These curves represent eÜectively the theoretical gain coefficient of a dye laser assuming the contributions from the absorption cross-sections of the lowest triplet state and the ground state are insigni–cant [see eqn.(1)]. This is justi–ed since (i) it has already been shown17 that no triplet states of rhodamine dyes can be observed upon direct excitation, the intersystem crossing yields being less than 0.02 and (ii) that there is very little ground state absorption in the wavelength range of the plots in Fig. 6, in fact, the curves correspond to the theoretical lasing condition where all ground state dye molecules have been converted to the S1 excited state.Hence, the plots can also be regarded as peff representing the maximum theoretical output of a particular rhodamine dye laser. It is, therefore, interesting to compare the experimental output of dye lasers with these theoretical plots. Such comparisons have been undertaken for the three dyes used in this work together with the three dyes investigated in an earlier study,4 viz. Rhodamine 6G, Rhodamine B and Rhodamine 101, using published output data.18 In all cases, the threshold Table 3 Wavelength absorption maxima (nm) and molar absorption coefficients (dm3 mol~1 cm~1) for the and S1 ^S0, S3 ^S1 S4 ^S1 transitions for a series of six rhodamine dyes in ethanol: data for Rhodamine 6G, Rhodamine B and Rhodamine 101 are taken from ref. 4 (estimated errors^20%) jmax(e) jmax(e) jmax(e) S1 ^S0 S3 ^S1 S4 ^S1 Rhodamine 6G 530(1.2]105) 532(6.4]104) 428(4.4]104) Rhodamine B 544(1.2]105) 566(3.8]104) 430(4.3]104) Rhodamine 101 575(1.2]105) 576(7.7]104) 452(3.7]104) Rhodamine 3B 554(1.1]105) 556(1.0]105) 444(4.6]104) Sulforhodamine B 556(1.1]105) 556(1.2]105) 446(3.4]104) Sulforhodamine 101 576(1.1]105) 578(1.2]105) 458(3.6]104) 198 J.Chem. Soc., Faraday T rans., 1998, V ol. 94Fig. 6 Plots of eÜective stimulated emission cross-section for (peff) Rhodamine 3B Sulforhodamine B (*) and Sulforhodamine 101 (K), All data is for ethanolic solutions. (=). wavelength for actual laser output is always at longer wavelengths than those suggested by the theoretical curves in Fig. 6. For example, the theoretical threshold wavelength for Sulforhodamine B and Rhodamine 6G are 570 and 545 nm, respectively. In practice, the respective threshold wavelengths are 590 and 560 nm, respectively. Similarly, there is also some truncation at longer wavelengths where, for example, the theoretical maximum wavelength output may be at 20 nm greater than that found in practice, this being the case for Sulforhodamine B, spectral output of a laser also depends considerably upon the lasing conditions.Here, laser output is aÜected by the type of pumping light source (pulsed, cw, spectral output), the solvent, the dye concentration and dye stability. Clearly, all these parameters could have a signi–cant eÜect on the actual spectral output of a laser. In particular, strong self-absorption by the dye, aggregation of the dye at the high dye concentrations typically employed as well as multiphoton events are expected to aÜect the spectral output of a laser.In the case of multiphoton events, we have already demonstrated that Rhodamine 123 photoionises readily amongst other biphotonic processes.19 In conclusion, therefore, we have used time-resolved picosecond laser —ash photolysis techniques with the charge transfer excited state of to characterise excited singlet state Ru(bpy)3 2 ` transitions for three rhodamine dyes for the –rst time. Taken together with our previous work in this –eld,4 we believe that the technique used here provides a reliable, and more straightforward, method than those adopted previously by other workers.authors would like to extend their thanks formally to the The staÜ of the Center for Fast Kinetics Research for their help and assistance during the course of these studies. The Center for Fast Kinetics Research being supported jointly by the Biomedical Research Technology Program of the Division of Research Resources of NIH (Grant RR00886) and by the University of Texas at Austin.One of us (D.G.J.) would like to acknowledge the award of an SERC CASE Studentship. Further –nancial support from British Nuclear Fuels plc is gratefully acknowledged. References 1 P. P. Sorokin and J. R. Lankard, IBM J. Res. Dev., 1976, 10, 162. 2 F. P. Schaé fer, T op. Curr. Chem., 1976, 61, 1. 3 L. G. Nair, Prog. Quantum Electron., 1982, 7, 153. 4 P. C. Beaumont, D. G. Johnson and B. J. Parsons, J. Chem. Soc., Faraday T rans., 1993, 89, 4185. 5 S. J. Atherton, S. M. Hubig, T. J. Callan, J. A. Duncanson, P. T. Snowden and M. A. J. Rodgers, J. Phys. Chem., 1987, 91, 3137. 6 J. Davilla and A. Harriman, Photochem. Photobiol., 1990, 51, 9. 7 U. Brackmann, in L ambdachrome L aser Dyes, Lambda-Physik GmbH, Goé ttingen, 1986. 8 T. Karstens and K. Kobs, J. Phys. Chem., 1980, 84, 1871. 9 J. N. Demas and D. G. Taylor, J. Inorg. Chem., 1979, 18, 3177. 10 M. Z. HoÜmann, J. Phys. Chem., 1988, 92, 3458. 11 D. Magde, S. T. GaÜney, and B. F. Campbell, IEEE J. Quantum Electron., 1981, 17, 489. 12 P. Venkateswarlu, M. C. George, Y. V. Rao, H. Jagannath, G. Chakrapani and A. Miahnahri, Pramana»J. Phys., 1987, 28, 59. 13 E. Sahar and D. Treeves, IEEE J. Quantum Electron., 1977, 13, 962. 14 P. R. Hammond, IEEE J. Quantum Electron., 1980, 16, 1157. 15 P. R. Hammond, IEEE J. Quantum Electron., 1979, 15, 624. 16 M. C. Gazeau, V. Wintgens, P. Valat, J. Kossanyi, D. Doizi, G. Sawetat and J. Jaraudias, Can. J. Phys., 1993, 71, 59. 17 P. C. Beaumont, D. G. Johnson and B. J. Parsons, J. Photochem. Photobiol. A: Chem., 1997, 107, 175. 18 D. M. Rayner, in Handbook of Organic Photochemistry, ed. J. C. Scaiano, CRC Press, Boca Raton, FL, 1989, vol. 1, p. 215. 19 M. W. Ferguson, P. C. Beaumont, S. E. Jones, S. Navaratnam and B. J. Parsons, Congress of the European Society for Photobiology, Stresa, Italy, 8»13th September 1997, p. 78. Paper 7/05692C; Received 5th August, 1997 J. Chem. Soc., Faraday T rans., 1998, V ol. 94 199

ISSN:0956-5000    

DOI:10.1039/a705692c

出版商:RSC    

年代:1998

数据来源: RSC

摘要:

Capillary electrophoresis with chemical reaction Effect of ionic strength D. H. J. Lindner,a M. Mareka and J. H. Merkinc S ã nita,a S ã evcó ï ç kovaç ,b a Department of Chemical Engineering and b Center for Nonlinear Dynamics of Chemical and Biological Systems, Prague Institute of Chemical T echnology, T echnicka 5, 166 28 Prague 6, Czech Republic c Department of Applied Mathematics, University of L eeds, L eeds, UK L S2 9JT A brief summary of the results of experimental observations of the eÜects of electric –elds on propagating reaction fronts and pulses is presented.A prototype ionic chemical system consisting of a substrate A` and an autocatalyst B` and two further non-reacting species C~ and D` is then considered when an electric –eld with a constant current is applied. An autocatalytic reaction between A` and B` with a quadratic rate law is assumed. Results obtained from extensive numerical simulations of the model are reported. These show that the system is capable of supporting a variety of propagating fronts ; ì kinetic wavesœ, ìKohlrausch boundariesœ and complete species separation are all observed as well as a new type of wave front in which there is a much enhanced reaction rate.The behaviour is characterized in terms of the applied electric current, the ionic strength, and the ratio of the diÜusion coefficients of the reacting species. 1 Introduction Chemical reactions with ionic species can form well de–ned spatial concentration structures (e.g.reaction fronts) and, when electric –elds are applied, the electrophoresis of the reaction components in combination with the reaction processes can lead to considerable modi–cation of these structures or even produce entirely diÜerent spatio-temporal behaviour. Experimental studies into the eÜects of electric –elds on the shape and time evolution of spatio-temporal concentration structures in ionic reacting systems often use isothermal autocatalytic reaction schemes as model systems to describe the formation of fronts and pulse concentration waves.1h10 The eÜects of applied electric –elds are re—ected in the clearly de–ned variations in the velocity of wave propagation and in the transformations of the wave pro–les, which can lead to wave stopping, to wave splitting or to reversal in the propagation direction depending on the electric –eld intensity and direction.3 Experiments performed on spiral waves have shown drift and shift of the spiral waves resulting from applying electric –elds5h7 as well as both changes in the spiral frequency8 and the collapse of a pair of spirals into a single pacemaker for circular waves.9 Both one-dimensional1h3 and two-dimensional4h12 reactors of diÜerent constructions are used experimentally. The eÜects of an electric –eld on a pulse wave, for example, have been studied in the catalytic oxidation of malonic acid by bromate (the Belousov»Zhabotinsky, BZ, reaction).1,3h12 Reaction fronts have been studied in the oxidation of arsenous acid by iodate.2 Capillary reactors are used for the investigation of the one-dimensional eÜects of dc electric –elds that are applied parallel to the direction of propagation of the reaction wave.1h3 The capillaries of circular cross-section, which were used originally,1,2 have been replaced by rectangular ones3 as these are much more suitable for the employment of optical monitoring and recording techniques.A schematic representation of a capillary reactor currently being used is drawn in Fig. 1. A rectangular glass cuvette (GC) made of optically clean glass (outer cross-section 7]7]84 mm) with a rectangular capillary channel (cross-sections of 1 mm2 and less are used) forms an essential part of the apparatus. Both ends of the cuvette are –xed in the –lling chambers (FC) made of organic glass. Electrode cells (EC) also made of organic glass are –lled with the reaction solution.Two pieces of silicon packing (SP) and a piece of microporous Te—on membrane (TM) are placed between the electrode cells and the –lling chambers and the whole apparatus is placed in a thermostated water bath. The cuvette is –lled with the reaction solution through the openings in the –lling chambers which are then closed by stoppers. The electrode cells are –lled with the same reaction mixture and planar (3]3]0.03 cm) electrodes made of platinum (PE) are immersed in the solutions.The microporous Te—on membranes separate the capillary reactor from the electrode cells and prevent the mixing of the products of the reactions at the electrodes with the reacting solution in the capillary. Front or pulse reaction waves can propagate in the capillary. Colour changes of either the starch indicator in the iodate»arsenous acid system or the form of the catalyst in the BZ reaction (ferroin/ferriin is often used) enable the propagating reaction zones to be followed optically using a CCD camera and further evaluated on a PC by image processing packages.An example of experimental observations for the iodate»arsenous acid system is shown in Fig. 2 where we show [Fig. 2(a)] a sequence of snapshots taken at equal time inter- Fig. 1 Capillary reactor. GC, rectangular glass cuvette ; EC, electrode cells ; FC, –lling chambers; SP, silicon packings; TM, microporous Te—on membranes; PE, Pt plate electrodes, x, spatial coordinate. J.Chem. Soc., Faraday T rans., 1998, 94(2), 213»222 213Fig. 2 EÜects of an applied electric –eld on two reaction fronts (dark stripes) propagating in opposite directions in the arsenous acid»iodate reaction medium. (a) Space»time plot. Two sequences of 27 snapshots of the fronts taken every 12 s. A dc electric –eld of intensity 1.8 V cm~1 was switched on between times and (b) Dependence of the t1 t2 . propagation velocity on the electric –eld intensity, see ref. 2. vals. The propagation away from each other of two reaction fronts (shown by the dark stripes formed by the starch indicator coloured by iodine, a reaction intermediate) can clearly be seen. With the electric –eld switched oÜ these propagate in opposite directions with the same speed (snapshots up to time The electric –eld causes the negatively charged iodate and t1). iodide ions to migrate to the right so that with the electric –eld switched on (times between and the front propagat- t1 t2) ing to the right travels faster than that propagating to the left.The dependence of propagation velocity v on electric –eld intensity E measured experimentally for this system is shown in Fig. 2(b). This –gure shows that considerable variations in velocity can be achieved by applying electric –elds and that, with a sufficiently strong (negative) –eld, propagation can be stopped. When an electric –eld is applied the diÜerential migration of the ionic components in a reaction mixture alters their local concentrations within the reaction region and, as a consequence, the local course of the reaction.Strong evidence for this eÜect is provided by the iodate»arsenous acid system shown in Fig. 2(a), where a dark band can be seen evolving behind the left-travelling front. The iodine, appearing only as an intermediate when the reaction is not in—uenced by electric –eld, is formed as a –nal product within the reaction region when the front is exposed to the external electric –eld.Electric –eld»chemical wave interactions are also studied theoretically by means of mathematical descriptions of the wave-supporting reaction systems which are investigated experimentally. Mass balances for a general reacting ionic system and the consequences of the imposed and/or selfgenerated electric –elds on the variety and complexity of nonlinear phenomena in reaction-transport systems have been discussed earlier.13,14 Our approach to studying the eÜects of electric –elds on reacting ionic systems is based on a mathematical model that employs a simple autocatalytic reaction with only one elementary reaction step.This allows for a detailed analytical investigation of the travelling front behaviour for a broad range of diÜusion coefficients, electric –eld intensitites and ionic strengths of the reaction mixture. The eÜects of electric –elds on travelling front waves in a three-component autocatalytic reaction system with a quadratic rate law have been discussed in ref. 15 and 16. The eÜects of an applied –eld on the reaction zone are of two basic types ; electric –elds of low intensities change only the propagation velocity of the wave, electric –elds of higher intensity (ì supercritical –eldsœ) change the global behaviour of the reaction. A ì kinetic concentration frontœ arises in the ì kinetic regionœ of parameter space where the eÜects of the electric –elds of low intensity are small.Electric –elds of strong intensity cause the formation of ìKohlrauschœ boundaries, where the eÜects of separation of the ionic components dominate (the ìtransport regionœ).17,18 Intermediate levels of electric –eld intensity lead to the strong interaction between the reaction and transport (migration) eÜects. These are connected with the transformation of the reaction front, possible reversal of the propagation direction or with a number of other interesting eÜects discussed below.Here, we summarise the results of a numerical and analytical study of the eÜects of an applied electric –eld on travelling fronts for a four-component autocatalytic reaction again with a quadratic rate law. We classify, in the parameter space of ionic strength»ratio of diÜusion coefficients»electric –eld intensity, the possible types of behaviour that this system can support and discuss their characteristic features from the point of view of reaction and separation. 2 Model We consider a system in which there is a quadratic autocatalytic reaction between the ionic species A` and B`, namely A`]B`]2B`, rate\kab (I) (where a and b are the concentrations of A` and B`, respectively, and k is the rate constant). We also assume that there are two further ionic species C~ and D` (with concentrations c and d) present in the system but not taking part in the reaction (the ionic charges on the four species can be reversed in an obvious way). The equations describing the model are obtained from local mass balances for the concentrations of the reacting species A`, B` and non-reacting species C~, D` following the general treatment given in ref. 13. Mass transport is assumed to arise from both molecular (Fickian) diÜusion and by migration of the ionic species in the electric –eld. The Nernst» Planck equation is used to describe the mass transfer. Source terms arise from chemical reaction (I). To complete the formulation we utilize the fact that the electric current can be held at a constant value I in a spatially one-dimensional system, which is what we limit our attention to.The assumption of local electroneutrality gives a]b[c]d\0 (1) which can be used to eliminate c from the system of equations. 214 J. Chem. Soc., Faraday T rans., 1998, V ol. 94We consider a situation in which the substrate A` is initially uniformly distributed throughout the system at concentration and that the non-reacting species C~ and D` also a0 have initial uniform concentrations and respec- a0]d0 d0 , tively [so that local electroneutrality, eqn.(1), is maintained]. The reaction is then initiated by the local introduction of some autocatalyst B` (again at a concentration so as to satisfy local electroneutrality). Wave fronts are then allowed to develop fully before the electric –eld is switched on. The original equations are made dimensionless by de–ning the variables, a6 \a/a0 , b 6 \b/a0 , c6 \c/a0 , d 6 \d/a0 , t6 \tka0 , x6 \xAka0 DAB1@2 , E1 \ EF RT ADA ka0B1@2 , I1 \ I Fa0 ADA ka0B1@2 , where x and t are space and time coordinates, and are x6 t6 dimensionless coordinates (measured in reaction time and reaction-diÜusion length), E is dimensional (dimensionless) (E1 ) electric –eld and I is dimensional (dimensionless) constant (I1 ) electric current intensity.We also introduce the parameter which gives a measure of the ionic strength of the d 6 0\d0/a0 system (a measure of the concentration of the non-reacting ionic species D` relative to that of A`).This leads to, on dropping the bars for convenience, the dimensionless equations for our model as da dt \d2a dx2 [ d dx (aE)[ab (2) db dt \dB d2b dx2 [dB d dx (bE)]ab (3) dd dt \dD d2d dx2 [dD d dx (dE) (4) for the dimensionless concentrations of A`, B` and D`, the concentration of C~ can then be found from eqn. (1). The (dimensionless) electric –eld E is given by E\ 1 G CI](1[dC) da dx ](dB[dC) db dx ](dD[dC) dd dxD (5) where G\(1]dC)a](dB]dC)b](dD]dC)d is the (dimensionless) conductivity. Here dB\DB/DA , dC\ and are the ratios of the diÜusion coeffi- DC/DA dD\DD/DA cients. 3 Travelling waves Our previous studies15,16 into the eÜects of electric –elds on autocatalytic wave propagation have shown that a prerequisite for understanding the full behaviour of the model is the determination of the conditions for the existence of travelling kinetic fronts. In these structures all the chemical species are functions of the single travelling coordinate y\x[vt, where v is the constant propagation speed, and are given by eqn.(2)»(5) expressed in terms of y. As we shall describe below, several types of waves can be supported by our model. We now present brie—y the conditions for the existence of kinetic waves in which reaction, diÜusion and electrochemical migration all have comparable eÜects. Using techniques similar to those described previously15,16 we can show that the velocity for these kinetic waves is v\2)dB] dB I (1]dC)](dC]dD)d0 (6) and that these waves will form provided the current satis–es the inequalities dB[1, I[[ 2)dB[dD(dB]dC)]d0 dB(dC]dD)][(1]dC)](dC]dD)d0] (dB2]2dB dC[dC)]d0 dB 2 (dC]dD) (7) dB\1, [ 2[(1]dC)](dC]dD)d0] )dB \I\ 2)dB[(1]dC)](dC]dD)d0] 1[dB (8) A full derivation of these conditions as well as further properties of these travelling waves is given in ref. 19. For these kinetic waves exist for all values of I and dB\1 have the same waveform as the equivalent wave without the electric –eld (i.e., with I\0), the only diÜerence is in the propagation speed (and this can be either positive or negative depending on the magnitude and direction of I).As the ionic strength parameter is increased we require d0 increasingly larger values of the current I to produce signi–- cant variations from what is observed without the electric –eld [as can be seen from eqn. (6)»(8), for example].In order to assess the eÜects of increasing more directly it is convenient d0 to work in terms of a relative velocity and a relative current v� which we now de–ne. As a reference velocity we take the Iå , velocity of the front with the electric –eld switched oÜ, v0\ and de–ne as 2)dB v� v� \ v v0 \ v 2)dB (9) From eqn. (6) we then have v� \1] I)dB 2[(1]dC)](dC]dD)d0] (10) We can identify the term G0\(1]dC)]d0(dC]dD) as the conductivity ahead of the wave. This then leads us to de–ne the relative current as Iå Iå \I )dB 2G0 \ I)dB 2[(1]dC)]d0(dC]dD)] (11) Thus when kinetic waves are formed eqn.(10) and (11) give the simple relation v� \1]Iå (12) Expression (12) holds for all values of the other parameters when For the divergence from this linear rela- dB\1. dBD1, tion between and gives a measure of how far the response v� Iå of the system is from a kinetic wave. We give the velocities for the other front structures that arise in tere no reaction is taking place in the Appendix. 4 Numerical simulations The numerical simulations to be described have been obtained from integrations of eqn. (2)»(5) with the initial con–guration of the system (before the electric –eld is switched on) being two symmetric fronts propagating in opposite directions away from each other. We will refer to these as the ìright-waveœ and the ìleft-waveœ in an obvious way. The system is in its unreacted state (a\1, b\0) ahead of these waves and in its fully reacted state (a\0, b\1) at their rear.We consider the eÜects that applying an electric –eld (with the current maintained constant) have on this basic state for various ionic strengths, as characterized by the parameter From sym- d0 . metry we need consider only positive values for I, the eÜect on the left-wave is equivalent to taking a negative current. Also, J. Chem. Soc., Faraday T rans., 1998, V ol. 94 215Fig. 3 Values of the relative velocity calculated from the numerical integrations of eqn.(2)»(5) plotted vs. the relative current shown by v� Iå , ), for (and for (a) and (b) The full line gives for the kinetic waves (K), from eqn. (13), the dot»dashed line in (a) dB\2 dC\dD\1) d0\0 d0\10. v� gives the relative velocity of the Kohlrausch boundary (E), from eqn. (A11), the broken line in (b) gives the relative velocity of the boundary in A`, from eqn. (A13), and the dot»dashed line in (b) gives the relative velocity of the boundary in B`, from eqn.(A13). Fig. 4 Spatial pro–le plots at equal time intervals for the (dimensionless) concentrations of the reacting species A`, B`, the non-reacting species C~, D`, the electric –eld E and its gradient (proportional to charge density) for and ] direction of propagation d0\10, Iå \0.25 dB\2; 216 J. Chem. Soc., Faraday T rans., 1998, V ol. 94Fig. 5 Spatial pro–le plots at equal time intervals for the (dimensionless) concentrations of the reacting species A`, B`, the non-reacting species C~, D`, the electric –eld E and its gradient (proportional to charge density) for and Iå \2.5, dB\2 d0\0 Fig. 6 Spatial pro–le plots at equal time intervals for the (dimensionless) concentrations of the reacting species A`, B`, the non-reacting species C~, D`, the electric –eld E and its gradient (proportional to charge density) for and Iå \2.5, dB\2 d0\10 J. Chem. Soc., Faraday T rans., 1998, V ol. 94 217Fig. 7 Values of the relative velocity calculated from the numerical integrations of eqn.(2)»(5) plotted vs. the relative current shown by v� Iå , ), for (and for (a) (b) and (c) The full line gives for the kinetic waves (K), from eqn. (13), the dB\0.5 dC\dD\1) d0\0, d0\10 d0\1000. v� broken line in (a) denotes the relative velocity of the Kohlrausch boundary (E), from eqn. (A12), the broken line in (b) denotes the relative velocity of the boundary in A`, from eqn. (A13), and the dot»dashed line in (b) gives the relative velocity of the boundary in B`, from eqn.(A13). for all the cases presented below, this means that the positively charged ions are attracted to the right (in the positive x-direction). As suggested by conditions [eqn. (7) and (8)] and as seen previously in ref. 15 and 16 qualitatively diÜerent features are to be expected depending on whether or and we dB[1 dB\1 discuss these cases in turn. Before doing so we note that when the only modi–cation to the basic initial state that the dB\1 applied electric –eld makes is to change the propagation speed of the waves (an increase for the right-wave and a decrease for the left-wave) without any change in the waveform.For sufficiently large currents the direction of propagation of the leftwave can be reversed. We consider four ionic strengths ; (where the system d0\0 reduces to a three species model), low ionic strength, d0\1, intermediate ionic strength, and high ionic strength, d0\10, Throughout we take d0\1000.dC\dD\1. (i) Here we took as a representative value, dB[1. dB\2 with condition (7) giving I[[ 4)2(3]4d0)(1]d0) 7]8d0 , Iå [[ 2(3]4d0) 7]8d0 (13) for the existence of kinetic waves. The results are summarized in Fig. 3 where we give plots of computed values of vs. for v� Iå (three species model) and the intermediate ionic d0\0 strength cases. These are shown by open diamonds (d0\10) in these and subsequent similar –gures. The equivalent plots for the low and high ionic strength cases are essentially the same as those for the intermediate ionic strength case.These –gures show that, when the existence of a kinetic wave (K) is predicted [with as calculated from eqn. (12) v� shown by the full line in the –gures], this is what is observed in the numerical simulations. This is brought out more clearly in the pro–le plots for the intermediate ionic strength case which are shown in Fig. 4 (for This –gure (and sub- Iå \0.25).sequent similar ones) gives pro–les at equally spaced time intervals of the concentrations of the reacting species A`, B`, the non-reacting species C~, D`, the electric –eld E and its gradient (this latter quantity being proportional to the charge density), with the initial con–guration as the electric –eld is switched on being the –rst set of pro–les. Plots for the other ionic strength cases are similar in form, the only substantial diÜerences between the cases being in the magnitude of the electric –eld and the concentrations of C~ and D` (though their variations from the initial state are very small and decrease in relative terms as is increased). d0 For this low current case the main feature is the two kinetic waves (K) propagating in opposite directions, with the velocities given by (right-wave) and by (left- Iå \0.25 Iå \[0.25 wave) in Fig. 3(b). There is a relatively small increase in the concentration of B` resulting from the right-wave and a small depletion in B` from the left-wave (the accumulation and depletion increase slightly as is increased).This eÜect can d0 be explained by the fact that the conductivity is higher in the region behind the right-wave than it is ahead of it. Then, since the migration —uxes of A` and B` are aE and respec- dB bE, tively, with there will be a build up in B` in the region dB[1 behind the kinetic wave. A similar argument shows that there will be a net depletion of B` at the rear of the left-wave.We 218 J. Chem. Soc., Faraday T rans., 1998, V ol. 94also note the formation of two small humps (denoted by asterisks in Fig. 4) in B`, C~ and D`. These humps (where no reaction is taking place) propagate slowly to the right with the applied current (for for the humps remain d0D0; d0\0 where the waves were when the electric –eld was switched on) and spread slowly by diÜusion. We next consider higher values for the current, taking Iå \ Now there is a diÜerence in behaviour depending on 2.5.whether (three species model) or (fully four d0\0 d0D0 species model). This is illustrated in Fig. 5 (for and in d0\0) Fig. 6 (for The right-wave is still a kinetic wave (K) d0\10). in both cases, now with an increased velocity and being more spread out. Humps (denoted by asterisks in Fig. 5) remain where the waves were when the electric –eld was switched on for They do not move and spread slowly by diÜusion. d0\0. However, it is perhaps the behaviour of the left-wave that is of most interest in this case.For the three species model (Fig. 5) a strongly focussed Kohlrausch boundary (E) is formed (in which the reaction is virtually extinguished). This front propagates in the positive x-direction (i.e., the direction of propagation of the wave is reversed) with a velocity given by eqn. (A11). For (all four species present), Fig. 6, complete d0D0 separation of A` and B` occurs anon stops. The separated boundaries for A` and B` both propagate in the positive x-direction with that of B` propagating faster (v� BIå ) than that of A` see eqn.(A13), giving an (v� BIå /dB\Iå /2), increasingly greater separation of the two species as time increases (see boundaries A and B in Fig. 6). These velocities are shown by the two points for a given value of in Fig. 3(b). Iå The reason for this diÜerence in behaviour of three and four components system lies in the fact that, for the three species case, A` and B` are the only positively charged ions present and local electroneutrality constrains the system to have both positively and negatively charged ions present everywhere [otherwise in–nite electric –elds would occur, from eqn. (5)] and so separation of the only two positively charged ions is not possible and strong focussing of the front occurs.This is not the case when all four species are present, electroneutrality in the region where there is no A` or B` can be maintained by the presence of the non-reacting species C~ and D` in this region.Another boundary in B` denoted as D in Fig. 6 is formed for the intermediate ionic strength case. (ii) For this case we took as a representa- dB\1. dB\0.5 tive value, with condition (8) giving [4)2(1]d0)\I\4)2(1]d0), [1\Iå \1 (14) for the existence of kinetic waves. The results for this case are summarized in Fig. 7, where we show (computed from the numerical simulations) plotted vs.v� for the three species case, intermediate and high ionic Iå strength cases [the graph for the low ionic strength d0\1, case, is essentially the same as that for Fig. 7(a)]. d0\0, Again we can see that when the existence of a kinetic wave is predicted (now only for a –nite range of this is what is Iå ) observed. In this case the concentration pro–les are essentially the same as for the low current case for (see Fig. 4) dB[1 with the only (minor) diÜerence being that the concentration of B` now builds up behind the left-wave and is depleted behind the right-wave.For higher values of the current the behaviour of the system depends strongly on the ionic strength. For the right- d0\0 wave evolves into a highly focussed Kohlrausch boundary (E) (and the reaction is virtually extinguished) propagating in the positive x-direction with a velocity see eqn. [v� \Iå /dB\2Iå , (27)] in excess of the corresponding kinetic wave speed. This can be seen in Fig. 7(a) and in Fig. 8, where we give concentration plots for The left-wave (K) evolves into a wave in Iå \2.5. which there is a considerable build up in the concentrations of Fig. 8 Spatial pro–le plots at equal time intervals for the (dimensionless) concentrations of the reacting species A`, B`, the non-reacting species C~, D`, the electric –eld E and its gradient (proportional to charge density) for and Iå \2.5, dB\2 d0\0 J. Chem. Soc., Faraday T rans., 1998, V ol. 94 219Fig. 9 Spatial pro–le plots at equal time intervals for the (dimensionless) concentrations of the reacting species A`, B`, the non-reacting species C~, D`, the electric –eld E and its gradient (proportional to charge density) for and Iå \2.5, dB\2 d0\10 Fig. 10 Spatial pro–le plots at equal time intervals for the (dimensionless) concentrations of the reacting species A`, B`, the non-reacting species C~, D`, the electric –eld E and its gradient (proportional to charge density) for and Iå \2.5, dB\2 d0\1000 220 J.Chem. Soc., Faraday T rans., 1998, V ol. 94both A` and B` (well above their initial values) and in which there is a much enhanced reaction rate. This wave propagates (relatively slowly) to the left (in the negative x-direction). No reversal in the direction of propagation was seen in any of the computations for this case as was increased further. This Iå feature can be explained by the fact that, though the –eld causes both positively charged ions to migrate to the right, the in—ow of the more mobile A` (since into the reaction dB\1) region (where A is converted to B) from the left is stronger than the out—ow of B` to the right.This results in a much enhanced reaction rate leading to more B` being produced. The slow out—ow of B` from the reaction region produces a build up in this component at the rear of the wave and the negative charge densities at the wave attracts A` increasing its concentration. The combination of these eÜects is to sustain the process and to increase greatly the reaction rate.The tendency of the autocatalytic reaction to move the reaction zone to the left into the unreacted region is then sufficient to overcome the tendency of the –eld to cause rightward migration, allowing the front to propagate to the left. Humps in the concentration pro–les (denoted by asterisks in Fig. 8) appear at the position where the waves were when the electric –eld was switched on. For these humps do not move and spread d0\0 slowly by diÜusion.However, in the four component system the right-wave evolves into fully separated boundaries in A` and B`, both propagating to the right. The velocity of the boundary in A` is larger than the velocity of the front in B` (v� ABIå /dB\2Iå ) see eqn. (A13). This eÜect is present in both the inter- (v� BBIå ), mediate and high ionic strength cases as (d0\10) (d0\1000) can be seen in Fig. 9 and 10 and by the pair of wave speeds for each (one for each boundary) shown in Fig. 7(b) and (c). Iå [1 These two boundaries (A and B) become increasingly separated with increasing time. The behaviour of the left-wave is diÜerent for increased ionic strengths. The enhanced reaction wave is still observed in the low ionic strength case again propagating to (d0\1), the left for all the considered. For the intermediate case [Fig. Iå 7(b)] there is a –nite range of values of (approximately Iå for which the left-propagating enhanced [2.2\Iå \[1) reaction wave is still observed.For larger values of (as for Iå the used in Fig. 9) a kinetic wave, now propagating to the Iå right with its original propagation direction reversed [equivalent to having a negative see Fig. 7(b)] is observed. v� , For the high ionic strength case [Fig. 7(c) and 10] no enhanced reaction waves are seen for The behaviour Iå \[1. is just a right-propagating kinetic wave (giving a change in the direction of propagation with respect to the original wave).In this case only right-propagating fronts evolve from the initial con–guration with the electric –eld eÜects being strong enough to overcome the natural tendency of the autocatalytic reaction to propagate the left-wave into the unreacted part of the system. A boundary in B`, C~ and D` (denoted by D in Fig. 9 and 10) moving to the right is observed in four component system. No reaction takes place in these boundaries. 5 Conclusions We have been able to identify clearly the general features that can arise when an electric –eld is applied to an ionic chemical system with an autocatalytic reaction.We have seen that there are essentially three basic parameters which determine the behaviour of our model system. There is the diÜusion coef- dB , –cient of the autocatalyst relative to that of the substrate. When these are the same (i.e., the eÜect of the applied dB\1) electric –eld is to change only the speed of propagating reaction front, reversal being possible for sufficiently strong –eld intensities, without altering the waveform.We can identify this as a ì critical œ case with qualitatively diÜerent behaviour arising depending on whether or There is the dB[1 dB\1. ionic strength, which we have expressed in terms of the parameter a measure of the initial concentration of the d0 , non-reacting species to that of the (active) substrate. Finally, tgnitude and direction of the applied current.The eÜect that this can have depends strongly on the ionic strength requiring increasingly larger currents to make a comparable eÜect as is increased. We have shown how this can d0 be accounted for by describing the behaviour in terms of the relative current and relative velocity de–ned in eqn. (9) Iå v� , and (11). For low –eld intensities (and the basic structures dBD1) that arise are kinetic (or reaction-diÜusion) fronts. The applied –eld plays only a minor role, producing small accumulations or depletions in autocatalyst concentration at the rear of these waves and in making only small changes to the propagation speed, the precise nature of which depending mostly on whether or \1 and the direction of the applied –eld.dB[1 For stronger –eld intensities there is a much greater interaction between reaction and molecular transport through diffusion and electrochemical migration. This results in a variety of propagating structures.Kinetic waves can still arise though their waveforms are substantially diÜerent to those for low –eld intensities. Now there are considerable accumulations/ depletions in autocatalyst concentration at the rear of the wave and their propagation speeds are greatly modi–ed, with reversal being possible. With (and when only A`, B` and C~ are the ionic d0\0 species present in the reactor) highly focussed Kohlrausch boundaries can form. In these boundaries the reaction is inhibited and sharp gradients in concentration and electric –eld occur.For sufficiently large (with now the further ionic d0 species D` also present) Kohlrausch boundaries are not formed. The equivalent behaviour is then complete separation of the reacting species, with distinct boundaries in A` and B` forming. For low ionic strengths and greater mobility of the substrate relative to the autocatalyst a propagating front (dB\1) can arise in which there is a substantial build up in the concentrations of both reacting species.This front propagates into the unreacted part of the reactor, against the direction induced by the electric –eld. This is a new type of propagating front and it is formed as a direct result of the interaction between an autocatalytic reaction of ionic species and applied electric –elds. The relative simplicity of our model has permitted a detailed systematic analysis to determine critical values [conditions (7) and (8)] where we could expect qualitatively diÜerent behaviour to emerge. These suggested the appropriate values to take in the numerical simulations and led to a full elucidation of the various propagating structures that the model could sustain.We do not expect these features to be con–ned speci–cally to the present model and can be expected in other ionic reacting systems which are governed, in part at least, by some autocatalytic reaction mechanism and where the complexity of the model may preclude the detailed considerations presented here.work was partly supported by grant No. VS96073 by This MSMT (Ministry of Education, Czech Republic) and a travel grant from the Leverhulme Trust. Appendix Here we give the velocities for the various non-reaction concentrations and fronts seen in the numerical simulations. If we introduce the travelling coordinate, y\x[vt, where v is a constant speed, eqn. (2)»(4) become with the reaction terms put to zero, 0\ d dy Ada dy [aE]avB (A1) J.Chem. Soc., Faraday T rans., 1998, V ol. 94 2210\ d dy AdB db dy [dB bE]bvB (A2) 0\ d dy AdD dd dy [dD dE]dvB (A3) where E is given by eqn. (5). We assume that at large distances from the front conditions are uniform. This gives the boundary conditions y]]O: da dy \db dy \dd dy ]0, a]aR , b]0, d]dR , E]ER (A4) y][O: da dy \db dy \dd dy ]0, a]0, b]bL , d]dL , E]EL (A5) where suffices R and L refer to the right and left sides of the boundary, respectively. Integration from [O to O gives, from eqn.(A1)»(A3) and conditions (A4) and (A5) 0\[ aR I aR(1]dC)]dR(dC]dD) ]aR v (A6) [ dB bL I bL(dB]dC)]dL(dC]dD) ]bL v\0 (A7) [ dD dL I bL(dB]dC)]dL(dC]dD) ]dL v \[ dD dR I aR(1]dC)]dR(dC]dD) ]dR v (A8) Expressions (A6) and (A7) then give [for and see eqn. (10) v� Iå , and (12)] v� \v� A\Iå 1 dB (1]dC)]d0(dC]dD) aR(1]dC)]dR(dC]dD) (A9) v� \v� B\Iå (1]dC)]d0(dC]dD) bL(dB]dC)]dL(dC]dD) (A10) We now consider expressions (A9) and (A10) for the various cases. (i) dR\0, dL\0, bL\1. Here v� \v� A\v� B , v� \Iå (1]dC) (dB]dC) (A11) (ii) dR\0, dL\0, aR\1. Here v� \v� A\v� B , v� \Iå 1 dB (A12) (iii) dR\dL\d0 ]O. Here v� A\Iå 1 dB , v� B\Iå (A13) References 1 H. and M. Marek, Physica D, 1983, 9, 140. Sã evcó ïç kovaç 2 H. and M. Marek, Physica D, 1984, 13, 379. Sã evcó ïç kovaç 3 H. M. Marek and S. C. Mué ller, Science, 1992, 257, Sã evcó ïç kovaç , 951. 4 R. Feeney, S. L. Schmidt and P. Ortoleva, Physica D, 1981, 2, 536. 5 O. Steinbock, J. Schué tze and S. C. Mué ller, Phys. Rev. L ett., 1992, 68, 248. 6 K. I. Agladze and P. De Kepper, J. Phys. Chem., 1992, 96, 5239. 7 A. P. Mun8 uzuri, M. Goç mez-Gesteira, V. Peç rez-Mun8 uzuri, V. I. Krinsky and V. Peç rez-Villar, Phys. Rev. E, 1994, 50, 4258. 8 V. erç rez-Mun8 uzuri, R. Aliev, B. Vaisev and V. I. Krinsky, Physica D, 1992, 56, 229. 9 S. C. Mué ller, O. Steinbock and J. Schué tze, Physica A, 1995, 188, 47. 10 P. Kasó taç nek, J. Kosek, D. I. Schreiber and M. Marek, Sã nita, Physica D, 1995, 84, 79. 11 H. J. Kosek and M. Marek, J. Phys. Chem., 1996, 100, Sã evcó ïç kovaç , 1666. 12 H. I. Schreiber and M. Marek, J. Phys. Chem., 1996, Sã evcó ïç kovaç , 100, 19153. 13 D. and M. Marek, Physica D, 1994, 75, 521. Sã nita 14 P. Ortoleva, Physica D, 1987, 26, 67. 15 D. H. M. Marek and J. H. Merkin, J. Phys. Sã nita, Sã evcó ïç kovaç , Chem., 1996, 100, 18740. 16 D. H. M. Marek and J. H. Merkin, Proc. R. Sã nita, Sã evcó ïç kovaç , Soc. L ondon, Ser. A, 1997, 453, 2325. 17 F. Kohlrausch, Ann. Phys. (L eipzig), 1897, 62, 209. 18 R. A. Mosher, D. A. Saville and W. Thormann, T he dynamics of electrophoresis, VCH, Weinheim, 1992. 19 D. J. Lindner, M. Marek and J. H. Merkin, Math. Comput. Sã nita, Modell. in press. Paper 7/05578A; Received 1 August, 1997 222 J. Chem. Soc.,

ISSN:0956-5000    

DOI:10.1039/a705578a

出版商:RSC    

年代:1998

数据来源: RSC

摘要:

Electrical properties of wood Determination of ionic transference numbers and electroosmotic water —ow in Pinus sylvestris L. (Scots pine) Paul J. Simons,a Michael Spiroa,* and John F. Levyb Departments of aChemistry and bBiology, Imperial College of Science, T echnology and Medicine, L ondon, UK SW 7 2AZ A novel technique has been developed for measuring the electrical transport of ions and of water through natural materials when a dc electric –eld is applied across them. The material studied was green sapwood of Pinus sylvestris L.(Scots pine). By means of a special cell the processes at the wood/solution interfaces were separated from those at the solution/electrode interfaces. Analyses of the electrode compartment solutions after the passage of known numbers of coulombs yielded the relative transference numbers of ions in the wood. Horizontal capillaries in the two electrode compartments enabled equal hydrostatic pressure to be maintained across the cell and allowed the simultaneous measurement of the electroosmotic water —ow.This provided a value for the zeta potential of the green sapwood. The experiments showed electroosmotic water —ow and ionic migration to be independent processes. The endogenous inorganic current carriers in the samples decreased in the sequence K`, Cl~, and values were Ca2`[Mg2`[Na`[NH4 `, SO4 2~ obtained for the hindered conductances of the major ionic carriers. The results are consistent with a cation-exchange model for the wood. Although dry wood is an excellent electrical insulator, with increasing moisture content the electrical conductivity rises steeply and by several orders of magnitude.1,2 It is generally agreed that this conductivity arises from the movement of ions but little is known about their relative contributions to the conduction process.Much of the work described in the literature for studying the electrical properties of wood contains features which complicate the interpretation of the results.Examples are the measurement only of changes in ash content rather than changes in individual salts,3,4 the clamping of electrodes such as copper5 or carbon6 directly onto the wood samples which produces unwanted chemical and electrical interactions, and the use of constant voltages rather than constant currents5,6 so that the number of faradays passed is unknown. The eÜects of hydrostatic and electroosmotic water —ows were often not considered sufficiently.4 The aim of the present work was therefore to design a modi–ed Hittorf7 cell and a mode of operation to overcome these and other problems. Experimental Materials Wood was taken from 60»70 year old healthy trees of Scots pine, Pinus sylvestris L.(Paddock Hurst, E. Sussex). Felled logs were cut up to provide straight-grained sapwood sticks which were closely packed into thick polythene bags and sealed. The bags were either refrigerated at 7 °C or deep frozen at 0 °C.Several of the bags were c-irradiated before cold storage. When required, the wood was turned on a lathe into cylinders along the longitudinal axis, with diameter 22.0^0.2 mm and either 50 or 100 mm in length. Electrolytes were prepared from BDH AnalaR materials. Copper electrodes were made by sealing 1 mm diameter Specpure copper wire (Johnson Matthey) into 10/19 Quick–t cones with Araldite. Silver and Ag o AgCl electrodes were prepared by electroplating onto 0.1 mm diameter platinum wire electrodes.Equipment Fig. 1 shows the essential elements of the cell. The two glass electrode compartments were made from SVL (Sovirel, Levallois-Perret, France) screw joint glass cylinders of 26 mm id and 138 mm length. The cylinders of wood were –tted into these by means of Sovirel screw cap attachments (40 mm od) with Sovirel silicon rubber O-rings (20 mm id) which had been stripped of their phenoplast covers. This procedure was essential for making a water-tight seal between the wood and the glass cell without contaminating the wood, and it allowed repeated re-use of the cell.Both electrode compartments were –tted with an open-ended horizontal capillary tube (2 mm id), each at the same height to ensure equal hydrostatic pressure across the wood. The cell was mounted on an aluminium platform standing above a heavy cast iron base. The platform was made truly horizontal by adjusting a knurled knob below it and employing a spirit level.Strong spring clips screwed on to the platform held the cell –rmly in position. A stable dc current was provided by a departmentally built constant current generator. Its maximum output was 23 mA and in most experiments a current of 10 mA was selected. The current was accurately measured with a digital multimeter (Solartron 7045) in the voltage mode placed across a standard 100 or 1000 ) resistor in series with the generator and the cell. Fig. 1 Elements of the basic electrical cell, shown in exploded and cut-away views: 1, horizontal capillary ; 2, vertical tube; 3, two-way Inter—on tap; 4, electrode port ; 5, screw-threaded joint ; 6, wood sample; 7, silicon rubber O-ring ; 8, phenoplast cap J.Chem. Soc., Faraday T rans., 1998, 94(2), 223»226 223Procedure The wood was always handled with clean disposable rubber gloves. If the cylinder had been refrigerated, it was allowed to equilibrate in its polythene wrapper for at least 2 h at room temperature.The O-rings were then slipped over each end of the sample and carefully screwed into the screw cap using a clean Sovirel screw-jointed glass tube. The electrode sections were screwed onto the phenoplast caps abutting onto the O-rings to make a tight junction with the wood. One of the electrode compartments and its corresponding cap were then twisted to align the capillary tubes parallel to each other. Next, the cell was clamped on to its support jig and aligned using a spirit level.The electrode compartments were –lled with the chosen electrolytes and solution was forced up into the capillary tubes to the desired extent by repeatedly plunging the electrodes into their respective ports. The electrodes were then inserted and the leads clipped on. Just before the current was switched into the cell, the position of the meniscus in each capillary was marked with a felt-tipped pen. Runs were abandoned under the following adverse conditions : erratic current, excessive ìsweatingœ on the wood surface, leakage of solution, disintegration of an electrode, or unwanted gassing at an electrode.When a pre-determined number of coulombs had been passed, the taps were closed and the electrodes were removed. The cell was tipped on its side and the electrode solutions collected in dry Pyrex boiling tubes. The taps were re-opened and the solutions in the capillaries also collected. The tubes were then sealed with Para–lm and analysed.Analytical methods employed included Dionex ion chromatography for both cations and anions, —ame photometry, atomic absorption, inductively coupled argon or helium plasma spectroscopy, and pH measurement. The wood cylinder was carefully examined for any changes after each run. Moisture contents (u) of wood samples were calculated from the formula u\100 (wu[w0)/w0 (1) where is the mass of the wood sample and that of the wu w0 sample after oven drying at 101 °C for 48 h.The inorganic content of the oven-dried wood was determined by milling chips of the wood into sawdust and oxidising oÜ all the organic matter by careful heating with a mixture of hydrogen peroxide and sulfuric acid. The resulting ash was dissolved in a known volume of distilled water and analysed by —ame photometry. A blank solution, obtained by following the same procedure but without the wood sample, was also analysed. The ac electrical resistances of wood samples were measured with a Wayne Kerr B905 autobalance bridge using circular platinum disc electrodes –rmly pressed against the ends of each wood cylinder.Results and Discussion General comments The transference number of any ion i of algebraic charge ti number migrating out of the wood into an electrode com- zi partment of volume V was calculated from ti\ci V o zi o /f (2) where was the change in molar concentration of i in the ci compartment after f faradays of electricity had been passed.After a typical run the values of were of order 1 lM»1 mM. ci The concentrations of the anolyte and catholyte electrolytes, chosen not to have ions in common with the wood ions, were usually much larger to keep Joule heating low. The difficulty of analysing low concentrations of some ions in the presence of a large concentration of others placed signi–cant strain on the analytical methods. Moreover, a natural variability in the results was to be expected with diÜerent pieces of wood.When changes in a particular parameter were to be tested, therefore, wood samples were chosen to be as similar in origin as possible. In the initial experiments beads of moisture (ìsweatœ) appeared on the exposed surface of the naked wood during the electrical runs. These droplets gradually enlarged, particularly on the underside of the wood, until a continuous –lm of moisture was formed which acted as a parallel conducting path. To overcome this problem several types of barrier material were tried, the most successful being the rubberbased emulsion Mobilcer R.Wood coated with a thin –lm of this emulsion showed no sign of sweating except when more than 50 C had been passed. Table 1 shows that the coating had no signi–cant eÜect on the transference numbers. Another problem with long runs was that the anolyte meniscus fell out of its capillary tube, so giving rise to unequal hydrostatic pressure across the sample.This was overcome either by using still longer capillary tubes or, more conveniently, by injecting fresh anolyte solution into the capillary with a long needle attached to a syringe. Transference numbers and ionic conductances It was important to check that the endogenous ions found in the electrode compartments had arrived there by electrical migration and not by other mechanisms such as diÜusion or ion exchange. Comparison of the results of zero-current and 10 mA runs in Table 2 con–rmed that migration was indeed the route by which most cations entered the cathode compartments.In long runs, ions from the electrode compartments migrated right through the wood. This is shown by the Cu2` ions from the anolyte in Fig. 2. The resultant trans- CuSO4 ference numbers are listed in Table 3. Typically, the transference numbers of K` were larger than those for Ca2` for small numbers of coulombs. The reverse was true when more Table 1 EÜect of coating 100 mm long wood with Mobilcer R, using a Pto Ag o AgCl cathode in and a Cu anode in and Bu4NI CuSO4 , passing 10 C wood treatment electrolyte conc./mM t(K`) t(Na`) uncoated 25 0.188 0.012 coated with Mobilcer R 25 0.158 0.032 uncoated 0.25 0.212 0.008 coated with Mobilcer R 0.25 0.208 0.012 Table 2 Blank experiments to test the eÜect of diÜusion on ion movement, using cells –tted with Pt o Ag o AgCl cathodes and Cu anodes endogenous ion conc.in catholyte/lM current/mA time/s anolyte catholyte K` Ca2` t(K`) t(Ca2`) 0 1000 0.025 M Li2SO4 0.05 M HCl (65 ml) 15 20 10 1000 0.025 M Li2SO4 0.05 M HCl (65 ml) 210 92 0.122 0.090 0 15000 0.05 M CuSO4 0.05 M HCl (80 ml) \10 \5 10 15000 0.05 M CuSO4 0.05 M HCl (80 ml) 3980 85 0.205 0.009 224 J.Chem. Soc., Faraday T rans., 1998, V ol. 94Fig. 2 Concentrations of cations found in the cathode compartment after the passage of 10 mA through 50 mm long wood for increasing periods of time, using the cell [Pt o Ag o AgCl o 0.05 M HCl o wood o 0.05 M CuSO4 o Cu] current had been passed because of the slower migration of the doubly charged cation through the wood sample.Potassium and calcium were the major endogenous current carriers, with smaller contributions by Mg2` and Na` ions (Table 4). Endogenous anions such as Cl~ and con- SO42~ tributed much less than the cations. No signi–cant amount of current was carried through the wood by H` or OH~ ions. The sum of the transference numbers of the endogenous mineral ions was always less than unity because, at each wood/electrolyte interface, part of the current was carried by exogenous ions (such as Cu2` and Cl~) entering the wood.As expected, therefore, the endogenous transference numbers rose when lower concentrations of bathing electrolyte were employed, as exempli–ed by the K` transference numbers in Table 1. The apparent decrease of the small Na` values is due to their much larger variability. However, low concentrations of catholyte or anolyte produced unwanted Joule heating.At the other extreme, when 1 M concentrations of catholyte and anolyte were employed, the K` transference numbers fell below 0.01. Compromise concentrations were therefore chosen in practice. Table 3 EÜect of closed cathode compartment on cation migration through 50 mm long wood, using a Pt o Ag o AgCl cathode in 0.05 M HCl and a Cu anode in 0.05 M CuSO4 no. of coulombs cathode compartment t(K`) t(Ca2`) t(Cu2`) 10 open 0.106 0.096 0 10 closed 0.100 0.077 0 150 open 0.032 0.150 0.143 150 closed 0.028 0.154 0.172 Table 4 Summary of ion concentrations, mean transference numbers and ionic conductances in the green sapwood ji(lit.)a ioni ci (ppm) ci/mM ti ji/S cm2 mol~1 /S cm2 mol~1 K` 473 5.45 0.18 8.7 73.5 Na` 22 0.43 0.015 9.2 50.1 Ca2` 549 6.17 0.09 3.8 119.0 Mg2` 139 2.58 0.013 1.3 106.1 Cl~ 34b 0.43 0.024 14.6 76.4 a Data from Robinson and Stokes8 at 25 °C.b Data from Will9 (see text).The mean transference numbers of the major endogenous current carriers in the wood samples are listed in the summary Table 4. To evaluate the molar conductances of the separate ion constituents in the wood we require also their concen- (ji) trations in the wood and the speci–c conductivity i of the wood, since ti\ci ji/&ci ji\ci ji/i (3) The resistance of the 50 mm wood samples of cross-sectional area 3.80 cm2 usually fell to ca. 5 k) after passing even small numbers of coulombs, whence i\2.63]10~4 )~1 cm~1.This is a typical value for wood of the moisture content used.1 The concentrations of the relevant ions were converted from parts per million in the oven-dried wood to mM in the ìwet œ wood by using the mean moisture content evaluated from eqn. (1) (122%) and a density of 1.00 g cm~3 for the green sapwood. The resulting molar conductances of the ions in the sapwood are compared in the last column of Table 4 with the limiting molar conductances of the same ions in water at 25 °C.8 The values show that, on application of an electric –eld, the singly charged Na` and K` ions migrate 5»8 times more slowly through the wood than through water while the doubly charged Mg2` and Ca2` ions move 30»80 times more slowly.This indicates that the doubly charged cations are held more tightly, consistent with cations migrating via cation exchange at negatively charged carboxyl and phenolic hydroxyl10 sites attached to the organic wood matrix.The chloride anions appear to migrate somewhat more freely than the singly charged cations, probably because the negative zeta potential of the wood samples was small (see below). However, the calculated chloride conductance in the wood depends on a concentration value in an old reference9 supported by a recent report11 of a chloride concentration of similar magnitude in Pinus densi—ora Sieb et Zucc. Electroosmosis During the electric runs, the volumes of the catholytes rose slightly while those of the anolytes fell linearly with increasing numbers of coulombs.In blank control experiments, in which no current was passed, both electrolyte volumes fell but at diÜerent rates. This is clearly illustrated in Fig. 3. Thus both non-electrical (diÜusion, osmosis) and electrical (electroosmosis) eÜects took place. Anolyte and catholyte volume changes due to electroosmosis were therefore evaluated from the diÜerences between the plots obtained with and without current. The extent of the volume changes as monitored with the long capillaries varied in diÜerent runs.In every case, however, there was a net uptake of liquid by the wood sample which explains the increase in its mass after runs of 1^1 wt.%. The water absorbed probably –lled void spaces in the wood structure. The net fall in electrolyte volume was less when low concentrations (0.25 mM) of electrolytes were used at each end because of expansion caused by Joule heating. Several experiments were carried out to compare the eÜects of leaving the cathode compartment either open or closed during a run.As Fig. 4 shows, there was no signi–cant diÜerence in the decrease in anolyte volumes. However, isolated beads of moisture broke through the Mobilcer R barrier –lm on the wood surface during the closed cathode runs, thereby releasing some of the electroosmotic pressure. Table 3 shows that closing the cathode compartment had no signi–cant eÜect on the transference numbers of the major cations.These had therefore migrated into the catholyte as a result of the electric –eld and not by being passively carried into it with the electroosmotic water —ow. Thus, for the –rst time, the electrical migration of ions and electroosmosis have been shown to be independent phenomena, contrary to the belief of earlier authors.3,4 J. Chem. Soc., Faraday T rans., 1998, V ol. 94 225Fig. 3 Changes in electrode compartment volumes with and without passing current through 100 mm long wood, using the same cell as in Fig. 2. Catholyte and anolyte, in the absence of current ; L, K, Ö, catholyte and anolyte with 10 mA current passed. =, A simple order-of-magnitude calculation also rules out the converse, namely that the changes in the electrode compartment volumes arose not from electroosmosis, but from the volume changes produced by the electrode reactions and the migration of ions with their associated water of hydration.The latter processes will have led to the following volume increase in the catholyte per faraday *V \V (Ag)[V (AgCl)]t(K`)V1 (KCl)]12t(Ca2`)V1 (CaCl2) (4) if for simplicity we focus only on the major endogenous K` and Ca2` ions. Here V are molar volumes and partial V1 molar volumes whose values have been given by Longsworth. 12 Insertion of the appropriate data gives *V \[9.7 cm3 faraday~1 or [10 mm3 per 100 C. This corresponds to a cathode capillary movement of [3.2 mm per 100 C, which is of opposite sign and far smaller in magnitude than the observed change in movement on passing current through the cell.An estimate of the zeta potential at the wood/water interface can be obtained from the rate of the electroosmotic —ow of water (v) using the Smoluchowski equation in SI units13 v\e0 er Ef/g (5) where is the permittivity of vacuum, the relative permit- e0 er Fig. 4 Changes in anolyte volume with the cathode compartment open or closed in runs with 50 mm long wood using the same (K) (=) cell as in Fig. 3 tivity of water and g the viscosity of water. Their values are listed in the literature.8 The electric –eld E across the wood is given by E\I/iA (6) where I is the current and A the cross-sectional area of the wood sample. The value of v can be calculated from the rate of electroosmotic movement of the menisci in the capillaries since the rate of volume —ow of water is the same (vcap) through the wood and through the capillaries, so that vA\vcapAcap (7) Combination of these equations leads to f\vcapAcap gi/e0 er I (8) Insertion of the numerical values of these parameters with the average values from Fig. 3 leads to a zeta potential of vcap [0.25 mV for the 100 mm long sapwood sample. The negative sign follows from the direction of —ow and shows that the wood matrix possessed a small negative charge. This will have arisen from partial dissociation of carboxyl and phenolic groups in the wood, largely shielded by endogenous and (once the runs were under way) by exogenous cations.The type and concentration of these ions are known to have a marked eÜect on the value of the zeta potential of wood.1b Few zeta potential data for woods have been published. The nearest example is a value of [6.1 mV for sapwood ì—ourœ of Pinus densi—ora Sieb. et Zucc. obtained by Kim et al.14 by streaming potential measurements. Conclusions Several previous workers5,6 have reported that application of an electric –eld to samples of wood leads to the migration of potassium, sodium and calcium ions towards the cathode and of halide ions towards the anode.The present study is the –rst one to provide more quantitative data and, in particular, to indicate the degree of hindrance experienced by these ions in migrating through wood. Moreover, the experimental arrangement employed has made it possible to separate electrochemical and electroosmotic eÜects and has provided a value for the zeta potential of the green sapwood.thank the SERC and Rentokil PLC for the award of a We CASE Research Studentship to P.J.S., Dr. D. J. Moore and D. Taplin of Rentokil for their help and support, and the staÜ of CERL, Courtaulds and British Gas for ion chromatography analyses. References 1 A. J. Stamm, (a) Ind. Eng. Chem., Anal. Ed., 1929, 1, 94; (b) W ood and Cellulose Science, Ronald Press, New York, 1964, ch. 21. 2 R. T. Lin, Forest Products J., 1965, 15, 506. 3 H. Bechhold and E. Heymann, Z. Elektrochem., 1927, 33, 161. 4 B. F. Schwarz, Bull. Inst. Pin, 1928 (no. 52), 215. 5 J. E. Langwig and J. A. Meyer, W ood Sci., 1973, 6, 39. 6 K. Minato, N. Kojima, Y. Ishimaru, Y. Katayama and A. Aoki, Mokuzai Gakkaishi, 1990, 36, 1089. 7 M. Spiro, in Physical Methods of Chemistry, V ol. II : Electrochemical Methods, ed. B. W. Rossiter and J. F. Hamilton, Wiley- Interscience, New York, 2nd edn., 1986, ch. 8. 8 R. A. Robinson and R. H. Stokes, Electrolyte Solutions, Butterworths, London, 2nd edn., 1959, pp. 457, 465. 9 H. Will, Z. Forst.- Jagdwesen, 1882, 14, 209. 10 R. Popper, Holzforschung, 1978, 32, 77. 11 N. Okada, Y. Katayama, T. Nobuchi, Y. Ishimaru and A. Aoki, Mokuzai Gakkaishi, 1993, 39, 1111. 12 L. G. Longsworth, J. Am. Chem. Soc., 1935, 57, 1185. 13 D. H. Everett, Basic Principles of Colloid Science, Royal Society of Chemistry, London, 1988, p. 91. 14 Y. Kim, K. Kuroda and Y. Inoue, J. Antibact. Antifung. Agents, 1985, 13, 389. Paper 7/06066A; Received 18th August, 1997 226 J. Chem. Soc., Faraday T rans., 1998, V ol. 94

ISSN:0956-5000    

DOI:10.1039/a706066a

出版商:RSC    

年代:1998

数据来源: RSC

摘要:

Circular dichroism (CD) study of peridininñchlorophyll a protein (PCP) complexes from marine dino—agellate algae The tetramer approach Mariusz Pilcha and Marek Pawlikowskib a Department of Computational Chemistry, Faculty of Chemistry, Jagiellonian University, 30-060 Krakow, Ingardena 3, Poland b Department of T heoretical Chemistry, Faculty of Chemistry, Jagiellonian University, 30-060 Krakow, Ingardena 3, Poland The absorption and circular dichroism spectra of PCP (peridinin»chlorophyll a protein) light-harvesting complexes from Glenodinium sp.and Gonyaulax polyedra are studied in terms of vibronic coupling theory. Analysis based on a tetramer model allows the determination of the relative positions of peridinin molecules in the PCP complexes studied. The tetrameric arrangement of four peridinins around the chlorophyll a is suggested to favour the efficient transfer of energy from the peridinin to the chlorophyll. The simple arguments presented suggest that the energy transfer from peridin to chlorophyll might occur from the states of the peridinin tetramer to the and states of the chlorophyll a.W1B Bx, By 1 Introduction The chiroptical properties of molecules play an in—uential role in the stereochemical and electronic structural characterization of large organic molecules and natural products. Studies of steroids, polypeptides, proteins and nucleic acids,1h5 to mention a few diÜerent families of molecules, can oÜer examples of historical signi–cance. At present, circular dichroism (CD) is routinely applied to gain information about the stereochemistry of large important molecules.6 Of the vast number of biologically important molecules, those containing two or more identical optically inactive chromophores are of especial interest and are convenient for theoretical studies.Structural studies on lobster shell pigments oÜer a classical example.7h10 For these types of molecule, the relationship between the intensity distribution in the CD spectra and the molecular structure is, at least in principle, very simple.This is because the optical activity of molecules containing identical chromophores is basically due to an asymmetrical arrangement of the chromophores and the interaction between them.11h14 Although the asymmetrical arrangement is required in order to generate the nonvanishing rotatory strength, the interaction that occurs results in splitting of the excited electronic states.However, this simple interpretation, very often employed for qualitative analysis of the CD experimental data, might be too severe for quantitative analysis if the totally symmetric vibrations exhibit their Franck»Condon (FC) activities in the absorption spectra of the chromophores. To be more speci–c, various complications can arise as the frequencies of the vibrational modes are typically of the same order of magnitude as the energy split of the excited states resulting from interchromophore interactions.As a result, the Born»Oppenheimer (BO) approximation can be violated even if it holds for the excited states of the separate chromophores. These aspects of CD spectroscopy have been discussed in some detail in a series of papers concerning the CD of naphthalene and anthracene dimers.15h18 One of the most intriguing relations between the molecular geometry and the in vivo biological processes has been reported and discussed for the peridinin»chlorophyll a protein (PCP) complexes extracted from the dino—agellate algae.19h21 The PCP complexes act as photosynthetic antenna pigments and their geometrical structure, proposed earlier19 (Fig. 1), was reported to be unique for the highly efficient energy transfer that occurs from the peridinin to the chlorophyll a.This conclusion was made under the assumption that four peridinin molecules are arranged into two pairs of non-interacting dimers located at opposite corners of the chlorophyll molecule. However, this is not the only possible arrangement of the four peridinins in the PCP complexes that could account for the efficient energy transfer, i.e., it is conceivable that the four peridinins form a rectangular (not planar) environment for the chlorophyll a.The aim of this paper is to consider an alternative geometry for the PCP complexes in order to reconstruct their CD and absorption spectra. To this end we treat the four peridinins as a tetramer, instead of as two pairs of non-interacting dimers.With the rectangular or topology, considered but not (D2 C2) favoured in earlier studies,19 we aim to show that the CD and absorption spectra of PCP complexes can be (semi) quantitatively interpreted in terms of a vibronic model. The reliability of the model predictions are then rationalized in terms of the CNDO-Cl1 method. The conditions that favour the energy transfer process are also brie—y discussed.A more complete analysis of this problem is the subject of a future paper. 2 Model Consider a molecule (tetramer) containing four identical and achiral units (chromophores) labelled by A, B, C and D. Further, and denote the excited and ground state of /m, a 0 /0, a 0 the ath chromophore. The corresponding energies (nuclear potential) are and For model simplicity we Em,a(Q) E0, a(Q). assume that the totally symmetric vibrational modes of the chromophores are represented by a set of harmonic oscillators, which are displaced (Franck»Condon eÜects) but not distorted in the excited states relative to the ground state of a chromophore. Therefore, in the absence of any interaction J.Chem. Soc., Faraday T rans., 1998, 94(2), 227»232 227Fig. 1 Topology of the PCP complex. Vectors and are subject to constraints : applied for k\A, B, C and D. RA , RB , RC RD Dk … Rk\0 between the chromophores, the excited electronic states of the tetramer and their corresponding potentials are given as /k\/m, k 0 < a(Ek) /0, a 0 (1a) Uk(Q)\E0] ; i/1 N um, i [Bm, iQk, i ]12(QA, i 2 ]QB, i 2 ]QC, i 2 ]QD, i 2 )] (1b) where is the ì vertical œ electronic excitation energy (the E0 ìcentre of gravityœ of the chromophore absorption band) and is the displacement (Franck»Condon) parameter of the Bm, i ith vibration in the mth electronic state. The four electronic functions, eqn.(1a), for k\A, B, C and D, represent the localized states of the tetramer resulting from the four possible localizations of the exciton on the chromophores.An interaction between the chromophores will tend to delocalize the excitation giving rise to splitting of the four-fold degeneracy. On the other hand, displacement of the excited state potentials along the totally symmetric vibration(s) will tend to localize the exciton on a chromophore. To describe these two competitive eÜects we express the total (vibronic) wavefunctions of the excited states of the tetramer as tv\/A mv(A)]/B mv(B)]/C mv(C)]/D mv(D) (2) 228 J.Chem. Soc., Faraday T rans., 1998, V ol. 94where v numbers the level of vibrational manifold and are mv ( i) the Q-dependent coefficients that satisfy equation: Hcmv(A) mv(B) mv(C) mv(D)d\Evcmv(A) mv(B) mv(C) mv(D)d (3) where the matrix Hamiltonian H, has the form H\cTN]UA VA VAC VAD VAB TN]UAB VBC VBC VAC VBC TN]UC VCD VAD VBD VCD TN]UDd (3a) where is the kinetic energy operator for the nuclei, is the TN Ev total (vibronic) energy corresponding to the wavefunctions, eqn.(2), and are the interchromophore interaction matrix Vab elements responsible for the exciton migration in the tetramer. In general, the six integrals are independent but some Vab relationships among them may arise when the tetramer has one or more symmetry elements. For the purpose of this paper we assume that the tetramer has a two-fold symmetry axis perpendicular to the ìplaneœ of the chlorphyll a (Fig. 1). In this case the tetramer belongs to the point group and C2(D2) the interchromophore interaction matrix elements are subject to the relations : and If the VCD\VAB , VBC\VAD VADVBD . tetramer also has a four-fold symmetry axis parallel to the two-fold symmetry one, the symmetry of the tetramer C4(D4) imposes the relations : and VAB\VCD\VBC\VAD VAC\VBD . With these symmetry restrictions, the tetramers belonging to the and point groups can be treated in the same C2(D2) C4(D4) calculational scheme.Now we are in position to calculate the absorption and CD characteristics associated with transitions in the t0,0 ]tv tetramer. For these transitions the absorption intensities I(0]v) and the rotatory strengths R(0]v) can be determined from5 I(0]v)\(St0, 0 oDotvT) … (Stv oDot0, 0T) (4a) R(0]v)\Im(St0, 0 oDotvT) … (Stv oMot0, 0T) (4b) where S T and ( ) denote integration over the electronic and nuclear coordinates, respectively, and D and M are the electric and magnetic dipole operators, respectively.Im is an abbreviation for the imaginary part. Under the assumption that the electronic functions, eqn. (1a), only slightly depend on the vibrational coordinates (Condon approximation), eqn. (4a) and (4b) can be rewritten as I(0]v)\;i ;j (m0 o mv ( i))I(i, j)(mv ( j) o m0) (5a) R(0]v)\;i ;j (m0 o mv ( i))F(i, j)(mv ( j) o m0) (5b) where the matrix elements I(i, j) and F(i, j)\ \Di … Dj depend only on the tetramer geometry.[Di … (Rj]Dj)E0 With the tetramer geometry given in Fig. 1, a simple but tedious analysis leads us to expressions : I\c 1 sin2 a [cos 2a sin 2a sin2 a 1 sin 2a [cos 2a [cos 2a sin2 a 1 sin 2a sin2 a [cos 2a sin 2a 1 dD0 2 (6a) and F\c0 Rx 2Rx Ry Ry 0 Ry 2Ry 2Rx Rx 0 Rx Ry 2Ry Ry 0 dD0 2 E0 sin a cos a (6b) Eqn. (3), (5a) and (5b) are the working equations for the remaining part of this paper. 3 Results and Discussion The quantitative determination of the absorption and CD spectra with the help of eqn.(5a) and (5b) requires the numerical solution to eqn. (3). Before drawing a conclusion from the results of the numerical treatment, we will consider, for illustrative purposes, a much simpler situation in which any vibrational activity can be ignored. In such a situation, the CD and absorption spectra are entirely of electronic origin. To proceed with this task let us put in eqn. (1b) and then let us Bm, i\0 transform Hamiltonian eqn. (3a) by means of unitary transformation S `HS\cE2` 0 0 0 0 E1` 0 0 0 0 E1~ 0 0 0 0 E2~d (7) It is easily to verify that eqn.(7) holds if the matrix S is of the form S\ 1 2 c1 1 1 1 1 [1 [1 1 1 1 [1 [1 1 [1 1 [1d (8) so that the electronic energies and are E2B E1B E2B\E0]VAC^(VAB]VAD) E1B\E0[VAC<(VAB[VAD) (9) The corresponding wavefunctions can be obtained from (t2`, t1` , t1~ , t2~)\(/A , /B , /C , /D)S (10) The rotatory strengths for the four possible transitions and can be now readily calculated from t0 ]t2B t0 ]t1B eqn.(4a) and (4b) where the vibronic wavefunctions and t0, 0 were replaced by the electronic ones, eqn. (10). So, inserting tv eqn. (8) into (10) and the result into eqn. (4) we get, with the help of the matrix in eqn. (6b) : R(0]2])\[(Rx]Ry)D0 2 sin 2a R(0]2[)\0 (11) R(0]1^)\12(Rx]Ry)D0 2 sin 2a The rotatory strength R(0]2[) vanishes at a result of cancellation of the transition dipole moment DA[DB]DC corresponding to the transition in the tetra- [DD t0 ]t2~ mer (Fig. 1). As follows immediately from eqn. (11), the rotatory strengths obey the sum rule,5 i.e., the total rotatory strength vanishes in the absorption region covering the four interacting states of the tetramer. Three special cases emerge immediately from eqn. (9) and (11). In the –rst, for the energies of the excited VAC\VAD\0, states are subject to equalities and so E2`\E1~ E2~\E1` that the CD spectrum is expected to show two bands with the rotatory strengths R(0]2])]R(0]1[) and R(2[)]R(1]) corresponding to the and t0 ]t2`(t1~) transitions.Since these rotatory strengths are t0 ]t2~(t1`) of the same magnitude but diÜer in sign, the situation resembles that known from the dimer theory of optical activity.5 Indeed, for the tetramer can be viewed as two VAC\VAD\0 pairs, (A,B) and (C,D), of non-interacting dimers. In the J. Chem. Soc., Faraday T rans., 1998, V ol. 94 229second case, when the exited states and VAB\VADD0, t1` are doubly degenerate due to the symmetry of the t1~ D4(C4) tetramer.An inspection of eqn. (11) reveals that three transitions, and carry the non- t0 ]t2` t0 ]t1`(t1~), vanishing rotatory strengths, but one transition, t0 ]t2~ , appears to be inactive. Once again the resulting CD spectra are expected to show two CD bands with rotatory strengths R(0]2]) and R(0]1])]R(0]1[) ; both twice as large as those for the dimer. In the –nal case, when the tetramer has symmetry, we put in eqn.(9) so that the C2(D2) VABDVADD0 degeneracy of the and states is removed. Now, three t1` t1~ transitions, and give rise to t0 ]t2`, t0 ]t1` t0 ]t1~ , the optical activity and the transition remains inac- t0 ]t2~ tive. As a result, the CD spectrum will show three Cotton bands with the rotatory strengths R(0]2]), R(0]1]) and R(0]1[), with R(0]2]) being twice as large as the other two and opposite in sign, which is exactly what we observe in the measured CD spectra of PCP complexes.Table 1 gives a comparison between the calculated and measured19 energies and (relative) rotatory strengths for two PCP complexes with a 4 : 1 peridinin to chlorophyll ratio. The empirical rotatory strengths and energies for the three lowenergy transitions were evaluated from the maxima and minima of the CD curves. Their theoretical counterparts were evaluated from eqn. (9) and (11) applied for cm~1, E0\22 500 cm~1, and cm~1. These VA\[2 200 VAC\0 VAD\[1 000 values for the parameters could be clearly derived by –tting to the experimental data.Although the model used to gain the values in Table 1 is apparently oversimpli–ed, the theoretical predictions appear to be fully consistent with experiment. Not only the transition energies but also the signs and relative intensities of the Cotton bands are correctly reproduced for both complexes, which suggests that the peridinin tetramers in the PCP complexes from Glenodinum sp. and Gonyanlax polydra are of C2 or symmetry.The basic functionality of the model in pre- D2 dicting the main features of the CD spectra of the PCP complexes was encouraging and we decided to go one step further and include the vibrational mode(s) of the peridinin in the considerations. This step requires the FC parameters, to Bm, i , be known from independent data. Since the FC parameters for the peridinin molecule are not thus far available from quantum chemical computations we can consequently attempt to acquire them from the experimental absorption spectrum of peridinin.The low-temperature absorption spectrum of the peridinin molecule, measured in the region 15 000»40 000 cm~1, is shown in Fig. 2. For a comparison the absorption spectrum of the PCP complex from Glenodinum sp. is also given. The three dipole-allowed 1A]nB (n\1, 2, 3) electronic transitions marked in Fig. 2 are due to one-electron promotions in the p»p* system of the conjugate carbon chain of the peridinin molecule.Of these transitions, the lowest energy one at ca. Table 1 Transition energies and relative rotatory strengths for PCP complexes from Glenodinum sp. (PCP-Glen) and Gonyanlax polydra (PCP-Gony) PCP-Glena PCP-Gonya theoryb R(0]2]) [1.00 [1.00 [1.00 E2`/cm~1 18 470 18 868 19 300 R(0]1]) 0.55 0.77 0.50 E1`/cm~1 21 489 21 622 21 300 R(0]1[) 0.65 0.73 0.50 E1~/cm~1 23 470 23 470 23 700 R(0]2[) » » 0.00 E2~/cm~1 » » 25 700 a Ref. 19 and 20. cm~1, cm~1, b E0\22 500 VAB\[2200 VAC\0, cm~1 and a\12.5°. VAD\[1000 Fig. 2 Absorption spectra of : (a) free peridinin and (b) PCP complex from Glenodinum sp. (from ref. 19, 20) 22 000 cm~1 is almost exactly polarized along the long axis of the peridinin chain22 and is responsible for the most prominent CD features observed in the CD spectra of the PCP complexes. The vibrational structure of the 1A]1B transition is dominated by a single vibration with an energy quantum of 1450 cm~1. In analogy to the other molecules with conjugate double-bond chains,23,24 this most FC active vibration can be assigned to a CxC stretching mode.There should also be two other moderately active vibrations of the same character but no clear evidence for their activity was found in the peridinin absorption spectrum (Fig. 2). So, we had to assume that the single (ìeÜectiveœ) vibration, u\1450 cm~1, builds the vibronic structure of the peridinin absorption spectrum. With this assumption, the FC parameter can be evaluated directly from the peridinin absorption spectrum; analysis yields B\1.47.In Fig. 3 we compare the calculated and the measured CD and absorption spectra for the PCP complex extracted from Glenodinum sp. The stick spectra give the results obtained for a\12.5° and and Since the electronic Rx\9 ” Ry\8.5 ”. structure of the CD spectrum is fully resolved the matrix elements and could be –rmly established from the VA , VAC VAD positions of the CD peaks; analysis yields : VAB\[2200 cm~1, cm~1, cm~1.It is worth VAC\[80 VAD\[1006 noting that angle a was evaluated somewhat arbitrarily but Fig. 3 (a) Experimental (curves) and the theoretical (sticks) absorption and (b) CD spectra of the PCP complex from Glenodinum sp. The calculation parameters are : cm~1, cm~1, VAB\[2200 VAC\[80 cm~1, B\1.47, a\12.5°, and VAD\[1006 Rx\9 ” Ry\8.5 ”. The experimental data were taken from ref. 19 and 20. 230 J. Chem. Soc., Faraday T rans., 1998, V ol. 94R (0 ® 1–) = 3.19 � 10–37 esu I (0 ® 1–) = 2.82 � 10–34 esu R (0 ® 1+) = 3.25 � 10–37 esu I (0 ® 1+) = 3.42 � 10–34 esu R (0 ® 2+) = –5.60 � 10–37 esu I (0 ® 2+) = 0.25 � 10–34 esu E1– = 20 459 cm–1 E1+ = 17 560 cm–1 E2+ = 17 202 cm–1 D D C C A B B A D C B A z z z x y y x y x D(1–) D(1+) D(2+) the choice of a\12.5° can be justi–ed when considering the zeroth and the –rst spectral moments ratio SET0 SET1 SET1 SET0 \E0](VAB]VAC]VAD)sin2 a[VAC cos 2a (12) obtainable from an analysis of the measured absorption spectra of the tetramer and peridinin.Careful analysis yields : cm~1 for peridinin and SET1/SET0\22 500 SET1/SET0\ cm~1 for the PCP complex; the former being equal to 22 150 Subtracting these two values we can see that the second E0 . term in eqn. (12) diÜers only slightly from the value of [81 cm~1 evaluated using the parameters applied to obtain the results presented in Fig. 3. This implies that angle a is not large, but has to diÜer from zero to ensure the non-vanishing optical activity of the peridinin tetramer.Although the agreement between theory and experiment is satisfactory, some bands in the CD spectrum cannot be explained in terms of the tetramer model, which only takes the 1B state of peridinin into account. While the low-energy CD peak at ca. 15 000 cm~1 can be assigned to the state of Qy chlorophyll a, the high-energy (negative) CD band at ca. 30 000 cm~1 can be attributed to other electronic states of peridinin.Fig. 2 reveals that a contribution from the less intense long axis polarized 1A]2B transition to the CD spectrum is very likely. Although the theoretical model used thus far oÜers a consistent and very simple interpretation of the CD and absorption data for apparently complex systems, it would be interesting to confront these results with others obtained from an independent method. Because of the size of the PCP complexes, application of quantum chemical method(s) to deal with the vibronic problems still remains beyond our computer capacity. Nevertheless, well-behaved semi-empirical quantum chemical methods, such as CNDO and MNDO, maybe useful in providing information about excited states, even for very large molecules.The transition energies, the rotatory strengths and the directions of the transition dipole moments determined from CNDO-CL1 calculations are given in Fig. 4 together with the schematic structure of the PCP complex. The calculations were done with the parameterization proposed by Del Bene and JaÜeç 25 and no attempt was made to adjust that parameterization for the actual purpose.The chlorophyll a was not included in the calculations. The tetramer geometry used in the computations was the same as that applied to calculate the CD and absorption spectra given in Fig. 3. From Fig. 4 one can see that the transition energies are uniformly smaller than those needed to reproduce quantitatively the CD and absorption spectra.However, the calculated energy gap cm~1 is not much smaller than E1[E2`\3257 the energy gap cm~1) estimated from the (E1[E2`\5000 experimental data. At the same time, the rotatory strengths for the and transitions keep exactly the same t0 ]t2` t0 ]t1` pattern as that observed in the CD spectra of the PCP complexes (Fig. 2). In particular, the signs and relative values of the rotatory strengths are very close to those predicted by the tetramer model and those found by experiment.It is worth noting that the energy splits of the tetramer excited states can be better reproduced when changing the CNDO parameterization25 in order to adjust it to the actual problem. More details of the quantum chemical calculations concerning the free peridinin, the peridinin tetramer and the peridinin» chlorophyll a complex will be presented elsewhere.22 Finally, we wish to comment brie—y on the energy transfer eÜect that occurs in the PCP complexes between the peridinin and the chlorophyll a.According to the classical theory of the radiationless transitions26 based on the BO approximation, the energy transfer processes are governed by the interactions between the donor (peridinin tetramer) and the acceptor Fig. 4 Transition energies (E), rotatory strengths (R) and absorption intensities (I) obtained from CNDO-Cl1 calculations. D(2]), D(1]) and D(1[) are the dipole moments vectors for the three low-energy allowed transitions.The symbols (x) represent the chromophore (peridinin) of the PCP complex. (chlorophyll a) in their excited electronic states. So, at the level of dipole»dipole approximation the interaction promoting the energy transfer can be simply evaluated as a scalar product of the transition dipole moments in the donor and the acceptor. A look at Fig. 4 reveals that the dipole moments of the transitions in the tetramer and these of the t0 ]t1B and transitions in chlorophyll a are /0 ]/(Bx) /0 ]/(By) polarized roughly in the same (x, y) plane of the PCP complex.Such a situation favours energy transfer from the tetramer states to the and Soret states of the t1B /(Bx) /(By) chlorophyll a. On the same grounds one can argue that a contribution from the state to the energy transfer is less t2` likely. This seems to suggest that the efficient energy transfer from peridinin to chlorophyll is due to a non-radiative path, which starts in the states of the tetramer and terminates t1B in the and states of the chlorophyll a. Work on the /(Bx) /(By) energy transfer processes occurring in the PCP complexes is now in progress in our group.So, within a vibronic formalism, which goes beyond BO approximation, we hope to return to the energy transfer problems in a forthcoming paper. 4 Conclusion In our opinion the results presented in this paper leave little doubt that the PCP complex from Glenodinum sp. is better characterized in terms of the tetramer model than in terms of the dimer one. This conclusion is based on a comparison between the experimental CD and absorption spectra and the theoretical d-function (stick) spectra generated by the vibronic coupling model.The same conclusion can be drawn when comparing the experimental CD spectrum to those calculated in the framework of the tetramer and dimer models as a superposition of the Gaussian band functions applied with (a priori) the same linewidths.§ The basic functionality of the § Available supplementary material (SUP 57319; 3 pp.) deposited with the British Library. Details are available from the editorial office.J. Chem. Soc., Faraday T rans., 19 231tetramer model can also be proved for the other PCP complexes with the same 4 : 1 peridinin to chlorophyll ratio. We have shown that the very characteristic sequence of CD bands observed for most of the PCP complexes is due to the exciton splitting of the 1B states of the peridinins arranged in the tetramer structure.The splitting was shown to be consistent with the symmetry of the tetramer. Although crystallo- C2(D2) graphic data for the PCP molecules are still not available, a suggestion that the PCP complex has a two-fold axis ìperpendicularœ to the chlorophyll plane is known from the literature.21 The angle between the main axes of the peridinin molecules located on the opposite sides of the tetrameric frame was estimated to be 2a\25°.This is a best tentative estimate so far available in the absence of crystallographic data. The geometrical structure deduced from the CD analysis was also found to favour the energy transfer process evidenced in the light-harvesting antenna complexes.19 These qualitative arguments suggest that the energy transfer from peridinin to chlorophyll occurs from the states of the tetramer to the t1B and Soret states of the chlorophyll a. Bx , By work has been supported by the Polish Committee for This Scienti–c Research (Grant PB1049).References 1 W. Kauzmann, Ann. Rev. Phys. Chem., 1957, 8, 413. 2 E. R. Blout, Optical Rotatory Dispersion : Applications to Organic Chemistry, McGraw-Hill, New York, 1960, ch. 17. 3 P. Doty, Rev. Mod. Phys., 1959, 31, 107; G. Holzwarth and P. Doty, J. Am. Chem. Soc., 1965, 87, 218. 4 B. Jirgensons, T etrahedron, 1961, 13, 166; J. Biol. Chem., 1963, 238, 2716; Makromol. Chem., 1964, 72, 119. 5 H. Eyring, H-C.Liu and D. Caldwell, Chem. Rev., 1968, 68, 525; also T. M. Lowry, Optical Rotatory Power, Longmans, Green and Co. Ltd., London, 1935. 6 B. Samori@ and E. W. Thulstrup, Polarized Spectroscopy of Ordered Systems, Kluwer, Dordrecht, 1988; K. Nakanishi, Cicular Dichroic Spectroscopy : Exciton Coupling in Organic Stereochemistry, Oxford University Press, Oxford, 1983. 7 M. Buchwald and W. P. Jancks, Biochemistry, 1968, 7, 844. 8 T. Y. Lee, J. Jung and P-S. Song, J. Biochem., 1980, 88, 663. 9 M. Pawlikowski, Acta Phys. Pol. A, 1988, 74, 145; 1988, 74, 295. 10 M. Pilch and M. Pawlikowski, Acta Phys. Pol. A, 1991, 79, 619. 11 O. J. Weigang, J. Chem. Phys., 1965, 43, 71. 12 R. Grinter and S. F. Mason, T rans. Faraday Soc., 1964, 60, 274. 13 S. F. Mason, R. H. Seal and D. R. Roberts, T etrahedron, 1974, 30, 1671. 14 N. Harada, Y. Takuma and H. Uda, J. Am. Chem. Soc., 1978, 100, 4029. 15 M. Pawlikowski and M. Z. Zgierski, J. Chem. Phys., 1982, 76, 4789. 16 M. Z. Zgierski and M. Pawlikowski, J. Chem. Phys., 1983, 79, 1616. 17 M. Pawlikowski and B. Rys, Chem. Phys., 1996, 202, 149. 18 R. L. Fulton and M. Gouterman, J. Chem. Phys., 1961, 35, 1059. 19 P-S. Song, P. Koka, B. B. Preç zelin and F. T. Haxo, Biochemistry, 1976, 15, 4422. 20 P. Koka and P-S. Song, Biochim. Biophys. Acta, 1977, 495, 220. 21 D. Carbonera, G. Giacometti and U. Segre, J. Chem. Soc., Faraday T rans., 1996, 92, 989. 22 M. Pawlikowski, in preparation. 23 L. C. Hoskins, Spectrochim. Acta, Part A, 1986, 42, 169. 24 L. C. Hoskins, A. X. Pham and G. C. Rutt, J. Raman Spectrosc., 1990, 21, 543. 25 J. Del Bene and H. H. JaÜeç , J. Chem. Phys., 1968, 48, 1807; 4050; 1968, 49, 1221; 1969, 50, 1126. 26 S. H. Lin, Proc. R. Soc. L ondon, Ser. A, 1973, 335, 51. Paper 7/05173E; Received 8th July, 1997 232 J. Chem. Soc., Faraday T rans., 1998, V ol. 94

ISSN:0956-5000    

DOI:10.1039/a705173e

出版商:RSC    

年代:1998

数据来源: RSC

摘要:

Becker&ndash;D&ouml;ring model of self-reproducing vesicles Peter V. Coveneya* and Jonathan A. D. Wattis a Schlumberger Cambridge Research High Cross Madingley Road Cambridge UK CB3 0EL and Department of T heoretical Physics Oxford University 1 Keble Road Oxford UK OX1 3NP b Department of T heoretical Mechanics University of Nottingham University Park Nottingham UK NG7 2RD Important developments have been made recently in the experimental study of self-reproducing supramolecular systems based on micelles and vesicles (or liposomes) ; the processes are related to possible prebiotic transformations involving the forerunners of biological cells. Here we construct and study a kinetic model which describes both the formation and self-reproduction of vesicles. Until now a detailed mechanistic understanding of vesicle formation has been lacking.Our approach is based on a novel generalisation of the Becker»Doé ring cluster equations which describe the stepwise growth and fragmentation of vesicular structures. The non-linear kinetic model we present is highly complex and involves many microscopic processes ; however by means of a systematic contraction of the complete set of kinetic equations to the macroscopic limit we show that the model correctly captures the experimentally observed behaviour. 1 Introduction The phenomenon of self-reproduction is an inherent feature of living systems. It is also central to the question of the origin of life itself. Much contemporary research concerned with the search for the origins of life is devoted to a consideration of the self-replicating properties of individual molecules including RNA DNA and their presumed progenitors.1h3 However self-reproduction is a form of autocatalysis and autocatalytic processes can be realised at higher levels than that of individual molecules.3h5 The present paper is concerned with the analysis of one example of such supramolecular (or ìemergentœ) self-reproduction.In the past few years signi–cant progress has been made in the experimental study of self-reproducing supramolecular systems mainly based on micelles and vesicles (or liposomes) ; the processes were subsequently connected to possible prebiotic transformations involving the forerunners of biological cells.6h10 These laboratory systems can be regarded as ful- –lling the conditions for ìminimal life œ as de–ned by Varela et al.11 The essential features of self-reproduction in these experiments involve the formation of bounded cell-like structures (either micelles or vesicles) at or within the boundaries of which the synthesis of further such structures is initiated.Some extensions of these experiments have even involved attempts at ìcore-and-shellœ reproduction in which both the ì cell œ membrane and RNA within the ìcell œ are simultaneously reproduced.12,13 The –rst such supramolecular self-reproduction experiments involved micelles. Immiscible ethyl caprylate was hydrolysed by aqueous sodium hydroxide as the concentration of caprylate monomer builds up the critical micelle concentration is reached at which point there is a dramatic acceleration in the rate of hydrolysis.The micelles in the aqueous phase dissolve large amounts of ethyl caprylate increasing the reaction rate which in turn produces more micelles through hydrolysis and so on. The reaction terminates when all the ethyl caprylate has been consumed. A subsequent reduction in the pH of the solution leads to the production of vesicles. Signi–cantly it was also found that if caprylic anhydride is used in place of * E-mail coveney=cambridge.scr.slb.com § E-mail Jonathan.Wattis=nottingham.ac.uk ethyl caprylate vesicles are formed directly at the lower solution pH resulting from its hydrolysis although the kinetics of the reaction are similar. Thus under these conditions the system is comprised of self-reproducing vesicles rather than self-reproducing micelles.It is worth remarking in passing that many vesicle systems are either thought or known to be metastable and generally require some form of energy input (such as sonication) for their preparation.14 Two experimental systems which lead to self-reproducing vesicles have been reported by Walde et al.8 In each case an immiscible liquid fatty acid anhydride is hydrolysed by an aqueous phase in the –rst system caprylic anhydride reacts with aqueous sodium hydroxide; in the second oleic anhydride is hydrolysed by a pH buÜered aqueous solution. The liquids are stirred throughout the reaction. The reason for the diÜerent conditions imposed on the caprylic and oleic anhydride systems stems from the fact that the vesicles that caprylate and oleate anions form are known to be stable under diÜerent conditions of pH.In a typical experiment one –nds that the concentration of produced surfactant monomer (caprylate or oleate) builds up gradually until a certain point whereupon the hydrolysis reaction rapidly accelerates (see Fig. 1 for a set of experimental results showing this eÜect). This is due to the existence in both systems of a surfactant critical aggregation concentration at which the monomers aggregate into vesicles in appreciable quantities. Once these vesicles are formed they solubilise the remaining immiscible anhydride molecules within the aqueous phase and hence accelerate the reaction rate owing to a vastly increased interfacial area of contact between anhydride and the hydrolysing hydrophilic species.Thus the reaction becomes autocatalytic overall since enhanced production of surfactant monomer leads to increased concentration of vesicles which further accelerate hydrolysis. The critical aggregation concentration (c.a.c.) in the case of vesicle-forming systems is analogous to the critical micelle concentration (c.m.c.) for surfactant systems that produce micellar aggregates. Although both these quantities are normally assumed to be unambiguously de–ned there is a considerable degree of arbitrariness about them. First of all it is important to recognise that they are concepts which are de–ned only at thermodynamic equilibrium.Focusing on the vesicle case it is known that as the equilibrium concentration 233 J. Chem. Soc. Faraday T rans. 1998 94(2) 233»246 Fig. 1 Graph showing the rise in caprylic acid concentration and corresponding fall in pH. This graph demonstrates the rapid acceleration of the hydrolysis reaction following an induction time of ca. 15 days [taken from Fig. 6(A) of Walde et al.8]. of monomers is increased within say an aqueous solution a point is reached where monomers associate into vesicles»this is the c.a.c. Beyond this point additional monomers contribute to an increasing concentration of vesicles while the concentration of free monomers remains essentially constant. However the critical aggregation concentration is not the location of a sharp phase transition ; instead it is the concentration of monomers at which the equilibrium fraction of monomers within vesicles reaches some arbitrary value usually taken to be 0.5.In fact the equilibrium fraction of monomers within vesicles is itself somewhat arbitrary since there is no clear-cut division between ì vesicles œ and smaller clusters that are not regarded as vesicles. The equilibrium fraction of monomers within vesicles varies very rapidly around the c.a.c. so that to an experimentalist it may appear to look like a phase transition. The same considerations apply in the case of the critical micelle concentration. While we have previously discussed the theoretical basis for the c.m.c. phenomenon, 15,16 we are not aware of any similar discussion of the c.a.c.in vesicle-forming —uids. The description of these supramolecular vesicular systems is a major theoretical challenge ; it is also clearly of considerable importance not only intrinsically but for origins-of-life studies and for the wider relevance and applications of these systems in pure and applied science. Indeed Farquhar et al.14 have recently suggested that at least for certain (bichained) surfactants vesicle formation is probably more common than has generally been thought to be the case. Based on their experimental observations they suggested a possible breakdown mechanism for vesicles in qualitative terms but doubted that formation occurs simply by reversing those processes. On the other hand we have recently put forward a detailed quantitative mathematical model of the kinetics of self-reproducing micelle experiments;15 in order to do so we have had to formulate a description of the processes involved in micelle formation in a more general manner than had previously been described.The approach is based on a novel application of the fully non-equilibrium Becker»Doé ring equations to micelle formation kinetics and is discussed further in Section 2. In the present paper we extend this development by formulating a new generalisation of the Becker»Doé ring model which is applicable to both vesicle formation and vesicle selfreproduction kinetics. Our model may also be applicable to certain micellar systems; however many micellar systems can be analysed using simpler models as we have demonstrated in J.Chem. Soc. Faraday T rans. 1998 V ol. 94 234 an earlier paper.15 To deal with self-reproducing vesicles requires a more complicated model from the start. Since here we are particularly interested in comparing our results with experimental observations from a vesicular system we shall refer to vesicles throughout the text. There are three challenges in the modelling of vesicular selfreproduction which we aim to address (a) to model vesicle formation on a microscopic level ; (b) to bridge the gap between microscopic and macroscopic models in a systematic manner; and (c) to analyse the resulting macroscopic model to show that it correctly captures experimentally observed behaviour. Sections 2 and 3 introduce the basic theory on which our models are based.Section 4 addresses the –rst challenge in providing a microscopic model of the mechanisms of vesicle formation; Sections 5»7 are necessary for (b) that is to handle the contraction from microscopic to macroscopic model. In these sections we derive a simple set of equations for macroscopic and hence observable quantities from the microscopic model. Sections 7 and 8 together with the appendices demonstrate that the solution of our macroscopic model has the correct properties. As stated above a detailed mechanistic understanding even of simple vesicle formation has until now been lacking.17,18 We emphasize that our model does not assume the existence of a c.a.c. ; rather that the phenomenon is a consequence of our model.The kinetic model we present is nonlinear and highly complex (far more so than our micellar model15) although it is still a simpli–ed description of these systems; however we are able to show that the model correctly captures the experimentally observed behaviour. (2.1) (2.2) 2 Components of the BeckerñDoé ring model cr(t) is used to denote the C containing r individual monomers The Becker»Doé ring equations were originally formulated to describe the kinetics of non-equilibrium gas»liquid phase transitions on the basis of the reversible processes of droplet formation and growth. Their main aim was to describe the number density or concentration of droplets of diÜering sizes as a function of time.The variable concentration of clusters r (atoms molecules ions etc.). Such a droplet or cluster can grow or reduce in size via the addition or subtraction of a single monomer at a time. In chemical notation the process may be written 1) Cr]C1HCr`1 This stepwise aggregation»fragmentation process is the central feature of the Becker»Doé ring model. Thus no cluster»cluster interactions are allowed in the model. This assumption is a good approximation in situations where relatively low cluster concentrations arise (and/or where the interactions are such that the micelles are known not to coalesce) and there are appreciable concentrations of monomers (C present. In mathematical terms the kinetics of this model are governed by the equations r\2 3 .. . dc dt r\Jr~1[Jr dc = dt 1\[J1[ ; Jr r/1 Jr\ar cr c1[br`1cr`1 r which are derived from eqn. (2.1) by applying the law of mass action. In eqn. (2.2) a represents the forward rate of reaction b the backward rate and J denotes the —ux from of (2.1) r`1 r clusters of size r to size r]1. Since the monomer unit C is 1 involved in every reaction there is a special equation for its concentration c1(t). The system of equations (2.2) has the following important properties which constrain the kinetics it describes. 1 A unique equilibrium solution exists. We denote this by Q is a cluster partition function It where r\Qr c6 1 r c6 (Q1\1). r is connected to the forward and backward rate coefficients by arQr\br`1Qr`1.2 The total number of monomers present including those that are free and those sequestered within clusters is constant. o\;r/1 = rcr(t) is con- In other words the matter density served. 3 The quantity V \;r/1 = cr[log(cr/Qr)[1] decreases monotonically with time. It thus quali–es as a Lyapunov function ; in physical terms it corresponds to the free energy of the system. 4 There is an alternative way of writing the in–nite set of ordinary diÜerential equations given an arbitrary sequence of numbers (2.3) g = r c5 r\ ; [gr`1[gr[g1]Jr MgrNr=/1 the following identity (ìweak formœ) holds ; = r/1 r/1 which is equivalent to the original diÜerential eqn. (2.2). 2.1 A generalisation of the BeckerñDoé ring scheme multi-component nucleation The basic Becker»Doé ring model can be generalised to cover a number of physically diÜerent systems.Previously we have used extensions and generalisations of the model to describe micelle formation15,19,20 and to provide a general theory of nucleation including inhibition for chemically reacting systems.21 In the present paper we shall construct another generalisation which can be used to model the formation and chemical transformations of liposomes. As an introduction to this we shall –rst formulate a model for multi-component micellisation in which there are two diÜerent monomer species present (A B) and mixed clusters can form. We shall denote a cluster containing r atoms of type A and s atoms of type B by Cr s . We still only allow a single monomer to be added or removed at a time but now there and type B are two monomers; type A denoted C1 0 denoted C0,1.Thus there two reactions that we have to account for C (2.4) r s]C1 0HCr`1 s Cr s]C0 1HCr s`1 In modelling this system mathematically we de–ne two —uxes one for the material growing by the addition of monomer A and a separate —ux (Jr s @ ) for growth by the addition of (Jr s) monomer B. The equations governing such a system are then [Jr s @ c5 r s\Jr~1 s[Jr s]Jr s~1 @ Gr\1 2 . . . s\1 2 . . . r\2 3 . . . c5 r 0\Jr~1 0[Jr 0[Jr 0 @ s\2 3 . . . c5 0 s\[J0 s]J@0 s~1[J0 @ s c5 1 0\[J1 0[J1 0 @ [; Jr s r s c5 0 1\[J0 1[J0 1 @ [; J@r s r s Jr s\ar s cr s c1 0[br`1 s cr`1 s (2.5) Jr s @ \ar s @ cr s c0 1[br s`1 @ cr s`1 ; signi–es summation of all values of rP0 and sP0 where r s with the exception of r\0\s.This set of equations was originally proposed by Carr et al. ;22 it has similar properties to the former system (2.2) viz There is a unique equilibrium solution s r c6 r s\Qr s c6 1 0 c6 0 1 and now satis–es Q a Q where r sQr s\br`1 sQr`1 s ar s @ Qr s\br s`1 @ r s (as well as Q1 0\1\Q0 1). r s`1 There are now two conserved quantities the density of A A\;r s rcr s o B\;r s scr s . and the density of B o and A Lyapunov function or free energy V \;r s cr s[log(cr s/Qr s)[1] exists which satis–es V0 \0. An alternative way of writing the equations as a set of identities also known as a ìweak formœ is as follows ; gr s c5 r s\; [gr`1 s[gr s[g1 0]Jr s r s (2.6) ] r s ; [gr s`1[gr s[g0 1]J@r s r s (In fact later on we shall not make use of these identities directly but we shall ensure that such a ìweak formœ still exists after any approximations we make.) In Section 4 this system will be generalised further to allow other chemical processes to occur.(3.1) (3.2) r/1 (3.3) 3 A coarse-graining approximation This section discusses the central approximation technique that we use throughout the current paper. The technique has been employed in our micelle formation and self-reproduction model15 as well as in our generalised nucleation theory (incorporating inhibition and chemical reactions)21 to reduce the number of equations we need to consider ; at the same time it reduces the number of (generally unknown) parameters contained in the model.It also has the advantage of producing simple kinetic equations for macroscopically observable quantities enabling the theory to be compared with experimental data. In the present section we summarise the application of the coarse-graining procedure to the basic Becker»Doé ring equations before extending it to the multicomponent equations in the next section. A more detailed account of the method can be found in our previous papers.15,21 The aim is to de–ne new variables x to replace the individ- r ual cluster concentrations c such that x represents an r r average over a certain number of the c variables thereby r reducing the overall number of ordinary diÜerential equations requiring solution.The number j is used to denote the number of c values we clump together to perform this r averaging»thus we aim to make the following de–nitions xr\ 1 j ; j c(r~2)j`j`1 (r[1) ; x1¿c1 j/1 c Here we have kept 14x1 separate from the rest of the concentrations since it has a special ro� le in the Becker»Doé ring system. In order to maintain the same Becker»Doé ring structure in the new system we will have new —uxes L from the group of clusters x to x r r r`1. Thus the diÜerential part of the system will be dx = dt \[L 1[ ; jL r 1 dx dt \L r~1[L r r Indeed only a system such as this can possibly conserve density and satisfy a set of identities similar to the original eqn.(2.3). The –nal relationship to determine is how the —ux L r x1 xr xr`1. On average j monomers need to be depends on added to a cluster in X to convert it into a cluster within r X Xr]jX1H r`1. This corresponds to the chemical reaction Xr`1 which can be incorporated into the mathematical model via the de–nitions L r\ar xr x1 j [br`1xr`1 where ar br`1 can be treated as new parameters. But to be more rigorous it can be shown that they are related to ar J. Chem. Soc. Faraday T rans. 1998 V ol. 94 235 c(r~1)j`2 c(r~1)j`3 . . . crj~2 from the giving b by eliminating r`1 equations for J(r~1)j`1 J(r~1)j`2 . . . Jrj~2 ar\a(r~1)j`1 a(r~1)j`2 ……… arj (3.4) br`1\b(r~1)j`2 b(r~1)j`3 ……… brj`1 From this it is possible to see that the new coefficients ar br`1 are connected to the cluster partition function Q in a similar r br`1 arQ(r~1)j`1\br`1Qrj`1.This procedure is a way to r discussed in more detail in Section V of ref. 21. The system (3.2 3.3) has all the required Becker»Doé ring properties its equilibrium solution is x6 r\Q(r~1)j`1x6 1 ( r~1)j`1 ; o\; by de–ning the density to be r/1 = [(r[1)j]1]xr the density is exactly conserved. V \;r/1 = xr[log(xr/Q(r~1)j`1)[1] is a decreasing function for all solutions of the system and hence is a Lyapunov function. Finally the identities (3.5) = gr x5 r\ ; [gr`1[gr[jg1]L r ; = r/1 r/1 hold for any sequence MgrN. Thus we have reduced the size of the Becker»Doé ring system by a factor of (1/j) whilst maintaining the same essential mathematical structure.The new system is of course an approximation to the original one but it is intended that solutions of the contracted system will give approximations to those of the full system; an elementary study of the accuracy of the course-graining procedure has been carried out by Wattis and King.23 This has been found to be a successful method in earlier and simpler although still highly non-trivial situations15,21 than the case of vesicle formation currently under consideration. (4.1) 4 A Becker-Doé ring model for vesicle formation We return now to the self-reproducing vesicle experiments.8,9 In these simple hydrolysis of anhydride occurs in the absence of vesicles ; chemically we write this step as S]2C1 0 where S represents caprylic anhydride and C the caprylate 1 0 monomer from which vesicles can be formed; C represents i n a vesicle of i monomers with n molecules of the anhydride absorbed.This latter notation was used by Mavelli and Luisi.24 Eqn. (4.1) is intended to represent the direct hydrolysis of the immiscible anhydride by aqueous acid or alkali which occurs mainly but not exclusively near the anhydride» water interface in the stirred reaction vessel.16 (It should be noted in passing that eqn. (4.1) asserts that two surfactant anions are produced rather than one anion and one acid moeity as stated in the model of Mavelli and Luisi.24) Fig. 3 Details of the various kinetic processes occurring in the Becker»Doé ring model of self-reproducing vesicle formation. Upper case letters denote micellar and vesicular species while rate constants are indicated in lower case letters.J. Chem. Soc. Faraday T rans. 1998 V ol. 94 236 We also have the usual Becker»Doé ring type of reversible aggregation process of stepwise addition of a monomer to a vesicle (4.2) C1 0]Ci nHCi`1 n and the stepwise incorporation of anhydride (4.3) Ci n]SHCi n`1 which has been previously introduced by Mavelli and Luisi ;24 k we shall denote the forward rate by i n f and the backward k rate by i n`1 b . (Note that this is treated as a reversible reaction. 24) It is the rate of formation and break-up of this new complex C which is rate-determining in the fast phase of the reaction. i n The crucial step (4.4) (nP1) Ci n ]Ci`1 n~1]C1 0 during which one adsorbed molecule of anhydride is converted to an additional surfactant molecule within the cluster together with a free surfactant monomer produces a long induction time before a sudden rapid reaction as the process (4.4) occurs much faster than (4.1).Fig. 2 shows the overall structure of the reaction scheme (4.1)»(4.4) whilst Fig. 3 displays a small portion of the vesicular part of the reaction scheme in much greater detail together with rate constants and the allowed pathways. In Fig. 2 each diÜerent superscript symbol indicates a diÜerent form of equation needed to describe the kinetics of that type of cluster. Vesicles are comprised overwhelmingly of surfactant monomers that is the important Ci n are those with iAn.For this reason we shall restrict the (i n) space to i[n. Fig. 2 Diagram showing the reaction scheme proposed as a model for vesicle formation. Each diÜerent superscript symbol indicates a diÜerent form of rate equation needed to describe the kinetics of that type of cluster. Putting the four rate processes of eqn. (4.1)»(4.4) together and writing down the diÜerential equations for the corresponding concentrations (in lower case letters) we –nd Ji n @ = s5 \[k0 s[ ; ; = n/0 i/n`2 = = Ji n] ; ; ki n ci n = = c5 1 0\2k0 s[J1 0[ ; ; n/1 i/n`1 i/n`1 n/0 c5 2 0\J1 0[J2 0[J2 0 @ c5 i 0\Ji~1 0[Ji 0]ki~1 1 ci~1 1[Ji 0 @ (iP3) [Ji @ n c5 i n\Ji~1 n[Ji n]Ji n~1 @ ]ki~1 n`1 ci~1 n`1[ki n ci n (nP1 iPn]3) c5 n`1 n\[Jn`1 n]J@n`1 n~1[kn`1 n cn`1 (nP1) (nP1) c5 n`2 n\Jn`1 n[Jn`2 n]Jn` @ 2 n~1 [kn`2 n cn`2 n [J@n`2 n Ji n\ai n ci n c1 0[bi`1 n ci`1 n (4.5) ci n`1 Ji n @ \ki n f ci n s[ki n`1 b Here the variables Ji n represent —uxes from clusters composed of i caprylate monomers and n caprylic anhydride molecules to those with one extra monomer; similarly Ji n @ represents the —ux to vesicles with one extra anhydride molecule.The forward rate coefficient for the addition of monomer is denoted ai n and the backward rate bi`1 n . For the addition of anhydride the forward rate is written the backward one as converted to caprylate monomer at the rate ki n f and ki b n`1. Caprylic anhydride is irreversibly k0 . Finally and crucially for the overall kinetic behaviour there is an alterna- C tive conversion mechanism namely that a C vesicle is con- i n vesicle and a monomer (C i`1 n~1 and is assumed to be an irreversible 1 0) ; this verted to a occurs at a rate ki n process.The system of eqn. (4.5) is a new generalisation of the Becker»Doé ring equations. Thus we must check that the Becker»Doé ring structure is preserved. Indeed we –nd the following properties. 1 There is an equilibrium state s6 \0 c6 i n\0 #nP1 c6 i 0\Qi c6 1 0 i . The cluster partition function Qi is related to Ci 0 and also to The the equilibrium chemical potential of cluster the rate constants other ai 0 bi`1 0 i 0Qi\bi`1 0Qi`1. via a ai ns and bi ns need satisfy no special relationship. 2 Density since the anhydride molecule has approximately twice the mass of a single caprylate monomer the quantity (4.6) = o\2s(t)] ; (i]2n)ci n (t) ; = n/0 i/n`1 3 The quantity should be conserved.(We note that in mixed-micelle and mixed-vesicle systems comprising two distinct monomeric forms which cannot mutate from one form to the other there will be two conserved quantities one corresponding to the conservation of each species.) n/1 = ;i=/n`1 nci n satis–es the V \s]; conditions for a Lyapunov function. Since there are trajectories over which V0 \0 this is not a strong Lyapunov function. Moreover it does not correspond to a free energy of the system (note the diÜerent form this V has from the previously quoted Lyapunov functions). 4 There is a weak form gi n c5 i n = g0,1s5 ] ; ; = n/0 i/n`1 (gi`1 n[gi n[g1 0)Ji n = \(2g1 0[g0,1)k0 s] ; ; = n/0 i/n`1 (gi n`1[gi n[g0,1)Ji n @ (4.7) (g = ] ; ; = n/0 i/n`2 ] ; = i`1 n~1[gi n]g1 0)ki n ci n ; = n/1 i/n`1 The complexity of the model (4.5) is obvious.Hence in Section 5 we shall investigate the possibility of reducing the number of diÜerential equations involved by invoking a coarse-graining technique. Before doing that we note some of the properties of the equilibrium solution of eqn. (4.5). 4.1 Equilibrium propertiesñvesicle formation without self-replication From point one above we see that at equilibrium there is no anhydride present in the system at all either in its original form or incorporated into vesicles.All the vesicles are of the ìpureœ form with concentrations denoted by ci 0 (the concentrations ci n with nP1 are all zero). There is simply a distribution of ìpureœ vesicles across a range of sizes ; we denote by i* the aggregation number where this distribution peaks. The cluster partition function Q can be related to the i chemical potential of the vesicles in a similar way to that which occurs in the treatment of micelles.15 We write the temperature as T Boltzmannœs constant as k and the chemical potential of a cluster of size i in its standard state as ki E; then the chemical potential of a vesicle of size i is (4.8) ki\ki E]kT log ci 0 If we arbitrarily set the standard chemical potential of mono- (k mers to zero 1 E\0) then the condition of thermodynamic equilibrium ki\ik1 implies that (4.9) ki E\[kT log Qi establishing a relationship between the cluster partition function (Q and the chemical potential of a cluster Ci 0 in its i) standard state.Since vesicular clusters comprising only a small number of monomers are highly unstable they have associated with them a large chemical potential implying in turn small values for Q and hence small concentrations at equilibrium. Small i vesicles tend to either break up into individual monomers or incorporate monomers to form larger more stable vesicles. In fact for geometrical reasons it is unlikely that very small vesicular clusters can form at all ; such transient clusters are more likely to exist as lamellar bilayers with high end energies due to the exposed hydrophobic tails of the individual surfactant molecules.Hence we expect the chemical potential of monomer and larger vesicles to be lower than for small vesicles. This implies the existence of an equilibrium cluster distribution function which shows the presence of some monomers a few dimers fewer trimers then stays very small for a considerable range of aggregation numbers before rising to a maximum at the most probable vesicle size i* and –nally reducing again (vesicles of arbitrarily large size are not found). The most important characteristics of this distribution are that there is a considerable number of monomers present a ìrare–edœ region where hardly any vesicular clusters of intermediate size are found and a region containing a well de–ned distribution of larger vesicles present in signi–cant concentrations.Such a size distribution is qualitatively similar to that encountered in spherical micelle systems and is a crucial J. Chem. Soc. Faraday T rans. 1998 V ol. 94 237 Fig. 4 Cluster size against aggregation number showing a reasonably strongly peaked distribution of vesicle sizes [taken from Fig. 5(B) of Walde et al.8] feature which enables the coarse-grained contraction procedure of Section 5 to be applied successfully. While in micellar systems one typically –nds that the distribution of larger clusters is sharply peaked about one cluster size that is the micelles are quite highly monodisperse in the case of vesicles the distribution function is normally broader owing to the fact that vesicle solutions are usually more polydisperse.See Fig. 4 for an example of such a size distribution curve. Before closing this section there are two further points we wish to make. The –rst concerns the metastable properties of many vesicular systems referred to in Section 1. In the present paper the thermodynamic stability of vesicles is controlled by the numerical values of their associated chemical potentials compared with that of monomers. The model on which our analysis is based eqn. (4.5) does not include the possibility that such vesicles can transform into micellar structures (spheres rods or disks) or lamellae although it is perfectly possible to include such transformations as well at the expense of greatly complicating the analysis.25 It is nevertheless intriguing to point out that some elements of the kinetic metastability of vesicles are captured by the current model (see the discussion in Section 8).The second point concerns the validity of the Becker» Doé ring scheme for modelling vesicle formation. As noted in Section 2 the approximation is good when the concentrations of clusters are low and the monomer concentration is high and we shall assume these conditions hold here. Whereas the one-step nature of the model has wide validity for aqueous spherical micelles comprised of ionic surfactants (for which the coulomb repulsion between polar head groups is large) the domain of validity of such an approximation for vesicular systems is more restricted.Under more general conditions the kinetic equations should then be based on the so-called coagulation»fragmentation equations of von Smoluchowski,26 which admit much more general aggregation and coalescence processes once again at the cost of increased analytical complexity.25 Indeed we note that some of the more remarkable observed features of self-reproducing vesicular systems which involve budding and ìbirthingœ,9 can only be described in these more general terms. 5 Contraction procedure In this section we introduce a simpli–cation that enables the vast array of eqn. (4.5) to be reduced to a manageable number. J. Chem. Soc. Faraday T rans. 1998 V ol. 94 238 The procedure makes a combination of assumptions which are quite reasonable in the context of vesicle formation and these we shall now describe.The –rst is that the various processes modelled take place over widely diÜering timescales. In particular there is the very slow dissolution of caprylic anhydride to form caprylate monomer; another slow process is the self-assembly of monomers into vesicles. Faster processes include the equilibration of the vesicle distribution at larger cluster sizes which is controlled by the rapid exchange of monomers between vesicles and the surrounding solution. The reason for the slow rate at which monomers aggregate into vesicles is that the intermediate stages of very small vesicles are highly unstable. They have a great propensity to break up (dissociate) and return their constituents to free monomeric form; thus their typical lifetime is short.It is for these reasons that the equilibrium distribution has very few vesicles of small size. Over shorter periods of time a vesicle is able to absorb or expel monomers (exchanging them with the surrounding solution) and so achieve equilibrium with its neighbouring vesicle sizes. This short-time relaxation we refer to as ì selfequilibrationœ or ì local equilibrationœ since it refers only to part of the system reaching a (quasi)equilibrium state. The system is still evolving on longer timescales so this is not a true global equilibrium state. As we mentioned above larger vesicles are more stable than very small ones; hence there is a natural separation in aggregation number between vesicles and free monomers.Thus we intend to focus on just two regions one determining the concentrations of very small clusters and a second covering the range of sizes in which vesicles are common. Since experimentalists are not often primarily concerned with the details of the polydispersity of the vesicle size distribution it is reasonable to have one variable describing the concentration of monomers and another providing an averaged description of the vesicle population. In summary our reduction method is based on a combination of the assumptions of (i) a separation of timescales and (ii) the existence of certain local equilibria. The separation of timescales gives the opportunity for a subset of the kinetic processes in our model to approach a state of local equilibrium.A global equilibrium solution of the full model carries over to a corresponding equilibrium solution of the reduced model. Although much of the following analysis assumes local equilibrium of certain parts of the system it never assumes the system is in a global equilibrium state or even close to such a state. 5.1 Derivation of contracted kinetic equations i`1[Ki\ji i Kn @ with K Kn`1 @ [Kn @ \ and so that K and Kn @ mark the position of the largest aggre- i c ji~1 kn~1 j m s rep- Following the contraction procedures carried out on simpler systems in previous papers,15,21 we suggest the following coarse-grained contraction for the kinetics of vesicle formation.The coarse-graining approximation is achieved by de–ning a new grid K kn ; gation numbers in the space of the and resent the size of the region averaged over to –nd xi n . Thus we think of the corresponding ìaveragedœ concentrations xi n as being de–ned by 1 (5.1) x cj m i n\ j ; K i K ; n @ i~1kn~1 j/Ki~1 m/Kn~1{ x x is then denoted by L and that i n i`1 n i n @ ; x i n x to L by x 1 i n and i,s n` respectively. Their eÜective forward and backthese quantities are strongly nonlinai n bi`1 n a@i n bi @ n`1. We now when the conversion to surfactant The —ux from to from ear in 1 ward rate constants are denote the rate coefficient for hydrolysis of anhydride by i k0 and by i instead of 0 i n occurs within clusters represented by xi n kn L i n @ = s5 \[i0 s[ ; ; = i/n`2 n/0 x5 ji L i n = 1 0\2i0 s[L 1 0[ ; ; = n/0 i/n`1 li n ii n xi n ] ; = ; = n/0 i/n`1 x5 2 0\L 1 0[L 2 0[L 2 0 @ x5 iP3 nP1 i 0\L i~1 0[L i 0[L i 0 @ ]ii~1 1 xi~1 1 [L i @ n iPn]3 x5 i n\L i~1 n[L i n]L i n~1 @ ]ii~1 n`1 xi~1 n`1[ii n xi n nP1 x5 n`1 n\[L n`1 n]L n` @ 1 n~1[in`1 n xn`1 n x5 n`2 n\L n`1 n[L n`2 n]L n` @ 2 n~1 nP1 [L @n`2 n[in`2 n xn`2 n L j i n\ai n xi n x1,i 0[bi`1 n xi`1 n (5.2) L (j i0 ii n the following identity relating the derivatives L i n L i n @ holds = = h0,1 s5 ] ; ; hi n x5 i n\(2h1 0[h0 1)i0 s (h n/0 i/n`1 ] ; = i`1 n[hi n[ji h1 0)L i n (h ; = n/0 i/n`1 ] ; = i n`1[hi n[kn h0 1 )L i n @ ; = n/0 i/n`2 = (5.3) =; (h i/n`1 ] ; n/1 tion of density provided (j ji\j i n\j.have K density is (5.4) = o\2s] ; ; = n/0 i/n`1 i,0 3 Equilibrium from the identities n\1 2 . . . then by setting the —uxes L a x6 i 0\QKi x6 1 0 Ki where i 0QKi\bi`1 0QKi`1 . –nd 4 Lyapunov function the function = V \s] ; jnxi n ; = n/1 i/n`1 G i n @ \ai n @ xi n skn[bi n`1 @ xi n`1 These equations contain arbitrary coarse-graining functions i kn) and extra parameters l which depend on the granu- i n larity. We now examine the Becker»Doé ring structure of this system to check that such a coarse-graining does not destroy any of the essential properties. 1 General identities for any sequence of numbers Mhi nN s5 x5 i n to i`1 n~1]li n h1 0[hi n)ii n xi n 2 Conservation of density as in previous contractions a minor rede–nition of density is required in our new coordinate system.Thus we de–ne o\2s(t)];n/0 = ;i=/n`1 (Ki ]2Kn @ )xi n(t). Then the weak identities (5.3) establish conservaji\ kn in other words we must use a i\kn\j). Conserva- K1\1 we square uniform coarse-graining mesh tion of o also requires l Since #i and i\(i[1)j]1 for iP1 and Kn @ \jn. Thus the [2jn]ji[j]1]xi,n s6 \0; x6 i n\0 for equal to zero we satis–es V0 O0. Thus the coarse-graining procedure will only work if the functions ji kn and li n satisfy certain constraints. To summarise the conditions on eqn. (5.2) being the correct contraction of (4.5) are (5.5) li n\j ji\j kn\j for all i n.Such a uniform mesh was described in our earlier paper on self-reproducing micelles.15 A general mesh where ji varies with i does not allow density to be conserved in the present case. Nevertheless such a mesh has previously been used to analyse nucleating systems in the presence of chemical reactions.21 Here however in order to conserve density our mesh must have the same spacing in both i and n directions. Eqn. (5.2) then represent the kinetics of the chemical reactions S]2X1 0 Xi n]jSHXi n`1 rate coeÜ.\i G 0 forward-rate coeÜ. \ai n @ backward-rate coeÜ.\bi @ n`1 (iPn]2) Xi n]jX1 0HXi`1 n Gforward-rate coeÜ. \a Xi n ]Xi`1 n~1]jX1 0 i n backward-rate coeÜ.\bi`1 n rate coeÜ.\ii n (nP1) (5.6) i n .L s @ 5 \[i0 s[jL 2 0 1 0\a1 0 x1 0 j`1[b2 0 x2 0 L 2 0 @ \a2 0 @ x2 0 sj[b2 1 @ x2 1 (6.1) (6.2) Fig. 5 Diagram showing reaction scheme of maximally contracted model 6 Maximal contraction In this section we aim to take the reduction procedure described earlier as far as possible without eliminating any of the rate-determining processes. Our aim is to obtain a system of equations that we can analyse theoretically ; thus we want to eliminate as many of the intermediate stages of reactions as possible without losing the essential kinetics of the process. This corresponds to taking j as large as possible while keeping at least one of the reactions with rate constants i Hence we shall attempt to analyse a system with just x1 0 variables as shown in Fig.5. x2 0 x3 0 and x2,1 The kinetics of this system are determined by the following equations x5 1 0\2i0 s[L 1 0[jL 1 0[jL 2 0]ji2 1 x2 1 L j 2 0\a2 0 x2 0 x1 0[b3 0 x3 0 x5 2 0\L 1 0[L 2 0[L 2 0 @ x5 3 0\L 2 0]i2 1x2 1 x5 2 1\L 2 0 @ [i2 1x2 1 This system has only one conserved quantity the total density o, o\2s]x1 0](j]1)x2 0](2j]1)x3 0](3j]1)x2 1 so we have to analyse a fourth-order system. This will be done by the use of matched asymptotic expansions noting that i0\v@1. We choose this notation to emphasize that i0 which is the uncatalysed rate of decay of anhydride to surfactant is a small parameter. In the remainder of this paper we simplify our notation as follows a2\a2 0 a1\a1 0 J.Chem. Soc. Faraday T rans. 1998 V ol. 94 239 b x2\b2 0 b3\b3 0 a@\a2 0 @ b@\b2 1 @ i\i2 1 x1\ 1 0 x2\x2 0 x3\x3 0 y\x2 1. Chemically the rate eqn. (6.1) corresponds to the reaction scheme S]2X1 backward rate coeÜ. KX1HX2 rate coeÜ.\v¿i Gforward-rate coeÜ. \a1¿a1 0 0 \b2¿b2 0 jS]X2HY G @ forward-rate coeÜ. \a@¿a2 0 backward-rate coeÜ.\b@¿b jX1]X2HX3 Gforward-rate coeÜ. \a2¿a2 0 2 1 @ backward-rate coeÜ.\b3¿b3 0 (6.3) rate coeÜ.\i¿i2 1 Y ]X3]jX1 where the variables label species as follows S\caprylic anhydride X1\caprylate monomer X2\vesicles of pure caprylate size K\j]1 molecules X3\vesicles of pure caprylate size M\2j]1 molecules Y \mixed vesicles comprising K molecules of caprylate with j adsorbed molecules of caprylic anhydride.(6.4) (X3) can also be formed by the The –rst reaction represents the slow irreversible conversion of caprylic anhydride to monomer. The monomer can then (reversibly) form vesicles as shown by the second step. The third shows the adsorption of caprylic anhydride onto the vesicles forming mixed vesicles (Y ). The last step shows that the mixed vesicles convert incorporated anhydride both to free monomer and monomer which forms part of a larger vesicle. These larger vesicles addition of monomer to smaller vesicles (X2) as shown in the penultimate step of (6.3). In physicochemical terms the approximation involved in the contraction procedure pulls out of the full in–nite set of possible chemical transformations (and associated rate equations) the smallest subset which describes the ratedetermining processes involved in the growth and selfreproduction of vesicles.As in the micellar model,15 on physical grounds we expect that the slowest timescale on which vesicle growth occurs is dictated by the passage of monomer through the ìbottleneckœ of intermediate aggregation numbers (which are very unstable and are only present in extremely low concentrations) into the regime of higher vesicle aggregation numbers. On both sides of this bottleneck matter can be assumed to equilibrate rapidly. 6.1 Comparison with the scheme of Mavelli and Luisi The approach adopted by Mavelli and Luisi24 in their attempt to model self-reproducing vesicles relies heavily on assumptions of thermodynamic equilibrium between species present in the reaction mixture.Our model diÜers from theirs in numerous ways. However the most important distinction lies at a fundamental level. As in our work on self-reproducing micelles,15 we begin from a kinetic description which makes no assumptions of thermodynamic equilibrium our concern is to provide a mechanism for how vesicles form and then selfreplicate. Mavelli and Luisi24 prefer to take as given the existence of self-assembled vesicles they do not attempt to describe the processes that must be involved in their formation from monomers. Furthermore they assume that these structures are essentially in a state of thermodynamic equilibrium with all other reaction components.J. Chem. Soc. Faraday T rans. 1998 V ol. 94 240 Thus none of the detailed multi-step processes which are present in our model (see Sections 4 and 5) appear in their formulation. In particular as regards the contracted model we derived in Section 5 de–ned by eqn. (6.3) above Mavelli and Luisi have no analogue to our vesicular growth and fragmentation processes KX1HX2 or X2]jX1HX3 . (7.1) sjB (7.2) (7.3) 7 Further reduction of the rate equations The fourth-order system of eqn. (6.1) although much simpler than our original model (4.5) is still too complex to analyse in detail. Thus in this Section we make a further simpli–cation to reduce the mathematical system of rate eqn. to a form analysable by the use of phase planes a common methodology in nonlinear dynamics which we previously invoked in our analysis of self-reproducing micelles.15 To achieve this simpli–cation we assume that the three (x types of vesicle small and pure (x 2) large and pure 3) and mixed (y) are all in local equilibrium with each other.Mathematically speaking this amounts to assuming a steady-state distribution of mass between these kinds of vesicles ; that is the —uxes between these three moieties are in balance such that L @2 0\iy\[L 2 0 Mathematically this approximation is the –rst term in an L asymptotic expansion where each of 2 0 L 2 0 @ and iy are L large but the combinations 2 0 and @ ]iy L2 0[iy are L close to zero relative to any one of 2 0 L 2 0 @ or iy. Time derivatives will enter in higher order terms but not at leading order thus simplifying two of the equations in (6.1) from differential equations to algebraic equations.The quantities x3 and y are then related to the rest of the system through simple relations involving x2 a situation which can be referred to as x and y being ìslavedœ to x2 .27 This subtle aspect of asymp- 3 totic analysis then enables the whole system to be analysed without recourse to numerical methods. Clearly this approximation will not always be valid under general nonequilibrium conditions ; it requires the rate of equilibration among the different types of vesicles to occur on a much faster timescale than any other process involved in the scheme. In particular it assumes that the release of monomer from caprylic anhydride and the formation of vesicles from monomers both occur on longer timescales than self-equilibration among vesicles.In fact for these surfactant-based self-reproducing systems this is a good approximation since micelle and vesicle aggregation processes are very fast in comparison with the slow rate of hydrolysis of aqueous anhydride. Solving the two equations in (7.1) we can write the concentrations y and x in terms of x2 3 y\ a@x2 sj i]b@ 3 i a@ x3\x2 b x1 j ] i]b@ b3 2 We then use the conservation of density o\2s]x1](j ]1)x2](2j]1)x3](3j]1)y to eliminate x2 from the system leaving just two ordinary diÜerential equations for x1 and s. This substitution amounts to x x D ]a@sj[(3j]1)b tions are 1 Aa 2\ b3 (i]b@)(o D [x1[2s) 3\ (o[x1[2s)[a2 ( D i]b@)x1 j ]a@isj] y\ (o[x1[2s)a@b3 sj D\b3 (j]1)(i]b@)]a2 x1 j (2j]1)(i]b@) 3](2j]1)i] The substitution s1\o[2s means that the initial condis (0)\0\x (0).Substituting eqn. (7.3) into the 1 equations for x s 5 1 and 5 from (6.1) we –nd that our system is governed by the two ordinary diÜerential equations x5 1\v(o[s1)[(j]1)a1x1K ] b3(s1[x1)[b2(j]1)(i]b@)]21~jja@i(o[s1)j] D (7.4) s5 1\v(o[s1)] 21~jb3 ja@i(s1 D [x1)(o[s1)j An analysis of the unperturbed system (that is when v\0) reveals that the initial condition is a critical (equilibrium) point. Hence we expect an induction-type behaviour characteristic of a chemical clock where very little happens at the start (cf.ref. 15 and 28). One of the eigenvalues at this point vanishes and the other is negative con–rming the existence of a centre manifold.29 We can use either matched asymptotic expansions as in ref. 21 or the perturbative centre-manifold procedure as carried out in ref. 15 to –nd approximate solutions. 8 Solution of the contracted kinetic equations for self-reproducing vesicles In this section we summarise approximate solutions to eqn. (7.4). Although to this point we have performed many approximations and simpli–cations albeit in a systematic and controlled manner the system is still too complex to –nd an exact explicit solution. However owing to the presence of a small parameter (v) it is possible to –nd a highly accurate approximate solution using the method of matched asymptotic expansions and a perturbative centre-manifold procedure.8.1 Solution by the method of matched asymptotic expansions In this method the temporal evolution of the system is split into a sequence of regions (four in this case). In each region some of the terms in these equations are insigni–cant and so can be neglected giving solvable equations for that time interval. These solutions are then ìmatchedœ to ensure that the system evolves smoothly from one region to the next and the system of equations is thus fully solved as we describe in 2](2j]1)x3](3j]1)y] is represented by v and outline here. The details of this process are provided in Appendix B. To simplify the procedure we use the variables u\s and v\s1[x1.This has the advantage that now there is only 1 one O(v) term in the diÜerential equation system. These variables are not simply mathematically convenient they represent macroscopic quantities of interest. The total vesicular mass [Kx u denotes the total surfactant mass (v]x1\o[2s). Our differential eqn. (7.4) become Kv(o[u)j u5 \v(o[u)] D0]D1(o[u)j]D2(u[v)j Bv (8.1) v5 \Ka1(u[v)K[ D0]D1(o[u)j]D2(u[v)j where the new constants are de–ned by B\b2 b3K(i]b@) K\21~jjia@b3 D0\b3(j]1)(i]b@) D1\2~ja@[(2j]1)i](3j]1)b3] (8.2) D2\a2(2j]1)(i]b@) Region I. A short region during which the precursor S is converted into monomer. The concentration of monomer (x grows linearly 1Bvot) and a very small concentration of vesicles is formed (mass in vesicles v\o[x1[2sBvK).Thus the concentration of anhydride falls linearly sB 12 [o[vot] and uBvot n! vB vKa1oKKK! exp([ht)[ ; K ([ht)n ([h)K`1 n/0 (8.3) u(t)BA Bvo KKa tD (8.4) B t 1 (8.6) v(t)Bv0[ (1]L v 0 L v 0) Kv Here v satis–es 0 (8.8) Ka1(o[v0)K\ D where h\B/(D0]D1oj). Region II. This region is the long induction region ; the asymptotic equations only balance if time is rescaled to consider time-intervals of O(v~j@K). During this region the variable v is ìslaved toœ u and u changes very slowly. Physically this means that the vesicular concentration passively follows the change in total caprylate concentration so that vesicles and monomers stay in equilibrium with each other 2cBAvjo2j B Ka1KB1@K B o 2 2 Co2 4 b jia 2(i] a@v b@ j )D1@K (8.5) As this time is approached both u and v appear to blow up.At this stage the rapid reaction starts and we need to revert to the original timescale to examine the kinetics in proper detail. Region III. This covers the rapid reaction region. Unfortunately the equations are too complex to solve here ; hence we only have approximations at the start and the end of the region. At the start a centre-manifold is identi–ed showing the dynamics are essentially nonlinear These solutions diverge and another approximation needs to be found for the concentrations as they approach their equilibrium values. This behaviour is also controlled by a centre manifold showing that nonlinear terms dominate the approach to equilibrium as well as the start of the reaction.This accounts for the extremely slow and unusual approach to equilibrium seen in the experimental results of Walde et al.8 Our results show that it is algebraic and not exponential decay which governs the time evolution in this region C D 0(j[1)(t[t2c)D1@(j~1) (8.7) and is the value of v at equilibrium. Region IV . In the –nal approach to equilibrium a slightly diÜerent set of terms control the kinetics. In this region more analytical progress can be made in understanding the dynamics. The approach to equilibrium occurs on a slow timescale with the vesicle concentration (v) slaved to the total C 1ojB1@K ZK~1CAKKa B 1 vjo2jB1@K v(t)BKa1(D0]D1oj)uK The region has an abrupt end as t]t2c where u(t)BA B [jKa1Koj(t2c[t)]B1@j v(t)B Ka1(D0]D1oj)B1@j [jKa1Koj(t2c[t)]K@j u(t)Bo[CD0]D2(o[v0)j Kv0(j[1)(t[t2c)D1@(j~1) 0]D2(o[v0)j Bv D0]D2(o[v)j 0 J.Chem. Soc. Faraday T rans. 1998 V ol. 94 241 concentration u. Physically this corresponds to the two quantities remaining in self-equilibrium with each other throughout the duration of the region (8.9) uBo[Cev(j~1)(t~C)[ v Kv D1@(j~1) 0/D= vBv0G1[ 1] L L v ev(j~1)(t~C)[ v Kv D1@(j~1)H (8.10) C 0 0/D= where D=\D0]D2(o[v0)j. As a result of this analysis we –nd that our solution has two regions before the main reaction»one short region where one variable reaches a pseudo-steady-state value followed by a second long region where it remains slaved to the second variable.This is the long induction period during which very little appears to happen. Region III is where the rapid reaction occurs. Even after ignoring terms in the asymptotic expansion the equations in this region are too complex to solve. Thus all we can manage is to write down an approximation for the start of the region and another approximation for the kinetics at the end of the region. This shows an unusually slow approach to equilibrium and undergoes a slight change as a fourth –nal region is entered describing the –nal stage of reaching equilibrium which also occurs over a long timescale. It must be recalled that all these results are obtained under the assumption stated in eqn.(7.1) namely that the three types of vesicles which are de–ned in the contracted Becker»Doé ring scheme (small and pure large and pure large and mixed the latter implying that anhydride molecules are adsorbed) are always in thermodynamic equilibrium with one another. The concentrations of mixed vesicles and large vesicles are then directly dependent on the concentration of small vesicles that is they are slaved by eqn. (7.2). For this to be the case the timescale over which they self-equilibrate must be much faster than any of the other processes concerned. The behaviour that results from typical choices of parameters is shown in Fig. 6 and can be seen to be in good agreement with the experimental observations of the hydrolysis of caprylic anhydride by Walde et al.;8 see also Mavelli and Luisi.24 With nine parameters in our model and very little quantitative experimental data it is impossible to –t parameters in a reliable manner. The values chosen are provided simply to show that our model supports the observed behaviour. x1 All the analysis presented thus far assumes the initial condi- (0)\0\x (0)\x (0)\y tions s\o/2. From the de–ni- 2 3 tions of u v together with eqn. (8.4) and (A2) below the monomer concentration is given by (8.11) x1(t)Bvot once a short self-equilibration region is passed (region I). Thus the time taken for the monomer concentration to reach a small quantity d is d/vo. If the system is now initiated with x(0)\d and s(0)\o/2 the total mass is o]d and the induction time will be shortened by d/v(o]d).The formula for the induction time is then modi–ed from (8.5) to tindBC B KvjKa1 model. in (o]d)2jD1@K [ v(o] d d) (8.12) kind our of behaviour is noted in experimental systems as well as This quantity drops to zero if d is sufficiently large indicating the existence of a critical aggregation concentration discussed earlier. Noting that v@1 the c.a.c. is x1 c.a.c.\dc.a.c.BA Bv K To a1 is summarised diagrammatically in Fig. scheme. é of version Koj~1B1@K (8.13) and self-reproduction the Becker»Do based ring kinetic on a substantially 2 and 3. The full generalised our scheme knowl- 9 Discussion We have proposed a detailed mechanism for vesicle formation J.Chem. Soc. Faraday T rans. 1998 V ol. 94 242 0\0.01 D1\1.99 D2\0.1 B\11.976 Fig. 6 Graph of total surfactant concentration vs. time showing the induction time and slow approach to equilibrium. Parameters v\0.012 o\1.0 j\20 D K\2.395 and a –xed by taking v 1 represent experimental results for the hydrolysis of caprylic anhydride 0\0.68 in eqn. (8.8). The circles as shown in Fig. 6(A) of Walde et al.8 8.2 Centre-manifold perturbation approach A search for critical points of the unperturbed system [eqn. (8.1) with v\0] leads to two such points u\v\0 which is the initial condition and u\o v\v0 which is the equilibrium con–guration of the system. In Appendix C we analyse each of these in turn using the perturbations of the centre-manifold.This is the same technique we used to solve the kinetic equations governing the formation of selfreproducing micelles in a previous paper.15 Here we con–ne ourselves to making a few remarks about the physicochemical interpretation of this mathematical solution which provides additional insights to those obtained from the foregoing asymptotic analysis. The fact that there is a centre-manifold emanating from the equilibrium con–guration shows that the vesicle distribution is only just stable and that a minor structural perturbation to the system could cause the equilibrium solution to become unstable or change form dramatically. This behaviour is gratifying in view of the known relative instability of many vesicles.Moreover the presence of a centre-manifold results in a very slow approach to equilibrium. States on the centremanifold evolve extremely slowly and so over short time intervals they appear to be at equilibrium. In mathematical parlance such states are often called metastable since if perturbed they quickly return to a quasi-static state and then continue to evolve towards equilibrium only very slowly. This edge this is the –rst model for the mechanism of formation of vesicles which takes into account the stepwise processes by means of which these structures self-assemble and then reproduce. Previous highly simpli–ed models have assumed the spontaneous emergence of fully-formed vesicles at the critical aggregation concentration and the omnipresence of thermodynamic equilibria between monomers micelles and vesicles.24,30 In order to make our general model analytically tractable as well as to eliminate the need to determine or –t a very large number of generally unknown rate coefficients for the individual molecular processes comprising the full reaction scheme we have developed a systematic contraction or coarsegraining approximation procedure which reduces the dimensionality of the kinetic equations while making them much more suitable for direct comparison with macroscopic data.This leads to a relatively simple macroscopic description of the system. The speci–c experiments and the model we have proposed here have possible relevance to the chemical origins of life,31 since the chemical processes involved provide a direct route to the formation of bounded cell-like structures under prebiotic conditions.The Becker»Doé ring model gives results that agree well with experimental data at least in part because it describes the existence of a critical aggregation concentration in a natural way. One manifestation of this is shown by the dependence of the induction time on the initial surfactant concentration when this reaches the c.a.c. the induction time falls to zero. It is possible to include more general aggregation and fragmentation processes than the one-step monomer attachment and detachment kinetics implied by the Becker»Doé ring scheme. Here this would considerably complicate an already difficult theoretical problem.However we hope to return in the future with an analysis of some related coagulation» fragmentation problems involving surfactants in which such a generalisation can be fruitfully studied.25 We are grateful to Pier Luigi Luisi Peter Walde Kenichi Morigaki Neville Boden Richard Harding and John Billingham for several helpful discussions and to Marco Maestro for making available to us a preprint of ref. 24. P.V.C. is grateful to Luigi Luisi for an invitation to visit the Institut fué r Polymere at E.T.H. Zué rich in June 1996 and for his kind hospitality ; also to Wolfson College and the subdepartment of Theoretical Physics at the University of Oxford for a Visiting Fellowship. J.A.D.W. is grateful to the Nuffield Foundation for the provision of computing equipment.(A1) (A2) n(O) can be calcu- Appendix A the function Zn(s) In ref. 15 we introduced the function Zn(s) de–ned by Zn(s)\Ps dx 1]xn 0 For convenience we summarise its properties again here. For small s the integrand can be expanded around x\0 to –nd Zn(s)\s 2F1A1 1 n n]1 [snB n Bs[ sn]1 n]1 ] 2 s n 2n` ] 1 1 ]… … … where 2F1(a b c x) is a hypergeometric function. Since the value of n that concerns us is large this can be approximated by 2F1(1 0 1 x)\1. For large s we note that the quantity Z lated by contour integration in the complex plane [Zn(O)\ n/n cosec(n/n)]. Further terms in the series for large s can be obtained by subtracting the contribution from (s O) (the summation only converges for s[1) Zn(s)\ n n nB[ n s1~ [ n 1 2F1A1 n[1 2n[1 [s~nB n n cosecAn (A3) Again since our value of n is large the hypergeometric func- 2F1(1 tion can be approximated by 1 2 x)\ [x~1 log(1[x) [Abramowitz and Stegun,32 eqn.(15.1.3)]. (B1) (B2) (B3) (B4) Ao (B6) (B7) Appendix B solution of eqn. (8.1) by matched asymptotic expansions We use subscripts on the u v variables to denote the scaled solution in each region. B1 region I The initial conditions are u(0)\0\v(0). Thus we seek a scaling for u and v which make both small this is consistent uBvu1 vBvKv1 tBv0q1 so that our leading order when equations are u5 1\o v5 1\Ka1u1K [ D Bv1 0]D1oj where D0 D1 are as de–ned in eqn.(8.2). The solution is 1\ot v1\Ka1oK e~ht Pt ehssK ds u 0 h\B/(D where 0]D1oj). This solution will break down when uB1 or when uBv or when vBv. The –rst two occur at tBv~1 the latter at tBv~j@K @v~1. When t reaches this second value uBv1@K and we need to start a new region. B2 region II uBv1@Ku2 vBvv2 and tBv~j@Kq2 . The leading order The correct scaling in this region is as described above; we put equations are then 2 @ \o] KoK B Ka1v2 0\Ka1u2K [ D Bv2 u 0]D1oj From the latter we see that v is slaved to u2 2 v2\ a1 b (D0]D1oj)u2K 2 b3(i]b@) The former eqn. (B3) can now be solved to provide an implicit solution q2\Pu2 o] du guK\ 1 gB1@K ZKAu2Co gD1@KB (B5) o 0 g\KKa1oj/B.See Appendix A for details of the func- where Z tends to the constant Z\n cosec(n/n)/n tion n(s). Since Zn(s) as s]O our solution blows up (u2 ]O) in –nite time (as q2 ]q2c) where q2cB o 2 2 Co2b2(i]b@)D1@K 4a@a1ji since in our applications K is large so (n/K)cosec(n/K)B1. Owing to the long timescale used here region II is the long induction period and has an abrupt ending. Formally the solution is 2(q2)\Ao 2BAb2 o2(i]b@)B1@K K~1Aoq2Co gD1@KB u Z 4a a@ij G1 v2(q2)\ a@b 2j~1D0 o ZK~1Aoq2Co gD1@KBHK 3 ojji J. Chem. Soc. Faraday T rans. 1998 V ol. 94 243 2 v2 ]O u At the end of region II both q2 ]q2c with as v2Bu2K from which we can –nd the scaling for the next region uB1Bv with the initial condition that u and v are both small and satisfy v2Pu2 j .The induction time is similar to which occurred in our modelling of generalised nucleation theory ;21 the underlying equations have the same mathematical structure a long induction region caused by one (fast) variable being slaved to another which is varying extremely slowly. B3 region III Following the conditions at the end of region II we expect that in region III both u and v are O(1) and vary by O(1) amounts when t varies by an O(1) amount. A direct asymptotic expansion of eqn. (8.1) then leads to the set of nonlinear equations Kv(o[u)j u5 \ D0]D1(o[u)j]D2(u[v)j Bv (B8) v5 \Ka1(u[v)K[ D0]D1(o[u)j]D2(u[v)j which involve too many terms to be solvable.Hence we shall consider only how the kinetics accelerate and slow down at the start and end of region III. Start of region III. Firstly let us consider just the start of region III. Since uBv1@K and vBv in region II our initial conditions in region III are going to be small and hence close to the critical point at u\0\v. Linearising about the origin we –nd the eigenvalues are zero and [B/(D0]D1oj) indicating the existence of a centremanifold which is itself stable. To –nd the centre-manifold we need to introduce w\Bu]Kojv in place of u to form a system whose linear part is diagonal. The centre-manifold is then found in a way similar to that presented in Section C1 (except that here we do not have to worry about v-corrections to the centre-manifold).Thus the centre-manifold is given by (B9) 0]D1oj wK B vBKa1 D BK A B to leading order. On the centre-manifold the equation of motion is (B10) 1ojAw BBK w5 \KKa which is solved by (B11) w(t)BA BK BKw0~j[jKa1ojKtB1@j Then v is found from eqn. (B9) and u from u\(w[Koj v)/B; see eqn. (8.6) for the formulae. Since we know u\o this solution breaks down owing to the presence of further nonlinear terms which are neglected in the above analysis. It is not possible to –nd a solution valid solution as for the entirety of region III but we can –nd the form of the uào as we shall now show. End of region III. In this region we introduce u3\o[u v3\v0[v and treat both of these as small but larger than v.Both are positive but approaching zero. The leading order terms in the equations for u are 3 Kv0 u3 j u5 3\ D0]D2(o[v0)j 3]L (v v5 3\ D 3[u3)D (B12) Then the centre-manifold can be written as Appendix C centre-manifold perturbation solution of eqn. (8.1) As stated in the main text a search for critical points of the unperturbed system [eqn. (8.1) with v\0] leads to two points u\v\0 which is the initial condition and u\o v\v0 which is the equilibrium con–guration of the system. C1 near the initial condition (u= ø= 0) Ignoring the O(v) terms the linear part of the system at the origin can be written as 1 (C1) \ v5 vB K [ o B jBAu D0]D1oj 0 which clearly has a zero eigenvalue (the other is negative indicating that the centre-manifold is stable and hence worth studying).We transform the variables to (v w) from (u v) via (C2) w\Kojv]Bu7u\ w[Kojv B so as to end up with a system whose linear part is diagonal. (C3) v\h(w)Bh0wP]h1wQ]vhv wR [Bv0 0]D2(o[v0)j v0 Cv J. Chem. Soc. Faraday T rans. 1998 V ol. 94 244 Once again we see that nonlinear terms dominate the behaviour of the system through the existence of a centre-manifold. To diagonalise the linear part of the system the variable w3\ (B13) w5 v3/v0]L (v3[u3) is used to eliminate v3 . We then –nd 3\[Pw3[Su3 2 with P and S as in eqn. (C17). The centre-manifold is given by w3 u \[Su32/P. To –nd the kinetics we –rst –nd 3 from (B12) 3(t)BCD0]D2(o[v0)j u Kv0(j[1)(t[C)D1@(j~1) (B14) This is only valid for t[C; hence to –nd a reasonable approximation to the solution we put C\t2c .Inverting the above transformations we –nd (B15) v3\ (w3 1 ] ] L u L v 3)v0B 1 L v ] 0 L v u3 ]O(u3 2) 0 hence 3 0 u and v both tend to zero at the same rate (with their 3 ratio being constant). B4 region IV and with scale When u3 j Bvu3 a new balance in eqn. (8.1) is obtained and a new region entered. In this region we again have a long time- 4\vt u\o[v1@(j~1)u v\v0[v1@(j~1)v4 . q 4 The leading order equations in this region are v4]L (v4[u4) (B16) u4 @ \[u4[ D Kv 0]D2(o[v0)j 0\ v0 0 u4 j Once again we have a slaved equation since the system is evolving on a slow timescale the vesicles are always in equilibrium with the monomer.The –rst equation above is a Bernoulli equation which can be integrated by separating variables to –nd (B17) 4\ [e(j~1)(q4~C)[Kv u 1 0/D=]1@(j~1) where D=\D0]D2(o[v0)j. The second equation then v4\L v0 u4/(1]L v0) ; as noted in the previous section 0[v) both tend to zero with a implies the quantities (o[u) and (v constant ratio. Au5 B A0 and the exponents P Q R and coefficients h0 h1 hv are found from substituting the asymptotic forms for v5 w5 into v5 \ h@(w)w5 w5 \Bvo]KojKa1Aw BBK [ jKoj~1wv D0]D1oj v5 \Ka1Aw BBK [ Bv D0]D1oj [ (D0]D1oj)2 (C4) jD1oj~1wv Balancing terms gives P\K Q\K]1 and R\K[1 so that the centre-manifold is given by B v\h(w)BKa1 0]D1oj wK BK AD ]C1[ vKo(D0]D1oj) w [ jD 0 1 ] oj D ~1 1o w j)D (C5) (D critical point is The equation of motion on the centre-manifold near to the w5 \Bvo]KojKa grated using the function Z 1(w/B)K.This can be inten( s) detailed in Appendix A to give t\Pw@B B ds Bvo]KojKa 0 (C6) 1 Z \ 1 B Bvo A Bvo B1@K KCw AKojKa B1@KD 1sK vo KojKa1 Inverting this expression for small w leads to (C7) wBBvotC1] Bvo(vot)K KojKa1(K]1)D The form of this function is a slow linear growth from w(0)\0 followed by a rapid take-oÜ at larger times caused by the second term in the square brackets. Using eqn. (C5) we can now –nd v(t) ; to leading order this is (C8) 0]D1oj (Bvot)K v(t)BKa1 B B AD (C9) u(t)BvotC1[KojKa BD (C10) t B Although introduced to simplify the mathematics this quantity represents the mass of vesicular material in the system and is hence an important quantity.It remains small for a long period of time before increasing dramatically as was observed with the amount of micellar material in the ethyl caprylate system studied previously.15 Having found w and v we are in a position to calculate u. As with v this was introduced to simplify the calculations but also has a direct relationship to the original system. It represents the total surfactant present in the system u\x1 ]Kx2](K]j)x3](K]2j)y\o[2s. It is this quantity which is plotted in Fig. 4 of Mavelli and Luisi.24 From eqn. (C2) we –nd 1(Bvot)jAD0]D1oj B This has the correct form expected it displays a long period of linear growth in time followed by a —attening out.A simple calculation shows that it reaches a zero gradient at B KojK2a1(D0]D1oj)D~1@j c\ 1 Bvo where uBvojtc/K. C1 C2 near equilibrium (u= q ø= ø0) We translate the system so that the equilibrium solution is at the origin and we work with the new variables u1\o[u v1\v[v0 in which the system of equations can be written as Ku1 j (v0]v1) u5 1\[vu1[ D0]D1u1 j ]D2(o[v0[u1[v1)j [Bv v5 1\ 1[A1[ u1]v1BKD 0 D0]D2(o[v0)j o[v0 [D (C11) v5 B B ]AK] 0 j ] D 0 2 D (o 2( [ o[ v0) v j 0)jBD 0 D (C12) ]L (u \[Ka v0 K] D L \A 1 BC 0 j ] D2 D (o 2( [ o[ v0) v j 0)jD (C13) 0 (C14) 1]L v (C15) (C16) w5 K1 \ D P\ D S\ 2(o[v 1 0) (C17) (C18) (C19) C ] B[D0 v0 u1 j [D0 v1]D2 v0(o[v0[u1[v1)j[D2 v0(o[v0)j] 0]D2(o[v0)j][D0]D1u1 j ]D2(o[v0[u1[v1)j] The only linear part of this system is in the v5 1 equations where an expansion around the equilibrium solution yields 1B[Ka1(o[v0)KCv v 1]Au o 1 [ ] v v1 1(o[v0)KCv1 1]v1)D where we have de–ned the new constant o[v0 As in the previous calculation we use this to transform coordinates so that the linear part of the system is diagonal.To do this we introduce w1\ v v 1]L (u1]v1)7v1\ (w1 1 [ ] L u L v 1)v0 0 1]v1\ u1]v0w1 u 0 Then our equations can be written as u5 1\vu1[K1 u1 j 1\[L vu1[Pw1[Su12[Qw12[Ru1w1[… … … for constants P Q R S K1 of which the most important are Kv0 0]D2(o[v0)j B(1]L v0) 0]D2(o[v0)j [jB[KD0]2D2(K]j)(o[v0)j] ] [D0]D2(o[v0)j][(o]jv0)D0](o]2jv0)D2(o[v0)j] Using the perturbed centre-manifold approach we seek a function w1\h(u1)Bh0 u1 n ]… … …]vhv u1 m]… … … with exponents n m and constants h0 hv such that the leading order terms in the system (C15)»(C16) balance.Firstly ignoring the O(v) terms we –nd n\2 and h0\[S/P; then from the O(v) terms we –nd m\1 and hv\[L /P. Thus the perturbed centre-manifold is w1B [ P 1 (Su12]L vu1) J. Chem. Soc. Faraday T rans. 1998 V ol. 94 245 Now that we know where the centre-manifold is we are in a position to –nd the form of the kinetics which occur on it.These are found by solving eqn. (C15) an equation which only 1 ]0 u1. We know that u involves as t]]O but the solution has a divergence at –nite time. We impose the boundary condition that this divergence occurs at t\trapid giving 1\A u K Chem. 1994 98 1160. Phys Ges . Ber 1 Mexp[v(j[1)( v t[trapid 13 P. L. Luisi P. Walde and T. Oberholzer 116 . . . J Luisi )][1NB1@(j~1) (C20) 12 P. Walde . Am A. Chem Goto Soc P-A. 1994 Monnard 7541. M. Wessicken Bunsenand . P. L. . From eqn. (C17) S\0 we see that w1[0 but more imporw 1@u1. Thus when we calculate v1 tantly eqn. (C19) implies from eqn. (C14) we –nd v1B [ 1] L v L v 0 u1 0 B[Cv0(1]j)D0]v0(1]2j)D2(o[v0)j (o]jv0)D0](o]2jv0)D2(o[v0)jD v K1 Mexp[v(j[1)(t[t ]A rapid O.22 9122. J. Carr D. G. Hall and Wattis D. A. J. 21 )][1NB1@(j~1) (C21) 20 J. A. D. Wattis unpublished and P. V. Coveney work. Penrose, J. personal Chem. Phys communication . 1997 106 Thus both the total surfactant (u) and total vesicular mass (v) approach equilibrium in the same manner. References 1 M. Eigen Naturwissenschaften 1971 58 465. 2 L. E. Orgel Sci. Am. 1994 Oct. 77. 3 Self-Production of Supramolecular Structures ed. G. Fleischaker S. Colonna and P. L. Luisi NATO ASI Series Kluwer Dordrecht 1994. 4 S. A. KauÜman T he Origins of Order Self-Organization and Selection in Evolution Oxford University Press New York 1993. 5 P. V. Coveney and R. R. High–eld Frontiers of Complexity Faber and Faber London; Fawcett New York 1995. 6 P. A. Bachmann P. Walde P. L. Luisi and J. Lang J. Am. Chem. Soc. 1990 112 8200. 7 P. A. Bachmann P. L. Luisi and J. Lang Nature (L ondon) 1992 357 57. J. Chem. Soc. Faraday T rans. 1998 V ol. 94 246 8 P. Walde R. Wick M. Fresta A. Mangone and P. L. Luisi J. Am. Chem. Soc. 1994 116 11 649. 9 R. Wick P. Walde and P. L. Luisi J. Am. Chem. Soc. 1995 117 1435. 10 K. Morigaki S. Dallavalle P. Walde S. Colonna and P. L. Luisi J. Am. Chem. Soc. 1997 119 292. 11 F. Varela H. Maturana and R. Uribe Biosystems 1974 5 187. 15 P. V. Coveney and J. A. D. Wattis Proc. R. Soc. L ondon Ser. A 14 K. D. Farquhar M. Misran B. H. Robinson D. C. Steytler P. Morini P. R. Garret and J. F. Holzwarth J. Phys Condens. Matter 1996 8 9397. 1996 452 2079. 16 P. V. Coveney A. N. Emerton and B. M. Boghosian J. Am. Chem. Soc. 1996 118 10 719. 17 D. D. Lasic Biochim. Biophys. Acta 1982 692 501. 18 D. D. Lasic J. Colloid Interface Sci. 1990 140 302. 19 J. Billingham and P. V. Coveney J. Chem. Soc. Faraday T rans. 1994 90 1953. 1993. 23 J. A. D. Wattis and J. R. King unpublished work. 24 F. Mavelli and P. L. Luisi J. Phys. Chem. 1996 100 16 600. 25 P. V. Coveney and J. A. D. Wattis unpublished work. 26 M. von Smoluchowski Phys. Z. 1916 117 557. 27 H. Haken Synergetics»An Introduction Springer-Verlag Berlin Heidelberg 2nd edn. 1978. 28 P. V. Coveney in Self-Production of Supramolecular Structures ed. G. Fleischaker S. Colonna and P. L. Luisi NATO ASI Series Kluwer Dordrecht 1994 pp. 157»176. 29 J. Carr Applications of Centre Manifold T heory Springer New York 1981. 30 Y. A. Chizmadzhew M. Maestro and F. Mavelli Chem. Phys. L ett. 1994 226 56. 31 E. Szathmaç ry and J. M. Smith Nature (L ondon) 1995 374 227. 32 M. Abramowitz and I. A. Stegun Handbook of Mathematical Functions Dover New York 1972. Paper 7/0348K; Received 20th May 1997

ISSN:0956-5000    

DOI:10.1039/a703483k

出版商:RSC    

年代:1998

数据来源: RSC

摘要:

Selective adsorption of metal cations onto AOT and dodecyl sulfate –lms at the air/solution interface Jamie C. Schulz and Gregory G. Warr* School of Chemistry University of Sydney NSW , 2006, Australia The selective binding of alkali and alkaline earth metal cations to adsorbed –lms of sodium bis(2,2@)ethylhexylsulfosuccinate (AOT) and sodium dodecyl sulfate (SDS) at air/solution interfaces has been studied by ion —otation. The selectivity orders obtained for both anionic surfactant –lms are Li`\Na`\K`\Rb`\Cs` and Mg2`\Ca2`\Sr2`\Ba2`, although diÜerences in absolute selectivities were found for the two surfactants. Selectivity was found to be determined by slight dehydration of the adsorbing ions.The selective adsorption of ions has long been an important concern in colloid science, and binding at surfactant interfaces has been extensively studied.1h8 The air/surfactant solution interface is of particular interest due to its association with numerous industrial applications.9h11 In particular, ion —otation or foam fractionation has been investigated to selectively remove ions or other impurities from dilute aqueous solution, however the techniques used to examine ions in foams are often tedious and subject to large errors.12,13 Recent advances in laboratory-scale ion —otation have enabled the reliable determination of ion selectivity coefficients at the air/solution interface, and this has been employed in our laboratory in several studies of cationic surfactants with numerous anions.14h18 The selective binding of cations to similarly adsorbed anionic surfactants has not been subject to the same attention.This is in spite of the greater industrial interest in anionic surfactants and the known in—uence of cation type on numerous important properties including solubility,19 micelle shape20 and viscosity. The equilibrium competitive adsorption of one counter-ion over another at an interface can be described by a selectivity coefficient.If the exchange of two homovalent cations An` and Bn` occurs at an interface as follows An`(ads)]Bn`(aq)HAn`(aq)]Bn`(ads) [where (aq) denotes the bulk concentration and (ads) denotes the concentration at the interface], then the selectivity coefficient can be expressed as KAn` Bn`\CBn`[An`] CAn`[Bn`] (1) The primary cause of counter-ion accumulation at the interface is electrostatic, but what determines the selectivity of one ion over another at the interface is not well understood.There have been several models proposed to explain selectivity. Jorneç and Rubin21 proposed an electrostatic model based on the size of the ions. They argued that the smaller the eÜective radius of the ion, the stronger the interaction with the charged interface would be. This model gives the correct selectivity order for alkali metals when the hydrated radii are used, however it is not consistent with results obtained for anions.17 Alkaline earth ions are expected to display little selectivity in this model as they all have approximately the same hydrated radius.22 The eÜect of solvent was –rst considered explicitly by Eisenman23 who suggested that an ion dehydrates when it adsorbs at the interface.Such ìcontact adsorptionœ is known to occur for halides from electrocapillarity measurements, but is unlikely for metal ions unless they have speci–c interactions with surface groups. In the case of contact adsorption exchange can be correlated with the diÜerence in the standard free energies of hydration of the exchanging species, A and B. *GA ° B\*Ghyd °A [*Ghyd °B (2) This idea was further developed by Morgan et al.,17 who introduced a parameter u, the degree of dehydration: 0 indicates full hydration and 1 indicates full dehydration of the ion at the interface.It was proposed that fractional dehydration is constant for ions in the same group (e.g. halides or alkali metals), and that this dominates the exchange mechanism. It should be noted that u is not the fraction of solvating water molecules lost on adsorption, but the fraction of the free energy of solvation.In this case, u is obtained from the slope of the line of best –t for a plot of vs. for a group. RT ln KBA (*Ghyd A [*Ghyd B ) Results from ion exchange resins indicate that the alkali and alkaline earth metals remain strongly hydrated on adsorption, with u\1%. Ion exchange results for the halides both at interfaces and on resins indicate that they dehydrate more readily upon adsorption, giving u of ca. 10%. This is consistent with the conventional picture of ion adsorption at an electri–ed interface derived from e.g. electrocapillarity. Numerous other mechanisms for ion selectivity have also been proposed, including higher order electrostatic and speci –c complexation eÜects. In general the free energy of ion exchange may be expressed as a sum of the various interaction terms *Ghyd ° \*Gelectrostatic ° ]*Ghydration ° ]other terms (3) For homovalent ions of approximately equal radius, the electrostatic term is negligible for ion exchange, so eqn.(3) becomes [RT ln KBA\u(*Ghyd B [*Ghyd A )]other terms (4) The objective of this work is to determine reliable selectivity coefficients for the competitive binding of pairs of alkali and alkaline earth metal ions at surfactant interfaces employing the ion —otation technique. These are used –rst to assess the validity of the partial dehydration model for the binding of monovalent and divalent metal cations, and where necessary to examine other mechanisms. The second eÜect addressed here is that of the surfactant headgroup on the selectivity coefficient.Benzenesulfonate groups on resins24 and sulfate from SDS at the air/solution interface25 have been compared previously. However in resins the selectivities depend on numerous factors such as crosslink J. Chem.Soc., Faraday T rans., 1998, 94(2), 253»257 253density, leading to substantial elastic work of swelling in the exchange. Ion exchange at interfaces is much simpli–ed. In this work we compare the selective binding of alkali metal and alkaline earth ions to the sodium salts of two anionic surfactants, dodecyl sulfate (SDS) and bis(2,2@)ethylhexylsulfosuccinate (AOT). Materials and methods Two anionic surfactants, dodecyl sulfate (SDS) and bis(2,2@) ethylhexylsulfosuccinate (AOT), were obtained as sodium salts from Sigma at [99% purity and were used as received.All experiments were performed well below the respective critical micelle concentrations : SDS 8]10~3 M and AOT 2.5]10~3 M. In addition to sodium, the counter-ions studied were the alkali metals ; lithium, potassium, rubidium (Merck [99%), and caesium (Sigma [99%) and the alkaline earth metals ; magnesium, calcium, strontium and barium (Ajax (99%), all as chloride salts. KraÜt temperatures of divalent AOT salts were determined by visual observation of the precipitation of the surfactant salt in solutions containing AOT at its critical micelle concentration and the divalent salt at a concentration equal to half the critical micelle concentration of sodium AOT. Solutions (1 l) of 3]10~4 M surfactant were prepared in Milli-Q water for each ion —otation experiment at 25 °C.The alkali metal salt solutions were prepared using equimolar concentrations of the Li` and K` salts, and 1.5]10~4 M Rb` and Cs` salts.For the alkaline earth ions Mg2` was used as a reference, added equimolar to the surfactant. The second ion was added at concentrations of 1.5]10~4 M for Ca2`, 3]10~5 M for Sr2`, and 5]10~6 M for Ba2`, due to coprecipitation with the surfactant at higher concentrations. Solutions were –ltered and degassed using a Millipore solvent –ltration apparatus prior to use. Ion —otation was carried out in a water-jacketed and thermostated —otation column, –tted with a porous frit through which nitrogen was passed at a —ow rate of 50 ml min~1.14 The solution (1 l) was placed in the —otation column under these conditions and allowed to foam for ca. 2»3 h. Samples (4 ml) were taken from the bulk solution at regular intervals. These samples were analysed using ion chromatography coupled with a conductivity detector. The ions in the samples were separated by the column and their concentrations obtained from peak areas. The selectivity constant is obtained from a —otation experiment by monitoring the change in solution concentration of the competing counter-ions as the experiment proceeds.As has been shown in previous work, a material balance on the —otation column leads to the following relationship between the concentrations of homovalent ions during a —otation experiment15 ln[An`]\KBA ln[Bn`]]C (5) where C is a constant which depends on initial solution conditions. is thus obtained from the slope of a plot of ln[An`] KBA vs.ln[Bn`]. Previous work has shown that this approach is more accurate than other methods, which involve the independent measurement of four concentrations and the explicit calculation of surface excesses to calculate directly from KBA eqn. (1).15 This method is, however, currently applicable only to the exchange of homovalent ions. In experiments involving alkaline earth ions there is also competitive adsorption between sodium and the two alkaline earth metal ions which cannot be interpreted at present.By considering solely the competitive adsorption between the two divalent species, the presence of sodium can, however, be ignored. Under the conditions used, the sodium concentration was observed to increase slightly throughout the —otation experiment, indicating that sodium was being excluded from the interface by the divalent ions. Results and Discussion Experimental results for the determination of selectivity coefficients of alkali metal ions over sodium at AOT and dodecyl sulfate –lms according to eqn.(5) are shown in Fig. 1 and 2. Selectivity coefficients thus obtained, are summarised in KNa X , Table 1. These clearly show that as one progresses down group 1, the selectivity coefficient increases. Results for alkali metals and SDS agree with ion —otation experiments of Grieves et al.25 which are also listed in Table 1. The selectivity coefficients obtained for the alkali metals are all close to 1, indicating that there is little discrimination between ions for either surfactant.This is very diÜerent from the behaviour of halides at quaternary ammonium surfactant interfaces,15,18 but similar to the selectivities of halides with primary ammonium ions.18 Results used for determination of selectivity coefficients of alkaline earth metal ions over magnesium are shown in Fig. 3 and 4. Selectivity coefficients, are listed in Table 2. Selec- KMg X , Fig. 1 Determination of selectivity coefficients, for the alkali KNa` X` , metals and AOT.Li` K` Rb` Cs` (+), (=), (>), (Ö). Fig. 2 Determination of selectivity coefficients, for the alkali KNa` X` , metals and SDS. Li` K` Rb` Cs` (+), (=), (>), (Ö). 254 J. Chem. Soc., Faraday T rans., 1998, V ol. 94Table 1 Selectivity coefficients for the alkali metals against sodium with the two surfactants AOT and SDS KNa X ion, X AOT DS DS25 DS micelles28 DS micelles29 Li` 0.77^0.02 0.90^0.04 0.92^0.09 » 1.0 K` 1.32^0.04 1.21^0.04 1.10^0.11 1.47 » Rb` 1.55^0.04 1.37^0.09 1.51^0.15 1.70 2.3 Cs` 1.62^0.04 1.58^0.06 1.65^0.16 2.05 2.7 tivities of these ions have not, to our knowledge, been reported previously for either micelles or bulk interfaces.Selectivity among the alkaline earth metal ions is much greater than among alkali metal ions, and each selectivity coefficient with Fig. 3 Determination of selectivity coefficients, for the alka- KMg2` X2` , line earth metals and AOT.Ca2` Sr2` Ba2` (Ö), (>), (=). Fig. 4 Determination of selectivity coefficients, for the alka- KMg2` X2` , line earth metals and SDS. Ca2` Sr2` Ba2` (Ö), (>), (=). Table 2 Selectivity coefficients for the alkaline earth metals against magnesium with the two surfactants AOT and SDS KMg X ion exchange ion, X AOT DS (C4H6SO3~)32 Ca2` 1.64^0.08 1.57^0.07 1.70 Sr2` 3.10^0.11 2.26^0.08 2.00 Ba2` 5.56^0.09 4.04^0.23 3.55 AOT is greater than the corresponding selectivity coefficient with SDS.Partial dehydration model It was shown by Morgan et al.15 that cation selectivity on ion exchange resins as well as anion selectivity at the air/solution interface is well described by partial dehydration of the counterions. In this model the extent of partial dehydration (u), presumed constant for ions from a particular group, is obtained from the free energy of exchange. Fig. 5(a) shows vs. for the alkali metal ions RT ln KBA (*Ghyd, A ° [*Ghyd, B ° )26 competitively adsorbed at dodecyl sulfate and AOT –lms.The observed correlation of the free energy of exchange for the alkali metals with the diÜerence in the standard free energy of hydration of the exchanging counter-ions is good for both surfactants, although it is somewhat better for AOT than for SDS. The extent of partial dehydration, u, is found to be u\0.9% for AOT and u\0.7% for SDS. This agrees reasonably well with the ion exchange resin values of u\1.5% on an 8% crosslinked sulfonated resin24 and u\1.1% on a 4% crosslinked sulfonated resin,27 and also with the generally accepted view that alkali metal ions remain virtually fully hydrated on adsorption.We expect the present case to be lower than either resin because of the negligible elastic work of expansion at an interface.17 Using the same approach with micellar selectivity coefficients, the extent of dehydration upon alkali metal binding to SDS micelles is found to be u\1.5%.28,29 The agreement with our results is again quite good, however selectivity coefficients derived from —otation include both bound and diÜuse layer ions in the surfaces excess30,31 [eqn.(1)], whereas micelle selectivity coefficients target only ions intimately associated with the micelle surface by some chemical or photochemical reactive trap. As homovalent diÜuse layer ions are not selectively bound, their in—uence should ensure that —otation selectivity coefficients are always less than or equal to those obtained from reactive trapping experiments. This is consistent with what we observe here : lower selectivity coefficients and hence lower u from —otation.The partial dehydration model also describes the alkaline earth data, as shown in Fig. 5(b). A –t to the partial dehydration model gives even lower values for partial dehydration than it does for the alkali metal ions : u\0.6% for AOT and u\0.5% for SDS. This agrees reasonably well with the ion exchange resin values of u\0.5% on a sulfonated resin24 and is, again, consistent with the expectation that these ions remain almost fully hydrated on adsorption.The wider range of hydration energies for alkaline earth ions provides a stronger test for the partial dehydration model, and a systematic deviation from linearity is evident in the data. Although the weak dependence of selectivity on hydration means that our conclusion that the counterions remain almost fully hydrated is justi–ed, the correlation in Fig. 5(b) is unsatisfactory and the plot clearly curves upwards. The most straightforward possibility is that the assumption of constant u is incorrect, and that the –tted u is merely an average value. The observed upward curvature for Fig. 5(b) clearly indicates that the more strongly hydrated ion has more J. Chem. Soc., Faraday T rans., 1998, V ol. 94 255Fig. 5 Degree of partial dehydration analysis for the selective ion —otation of (a) alkali and (b) alkaline earth metals with the two surfactants : and a sulfonated ion exchange resin32 AOT(=), SDS(>) (+), according to eqn (4).For the alkali metals B\Na` and A\Li`, Na`, K`, Rb`, Cs`. For the alkaline earth metals B\Mg2` and A\Mg2`, Ca2`, Sr2`, Ba2`. fractional dehydration. We would expect that a more strongly hydrated ion would experience less dehydration on adsorption, not more, implying that variations in u do not explain the upward curvature.Although the bulk concentrations were well below the solubility product of the surfactant salts, some precipitation was observed in the collapsed foam. This may indicate that the selectivity mechanism is precipitation rather than partial dehydration, or that the measured selectivity coefficients are altered by precipitation in the foam. Certainly the selectivity coefficients correlate well with the solubilities of the dodecyl sulfate salts. Selectivity enhancement would arise as the foam obtained might thus alter the concentration ratio of ions returning into the column, and hence the material balance on which eqn.(5) rests. The apparent rate of extraction of the soluble ion would be then reduced, yielding a higher KBA . Experimentally determined KraÜt temperatures for the divalent salts of AOT are shown in Table 3. KraÜt temperatures obtained for SDS by Miyamoto19 are also shown in Table 3 KraÜt temperatures for the alkaline earth salts of the two surfactants AOT and SDS KraÜt temperature/°C ion SDS19 AOT Mg2` 20 28 Ca2` 55 59 Sr2` 64 74 Ba2` [100 85 Table 3.The KraÜt temperatures of AOT and DS salts increase in the same order indicating that the solubilities at 25 °C behave likewise. If we assume selectivity to be solely due to precipitation in the foam, then the ratio of the counter-ions on the rising bubble is the same as in solution CB CA \ [B2`] [A2`] (6) Note that the more strongly bound (and less soluble) cation, B, is always present at lower concentration in our experiment. Drainage of solution from the foam has no eÜect on concentration ratios, but precipitation occurs when the surfactant and counterion have accumulated so that the solubility is exceeded.Precipitation within the foam could then aÜect the ratio in which they were returned to the column by further drainage giving an apparent selectivity [1. In this case a long induction time during which would be expected. This KBA\1 is not observed in any of our experiments. We further note that a precipitation mechanism should give rise to lower selectivity for AOT compared to DS, due to the lower AOT KraÜt temperatures.This is again at odds with experiment, and argues against a precipitation based selectivity. Results for divalent metal ion exchange on sulfonated resins show a similar upward curvature to our results,32 this again indicates a common mechanism for ion exchange on resins and at surfaces, and also argues against a precipitation eÜect in selectivity.The similarity between the present data and that for resins also excludes solution complexes or ion pairs as causes of selectivity, although they have been proposed in the past, particularly for divalent ions.33 Some other interactions between the ions and the interface must be at work. Further work will be required to determine its origin. EÜect of head group on selectivity The selectivity coefficients for the alkaline earth metals with AOT are consistently greater than the selectivity coefficients for SDS (Tables 1 and 2).The surfactant clearly has a role in determining the extent of selectivity observed. As before, an electrostatic model is unable to explain this observation. However the dehydration mechanism can yield a head-group dependence. Rather than regarding the fractional dehydration as being purely that of the ion, we explain this simply by assuming that a mutual dehydration of exchange group plus counter-ion occurs with ion exchange.DiÜerences in the head group hydration of AOT and dodecyl sulfate would permit this to occur. The direct evidence of this eÜect of head group on selectivity is apparent in the alkaline earth metal ion system where ion discrimination is more apparent than in the alkali metal ion system. Table 2 shows that the selectivity coefficients of AOT for the alkaline earth metal ions are greater than the corresponding selectivity coefficients for SDS.Within the alkali metal ion system ion discrimination is 256 J. Chem. Soc., Faraday T rans., 1998, V ol. 94minimal, hence this eÜect of the head group is not obvious in this system. Conclusions The selectivity orders of the two surfactants AOT and SDS are Li`\Na`\K`\Rb`\Cs` and Mg2`\Ca2`\ Sr2`\Ba2`. For the alkali metal ions, counter-ion discrimination is minimal, whereas in the alkaline earth ions it is more apparent. Partial dehydration theory adequately describes selectivity both for the alkali and the alkaline earth ion series at the air/solution interface, which is consistent with the interpretation of Morgan et al.17 for metal ion selectivity on ion exchange resins.The alkaline earth ion systems do show some systematic deviations which remain unexplained. We have also demonstrated that the surfactant plays a role in determining the extent of selectivity observed in ion exchange, previously considered to be negligible.The partial dehydration description can account for the eÜect of the diÜerent surfactants upon selectivity. References 1 E. A. Lissi, E. B. Abuin, A. Zanocco, C. A. Backer and D. G. Whitten, J. Phys. Chem., 1989, 93, 4886. 2 D. L. Ban–eld, I. H. Newson and P. J. Alder, AIChE.-I.Chem.E. Symp. Ser., 1965, 1, 3. 3 C. Walling, E. E. RuÜ and J. L. Thornton, J. Phys. Chem., 1957, 61, 486. 4 L. S. Romsted, C. A. Bunton, F. Nome and F. H. Quinta, Acc. Chem. Res., 1991, 24, 357. 5 J. A. Loughlin and L. S. Romsted, Colloids Surf., 1990, 48, 123. 6 F. Nome, M. da Graca Nascimento and S. A. Miranda, J. Phys. Chem., 1986, 90, 3366. 7 E. B. Abuin and E. J. Lissi, J. Colloid Interface Sci., 1983, 96, 293. 8 C. J. Drummond and F. Grieser, J. Colloid Interface Sci., 1989, 127, 281. 9 K. P. Galvin, S. K. Nicol and A. G. Waters, Colloids Surf., 1992, 64, 21. 10 R. Lemlich, in Adsorptive Separation T echniques, Academic Press, New York, 1972. 11 In Foams: T heory, Measurements, and Applications, ed.R. K. Prudœhomme and S. A. Khan, Marcel Dekker, Inc., New York, 1996. 12 K. Shinoda and M. Fujihira, Adv. Chem. Ser., 1967, 79, 198. 13 M. C. Morales, I. Waissbluth and F. H. Quina, Bol. Soc. Chil. Quim., 1990, 35, 19. 14 J. D. P. Morgan, D. H. Napper, G. G. Warr and S. K. Nicol, L angmuir, 1992, 8, 2124. 15 J. D. P. Morgan, D. H. Napper, G. G. Warr and S. K. Nicol, L angmuir, 1994, 10, 797. 16 L. Evans, B. P. Thalody, J. D. Morgan, S. K. Nicol, D. H. Napper and G. G. Warr, Colloids Surf., 1995, 102, 81. 17 J. D. Morgan, D. H. Napper and G. G. Warr, J. Phys. Chem., 1995, 99, 9458. 18 L. Kellaway and G. G. Warr, J. Colloid Interface Sci., 1997, 193, 312. 19 S. Miyamoto, Bull. Chem. Soc. Jpn., 1960, 33, 371. 20 G. Roux-Desranges, S. Bordere and A. H. Roux, J. Colloid Interface Sci., 1994, 162, 284. 21 J. Jorneç and E. Rubin, Sep. Sci., 1969, 4, 313. 22 R. Kunin and R. J. Myers, in Ion Exchange Resins, John Wiley & Sons, 1950, p. 24. 23 G. Eisenman, Biophys. J., 1962, 2, 259. 24 Y. Marcus and D. G. Howery, in Ion Exchange Equilibrium Constants, Butterworth, London, 1975. 25 R. B. Grieves, K. E. Burton and J. A. Craigmyle, Sep. Sci. T echnol., 1987, 22, 1597. 26 H. Friedman and C. V. Krishnan, in W ater : A Comprehensive T reatise, Plenum Press, New York, 1973, vol. 3. 27 F. HelÜrich, in Ion Exchange, McGraw-Hill, New York, 1975. 28 Z. He, P. J. OœConnor, L. S. Romsted and D. J. Zanette, J. Phys. Chem., 1989, 93, 4219. 29 A. Ha–ane, L. Issid and D. Lemordant, J. Colloid Interface Sci., 1991, 142, 167. 30 B. Thalody and G. G. Warr, J. Colloid Interface Sci., 1997, 188, 305. 31 G. G.Warr, L angmuir, 1997, 13, 1451. 32 D. S. Flett and P. Mears, T rans. Faraday Soc., 1966, 44, 2139. 33 R. B. Grieves and D. Bhattacharyya, Anal. L ett., 1971, 4, 603. Paper 7/06680E; Received 15th September, 1997 J. Chem. Soc., Faraday T rans., 1998, V ol. 94 257

ISSN:0956-5000    

DOI:10.1039/a706680e

出版商:RSC    

年代:1998

数据来源: RSC

摘要:

Light-induced formation of 2,5-dihydroxy-p-benzoquinone from hydroquinone in photoirradiated silver-loaded zirconium phosphate suspension Hirokazu Miyoshi,a,* Hiroki Kouraib and Takuya Maedab a Department of Radiological T echnology, School of Medical Sciences, T he University of T okushima, 3-18-15 Kuramoto-cho, T okushima 770, Japan b Department of Bioscience and T echnology, Faculty of Engineering, T he University of T okushima, 2-1 Minamijousanjima-cho, T okushima 770, Japan Silver-loaded zirconium phosphate has shown photocatalytic activity concerning the generation of [Ag1~xHxZr2(PO4)3] OH~ and the hydroxylation of hydroquinone (HQ) to 2,5-dihydroxy-p-benzoquinone HQ was initially oxidized to p- (DHQH2).benzoquinone (BQ) by Ag` on the surface of in the dark and by photogenerated during visible-light Ag1~xHxZr2(PO4)3 OH~ irradiation. As an intermediate, a semiquinone radical was detected by EPR measurements in both cases. Furthermore, BQH~ under visible-light irradiation, was identi–ed by its absorption spectrum and thin layer chromatography.The amount of DHQH2 increased and BQ decreased with irradiation time. The total amount of BQ and under visible-light irradiation DHQH2 DHQH2 agreed with that of BQ in the dark. Consequently, appeared to form from generated by the oxidation of HQ and DHQH2 BQH~ the reduction of BQ by photogenerated e~. From the XPS and FT-Raman technique analyses, it was found that the addition of the photogenerated to occurred at the surface of This indicated that both the and OH~ BQH~ Ag1~xHxZr2(PO4)3 .OH~ HBQ~ were stabilized on the surface of Ag1~xHxZr2(PO4)3 . Silver-loaded zirconium phosphate has [Ag1~xHxZr2(PO4)3] been prepared as an antibacterial reagent by Kourai et al.1 was obtained by ion-exchanging Na` in Ag1~xHxZr2(PO4)3 sodium zirconium phosphate with Ag`. [NaZr2(PO4)3] has been reported to be a three-dimensional NaZr2(PO4)3 structure composed of and by Goodenough et al.2 ZrO6 PO4 Also, the crystal data has been indicated by Hagman and Kierkegaard.3 Antibacterial action towards Esherichia coli K12 W 3110 occurred during visible-light irradiation.1,4 The active species were found to be as a DMPO-OH adduct OH~ using a spin-trapping technique.5 The generation mechanism of was investigated and it was clari–ed that a charge OH~ separation occurred as a result of light irradiation of zirconium phosphate.A photocathodic current was observed for the zirconium phosphate-modi–ed Pt electrode in 0.1 mol dm~3 aqueous solution using a 500 W Xe lamp.5 Na2SO4 The generation rate of DMPO-OH increased with the relative concentration of Ag/Zr on the surface.It seemed that Ag` on the surface acted as an electron pool like Ag 6 which leads to an eÜective charge separation. Furthermore, the addition of I~ to that suspension reduced the amount of and the OH~ signal of appeared. This indicated that an elec- DMPO-O2~~ tron and a hole generated by the charge separation reduced and oxidized OH~, respectively.The reaction mechanism O2 has been proposed to be as follows.5 Ag1~xHx Zr2(PO4)3 ] h l Ag1~xHx Zr2(PO4)3(e~]h`) (1) e~](Agsurface ` )wO2 ](Agsurface 0 )wO2 ]O2~~]Agsurface ` (2) h`]OH~]OH~ (3) DMPO]O2~~] k 1 DMPO[O2~ (4) OH~]DMPO] k 2 DMPO[OH (5) OH~]I~] k 3 OH~]12 I2 (6) where the rate constants and are known to be 16.9 k1, k2 k3 dm3 mol~1 s~1,7 3.4]109 dm3 mol~1 s~1 7 and 1.0]1010 dm3 mol~1 s~1.8 represents a semi-reduced Ag` on Agsurface ` the surface of as an electron pool.5 Ag1~xHxZr2(PO4)3 was only detected in the presence of I~.In the DMPO-O2~~ absence of I~, DMPO traps almost exclusively because OH~ the rate constant was much larger than If instead of k2 k1. DMPO, hydroquinone (HQ) was added to the suspension and irradiated by visible light then the rate constant for reaction of and HQ was reported to be 2.1]1010 dm3 mol~1 s~1 at HO~ pH 6»7.8 In this study, when a suspension Ag1~xHxZr2(PO4)3 and HQ was irradiated by visible light, 2,5-dihydroxy-pbenzoquinone was formed.Generally, is (DHQH2) DHQH2 synthesized from hydroquinone in alkaline solution by addition of at \323 K.9 Since is stable in alkaline H2O2 BQH~ solution, during the synthesis of it seems that the DHQH2 , stabilization of the semiquinone radical as an interme- BQH~ diate of hydroquinone is required. Therefore, it seems that the surface of may stabilize both and Ag1~xHxZr2(PO4)3 OH~ BQH~.In this study, trapping of the photogenerated was OH~ attempted using a hydroquinone. As a result, since DHQH2 formed with BQ during irradiation and in the dark, only BQ was generated. Its irradiation time dependence was investigated with respect to the concentration of BQ and DHQH2 . Furthermore, the reaction mechanism and the role of the surface of were investigated using XPS, Ag1~xHxZr2(PO4)3 EPR and FT-Raman techniques. Also, the usefulness of as a photocatalyst for the formation of Ag1~xHxZr2(PO4)3 from HQ is discussed.DHQH2 Experimental Silver-loaded zirconium phosphate (Ag Ag1~xHxZr2(PO4)3 content\11 wt.%) was provided by Toa Gousei Co., Ltd. 5,5-Dimethylpyrrolidine-N-oxide (DMPO, LC-9130) and 2,2, 6,6-tetramethyl-1-piperidine-N-oxyl nitroxide (TEMPO) were J. Chem. Soc., Faraday T rans., 1998, 94(2), 283»287 283obtained from Labotec Co., Ltd. Hydroquinone (reagent grade) was purchased from Wako Pure Chemical Industries, Ltd.These reagents have been directly used in our investigations without further puri–cation. 2,5-Dihydroxy-p-benzoquinone as a standard was synthesized as (DHQH2) previously reported9 and was recrystallized from ethanol. A phosphate buÜer solution of pH 6.0 was prepared with and NaOH. KH2PO4 The oxidation of hydroquinone (HQ) was investigated in the dark and under irradiation. After the sample (2 mg) was dispersed in a 2.125 cm3 phosphate buÜer solution (pH 6.0) containing 5.9 mmol dm~3 HQ, this solution in a Pyrex tube was irradiated with a Xe lamp (UV-37 and UV-25 cut-oÜ –lters, Toshiba Glass Co., Ltd.) or allowed to stand in the dark for certain times.The absorption spectra of the solutions, which were diluted to 1/30 or undiluted (]1), in 10 mm cells were measured using a Hitachi U-2000 spectrophotometer. The concentration of p-benzoquinone (BQ) was calculated from the absorbance at 246 nm10 and its log e(j/246 nm)\ and that of was from the absorbance at 490 nm 4.411 DHQH2 and its was determined log e(j/490 nm)\3.0 ; log e(j/490 nm) using of 83.3 lmol dm~3 A(j/490 nm)\0.087 DHQH2 .Thin layer chromatography was performed using a Merk Art. 15389 DC-Fertigplatten RP-18 F 254 S. Its 9.8]5.0 cm plate (the baseline is 0.1 cm from the bottom) was prepared and methyl alcohol, ethyl acetate and isopropyl alcohol were used as the developing solvents. EPR spectral measurements were performed with a JEOL TE-300 and ESPRIT-425 data system. 5,5- Dimethylpyrrolidine-N-oxide (DMPO) was used as the spin trap reagent. The EPR spectra (X-band) of a semiquinone radical and DMPO adducts were measured with a (HBQ~) JEOL DATUM LC12 quartz oblique cell (ca. 0.2 cm3) for the aqueous solution. Concentrations of and DMPO-OH HBQ~ were determined by comparing their peak area in their EPR spectra to that of a 3.2 lmol dm~3 TEMPO aqueous solution as the standard. A 0.2 mg/0.2 cm3 sample of an powder suspension was mixed with 0.02 Ag1~xHxZr2(PO4)3 cm3 DMPO spin trapping reagent (9.0 mol dm~3) and added to the cell.The concentration of DMPO in the suspension was 0.8 mol dm~3. The EPR spectra were measured during irradiation with a 500 W Xe lamp (Ushio, UI-501C) with UV-25 and UV-37 cut-oÜ –lters (Toshiba Glass Co., Ltd.), UV-37 cut-oÜ and KL-40 interference –lters (Toshiba Glass Co., Ltd.), or in the dark at room temperature with the following conditions : 8 mW power, 79 lT modulation width, MnII/ MgO external standard for g values, and ^5 mT sweep width.XPS spectra of the (Ag content\11 Ag1~xHxZr2(PO4)3 wt.%) powders were measured with a Shimadzu ESCA- 1000AX instrument. Mg-Ka radiation (1253.6 eV) was employed as the X-ray source. Data processing12 was carried out with an HP 340 computer (Hewlett-Packard Co., Ltd.), which was attached to the Shimadzu ESCA-1000AX. The ESCA-1000AX was operated at 10 kV and 30 mA under a pressure of 10~6»10~7 Pa.The binding energy was cali- (Eb) brated with C ls\285 eV from contaminant C. The sampling time was 200 ms and the number of accumulations was 20 for the Ag peak while for other elements, the number of 3d5@2 accumulations was 1. The Savitzky method13 was used for the smoothing. The sample was pelletized and attached to the sample probe with carbon tape. Measurements of the FT-Raman spectra were performed with a Nihon Bunko NR-1800 instrument at room temperature. The FT-Raman spectra of the Ag1~xHxZr2(PO4)3 (Ag content\11 wt.%) powders were measured with an Ar ion laser (514.5 nm, 30 mW power) and triple monochromator. The sample powders were put on the glass plate and simply arranged on its surface with another glass plate : entrance slit 500 lm, sensitivity 1.0 (nA/full scale)]100, scan speed 600 cm~1 min~1, and accumulation number 3.Results and Discussion A visible-light irradiated silver-loaded zirconium phosphate generated and from aqueous Ag1~xHxZr2(PO4)3 OH~ O2~~ solution in air as shown in eqn. (1)»(6) earlier.5 Their radicals formed DMPO-OH and adducts with DMPO DMPO-O2~ as the spin trap reagent.However, since the reaction rate of DMPO and is much larger than that of DMPO and OH~ only DMPO-OH was detected by the EPR measure- O2~~, ment. In a separate experiment, instead of DMPO, HQ was added and its suspension was irradiated. The reaction rate of HQ and has been reported to be 2.1]1010 dm3 mol~1 OH~ s~1.8 After irradiation, the solution turned from yellow to red, Fig. 1(a) and (b) show the absorption spectra of HQ and the product. As shown in Fig. 1(a), in the dark, the absorption peak of BQ at 246 nm (log e\4.4, in hexane)11 increased with the amount of [0 mg (a) to 30 mg (e)] Ag1~xHxZr2(PO4)3 present. As shown in Fig. 2(b), during light irradiation, peaks at 490 and 246 nm grew. The peak at 490 nm corresponded to in aqueous solution. The value from a thin layer DHQH2 Rf chromatogram for the solutions was measured using ethyl acetate and isopropyl alcohol as the developing solvents. Table 1 lists the values of products in unirradiated and Rf irradiated solutions. The value (0) for the irradiated sample Rf Fig. 1 (a) Absorption spectra of hydroquinone in supernatant after mixing with 0 mg (a), 2 mg (b), 10 mg (c), 20 mg (d) and 30 mg (e) for 2»3 h in the dark. Each amount of Ag1~xHxZr2(PO4)3 was suspended in 2.125 cm3 of 5.9 mmol dm~3 Ag1~xHxZr2(PO4)3 hydroquinone phosphate buÜer solution (pH 6.0) and mixed for 2»3 h in the dark.After the reaction, the suspension was centrifuged at 3000 rpm for 5 min. The obtained supernatant was diluted to 1/30 and its absorption spectrum was measured. The concentration of pbenzoquinone was calculated using to be 4.8 log e(j/246 nm)\4.4 lmol dm~3, 22.9 lmol dm~3, 36.9 lmol dm~3 and 75.5 lmol dm~3, respectively. (b) Absorption spectra of hydroquinone in supernatant after mixing with 0 mg (a) and 2 mg (b) for 1 h Ag1~xHxZr2(PO4)3 under light irradiation. 2 mg of was suspended in Ag1~xHxZr2(PO4)3 2.125 cm3 of 5.9 mmol dm~3 hydroquinone phosphate buÜer solution (pH 6.0) and mixed for 1 h under light irradiation using a 500 W Xe lamp (UV-25 and UV-35 cut-oÜ –lters). After the reaction, the suspension was centrifuged at 3000 rpm for 5 min. The absorption spectra of the supernatant, which was diluted to 1/30 and undiluted (]1), were measured. The concentration of p-benzoquinone was calculated to be 2.3 lmol dm~3 and that of 2,5-dihydroxy-p-benzoquinone using to be 12.5 lmol dm~3.log e(j/490 nm)\3.0 284 J. Chem. Soc., Faraday T rans., 1998, V ol. 94Fig. 2 Plot of amount of products vs. the reaction time in the dark and during irradiation. The products were p-benzoquinone in the dark p-benzoquinone during light irradiation and 2,5- (>), (|) dihydroxy-p-benzoquinone during light irradiation (L). (2 mg) was suspended in 2.125 cm3 phosphate Ag1~xHxZr2(PO4)3 buÜer solution (pH 6.0) containing 5.9 mmol dm~3 HQ and irradiated using a 500 W Xe lamp with UV-37 and UV-25 cut-oÜ –lters.indicated the presence of which was absent in the DHQH2 unirradiated sample. Although the values of HQ and BQ Rf could not be distinguished in this experiment, the formation of BQ could be identi–ed from the absorption peak at 246 nm. In the dark the generation of BQ was due to the oxidation of HQ by Ag` on the surface of (the redox Ag1~xHxZr2(PO4)3 potential for Ag`/Ag0 14 is ]0.799 V vs.NHE and that for BQ/HQ15 is ]0.70 V vs. NHE). Consequently, as shown in Fig. 1(a), the formation of BQ depended on the amount of Ag1~xHxZr2(PO4)3 . Fig. 2 shows the relation between the amount of products and the reaction time in the dark and during irradiation. In the dark, the amount of BQ increased with reaction time. During irradiation, the amount of BQ decreased and that of increased with irradiation time. Up to ca. 50 min, the DHQH2 amount of BQ was the same as that in the dark.Since was also generated with BQ at the same time, the DHQH2 formation of BQ during irradiation would be due to the oxidation by Ag` and the photogenerated on the surface. OH~ On the other hand, a decrease in the concentration of BQ was seen from 0.08 to 0.04 mmol dm~3 for an irradiation time of 50 to 240 min. The generated BQ was re-reduced by the photogenerated e~ from and was Ag1~xHxZr2(PO4)3 HBQ~ reformed. Subsequently, was hydroxylated to HBQ~ DHQH2 by the photogenerated on the surface and the that OH~ HBQ~ originated from BQ would be consumed.Therefore, the amount of BQ tended to decrease with the formation of These facts indicate that needs to form DHQH2 . HBQ~ and increases with irradiation time (see Fig. DHQH2 HBO~ 4). The total of BQ and almost agreed with that of DHQH2 BQ in the dark as shown in Fig. 2. The formation of BQ is known to occur by a disproportionation of as an HBQ~ intermediate.was detected by EPR measurements in HBQ~ both irradiated and non-irradiated suspensions. Fig. 3 shows the observed radicals formed during irradiation of values of products in suspension Table 1 Rf Ag1~xHxZr2(PO4)3 containing 5.9 mmol dm~3 HQ in the dark and under irradiation using thin layer chromatographya Rf light 0 0.9 dark » 0.89 HQ » 0.9 DHQH2 0 » a Developing solvent : ethyl acetate or isopropyl alcohol. Fig. 3 EPR spectra of semiquinone free radical in (a) and (b) suspensions containing 5.9 Ag1~xHxZr2(PO4)3 HZr2(PO4)3 mmol dm~3 hydroquinone during 500 W Xe lamp (UV-37 and UV-25 cut-oÜ –lters) irradiation.(2 mg) or Ag1~xHxZr2(PO4)3 HZr2(PO4)3 was suspended in 2.125 cm3 of the phosphate buÜer solution (pH 6.0) containing 5.9 mmol dm~3 hydroquinone. Mn2`(3) and Mn2`(4) occur at g\2.033 and 1.981, respectively. Sampling time was 10 s and accumulation was 30. and Spectrum (a) was Ag1~xHxZr2(PO4)3 HZr2(PO4)3 . assigned to that of the p-semiquinone free radical.16 For in the dark or during irradiation, the semi- HZr2(PO4)3 quinone radical could not be detected.Fig. 4 shows the reaction time dependence of the concentration of in the HBQ~ dark and during irradiation. The concentration of was HBQ~ estimated from the peak area and compared to that of TEMPO as a standard. Its concentration upon irradiation was higher than that in the dark and saturated at ca. 0.24 lmol dm~3 whereas in the dark, its concentration was ca. 0.05»0.06 lmol dm~3. This indicates that is stabilized HBQ~ on the surface of In the absence of Ag1~xHxZr2(PO4)3 . direct light-irradiation to an HQ solution Ag1~xHxZr2(PO4)3 , (pH 6.0) led to the formation of but as soon as the light HBQ~, was turned oÜ, immediately disappeared. Therefore, the HBQ~ surface of stabilizes the radical. Such sta- Ag1~xHxZr2(PO4)3 bilization was also observed in the case of the photogenerated Fig. 5 shows the relation between the concentration of OH~. DMPO-OH and the amount of The Ag1~xHxZr2(PO4)3 .spectra of DMPO-OH were measured immediately after the addition of DMPO to the 45 min pre-irradiated suspension. The signal of DMPO-OH Ag1~xHxZr2(PO4)3 appeared and its concentration depended on the amount of This indicates that the photogenerated Ag1~xHxZr2(PO4)3 . is stabilized on the surface in the dark. Therefore, both OH~ and photogenerated are stabilized on the surface HBQ~ OH~ of Generally, is prepared from Ag1~xHxZr2(PO4)3 .DHQH2 Fig. 4 Plot of concentration of semiquinone radical vs. the reaction time in the dark and during irradiation using a 500 W Xe (=) (Ö) lamp with UV-37 and UV-25 cut-oÜ –lters. (2 mg) Ag1~xHxZr2(PO4)3 was suspended in 2.125 cm3 of 5.9 mmol dm~3 hydroquinone phosphate buÜer solution at pH 6.0. J. Chem. Soc., Faraday T rans., 1998, V ol. 94 285Fig. 5 Plot of concentration of DMPO-OH vs. amount of Each amount of was dis- Ag1~xHxZr2(PO4)3. Ag1~xHxZr2(PO4)3 persed in 0.2 cm3 of distilled water and irradiated using 400 nm light from a 500 W Xe lamp (UV-37 cut-oÜ and KL-40 interference –lters) for 45 min.Then, 0.02 cm3 of DMPO (9 mol dm~3) was added to the suspension and the EPR spectrum was measured. The concentration of DMPO in the suspension was 0.8 mol dm~3. Sampling time was 5 s and accumulation was 40. the sodium salt of HQ and in alkaline solution in which H2O2 is stable. Thus the addition of to the stabilized HBQ~ OH~ seems to be important and supports the above result in HBQ~ this study, and a reaction scheme is proposed in Fig. 6. HQ is oxidized by Ag` or photogenerated on the surface to OH~ form [eqn (7)]. The two generated molecules dis- HBQ~ HBQ~ proportionate to BQ and HBQ~ in the dark [eqn. (9)] whereas under irradiation they disproportionate to DHQH2 , Fig. 6 Reaction scheme of conversion of HQ to BQ and in DHQH2 the suspension in the dark and during irradiation Ag1~xHxZr2(PO4)3 which was formed by the addition of to and OH~ HBQ~ HBQ~ [eqn.(10)]. The amount of linearly increased DHQH2 and that of BQ decreased with irradiation time as shown in Fig. 2, and this indicates that is also formed from the HBQ~ reduction of BQ by photogenerated e~ [eqn. (8)]. After the reaction in the dark or during irradiation, surface analysis of the used powders was per- Ag1~xHxZr2(PO4)3 formed using XPS. The C 1s XPS spectra for the used sample was diÜerent from that of the original sample (c) as shown in Fig. 7 in which the peak at 285 eV was due to contaminant C used as a reference. Peaks at 293 and 296 eV were assigned to K appearing to originate from the phos- 2p3@217 KH2PO4 phate buÜer solution (pH 6.0). A new peak was observed at ca. 280 eV in the dark and decreased in intensity in the irradiated sample. After the reaction in the dark and during irradiation, HQ, BQ and may be adsorbed on the surface. From DHQH2 the result shown in Fig. 2, the concentration of BQ increased in the dark while during irradiation it decreased.Therefore, the peak at 280 eV appears to be due to that of BQ. The binding energy of C 1s for has been reported to be Eb C6H6 284.9 eV.17 The lower of BQ compared to that of Eb C6H6 would be due to the high reactivity of BQ. Table 2 lists the binding energies of Ag O 1s, P 2p and Zr and the 3d5@2, 3s1@2 atomic ratio of the surface region determined by the XPS technique. In the unirradiated sample, values were ca. 0.6 Eb eV higher than that of the unreacted sample. In the irradiated sample, only the value of Zr was shifted to higher Eb 3s1@2 energy by ]0.4 eV. The atomic ratios of Ag/P, Zr/P and Ag/Zr were the same values for the unreacted and the irradiated samples. In the dark Ag/P and Zr/P decreased while Ag/Zr was unchanged. The high values for the unirradiated Eb sample and the decrease in the atomic ratio seems to be due to the adsorption of BQ on the surface, because the surface atoms constituting were recovered by Ag1~xHxZr2(PO4)3 adsorbed species and were stabilized.The decrease in Ag/P Fig. 7 XPS spectra of C 1s on powders used in Ag1~xHxZr2(PO4)3 the experiment of Fig. 2; (a) after the reaction in the dark, (b) after the reaction during irradiation and (c) before the reaction. The peak at 285 eV was due to contaminant C, those at 293 and 295 eV were due to K 2p3@2 . Table 2 Binding energies and the atomic ratio of surface region determined by XPS Ag 3d5@2 O 1s P 2p Zr 3s1@2 eV Ag/P Zr/P Ag/Zr Ag1~xHxZr2(PO4)3 a dark 369 532.2 134.3 434.5 0.054 0.32 0.17 light 368.3 531.7 133.7 434.4 0.062 0.36 0.17 unreacted 368.4 531.6 133.6 434 0.06 0.36 0.17 powder after reaction in the dark, during irradiation, and before the reaction shown in Fig. 2. a Ag1~xHxZr2(PO4)3 286 J. Chem. Soc., Faraday T rans., 1998, V ol. 94Fig. 8 Raman spectra of powders used in the Ag1~xHxZr2(PO4)3 experiment of Fig. 2; (a) after the reaction in the dark, (b) after the reaction during irradiation and (c) before reaction and Zr/P suggests that BQ was adsorbed on the Ag and Zr atoms on the surface.Raman spectra of the adsorbed species were measured by the FT-Raman technique. Fig. 8 shows the Raman spectra of powders before and after reaction in the Ag1~xHxZr2(PO4)3 dark and under irradiation. As shown in Fig. 8, compared to the unreacted sample, both samples in the dark and during irradiation showed enhanced peak intensities at 104 and 119 cm~1 due to zirconium phosphate.5 The reason why these peaks were enhanced could not be determined.In the dark, a new broad peak at ca. 1370 cm~1 appeared, and for the irradiated sample, its peak intensity decreased. These Raman shifts are characteristic of BQ and HQ;18,19 for BQ, peaks at 1394 and 1299 cm~1 are assigned to CwC stretching vibrations while for HQ, peaks at 1370 and 1260 cm~1 are assigned to the CwH bending and CwO stretching vibrations, respectively.These indicate the existence of the adsorbed species in the dark. Considering XPS and the Raman spectra of the sample in the dark, the peak at 280 eV in the XPS spectrum and that at 1370 cm~1 in the Raman spectra seemed to originate from the same species. Since the product in the dark was BQ (Fig. 2), the peak in the Raman and XPS spectra is due to BQ. On the other hand, the peaks based on in the Raman spectra decreased in the Ag1~xHxZr2(PO4)3 dark, but during irradiation, clearly remained.Furthermore, since the surface had few adsorbed species during irradiation according to the surface analysis by XPS and FT-Raman spectroscopy, was concluded to be able to Ag1~xHxZr2(PO4)3 act as a photocatalyst for the formation of from HQ. DHQH2 Conclusion 2,5-Dihydroxy-p-benzoquinone formed via from HQ HBQ~ upon irradiation of an suspension. Ag1~xHxZr2(PO4)3 HBQ~ was generated from HQ by the oxidation of Ag` and the photogenerated and from BQ by the reduction of the photo- OH~ generated e~ on the surface.The formation of was DHQH2 required in order to stabilize both and on the OH~ HBQ~ surface of Surface analysis indicated the Ag1~xHxZr2(PO4)3 . characteristic peaks of the products in the XPS and FTRaman spectra after the reaction in the dark. The peaks were assigned to BQ considering the products formed in the dark. Therefore, the peak of BQ adsorbed on the surface of was observed at 280 eV in the XPS Ag1~xHxZr2(PO4)3 spectra.Since these spectra showed no peaks for products during irradiation, was indicated to be Ag1~xHxZr2(PO4)3 able to act as a photocatalyst for the formation of DHQH2 from HQ. thank Toa Gousei Co., Ltd., in Japan, for supplying the We zirconium phosphate samples as well as the silver-loaded samples (Ag content\11 wt.%) used in this work. The FTRaman spectra were measured at the Center for Cooperative Research at Tokushima University. We also thank Dr Shigeru Sugiyama for the ESCA measurements and useful discussions.References 1 H. Kourai, K. Nakagawa and Y. Yamada, J. Antibact. Antifung. Agents, 1993, 21, 77. 2 J. B. Goodenough, H. Y-P. Hong and J. A. Kafalas, Mater. Res. Bull., 1976, 11, 203. 3 L. O. Hagman and P. Kierkegaard, Acta Chem. Scand., 1968, 22, 1822. 4 H. Kourai, Y. Manabe and Y. Yamada, J. Antibact. Antifung. Agents, 1994, 22, 595. 5 H. Miyoshi, M. Ieyasu, T. Yoshino and H. Kourai, J. Photochem. Photobiol : A Chem., submitted. 6 A. Henglein, J. Phys. Chem., 1979, 83, 2209. 7 E. Finkelstein, G. M. Rosen and E. J. Rauckman, Arch. Biochem. Biophys., 1980, 177, 1. 8 G. V. Buxton, C. L. Greenstock, W. P. Helman and A. B. Ross, J. Phys. Chem. Ref. Data, 1988, 17, 513. 9 R. G. Jones and H. A. Shonle, J. Am. Chem. Soc., 1945, 67, 1034. 10 X. Zao, H. Imahori, C.-G. Zhau, Y. Sakata, S. Iwata and T. Kitagawa, J. Phys. Chem. A, 1997, 101, 622. 11 Sadtler Standard Ultraviolet Spectra, 1961, Sadtler Res. Lab. 12 ESPAC 1000, Userœs Manual, Shimadzu. 13 A. Savitsky and M. J. E. Golay, Anal. Chem., 1964, 36, 1627. 14 A. J. Bard, R. Parsons and J. Jordan, Standard Potentials in Aqueous Solution, Marcel Dekker, New York and Basel, 1985, p. 311. 15 W. M. Clark, Oxidation»Reduction Potentials of Organic Systems, R. E. Krieger, New York, 1972. 16 I. Yamazaki, H. S. Mason and L. Piette, J. Biol. Chem., 1960, 235, 2444. 17 D. Briggs and M. P. Seach, Practical Surface Analysis, Auger and X-ray Photoelectron Spectroscopy, John Wiley & Sons, New York, 2nd edn., 1990, vol. 1. 18 P. Mohandas and S. Umapathy, J. Phys. Chem. A, 1997, 101, 4449. 19 M. Nonella, J. Phys. Chem. B, 1997, 101, 1235. Paper 7/05949C; Received 13th August, 1997 J. Chem. Soc., Faraday T rans., 1998, V ol. 94 287

ISSN:0956-5000    

DOI:10.1039/a705949c

出版商:RSC    

年代:1998

数据来源: RSC

摘要:

Interaction of a model epoxy resin compound, diethanolamine, with aluminium surfaces studied by static SIMS and XPS Stanley AÜrossman,* Robert F. Comrie and Susan M. MacDonald Department of Pure and Applied Chemistry, University of Strathclyde, Glasgow, Scotland, UK, G1 1XL The interaction of diethanolamine, a model epoxy resin compound, with aluminium surfaces is characterised using static secondary ion mass spectrometry (SIMS) and X-ray photoelectron spectroscopy (XPS). Diethanolamine does not adsorb on c-alumina but does adsorb on phosphoric acid anodised aluminium, suggesting that the adsorption site is a acid. A static SIMS Br‘nsted spectrum is obtained consistent with a protonated species and the XPS N 1s signal shows two states for the adsorbate.Diethanolamine on an ion-bombarded aluminium surface does not show the characteristic SIMS spectrum observed with the anodised substrate. It is postulated that the hydroxy groups of the diethanolamine form a dialkoxide covalently bound to the ion-bombarded aluminium.The corresponding XPS N 1s signal showed a single binding energy in the range of Lewis site interactions on alumina. The interaction of all three functionalities of the diethanolamine with the anodised aluminium surface results in stronger adsorption than for a similar difunctional compound, (methylamino)ethanol, indicating that both hydroxy groups are involved in hydrogen bonding to surface acid sites The presence of covalent bonds across the adhesive/metal (oxide) interface is regarded as providing enhancement of the durability of a metal»adhesive»metal joint, and several studies have been made of the nature of the polymer/metal interface.Many of these investigations have avoided the experimental problems of examining the buried interface by utilising model adhesive compounds as adsorbates,1h8 and this approach is used in the present work, continuing the study of amine cured epoxy resins on aluminium subtrates.Amine cured epoxy mimics contain the characteristic grouping, formed from reaction of an wC(OH)CH2NHw epoxide ring and the active hydrogen of an amine group, and simple model compounds which have been used as resin mimics are ethanolamine7 and (methylamino)ethanol.8 Diethanolamine has also been used as a model compound,4 corresponding to the stage when the active hydrogens of a primary amine functionality react with two epoxide groups. None of these compounds are strictly resin mimics, diÜering from the ì real œ resin in that the alcohol groups are primary instead of secondary and active hydrogen remains on the amine, though the latter is found in partially cured resin.Diethanolamine does, however, provide the opportunity of exploring the stereochemical aspects of the adsorption, having three interactive groups in close proximity. The interaction of diethanolamine, on air-oxidised copper, aluminium and phosphoric acid anodised aluminium was studied previously by Kelber and Brow4 using temperatureprogrammed desorption (TPD) and X-ray photoelectron spectroscopy (XPS). They concluded that the reaction of di ethanolamine with air-oxidised or anodised aluminium was with the nitrogen groups on the molecule via a acid Br‘nsted interaction, based on observations of the N 1s binding energy and the retention of the species to high temperatures ([500 °C).The assignment of adsorbate bonding (Lewis/ from the N 1s binding energies is not straightfor- Br‘nsted) ward.Several investigations of the relationship between acidity and N 1s binding energies have been made, notably by Borade et al.9h13 They correlated IR data for pyridine on zeolites, which delineates or Lewis acidity, with XPS N Br‘nsted 1s binding energies. Guimon et al.14 made a similar study using N 1s binding energies and TPD of ammonia on faujasites. There is agreement that there is generally a distribution of sites and binding to sites corresponds to the Br‘nsted higher, and Lewis to the lower, N 1s binding energies, though the diÜerence between the probe depths between XPS and IR/TPD should be borne in mind. The binding energy alone is not sufficient to distinguish between and Lewis sites Br‘nsted e.g.an N 1s component at 400.0 eV is assigned to a Br‘nsted site on ZSM-59 whilst a component at 400.2 eV is postulated to be a Lewis site interaction on beta zeolite.10 An additional de–ciency with XPS is that information on the interaction of the hydroxy group is difficult to obtain because of the overlap of the adsorbate O 1s signal with those of substrate oxygen functionalities and the small O 1s binding energy range.Static secondary ion mass spectrometry (SIMS) can provide additional valuable data on the nature of chemisorbed species.6,15h18 The advantages of this technique lie in its high sensitivity and detailed molecular structural information.SIMS and XPS therefore provide, respectively, complementary qualitative and quantitative information, and are used here to investigate the adsorption of diethanolamine on various aluminium substrates, and to compare the relative strength of adsorption of trifunctional diethanolamine with that of difunctional (methylamino)ethanol. Experimental Materials Pure aluminium (Goodfellows) substrates were treated by the full Boeing Process19 to give an oxide coating of several hundred nm [phosphoric acid anodised (PAA) aluminium], or were exposed to an argon ion beam of 6 kV kinetic energy to produce the ion bombarded samples.The cleanliness of the latter was monitored using the XPS Al 2p, N 1s, O 1s and C 1s signals. The pure c-alumina was Degussa grade C, a non-porous alumina; diethanolamine (Fisons), methylaminoethanol (Aldrich) and diethylamine hydrochloride (Fluka) were used without further puri–cation. The SIMS spectrum of diethylamine hydrochloride was obtained from the powder coated on to double-sided sellotape.Overlayers on PAA aluminium were obtained by evaporation of 1»3 drops of 0.05 M solutions of the model compounds, in methanol or in toluene, on to the anodised substrates. The ion bombarded aluminium was exposed to the J. Chem. Soc., Faraday T rans., 1998, 94(2), 289»294 289vapour of the model compound within the surface analysis instrument, after degassing the diethanolamine by a series of freeze»pump»thaw cycles.Molecular modelling Molecular structures of diethanolamine and (methylamino) ethanol were constructed using the HyperCHEM program, Version 4.520 on a stand alone personal computer. The molecular geometries were optimised using the semiempirical AM1 method21 for all atoms at the restricted Hartree»Fock (RHF) level. No molecular symmetry constraint was applied and full optimisation of all bond lengths and angles were carried out under the AM1 conditions. The charges on the atoms were determined.Surface analysis For static SIMS, samples were irradiated with a Vacuum Science Workshop ion gun, using a 3 keV argon ion beam, with a current of 2]10~10 A measured at the gun exit, over an area of ca. 5 mm2. Spectra were obtained with a Vacuum Generators 12»12 quadropole. Sample charging was compensated by an electron gun providing a 30 eV electron beam. XPS data were obtained with a Vacuum Science Workshop 100 mm hemispherical analyser and X-ray anode, using aluminium or magnesium Ka radiation.XPS binding energy referencing XPS binding energies for diethanolamine were referenced to the C 1s envelope which spans (wCwCw) to (wCwOw) type carbons. The latter are shifted by 1.6 eV relative to a (wCwCw) binding energy.22 A (wCwNw) C 1s has a variable binding energy, i.e. ca. 0.9 eV higher than a (wCwCw) C 1s for a neutral amine but the diÜerence will be increased if charge transfer or protonation of the nitrogen occur on adsorption.23 Because of the relatively low resolution of the XPS instrument, the carbons were assigned only to (wCwCw) or (wCwO/Nw).The measured binding energy of the (wCwOw) C 1s peak, which is assumed to encompass the (wCwNw) C 1s signal, will be decreased because of the (wCwNw) contribution, in the worst case (neutral amine» alcohol) by ca. 0.3 eV, the (wCwNw) and (wCwOw) concentrations being equal. For calibration, the (wCwOw) C 1s peak was –xed at a nominal (284.6]1.5)\286.1 eV.Contamination would be expected mainly to increase the (wCwCw) contribution and, though adsorption of the diethanolamine was low and contamination was therefore proportionately high, the (wCwCw) C 1s binding energies were 284.6^0.2 eV, indicating that diÜerential charging between adsorbates was not a problem. The charging reference for the adsorbed diethylamine was referenced to the (wCwCw) C 1s signal at 284.6 eV because of the absence of a (wCwOw) contribution. Signal intensities were corrected for cross-sections and escape depths using Wagnerœs sensitivity factors24 adjusted for our spectrometer.The Al 2p, O 1s, P 2p, C 1s and N 1s signals were measured at a take-oÜ angle normal to the surface, and spectra were smoothed and deconvoluted using the software of Evans.25 Peak shapes for deconvolution were taken from spectra with signals from single carbon or nitrogen species. Although no deconvolutions are unique, the C 1s envelopes were –tted by a minimum number of components and were chemically reasonable i.e.the adventitious contribution could be readily recognised. The N 1s envelopes contained no analogous common feature. Thus, they were –tted with the minimum number of standard peaks though the peak width of the components had to be increased by up to 0.4 eV to match the N 1s envelope. This could result from diÜerential charging or a distribution of energies of surface sites, and in view of the C 1s data the latter is considered more probable.Results Diethylamine hydrochloride Before investigating the adsorption of diethanolamine on aluminium, it is appropriate to consider the interaction of diethylamine, which has a similar secondary nitrogen functionality but no alcohol groups. Firstly, the hydrochloride salt was examined. Attempts to form a thin layer of the salt from aqueous or methanol solution were unsuccessful : an oily layer was formed which evaporated in the spectrometer.The salt powder was spread therefore on double-sided sellotape and a good SIMS spectrum was recorded. The XPS data showed a broadened N 1s signal (there should be only one species) which was attributed to diÜerential charging between the particles, and the sample also desorbed under the X-ray source causing an increase in pressure. Presumably the material sublimes, like ammonium chloride, with the heat of the X-ray source and the low pressure. Thus, only the SIMS data are described.The SIMS spectrum of the diethylamine salt is given in Fig. 1(a). The very dominant feature is the protonated amine fragment (M]H)` at m/z 74. Minor contributions are at m/z 44 from scission of awCwNw linkage and at m/z 30 from the eventual breakdown to The m/z 18 peak is from CH2NH2 `. which is difficult to remove from the salt once H2O`, absorbed. The failed attempts to deposit a thin layer from water or methanol solution were probably caused by decomposition of the salt because of the strong interaction with the solvent.Fig. 1 (a) SIMS spectrum of diethylamine hydrochloride, (b) SIMS spectrum of diethylamine on PAA aluminium and (c) XPS data for diethylamine on PAA aluminium 290 J. Chem. Soc., Faraday T rans., 1998, V ol. 94Diethylamine adsorbed on PAA aluminium We have reported XPS and SIMS data for diethylamine on PAA aluminium previously.6 The XPS data were referenced to Al and were not deconvoluted. In accordance with the current scheme, the data are reanalysed and presented in Table 1 and Fig. 1(c).The C 1s envelope is deconvoluted to give two components at 284.6 eV (–xed) and 286.3 eV. The ratio of carbon at 286.3 eV to the total nitrogen is 5 : 1 compared to the theoretical 2 : 1, with the discrepancy probably caused by the errors in measurement of the small signals and contamination by (wCwOw) species. Using the standard N 1s peak shape, the N 1s envelope can be –tted by two components at 398.7 and 401.1 eV and relative intensities of 30 and 70% respectively. Borade et al.11 have examined the adsorption of pyridine on c-alumina, concluding that there is a range of Lewis acid sites, three N 1s species being identi–ed with binding energies of 397.8, 399.5 and 401.3 eV, respectively with the middle one being the dominant component.In PAA aluminium phosphate is retained in the surface region, as con- –rmed by XPS (Table 1), and will introduce activity. Br‘nsted Thus, it is probable that the major component at 401.3 eV for diethylamine on PAA aluminium corresponds to adsorption on a site. The minor component at 398.7 eV may Br‘nsted arise from weaker or Lewis sites. Br‘nsted The SIMS spectrum of diethylamine on PAA aluminium6 is reproduced in Fig. 1(b) for comparison with the amine hydrochloride. The marked (M]1)` peak at m/z 74 signal shows unequivocally that diethylamine is adsorbed intact. A fragment at m/z 45 corresponds to and possibly (M]1[C2H5)` to PN`, and is not signi–cant in the spectrum of the salt.Adsorption of diethanolamine on alumina Pure c-alumina was heated overnight at 773 K, cooled to 298 K and exposed to a solution of diethanolamine. The strongest Lewis sites would be rapidly deactivated on exposure to atmosphere but the alumina will remain partially activated. No adsorption was detected by SIMS or XPS. Diethanolamine adsorbed on PAA aluminium The XPS data for diethanolamine adsorbed on PAA aluminium are given in Fig. 2(a) and Table 1. Two nitrogen species can be observed at 399.2 and 401.0 eV, similar to the diethylamine data, but in this case the low binding energy component is the larger. The ratio of carbon at 286.1 eV to the total nitrogen is 4 : 1, in agreement with the molecular structure which suggests, in turn, that both nitrogen species relate to adsorbed diethanolamine. Before considering the SIMS data for adsorbed diethanolamine, the mass spectrum of gaseous diethanolamine from electron beam ionisation26 is discussed, Fig. 2(b). Scission a to both the nitrogen and a hydroxy gives the dominant m/z 74 fragment, with further breakdown to m/z 56, 42 and, Fig. 2 (a) XPS data for diethanolamine on PAA aluminium, (b) mass spectrum of diethanolamine (from data of ref. 24), (c) SIMS spectrum of diethanolamine on PAA aluminium and (d) fragmentation patterns for diethanolamine Table 1 Binding energies for diethylamine on PAA and diethanolamine on PAA and on ion-bombarded aluminium adsorbate diethylamine diethanolamine diethanolamine substrate PAA aluminium PAA aluminium IB aluminium Eb/eV FWHH/eV atom ratioa Eb/eV FWHH/eV atom ratioa Eb/eV FWHH/eV atom ratioa N 1s (1st peak) 398.7 2.4 0.3 399.2 2.1 0.7 399.8 2.5 1 N 1s (2nd peak) 401.1 2.4 0.7 401.0 2.1 0.3 » » » C 1s (1st peak) 284.6b 2.0 8 284.7 2.0 5.5 284.8 2.0 8.5 C 1s (2nd peak) 286.3 2.0 5 286.1b 2.0 4.5 286.1b 2.0 5.5 O 1s 531.8 3.1 33 530.5 3.1 20 530.6 2.8 28 Al 2p (1st peak) » » » » » » 70.7 1.7 41 Al 2p (2nd peak) 74.1 2.4 17 73.1 2.5 13 73.3 2.0 17 P 2p 134.0 » 3 133.5 » 1 » » » a Atom ratio relative to total nitrogen.b Reference Eb . J. Chem. Soc., Faraday T rans., 1998, V ol. 94 291eventually m/z 30 fragments. The m/z 45 species can be formed directly from scission of the parent molecule at a CwN linkage. Though the (N)wCwCw(O) linkage is readily broken, diethanolamine does not fragment like aliphatic alcohols, which give a major species at m/z 31. The SIMS spectrum of the molecule adsorbed on PAA is shown in Fig. 2(c) and notable features are the appearance of the parent at (M]1)` and the much decreased m/z 74 fragment. The fragmentation scheme for diethanolamine is shown in Fig. 2(d) and proceeds via loss of a hydroxy group or water from the protonated molecule, (M[OH)` or (M]H to give a fragment at m/z 88, similar to the mechan- [H2O)` ism for difunctional amine-alcohols.8 In this case, one or both hydroxys are removed, and the fragment at m/z 70 arises from a Scission of the protonated molecule (M]H[2H2O)`.would give a signal at m/z 75 which is not observed, although a minor signal at m/z 74 may arise from neutral molecules or molecules protonated at an oxygen. The fragment at m/z 45 can be formed directly by cleavage of a CwN bond of the protonated or neutral molecule.The SIMS spectrum shows that the behaviour is similar to that of (methylamino)ethanol8 on PAA, i.e.at least part of the adsorbate lies intact on a acid site with a proton donated to the amine group. Br‘nsted Coadsorption of diethanolamine and (methylamino)ethanol In order to evaluate the relative strength of the interaction of the diethanolamine compared to methylaminoethanol, a PAA aluminium substrate was exposed to an equimolar solution of both compounds. The SIMS spectrum (Fig. 3) from the coadsorption experiment distinctly shows the fragments corresponding to diethanolamine, but the absence of a signal at m/z Fig. 3 SIMS spectrum from the coadsorption of diethanolamine and (methylamino)ethanol on PAA aluminium 76, (M]1)` for (methylamino)ethanol, indicates that adsorption of the latter is blocked by diethanolamine. (Methylamino)ethanol and diethanolamine are comparable small molecules. Therefore, the preferential adsorption of diethanolamine must result from the extra hydroxy functionality. If the eÜect of the extra hydroxy group was to increase the electron charge density on the nitrogen, then the basicity of the molecule would be increased.Calculation of the charges on the nitrogen atoms of diethanolamine and (methylamino)ethanol using molecular modelling gave values of [0.287 and [0.308 respectively, i.e. diethanolamine is less basic. The hydroxy group must therefore interact with the surface directly to cause the preferential adsorption. A conformer of the quaternised molecule, which is apparently the adsorbed species, was constructed and rotation of the appropriate bonds showed that all three functionalities can approach the surface simultaneously.Diethanolamine adsorbed on ion-bombarded aluminium Ion bombarding an aluminium substrate results in loss of much of the surface oxide/hydroxide overlayer, and most of any carbon contamination. The oxide overlayer is not reduced to zero because of the strong gettering power of clean aluminium and the medium vacuum in the analyser chamber, (ca. 10~9 Torr). Exposure of the ion bombarded sample to diethanolamine increases the O : Al ratio, but the Al 2p signal, Fig. 4, shows that Al metal is present within the top 4 nm of the substrate. The nitrogen signal is small but comparable to that on PAA aluminium and there is a marked adventitious carbon signal acquired during exposure to the adsorbate vapour within the instrument. Only a single N 1s species is observed with a binding energy of 399.8 eV. A blank run, without diethanolamine, gave a similar carbon contamination but a much reduced N 1s signal. The SIMS spectrum of an ion-bombarded aluminium surface, shown in Fig. 5(a), has a strong Al` signal.Minor contributions from AlO`, AlOH` (m/z 43, 44) will contain an unknown fraction of contaminent signals. The spectrum of diethanolamine adsorbed on ion-bombarded aluminium is given in Fig. 5(b). Comparing the data from the PAA aluminium surface to that from the ion-bombarded metal, it is seen that the parent (M]1)` signal is missing for the latter.Also, no useful fragment ions were observed at lower masses, i.e. these could not be safely distinguished from contaminent signals. In the previous study8 of (methylamino)ethanol on an ion-bombarded aluminium no parent signal was obtained but the species was observed. The correspond- (M]H[H2O)` Fig. 4 XPS data for diethanolamine on ion-bombarded aluminium 292 J. Chem. Soc., Faraday T rans., 1998, V ol. 94Fig. 5 (a) SIMS spectrum of clean ion-bombarded aluminium and (b) SIMS spectrum of diethanolamine on ion-bombarded aluminium ing fragments for diethanolamine, and (M (M]H[H2O)` are not seen on ion-bombarded aluminium ]H[2H2O)` though they were detected on the PAA aluminium. The XPS data suggest that diethanolamine adsorbs on ionbombarded aluminium (containing a small oxide overlayer), but SIMS shows that the interaction with the ion-bombarded aluminium diÜers from that with PAA. Discussion In general our XPS data are similar to those of Kelber and Brow,4 showing that diethanolamine adsorbs on both PAA and ion-bombarded aluminium.The assignment of binding energies diÜers because they referenced to the Al 2p signal, discarding the C 1s data, and the N 1s envelope was not deconvoluted. Comparing the data for diethanolamine on PAA aluminium, the diÜerence between their Al 2p and O 1s values and ours is 2.3^0.1 eV, which also brings the N 1s values into agreement (taking our major N 1s peak).For diethanolamine on the ion-bombarded substrate the diÜerence between the AlO 2p assignments is 1.7 eV. The AlIII 2p and O 1s binding energy diÜerentials for ion-bombarded aluminium depend on the degree of oxidation of a particular sample and any further diÜerential through the oxide overlayer. In this case, a total of 2.2^0.1 eV accounts for the diÜerence in AlIII 2p and O 1s values. Thus, the issue is whether diÜerential charging occurs between the substrate and adsorbate, a problem that has been discussed in ref. 8. It is difficult to ascertain the magnitude of any charge diÜerential, or to know whether it applies equally to the whole adsorbate, with the possible exception of the relationship between adventitious carbon and the AlO signal for ion-bombarded aluminium. Assuming that part of the adventitious carbon is (wCwCw) type, both binding energies are known. Our data for diethanolamine on the ion-bombarded aluminium then gives a diÜerential charge of 2.4^0.1 eV in agreement with the 2.2^0.1 eV diÜerence between our assignments and those of Kelber and Brow.4 If the assumption is made that there is no signi–cant charge diÜerential across the surface, XPS can give at least the relative environments of an adsorbate from the peak shape, i.e.the occupancy and relative binding energy. It is apparent that the SIMS data for diethanolamine on PAA aluminium show that the adsorbate is present and retains the molecular structure.Interaction of the nitrogen at a weak Lewis site plus hydrogen bonding at both alcohol functionalities would give an adsorbed species similar to an overlayer of frozen molecules and thus would be expected to give an (M]1)` signal with SIMS.27 However, the lack of adsorption of diethanolamine on c-alumina suggests that acidity introduced by the phosphate is responsible Br‘nsted for the adsorption on PAA aluminium. The XPS N 1s data show that there is more than one environment and the minor N 1s contribution (401.0 eV) would therefore correspond to protonated amine. By the same argument, the major component at 399.2 eV probably corresponds to interaction of the nitrogen with a weaker site, but two alternative Br‘nsted adsorption mechanisms cannot be entirely excluded: (a) protonation of some molecules at the hydroxy, not at the nitrogen, though diethylamine, without hydroxys, shows two binding states with similar N 1s binding energies ; (b) bonding via alkoxy linkages.Breakage of the alkoxy bond is unlikely to give an (M]1)` ion with SIMS and the SIMS spectrum showed only fragments which could be assigned to an associatively adsorbed species, though in view of the simplicity of the molecule and the presence of two alcohol groups, and therefore two alkoxide links, fragmentation of the alkoxide may give only low molecular weight ions common in the background spectrum. Alkoxide formation is more probable on the ion bombarded aluminium.Ion bombarded-aluminium is oxygen de–- cient and surface aluminium metal atoms can dissociate the hydroxy groups of the adsorbate to give alkoxide linkages. Noting that no adsorption was observed on activated alumina, it may be concluded that a small adsorption of oxygen on clean aluminium does not give a sufficiently coherent oxide overlayer to prevent migration and reaction of aluminium with adsorbates.The lack of identi–able signals in the SIMS spectrum of diethanolamine on ion-bombarded aluminium shows that the adsorption mode diÜers from that on PAA aluminium and precludes a protonated molecule adsorbate.Alkoxide formation would give an adsorbed species which would fragment to lower molecular weight species but, unlike (methylamino)ethanol8 on ion-bombarded aluminium, the (M[OH)` [or (M[2OH)`] are not observed, which may be evidence for reaction of both alcohol groups to form alkoxy bonds. The XPS data for diethanolamine on the ionbombarded aluminium showed a single nitrogen species at 399.8 eV, which is consistent with a Lewis interaction of the nitrogen, cf.c-alumina.11 Consequently, the adsorbate would be bound to the surface at three molecular sites, two covalently, and desorption during SIMS would give only minor fragments. The adsorption of diethanolamine on PAA or ionbombarded aluminium follows the same pattern as that of (methylamino)ethanol with associative adsorption on the former and dissociative on the latter substrate. The calculated molecular conformation of diethanolamine showed that the adsorbate geometry allows all three functionalities to approach the surface and the results for competitive adsorption have shown that the substrate site geometry is favourable for reaction with all three functionalities simultaneously, giving diethanolamine an advantage over (methylamino) ethanol.The competitive adsorption results in this study, and in previous work on (methylamino)ethanol and diethylamine on PAA,6,8 enable an order of adsorption to be established. The progression of adsorption strength is CH3CH2NHCH2CH3\HOCH2CH2NHCH3 \HOCH2CH2NHCH2CH2OH which con–rms the importance of the hydroxy group interactions. The extra adsorption energy conferred by the hydroxy group is therefore signi–cant in dictating the species adsorbed in a competitive situation, even though on surfaces, Br‘nsted as seen from the SIMS which con–rms a molecular adsorbate, it adds only a hydrogen bond.is grateful to EPSRC for S.M.MacD. funding. J. Chem. Soc., Faraday T rans., 1998, V ol. 94 293References 1 N. M. D. Brown, R. J. Turner and D. G. Walmsley, J. Mol. Struct., 1982, 79, 163. 2 N. M. D. Brown, R. J. Turner, S. AÜrossman, I. R. Dunkin, R. A. Pethrick and C. J. Shields, Spectrochim. Acta, Part B, 1985, 40, 847. 3 S. AÜrossman, J. M. R. MacAllister, R. A. Pethrick, B. Thomson, N. M. D. Brown and B.J. Meenan, in Polymer surfaces and interfaces, ed. W. J. Feast and H. S. Munro, John Wiley, Chichester, 1987, p. 99. 4 J. A. Kelber and R. K. Brow, Appl. Surf. Sci., 1992, 59, 273. 5 M. Nakazawa and G. A. Somorjai, Appl. Surf. Sci., 1993, 68, 539. 6 S. AÜrossman and S. M. MacDonald, L angmuir, 1994, 10, 2257. 7 C. Fauquet, P. Dubot, L. Minel, M. Villatte and M. G. Barthes Labrousse, Appl. Surf. Sci., 1994, 81, 435. 8 S. AÜrossman and S. M. MacDonald, L angmuir, 1996, 12, 2090. 9 R.B. Borade, A. Sayari, A. Adnot and S. Kaliaguine, J. Phys. Chem., 1990, 94, 5989. 10 R. B. Borade and A. Clear–eld, J. Phys. Chem., 1992, 96, 6729. 11 R. B. Borade, A. Adnot and S. Kaliaguine, J. Chem. Soc., Faraday T rans., 1990, 86, 3949. 12 R. B. Borade, A. Adnot and S. Kaliaguine, J. Catal., 1990, 126, 26. 13 R. B. Borade, A. Adnot and S. Kaliaguine, Zeolites, 1991, 11, 710. 14 C. Guimon, A. Zouiten, A. Boreave, G. P–ster-Guillouzo, P. Schulz, F. Fitoussi and C. Quet, J. Chem. Soc., Faraday T rans., 1994, 90, 3461. 15 S. AÜrossman, J. M. R. MacAllister, M. A. Morris, R. A. Pethrick and J. M. Rynkowski, Surf. Sci., 1987, 180, 633. 16 J. M. R. Rynkowski, S. AÜrossman, J. M. R. MacAllister and R. A. Pethrick, Surf. Sci., 1987, 182, 1. 17 M. A. Karolewski and R. G. Cavell, Surf. Sci., 1989, 219, 249; 261. 18 G. J. Leggett, M. C. Davies, D. E. Jackson and S. J. B. Tendler, J. Chem. Soc., Faraday T rans. 1, 1993, 89, 179; J. Phys. Chem., 1993, 97, 5348. 19 G. S. Kabayashi and D. J. Donnelly, Boeing Co. Rept. No. DG- 41517, 1974. 20 HyperCHEMTM Release 4.5, Hypercube Inc., 419, Phillip Street, Waterloo, Ontario, 1994. 21 M. J. Dewar, E. G. Zoebisch, E. F. Healy and J. J. P. Stewart, J. Am. Chem. Soc., 1985, 107, 3902. 22 Practical Surface Analysis, ed. D. Briggs and M. P. Seah., John Wiley, Chichester, vol. 1, 1990. 23 A. G. Shard, L. Sartore, M. C. Davies, P. Ferruti, A. J. Paul and G. Beamson, Macromolecules, 1995, 28, 8259. 24 C. D. Wagner, H. A. Six, W. T. Jansen and J. A. Taylor, Appl. Surf. Sci., 1981, 9, 203. 25 S. Evans, Surf. Interface Anal., 1991, 17, 85. 26 Atlas of Mass Spectral Data, ed. E. Stenhagen, S. Abrahamsson and F. W. McLaÜerty, Interscience, New York, 1969, p. 313. 27 M. Barber, J. C. Vickerman and J. Wolstenholme, J. Chem. Soc., Faraday T rans. 1, 1980, 76, 549. Paper 7/06261C; Received 27th August, 1997 294 J. Chem. Soc., Faraday T rans., 1998, V ol. 94

ISSN:0956-5000    

DOI:10.1039/a706261c

出版商:RSC    

年代:1998

数据来源: RSC

摘要:

Preparation and characterization of anatase powders Athanassios Tsevis,a Nikos Spanos,a Petros G. Koutsoukos,a Ab J. van der Lindeb and Johannes Lyklemab a Institute of Chemical Engineering and High T emperature Chemical Processes (ICEHT -FORT ) and the Department of Chemical Engineering, University of Patras, University Campus, GR-265 00 Patras, Greece b Department of Physical and Colloid Chemistry, W ageningen Agricultural State University, Dreyenplein 6, 6703 HB W ageningen, T he Netherlands Anatase powders have been prepared by precipitation and by sol»gel methods.In the former, titania was continuously precipitated at 25 °C, pH 1.97 in a stirred reactor by mixing and potassium hydroxide so as to keep solution supersaturation TiOSO4 constant throughout the precipitation process. The preparations were performed in the absence and in the presence of Li`, Nb5` and W6` ions. In all cases anatase was the sole phase forming. The presence of these metal ions (1»7]10~5 M) did not in—uence the precipitation kinetics, which was controlled by surface integration.XPS analysis showed that the dopant ions were incorporated into the anatase lattice for the preparations in supersaturated solutions. Microelectrophoresis experiments did not show any diÜerentiation of the electric charge of the preparations in the presence and in the absence of these ions. The relatively high speci–c surface area (SSA) of the anatase obtained (135 m3 g~1) increased (up to 250 m2 g~1) by the incorporation of the dopant ions.In the sol»gel preparations the process was found to depend on the supersaturation of the sol with respect to the solid phase forming. A threshold sol composition corresponding to a total titanium concentration of M (25 °C, pH\2.5»3.0) was CTi\0.06 found to be critical for the formation of the gel. Anatase was exclusively formed both in the absence and in the presence of dopant ions in the gel. The SSA obtained was low although it increased in the presence of dopant metal ions.Electrokinetic measurements of the solids formed by the sol»gel method, suggested that the dopant ions tend to accumulate on the surface of the anatase particles. Introduction Titania powders are used as supports for the preparation of catalysts for the reduction of nitrogen oxides.1 Since the process involves redox reactions, the electronic structure and the interactions of the adsorbed species with the substrate, are expected to play an important role.Doping of the solid TiO2 with altervalent ions but with similar size to TiIV, may improve greatly the catalytic activity of the catalysts prepared. 2h6 Moreover, since extensive work has been carried out concerning the photocatalytic activity of in various TiO2 forms (powder, –lms, etc.) the interface is of great TiO2/water interest for the regulation of the surface potential and hence the aggregation and/or adsorption of charged species.On the basis of ion size considerations, ions such as Li`, Mg2`, W6` and Nb5` may be introduced into the titania lattice. The introduction into the lattice of powdered titania of these ions is eÜected by heating mixtures of titania powders with small volumes of concentrated dopant solutions (dry or wet impregnation). The calcination process results not only in the loss of speci–c surface area due to sintering but also in solid phase transformations. Titanium oxide exists in three polymorphic phases: rutile (tetragonal, density\4.250 Mg m~3), anatase (tetragonal, 3.890 Mg m~3) and brookite (orthorhombic, 4.120 Mg m~3).The lower density solid phases are less stable and undergo transformation into rutile in the solid state. The transformation is accelerated by heat treatment and occurs at temperatures between 450 and 1200 °C7 while it depends on the nature, the structure and the preparation conditions of the precursor phase. Anatase doped with various metal ions has also been reported at low temperatures either by hydrolysis of titanium(IV) tetrachloride or/and titanium tetraisopropoxide in the presence of dopant ions8,9 or by adsorption from solution and coprecipitation.10 The problem with the preparation methods reported in the literature is the lack of control of the conditions during the formation of the new anatase nuclei and their further crystal growth.It is important to note that the kinetics of the formation of precipitates is very important both for the reproducibility of the preparations and for their –nal physicochemical characteristics.11 While pure anatase is prepared by hydrolysis of in TiCl4 solution and in the gas phase12 or by sol»gel methods13h17 there are very limited reports on the quanti–cation of the preparation conditions and their relative importance with respect to the physicochemical characteristics of the preparations.In the present work we have studied the kinetics of formation of anatase in aqueous solutions of titanyl ions as a function of the solution composition both in the absence and in the presence of Li`, Nb5` and W6` dopant ions.For maximum precision in the measurement of the rates of formation the investigation was done by continuous crystallization at constant supersaturation (C4S). Moreover, anatase was prepared by sol»gel methods in the absence and in the presence of dopant ions focusing on the importance of the composition of the precursor components.The oxide preparations (with and without the dopant ions) were characterized by measurements of their electrophoretic mobility in electrolyte solutions of diÜerent concentrations. The latter measurements aimed at investigating the eÜect of the preparation methods and of the presence of metal ions in the crystallizing medium on the phase stability and the surface charge of the precipitated titania. J. Chem. Soc., Faraday T rans., 1998, 94(2), 295»300 295Experimental Preparation by continuous crystallization at constant supersaturation (C4S) Titania powders were batchwise prepared, magnetically stirred, in a double walled glass reactor, of volume ca. 0.25 dm3.The temperature was controlled via circulation of thermostatted water at 25.0^0.1 °C. Titanium stock solutions were prepared from crystalline oxotitanium sulfate sulfuric acid complex hydrate (Aldrich) dissolved in standard 1 M hydrochloric acid (Merck, Titrisol).The solution was –ltered prior to use through membrane –lters (0.22 lm, Millipore). The standardization of the stock solutions was done spectrophotometrically measuring the absorption at 420 nm of the complex formed between TiIV ions and sulfuric acid.18 In this preparation, the eÜect of Li`, Nb5` and W6` ions was investigated. Standard stock solutions of these ions were prepared from (Merck, pro analisi), (Alfa) and Li2CO3 K2NbF7 (Alfa) crystalline reagents, respec- (NH4)10W12O41 … 5H2O tively.The preparation of the working solutions was as follows : a small volume of the stock titanium solution was transferred to a 0.2 dm3 volumetric —ask –lled with triply distilled, CO2-free water. For experiments in the presence of dopant ions, prior to –lling the —ask, the appropriate volumes of the dopant ions stock solutions were added. Then the solution was transferred to the reactor. The pH of the solution was measured by a combination glass/saturated calomel electrode standardized before and after each experiment by NBS standard buÜer solutions at pH 4.001 (25 °C, 0.05 M potassium hydrogen phthalate) and pH 7.413 (25 °C, 0.008 695 M KH2PO4» 0.030 43 M The pH of the working solution was Na2HPO4).19 adjusted in the reactor by the slow addition of standard KOH solution (Merck, Titrisol) to 1.97 at a constant stirring rate of ca. 400 rpm, adequate for obtaining a well mixed suspension. Ammonium nitrate was used as background electrolyte and the appropriate concentrations were obtained by adding a weighed mass of the crystalline reagent (Merck, Puriss.) in the working solution.Following pH adjustment of the working solution precipitation started immediately without any appreciable induction period. The formation of the solid precipitate according to eqn. (1) : TiO2`(aq)]2OH~(aq)]TiO(OH)2(s) (1) resulted in the release of protons in the solution. A pH drop as low as 0.005 pH units triggered the addition of titrant solutions and KOH at concentrations according to the TiOSO4 stoichiometry TiO : OH\1 : 2 of the precipitating solid.The titrant solutions added from two coupled syringe pumps were made up as follows : solution 1: (nC1]2C1]2C3) M TiOSO4 (2) solution : 2: (2nC1]2C2[C4) M KOH (3) where is the total titanyl concentration in the working C1 solution, is the KOH concentration needed for pH adjust- C2 ment at the desired value, the total concentration of the C3 dopant ions and the KOH concentration required for the C4 neutralization of hydrochloric acid contained in the eÜective titrant in burette 1.n is a constant, determined by pre- nC1 liminary experiments, and depends on the concentration needed to maintain the solution pH at the desired value (avoiding over- or under-shooting during the addition of the titrant solutions). In our experiments, n\24. The control of the addition was done via the impulsomat of an automatic titrator (Metrohm 614) while the solution pH was monitored by a pH meter (Metrohm 691).The coefficient 2 before C1, C2 and was a consequence of the use of two syringes. During C3 the course of precipitation the level of the working solution was kept constant by withdrawing from the solution front of the titania slurry. The slurry was –ltered through membrance –lters and the –ltrates were analyzed for total titanium by atomic absorption spectroscopy (AAS, Perkin-Elmer 305 A) and/or by spectrophotometric measurements. The solids collected on the –lters were further characterized by powder X-ray diÜraction (Philips PW 1840/30), scanning electron microscopy (SEM, JEOL JSM 5200) and measurements of the speci–c surface areas by nitrogen adsorption using a multiple point BET methodology (Sorptomatic 1900, Fisons).The volume of titrants added as a function of time was continuously recorded by a strip chart recorder and from the traces, the rates of precipitation were measured directly. The operation of the continuous crystallizer was continued to obtain the desired quantity.Finally the process was interrupted and the slurry in the reactor was immediately transferred in a centrifuge and the solid was separated at 4000 rpm for 3 min. Extensive washing of the precipitates was carried out to avoid contamination from the counter-ions of the salts used for the dopant ions. The mother-liquor was decanted and the solid was dried under vacuum.The experimental set-up for the preparation of titania powders by the C4S methodology is shown in Fig. 1. Solñgel preparation Titanium tetraisopropoxide (Merck-Schuchardt) Ti(OPri)4 dissolved in isopropyl alcohol (Merck) was hydrolysed with water. A quantity of a 0.2 M stock solution of was Ti(OPri)4 mixed with water in a ratio of 1 : 4. For preparation Ti : H2O of doped specimens, the appropriate concentrations of Li`, Nb5` and W6` were dissolved in water which was mixed with Ti.Then the clear solution containing and water Ti(OPri)4 with or without dopant ions was acidi–ed with concentrated nitric acid (65%, Merck) and the pH was adjusted between 2.5»3.0 at 25 °C. During the acidi–cation process, the solution remained clear without any solid formation. The solutions were left unstirred in a beaker covered with a lid and the gelation process proceeded until no liquid remained. Next, the gel was heated overnight at 80 °C to remove the solvent completely.After this stage, the powder obtained from the gel was heated in the presence of oxygen at 480 °C for 40 h resulting in the removal of the organic phase. The titania preparations by the C4S and sol»gel methods are summarized in Table 1. Electrophoretic mobility measurements The electrophoretic mobilities of the titania particles were measured in 0.01 M potassium chloride solutions at 2 °C as a Fig. 1 Experimental set-up for the preparation of titania by continuous crystallization at conditions of constant supersaturation (C4S) 296 J.Chem. Soc., Faraday T rans., 1998, V ol. 94Table 1 Titania preparations in the absence and in the presence of doping ions sample preparation method dopant ion (M/Ti)/M 1a C4S » » 1b C4S WVI 5]10~5/1]10~3 1c C4S NbV 5]10~5/1]10~3 1d C4S LiI 5]10~5/1]10~3 2a sol»gel » » 2b sol»gel WVI 1.0]10~5/0.2 2c sol»gel WVI 1.5]10~3/0.2 2d sol»gel NbV 1.0]10~4/0.2 2e sol»gel LiI 1.0]10~4/0.2 M/Ti is the concentration ratio of metal ion/total titanium in the solution.function of pH with a laser-Doppler velocimetric device (Zetasizer 3, Malvern Instruments Ltd., Worcestershire, UK) with an applied –eld strength of ca. 80 V cm~1. Velocity measurements were performed at the center of the capillary. To avoid polarization of the electrodes and to eliminate electroosmosis, the polarity of the electrodes was reversed at a frequency of 50 Hz.20 The concentration of the suspensions was adjusted within the operational limits of the instrument and the suspension pH was adjusted by the addition of standard solutions of hydrochloric acid or potassium hydroxide (Merck, Titrisol). The suspension pH value was measured before and after the mobility measurements. The reported electrophoretic mobilities are the averages of at least ten measurements (spread of values ^10% of the reported mean values).Results and Discussion The driving force for the precipitation in a supersaturated solution is the change of chemical potential on going from the supersaturated solution to equilibrium which (per mol) is : NA *k\*G\[ RT 3 ln (TiO2`)(OH~)2 Ks0 (4) where is Avogadroœs number, R is the gas constant, T the NA absolute temperature and the thermodynamic solubility Ks0 product of the precipitated solid. Parentheses denote the activities of the corresponding ions calculated from the mass balance for titanium, the solution pH and the charge balance by an iterative procedure in which the free energy of the system is minimized through successive approximations for the ionic strength.21 The extended Debye»Hué ckel equation corrected for ion interactions was used for the calculation of the activity coefficients.The ratio : X\ (TiO2`)(OH~)2 Ks0 (5) is de–ned as the supersaturation ratio. The initial conditions and the rates obtained with the C4S method both in the absence and in the presence of doping ions are presented in Table 2.From the powder X-ray diÜraction spectra of the solid precipitates by the C4S methodology shown in Fig. 2 it was concluded that the solid phase consisted of anatase with a relatively large content of amorphous titanium oxide. It should be noted that the presence of the amorphous band in the X-ray spectrum may be due to the very small particle size of the anatase powder precipitated. Moreover, diÜerential thermal analysis of the undoped titania preparations showed only one exothermic peak at 420 °C suggesting the presence of anatase only.Upon heating the precipitate at 500 °C for 20 h the peaks characteristic for anatase became sharper indicating improved crystallinity. The calcination conditions were selected as appropriate for the operation conditions of deNOx catalyst supports. The kinetics analysis was consequently performed on the basis of anatase formation and the corresponding solubility product of 2.5]10~23 mol3 dm~9 was used.22 As can be seen in Table 2, in the absence of dopant ions the Fig. 2 Powder X-ray diÜraction spectra of anatase prepared by the C4S methodology; (a) following drying at 80 °C overnight and (b) after heating at 500 °C for 20 h Table 2 Experimental conditions and measured rates for the precipitation of titania from supersaturated solutions at constant supersaturation, 25 °C, pH 1.97 expt. Tit a/10~3 M pH dopant Cdopant/10~5 M XTiO(OH)2/1014 rate/10~6 mol min~1 1 0.85 1.97 » » 1.62 2.3 2 0.85 1.97 WVI 1.0 1.62 1.2 3 0.85 1.96 WVI 3.0 1.62 1.9 4 0.85 1.97 WVI 5.0 1.62 1.7 5 0.85 1.97 WVI 7.0 1.62 2.1 6 0.85 1.97 NbV 1.0 1.62 2.5 7 0.85 1.96 NbV 3.0 1.62 2.8 8 0.85 1.97 NbV 5.0 1.62 1.0 9 0.85 1.97 NbV 7.0 1.62 1.7 10 1.26 1.97 » » 2.38 8.5 11 1.26 1.97 WVI 1.0 2.23 5.6 12 1.26 1.96 WVI 3.0 2.38 5.9 13 1.26 1.97 WVI 5.0 2.38 4.3 14 1.26 1.97 WVI 7.0 2.38 6.0 15 1.26 1.96 NbV 1.0 2.38 7.1 16 1.26 1.97 NbV 3.0 2.38 12.6 17 1.26 1.97 NbV 5.0 2.38 13.3 18 1.26 1.96 NbV 7.0 2.38 13.7 titanium in solution.a Tit\total J. Chem. Soc., Faraday T rans., 1998, V ol. 94 297rate was found to depend on the relative solution supersaturation, p: p\X1@3[1 (6) The power law: Rp\kp pn (7) was used to –t the kinetics data. In eqn. (7), is the rate of Rp precipitation, the rate constant and n the apparent order of kp the precipitation process. is a function of the active growth kp sites, which during crystal growth remains constant. Logarithmic plots according to eqn.(7) both in the absence and in the presence of Nd5` and W6` ions are shown in Fig. 3. The value calculated from the slope is ca. 12^0.5, while the presence of the doping metal ions did not aÜect the kinetics of precipitation. The high value found for the apparent order for the precipitation suggested a surface integration mechanism. 23h25 According to the classical nucleation theory, there is a linear relationship between the logarithm of the rate of precipitation and the inverse square of the logarithm of the supersaturation ratio according to eqn.(8) :26 ln Rp\A[ bc3v2 (kT )3 1 (ln X)2 (8) where b is a shape factor (\15n/3 in our case, corresponding to spheres), v the molecular volume of anatase [v\formula weight/(density]Avogadroœs number)\3.41]10~29 m3], k the Boltzmannœs constant and c the surface energy of the growing phase. A typical plot of the kinetics data according to eqn. (8) is shown in Fig. 4. From the slope of the line a value of c\650 mJ m~2 was obtained for the surface energy of the forming anatase.The phase forming was anatase consisting of small crystallites with sizes \0.1 lm aggregated in the form of larger spherullitic particles (ca. 10 lm), as may be seen in the Fig. 3 Plots of the logarithm of the rates of precipitation of anatase as a function of the logarithm of the relative solution supersaturation measured at constant supersaturation conditions ; pH 1.97, 25 °C Fig. 4 Plot of the precipitation rates of anatase as a function of the inverse square of the logarithm of the relative supersaturation at conditions of constant supersaturation pH 1.97, 25 °C Fig. 5 Scanning electron micrographs of anatase crystallites formed by the C4S method; (a) aggregated anatase particles and (b) cracked spherullitic anatase aggregate showing composition of submicrometer particles electron migrographs of Fig. 5(a) and (b). It should be noted that the concentration of the dopant ions in solutions were selected so that precipitation of the oxides of these ions was precluded. The presence of the dopant ions examined did not cause any change in the particles morphology.The speci–c surface areas (SSAs) for the preparations are summarized in Table 3 where the atomic ratios of oxygen relative to titanium determined by XPS analysis are also listed. As may be seen, the presence of the dopant ions in the precipitation medium resulted in the replacement of the titanium ions in the anatase lattice while the SSA increased in the case of Li and Nb Table 3 Speci–c surface areas and ratios of oxygen relative to titanium determined by XPS analysis for anatase preparations with the C4S technique sample SSA/m2 g~1 O:Ti TiO2 (1a)a 139 2.05 TiO2 b (1a) 80 » TiO2»Li (1d) 252 2.19 TiO2»Lib (1d) 81 » TiO2»W (1b) 120 2.29 TiO2»Wb (1b) 60 » TiO2»Nb (1c) 209 » TiO2»Nbb (1c) 85 » a Sample numbers (Table 1) in parentheses.b After heating for 20 h at 500 °C 298 J.Chem. Soc., Faraday T rans., 1998, V ol. 94doping while it remained practically unchanged in the case of WVI doping. Upon heat treatment of the samples their SSA was markedly reduced, most likely because of extensive sintering. It should be noted that heat treatment (20 h at 500 °C) did not cause any phase change. The limitations of the preparative method of precipitation consist mainly in the relatively low rates of precipitation and the low limits of the dopant ions able to be used.Alternatively we have attempted to prepare both undoped and doped titania by sol»gel methods which may allow the use of higher levels of dopant ions which by diÜusion may be incorporated into the lattice of the forming oxide. The formation of gels depends critically on the supersaturation of the solution which is de–ned according to eqn. (5) by the total titanium concentration and the pH of the sol. As may be seen in Fig. 6, there is a critical supersaturation below which the gel cannot form, a solid oxide precipitate forming prior to the formation of the gel. Above this threshold, the gel is formed beyond an induction time which in inversely proportional to the solution supersaturation.The speci–c surface areas and the XPS analysis results for the anatase preparations according to the sol»gel technique are listed in Table 4. It is interesting to note the low SSA obtained for the preparations by the sol»gel method.It is possible that two factors contribute to the low SSA: slow formation by diÜusion of TiIV and OH~ ions through the gel and further sintering during the heating stage during the removal of the organic phase. The powder X-ray diÜraction of the oxide prepared was amorphous (the gel phase is predominant) but after heat treatment at 480 °C for 40 h it showed sharp anatase peaks as can be seen in the diÜractograms shown in Fig. 7. It is interesting however to note that the presence of dopant ions in the sol»gel process resulted both in the replacement of Ti ions and in a marked increase of the SSA of anatase with the exception of WVI at very low concentrations (10 lM), which caused a –vefold decrease of the anatase SSA.Consistent results were obtained for –ve diÜerent independent sample preparations at these conditions.27,28 Fig. 6 Preparation of by sol»gel methods; dependence of TiO2 gelation time as a function of the initial total titanium concentration at 25 °C Table 4 Speci–c surface areas and ratios of oxygen relative to titanium determined by XPS analysis for anatase preparations according to the sol»gel technique sample SSA/m2 g~1 O:Ti TiO2 (2a)a 2.5 2.01 TiO2»Li (2e) 14.2 2.02 TiO2»W1 (2b) 0.5 2.11 TiO2»W2 (2c) 76 2.22 TiO2»Nb (2d) 35.0 2.09 a Sample numbers (Table 1) in parentheses.All samples were subjected to heating at 480 °C for 40 h. Fig. 7 Powder X-ray diÜraction spectra of anatase prepared by the sol»gel method; (a) gel dried at 80 °C overnight (only solvent is removed) and (b) after heat treatment at 480 °C for 40 h The important diÜerences in the physicochemical properties of the oxide preparations are also expected to in—uence their electrical double layer which is very important for the most efficient deposition of the active phase in the catalyst preparation process.29,30 Measurement of the electrokinetic potential (f potential) is often calculated by applying the well known Helmholtz»Smoluchowski relation given by eqn.(9) : u\ ef g (9) where u is the electrophoretic mobility, where and e\erese0 eres are the relative permittivities of the electrolyte solution and e0 of vacuum, respectively, and g the viscosity of the solution.31 The applicability of eqn. (9) rests on a number of assumptions such as the following. (i) The radius of curvature of the particle surface is large compared to the Debye-screening length (K~1), (ii) the particle surface is non-conducting, (iii) the applied electric –eld strength and the –eld of the double layer are additive (iv) the charge is homogeneously distributed over the surface and (v) the viscosity, relative permittivity and ion conductivities in the double layer outside the plane of shear are equal to their bulk values.32 For anatase particles formed in the presence of the dopant ions, the validity of these assumptions is uncertain. It is preferable therefore, instead of f potentials, to present the electrophoretic mobilities of the anatase preparations which are shown in Fig. 8 and 9 for the C4S and sol»gel preparations, respectively. As may be seen, the i.e.p. of the samples prepared by the C4S methodology was at pH 6.7^0.1 irrespective of Fig. 8 Electrophoretic mobility of anatase particles prepared by C4S methodology as a function of the suspension pH; 0.01 M KCl, 25 °C J. Chem. Soc., Faraday T rans., 1998, V ol. 94 299Fig. 9 Electrophoretic mobility of anatase particles prepared by the sol-gel methodology, suspended in 0.01 M KCl at 25 °C.Numbers in parentheses refer to samples shown in Table 1; 2e, 2d, (\) 2b, (K) (|) 2a, 2c. (L) ()) doping with Li`, Nb5` or W6` ions. This result may be due to either the fact that the ions are incorporated inside the anatase lattice thus not aÜecting signi–cantly their surface charge, or to the low extent of their incorporation and presence on the surface. The anatase preparations by the sol»gel technique however show a markedly diÜerent behaviour as seen in Fig. 9. In the absence of doping with ions a small shift in the i.e.p. was observed from pH 6.7 found for the C4S preparations to 5.6 for the sol»gel preparations. The presence of ions such as Li`, Nb5` and W6` caused a shift of the i.e.p. to pH 6.4, i.e. to the same value as for the C4S preparations. This behaviour may be interpreted as indicative of the fact that in the sol»gel preparations the ions are more concentrated on the surface of the anatase particles causing the shift of the i.e.p.to more alkaline values. In the case of high concentrations of W6` in the gelation process a marked shift of the i.e.p. to pH 4.5 was observed. Since the pH of the sol»gel preparation favored the presence of polymeric, negatively charged tungstate anions it is possible that they have been mostly absorbed on the anatase surface causing a shift of the i.e.p. to more acidic pH values.33 Further studies concerning the role of the dopant ions on the determination of the surface charge of anatase particles prepared by various methods is currently being undertaken by potentiometic titrations and streaming potential measurements.Conclusions Polycrystalline titania catalyst supports were prepared by a continuous precipitation method at conditions of constant supersaturation (C4S) and by sol»gel methods both in the absence and in the presence of Li`, Nb5` and W6` dopant ions.In all cases the only phase forming was anatase. In the C4S methodology the reaction was controlled by the rate of integration of the growth units on the surface of the growing crystallites and the metal ions present were incorporated into the anatase lattice. A high apparent order for the dependence of the rates of precipitation on the solution supersaturation with respect to anatase was found. The high SSAs obtained were increased by the incorporation of the dopant ions.In the sol»gel preparations, the SSAs obtained for the anatase preparations were low but increased in the presence of dopant ions. The formation of gels preceding anatase formation was found to depend critically on the sol supersaturation. The induction times required for the formation of gels were inversely proportional to the sol supersaturation beyond a threshold value. Electrophoretic mobility measurements of the anatase particles suggested that in the preparations by the sol»gel method the ions are adsorbed on the surface rather than incorporated into the crystal lattice.authors wish to thank Professor J. L. G. Fierro at ICP, The Madrid, Spain for the XPS analyses and the European Comission for –nancial support of this work (contract CHR-X-CT- 94-0448-8). 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ISSN:0956-5000    

DOI:10.1039/a706608b

出版商:RSC    

年代:1998

数据来源: RSC