J. Chem. Soc., Faraday Trans. I, 1989, 85(2), 175-185 An Aluminium-27 Nuclear Magnetic Resonance Study of Chemical Exchange between Different Polyatomic Species in Butylpyridinium Chloride-AlC1, Me1 t s Kazuhiko Ichikawa," Takashi Jin and Toshiyuki Matsumoto Department of Chemistry, Faculty of Science, Hokkaido University, Sapporo 060, Japan 27A1 n.m.r. measurements have been made for molten n-butylpyridinium chloride-AIC1, mixtures at 61 and 66mol% AlCl, and at various temperatures between 20 and 100 "C. The time evolution of the 27Al longitudinal magnetization recovery (1.m.r.) was obtained from the free- induction decays measured using the inversion recovery method. The observed 27Al 1.m.r. and n.m.r. spectrum consisted of two contributions which were attributed to A1,Cl; (A) and AlCl, (B).The experimental results of the 27Al 1.m.r. and n.m.r. spectrum were reproduced with the aid of the general theory describing the effect of chemical exchange on 1.m.r. and lineshape. Thus the kinetic and equilibrium properties of the chemical exchange process were determined from the temperature dependences of the fractional population, f,, and the lifetime t, (a = A or B), which ranged from 10-3-10-1 s. The rate of the exchange reaction A1 (in B)+AI (in A) is not very fast, since it is small compared with I?:, A (> I?:,.) even at high temperatures for 61 mol% AlC1,. The observed rate of 1.m.r. at high temperatures under the influence of chemical exchange between the different polyatomic species B and A was not equal to the spin-lattice relaxation rates I?;".* and Rr,R.In molten mixtures of AlCl, and 1 -butylpyridinium chloride (BPCl), alkylimidazolium chloride (IMCl) or alkali-metal chloride the predominant equilibria reactions may be expressed as (1) (2) 2 AlCl, g A1,Cl; + C1- 2 AlCl, + Al,CI, e 2 AI,Cl; over the region of a formal AlC1,:MCl mole ratio, x, of 1.0 (i.e. MAlCl, melt or 50 mol YO AlCl,) to 2.0 (i.e. MAl,Cl, melt or 66.7 mol '/O AlCl,). The chloroaluminate melts consist of aluminum tetrachloride and dialuminum heptachloride ions, AlCl, and Al,Cl;, as the major chloroaluminate species, at 1 < x < 2. A Raman spectroscopic study showed that the bands assigned to Al,Cl, or higher polymers (e.g. Al,Cl;,,) did not appear in the observed spectra as far as the available sensitivity permitted us to The potentiometric determination of the equilibrium constant Keq for eqn (1) was carried out using the electrochemical concentration cell and the solvent acid-base properties were also Keq was determined to be ca.at 30 "C and 1 < x < 2 for the BPCl-AlC1, melts because of the very small value of [Cl-] (ca. The aluminium-27 n.m.r. spectrum and 1.m.r. on MCl(M+ = BP+, Im+)-AlCl, melts were measured, and an equilibrium between the principal chloroaluminate species was discussed as far as the available n.m.r. sensitivity permitted us to Proton and carbon chemical shifts at the different sites of IM+ in MeEtIMCl-AlCl, (1 < x < 2) 175 7-2176 Butylpyridinium Chloride-AlC1, Melts melts were obtained from least-squares fits to the observed shift as the average of the unresolved multiplet using the calculated anion mole fractions of B and A under the assumption that [Cl-] << [complex anion] and [All = [B] + 2[A].*, lo The fractional population of B and A was determined by non-linear least-squares fits to the observed 1.m.r.using as a model the effect of rather slow chemical-exchange on its time evolution.1° On the other hand, the spin-lattice relaxation, and the equilibrium and kinetic properties of the dynamic equilibrium reaction associated with the ligand exchange between H,O and SO:- in the inner-sphere shell of aqueous 27A111*,11 were characterized by reproducing the experimental results for the 1.m.r. and n.m.r. spectrum with the aid of the general theory describing the effects of chemical exchange on 1.m.r.12 as well as on lineshape.', The theory showed an exact solution of the coupled expressions for the time evolution of each of the longitudinal magnetizations in two different environments.This paper describes how n.m.r. spectroscopy enables us to characterize an exchange process between different polyatomic species on the basis of experimental and theoretical studies. One can see an exchange process only between B and A in the observed 27Al n.m.r. lineshapes and 1.m.r. at 1 < x < 2, as far as the available sensitivity permitted us to determine. We reproduce their experimental results with the aid of the theory describing the effects of chemical exchange on 1.m.r. and lineshapes. This paper also reports the temperature dependences of the fractional population between B and A, their chemical exchange lifetimes, and the spin-lattice relaxation rates of 27Al in B and A, as well as the equilibrium and kinetic properties for the exchange reaction of B and A.Experimental Materials The preparation of crystalline BPCl and aluminum trichloride has been described previously." The manipulation of all materials was performed under an argon atmosphere in a glove box. The composition of molten BPCl-AlC1, was determined for aluminum by the 8-hydroxyquinoline method with the aid of the absorption spectrum and for chlorine by the precipitation titration method. N.M.R. Measurements We carried out the n.m.r. measurements of molten BPCl-AlCl, at 61 1 and 66f 1 mol% AlCl, between 20 and 100 "C. The melts consist of B and A as the major chloroaluminate species, as mentioned above.The 27Al resonance frequency and the time interval td between the last 90" pulse and the onset of data acquisition were ca. 52.1 MHz and 30 ps or 1 ms on a Varian XL-200, and ca. 130.2 MHz and 400 ps on a JEOL GX-500, respectively. The observed magnetization M,(z) was obtained from the initial intensity of the free-induction decays measured at td = 30 ps, using the inversion recovery (or 18O0-z-9O") method for ca. 10 values of z until M,(z)/M; reached ca. 0.65.l' Thus the experimental points of 1.m.r. were obtained as a function of z. Results The 27Al n.m.r. spectra of molten BPCl-AlCl, at 61 k 1 and 66 k 1 mol % AlCl, between 20 and 100 "C are shown in fig. 1 and 2. The ,'A1 n.m.r. spectra at 61 1 mol O/O AlCl, (ie.x = 1.56, see fig. 1) were partially resolved into two components corresponding to B and A, where the resonance line assigned to the former was located to high field. Previous studies have reported the measurements of the partially resolved lineshapes ofK. Ichikawa, T. Jin and T. Matsumoto 177 100 ~ 52.1401 52.1201 VIMHZ Fig. 1. 27A1 spectra recorded at 52.1 MHz, t, = 30 ps and 61 & 1 mol % AICI, between 30 and 100 "C. The spectra are displayed isometrically on a scale. 27Al in the BPCl or IMCl-AlC1, melts over the region 1 < x < 2 . 7 9 8 9 1 3 * 1 4 Increasing the temperature gives rise to an increase in the concentration of A as well as the motional narrowing of the lineshapes. We can recognize that the chemical exchange rate between B and A in eqn (1) is not larger than the resonance-frequency separation of the two lines Av(= v,-vv,).The effect of chemical exchange on the 1.m.r. is small, but it is still important. The 27Al resonance line was found to depend upon the delay time t, at 66 mol YO AICl, and v,, = 52.1 MHz, as shown in fig. 2(a) and (b). Each of the spectra showed a single peak for t , = 30 ps, because of the BPA12C17 melt (i.e. x = 2), which consisted of the two species BP+ and A; the large signal attributed to 27Al in A masked a much smaller contribution from B. For t, = 1 ms partially resolved peaks were observed [see fig. 2(b)], where a large number of transient accumulations (i.e. 500) were necessary to obtain a good signal-to-noise (SIN) ratio. On the other hand, for v,, = 130.2 MHz and td = 400 ps, clearly resolved peaks were observed at all the temperatures for each of 16 times that the signal was augmented [see fig.2(c)]. The experimental points of the 1.m.r. at 61 and 66 mol YO AlCl, are shown in fig. 3 and 4, respectively. Once we were able to observe the free-induction decays at vAl = 52.1 MHz and t d = 30ps using the inversion recovery method, we were then able to obtain the longitudinal magnetization Mz(z) as a function of time interval z between the 180 and 90" pulses, as mentioned in the Experimental section. At the lower temperatures the non-linear logarithmic longitudinal magnetization originated from the slow exchange rates ; at high temperature single-exponential decays were observed, although the 27Al spectra showed some partially resolved peaks (see fig.1). The 1.m.r. data for the whole signal did not enable us to determine the spin-lattice relaxation rates of 27Al in A (B) R:,, (> without the aid of the theory describing the effects of chemical exchange on the 1.m.r. and n.m.r. spectrum, as mentioned below. Discussion We focus here on the chemical-exchange process between different polyatomic species A and B in BPCI-AICI, melts. We will characterize its equilibrium and kinetic properties178 Bu ty lpy r idin iurn Chloride- Al C1 Melts 100 80 40 21 4 I I I I I 52.1401 V I M H Z 52.12 01 100 - 80 I I I I I I 52.140 52.1201 V I M H Z 90 I I I 1 I 1 130.22 V I M H Z 130.23 Fig. 2. 27A1 spectra at 66k 1 mol YO AlCl, between 20 and 100 "C; (a) for v,, = 52.1 MHz and t, = 30 ,us, (6) for v,, = 52.1 MHz and t , = I ms and (c) for v,, = 130.2 MHz and t, = 400 ,us.K.Ichikawa, T. Jin and T. Matsumoto I79 I I I 1 I 1 - 0 2 4 6 8 10 104 zls Fig. 3. Experimental points of the longitudinal magnetization recovery at 61 f 1 mol YO between 30 and 100 "C. The dashed line is a fit of the data to the theory. v,, = 52.1 td = 30 p ~ . AlCI, M Hz, \ I I I I 1 * - 2 0 2 4 6 0 10 104 zjs Fig. 4. Experimental points of the longitudinal magnetization recovery at 66k 1 mol YO AICl, BPAl,CI, melt between 21 and 100 "C. The dashed line is as for fig. 3. v,, = 52.1 MHz, td = 30 ,us. and obtain the spin-lattice relaxation rates of 27AI in the species by using the theory describing the effects of chemical exchange on 1.m.r. and the n.m.r.spectrum:l2. l3 Calculations of L.M.R. and Lineshape In the case of 27Al n.m.r. experiments the predominant equilibria (1) and (2) can be simplified to (3) 27Al (in B) g 27Al (in A). Here, we assume for simplification that no contributions from AI,CI, or higher polymers appear in the n.m.r. data of the chloroaluminate melts over the region I < x < T7* * * 13, l4 Note that no Raman bands assigned to species such as A12Cl, and A13CI;o were180 Butylpyridiniurn Chloride-AlC1, Melts I I 1 1 1 I I 1 1 I V I M H Z 52.1381 VA VB 52.1221 Fig. 5. Experimental spectra (-) and their simulation (**.*.) at 61 +_ I mol % AlCl, at 50, 70 and 100 "C. (--) and (---) show the individual components of A and B. The parameters used for the simulation are given in fig.8 and 9 (later). Under conditions of chemical exchange between the two sites A and B the time evolution of their longitudinal magnetizations Mz, A(z) and Mz, A(z) and the total magnetization Mz(z) is given by and MZ(') = M Z , A(') + M Z , B(')' (6) Here the coefficients of and the inverse time constant describing the time evolution of the observed M,(z) or MZJz), R,,,(a = A or B) are expressed in terms of the spin-lattice relaxation rate R:, A(R:, B) of A1 in site A (and site B), the lifetime of chemical exchange of site a, z,, and the fractional population of nuclei (e.g. 27Al) between sites A and B (fA = 1 -fB), as shown in eqn (8)-(10) and (13)-(17) in ref. (12). Since there is supposed to be equilibrium in solution between the main A and B species, the relation between f A , and zA, is expressed as 'BfA = ' A f B ' (7)K.Ichikawa, T. Jin and T. Matsumoto 181 J I I I I II I I 130.228 UA U S 130.222 V I M H Z Fig. 6. Experimental spectra (-) as shown in fig. 2(c) and their simulation (-.*.*) at 66f 1 mol YO AlCl, at 50, 70 and 90 "C. (--) and (---) are as for fig. 6. z, used for the simulation is given in fig. 10 (later). 1001 I I I I I I I I 1 1 1.9 Fig. 7. 0 0 0 a I 0 0 I 1 1 1 1 1 1 1 1 1 1 1 7 . 4 0 50 100 T I T Temperature dependences R:,, t, (a) and t, Av (0) at 61 mol % AlCl,. We have been able to investigate the influence of chemical exchange on the 1.m.r. for slow, intermediate or rapid exchange, kBA(ril, k,, = ~i'), for the forward and backward exchange processes. Hence the simulation of the n.m.r.spectrum and the 1.m.r. provides the equilibrium and kinetic parameters of the exchange reaction in eqn (3) as well as the spin-lattice relaxation rate.182 lo-* Y) 1 n W 8 8 n W Butylpyridinium Chloride-AlC1, Melts 1 1 1 1 ~ 1 1 l I - - - - - - 0 Q 0 0 I , , ,j 0 - I 1 1 TIOC i + - 1 % 1 0*- 2.6 2.8 3.0 3.2 3.4 3.6 103 KIT Fig. 8. Temperature dependences of Rl, A (O), R l , , (O), R:, A (@) and R:. , (a) at 61 & 1 rnol % AICI,. We simulated the experimental points of 1.m.r. as shown by the dashed lines in fig. 3 and 4; the observed lineshapes were also simulated, as shown by the dotted lines in fig. 5 and 6, between 21 and 100 "C at 61 and 66 mol O h AlCl,, using equations that appear in ref. (12) and (13). The effect of a delay on the observed free-induction decay was accounted for in the simulation of the recovery curve and the lineshape, since the data were recorded with the delay.', Fig.7 shows the temperature dependence of the product parameters 2, Av and R:,* z, at 61 mol YO AlCl,, where Av = 501 _+ 1 MHz at vAl = 52.1 MHz. The fact that Rf,A z, ranged from 3 to 20 above ca. 40 "C at 61 mol YO AlCl, showsK. Ichikawa, T. Jin and T. Matsumoto 183 I I I 50 60 70 80 90 T I T Fig. 10. Temperature dependences of t, (0) and T~ (0) at 66+ 1 mol % AlCl,. Table 1. Kinetic properties of the exchange reaction of eqn (3) at 61 f 1 mol % AlCl, between 30 and 100 "C forward process backward process AH;,,/kJ mo1-' AS&/J K-I mol-' AHz,/kJ mol-' AS:,/J K-' mol-' 15.5k 1.3 - 149&4 -0.83 & 0.20 - 195+ 1 the effects of the chemical exchange on the 1.m.r.and lineshape to be small but important. Rr,, (a = A or B), z, and f,, which reproduced the data of 1.m.r. and the n.m.r. spectrum as shown in fig. 3-6, are discussed below. The Rate (&,) and Spin-Lattice Relaxation Rate The spin-lattice relaxation mechanism for 27Al is expressed in terms of the interaction of the nuclear electric quadrupolar moment with the fluctuating electric-field gradients (e.f.g.). The local e.f.g. at 27Al in B is much smaller than that in A, because an AlC1; species is characterized by regular symmetry, while the electronic density around 27Al in A1,Cl; with a double tetrahedron sharing one corner is not symmetrica1.2,15*'6 It is reasonable to conclude that R:,, is much larger than R:,, at 61 mol O/O AlC1, (fig.8). The exchange rate between A and B in the BPCl-AlCI, melts is not fast at 61 mol% AlCl, [ie. R;,, z, > 1 (as fig. 7)]. Both R1,* and R l , , become nearly equal to R:,, and R:, , respectively, below ca. 60 "C at 61 mol YO AlC1, (fig. 8), because of the very small effect of the chemical exchange on the 1.m.r. of 27A11*1 Kinetic and Equilibrium Properties of Chemical Exchange between Different Polyatomic Species In our n.m.r. study the lifetimes of A and B, z, and z,, were obtained at 61 and 66 mol YO AlCl, (fig. 9 and 10). z, and z, at 61 mol YO AlC1, range from lo-, to s and cross over; 5, is larger than z, above ca. 50 "C. For all the temperatures at 66 rnol YO AICl, 5, x tA/ 100 because of the fractional population of 27Al in A fA x 0.99.By applying the184 Butylpyridinium Chloride-AlC1, Melts T/OC Fig. 11. Temperature dependences of the anion fractions between A (0) and B (0) at 61 f 1 mol YO AlCl,. theory of rate processes1' we obtained the activation enthalpy and entropy AHiA (AHZB) and ASiA(AS:B) at 61 mol% AlCl, from the temperature dependence of kBA( = ~ i l , kAB = T ; ~ ) , as shown in table 1, for the forward (and backward) path in eqn (3). The large negative value of AS:, for both forward and backward paths in the exchange process between B and A may mean an increase in the coordination number in the activated complex, i.e. an associative mechanism or S , 2 displacement mechanism. l8 MNDO calculations also led us to conclude that in the transition-state geometry one of the four chloride ions in B attacked an A1 in A.19 The temperature dependence of the anion fraction X(a) between A and B at 61 mol O/O AlCl, was obtained fromf, (fig.11); X(A) and X(B) crossed over at ca. 90 "C and X(A) became larger than X(B). For 66 mol% AlCl, X(A) ranged from 0.995 to 0.998. X(a) is not the concentration of the aluminum-containing species present in the melt, since X(a) is obtained from the n.m.r. data which showed the contributions from the major species B and A as far as the experimental sensitivity permitted us to determine. When X(a) was assumed to be equal to the concentration of species present (i.e. [Al'"] = [B] + 2[A] and [Cl] = 4[B] + 7[A])1° we were unable completely to reproduce the formal concentration 61 f 1 mol Yo AlC1, between 30 and 100 "C (i.e.the calculation showed 57 mol YO AlCl, at 30 "C and 61 mol O/O at 100 "C). The equilibrium constant Kn.m.r, for the chemical-exchange reaction of eqn (3) is given by (8) K . m . r . = k A B / k B A = 2X(A)/X(B). The difference AGO( = Gl- G i ) between the Gibbs free energies of the two equilibrium sites in eqn (3) is given by AGO = -RTln Kn.m.r. (9) and the differences in enthalpy and entropy, AH" and AS", can be obtained from the thermodynamical relations between Kn.m.r. and 7'. AH" = 16.0 0.9 kJ mol-1 and AS" = 49.7 f 2.7 J K-' mol-' at 61 mol %. The Gibbs free-energy inter-relations between AGO and AG&, were confirmed at 61 mol YO AlCl,, although the equilibrium and kinetic parameters were obtained independently. The forward reaction in eqn (3) was endothermic.The product A1,Cl; is, however, more stable than the reactant AlCI, at the higher temperatures because of the high entropy contribution.K. Ichikawa, T. Jin and T. Matsumoto 185 Professor T. Ishikawa (Faculty of Engineering) for the loan of the crystalline AlCI,. The n.m.r. measurements were carried out with a Varian XL-200 and a JEOL GX-500 installed in the two n.m.r. Laboratories of the Faculties of Engineering and Science. This work was supported in part by a Grant-in-Aid for Scientific Research no. 61470040 from the Japanese Ministry of Education, Science and Culture. References 1 G. Torsi, G. Mamantov and G. M. Begun, Inorg. Nucl. Chem. Lett., 1970, 6, 553. 2 E. Rytter, H. A. Oye, S. J. Cyvin, B. N. Cyvin and P. Klebol, J. Inorg. Nucl. Chem., 1973, 35, 1185. 3 R. J. Gale, B. Gilbert and R. A. Osteryoung, Inorg. Chem., 1978, 17, 2728. 4 G. Torsi and G. Mamantov, Inorg. Chem., 1971, 10, 1900; 1972, 11, 1439. 5 L. G. Boxall, H. L. 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Eyring, The Theory of Rate Processes (McGraw-Hill, New York, 18 M. Eigen, Ber. Bunsenges Phys. Chem., 1963, 67, 753. 19 L. P. Davis, C. J. Dymek Jr, J. J. P. Stewart, H. P. Clark and W. J. Lauderdale, J. Am. Chem. Soc., 1941). 1985, 107, 5041. Paper 712122; Received 30th November, 1987