J. Phys. Chem. 1992, 96, 1482-1490
1482
a secondary micelle from two primary micelles: M,+ M,* M, K
(29)
Accepting that yc = ya i.e., Ay = 0 and n, = ns, we deduce that
K = ~(n)/[Ks(ns)l*
(30)
or
K = exp(-n8Awo/kBn
(31)
Mazer et report an aggregation number of 10 for the formation of a primary micelle, Le., n, = 10. Accepting our Awo values and AGO = -RT In K,it is deduced that AGO varies in the range -1.3 to -6.7 kcal/mol. Although several simplifications are involved, such values are very close to those obtained by Mazer et al. (from -3.8 to -6.7 depending on experimental conditions) for the above-mentioned bile salts. Giglio et al.” have demonstrated the advantages of the helical model compared with the Small model for deoxycholate derivatives. The previous aggreement could mean that such a model is also valid for other bile salts.
The effect of the electrolyte anion on the value of Ay found in this paper has not been considered in KS model and further developments are required. Acknowledgment. We thank the Xunta de Galicia for financial support (project XUGA29906A90). Glossary cmc critical micelle concentration QLS quasi-elastic light scattering NaDC sodium deoxycholate NaC sodium cholate NaDHC sodium dehydrocholate NaTDC sodium taurodeoxycholate TC taurocholic acid TDC taurodeoxycholic acid TCDC taurochenodeoxycholic acid TUDC tauroursodeoxycholic acid Salsalicylate anion M mol d n i 3 mM mol m-’ Registry No. NaDC, 302-95-4; NaCI, 7647-14-5;NaClO,, 7647-14-5; Nasal, 54-21-7.
Molecular Dynamics Studies on Zeolites. 6. Temperature Dependence of Diffusion of Methane In Siiicaiite P. Demontis, G.B. Suffritti,* Dipartimento Chimica, Universith di Sassari, Via Vienna 2, I-071 00 Sassari, Italy
E.S . Fois, Dipartimento di Chimica Fisica ed Elettrochimica, Uniuersith di Milano, Via Golgi 19, I-20133 Milano, Italy
and S. Quartieri Istituto di Mineralogia e Petrografa, Universitd di Modena, Via S. Eufemia 19, I-41 100 Modena, Italy (Received: June 20, 1991)
The effect of the temperature on the diffusion of methane in silicalite was studied by molecular dynamics both using a model where the vibrations of the zeolite framework are taken into account and keeping the framework Fled. Methane molecules were represented by Lennard-Jones particles. The diffusion coefficients were evaluated at four different temperatures in the range 150450 K and resulted in good agreement with experiment. The effect of the vibrating framework on the diffusive process is discussed and a detailed analysis of the behavior of methane molecules in silicalite is reported.
Introduction The elucidation of the behavior of fluids within narrow pores and cavities has received much recent attention.I-l0 Among the (1) Rowlinson, J. S.;Widom, B. Molecular theory of capillarity: Clarendon Press: Oxford, 1982. (2) Henderson, J. R. Mol. Phys. 1983, 50, 741. (3) Walton, J. P. R. B.; Quirke, N. Chem. Phys. Lett. 1986, 129, 382. (4) Davis, H. T. Chem. Phys. 1987.86, 1474. Vanderlick, T. K.; Davis, H.T.J. Chem. Phys. 1987,87.1791. Vanderlick, T. K.; Scriven,L. E.;Davis, H. T. J. Chem. Phys. 1989,90, 2422. ( 5 ) Snook, I. K.; van Megen, W. J. Chem. Phys. 1980, 72,2907. (6) Magda, J. J.; Tirrell, M.; Davis, H. T. J. Chem. Phys. 1985,83, 1888. ( 7 ) Heffelfinger, G. S.;van Swol, F.;Gubbins, K. E. Mol. Phys. 1987,61, 1381. (8) Panagiotopoulos, A. 2.Mol. Phys. 1987, 62, 701. (9) Woods, G. B.;Panagiotopoulos, A. Z.; Rowlinson, J. S . Mol. Phys. 1988, 63, 49. (10) Heffelfinger,G. S.; van Swol, F.; Gubbins, K. E. J. Chem. Phys. 1988, 89, 5202.
different methods employed to study this topic, computer simulation experiments are playing an increasingly important role, because many properties of fluids in porous media become inaccessible to experimental measurements when the characteristic dimensions of the confining medium approaches molecular scale. These techniques have been mostly employed within idealized representations of pores, generally a slit, a cylinder, or a sphere, in order to confirm the results of some theoretical approaches. In this paper we attempt to model a real microporous material, namely a molecular sieve (zeolite), in order to compare an atomic description with the available experimental results. The importance of zeolites, a variety of porous aluminosilicates which are well-known for their industrial applications as adsorbants, molecular sieves, and catalysts, has stimulated conspicuoustheoretical work*I-l3 in order to elucidate their interesting properties. (11) Sauer, J.; Zahradnik, R. Inr. J. Quantum. Chem. 1984, 26, 793. (12) Suffritti, G. B.; Gamba, A. Int. Reu. Phys. Chem. 1987, 6, 299.
0022-365419212096-1482$03.00/00 1992 American Chemical Society
Molecular Dynamics Studies on Zeolites Quantum mechanical studies, empirical energy calculations and statistical models have been developed, and, more recently, molecular dynamics14J5(MD) was applied to the simulation of structural and dynamic properties of zeolites.13 Besides the papers quoted in refs 13 and 16, molecular dynamics simulations were recently reported by Gamba et al.” about the structural changes in the silicalite framework, by Song et al.18*19 on the effect of the temperature upon the stability of the framework of zeolite A, by June et aLzofor the diffusion of xenon and methane in silicalite, and by Fritzsche et al?l on the diffusion of methane in ZK4 zeolite. In the last two works, fixed framework models were adopted. Finally, three MD simulations of zeolites were presented to the Faraday Symposium No. 26 on molecular transport in confined regions and membranes. The first, by Catlow et alaz2reported some preliminary results of the diffusion of methane and ethane in silicalite, using a vibrating framework model; the second, by Goodbody et al,,23was a study of the behavior of methane and butane sorbed again in silicalite, and the last, concerning the diffusion of water in ferrierite-type zeolites, was discussed by Leherte et aLz4 MD calculations on the diffusive motion of methane in silicalite (ZSM-5)2527at room temperature had been performed in this laboratory16and by Trouw and Iton.28 Good agreement with experimental diffusion coefficient was obtained, but the temperature dependence of this quantity, when derived from MD simulation, had to be checked. This problem was discussed, among others, in the above quoted paper by June et which was published when this work was nearly over. However, a structured model for the methane molecule different from that adopted in this work (a soft sphere) was usad. On the contrary, in the more recent paper by Goodbody et al.= the model for methane was like the one of the present work, but only fixed framework calculations were performed. In both refs 20 and 23 the results were good, and a comparison with the calculations reported in this paper will be interesting. In ref 16 the influence of vibrating or fixed framework on the diffusion of methane was also checked. The more relevant result was that, at room temperature, the moving framework acted as a thermal bath on the sorbed molecules, whose statistics was close to that of a small canonical ensemble, while, in the case of the fixed framework, the distribution of the temperature of methane molecules was markedly narrower. However, some computed properties,like the diffusion coeffcients, were affected only slightly by the model used for the framework. A simulation of the bare (13) Demontis, P.; Suffritti, G. B. In Modelling of Structure and Reacriuity in Zeolites; Catlow, C. R. A., Vetrivel, R., Us.; Academic Press: London, in press. (14) Ciccotti, G., Frenkel, D., McDonald, I. R., E&. Simulations of Liquids and Solids; North-Holland: Amsterdam, 1987. (15) Allen, M. P.; Tildesley, D. J. Computer simulation of liquids; Clarendon Press: Oxford, 1987. (16) Demontis, P.; Suffritti,G. B.; Fois, E. S.;Quartieri,S.J. Phys. Chem. 1990, 94,4329. (17) Demontis, P.; Suffritti, G. B.; Fois, E. S.;Quartieri, S.;Gamba, A. J . Chem. Soc., Faraday Trans. 1991,87, 1657. (18) Song, M. K.; Shin, J. M.; Chon, H.; Jhon, M. S.J. Phys. Chem. 1989, 93, 6463. (19) Song, M. K.; Chon, H.; Jhon, M. S.J. Phys. Chem. 1990,94,7671. (20) June, R. L.; Bell, A. T.; Thcodorou, D. N. J. Phys. Chem. 1990,94, 8232. (21) Fritzsche,S.;Haberlandt,R.; Kaerger, J.; Pfeifer. H.; Wolfberg, M. Chem. Phys. Lett. 1990, 171, 109. (22) Catlow, C. R. A.; Freeman, M. C.; Vessal, B.; Tomlinson, S. M.; Leslie, M. J . Chem. Soc., Faraday Trans. 1991, 87, 1947. (23) Goodbcdv, S. J.; Watanabe, K.: MacGowan. D.: Walton. J. P. R. B.: Quirk,, N. J . C h . Soc., Faraday Trans. 1991,87, 1951. (24) Leherte, L.; AndrC, J.-M.; Derouane, E. G.; Vercauteren, D. P. J . Chem. Soc., Faraday Trans. 1991,87, 1959. (25) Kokotailo, G. T.; Lawton, S.T.; Olson, D. H.; Meier, W. Nature (London) 1978, 272,437. (26) Olson, D. H.; Kokotailo, G. T.; Lawton, S.T.; Meier, W. J . Phys. Chem. 1981.85, 2238. (27) Lermer, H.; Draeger, M.; Steffen, J.; Unger, K. K. Zeolites 1985, 5, 131. (28) Trouw, F. R.; Iton, L. E. In Zeolitesfor the nineties, Recent Research Report; Jansen, J. C., Moscou, L., Past, M. F. M., Eds. Presented at the 8th International Zeolite Conference, Amsterdam, The Netherlands, July 1989; . p309.
The Journal of Physical Chemistry, Vol. 96, No. 3, 1992 1483 silicalite was also performed in this laboratory.” In spite of the simple model used, slight structural changes in the framework induced by the sorbate and detected also by X-ray and spectroscopic experiments were found also in the simulated system. In this paper, the results of a MD simulation of the diffusion of methane in silicalite at different temperatures are reported and the influence of the vibrating framework upon the diffusive process is discussed in detail. Silicalite is a well-known synthetical aluminum-free zeolite derived from ZSM-5 ze0lits5and it is characterized by cylindrical straight channels parallel to [OlO], which are intersected at right angles by sinusoidal channels along [ 1001. Diffusion along the [001] direction can take place between the overlapping channels parallel to [100] and [OlO]. Accurate experimental data on the diffusion of methane in ZSM-5 and silicalite were obtained for temperatures ranging from 150 to 300 K by Car0 et al.2e31and by Kaerger et a1.3233using NMR pulsed field gradient technique and by Jobic et a1.30*34 with inelastic neutron scattering (INS). Moreover, calorimetric measurements of the heat of sorption of CH4 in the same zeolite by Papp et al.,35 by Vigne-Maeder and A u ~ o u xand , ~ ~by Chiang et aL3’ are available. The same model potential (harmonic form) that was used for anhydrous natrolite and zeolite A was adopted also for the silicalite framework, while methane molecules were represented by point particles interacting with the framework and among themselves via suitable Lennard-Jones potentials. In order to reproduce experimental results, the loading of the methane was 12 molecules per crystallographic cell, while the maximum loading can be estimated as about 18 molecules per cell at high pressureaz4The motion of the methane particles was slow and highly irregular, so that statistics and averaging problems suggested us to extend the length of the runs up to 200 ps, or 0.2 ns.
Method and Model The model potential for the zeolite framework proposed by the authors and used for MD calculations on anhydrous natrolite and zeolite A was adopted, in the harmonic form, also for silicalite. This model is described in detail in refs 38 and 39 and assumes that the potentials for Si-0 and 0-0 interactions are represented by quadratic functions of the displacement from a given equilibrium bond distance. No other possible contacts are included, the initial topology of the framework bonds is retained during the MD simulation, and only first neighbors are considered as interacting atoms. The parameters used for silicalite were the same as for zeolite A.39 This model is certainly crude and may be interpreted as a second-order approximation of a Taylor expansion of a realistic potential which, when used in MD simulations, could be unmanageable. On the other hand, it has been shown in our previous works that it can describe reasonably the structural and dynamical features of zeolitic frameworks, so that the effects of the vibrations of the framework upon the diffusion of methane would be satisfactorily reproduced. We stress that this model is not stochastic and that the motion of the atoms is not independent, they being linked by a tridimensional network of “springs”. As (29) Caro, J.; Hocevar, S.;Kaerger, J.; Riekert, L. Zeolites 1986.6, 213. (30) Jobic, H.; Bk,M.; Caro, J.; Kaerger, J. In Zeolites for the nineties, Recent Research Report; Jansen, J. C., Moscou, L., Post, M. F. M., Eds. Prcsented at the 8th International Zeolite Conference, Amsterdam, The Netherlands, July 1989; p 309. (31) Zibrowius, B.; Caro, J.; Kaerger, J. Z . Phys. Chem. ( k i p z i g ) 1988, 269, 1101. (32) Hong, U.; Kaerger, J.; Kramer, R.; Pfeifer, H.; Mueller, U.; Unger, K. K.; Lueck, H. B. Submitted for publication in Zeolites. (33) Kaerger, J.; Pfeifer, H. J . Chem. Soc., Faraday Trans. 1991, 87, 1989. Kaerger, J. J . Phys. Chem. 1991, 95, 5558. (34) Jobic, H.; B€e, M.; Kearley, J. Zeolites 1989, 9, 312. (35) Papp, H.; Hinsen, W.; Do,N . T.; Baerns, M. Themochim. Acta 1984, 82, 137. (36) VignC-Maeder, F.; Auroux, A. J. Phys. Chem. 1990, 94, 316. (37) Chiang, A.; Duon, A. G.;Ma, Y. H. Chem. Eng. Sci. 1984,39, 1451, 1461. .~ (38) Demontis, P.; Suffritti, G. B.; Fois, E. S.;Quartieri, S.;Gamba, A. Zeolites 1987, 7, 522. (39) Demontis, P.; Suffritti, G. B.; Fois, E. S.; Quartieri, S.;Gamba, A. J . Phys. Chem. 1988, 92, 867. ~
1484 The Journal of Physical Chemistry, Vol. 96, No. 3, 1992
in the case of anhydrous Natrolite38and zeolite A,39not only the averaged atomic positions but also the mean square vibrational amplitudes and the simulated IR spectrum of silicalite are in agreement with the experiment, as shown in ref 17. Fixed framework simulations were performed in order to get insight into the effect of the vibrating framework on the diffusive process. In a previous workI6it was argued that the vibrating framework, at room temperature, acts as an effective thermal bath for the sorbed molecules by comparing the fluctuation of the calculated temperature of methane molecules with the one predicted by statistical mechanics for a canonical ensemble (NVT), where number of particles, volume, and temperature are constant. Indeed, Lebowitz et a1.40showed that the mean-square fluctuation of the temperature of a particle i, U’T = ( ( T i- ( T i ) ) 2 ) , in a canonical ensemble containing N particles, is given by where T, is the temperature of the ith particle ( i = 1, ..., N). For a microcanonical ensemble (NVE), where total energy, volume, and N are constant, the mean-square fluctuation of the temperature is smaller than in the case of canonical ensemble, and it depends on the specific heat C,. The resulting formula is the following: QZT = (2/3N)( Tj)’(l
- (3Nk/2CV))
Therefore, if methane particles were subjected to an effective thermal bath which keeps constant their mean temperature, they should behave as a small canonical ensemble, and the mean square fluctuation of their temperature would match eq 1. This was the case for the room temperature simulation with vibrating framework reported in ref 16, while for the fmed framework simulation, where the total energy of the methane molecules was constant, the fluctuation was smaller (about half of the one for the vibrating framework), in agreement with the theoretical predictions. However, a test at different temperatures would cast more light on this topic. Methane molecules were represented by soft spherical particles, mainly because attention was focused on the general features of the diffusion, so that a model as simple as possible allowing long simulation runs was desirable. The rationale for this approximation is in line with the calculations by Trouw and Iton2*who showed that for structured methane molecules there was not translational rotational coupling in the overall motion of methane in silicalite. Methanemethane interactions were represented by a 20-6 Lennard-Jones potential between the centers of the molecules, derived by Matthews and Smith41from experimental data. For the methaneframework potential a slight modification (neglecting the polarization term) of the one used by Ruthven and Derrah42for a transition state theory study of the diffusion of CH4 in 5A zeolite was adopted. No adjustment of the original parameters for both methanemethane and methaneframework potentials was attempted. Their analytical form and parameters are reported in ref 16. This model is slightly different from the one used in ref 23, where both CH4-CH4and CH4-framework potentials are of the usual 12-6 Lennard-Jones form, and minimum distances and depths are 3.73 (3.88) A and 3.214 (3.885) A and 0.281 (0.431) kcal/mol and 0.264 (0.194) kcal/mol, respectively (the values in parentheses are those adopted in the present work). In the MD calculations on silicalite with vibrating framework, all the atoms were left free to move without symmetry constraints under the action of the above described potentials. A series of calculations was also performed by keeping the framework atoms fixed at the experimental positions and by letting the methane molecules move freely. The periodicity of the crystal was simulated by the usual minimum image convention and the equations of motion were integrated by means of a modified Verlet’s alg~rithm!~ Structural analysis was performed separately (40) Lebowitz, J . L.; Percus, J. K.; Verlet, L. Phys. Rev. 1967, 153, 250. (41) Matthews, G. P.; Smith, E. B. Mol. Phys. 1976, 32, 1719. (42) Ruthven, D. M.; Derrah, M. I. J. Chem. Soc., Faraday Truns.1 1972, 68, 2332.
Demontis et al. for the zeolite framework and for methane particles. The former one is illustrated in refs 16 and 17, while, to elucidate some features of the methane diffusion, radial distribution functions (rdf) were used. Indeed, methanemethane rdf can yield information about dimers or clusters that can be formed in the cavities, and metha n d f (where Of are the oxygen atoms of the framework) rdf can explain some properties of the diffusive motion, like the average distance from the walls of the channels. A more detailed analysis of the diffusion mechanism was devised in order to elucidate the relative motion of the sorbed molecules: the distribution of dimers, trimers, ..., n-mers (up to n = 24) simultaneously present was evaluated, along with the distributions of the time of life of the n-mers from which the mean lives were derived. Also the distribution of the interaction energy between methane molecules was evaluated. The methane molecules n-mers can be considered as collisions or encounters if the cutoff distance which defines them is so small that the CH4-CH4interaction is repulsive. The number of collisions can then be compared with the corresponding value for a gas as derived from the collision theory of common use in chemical kinetics (see, e.g., ref 44). Moreover, the velocity autocorrelation function of the methane molecules and the distribution of their velocities and temperatures were computed. The diffusion coefficient of methane in zeolite channels was evaluated by using the well-known Einstein formula. However, some comment must be deserved to the physical meaning of the Einstein formula for the diffusion of molecules in zeolites. As it was remarked in ref 16, this formula is valid for Brownian motion in a tridimensional homogeneous medium, but the molecules diffusing in zeolite channels and cavities are constrained to move in a biased or hindered way, so that isotropic diffusion coefficients cannot be defined microscopically. Therefore, since in most cases experimental measurements of diffusion coefficients are performed in polycrystalline or powdered samples by means of various techniques giving an average over all directions and on a scale for which the internal structure of the zeolite is not resolved, the use of the Einstein formula to obtain the diffusion coefficients of molecules sorbed in zeolites from MD simulations could be justified if the only meaning attributed to that quantity is the possibility of comparison with experimental data. This problem will be the object of further study in future. Recently, Zibrowius et al.” proposed an application of NMR spectroscopy to study diffusion anisotropy in polycrystalline materials. By measuring spin-echo attenuation due to anisotropic diffusion in an assembly of randomly oriented subregions, in terms of the field gradient intensity parameter, it is possible to detect a characteristic deviation from the behavior for isotropic diffusion, and an estimate of the ratio between the maximum principal element of the diffusion tensor and the average of the two other principal elements can be derived. Finally, Kaerger et a1.32J3were able to evaluate the diffusion anisotropy of methane in H-ZSM-5 by performing NMR measurements with oriented crystallites. These methods are still semiquantitative,because experimental errors are too large to yield good a c c u r a ~ y , but ~ ’ ~they ~ ~ can give some interesting information about the physics of the diffusion process.
MD Simulations Single-crystalX-ray studies of ZSM-5 structure were carried out by Kokotailo and c o - w ~ r k e r and s ~ ~by~ Lermer ~~ et al.27 The resulting diffraction patterns are consistent with the orthorhombic Pnma space group. However, sorbate-induced change of the crystal symmetry of ZSM-5 from orthorhombic to monoclinic space groups have been o b ~ e r v e d ,though ~ ~ - ~ with minor shifts in cell parameters (in particular the B angle was reported in the range 90.4-90.6°).45 It was found that the MD simulations were (43) Swope, W. C.; Andersen, H. C.; Berens, P. H.; Wilson, K. R. J . Chem. Phys. 1982, 76,637. (44) Moore, J. W.; Pearson, R. J. Kinetics and mechunism; John Wiley & Sons: New York, 1981. (45) Wu, E. L.; Lawton, S. L.; Olson,D. H.; Rohman, A. C., Jr.; Kokotailo, G. T. J . Phys. Chem. 1979, 83, 2717. (46) Fyfe, C. A.; Kennedy, G. J.; De Schutter, C. T.; Kokotailo, G. T. J . Chem. SOC.,Chem. Commun. 1984, 541.
The Journal of Physical Chemistry, Vol. 96, No. 3, 1992 1485
Molecular Dynamics Studies on Zeolites somewhat able to reproduce this effect. Indeed, as reported in refs 16 and 17,a monoclinic unit cell was assumed for silicalite containing methane and the angle /3 was optimized by " i z i n g the total energy of the system. The best value for @was90.4O, in agreement with experiment. For MD simulations, a system corresponding to two crystallographiccells, superimposed, along c, with cell parameters u = 20.076,b = 19.926,c = 13.401 A, and /3 = 90.4O was used. Thermal variation of cell parameters was neglected, but in zeolites it is small and can hardly affect the diffusion of sorbed molecules. The framework atoms were 576 (192Si and 384 0).The spherical particles representing CH4 molecules were initially located in positions occupied by CH3 and CH2groups in tetrapropylammonium ZSM-5, whose single crystal structure was studied by van Koningsveld et a!7l and by Chao et aLQ In d e r to compare simulated and experimental diffusion coefficients,threemethane molecules per channel intersection were included in the MD system, Le. 12 molecules per unit cell, resulting in a total of 600 particles. The time step used in MD runs was 1 fs. The fluctuations of total energy were less than 0.1%. Four MD simulations 200 ps long were performed with vibrating framework at temperatures of 446, 290, 221, and 167 K, respectively. In order to obtain a direct comparison among simulations at different temperatures, the mean coordinates of the framework resulting from the room temperature simulation described in ref 16 were used as a starting point of the new MD runs, and they were generated from the same structure by equilibrating to the selected temperatures for 12 ps. Four MD runs (always 200 ps long) were carried out with fixed framework, in order to verify the effect of the moving framework upon the diffusion at different temperatures: 451, 304,202,and 169 K.
300
L300
8
O O0-
-
O O
time (ps)
40 60 time (ps)
20
Figure 1. Mean square displacements of the methane molecules (Az) vs time (ps) for simulations at different temperatures for vibrating framework (vf) (continuous line) and fixed framework (ff) (dashed line): (a) vf 167 K, ff 169 K (b) vf 221 K, ff 202 K (c) vf 290 K, ff 298 K (d) vf 446 K, ff 451 K.
Results and Discussion The experimental data on the diffusive process of methane in silicalite are essentially of two kinds: evaluation of the diffusion coefficients and calorimetric measurement of the sorption heat. Self-diffusion coefficients of methane in silicalite and in several samples of ZSM-5 with various aluminum content have been determined by Caro et al?e31 by the NMR pulsed field gradient technique and by Jobic et a1.30,34using INS for temperatures ranging from about 150 to 300 K, so that the temperature dependence of the calculated diffusion coefficient can be checked. Their range was from 1 X lo+' to 7 X lo+ m2 s-', with deviations of the order of lo4 mz s-l. Zibrowius et al.31were able to estimate, by means of NMR spin-echo attenuation technique (see above), an upper bound for the ratio between the diffusion tensor principal element related to the motion along y and the average of the two other principal elements. This ratio was estimated to be less than 5 at room temperature for a loading of eight molecules of methane per unit cell. Finally, Kaerger et performed NMR measurements with oriented H-ZSM-5 crystallites and found that the mean diffusivity in the direction of the two channel systems (straight and sinusoidal) should not be larger than a factor of 4.5 of the diffusivity in the third direction, orthogonal to them. Sorption heat of methane in H-ZSM-5 was measured by Papp et by VignE-Maeder and A u ~ o u xand , ~ ~by Chiang et al.37 for methane in silicalite and was quoted as 6.7, 5.0, and 4.8 kcal/mol, respectively. From the calculations reported in this work following the procedure of June et a1.,2O a value of 4.4kcal/mol was obtained. This value includes the correlation (0.1kcal/mol) for the truncation of the CH4-01 potential at 7 A, estimated by extending the cutoff distance to about 30 A in a suitably larger system. The calculated sorption heat is in agreement with the values of 4.0 and 4.3 kcal/mol computed by June et al.20 and Goodbody et ~ 1 . : ~respectively, compares favorably with the data of refs 36 and 37 for silicalite, and can be considered reasonably good, because the value of ref 35 concerns the H-ZSM-5, where extra polarization energy due to the acidic sites is present. In d e r ~
1
.
~
~
9
~
~
(47) van Koningsveld, H.; van Bekkum, H.; Jansen, J. C. Acta Crysrullop., Sect. B 1987, 843, 127. (48) Chao, K.-J.; Lin, J.-Ch.; Wang, Y.;Lee, G. H.Zeolites 1986,6, 35.
* .o
. @ *. *
*
. * .*
-20 -
..a.
* *
. . I
.21
1
I
I
I
1
3
4
5
6
ii-r~io~
Figure 2. log plot of diffusion coefficients for 12 molecules of methane per unit cell: computed from MD simulations, (0)vibrating framework, ( 0 )fixed framework;experimentalvalues2e3' for ZSM-5 with various aluminum content and crystal size (+) and silicalite ( a )vs 1/T.
to discuss the results of the MD simulation of diffusion of methane in silicalite, we first consider the trend of the mean square displacements of methane vs time, which is shown in Figure 1. It appears that (Ir(t)- r(0)12) behaves approximately as a straight line, with slight oscillations, for the four simulations at different temperatures. An estimate of the self-diffusion coefficients was obtained using the Einstein formula. Their values are reported in Table I, and they are in good agreement with the experimental data as shown in Figure 2,where both calculated and values are reported. The errors on the computed values can be estimated from the oscillations of the mean square displacements vs time and are of the order of some 1Wl0m2 s-'. In Figure 3 the trends of mean quare displacements of methane along the Cartesian coordinates vs time are reported for the simulations at different temperatures. It appears that the diffusion is larger along y, corresponding to the direction of the straight channels of ZSM-5, is smaller but relevant along x, the direction of the sinusoidal channels, and is almost negligible along z, for which no channel is present, but some diffusion is possible through
1486 The Journal of Physical Chemistry, Vol. 96, No. 3, 1992
Demontis et al.
TABLE I: ComDuted end Exwrimental Diffusion Coefficients and Related Owntities ~~
D, lo4 m2 s-I
exptl”
D, lo4 m2 s-’
calcd calcdb calcd calcdb calcd calcdb exptlC calcd calcdb calcd calcdb exptlc calcd calcdb exPtlC calcd calcdb
DX DY 0, Dy/(]/2)(Dx+ 0,) ‘/z(Dx + 0,) 1 / 2 ( D x+ D,)/D,
446 K 11.7 8.3
vibrating framework 290K 221 K 6.7 4.1 6.9
6.2
167 K 2.1
451 K 11.8
304 K 7.2
3.0
8.6
5.5
fixed framework 298 K 202K 7.0 3.3
169 K 2.1
4.5
2.9
3.4
2.5
9.3
5.5
0.9
0.8
4.3
3.3
6.3
4.0
7.0
5.0
4.6 7.8
5.5
5.3
3.1
6.2
5.2 4.9
15.2
14.1
12.0
5.2
18.0
9.8 7.1
1.8
1.6 1.1
1.2
0.7
1.6 1.5
1.5
1.7 3.2
4.3
3.7
2.8
2.9
4.7
2.2 11.5 6.4
1.2 9.8 4.5 8.9
8.6 1.2
4.1
7.2 7.5
12.1
5.8
6.0 4.5
4.5 5.0
8.1
3.5
Derived from Arrhenius plot interpolation of experimental data for s i l i ~ a l i t e . ~Reference ~ 23. CReferences32 and 33.
the intersections of the channels along x and y. The differences among the diffusion along the Cartesian coordinates can be evidenced by computing the monodimensionaldiffusion coefficients from the slopes of the curves reported in Figure 3. They are collected in Table I. The values of D, and ‘/*(D,+ 0,)at room temperature were recently estimated by Kaerger et a1.32,33by means of NMR measurements with oriented crystallites and are reported in Table I. Computed values are higher than experimental ones, but both are affected by some error33and, in our opinion, this trend cannot be considered as definitively assessed. In Table I we report also the results obtained by Goodbody et al.23from MD simulations, whose trend is similar to that of ours. It is possible that the low value of computed D, and other related quantities depends on the simplified model of the methane molecule as well as on the simulation length, which could affect the statistics, the diffusion along z being a relatively rare event. The monodimensional diffusion coefficients, for a system of orthogonal channels (as in the present case to a good approximation), correspond to the principal elements of the diffusion tensor, and the ratio C = D,/[’/,(D, + D,)] for the room temperature simulation, C = 4.3 for vibrating framework simulation, and C = 2.9 (this work) or C = 2.2 (ref 23) for fixed framework simulations, can be compared with the experimental upper bound C C 5 for 8 molecules per unit cell.3’ The agreement is good, as diffusion coefficients for 8 and 12 molecules per cell are similar. The comparison of D values between fixed and vibrating framework simulationsshows no regular trend, possibly because of statistical errors, but in any case they are similar. The diffusion rate should be controlled by collisions between methane molecules and then should increase by lowering the loading, and in fact, this effect is observed in INS and NMR measurements2e3’ and in MD simulation^.^^*^^ When In D is plotted vs 1/T, both experimental and calculated results show the characteristic Arrhenius behavior, suggesting that diffusion is an activated process. Orientationally averaged activation energies can be easily derived for experimental and theoretical data and their comparison can be useful to check the validity of the model (indeed they are -0.9 kcal/mol for experimental results and -0.5 kcal/mol for both the vibrating and the fixed framework calculations), but because silicalite is anisotropic, more interesting are the computed values of the activation energies for the diffusion along the Cartesian axes. They are reported in Table I1 and compare fairly with the values reported in a paper by Vign€-Maederand A u ~ o u xwhere , ~ ~ a theoretical potential energy for methane in silicalite channels is mapped. Indeed, they estimated the potential barrier for translational motion to about 2 kcal/mol (at 0 K) both for straight and sinusoidal channels, while from MD simulations activation energies are about 0.6 kcal/mol for the straight channels and 0.5
fixed framework
vibrating framework
LioL-----i
0
12
24
36
48
60
0
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48
60
h
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-
Molecular Dynamics Studies on Zeolites
The Journal of Physical Chemistry, Vol. 96, No. 3, 1992 1487
uu
' 0
2
4
6
8 1 0
r/A
' 0
2
4
6
8 1 0
r/A
Figure 4. Methane-oxygen atoms of the framework radial distribution functions: continuous, dashed, dotted, and dash-dotted lines with the same meaning as in Figure 3; (a) vibrating framework, (b) fixed framework. TABLE II: Arrhenius Activation Energies E , and heexponential Factors D , for the Diffusion of Methane in Sicalite vibrating fixed frameframeexptl work work E,, kcal/mol total 0.92 0.52 0.52 0.47 0.49 along x along y 0.56 0.58 along z 0.48 0.38 Do, IO4 m2 s-I 32.9 16.5 14.9 13.4 11.2 DO, 33.9 31.9 Do, 3.0 2.5 DO,
conclusions of Pickett et al.49that the small diffusion coefficient along z is due not to a higher energy barrier but to the more tortuous path that the methane molecules must cover, entailing a smaller cross section for the diffusive process. More information about the behavior of methane in silicalite channels can be obtained by considering radial distribution functions (rdf s). From the methane+ radial distribution functions at different temperatures (Figure 4) it can be deduced that methane molecules move preferentially close to the axes of the channels. Indeed, the fmt maximum in the rdf occurs at about 4.1 A, a distance close to the channel radius (measured as half the distance between the wall oxygen nuclei), while the second maximum (at 5.8 A) corresponds to the distances with the other oxygen atoms of the eight-membered rings of the channels, and the third maximum, at 8.2 A, can be referred to a cylindrical shell containing, among the other ones, the surface oxygens of the adjacent channels. The dependence of the rdf on the temperature is small, suggesting that no qualitative change of the diffusive process in the considered temperature range occurs. Moreover these rdfs are nearly unaffected by keeping the framework fixed. The distributions of methane molecules along the channel axes were evaluated. They can be compared with those in Figure 5 of ref 49 for xenon in silicalite with different loadings. As the energies of sorption and the dimensions of xenon and methane are similar, one could expect that also their distributions along the channels are not very different, for the same loading. Indeed, this is the case. The occupancies are smeared out as the temperature increases, but at least up to about 450 K, they are not yet flat. Finally, they are slightly more peaked for fmed framework calculations at corresponding temperatures. On the other hand, by comparison of the tridimensional plots of sorbate distributions proposed by June et al?Ov50 with the projection of the occupancies along the axes, it appears that the monodimensional representations can give deceptive information about preferential sites of the sorbed molecules, and they are not reported here. The distributions of kinetic energy along the channels were also evaluated, and, contrary to the occupancies, they are uniform with (49) Pickett, S. D.; Nowak, A. K.; Thomas, J. M.; Peterson, B. K.; Cheetham,A. K.; den Ouden, C. J. J.; Smit, B.; Post, M. F. M. J . Phys. Chem. 1990, 94, 1233. (50) June, R. L.; Bell, A. T.; Theodorou, D. N. J . Phys. Chem. 1990,94, 1508.
A'4
A ,b r/A
u
' 0
2
4
6
8
10
riA
Figure 5. Methane-methane radial distribution functions: continuous, dashed, dotted, and dash-dotted lines with the same meaning as in Figure 3; (a) vibrating framework, (b) fixed framework. It is important to remark that, while the radial distribution function was evaluated in the usual way, it is not possible to obtain from it the nearest neighbors number by the usual integration scheme because of the anisotropy of the system, which reduces the volume accessible to the molecules surrounding the reference. The number of nearest neighbors should be evaluated by direct integration.
small statistical fluctuations, both for fixed and vibrating framework. Therefore, where the concentrations of methane molecules are higher, also the frequency of the collisions is higher. This effect could enhance reactivity in the channels of zeolites. The methane-methane rdfs (Figure 5), for both vibrating and fixed framework, exhibit a unique maximum at r = 3.7 A, a distance slightly smaller than the minimum of the CH4-CH4 potential function, and their dependence on temperature is small in the explored range. This maximum could reflect frequent collisions as well as permanent or transient methane dimers or clusters. In order to elucidate this point, as in ref 16, a detailed analysis of the methane particles trajectories was performed. First of all, a clear-cut definition of "methane dimer" was required. From direct inspection of the trajectories, it is reasonable to state that a dimer exists when two methane molecules remain closer than 4.5 A. Many dimers oscillating without exceeding this distance were found. Moreover, clusters containing three, four, or more methane molecules, linear or branched (the last near channel intersections), were observed. For each cluster of n molecules (n = 2, ..,,24) it was assumed that all its subclusters made of n'< n molecules did not enter in the number of the cluster of n'molecules (e.g., the two or three dimers discernible in a trimer were not enumerated as dimers). It should be reminded that in a channel cross section only one methane molecule can be accommodated, and by setting the 24 disposable particles evently spaced in the channels, their mean distance would be about twice a molecular diameter so, that moving molecules are forced to collide very frequently. Moreover, in particular for the vibrating framework model, kinetic energy exchange with the channel wall atoms is sufficiently large and slow to favor the forming of more or less long-lived dimers or clusters. This picture of the diffusive process of methane in silicalite emerges from the following analysis of the methane trajectories. Henceforth, for simplicity a cluster containing n methane molecules will be called %-mern. From the frequencies of the number of n-mers simultaneouslypresent in the simulated system, it appears that, for both vibrating and fmed framework models, at rmm temperature the most probable number of isolated molecules present in an instant is about eight, while for dimers the same number is two, and only one for the n-mers with n > 2. For n > 9 the frequencies are negligible. The effect of lowering the temperature is to sharpen slightly the distributions, and the only noticeable effect is that, for n = 1, the maximum is closer to 7 than to 8. One may conclude that, in the considered temperature range, about one-third of the diffusing molecules are on the average, isolated, while the others are associated in clusters, two of which, at least, are dimers, and that lowering the temperature is slightly favorable to the relative Occurrence of clusters. The largest cluster observed (lasting only a few time steps) contained 15 molecules. In Figure 6, the mean lives of the n-mers derived from the distributions of the lifetime of the n-mers vs temperature for the vibrating and fmed framework
Demontis et al.
1408 The Journal of Physical Chemistry, Vol. 96, No. 3, 1992
TABLE IIk Temperature Fluctuations and Specific Heats for the Sorbed Molecules
((AT)2)1/2(K)
C,lNk€Ib
calcd theola theof
446 K 71 74
vibrating framework 290 K 221 K 47 35 48 37
167 K 26 28
451 K 38 0.5
fixed framework 304K 202K 27 19
169 K 17
0.7
0.5
0.9
“Computed from eq 3.10 of ref 40. bCi = C,- (3/2)NkB; see ref 40. ‘Computed from eq 3.9 of ref 40, for the N = 24 methane molecules.
8
0.5
I
I
I
I
I
220
290
360
430
500
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t
I I -Os5
’
l o
0 0
0 8
8
I
I
I
I
J
220
290
360
430
500
Temperature (K)
Figure 6. Mean lifetimes of the clusters made of methane molecules vs temperatures: (a) vibrating framework, (b) fixed framework; (W) monomers, ( 0 )dimers, (0)trimers, (0)tetramers.
models are reported. The mean lives decrease by raising the temperaturesso that, for the vibrating framework, they are about 40-5W0 longer at 167 K than at room temperature. It is noticeable that, even at room temperature, detectable fractions of monomers last up to about 1.5 ps before being captured to form a cluster. For dimers, the maximum lifetime is about 5.5 ps, with mean lives which are sufficient to allow the dimers to oscillate a few times. The mean lives of trimers and tetramers are shorter than 0.15 and 0.13 ps, respectively, and most of them can be considered the result of multiple collisions, as they, on the average, hardly oscillate before they decompose. For the fmed framework simulations the mean lives of the n-mers are longer than in the case of vibrating framework, and they decrease in particular for monomers and dimers, when the temperature is raised. At about 170 K the mean lives of monomers and dimers are approximately 1.5 times the corresponding ones for the vibrating framework model. This is the first evident difference between fixed and vibrating framework simulations reported so far and will be discussed in the next section. Further features of the dynamical behavior of the diffusing particles can be outlined by considering the velocity autocorrelation functions (vacf s), which are reported in Figure 7. Their dependence on temperature is small, but not meaningless, and the differences between simulations with fixed or vibrating framework (maxima are higher and minima are deeper with fmed framework) are interesting. Both effects are discussed in the next section. The methane vacf s show a damped oscillatory trend and are more like a vacf for a onedimensional system of Lennard-Jones particles than a vacf typical of Lennard-Jones liquid,51as should (51) Beme, B. J. In Physical Chemistry, an Aduanced Treatise; Eyring, H., Henderson, D., Jost, W., Eds.; Academic Press: New York, 1971; Vol. VIIIB, p 652 ff.
-Oe5 -1
-
t-I t -Oe5
-1
0
1
2
time (ps)
0
1
2
time (ps)
Figure 7. Velocity autocorrelation functions for methane molecules. Symbols are the same as those used in Figure 1.
be expected because the methane molecules are constrained to move in narrow channels. Another point of interest for the study of the dynamics of diffusing particles is the distribution of velocities and temperatures. The large number of collisions allowed a good equilibration of the simulated system, and the calculated distributions of the methane velocities at the three temperatures resulted to be Maxwellian-like. It appears that the vibrating framework acts by exchanging kinetic energy with the diffusing molecules and broadening the velocity distribution. As stated above on the basis of the room temperature results, the methane molecule system behaves like a small canonical ensemble in the thermal bath of the vibrating framework. This statement can be verified by comparing the theoretical mean-square fluctuation of the temperature of the methane molecules (more precisely its square root) given by eq 1 with the corresponding ones derived from MD simulations. They are reported in Table 111. The agreement with theoretical values is good, and the slight discrepancies can be ascribed to the small number of methane molecules, while eq 1 should hold, in principle, for systems with a large number of particles. Also for the fixed framework simulations, the square root of the mean-square fluctuation was evaluated (seeTable 111), and it could be compared with the results of eq 2, but the presence of the specific heat in this equation hinders a strictly theoretical prediction. However, following Lebowitz et a1.,40 the constantvolume specific heat C, can be considered as the sum of an ideal-gas term, 3/2Nk,and a term Cidepending on the interactions among the particles, more precisely proportional to the mean square fluctuations of the intermolecular potential. The second term could be computed directly from the MD trajectories, but in view of the small number of particles and the need for good statistics (see ref 40 on this particular point), we preferred to attempt only a qualitative check of the trend of Civs temperature.
The Journal of Physical Chemistry, Vol. 96, No. 3, 1992 1489
Molecular Dynamics Studies on Zeolites
g 4000 0 N 0
.-E .v)
0
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2000
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6
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8
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--0
1
2
Energy (kcal mol-')
Figure 8. Normalized distributionsof pair potential energies for methane molecules: vibrating framework (vf) (continuous line) and fixed framework (ff) (dashed line); (a) vf 167 K, ff 169 K, (b) vf 290 K, ff 298 K; (c) vf 446 K, ff 451 K.
From the values of C,obtained from eq 2, an estimate of Ci = C,- 3/2Nkwas derived. The results are reported in Table 111, and the Ci values show a qualitative temperature dependence in agreement with the calculations of Lebowitz et al.,40 Le. they decrease when temperature increases. The last statistical tool that we consider in the present paper for the study of the diffusive process is the distribution of the interaction potential energy between pairs of methane molecules (Figure 8). The distributions for fixed and vibrating framework simulationsare markedly different though they are consistently normalized. When the framework is held fixed, the distributions for negative energies are lower, but long tails in the positive regions are present. Figure 8 cuts at 2 kcal/mol, but even at 10 kcal/mol the distributions are not yet zero. This finding is discussed in the next section.
Effects of the Vibrating Framework In the previous section it was remarked that some properties of the sorbate molecules are almost unaffected by switching off the vibrations of the framework, namely the diffusion coefficients, the activation energies, and the radial distribution functions. Some other computed quantities, like the velocity autocorrelation functions, show small differences but definite trends. Finally, the differences become evident or dramatic when the mean lives of the clusters and the distributions of the pair interaction energies and of the temperatures are considered. The changes in the temperature distributions are explained in terms of the effect of a thermal bath generated by the vibrations of the framework, as discussed above, but this collective property does not give suggestions about the details of the behavior of the particles in the two cases. Interesting evidence comes from considering the pair interaction energy distributions (Figure 8). The long tails in the repulsive energy region shown by these distributions for the fixed framework simulations can be interpreted as deriving from a relevant number of high-energy collisions. This finding can be
Figure 9. Number of collisions between methane molecules in 200 ps: (0) vibrating framework; ( 0 )fixed framework; (H) number of binary collisions for 24 particles in a volume corresponding to the MD simulation box interacting with a hard sphere + r4 potential close to the methane-methane potential. At room temperature, the pressure of this reference gas model is about 70 bar following the van der Waals equation.
explained by considering the elastic backscattering of the sorbed molecules colliding with the fixed framework walls, while, in the case of vibrating framework the backscattering is damped by soft walls. Another argument in favor of this hypothesis becomes apparent by reminding that,5ZS3when backscattering occurs,the correlations of the velocities of the colliding particles are negative and become positive again when the backscattering particle collides with a third molecule or with the framework walls. Indeed, by inspection of the vacf s shown in Figure 7, it is clearly seen that the effect of the rigid framework on the velocity relaxation is to enhance the amplitude of the negative and positive correlation in the first and second peak of the vacf s. This effect decreases as temperature increases. Moreover, the behavior of the vacf s can explain why, notwithstanding the differences between fixed and vibrating framework simulations, the computed diffusion coefficients are similar. Since diffusion coefficients are proportional to the time integral of the vacf s, and the main contributions to this integral come from the first and second peak, the more negative first peak cancels the effect of the more positive second peak in the fixed framework vacf s, and the net result is almost the same as for the vibrating framework. As stated above, the mean lifetimes of monomers, dimers, and clusters (see Figure 6) are higher for the fixed framework simulations. This effect is more evident at low temperatures and can be explained by the energy exchange with the vibrating framework walls. From the above considerations, a picture of the effect of keeping the framework rigid emerges. Owing to elastic backscattering from the walls, sorbed particles are compelled to come together closer and to collide with relative energy higher than in the case of the vibrating framework, and the resulting clusters decomposed more slowly once formed. Therefore, an unphysical clustering effect is detected in fixed framework simulations, or (52) Wijeyesekera, S. D.; Kushick, J. N. J. Chem. Phys. 1979, 71, 1397. (53) Dean, D. P.; Kushick, J. N. J. Chem. Phys. 1982, 76, 619.
1490
J. Phys. Chem. 1992,96, 1490-1494
from another point of view, lattice vibrations disoourage clustering. Further evidence of this picture comes from the different number of binary and multiple collisions. While the total number of collisions is similar for fmed and vibrating framework models, the enhanced clustering observed in the fixed framework simulations yields a very large number of multiple colliiions, which are almost lacking when the framework vibrates, as shown in Figure 9.
Concluding Remarks From the results reported in this paper, a description for the diffusion mechanism, OcCuRing through frequent collisionsbetween sorbed particles and the walls of the channels and through the presence of short-lived dimers or clusters, has been clarified for methane in silicalite in a wide range of temperatures. Moreover, the effectiveness of the zeolitic framework as thermal bath has been assessed, and its role in influencing the diffusion along the channels has been illustrated. These effects are confirmed by comparison with the results of the fiied framework simulations. The activation energies for the diffusive process along the different directions have been evaluated and their influence on
the diffusive motion has been discussed. Consideration of all these details of the methane molecule diffusion in silicalite can give suggestions about some aspects of the effectiveness of zeolites as molecular sieves and about the reaction mechanisms of the molecules sorbed in zeolites. Work is in progress to extend the study of diffusion kinetics to zeolites with different loading and topology5e56 and to attempt a molecular dynamics simulation of other phenomena related more directly to the zeolite-catalyzed chemical reactions.
Acknowledgment. This research is supported by MURST (60% and 40%) and by Consiglio Nazionale delle Ricerche, Grant 89.00030.69. Registry No. Methane, 74-82-8. (54) Yashonath, S.;Demontis, P.; Klein, M. L. J . Phys. Chem. 1991.95, 5881. (55) Yashonath, S. Chem. Phys. Left. 1991, 177, 54. (56) Yashonath, S . J . Phys. Chem. 1991, 95, 5877.
Infrared and Raman Studies of Poly(ppheny1enevinylene) and Its Model Compounds Akita Sakamoto, Yukio FurUkawa, and Mitsuo Tasumi* Department of Chemistry, Faculty of Science, The University of Tokyo, Bunkyo-ku, Tokyo 113, Japan (Received: July 29, 1991)
The infrared and Raman spectra of polyb-phenylenevinylene) (PPV) and its low molecular weight model compounds CH3(C6H4CH=CH),C6H4CH3(n = 1-3) have been studied, and the following points have been made clear. (1) The vinylene groups in PPV are slightly distorted from a planar trans form, so that the PPV molecule has approximate C, symmerry. (2) Extensive ?r-electron conjugation takes place between the phenylene and vinylene groups, and the degree of conjugation increases with increasing chain length. (3) The positions and relative intensities of the infrared and Raman bands of the model compounds change regularly as the chain length increases and rapidly converge on those of PPV, which are considered to be practically identical to those of an infinitely long chain. (4) The positions of the Raman bands of PPV slightly shift with the excitation wavelength. The 363.8-nm-excited Raman spectrum seems to arise from segments whose lengths are of the order of the model compound n = 3, whereas the Raman spectra excited at longer wavelengths correspond to longer segments which are dominant in quantity.
Introduction Several classes of organic polymers exhibit electrical properties of semiconductors or metals when suitably doped with a donor or acceptor species.l Spectroscopic techniques are widely used for structural studies of these materials before and after the doping process.* Poly@-phenylenevinylene)(Figure la, abbreviated PPV) is an interesting material because of its nonlinear optical properties3 and high electric conductivities upon doping."-' PPV can be prepared via pyrolysis of a soluble precursor pol~mer.~-lOSuch (1) Handbook of Conducting Polymers; Skotheim, T. A., Ed.; Dekker: New York, 1986; Vol. 1 and 2. (2) Harada, I.; Furukawa, Y. In Vibrational Spectra andStructure; Dung, J. R., Ed.; Elsevier: Amsterdam, 1991; Vol. 19, pp 369-469. (3) Kaino, T.; Kubodera, K.; Tomaru, S.;Kurihara, T.; Saito, S.;Tsutsui, T.; Tokito, S . Electron. Lett. 1987, 23, 1095. (4) Murase, I.; Ohnishi, T.; Noguchi, T.; Hirooka, M. Polym. Commun. 1984, 25, 327. (5) Gagnon, D. R.; Capistran, J. D.; Karasz, F. E.; Lenz, R. W. Polym. Bull. 1984, 12, 293. (6) Murase, I.; Ohnishi, T.; Noguchi, T.; Hirooka, M. Synth. Mer. 1987, 17, 639. (7) Hirooka, M.; Murase, I.; Ohnishi, T.; Noguchi, T. In Frontiers of Macromolecular Science; Saegusa, T., Ed.; Blackwell Scientific Publications: Oxford, U.K.,1989; p 425. (8) Kanbe, M.; Okawara, M. J . Polym. Sci., Polym. Chem. Ed. 1968, 6, 1058. (9) Wessling, R. A.; Zimmermann, R. G. US.Patent 3,401,152, 1968. (10) Wessling, R. A,; Zimmermann, R. G. U.S. Patent 3,706,677, 1972.
a method of preparation enables us to prepare this polymer in various forms and to control its higher order structure by stretching the precursor polymer. The electrical conductivity of a highly stretched film of PPV after treatment with concentrated sulfuric acid has been reported to become as high as 1.12 X lo4 S cm-'.' To obtain information on the molecular and electronic structure of this polymer in the pristine and doped states, infrared and Raman spectroscopy provides a useful tool, and in fact a few papers have already been published on vibrational studies of PPV.'1-13 However, the structurespectrum correlation for PPV has not been established yet. The vibrational spectra of a polymer can only be unambiguously interpreted on the basis of careful studies on low molecular weight model compounds. For example, assignments of the vibrational bands of pristine poly@phenylenesulfide) have been made by comparing them with those of several low molecular weight model compound^.'^ The structure of polyaniline upon doping has been elucidated on the basis of vibrational key bands derived from studies of model compounds.15 Moreover, from the dependence of the electronic (1 1) Bradley, D. D. C.; Friend, R. H.; Lindenberger, H.; Roth, S. Polymer 1986, 27, 1709. (12) Lefrant, S.; Perrin, E.; Buisson, J. P.; Eckhardt, H.; Han, C. C. Synth. Met. 1989, 29, E91. (13) Furukawa, Y . ;Sakamoto, A.; Tasumi, M. J . Phys. Chem. 1989, 93, 5354. (14). Piaggio, P.; Cuniberti, C.; Dellepiane, G.;Campani, E.;
Gorini, G.;
Masetti, G.; Novi, M.; Petrillo, G. Spectrochim. Acta 1989, 45A, 347.
0022-3654/92/2096-1490%03.00/0 0 1992 American Chemical Society
