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Dielectric Relaxation in Na-MFI Zeolite
J. Weilkamp, H.G. Karge, H. Pfeifer and W. Holderich (Eds.) Loliies and Relared Microporous Materials: Stare of rhe Art 1994 Studies in Surface Science and Catalysis, Vol. 84 0 1994 Elsevier Science B.V. All rights reserved.
883
DIELECTRIC RELAXATION IN Na-MFI ZEOLITE F. Ferntindez-Gutierrez', M. Herntindez-Velez', and R. Roque-Malherbe'
' Instituto Pedag6gico Superior E.J. Varona, C. Libertad, Marianao, Havana, Cuba. # Instituto de Tecnologia Quimica UPV-CSIC, Camino de Vera, s/n 46071 Valencia, Spain. Telefax: 34-6-3877996. Dielectric methods are possible to be used as fingerprint techniques in the study of zeolites. In the present case a ZSM-5 zeolite is studied with the help of thermodielectric analysis and dielectric spectrometry. Both methods provides information for the characterization of the zeolite.
INTRODUCTION Na-MFI zeolite is a material used for the preparation of catalysts for the petrochemical industry (1,2). Its structure (3-6) consist fundamentally of a 2 interconnected set of channels with 10-ring openings. One set of channels run parallels to the [OlO] axis with 10-ring openings of 5.4 x 5.6 A, these channels are intersected by a second set of sinusoidal channels the entrance of which have also 10-rings with openings of 5.1 X 5.5 A, parallel to the [loo] direction. The unitary cell composition is: Na,A1,Sig6-,0,g,.16 H,O (6); charge compensation is carried out by sodium cations in 2 extra-framework sites: SI and SII, respectively located in 6-rings and in the intersections of the channels with 10ring openings (7-9), with 8 extra-framework sites per unit cell (9). The dielectric relaxation phenomena in zeolites are linked to charge transport mechanisms (10-15) and are accepted to be present in the dielectric absorption spectra a domain at low frequency (10-103 Hertz) related with the Maxwell Wagner effect, d.c. conduction, electrode effects or low frequency dispersion phenomena; a second domain at medium frequency range (103-106 Hertz) is related to cation hopping and a high frequency domain
884
related to water (16,17). In fact dielectric relaxation phenomena in zeolites brings information about the movement and location of cations (17-22), zeolitic water (23,24) and template agents (25); hence the aim of the present paper is to infer analytical information from dielectrical relaxation phenomena, etc.
EXPERIMENTAL Na-MFI was given by Dr. H.K. Beyer (Central Research Institute for Chemistry, Budapest) its crystallinity determined by X ray diffraction (Carl Zeiss TUR M-62 equipment, using the Cu K a radiation) and was found to be around 95%. The Si/A1 determined with the help of absorption spectrometry (PYE UNICAM SP-1900 equipment) was 25. The sample was used in the calcined form and was dehydrated in the measurements of the dielectric dispersion and absorption spectra. For thermodielectrical measurements the sample was used in hydrated form as-synthesized or calcined. Calcination was carried out at 723 K in air flow overnight; hydration was ensured by adsorption of water vapor at 300 K and dehydration executed in vacuum (lo-' Pa) at 650 K overnight. The measurement of the dielectric dispersion and absorption spectra of dehydrated and calcined Na-MFI at different temperatures (300, 373, 423 and 473 K) were carried out in a dielectric spectrometer designed and constructed in our laboratory (19,29) which consist of two parts: a vacuum system which evacuate a cylindrical capacitor where the zeolite powder (12 g of powder with grain size between 0.2 to 0.5 mm) is deposited and a measuring device consisting of an operational amplifier (26,27) which compare the capacitance of a standard and a sample capacitor. The dielectric permittivity is calculated using the relation E' (w) = C,/C, where: E' (w) is the value of the real part of the dielectric permittivity of the zeolite powder with respect to frequency (30 Hz c w c lo6 Hz)), C, is the capacitance of the cylindrical capacitor full of zeolite powder and C, is the capacitance of the same capacitor but empty. Hence, with the help of the relation: E' (W) = E (03) + x '(w) is possible to calculate the value of the real part of the dielectric susceptibility of the zeolite powder (x '(w)); the value of the imaginary part of the dielectric permittivity of the zeolite powder was obtained using a program which calculates E" (w) with the help of Kramers-Kronig relations (28). The calculated results were compared with experimental values of loss angle measured with the help of the phase of the input and output signals.
885
The thermodielectrical thermograms of hydrated samples were obtained with an equipment designed and constructed in our laboratory which registers the relation between scanned temperature and the output voltage (V,) of a circuit which differentially compares the impedance of the sample under test and a reference (A1,0,) (29). The thermograms show low temperature effects (300-623 K) related to the polarization of zeolitic water (23,24) and the polarization related to cation hopping (19), an effect related to template removal at intermediate temperatures (25) and a high temperature effect (673-1 173 K) related to long range charge carrier transport (21,22). The thermodielectric analyzer uses the same measuring device described for the dielectric spectrometer but instead of scanning frequency at constant temperature, it scans temperature at constant frequency (400 Hz) (29).
RESULTS AND DISCUSSION In figure 1 the dispersion spectra of dehydrated Na-MFI at different temperatures are reported.
5
10
In w
Figure 1. Dielectric dispersion spectra of calcined dehydrated Na-MFI at a: 300 K, b: 373 K, c: 423 K and d: 473 K.
886
The first fact noted is the very low value reported for the dielectric permittivity at 300 K. This is related with the high Si/Al relation of the studied Na-MFI (%/A1 = 25), which implies that the number of charge compensating cations per unit cell (n) is low for the studied Na-MFI ( ~ ~ 3 . 7The ) . other effect easily observed from figure 1 is the increase in the permittivity values with temperature. This increase is clearly connected with the intensity of cationic movements at higher temperatures. The thermodielectricprofile of hydrated-calcined Na-MFI (Fig.2) exhibits no low temperature effect, for hydrated-as-synthesized Na-MFI a peak of template agent removal is observed at 650-800 K (Fig. 2.), i.e. thermodielectric analysis is not sensitive to the polarization effects of Na cations and water inside the Na-MFI structure because of the low quantity of present cations and the recognized hydrophobic character of Na-MFI, but detect the presence of the template agent.
In figure 3 it is possible to observe the calculated dielectric absorption spectra for calcined-dehydrated Na-MFI (a good coincidence exists between calculated and experimentally obtained spectra, and only at low frequencies a difference related with a negligible d.c. component (30) is observed).
"0
-
b
500
1000
Figure 2. Thermodielectrical profile (Output Voltage V, versus Temperature for a: hydrated calcined Na-MFI at a : 300 K, b: hydrated as synthesized Na-MFI.
887
Table 1. Temperature Dependence of Maximum Frequencies
w,(Hz)
Temperature 373
91
423
1556
473
11339
The spectra show the presence of maxima whose frequency are dependent of temperature. In table 1 the dependence between temperature and the frequency of the maximum (W,) are reported. The absence of the absorption peak for dielectric relaxation at 300 K in the frequency range measured is related with the presence of this maxima for lower frequencies.
If we make an Arrhenius plot with the data reported in table 1 we obtain the following value for the activation energy of the predominant relaxation process: E, = 70 kJ/mol. Let us suppose now that the predominant relaxation process for dehydrated-calcined Na-MFI is cation hopping. In a previous paper, it was shown that the frequency dependence for the dielectric susceptibility for a cation hopping mechanism is (20): x (w) = x '(0)/ (1 t i w/wo) (1)
0
5
10
In w
Figure 3. Calculated dielectric absorption spectra of calcined dehydrated NaMFI at a: 300 K, b: 373 K, c: 423 and d: 473 K.
888
where: x '(0) is the static dielectric susceptibility and w, = Q D where Q is a constant and D = Do exp -(Ea/RT) is the diffusion coefficient for cation hopping. Hence if cation hopping is the fundamental relaxation mechanism the obtained results must follow equation "1" and in fact the obtained data is fairly adjusted by the real and imaginary parts of equation "1" in the appropriate frequency range (see Fig. 4). If we make a normalization of the spectra reported in Fig. 3 for the appropriate frequency range (Fig. 4) it is evident the superposition of the peaks, which is a consequence of the presence of only one relaxation mechanism for this frequency range i.e. cation hopping (10-20) and consequently the measured activation energy is related with cationic diffusion in the Na-MFI channels. As was pointed out previously, the Na-MFI zeolite in its structure contains 2 extra-framework sites, one of them is located in the 6 rings openings where diffusion is difficult because of steric restrictions in comparison with diffusion in 10 member ring opening channels, then because of the small reported value for the activation energy it is possible to propose that cationic diffusion occurs through 10 member ring opening channels.
&" &;
1 d ,/'c
0.5
-4
-2
0
2
4
)"1
Figure 4. Normalization of the spectra reported in figure 3.
W
889
At high temperature long range charge carrier transport becomes the predominant effect (T > 700 K) (21-23) i.e. a high temperature effect is evident in thermodielectric analysis for hydrated-calcined and hydrated as synthesized Na-MFI, this effect occurs for Na-MFI (Si/A1=25) at temperatures higher than those corresponding to Na-FAU, Na-LTA, Na-HEU (19,21-23).
In conclusion, it is possible to state that dielectric methods could be used as finger print techniques in the study of ZSM-5 zeolite, by the following facts (19-25): 1. 2. 3.
4.
The absence of the low temperature effect is only related with hydrophobic samples with a low quantity of charge carriers. The presence of the medium temperature effect indicates the existence of a template agent. The position of the high temperature effect indicates too a low quantity of charge carriers if the sample is in the Na form. The value reported for the activation energy of the diffusion process of Na' cation in the zeolite channels in a numerical characteristics related with the zeolite
REFERENCES 1.
2. 3. 4. 5.
6. 7.
8. 9.
A. Corma, in Zeolites: Facts, Figures, Future, eds. P.A. Jacobs and R.A.
van Santen, Elsevier Amsterdam, 1989, p.49. P. Ratnasamy, in: Advances in Catalyst Desing, eds. M. Graziani and C.N.R. Rao, World Scientific, Singapore, 1991, p.67. G.T. Kokotailo, S.L. Lawton, D.H. Olson and W.M. Meier, Nature 27 (1978) 437. D.H. Olson, G.T. Kokotailo, L.S. Lawton and W.M. Meier, J. Phys. Chem. 85 (1981) 2238. H. van Kononngsveld, H. van Bekkum and J.C. Jansen, Acta Cryst. B34 (1987) 127. W.M. Meier and D.H. Olson, Atlas of Zeolite Structure Types Butterworth-Heinemann, London, 1992, 138. W.J. Mortier, Compilation of Extraframework Sites in Zeolites Butterworth, London, 1982, p.53. C.E. Sass and L. Kevan, J. Phys Chem. 92 (1988) 5192. L. Zhenyi, Z. Wangjin, Y. Qin and L. Guanglie, in: Proceedings of the 7" International Zeolite Conference, eds. Y. Murakami, A. Ijima and J.W. Ward, Elsevier-Kodansha, Tokyo, 1986, p. 415.
890
10. 11.
12. 13. 14. 15. 16. 17. 18.
19. 20. 21. 22. 23. 24. 25. 26. 27. 28. 29. 30.
A. Chapoton, Rev. Phys. Appl. 10 (1975) 153. W.A. Hauffe and H. Gunser, Z. Phys. Chem. Chemie Neue Folge 104 (1977) 249. M.F. Rakitinskaya and B.M. Fedorov, Zh. Fiz. Xim. (1982) 2626. A.R. Haidar and A.K. Jonscher, J. Chem. SOC.Far. Trans I. 82 (1986) 132. T. Ogushi, Bull. Chem. SOC.Japan 61 (1988) 1109. T. Ogushi, H. Nonaka and T. Watanabe, Bull. Chem. SOC.Japan 61 (1988) 1797. P. Tabourier, J.c. Carru and J. W. Wacrenier, J. Chim. Phys. 87 (1990) 43. A.K. Jonscher, Dielectric Relaxation in Solids, Chelsea Dielectric Press, London, 1983, Chapter 2. A. Szasz, S. Sabet A1 Rahim and J. Lisz, Acta Chimica Hungarica 125 (1988) 37. R. Roque-Malherbe and M. Hernandez-Velez, J. Thermal Analysis 36 (1990) 1025. R. Roque-Malherbe and M. Hernandez-Velez, J. Thermal Analysis 36 (1990) 2455. R. Roque-Malherbe, C. de las Pozas and J. Castillo, J. Thermal Analysis 32 (1987) 321. R. Roque-Malherbe, C. de las Pozas and M. Carreras, J. Thermal Analysis 34 (1988) 1113. R. Roque-Malherbe, and A. Montes, J. Thermal Analysis 31 (1986) 517. M. Carreras, R. Roque-Malherbe and C. de las Pozas, J. Thermal Analysis 32 (1987) 1271. R. Roque-Malherbe, C. de las Pozas and M. Carreras, J. Thermal Analysis 37 (1991) 2423. R. Roque-Malherbe, A. Rodriguez, M. Hernandez-Velez and A. Montes, Cuban Patent Certificate 21746 (1988). M. Hernandez-Velez and R. Roque-Malherbe, in: Proceedings of the 6'h International Symposium on Electrets, eds. D.K. Gas-Gupta and A. W. Patullo (IEEE Service Center, Piscatawauy, N.J. USA, (1988) p.576. A.K. Jonscher, Dielectric Relaxation in Solids (Chelsea Dielectric Press, London, 1983) appendix. A. Montes, R. Roque-Malherbe and E.D. Shchukin, J. Thermal Analysis 31 (1986) 41. 0. Vigil, M. Hernandez-Velez, J. Fundora, H. Villavicencio and R. Roque-Malherbe, J. Materials Science Letters 11 (1992) 1725.
883
DIELECTRIC RELAXATION IN Na-MFI ZEOLITE F. Ferntindez-Gutierrez', M. Herntindez-Velez', and R. Roque-Malherbe'
' Instituto Pedag6gico Superior E.J. Varona, C. Libertad, Marianao, Havana, Cuba. # Instituto de Tecnologia Quimica UPV-CSIC, Camino de Vera, s/n 46071 Valencia, Spain. Telefax: 34-6-3877996. Dielectric methods are possible to be used as fingerprint techniques in the study of zeolites. In the present case a ZSM-5 zeolite is studied with the help of thermodielectric analysis and dielectric spectrometry. Both methods provides information for the characterization of the zeolite.
INTRODUCTION Na-MFI zeolite is a material used for the preparation of catalysts for the petrochemical industry (1,2). Its structure (3-6) consist fundamentally of a 2 interconnected set of channels with 10-ring openings. One set of channels run parallels to the [OlO] axis with 10-ring openings of 5.4 x 5.6 A, these channels are intersected by a second set of sinusoidal channels the entrance of which have also 10-rings with openings of 5.1 X 5.5 A, parallel to the [loo] direction. The unitary cell composition is: Na,A1,Sig6-,0,g,.16 H,O (6); charge compensation is carried out by sodium cations in 2 extra-framework sites: SI and SII, respectively located in 6-rings and in the intersections of the channels with 10ring openings (7-9), with 8 extra-framework sites per unit cell (9). The dielectric relaxation phenomena in zeolites are linked to charge transport mechanisms (10-15) and are accepted to be present in the dielectric absorption spectra a domain at low frequency (10-103 Hertz) related with the Maxwell Wagner effect, d.c. conduction, electrode effects or low frequency dispersion phenomena; a second domain at medium frequency range (103-106 Hertz) is related to cation hopping and a high frequency domain
884
related to water (16,17). In fact dielectric relaxation phenomena in zeolites brings information about the movement and location of cations (17-22), zeolitic water (23,24) and template agents (25); hence the aim of the present paper is to infer analytical information from dielectrical relaxation phenomena, etc.
EXPERIMENTAL Na-MFI was given by Dr. H.K. Beyer (Central Research Institute for Chemistry, Budapest) its crystallinity determined by X ray diffraction (Carl Zeiss TUR M-62 equipment, using the Cu K a radiation) and was found to be around 95%. The Si/A1 determined with the help of absorption spectrometry (PYE UNICAM SP-1900 equipment) was 25. The sample was used in the calcined form and was dehydrated in the measurements of the dielectric dispersion and absorption spectra. For thermodielectrical measurements the sample was used in hydrated form as-synthesized or calcined. Calcination was carried out at 723 K in air flow overnight; hydration was ensured by adsorption of water vapor at 300 K and dehydration executed in vacuum (lo-' Pa) at 650 K overnight. The measurement of the dielectric dispersion and absorption spectra of dehydrated and calcined Na-MFI at different temperatures (300, 373, 423 and 473 K) were carried out in a dielectric spectrometer designed and constructed in our laboratory (19,29) which consist of two parts: a vacuum system which evacuate a cylindrical capacitor where the zeolite powder (12 g of powder with grain size between 0.2 to 0.5 mm) is deposited and a measuring device consisting of an operational amplifier (26,27) which compare the capacitance of a standard and a sample capacitor. The dielectric permittivity is calculated using the relation E' (w) = C,/C, where: E' (w) is the value of the real part of the dielectric permittivity of the zeolite powder with respect to frequency (30 Hz c w c lo6 Hz)), C, is the capacitance of the cylindrical capacitor full of zeolite powder and C, is the capacitance of the same capacitor but empty. Hence, with the help of the relation: E' (W) = E (03) + x '(w) is possible to calculate the value of the real part of the dielectric susceptibility of the zeolite powder (x '(w)); the value of the imaginary part of the dielectric permittivity of the zeolite powder was obtained using a program which calculates E" (w) with the help of Kramers-Kronig relations (28). The calculated results were compared with experimental values of loss angle measured with the help of the phase of the input and output signals.
885
The thermodielectrical thermograms of hydrated samples were obtained with an equipment designed and constructed in our laboratory which registers the relation between scanned temperature and the output voltage (V,) of a circuit which differentially compares the impedance of the sample under test and a reference (A1,0,) (29). The thermograms show low temperature effects (300-623 K) related to the polarization of zeolitic water (23,24) and the polarization related to cation hopping (19), an effect related to template removal at intermediate temperatures (25) and a high temperature effect (673-1 173 K) related to long range charge carrier transport (21,22). The thermodielectric analyzer uses the same measuring device described for the dielectric spectrometer but instead of scanning frequency at constant temperature, it scans temperature at constant frequency (400 Hz) (29).
RESULTS AND DISCUSSION In figure 1 the dispersion spectra of dehydrated Na-MFI at different temperatures are reported.
5
10
In w
Figure 1. Dielectric dispersion spectra of calcined dehydrated Na-MFI at a: 300 K, b: 373 K, c: 423 K and d: 473 K.
886
The first fact noted is the very low value reported for the dielectric permittivity at 300 K. This is related with the high Si/Al relation of the studied Na-MFI (%/A1 = 25), which implies that the number of charge compensating cations per unit cell (n) is low for the studied Na-MFI ( ~ ~ 3 . 7The ) . other effect easily observed from figure 1 is the increase in the permittivity values with temperature. This increase is clearly connected with the intensity of cationic movements at higher temperatures. The thermodielectricprofile of hydrated-calcined Na-MFI (Fig.2) exhibits no low temperature effect, for hydrated-as-synthesized Na-MFI a peak of template agent removal is observed at 650-800 K (Fig. 2.), i.e. thermodielectric analysis is not sensitive to the polarization effects of Na cations and water inside the Na-MFI structure because of the low quantity of present cations and the recognized hydrophobic character of Na-MFI, but detect the presence of the template agent.
In figure 3 it is possible to observe the calculated dielectric absorption spectra for calcined-dehydrated Na-MFI (a good coincidence exists between calculated and experimentally obtained spectra, and only at low frequencies a difference related with a negligible d.c. component (30) is observed).
"0
-
b
500
1000
Figure 2. Thermodielectrical profile (Output Voltage V, versus Temperature for a: hydrated calcined Na-MFI at a : 300 K, b: hydrated as synthesized Na-MFI.
887
Table 1. Temperature Dependence of Maximum Frequencies
w,(Hz)
Temperature 373
91
423
1556
473
11339
The spectra show the presence of maxima whose frequency are dependent of temperature. In table 1 the dependence between temperature and the frequency of the maximum (W,) are reported. The absence of the absorption peak for dielectric relaxation at 300 K in the frequency range measured is related with the presence of this maxima for lower frequencies.
If we make an Arrhenius plot with the data reported in table 1 we obtain the following value for the activation energy of the predominant relaxation process: E, = 70 kJ/mol. Let us suppose now that the predominant relaxation process for dehydrated-calcined Na-MFI is cation hopping. In a previous paper, it was shown that the frequency dependence for the dielectric susceptibility for a cation hopping mechanism is (20): x (w) = x '(0)/ (1 t i w/wo) (1)
0
5
10
In w
Figure 3. Calculated dielectric absorption spectra of calcined dehydrated NaMFI at a: 300 K, b: 373 K, c: 423 and d: 473 K.
888
where: x '(0) is the static dielectric susceptibility and w, = Q D where Q is a constant and D = Do exp -(Ea/RT) is the diffusion coefficient for cation hopping. Hence if cation hopping is the fundamental relaxation mechanism the obtained results must follow equation "1" and in fact the obtained data is fairly adjusted by the real and imaginary parts of equation "1" in the appropriate frequency range (see Fig. 4). If we make a normalization of the spectra reported in Fig. 3 for the appropriate frequency range (Fig. 4) it is evident the superposition of the peaks, which is a consequence of the presence of only one relaxation mechanism for this frequency range i.e. cation hopping (10-20) and consequently the measured activation energy is related with cationic diffusion in the Na-MFI channels. As was pointed out previously, the Na-MFI zeolite in its structure contains 2 extra-framework sites, one of them is located in the 6 rings openings where diffusion is difficult because of steric restrictions in comparison with diffusion in 10 member ring opening channels, then because of the small reported value for the activation energy it is possible to propose that cationic diffusion occurs through 10 member ring opening channels.
&" &;
1 d ,/'c
0.5
-4
-2
0
2
4
)"1
Figure 4. Normalization of the spectra reported in figure 3.
W
889
At high temperature long range charge carrier transport becomes the predominant effect (T > 700 K) (21-23) i.e. a high temperature effect is evident in thermodielectric analysis for hydrated-calcined and hydrated as synthesized Na-MFI, this effect occurs for Na-MFI (Si/A1=25) at temperatures higher than those corresponding to Na-FAU, Na-LTA, Na-HEU (19,21-23).
In conclusion, it is possible to state that dielectric methods could be used as finger print techniques in the study of ZSM-5 zeolite, by the following facts (19-25): 1. 2. 3.
4.
The absence of the low temperature effect is only related with hydrophobic samples with a low quantity of charge carriers. The presence of the medium temperature effect indicates the existence of a template agent. The position of the high temperature effect indicates too a low quantity of charge carriers if the sample is in the Na form. The value reported for the activation energy of the diffusion process of Na' cation in the zeolite channels in a numerical characteristics related with the zeolite
REFERENCES 1.
2. 3. 4. 5.
6. 7.
8. 9.
A. Corma, in Zeolites: Facts, Figures, Future, eds. P.A. Jacobs and R.A.
van Santen, Elsevier Amsterdam, 1989, p.49. P. Ratnasamy, in: Advances in Catalyst Desing, eds. M. Graziani and C.N.R. Rao, World Scientific, Singapore, 1991, p.67. G.T. Kokotailo, S.L. Lawton, D.H. Olson and W.M. Meier, Nature 27 (1978) 437. D.H. Olson, G.T. Kokotailo, L.S. Lawton and W.M. Meier, J. Phys. Chem. 85 (1981) 2238. H. van Kononngsveld, H. van Bekkum and J.C. Jansen, Acta Cryst. B34 (1987) 127. W.M. Meier and D.H. Olson, Atlas of Zeolite Structure Types Butterworth-Heinemann, London, 1992, 138. W.J. Mortier, Compilation of Extraframework Sites in Zeolites Butterworth, London, 1982, p.53. C.E. Sass and L. Kevan, J. Phys Chem. 92 (1988) 5192. L. Zhenyi, Z. Wangjin, Y. Qin and L. Guanglie, in: Proceedings of the 7" International Zeolite Conference, eds. Y. Murakami, A. Ijima and J.W. Ward, Elsevier-Kodansha, Tokyo, 1986, p. 415.
890
10. 11.
12. 13. 14. 15. 16. 17. 18.
19. 20. 21. 22. 23. 24. 25. 26. 27. 28. 29. 30.
A. Chapoton, Rev. Phys. Appl. 10 (1975) 153. W.A. Hauffe and H. Gunser, Z. Phys. Chem. Chemie Neue Folge 104 (1977) 249. M.F. Rakitinskaya and B.M. Fedorov, Zh. Fiz. Xim. (1982) 2626. A.R. Haidar and A.K. Jonscher, J. Chem. SOC.Far. Trans I. 82 (1986) 132. T. Ogushi, Bull. Chem. SOC.Japan 61 (1988) 1109. T. Ogushi, H. Nonaka and T. Watanabe, Bull. Chem. SOC.Japan 61 (1988) 1797. P. Tabourier, J.c. Carru and J. W. Wacrenier, J. Chim. Phys. 87 (1990) 43. A.K. Jonscher, Dielectric Relaxation in Solids, Chelsea Dielectric Press, London, 1983, Chapter 2. A. Szasz, S. Sabet A1 Rahim and J. Lisz, Acta Chimica Hungarica 125 (1988) 37. R. Roque-Malherbe and M. Hernandez-Velez, J. Thermal Analysis 36 (1990) 1025. R. Roque-Malherbe and M. Hernandez-Velez, J. Thermal Analysis 36 (1990) 2455. R. Roque-Malherbe, C. de las Pozas and J. Castillo, J. Thermal Analysis 32 (1987) 321. R. Roque-Malherbe, C. de las Pozas and M. Carreras, J. Thermal Analysis 34 (1988) 1113. R. Roque-Malherbe, and A. Montes, J. Thermal Analysis 31 (1986) 517. M. Carreras, R. Roque-Malherbe and C. de las Pozas, J. Thermal Analysis 32 (1987) 1271. R. Roque-Malherbe, C. de las Pozas and M. Carreras, J. Thermal Analysis 37 (1991) 2423. R. Roque-Malherbe, A. Rodriguez, M. Hernandez-Velez and A. Montes, Cuban Patent Certificate 21746 (1988). M. Hernandez-Velez and R. Roque-Malherbe, in: Proceedings of the 6'h International Symposium on Electrets, eds. D.K. Gas-Gupta and A. W. Patullo (IEEE Service Center, Piscatawauy, N.J. USA, (1988) p.576. A.K. Jonscher, Dielectric Relaxation in Solids (Chelsea Dielectric Press, London, 1983) appendix. A. Montes, R. Roque-Malherbe and E.D. Shchukin, J. Thermal Analysis 31 (1986) 41. 0. Vigil, M. Hernandez-Velez, J. Fundora, H. Villavicencio and R. Roque-Malherbe, J. Materials Science Letters 11 (1992) 1725.