J. Phys. Chem. B 1998, 102, 3749-3753
3749
Na+/Mordenite Interaction Energy Determined by Thermally Stimulated Depolarization Current S. Devautour,† J. Vanderschueren,‡ J. C. Giuntini,† F. Henn,*,† J. V. Zanchetta,† and J. L. Ginoux§ Laboratoire de Physicochimie de la Matie` re Condense´ e (UMR 5617 CNRS), UniVersite´ de Montpellier II, Place E. Bataillon, 34095 Montpellier, Cedex 05, France, Laboratoire de Chimie Mole´ culaire et de Physique, National Fund for Scientific Research, Institut de Chimie au Sart-Tilman, 4000 Lie` ge, Belgium, and Laboratoire d’Electrochimie et de Physicochimie des Mate´ riaux et des Interfaces, ENSEEG, Domaine UniVersitaire, 38402 Saint Martin d’He` res Cedex, France ReceiVed: October 28, 1997; In Final Form: January 22, 1998
The evolution of thermally stimulated depolarization current (TSDC) measured on a mordenite Na zeolite is examined as a function of the Na+ exchange degree. According to this investigation, the dipolar reorientation is due to Na+, and the TSDC signal analysis leads to an assessment of the interaction energies between the hopping Na+ ions and the zeolitic lattice. The values of these energies are found to be between 0.7 and 0.9 eV. According to the Na+ exchange degree and the nature of the occupied Na+ sites, a quantitative and qualitative characterization of each site is given.
I. Introduction The use of zeolites in catalysis,1 electrochemistry,2 and other applications strongly depends on their ionic exchange capacity, which is related to the specific crystalline structure consisting of channels and cages. The anionic character of the lattice, built from SiO4 and AlO4 tetrahedrons, is neutralized by cations localized in different sites according to the amount and the nature of the exchanged cation. When these sites are located at the surface of the zeolite, they play a key role in its property of gas or liquid adsorption.3,4 The aim of the present work is to determine the energy of the different Na+ sites in a mordenite with different sodium concentrations and therefore to obtain information regarding the surface properties of this zeolite. For this purpose, thermally stimulated depolarization current (TSDC) spectroscopy can be used, since it allows the determination of the interaction energy5 between the sodium and the lattice and of the concentration distribution of the charge carriers in the different sites of the framework. As far as we know, this is the first time that such an experimental technique has been tested for the study of mordenite-type zeolites, and it confirms that TSDC is a powerful method for analyzing the behavior of ionic dipoles on the surface of aluminosilicate. II. Sample Preparation Mordenite is a very high-silica zeolite. Its aluminosilicate network has a porous structure6 (Figure 1), which consists of primary straight channels, parallel to [001], having a slightly elliptical cross section of 6.5 Å × 7.0 Å with 12-member windows, and connected with secondary channels, parallel to [010] of 2.8 Å free diameter, so-called side-pockets with 8-member windows.
Figure 1. Mordenite structure.
The mordenite was originally in the hydrogen form (MH) with the chemical structural formula Na0.09H7.29Al7.38Si40.61O96‚ 27H2O. The partial or total substitution of protons H+ by Na+ was obtained by mixing the zeolite for 12 h in an aqueous solution of NaOH at ambient temperature to achieve the following equilibrium:7
MH + xNaOH S MNaxH1-x + xH2O Different exchanged samples (x ) 0, 0.35, 0.50, 0.75, 1) were prepared (by changing the NaOH concentration from 0.2 to 0.1 mol L-1 in the experimental process) and verified by atomic absorption spectrometry. Each type of exchanged zeolite powder was introduced into a die and compressed up to 4 × 108 Pa. The obtained diskshaped samples (diameter ) 133 mm2, thickness ≈ 1 mm) were treated at 200 °C under vacuum (103 Pa) for 24 h to obtain a dehydrated zeolite prior to carring out the TSDC experiments. III. TSDC Method
* To whom correspondence should be addressed. Telephone: 33-4-6714-46-53. E-mail:
[email protected]. † Universite ´ de Montpellier II. ‡ Institut de Chimie au Sart-Tilman. § ENSEEG.
III. 1. Principle. The TSDC method is a technique developed by Bucci and Fieschi8 and later improved by Van Turnhout,9 Gasiot and Vanderschueren,10 and Lacabanne.11
S1089-5647(97)03478-0 CCC: $15.00 © 1998 American Chemical Society Published on Web 04/17/1998
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Although it was originally developed for the measurement of ionic thermocurrents in insulators, it was extensively used to study the dielectric relaxation in polymers or the electron detrapping in semiconductors.12,13 Basically, TSDC spectroscopy consists of measuring the depolarization current when a dipolar solid, which was first polarized, returns to the equilibrium state under a controlled heating ramp. If the studied material is not a pure dielectric but exhibits a nonnegligeable dc conductivity, it is inserted between two thin films of Teflon before being placed between two metallic electrodes. The mordenite samples were heated at the polarization temperature Tp ) 100 °C and polarized under a constant electrical field of 450 V. The system is then maintained under these conditions for a length of time tp of sufficient duration so that polarization reaches a steady value, i.e., tp . τ(Tp), where τ(Tp) characterizes the relaxation time at temperature Tp at which the polarization takes place. Afterward, the system is rapidly cooled to temperature T0 and the electrical field switched off. T0 is usually close to 77 K to slow down as much as possible the spontaneous depolarization and to stabilize the sample in a “frozen-in” state. Finally, the system is warmed by use of a constant heating rate, viz., 7 °C/min, in our experimental procedure. The return to the equilibrium state of the dipoles gives rise to a depolarization current JD measured as a function of the temperature and characteristic of the material under consideration. III.2. Equations for the TSDC Simulation. Under isothermal conditions, the depolarization function characterizing the return to equilibrium of a system, characterized by a single relaxation time τ, can be written according to a first-order kinetic process (Debye process):
( τt )
P(t) ) Pe exp -
(1)
where Pe is the polarization at time zero. The corresponding depolarization current jD is defined as follows:14,15
jD(t) ) -
dP(t) P(t) ) dt τ
(2)
If the sample is heated using a constant rate q, the variable temperature T is related to the time t via the relation
T ) T0 + qt
(3)
Assuming that the relaxation time τ follows an Arrhenius law, it takes the following form:
(∆E kT )
τ ) τ0 exp
(4)
where k is Boltzmann’s constant, ∆E the potential barrier associated with the dipole reorientation, and τ0 the inverse of the oscillation frequency ν0 οf a charge carrier trapped in its site. Following a statistical thermodynamic calculation, τ0 has been determined and fixed at 2.6 × 10-12 s.5 Then in the first stage, when the ion/ion Coulombic interactions are neglected, the measured polarization current can be considered as the contribution of a dipole population characterized by a distribution of relaxation times. Equation 4 shows that this corresponds to a distribution of energy G(∆Ei).
Figure 2. Evolution of the depolarization current JD vs the temperature T for different sodium contents. Arrows indicate the space charge contribution.
Therefore, the global depolarization current JD can be written as
JD(T) )
Pe(T) τ0
( ) [ ]∫ ( )
∑i G(∆Ei) exp
-∆Ei kT
-1
exp
qτ0
×
T
exp T 0
-∆Ei kT
dT (5)
In ionic materials, such as in zeolites, there exist several types of sites that can be, in terms of energy, very close to one another. In such cases, the distribution function G(∆Ei) appears to be a convolution of simple Gaussian functions gk(∆Ei), which can be written as
G(∆Ei) ) a1g1(∆Ei) + a2g2(∆Ei) + ...
(6)
where ai is a coefficient of proportionality. In practical cases, the number of terms akgk(∆Ei) is restricted to between one and three or four terms. In short, from the deconvolution and the fitting of the TSDC signal, we can obtain two types of significant information for the case of a zeolite having different sites: (1) the potential barrier ∆Ee, characterizing the interaction energy between the charge carrier in a given site and its environment and corresponding to the centered value introduced in the Gaussian functions and being equal to the energy difference between two levels ∆Εe ) h - e, where e is the most probable energy level of the ion embedded in its site, i.e., the equilibrium state, and h is the energy level to be reached in order that the hopping process takes place; (2) the site population, obtained from the ratio of each site contribution. IV. Results and Discussion IV.1. Data Treatment. Figure 2 illustrates the evolution of the current density JD as a function of temperature for different Na+ concentrations. From this figure, three general conclusions can be drawn: (i) In the studied temperature domain, the TSDC signal is most likely due to the Na+ ions, since MH exhibits no signal. (ii) When the Na+ content increases, the signal shifts toward the lower temperatures. (iii) The peaks denoted by an arrow correspond to the depolarization of space charges10 and do not characterize the bulk response of the material. The procedure of data treatment consists of fitting each experimental signal using eq 5 by adjusting the value of ∆Ei
Na+/Mordenite Interaction Energy
J. Phys. Chem. B, Vol. 102, No. 19, 1998 3751
Figure 3. (a) Comparison between the calculated JD signal (solid line) and the experimental data (0) obtained on a totally exchanged mordenite. (b) Line shape of the distribution function G(∆E) used for the calculation of JD(T). Solid and dotted lines represent the global G(∆E) and the g(∆E) assigned to each site, respectively.
TABLE 1: Parameter ∆Ee of the Gaussian Functions G(∆Ei) ) {a/[γ(2π)1/2]}exp[-(∆Ei - ∆Ee)2)/γ2], Where ∆Ee is the Centered Value of Each Gaussian Function Corresponding to the Most Probable Interaction Energy, γ the Width of the Gaussian Function, and a/[γ(2π)1/2] the Proportionality Coefficient between Each Gaussian Functiona MNa1H0 MNa0.75H0.25 MNa0.5H0.5 MNa0.35H0.65
a
Gaussian
∆Ee ( 0.01 (eV)
1 2 3 1 2 3 1 2 3 1 2 3
0.72 0.77 0.80 0.74 0.80 0.82 0.75 0.81 0.84 0.81 0.88 0.90
The error in the value of ∆Ee was estimated to be (0.01 eV.
and G(∆Ei). Figure 3a shows the comparison between a calculated signal JD(T) and an experimental curve. The discrepancy observed at the high-temperature part of this curve is due to the space charge peak, which was not taken into account in the simulation. To obtain a good agreement between the experimental data and the simulated curves, G(∆Ei) appears as a convolution of three Gaussian functions centered around three different values of ∆Ee (Figure 3b). Fitting parameters are summarized in Table 1. These Gaussian functions would correspond to the different sites occupied by the charge carriers, since, as was claimed by Mortier,16 Na+ ions of MNa1 are
localized in three sites, i.e., I, IV, and VI (see Figure 1), characterized by different potential energies. However, since neither theoretical nor experimental information is given for the other Na+-exchanged mordenites, we assume that these three sites coexist whatever the exchange degree and continue to use the three Gaussian functions for recovering all experimental data. IV.2. Determination of the Site Potential Barrier ∆Ee. To explain and to clarify the different values of ∆Ee (Table 1), we have to consider two parameters: the cation coordination by the oxygen atoms in each site,17-19 and the site geometry. In fact, nonframework cations in dehydrogenated zeolite are located near Al atoms, where there is an excess of negative charge on the oxygen atoms. Thus, knowledge of the Al distribution can be helpful to determine the interaction energy between the Na+ and the oxygen atoms. Taking into account these considerations, it has been emphasized that sites I and IV contain much more oxygen, i.e., more negative charge, than site VI. In fact, Na+ ions located in sites I and IV are linked to six oxygen atoms, whereas they are only associated with four oxygens in site VI.18 As a consequence, the Na+ ion trapped in the latter site is submitted to the weaker negative charge of the oxygen atoms, and its interaction energy with the zeolitic lattice decreases. This approach can explain the energy difference between sites I and IV and site VI. Furthermore, the fact that site VI corresponds to a one-sided coordination, resulting from an off-center position in an eight-ring17 at the surface of the main channel, results in an energy even weaker than expected. To explain the energy difference between sites I and IV, which have the same coordination, we must refer to the geometry of each site. Since site I is embedded in the side pockets and since site IV is located at the entry of the narrow channel,16 without neighbors on one side, it is reasonable to obtain a higher interaction energy for site I than for site IV. However, if we compare the energy differences between the sites, we remark that the factor of coordination near the Na+ cation is predominant in the evaluation of the interaction energy Na+/zeolitic lattice. This description can be compared with the data proposed by Tyburce,20 who also defined the site energy sequence from the negative charge distribution: ∆E(I) > ∆E(IV) > ∆E(VI). Moreover, we emphasize that the TSDC technique can be used to determine quantitatively the potential barrier associated with each site in the zeolites. However, TSDC being the only technique that enables an experimental determination of this energy, a comparison is not yet possible. IV.3. Determination of the Site Population. From the fitting of our experimental spectra, it is also possible to assess the occupation degree of each site by calculating the ratio of the integral of each single distribution function gk(∆Ei) to the integral of the global distribution function G(∆Ei). When this occupation degree is known, the population of each site can be calculated from the structural formula of the mordenite, since MNa1, MNa0.75H0.25, MNa0.5H0.5, and MNa0.35H0.65 correspond to 7.38, 5.53, 3.69, and 2.58 Na+ ions per unit cell, respectively. Then by comparison of our calculation with those of the previous studies reported in the literature, it is possible to assign each peak to a given site. The results reported in Table 2 on MNa1 compare favorably with the data given by Mortier,16 Tyburce,20 and Coughlan.21 Only one discrepancy is noticeable: there is a maximum of four sites I occupied by Na+ per unit cell, whereas the simulation gives 4.5. This difference is likely to be related to the fitting approach. By comparison with the population of each site, the
3752 J. Phys. Chem. B, Vol. 102, No. 19, 1998
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TABLE 2: Number of Sodium Atoms per Unit Cell for Each Type of Sitea
site I site IV site VI
Tyburce20
Mortier16
Coughlan21
TSDC (this study)
4 3 1 ∑)8
3.1 2.6 1.5 ∑ ) 7.2
4 2.6 1.5 ∑ ) 8.1
4.5 2.2 0.68 ∑ ) 7.38
a By comparing the occupation degree obtained by TSDC with the results of different authors, we can attribute the Gaussian functions numbered 3, 2, and 1 to the response of sites I, IV, and VI, respectively.
Figure 5. Evolution of ∆Ee vs the exchange degree for sites I, IV, and VI respectively denoted by 9, 2, and b. The error of the measured data is the size of the symbols and is about (0.01 eV.
Figure 4. Evolution of the number of sodum atoms, NNa. per unit cell as a function of the exchange rate. Sites I, IV, and VI are represented by 9, 2, and b, respectively. The error made in the occupation degree is estimated to be 10%.
occupation degree is proportional to the site potential energy and therefore decreases from site I to site VI. IV.4. Evolution of the Site Occupation with the Exchange Degree. Figure 4 represents the evolution of the site occupancy as a function of the exchange degree, remembering that the numbers reported here (see Table 2) are indicative values that must be interpreted as a tendency and not as absolute values. Since site I is the deepest site, it is always the most occupied site and its occupancy as a function of the Na+ concentration is approximatively linear. The same assumption can be employed to explain the site IV occupancy, which also evolues linearly with respect to the Na+ content but with a slope weaker than that of site I. As a result of the low interaction energy of site VI, its occupation degree remains low and, within the errors of determination, almost constant with the exchange degree. Finally, we remark that each type of site is occupied whatever the exchange degree. IV.5. Evolution of the Site Energy with the Exchange Degree. Figure 5 shows the evolution of the site energies ∆Ee with respect to the exchange degree. We note that the interaction energy ∆Ee between the sodium atoms and the zeolitic network decreases when the exchange degree increases. These results can be explained by considering the following interpretation. Before being exchanged, the proton located at the zeolite surface is in equilibrium at its site. This equilibrium can be described by using the concept of electronegativity, as proposed by Mulliken and Jaffe.22,23 In this approach, the electronegativity χ is proportional to the first derivative of the potential energy as a function of the effective charge of a given atom involved in the bond under consideration. This representation can be extended to the characterization of the surface sites, considering the interaction between the exchangeable cation and
Figure 6. Schematic representation of the charge distribution of the oxygen network δ′O and of the cations δ+N and δ+H as a function of the exchange degree. This figure is a qualitative description. For the sake of simplicity, we have reported four sites having the same interaction energy before the H+/Na+ exchange and corresponding to the following compositions: (a) MH1; (b) MNa0.25H0.75; (c) MNa0.50H0.50; (d) MNa1.
the network, if we assume that a zeolite site, having a negative charge, could be regarded as a soft polyanion. In this approach, the parameter, i.e., the charge distribution characterizing the equilibrium state, will be very dependent on the “ionic strength” of the exchanged cation and, of course, on its concentration. This can be illustrated by the evolution of the interaction energy, occurring by interaction between sodium and oxygen when the hydrogen cation is replaced by sodium. A schematic representation is given in Figure 6, where four “situations” are examined corresponding to four compositions of the solid. The pure hydrogenated solid is reported in Figure 6a, showing that all four representative situations of the hydrogen in the netwok are energetically equivalent. It is wellknown that the potential of sodium ionization is lower than that of hydrogen. Therefore, the effective charge of the sodium δ+Na1 is more important than the charge located on the exchanged
Na+/Mordenite Interaction Energy
Figure 7. Schematic representation of the energy difference ∆Ee
measured in TSDC. proton δ+Η0 (δ+Na1 > δ+Η0). In Figure 6b it is shown that the negative charge localized on the oxygen δ-O1 facing the sodium atom is necessarily higher than that facing the hydrogen H0 in Figure 6a. The excess of charge due to the introduction of a sodium atom in the network creates an induction effect with modification of the partial charge of the remaining hydrogens and oxygens. Therefore, δ+Na1 > δ+H0 implies δ-O1 > δ-O1′. Of course, the induction effect becomes less important when the distance between the ions increases. Analysis of cases c and d is analogous, if we remark, as an example, that in c δ+Na2 > δ+Na1. As a consequence, the partial charge of the sodium atoms is an increasing function of their number after exchange. Indeed, these atoms have more difficulty dissipating their charges, and therefore, the charge of the oxygen atoms increases as shown in Figure 6d, where δ-O3 ) δ-O3′ ) δ-O3′′ ... > δ-O2 .... In short, this means that the charge located on Na+ in the case of a totally exchanged mordenite is higher than the charge related to a partial exchange. Therefore, the ionicity of the Na+/ oxygen network bond increases with the exchange, and Na+ becomes more mobile. This trend, as schematically represented in Figure 7, corresponds to the evolution of the TSDC signal for which the calculated interaction energy decreases with increasing exchange degree (Figure 5). V. Conclusion In this work we have shown that the TSDC technique can be used to study a mordenite and to obtain important quantitative data: (i) the number and type of sites occupied by the compensating ions; (ii) the occupancy degree of each site; (iii) the site energy. The last, which characterizes the interaction energy between the charge carrier and the zeolitic lattice, was found to vary from 0.72 to 0.90 eV. Such quantitative
J. Phys. Chem. B, Vol. 102, No. 19, 1998 3753 information usually cannot be obtained from methods of structural analysis. Furthermore, we have attempted to explain, by using a simple model based on electronegativity and induction concepts, the decrease of the interaction energy with increasing exchange degree. Since adsorption properties of liquid or gas on zeolites are strongly related to these energy values, TSDC appears to be a powerful technique for surface characterization. The same approach on hydrated mordenite is currently being undertaken, and the corresponding results should be of great interest for understanding the interfacial phenomenon. These results will also be compared with the heat of adsorption measured by calorimetric experiments. Acknowledgment. This article is dedicated to the memory of the late Dr. J. L. Ginoux. References and Notes (1) Mortier, W. M.; Pluth, J. J.; Smith, J. V. Natural Zeolite Occurrence Properties; Pergamon Press: New York, 1978. (2) Ozin, G. A.; Kuperman, A.; Stein, A. Angew. Chem., Int. Ed. Engl. 1989, 28, 359. (3) Mamy, J. Ph.D Thesis, P. et M. Curie University, Paris, 1965. (4) Fripiat, J. J.; Jelli, A.; Poncelet, A.; Andre, J. J. Phys. Chem. 1965, 62, 2185. (5) Devautour, S.; Vanderschueren, J.; Giuntini, J. C.; Henn, F.; Zanchetta, J. V. J. Appl. Phys. 1997, 82, 5057. (6) Meier, W. M. Z. Kristallogr. 1961, 115, 439. (7) Nguyen, P. Ph.D Thesis, J. Fourrier University, Grenoble, 1993. (8) Bucci, C.; Fieshi, R. Phys. ReV. Lett. 1964, 12, 16. (9) Van Turnhout, J. J. Phys. D.: Appl. Phys. 1975, 8, 268. (10) Vanderschueren, J.; Gasiot, J. Thermally Stimulated Relaxation in Solids; Braunlich, P., Ed.; Springer-Verlag: Berlin, 1979. (11) Lacabanne, C. Ph.D. Thesis, P. Sabatier University, Toulouse, 1979. (12) Miller, S. L.; Fleetwood, D. M.; McWhorter, P. J. Philos. Mag. 1992, B66, 77. (13) Gasiot, J.; de Murcia, M.; Fillard, J. P. J. Appl. Phys. 1979, 50, 167. (14) Ibar, J. P. Fundamentals of Thermally Stimulated Current and Relaxation Map Analysis; SLP New Canaan, 1993. (15) Bucci, C.; Fieshi, R.; Guidi, G. Phys. ReV. 1966, 148, 816. (16) Mortier, W. J. Compilation of Extraframework Sites in Zeolites; Butterworth: Guildford, 1982. (17) Schlenker, J. L.; Pluth, J. J.; Smith, J. V. Mater. Res. Bull. 1979, 14, 751. (18) Takaishi, T.; Kato, M.; Itabashi, K. Zeolites 1995, 15, 21. (19) Shiokawa, K.; Ito, M.; Itabashi, K. Zeolites 1989, 9, 170. (20) Tyburce, B.; Kappenstein, C.; Cartraud, P.; Garnier, E. J. Chem. Soc., Faraday Trans. 1991, 87 (17), 2849. (21) Coughlan, B.; Carrol, W. M.; McCann, W. A. J. Chem. Soc., Faraday Trans. 1977, 73, 1612. (22) Mulliken, R. S. J. Chem. Phys. 1935, 3, 573. (23) Hinze, J.; Whitehead, M. A.; Jaffe´, H. H. J. Am. Chem. Soc. 1963, 85, 148.
