- Email: [email protected]
Mobility of CD4 molecules in nanoscale cages of zeolites as studied by deuteron NMR relaxation
Chemical Physics 311 (2005) 299–305 www.elsevier.com/locate/chemphys
Mobility of CD4 molecules in nanoscale cages of zeolites as studied by deuteron NMR relaxation A.M. Korzeniowska a, Z.T. Lalowicz a
a,*
, A. Gutsze
b,z
H. Niewodniczan´ski Institute of Nuclear Physics of Polish Academy of Sciences, ul. Radzikowskiego 152, 31-342 Krako´w, Poland b Biophysics Department, Medical Academy, Bydgoszcz, Poland Received 15 October 2004; accepted 10 November 2004 Available online 8 December 2004
Abstract Deuteron spin–lattice relaxation was applied to study mobility of CD4 molecules trapped in the cages of zeolite NaY. There are two, interconnected sets of cages: a-cages and b-cages with 1.16 and 0.74 nm diameter, respectively. The relaxation temperature dependence, measured between 4 and 300 K, can be divided into four ranges with characteristic motional parameters. At higher temperatures exchange between cages dominates. Increasing rate of translational motion leads to a significant reduction of the relaxation rate. Features typical for quantum rotors were observed at low temperatures. Molecules in the a-cages exhibit reorientational freedom, while motion of these in b-cages is significantly restricted. Increasing abundance of molecules in b-cages indicates slow diffusion down to low temperatures. 2004 Elsevier B.V. All rights reserved.
1. Introduction Molecular dynamics studies were carried out by NMR methods in every state of matter. Moving from solid state through liquids to gases, apart from rotational dynamics, translational motion appears. Methane provides good example of such studies. Placing CD4 molecules in zeolite cages creates exceptional possibilities for research of rotational and translational dynamics. It is possible to choose cages different in size, surface properties and the level of filling. The basic issue of cognitive significance is observation of free rotors in wide range of temperatures. Both CH4 and CD4 were studied by NMR in the form of molecular crystals at low temperatures [1,2], dissolved in, e.g., liquid crystals [3,4], and in gaseous form at high temperatures. Deuteron relaxation of CD4 was * Corresponding author. Tel.: +48 12 6628 259; fax: +48 12 6628 458. E-mail address: [email protected] (Z.T. Lalowicz). Deceased author. z
0301-0104/$ - see front matter 2004 Elsevier B.V. All rights reserved. doi:10.1016/j.chemphys.2004.11.009
studied in gaseous and liquid state [5]. Molecular reorientations make the intramolecular spin interactions time dependent and provide the relaxation mechanism. Various models of reorientations produced by molecular collisions were considered ([5] and references therein). Liquid methane freezes into a molecular crystal phase I at 90 K, where molecules occupy fcc sites, but can rotate freely. At lower temperatures there is the next phase transition at 27 K for CD4, to the ordered fcc phase II. At 22.1 K, CD4 undergoes a transition to phase III, where all molecules are rotationally hindered [2,6,7]. Molecular field theory predicts phase transitions in methane by taking into account the electric octupole– octupole interaction as dominating intermolecular interaction [8,9]. A more thorough discussion can be found in the comprehensive review by Press [10]. No change in the relaxation rate was observed at the melting point for CD4, but there is a discontinuity at transition to phase II [1]. Correlation time sc, defined as a mean time between molecular jumps, can be derived from temperature
300
A.M. Korzeniowska et al. / Chemical Physics 311 (2005) 299–305
dependence of the spin–lattice relaxation rate . An exponential correlation function exp(jsj/sc) was assumed for molecular reorientations. Arrhenius relation sc ¼ s0 expðEkTa Þ allows us to obtain the activation energy Ea from the temperature dependence of the correlation time. However, in gaseous methane [11] and its solid phase below 15 K some more specific features appear [1]. In the former case collisions of free rotors play important role, in the latter case transition between low rotational levels introduced a temperature dependence of an apparent activation energy [1,12]. Generally, the spacing between rotational levels is large compared to the energy of anisotropic interactions between molecules being responsible for molecular reorientation. We aim to study deuteron spin–lattice relaxation for CD4 molecules isolated in nanoscale cages in zeolites. It provides an unique possibility to study dynamics of single free rotor in limited space and intermolecular interactions on increasing number of molecules. Then on decreasing temperature molecular collisions decay and molecules solidify on cage walls, subjected, apart from eventual intermolecular interactions, to interaction with adsorption centers. Our results differ significantly with respect to observation for CD4 gas and disagree with the prediction of the Debye rotation diffusion model [12].
2. Theoretical overview 2.1. Rotational levels of a tetrahedral molecule The orientational states of a molecule with tetrahedral symmetry, like CD4 and NDþ 4 , are labelled by irreducible representations A, T and E of Td symmetry group. The total wave functions, the product of space and spin wavefunctions, must transform according to the A representation. Therefore, for respective symmetry species only specified spin configurations with a total spin I are allowed: A(I = 0, 2, 4), 3T(I = 1, 1, 2, 3), E(I = 0, 2). The rotational levels of CD4 molecules associated with each spin species are as follows: A(J = 0, 3, 4, . . .), 3T(J = 1, 2, 3, 4, . . .), E(J = 2, 4, 5, . . .) [13]. The tunnelling splitting is defined as an energy difference between A(J = 0) and 3T(J = 1) state. The tunnelling splitting depends exponentially on the ratio V0/ B of the potential V0 and rotational constant B = h2/ 2I, where I is the molecular moment of inertia [14, and references therein]. Therefore, the tunnelling splitting for deuterated and protonated rotors may differ by a factor in the range 10–300 [15]. There are fast symmetry conserving vibrational transitions among rotational levels, which maintain their Boltzmann populations. Rotational dynamics of molecular rotors depends on the local potential. Deuterated rotors, when subjected a high potential, e.g. higher than 8 kJ/mol in the case of
NDþ 4 [14], perform classical reorientation at high temperatures and become immobile on the timescale of spin interactions at sufficiently low temperature. The tunnelling splitting, amounts, e.g., 7.5 MHz for NDþ 4 ions subjected to the potential 5 kJ/mol [16]. For diminishing potential the free rotor states are approached. The activation energy Ea = 0.83 kJ/mol was obtained in solid CD4 below 10 K [12]. As the activation energy we define the energy difference from the ground level to the top of a barrier and therefore V0 = Ea + E0, where E0 represents a zero point motion energy. In the case of CD4 in a very low potential we take rather the lowest rotational level energy. With the resulting V0 1 kJ/mol we estimate the tunnelling frequency to be about 15.7 GHz for CD4. It justifies considering only the lowest rotational levels (J = 0, 1) in the theory of relaxation for CD4 [17]. The tunnelling frequency falls down to 4.4 GHz for the potential V0 = 1.5 kJ/mol. 2.2. Spin–lattice relaxation The spin–lattice relaxation rate for CD4 can be written as the sum 1 1 1 1 ¼ þ inter þ SR T 1 T intra T T 1 1 1
ð1Þ
of contributions from intramolecular dipolar and quadrupolar interactions, intermolecular dipolar interactions and the spin–rotational interactions [1]. The quadrupolar interaction dominates in the intra terms and can be written as [18,19] 1 3 x2Q ¼ ½J ðx0 Þ þ 4J ð2x0 Þ, 40 x0 TQ 1
ð2Þ
where we define here the reduced density function as x0 sc J ðx0 Þ ¼ : 1 þ x20 s2c Such definition allows us to write down the relaxation rate at the maximum conditions x0sc = 0.615 as ! 1 3 x2Q ¼ ½1:425, ð3Þ 40 x0 TQ 1 max
which is the convenient formulation for comparing values measured at different frequencies. Assuming xQ = 2p Æ 1.68 Æ 105 s1 and x0 = 2p Æ 46 Æ 106 s1 we get ðT1Q Þmax ¼ 411 s1 . Such value can be anticipated 1 for a deuteron or CD4 molecule undergoing classical isotropic reorientation. Tunnelling splitting, i.e. considering a scheme of rotational energy levels, has several important consequences. The reduction of relaxation rate results from elimination of contribution to relaxation from numerous (xt ± nx0) transitions. Only ±nx0 (n = 1, 2) transitions due to motionally perturbed intramolecular spin interactions
A.M. Korzeniowska et al. / Chemical Physics 311 (2005) 299–305
contribute. As the spin interactions vanish for A and E species of CD4, relaxation appears only within T levels manifold. Additionally T symmetry species happen to be significantly more ordered. That may lead to differences in Ea values obtained by different methods. In the case of CD4 placed in such a weak potential of tetrahedral symmetry that xt x0, we have to introduce a reduction factor 7/18 [17,19], what leads to the relaxation rate ! 1 7 x2Q ¼ ½1:425 ¼ 160 s1 : ð4Þ 240 x TQ 0 1 max
Moreover, T levels may split up in a potential of lower symmetry and several specific structures can be considered. Calculations show, that for realistic potentials, the reduction factor between 0.33 and 0.85 may be expected. Therefore, the range of expectable relaxation rate values falls between 53 and 136 s1 for CD4 molecules as slightly hindered quantum rotors. Any further reduction of the relaxation rate must involve spatial limitations of molecular reorientations. An useful theory of relaxation was worked out for NDþ 4 ions undergoing limited jumps [19]. It was assumed that motion of N–D vectors is restricted to a cone with an opening angle 2D. The angle can be evaluated from the ratio of relaxation rates at the maxima for restricted motion Rrestr and for molecular reorientation Rreor Rrestr ¼ 3sin2 Dcos2 D: ð5Þ Rreor The intermolecular relaxation rate due to dipolar interaction requires special, model dependent treatment [18,20,21]. The model includes the modulation of the interaction via site-to-site translational jumps. Reorientation of molecules may contribute too, when these are ineffective. Both intra- and intermolecular dipolar interaction contributions to the relaxation are much smaller, by a factor about 105, than the quadrupolar contribution. Contribution from spin-rotational interaction may also be neglected in the case of CD4 [11]. Molecules placed in a heterogenous environment, such as zeolites cages, may exhibit a distribution of mobilities. Effects of the distribution of correlation times may be detected from relaxation and spectra. We consider a case where there are two sites characterized by different relaxation times T1a T1b. Assuming slow exchange between these regions the magnetization is expected to evolve on time as t t MðtÞ ¼ wa exp þ wb exp , ð6Þ T 1a T 1b
301
dition wsaa ¼ wsbb , relaxation appears to be exponential with an average relaxation rate 1 wa wb ¼ þ : ð7Þ T 1 AV T 1a T 1b Intermediate cases were also analyzed [22]. 2.3. Spectra Narrow lines were observed for solid CD4 and very little attention was devoted to their analysis. Features expectable in CD4 spectra will be discussed on the basis of theory outlined for NDþ 4 ions [16,23]. Spin species A, T and E contribute distinguishable components to the spectra. Intramolecular spin interactions (first order dipolar and quadrupolar) vanish for A spin species, which contribute therefore rather narrow central line. There exists, however, a doubled structure related to second order terms of the quadrupole interaction. The doublet separation is inversely proportional to the tunneling splitting and with values above 10 MHz it falls below the natural linewidth of about 1 kHz. The T species may contribute a central line with a width about 10 kHz and a flat background. That spectral component is subjected to motional narrowing.
3. Experimental
r¼
with weights wa + wb = 1, related to an abundance of the sites. In the limit of fast exchange, T1a sa, T1b sb, where sa and sb are mean life-times and equilibrium con-
3.1. Materials and methods A synthetic faujasite-type zeolite NaY with Si/Al = 2.4 was used. The sample of the zeolite has a form of powder, composed of small grains with diameter between 1 and 100 lm. There are two interconnected three-dimensional pore systems in the structure of the faujasite. Large a-cages have mean free diameter 1.16 nm, are arranged tetrahedrally and connected through windows of 0.74 nm diameter. Smaller b-cages have 0.6 nm diameter and are connected through hexagonal prisms. For comparison, CD4 molecule has 0.216 nm diameter. About 120 mg of the zeolite was placed in a 5 mm thin-wall glass tube and attached to an all steel high-vacuum device. The sample was heated in vacuum up to 673 K with a heating rate 50 K/h and kept at this temperature for 12 h under the vacuum p < 105 hPa. After cooling down the sample was loaded with the calibrated amount of CD4 and sealed. The NMR experiments were performed on a homebuilt pulse NMR spectrometer, operating on the 7.04 T/89 mm superconducting magnet and thus of deuteron resonance frequency 46 MHz. A low temperature NMR probe was placed inside the Oxford CF1200 continuous flow cryostat, and the temperature was regulated by the
A.M. Korzeniowska et al. / Chemical Physics 311 (2005) 299–305
Oxford CT503 Temperature Controller. The temperature accuracy and stability were within ±0.1 K in the whole temperature range. The spin–lattice relaxation time was measured by the saturation recovery method. An aperiodic 10-pulse saturating sequence was followed by 2 ls r.f. sensing pulse after a variable time delay. The amplitude of the magnetization, recovered during the delay, was determined by recording the free induction decay (FID). In order to achieve a satisfactory S/N ratio it was necessary to accumulate the signal due to a low concentration of CD4 molecules in the zeolite. After Fourier transformation of the FID, phase and baseline correction, the signal intensity was determined by integration of the whole spectral line. A typical number of delays determining the magnetization recovery curve was about 25, chosen in such a way that they uniformly covered the range from 0 to about 3T1 in the logarithmic scale. An additional data point was measured at a time much longer than 5T1, in order to determine precisely the equilibrium magnetization. This approach was found to improve the accuracy of the three-parameter single-exponential fit to the data.
c d 100
c' 1/T1[s-1]
302
10
d'
b a
1
0.1 0
10
20
30
40
50
60
70
80
90
100
110
1000/T [K-1]
Fig. 1. Temperature dependence of deuteron spin–lattice relaxation rate for sample I. The single time constant in the exponential relaxation range is depicted with (), short and long relaxing components are marked (m) and (,), respectively.
c 100
d c'
3.2. Samples We have selected here first three examples for presentation: 1. Sample I: one CD4 molecule per cage of NaY zeolite. 2. Sample II: four CD4 molecules per cage of NaY zeolite. 3. Sample III: four CD4 molecules per cage of NaY(NaBr) zeolite, where b-cages had been filled by NaBr.
1/T1 [s-1]
b' 10
d'
b 1
a
0.1 0
10
20
30
40
50
60
70
80
90
100
110
1000/T [K-1]
Fig. 2. Temperature dependence of deuteron spin–lattice relaxation rate for sample II. Symbols are used as in Fig. 1.
3.3. Results
c 100
b'
1/T1[s-1]
Measured spin–lattice relaxation rates are shown in Fig. 1–3, respectively. Continuous lines show fits using Eq. (1) with appropriate reduction factors explained in the following. Figs. 4 and 5 show the temperature dependence of weights wx(x = a,b) of respective time constants in the non-exponentiality range for samples I and II, respectively. Fig. 6 presents the half-width of the spectra for all samples. We divided the observed temperature dependence of the spin–lattice relaxation into ranges with common labels. The derived motional parameters: activation energy Ea and the pre-exponential factor s0, are compiled in the Table 1. Activation energies Ea were obtained from the slope in the range a under condition x0sc 1. At a transition temperature, labelled TTR, there is a turning point to the
10
b a
1
0,1 0
10
20
30
40
50
60
70
80
90
100
110
1000/T [K-1]
Fig. 3. Temperature dependence of deuteron spin–lattice relaxation rate for sample III. Symbols are used as in Fig. 1.
A.M. Korzeniowska et al. / Chemical Physics 311 (2005) 299–305 Table 1 Motional parameters: Ea (kJ/mol), s0 (s), T (K)
1.0 0.9 0.8
a TTR b
0.7 0.6
wa, wb
303
0.5
Sample I
Sample II
Sample III
Ea = 1.5 110 Ea = 2.7 s0 = 3.5 · 1013
Ea = 1.4 181 Ea = 2.6 s0 = 5.9 · 1011 Ea = 1.3 s0 = 1.5 · 1011 25 Ea = 0.4 s0 = 9.8 · 1010 Ea = 0.7 s0 = 1.3 · 1010 Ea = 0.008 Ea = 0.056
Ea = 0.76 166 Ea = 2.4 s0 = 1.6 · 1011 Ea = 1.5 s0 = 4.8 · 1012
b0
0.4
TNE c
0.3 0.2
c0
0.1 0.0 0
20
40
60
80
100
120
140
160
180
200
d d0
43 Ea = 1.2 s0 = 3.5 · 1011 Ea = 1.0 s0 = 6.1 · 1011 Ea = 0.3 Ea = 0.67
Ea = 0.4
1000/T [K-1]
Fig. 4. Temperature dependence of weights wa (m) of the fast relaxing component and wb (,) of the slow relaxing component for sample I (compare Fig. 1).
1.0 0.9 0.8 0.7
wa, wb
0.6 0.5 0.4 0.3 0.2 0.1 0.0 0
20
40
60
80
100
-1
1000/T [K ]
Fig. 5. Temperature dependence of weights wa (m) of the fast relaxing component and wb (,) of the slow relaxing component for sample II (compare Fig. 2).
2.0 1.8 1.6
range where the condition x0sc 1 was assumed. Relaxation process appears to be bi-exponential below a transition temperature TNE. The relaxation rate maxima are fitted using Eq. (2) with adjusted reduction factors. The maximum value in the range c correlates well with the value predicted by Eq. (4). The range c 0 shows reduced value of the relaxation rate, by a factor 10 in the case of sample I and a factor 5 in the case of sample II. Using Eq. (5) we may estimate the angle of the cone to be equal to 21.5 and 31, respectively. At lowest temperatures, the slope provides the activation energy under the condition x0sc 1. The spectra remain narrow down to the lowest temperature (Fig. 6). Their width (fwha) increases from about 0.1 kHz at high temperatures up to about 2 kHz at most. It indicates that intramolecular spin interactions do not contribute. We must consider therefore the intermolecular interactions between molecules or molecules and walls. While the broadening of spectra appears at about 70 K for samples II and III, it begins already at about 150 K for sample I. It may indicate that the contribution from interaction with walls dominates in the sample I, where molecules spend a time long enough at the walls. That is not possible due to molecular scattering in samples II and III.
h1/2[kHz]
1.4 1.2
4. Discussion
1.0 0.8 0.6 0.4 0.2 0.0 0
20
40 60 80 100 120 140 160 180 200 220 240 260 280 300
T [K]
Fig. 6. Temperature dependence of the half-width of the spectra (fwha), sample I (s), sample II (), and sample III (h).
Deuteron spin–lattice relaxation was found to be the very sensitive method providing information on dynamics of CD4 molecules in zeolite cages. Observed features depend both on shape and size of cages as well as the filling factor. We begin our analysis from the intermediate range of temperatures. The key point lays in explaining the cause of non-exponentiality. Results on sample III provide the solution. The b-cages are filled up by NaBr and thus
304
A.M. Korzeniowska et al. / Chemical Physics 311 (2005) 299–305
are not accessible for CD4 molecules. Absence of nonexponentiality allows us to conclude that relaxation rates in the range c 0 for samples I and II come from CD4 molecules trapped in b-cages. The maximum value of the relaxation rate in the range c indicates that it comes from quantum rotors subjected to a weak potential in a-cages. Mobility of CD4 molecules in b-cages appear to be significantly reduced due to spatial limitations. A slow exchange is the condition for observation of non-exponentiality and thus we conclude that diffusion of molecules between cages is slow below TNE. It is the a common feature for quantum rotors that at temperatures well below maxima, typically below 20 K, in d range here, the temperature dependence of the relaxation rate levels down. Thermally activated motions are ineffective in relaxation and incoherent tunnelling prevails. Very low values of apparent activation energy characterize this process. It was interesting to follow the temperature dependence of relative weights of the time constants. These show some temperature dependence in spite of the condition of slow exchange. Thus molecules may undergo slow translational motion along the walls of cages in a gradient of potential, as it was observed in case of benzene [24] and considered to be a general feature [25]. At higher temperatures abundance of a-cages prevails, while at lowest temperature most of CD4 are trapped in b-cages (Fig. 4 and 5). Non-exponentiality appears at TNE = 43 and 25 K for samples I and II, respectively. At these temperatures exchange of molecules between cages becomes slow enough for observing two relaxation rates. Single molecules in sample I achieve that condition at higher temperatures. These experience a stronger bonding to the walls, what results also in line-broadening at higher temperatures. Molecular scattering, appearing with more molecules per cage, shifts observation of both effects down to lower temperatures. Efficiency of the relaxation process is related to a modulation of intramolecular spin by molecular reorientations. Two factors can be pointed out in a simplified picture: amplitude of the perturbation introduced by a single jump and a correlation time, defined as a mean time separating jumps between symmetry positions. The temperature dependence of the relaxation rate obtained for a rotor in a solid compound provides information on the correlation time sc [18]. It commonly has form of a maximum with slopes characterized by conditions x0sc 1 and x0sc 1, for high and low temperature sides, respectively. The respective dependence the relaxation rate on sc are as follows: 1/T1sc and 1/ T11/sc (2). Thus the slopes provide, usually the same, activation energy value. The relaxation rate maximum appears at a temperature where x0sc = 0.615 condition
is fulfilled , and with known Ea, s0 value is derived as the only adjustable parameter. That standard approach was used to analyze our results, but it leads here to a visualization of many, well distinguishable temperature ranges, characterized by different motional parameters (Table 1). The new features in relaxation, making CD4 in zeolites the special case, are related to their translational freedom. It evolves from free flight across cages at about 300 K to a very slow or no diffusion along walls of cages below 10 K. Rotors in the solid state experience a well defined potential, with a depth and symmetry resulting from interactions with surrounding ions or molecules. Combined translation and rotation of CD4 lead to a much less specified meaning of the apparent activation energy obtained experimentally. Data in Table 1 indicate that we have different values of the activation energy for different temperature ranges. Reorientations are detected by the relaxation method directly within the spectroscopic window. Translational motion influences the relaxation and the motional parameters indirectly. At temperatures above TTR the effective sc is very long and below TTR is very short compared to the Larmor precession period 1/x0. Above TTR most of molecules fly freely and their collisions introduce reorientations only by small angles. Below TTR most of molecules roll over, closer and closer to cages walls, what provides much more effective relaxation mechanism. One can point out that there is an activation energy common for all samples in the range b, and for higher filling also in the range b 0 . Molecules commute frequently enough between cages. Then above TNE, which is much lower for more than one molecule per cages, molecules become localized on the timescale of NMR and perform reorientations reflecting features of the surroundings. Single molecules (sample I) are located close to adsorption centers and their mobility is consistent with Ea = 1 kJ/mol. Moreover those in bcages experience some spatial limitations, which make their relaxation much less effective. The positions at adsorption centers can not be occupied long enough with more molecules in a-cages and the apparent activation energy is much lower. The related changes in Ea and the rotation angles after introducing more molecules are smaller for molecules in b-cages due to the smaller inner space.
5. Conclusion Several new features were observed in the relaxation rate of CD4 molecules in NaY zeolite. The molecule exhibit features of a quantum rotor at low temperatures. While these in a-cages are almost free rotors, molecules in b-cages exhibit effects of limited mobility. It is inter-
A.M. Korzeniowska et al. / Chemical Physics 311 (2005) 299–305
esting to compare observed relaxation rate with that obtained by de Wit and Bloom in solid CD4 [1]. The maximum of the spin–lattice relaxation time 8.2ms was measured at 4.4 MHz and 15 K. This value refers to spin–lattice relaxation rate 11.7 s1, when recalculated to our resonance frequency 46 MHz. This value comes close to the rate obtained for CD4 in b-cages and in terms of our approach it would give 2D = 18.5. It may indicate some spatial restrictions of molecular reorientation even in solid methane. That statement may be rather considered as an indication of an interesting subject than an unique conclusion. Fast exchange between cages leads to exponential relaxation at temperature above TNE. On temperature increasing further molecules acquire more kinetic energy and can fly across cages. Scattering on walls or other molecules seam to provide much less effective perturbation to the intramolecular spin interactions and the relaxation process. At a transition temperature TTR there is an abrupt change of relaxation conditions from x0sc 1 to x0sc 1. Also for a single D2 molecule in cages of NaY zeolite such transition was observed at TTR = 110 K [26]. That is related to a significant inefficiency of molecular collisions in relaxation, but conditions for such transition can not be specified yet.
Acknowledgments This project benefited a lot from many discussions of ZTL with Matti Punkkinen of Turku University. This project was supported, during 2002–2005, by the State Committee for Scientific Research Grant No. 2 P03B 135 23.
305
References [1] G.A. De Wit, M. Bloom, Can. J. Phys. 47 (1969) 1195. [2] S. Buchman, W.T. Vetterling, D. Candela, R.V. Pound, Phys. Rev. B 26 (1982) 4826. [3] A. Loewenstein, Chem. Phys. Lett. 38 (1976) 543. [4] J.G. Snijders, C.A. Lange, E.E. Burnell, J. Chem. Phys. 77 (1982) 5386. [5] P.A. Beckmann, M. Bloom, E.E. Burnell, J. Chem. Phys. 84 (1986) 5898. [6] J.H. Colwell, E.K. Gill, J.A. Morrison, J. Chem. Phys. 39 (1963) 3. [7] M. Prager, W. Press, B. Asmussen, J. Combet, Appl. Phys. A 74 (Suppl.) (2002) S1360. [8] H.M. James, T.A. Keenan, J. Chem. Phys. 31 (1959) 12. [9] T. Yamamoto, Y. Kataoka, K. Okada, J. Chem. Phys. 66 (1977) 2701. [10] W. Press, Single Particle Rotation in Molecular SolidsSpringer Tracts in Modern Physics, vol. 82, Springer, Berlin, 1981. [11] M. Bloom, F. Bridges, W.H. Hardy, Can. J. Phys. 45 (1967) 3533. [12] G.A. De Wit, M. Bloom, Can. J. Phys. 43 (1965) 986. [13] E.B. Wilson, J. Chem. Phys. 3 (1935) 276. [14] A. Birczyn´ski, Z.T. Lalowicz, Z. Łodziana, Chem. Phys. 299 (2004) 113. [15] M. Prager, A. Heidemann, Chem. Rev. 97 (1997) 2933. [16] L.P. Ingman, E. Koivula, Z.T. Lalowicz, M. Punkkinen, E.E. Ylinen, J. Chem. Phys. 88 (1988) 58. [17] D. Van der Putten, N.J. Trappeniers, Physica A 129 (1985) 302. [18] A. Abragam, The Principles of Nuclear Magnetism, New York, 1961. [19] L.P. Ingman, E. Koivula, M. Punkkinen, E.E. Ylinen, Z.T. Lalowicz, Physica B 162 (1990) 281. [20] H.C. Torrey, Phys. Rev. 92 (1953) 962. [21] P.S. Hubbard, Phys. Rev. 131 (1963) 275. [22] H. Pfeifer, Phys. Lett. C 26 (1976) 293. [23] Z.T. Lalowicz, Z. Naturforsch. A 43 (1988) 895. [24] B. Gil, O. Isfort, B. Boddenberg, D.E. Favre, B.F. Chmelka, F. Fujara, J. Chem. Phys. 116 (2002) 2184. [25] H.A. Resing, Advan. Mol. Relax. Processes 1 (1968) 109. [26] J.S. Blicharski, A. Gutsze, A.M. Korzeniowska, Z.T. Lalowicz, Z. Olejniczak, Appl. Magn. Reson. 27 (in print).
Mobility of CD4 molecules in nanoscale cages of zeolites as studied by deuteron NMR relaxation A.M. Korzeniowska a, Z.T. Lalowicz a
a,*
, A. Gutsze
b,z
H. Niewodniczan´ski Institute of Nuclear Physics of Polish Academy of Sciences, ul. Radzikowskiego 152, 31-342 Krako´w, Poland b Biophysics Department, Medical Academy, Bydgoszcz, Poland Received 15 October 2004; accepted 10 November 2004 Available online 8 December 2004
Abstract Deuteron spin–lattice relaxation was applied to study mobility of CD4 molecules trapped in the cages of zeolite NaY. There are two, interconnected sets of cages: a-cages and b-cages with 1.16 and 0.74 nm diameter, respectively. The relaxation temperature dependence, measured between 4 and 300 K, can be divided into four ranges with characteristic motional parameters. At higher temperatures exchange between cages dominates. Increasing rate of translational motion leads to a significant reduction of the relaxation rate. Features typical for quantum rotors were observed at low temperatures. Molecules in the a-cages exhibit reorientational freedom, while motion of these in b-cages is significantly restricted. Increasing abundance of molecules in b-cages indicates slow diffusion down to low temperatures. 2004 Elsevier B.V. All rights reserved.
1. Introduction Molecular dynamics studies were carried out by NMR methods in every state of matter. Moving from solid state through liquids to gases, apart from rotational dynamics, translational motion appears. Methane provides good example of such studies. Placing CD4 molecules in zeolite cages creates exceptional possibilities for research of rotational and translational dynamics. It is possible to choose cages different in size, surface properties and the level of filling. The basic issue of cognitive significance is observation of free rotors in wide range of temperatures. Both CH4 and CD4 were studied by NMR in the form of molecular crystals at low temperatures [1,2], dissolved in, e.g., liquid crystals [3,4], and in gaseous form at high temperatures. Deuteron relaxation of CD4 was * Corresponding author. Tel.: +48 12 6628 259; fax: +48 12 6628 458. E-mail address: [email protected] (Z.T. Lalowicz). Deceased author. z
0301-0104/$ - see front matter 2004 Elsevier B.V. All rights reserved. doi:10.1016/j.chemphys.2004.11.009
studied in gaseous and liquid state [5]. Molecular reorientations make the intramolecular spin interactions time dependent and provide the relaxation mechanism. Various models of reorientations produced by molecular collisions were considered ([5] and references therein). Liquid methane freezes into a molecular crystal phase I at 90 K, where molecules occupy fcc sites, but can rotate freely. At lower temperatures there is the next phase transition at 27 K for CD4, to the ordered fcc phase II. At 22.1 K, CD4 undergoes a transition to phase III, where all molecules are rotationally hindered [2,6,7]. Molecular field theory predicts phase transitions in methane by taking into account the electric octupole– octupole interaction as dominating intermolecular interaction [8,9]. A more thorough discussion can be found in the comprehensive review by Press [10]. No change in the relaxation rate was observed at the melting point for CD4, but there is a discontinuity at transition to phase II [1]. Correlation time sc, defined as a mean time between molecular jumps, can be derived from temperature
300
A.M. Korzeniowska et al. / Chemical Physics 311 (2005) 299–305
dependence of the spin–lattice relaxation rate . An exponential correlation function exp(jsj/sc) was assumed for molecular reorientations. Arrhenius relation sc ¼ s0 expðEkTa Þ allows us to obtain the activation energy Ea from the temperature dependence of the correlation time. However, in gaseous methane [11] and its solid phase below 15 K some more specific features appear [1]. In the former case collisions of free rotors play important role, in the latter case transition between low rotational levels introduced a temperature dependence of an apparent activation energy [1,12]. Generally, the spacing between rotational levels is large compared to the energy of anisotropic interactions between molecules being responsible for molecular reorientation. We aim to study deuteron spin–lattice relaxation for CD4 molecules isolated in nanoscale cages in zeolites. It provides an unique possibility to study dynamics of single free rotor in limited space and intermolecular interactions on increasing number of molecules. Then on decreasing temperature molecular collisions decay and molecules solidify on cage walls, subjected, apart from eventual intermolecular interactions, to interaction with adsorption centers. Our results differ significantly with respect to observation for CD4 gas and disagree with the prediction of the Debye rotation diffusion model [12].
2. Theoretical overview 2.1. Rotational levels of a tetrahedral molecule The orientational states of a molecule with tetrahedral symmetry, like CD4 and NDþ 4 , are labelled by irreducible representations A, T and E of Td symmetry group. The total wave functions, the product of space and spin wavefunctions, must transform according to the A representation. Therefore, for respective symmetry species only specified spin configurations with a total spin I are allowed: A(I = 0, 2, 4), 3T(I = 1, 1, 2, 3), E(I = 0, 2). The rotational levels of CD4 molecules associated with each spin species are as follows: A(J = 0, 3, 4, . . .), 3T(J = 1, 2, 3, 4, . . .), E(J = 2, 4, 5, . . .) [13]. The tunnelling splitting is defined as an energy difference between A(J = 0) and 3T(J = 1) state. The tunnelling splitting depends exponentially on the ratio V0/ B of the potential V0 and rotational constant B = h2/ 2I, where I is the molecular moment of inertia [14, and references therein]. Therefore, the tunnelling splitting for deuterated and protonated rotors may differ by a factor in the range 10–300 [15]. There are fast symmetry conserving vibrational transitions among rotational levels, which maintain their Boltzmann populations. Rotational dynamics of molecular rotors depends on the local potential. Deuterated rotors, when subjected a high potential, e.g. higher than 8 kJ/mol in the case of
NDþ 4 [14], perform classical reorientation at high temperatures and become immobile on the timescale of spin interactions at sufficiently low temperature. The tunnelling splitting, amounts, e.g., 7.5 MHz for NDþ 4 ions subjected to the potential 5 kJ/mol [16]. For diminishing potential the free rotor states are approached. The activation energy Ea = 0.83 kJ/mol was obtained in solid CD4 below 10 K [12]. As the activation energy we define the energy difference from the ground level to the top of a barrier and therefore V0 = Ea + E0, where E0 represents a zero point motion energy. In the case of CD4 in a very low potential we take rather the lowest rotational level energy. With the resulting V0 1 kJ/mol we estimate the tunnelling frequency to be about 15.7 GHz for CD4. It justifies considering only the lowest rotational levels (J = 0, 1) in the theory of relaxation for CD4 [17]. The tunnelling frequency falls down to 4.4 GHz for the potential V0 = 1.5 kJ/mol. 2.2. Spin–lattice relaxation The spin–lattice relaxation rate for CD4 can be written as the sum 1 1 1 1 ¼ þ inter þ SR T 1 T intra T T 1 1 1
ð1Þ
of contributions from intramolecular dipolar and quadrupolar interactions, intermolecular dipolar interactions and the spin–rotational interactions [1]. The quadrupolar interaction dominates in the intra terms and can be written as [18,19] 1 3 x2Q ¼ ½J ðx0 Þ þ 4J ð2x0 Þ, 40 x0 TQ 1
ð2Þ
where we define here the reduced density function as x0 sc J ðx0 Þ ¼ : 1 þ x20 s2c Such definition allows us to write down the relaxation rate at the maximum conditions x0sc = 0.615 as ! 1 3 x2Q ¼ ½1:425, ð3Þ 40 x0 TQ 1 max
which is the convenient formulation for comparing values measured at different frequencies. Assuming xQ = 2p Æ 1.68 Æ 105 s1 and x0 = 2p Æ 46 Æ 106 s1 we get ðT1Q Þmax ¼ 411 s1 . Such value can be anticipated 1 for a deuteron or CD4 molecule undergoing classical isotropic reorientation. Tunnelling splitting, i.e. considering a scheme of rotational energy levels, has several important consequences. The reduction of relaxation rate results from elimination of contribution to relaxation from numerous (xt ± nx0) transitions. Only ±nx0 (n = 1, 2) transitions due to motionally perturbed intramolecular spin interactions
A.M. Korzeniowska et al. / Chemical Physics 311 (2005) 299–305
contribute. As the spin interactions vanish for A and E species of CD4, relaxation appears only within T levels manifold. Additionally T symmetry species happen to be significantly more ordered. That may lead to differences in Ea values obtained by different methods. In the case of CD4 placed in such a weak potential of tetrahedral symmetry that xt x0, we have to introduce a reduction factor 7/18 [17,19], what leads to the relaxation rate ! 1 7 x2Q ¼ ½1:425 ¼ 160 s1 : ð4Þ 240 x TQ 0 1 max
Moreover, T levels may split up in a potential of lower symmetry and several specific structures can be considered. Calculations show, that for realistic potentials, the reduction factor between 0.33 and 0.85 may be expected. Therefore, the range of expectable relaxation rate values falls between 53 and 136 s1 for CD4 molecules as slightly hindered quantum rotors. Any further reduction of the relaxation rate must involve spatial limitations of molecular reorientations. An useful theory of relaxation was worked out for NDþ 4 ions undergoing limited jumps [19]. It was assumed that motion of N–D vectors is restricted to a cone with an opening angle 2D. The angle can be evaluated from the ratio of relaxation rates at the maxima for restricted motion Rrestr and for molecular reorientation Rreor Rrestr ¼ 3sin2 Dcos2 D: ð5Þ Rreor The intermolecular relaxation rate due to dipolar interaction requires special, model dependent treatment [18,20,21]. The model includes the modulation of the interaction via site-to-site translational jumps. Reorientation of molecules may contribute too, when these are ineffective. Both intra- and intermolecular dipolar interaction contributions to the relaxation are much smaller, by a factor about 105, than the quadrupolar contribution. Contribution from spin-rotational interaction may also be neglected in the case of CD4 [11]. Molecules placed in a heterogenous environment, such as zeolites cages, may exhibit a distribution of mobilities. Effects of the distribution of correlation times may be detected from relaxation and spectra. We consider a case where there are two sites characterized by different relaxation times T1a T1b. Assuming slow exchange between these regions the magnetization is expected to evolve on time as t t MðtÞ ¼ wa exp þ wb exp , ð6Þ T 1a T 1b
301
dition wsaa ¼ wsbb , relaxation appears to be exponential with an average relaxation rate 1 wa wb ¼ þ : ð7Þ T 1 AV T 1a T 1b Intermediate cases were also analyzed [22]. 2.3. Spectra Narrow lines were observed for solid CD4 and very little attention was devoted to their analysis. Features expectable in CD4 spectra will be discussed on the basis of theory outlined for NDþ 4 ions [16,23]. Spin species A, T and E contribute distinguishable components to the spectra. Intramolecular spin interactions (first order dipolar and quadrupolar) vanish for A spin species, which contribute therefore rather narrow central line. There exists, however, a doubled structure related to second order terms of the quadrupole interaction. The doublet separation is inversely proportional to the tunneling splitting and with values above 10 MHz it falls below the natural linewidth of about 1 kHz. The T species may contribute a central line with a width about 10 kHz and a flat background. That spectral component is subjected to motional narrowing.
3. Experimental
r¼
with weights wa + wb = 1, related to an abundance of the sites. In the limit of fast exchange, T1a sa, T1b sb, where sa and sb are mean life-times and equilibrium con-
3.1. Materials and methods A synthetic faujasite-type zeolite NaY with Si/Al = 2.4 was used. The sample of the zeolite has a form of powder, composed of small grains with diameter between 1 and 100 lm. There are two interconnected three-dimensional pore systems in the structure of the faujasite. Large a-cages have mean free diameter 1.16 nm, are arranged tetrahedrally and connected through windows of 0.74 nm diameter. Smaller b-cages have 0.6 nm diameter and are connected through hexagonal prisms. For comparison, CD4 molecule has 0.216 nm diameter. About 120 mg of the zeolite was placed in a 5 mm thin-wall glass tube and attached to an all steel high-vacuum device. The sample was heated in vacuum up to 673 K with a heating rate 50 K/h and kept at this temperature for 12 h under the vacuum p < 105 hPa. After cooling down the sample was loaded with the calibrated amount of CD4 and sealed. The NMR experiments were performed on a homebuilt pulse NMR spectrometer, operating on the 7.04 T/89 mm superconducting magnet and thus of deuteron resonance frequency 46 MHz. A low temperature NMR probe was placed inside the Oxford CF1200 continuous flow cryostat, and the temperature was regulated by the
A.M. Korzeniowska et al. / Chemical Physics 311 (2005) 299–305
Oxford CT503 Temperature Controller. The temperature accuracy and stability were within ±0.1 K in the whole temperature range. The spin–lattice relaxation time was measured by the saturation recovery method. An aperiodic 10-pulse saturating sequence was followed by 2 ls r.f. sensing pulse after a variable time delay. The amplitude of the magnetization, recovered during the delay, was determined by recording the free induction decay (FID). In order to achieve a satisfactory S/N ratio it was necessary to accumulate the signal due to a low concentration of CD4 molecules in the zeolite. After Fourier transformation of the FID, phase and baseline correction, the signal intensity was determined by integration of the whole spectral line. A typical number of delays determining the magnetization recovery curve was about 25, chosen in such a way that they uniformly covered the range from 0 to about 3T1 in the logarithmic scale. An additional data point was measured at a time much longer than 5T1, in order to determine precisely the equilibrium magnetization. This approach was found to improve the accuracy of the three-parameter single-exponential fit to the data.
c d 100
c' 1/T1[s-1]
302
10
d'
b a
1
0.1 0
10
20
30
40
50
60
70
80
90
100
110
1000/T [K-1]
Fig. 1. Temperature dependence of deuteron spin–lattice relaxation rate for sample I. The single time constant in the exponential relaxation range is depicted with (), short and long relaxing components are marked (m) and (,), respectively.
c 100
d c'
3.2. Samples We have selected here first three examples for presentation: 1. Sample I: one CD4 molecule per cage of NaY zeolite. 2. Sample II: four CD4 molecules per cage of NaY zeolite. 3. Sample III: four CD4 molecules per cage of NaY(NaBr) zeolite, where b-cages had been filled by NaBr.
1/T1 [s-1]
b' 10
d'
b 1
a
0.1 0
10
20
30
40
50
60
70
80
90
100
110
1000/T [K-1]
Fig. 2. Temperature dependence of deuteron spin–lattice relaxation rate for sample II. Symbols are used as in Fig. 1.
3.3. Results
c 100
b'
1/T1[s-1]
Measured spin–lattice relaxation rates are shown in Fig. 1–3, respectively. Continuous lines show fits using Eq. (1) with appropriate reduction factors explained in the following. Figs. 4 and 5 show the temperature dependence of weights wx(x = a,b) of respective time constants in the non-exponentiality range for samples I and II, respectively. Fig. 6 presents the half-width of the spectra for all samples. We divided the observed temperature dependence of the spin–lattice relaxation into ranges with common labels. The derived motional parameters: activation energy Ea and the pre-exponential factor s0, are compiled in the Table 1. Activation energies Ea were obtained from the slope in the range a under condition x0sc 1. At a transition temperature, labelled TTR, there is a turning point to the
10
b a
1
0,1 0
10
20
30
40
50
60
70
80
90
100
110
1000/T [K-1]
Fig. 3. Temperature dependence of deuteron spin–lattice relaxation rate for sample III. Symbols are used as in Fig. 1.
A.M. Korzeniowska et al. / Chemical Physics 311 (2005) 299–305 Table 1 Motional parameters: Ea (kJ/mol), s0 (s), T (K)
1.0 0.9 0.8
a TTR b
0.7 0.6
wa, wb
303
0.5
Sample I
Sample II
Sample III
Ea = 1.5 110 Ea = 2.7 s0 = 3.5 · 1013
Ea = 1.4 181 Ea = 2.6 s0 = 5.9 · 1011 Ea = 1.3 s0 = 1.5 · 1011 25 Ea = 0.4 s0 = 9.8 · 1010 Ea = 0.7 s0 = 1.3 · 1010 Ea = 0.008 Ea = 0.056
Ea = 0.76 166 Ea = 2.4 s0 = 1.6 · 1011 Ea = 1.5 s0 = 4.8 · 1012
b0
0.4
TNE c
0.3 0.2
c0
0.1 0.0 0
20
40
60
80
100
120
140
160
180
200
d d0
43 Ea = 1.2 s0 = 3.5 · 1011 Ea = 1.0 s0 = 6.1 · 1011 Ea = 0.3 Ea = 0.67
Ea = 0.4
1000/T [K-1]
Fig. 4. Temperature dependence of weights wa (m) of the fast relaxing component and wb (,) of the slow relaxing component for sample I (compare Fig. 1).
1.0 0.9 0.8 0.7
wa, wb
0.6 0.5 0.4 0.3 0.2 0.1 0.0 0
20
40
60
80
100
-1
1000/T [K ]
Fig. 5. Temperature dependence of weights wa (m) of the fast relaxing component and wb (,) of the slow relaxing component for sample II (compare Fig. 2).
2.0 1.8 1.6
range where the condition x0sc 1 was assumed. Relaxation process appears to be bi-exponential below a transition temperature TNE. The relaxation rate maxima are fitted using Eq. (2) with adjusted reduction factors. The maximum value in the range c correlates well with the value predicted by Eq. (4). The range c 0 shows reduced value of the relaxation rate, by a factor 10 in the case of sample I and a factor 5 in the case of sample II. Using Eq. (5) we may estimate the angle of the cone to be equal to 21.5 and 31, respectively. At lowest temperatures, the slope provides the activation energy under the condition x0sc 1. The spectra remain narrow down to the lowest temperature (Fig. 6). Their width (fwha) increases from about 0.1 kHz at high temperatures up to about 2 kHz at most. It indicates that intramolecular spin interactions do not contribute. We must consider therefore the intermolecular interactions between molecules or molecules and walls. While the broadening of spectra appears at about 70 K for samples II and III, it begins already at about 150 K for sample I. It may indicate that the contribution from interaction with walls dominates in the sample I, where molecules spend a time long enough at the walls. That is not possible due to molecular scattering in samples II and III.
h1/2[kHz]
1.4 1.2
4. Discussion
1.0 0.8 0.6 0.4 0.2 0.0 0
20
40 60 80 100 120 140 160 180 200 220 240 260 280 300
T [K]
Fig. 6. Temperature dependence of the half-width of the spectra (fwha), sample I (s), sample II (), and sample III (h).
Deuteron spin–lattice relaxation was found to be the very sensitive method providing information on dynamics of CD4 molecules in zeolite cages. Observed features depend both on shape and size of cages as well as the filling factor. We begin our analysis from the intermediate range of temperatures. The key point lays in explaining the cause of non-exponentiality. Results on sample III provide the solution. The b-cages are filled up by NaBr and thus
304
A.M. Korzeniowska et al. / Chemical Physics 311 (2005) 299–305
are not accessible for CD4 molecules. Absence of nonexponentiality allows us to conclude that relaxation rates in the range c 0 for samples I and II come from CD4 molecules trapped in b-cages. The maximum value of the relaxation rate in the range c indicates that it comes from quantum rotors subjected to a weak potential in a-cages. Mobility of CD4 molecules in b-cages appear to be significantly reduced due to spatial limitations. A slow exchange is the condition for observation of non-exponentiality and thus we conclude that diffusion of molecules between cages is slow below TNE. It is the a common feature for quantum rotors that at temperatures well below maxima, typically below 20 K, in d range here, the temperature dependence of the relaxation rate levels down. Thermally activated motions are ineffective in relaxation and incoherent tunnelling prevails. Very low values of apparent activation energy characterize this process. It was interesting to follow the temperature dependence of relative weights of the time constants. These show some temperature dependence in spite of the condition of slow exchange. Thus molecules may undergo slow translational motion along the walls of cages in a gradient of potential, as it was observed in case of benzene [24] and considered to be a general feature [25]. At higher temperatures abundance of a-cages prevails, while at lowest temperature most of CD4 are trapped in b-cages (Fig. 4 and 5). Non-exponentiality appears at TNE = 43 and 25 K for samples I and II, respectively. At these temperatures exchange of molecules between cages becomes slow enough for observing two relaxation rates. Single molecules in sample I achieve that condition at higher temperatures. These experience a stronger bonding to the walls, what results also in line-broadening at higher temperatures. Molecular scattering, appearing with more molecules per cage, shifts observation of both effects down to lower temperatures. Efficiency of the relaxation process is related to a modulation of intramolecular spin by molecular reorientations. Two factors can be pointed out in a simplified picture: amplitude of the perturbation introduced by a single jump and a correlation time, defined as a mean time separating jumps between symmetry positions. The temperature dependence of the relaxation rate obtained for a rotor in a solid compound provides information on the correlation time sc [18]. It commonly has form of a maximum with slopes characterized by conditions x0sc 1 and x0sc 1, for high and low temperature sides, respectively. The respective dependence the relaxation rate on sc are as follows: 1/T1sc and 1/ T11/sc (2). Thus the slopes provide, usually the same, activation energy value. The relaxation rate maximum appears at a temperature where x0sc = 0.615 condition
is fulfilled , and with known Ea, s0 value is derived as the only adjustable parameter. That standard approach was used to analyze our results, but it leads here to a visualization of many, well distinguishable temperature ranges, characterized by different motional parameters (Table 1). The new features in relaxation, making CD4 in zeolites the special case, are related to their translational freedom. It evolves from free flight across cages at about 300 K to a very slow or no diffusion along walls of cages below 10 K. Rotors in the solid state experience a well defined potential, with a depth and symmetry resulting from interactions with surrounding ions or molecules. Combined translation and rotation of CD4 lead to a much less specified meaning of the apparent activation energy obtained experimentally. Data in Table 1 indicate that we have different values of the activation energy for different temperature ranges. Reorientations are detected by the relaxation method directly within the spectroscopic window. Translational motion influences the relaxation and the motional parameters indirectly. At temperatures above TTR the effective sc is very long and below TTR is very short compared to the Larmor precession period 1/x0. Above TTR most of molecules fly freely and their collisions introduce reorientations only by small angles. Below TTR most of molecules roll over, closer and closer to cages walls, what provides much more effective relaxation mechanism. One can point out that there is an activation energy common for all samples in the range b, and for higher filling also in the range b 0 . Molecules commute frequently enough between cages. Then above TNE, which is much lower for more than one molecule per cages, molecules become localized on the timescale of NMR and perform reorientations reflecting features of the surroundings. Single molecules (sample I) are located close to adsorption centers and their mobility is consistent with Ea = 1 kJ/mol. Moreover those in bcages experience some spatial limitations, which make their relaxation much less effective. The positions at adsorption centers can not be occupied long enough with more molecules in a-cages and the apparent activation energy is much lower. The related changes in Ea and the rotation angles after introducing more molecules are smaller for molecules in b-cages due to the smaller inner space.
5. Conclusion Several new features were observed in the relaxation rate of CD4 molecules in NaY zeolite. The molecule exhibit features of a quantum rotor at low temperatures. While these in a-cages are almost free rotors, molecules in b-cages exhibit effects of limited mobility. It is inter-
A.M. Korzeniowska et al. / Chemical Physics 311 (2005) 299–305
esting to compare observed relaxation rate with that obtained by de Wit and Bloom in solid CD4 [1]. The maximum of the spin–lattice relaxation time 8.2ms was measured at 4.4 MHz and 15 K. This value refers to spin–lattice relaxation rate 11.7 s1, when recalculated to our resonance frequency 46 MHz. This value comes close to the rate obtained for CD4 in b-cages and in terms of our approach it would give 2D = 18.5. It may indicate some spatial restrictions of molecular reorientation even in solid methane. That statement may be rather considered as an indication of an interesting subject than an unique conclusion. Fast exchange between cages leads to exponential relaxation at temperature above TNE. On temperature increasing further molecules acquire more kinetic energy and can fly across cages. Scattering on walls or other molecules seam to provide much less effective perturbation to the intramolecular spin interactions and the relaxation process. At a transition temperature TTR there is an abrupt change of relaxation conditions from x0sc 1 to x0sc 1. Also for a single D2 molecule in cages of NaY zeolite such transition was observed at TTR = 110 K [26]. That is related to a significant inefficiency of molecular collisions in relaxation, but conditions for such transition can not be specified yet.
Acknowledgments This project benefited a lot from many discussions of ZTL with Matti Punkkinen of Turku University. This project was supported, during 2002–2005, by the State Committee for Scientific Research Grant No. 2 P03B 135 23.
305
References [1] G.A. De Wit, M. Bloom, Can. J. Phys. 47 (1969) 1195. [2] S. Buchman, W.T. Vetterling, D. Candela, R.V. Pound, Phys. Rev. B 26 (1982) 4826. [3] A. Loewenstein, Chem. Phys. Lett. 38 (1976) 543. [4] J.G. Snijders, C.A. Lange, E.E. Burnell, J. Chem. Phys. 77 (1982) 5386. [5] P.A. Beckmann, M. Bloom, E.E. Burnell, J. Chem. Phys. 84 (1986) 5898. [6] J.H. Colwell, E.K. Gill, J.A. Morrison, J. Chem. Phys. 39 (1963) 3. [7] M. Prager, W. Press, B. Asmussen, J. Combet, Appl. Phys. A 74 (Suppl.) (2002) S1360. [8] H.M. James, T.A. Keenan, J. Chem. Phys. 31 (1959) 12. [9] T. Yamamoto, Y. Kataoka, K. Okada, J. Chem. Phys. 66 (1977) 2701. [10] W. Press, Single Particle Rotation in Molecular SolidsSpringer Tracts in Modern Physics, vol. 82, Springer, Berlin, 1981. [11] M. Bloom, F. Bridges, W.H. Hardy, Can. J. Phys. 45 (1967) 3533. [12] G.A. De Wit, M. Bloom, Can. J. Phys. 43 (1965) 986. [13] E.B. Wilson, J. Chem. Phys. 3 (1935) 276. [14] A. Birczyn´ski, Z.T. Lalowicz, Z. Łodziana, Chem. Phys. 299 (2004) 113. [15] M. Prager, A. Heidemann, Chem. Rev. 97 (1997) 2933. [16] L.P. Ingman, E. Koivula, Z.T. Lalowicz, M. Punkkinen, E.E. Ylinen, J. Chem. Phys. 88 (1988) 58. [17] D. Van der Putten, N.J. Trappeniers, Physica A 129 (1985) 302. [18] A. Abragam, The Principles of Nuclear Magnetism, New York, 1961. [19] L.P. Ingman, E. Koivula, M. Punkkinen, E.E. Ylinen, Z.T. Lalowicz, Physica B 162 (1990) 281. [20] H.C. Torrey, Phys. Rev. 92 (1953) 962. [21] P.S. Hubbard, Phys. Rev. 131 (1963) 275. [22] H. Pfeifer, Phys. Lett. C 26 (1976) 293. [23] Z.T. Lalowicz, Z. Naturforsch. A 43 (1988) 895. [24] B. Gil, O. Isfort, B. Boddenberg, D.E. Favre, B.F. Chmelka, F. Fujara, J. Chem. Phys. 116 (2002) 2184. [25] H.A. Resing, Advan. Mol. Relax. Processes 1 (1968) 109. [26] J.S. Blicharski, A. Gutsze, A.M. Korzeniowska, Z.T. Lalowicz, Z. Olejniczak, Appl. Magn. Reson. 27 (in print).