Translational and Rotational Dynamics of Molecules Confined in

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Translational and Rotational Dynamics of Molecules Confined in Zeolite Nanocages by Means of Deuteron NMR Zdzislaw T. Lalowicz, Artur Birczynski, and Artur Krzy#ak J. Phys. Chem. C, Just Accepted Manuscript • DOI: 10.1021/acs.jpcc.7b06894 • Publication Date (Web): 03 Nov 2017 Downloaded from http://pubs.acs.org on November 7, 2017

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The Journal of Physical Chemistry

Translational and Rotational Dynamics of Molecules Confined in Zeolite Nanocages by Means of Deuteron NMR Z. T. Lalowicz,∗,† A. Birczyński,† and A. Krzy˙zak‡ †H. Niewodnicza´ nski Institute of Nuclear Physics PAS, ul. Radzikowskiego 152, 31-342 Kraków, Poland ‡Faculty of Mining and Geoengineering, AGH University of Science and Technology, al. Mickiewicza 30, 30-059 Kraków, Poland E-mail: [email protected] Phone: +48 12 6628259. Fax: +48 12 6628458

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Abstract The main aim of our approach is to gain a comprehensive view of mobility of small molecules in confinement as reported by 2 H NMR spectroscopy. The spectra and spin-lattice relaxation were measured in a wide range of temperature. A set of molecules: D2 , CD4 , D2 O, ND3 , CD3 OD and (CD3 )2 CO, was chosen and introduced into NaX and NaY zeolites. A wide range of loadings provides another dimension in studies of molecular mobility in confinement. Observed features reflect evolution on decreasing temperature of molecular dynamics from gaseous state over liquid-like rotational phase to immobilized molecules. Molecules become immobilized below the temperature TS , which appears to be an important parameter related to the strength of interactions with zeolite framework. For chosen zeolites NaX and NaY, hydrogen bonding and electrostatic interaction dominate, respectively. We restrict ourselves in reporting results above TS , as below molecular mobility is reduced to internal rotations when possible. The existence of D2 O clusters and trimers of CD3 OD gave particularly significant evidence for importance of their mutual interactions. A transition from translational to rotational mobility on decreasing temperature was a common observation, with transition temperature TT R as a significant parameter. Fast magnetization exchange between these two mobilities was considered as a model in analysis of the relaxation temperature dependence. We point out the effective value of the quadrupole coupling constant as justification for using the exchange model. A wealth of observed features proves particular sensitivity of 2 H NMR spectroscopy in studies of molecular dynamics.

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Introduction Duteron NMR spectroscopy was applied to study molecular reorientations at early eighties, and soon, with development of pulse methods, become irreplaceable. Pioneering contributions of Eckman and Vega 1,2 introduced dynamics of adsorbed molecules in zeolites as an interesting subject. Multinuclear NMR spectroscopy considers nuclei in zeolite framework and in adsorbed molecules and put emphasis on the basic point of interest: their mutual interactions. 3 Studies of molecular dynamics in zeolites lead us into that direction. Such studies, which followed, were aimed at understanding of molecular mobility in confinement, such as reorientations and diffusion, which are of basic importance for assessment of guest/host systems applicability for molecular separation, catalysis, adsorbtion and finding new functional materials. Choice of molecules for studies of mobility in zeolites is usually related to their important role in catalysis and separation of hydrocarbons. Topics of numerous publications of A. Stepanov and collaborators follow that principle. For example mobility of iso-butyl alcohol in H-ZSM-5 was studied by 2 H NMR spectroscopy at 115–293 K. 4 References in there may guide over related publications on dynamics of aromatic molecules, alcohols, olefins and alcanes in confinement. Studies of dynamics of n-hexane in silicalite 5 and isobutene in ZSM-5 6 show ways to disentangle intramolecular rotations and large amplitude reorientations of molecules as a whole. No direct effects of translational mobility were observed in NMR, however that aspect of research belongs to main topics of this contribution. Quasielastic neutron scattering (QENS) was used to fill that gap. It was shown how 2 H NMR and QENS methods complement each other in building up a detailed picture of benzene-d6 rotational and translational mobility in MOF 7 and ZIF-8. 8 Translational jump diffusion between neighboring cages was characterized by activation energy 27 kJ/mol and 38 kJ/mol, respectively. QENS was applied to study diffusion of water in zeolites NaX and NaY. 9 Activation energies were found decreasing on increasing loading, alternatively diffusion coefficients were 3



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found increasing on increasing loading and temperature. That makes the view of diffusion process on microscopic scale more detailed. Pulsed field gradient nuclear magnetic resonance (PFG NMR), QENS and MD simulations provide values of diffusion coefficients remarkably consistent. 9 A stepwise increase of self-diffusion coefficient of ammonia in H-ZSM-5 obtained with PFG NMR was correlated with the interaction between ammonia and the limited number of acid sites. 10 Deep insight into PFG NMR technique along with numerous important results can be found in the book. 11 Recent application of deuteron NMR spectroscopy in studies of slow and fast librational motion. covering broad rnage of time scale 103 –10−11 s, confirms in a remarkable way capabilities of the technique. 12 Recent review articles confirm the continuous importance of porous media and their applications. Buntkowsky et al. 13 outlined the applicability of NMR techniques (15 N and 2 H spectroscopy, MAS NMR, NMR diffusometry) for studies of molecular mobility in confinement, pointing out a wealth of involved interactions. Some more concepts were summarized in a more recent review from the same group. 14 NMR-crystallography, isotopically-labelled materials, NMR spectra of paramagnetic microporous materials and other methods discussed in Ref., 15 may guide studies of substrates. Moreover, mesoporous silica materials with large surface areas and uniform pore distribution constitute model systems which have been investigated by various 1 H NMR techniques. Gr¨ unberg et al. 16 studied MCM-41 and SBA-15 samples with a variable water filling of mesopores by 1 H MAS NMR. They attributed observed differences in the spectra to distinct mechanisms of pore filling. D’Agostino et al. 17 and Krzy˙zak et al. 18 applied High Field and Low Field 1 H NMR relaxometry, and found the correlation between the T1 /T2 ratio and a maximum activation energy of desorption, which yields information about water-surface interaction strength. Different adsorption properties, e.g. of polar and nonpolar molecules, were studied by means of field cycling relaxometry. 19 Discrimination was based on the shape of relaxation dispersion curve, steep or flat, respectively. The majority of measurements were performed

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for protons, however suitable properties of deuterons were pointed out. 20 Frequency dependence of the spin-lattice relaxation time is strongly determined by adsorption properties. Quantitative analysis considers Lévy-walks involving consecutive steps in molecule displacement: desorption, fast diffusion within the bulk liquid, and readsorption at another location on the surface. 21 Water diffusivity and velocity, adsorption depth are among derived parameters. 20 Methods for the determination of the pore-size distribution, based on size-dependent reduction of the adsorbate freezing temperature, were proposed. 22–24 Usage of deuterated adsorbates was found particularly reliable. 25 Porous media fully filled with selected liquids were the subject of studies, mentioned above and selected from numerous contributions. Zeolites are porous inorganic crystals, basically with the atomic formula TO4 , where the shared oxygens are arranged tetrahedrally around the central atom T, where T represents silicon or aluminum atoms. Zeolites NaX and NaY have a well-defined pore system. Their unit cell consists of eight supercages and eight sodalite cages. The supercages of 1.16 nm inner diameter are interconnected by 12-oxygen rings of 0.74 nm diameter. The smaller sodalite cages of inner diameter 0.66 nm are connected to supercages by 6-oxygen rings. 26 The compositions of typical zeolites NaX and NaY are Na86 [(SiO2 )106 (AlO2 )86 ] and Na56 [(SiO2 )136 (AlO2 )56 ], respectively. The ratio of Si/Al amounts to 1.3 for zeolite NaX and 2.4 for NaY. Chosen zeolites allow to take advantage of differences in bonding of molecules. Due to the higher density of AlO− 4 in zeolite NaX the framework oxygen atoms are more negative. Therefore hydrogen bonding of molecular deuterons is relatively stronger. The electrical charge on sodium cations is practically neutralized by oxygen atoms. The degree of neutralization is smaller in NaY and the electrical charge is higher. 27 The interaction of a free electron pair with the more positive charge of sodium cation is stronger than in NaX. For example, hydrogen bonding of methanol plays more important role in NaX. 28 We develop and follow application of 2 H NMR spectroscopy methods outlined before. 29 Translational mobility related features are detected as a set of small molecules was chosen.

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Shape of motionally averaged spectra displays features related to molecular mobility. Observed Lorentzian or Gaussian shapes refer to temperature ranges with translational freedom or restricted mobility, respectively. Width and contributions are followed in temperature dependence of spectra. Most of the attention is devoted here to analysis of the spin-lattice relaxation. Conditions for the application of the exchange model 30 are specifed. Evolution of translational and rotational mobilities is the main target. Data for D2 O 29 are reanalysed and summarized together with complementary new results. We extend our approach to ammonia, methanol and acetone at low loadings. We restrict ourselves to the range above that temperature where molecules become localized, which is significantly lower than the freezing temperature for filled pores. For the latter systems T1 /T2 ratio at a given temperature was considered as meaningful parameter for e.g. water in mesoporous silicas. 17 In spite of basic differences, such as proton versus deuteron NMR, filling factor and size of pores, we took T1 /T2 ratio into consideration. Parameters collected in Tables allow to make a judgement about their sensitivity to molecular mobility. Examination of e.g. activation energy for different zeolites and loadings indicates dominating interaction.

Theory Deuteron NMR is particularly suitable for the investigation of molecular mobility for a number of reasons. First, the quadrupole coupling constant is two orders of magnitude larger than the dipole-dipole coupling constant for protons. Second, the value of the quadrupole coupling constant depends on deuteron location and may provide information on the local structure and bonding. Third and most importantly, since the quadrupole coupling involves only one spin, information on molecular reorientation is not affected by the presence of neighboring nuclei. Therefore, motional averaging of the quadrupole interaction allows the clear discrimination between possible motional models. 31 Deuteron NMR obsevables are void

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of paramagnetic species influence. Molecular reorientations, rendering the intramolecular quadrupole interaction time-dependent and inducing transitions between nuclear Zeeman levels, drive the deuteron NMR relaxation. The spin-lattice relaxation rate is given as a linear combination of spectral density functions weighted by the coefficient A = (3/10)π 2CQ2 , where quadrupolar coupling constant CQ = e2 qQ/h. For reorientations characterized by the exponential autocorrelation function with a single correlation time τc , the spin-lattice relaxation rate constant is given by: 32

R1 =

1 = A [J(τc , ω0 ) + 4J(τc , 2ω0)] , T1

(1)

where J(τc , ω0 ) = τc /(1 + τc2 ω02 ) is the spectral density function, being the Fourier transform of the autocorrelation function, with ω0 /2π equal to the Larmor frequency. The correlation time τc is assumed to follow the Arrhenius formula τc = τ0 exp(Ea /kT ) with the activation energy Ea . The temperature dependence of the relaxation rate has an inverted V shape with the maximum at temperature fulfilling the condition ω0 τc = 0.616, which leads to

1 T1

= 1.425

max

A . ω0

(2)

Fast motions, obeying ω0 τc ≪ 1, contribute to the high temperature side of the maximum, while the low temperature side represents the relation ω0 τc ≫ 1. The slopes, in some cases unequal, provide the value of the activation energy Ea . Moreover, the value of τ0 and CQ can be calculated from the known position of the maximum and its absolute value. For reasons explained below, we will call the quadrupole coupling constant derived on this way as the effective one CQef f . In the following a spin system will be assumed to consist of two subsystems characterized by siginficantly different mobilities with intrinsic relaxation rates R1′ (rotation) and R1′′ (translational), respectively. At the limit of the fast magnetization exchange between the subsystems a single relaxation rate can be observed: 30

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R1 = W R1′ + (1 − W )R1′′ ,

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(3)

where W depends on relative abundances of molecules in both subsystems, and R1′ and R1′′ are expressed by eq 1, however for different correlation times. A eq 3 is valid for T > TS . Temperature TS by definition separates two ranges with different mobility. Down to TS high mobility of molecules takes place and narrow spectra observed. Below TS a substantial, step-wise broadening of deuteron spectra appears, and magnetization recovery becomes nonexponential, 33 as moelcules are localized at fixed positions. Generally, NMR spectra are sensitive to molecular reorientations on the NMR time scale, 34,35 which is reflected in the condition for the narrowing of spectra expressed as δτc ∼ 1, where δ is the width of a given spectrum and τc is the temperature-dependent correlation time. For a typical width of a deuteron spectrum, δ = 135 kHz for CQ = 180 kHz, the condition δτc ∼ 1 leads to the correlation time τc ≈ 10−6 s. For τc ≫ 10−6 s deuterons are considered to be immobile and the Pake doublet is observed. The doublet separation equals (3/4)CQ, which can be used to provide the value of the quadrupole coupling constant. Narrowed spectra result for τc ≪ 10−6 s. Deuteron NMR spectra are inhomogenous 36 and consist of the doublets covering the whole spectral range. The doublets undergo motional narrowing sequentially at somewhat different temperatures for differently oriented deuterons. For example, deuteron NMR spectra of polycrystalline ND4 VO3 measured between 60 K and 83 K were found to be sensitive to correlation frequencies in the range 210 kHz to 1 kHz (corresponding to correlation times in the range 7.6 × 10−7 s ≤ τc ≤ 1.6 × 10−4 s). 37 This result shows that the range of molecular mobilities, where the spectra can be considered to be in the intermediate narrowing regime, is quite broad. 16,38

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Experimental Section Zeolites NaX (supplied by Sigma–Aldrich) and NaY (purchased from Linde company) were activated in situ in an NMR cell. First, the samples were evacuated at room temperature for 30 min, then temperature was raised with the rate 5 K/min up to 700 K and kept at this temperature in vacuum for 1 h. The doses of selected compounds were sorbed in zeolites NaX and NaY up to e.g. 100% of the total coverage of Na+ ions. The samples were sealed in 24 mm long glass tubes with the outside diameter 5 mm. The NMR experiments were carried out over a range of temperatures regulated by the Oxford Instruments CT503 Temperature Controller to the accuracy of ±0.1 K. The static magnetic field 7 T was created by the superconducting magnet made by Magnex, and the 2 H resonance frequency was equal to 46 MHz. The NMR probe was mounted inside the Oxford Instruments CF1200 Continuous Flow Cryostat. Pulse formation and data acquisition were provided by Tecmag Apollo 500 NMR console. The dwell time was set to 2 µs. The π/2 pulse equal to 3 µs assured the uniform excitation 39 for our 200 kHz spectra. NMR spectra were obtained by the Fourier Transformation of the free induction decay (FID) or quadrupole echo (QE) signal for narrow and broad ones, respectively. For the wide spectra the sequence (π/2)x —τ —(π/2)y —t with separation time τ of the order of 50 µs was used. The pulse separation time τ was adjusted by means of the home-designed code for Tecmag console in order to optimize QE signal intensity for each temperature. The phase cycling sequence was applied and focused on the FID signal cancellation in the overall signal after the QE sequence. Temperature defined as TS separates two commonly observed ranges. Above TS narrow spectra are measured with FID. Alternatively broad spectra below TS are measured with QE sequence. Molecules become localized at TS and its value indicates the value of the binding strength to zeolite framework. 33

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Results and discussion Nuclear magnetic resonance provides the means to study molecular dynamics in every state of matter. Molecules in confinement exemplify a particularly rewarding system, as with a single sample we may observe on increasing temperature immobilized molecules, then the onset of molecular reorientation and, in some cases, translational diffusion. We selected a set of molecules with diverse properties leading to a wealth of specific features in mobility. We restrict ourselves to NaX and NaY zeolites and have a common environment in terms of size and structure of nanocages.

D2 and CD4 Spin-lattice relaxation rate was measured for zeolite NaY with one D2 molecule per supercage in the range 66–310 K. The theory of deuteron spin-latice relaxation for free D2 quantum rotators was developed leading to sucessful fits. 40 Relaxation rates were calculated for orthoand para-D2 . The spin-rotational interaction as well as quadrupole and dipole-dipole interactions under interference condition were taken into account. Relaxation rates were derived as weighted sums of contributions from rotational states according to their Boltzmann population. In the result the observed relaxation rates at high temperature range were surpassing values defined by the quadrupole coupling constant, and this was an unique case. The low temperature slope of the relaxation rate was observed at temperature above 110 K, indicating ω0 τc ≫ 1 condition, thus long correlation times. Molecules diffuse freely in the space of cages. Only collisions, among them and with cage walls, change their orientation. Many collisions are necessary to provide an effective relaxation mechanism and therefore effective correlation times are relatively long. Below 110 K molecules stay close to the surface of cages and undergo reorientation in a surface mediated diffusion. Displacement on the surface was commonly observed before and termed ”reorientations mediated by translational displacements” (RMTD). 41 Effective correlation time decreases by about three orders of magnitude

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in a stepwise manner. The spin-lattice relaxation rate was measured for CD4 molecules with 4 molecules per supercage in zeolites HY, NaA and NaMord in the range 10–310 K. 42 The transition from translational to rotational mechanism of relaxation was observed at 150 K for HY and at about 200 K for NaA and NaMord zeolites. Also for CD4 basic features in relaxation are related to quantum effects for free rotators. The theory was fitted in all cases with somewhat different parameters. We report here about HY sample only for consistency with the principle of common environment. The relaxation rate depends strongly on the rotational states of CD4 . These are labelled by the irreducible representations A, T and E of the tetrahedral point group. The symmetry of the total wave functions, being a product of the rotational and spin functions, requires a population of rotational states with selective spin isomers A, T and E. Expressions were derived for relaxation rates of magnetizations MT and MAE via the intra- and intermolecular quadrupole couplings. Exchange between two locations averages the relaxation rates within the symmetry species. Moreover the spin conversion transitions couple the relaxation of MT nad MAE . Two relaxation rates with two maxima in each case were explained with these postulates. Incoherent tunnelling was attributed to relaxation rates below 15 K.

Water D2 O The methods applied here in the analysis of deuteron NMR data, obtained for water molecules in confinement, were developed and described before. 29 Some of previous results, supplemented by additional measurements, are summarized in Table 1. The effective quadrupole coupling constant CQef f is a fraction of the static value which amounts 260 kHz. 29 Two Gaussian components in the spectra were observed in majority of cases. Eventual Lorentzian line at high temperature was considered as a fingerprint of efficient translational motion. 29 Contributions of Gaussians change on decreasing temperature, that of narrower 11



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Table 1: Water D2 O. Sample (Si/Al) loading NaX (1.3) 100% NaY (1.8) 100% NaY (2.4) 100% NaX (1.3) 200% NaY (2.4) 200% NaX (1.3) 300% NaY (1.8) 300% NaY (2.4) 300% NaX (1.3) 500% NaY (2.4) 500%

T1 /T2 14.8 42.4 36.5 5.9 9.3 24.1 10.3 8.0 24.4 16.0

DY 100%

37.5

245.0

200.0

DY 500%

22.8

240.0

205.0

T50 [K] TS [K] 245.0 220.0 311.0 235.0 305.0 225.0 293.0 215.0 232.5 220.0 305.0 233.0 260.0 210.0 235.0 205.0 294.0 227.0 250.0 218.0

CQef f

[kHz] 143.3 241.2 87.8 139.9 162.2 136.1 139.4 149.4 133.0 153.7 98.6 148.6

153.3 180.0

Ea [kJ/mol] R1 R1′ 18.6 18.6 9.0 14.0 9.8 13.5 18.4 18.4 29.1 29.0 11.4 13.0 14.3 14.0 23.3 23.0 11.0 13.0 31.7 LT 31.5 LT 36.5 HT 36.5 HT 23.0 LT 23.0 LT 9.8 HT 23.5 LT 23.0 LT 18.0 HT 18.0 HT

R1′′ W ≥ 37.0 0.30 30.0 0.75 ≥ 37.0 0.115 ≥ 37.0 0.30 ≥ 42.0 0.40 ≥ 37.0 0.30 ≥ 40.0 0.28 ≥ 34.0 0.33 ≥ 37.0 0.27 ≥ 46.0 0.35 LT ≥ 46.0 0.15 HT ≥ 37.0 0.32 ≥ 40.0 0.35 LT ≥ 40.0 0.30 HT

one is decreasing. Temperature T50 , where their contributions are equal, was proposed as a significant parameter related to the adsorption strength; higher when T50 is higher. T50 is higher for NaY zeolite at 100% loading as expected for relatively stronger bonding to sodium cations. However, that scheme brakes down due to cluster formation at higher loadings. Certain correlation may be seen between T1 /T2 and T50 , but we leave that aspect for a further study. Values of TS seam to be not sensitive either to zeolite type or to loading. There is thus no preference in location of water molecules on the framework for hydrogen bonding to oxygens and bonding to sodium cations. Considerable attention has been given to the spin-spin relaxation rate R2 in the previous study. 29 The aim was, as in other ways of data analysis, to determine activation energy as a useful parameter. Moreover, in more quantitative terms, the relaxation rate R2 offers susceptibility to fine changes in mobility. Temperature dependence of R2 reflects evolution of water dynamics, depending on Si/Al ratio and loading. Effects due to reduced translational mobility are most significant, and related to formation of water clusters. The hysteresis 12


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observed in both relaxation rates at high loadings, may be attributed to decomposition into smaller clusters with higher mobility at a temperature that is higher than the temperature required for the stable cluster formation. Cluster formation leads to a step in the spin-lattice relaxation rate, and the exchange model procedure was applied separately. Therefore results above and below it are labelled as HT and LT, respectively (Table 1). The rotation of water molecules may be executed by tetrahedral jumps between inversion related orientations, proposed as responsible for effects observed in low temperature spectra. 33 As the representative example of the exchange model we show results for NaY (1.8) with 300% loading (Figure 1). 1000

R’’ 1

-1

relaxation rates [s ]

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R’1

100

3

4

5

-1

1000/T [K ]

Figure 1: Temperature dependence of deuteron spin-lattice relaxation rate for NaY (1.8) sample with 300% loading of D2 O (◦). Relaxation rate R1 (eq 3) with W = 0.28 is shown with the dashed line. Rotational dynamics dominates in the experimental range. Activation energies obtained with R1 and R1 are identical in this case or comparable in other cases (Table 1). Fitting the experimental data with R1 is possible with highly reduced quadrupole coupling constant CQef f = 149.4 kHz. Various values obtained for other cases cover a wide range. We take it as a fingerprint of an otherwise hidden translational mobility. We take CQ = 260 kHz for relaxation rates R1′ and R1′′ and succesfully fit the experimental results with R1 (Figure 1). To our best knowledge only exchange model may explain versatile values of CQef f . High activation energies characterizing R1′′ relaxation rates indicate highly reduced efficiency of 13



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translational mobility in relaxation as related weighting factor is high (Table 1). All that makes water in cationic zeolites a special case. Bonding to the framework at low loading, then formation of clusters on increasing loading are the specific features of water in confinement.

Ammonia ND3 Deuteron NMR spectra and spin-lattice relaxation were measured for the set of zeolites and loadings listed in Table 2. √ Spectra consist of two Gaussian components, with the shape defined by 1/(σ 2π) exp(−(ν− ν0 )2 /(2σ 2 )), with different width in majority of cases. Linear dependence of their width h(FWHA) = 2(2 ln 2)−1/2 σ in function of 1000/T indicates Arrhenius process, where the slope defines the activation energy. In some cases two different values were obtained at higher and lower temperatures for narrow and broad Gaussians, respectively (Table 2). Lorentzian components, observed in some cases at highest temperature, indicate the dominating role of translational mobility. The quadrupole constant for ND3 was estimated to be 217.5 kHz, 45 or in the range 221.1– 239.1 kHz. 43 We take 228 kHz as a common value on the basis of our study of spectra at low temperature. As the representative example we take the spin-lattice relaxation results for NaY with 300% loading (Figure 2). Three-fold rotation of ammonia reduces the quadrupole coupling constant to 76 kHz. The final fit with eq 3 indicates on molecular jumps between two dynamic states described by the relaxation rate R1′ with parameters τ0′ = 2.5·10−12 s, Ea′ = 5.0 kJ/mol, and R1′′ with τ0′′ = 2.0 · 10−11 s, Ea′′ = 10.0 kJ/mol. The final fit was obtained for W = 0.72. Activation energies are siginificantly lower than in the case of D2 O and the relaxation rate R1′′ appears in the experimental range of temperature. The weighting factor W = 0.7 reveals the dominating role of reorientations over translational mobility in all cases (Table 2). F. Gilles in a scarce paper on ND3 mobility by NMR postulated translational jumps 14


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100 -1


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R’’ 1

R’1

10

1

3

4

5 6 -1 1000/T [K ]

7

8

Figure 2: Temperature dependence of deuteron spin-lattice relaxation rate for NaY sample with 300% loading of ND3 (◦). Relaxation rate R1 (eq 3) with W = 0.72 (dashed line). Table 2: Ammonia ND3 . Sample (Si/Al) loading NaX (1.3) 100% NaX (1.3) 300% NaY (2.4) 100% NaY (2.4) 300% DX 100% DX 200% DY 100% DY 200%

T1 /T2 T50 [K] TS [K] CQef f [kHz] 197.9 > 260 200.0 107.3 270 210.5 41.7 250 195.0 17.5 190 140.0 41.5 509.1 265.0 1272.5 42.1 170.0 60.4 442.2 216.0 1243.8 18.7 135.0 70.9

Ea [kJ/mol] h R1 narrow broad 14.5 11.0 19.1 14.5 7.9 22.1 21.4 10.1 10.4 10.4 16.2 1.5 1.0

R1′ 3.9 3.2 5.8 5.0 -

R1′′ 14.0 12.7 15.2 10.0 -

W 0.70 0.70 0.70 0.72 -

9.4 6.3

9.0 0.1

4.2 0.1

6.0 -

8.0 -

0.25 -

9.2

7.6

2.9

8.0 11.0 0.20

between adsorption centers in cationic zeolites. 43 Ammonia molecules interact with the counter-ions via their nitrogen and deuterons may be involved in hydrogen bonds to the framework oxygens. 44 Both interactions will be considered in analysis of results below. Activation energy of ammonia rotations is directly related to the strength of the hydrogen bond of molecular deuteron with a framework oxygen (Figure 2 in Ref. 43 ). More restricted mobility of ammonia was detected in DY. Application of QE sequence

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32 K

292.2 K -50

0

50 ν [kHz]

100

150

Figure 3: Deuteron spectrum of ammonia confined in DY zeolite at 100% ND3 loading. Spectral components resulting from the numerical decomposition of the total spectra are shown. was necessary to receive deuteron spectra already at about 300 K. The spectrum obtained at 292.2 K consists of well defined components (Figure 3). Two narrow Gaussian lines dominate with contributions 40% and 28% and width h = 7.1 kHz and 21.2 kHz, respectively. The doublet with contribution 10% comes from ND3 undergoing uniaxial rotation. Contributions of the doublet and the broad component are more clearly seen at 32 K (Figure 3) with contribution 18% and 64%, respectively. It allows a better recognization of the broad component shape. Its shape was reproduced using WEBLAB package 46 for localized ammonia performing torsional jumps with 56◦ amplitude about the 3-fold axis. The structure with ammonia nitrogen at the framework deuterium may be seen as the 16


Page 17 of 36

formation of a quasi-ammonium ion. Such singly bonded state 49,50 allows free 3-fold rotation of ammonia. Triply bonded structure (Figure 6c in Ref. 49 ) refer to localized, performing torsional oscillations ammonia in a high potential with the 3-fold symmetry. We are tempted in this case to discuss mobility also below TS . Lowering of temperature leads to dfferent evolution of contributions of the spectral components (Figure 4). There is seen basically transfer from Gaussian to broader components. Below about 100 K contribution of rotating ammonia stays constant, but contribution of those performing torsional oscillation increases and dominates. Broad Gaussian component with a contribution about 7% is there down to lowest temperature. The component attributed to tunnelling ammonia was found below 20 K with the shape calculated before. 51 1

contribution

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


0.1

TS 0.01 10

20 30 -1 1000/T [K ]

40

Figure 4: Temperature dependence of the contributions of the following spectral components of ammonia confined in DY zeolite at 100% ND3 loading: () Pake doublet, (•) C3 rotation, (∗) torsional, (H) narrow Gaussian, (△) broad Gaussian. The spin-lattice relaxation for DY with 100% loading was also measured using QE sequence (Figure 5). Two time constants above TS , the smaller with weight 68% may be attributed to mobile molecules (Gaussians), and the bigger one to rotating ND3 . Below TS = 216 K we show results for localized molecules in DY as an example of a common feature for all cases of molecules in confinement. The characteristic three time constants, spanned over three orders of magnitude, indicate a wide distribution of correlation times.

17



The conclusion is based on the theoretical procedure worked out before. 47,48 The main contribution to relaxation comes from the 3-fold rotation of localized ammonia. On shorter correlation time side dominate more freely moving ammonia contributing to Gaussian components. Alternatively at long correlation time range one may expect a contribution from torsional oscillations about the 3-fold axis. Motionless ammonia (Pake doublet) do not contribute to the relaxation. 100

-1


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10

1

TS 0.1 3

4

5 -1 1000/T [K ]

6

Figure 5: Temperature dependence of deuteron spin-lattice relaxation rate for DY sample with 100% loading of ND3 . The electrical charge of Na+ in NaY is higher and bonding of nitrogen is stronger than in NaX. Activation energies from R1′′ (Table 2) do not confirm that relation as interaction of molecules with zeolite framework has no effect on translational mobility. On the other hand however, inspection of TS temperatures corroborate the importance of N-Na+ interaction. Also activation energies from R1′ clearly point out N-Na+ interaction influence on rotational mobility. The ratio T1 /T2 was taken from results at room temperature with 1/T2 = h(ln 2)−1/2 /4. The ratio depends strongly on the width of Gaussian spectra as for T1 similar values were found for different loadings. Isotropic reorientation leads to narrow spectra as, by definition, intramolecular spin interactions are averaged out. Increased width may result from reduced efficiency of reorientations due to collisions of freely reorienting molecules with zeolite cage 18


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walls, and their mutual collisions at higher loading. Thus high values of the ratio provide an evidence for the scale of limited mobility. Higher values of the ratio and higher temperatures of T50 indicate stronger effect of collisions for NaX compared to NaY (Table 2). At low loadings, where N-Na+ interaction may be perturbed via collisions, higher activation energies were obtained for NaY from spectra and relaxation. Activation energies are lower for higher loadings due to mutual collisions. The loading plays even more important role which is reflected in ammonia mobility. The mobility at low loadings is highly reduced and diversified in DY an DX. Mutual collisions play an important role at high loadings, leading to effects in spectra and relaxation similar to observed for cationic zeolites: narrow spectra and one time constant in relaxation. Activation energies for translational and rotational mobility are relatively closer to each other for DY and DX at 200% loading. It is worth pointing out that W parameter indicates dominating role of translational mobility, while for cationic zeolites rotational mobility prevails.

Methanol CD3OD As a key example we take NaY zeolite with 100% loading. Two time constants are observed in the temperature dependence of the spin-lattice relaxation (Figure 6). The faster relaxation rate was fitted with eq 1 and coefficient CQef f = 142.6 kHz, being closed to values attributed to CD3 and OD. 28 At about 260 K its contribution comes to zero from about 25% at highest temperature.The slower relaxation rate, characterized by CQef f = 28.3 kHz is dominating down to TSs = 215 K. At this point spectrum broadens significantly, indicating immobilization of all molecules. While the fast relaxation rate refers to localized methanol molecule with rotating CD3 and OD, the slower relaxation rate is attributed to molecules performing reorientation with internal rotation of CD3 and OD. The motional reduced quadrupole constant is equal to 53.3 kHz, while CQef f = 28.3 kHz. Thus application of the exchange model is necessary. The resulting fit is shown in Figure 6 and obtained parameters are found in Table 3. 19



f

TS -1


1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

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100

R’1

10

s

1

TS

R’’ 1 3

4

5

-1

1000/T [K ]

Figure 6: Temperature dependence of deuteron spin-lattice relaxation rate for NaY sample with 100% loading of CD3 OD. Symbols △, and ▽, refer to fast and slow relaxation rates, respectively. Relaxation rate R1 (eq 3) resulting from the exchange model, with dashed line. In the case of NaX with 100% loading the TSf temperature is lower than for NaY and equals 190 K, 28 thus the binding energy is lower. Activation energy is also significantly lower. From the relation between binding energies we may point out the location of methanol molecules with oxygens at Na+ cations, as their electrical charge is higher in NaY compared to NaX. Thus the first adsorption layer consists of molecules at so called horizontal position. 28 The conclusion directs us to an explanation of observed relaxation rates based on a common view of molecular mobility. A fraction of methanol molecules face a reduced mobility in a sort of a first adsorption layer in the vicinity of Na+ cations. The fast relaxation rate, with high CQef f value, is driven by rotating OD and CD3 groups in absence of any overall mobility. The slower relaxation rate refers to majority of molecules moving freely in the space of cages, performing isotropic reorientations accompanyed with internal fast rotations of both OD and CD3 . There are two components in the spectra for the NaY sample with 100% loading of CD3 OD, narrow and broader, referred to as N and B in Table 3, respectively. Contributions of the narrow and broader components amount to about 40% and 60% at higher temperatures. The contribution of the broader component increases significantly below TSf = 260 K. The width of the narrow component does not change significantly in the whole range of 20


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Table 3: Methanol CD3 OD. Sample (Si/Al) loading NaX (1.3) 100% NaY (2.4) 100% NaX (1.3) 200%

T1 /T2 110.3 N 20.1 B 18.7 N 2.7 B 128.4 N 304.2 B

T50 [K] TS [K] 250.0 190.0 245.0 260.0 260.0 215.0 166.7 153.8 -

NaY (2.4)200%

CQef f

[kHz] 123.0 24.3 142.6 28.3 120.8 94 8

Ea [kJ/mol] R1 h R1′ 20.7 f 8.6 s 8.6 32.3 f 31.2 N 14.5 s 23.4 B 14.5 12.7 OD 14.0 10.4 CD3 14.0 11.5 OD 13.3 11.7 CD3 13.0

R1′′ 32.0 37.0 13.0 13.0 18.3 18.0

temperature, while for the broader component a continuous increase is observed (Figure 7). 5

4

h [kHz]

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


3

s

f

TS

TS

2 1 0

220

240

260 T [K]

280

300

Figure 7: NaY sample with 100% loading of CD3 OD. Temperature dependence of spectral width h (FWHA) for narrow (▽) and broad (△) Gaussian lineshapes, respectively. The comprehensive view of molecular mobility in confinement must involve the basic assumption of a broad distribution of correlation times. As pointed out above we have τc ≈ 10−6 s as boundary condition for narrowing of deuteron spectra. Molecules with longer τc contribute to broad lines, alternative those with shorter provide narrow lines, thus using FID method we detect signal from a fraction of molecules with higher mobility. The features observed in relaxation at 200% loading are substantially different. Evidence for translation to reorientation transition was particularly prominent. Existence of methanol 21


W 0.20 0.30 0.30 0.30 0.35 0.35


trimers was the key point in explaining them. 28 Results of exchange procedure are included in Table 3 to complete the case.

Acetone (CD3)2CO Relaxation rates are shown for NaX and NaY with 100% loading of acetone in Figure 8 and 9, respectively. There are significant differences. Results of the exchange model shown there will be discussed below.

R’’ 1

-1


1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

R’1

10

TS 1 2

3

4 5 -1 1000/T [K ]

6

Figure 8: Temperature dependence of deuteron spin-lattice relaxation rate for NaX sample with 100% loading of (CD3 )2 CO (◦). Relaxation rate R1 (eq 3) resulting from the exchange model is depicted with dashed line.

Features observed in relaxation may be related to reorientation of acetone molecules as whole, i.e. to reorientation of C=O bond in space. However, when a fraction of acetone molecules become localized, relaxation driven by methyls rotations may dominate. The quadrupole coupling constant equals 160 kHz and 53.3 kHz for static and performing 3-fold rotation CD3 groups, respectively. The reduced quadrupole coupling constant equals 26.7 kHz, and the activation energy 11.6 kJ/mol were obtained by fitting the maximum in the relaxation rate with eq 1 in Figure 8. We apply therefore the exchange model with the following parameters for R1′ : CQ′ = 53.3 kHz, τ0′ = 3.3 · 10−12 s, Ea′ = 11.6 kJ/mol, and R1′′ : CQ′′ = 53.3 kHz, τ0′′ = 1.0 · 10−11 s, Ea′′ = 28.0 kJ/mol, W = 0.25. Exchange takes place at a 22


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Page 23 of 36

100 -1


1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


10

R’’ 1

R’1

1

TS 0.1

3

4 5 -1 1000/T [K ]

6

Figure 9: Temperature dependence of deuteron spin-lattice relaxation rates: slow (◦) and fast () for NaY sample with 100% loading of (CD3 )2 CO. Relaxation rate R1 (eq 3) resulting from the exchange model, with dashed line. See text for more details. high rate between isotropic reorientation, and translational mobility against a high potential. Evidence for an effect of the latter might be observed more clearly at higher temperatures. We apply the exchange model to the dominating long relaxation rate obtained for NaY sample (Figure 9) with the following parameters R1′ : CQ′ = 53.3 kHz, τ0′ = 5.0 · 10−13 s, Ea′ = 8.7 kJ/mol, and R1′′ : CQ′′ = 53.3 kHz, τ0′′ = 1.6 · 10−11 s, Ea′′ = 25.0 kJ/mol, W = 0.30. As for NaX reorientation of molecules is perturbed by translational jumps, with however much lower activation energies for both mobilities. That leads to lower relaxation rates in the experimental range of temperature. A minimum in the relaxation rate is seen more clearly. There appears an additional higher relaxation rate from about 15% of molecules. Fitting with eq 1 to a range (dotted line in Figure 9) gives the parameters τ0 = 7.0 · 10−14 s, Ea = 15.0 kJ/mol. Higher relaxation rate for a fraction of acetone molecules indicates on dominating role of methyl groups rotation as we have to take into account the quadrupole coupling constant CQ = 160 kHz. Thus the range of relaxation rates covered by the dotted line represents the high temperature side of a maximum R1 = 373.9 s−1 at T = 142.2 K (with parameters τ0 = 3.2 · 10−15 s and Ea = 15.9 kJ/mol) observed when there were no changes in molecular mobility at TS . Here we have, similarly to CD3 OD at low loading in NaY, 23



1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

where a maximum close to the predicted above value was observed (Figure 6), the fraction of molecules immobilized at a first absorption layer with intramolecular rotation of methyl groups driving the relaxation. There are also significant differences in the spectra and their temperature dependence. Reorientation of acetone molecules with internal rotation of methyl groups leads to narrow lines. Spectra are composed of two Gaussians with somewhat different width and its temperature dependence providing Ea values (narrow and broad, labeled N and B in Table 4, respectively). Both Gaussians broaden significantly below 260 K in the case of NaX. Deuterons are subjected to stronger hydrogen bonding to framework oxygens, when compared to NaY. Narrower spectra than for NaX are therefore observed for NaY, with a very weak temperature dependence, down to TS . Table 4: Acetone (CD3 )2 CO. Sample (Si/Al) loading NaX (1.3) 100% NaY (2.4) 100%

T1 /T2 73.4 237.3 129.8 323.4

T50 [K] TS [K] 255 164.0 250

CQef f

[kHz] 26.7

159.0

-

Ea [kJ/mol] R1 h R1′ R1′′ W 11.6 24.3 N 11.6 28.0 0.25 20.5 B 2.7 N 8.7 25.0 0.30 1.9 B

Acetone adsorbs on Lewis acid sites, where the carboxyl oxygen of acetone interacts with the offsite Al atom, and a coordination adsorption complex is created. 52,53 Temperature TS indicates a stronger interaction with Lewis sites in the case of NaY (Table 4). Existence of a fraction of localized molecules makes that argument even stronger. Molecules rolling over cage walls interact with the framework via deuterium - oxygen hydrogen bonding, siginificantly stronger for NaX. An effect into the same direction appears due to different abundance of molecules. There are 86 and 56 molecules per unit cell at 100% loading in NaX and NaY samples, respectively. Their collisions between themselves and with cage walls are more frequent and have stronger effect on relaxation in NaX. Thus apparent 24


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activation energy is higher, and the relaxation rate maximum is moved to significantly higher temperature in the experimentally accessible range.

Translation to rotation transition Spin-lattice relaxation rates are consistent with the model of the fast magnetization exchange between two dynamically different deuteron populations: translational and rotational mobility dominates at high and lower temperatures, respectively. Temperature at the minimum of the effective relaxation rate R1 is labelled as TT R . Effective correlation times are long (ω0 τc ≫ 1) and the low temperature slope, thus below the relaxation rate maximum for translations (R1′′ ), is observed above temperature TT R , while below it the high temperature slope, thus above the relaxation rate maximum for rotations (R1′ ), indicates that correlation times are significantly shorter. The transition at TT R may be visualized as a transfer from surface free (including transfer of molecules between cages) to surface mediated (molecules rolling over the surface of cages) diffusion. In this picture, intramolecular spin interaction is perturbed via molecular collisions and collisions of molecules with zeolite cage walls above the transition temperature, where diffusion dominates. Many such collisions are necessary to drive spin-lattice relaxation and the effective correlation time is long. On the other hand the rotation of molecules provides an efficient spin-latice relaxation mechanism below the transition temperature TT R . There is a change in effective correlation time by three or four orders of magnitude at TT R . Values of the transition temperature TT R are collected in Table 5. Low temperatures TT R in the case of D2 and CD4 indicate very weak (physisorbtion) interaction with the zeolite framework. Significantly higher TT R for water and ammonia in NaX than in NaY points out stronger hydrogen bonding. Such feature is particularly significant in the case of acetone (Table 5).

25



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Table 5: Translation to rotation transition temperature TT R [K] NaX D2 CD4 D2 O (100%) D2 O (200%) D2 O (300%) D2 O (500%) ND3 (100%) ND3 (300%) CD3 OD (100%) CD3 OD (200%) (CD3 )2 CO (100%)

395.3 335.6 333.3 333.3 261.0 259.0 384.6 245.0 344.8

NaY HY/DY NaA 110.0 150.0 200.0 322.6 324.1 342.5 304.9 343.6 327.9 235.0 157.0 444.4 230.0 266.6

Conclusion Applicability of deuteron NMR methods in studies of molecular mobility was tested on a series of small molecules confined in nanocages of NaX and NaY zeolites in a wide range of temperature. The temperature defined as TS separates two ranges with basically different mobility. High mobility, both translational and rotational, is responsible for features observed in spectra and relaxation at temperatures above TS . That range of temperature was chosen also for most of studies of hydrocarbons in confinement, listed in Introduction. Rotational and translational mobilities were observed as parallel processes by 2 H NMR and e.g. QENS, respectively. Higher translational mobility of small molecules allows us to trace their competing influence on NMR observables. The transition temperature TRT is related to the strength of mutual interactions in guest/host systems. At temperatures below TS molecules become localized and effects due to internal rotations are the point of interest. We use our own procedures 33 to analyse the structure of spectra, and we can follow a temperature dependence of contributions for a given set of components. Expectable transfer, on increasing temperature, between components resulting from increasing mobility, e.g. evolution from immobile to rotating methyl group spectrum,

26


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is not the main feature. In general, a site related mobility observed over a wide range of temperature, was a common observation. Results in this range were shown here for ammonia. Two components for ammonia molecules, rotating and subjected to torsional jumps, coexist and dominate the spectra in the whole temperature range. An evidence for torsional jumps was given as a spectral component shows asymmetry parameter η 6= 0. Previous explanation of such feature, such as a distortion of the methyl geometry, 54,55 are considered as unrealistic. Three time constants in the spin-lattice relaxation, spanned over three orders of magnitude, indicate a wide distribution of correlation times for localized ammonia. Spectra at intermediate mobility were therefore not observed for molecules in confinement. The main scope of our study refers to temperatures above TS . The exchange model was applied to fit the spin-lattice relaxation rate. The reduced value of quadrupole coupling constant, reduced with respect to the value expected for rotational mobility, underlines that decision. That point was overlooked in many previous studies when fitting observed relaxation rates. The emerging picture reflects combined translational and rotational mobility. The weighting factor W , and activation energies for respective mobilities characterize individual cases. High activation energies were obtained for translational mobility, however on a much simpler way, compared to other methods (QENS, PFG NMR). Other derived quantities, such as T1 /T2 , T50 and TS , were analyzed for each considered molecule and guided efforts to unravel involved interactions with their relative strength. The case of each cosidered molecule appears to be a distinctive one. Mutual interactions and interactions with adsorbtion centers on the cage walls, play direct and indirect role in features observed for NMR observables. These involved, for example, formation of water clusters, location at Levis sites for ammonia and acetone, hydrogen bonding hindering rotation of ammonia, methanol molecules at sodium cations and methanol trimers, and low and high loading, respectively. All together supplies guidance for future applications of deuteron NMR in studies of molecular interactions and dynamics in confinement.

27



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Acknowledgement The work was financed by the National Centre for Research and Development, contract No. PBS2/A2/16/2013. The sample preparation by Dr. Kinga Góra-Marek (Jagellonian University) is acknowledged.

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Translational and Rotational Dynamics of Molecules Confined in

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