Dynamics of molecules confined in nanocages. A deuteron NMR study at high temperature

TL;DR

This study uses deuteron NMR spectroscopy to investigate molecular mobility within nanocages of zeolites at high temperatures, revealing transitions from translational to rotational motion and the effects of interactions on molecular dynamics.

Contribution

It provides new experimental insights into molecular behavior in nanoconfined environments and discusses the applicability limits of NMR methods for such studies.

Findings

Transition from translational to rotational mobility with decreasing temperature

Evidence of D2O clustering and CD3OD trimer formation

Correlation between molecule immobilization temperature and interaction strength

Abstract

Our published and new experimental results by means of deuteron NMR spectroscopy in studies of molecular mobility in confinement are summarized and annalysed. Conclusions about limits of applicability of methods in disclosing several features are achieved. A set of molecules: D2, CD4, D2O, ND3, CD3OD and (CD3)2CO was chosen and introduced into zeolites with faujasite structure. Measurements of deuteron spectra and relaxation in function of loading and temperature provide a wealth of cases. A tranistion from translational into rotational mobility on decreasing temperature was a common obsevation. Fast magnetization exchange between two subsystems with different mobility was considered as a model. Existence of D2O clusters and trimers of CD3OD was a particularly significant evidence for importance of mutual ineractions. Evolution of spectral components, derivation of the activation energy and T1/T2 ratio are among analysed features. Choice of the zeolite, eg. NaY or NaX, introduces specific inertactions with the zeolite framework. Temperature at wich molecules become immobilized on cage walls is related to the strength of the interactions. On increasing temperature we may observe features like for layers of liquid on cage walls and gaseus state. In general properly chosen molecules may be used for characterization of host microporous systems.

Tables

Table 1. Table 1: Water D 2 ​ O subscript D 2 O \rm D_{2}O .

Sample					$E_a$ [kJ/mol]
(loading)	$T_1/T_2$	$T_{50}$ [K]	$T_S$ [K]	$C_Q^{eff}\left[\mathrm{kHz}\right]$	$T_1$	$R_1^{\prime }$	$R_1^{\prime \prime }$	$W$
NaX(1.3) (100%)	14.8	245.0	220.0	143.3	18.6	18.6	$\ge 37.0$	0.3
NaY(1.8) (100%)	42.4	311.0	235.0	241.2	9.0	14.0	30.0	0.75
NaY(2.4) (100%)	36.5	305.0	225.0	87.8	9.8	13.5	$\ge 37.0$	0.115
NaX(1.3) (200%)	59.4	293.0	215.0	139.9	18.4	18.4	$\ge 37.0$	0.3
NaY(2.4) (200%)	9.3	232.5	220.0	162.2	29.1	29.0	$\ge 42.0$	0.4
NaX(1.3) (300%)	24.1	305.0	233.0	136.1	11.4	13.0	$\ge 37.0$	0.3
NaY(1.8) (300%)	10.3	260.0	210.0	139.4	14.3	14.0	$\ge 40.0$	0.28
NaY(2.4) (300%)	8.0	235.0	205.0	149.4	23.3	23.0	$\ge 34.0$	0.33
NaX(1.3) (500%)	24.4	294.0	227.0	133.0	11.0	13.0	$\ge 37.0$	0.27
NaY(2.4), 500%)	16.0	250.0	218.0	153.7	31.7 LT	31.5 LT	$\ge 34.0$	0.35 LT
					9.8 HT	36.5 HT		0.15 HT
DY (100%)	37.5	245.0	200.0	148.6	23.0 LT	23.0	$\ge 37.0$	0.32
					9.8 HT
DY(2.4) (500%)	22.8	240.0	205.0	153.3	23.7 LT	23.0 LT	$\ge 40.0$	0.35 LT
					9.8 HT	18.0 HT		0.3 HT

Table 2. Table 2: Ammonia ND 3 subscript ND 3 \rm ND_{3} .

				$E_a$ [kJ/mol]
Sample				$h$
loading	$T_1/T_2$	$T_{50}$ [K]	$T_S$ [K]	HT	LT		$R_1^{\prime }$	$R_1^{\prime \prime }$	$W$
NaX (100%)	197.7	$>260$	200	14.5	11		3.9	14.0	0.7
NaX (300%)	107.3	270	210.5	19.2	14.5		3.2	12.7	0.7
NaY (100%)	41.7	250	195	22.1	21.4		5.8	15.2	0.7
NaY (300%)	17.5	190	140	10.4	10.4		5.0	10.0	0.72
DX (100%)	20.0		172	-	-		7.0	20.0	0.88
DY (100%)	$8.5\cdot {10}^3$	-	216	-	-		-	-	-

Table 3. Table 3: Methanol CD 3 ​ OD subscript CD 3 OD \rm CD_{3}OD .

					$E_a$ [kJ/mol]
Sample, l.	$T_1/T_2$	$T_{50}$ [K]	$T_S$ [K]	$C_Q^{eff}$	$T_1$	l. width	$R_1^{\prime }$	$R_1^{\prime \prime }$	W
NaX, 100%	110.3 N	250.0	190.0	123.0	20.7	-
	20.1 B			24.3	8.6	-
NaY, 100%	18.7 N	260.0	215.0	142.6	32.3	31.2 N
	2.7 B			28.3	14.5	23.4 B
NaX, 200%	128.4 N	-	166.7	-	12.7 OD	-	14.0 OD	13.0 OD	0.3
	304.2 B			-	10.4 ${\mathrm{CD}}_3$	-	14.0 ${\mathrm{CD}}_3$	13.0 ${\mathrm{CD}}_3$	0.3
NaY, 200%	-	-	153.8	120.8	9.7 OD	-	13.3 OD	18.3 OD	0.35
	-			-	11.3 ${\mathrm{CD}}_3$	-	13.0 ${\mathrm{CD}}_3$	18.0 ${\mathrm{CD}}_3$	0.35

Table 4. Table 4: Acetone ( CD 3 ) 2 ​ CO subscript subscript CD 3 2 CO \rm(CD_{3})_{2}CO .

				$E_a$ [kJ/mol]
Sample, loading	$T_1/T_2$	$T_{50}$ [K]	$T_S$ [K]	$T_1$	line width	$R_1^{\prime }$	$R_1^{\prime \prime }$	W
NaX, 100%	206.0	255	165	9.2	20.5	9.2	37.0	0.12
	74.5				24.3
NaY, 100%	-	250	155	-	21.0	8.7	25.0	0.15

Table 5. Table 5: Translation to rotation transition temperature T T ​ R subscript 𝑇 𝑇 𝑅 T_{TR} [K]

	NaX	NaY	HY/DY	NaA
$D_2$		110.0
${\mathrm{CD}}_4$			150.0	200.0
$D_{2}O$ (100%)	318.0	322.6	34.1
$D_{2}O$ (200%)	335.6	342.5
$D_{2}O$ (300%)	333.3	304.9
$D_{2}O$ (500%)	333.3	343.6	327.9
${\mathrm{ND}}_3$ (100%)	261.0	235.0	191.0
${\mathrm{ND}}_3$ (300%)	259.0	157.0
${\mathrm{CD}}_3\mathrm{OD}$ (200%)	245.0	230.0
${\left({\mathrm{CD}}_3\right)}_2\mathrm{CO}$ (100%)	416.6	266.6

Equations

$$R_1=\frac{1}{T_1}=A\left[J({\tau }_c,{\omega }_0)+4J({\tau }_c,2{\omega }_0)\right],$$

$${\left(\frac{1}{T_1}\right)}_{max}=1.425\frac{A}{{\omega }_0}.$$

$$R_1=W{R}_1^{\prime }+(1-W)R_1^{\prime \prime },$$

Full text

Keywords: water clusters, hydrogen bonding, molecular dynamics, activation energy, phase transition, hysteresis

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1 Introduction

Recent review articles proove continuous importance of porous media and their applications. Buntkowsky et al. 1 outlined applicability of NMR technique ($\rm{}^{15}N$ and $\rm{}^{2}H$ spectroscopy, MAS NMR, NMR diffusometry) for studies of the moleculs dynamics in confinement reflecting a wealth of interactions. Some more apsects were summarized in a more recent review from the same group 2. NMR-crystallography, isotopically-labelled materials, NMR spectra of paramagnetic microporous materials and other methods discussed in 3, may guide studies of substrates. We concentrate in our approach on deuteron NMR studies of selected molecules cofined in cages of zeolites with faujasite structure.

Zeolites are porous inorganic crystals basically with the atomic formula $\rm TO_{2}$, where the oxygens are arranged tetrahedrally around the central atom T (T represents silicon or aluminum atoms in the more common zeolites). Zeolite Y of the faujasite type has a well defined pore system. The supercages of 1.16 nm inner diameter are interconnected by 12-oxygen rings of 0.74 nm diameter. Moreover, there are also smaller sodalite cages of inner diameter of 0.66 nm connected to supercages by windows of 0.25 nm diameter formed by 6-oxygen rings. The unit cell of Y zeolite consists of eight supercages and eight sodalite cages and contains 192 T atoms and 384 oxygen atoms 4.

Hydroxyl protons in zeolite HY are attached to oxygens bridging tetrahedrally coordinated silicon and aluminum atoms. These protons compensate the negative framework charges introduced by tetrahedrally coordinated aluminums, alternatively the same role is played by sodium cations. Thus OH groups are named as structural or bridging OH groups (SiOHAl). In real crystals some imperfections can be found in a form of silanol (SiOH) groups or OH groups associated with some extra-framework aluminum species 5.

The unit cell of zeolite Y contains 384 oxygen atoms at four crystallographically inequivalent positions from O1 to O4. One can therefore expect four different types of bridging hydroxyl groups with protons at the positions from H1 to H4. The protons H1 and H4 point into supercages while the protons H2 and H3 are directed towards the 6-oxygen rings. Czjzek et al. 6 used neutron diffraction to determine the following abundances of protons at respective positions in the unit cell: $n(1)=28.6$, $n(2)=9.5$ and $n(3)=15$ in zeolite HY (${\rm Si/Al}=2.4$). No H4 protons were detected. The positions H1 and H3 are occupied preferentially and that confirms the results of quantum mechanical calculations 7, 8.

2 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 9.

Molecular reorientations rendering the quadrupole interaction time–dependent and inducing transitions between nuclear Zeeman levels drive the deuteron NMR relaxation. The spin-spin and spin-lattice relaxation rate constants are given as different linear combinations of spectral density functions weighted by the coefficient $A=(3/10)\pi^{2}C_{Q}^{2}$, where quadrupolar coupling constant $C_{Q}=e^{2}qQ/h$. In the simplest case of isotropic diffusion characterised by exponential autocorrelation function with a single correlation time $\tau_{c}$, the spin-lattice relaxation rate constant is given by 10:

[TABLE]

where $J(\tau_{c},\omega_{0})=\tau_{c}/(1+\tau_{c}^{2}\omega_{0}^{2})$ is the spectral density function, being the Fourier transform of the autocorrelation function, with $\omega_{0}/2\pi$ equal to the Larmor frequency. The correlation time $\tau_{c}$ is assumed to follow the Arrhenius formula $\tau_{c}=\tau_{0}\exp(E_{a}/kT)$ with the activation energy $E_{a}$. The temperature dependence of the relaxation rate has an inverted V shape with the maximum at temperature fulfilling the condition $\omega_{0}\tau_{c}=0.616$ which leads to

[TABLE]

Fast motions, obeying $\omega_{0}\tau_{c}\ll 1$, contribute to the high temperature side of the maximum, while the low temperature side represents the relation $\omega_{0}\tau_{c}\gg 1$. The slopes, in some cases unequal, provide the value of the activation energy $E_{a}$. Moreover, the value of $\tau_{0}$ and $C_{Q}$ can be calculated from the known position of the maximum and its absolute value.

In the following a spin system will be assumed to consist of two subsystems characterized by a fast and slow motional regime with intrinsic relaxation rates $R_{1}^{\prime}$ and $R_{1}^{\prime\prime}$, respectively. In the limit of the fast magnetization exchange between the subsystems a single apparent relaxation rate can be observed 11:

[TABLE]

where $W$ depends on relative abundances of molecules in both subsystems and $R_{1}^{\prime}$ and $R_{1}^{\prime\prime}$ are expressed by eq 1, however for different correlation times. Experimentally, the limit of the applicability of eq 3 is described by the temperature $T_{S}$. Above $T_{S}$ narrow deuteron NMR lines are observed. Below $T_{S}$ a substantial, step-wise broadening of deuteron spectra appears, and magnetization recovery becomes nonexponential 12.

Generally, NMR spectra are sensitive to molecular reorientations on the NMR time scale 13, 14, which is reflected in the condition for the narrowing of spectra expressed as $\delta\tau_{c}\sim 1$, where $\delta$ is the width of a given spectrum and $\tau_{c}$ is the temperature-dependent correlation time. For a typical width of a deuteron spectrum, $\delta=135\rm\,kHz$ for $C_{Q}=180\rm\,kHz$, the condition $\delta\tau_{c}\sim 1$ leads to the correlation time $\tau_{c}=10^{-6}\rm\,s$. For $\tau_{c}\gg 10^{-6}\rm\,s$ deuterons are considered to be immobile and the Pake doublet is observed. The doublet separation equals $(3/4)C_{Q}$, which can be used to provide the value of the quadrupole coupling constant. Narrowed spectra result for $\tau_{c}\ll 10^{-6}\rm\,s$. Deuteron NMR spectra are inhomogenous 15 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 $\rm ND_{4}VO_{3}$ 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 $7.6\times 10^{-7}{\rm\,s}\leq\tau_{c}\leq 1.6\times 10^{-4}\rm\,s$) 16. 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 17, 18.

3 Experimental

Zeolites NaX (supplied by Sigma–Aldrich) and NaY (purchased from Linde company) were activated in situ in an NMR cell. First, 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 100% and 200%, of the total coverage of $\rm Na^{+}$ 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 $\pm 0.1\rm\,K$. The static magnetic field 7 T was created by the superconducting magnet made by Magnex, and the 2H 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 $2\,\mu\rm s$. The $\pi/2$ pulse equal to $3\,\mu\rm s$ assured the uniform excitation 19 for our 200 kHz spectra.

NMR spectra were obtained by the Fourier transformation of the free induction decay (FID). For eliminating spectral baseline distortion an extension 20 of Heuers method 21 dedicated to wide spectra was used. The nature of quadrupole interaction for deuterons allows us to expect symmetric spectra. Thus, the zeroing of the imaginary signal was possible at the final stage of signal processing. An acceptable signal-to-noise ratio in the spectra was achieved by signal averaging over several thousands of accumulations depending on loading. Repetition time was kept at least 5 times longer than the time constant observed in relaxation.

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 FID and QE spectra the sequences $(\pi/2)_{x}$—$t$ and $(\pi/2)_{x}$—$\tau$—$(\pi/2)_{y}$—$t$ were used with separation time $\tau$ of the order of $50\,\mu\rm s$ in the QE sequence. The pulse separation time $\tau$ 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 quadrupole echo sequence.

4 Results and discussion

Nuclear magnetic resonance provides means to study molecular dynamics in every state of matter. Molecules in cofinement provide a particularly rewarding system as with a single sample we may observe on increasing temperature immobilized molecules, then 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 fetaures in mobility. We restrict ourselves to zeolites of faujasite structure and have a common enviromemt in terms of size and structure.

4.1 $\rm D_{2}$ and $\rm CD_{4}$

Spin-lattice relaxation rate was measured for zeolite NaY with one $\rm D_{2}$ molecule per supercage in the range 310 K to 66 K. The theroy of deuteron spin-latice relaxation for free $\rm D_{2}$ quantum rotators was developed leading to sucessful fits 22. Relaxation rates were calculated for ortho-$\rm D_{2}$ and para-$\rm D_{2}$. 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 result of that we observed that relaxation rates surpass values defined by the quadrupole coupling constant. That is unique case. The low temperature slope of the relaxation rate was observed at temperature above 110 K, indicating $\omega_{0}\tau_{c}\gg 1$ 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 effictive relaxation mechanism and effective correlation times are relatively long. Below 110 K molecules stay close to the surface of cages and undergo reorienation in a surface mediated diffusion. Effective correlation time decreases by about three orders of magnitude in a stepwise manner.

The spin-lattice relaxation rate was measured for $\rm CD_{4}$ molecules with 4 molecules per supercage in zeolites HY, NaA and NaMord in the range 10 K to 310 K 23. The transition from transaltional to rotational mechanism of relaxation was observed at 150 K for HY and at about 200 K for NaA and NaMord zoelites. Also for $\rm CD_{4}$ basic features in relaxation are related to quantunm effects for free rotators. The theory was fitted in all cases with somewhat different parameters. We report here about HY only for consistency with the principle of common enviroment.

The relaxation rate depends strongly on the rotational states of $\rm CD_{4}$. 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 population of rotational states with selected spin isomers A, T and E. Expressions were derived for relaxation rates of magnetizations $M_{T}$ and $M_{AE}$ via the intra- and external quadrupole couplings. Exchange between two locations averages the relaxation rates within the symmetry species. Moreover the spin conversion transitions couple the relaxation of $M_{T}$ nad $M_{AE}$. Two relaxation rates with two maxima in each case were explained with these postulates. Incoherent tunnelling was attributed to relaxation rates below 15 K.

4.2 Water $\rm D_{2}O$

Applied here methods in analysis of deuteron NMR data, obtained for moelcules in confinement, were developed and described before for the case of water 24. Some of previous results, supplemented by additional measurements, are summarized in Table LABEL:table_water.

Two Gaussian components in the spectra were observed in majority of cases. Eventual Lorentzian line at high temperature was considered as a fingerpoint of efficient translational motion.

Contributions of Gaussians depend on decreasing temperature, that of narrower one is decreasing. Temperature $T_{50}$, where their contributions are equal, was proposed as a parameter related to the adsorbtion strength; higher when $T_{50}$ is higher. Inspection of $T_{S}$ leads to similar conclusions (Table LABEL:table_water).

Results of direct application of eq 1 in analysis of the spin-lattice relaxation (activation energy and $C_{Q}^{eff}$) point to necessity of application of the exchange model. High activation energies were attributed to less mobile fraction of molecules. In most cases, irrespective of Si/Al ratio and loading, that fraction dominates (Table LABEL:table_water). All that make water in cationic zeolites a special case. Bonding to the framework alt low loading, then formation of clusters are the specific features of water in confinement.

4.3 Ammonia $\rm ND_{3}$

Deuteron NMR spectra and spin-lattice relaxation were measured for the set of zeolites and loadings listed in Table LABEL:table_ammonia. Measurements were performed down to the temperature $T_{S}$, which is significantly higher for NaX than for NaY for respective loadings. Higher $T_{S}$ indicates stronger bonding to adsorption centers.

Analysis of relaxation supplies activation energies. Spectra consist of two components, Gaussian in shape in majority of cases. Linear dependence of their width $h$ (FWHA) 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 (HT) and lower temperature (LT) (Table LABEL:table_ammonia).

An apparent fit of spin-lattice relaxation rates with eq 1 was possible only in two cases, NaY (300%) and DY (100%), where a maximum was observed. Reduced values of the quadrupole coupling constant and necessity of finding a common mobility model in all cases leads us to application of the exchange model.

F. Gilles in a scarce paper on $\rm ND_{3}$ mobility study by NMR postulated translational jumps between adsorption centers in some $\rm Na^{+}$-faujasites 25. Ammonia molecules adsorbed in the cationic zeolites interaction with the counter-ions via their nitrogen and deuterons may be involved in hydrogen bonds to the framework oxygens 26. Both interactions will be considered in analysis of results below. The quadrupole constant for $\rm ND_{3}$ was estimated to be 217.5 kHz 27, or in the range 221.1–239.1 kHz 25. We take 228 kHz as a common value on the basis of our study.

As the representative example we take the spin-lattice relaxation results for NaY with 300% loading (Figure 1). 3-fold rotation of ammonia reduces the effective 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 $R^{\prime}$ with parameters $\tau_{0}^{\prime}=2.5\cdot 10^{-12}\rm\,s$, $E_{a}^{\prime}=5.0\rm\,kJ/mol$, and $R^{\prime\prime}$ with $\tau_{0}^{\prime\prime}=2.0\cdot 10^{-11}\rm\,s$, $E_{a}^{\prime\prime}=10.0\rm\,kJ/mol$. The final fit was obtained for $W=0.72$. The direct fit with eq 1 provided $C_{Q}^{eff}=41.5\rm\,kHz$. Results for exchange model for other cationic zeolites are collected in Table LABEL:table_ammonia.

DX zeolite with 100% loading we find as a different case (Figure 2). Here we have: $R^{\prime}$ with parameters $C_{Q}=76.0\rm\,kHz$, $\tau_{0}^{\prime}=2.0\cdot 10^{-11}\rm\,s$, $E_{a}^{\prime}=7.0\rm\,kJ/mol$, and $R^{\prime\prime}$ with $C_{Q}=228.0\rm\,kHz$, $\tau_{0}^{\prime\prime}=1.5\cdot 10^{-10}\rm\,s$, $E_{a}^{\prime\prime}=20.0\rm\,kJ/mol$. Exchange takes place between immobile molecules (static value of $C_{Q}$) and more abundant rotating molecules (reduced value of $C_{Q}$) as $W=0.88$. Narrow lines were observed in the whole temperature range.

More restricted mobility of ammonium than in DX was detected in DY. Application of QE sequence was necessary to receive deuteron spectra already at about 300 K. The spectrum obtained at 293 K consists of well defined components (Figure 3). Two Gaussian lines (the shape defined by $1/(\sigma\sqrt{2\pi})\exp(-(\nu-\nu_{0})^{2}/(2\sigma^{2}))$ dominate with contributions 40% and 28% and width $\sigma=3\rm\,kHz$ and 9 kHz, respectively. The doublet with contribution 10% comes from $\rm ND_{3}$ undergoing 3-fold rotation. The broad component, contrbuting 22% of the signal was derived for localized ammonia performing torsional oscillations with $56^{\circ}$ amplitude. The spectrum was calculated using WEBLAB package 28.

The spin-lattice relaxation for DY with 100% loading was also measured using QE sequence (Figure 4) shown together with results for DX (top range) for comparison. Significant difference in $T_{S}$ indicates stronger bonding for $\rm ND_{3}$ in DY.

Two time constants above $T_{S}$, the shorter with weight 68% may be attributed to mobile molecules (Gaussians), and the longer one to rotating $\rm ND_{3}$. Below $T_{S}=216\rm\,K$ we show, as an example of a common for all cases of molecules in confinement feature, results for localized molecules in DY. Characteristic three time constants, spanned over three orders of magnitude range, indicate on a distribution of correlation times. The conclusion is based on the theoretical procedure worked out before 29, 30.

As a basic location of ammonia in cationic zeolites one may take the one with molecular nitrogen in the vicinity of the cation. The hydrogen bond of molecular deuteron with a framework oxygen is also possible (Figure 2 in Ref. 25).

Electrical charge of $\rm Na^{+}$ in NaY is stronger and nitrogen bonding stronger than in NaX. Activation energies from $R^{\prime\prime}$ ((Table LABEL:table_ammonia) do not confirm that expectation clearly enough. On the other hand however, inspection of $T_{S}$ temperatures corroborate importance of N-$\rm Na^{+}$ interaction.

Experimental results indicate that molecular mobility in DX and DY appears to be significantly different. The structure with ammonia nitrogen at the framework deuterium may be seen as formation of a quasi-ammonium ion. Such singly bonded state 31, 32 allows free 3-fold rotation of ammonia and appears to be more abundant in NaX. Triply bonded structure (Figure 6c in Ref. 31) refer to localized, performing torsional oscillations ammonia in a strong potential with the 3-fold symmetry.

Hydrogen bonds are relatively weaker in DY, however the exchange model was not applicable in this case. Majority of molecules (Gaussian components amount to 68%) perform almost isotropic reorientation, however with highly restricted translational diffusion. Juast a fraction is fully localized with the single bond (3-fold rotation) or triply bonded (torsional oscillations). The loading 100% means that we have 86 or 56 molecules in the unit cell in DX and DY, respectively. It leads to an additional concept that more frequent collisions between more abundant molecules in the space of DX cages may overshadow features related to bonding and settle the final view of molecular mobility in confinement.

4.4 Methanol $\rm CD_{3}OD$

As the key example we take NaY zeolite with 100% loading. Two time constants are observed in the temperature dependence of the spin-lattice relaxation (Figure 5). The higher relaxation rate was fitted with $C_{Q}^{eff}=142.6\rm\,kHz$ in eq 1. At about 260 K its contribution comes to zero from about 25% at highest temperature. The slower rrelaxation rate, characterized by $C_{Q}^{eff}=28.3\rm\,kHz$ is dominating down to $T_{S}=215\rm\,K$. At this point spectrum broadens significantly, indicating immobilization of all molecules.

In the case of NaX with 100% loading $T_{S}$ temperature is lower than for NaY and equals 190 K (Table LABEL:table_methanol, Ref. 33), thus the binding energy is lower. From relaxation between binding energies we may point out the location of methanol molecules with oxygens at $\rm Na^{+}$ 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 33. The conclusion directs us to an expalantion of obeserved relaxation rates based on a common view of molecular mobility. A fractional methanol molecules face a reduced mobility in a sort of first adsorption layer in the vicinity of $\rm Na^{+}$ cations. The fast relaxation rate, with high $C_{Q}^{eff}$ value, is driven by rotating OD and $\rm CD_{3}$ groups in absence of any overall reorientation. Increasing width of spectra eliminates that time constant from detection using FID below 260 K.

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 $\rm CD_{3}$. Solidification temperatures for molecules contributing to the fast and slow relaxation rates, 260 K and 215 K, respectively, are resulting from difference in binding energy (respective activation energies are equal 32.3 kJ/mol and 14.5 kJ/mol (Table LABEL:table_methanol). There are two exponents in the spectra, narrow and broader, being referred to as N and B in Table LABEL:table_methanol, respectively. Contributions of the narrow and broader components amount to about 40% and 60% at higher temperature. The contribution of the broader exponent increases significantly below $T_{50}=260\rm\,K$. The width of the narrow component does not change significantly in the whole range of temperature, while for the broader component a continuous increase is observed (Figure 6).

The comprehensive view of molecular mobility in confinement must involve the basic assumption of a broad distribution of correlation time. As pointed out above we have $\tau_{c}=10^{-6}\rm\,s$ as boundary condition for narrowing of deuteron spectra. Molecules with longer $\tau_{c}$ contribute broad lines, alternative those with shorter provide narrow lines, thus using FID method we detect signal from a fraction of molecules with higher mobility. Application of QE methods would be necessary in order to get a complete view with both fractions of molecules.

The features observed in relaxation at 200% loading are substantially different. Existence of methanol trimers was the key point in explaining them.

4.5 Acetone $\rm(CD_{3})_{2}CO$

Relaxation rates are shown in Figure 7 and 8 for NaX and NaY, respectively. There are significant differences, however no obvious interpretation appears. We may search for differences in molecular mobility in deuteron spectra below $T_{S}$. Rotation of methyl groups takes place down to low temperature. Therefore, in the temperature range considered here, its contribution to relaxation is neglibile.

Mobility of acetone molecule consists of torsional oscillations about the 2-fold symmetry axis ($z$), the axis in the molecular plane ($y$), and about the axis perpendicular to the plane ($x$). Oscillations are induced on increasing temperature in this order. All of them are effective in NaX just below $T_{S}$. Therefore we may expect above $T_{S}$ uniform istopic reorientations of acetone molecules. The maximum in spin-lattice relaxation rate provides the activation energy 9.2 kJ/mol.

Spectral component related to 2-fold oscillations dominate in the spectra of NaY just below $T_{S}$. Another one with about 15% contribution indicates on consecutive oscillations about $z$ and $y$ axes. Acetone molecules are subjected to hindrance by a local potential with lower symmetry in this case. The time constants in the spin-lattice relaxation rate reflect complexity of molecular dynamics above $T_{S}$, where 2-fold oscillations may evolve into rotational jumps. Their weights, 85% and 15% for shorter and longer one in the whole temperature range, respectively confirm domination of mobility about $z$ axis, acompanied by rotational mobility also about $y$ axis for the fraction of molecules.

Spectra are composed of two Gaussians. Their width shows in significant temperature dependence (Figure 8). Alternatively for NaX spectra are broader and high activation energy was derived (Table LABEL:table_acetone). Exchange of methyl groups in acetone via 2-fold rotation was proposed before 34. Extensive studies of acetone adsorbtion were performed using $\rm{}^{13}C$ chemical shift 35, 36. A relation was found between the $\rm{}^{13}C$ chemical shift and acid strength of Brønsted and Lewis acid sites. Effects of molecular reorientations were detected 36. When acetone adsorbs on Lewis acide sites, the carboxyl oxygen of acetone interacts with the Al atom of the zeolite framework to form a coordination adsorbtion complex. Such geometry is basic in the case of NaX and NaY. Molecular reorientations and their activation energy as well as $T_{S}$ indicate on stronger interaction of acetone with Lewis sites in the case of NaY (Table LABEL:table_acetone).

4.6 Translation to rotation transition

Spin-lattice relaxation rates are consistent with the model of the fast magentization exchange between two dynamically different deuteron populations. Effective correlation times are long ($\omega_{0}\tau_{c}\gg 1$) and the low temperature slope is observed. The observed relaxation behaviour in temperature depnedence is most likely an effect of the transition friom translational to rotational diffusion as the major relaxation mechanism. In the transition may be visualized as a transfer from surface free (collisions) to surface mediated (molecules rolling over the surface of cages) diffusion. A change in effective correlation time by three or four orders of magnitude stays behind the transition in terms of relaxation efficiency.

5 Conclusion

Applicability of deuteron NMR methods in studies of molecular mobility was tested on a series of molecules confined in cages of zeolites with the faujasite structure. Several paramaters related to their interaction, mutual and with the zeolite framework, were obtained and compared. Each case appears to be the unique one. Obtained parameters reflect distinct influence of adsorbtion centers and, on increasing loading, also on variety of mutual interactions. Particularly formation of molecular aggregates like water clusters or assembling of ammonia gave most rewarding features in deuteron NMR observables. All together supplies guidance for future applications of deuteron NMR in studies of molecular dynamics in confinement and proofs it to be the usful tool.

\acknowledgement

The work was financed by the National Centre for Research and Development, contract No. PBS2/A2/16/2013.