Nuclear spin relaxation as a probe of zeolite acidity: a combined NMR and TPD investigation of pyridine in HZSM-5 †

The relative surface aﬃnities of pyridine within microporous HZSM-5 zeolites are explored using two-dimensional 1 H nuclear magnetic resonance (NMR) relaxation time measurements. The dimensionless ratio of longitudinal-to-transverse nuclear spin relaxation times T 1 / T 2 is shown to exhibit strong sensitivity to the silica/alumina ratio (SAR) of these zeolites, which is indicative of material acidity. This trend is interpreted in terms of increased pyridine surface aﬃnity with decreasing SAR. Temperature programmed desorption (TPD) analysis corroborates this observation, revealing a distinct increase in the heat of desorption associated with adsorbed pyridine as a function of decreasing SAR. A direct correlation between NMR and TPD data suggests NMR relaxation time analysis can be a valuable tool for the non-invasive characterisation of adsorption phenomena in microporous solids. 1 / T 2 ratios exhibited by pyridine confined to the microporous zeolite HZSM-5 with varying silica/alumina ratios (SAR, a measure of zeolite acidity). Through a direct comparison with TPD analysis our results demonstrate for the first time a clear correlation between nuclear spin relaxation characteristics, SAR and pyridine desorption energetics.


Introduction
Microporous solids (exhibiting pore diameters o2 nm) such as zeolites and metal organic frameworks have potential applications across a variety of processes including chemical conversion, storage, sensing and separations. 1,2 In the field of heterogeneous catalysis zeolites are regularly applied to facilitate a range of reactions such as cracking, 3,4 alkylation 5 and dehydration. [6][7][8] A key feature regarding the activity of such materials is that of surface acidity, characterised by the presence of Brønsted (proton donating) and/or Lewis (electron accepting) acid sites within the micropore network, and across the external material surface. As both the accessibility and acidity of these sites dictate the potential catalytic activity of zeolitic materials, extensive research efforts have been directed towards their characterisation. 9,10 Established techniques used to investigate the surface acidity of zeolites include infrared (IR) spectroscopy, temperature programmed desorption (TPD) and nuclear magnetic resonance (NMR) spectroscopy. The use of IR spectroscopy with pyridine as a probe molecule, for example, is particularly powerful since the assignment of vibrational modes associated with pyridinium ions at Brønsted sites and the coordination of complexes at Lewis sites are well-established. [11][12][13] Quantitative analysis in terms of adsorbate density is also possible if molar extinction coefficient values are known. 14 TPD analysis -again utilising basic probe molecules such as ammonia and pyridine -is also widely applied. [15][16][17][18][19] Typical TPD spectra report the desorption rate of the chosen probe molecule as a function of temperature; the area beneath such a curve is proportional to the amount of adsorbate present, providing quantification of acid site density, while the position of desorption peaks provides information on acid site strength. Magic angle spinning (MAS) solid state NMR spectroscopy measurements of zeolitic materials are extensively reported; such measurements provide a direct and quantitative probe of Brønsted acid site density via 1 H (proton) analysis and utilise the observed 1 H chemical shift values to both characterise site acidity 20 and differentiate between bridging (Si-OH-Al) and terminal (Al-OH or Si-OH) groups. 21 The measurement of 29 Si and 27 Al spectra also allows quantification of the material silica/alumina ratio (SiO 2 /Al 2 O 3 ), which is considered an analogue of zeolite acidity. 22 Indirect measurements of acid site characteristics are again possible via the use of probe molecules and facilitate the investigation of site accessibility. While 1 H chemical shift features may be exploited to detail probe molecule interactions, a wide range of heteronuclear MAS NMR experiments (including 13 C, 15 N and 31 P) have also been used to resolve adsorbate resonances. [23][24][25][26][27] In the present work we detail an alternative magnetic resonance technique for the comparison and characterisation of zeolitic acidity based on analysis of the 1 H nuclear spin relaxation characteristics of a liquid-phase basic probe molecule. The past decade has seen a rapid evolution in the application and interpretation of nuclear spin relaxation phenomena as a probe of surface affinity and adsorbate behaviour within catalytically active porous media. 28,29 These measurements exploit relevant NMR pulse sequences to determine the rates longitudinal and/or transverse nuclear spin relaxation processes, which are characterised by the time constants T 1 and T 2 , respectively. Within the unrestricted bulk liquid phase these time constants are known to conform to well-established relationships with molecular rotational and translational dynamics. 30 For liquids imbibed within porous solids, however, the correspondence between time constants and molecular dynamics is influenced by the pore structure and surface chemistry properties of the confining material, providing a potential route for the non-destructive characterisation of adsorption phenomena and confinement effects.
For fluids confined to catalytically active porous media the evaluation and interpretation of dimensionless relaxation time ratios is often of particular utility. 31,32 The ratio of longitudinal-totransverse nuclear spin relaxation time constants T 1 /T 2 is now established as a non-invasive probe of surface affinity, 33 and is a regularly sought metric to aid in the evaluation mesoporous catalyst materials. [34][35][36][37][38] Most notably, this ratio has been shown to correlate with the desorption energetics of liquids imbibed within mesoporous oxide materials as evaluated via both experimental 32 (TPD) and theoretical 39 (density functional theory) methods, and has been demonstrated as a useful probe of competitive adsorption processes in liquid-phase catalytic systems. [40][41][42] It is of interest to note, however, that this approach is yet to be applied to the evaluation of liquid-saturated microporous materials, with previous relaxation studies instead focussing on the investigation of gas admission and storage phenomena, [43][44][45][46] surface area screening protocols 47,48 and the study of confinement effects. [49][50][51][52] To this end, we detail here the measurement and interpretation of T 1 /T 2 ratios exhibited by pyridine confined to the microporous zeolite HZSM-5 with varying silica/alumina ratios (SAR, a measure of zeolite acidity). Through a direct comparison with TPD analysis our results demonstrate for the first time a clear correlation between nuclear spin relaxation characteristics, SAR and pyridine desorption energetics.

Relaxation theory
For fluids confined to porous media the observed rates of nuclear spin relaxation T i À1 (with i A {1,2}) may be expressed as a linear combination of unrestricted bulk, surface, and topological contributions, 53 1 Additional terms may also be required to fully describe transverse relaxation (i = 2) rates due to the influence of magnetic susceptibility differences between the confining solid and imbibed fluid. 54,55 Here T i,bulk À1 and D are the relaxation rates and self-diffusion coefficient of the unrestricted bulk fluid, respectively, a is a shape parameter that takes values of 1, 2 or 3 for planar, cylindrical or spherical pores, respectively, and d p is the pore diameter. The surface relativities r i = dT i,surf À1 are defined by the relaxation rates of species at the pore surface T i,surf À1 weighted by the length-scale of the adsorbed surface layer d. 56 Enhanced rates of relaxation occur at the solid-liquid interface due to the reduction in rotational and translational molecular mobility upon adsorption 35,57 and through interactions with any paramagnetic species imbedded within the solid matrix, 58,59 such that . As T i,surf exhibits sensitivity to the surface chemistry of the porous medium under investigation, 60-62 this parameter is central to the characterisation of surface interactions using nuclear spin relaxation measurements. 63 There exists two limiting cases for eqn (1), which may be defined according to the dimensionless parameter 59 If k c 1 a diffusion-limited condition arises, typically associated with large pores, slowly diffusing probe molecules and/or large surface relaxivities. In this case eqn (1) reduces to such that the observed relaxation rates are dominated by the topology of the confining pore structures and the diffusive characteristics of the probe fluid. 59 Diffusion-limited relaxation has been observed for water confined between SiC grains exhibiting a high surface concentration of paramagnetic Fe 3+ ions, resulting in large r 1 and r 2 values. 64 Sensitivity to the term d p À2 means this regime is also of relevance to porous structures exhibiting small pore diameters on the same length scale as the probe molecules employed, as has been evidenced using calibrated microporous silica glasses. 51,52 Alternatively, if k { 1 a surface-limited condition arises, associated with the presence of rapidly diffusing species and/or slow rates of surface relaxation. In this regime the rate of mixing between surface and bulk populations is rapid compared to the rates of surface relaxation and eqn (1) reduces to such that the observed rates of relaxation exhibit sensitivity to the surface relaxivities r i . Furthermore, as the regularly applied assumption of spherical pores (a = 3) gives ‡ where S/V is the surface-to-volume ratio of the confining pore structure, r i is often considered a scaling parameter between observed relaxation characteristics and pore size. 65,66 In the case of microporous zeolites careful consideration of an appropriate form of such expressions is required. In the present case, that of pyridine relaxation within HZSM-5 with various SAR, we note that the micropore diameter (d p = 5.1-5.6 Å) 67 and molecular kinetic diameter (d k E 5.3 Å) 68 are essentially identical, such that there will be no contribution to the observed relaxation rates from bulk liquid away from the pore walls. An appropriate relaxation expression is therefore comprising only the surface and topological terms of eqn (1). A value of a = 2 is suggested as a sensible shape parameter choice given the cylindrical pore structure exhibited by ZSM-5 zeolites, 69 such that this equation might be written The corresponding ratio of observed relaxation time constants then becomes where the equivalence between d k and d p means the surface relaxivities may be expressed . For a range of HZSM-5 materials differing only in SAR (assumed here to influence only pore surface chemistry and maintain a constant d p ) and characterised by the same probe molecule (constant D and d k ), we note that changes in this ratio will be dominated by changes in r 2 /r 1 = T 1,surf /T 2,surf ; this ratio is considered a probe of molecular mobility at the solid/liquid interface and is therefore sensitive to surface affinity. 32 [70][71][72] Samples for TPD and NMR analysis were first prepared by pressing each zeolite powder into tablets using a manual hydraulic press. A 2 tonne compressive force was applied to approximately 250 mg of powder in each case, forming cylindrical tables measuring around 13 mm in dimeter and 1 mm in thickness. The tablets were then broken into approximately 10 mg pieces so as to fit within the active regions of the TPD and NMR equipment. Each material was dried in N 2 (Air Liquide, 100 mL min À1 ) at 673 K for 1 hour to remove any adsorbed water, and soaked in excess pyridine under ambient conditions for at least 24 hours.

NMR relaxation measurements
1 H NMR relaxation measurements were performed using a Bruker DMX 300 spectrometer equipped with a 7.1 T superconducting magnet, corresponding to a 1 H frequency of 300.13 MHz. Experiments were performed under ambient pressure and at 298 AE 1 K as controlled by a Bruker Variable Temperature (BVT 3000) unit.
Pyridine-saturated zeolite materials were first placed onto a pre-soaked filter paper to remove any excess liquid on the external surface, then transferred to sealed 5 mm NMR tubes. To minimise experimental uncertainties associated with the evaporation of pyridine from the zeolite structures during NMR analysis, the atmosphere within each NMR tube was saturated by placing a pyridine-soaked plug of filter paper beneath the cap. Each sample was left within the magnet bore for at least 15 minutes prior to analysis to attain thermal equilibrium.
T 1 -T 2 correlation data was acquired by applying the two-dimensional (2D) NMR pulse sequence in Fig. 1, which comprises an inversion recovery component followed by a CPMG echo train. 73 The indirect (T 1 ) dimension was encoded using m = 16t recovery times between 1 ms and 10 s, while data in the direct (T 2 ) dimension was acquired by taking the magnitude of n = 512 spin echoes separated by an echo time of t e = 0.5 ms. Echo magnitudes S(t,nt e ) were acquired as a single data point (white data point in Fig. 1) generating an m Â n data matrix with no spectral resolution. Each experiment took approximately 30 minutes to complete and included 16 repeat scans separated by a recycle delay of 5T 1 .
The acquired 2D NMR relaxation data may be described by a Fredholm integral equation of the first kind, 74 Sðt;nt e Þ Sðt!1;0Þ ¼ ðð K t;T 1 ;nt e ;T 2 ð Þ F T 1 ;T 2 ð Þd logðT 1 Þd log T 2 ð Þ þeðt;nt e Þ: Here S(t,nt e )/S(t -N,0) is the normalised spin echo magnitude and e(t,nt e ) represents the experimental noise, assumed Gaussian with zero mean. The kernel function K(t,T 1 ,nt e ,T 2 ) describes the predicted forms of T 1 and T 2 relaxation, and for the NMR pulse sequence in Fig. 1 takes the form 75 Finally, F(T 1 ,T 2 ) represents the desired 2D distributions of T 1 and T 2 relaxation time constants; distributions were obtained by applying a numerical inversion of the acquired 2D relaxation data according to the above expressions. As this is an ill-posed problem, 76 stability of the inverted distributions in the presence of experimental noise was achieved through the use of Tikhonov regularisation, 77 with the magnitude of the smoothing parameter chosen according to the Generalised Cross-validation method. 78 Inverted distributions were bound within the range {10 À3 , 10 2 } s and corrected for the influence of

TPD measurements
TPD measurements were performed using a Hidden Analytical CATLAB-PCS comprising a microreactor module and integrated mass spectrometer. Zeolite samples imbibed with pyridine were placed within a glass microreactor under a constant 40 mL min À1 flow of high-purity helium and left for 2 hours at 432 K; after this time the mass spectrometer signal was observed to have returned to its baseline, indicating removal of all physiosorbed and excess pyridine. TPD curves were then acquired across the temperature range 423-1273 K with heating rates of b = 2, 5, 10, 15 and 20 K min À1 . Data from the mass fragments m/z = 52 and m/z = 79 were recorded, with each experiment repeated twice to ensure reproducibility; the acquisition of each TPD curve took between 4 and 10 hours.  80 The correlation peak obtained from bulk pyridine can been seen close to this diagonal, consistent with the expectation that T 1 = T 2 in the absence of surface interactions or confinement effects. Correlation peaks away from this diagonal are characterised by T 1 /T 2 4 1; as suggested by eqn (8), the position of these peaks is expected to be dictated by the relative surface affinities of pyridine within these structures. The T 1 /T 2 values obtained from the logarithmic mean of these correlation peaks are summarised in Table 1 and discussed further below.

Temperature programmed desorption
Example TPD spectra for pyridine with the range of HZSM-5 zeolites studied are shown in Fig. 3. For HZSM-5 with SAR = 23 three desorption rate maxima are evident, labelled (i), (ii) and (iii), suggesting pyridine desorbs from three distinct sites Correlation peaks indicate the relative probability density of each pyridine/zeolite system exhibiting a given combination of T 1 and T 2 times, as indicated by the colour bar. The solid diagonal line indicates the parity ratio T 1 /T 2 = 1. The red arrow indicates the direction of increasing T 1 /T 2 ratio, which is interpreted here as indicative of surface interaction strength. SAR values are indicated next to each correlation peak; bulk pyridine data is also shown.  23  32  150  30  25  141  50  17  132  80  14  126  300 12 110 within this material. While peaks (ii) and (iii) are also evident at SAR = 30, only a single spectral desorption peak (peak (i)) is observed for the remaining materials, characterising the temperatures associated with the maximum pyridine desorption rates across these zeolites, T p . Given the NMR relaxation time ratio T 1 /T 2 is conjectured to be sensitive to the strongest adsorption sites present across a surface, 32 we focus here on the consideration of this maximum desorption rate temperature across the five materials investigated, and a comparison of the associated desorption energetics with our acquired NMR relaxation data. Analysis of our TPD data was performed using the variable heating rate method of Cvetanović and Amenomiya, 81,82 which has been applied to a variety of acidic zeolitic systems elsewhere. [83][84][85][86][87] The relationship between desorption peak temperature T p , heating rates b and the probe molecule heat of desorption DH des may be written where R is the gas constant. A series of measurements utilising different heating rates therefore facilitates a plot of 2ln(T p ) À ln(b) against 1/T p , yielding a gradient equal to DH des /R; this gradient is independent of the intercept parameter C, which is discussed further in the ESI. † Fig. 4 summarises our acquired TPD data, obtained using a range of heating rates between b = 2 K min À1 and b = 20 K min À1 . Solid lines indicate a fit to eqn (11) in each case, yielding values of DH des for each SAR. These values, together with the T 1 /T 2 ratios extracted from the data within Fig. 2, are summarised in Table 1.

Correlating NMR relaxation with desorption energetics
We now provide a comparison of our acquired NMR relaxation data with the heats of desorption obtained from TPD analysis. The aim of this comparison is to validate the use of nuclear spin relaxation measurements for the comparison of zeolitic materials exhibiting different acidities, and more generally to extend the potential of such measurements -applied previously as a non-destructive probe of surface affinities in mesoporous systems -to microporous media.
The data within Table 1 reveals clear and notable correlations between SAR, T 1 /T 2 ratios and DH des values. In particular, an increase in DH des , which correlates with decreasing SAR due to an increase in the number of Brønsted acid sites, 71 can be seen to correlate with an increase in T 1 /T 2 ratio; this observation indicates the measurement of nuclear spin relaxation phenomena associated with basic probe molecules imbibed within such systems provides a useful method for the evaluation and comparison of zeolitic materials in terms of their acidity. Following our derivation of eqn (8) we attribute this observation to an increase in the ratio T 1,surf /T 2,surf with enhanced DH des .
In previous work an empirical theory was developed to formally relate the ratio T 1,surf /T 2,surf with probe molecule desorption energetics. 32 It was found that a linear correlation is expected to exist between desorption energetics and the inverse relaxation time ratio ÀT 2 /T 1 . This relationship has been verified for a range of water 32 and short-chain hydrocarbons 39 imbibed within mesoporous catalyst support materials. To explore whether this relationship also holds within microporous structures we provide in Fig. 5 a comparison of this inverse ratio, obtained from our NMR data in Table 1 as ÀT 2 /T 1 = À1/(T 1 /T 2 ), with our DH des values. An extremely strong correlation is observed between these metrics, providing evidence that NMR relaxation data obtained from liquidsaturated microporous materials can provide a quantitative indication of surface interaction phenomena associated with the strongest adsorption sites present.  Data points indicate values of the maximum desorption rate temperature T p obtained across multiple heating rates between b = 2 K min À1 and b = 20 K min À1 . Solid lines indicate a fit to eqn (11) in each case, which yields values of the pyridine heat of desorption DH des ; the acquired values of DH des are detailed in Table 1.

PCCP Paper
Open Access Article.

Conclusions
We have detailed an investigation into the application of nuclear spin relaxation measurements as a probe of sorption energetics within microporous HZSM-5 zeolites of varying SAR. Through a direct comparison with TPD analysis our results indicate that the dimensionless ratio of relaxation time constants T 1 /T 2 , obtained here through the analysis of 2D 1 H T 1 -T 2 correlation data, provides a non-invasive probe of surface affinity in microporous solids. For the specific case explored here, clear sensitivity of this relaxation time ratio to zeolite acidity has been demonstrated. Overall, our analysis method is of interest as it is rapid, non-destructive and simple to implement, and may be readily translated to portable and low-field benchtop NMR systems employed for materials screening and quality control. Measurements take on the order of tens of minutes to perform, reducing significantly the required experimental time required for such analysis compared to typical TPD analysis protocols, which may take 4100 hours. Relaxation measurements may therefore be employed in standalone form to provide a rapid, qualitative indication of increasing surface interaction strength across a given material series, or performed in combination with at least two TPD calibration measurements to yield quantitative measures of surface interact strength, significantly reducing the required experimental time for such analysis. These factors suggest such relaxation time measurements represent a valuable tool for the characterisation of microporous materials.

Conflicts of interest
There are no conflicts to declare.