NMR Investigation into the Influence of Surface Interactions on Liquid Diffusion in a Mesoporous Catalyst Support
Abstract
Pulsed field gradient NMR diffusion measurements provide a non-invasive measure of the mass transport (self-diffusion) characteristics of liquids confined to porous catalyst materials. Here we explore the ability of this technique to probe the diffusive behaviour of a series of short-chain primary alcohols within a mesoporous catalyst support material; through the comparison of our results with highly surface-sensitive NMR relaxation data, we show that the evaluation of bulk-pore diffusion dynamics may provide a simple and indirect method to access and explore surface interaction phenomena occurring at the catalyst-liquid interface.
Keywords
NMR Diffusion Adsorption Alcohols Tortuosity1 Introduction
It is well-established that the implementation of heterogeneous catalytic process is fundamental to the future of sustainable chemistry [1, 2]. The development of liquid-phase reaction processes is of particular importance regarding the enhanced utilisation of biomass—waste organic matter derived from food refuse, animal waste and used vegetable oils—which may be processed to produce renewable platform chemicals and fuels [3, 4, 5]. While it is clear that relevant catalytic processes are necessary to facilitate such transformations [6, 7, 8, 9], such reaction systems can differ significantly from the gas-phase processes encountered in more traditional catalyst applications [10]. Most notably, biomass-derived compounds typically possess multiple polar functional groups; the resulting intermolecular interactions lead these materials to exhibit notably low volatilities and vapour pressures, such that effective transportation relies heavily on the addition of solvents [11]. It follows that the relevant chemistry and mass transport phenomena are dominated by the liquid-phase; while this is favourable for efficient macrokinetic transport processes, the high molecular density within such systems can lead to complex and competitive dynamics at the catalyst surface [11]. As a result, the development of robust approaches for the investigation of liquid-phase dynamics within catalytically relevant porous media has become a significant goal within modern catalytic research.
Nuclear magnetic resonance (NMR) relaxation and diffusion measurements have shown significant promise in this area [12]. Obtaining useful insight from traditional NMR chemical shift phenomena is challenging when considering liquid-saturated porous material as a result of significant line-broadening effects due to adsorption interactions and magnetic susceptibility differences at the solid–liquid interface. While such effects may be mitigated through the observation of nuclei known to exhibit a wide range of chemical shift values (e.g. 13C), the resolution of such measurements is often limited by their inherently low natural abundance. The measurement of nuclear spin relaxation rates and molecular self-diffusion coefficients are, however, broadly independent of observable chemical shift phenomena. Rather, such measurements depend on the rate of decay of relevant NMR signals as a result of molecular dynamics. NMR relaxation studies have been particularly successful in determining adsorption phenomena within liquid-saturated catalyst materials; such measurements probe the longitudinal (\(T_{1}\)) and/or transverse (\(T_{2}\)) relaxation time constants of the confined liquid. Notably, the ratio of these time constants \(T_{1} /T_{2}\) is now well-established as a measure of relative surface affinity exhibited by liquids and liquid mixtures at the catalyst pore surface [13, 14, 15], and we have recently extended such analysis to demonstrate that this ratio may be interpreted as a quantitative indicator of adsorption energetics [16, 17].
Alternatively, pulsed field gradient (PFG) NMR diffusion measurements rely on the application of a series of short magnetic field gradient pulses to encode and then decode the position of nuclear spins either side of an observation period (see Sect. 2). Such measurements have been widely applied to the elucidation of mass transport phenomena in materials of relevance to heterogeneous catalysis [18], including mass-transfer limitations [19] and the influence of pore structure design [20, 21, 22]. Intriguingly, we note that liquids confined to porous materials will be subject to significant and repeated interactions with the pore walls, such that the measurement of their diffusive characteristics may present a potential method for the elucidation of surface interaction phenomena. While PFG NMR diffusion measurements have previously been applied to obtain direct insight into surface diffusion phenomena within liquid-saturated catalyst materials [23], the direct observation of dynamics associated with the adsorbed surface layer is challenging due to its small population and self-diffusion coefficient, as well as the inherently rapid rates of nuclear spin relaxation of species near the pore surface; such characteristics significantly reduce the observable signal from this layer, relative to that obtained from the bulk-pore population. It follows that this approach is only possible with access to NMR hardware capable of producing both large static magnetic fields and field gradient pulses ranging in the several \({\text{T m}}^{ - 1}\). Herein, with the aid of preliminary diffusion data obtained from a series primary alcohols within a silica catalyst support, we discuss how the observation of self-diffusion phenomena associated with the bulk-pore population of confined liquids may be utilised as an indirect method for the elucidation of surface phenomena within liquid-saturated mesoporous materials. This approach is predicted to be applicable to experiments using a range of NMR hardware, including low magnetic field benchtop systems [24].
2 Theory
2.1 Pulsed Field Gradient NMR
2.2 Diffusion in Restricted Systems
For weakly interacting non-viscous liquids (such as short-chain alkanes) restricted within mesoporous media this ratio is often considered equal to the tortuosity of the accessible pore network, \(\xi = \tau\) [32]. The observation that \(\xi > \tau\) may be facilitated by non-negligible adsorption interactions at the solid liquid interface, or by the occurrence of hindered diffusion, whereby region of the porous materials exhibit pore diameters of a similar size to the diffusion probe molecule employed. Prevalent examples of such are configurational diffusion through the pore network of zeolites, and the effects of coke deposition [33, 34]. Conversely, the observation that \(\xi < \tau\) has been proposed to originate from the disruption of dynamic hydrogen bonding networks by the presence of the pore walls [20, 32]. Herein, we present a brief investigation into the PFG interaction parameter presented by a homologous series of short-chain primary alcohols within an industrial silica catalyst support; the diffusion of cyclohexane is also investigated as a weakly interacting reference, and the assumption that such liquids may be used to provide an estimate of the pore structure tortuosity addressed.
3 Materials and Methods
3.1 Sample Preparation
Textural properties of the mesoporous silica catalyst support material used in this study
BET surface area (m2 g−1) | 272 |
BJH average pore diameter, \(d_{pore}\) (nm) | 15 |
BJH pore volume (cm3 g−1) | 1.3 |
3.2 Pulsed Field Gradient NMR Measurements
Summary of the PFG NMR acquisition parameters employed in this work
Unrestricted liquids | Restricted liquids | |
---|---|---|
Pulse sequence | PGSTE | APGSTE |
Observation time, \(t_{{{\Delta }}}\) (ms) | 50 | 100 |
Effective gradient pulse duration, \(t_{g}\) (ms) | 1 | 1 |
Maximum gradient pulse strength, \(g_{max}\) (T m−1) | 0.6–1.5 | 0.75–1.7 |
Gradient rise and fall times (ms) | 0.2 | 0.2 |
Gradient stabilisation time, \(t_{\delta 1,2}\) (ms) | 1 | 1 |
Echo time, \(\tau_{e}\) (ms) | 3.2 | 2.7 |
Homospoil gradient duration, \(t_{H}\) (ms) | 5 | 10 |
Homospoil gradient strength (T m−1) | \(g_{max} /3\) | \(g_{max} /3\) |
Number of gradient steps | 16 | 16 |
Number of repeat scans | 16 | 32 |
PFG NMR diffusion pulse sequence diagrams for a PGSTE and b APGSTE analysis. Each pulse sequence consists of a radio frequency (RF) and gradient pulse (\(\mathrm{g}\)) axis. All remaining symbols are defined within the main text and Table 2
Our PGSTE measurements were performed by holding \(t_{g} = 1\) ms constant and varying the magnetic field gradient strength; 16 linearly spaced \(g_{z}\) values were employed while the observation time was set to \(t_{\Delta } =\) 50 ms. Trapezoidal gradient pulses of area \(t_{g} g_{z}\) were employed to ensure consistent pulse shaped across all values of \(g_{z}\). A homospoil gradient of magnitude \(g_{max} /3\) (where \(g_{max}\) is the magnitude of the maximum applied gradient) and length \(t_{H} =\) 5 ms was also applied during the storage interval \({\text{T}}\) to remove any remaining coherent transverse magnetisation. The echo time was \(\tau_{e} =\) 3.2 ms.
In analogy to our PGSTE experiments, APGSTE analysis was carried out by holding \(t_{g} =\) 1 ms constant and varying \(g_{z}\) across 16 linearly spaced values; in this case, however, the observation time was set to \(t_{\Delta } =\) 100 ms to allow for sufficient self-diffusion throughout the silica pore network. Trapezoidal gradient pulse lobes (in this case of area \(t_{g} g_{z} /2\)) and a homospoil gradient of magnitude \(g_{max} /3\) and length \(t_{H} =\) 10 ms were employed, while the echo time was \(\tau_{e} =\) 2.7 ms.
4 Results and Discussion
PFG NMR signal attenuation data for short-chain primary alcohols and cyclohexane in a the unrestricted bulk and b restricted within mesoporous silica. Solid lines in a represent a fit to Eqs. (16) and (17) while solid lines in b represent a fit to Eqs. (18) and (19). The resultant self-diffusion coefficients are detailed in Table 3
Summary of the PFG NMR diffusion characteristics obtained from Fig. 2
Liquid | \(D_{0} \times 10^{10}\) (m2s−1) | \(D_{eff} \times 10^{10}\) (m2s−1) | \(\sqrt {2t_{\Delta } D_{eff} }\) (µm) | \(\sqrt {2t_{\Delta } D_{eff} } /d_{pore}\) (pores) | \({{\Xi }}\) (106) | \(\xi\) | \(T_{1} /T_{2}\) |
---|---|---|---|---|---|---|---|
Methanol | 21.40 ± 0.03 | 12.6 ± 0.3 | 1.59 ± 0.04 | 106 ± 2 | 3.8 | 1.70 ± 0.04 | 3.8 ± 0.3 |
Ethanol | 9.52 ± 0.01 | 5.3 ± 0.1 | 1.03 ± 0.02 | 69 ± 2 | 1.7 | 1.79 ± 0.04 | 4.9 ± 0.4 |
1-Propanol | 5.72 ± 0.01 | 2.0 ± 0.1 | 0.77 ± 0.02 | 51 ± 1 | 1.0 | 1.93 ± 0.04 | 6.1 ± 0.5 |
1-Butanol | 4.10 ± 0.01 | 2.1 ± 0.1 | 0.64 ± 0.01 | 43 ± 1 | 0.7 | 2.00 ± 0.05 | 6.6 ± 0.5 |
Cyclohexane | 12.91 ± 0.02 | 8.6 ± 0.2 | 1.31 ± 0.03 | 87 ± 2 | 2.3 | 1.50 ± 0.03 | 1.9 ± 0.1 |
Comparison of the PFG interaction parameter \(\xi\) with ratio of NMR relaxation time constants \(T_{1} /T_{2}\) (a measure of surface affinity) obtained for these same adsorbate/adsorbent systems. NMR relaxation data is taken from Ref [17]
In this case a single self-diffusion coefficient \(D\) is observed, defined by the weighted average of the rates of diffusion within the two populations. Given the long diffusion observation time employed in our APGSTE measurements it is reasonable to assume that this biphasic fast-exchange approach is applicable to the self-diffusion processes explored here; this interpretation is supported by the log-attenuation plots in Fig. 2, which present a single diffusion coefficient as characterised by a straight line on the log-scale.
5 Conclusion
This work has detailed a brief evaluation of the diffusive characteristics of a series of short-chain primary alcohols and cyclohexane within a commercial mesoporous silica catalyst support material. Through the application of PFG NMR diffusion measurements we have revealed a distinct inequality in the ratio of unrestricted-to-restricted self-diffusion coefficients across the series of liquids investigated. Indeed, while this ratio is often defined as a measure of the tortuosity of the accessible pore space, our results illustrate a notable increase in this parameter with increasing carbon chain length. A direct comparison of this data with the results of nuclear spin relaxation measurements reported previously reveal a strong, positive correlation, and suggests that our NMR diffusion data is sensitive to adsorption interactions occurring at the solid–liquid interface. A biphasic fast-exchange theory has been presented which suggests that the sensitivity of bulk-pore diffusivity to surface phenomena occurs as a result of the influence of a surface diffusion term. Overall, the results described here demonstrate that such measurements may be a potential source of additional insight for providing rational connections between adsorption phenomena and mass transfer characteristics within systems of relevance to heterogeneous catalysis.
Notes
Acknowledgements
N.R. acknowledges the Catalysis@Cambridge initiative, University of Cambridge, for the award of a studentship. The authors also thank Prof Lynn F. Gladden, University of Cambridge, for access to the NMR equipment.
Compliance with Ethical Standards
Conflict of interest
The authors have no conflicts of interest to declare.
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