A General Correlation for the ¹²⁹Xe NMR Chemical Shift−Pore Size Relationship in Porous Silica-Based Materials

Abstract

A general correlation for the 129 Xe NMR chemical shift-pore size relationship (δ versus D) in porous silica-based materials over the range 0.5-40 nm has been demonstrated: δ ) δs/(1 + D/b), with δs ) 116 ( 3 ppm and b ) 117 ( 8 Å for the 34 materials studied. The correlation may be used in the characterization of silica samples with unknown pore structure. Even within this general correlation, subsets of materials of similar origin display finer correlations that indicate an acute sensitivity to details of the pore surfaces.The NMR spectroscopy of adsorbed 129 Xe has evolved into a sophisticated scientific tool for the study of different aspects of the structure and topology of internal voids in porous substances. 1 Although some disadvantages of the technique have been noted, 2 it remains attractive and popular, as judged by the fact that in 2001 about 50 Xe NMR-related papers were published. The latest improvements include the production of hyperpolarized xenon (HP Xe), 3 which gives a dramatic increase in the sensitivity for a variety of applications. 4 Besides such practical novelties, important theoretical developments directed at a much needed understanding of chemical shielding phenomena of confined 129 Xe are in progress. 5 For example, through empirical correlations were proposed between isotropic Xe chemical shifts and the pore size (δ-D correlation) in zeolites 6a as well as clathrates and solid Xe, 6b there is still no clear quantitative appreciation of the origin of this behavior. Attempts to extend it beyond zeolites have failed, and it has been pointed out that different correlations must exist for small pores, with a diameter less than about twice the diameter of a Xe atom, and large pores, as in the latter case account must be taken of Xe not adsorbed on the pore walls. 7We have shown previously that a simple fast exchange model explains a qualitatively similar, yet distinct, δ-D correlation found for mesoporous amorphous silica gels with a wide range of mean pore diameters from 2 to 40 nm. 8 Assuming that the 129 Xe NMR chemical shift of xenon adsorbed in mesoporous silica is a dynamic average between the gas and adsorbed states, it is straightforward to derive a parabolic dependence of the 129 Xe NMR chemical shift, δ (ppm), on the mean pore diameter, D (Å), where δ s is the chemical shift characteristic of interactions of Xe with the silica surface, and the parameter b depends on the pore geometry (η), the adsorption constant (K), and the temperature (T), as 8The mean pore diameter (D) is usually given through the volume-to-surface ratio as D ) ηV/S, where the geometry factor η is dependent on the model adopted for the pores. It can vary from 2.8 in a model of randomly packed globular particles (D ) 2.8V/S), to 4 for cylindrical pores (D ) 4V/ S) or 6 for unconnected spherical pores (D ) 6V/S).In this work we show that the model is more generally applicable by extending the range of silica-based porous materials, and we illustrate the correlation with previous work 8, 9 and new results 10 on...

Pore Structure and Interconnectivity of CdS Aerogels and Xerogels by Hyperpolarized Xenon NMR

“…These correspond to xenon gas adsorbed in void spaces of different dimensions within the aerogel matrix, with the breadth indicative of a chemical shift distribution from xenon gas sampling a range of similar environments at a rate slower than the NMR experiment time scale. The chemical shift range (27-55 ppm) over which these peaks are located is generally indicative of the void spaces being in the mesopore size regime, 55 in accordance with the nitrogen physisorption data.…”

“…Alternatively, the discrepancy we observe in pore size may arise from sampling of the space between the powdered aerogel grains, an effect that has been noted in mesoporous silica materials with submicrometer grain sizes and which is known to result in the broadening and a shift of the 129 Xe NMR line upfield, thereby resulting in an underestimation of pore size. 55 A similar effect has been noted in silica aerogels. 40 Regardless, the nitrogen physisorption and 129 Xe NMR data are consistent with the conclusion that the CdS aerogels consist largely of mesopores (i.e., pores of 2-50 nm), an advantageous pore size regime for molecular transport through the matrix.…”

“…55 This is achieved by fitting the chemical shift as a function of temperature to yield the heat of adsorption of xenon from which the diameter of the void spaces can be estimated using an empirical chemical shift-pore size correlation geometrical model. 54,58 We have applied this model to the CdS aerogels.…”

“…The validity of this method has been demonstrated for a wide variety of silica materials, including those with ordered or random pore networks, and with micropores and/or mesopores. 55 …”

129Xenon NMR: Review of recent insights into porous materials

“…The various values of the chemical shift observed for many different structures allowed some of us to establish a relationship between the chemical shift δ s (obtained by extrapolating, at zero Xe loading, the chemical shift measured as a function of Xe pressure) and the pore dimension, via the mean free path of a Xe atom diffusing in the pores [88]. Analogous relationship has been obtained later for mesoporous silica and silica-alumina materials [89].…”