Measuring nanopore size from the spin–lattice relaxation of CF4 gas

Abstract

The NMR 19 F spin-lattice relaxation time constant T 1 for CF 4 gas is dominated by spin-rotation interaction, which is mediated by the molecular collision frequency. When confined to pores of approximately the same size or smaller than the bulk gas mean free path, additional collisions of molecules with the pore walls should substantially change T 1 . To develop a method for measuring the surface/volume ratio S/V by measuring how T 1 changes with confinement, we prepared samples of known S/V from fumed silica of known mass-specific surface area and compressed to varying degrees into cylinders of known volume. We then measured T 1 for CF 4 in these samples at varying pressures, and developed mathematical models for the change in T 1 to fit the data. Even though CF 4 has a critical temperature below room temperature, we found that its density in pores was greater than that of the bulk gas and that it was necessary to take this absorption into account. We modeled adsorption in two ways, by assuming that the gas condenses on the pore walls, and by assuming that gas in a region near the wall is denser than the bulk gas because of a simplified attractive potential. Both models suggested the same two-parameter formula, to which we added a third parameter to successfully fit the data and thus achieved a rapid, precise way to measure S/V from the increase in T 1 due to confinement in pores.

Oxygen Sensing with Perfluorocarbon-Loaded Ultraporous Mesostructured Silica Nanoparticles

“…The T 1 relaxation times are sensitive to the magnetic field, temperature, and the PFC microenvironment. In this case, the nanoparticles themselves could be affecting the relaxation of PFCs, likely due to both a decrease in molecular mobility of PFC inside of UMNs and the molecular interactions between the SiO 2 cage and PFC. , Degradation of the silica nanoparticles may change the response curve of PFC to oxygen. As an initial evaluation of the PERFUMN stability, a preliminary analysis in whole blood is described in the section PERFUMN Oxygen Measurements in Whole Blood.…”

Strategies for Solid-State NMR Studies of Materials: From Diamagnetic to Paramagnetic Porous Solids

“…Other NMR approaches, developed recently, are based on relaxation behavior of gases when they saturate pores of materials. For example, the 19 F T 1 times of CF 4 gas, typically measured as 0.2 to 5−6 ms and dominated by spin-rotation interaction, have been applied for pore-size measuring . The relaxation measurements have shown that the gas, condensed on the pore walls and in a region near the wall, is denser than the bulk gas.…”

NMR Relaxation of Gas Adsorbed in Microporous Material

“…This can be explained by increased collisions among adsorbed gas molecules with a higher density and also collisions with the pore surface. 48 The gas−gas collision rate can be estimated by…”

“…For the relaxation induced by the gas molecules, simulation results show that the spin–rotational interaction still dominates, as in the bulk phase, but is smaller than that of the bulk phase over an order of magnitude (Figures S5–S7 in Supporting Information). This can be explained by increased collisions among adsorbed gas molecules with a higher density and also collisions with the pore surface . The gas–gas collision rate can be estimated by ω g = 2 v̅ π d M 2 w / V normalc normala normalg normale where v̅ is the mean velocity, d M is the kinetic diameter of the CH 4 molecule, w is the number of molecules per cage, and V cage is the volume of a ZIF-8 cage.…”

“…The gas–gas collision rate can be estimated by ω g = 2 v̅ π d M 2 w / V normalc normala normalg normale where v̅ is the mean velocity, d M is the kinetic diameter of the CH 4 molecule, w is the number of molecules per cage, and V cage is the volume of a ZIF-8 cage. The gas–surface collision rate can be estimated by ω s = v̅ S normalc normala normalg normale / 4 V normalc normala normalg normale where S cage is the inner surface area of the cage . When the extreme narrowing limit is achieved (the correlation time is much smaller than the inverse of the Larmor frequency), the spin–rotational relaxation rate is proportional to the correlation time of the collision-induced alteration of the angular momentum, so with a further assumption that collisions in the cage have the same efficiency of altering the angular momentum as the collisions in the bulk phase, the gas-induced relaxation rate will be R 1 , 2 G = R 1 , 2 B 2 π d M 2 n 2 π d M 2 w / V normalc normala normalg normale + S normalc normala normalg normale / 4 V normalc normala normalg normale where R 1,2 B is the bulk-phase spin–rotational relaxation ra...…”