Measuring nanopore size from the spin–lattice relaxation of CF 4 gas

Abstract

The NMR 19F 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.