Confinement effects on dipolar relaxation by translational dynamics of liquids in porous silica glasses

Abstract

A theory of dipolar relaxation by translational diffusion of a nonwetting liquid confined in model porous media is presented. We obtain expressions of the rates of spin-lattice relaxation 1/T1, spin–spin relaxation 1/T2, and spin-lattice relaxation in the rotating frame 1/T1ρ, which depend on the average pore size d. The frequency variations of these rates are intermediate between the two-dimensional and three-dimensional results. At small frequency they vary logarithmically for small d and tend progressively to a constant with increasing d. For small pore sizes we obtain quadratic confinement dependences of these rates (∝1/d2), at variance with the linear (∝1/d) relation coming from the biphasic fast exchange model usually applied for a wetting liquid in porous media. We apply such a theory to the 1H NMR relaxation of methylcyclohexane liquid in sol-gel porous silica glasses with a narrow pore-size distribution. The experiments confirm the theoretical predictions for very weak interacting solvent in porous silica glasses of pore sizes varying in the range of 18.4–87.2 Å and in the bulk. At the limit of small pores, the logarithmic frequency dependencies of 1/T1ρ and 1/T1 observed over several decades of frequency are interpreted with a model of unbounded two-dimensional diffusion in a layered geometry. The leveling off of the 1/T1ρ low-frequency dependence is interpreted in terms of the bounded two-dimensional diffusion due to the finite length L of the pores. An estimate of a finite size of L=100 Å is in excellent agreement with the experimental results of the transmission electron microscopy study of platinium-carbon replicated xerogels.