Chemical Engineering Science 63 (2008) 1929 – 1940 www.elsevier.com/locate/ces Determination of the percolation properties and pore connectivity for mesoporous solids using NMR cryodiffusometry Emily L. Perkins a , b , John P. Lowe b , Karen J. Edler b , Nuradeen Tanko a , Sean P. Rigby a , ∗ a Department of Chemical Engineering, University of Bath, Claverton Down, Bath BA2 7AY, UK b Department of Chemistry, University of Bath, Claverton Down, Bath BA2 7AY, UK Received 30 August 2007; received in revised form 17 December 2007; accepted 17 December 2007 Available online 23 December 2007 Abstract Using a model disordered mesoporous solid with a spatial arrangement of pore sizes analogous to a macroscopic ‘ink-bottle’, it has been shown that the hysteresis observed in NMR cryoporometry can be deconvoluted into separate single pore and pore-blocking contributions. The suggestion of pore-blocking effects has been confirmed using PFG NMR. Hence, percolation theory has been used, for the first time with cryoporometry, to analyse the pore-blocking contribution to the hysteresis to determine the accessibility function and pore connectivity of the void space of a mesoporous sol–gel silica catalyst support pellet. This work demonstrates that NMR cryoporometry can be used to obtain a full range of void space descriptors, and thus offers a full, and potentially better understood, complementary pore structure characterisation method to gas sorption and mercury porosimetry.  2008 Elsevier Ltd. All rights reserved. Keywords: Catalyst support; Phase change; Porous media; Voidage; NMR cryoporometry; PFG NMR 1. Introduction Cryoporometry, also known as thermoporometry, is a tech- nique often used to determine pore size distributions for porous media. It is based upon the phenomenon that the melting or freezing point of a fluid imbibed within a porous solid is de- pressed below that of the bulk solid by an amount inversely proportional to pore size. Common probe fluids used in cry- oporometry include water, cyclohexane and benzene. In this work water will be used as the probe fluid. The choice of probe fluid is limited by several criteria, such as the requirement that no part of the sample be soluble in the probe fluid. The cryoporometry technique can be performed using either NMR spectroscopy (Gane et al., 2004) or calorimetry (Denoyel et al., 2004). In the former, the volume fraction of molten phase in a partially molten sample is assessed from the reduction in the NMR signal intensity relative to a fully molten sample, while in the latter it is assessed from the heat flow to/from the ∗ Corresponding author. Tel.: +44 1225 384978. E-mail address: S.P.Rigby@bath.ac.uk (S.P. Rigby). 0009-2509/$ - see front matter  2008 Elsevier Ltd. All rights reserved. doi:10.1016/j.ces.2007.12.022 sample. Hence, cryoporometry can be used to determine the same pore size distribution descriptor as is obtained from nitro- gen adsorption (Barrett et al., 1951) or the mercury porosimetry mini-loop method (Portsmouth and Gladden, 1991, 1992). In common with both gas sorption and mercury porosimetry, hysteresis effects are also observed in cryoporometry (Denoyel et al., 2004). In a cryoporometry experiment the freezing curve does not generally overlay the melting curve. As with gas sorp- tion and mercury porosimetry, several theories have been ad- vanced to explain the presence of hysteresis in cryoporometry (Petrov and Furó, 2006). The first main theory proposes that the probe fluid may become supercooled, as occurs for bulk fluids, until homogeneous nucleation initiates freezing. The second theory of hysteresis suggests freezing within the void space may be heterogeneously nucleated by the presence of bulk ice surrounding the exterior of the porous solid but penetration of the ice front into the interior of the sample is delayed by pore- blocking effects. Thirdly, the hysteresis may arise from a free- energy barrier, which separates metastable states of a confined material from stable ones, akin to that proposed by Broekhoff and De Boer (1967) for gas adsorption–desorption hysteresis.