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60 We have recently used the macropore/nanopore model to describe the relative apparent
61 diffusion coefficients Da,,/Do of water and cations (Na+, Sr2+) in compacted water-saturated
62 bentonite (Bourg et al., 2006, 2007) with the equation:
63 ~ -,a arpr + ainterlayer 'interlayer) (1)
0 1
64 In equation 1, Da,, is a tracer diffusion coefficient of a species along the direction x,, i.e., the ith
65 diagonal element of the apparent diffusion coefficient tensor, Da; Do is the diffusion coefficient
66 of the species in bulk liquid water; G, (> 1) is a "geometry factor" that accounts for the influence
67 of pore network geometry on Da,,; binterlayer ( 1) is a "constrictivity factor" that accounts for the
68 slower diffusion of the species of interest in nanopores relative to macropores or bulk water. The
69 parameters amacropore and ainterlayer are the mole fractions of the species of interest in macropores
70 and nanopores, respectively; they are subject to the constraint amacropore + ainterlayer = 1 if
71 adsorption on montmorillonite edge surfaces or on non-montmorillonitic minerals is negligible.
72 In essence, equation 1 is a weighted sum of diffusive retardation factors for macropores
73 (1/G) and nanopores (binteriayer/Gi), with weighting being by the mole fraction of the species of
74 interest in these two compartments. It is strictly valid only if the mass of montmorillonite per
75 combined volume of montmorillonite and pore space, i.e., the partial montmorillonite dry density
76 pb,mont (Liu et al., 2003; Sato and Suzuki, 2003), is greater than or equal to 0.98 kg dm-3, the
77 threshold value at which X-ray diffraction (XRD) reveals the existence of nanopores in Na-
78 bentonite (Kozaki et al., 1998, 2001). Equation 1 also assumes that the two- and three-layer
79 hydrates (observed by XRD in the range 0.98 < pb,mont < 1.76 kg dm-3) and the external basal
80 surfaces of montmorillonite stacks can be modeled as a single nanopore compartment (Bourg et
81 al., 2007). For 0.2 < pb,mont < 1.7 kg dm-3 (i.e., ranging from a dilute montmorillonite gel to a
82 compacted bentonite with most of its pore space located in nanopores), equation 1 accurately
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