The interlayer pore width of the osmotic swelling is calculated from a regression curve (Equations (11) and (12)) in Figure 2 plotting the relation between the effective montmorillonite density and basal spacing. The basal spacing of the mixed state of the osmotic and crystalline swelling was at 700 kg/m^{3} ≤ *ρ*_{em} < 1,000 kg/m^{3} for Na-montmorillonite. As the abundance ratio of the number of stacks attributed to the osmotic or crystalline swelling was difficult to evaluate precisely, we assumed that the osmotic swelling stacks had an abundance ratio of 100% at *ρ*_{em} = 700 kg/m^{3} and 0% at *ρ*_{em} = 1,000 kg/m^{3}, and *vice versa* for the crystalline swelling. The abundance ratio of the stacks between these densities was calculated from linear interpolation. The basal spacing of the mixed state consisting of the 3WH and 2WH states was estimated at 1,300 kg/m^{3} < *ρ*_{em} < 1,600 kg/m^{3} for Na-montmorillonite and Ca-montmorillonite. We assumed that the stacks had an abundance ratio of 100% at *ρ*_{em} = 1,300 kg/m^{3} and 0% at *ρ*_{em} = 1,600 kg/m^{3} for the 3WH state, and *vice versa* for the 2WH state. Between these densities, the abundance ratio of the stacks was calculated in the same manner used for Na-montmorillonite at 700 kg/m^{3} ≤ *ρ*_{em} < 1,000 kg/m^{3}. The external pore width was calculated by Equations (1), (11), (12), and (20) using the calculation parameters as shown in Table 1. The external pore width decreases as the effective montmorillonite density increases, and also as the number of laminations in the stack (*n*) decreases (Figure 5). If the number of laminations exceeds 4 for Na-montmorillonite, the external pore width at *ρ*_{em} = 1,000 kg/m^{3} is larger than that at *ρ*_{em} = 700 kg/m^{3}, based on the assumed ratio of the osmotic swelling to the 3WH states. Having a large external pore width implies that the specimen has enough space for montmorillonite swelling. Since only crystalline swelling was observed at *ρ*_{em} = 1,000 kg/m^{3} (Kozaki *et al.* 1998), it would be unreasonable to assume that the external pore width at *ρ*_{em} = 1,000 kg/m^{3} is larger than that at *ρ*_{em} = 700 kg/m^{3}. In contrast to the unreasonable behavior observed for Na-montmorillonite with an *n* over 3, the external pore width in the case of Ca-montmorillonite decreases monotonically as the effective montmorillonite density increases in every lamination number. This difference between Na-montmorillonite and Ca-montmorillonite was due to the difference in their swelling behavior. Although Na-montmorillonite could form the osmotic state (the *d-*value was over 3.2 nm) under any effective montmorillonite density condition other than 1,000 kg/m^{3} ≤ *ρ*_{em}, Ca-montmorillonite could swell only up to the 3WH state (the *d-*value was 1.88 nm) under the density condition of *ρ*_{em} < 1,000 kg/m^{3}. Therefore, we determined that the number of laminations for Na-montmorillonite was 2 and 3, while that for Ca-montmorillonite was an arbitrary number above 2.

Table 1

Diameter of montmorillonite particle (2R) | 3.91 × 10^{−7} [m] (Suzuki et al. 2012) |

Thickness of montmorillonite particle (t) | 9.55 × 10^{−10} [m] (Tournassat et al. 2003) |

Particle density of montmorillonite (ρ) _{m} | 2,770 (kg/m^{3}) (Komine 2008) |

Diameter of montmorillonite particle (2R) | 3.91 × 10^{−7} [m] (Suzuki et al. 2012) |

Thickness of montmorillonite particle (t) | 9.55 × 10^{−10} [m] (Tournassat et al. 2003) |

Particle density of montmorillonite (ρ) _{m} | 2,770 (kg/m^{3}) (Komine 2008) |

Figure 5

This site uses cookies. By continuing to use our website, you are agreeing to our privacy policy.