Ion-exchange modeling is used widely to describe and predict ion-adsorption data on clay minerals. Although the model parameters are usually optimized by curve fitting experimental data, this approach does not confirm the identity of the adsorption sites. The purpose of the present study was to extend to divalent cations a previous study on the retention of monovalent cations on Na-saturated montmorillonite (NaMnt) which optimized some of the model parameters using density functional theory (DFT) simulations. The adsorption strength of divalent cations increased in the order Mg²⁺ < Cd²⁺ < Ca²⁺ < Sr²⁺ < Ba²⁺. After adding adsorption of metal hydroxide species (MOH⁺), the three-site ion-exchange model was able to describe adsorption data over a wide pH range (pH 1–10) on NaMnt. X-ray diffraction (XRD) analyses were conducted to investigate the interlayer dimension of clay samples under various conditions. The cation retention strengths of divalent cations did not correlate with interlayer dimensions. The XRD analyses of the Mnt showed a d₀₀₁ value of 19.6 Å when saturated with alkaline earth cations, 22.1 Å with Cd²⁺, 15.6 Å with Na⁺, and 15.2 Å with H⁺. In the case of Na⁺, the 15.6 Å peak decreased gradually and disappeared, and new peaks at 22.1 and 19.6 Å appeared when the percentages of Mg²⁺ and Ba²⁺ adsorbed increased on NaMnt. The peak shifted from 22.1 to 20.3 and 19.6 Å when the pH increased for all cations except Cd²⁺, which stayed constant at 22.1 Å. The coexistence of multiple d₀₀₁ peaks in the XRD patterns suggested that the interlayer cations were segregated, and that the interlayer ion–ion interactions among different types of ions were minimized.

离子交换模型广泛用于描述和预测粘土矿物的离子吸附数据。虽然模型参数通常通过曲线拟合实验数据进行优化，但这种方法并不能确认吸附位点的身份。本研究的目的是将先前关于单价阳离子保留在 Na 饱和蒙脱石 (NaMnt) 上的研究扩展到二价阳离子，该研究使用密度泛函理论 (DFT) 模拟优化了一些模型参数。二价阳离子的吸附强度按照Mg ²⁺ < Cd ²⁺ < Ca ²⁺ < Sr ²⁺ < Ba ²⁺的顺序增加。加入吸附金属氢氧化物后的物种（M OH ⁺)，三中心离子交换模型能够描述 NaMnt 上宽 pH 范围 (pH 1-10) 的吸附数据。进行 X 射线衍射 (XRD) 分析以研究粘土样品在各种条件下的层间尺寸。二价阳离子的阳离子保留强度与层间尺寸无关。Mnt 的 XRD 分析表明，当碱土金属阳离子饱和时，d ₀₀₁值为 19.6 Å，Cd ^{2+ 为}22.1 Å，Na ^{+ 为}15.6 Å，H ^{+ 为}15.2 Å 。在 Na ⁺的情况下，15.6 Å 峰逐渐减小并消失，当 Mg ²⁺和 Ba ²⁺的百分比增加时，在 22.1 和 19.6 Å 处出现新峰NaMnt 上的吸附量增加。当除 Cd ²⁺之外的所有阳离子的 pH 值增加时，峰值从 22.1 移至 20.3 和 19.6 Å，Cd ²⁺保持恒定在 22.1 Å。XRD 图中多个d ₀₀₁峰的共存表明层间阳离子被隔离，并且不同类型离子之间的层间离子-离子相互作用被最小化。