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高温下钙蒙脱石膨胀特性的分子动力学模拟

杨亚帆 王建州 商翔宇 王涛 孙树瑜

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高温下钙蒙脱石膨胀特性的分子动力学模拟

杨亚帆, 王建州, 商翔宇, 王涛, 孙树瑜

Molecular dynamics simulation of swelling properties of Ca-montmorillonite at high temperatures

Yang Ya-Fan, Wang Jian-Zhou, Shang Xiang-Yu, Wang Tao, Sun Shu-Yu
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  • 高温下蒙脱石的膨胀特性在核废料深部封存、二氧化碳封存及页岩气开发等应用中有着重要影响, 但相关机理尚不明确. 本工作使用分子动力学模拟为技术手段计算5 MPa和298—500 K等条件下, 1.40—4.00 nm晶面间距(d)的一系列饱和钙蒙脱石的膨胀压力. 以模拟所得的数值结果为依据, 基于水化效应、双电层效应和离子关联效应等模型推演膨胀压力随温度与d的变化规律, 并与相应的实验数据进行对比. 模拟结果表明, 当d较小时, 因为高温会弱化水化力的强度, 钙蒙脱石膨胀压力震荡的幅度降低, 同时水化力作用的d的范围减小. 当d较大时, 因为高温强化离子关联效应, 膨胀压力降低, 同时双电层力的作用的d的范围增加. 在较高温度和较大d时, 膨胀压力为收缩力, 阻碍膨胀. 这些膨胀压力的变化规律与前期钠蒙脱石体系的研究类似. 然而, 通过对比两种蒙脱石体系的模拟结果, 发现两种体系存在显著的差异—钙蒙脱石比钠蒙脱石更难膨胀到较大的d.此模拟结果与前人实验观测的结果相符. 我们进一步将此差异归于钙蒙脱石的离子关联效应要远大于钠蒙脱石. 有别于分子模拟中对于离子关联效应的精确描述, 连续化的Poisson-Boltzmann方程因为忽略了离子关联效应, 从而无法表达出与两种体系模拟结果都相吻合的膨胀压力变化规律.
    The swelling of Ca-montmorillonite at elevated temperatures is important for many applications including geological disposal of radioactive waste, subsurface carbon sequestration, and shale gas exploration. However, the experimentally observed swelling behaviors of Ca-montmorillonite contacting liquid water and the temperature effects on the swelling pressure are not well understood. In this work, molecular dynamics simulations are carried out to study the swelling of Wyoming Ca-montmorillonite with a d-spacing (d) range of 1.40–4.00 nm at 5 MPa and various temperatures (298–500 K). The ClayFF and SPC are adopted for modeling Ca-montmorillonite and water, respectively. The simulation box is measured to be 11.15, 3.66, and 28.00 nm in the x-, y-, and z-direction. Atomistic pistons are used to control the bulk pressure of the water environment, and the implicit walls are implemented for preventing the ions from leaking from the pore into the water environment. The clay atoms are fixed during the simulation and the swelling pressure is calculated through dividing the force by the area. The equilibrium time is at least 20 ns and the production time falls in a range of 50–88 ns. The swelling pressure results show that for small d, high temperature reduces the magnitude of the oscillating curve of swelling pressure and also reduces the range of d where hydration force dominates the swelling pressure. This temperature effect is due to the weakened hydration force as evidenced from the weakened water density distributions inside the pore. For large d, high temperature reduces the swelling pressure, which is consistent with the experimental result, and increases the range of d where double layer force dominates the swelling pressure. The reduction of the swelling pressure can be explained by the enhanced ion correlation that reduces the double layer force according to the strong coupling theory, given that the calculated coupling parameters at higher temperatures are smaller. The swelling pressures are negative at elevated temperatures and large d, which prevents the clay from further swelling. However, the classical Poisson-Boltzmann (PB) equation predicts the positive double layer force since the ion correlation effect is not considered in the PB equation. Furthermore, the calculated swelling free energy curve shows that at 298 K and 5 MPa, it is difficult for Ca-montmorillonite to swell beyond a d-spacing of around 1.9 nm, which is in good agreement with the experimental result. The energy barrier for Ca-montmorillonite to swell to large d is larger than that for Na-montmorillonite, which means that it is more difficult for Ca-montmorillonite to swell to large d. This behavior is consistent with experimental observation and can be explained by the larger ion correlation effect in the Ca-montmorillonite system. These findings enhance the understanding of swelling of Ca-montmorillonite at elevated temperatures and could help to engineer better barrier materials for nuclear waste storage.
      通信作者: 杨亚帆, yafan.yang@cumt.edu.cn ; 孙树瑜, shuyu.sun@kaust.edu.sa
    • 基金项目: 国家自然科学基金重点项目(批准号: 51936001)、国家自然科学基金(批准号: 51874262)、阿卜杜拉国王科技大学(批准号: BAS/1/1351-01, URF/1/4074-01, URF/1/3769-01)和中国矿业大学引进人才科研启动经费(批准号: 102521155)资助的课题
      Corresponding author: Yang Ya-Fan, yafan.yang@cumt.edu.cn ; Sun Shu-Yu, shuyu.sun@kaust.edu.sa
    • Funds: Project supported by the Key Program of the National Natural Science Foundation of China (Grant No. 51936001), the National Natural Science Foundation of China (Grant No. 51874262), the King Abdullah University of Science and Technology (Grant Nos. BAS/1/1351-01, URF/1/4074-01, URF/1/3769-01), and the Talent Introduction Scientific Research Startup Foundation of China University of Mining and Technology, China (Grant No. 102521155)
    [1]

    Yang Y, Qiao R, Wang Y, Sun S 2021 Appl. Clay Sci. 201 105924Google Scholar

    [2]

    Pusch R 1992 Clay Miner. 27 353Google Scholar

    [3]

    Higgo J 1987 Prog. Nucl. Energy 19 173Google Scholar

    [4]

    Morodome S, Kawamura K 2011 Clays Clay Miner. 59 165Google Scholar

    [5]

    Ferrage E, Lanson B, Sakharov B A, Geoffroy N, Jacquot E, Drits V A 2007 Am. Mineral. 92 1731Google Scholar

    [6]

    Karnland O 1997 Bentonite Swelling Pressure in Strong NaCl Solutions. Correlation between Model Calculations and Experimentally Determined Data Report

    [7]

    Komine H, Ogata N 1996 Can. Geotech. J. 33 11Google Scholar

    [8]

    Norrish K 1954 Discuss. Faraday Soc. 18 120Google Scholar

    [9]

    Yong R 1999 Eng. Geol. 54 3Google Scholar

    [10]

    Posner A M, Quirk J P 1964 J. Colloid Sci. 19 798Google Scholar

    [11]

    Norrish K, Quirk J 1954 Nature 173 255Google Scholar

    [12]

    Pusch R, Karnland O, Hökmark H 1990 GMM-a General Microstructural Model for Qualitative and Quantitative Studies of Smectite Clays Report

    [13]

    Villar M V, Lloret A 2004 Appl. Clay Sci. 26 337Google Scholar

    [14]

    Akinwunmi B, Hirvi J T, Kasa S, Pakkanen T A 2020 Chem. Phys. 528 110511Google Scholar

    [15]

    Akinwunmi B, Sun L, Hirvi J T, Kasa S, Pakkanen T A 2019 Chem. Phys. 516 177Google Scholar

    [16]

    Honorio T, Brochard L, Vandamme M 2017 Langmuir 33 12766Google Scholar

    [17]

    Yang Y, Narayanan Nair A K, Sun S 2019 ACS Earth Space Chem. 3 2635Google Scholar

    [18]

    Li Y, Narayanan Nair A K, Kadoura A, Yang Y, Sun S 2019 Ind. Eng. Chem. Res. 58 1396Google Scholar

    [19]

    那平, 张帆, 李艳妮 2006 物理化学学报 22 1137Google Scholar

    Na P, Zhang F, Li Y N 2006 Acta Phys. -Chim. Sin. 22 1137Google Scholar

    [20]

    王进, 王军霞, 曾凡桂, 吴秀玲 2010 化学学报 16 1653

    Wang J, Wang J X, Zeng F G, Wu X L 2010 Acta Chim. Sin. 16 1653

    [21]

    王进, 曾凡柱, 王军霞 2006 化学学报 64 1654Google Scholar

    Wang J, Zeng F Z, Wang J X 2006 Acta Chim. Sin. 64 1654Google Scholar

    [22]

    李丽丽, 张晓虹, 王玉龙, 国家辉, 张双 2016 物理学报 65 19620201Google Scholar

    Li L L, Zhang X H, Wang Y L, Guo J H, Zhang S 2016 Acta Phys. Sin. 65 19620201Google Scholar

    [23]

    Plimpton S 1995 J. Comput. Phys. 117 1Google Scholar

    [24]

    Cygan R T, Liang J-J, Kalinichev A G 2004 J. Phys. Chem. B 108 1255Google Scholar

    [25]

    Berendsen H, Grigera J, Straatsma T 1987 J. Phys. Chem. 91 6269Google Scholar

    [26]

    Ryckaert J-P, Ciccotti G, Berendsen H J 1977 J. Comput. Phys. 23 327Google Scholar

    [27]

    Hockney R W, Eastwood J W 2021 Computer Simulation using Particles (Boca Raton: CRC Press)

    [28]

    Shinoda W, Shiga M, Mikami M 2004 Phys. Rev. B 69 134103Google Scholar

    [29]

    Allen M P, Tildesley D J 2017 Computer Ssimulation of Liquids (Oxford University Press)

    [30]

    Israelachvili J N 2015 Intermolecular and Surface Forces (Cambridge: Academic Press) p291

    [31]

    Schlaich A, Dos Santos A P, Netz R R 2018 Langmuir 35 551

    [32]

    Bourg I C, Sposito G 2011 J. Colloid Interface Sci. 360 701Google Scholar

    [33]

    Sposito G, Skipper N T, Sutton R, Park S H, Soper A K, Greathouse J A 1999 Proc. Natl. Acad. Sci. U. S. A. 96 3358Google Scholar

    [34]

    Fang C, Sun S, Qiao R 2019 Langmuir 35 10341Google Scholar

    [35]

    Moreira A G, Netz R R 2001 Phys. Rev. Lett. 87 78301Google Scholar

    [36]

    Netz R R 2001 Eur. Phys. J. E 5 557Google Scholar

    [37]

    Moreira A, Netz R 2002 Eur. Phys. J. E 8 33Google Scholar

    [38]

    Whitley H D, Smith D E 2004 J. Chem. Phys. 120 5387Google Scholar

    [39]

    Tambach T J, Bolhuis P G, Hensen E J, Smit B 2006 Langmuir 22 1223Google Scholar

    [40]

    Seppälä A, Puhakka E, Olin M 2016 Clay Miner. 51 197Google Scholar

    [41]

    Brochard L, Honório T, Vandamme M, Bornert M, Peigney M 2017 Acta Geotech. 12 1261Google Scholar

  • 图 1  研究饱和钙蒙脱石膨胀压力的分子体系; 蒙脱石原子类型与颜色关系: 橙: 钙离子, 红: 氧, 白: 氢, 黄: 硅, 蓝: 铝, 粉: 镁; 体系中的水分子不作具体展示

    Fig. 1.  Molecular system for studying the swelling pressure of Ca-montmorillonite in water. The color code for clay atoms: orange: Ca ion, red: O, white: H, yellow: Si, cyan: Al, pink: Mg. Water molecules are not explicitly shown.

    图 2  饱和蒙脱石在298 K和5 MPa下膨胀压力曲线; 钠蒙脱石的数据源于文献[1]

    Fig. 2.  Swelling pressure curves of saturated montmorillonite at 298 K and 5 MPa. Data for Na-montmorillonite is taken from Ref. [1].

    图 3  在298 K和5 MPa下, 水在孤立钙蒙脱石表面($ d\to \infty $)的平衡密度分布(a)和钙蒙脱石层间水在不同晶面间距下的平衡密度分布((b)—(l)); 在((b)—(l))图中, 虚线(点线)为平移后的(a)图中的密度分布; x = 0 对应孔的中心

    Fig. 3.  Equilibrium density profiles of water near one quasi-isolated clay surface (a) and inside Ca-montmorillonite pore with various d-spacings ((b)–(l)) at 298 K and 5 MPa. In ((b)–(l)), the shifted density profile from (a) are plotted as dashed(dotted) lines. x = 0 corresponds to the center of the pore.

    图 4  在298 K和5 MPa下, 钙离子在孤立钙蒙脱石表面($ d\to \infty $)的平衡密度分布(a)和钙蒙脱石层间钙离子在不同晶面间距下的平衡密度分布((b)—(l)); 在((b)—(l))图中, 虚线(点线)为平移后的(a)图中的密度分布; x = 0 对应孔的中心

    Fig. 4.  Equilibrium density profiles of Ca ion near one quasi-isolated clay surface (a) and inside Ca-montmorillonite pore with various d-spacings ((b)–(l)) at 298 K and 5 MPa. In ((b)–(l)), the shifted density profile from (a) are plotted as dashed(dotted) lines. x = 0 corresponds to the center of the pore.

    图 5  饱和蒙脱石在298 K和5 MPa下的膨胀自由能曲线

    Fig. 5.  Swelling free energy curves of saturated montmorillonite at 298 K and 5 MPa.

    图 6  饱和钙蒙脱石在不同温度和5 MPa下膨胀压力曲线

    Fig. 6.  Swelling pressure curves of saturated Ca-montmorillonite at various temperatures and 5 MPa.

    图 7  在5 MPa下, 水在孤立钙蒙脱石表面($ d\to \infty $)的平衡密度分布(a)和钙蒙脱石层间水在不同晶面间距下的平衡密度分布((b)—(l)); 在((b)—(l))图中, 虚线(点线)为平移后的(a)图中的密度分布. x = 0 对应孔的中心

    Fig. 7.  Equilibrium density profiles of water near one quasi-isolated clay surface (a) and inside Ca-montmorillonite pore with various d-spacings ((b)–(l)) at 5 MPa. In ((b)–(l)), the shifted density profiles from (a) are plotted as dashed(dotted) lines. x = 0 corresponds to the center of the pore.

    图 8  饱和钙蒙脱石在不同温度和5 MPa下的膨胀自由能曲线

    Fig. 8.  Swelling free energy curves of saturated Ca-montmorillonite at various temperatures and 5 MPa.

    表 1  水、蒙脱石和离子的Lennard-Jones参数和电荷

    Table 1.  Lennard-Jones parameters and partial charges of water, montmorillonite, and ion.

    原子种类尺度参数$ {\sigma }_{i}/$nm能量参数$ {\varepsilon }_{i}/$(kcal·mol–1)电荷q/e
    O0.316561.554 × 10–1–0.8200
    H0.000000.0000.4100
    蒙脱石羟基O0.316561.554 × 10–1–0.9500
    有取代的羟基O0.316561.554 × 10–1–1.0808
    羟基H0.000000.0000.4250
    桥联O0.316561.554 × 10–1–1.0500
    有八面体取代的桥连O0.316561.554 × 10–1–1.1808
    有四面体取代的桥连O0.316561.554 × 10–1–1.1688
    四面体Si0.330201.841 × 10–62.1000
    四面体Al0.330201.841 × 10–61.5750
    八面体Al0.427121.330 × 10–61.5750
    八面体Mg0.526439.030 × 10–71.3600
    离子Ca0.287201.000 × 10–12.0000
    下载: 导出CSV

    表 2  在不同温度和晶面间距下, 分子动力学模拟计算的钙蒙脱石的膨胀压力及预测误差

    Table 2.  Swelling pressures of Ca-montmorillonite at different temperatures and d-spacings and the corresponding standard deviations obtained from molecular dynamics simulations.

    晶面间距/nm膨胀压力/MPa 膨胀压力的标准差/MPa
    T = 298 KT = 400 KT = 500 KT = 298 KT = 400 KT = 500 K
    1.40577.940275.174263.519 27.58315.8862.875
    1.5075.841110.869157.5692.7845.2794.072
    1.6040.63784.61792.1471.8870.7190.482
    1.70–6.80010.74423.4760.6890.1550.609
    1.7510.57516.78120.1060.3490.4080.445
    1.8022.74925.89023.4490.1950.2860.401
    1.8513.27514.24113.8840.2851.1860.364
    1.903.8935.9136.1740.4820.6290.077
    1.95–4.018–2.3070.1210.3690.1490.858
    2.00–2.926–0.923–0.7300.3250.3500.142
    2.103.3133.1420.6640.5830.1840.423
    2.152.2761.388–1.3760.3610.4110.401
    2.201.044–0.584–2.0340.2200.1440.177
    2.30–0.5280.103–1.7140.4040.4420.176
    2.40–0.246–0.184–1.7630.1260.2910.204
    2.600.844–0.639–2.0680.4020.1980.291
    3.00–0.082–0.502–1.0840.1300.2230.244
    3.500.050–0.331–0.5720.1070.1250.060
    4.000.0480.003–0.0840.1930.0570.158
    下载: 导出CSV

    表 3  水在5 MPa和不同温度下的介电常数和耦合参数

    Table 3.  Water dielectric constants and coupling parameters at 5 MPa and various temperatures.

    温度T/K298400500
    水介电常数 $ {\varepsilon }_{\mathrm{b}} $63.58a40.01a23.23a
    耦合参数 ${\Xi }$30.3842.5880.84
    a数据源于文献[1].
    下载: 导出CSV
  • [1]

    Yang Y, Qiao R, Wang Y, Sun S 2021 Appl. Clay Sci. 201 105924Google Scholar

    [2]

    Pusch R 1992 Clay Miner. 27 353Google Scholar

    [3]

    Higgo J 1987 Prog. Nucl. Energy 19 173Google Scholar

    [4]

    Morodome S, Kawamura K 2011 Clays Clay Miner. 59 165Google Scholar

    [5]

    Ferrage E, Lanson B, Sakharov B A, Geoffroy N, Jacquot E, Drits V A 2007 Am. Mineral. 92 1731Google Scholar

    [6]

    Karnland O 1997 Bentonite Swelling Pressure in Strong NaCl Solutions. Correlation between Model Calculations and Experimentally Determined Data Report

    [7]

    Komine H, Ogata N 1996 Can. Geotech. J. 33 11Google Scholar

    [8]

    Norrish K 1954 Discuss. Faraday Soc. 18 120Google Scholar

    [9]

    Yong R 1999 Eng. Geol. 54 3Google Scholar

    [10]

    Posner A M, Quirk J P 1964 J. Colloid Sci. 19 798Google Scholar

    [11]

    Norrish K, Quirk J 1954 Nature 173 255Google Scholar

    [12]

    Pusch R, Karnland O, Hökmark H 1990 GMM-a General Microstructural Model for Qualitative and Quantitative Studies of Smectite Clays Report

    [13]

    Villar M V, Lloret A 2004 Appl. Clay Sci. 26 337Google Scholar

    [14]

    Akinwunmi B, Hirvi J T, Kasa S, Pakkanen T A 2020 Chem. Phys. 528 110511Google Scholar

    [15]

    Akinwunmi B, Sun L, Hirvi J T, Kasa S, Pakkanen T A 2019 Chem. Phys. 516 177Google Scholar

    [16]

    Honorio T, Brochard L, Vandamme M 2017 Langmuir 33 12766Google Scholar

    [17]

    Yang Y, Narayanan Nair A K, Sun S 2019 ACS Earth Space Chem. 3 2635Google Scholar

    [18]

    Li Y, Narayanan Nair A K, Kadoura A, Yang Y, Sun S 2019 Ind. Eng. Chem. Res. 58 1396Google Scholar

    [19]

    那平, 张帆, 李艳妮 2006 物理化学学报 22 1137Google Scholar

    Na P, Zhang F, Li Y N 2006 Acta Phys. -Chim. Sin. 22 1137Google Scholar

    [20]

    王进, 王军霞, 曾凡桂, 吴秀玲 2010 化学学报 16 1653

    Wang J, Wang J X, Zeng F G, Wu X L 2010 Acta Chim. Sin. 16 1653

    [21]

    王进, 曾凡柱, 王军霞 2006 化学学报 64 1654Google Scholar

    Wang J, Zeng F Z, Wang J X 2006 Acta Chim. Sin. 64 1654Google Scholar

    [22]

    李丽丽, 张晓虹, 王玉龙, 国家辉, 张双 2016 物理学报 65 19620201Google Scholar

    Li L L, Zhang X H, Wang Y L, Guo J H, Zhang S 2016 Acta Phys. Sin. 65 19620201Google Scholar

    [23]

    Plimpton S 1995 J. Comput. Phys. 117 1Google Scholar

    [24]

    Cygan R T, Liang J-J, Kalinichev A G 2004 J. Phys. Chem. B 108 1255Google Scholar

    [25]

    Berendsen H, Grigera J, Straatsma T 1987 J. Phys. Chem. 91 6269Google Scholar

    [26]

    Ryckaert J-P, Ciccotti G, Berendsen H J 1977 J. Comput. Phys. 23 327Google Scholar

    [27]

    Hockney R W, Eastwood J W 2021 Computer Simulation using Particles (Boca Raton: CRC Press)

    [28]

    Shinoda W, Shiga M, Mikami M 2004 Phys. Rev. B 69 134103Google Scholar

    [29]

    Allen M P, Tildesley D J 2017 Computer Ssimulation of Liquids (Oxford University Press)

    [30]

    Israelachvili J N 2015 Intermolecular and Surface Forces (Cambridge: Academic Press) p291

    [31]

    Schlaich A, Dos Santos A P, Netz R R 2018 Langmuir 35 551

    [32]

    Bourg I C, Sposito G 2011 J. Colloid Interface Sci. 360 701Google Scholar

    [33]

    Sposito G, Skipper N T, Sutton R, Park S H, Soper A K, Greathouse J A 1999 Proc. Natl. Acad. Sci. U. S. A. 96 3358Google Scholar

    [34]

    Fang C, Sun S, Qiao R 2019 Langmuir 35 10341Google Scholar

    [35]

    Moreira A G, Netz R R 2001 Phys. Rev. Lett. 87 78301Google Scholar

    [36]

    Netz R R 2001 Eur. Phys. J. E 5 557Google Scholar

    [37]

    Moreira A, Netz R 2002 Eur. Phys. J. E 8 33Google Scholar

    [38]

    Whitley H D, Smith D E 2004 J. Chem. Phys. 120 5387Google Scholar

    [39]

    Tambach T J, Bolhuis P G, Hensen E J, Smit B 2006 Langmuir 22 1223Google Scholar

    [40]

    Seppälä A, Puhakka E, Olin M 2016 Clay Miner. 51 197Google Scholar

    [41]

    Brochard L, Honório T, Vandamme M, Bornert M, Peigney M 2017 Acta Geotech. 12 1261Google Scholar

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出版历程
  • 收稿日期:  2021-08-24
  • 修回日期:  2021-09-29
  • 上网日期:  2022-02-10
  • 刊出日期:  2022-02-20

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