土壤电场对土壤中离子扩散/吸附动力学的影响
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摘要
目前关于土壤中离子扩散/吸附动力学已开展了一些研究,大家普遍认为离子扩散与离子交换是两个完全不同的过程,并认为离子的扩散往往是离子交换过程的控制速率步骤；而且,不论是在离子扩散问题还是在离子交换的动力学研究中,人们都直接应用Fick扩散定律来处理土壤中的离子扩散与交换,而忽略了土壤电场这一重要影响因素。本研究的主要目标是在“场”理论的基础上,提出土壤电场作用下离子扩散/吸附动力学的新机理,并在此基础上准确测定离子扩散/吸附的速率及相关参数,从而实现土壤电场作用下离子扩散/吸附动力学的定量评估,最终明确土壤电场在土壤离子传输中的主导作用。
为了实现这个研究目标,首先从理论上讨论了恒流法与平衡法中离子发生吸附、解吸时DDL(扩散双电层)中离子的动力学分布方程。这一系列方程反映了,当吸附解吸过程发生时离子浓度在DDL与本体溶液不同位置中随时间的变化关系。结果表明,当吸附解吸过程达到平衡时,自然而然地就会得到Boltzmann分布方程,从而引入了一个关于离子交换与离子扩散的新概念,即DDL中离子的交换过程的本质是各种离子在外电场中由“活度梯度”推动下的相互扩散过程。
然后从Li和Wu提出的考虑黏土矿物的表面电场时的由非线性的Fokker-Planck微分方程转化成的线性方程入手,根据扩散过程中的瞬时松弛近似,得出土壤电场作用下的离子扩散/吸附动力学新模型,并且同时从理论和实验上证实土壤中的离子扩散与交换确实是同一过程,而且土壤颗粒表面电场将大大加速离子的吸附过程。
论文还通过不同强弱静电力作用下离子的吸附/扩散动力学研究,提出了描述不同强弱静电力作用下离子扩散/吸附的速率方程,根据理论分析,我们用“蒙脱石K饱和样”、“蒙脱石Ca饱和样”、“中性紫色土K饱和样”和“黄壤K饱和样”作为实验材料来研究离子的扩散/吸附动力学。实验结果表明,当离子交换过程中同时存在强力吸附(强静电力吸附或化学键吸附)和弱力吸附时,在离子扩散/吸附的初期,将出现零级动力学过程,随后转为一级动力学过程,并且零级和一级动力学过程中存在着明显的转折点。随后,本部分的研究结果通过考虑土壤颗粒电场与不考虑土壤颗粒电场时离子的扩散速率的比较,说明了土壤颗粒电场强烈地影响着离子的扩散/吸附速率。这进一步说明了,土壤颗粒表面电荷引起的电场是土壤带电离子吸附的主要推动力,离子交换吸附和离子扩散完全是同一个过程,即扩散双电层中的离子交换过程的本质是各种离子在外电场中由活度梯度(包含浓度梯度和电位梯度)推动下的“混合”过程。说明过去认为离子交换与离子扩散是两个不同的过程的观点是完全错误的。
论文还通过土粒表面静电力作用下不同离子扩散/吸附动力学研究,分别考虑了表面电场作用下的Ca2+-K+、Mg2+-K+体系中,Ca2+Ca2+在固/液相界面中的吸附动力学,通过不同电解质条件下的扩散速率,Mg2+、Ca2+在土壤表面的覆盖度以及当Mg2+、Ca2+扩散/吸附达到平衡时离子的活度系数的分析,结果表明,在相同支持电解质浓度的条件下,实验结果表现出初期阶段强静电力作用下快速吸附的零级动力学过程和一定反应时间后的弱静电力作用下的一级动力学过程,而且零级速率过程和一级速率过程之间存在明显的转折点,且Ca2+-K+交换的零级与一级过程比Mg2+-K+交换持续时间更久,扩散速率更快,在土壤表面的覆盖度更大,吸附达到平衡时离子的平均活度系数更小。通过对土壤表面电荷性质的分析,我们发现,在本研究中,离子水化半径、离子的相对有效电荷系数与土壤颗粒电场是造成各体系中Ca2+、Mg2+吸附动力学有差别的根本原因。同时,根据本文中离子吸附的理论模型,提供了一个测定吸附态离子的平均活度系数的新方法。并且可以计算出土壤颗粒电场作用下离子吸附动力学的一些重要参数,比如,吸附态离子的吸附速率系数、离子的平衡吸附量、离子在土壤颗粒表面表现的概率与覆盖度以及固定液的体积。这些参数可以定量反映土壤颗粒表面电场对离子吸附动力学的影响。本部分的研究结果再一次从不同离子的扩散／吸附动力学角度,明确了土壤电场在离子扩散／吸附动力学过程中起的主导地位,证明了离子交换吸附和离子扩散完全是同一个过程,即扩散双电层中的离子交换过程的本质是各种离子在外电场中由活度梯度(包含浓度梯度和电位梯度)推动下的“混合”过程。
总之,本研究首次从多个角度(包括扩散通量、扩散速率、表面电荷性质、离子在土壤颗粒表面的覆盖度、离子扩散/吸附达平衡时的活度系数等)定量地,而且是较系统地考察土壤外电场对离子扩散传输的影响。进一步得出“扩散双电层中的离子交换过程的本质是各种离子在外电场中由活度梯度(包含浓度梯度和电位梯度)推动下的“混合”过程的结论。
At present, a great number of researches related to the ion diffusion/adsorption kinetics in soil have been carried out, and most researchers accept the opinion that ion diffusion and ion exchange via electrostatic attractive forces occurring in DDL were two different and separate processes, and the reaction rate is limited by ion diffusion; Furthermore, Most of them directly employed Fick's first and second laws to describe ionic diffusion in the soil, and the electric potential from charged clay surface was neglected. The main target of this research is putting forward a new equation for describing cation exchange kinetics on the basis of the theory of "field", then determining the ion diffusion/adsorption rate and related parameters, so as to evaluate quantitatively the influence on ion diffusion/adsorption dynamics of soil surface potential, and at last to identify the leading position of the soil surface potential in ion diffusion/adsorption in the soil.
In order to fulfill this task, firstly, the dynamic distribution equations of ion in DDL in both of adsorption and desorption process in the experiment of the miscible displacement and the batch technique have been established theoretically in this paper. Those equations can give us the clear pictures how the concentration of ions changes with time at different position both in DDL and in bulk solution when the adsorption and desorption are progressing. The results showed that, when the equilibrium of adsorption or desorption to be reached, the dynamic distribution will naturally change to the equilibrium distribution:the Boltzmann distribution. Thus, a new concept of ion diffusion/adsorption in DDL is introduced, that is, the process of ion exchange occurring in the diffuse double layer will be essentially a mutual diffusion driven by the gradient of the apparent concentration.
Then, starting with the linear equation transformed from non-linear Fokker-Planck differential equation which the soil surface potential considered, and based on the instantaneous relaxation approximation in the ion diffusion process, we established the theoretical models that well describe the exchange process of ions in the soil under steady flow conditions, both theoretical analysis and experimental data in this paper demonstrated that ion exchange and ion diffusion in the electric field of DDL are not two different processes, they are one, the obtained results showed that the electric field in EDL exerted a significant influence on the ion exchange/diffusion.
Based on the theoretical analysis, we also advanced the rate equations of ion diffusion/adsorption kinetics in different intensity soil surface field. For further reveal the influence of electric field from soil particle surface on cation exchange, in this study, three types of permanently charged materials, the K-saturated neutral purple soil and the K-saturated montmorillonite and the Ca-saturated montmorillonite, and K-saturated yellow soil with variable charge were used. The results showed that when strong forces adsorption (strong electrostatic adsorption or chemical bond adsorption) exist on soil particle surface, in the initial stage of diffusion/adsorption, the diffusion/adsorption process will appear the zero-order kinetics, and then transfer to the first-order kinetics, and the turning point from the zero-order to the first-order was very sharp for each system. Subsequently, By comparing the rate coefficient of ion as the electric field from particle surface not to be considered and the rate coefficient as the electric field to be considered, showing that, the electric field from soil particle surface strongly increases the diffusion/adsorption rate, and thus further explains that the soil surface potential is the main driving force of ion diffusion/adsorption process in soil, the exchange and the diffusion processes occurring in external electric field of DDL are really essentially the one process, that is ion exchange occurring in DDL via electrostatic attractive forces may be essentially a mutual diffusion process driven by the activity gradient of the ion (including the concentration gradient and the potential gradient), the opinion that ion diffusion and ion exchange via electrostatic attractive forces occurring in DDL were taken as two different and separate processes was absolutely mistake.
By the comparative study of different ion exchange kinetics process on soil particle electric field at solid-liquid interface, Mg~(2+), Ca~(2+) adsorption kinetic in different particle surface potential was also studied. In this study, some important parameters such as ion diffusion/adsorption rate coefficient in different electrolyte solutions, the adsorption quantities, the surface coverage of the adsorbed ions and the average activity coefficients as the ion diffusion/adsorption equilibrium reached were studied. The experimental data showed that, in the initial stage of experiment, the adsorption process will appear the zero-order kinetics for the strong force adsorption, and then transfer to the first-order kinetics of the weak force adsorption, and the turning point from the zero-order to the first-order was very sharp for each system. When the supporting electrolyte concentration is equal, the adsorption rate of Ca~(2+) is obviously faster than Mg~(2+), the duration of the zero-order kinetics and the first-order kinetics process of Ca~(2+) is much longer than Mg~(2+), and the equilibrium adsorption capacity of Ca~(2+) is more than Mg~(2+), the average activity coefficients of Ca~(2+) on soil solid particle surface is also lower than Mg~(2+). By the analysis of the soil surface charge characters, we also found that in this paper, the differences of the relative effective charge coefficient and the surface electrochemical properties are the basic reason why the Ca~(2+)、Mg~(2+) adsorption kinetics process different. At the same time, based on the theory and method in this research, we also can figure out some important properties for the adsorbed ions of the different adsorption forces respectively, such as the average activity coefficients, the rate coefficients, the adsorption quantities, the surface coverage of the adsorbed ions and the distributed space in the fixed liquid film of the adsorbed ions. These parameters make us possible in future to evaluate quantitatively the effects of different colloid surface potential on the ion diffusion/adsorption kinetics theoretically. The results once again makes clear the leading position of the soil surface potential in ion diffusion/adsorption in the soil from the different ion diffusion/adsorption kinetics process, prove the exchange and the diffusion processes occurring in external electric field of DDL are really essentially the one process, that is ion exchange occurring in DDL via electrostatic attractive forces may be essentially a mutual diffusion process driven by the activity gradient of the ion (including the concentration gradient and the potential gradient).
In conclusion, this paper for the first time can evaluate quantitatively the effects of different colloid surface potential on the ion diffusion/adsorption kinetics theoretically from many ways such as the average activity coefficients, the rate coefficients, the adsorption quantities, the surface coverage of the adsorbed ions, etc. It is further concluded that ion exchange occurring in DDL via electrostatic attractive forces may be essentially a mutual diffusion process driven by the activity gradient of the ion.
为了实现这个研究目标,首先从理论上讨论了恒流法与平衡法中离子发生吸附、解吸时DDL(扩散双电层)中离子的动力学分布方程。这一系列方程反映了,当吸附解吸过程发生时离子浓度在DDL与本体溶液不同位置中随时间的变化关系。结果表明,当吸附解吸过程达到平衡时,自然而然地就会得到Boltzmann分布方程,从而引入了一个关于离子交换与离子扩散的新概念,即DDL中离子的交换过程的本质是各种离子在外电场中由“活度梯度”推动下的相互扩散过程。
然后从Li和Wu提出的考虑黏土矿物的表面电场时的由非线性的Fokker-Planck微分方程转化成的线性方程入手,根据扩散过程中的瞬时松弛近似,得出土壤电场作用下的离子扩散/吸附动力学新模型,并且同时从理论和实验上证实土壤中的离子扩散与交换确实是同一过程,而且土壤颗粒表面电场将大大加速离子的吸附过程。
论文还通过不同强弱静电力作用下离子的吸附/扩散动力学研究,提出了描述不同强弱静电力作用下离子扩散/吸附的速率方程,根据理论分析,我们用“蒙脱石K饱和样”、“蒙脱石Ca饱和样”、“中性紫色土K饱和样”和“黄壤K饱和样”作为实验材料来研究离子的扩散/吸附动力学。实验结果表明,当离子交换过程中同时存在强力吸附(强静电力吸附或化学键吸附)和弱力吸附时,在离子扩散/吸附的初期,将出现零级动力学过程,随后转为一级动力学过程,并且零级和一级动力学过程中存在着明显的转折点。随后,本部分的研究结果通过考虑土壤颗粒电场与不考虑土壤颗粒电场时离子的扩散速率的比较,说明了土壤颗粒电场强烈地影响着离子的扩散/吸附速率。这进一步说明了,土壤颗粒表面电荷引起的电场是土壤带电离子吸附的主要推动力,离子交换吸附和离子扩散完全是同一个过程,即扩散双电层中的离子交换过程的本质是各种离子在外电场中由活度梯度(包含浓度梯度和电位梯度)推动下的“混合”过程。说明过去认为离子交换与离子扩散是两个不同的过程的观点是完全错误的。
论文还通过土粒表面静电力作用下不同离子扩散/吸附动力学研究,分别考虑了表面电场作用下的Ca2+-K+、Mg2+-K+体系中,Ca2+Ca2+在固/液相界面中的吸附动力学,通过不同电解质条件下的扩散速率,Mg2+、Ca2+在土壤表面的覆盖度以及当Mg2+、Ca2+扩散/吸附达到平衡时离子的活度系数的分析,结果表明,在相同支持电解质浓度的条件下,实验结果表现出初期阶段强静电力作用下快速吸附的零级动力学过程和一定反应时间后的弱静电力作用下的一级动力学过程,而且零级速率过程和一级速率过程之间存在明显的转折点,且Ca2+-K+交换的零级与一级过程比Mg2+-K+交换持续时间更久,扩散速率更快,在土壤表面的覆盖度更大,吸附达到平衡时离子的平均活度系数更小。通过对土壤表面电荷性质的分析,我们发现,在本研究中,离子水化半径、离子的相对有效电荷系数与土壤颗粒电场是造成各体系中Ca2+、Mg2+吸附动力学有差别的根本原因。同时,根据本文中离子吸附的理论模型,提供了一个测定吸附态离子的平均活度系数的新方法。并且可以计算出土壤颗粒电场作用下离子吸附动力学的一些重要参数,比如,吸附态离子的吸附速率系数、离子的平衡吸附量、离子在土壤颗粒表面表现的概率与覆盖度以及固定液的体积。这些参数可以定量反映土壤颗粒表面电场对离子吸附动力学的影响。本部分的研究结果再一次从不同离子的扩散／吸附动力学角度,明确了土壤电场在离子扩散／吸附动力学过程中起的主导地位,证明了离子交换吸附和离子扩散完全是同一个过程,即扩散双电层中的离子交换过程的本质是各种离子在外电场中由活度梯度(包含浓度梯度和电位梯度)推动下的“混合”过程。
总之,本研究首次从多个角度(包括扩散通量、扩散速率、表面电荷性质、离子在土壤颗粒表面的覆盖度、离子扩散/吸附达平衡时的活度系数等)定量地,而且是较系统地考察土壤外电场对离子扩散传输的影响。进一步得出“扩散双电层中的离子交换过程的本质是各种离子在外电场中由活度梯度(包含浓度梯度和电位梯度)推动下的“混合”过程的结论。
At present, a great number of researches related to the ion diffusion/adsorption kinetics in soil have been carried out, and most researchers accept the opinion that ion diffusion and ion exchange via electrostatic attractive forces occurring in DDL were two different and separate processes, and the reaction rate is limited by ion diffusion; Furthermore, Most of them directly employed Fick's first and second laws to describe ionic diffusion in the soil, and the electric potential from charged clay surface was neglected. The main target of this research is putting forward a new equation for describing cation exchange kinetics on the basis of the theory of "field", then determining the ion diffusion/adsorption rate and related parameters, so as to evaluate quantitatively the influence on ion diffusion/adsorption dynamics of soil surface potential, and at last to identify the leading position of the soil surface potential in ion diffusion/adsorption in the soil.
In order to fulfill this task, firstly, the dynamic distribution equations of ion in DDL in both of adsorption and desorption process in the experiment of the miscible displacement and the batch technique have been established theoretically in this paper. Those equations can give us the clear pictures how the concentration of ions changes with time at different position both in DDL and in bulk solution when the adsorption and desorption are progressing. The results showed that, when the equilibrium of adsorption or desorption to be reached, the dynamic distribution will naturally change to the equilibrium distribution:the Boltzmann distribution. Thus, a new concept of ion diffusion/adsorption in DDL is introduced, that is, the process of ion exchange occurring in the diffuse double layer will be essentially a mutual diffusion driven by the gradient of the apparent concentration.
Then, starting with the linear equation transformed from non-linear Fokker-Planck differential equation which the soil surface potential considered, and based on the instantaneous relaxation approximation in the ion diffusion process, we established the theoretical models that well describe the exchange process of ions in the soil under steady flow conditions, both theoretical analysis and experimental data in this paper demonstrated that ion exchange and ion diffusion in the electric field of DDL are not two different processes, they are one, the obtained results showed that the electric field in EDL exerted a significant influence on the ion exchange/diffusion.
Based on the theoretical analysis, we also advanced the rate equations of ion diffusion/adsorption kinetics in different intensity soil surface field. For further reveal the influence of electric field from soil particle surface on cation exchange, in this study, three types of permanently charged materials, the K-saturated neutral purple soil and the K-saturated montmorillonite and the Ca-saturated montmorillonite, and K-saturated yellow soil with variable charge were used. The results showed that when strong forces adsorption (strong electrostatic adsorption or chemical bond adsorption) exist on soil particle surface, in the initial stage of diffusion/adsorption, the diffusion/adsorption process will appear the zero-order kinetics, and then transfer to the first-order kinetics, and the turning point from the zero-order to the first-order was very sharp for each system. Subsequently, By comparing the rate coefficient of ion as the electric field from particle surface not to be considered and the rate coefficient as the electric field to be considered, showing that, the electric field from soil particle surface strongly increases the diffusion/adsorption rate, and thus further explains that the soil surface potential is the main driving force of ion diffusion/adsorption process in soil, the exchange and the diffusion processes occurring in external electric field of DDL are really essentially the one process, that is ion exchange occurring in DDL via electrostatic attractive forces may be essentially a mutual diffusion process driven by the activity gradient of the ion (including the concentration gradient and the potential gradient), the opinion that ion diffusion and ion exchange via electrostatic attractive forces occurring in DDL were taken as two different and separate processes was absolutely mistake.
By the comparative study of different ion exchange kinetics process on soil particle electric field at solid-liquid interface, Mg~(2+), Ca~(2+) adsorption kinetic in different particle surface potential was also studied. In this study, some important parameters such as ion diffusion/adsorption rate coefficient in different electrolyte solutions, the adsorption quantities, the surface coverage of the adsorbed ions and the average activity coefficients as the ion diffusion/adsorption equilibrium reached were studied. The experimental data showed that, in the initial stage of experiment, the adsorption process will appear the zero-order kinetics for the strong force adsorption, and then transfer to the first-order kinetics of the weak force adsorption, and the turning point from the zero-order to the first-order was very sharp for each system. When the supporting electrolyte concentration is equal, the adsorption rate of Ca~(2+) is obviously faster than Mg~(2+), the duration of the zero-order kinetics and the first-order kinetics process of Ca~(2+) is much longer than Mg~(2+), and the equilibrium adsorption capacity of Ca~(2+) is more than Mg~(2+), the average activity coefficients of Ca~(2+) on soil solid particle surface is also lower than Mg~(2+). By the analysis of the soil surface charge characters, we also found that in this paper, the differences of the relative effective charge coefficient and the surface electrochemical properties are the basic reason why the Ca~(2+)、Mg~(2+) adsorption kinetics process different. At the same time, based on the theory and method in this research, we also can figure out some important properties for the adsorbed ions of the different adsorption forces respectively, such as the average activity coefficients, the rate coefficients, the adsorption quantities, the surface coverage of the adsorbed ions and the distributed space in the fixed liquid film of the adsorbed ions. These parameters make us possible in future to evaluate quantitatively the effects of different colloid surface potential on the ion diffusion/adsorption kinetics theoretically. The results once again makes clear the leading position of the soil surface potential in ion diffusion/adsorption in the soil from the different ion diffusion/adsorption kinetics process, prove the exchange and the diffusion processes occurring in external electric field of DDL are really essentially the one process, that is ion exchange occurring in DDL via electrostatic attractive forces may be essentially a mutual diffusion process driven by the activity gradient of the ion (including the concentration gradient and the potential gradient).
In conclusion, this paper for the first time can evaluate quantitatively the effects of different colloid surface potential on the ion diffusion/adsorption kinetics theoretically from many ways such as the average activity coefficients, the rate coefficients, the adsorption quantities, the surface coverage of the adsorbed ions, etc. It is further concluded that ion exchange occurring in DDL via electrostatic attractive forces may be essentially a mutual diffusion process driven by the activity gradient of the ion.
引文
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Chien, S. H., Clayton, W. R., Application of Elovich equation to the kinetics of phosphate release and sorption in soils. Soil Sci. Soc. Am. J.,1980,44:265～268
Conkling,B.L.Blanchar,R.W.Estimation of calcium diffusion problems related to soil by conductometric techniques. Soil Sci. Soc. Am.J.1986.50:6,1455-1549.
De Bokx; P. K.; Boots, H. M. The Ion-Exchange Equilibrium. J. Phys. Chem.1989,93, 8243.
Elkhatib, E.A., Hern, J.L., Kinetics of phosphorus desorption from Appalachian soils. Soil Sci.,1988,145:222～229
Eriksson, E. Cation-exchange equilibrium on clay minerals. Soil Sci.1952,74,103-111.
Gaines, G. L. J.; Thomas, H. C. Adsorption studies on clay minerals:Ⅱ. A formulation of the thermodynamics of exchange adsorption. J. Phys. Chem.1953,21,714-718.
Graul, T. W.; Li, M; Schlenoff, J. B. Ion exchange in ultrathin films. J. Phys. Chem. B. 1999,103,2718-2723.
Hachiya, K.; Sasaki, M.; Nabeshima, Y.; Mikami, N. Yasunaga, T. Ion-Exchange Kinetics on Ion Exchanger Using the Pressure-Jump Technique. J. Phys. Chem. 1984,88(8),1623-1627.
Holford I.C.R., Mattingly G.E.G.1976, A model for the behaviour of labile phosphate requirements of plants. Plant and Soil.44(1):219-229
He, R.; Chen, S.L.; Yang, F.; Wu, B. L. Dynamic Diffuse Double-Layer Model for the Electrochemistry of Nanometer-Sized Electrodes. J.Phys. Chem. B, 2006,110,3262-3270
P.Somasundaran, B. Markovic, S. Krishnakumar and X. Yu.1997:Chapter 14, Handbook of surface and colloid chemistry. CRC Press LLC, New York.
Hou, J.; Li, H.; Wu, L.S..; Zhu, H.L. Determination of Clay Surface Potential:A More Reliable and Widely Applicable Approach. Soil Sci. Soc. Am. J.,2009,73:1658.
Hui, T. W.; Baker, M. D. Ion exchange and electron turansport at methyl viologen Y modified electrodes. J. Phys. Chem. B.2001,105,3204
Huertas, F. J.; Carretero, P.; Delgado, J.; Linares, J.; Samper, J. An experimental study on the ion exchange behavior of the FEBEX bentonite. J. Coll. Inter. Sci.2001,
239,409-416.
Jardine, P. M., and D. L. Sparks. Potassium-calcium exchange in multireactive soil system:I. Kinetics. Soil Sci. Soc. Am. J.1984,48:39-45.
Jui Hsin-wang. Radioactivity applied to self-diffusion studies. Radioactivity Applied to Chemistry. John Wilkey&Sons,1951.New York.
Kemper, W. D., and J. C. Van Schaik.1966. Diffusion of salts in clay-water systems. Soil Sci. Soc. Am. Proc.30:534-540.
Li. H., Shiqiang Wei, Changle Qing, and Jinshan Yang. Discussion on the position of the shear plane. Colloid and Interface Science.2003,258:40-44.
Li. H, Changle Qin, Shiqiang Wei, et al,:An approach to the method for determination of surface potential on solid/liquid interface, J. Coll..Inter. Sci.2004,275, 172-176.
Li, H.; Qing, C.L.; Wei, S.Q.; Jiang, X.J. Discussion on the position of the shear plane, J. Colloid Interface Sci.,2003,258:40-44
Li, H., and L. Wu. On the relationship between thermal diffusion and molecular interaction energy in binary mixtures. J. Phys. Chem.2004.3108:13821-13826.
Li, H.; Wu, L. S. A New Approach to Estimate Ion Distribution between the Exchanger and Solution Phases. Soil Sci. Soc. Am. J.,2007,71:1694-1698.
Li, H. and L. Wu.2007. A generalized linear equation for non-linear diffusion in external fields and non-ideal systems. New Journal of Physics.9:357.
Li, H.; Wu, L. S.; Zhu, H. L.; Hou, J. J. Phys. Chem. C,2009,113,13241-13248.
Li, H.; Li, R.; Zhu,H. L. and Wu, L.:Influence of Electrostatic Field Originated from Surface Charges of Soil Particles on Ion Adsorption/Diffusion. Soil Sci. Soc. Am. J., 2010 (in press)
Low P.F.,著.薛家骅等译.土壤物理化学.北京：农业出版社,1981,112-120.
Morgan, J.D.; Napper, D.H.; Warr. G.G. Thermodynamics of ion exchange selectivity at interfaces. Journal of Physical Chemistry,1995,99:9458-9465
Myers, G. E.; Boyd, G. E. A Thermodynamic Calculation of Cation Exchange Selectivities. J. Phys. Chem.1956,60,521-529.
Nkedi-Kizza, P., P. S. C. Rao, R. E. Jessup, and J. M. Davidson. Ion exchange and diffusive mass transfer during miscible displacement. Soil Sci. Soc. Am. J.1982, 46:471-4476.
Ogwada, R. A.; Sparks, D. L.Kinetics of ion exchange on clay minerals and soil. Ⅱ. Elucidation of rate-limiting steps. Soil Sci. Soc. Am. J.,1986,50:1162-1164.
Olsen, S. R. and Watanable, F.S. A method to determine a phosphorus-adsorption maximum of soils as measured by the Langmuir isotherm. Soil.Sci.Soc.Am.Proc. 1957,21,144-149.
Olsen, S. R., W. D. Kemper, and R. D. Jackson. Phosphate diffusion to plant roots. Soil Sci. Soc. Am. Proc.1962,26:222-226.
Porter, L. K., W. D. Kemper, R. D. Jackson, and B. A. Stewart. Chloride diffusion in soils as influenced by moisture content. Soil Sci. Soc. Am. Proc.1960, 24:460-463.
Rao, P. S. C., D. E. Rolston, R. E. Jessup, and J. M. Davidson. Solute transport in aggregated porous media:theoretical and experimental evaluation. Soil Sci. Soc. Am.J.1980,44:1139-1145.
R. A. Griffin and A. K. Au. Lead Adsorption by Montmorillonite Using A Competitive Langmuir Equation. Soil Sci Soc Am J.1977,41:880-882
Reddy, M. M.; Marinsky, J. A.; Ion-exchange selectivity coefficients in the exchange of calcium, strontium, cobalt, nickel, zinc, and cadmium ions with hydrogen ion in variously cross-linked polystyrene sulfonate cation exchangers at 25 25℃. J. Macromol. Sci. Phys.1971, B5(1),135.
Rhue, D., Coupled Diffusion of Exchangeable Cations in Soil. Soil Sci. Soc. Am.J., 1992,56,683-689.
Ryden, J, C., Mclaughlin, J. R.and Syers, J. K., Mecha-nisms of phosphate adsorption by soils and hydrous ferricoxide gel. J. Soil Sci.,1977; 28:62～92
Saeki, K; Wada, S. L.; Shibata, M. Ca~(2+)-Fe~(2+) and Ca~(2+)-Mn~(2+( exchange selectivity of kaolinite, montmorillonite and illte. Soil Sci.2004,169,125-132.
Samson, E.; Marchand, J.; Robert, J. L.; Bournazel, J. P. Modelling of ion diffusion mechanisms in porous media, Internation Journal for Numerical Methods in Engineering 46,1999,2043-2060
Siyasubramaniam, S., and O. Talibudeen.1972. Potassium-aiuminum exchange in acid soil:I. Kinetics. J. Soil Sci.23:163-176.
Schofield, R.K.,Graham-Bryce,I,J. Diffusion of ions in soils. Nature.1960,188, 1048-1049.
Skopp, J.,D. McCallister. Chemical kinetics from a thin disc flow system:Theory. Soil Sci. Soc. Am. J.1986,50:617-623.
Sposito G. The thermodynamics of soil solutions. Oxford University Press,1981a, Oxford, England)
Sposito G. The operational definition of the zero point of charge in soils. Soil Science Society of America Journal.1981b,45,292-297.
Sposito G. Ion exchange phenomena, HANDBOOK OF SOIL SCIENCE, CRC Press, 2000,pp:B241-B263.
Sparks, D.L. Soil physical chemistry, CRC Press, Bocaraton, F.,1986, p70-200.
Sparks, D. L. Kinetics of reactions in pure and mixed systems. Soil physical chemistry. 2rd,11ed. CRC Press. Boca Raton, FL.1999, p83-178.
Sparks, D. L., L. W. Zalazny, D. C. Martens. Kinetics of potassium desorption in soil using miscible displacement. Soil Sci. Soc. Am. J.1980,44:1205-1208.
Sparks, D. L. Kinetics of soil chemical processes. Academic Press, Inc. San Dieog, California.1990.
Sparks, D. L., Structure and surface reactions of soil particles, Edited by P. M. Huang, N. Senesi and J. Buffle. John Wiley & Sons Ltd. New York.1998. Chapter 11.
Sparks, D.L.,著.尉庆丰,张一平等译.土壤物理化学.天则出版社,1986,55-69.
Skopp, J., D. McCallister. Chemical kinetics from a thin disc flow system:Theory. Soil Sci. Soc. Am. J.1986,50:617-623.
Suresh, G.; Scindia, Y. M.; Pandey, A. K.; Goswami, A. Isotopic and ion-exchange kinetics in the Nafion-117 membrane. J. Phys. Chem. B 2004,108:4104-4110.
Tang, L. Y.; Sparks, D. L. Cation-exchange kinetics on montmorillonite using pressure-jump relaxation. Soil Sci. Soc. Am. J.,1993,57:42-46.
Tanioka, A.; Kawaguchi, M.; Hamada, N.; Yoshie, K. Dissociation constant of weak electrolyte in charged membrane. J. Phys. Chem.B,1998,102,1730-1736.
Van Schaik, J. C., W. D. Kemper, and S. R. Olsen.1966. Contribution of adsorbed cations to diffusion in clay-water systems. Soil Sci. Soc. Am. Proc.30:17-22.
吉林大学编.物理化学(下册).北京：人民教育出版社,1979：240
胡纪华,杨兆禧,郑忠.胶体与界面化学.广州：华南理工大学出版社,1997：199
李韵珠,李保国,1998：土壤溶质运移,科学出版社。
李航,薛家骅.土壤中离子扩散的动力学研究,土壤学报,1996：33,327-336。
李航,薛家骅.离子扩散与交换的一级动力学方程中平衡吸附量的讨论与确定,土
壤学报,1997,34(4)：353-358.
李航,薛家骅.土壤中离子扩散的基本方程与实验验证,土壤学报,1998：35：321～327
李航,陈明树.带电胶体离子扩散与交换动力学的比较.物理化学学报,1998,14(3)：278-282
李航.土壤界面电化学性质测定的动力学方法研究[博士学位论文],重庆：西南农业大学,2000,15-27.
李学垣.土壤化学.北京：高等教育出版社2001,101
李学垣.土壤化学.北京：高等教育出版社2001,66-67
林玉锁,薛家骅,1989：几种动力学用于描述土壤中锌吸持动力学特性比较,南京农业大学学报,1期,第111-117页。
林玉锁,薛家骅,1989：锌在石灰性土壤中吸持动力学初步研究,环境科学学报,2期,144-148页。
熊毅,陈家坊等.土壤胶体(第三册).北京：科学出版社1990,28
杨邦杰,隋红建,1997：土壤水热运动模型及其应用,中国科学技术出版社。
杨兴伦,李航.三种紫色土表面电荷性质研究.土壤学报,2004,41(4)：577-583.
杨亚提,张一平.陪伴离子对土壤胶体吸附Cu2+和pb2+的影响.土壤学报,2003,40(2)：218-223
杨亚提,张一平.离子强度对恒电荷土壤胶体吸附Cu2+和pb2+的影响.环境化学,2001,20(6)：566-571
张正斌等.海洋物理化学.北京：科学出版社,1989
赵芳,吴晓芙,周海兰,赵崇,芦鹏,于旭彪.液／固相单一离子吸附体系的动力学预测模型.环境化学,2009,28(1)：62
Aharoni, C., D. L. Sparks, L. Levinson, and I. Ravina.1991. Kinetics of soil chemical reactions:relationships between empirical equations and diffusion models. Soil Sci. Soc. Am. J.55:1307-1312.
Biesuz, R; Zagorodni, A. A.; and Muhammed,M. Estimation of Deprotonation Coefficients for Chelating Ion Exchange Resins. Comparison of Different Thermodynamic Model. J. Phys. Chem. B.2001,105,4721-4726.
Bloksma,A.H. The diffusion of Na~+ and I~-, and of urea in clay paste. J.Coll.Sci,1957,12,40-52.
Bolt, G H. Ion adsorption by clays. Soil Sci.1954,76,267-276.
Bolt, G. H. Soil Chemistry, B. Physical-Chemical Models. Elsevier, Amsterdam.1979.
Buckingham, E.Contribution to our knowledge of the areation of the soils. USDA Bur. Soil Bull.1904,25.
Chan, D. Y. C.; Hughes, B. D. J. Stat. Phys.1988,52,383-394
Chan, D. Y. C.; Halle, B. The Smoluchowski-Poisson-Boltzmann description of ion diffusion at charged interface. Biophys. J.1984,46(3),387-407
Chien, S. H., Clayton, W. R., Application of Elovich equation to the kinetics of phosphate release and sorption in soils. Soil Sci. Soc. Am. J.,1980,44:265～268
Conkling,B.L.Blanchar,R.W.Estimation of calcium diffusion problems related to soil by conductometric techniques. Soil Sci. Soc. Am.J.1986.50:6,1455-1549.
De Bokx; P. K.; Boots, H. M. The Ion-Exchange Equilibrium. J. Phys. Chem.1989,93, 8243.
Elkhatib, E.A., Hern, J.L., Kinetics of phosphorus desorption from Appalachian soils. Soil Sci.,1988,145:222～229
Eriksson, E. Cation-exchange equilibrium on clay minerals. Soil Sci.1952,74,103-111.
Gaines, G. L. J.; Thomas, H. C. Adsorption studies on clay minerals:Ⅱ. A formulation of the thermodynamics of exchange adsorption. J. Phys. Chem.1953,21,714-718.
Graul, T. W.; Li, M; Schlenoff, J. B. Ion exchange in ultrathin films. J. Phys. Chem. B. 1999,103,2718-2723.
Hachiya, K.; Sasaki, M.; Nabeshima, Y.; Mikami, N. Yasunaga, T. Ion-Exchange Kinetics on Ion Exchanger Using the Pressure-Jump Technique. J. Phys. Chem. 1984,88(8),1623-1627.
Holford I.C.R., Mattingly G.E.G.1976, A model for the behaviour of labile phosphate requirements of plants. Plant and Soil.44(1):219-229
He, R.; Chen, S.L.; Yang, F.; Wu, B. L. Dynamic Diffuse Double-Layer Model for the Electrochemistry of Nanometer-Sized Electrodes. J.Phys. Chem. B, 2006,110,3262-3270
P.Somasundaran, B. Markovic, S. Krishnakumar and X. Yu.1997:Chapter 14, Handbook of surface and colloid chemistry. CRC Press LLC, New York.
Hou, J.; Li, H.; Wu, L.S..; Zhu, H.L. Determination of Clay Surface Potential:A More Reliable and Widely Applicable Approach. Soil Sci. Soc. Am. J.,2009,73:1658.
Hui, T. W.; Baker, M. D. Ion exchange and electron turansport at methyl viologen Y modified electrodes. J. Phys. Chem. B.2001,105,3204
Huertas, F. J.; Carretero, P.; Delgado, J.; Linares, J.; Samper, J. An experimental study on the ion exchange behavior of the FEBEX bentonite. J. Coll. Inter. Sci.2001,
239,409-416.
Jardine, P. M., and D. L. Sparks. Potassium-calcium exchange in multireactive soil system:I. Kinetics. Soil Sci. Soc. Am. J.1984,48:39-45.
Jui Hsin-wang. Radioactivity applied to self-diffusion studies. Radioactivity Applied to Chemistry. John Wilkey&Sons,1951.New York.
Kemper, W. D., and J. C. Van Schaik.1966. Diffusion of salts in clay-water systems. Soil Sci. Soc. Am. Proc.30:534-540.
Li. H., Shiqiang Wei, Changle Qing, and Jinshan Yang. Discussion on the position of the shear plane. Colloid and Interface Science.2003,258:40-44.
Li. H, Changle Qin, Shiqiang Wei, et al,:An approach to the method for determination of surface potential on solid/liquid interface, J. Coll..Inter. Sci.2004,275, 172-176.
Li, H.; Qing, C.L.; Wei, S.Q.; Jiang, X.J. Discussion on the position of the shear plane, J. Colloid Interface Sci.,2003,258:40-44
Li, H., and L. Wu. On the relationship between thermal diffusion and molecular interaction energy in binary mixtures. J. Phys. Chem.2004.3108:13821-13826.
Li, H.; Wu, L. S. A New Approach to Estimate Ion Distribution between the Exchanger and Solution Phases. Soil Sci. Soc. Am. J.,2007,71:1694-1698.
Li, H. and L. Wu.2007. A generalized linear equation for non-linear diffusion in external fields and non-ideal systems. New Journal of Physics.9:357.
Li, H.; Wu, L. S.; Zhu, H. L.; Hou, J. J. Phys. Chem. C,2009,113,13241-13248.
Li, H.; Li, R.; Zhu,H. L. and Wu, L.:Influence of Electrostatic Field Originated from Surface Charges of Soil Particles on Ion Adsorption/Diffusion. Soil Sci. Soc. Am. J., 2010 (in press)
Low P.F.,著.薛家骅等译.土壤物理化学.北京：农业出版社,1981,112-120.
Morgan, J.D.; Napper, D.H.; Warr. G.G. Thermodynamics of ion exchange selectivity at interfaces. Journal of Physical Chemistry,1995,99:9458-9465
Myers, G. E.; Boyd, G. E. A Thermodynamic Calculation of Cation Exchange Selectivities. J. Phys. Chem.1956,60,521-529.
Nkedi-Kizza, P., P. S. C. Rao, R. E. Jessup, and J. M. Davidson. Ion exchange and diffusive mass transfer during miscible displacement. Soil Sci. Soc. Am. J.1982, 46:471-4476.
Ogwada, R. A.; Sparks, D. L.Kinetics of ion exchange on clay minerals and soil. Ⅱ. Elucidation of rate-limiting steps. Soil Sci. Soc. Am. J.,1986,50:1162-1164.
Olsen, S. R. and Watanable, F.S. A method to determine a phosphorus-adsorption maximum of soils as measured by the Langmuir isotherm. Soil.Sci.Soc.Am.Proc. 1957,21,144-149.
Olsen, S. R., W. D. Kemper, and R. D. Jackson. Phosphate diffusion to plant roots. Soil Sci. Soc. Am. Proc.1962,26:222-226.
Porter, L. K., W. D. Kemper, R. D. Jackson, and B. A. Stewart. Chloride diffusion in soils as influenced by moisture content. Soil Sci. Soc. Am. Proc.1960, 24:460-463.
Rao, P. S. C., D. E. Rolston, R. E. Jessup, and J. M. Davidson. Solute transport in aggregated porous media:theoretical and experimental evaluation. Soil Sci. Soc. Am.J.1980,44:1139-1145.
R. A. Griffin and A. K. Au. Lead Adsorption by Montmorillonite Using A Competitive Langmuir Equation. Soil Sci Soc Am J.1977,41:880-882
Reddy, M. M.; Marinsky, J. A.; Ion-exchange selectivity coefficients in the exchange of calcium, strontium, cobalt, nickel, zinc, and cadmium ions with hydrogen ion in variously cross-linked polystyrene sulfonate cation exchangers at 25 25℃. J. Macromol. Sci. Phys.1971, B5(1),135.
Rhue, D., Coupled Diffusion of Exchangeable Cations in Soil. Soil Sci. Soc. Am.J., 1992,56,683-689.
Ryden, J, C., Mclaughlin, J. R.and Syers, J. K., Mecha-nisms of phosphate adsorption by soils and hydrous ferricoxide gel. J. Soil Sci.,1977; 28:62～92
Saeki, K; Wada, S. L.; Shibata, M. Ca~(2+)-Fe~(2+) and Ca~(2+)-Mn~(2+( exchange selectivity of kaolinite, montmorillonite and illte. Soil Sci.2004,169,125-132.
Samson, E.; Marchand, J.; Robert, J. L.; Bournazel, J. P. Modelling of ion diffusion mechanisms in porous media, Internation Journal for Numerical Methods in Engineering 46,1999,2043-2060
Siyasubramaniam, S., and O. Talibudeen.1972. Potassium-aiuminum exchange in acid soil:I. Kinetics. J. Soil Sci.23:163-176.
Schofield, R.K.,Graham-Bryce,I,J. Diffusion of ions in soils. Nature.1960,188, 1048-1049.
Skopp, J.,D. McCallister. Chemical kinetics from a thin disc flow system:Theory. Soil Sci. Soc. Am. J.1986,50:617-623.
Sposito G. The thermodynamics of soil solutions. Oxford University Press,1981a, Oxford, England)
Sposito G. The operational definition of the zero point of charge in soils. Soil Science Society of America Journal.1981b,45,292-297.
Sposito G. Ion exchange phenomena, HANDBOOK OF SOIL SCIENCE, CRC Press, 2000,pp:B241-B263.
Sparks, D.L. Soil physical chemistry, CRC Press, Bocaraton, F.,1986, p70-200.
Sparks, D. L. Kinetics of reactions in pure and mixed systems. Soil physical chemistry. 2rd,11ed. CRC Press. Boca Raton, FL.1999, p83-178.
Sparks, D. L., L. W. Zalazny, D. C. Martens. Kinetics of potassium desorption in soil using miscible displacement. Soil Sci. Soc. Am. J.1980,44:1205-1208.
Sparks, D. L. Kinetics of soil chemical processes. Academic Press, Inc. San Dieog, California.1990.
Sparks, D. L., Structure and surface reactions of soil particles, Edited by P. M. Huang, N. Senesi and J. Buffle. John Wiley & Sons Ltd. New York.1998. Chapter 11.
Sparks, D.L.,著.尉庆丰,张一平等译.土壤物理化学.天则出版社,1986,55-69.
Skopp, J., D. McCallister. Chemical kinetics from a thin disc flow system:Theory. Soil Sci. Soc. Am. J.1986,50:617-623.
Suresh, G.; Scindia, Y. M.; Pandey, A. K.; Goswami, A. Isotopic and ion-exchange kinetics in the Nafion-117 membrane. J. Phys. Chem. B 2004,108:4104-4110.
Tang, L. Y.; Sparks, D. L. Cation-exchange kinetics on montmorillonite using pressure-jump relaxation. Soil Sci. Soc. Am. J.,1993,57:42-46.
Tanioka, A.; Kawaguchi, M.; Hamada, N.; Yoshie, K. Dissociation constant of weak electrolyte in charged membrane. J. Phys. Chem.B,1998,102,1730-1736.
Van Schaik, J. C., W. D. Kemper, and S. R. Olsen.1966. Contribution of adsorbed cations to diffusion in clay-water systems. Soil Sci. Soc. Am. Proc.30:17-22.
吉林大学编.物理化学(下册).北京：人民教育出版社,1979：240
胡纪华,杨兆禧,郑忠.胶体与界面化学.广州：华南理工大学出版社,1997：199
李韵珠,李保国,1998：土壤溶质运移,科学出版社。
李航,薛家骅.土壤中离子扩散的动力学研究,土壤学报,1996：33,327-336。
李航,薛家骅.离子扩散与交换的一级动力学方程中平衡吸附量的讨论与确定,土
壤学报,1997,34(4)：353-358.
李航,薛家骅.土壤中离子扩散的基本方程与实验验证,土壤学报,1998：35：321～327
李航,陈明树.带电胶体离子扩散与交换动力学的比较.物理化学学报,1998,14(3)：278-282
李航.土壤界面电化学性质测定的动力学方法研究[博士学位论文],重庆：西南农业大学,2000,15-27.
李学垣.土壤化学.北京：高等教育出版社2001,101
李学垣.土壤化学.北京：高等教育出版社2001,66-67
林玉锁,薛家骅,1989：几种动力学用于描述土壤中锌吸持动力学特性比较,南京农业大学学报,1期,第111-117页。
林玉锁,薛家骅,1989：锌在石灰性土壤中吸持动力学初步研究,环境科学学报,2期,144-148页。
熊毅,陈家坊等.土壤胶体(第三册).北京：科学出版社1990,28
杨邦杰,隋红建,1997：土壤水热运动模型及其应用,中国科学技术出版社。
杨兴伦,李航.三种紫色土表面电荷性质研究.土壤学报,2004,41(4)：577-583.
杨亚提,张一平.陪伴离子对土壤胶体吸附Cu2+和pb2+的影响.土壤学报,2003,40(2)：218-223
杨亚提,张一平.离子强度对恒电荷土壤胶体吸附Cu2+和pb2+的影响.环境化学,2001,20(6)：566-571
张正斌等.海洋物理化学.北京：科学出版社,1989
赵芳,吴晓芙,周海兰,赵崇,芦鹏,于旭彪.液／固相单一离子吸附体系的动力学预测模型.环境化学,2009,28(1)：62