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The Electrostatic Field Effect from Surface Charges on Ion Diffusion/Adsorption in Soil

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Molecular Environmental Soil Science

Part of the book series: Progress in Soil Science ((PROSOIL))

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Abstract

Soil is a system exhibiting strong electrostatic field in aqueous solution, even though it is electrically neutral macroscopically. Therefore, the gradient of electric potential will be the main driving forces for ions transportation, adsorption/desorption in the soil. In this chapter, we will firstly discuss the theoretical descriptions for mass diffusion in a system with multi-potential fields. Based on macroscopic thermodynamic analysis, a generalized linear theory for describing non-linear diffusion in external fields and non-ideal systems, such as soil, can be established, and this theory included: a generalized linear flux equation for non-linear diffusion; an apparent mass conservation equation and a generalized linear non-steady state equation for non-linear diffusion. This section is critical in ion diffusion/adsorption study in soil, because in this theory the coupling diffusion with multiple driving forces in soil have been unified to a single force: the apparent concentration gradient, and which changes the complex non-linear diffusion problem of ions in soil to linear. In the second section, we will discuss the electrostatic field effect from surface charges of soil particles on ion exchange equilibrium. In this section, we will show that, the electrostatic adsorption of cations in soil can be treated as a diffusion process driven by the apparent concentration gradient of ions in the external electric field from soil particle surface. Therefore the electrostatic adsorption/desorption process and the diffusion process in the electric field of soil are essentially the same process, and can be treated as one. Based on this concept, new ion equilibrium distribution equations for describing ion exchange equilibrium can be obtained, and those equation clearly show how the surface charges, the electric field strength, ionic volume and ionic interaction in soil solution influence the exchange. In the last section, we will discuss the electrostatic field effect from surface charges of soil particles on ion adsorption/diffusion kinetics. In this section, we will show that, the electric field in the soil exerts a significant influence on ion adsorption and diffusion kinetics. By considering the electric field from soil particle surface, new exact kinetic equations for describing cation adsorption can be developed. The new equations show that, when both strong force adsorption and weak force adsorption coexist in an exchange experiment, the initial stage of strong force adsorption can be described by the zero-order kinetics. The adsorption then shifts to the first-order kinetics of the weak force adsorption. The new kinetic equations are mathematically precise, and they were derived from the actual physical mechanism of cation adsorption. Thus, those new equations are fundamentally different from the classic apparent kinetic equations. All the parameters in the new equations have definite physical significance. Therefore, using the new equations, some important dynamic and thermodynamic parameters in cation exchange can be estimated from the experimental data.

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References

  • Abell GC, Mozumber A (1972) Application of diffusion model for recombination of isolated pairs in condensed media. J Chem Phys 56:4079

    Article  Google Scholar 

  • Abell GC, Mozumder A, Magee JL (1972) Laplace transformation method in theory of ion neutralization–Application to scavenging probability in gamma-radiolysis of dielectric liquids. J Chem Phys 56:5422

    Article  Google Scholar 

  • Achari G, Chatterji S, Joshi RC, Bentley LR (1997) Effect of ion concentration on diffusion through clay. Soil Sci 162:51

    Article  Google Scholar 

  • Aharoni C, Sparks DL, Levinson L, Ravina I (1991) Kinetics of soil chemical reactions: relationships between empirical equations and diffusion models. Soil Sci Soc Am J 55:1307–1312

    Article  Google Scholar 

  • Ǻkesson B, JÅ‘nsson B, Chan DYC (1986) Ion diffusion at charged interfaces – A stochastic dynamics simulation test of the Smoluchowski-Poisson-Boltzmann approximation. Mol Phys 57:1105

    Article  Google Scholar 

  • Ben Y, Chang HC (2002) Nonlinear Smoluchowski slip velocity and micro-vortex generation. J Fluid Mech 461:229

    Article  Google Scholar 

  • Benesi AJ (1986) Diffusion in potentials-A method for solving the Smoluchowski equation. J Chem Phys 85:374

    Article  Google Scholar 

  • Berber-Mendoza MS, Leyva-Ramos R, Alonso-Davila P, Fuentes-Rubio L, Guerrero-Coronado RM (2006) Comparison of isotherms for the ion exchange of Pb(II) from aqueous solution onto homoionic clinoptilolite. J Colloid Interf Sci 301:40–45

    Article  Google Scholar 

  • Berezhkovskii AM, D’yakov YuA (1998) Smoluchowski equation with a sink term: Analytical solutions for the rate constant and their numerical test. J Chem Phys 109:4182

    Article  Google Scholar 

  • Biesuz R, Zagorodni AA, Muhammed M (2001) Estimation of deprotonation coefficients for chelating ion exchange resins: comparison of different thermodynamic models. J Phys Chem B 105:4721–4726

    Article  Google Scholar 

  • Bolt GH (1955) Ion adsorption by clay. Soil Sci 79:267–276

    Article  Google Scholar 

  • Butler PR, Pilling MJ, Rice SA, Stone TJ (1977) Numerical investigation of tunneling contributions to electron scavenging reactions in liquids at short times. Can J Chem 55:2124

    Article  Google Scholar 

  • Chan DYC (1987) Ion diffusion near charged surfaces – Exact analytical solutions. J Chem Soc Faraday Trans 83:2271

    Article  Google Scholar 

  • Chan DYC, Halle B (1984) The Smoluchowski-Poisson-Boltzmann description of ion diffusion at charged interface. Biophys J 46:387

    Article  Google Scholar 

  • Chan DYC, Hughes BD (1988) Ion diffusion in Coulombic field. J Stat Phys 52:383

    Article  Google Scholar 

  • Chatterji S (2004) Ionic diffusion through thick matrices of charged particles. J Colloid Interface Sci 269:186–191

    Article  Google Scholar 

  • Chavanis PH (2003) Generalized thermodynamics and Fokker-Planck equations: Applications to stellar dynamics and two-dimensional turbulence. Phys Rev E 68:036108

    Article  Google Scholar 

  • Clifford P, Green NJB, Pilling MJ (1984) Analysis of the Debye-Smoluchowski equation – Approximation for high-permittivity solvents. J Phys Chem 88:4171

    Article  Google Scholar 

  • Crank J (2001) The mathematics of diffusion. Oxford Science, New York

    Google Scholar 

  • De Bokx PK, Boots HMJ (1989) The ion-exchange equilibrium. J Phys Chem 93:8243–8248

    Article  Google Scholar 

  • Delaire JA, Croc E, Cordier P (1981) J Phys Chem 85:1549

    Google Scholar 

  • Eriksson E (1952) Cation-exchange equilibrium on clay minerals. Soil Sci 74:103–111

    Article  Google Scholar 

  • Fatin-Rouge N, Milon A, Buffle J, Goulet RR, Tessier A (2003) Diffusion and partitioning of solutes in agarose hydrogels: The relative influence of electrostatic and specific interactions. J Phys Chem B 107:12126

    Article  Google Scholar 

  • Gitterman M, Weiss GH (1993) Small-noise approximations to the solution of the Smoluchowski equation. Phys Rev E 47:976

    Article  Google Scholar 

  • Graul TW, Li M, Schlenoff JB (1999) Ion exchange in ultrathin films. J Phys Chem B 103:2718–2723

    Article  Google Scholar 

  • Hanggi P, Luczka J, Talkner P (2005) Statistics of transition times, phase diffusion and synchronization in periodically driven bistable systems. New J Phys 7

    Google Scholar 

  • Hong KM, Noolandi J (1978a) Solution of Smoluchowski equation with a Coulomb potential. 1. General results. J Chem Phys 68:5163

    Article  Google Scholar 

  • Hong KM, Noolandi J (1978b) Solution of Smoluchowski equation with a Coulomb potential. 2. Application to fluorescence quenching. J Chem Phys 68:5172

    Article  Google Scholar 

  • Hui TW, Baker MD (2001) Ion exchange and electron transport at methyl viologen Y modified electrodes. J Phys Chem B 105:3204–3210

    Article  Google Scholar 

  • Jacob AM, Reddy MM (1991) Employment of gibbs-donnan-based concepts for interpretation of the properties of linear polyelectrolyte solutions. J Phys Chem 95:10208–10214

    Article  Google Scholar 

  • Jardine PM, Sparks DL (1984) Potassium-calcium exchange in multireactive soil system: I. Kinetics. Soil Sci Soc Am J 48:39–45

    Article  Google Scholar 

  • Jenny H (1932) Studies on the mechanism of ion exchange in colloidal aluminum silicates. J Phys Chem 36:2217–2258

    Article  Google Scholar 

  • Jenny H (1936) Simple kinetic theory of ion exchange. I. Ions of equal valency. J Phys Chem 40:501–517

    Article  Google Scholar 

  • Jones RB (2003) Adiabatic change in the Smoluchowski equation: Orientational diffusion of polar particles. J Chem Phys 119:1517

    Article  Google Scholar 

  • Kemper WD, Van Schaik JC (1966) Diffusion of salts in clay-water systems. Soil Sci Soc Am Proc 30:534–540

    Article  Google Scholar 

  • Klik I, Yao YD (2000) Solution of a separable Smoluchowski equation in one spatial dimension. Phys Rev E 62:4469

    Article  Google Scholar 

  • Li R (1986) Non-equilibrium thermodynamics and dissipative structure. Qinghua University Press, Beijing (In Chinese)

    Google Scholar 

  • Li R, Li H (2010) Comparison study between Mg/K and Ca/K exchange kinetics under electric fields at the solid/liquid interface of soil. Acta Phys-Chim Sin 26(3):552–560

    Google Scholar 

  • Li H, Wu L (2004) On the relationship between thermal diffusion and molecular interaction energy in binary mixtures. J Phys Chem B 108:13821

    Article  Google Scholar 

  • Li H, Wu L (2007a) A generalized linear equation for non-linear diffusion in external fields and non-ideal systems. New J Phys 9:357

    Article  Google Scholar 

  • Li H, Wu L (2007b) A new approach to estimate ion distribution between the exchanger and solution phases. Soil Sci Soc Am J 71:1694–1698

    Article  Google Scholar 

  • Li H, Xue JH (1996) Study on ion diffusion kinetics in soil systems. Acta Pedologica Sinica 33(4):327–336 (in Chinese)

    Google Scholar 

  • Li H, Zhang H (2001) Mathematics in soil science. Agricultural Press, Beijing

    Google Scholar 

  • Li H, Qing CL, Wei SQ, Jiang XJ (2004) An approach to the method for determination of surface potential on solid/liquid interface: theory. J Colloid Interface Sci 275:172–176

    Article  Google Scholar 

  • Li H, Zhu HL, Jia MY, Wu LS (2009a) Some new features of linear theory for describing non-linear diffusion. Commun Theor Phys 52:269–273

    Article  Google Scholar 

  • Li H, Laosheng Wu, Zhu H, Hou J (2009b) Ion diffusion in the time-dependent potential of the dynamic electric double layer. J Phys Chem C 113:13241–13248

    Article  Google Scholar 

  • Li H, Li R, Zhu H, Wu L (2010) Influence of electrostatic field from soil particle surfaces on ion adsorption–diffusion. Soil Sci Soc Am J 74:1129–1138

    Article  Google Scholar 

  • Li H, Hou J, Liu X, Li R, Zhu H, Wu W (2011a) Combined determination of specific surface area and surface charge properties of charged particles from a single experiment. Soil Sci Soc Am J 75(6):2128–2135

    Article  Google Scholar 

  • Li R, Li H, Zhu H, Wu L (2011b) Kinetics of cation adsorption on charged soil mineral as strong electrostatic force presence or absence. J Soils Sedim 11(1):53–61

    Article  Google Scholar 

  • Liu X, Li H, Li R, Hou J (2012) A new theory on cation exchange equilibrium of hydrated. J Soil Sediments (accepted)

    Google Scholar 

  • Magee JL, Tayler AB (1972) Recombination of ions in a Coulomb field in presence of a scavenger. J Chem Phys 56:3061

    Article  Google Scholar 

  • Monchick L (1956) Note on the theory of diffusion controlled reactions – Application to photodissociation in solution. J Chem Phys 24:381

    Article  Google Scholar 

  • Montroll EW (1946) A note of the theory of diffusion controlled reactions with application of the quenching of fluorescence. J Chem Phys 14:202

    Article  Google Scholar 

  • Morgan JD, Napper DH, Warr GG (1995) Thermodynamics of ion exchange selectivity. J Phys Chem 99:9458–9465

    Article  Google Scholar 

  • Mozumder A (1968) Theory of neutralization of an isolated ion pair – Application of method of prescribed diffusion to random walk in Coulomb field. J Chem Phys 48:1659

    Article  Google Scholar 

  • Nkedi-Kizza P, Rao PSC, Jessup RE, Davidson JM (1982) Ion exchange and diffusive mass transfer during miscible displacement. Soil Sci Soc Am J 46:471–4476

    Article  Google Scholar 

  • Ogwada RA, Sparks DL (1986a) A critical evaluation on the use of kinetics for determining thermodynamics of ion exchange in soils. Soil Sci Soc Am J 50:300–305

    Article  Google Scholar 

  • Ogwada RA, Sparks DL (1986b) Kinetics of ion exchange on clay minerals and soil: I. Evaluation of methods. Soil Sci Soc Am J 50:1162–1166

    Article  Google Scholar 

  • Olsen SR, Kemper WD, Jackson RD (1962) Phosphate diffusion to plant roots. Soil Sci Soc Am Proc 26:222–226

    Article  Google Scholar 

  • Pauley JL (1953) Prediction of cation-exchange equilibria. J Am Chem Soc 76:1422–1425

    Article  Google Scholar 

  • Pechukas P, Ankerhold J, Grabert H (2001) Quantum Smoluchowski equation II: The overdamped harmonic oscillator. J Phys Chem B 105:6638

    Article  Google Scholar 

  • Pedersen JB, Freed JH (1973) Theory of chemically induced dynamic electron polarization. J Chem Phys 58:2746

    Article  Google Scholar 

  • Porter LK, Kemper WD, Jackson RD, Stewart BA (1960) Chloride diffusion in soils as influenced by moisture content. Soil Sci Soc Am Proc 24:460–463

    Article  Google Scholar 

  • Rao PSC, Rolston DE, Jessup RE, Davidson JM (1980) Solute transport in aggregated porous media: theoretical and experimental evaluation. Soil Sci Soc Am J 44:1139–1145

    Article  Google Scholar 

  • Rice SA, Butler R, Pilling MJ, Baird JK (1979) Solution of the Debye-Smoluchowski equation for the rate of reaction of ions in dilute solution. J Chem Phys 70:4001

    Article  Google Scholar 

  • Samson E, Marchand J, Robert JL, Bournazel JP (1999) Modelling ion diffusion mechanisms in porous media. Int J Numer Meth Eng 46:2043

    Article  Google Scholar 

  • Schulten Z, Schulten K (1977) General, diffusion, spin motion, and recombination of redical pairs in solution in nano second time domain. J Chem Phys 66:4616

    Article  Google Scholar 

  • Shainberg I, Kemper WD (1966) Hydration status of adsorbed cations. Soil Sci Soc Am Proc 30:707–713

    Article  Google Scholar 

  • Sibani P, Boiden JP (1981) A perturbation solution of the smoluchowski equation in the weak potential region. J Chem Phys 74:6934

    Article  Google Scholar 

  • Sparks DL (1989) Kinetics of soil chemical processes. Academic Press, Inc., San Diego/New York/Berkeley/Boston/London/Sydney/Tokyo/Toronto

    Google Scholar 

  • Sparks DL (1998a) Soil physical chemistry, 2nd edn. CRC Press, Boca Raton/Boston/London/New York/Washington, DC, p 17

    Google Scholar 

  • Sparks DL (1998b) Chapter 11. In: Huang PM, Senesi N, Buffle J (eds) Structure and surface reactions of soil particles. Wiley, New York

    Google Scholar 

  • Sparks DL, Jardine PM (1984) Comparison of kinetics equations to describe K-Ca exchange in pure and in mixed systems. Soil Sci 138:115–122

    Article  Google Scholar 

  • Sparks DL, Zalazny LW, Martens DC (1980) Kinetics of potassium desorption in soil using miscible displacement. Soil Sci Soc Am J 44:1205–1208

    Article  Google Scholar 

  • Sposito G (1981) The thermodynamics of soil solution. Oxford University Press, New York, pp 126–150

    Google Scholar 

  • Sposito G (1984) The surface chemistry of soils. Oxford University Press, New York

    Google Scholar 

  • Su WD (1986) Electro-chemistry. In: Jilin University (ed) Physical chemistry. Education Press, Beijing, pp 212–318

    Google Scholar 

  • Suresh G, Scindia YM, Pandey AK, Goswami A (2004) Isotopic and ion-exchange kinetics in the Nafion-117 membrane. J Phys Chem B 108:4104–4110

    Article  Google Scholar 

  • Tachiya M (1979) Recombination of geminate species in the presence of a scavenger. J Chem Phys 70:238

    Article  Google Scholar 

  • Tan KH (1982) Principle of soil chemistry. Marcel Dekker Inc., New York/Basel, pp 162–171

    Google Scholar 

  • Tang LY, Sparks DL (1993) Cation-exchange kinetics on montmorillonite using pressure-jump relaxation. Soil Sci Soc Am J 57:42–46

    Article  Google Scholar 

  • Tanioka A, Kawaguchi M, Hamada M, Yoshie K (1998) Dissociation constant of a weak electrolyte in charged membrane. J Phys Chem B 102:1730–1735

    Article  Google Scholar 

  • Van Duijvenbode RC, Koper GJM (2001) Fast adsorption on nonideal surfaces. J Phys Chem B 105:11729

    Article  Google Scholar 

  • Van Schaik JC, Kemper WD, Olsen SR (1966) Contribution of adsorbed cations to diffusion in clay-water systems. Soil Sci Soc Am Proc 30:17–22

    Article  Google Scholar 

  • Xiong YT (1981) Statistic physics. Peoples Educational Press, Beijing (in Chinese)

    Google Scholar 

  • Zhang T (2007) Statistical dynamics and its applications. Metallurgical Industry Press, Beijing

    Google Scholar 

  • Zientara GP, Freed JH (1979) J Chem Phys 70:2587

    Google Scholar 

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Authors and Affiliations

  1. College of Resources and Environment, Southwest University, Chongqing, PR China

    Hang Li, Rui Li, Xinmin Liu & Jie Hou

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  1. Hang Li
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  2. Rui Li
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Correspondence to Hang Li .

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Editors and Affiliations

  1. Institute of Soil and Water Resources, Zhejiang University, Hangzhou, China, People's Republic

    Jianming Xu

  2. Delaware Environmental Institute, University of Delaware, Newark, Delaware, USA

    Donald L. Sparks

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Li, H., Li, R., Liu, X., Hou, J. (2013). The Electrostatic Field Effect from Surface Charges on Ion Diffusion/Adsorption in Soil. In: Xu, J., Sparks, D. (eds) Molecular Environmental Soil Science. Progress in Soil Science. Springer, Dordrecht. https://doi.org/10.1007/978-94-007-4177-5_9

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