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RESEARCH ARTICLE

An algorithm to calculate the cationic composition of soil solutions. 1. Theory and structure

Jeff B. Reid https://orcid.org/0000-0002-3269-7151
+ Author Affiliations
- Author Affiliations

The New Zealand Institute for Plant and Food Research Limited, Private Bag 1401, Havelock North, New Zealand. Email: jeff.reid@plantandfood.co.nz

Soil Research - https://doi.org/10.1071/SR20226
Submitted: 13 August 2020  Accepted: 23 September 2020   Published online: 28 October 2020

Abstract

Difficulties forecasting cation exchange processes may limit the use of soil solution analyses in routine soil testing for agriculture. An important part of those difficulties is the need for much data and expertise to parameterise existing models that can be used for variable charge soils. This paper proposes an algorithm to simulate concentrations of the major nutrient cations in the soil solution. It is designed to have only modest data requirements, be applicable for variable charge soils, and be simple to implement in crop and environment simulation packages. It is based on a Gaines–Thomas type approach to cation exchange, adapted to allow for variations in cation exchange capacity. It includes interactions with anions and anion exchange, which may affect cation behaviour in variable charge soils. Assumptions and limitations of the approach are described, and some issues associated with parameterisation, implementation, and future extension are discussed.

Keywords: algorithm, cation exchange, soil acidity, soil solution, variable charge soils.


References

Adams F (1971) Ionic concentrations and activities in soil solutions. Soil Science Society of America Journal 35, 420–426.
Ionic concentrations and activities in soil solutions.Crossref | GoogleScholarGoogle Scholar |

Adams F (1974) Soil solution. In ‘The plant root and its environment’. (Ed. EW Carson) pp. 441–481. (University Press of Virginia: Charlottesville).

Adams F, Burmester C, Hue NV, Long FL (1980) A comparison of column-displacement and centrifuge methods for obtaining soil solutions. Soil Science Society of America Journal 44, 733–735.
A comparison of column-displacement and centrifuge methods for obtaining soil solutions.Crossref | GoogleScholarGoogle Scholar |

Aitken RL, Outhwaite RJ (1987) A modified centrifuge apparatus for extracting soil solution. Communications in Soil Science and Plant Analysis 18, 1041–1047.
A modified centrifuge apparatus for extracting soil solution.Crossref | GoogleScholarGoogle Scholar |

Appelo C, Parkhurst D (2002) Calculating cation exchange with PHREEQC (version 2). Available at https://www.hydrochemistry.eu/a&p/6/exch_phr.pdf [verified 10 August 2020].

Arai Y, Elzinga EJ, Sparks DL (2001) X-ray absorption spectroscopic investigation of arsenite and arsenate adsorption at the aluminum oxide–water interface. Journal of Colloid and Interface Science 235, 80–88.
X-ray absorption spectroscopic investigation of arsenite and arsenate adsorption at the aluminum oxide–water interface.Crossref | GoogleScholarGoogle Scholar | 11237445PubMed |

Argo WR, Weesies BJ, Bergman EM, Marshal M, Biernbaum JA (1997) Evaluating rhizon soil solution samplers as a method for extracting nutrient solution and analyzing media for container-grown crops. HortTechnology 7, 404
Evaluating rhizon soil solution samplers as a method for extracting nutrient solution and analyzing media for container-grown crops.Crossref | GoogleScholarGoogle Scholar |

Bennett A, Adams F (1972) Solubility and solubility product of gypsum in soil solutions and other aqueous solutions. Soil Science Society of America Journal 36, 288–291.
Solubility and solubility product of gypsum in soil solutions and other aqueous solutions.Crossref | GoogleScholarGoogle Scholar |

Black AS, Campbell AS (1982) Ionic strength of soil solution and its effect on charge properties of some New Zealand soils. Journal of Soil Science 33, 249–262.
Ionic strength of soil solution and its effect on charge properties of some New Zealand soils.Crossref | GoogleScholarGoogle Scholar |

Bolan NS, Syers JK, Sumner ME (1993) Calcium-induced sulfate adsorption by soils. Soil Science Society of America Journal 57, 691–696.
Calcium-induced sulfate adsorption by soils.Crossref | GoogleScholarGoogle Scholar |

Bouldin DR (1989) A multiple ion uptake model. Journal of Soil Science 40, 309–319.
A multiple ion uptake model.Crossref | GoogleScholarGoogle Scholar |

Cornforth IS, Sinclair TR (1984) ‘Fertilizer recommendations for pastures and crops in New Zealand.’ (New Zealand Ministry of Agriculture and Fisheries: Wellington)

Curtin D, Trolove S (2013) Predicting pH buffering capacity of New Zealand soils from organic matter content and mineral characteristics. Soil Research 51, 494–502.
Predicting pH buffering capacity of New Zealand soils from organic matter content and mineral characteristics.Crossref | GoogleScholarGoogle Scholar |

Curtin D, Selles F, Steppuhn H (1998) Estimating calcium-magnesium selectivity in smectitic soils from organic matter and texture. Soil Science Society of America Journal 62, 1280–1285.
Estimating calcium-magnesium selectivity in smectitic soils from organic matter and texture.Crossref | GoogleScholarGoogle Scholar |

Davies CW (1962) ‘Ion association.’ (Butterworths: London)

Davis JG, Burgoa B (1995) Interactive mechanisms of anion adsorption with calcium leaching and exchange. Soil Science 160, 256–264.
Interactive mechanisms of anion adsorption with calcium leaching and exchange.Crossref | GoogleScholarGoogle Scholar |

Defra (2010) ‘Fertiliser manual (RB209)’. 8th edn. (Agriculture and Horticulture Development Board: Norwich, England)

Donn MJ, Menzies NW (2005) The effect of ionic strength variation and anion competition on the development of nitrate accumulations in variable charge subsoils. Soil Research 43, 43–50.
The effect of ionic strength variation and anion competition on the development of nitrate accumulations in variable charge subsoils.Crossref | GoogleScholarGoogle Scholar |

Dudal Y, Gérard F (2004) Accounting for natural organic matter in aqueous chemical equilibrium models: a review of the theories and applications. Earth-Science Reviews 66, 199–216.
Accounting for natural organic matter in aqueous chemical equilibrium models: a review of the theories and applications.Crossref | GoogleScholarGoogle Scholar |

Dufey JE, Delvaux B (1989) Modeling potassium-calcium exchange isotherms in soils. Soil Science Society of America Journal 53, 1297–1299.
Modeling potassium-calcium exchange isotherms in soils.Crossref | GoogleScholarGoogle Scholar |

Edmeades DC, Judd MJ (1980) The effects of lime on the magnesium status and equilibria in some New Zealand topsoils. Soil Science 129, 156–161.
The effects of lime on the magnesium status and equilibria in some New Zealand topsoils.Crossref | GoogleScholarGoogle Scholar |

Elkhatib EA, Bennett OL, Baligar VC, Wright RJ (1986) A centrifuge method for obtaining soil solution using an immiscible liquid. Soil Science Society of America Journal 50, 297–299.
A centrifuge method for obtaining soil solution using an immiscible liquid.Crossref | GoogleScholarGoogle Scholar |

Fageria NK, Baligar VC, Jones CA (2011) ‘Growth and mineral nutrition of field crops.’ 3rd edn. (CRC Press: Boca Raton, FL)

Fest EPMJ, Temminghoff EJM, Griffioen J, Van Riemsdijk WH (2005) Proton buffering and metal leaching in sandy soils. Environmental Science & Technology 39, 7901–7908.
Proton buffering and metal leaching in sandy soils.Crossref | GoogleScholarGoogle Scholar |

Galindo GG, Bingham FT (1977) Homovalent and heterovalent cation exchange equilibria in soils with variable surface charge. Soil Science Society of America Journal 41, 883–886.
Homovalent and heterovalent cation exchange equilibria in soils with variable surface charge.Crossref | GoogleScholarGoogle Scholar |

Gebhardt H, Coleman NT (1974) Anion adsorption by allophanic tropical soils: I. Chloride adsorption. Soil Science Society of America Journal 38, 255–259.
Anion adsorption by allophanic tropical soils: I. Chloride adsorption.Crossref | GoogleScholarGoogle Scholar |

Gillman GP (1981) Effects of pH and ionic strength on the cation exchange capacity of soils with variable charge. Australian Journal of Soil Research 19, 93–96.
Effects of pH and ionic strength on the cation exchange capacity of soils with variable charge.Crossref | GoogleScholarGoogle Scholar |

Goldberg S (1995) Adsorption models incorporated into chemical equilibrium models. In ‘Chemical equilibrium and reaction models’. (Eds RH Loeppert, AP Schwab, S Goldberg) pp. 75–95. (Soil Science Society of America and American Society of Agronomy: Madison, WI)

Goldberg S, Criscenti LJ (2007) Modeling adsorption of metals and metalloids by soil components. In ‘Biophysico‐chemical processes of heavy metals and metalloids in soil environments’. (Eds A Violante, PM Huang, JM Gadd) pp. 215–264. (Wiley Online Library: Hoboken, NJ)

Havlin J, Tisdale SL, Nelson WL, Beaton JD (2016) ‘Soil fertility and fertilizers: an introduction to nutrient management’ (Pearson: London)

Haynes WM (2014) ‘CRC handbook of chemistry and physics.’ 95th edn. (CRC Press: Boca Raton, FL)

Hodson ME, Donner E (2013) Managing adverse soil chemical environments. In ‘Soil conditions and plant growth’. (Eds PJ Gregory, S Nortcliff) pp. 195–237. (Wiley-Blackwell: Oxford, UK)

Ishiguro M, Makino T, Hattori Y (2006) Sulfate adsorption and surface precipitation on a volcanic ash soil (allophanic Andisol). Journal of Colloid and Interface Science 300, 504–510.
Sulfate adsorption and surface precipitation on a volcanic ash soil (allophanic Andisol).Crossref | GoogleScholarGoogle Scholar | 16750540PubMed |

Jalali M (2013) Using chemical analysis and modeling to enhance the understanding of soil solution of some calcareous soils. Environmental Earth Sciences 68, 2041–2049.
Using chemical analysis and modeling to enhance the understanding of soil solution of some calcareous soils.Crossref | GoogleScholarGoogle Scholar |

Johnston J (2005) ‘Assessing soil fertility: the importance of soil analysis and its interpretation’ (Potash Development Association: York)

Karberg NJ, Pregitzer KS, King JS, Friend AL, Wood JR (2005) Soil carbon dioxide partial pressure and dissolved inorganic carbonate chemistry under elevated carbon dioxide and ozone. Oecologia 142, 296–306.
Soil carbon dioxide partial pressure and dissolved inorganic carbonate chemistry under elevated carbon dioxide and ozone.Crossref | GoogleScholarGoogle Scholar | 15378342PubMed |

Katou H (2002) A pH-dependence implicit formulation of cation- and anion-exchange capacities of variable-charge soils. Soil Science Society of America Journal 66, 1218–1224.
A pH-dependence implicit formulation of cation- and anion-exchange capacities of variable-charge soils.Crossref | GoogleScholarGoogle Scholar |

Kinniburgh DG, Syers JK, Jackson ML (1975) Specific adsorption of trace amounts of calcium and strontium by hydrous oxides of iron and aluminum. Soil Science Society of America Journal 39, 464–470.
Specific adsorption of trace amounts of calcium and strontium by hydrous oxides of iron and aluminum.Crossref | GoogleScholarGoogle Scholar |

Kolahchi Z, Jalali M (2006) Simulating leaching of potassium in a sandy soil using simple and complex models. Agricultural Water Management 85, 85–94.
Simulating leaching of potassium in a sandy soil using simple and complex models.Crossref | GoogleScholarGoogle Scholar |

Koopal LK, Saito T, Pinheiro JP, van Riemsdijk WH (2005) Ion binding to natural organic matter: General considerations and the NICA–Donnan model. Colloids and Surfaces. A, Physicochemical and Engineering Aspects 265, 40–54.
Ion binding to natural organic matter: General considerations and the NICA–Donnan model.Crossref | GoogleScholarGoogle Scholar |

Kopittke PM, Menzies NW (2007) A review of the use of the basic cation saturation ratio and the “ideal” soil. Soil Science Society of America Journal 71, 259–265.
A review of the use of the basic cation saturation ratio and the “ideal” soil.Crossref | GoogleScholarGoogle Scholar |

Lindsay WL (1979) ‘Chemical equilibria in soils.’ 1st edn. (Wiley-Interscience: New York)

Liu X, Li H, Li R, Tian R, Hou J (2012) A new model for cation exchange equilibrium considering the electrostatic field of charged particles. Journal of Soils and Sediments 12, 1019–1029.
A new model for cation exchange equilibrium considering the electrostatic field of charged particles.Crossref | GoogleScholarGoogle Scholar |

Matschonat G, Vogt R (1997) Effect of changes in pH, ionic strength, and sulphate concentration on the CEC of temperate acid forest soils. European Journal of Soil Science 48, 163–171.
Effect of changes in pH, ionic strength, and sulphate concentration on the CEC of temperate acid forest soils.Crossref | GoogleScholarGoogle Scholar |

Mau Y, Porporato A (2015) A dynamical system approach to soil salinity and sodicity. Advances in Water Resources 83, 68–76.
A dynamical system approach to soil salinity and sodicity.Crossref | GoogleScholarGoogle Scholar |

Meijboom F, van Noordwijk M (1991) Rhizon soil solution samplers as artificial roots. In ‘Root Ecology and its Practical Application 3. ISRR Symposium. Verein für Wurzelforschung, A-9020 Klagenfurt Austria’, pp. 793–795. (International Society of Root Research: Vienna)

Mercl F, Tejnecký V, Száková J, Hubová P, Tlustoš P (2017) Influence of Rhizon MOM suction cup and Triticum aestivum L. on the concentration of organic and inorganic anions in soil solution. Journal of Soils and Sediments 17, 820–826.
Influence of Rhizon MOM suction cup and Triticum aestivum L. on the concentration of organic and inorganic anions in soil solution.Crossref | GoogleScholarGoogle Scholar |

Molina F (2014) ‘Soil colloids.’ (CRC Press: Boca Raton, FL)

Mott CJB (1988) Surface chemistry of soil particles. In ‘Russell’s soil conditions and plant growth’. (Ed. AJ Wild) pp. 239–281. (Longman Scientific and Technical: Harlow)

Munns DN (1976) Heterovalent cation exchange equilibria in soils with variable and heterogeneous charge. Soil Science Society of America Journal 40, 841–845.
Heterovalent cation exchange equilibria in soils with variable and heterogeneous charge.Crossref | GoogleScholarGoogle Scholar |

Nederlof MM, Venema P, Van Riemsdijk WH, Koopal LK (1991) Modelling variable charge behaviour of clay minerals. In ‘Seventh Euroclay Conference’, Dresden. pp. 795–800. (Ernst-Moritz-Arndt-Universität: Greiswald)

Nye PH (1972) The measurement and mechanisms of ion diffusion in soils VIII — A theory for the propagation of changes of pH in soils. Journal of Soil Science 23, 82–92.
The measurement and mechanisms of ion diffusion in soils VIII — A theory for the propagation of changes of pH in soils.Crossref | GoogleScholarGoogle Scholar |

Parfitt R (1978) Anion adsorption by soils and soil materials. Advances in Agronomy 30, 1–50.

Parkhurst DL, Wissmeier L (2015) PhreeqcRM: A reaction module for transport simulators based on the geochemical model PHREEQC. Advances in Water Resources 83, 176–189.
PhreeqcRM: A reaction module for transport simulators based on the geochemical model PHREEQC.Crossref | GoogleScholarGoogle Scholar |

Ponthieu M, Juillot F, Hiemstra T, van Riemsdijk WH, Benedetti MF (2006) Metal ion binding to iron oxides. Geochimica et Cosmochimica Acta 70, 2679–2698.
Metal ion binding to iron oxides.Crossref | GoogleScholarGoogle Scholar |

Reddy KJ, Lindsay WL, Workman SM, Drever JI (1990) Measurement of calcite ion activity products in soils. Soil Science Society of America Journal 54, 67–71.
Measurement of calcite ion activity products in soils.Crossref | GoogleScholarGoogle Scholar |

Reid JB, Morton JD (2019) ‘Nutrient recommendations for vegetable crops in NZ.’ (Horticulture New Zealand Inc.: Wellington)

Reid JB, Trolove SN, Tan Y (2020) An algorithm to calculate the cationic composition of soil solutions 2. Parameterisation and test. Soil Research
An algorithm to calculate the cationic composition of soil solutions 2. Parameterisation and test.Crossref | GoogleScholarGoogle Scholar |

Rhue RD, Mansell RS (1988) The effect of pH on sodium-calcium and potassium-calcium exchange selectivity for Cecil soil. Soil Science Society of America Journal 52, 641–647.
The effect of pH on sodium-calcium and potassium-calcium exchange selectivity for Cecil soil.Crossref | GoogleScholarGoogle Scholar |

Rieu M, Vaz R, Cabrera F, Moreno F (1998) Modelling the concentration or dilution of saline soil-water systems. European Journal of Soil Science 49, 53–63.
Modelling the concentration or dilution of saline soil-water systems.Crossref | GoogleScholarGoogle Scholar |

Robbins CW (1986) Carbon dioxide partial pressure in lysimeter soils. Agronomy Journal 78, 151–158.
Carbon dioxide partial pressure in lysimeter soils.Crossref | GoogleScholarGoogle Scholar |

Robbins CW, Jurinak JJ, Wagenet RJ (1980) Calculating cation exchange in a salt transport model. Soil Science Society of America Journal 44, 1195–1200.
Calculating cation exchange in a salt transport model.Crossref | GoogleScholarGoogle Scholar |

Ross DS, Matschonat G, Skyllberg U (2008) Cation exchange in forest soils: the need for a new perspective. European Journal of Soil Science 59, 1141–1159.
Cation exchange in forest soils: the need for a new perspective.Crossref | GoogleScholarGoogle Scholar |

Rowell DL (1988) Soil acidity and alkalinity. In ‘Russell’s soil conditions and plant growth’. (Ed. AJ Wild) pp. 844–898. (Longman Scientific and Technical: Harlow)

Sagoo L, Huckle A, Atwood J, Rahn C, Lillywhite R, Stavridou E (2016) Review of evidence on the principles of crop nutrient management and nutrition for horticultural crops. Research Review No. 3110149017, Agriculture & Horticulture Development Board, Kenilworth, UK.

Sawhney B (1972) Selective sorption and fixation of cations by clay minerals: a review. Clays and Clay Minerals 20, 93–100.
Selective sorption and fixation of cations by clay minerals: a review.Crossref | GoogleScholarGoogle Scholar |

Schneider A, Mollier A (2016) Modelling of K/Ca exchange in agricultural soils. Geoderma 271, 216–224.
Modelling of K/Ca exchange in agricultural soils.Crossref | GoogleScholarGoogle Scholar |

Schulthess CP, Hu Z (2001) Impact of chloride anions on proton and selenium adsorption by an aluminum oxide. Soil Science Society of America Journal 65, 710–718.
Impact of chloride anions on proton and selenium adsorption by an aluminum oxide.Crossref | GoogleScholarGoogle Scholar |

Selim H, Mansell R, Gaston L, Flühler H, Schulin R (1990) Prediction of cation transport in soils using cation exchange reactions. In ‘Field-Scale Water and Solute Flux in Soils. Monte Verità (Proceedings of the Centro Stefano Franscini Ascona)’. (Eds Roth, K., WA Jury, H Flühler, JC Parker) pp. 223–238. (Birkhäuser: Basel)

Serrano S, O’Day PA, Vlassopoulos D, García-González MT, Garrido F (2009) A surface complexation and ion exchange model of Pb and Cd competitive sorption on natural soils. Geochimica et Cosmochimica Acta 73, 543–558.
A surface complexation and ion exchange model of Pb and Cd competitive sorption on natural soils.Crossref | GoogleScholarGoogle Scholar |

Sillen LG, Marttell AE (1971) Stability constants of metal-ion complexes. Supplement No 1 to Special Publication No 17. 3rd edn., The Chemical Society, London.

Sparks DL (2003) 10 - The chemistry of saline and sodic soils. In ‘Environmental soil chemistry’. 2nd edn. (Ed. DL Sparks) pp. 285–300. (Academic Press: Burlington, MA)

Sposito G (1977) The Gapon and the Vanselow selectivity coefficients. Soil Science Society of America Journal 41, 1205–1206.
The Gapon and the Vanselow selectivity coefficients.Crossref | GoogleScholarGoogle Scholar |

Sposito G (1994) ‘Chemical equilibria and kinetics in soils.’ (Oxford University Press: Oxford)

Sposito G, Coves J (1988) ‘SOILCHEM: A computer program for the calculation of chemical equilibria in soil solutions and other natural water systems.’ (University of California Riverside and Berkely, Kearney Foundation of Soil Sciences: Waterside, CA)

Sposito G, Fletcher P (1985) Sodium-calcium-magnesium exchange reactions on a montmorillonitic soil: III. Calcium-magnesium exchange selectivity. Soil Science Society of America Journal 49, 1160–1163.
Sodium-calcium-magnesium exchange reactions on a montmorillonitic soil: III. Calcium-magnesium exchange selectivity.Crossref | GoogleScholarGoogle Scholar |

Sposito G, Holtzclaw KM, Charlet L, Jouany C, Page AL (1983a) Sodium-calcium and sodium-magnesium exchange on Wyoming bentonite in perchlorate and chloride background ionic media. Soil Science Society of America Journal 47, 51–56.
Sodium-calcium and sodium-magnesium exchange on Wyoming bentonite in perchlorate and chloride background ionic media.Crossref | GoogleScholarGoogle Scholar |

Sposito G, Holtzclaw KM, Jouany C, Charlet L (1983b) Cation selectivity in sodium-calcium, sodium-magnesium, and calcium-magnesium exchange on Wyoming bentonite at 298 K. Soil Science Society of America Journal 47, 917–921.
Cation selectivity in sodium-calcium, sodium-magnesium, and calcium-magnesium exchange on Wyoming bentonite at 298 K.Crossref | GoogleScholarGoogle Scholar |

Sposito G, Jouany C, Holtzclaw KM, LeVesque CS (1983c) Calcium-magnesium exchange on Wyoming bentonite in the presence of adsorbed sodium. Soil Science Society of America Journal 47, 1081–1085.
Calcium-magnesium exchange on Wyoming bentonite in the presence of adsorbed sodium.Crossref | GoogleScholarGoogle Scholar |

Stockdale EA, Goulding KWT, George TS, Murphy DV (2013) Soil fertility. In ‘Soil conditions and plant growth’. (Eds PJ Gregory, S Nortcliff) pp. 49–85. (Wiley-Blackwell: Oxford, UK)

Taubaso C, Dos Santos Afonso M, Torres Sánchez RM (2004) Modelling soil surface charge density using mineral composition. Geoderma 121, 123–133.
Modelling soil surface charge density using mineral composition.Crossref | GoogleScholarGoogle Scholar |

Tazi S, Rotenberg B, Salanne M, Sprik M, Sulpizi M (2012) Absolute acidity of clay edge sites from ab-initio simulations. Geochimica et Cosmochimica Acta 94, 1–11.
Absolute acidity of clay edge sites from ab-initio simulations.Crossref | GoogleScholarGoogle Scholar |

Tertre E, Prêt D, Ferrage E (2011) Influence of the ionic strength and solid/solution ratio on Ca(II)-for-Na+ exchange on montmorillonite. Part 1: Chemical measurements, thermodynamic modeling and potential implications for trace elements geochemistry. Journal of Colloid and Interface Science 353, 248–256.
Influence of the ionic strength and solid/solution ratio on Ca(II)-for-Na+ exchange on montmorillonite. Part 1: Chemical measurements, thermodynamic modeling and potential implications for trace elements geochemistry.Crossref | GoogleScholarGoogle Scholar | 20932535PubMed |

Tinker PB, Nye PH (2000) ‘Solute movement in the rhizosphere.’ (Oxford University Press: New York)

Tournassat C, Gailhanou H, Crouzet C, Braibant G, Gautier A, Lassin A, Blanc P, Gaucher EC (2007) Two cation exchange models for direct and inverse modelling of solution major cation composition in equilibrium with illite surfaces. Geochimica et Cosmochimica Acta 71, 1098–1114.
Two cation exchange models for direct and inverse modelling of solution major cation composition in equilibrium with illite surfaces.Crossref | GoogleScholarGoogle Scholar |

Van Den Ende J (1991) Supersaturation of soil solutions with respect to gypsum. Plant and Soil 133, 65–74.
Supersaturation of soil solutions with respect to gypsum.Crossref | GoogleScholarGoogle Scholar |

Vaughan PJ (2002) Evaluation of numerical techniques applied to soil solution speciation including cation exchange. Soil Science Society of America Journal 66, 474–478.
Evaluation of numerical techniques applied to soil solution speciation including cation exchange.Crossref | GoogleScholarGoogle Scholar |

Venema P, Hiemstra T, van Riemsduk WH (1996) Comparison of different site binding models for cation sorption: Description of pH dependency, salt dependency, and cation–proton exchange. Journal of Colloid and Interface Science 181, 45–59.
Comparison of different site binding models for cation sorption: Description of pH dependency, salt dependency, and cation–proton exchange.Crossref | GoogleScholarGoogle Scholar |

Viets FJ (1980) ‘Present status of soil and plant analysis for fertilizer recommendations and improvement of soil fertility. FAO Soils Bulletins 38/1.’ (Food and Agriculture Organization of the United Nations: Rome)

Voegelin A, Vulava VM, Kuhnen F, Kretzschmar R (2000) Multicomponent transport of major cations predicted from binary adsorption experiments. Journal of Contaminant Hydrology 46, 319–338.
Multicomponent transport of major cations predicted from binary adsorption experiments.Crossref | GoogleScholarGoogle Scholar |

Vulava V, Kretzschmar R, Rusch U, Grolimund D, Westall J, Borkovec M (2000) Cation competition in a natural subsurface material: modeling of sorption equilibria. Environmental Science & Technology 34, 2149–2155.
Cation competition in a natural subsurface material: modeling of sorption equilibria.Crossref | GoogleScholarGoogle Scholar |

Wada S-I, Seki H (1994) Ca-K-Na exchange equilibria on a smectitic soil: Modeling the variation of selectivity coefficient. Soil Science and Plant Nutrition 40, 629–636.
Ca-K-Na exchange equilibria on a smectitic soil: Modeling the variation of selectivity coefficient.Crossref | GoogleScholarGoogle Scholar |

White PJ, Greenwood DJ (2013) Properties and management of cationic elements for crop growth. In ‘Soil conditions and plant growth’. (Eds PJ Gregory, S Nortcliff) pp. 160–194. (Wiley-Blackwell: Oxford, UK)

Wijnja H, Schulthess CP (2001) Carbonate adsorption mechanism on goethite studied with ATR–FTIR, DRIFT, and proton coadsorption measurements. Soil Science Society of America Journal 65, 324–330.
Carbonate adsorption mechanism on goethite studied with ATR–FTIR, DRIFT, and proton coadsorption measurements.Crossref | GoogleScholarGoogle Scholar |

Zachara JM, Westall JC (1998) Chemical modeling of ion adsorption in soils. In ‘Soil physical chemistry’. (Ed. DL Sparks) pp. 47–93. (CRC Press: Baton Rouge, FL)