Theory to describe incomplete ion exchange in charged heterogeneous systems

  • Wei Du
  • Xinmin Liu
  • Rui Li
  • Rui TianEmail author
  • Wuquan Ding
  • Hang Li
Soils, Sec 3 • Remediation and Management of Contaminated or Degraded Lands • Research Article



Incomplete ion exchange state in charged heterogeneous systems has been observed for a long time, but no general theory to describe this seemingly ordinary yet important phenomenon has been developed. The purposes of this study were to verify the effects of specific ions on the incomplete ion exchange and establish a theory to describe the incomplete ion exchange state.

Materials and methods

Permanently charged montmorillonite were pre-saturated with KNO3. K+-saturated montmorillonite (~ 0.5 g) were evenly spread in the exchange chamber. Exchange solutions (CsNO3, NaNO3, and LiNO3) with electrolyte concentrations of 0.0001, 0.001, 0.01, 0.02, and 0.03 mol L−1 concentrations flowed across the sample layer with a constant flow rate of 0.5 mL min−1, respectively. The adsorption amount for each cation species was calculated based on the concentration difference before and after each experiment.

Results and discussion

There were great differences between the adsorption amounts of Cs+, Na+, and Li+. The adsorption amounts of different ions were smaller than the cation exchange capacity of montmorillonite, aside from the Cs+ adsorption at the maximum Cs+ concentration of 0.03 mol L−1. Therefore, the observed adsorption equilibrium of cations was actually in an incomplete ion exchange state rather than a complete ion exchange state. The amounts of adsorbed cations at the incomplete ion exchange state displayed the order of Cs+ > Na+ > Li+, which means that the activation energies of cation exchange adsorption possessed the order of Cs+ < Na+ < Li+.


The potential barrier of diffusion for the adsorption and desorption ions in the electric field resulted in the incomplete ion exchange state. There is a basic rule for the incomplete ion exchange-exhibited specific ion effects: the ratio of the adsorption rate constants of an ion under two ionic concentrations will equal the ratio of the two concentrations.


Incomplete ion exchange Ion adsorption rate Ion non-classical polarization Smoluchowski equation Specific ion effects 



This work was supported by the National Natural Science Foundation of China (41501241 and 41530855). We also thank the two anonymous reviewers for their constructive comments on this study.


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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Chongqing Key Laboratory of Soil Multi-Scale Interfacial Processes, College of Resources and EnvironmentSouthwest UniversityChongqingPeople’s Republic of China
  2. 2.College of Natural Resources and EnvironmentNorthwest A&F UniversityYanglingPeople’s Republic of China
  3. 3.Chongqing Key Laboratory of Environmental Materials & Remediation TechnologiesChongqing University of Arts and ScienceChongqingPeople’s Republic of China

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