scholarly journals Studies of Polyelectrolyte Solutions V. Effects of Counterion Binding by Polyions of Varying Charge Density and Constant Degree of Polymerization

1994 ◽  
Vol 26 (5) ◽  
pp. 539-550 ◽  
Author(s):  
Eckhard Nordmeier
Keyword(s):  
Charge Density ◽  
Degree Of Polymerization ◽  
Counterion Binding ◽  
Constant Degree ◽  
Polyelectrolyte Solutions

Electric condensation of divalent counterions by humic acid nanoparticles

2016 ◽  
Vol 13 (1) ◽  
pp. 76 ◽  
Author(s):  
Herman P. van Leeuwen ◽  
Raewyn M. Town
Keyword(s):  
Humic Acid ◽  
Charge Density ◽  
Double Layer ◽  
Ion Pairs ◽  
Ion Pairing ◽  
Counterion Condensation ◽  
Counterion Binding ◽  
Satisfactory Description ◽  
Poisson Boltzmann ◽  
Very High

Environmental context Humic acids are negatively charged soft nanoparticles that play a governing role in the speciation of many ionic and molecular compounds in the environment. The charge density in the humic acid nanoparticle can be very high and the binding of divalent cations such as Ca2+ appears to go far beyond traditional ion pairing or Poisson–Boltzmann electrostatics. A two-state approach, combining counterion condensation in the intraparticulate double layer and classical Donnan partitioning in the bulk of the particle, provides a satisfactory description of the physicochemical speciation. Abstract Experimental data for divalent counterion binding by soil humic acid nanoparticles are set against ion distributions as ensuing from continuous Poisson–Boltzmann electrostatics and a two-state condensation approach. The results demonstrate that Poisson–Boltzmann massively underestimates the extent of binding of Ca2+ by humic acid, and that electric condensation of these counterions within the soft nanoparticulate body must be involved. The measured stability of the Ca2+–humic acid associate is also much greater than that predicted for ion pairing between single Ca2+ ions and monovalent negative humic acid sites, which also points to extensive electrostatic cooperativity within the humic acid particle. At sufficiently high pH, the charge density inside the humic acid entity may indeed become so high that the bulk particle attains a very high and practically flat potential profile throughout. At this limit, all the intraparticulate Ca2+ is at approximately the same electrostatic potential and the status of individual ion pairs has become immaterial. A two-state model, combining counterion condensation in the charged intraparticulate part of the double layer at the particle–medium interface and Donnan partitioning in the uncharged bulk of the humic acid particle, seems to lead the way to adequate modelling of the divalent counterion binding for various particle sizes and different ionic strengths.

Dependence of Structural Forces in Polyelectrolyte Solutions on Charge Density:  A Combined AFM/SAXS Study

2003 ◽  
Vol 36 (18) ◽  
pp. 6878-6883 ◽  
Author(s):  
Dan Qu ◽  
Damien Baigl ◽  
Claudine E. Williams ◽  
Helmuth Möhwald ◽  
Andreas Fery
Keyword(s):  
Charge Density ◽  
Structural Forces ◽  
Polyelectrolyte Solutions

Improved numerical modelling of competitive counterion binding in polyelectrolyte solutions

Polymer ◽  
1991 ◽  
Vol 32 (8) ◽  
pp. 1504-1509 ◽  
Author(s):  
William F. Moss ◽  
H.Garth Spencer ◽  
George B. Savitsky ◽  
Carl M. Riedl
Keyword(s):  
Numerical Modelling ◽  
Counterion Binding ◽  
Polyelectrolyte Solutions
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