SED & PREDOM / Ionic Strength / Activity Coefficient Models

SIT - Specific Ion interaction Theory

This model was adopted by the OECD-NEA thermodynamic database (TDB) project, and it is described in its published reviews and books, see list of references.

In the SIT model the activity coefficient of an ion “i” with electric charge Z_i is given by:

log γi =

−Aγ Zi2 (√I  /  (1 + åBγ √I )) + ∑j ε(i,j) mj

where I is the ionic strength; A_γ and B_γ are the Debye-Hückel parameters, and the ion-size parameter å is selected to give åB_γ = 1.5 (mol/kg)^−½ at 25°C.

ε(i,j) are the specific interaction parameters between an ion “i” and another ion “j” of opposite charge sign; that is, the summation is taken over all ions j such that Z_i×Z_j > 0. Often the ε-values are assumed to be independent of the ionic strength. A fundamental principle of the SIT model is that ε(i,j) = ε(j,i), that is, the specific ion interactions are symmetrical. When making a diagram, the values of ε(i,j) are read from a separate file (see below).

The temperature dependence of åB_γ (= 1.5 (mol/kg)^−½ at 25°C) and of the ε(i,j) values is discussed by Lemire et al. (2020) (Section B.1.2), as well as by Bretti et al. (2004), Xiong (2006) and Plyasunov and Popova (2013).

See Table of Debye-Hückel parameters at different temperatures. See also temperature in DATABASE/SPANA.

The activity of water (H₂O) is given by:

log aH2O =

− Φ ∑mk / (ln(10) 55.508)

where “k” are all solute species in the aqeuous solution, and “Φ” is the osmotic coefficient, calculated using the SIT as follows:

Φ =

1 − (2 AΦ I3/2 (1/∑mk) σ(åBγ √I)) + (ln(10)/∑mk) ∑i ∑j ε(i,j) mi mj

where A_Φ = (1/3) ln(10) A_γ and “i” are cations or neutral species and “j” are anions, and

σ(x) =

(3/x3) ((1+x) − 1/(1+x) − 2 ln(1+x))

Note: in the calculations the values of log γ_i are cut-off to be in the range ±(20 Z_i²), and log a_H2O is cut-off to be in the range ±4. Also the concentrations m_i are cut-off at 100 molal. The ionic strength is nevertheless calculated without restrictions in the values of m_i.

The ε-values:

When making a diagram the ε-values are first searched in a file named:

“SIT-coefficients.dta”

This is a text file that is distributed and stored in the installation folder. The format of the data in this file is described in the file itself. If you wish to add or to change ε-coefficients you can create a copy of the file (with the same name) and store it either in your user directory (system dependent, shown with the “Help / About” menu), or in the “working” directory (where your input data file is located). Any ε-values in the “working” directory will supersede those in the user directory, and the data in the user directory will supersede those in the installation directory.

If the first non-comment line in any of the three ε-files described above is equal to “NoDefaults” (not case-sensitive) then all undefined ε-values will be set to zero. Otherwise all undefined ε-values will be set to the default values as follows:

• Default ε-values between any ion and either Na⁺, Cl⁻ or ClO₄⁻ are assigned with the estimation method proposed by Hummel (2009):

  ε(Na⁺,X^Y) = 0.05 Y

  ε(M^Z,Cl⁻) = −0.05 + (0.1 Z)

  ε(M^Z,ClO₄⁻) = 0.2 Z

  where Z and Y are the electric charges for the cation (Z>0) and anion (Y<0), respectively. For example, ε(Sr²⁺,Cl⁻) = 0.15, and ε(Na⁺,MoO₄²⁻) = −0.1.

• Any ε-value not yet defined is set to:

  ε(M^Z,X^Y) = 0.15 + 0.15 (Z + Y)

  where Z and Y are the electric charges for the cation (Z>0) and anion (Y<0), respectively. For example: ε(K⁺,MoO₄²⁻) = 0, and ε(H⁺,OH⁻) = 0.15.

• For neutral species ε-values not yet defined are set to:

  ε(N⁰,M^Z) = ε(N⁰,X^Y) = 0.1

  where “N” is a neutral species, Z and Y are the electric charges for the cation (Z>0) and anion (Y<0), respectively. For example: ε(CO₂,Na⁺) = ε(HAc,OH⁻) = 0.1

Convergence problems

The nature of the SIT equation is such that in concentrated solutions some of the values of log γ_i become linearly dependent on the concentrations being calculated. This may create convergence problems in the calculations, especially when making diagrams where the pH is very high or very low, or where the redox potential, Eh, is outside the stability range of H₂O. If the redox potential is very high or very low, then unrealistically large amounts of O₂(aq) or of of H₂(aq) are calculated, respectively. As a consequence, the calculated ∑m_k in the equations above also becomes unrealistically large.

References

• Bretti C, Foti C, Sammartano S (2004) Chem. Speciat. Bioavailab., 16, 105–110. doi: 10.3184/095422904782775036
• Giffaut E, Vitorge P, Capdevila H (1994) J. Alloys Compd., 213–214, 278–285. doi:10.1016/0925-8388(94)90916-4
• Grenthe I, Fuger J, Konings R J M, Lemire R J, Muller A B, Nguyen-Trung C, Wanner H (1992) Chemical Thermodynamics of Uranium. Amsterdam, The Netherlands: North-Holland, Elsevier Sci. Publ.
• Grenthe I, Plyasunov A (1997) Pure Appl. Chem., 69, 951–958. doi: 10.1351/pac199769050951
• Grenthe I, Plyasunov A V, Spahiu K (1997) Estimations of medium effects on thermodynamic data. In: Modelling In Aquatic Chemistry (I. Grenthe & I. Puigdomenech, eds.), pp.325-426. Paris, France: OECD Nuclear Energy Agency (NEA).
• Hummel W (2009) Ionic strength corrections and estimation of SIT ion interaction coefficients, Report PSI-TM-44-09-01. Paul Scherrer Institut, Switzerland.
• Lemire R J, Palmer D A, Taylor P, Schlenz H (2020) Chemical Thermodynamics of Iron. Part 2. Paris, France: OECD Nuclear Energy Agency (NEA).
• Plyasunov A V, Popova E S (2013) J. Solution Chem., 42, 1320–1335. doi: 10.1007/s10953-013-0029-3
• Xiong Y (2006) Geochem. Trans., 7, 4. doi: 10.1186/1467-4866-7-4

 Models for activity coefficients

 Comparison between experimental data and models