Jones Dole equation
The Jones-Dole equation or Jones-Dole expression is an empirical expression that describes the relationship between the viscosity of a solution and the concentration of solute within the solution (at a fixed temperature and pressure).[1] The Jones-Dole equation is written as:[2][math]\displaystyle{ \frac{\eta}{\eta_0} = 1 + A C^\frac{1}{2}+ B C }[/math]where
- η is the viscosity of the solution (at a fixed temperature and pressure)
- η0 is the viscosity of the solvent at the same temperature and pressure
- A is a coefficient that describes the impact of charge-charge interactions on the viscosity of a solution (it is usually positive) and can be calculated from Debye-Hückel theory.
- B is a coefficient that characterises the solute-solvent interactions at a defined temperature and pressure.
- C is the solute concentration
The Jones-Dole B coefficient[3] is often used to classify ions as either structure makers (kosmotropes) or structure breakers (chaotropes) according to their supposed strengthening or weakening of the hydrogen-bond network of water.[4][5] The Jones-Dole expression works well up to about 1 M but at higher concentrations breaks down as the viscosity of all solutions increase rapidly at high concentrations.
The large increase in viscosity as a function of solute concentration seen in all solutions above about 1 M is the effect of a jamming transition at a high concentration. As a result, the viscosity increases exponentially as a function of concentration and diverges at a critical concentration. This has been referred to as the Mayonnaise Effect[6] as the viscosity of mayonnaise (essentially a solution of oil in water) is extremely high because of the jamming of micrometer scale droplets.
References
- ↑ http://www.le.ac.uk/chemistry/thermodynamics/pdfs/3000/Topic2930.pdf
- ↑ Jones, Grinnell; Dole, Malcolm (1929-10-01). "THE VISCOSITY OF AQUEOUS SOLUTIONS OF STRONG ELECTROLYTES WITH SPECIAL REFERENCE TO BARIUM CHLORIDE". Journal of the American Chemical Society 51 (10): 2950–2964. doi:10.1021/ja01385a012. ISSN 0002-7863. https://dx.doi.org/10.1021/ja01385a012.
- ↑ Jenkins, H. Donald B.; Marcus, Yizhak. (1995-12-01). "Viscosity B-Coefficients of Ions in Solution". Chemical Reviews 95 (8): 2695–2724. doi:10.1021/cr00040a004. ISSN 0009-2665. https://dx.doi.org/10.1021/cr00040a004.
- ↑ Marcus, Yizhak (2009-03-11). "Effect of Ions on the Structure of Water: Structure Making and Breaking". Chemical Reviews 109 (3): 1346–1370. doi:10.1021/cr8003828. ISSN 0009-2665. https://dx.doi.org/10.1021/cr8003828.
- ↑ Ball, Philip; Hallsworth, John E. (2015-03-23). "Water structure and chaotropicity: their uses, abuses and biological implications" (in en). Physical Chemistry Chemical Physics 17 (13): 8297–8305. doi:10.1039/c4cp04564e. ISSN 1463-9084. http://xlink.rsc.org/?DOI=C4CP04564E.
- ↑ Wynne, Klaas (2017-12-08). "The Mayonnaise Effect". The Journal of Physical Chemistry Letters: 6189–6192. doi:10.1021/acs.jpclett.7b03207. ISSN 1948-7185. https://dx.doi.org/10.1021/acs.jpclett.7b03207.
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