Szyszkowski equation

${\displaystyle \sigma _{m}=\sigma _{w}\left(1-0.411\log \left(1+{\frac {x}{a}}\right)\right)}$

with:

• σ_m is surface tension of the mixture
• σ_w is surface tension of pure water
• a is component specific constant (see table below)
• x is mole fraction of the solvated component

The equation can be rearranged to be explicit in a:

${\displaystyle {\begin{aligned}a&={\frac {x}{10^{\left(-1+{\frac {{\frac {\sigma _{m}}{\sigma _{w}}}-1}{-0.411}}\right)}}}\\&=x10^{\left(1+{\frac {{\frac {\sigma _{m}}{\sigma _{w}}}-1}{0.411}}\right)}\end{aligned}}}$

This allows the direct calculation of that component specific parameter a from experimental data.

The equation can also be written as:

${\displaystyle \gamma =\gamma _{0}-{\frac {RT}{\omega }}\ln(1+K_{ad}c)}$

with:

• γ is surface tension of the mixture
• γ₀ is surface tension of pure water
• R is ideal gas constant 8.31 J/(mol*K)
• T is temperature in K
• ω is cross-sectional area of the surfactant molecules at the surface

The surface tension of pure water is dependent on temperature. At room temperature (298 K), it is equal to 71.97 mN/m ^[4]

Meissner and Michaels published the following a constants:

Szyszkowski Equation Constants

Compound	a.104	Compound	a.104
Propionic acid	26	n-Propyl alcohol	26
Isopropyl alcohol	26	Methyl acetate	26
n-Propyl amine	19	Methyl ethyl ketone	19
n-Butyric acid	7	Isobutyric acid	7
n-Butyl alcohol	7	Isobutyl alcohol	7
Propyl formate	8.5	Ethyl acetate	8.5
Methyl propionate	8.5	Diethyl ketone	8.5
Ethyl propionate	3.1	Propyl acetate	3.1
n-Valeric acid	1.7	Isovaleric acid	1.7
n-Amyl alcohol	1.7	Isoamyl alcohol	1.7
Propyl propionate	1.0	n-Caproic acid	0.75
n-Heptanoic acid	0.17	n-Octanoic acid	0.034
n-Decanoic acid	0.0025