Table 4 Physico-chemical parameters of mixed micelles

The critical micelle concentration of ideal mixtures (cmc^id) according to Clint [30]

cmc ^id

$\frac{1}{cm{c}^{id}}=\sum _i\frac{{\alpha }_i}{cm{c}_i}$

(1)

The mole fraction of the more hydrophobic surfactant in the ideal mixed micelle (x^id ), according to Motomura[31]:

x ^id

$x^{id}=\frac{cm{c}_2\alpha }{cm{c}_2\alpha +cm{c}_1\left(1-\alpha \right)}$

(2)

The mole fraction of the more hydrophobic surfactant in the real mixed micelle according to Rubingh [32]

x ₁

$\frac{x_1^2\text{ln (}cm{c}^{ex}\alpha /cm{c}_1{x}_{\text{1}}\text{)}}{{(1-x_1)}^2\text{ln}[{cmc}^{ex}(\text{1-}\alpha ){\text{/}cmc}_{\text{2}}({\text{1-x}}_{\text{1}})]}$

(3)

The β interaction parameter, according to Rubingh [32]

β

$\beta =\frac{\mathsf{\text{ln (}}cm{c}^{ex}\alpha ∕cm{c}_1{x}_{\mathsf{\text{1}}}\mathsf{\text{)}}}{{\left(1-x_1\right)}^2}$

(4)