Table 6 Values of langmuir, freundlich, DKR, TEMKIN, and R² for the adsorption of aniline blue dye on nano magnesium silicate nanoparticles.

Langmuir isotherm

\(\:{q}_{max}\)= 22.52 ± 2.86 mg/g

b = 0.52 ± 0.22 L/mg

R² = 0.90

\(\:{\chi\:}^{2}\) = 4.828

Freundlich isotherm

K_f = 9.02 ± 0.71 (mg g^− 1) (L g^− 1)^1/n

n = 3.17 ± 0.40

1/n = 0.32 ± 0.04

R² = 0.96

\(\:{\chi\:}^{2}\) = 1.683

Temkin isotherm

B = 3.43 ± 0.52

b = 722.32 ± 95.10 J mol^− 1

A = 18.7 ± 11.38 L/mol

R² = 0.916

\(\:{\chi\:}^{2}\) = 3.582

DKR isotherm

E = 4.29 × 10^− 4 ± 0.86 × 10^− 4 kJ mol^− 1

q_max = 18.87 ± 1.87 mg/g

R² = 0.82

\(\:{\chi\:}^{2}\) = 7.661