Table 6 Kinetic and isotherm parameters of Cr(VI) adsorption by AgNps-DE and PDE. Kinetic data have been obtained at an initial concentration of 50 mg/L.

Freundlich

K_F (mg/g)(L/mg)^1/n

1.41

0.42

n

1.68

1.73

R²; R²-Adj

0.9995; 0.9994

0.9998; 0.9998

χ²; Δq (%); Hybrid

0.37; 20.27; 6.0

0.09; 12.3; 2.9

Langmuir

q_m (mg/g)

10.99

5.76

K_L (L/mg)

0.11

0.04

R²; R²-Adj

0.9999; 0.9998

0.9999; 0.9999

χ²; Δq (%); Hybrid

0.08; 6.28; 1.0

0.03; 6.21; 1.4

Tempkin

K_T (L/mg)

3.64

1.01

B

1.57

0.913

R²; R²-Adj

0.9985; 0.9981

0.9997; 0.9997

χ²; Δq (%); Hybrid

1.42; 29.9; 9.4

0.49; 20.6; 5.1

D.R

q_s (mg/g)

5.41

2.86

E (KJ/mol)

0.1044

0.0767

R²; R²-Adj

0.9929; 0.9911

0.9972; 0.9965

χ²; Δq (%); Hybrid

16.60; 67.59; 15.4

4.12; 106.8; 45.8

Sips

q_m (mg/g)

12.30

7.42

\(\:n\)

1.08

1.18

K_S (Lⁿ/mgⁿ)

0.0884

0.0227

R²; R²-Adj

0.9999; 0.9998

1.000; 1.000

χ²; Δq (%); Hybrid

0.07; 4.48; 0.22

0.01; 1.48; 0.02

q_{e, exp} (mg/g)

N-PFO

k₁ (1/min)

4.19

2.18

q_e (mg/g)

0.275

0.132

R²; R²-Adj

0.9887; 0.9858

0.9977; 0.9971

χ²; Δq (%); Hybrid

0.11; 5.32; 2.08

0.18; 8.27; 4.48

Ritche

q_e (mg/g)

4.61

2.72

K_R (1/min)

0.371

0.128

R²; R²-Adj

0.9993; 0.9991

0.9997; 0.9996

χ²; Δq (%); Hybrid

0.01; 1.74; 0.25

0.03; 4.96; 0.70

Avrami

q_e (mg/g)

4.30

2.47

\(\:{\text{n}}_{\text{a}\text{v}}\)

0.728

0.762

\(\:{K}_{av}\)(1/min)

0.247

0.091

R²; R²-Adj

0.9975; 0.9964

0.9958; 0.9993

χ²; Δq (%); Hybrid

0.02; 2.41; 0.71

0.06; 7.45; 1.2

N-PSO

k₂ (g/mg.min)

4.61

2.66

q_e.cal (mg/g)

0.080

0.051

R²; R²-Adj

0.9992; 0.9990

0.9998; 0.9997

χ²; Δq (%); Hybrid

0.01; 1.68; 0.11

0.02; 5.12; 0.83

Elovich

α (mg/g.min^1/2)

6.95

0.57

β (g.mg)

1.33

1.57

R²; R²-Adj

0.9721; 0.9651

0.9991; 0.9988

χ²; Δq (%); Hybrid

0.26; 9.12; 3.73

0.10; 11.09; 3.55

Intra-particle diffusion

k_ip,1; k_ip,2; k_ip,3;

1.352; 0.422; 0.128

0.636; 0.219; 0.133

C₁; C₂; C₃

−0.012; 2.315; 3.496

−0.373; 0.950; 1.390

R²₁; R²₂; R²₃

1.000; 1.000; 0.996

0.990; 0.990; 0.977