Table 1.

Kinetics models for P release from classical fertilizers (control) and NEF in water and soil

Models release kinetics	Description	Parameter	Water			Soil
			nDPF1	nDPF2	C	nDPF1	nDPF2	C
First order Ln (q0–qt) = a − (Kd * T)	q0 = amount of P released at equilibrium mg·g−1, q or qt = amount of P released at time t (h) mg·g−1, Kd = Solubility rate (h−1) a = constant (mg.g−1)	Kd a R2 SE	0.012 5.835 0.927 0.214	0.012 5.291 0.925 0.215	0.013 6.442 0.942 0.206	0.007 2.835 0.953 0.171	0.006 2.569 0.940 0.191	0.007 3.738 0.967 0.151
Elovich qt = (1/β)ln(αβ) + (1/β)lnt	α = initial desorption rate of P (mg/g·h) β = constant related to P release (mg.g−1)	α β R2 SE	20.58 0.020 0.742 56.36	11.44 0.034 0.739 32.89	60.59 0.010 0.789 94.78	0.187 0.196 0.961 2.608	1E-01 0.261 0.942 2.417	4E-01 0.080 0.973 1.581
Parabolic diffusion q = a + kdt 1/2	a = constant (mg.g−1) Kd = apparent diffusion rate coefficient (mg/g.h1/2.)	Kd a R2 SE	22.44 43.88 0.948 25.27	12.99 26.66 0.946 14.95	42.20 36.07 0.969 36.03	0.840 2.201 0.994 1.009	0.634 2.268 0.989 1.029	2.051 7.405 0.998 1.489
Power functiona logq = logkdCο + 1/m logt	Kd = apparent desorption rate coefficient(h−1) 1/m = constant Co = initial P concentration	Kd 1/m R2 SE	6.380 0.705 0.978 0.087	2.764 0.765 0.978 0.096	38.17 0.492 0.964 0.078	0.316 0.643 0.993 0.018	0.164 0.696 0.995 0.016	0.410 0.743 0.993 0.021
Second order qt = kdqe2t /1 + kdqet	kd = apparent desorption rate coefficient (h−1)	Kd qe R2 SE	0.127 500 0.508 0.149	0.077 344.8 0.451 0.248	0.372 714.3 0.784 0.084	0.017 24.88 0.956 1.094	0.011 20.75 0.912 1.902	0.019 69.93 0.983 0.239

C = Classical fertilizers (control) ^aSE|≤ 0.1 in all the parameters