Table 2.

Kinetics models for K 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 K released at equilibrium mg·g−1, q or qt = amount of K released at time t (h) mg·g−1, Kd = Solubility rate (h−1) a = constant (mg.g−1)	Kd a R2 SE	0.017 6.805 0.933 0.289	0.016 6.490 0.872 0.386	0.019 7.352 0.908 0.399	0.007 4.031 0.939 0.205	0.006 3.111 0.903 0.220	0.005 5.582 0.942 0.151
Elovich qt = (1/β)ln(αβ) + (1/β)lnt	α = initial desorption rate of K (mg/g·h) β = constant related to K release (mg.g−1)	α β R2 SE	103.6 0.007 0.818 122.5	65.39 0.011 0.740 102.4	194.1 0.004 0.865 175.4	0.380 0.063 0.940 3.069	1E-01 0.153 0.887 1.770	2E-01 0.012 0.893 22.01
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	58.82 17.68 0.974 46.76	40.31 26.17 0.934 51.48	98.65 6.99 0.990 46.83	2.652 14.16 0.991 1.206	1.098 7.185 0.962 1.016	13.70 79.07 0.963 12.81
Power functiona logq = logkdCο + 1/m logt	Kd = apparent desorption rate coefficient (h−1) 1/m = constant Co = initial K concentration	Kd 1/m R2 SE	67.80 0.457 0.973 0.063	46.15 0.444 0.930 0.101	124.2 0.449 0.985 0.046	0.180 0.902 1.000 0.006	0.288 1.054 0.998 0.016	0.900 0.902 0.993 0.024
Second order qt = kdqe2t /1 + kdqet	kd = apparent desorption rate coefficient (h−1)	Kd qe R2 SE	0.561 1000 0.849 0.084	0.361 714.3 0.717 0.168	0.875 1666 0.913 0.075	0.028 2000 0.955 0.014	0.011 1000 0.787 0.066	31.62 11,111 0.472 0.032

C = Classical fertilizers (control) ^a SE|≤ 0.101 in all the parameters