Table 1. Obtained Fitting Theoretical Parameters of the Studied Kinetic, Classic Equilibrium, Advanced Equilibrium, Van’t Hoff Equation, and Release Kinetic Models.

model	parameters	Mg·HAP	β-CD/HAP
Kinetic Models
pseudo-first-order	K1 (min–1)	0.415	0.597
	Qe(Cal) (mg/g)	99.0	155.1
	R2	0.88	0.96
	X2	2.75	0.54
pseudo-second-order	k2 (g mg–1min–1)	0.0031	0.0038
	Qe(Cal) (mg/g)	124.0	180.4
	R2	0.83	0.89
	X2	4.01	1.68
Isotherm Models
Langmuir	Qmax (mg/g)	166.4	267.4
	b (L/mg)	1.17 × 10–7	8.61 × 10–8
	R2	0.99	0.99
	X2	0.146	0.104
	RL	0.99	0.99
Freundlich	1/n	0.36	0.30
	kF (mg/g)	165.1	256.6
	R2	0.99	0.99
	X2	0.027	0.01
D–R model	β (mol2/kJ2)	0.02897	0.01165
	Qm (mg/g)	173.28	275.8
	R2	0.99	0.97
	X2	0.31	1.67
	E (kJ/mol)	4.15	6.55
monolayer model of one energy	n	3.89	4.45
	Nm (mg/g)	42.4	61.2
	Q(sat) (mg/g)	164.9	272.3
	ΔE (kJ/mol)	–7.54	–8.13
Thermodynamics
ΔG° (kJ mol–1)	293.13	–12.83	–14.24
	303.13	–13.14	–14.64
	313.13	–13.30	–15.04
	323.13	–13.27	–15.33
ΔH° (kJ mol–1)		–8.31	–4.23
ΔS° (J K–1 mol–1)		15.65	34.3

release kinetics
	determination coefficient
	Mg·HAP		β-CD/HAP
models	gastric fluid (pH 1.2)	intestinal fluid (pH 7.4)	gastric fluid (pH 1.2)	intestinal fluid (pH 7.4)
zero-order	0.78	0.89	0.90	0.80
first order	0.93	0.96	0.93	0.98
Higuchi	0.92	0.97	0.98	0.94
Hixson–Crowell	0.99	0.98	0.99	0.99
Korsmeyer–Peppas	0.95	0.98	0.95	0.96
n	0.64	0.73	0.64	0.64