Table 1 The kinetics models of ARI release from NIOs/ARI

Zero-order

\(F={k_0}{\kern 1pt} t\)

First order

\(\ln (1 - F)= - {k_f}{\kern 1pt} t\)

Higuchi

\(F={k_H}\sqrt t\)

Power law^a

\(\ln F=\ln {k_P}+P\ln t\)

Square root of mass

\(1 - \sqrt {1 - F} ={k_{1/2}}{\kern 1pt} t\)

Hixson-Crowell

\(1 - \sqrt[3]{{1 - F}}={k_{1/3}}{\kern 1pt} t\)

Three seconds’ root of mass

\(1 - \sqrt[3]{{{{(1 - F)}^2}}}={k_{2/3}}{\kern 1pt} t\)

Weibull^b

\(\ln ( - \ln (1 - F))= - \beta \ln {t_d}+\beta \ln t\)

Reciprocal powered time^c

\(\left( {\frac{1}{F} - 1} \right)=\frac{m}{{{t^b}}}\)