Nonlinear estimation of kinetic parameters for solid-state hydrolysis of water-soluble drugs

Nonlinear-regression analysis was applied to estimate the kinetic parameters for the solid-state hydrolysis of meclofenoxate hydrochloride [2-(dimethylamino)ethyl (4-chlorophenoxy)acetate hydrochloride; 1] and propantheline bromide [(2-hydroxyethyl)diisopropylmethylammonium bromide xanthene-9-carboxylate; 2]. The percent decomposed (x) at the initial stage of decomposition was found to conform to the empirical equation x = ktn, where n and k are constants. The goodness of fit of the data was better than with the Prout-Tompkins equation. The parameters indicating the dependence of the rate on temperature (T) and water vapor pressure (P) were estimated by nonlinear-regression analysis based on the equation: x = x0 exp[(Ea/R)(1/298-1/T)] (P/18.167)s(t/50)n, where xo is the percent decomposed at t = 50 d, T = 298 K and P = 18.167 mmHg, and Ea (activation energy), s, and n are constants. For the hydrolysis at a relative humidity (RH) above the critical relative humidity (CRH), nonlinear parameter estimation provided statistically meaningful estimates of Ea, s, x0, and n, and it was suggested that these parameters could be regarded as constants in the experimental range. For the hydrolysis at RH below the CRH, however, the parameters could not be converged by nonlinear-regression analysis, and Ea and/or s were assumed not to be constant in this RH range.