Modelling phase transition kinetics of chenodeoxycholic acid with the Runge-Kutta method

The phase transition kinetics of two chenodeoxycholic acid polymorphic modifications-form I (stable at high temperature), form III (stable at low temperature) and the amorphous phase has been examined under various conditions of temperature and relative humidity. Form III conversion to form I was examined at high temperature conditions and was found to be non-spontaneous, requiring seed crystals for initiation. The formation kinetic model of form I was created incorporating the three-dimensional seed crystal growth, the phase transition rate proportion to the surface area of form I crystals, and the influence of the amorphous phase surface area changes with an empirical stage pointer q that contained the incomplete transition of the amorphous phase to form I with a residue omega(A)(infinity). The extent of transition and the phase transition rate constant depended on form I seed crystal amount in the raw mixture, and on the sample preparation. To describe phase transition kinetic curves, we employed the Runge-Kutta differential equation numeric solving method. By combining the Runge-Kutta method with the multi-point optimization method, the average quadratic deviation of the experimental results from one calculated series was under 2%.