Crystal Growth Kinetics of Piracetam Polymorphs in Ethanol and Isopropanol

Abstract

The crystal growth kinetics of two different polymorphs of Piracetam have been investigated in ethanol and isopropanol. Isothermal seeded desupersaturation experiments were carried out at supersaturation ratios below 1.2 within the range of temperature 283–308 K. Liquid concentration was determined by in situ ATR-FTIR spectroscopy by a calibration-free method using principal component analysis. The power law equation and the BCF and B+S models were fitted to the experimental desupersaturation data by nonlinear optimization. The growth rates ranged 10–7–10–8 m/s, the growth rate order is clearly higher than unity, and the activation energies are in the range 39–66 kJ/mol for all the systems studied suggesting surface integration control. The growth of the metastable polymorph is faster than that of the stable form in both solvents. The crystal growth proceeds faster in ethanol than in isopropanol for both polymorphs. The solid–liquid interfacial energy is lower for the metastable form and is for both forms lower in ethanol than in isopropanol. The surface diffusion mass transfer rate is higher for the metastable form compared to the stable form and higher in ethanol than in isopropanol.

Crystal Growth, Dissolution, and Agglomeration Kinetics of Sodium Chlorate

“…According to the Burton, Cabrera, and Frank (BCF) surface diffusion model, which is thought to dominate at moderate supersaturations, screw dislocations present on the crystal surface function as self-perpetuating growth steps (spiral growth) whose advancement rate determines the overall crystal growth rate. According to this model, the growth rate of a crystal face G BCF in m s –1 is given by , where A and B are complex temperature-dependent constants which include parameters dependent on step spacings and surface properties , …”

“…Since crystal growth mechanisms may differ for different crystal faces, can be active on the same crystal face simultaneously, and can change during the course of the experiment, often simpler power law (PL) expressions are used to describe the overall change in the characteristic crystal dimension (m s –1 ). Such expressions often take the form of eq , where k g is the crystal growth rate constant and g is the so-called growth order (which contrary to reaction kinetics is purely empirical and does not reflect the number of elementary reaction steps present). …”

“…In such cases, the overall molar flux to the growing crystals R g (mol m –2 s –1 ) can be expressed as a simple function of the dimensionless thermodynamic driving force σ, if it is assumed that the concentration at the interface is approximately equal to the bulk solution concentration, as , where k d is the mass-transfer coefficient (mol m –2 s –1 ). From eq , the overall linear growth rate under diffusion control G diff (m s –1 ) can be estimated as ,, where k a and k v are the surface and volume shape factors (taken here as k a = 6 and k v = 1 for the cubic sodium chlorate crystals), ρ c is the crystal density (taken as 2500 kg m –3 for sodium chlorate), and M is the molecular weight (106.44 g mol –1 for sodium chlorate). The unknown parameters k d or directly k d ′ (m s –1 ) can be estimated based on empirical correlations, taking into account the fluid dynamics of the stirred crystallizer or by dissolution experiments, if it can be proved (or assumed) that the dissolution process is purely diffusion controlled.…”

“…where A and B are complex temperature-dependent constants which include parameters dependent on step spacings and surface properties 38,39 A kT D x…”

“…where k d is the mass-transfer coefficient (mol m −2 s −1 ). From eq 16, the overall linear growth rate under diffusion control G diff (m s −1 ) can be estimated as 39,42,43…”