Fractal analysis of pharmaceutical particles by atomic force microscopy

Purpose. Reliable methods are needed to characterize the surface roughness of pharmaceutical solid particles for quality control and for finding the correlation with other properties. In this study, we used fractal analysis to describe the surface roughness. Methods. Atomic force microscopy (AFM) was used to obtain three-dimensional surface profiles. The variation method was used to calculate fractal dimensions. We have measured fractal dimensions of four granule samples, four powders, and two freeze-dried powders. Results. A computer program was written to implement the variation method. The implementation was verified using the model surfaces generated by fractional Brownian motion. The fractal dimensions of most particles and granules were between 2.1 and 2.2, and were independent of the scan size we measured. The freeze-dried samples. however, showed wide variation in the values of fractal dimension, which were dependent on the scan size. As scan size increased, the fractal dimension also increased up to 2.5. Conclusions. Fractal analysis can be used to describe surface roughness of pharmaceutical particles. The variation method allows calculation of reliable fractal dimensions of surface profiles obtained by AFM. Careful analysis is required for the estimation of fractal dimension, since the estimates are dependent on the algorithm and the digitized model size (i.e., number of data points of the measured surface profile) used. The fractal dimension of pharmaceutical materials is also a function of the observation scale (i.e., the scan size) used in the profile measurement. The multi-fractal features and the scale-dependency of fractal dimension result from the artificial processes controlling the surface morphology.