Application of fractal dimension to the study of the surface ruggedness of granular solids and excipients

Thibert, Roch; Akbarieh, Mostafa; Tawashi, R.

doi:10.1002/jps.2600770817

Cited by 36 publications

(10 citation statements)

References 9 publications

Supporting

Mentioning

Contrasting

Unclassified

Order By: Relevance

“…An ideal fractal structure should produce a linear plot at all resolutions, when ln L δ is plotted against ln δ; D is the linear fractal dimension obtained by the slope given by s ) (1 -D) and represents the degree of irregularity of the particle silhouette. 14 The fractal dimension can apply to a line (D l ), such as in the case already described, as well as to a surface (D S ), related to D l as follows: D S ) (D l + 1). So while D l is experimentally determined, D S is a derived parameter.…”

Section: Theoretical Sectionmentioning

confidence: 99%

Fractal Analysis of Sodium Cholate Particles

Fini¹,

Fazio²,

Fernández-Hervás³

et al. 1996

Journal of Pharmaceutical Sciences

View full text Add to dashboard Cite

A fractal analysis was carried out on the powder particles of two samples of sodium cholate. A commercial sample had very irregular particles agglomerated, and accordingly the fractal dimension of the surface was 2.98, suggesting a noteworthy roughness of the particle surface; scanning electron microscopy showed that this was due to irregularities caused by a disordered agglomeration of very small particles, resulting in larger particles showing polygonal and smooth but limited facets. A second sample was obtained by recrystallization from ethanol of the commercial sodium cholate and contained large and regular particles, with very smooth surfaces. The fractal dimension therefore was accordingly low. Despite these differences, the two samples had similar, high reactive dimension values to dissolution (2.96 and 2.76, respectively), suggesting that the surfactant behavior of sodium cholate is an important parameter in driving the dissolution of the solid particles and leveling the surface defects.

show abstract

Section: Theoretical Sectionmentioning

confidence: 99%

Fractal Analysis of Sodium Cholate Particles

Fini¹,

Fazio²,

Fernández-Hervás³

et al. 1996

Journal of Pharmaceutical Sciences

View full text Add to dashboard Cite

show abstract

“…The fractal dimension can apply to a line with fractal dimension D l as well as to a surface with D s , related to D l as follows (Thibert et al 1988, Avnir 1989, Farin and Avnir 1992):…”

Section: Boundary Fractals Of Profilesmentioning

confidence: 99%

“…The fractal analysis relies on the fact that the perimeter of a silhouette edge is dependent on the step length with which it was measured. The smaller the step length is, the larger is the perimeter measured, because more details of the structure are taken into account (Thibert et al 1988). Decreasing the magnification therefore decreases the resolution power of SEM, and a longer step is thus used to measure a shorter perimeter.…”

Section: Boundary Fractals Of Profilesmentioning

confidence: 99%

Fractal analysis in particle dissolution: a review

Bao

Long

et al. 2014

Reviews in Chemical Engineering

View full text Add to dashboard Cite

Abstract:Fractal is a geometric language to describe the objects, the systems, and the phenomenon spatially and temporally. This paper reviews the literature on fractal models developed to describe the dissolution of particles. Dissolution, the process by which a solid forms a homogeneous mixture with a solution, is the behavior of a population of particles rather than a single one in most of the cases. The fractal models developed for the particle population are reviewed on the basis of two key particle surface properties, namely, the surface fractal nature and the chemical reactivity of particle surfaces. In terms of the surface fractal nature, fractals have been used to describe the change in the superficial roughness of particles, surface area-particle size relation, and particle size distribution (PSD). In terms of the reactive fractal dimensions, the models that describe the dissolution process have been developed to obtain the empirical noninteger exponent, the reactive fractal dimension that can dictate the chemical reactivity of a solid surface. The comparison between the surface fractal dimension and the reactive fractal dimension provides the dissolution mechanisms in many aspects of surface morphology. Further research is necessary to modify the current models to coincide with the real industrial processes and production and to develop the specific models for a better understanding of many processes involving the dissolution of particles encountered in many areas, including pharmaceutical and chemical applications and hydrometallurgy.

show abstract

“…Insofar as the surface material is fractal on a molecular scale, 3 the parameter dictating the chemical reactivity of a solid surface can be quantified with an empirical noninteger exponent: the reaction dimension D R . 4,5 This reaction dimension can be calculated using the modified form of the Noyes-Whitney equation proposed by D. Farin and D. Avnir, according to Wenzel's law (1777) on surface reactivity: 6 -dQ/dt ) K(Q/Q 0 ) D R /3 with K ) kQ e (1) and -dQ/dt ) K′R D R -3 with K′ ) k′Q 0 (2) where k and k′ are constants dependent on the hydrodynamic conditions. The reactive fractal dimension D R reflects the roughness of the reactive surface involved in dissolution.…”

Section: Introductionmentioning

confidence: 98%

Study of Morphology of Reactive Dissolution Interface Using Fractal Geometry

Tromelin

Gnanou

Andrés

et al. 1996

Journal of Pharmaceutical Sciences

View full text Add to dashboard Cite

0 The determination of reactive fractal dimension was carried out using two forms of the Noyes−Whitney equation, −dQ/dt ) K(Q/ Q 0 ) D R /3 and −dQ/dt ) K′R D R -3 using the Richardson plot on the basis of previous data obtained by dissolution of an orthoboric acid powder. The correlation of the results provided by the two ways of calculation allows proposal of the hypothesis that dissolution begins on a specific population of reactive sites and probably promotes the formation of microporous volumes or cracks.

show abstract

Application of fractal dimension to the study of the surface ruggedness of granular solids and excipients

Cited by 36 publications

References 9 publications

Fractal Analysis of Sodium Cholate Particles

Fractal Analysis of Sodium Cholate Particles

Fractal analysis in particle dissolution: a review

Study of Morphology of Reactive Dissolution Interface Using Fractal Geometry

Contact Info

Product

Resources

About