Effect of aspect ratio on the x-ray attenuation of nanoparticles: A theoretical study

Abstract

Purpose: There has been a significant focus on the potential applications of nanoparticle suspensions in the past few decades particularly as targeted contrast agents for specific pathological conditions. However, the question of optimal size and shape of nanoparticles for contrast enhancement is inadequately addressed. Methods: We present a comprehensive and conclusive theoretical analysis using first principles by considering the attenuating property of a single nanoparticle of any arbitrary shape. As a special case, ellipsoidal nanoparticles and nanorods are considered, for two independent directions of incidence of x-rays. These results are extended for a suspension of nanoparticles in a liquid. Results: It is seen that for a nanoparticle with dimensions much less than 1/μ(E), where μ(E) is the attenuation coefficient of the material, the attenuation by the nanoparticle is independent of its shape and size; and attenuation per unit mass reduces as the nanoparticle size increases. Conclusions: To achieve maximum attenuation, the nanoparticle sizes should be as small as possible, immaterial of the shape, as long as the dimensions are smaller than 150 nm.