The theoretical molecular weight of NaYF ₄ :RE upconversion nanoparticles

Upconversion nanoparticles (UCNPs) are utilized extensively for biomedical imaging, sensing, and therapeutic applications, yet the molecular weight of UCNPs has not previously been reported. Herein, we present a theory based upon the crystal structure of UCNPs to estimate the molecular weight of UCNPs: enabling insight into UCNP molecular weight for the first time. We estimate the theoretical molecular weight of various UCNPs reported in the literature, predicting that spherical NaYF4 UCNPs ~ 10 nm in diameter will be ~1 MDa (i.e. 10⁶ g/mol), whereas UCNPs ~ 45 nm in diameter will be ~100 MDa (i.e. 10⁸ g/mol). We also predict that hexagonal crystal phase UCNPs will be of greater molecular weight than cubic crystal phase UCNPs. Additionally we find that a Gaussian UCNP diameter distribution will correspond to a lognormal UCNP molecular weight distribution. Our approach could potentially be generalised to predict the molecular weight of other arbitrary crystalline nanoparticles: as such, we provide stand-alone graphic user interfaces to calculate the molecular weight both UCNPs and arbitrary crystalline nanoparticles. We expect knowledge of UCNP molecular weight to be of wide utility in biomedical applications where reporting UCNP quantity in absolute numbers or molarity will be beneficial for inter-study comparison and repeatability.