Rare-earth-doped upconversion nanoparticles (UCNPs) have often been used in combination with fluorescent dyes for sensing applications. In these systems, sensing can be achieved through the modulation of Förster resonant energy transfer (FRET) between the dye and the UCNP. The effects of FRET in such cases are complex, as the extent to which FRET is experienced by the rare-earth ions is dependent on their position within the nanoparticle. Here, we develop an analytical model to accurately describe the effects of FRET for such a system. As a proof of principle, we verify our model by considering the case of a pH sensor comprised of fluorescein isothiocyanate and Tm3+-doped UCNPs. We extend our model to the case of core–shell UCNPs and discuss the design of an optimal FRET-based biosensor using UCNPs.

A plasmonic nanostructure with lanthanide-doped upconversion nanoparticles for an improved ratiometric sensing platform.

Among the most promising sensors being developed are those that rely on Förster resonance energy transfer (FRET). FRET is a non-radiative process where energy can be transferred from a donor (ion or molecule) to an acceptor. [3][4][5] The rate of this exchange is highly distance-dependent and fades rapidly with increasing donoracceptor separation. Thus sensors that utilize FRET are capable of measuring local variations in critical biological parameters.Of the possible FRET-based sensors, those based on upconverting nanoparticles (UCNPs) are among the most promising. UCNPs are unique nanoparticles that can emit at several distinct visible wavelengths from a single, near-infrared excitation source. UCNPs exhibit many advantageous characteristics for bioimaging and sensing such as no photobleaching, no blinking, and no background autofluorescence. [6,7] In particular, many groups have attempted to utilize UCNPs as a FRET-based sensor by conjugating a fluorescent dye to the UCNP surface. [8][9][10][11][12][13][14][15][16][17][18][19][20][21][22][23][24][25] The key advantage of this configuration over other FRET-based schemes is that the multimodal emission of UCNPs allows for ratiometric sensing in which the relative intensities of two distinct peaks are compared rather than just the enhancement or quenching of a single one. Such ratiometric sensing reduces the sensing error due to variations in excitation intensity or nanoparticle concentrations, and thus makes these sensors much more robust against both sensor inhomogeneity and environmental noise. [26] However, FRET is not the sole process occurring that can affect the collected emissions. Unless a single UCNP can be measured directly, there exists a non-negligible chance that a photon emitted by one UCNP can be absorbed by a dye molecule on another nanoparticle. Such photon reabsorption (PR) would in turn lead to a decrease in the collected emission, thereby obscuring the true, localized FRET response of the original nanoparticle. An additional complication also arises from the fact that many of the visible UCNP emission lines originate from the same energy level. Since FRET acts as a decay pathway for an excited state electron, all emissions from this level should be affected equally by FRET, not just the one that overlaps with the dye's absorption band. To our knowledge, although the distinction between FRET and photon reabsorption has been discussed before, [27][28][29] no FRET-UCNP sensor has yet been proposed that accurately accounts for these complications.

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