Lanthanide-Based Nanosensors: Refining Nanoparticle Responsiveness for Single Particle Imaging of Stimuli

Abstract

Lanthanide nanoparticles (LNPs) are promising sensors of chemical, mechanical, and temperature changes; they combine the narrow-spectral emission and long-lived excited states of individual lanthanide ions with the high spatial resolution and controlled energy transfer of nanocrystalline architectures. Despite considerable progress in optimizing LNP brightness and responsiveness for dynamic sensing, detection of stimuli with a spatial resolution approaching that of individual nanoparticles remains an outstanding challenge. Here, we highlight the existing capabilities and outstanding challenges of LNP sensors, en-route to nanometer-scale, single particle sensor resolution. First, we summarize LNP sensor read-outs, including changes in emission wavelength, lifetime, intensity, and spectral ratiometric values that arise from modified energy transfer networks within nanoparticles. Then, we describe the origins of LNP sensor imprecision, including sensitivity to competing conditions, interparticle heterogeneities, such as the concentration and distribution of dopant ions, and measurement noise. Motivated by these sources of signal variance, we describe synthesis characterization feedback loops to inform and improve sensor precision, and introduce noise-equivalent sensitivity as a figure of merit of LNP sensors. Finally, we project the magnitudes of chemical and pressure stimulus resolution achievable with single LNPs at nanoscale resolution. Our perspective provides a roadmap for translating ensemble LNP sensing capabilities to the single particle level, enabling nanometer-scale sensing in biology, medicine, and sustainability.

Graphical Abstract

Sensors that noninvasively report on the chemical, electrical, thermal, or mechanical conditions of complex systems have proven indispensable for diagnosing and predicting failures. From optical noncontact sensing of the structural soundness of bridges¹ to detecting cornea health in eyes with optical coherence tomography,^2,3 noninvasive optical sensing provides critical feedback to improve safety and health. To date, numerous sensors have been developed to monitor both normal and abnormal functioning of macroscale systems. However, for systems where the relevant processes are operative within the micro- or nanometer size regimes, the process of noninvasive information extraction is significantly more challenging. For example, development of efficient catalysts for renewable energy generation would benefit from nanometer resolution mapping of surface species, temperature, and pressure during reactor operation.⁴ As a second example, within the immunological synapse, accessing the mechanical information transmitted between individual membrane-associated ligands and their receptors could unravel the signaling pathways necessary for pathogen recognition, potentially advancing immunotherapies.⁵ Third, mechanical forces in the nervous system may be critical for growth and development, such as the migration of developing neurons in response to stiffness gradients, but noninvasive, robust sensors are needed to map mechanical information over the long time scales of neuron development.⁶ Our understanding of these systems, and ultimately our ability to improve them, depends not only on our ability to extract information but to distinguish that information with near nanometer resolution. Luckily, nanoscale optical sensors provide noninvasive methods of measuring such events with high spatial and temporal resolution. Lanthanide-doped nanoparticles (LNPs), which have proven to be effective sensors for a variety of environmental conditions on the ensemble level, have recently become bright enough to detect at the single particle level, making them particularly attractive for monitoring and diagnosing the functioning of complex micro- or nanoscale systems.

LNPs capitalize on the narrow emission lines and long lifetimes of lanthanide dopants embedded in a ceramic host lattice to measure temperature and pressure^7–10 or detect chemical species and biomarkers.^11–20 Here we use the term LNPs to refer to nanoparticles that are doped with lanthanide ions and are utilized for their upconversion (anti-Stokes), downconversion (Stokes), or other luminescent emission.^10,16–28 Their large Stokes and anti-Stokes shifts transduce absorbed light into emission lines spanning the infrared, visible, and ultraviolet depending on the chosen lanthanide dopants (Figure 1a).^15,29–31 The ladder-like energy structures of LNPs (Figure 1b) allow for tailored energy transfer,^32–35 minimal interferences from short-lived fluorescence,^18,36,37 and emission color control via dopant type and concentration (Figure 1c–d).^38–42 Moreover, LNPs possess a photostability that far exceeds that of other organic and inorganic fluorescent probes, such as dyes, fluorescent proteins, and quantum dots; for example, optimized LNPs can exhibit stable emission for 5 h.^43–46 Several recent reviews provide in-depth comparisons between the optical response of nanoscale organic and inorganic optical emitters.^47,48 Capitalizing on these intrinsic photophysical advantages, the LNP community has spent the last two decades engineering highly monodisperse, biocompatible, and functionalizable nanoparticle architectures (Figure 1e).^40,49–52 These advances have made LNPs luminescent probes that rival and exceed the capabilities of traditional platforms,^53–60 with diverse and impactful applications spanning super-resolution microscopy,⁶¹ monitoring of protein–protein interactions via FRET,⁶² ophthalmology,⁶³ and optogenetics.^64–66

Figure 1.

(a) Some of the prominent transitions of lanthanide elements spanning the ultraviolet to the infrared.^29–31 (b) Jablonski diagram showing energy structure and key energy transfer processes for Yb³⁺/Er³⁺ upconversion and downconversion. (c) Illustration of inorganic nanocrystal doped with lanthanide ions. (d) Control of nanoparticle emission via dopant type and concentration for downconversion of LiYF₄: 13% Ce³⁺, 14% Tb³⁺, 0–5% Eu³⁺ nanoparticles in polydimethylsiloxane (top) and upconversion in various sandwich-structured nanoparticles of NaGdF₄ and NaNdF₄ doped with Yb³⁺, Tm³⁺, Er³⁺, and Eu³⁺ (bottom). (e) Transmission electron microscope image of multishelled LNPs. (f) Confocal scan image of single nanoparticle emission and (g) colocalization of single nanoparticles via scanning electron microscopy. Panel d adapted with permission from ref 67, copyright 2015 Springer Nature, and ref 34, copyright 2013 John Wiley and Sons,³⁴ Panels e–g adapted with permission from ref 68, copyright 2019 American Chemical Society.

If the 2010s witnessed the adoption of LNP ensembles as pre-eminent luminophores, we believe the coming decade will see them emerge as a premier sensing platform for mapping spatiotemporal dynamics of pressure, temperature, and chemical composition at the single particle level; accordingly, this perspective focuses specifically on LNP’s promise as sensors. Biological tracking, so far done predominantly with bright and highly efficient single luminescent molecules^53,69 or quantum dots,^47,70–72 has revealed fascinating, nanometer scale insights into protein folding,⁷³ translation,⁷⁴ and myosin motor dynamics⁷⁵ to name a few examples. LNPs have the potential to track spatial position while also quantifying local conditions of temperature, pressure, and chemical composition. This potential would allow them to track phenomena that occur over long time scales and do so with sensitivity to local stimuli, here defined as any events or changes in environmental conditions such as temperature, pressure, or presence of chemical species that induce a response from the optical probe. In addition, the LNP’s ceramic host lattice provides stability against high temperature and pressure, making them ideal for monitoring nanoscale phenomena over time in more demanding and “extreme” environments like chemical reactors.⁴ LNPs are uniquely suited as high resolution sensors for a broad range of processes from biology to industry and consumer technology.^{4,13,21,76,77} However, doing so requires a translation from the ensemble regime, where output signal is often based off of millions to billions of nanoparticles, to the single particle regime (Figure 1f–g). The drastic reduction in output signal upon translation to the single particle regime presents a brightness challenge, one which is exacerbated by quenching when working in aqueous solutions.^78,79 Recent advances in nanoparticle design including passivation strategies^40,51,52,79 and enhancement via thermal treatments⁸⁰ and molecular dye antennas⁸¹ help overcome this challenge to maximize brightness. In parallel with improvements to brightness, achieving the vision of accurate and precise reporting of external stimuli by a single LNP requires ensuring identical optical behavior from any selected single particle.

This perspective focuses on describing ways to analyze the sensitivity and hence improve the precision and accuracy of LNP sensors. Note that precision is defined as how small of a change in an external stimuli can be correctly reported, and accuracy is how close the value of the stimuli reported is to the true value. First, we establish the photophysical basis for the environmental sensitivity of the platform and its common signal readout modalities, including luminescence intensity, ratiometric spectral changes, wavelength (λ) shift, and luminescence lifetime. Then we provide a discussion of the relevant physical parameters that broaden the variance of these four optical measurements when sensing with a single LNP. We group these sources of imprecision under three broad categories: (1) sensitivity to competing conditions, which includes the confluence of uncontrolled inputs such as temperature and laser power with the input under investigation, (2) interparticle heterogeneities, which stem from the unique concentration and distribution of dopant ions, defects, and other structural parameters in single nanoparticles, and (3) measurement noise, which includes the shot noise that ultimately dictates the lowest achievable stimulus sensitivity. We then suggest methods of characterizing and reporting these sources of imprecision with the goal of contributing to a better working knowledge of structure–property relationships at the single particle level and informing future synthetic efforts. We leave the reader with an estimate of the magnitude of stimulus resolution achievable with a single LNP at nanoscale resolution if the issue of precision and accuracy is undertaken in earnest.

SENSING WITH ENSEMBLES OF LANTHANIDE NANOPARTICLES

LNPs are sensitive to their environment, making them excellent sensors of pressure,^104–109 chemical and biomolecular concentration,^12,110 and temperature.⁷ In sensing, LNP emission can be modified via three distinct mechanisms: changes in radiative rates, nonradiative rates, and state population. The radiative rates of lanthanide nanoparticle emission are dictated by the Laporte selection rules, which are the basis for the low probability of f–f transitions and correspondingly long lifetimes (microseconds to milliseconds).¹⁵ These rules can be relaxed, often via changes in local crystal symmetry.^111–113 Alternatively, there are a number of ways to introduce or change nonradiative pathways such as energy transfer with an external luminescent species or changes in the phonon energies associated with nanoparticle surface defects, coordinated ligands, or solvent molecules.^11,114,115 Finally, the population of states can increase or decrease due to effective changes in the local temperature or incident photon flux.^{7,8,35,116–118} The energy transfer networks among the constituent lanthanide ions of a single nanoparticle possess a large number of possible transitions and complex dynamics; these present a broad phase-space for optimizing sensor precision, but can also make it difficult to disentangle the mechanisms of sensing.¹¹⁹ Figure 2a shows how different types of stimuli including temperature, chemical environment, pressure, and incident power affect the transition rates and population of lanthanide states, ultimately dictating the unique optical response.

Figure 2.

LNPs are sensitive to a range of external stimuli. (a) External parameters such as temperature, chemical signals, mechanical signals, and laser power adjust the optical emission of the nanoparticles. Emission from LNPs can change via alterations in the radiative rate of emission, nonradiative energy transfer, and population of energy levels. The resulting optical signal includes intensity changes, ratiometric changes between emission lines, wavelength (λ) shifts, and lifetime changes. (b) The detection limit for a range of analytes using LNPs reported vs their readout method.^82–103 (c) Resolution in pressure sensing for LNPs in a diamond anvil cell plotted versus reported readout mechanism.^104–108 Details on particle composition and experimental parameters for panels b and c are found in the Supporting Information.

Four common readout schemes for LNP sensors include luminescence intensity, ratiometric spectral changes, wavelength (λ) shift, and luminescence lifetime measurements. These sensing measurement techniques each have their own advantages and drawbacks. Luminescence intensity, which we define as the emitted photon count rate from LNPs without distinguishing spectral or temporal information, is commonly employed because of its simplicity, speed, and versatility. However, data obtained this way can be easily convoluted by a variety of factors, including changes in local excitation power and tissue thickness.^25,120,121 Ratiometric and λ-shift measurements employ spectral information to overcome these issues. The former compares the emission between two or more discrete wavelength ranges, while the latter relies on a shift in the central transition energy. The potential to normalize the signal against a standard spectral region provides both ratiometric¹²² and λ-shift measurements^106,107 a built-in control against power density changes. Finally, lifetime measurements collect time-dependent emission from lanthanide nanoparticles to measure an effective decay lifetime. Lifetime data are demonstrably robust to changes in excitation power density due to attenuation from up to 8 mm of intralipid medium and up to 4 mm of bone, as shown by Fan et al.²⁵ It also provides ample opportunity for multiplexing.^18,36,39,123 We compare the resolution for state-of-the-art chemical (Figure 2b) and pressure (Figure 2c) sensing with LNPs across the four discussed measurement techniques. Although LNPs also make excellent temperature sensors, we consider it outside the scope of this perspective and provide references to the many existing reviews for the interested reader.^{7,8,116,124–128} Tables S1 and S2 in the Supporting Information (SI) provide details about the LNPs used for sensing in Figure 2b,c, including host material, lanthanide constituent and concentration, architecture, excitation wavelength, and collection wavelengths.

Changes in chemical composition are relevant to applications ranging from biology^129–132 to consumer goods.^77,133 LNPs have shown promise in detecting inorganic ions and organic molecules, in some cases with femtomolar detection limits (Figure 2b).^82,83 Certain chemical species that come near to or bind to the surface of the LNPs will perturb energy transfer, and thereby tune emission. Often the nanoparticles are functionalized with an energy transfer donor or acceptor species which is sensitive to the chemical in question to help ensure selectivity of sensing.^11,84,99,100 Alternatively, Liu et al. achieved selectivity by coating LNPs designed for K⁺ sensing with a K⁺-selective filter membrane, thereby excluding interference from other cations.⁹⁴ The particles are either suspended in liquid^{82,84–86,88–97,99,100,102,103} or bound to a thin film^{83,98,101,134,135} based sensing platform. There are many reviews and resources detailing the state-of-the-art in chemical sensing and techniques with LNPs.^{11,12,136,137}

LNPs could also be applied to real time pressure sensing in biological systems and chemical reactors.^4,105,122 The pressure response of LNPs is commonly calibrated in a diamond anvil cell with resolution down to tens of MPa (Figure 2c) for high pressure (~GPa) measurements.^104–108 In addition to high pressure sensing applications, LNPs have also been used to detect pressure changes in a vacuum with resolution below 1 Pa.¹⁰⁹

Sensing is complicated by competing external parameters, stimuli that are not of interest to the experiment but have an impact on the emission response. Competing external parameters include incident power density fluctuations due to changes in the laser path length (through tissue or other absorbing/scattering media for example), sample temperature, different types of molecules that may interact with a sensor, and changes in pH in the sensing environment. To demonstrate the appropriateness of a sensor, researchers must show that these competing external parameters have been investigated and produce little or no response compared to the response of the desired stimuli. The relevant competing conditions differ for different sensing applications. As an example, Lay et al. show how the pH and buffer environment affect the optical properties of LNPs compared to the desired mechanosensitive response, all in the context of pressure sensing in the digestive tract of C. elegans.¹³⁸ For highly selective detection of a molecule or biomarker, functionalizing the particle to ensure only the molecule of interest binds to the surface can reduce the impact of other present molecules. As stated earlier, particles can be coated with a chemically selective luminescent marker which can couple into the energy transfer pathways in the LNP.¹¹⁴ While these great strides in sensing have enabled incredible work at ensemble levels, it is still challenging to bring sensing capabilities of LNPs to single particle measurements.

SOURCES OF IMPRECISION IN SINGLE PARTICLE SENSING

Realizing single particle LNP sensing necessitates elucidating sources of imprecision and inaccuracy. Over the past decade, syntheses aimed at single LNP sensing have mainly focused on maximizing signal output, usually through adjusting dopant ratios^139,140 or engineering complex architectures to control the nonradiative propagation of energy within the particle.^68,141,142 The impressive strides in brightness make it feasible to detect the presence of a single nanoparticle for labeling applications.^143,144 These studies range from characterizing single nanoparticles for super resolution microscopy,^33,48,145 particle tracking in biological systems,¹⁴⁶ and bioassays.¹⁴³ However, the utility of a sensing platform lies not just in its ability to produce a detectable signal, but also in the ability of that signal to precisely reflect a change in the system under inspection (i.e., precision). With that in mind, we believe optimizing sensor precision is comparable in importance to optimizing sensor brightness. The first step toward optimizing precision involves characterizing any sources of imprecision. We organize imprecision into three main categories, namely, measurement noise, interparticle heterogeneities, and competing external parameters.

We begin by outlining the measurement noise considerations that are relevant when developing a single particle sensor: (1) single particles must be bright enough to detect above the background, (2) the response must be larger than any noise in the signal, and (3) the response must be unique and unaffected by other parameters in the environment. It is challenging to compare the quality of sensors reported in the literature due to the variations in responsiveness, brightness, and selectivity from sensor to sensor. To compare the responsiveness and signal of sensors, we propose that authors present noise equivalent sensitivity (NES) as an essential figure of merit for their sensors. NES is a fundamental limit on the sensing capability of the nanoparticles, and one can think of this value as the smallest detectable change after integrating for 1 s. A more stringent definition is the response in a 1 Hz bandwidth with a signal-to-noise ratio of 1. For an optical probe whose photons are emitted with a Poisson distribution, the noise will scale with the square root of the number of photons collected; the unit of NES is sensing unit/√Hz.¹⁴⁷

This NES figure of merit is often used for magnetometers,¹⁴⁸ photoacoustic measurements,¹⁴⁹ and bolometers.¹⁴⁷ For a photodetector, it is sometimes quoted as the noise equivalent power (NEP) in units W/√Hz. NES combines the effect of particle brightness with particle response into a single value that is fundamental to the particles being studied.

Table 1 gives examples of changes in LNP brightness, spectra, and lifetime due to an external stimulus and a simple calculation to detect the NES of each feature. Here, we assume the response can be fit to a linear curve also given in the table. Derivations of these parameters are provided in the Supporting Information. We would like the reader to note that for any optical measurement the NES will scale with the inverse square root of the photon count rate (1/√I) and linearly with the inverse of the response (1/R). Therefore, once a particle becomes bright enough to sense, it is often advantageous to enhance the response of the sensor rather than continuing to enhance brightness.

Table 1.

Simple Noise Equivalent Sensitivity (NES) Calculations for Different Readout Optical Mechanisms^a

Technique	Signal	NES
Intensity	I0t(l + RF)	$\frac{1}{|\text{R}|\sqrt{{\text{I}}_0}}$
Ratiometric	α0(l + RF)	$\frac{1}{|\text{R}|\sqrt{{\text{I}}_0}}\cdot \frac{1+\alpha }{\sqrt{\alpha }}$
Lifetime	τ0(l + RF)	$\frac{2.37}{|\text{R}|\sqrt{{\text{I}}_0\cdot \text{DutyCycle}}}$
λ-shift	λ0(l + RF)	$\frac{1\sqrt{\text{G}({\lambda }_{\text{m},}{\lambda }_{\text{c}})}}{\sqrt{{\text{I}}_{\text{max}}}\frac{\text{dG}(\lambda ,{\lambda }_{\text{c}})}{\text{d}\lambda }{|}_{\lambda ={\lambda }_{\text{m}}}}\frac{1}{\text{R}{\lambda }_0}$

^aI₀ is the starting photon count rate of the particle, R is the respective response for each measurement, F is the strength of the external stimuli being sensed, α₀ is the starting intensity ratio of the emission lines being compared, τ₀ is the starting lifetime, duty cycle is the fraction of detection time per measurement period, λ₀ is the starting wavelength, G is the function defining the shape of the peaks, λ_c is the center wavelength of the peak, and λ_m is the wavelength with the largest slope. The calculations for NES are found in the Supporting Information.

Measurement noise will further affect the resolution of a sensing measurement. We attribute measurement noise to power fluctuations in the excitation laser, dark counts and electronic noise in the photon detector, and background fluorescence. This noise will add in quadrature with the shot noise of the nanoparticles. Because of the low count rates of single LNP measurements, commonly less than 100 kcps, shot noise is often the dominant source of measurement error. When designing an experiment, it is ideal for any excess measurement noise to be below the optical shot noise.

In an attempt to collate the influence of shot noise on the variance of optical properties as it appears in the available single LNP literature, we extracted coefficients of variation (standard deviation normalized by the mean) in single particle brightnesses across 29 distinct LNP batches, across 4 orders of magnitude of excitation power from four separate papers (Figure 3, SI Table S3).^{68,139,141,142} Here, batch refers to nanoparticles synthesized under identical conditions, and having identical average optical, structural, and compositional properties across repeated syntheses. Assuming a 1 s integration time when not specified in the respective study, we calculated the minimum percentage of that coefficient of variation attributable to shot noise (plotted in yellow for each batch). As is evident in Figure 3, the majority of the relative variance in the single particle brightness of each batch cannot be attributed to mere shot noise. Given the care that the experimenters took to control for fluctuations in experimental parameters like input power and the fact that shot noise is the dominant measurement noise in this low signal regime, we attribute this remaining variance to intrinsic heterogeneities in structure and elemental distribution across individual LNPs. In the absence of thousands to billions of other particles over which to average the measured response, a single particle experiment is limited by the intrinsic heterogeneity of the nanoparticles. What follows is an exploration of potential variations in composition across individual nanoparticles, lanthanide based or otherwise, which can inform eventual efforts to maximize precision.

Figure 3.

Coefficients of variation (CV), standard deviation normalized by mean, for sampling distributions of single particle intensity for 29 different particles across 4 papers,^{68,139,141,142} each with a different excitation power, that performed colocalization verification, showing the potential to increase measurement precision (see SI Table S3 for specific details on each batch). Attributions made to measurement noise were calculated based exclusively on the noise equivalent sensitivity for a 1 Hz brightness measurement. The remainder is attributable to interparticle heterogeneity, as considerable care was taken to control for competing conditions during the measurements. In cases where raw data were not available, means and standard deviations were estimated from figures using GraphClick software. The histograms to the right of the bar graph shows examples of raw data from two of the batches, ref 68. Batches 1 and 6.

First, size variability between particles causes variation in brightness and hence limits the precision of sensing. Routine transmission electron microscopy (TEM) and scanning electron microscopy (SEM) measurements have made it clear that size dispersions exist on the individual single particle level.⁶⁸ There is a well-documented relationship between nanoparticle size dispersions and the stochastic kinetics of nucleation and growth in colloid synthesis.¹⁵⁰ These disparities in size can couple into optical properties by affecting the density of defect states and the proximity of dopant ions to the quenching centers located on the surface.¹⁵¹ Surface quencher proximity can even be variable within an individual core–shell particle when the shell growth is anisotropic.¹⁵² The size can also influence the absolute number of donors within optically active layers, potentially affecting the absorptivity of a particle.

Second, we hypothesize that there are crystal field differences between individual particles, creating variation in brightness and optical response of the particles. Photophysical dynamics are dictated in part by the crystal field experienced by an electronic center,^15,153,154 which can be tuned globally by the host lattice space group as well as locally by defects in the crystal. The host lattice symmetry has a significant effect on the quantum yield, as demonstrated by the phase dependent quantum yield of cubic (α) versus hexagonal (β) NaYF₄ (O_h vs C_3h).^151,153,154 Defects, broadly defined as structural and surface heterogeneities, can also affect the photophysical dynamics by altering the crystal field of the electronic center locally. Some of the many defects that have been directly identified in nanoparticles (lanthanide-based or otherwise) include point defects,¹⁵⁵ grain boundaries,¹⁵⁶ lattice mismatch at core–shell or shell–shell interfaces,^105,157,158 and surface defects.¹⁵⁹ The unique strain fields experienced at each electronic center weakly affect the splitting of degenerate 4f states and the selection rules that dictate the allowable transitions between them. Indeed, ab initio calculations based on experimental tomographic data from single bimetallic nanoparticles suggest that unique strain environments translate to unique magnetic properties on the single particle level.¹⁵⁶ Apart from altering electrostatic potential environments around electronic centers, defects in the host lattice and on the surface can introduce high energy phonon modes that encourage nonradiative quenching.¹⁶⁰

Third, distance dependent efficiency of resonant energy transfer (RET), which is related to both the concentration and distribution of dopant ions within an individual nanoparticle, presents a limitation on sensor precision. Indeed, the many diverse efforts aimed at optimizing dopant concentrations, and partitioning them within complex architectures, ultimately aim to achieve the same thing: an average nearest neighbor distance that maximizes productive RET (such as energy transfer upconversion) while minimizing deleterious RET (such as cross relaxation and phonon assisted quenching) for a fixed excitation power density. For Er³⁺ dopants in the canonical β-NaYF₄ host lattice, the optimum between these extremes occurs between 20 and 30% in the low power regime (irradiance < 1W/cm²), corresponding to an average nearest neighbor Er³⁺–Er³⁺ distance of 6.3–7.2 Å.¹⁶¹ However, these models rely on the assumption that dopants are randomly distributed spatially within the optically active layer. Any clustering or dispersion of ions away from this ideal randomness could yield local pockets of unique composition. The separation-dependent RET dynamics are perturbed in these pockets, resulting in nonuniform spectral and intensity output across individual lanthanide doped particles.^162–164 For example, the intentional clustering of donor Yb³⁺ ions in a novel Er³⁺ doped orthorhombic KYb₂F₇ architecture yielded a unique preference for a 5-photon violet emission via highly localized energy transfer.¹⁶⁵

Estimates of nearest neighbor distances also rely on the assumption that dopants are confined to their optically active layers in multilayer architectures. However, X-ray based measurements at the ensemble level and electron microscopy (EM) based measurements at the single particle level provide compelling evidence for cation exchange throughout the particle volume, leading to concentration gradients around interfaces.^166,167 This further exacerbates uncertainties in single particle doping concentrations and nearest neighbor RET pair separations.

The final impediment to precise measurement originates from the large input space of the sensor. As was discussed in the section Sensing with Ensembles of Lanthanide Nanoparticles, the same sensitivity that gives LNP platforms the utility to sense any one of a large variety of environmental conditions hinders their ability to measure any with absolute selectivity.

METHODS AND METRICS FOR CHARACTERIZING SINGLE PARTICLE VARIANCES

In order to create highly precise and accurate LNP sensors, it is critical to report the structure and properties of individual particles and feed this information back into synthetic efforts. In this section, we propose metrics that could illuminate structure–property relationships at the single particle level, including their benefits, their drawbacks, and the measurement techniques necessary to acquire them. Some of these metrics, such as single particle brightness and size, routinely appear in LNP literature, while others are only beginning to be reported. We also propose a metric, Ripley’s K Function, for quantifying RET pair separation, that, to our knowledge, the community has not reported on at either the ensemble or single particle level. We aim for these characterization methods to be used in conjunction with synthetic strategies, such as those provided here for reference,^52,168–171 to minimize heterogeneities from particle to particle.

Single LNPs can sense using the same measurement techniques discussed in Sensing with Ensembles of Lanthanide Nanoparticles so their optical characterization is analogous (i.e., intensity, ratiometric, λ-shift and lifetime). Highly sensitive detectors including avalanche photodiodes (APD) and photomultiplier tubes (PMT) can be coupled with a pulsed or chopped excitation laser to achieve temporal resolution for lifetime measurements. Ratiometric or λ-shift measurements require a way of separating spectral components, such as with a spectrometer, or, in the case of ratiometric measurements, by placing dichroic filters upstream of multiple detectors. In all cases, characterizing single LNP optical properties requires being able to confirm that only one particle is being imaged in a diffraction limited spot. Often this requires correlating optical images with TEM,¹⁷² SEM,^68,141 or AFM⁴⁴ measurements.

In order to connect particle structure to performance, we propose using correlated optical and electron microscopy techniques. High-throughput size and morphological analysis of LNPs using nonaberration corrected TEM have been routine for nearly two decades.¹⁷³ Thanks to the emergence of data processing tools, the calculation of size and morphological indices is trivially scalable to thousands of single particles. TEMs can also be used to calculate local lattice spacings, which could provide qualitative insights into the impact of interfacial defects and strains on nonradiative quenching.¹⁵⁸ However, limited Z-contrast makes it difficult to distinguish layers with similar elemental composition. This kind of elemental discrimination is possible with the more specialized EM techniques discussed below, but they come with an important caveat. Namely, the ionic lattices that comprise the vast majority of LNPs are relatively sensitive to electron beam induced damage. In some cases, this damage can result in ion diffusion and structural remodeling of the nanoparticle, thus effectively limiting spatial resolution.^174,175 Luckily, direct electron detectors exist having high detective quantum efficiency for imaging at low absolute doses or dose rates, where damage is minimized.¹⁷⁶ Cryomicroscopy techniques, often used to prevent the beam induced damage of organic biological samples while imaging, can effectively stabilize sensitive inorganic materials like batteries as well.¹⁷⁷ Finally, studying the mechanisms of radiation damage (e.g., radiolysis, knock-on displacement, charging) for a particular LNP architecture can help inform the appropriate hardware and sample preparation requirements.¹⁷⁸

Quantifying elemental distributions and defect densities can enhance our understanding of structure–property relationships. With appropriate aberration-correction, this high resolution information is accessible using imaging methods such as high angle annular dark field scanning transmission electron microscopy (HAADF-STEM), energy dispersive X-ray spectroscopy in STEM mode (STEM EDX), and electron energy loss spectroscopy in STEM mode (STEM EELS). The former technique relies on the contrast of elastically scattered electrons, while the latter two measure the energy of emitted X-rays (EDX) and inelastically scattered electrons (EELS) to distinguish between elements. As previously mentioned, most of the techniques for rapidly quantifying single particle structures at high resolution were developed and refined on metallic nanoparticles.^179,180 Nevertheless, these techniques have begun to gain a foothold in the LNP community within the last several years. HAADF was deployed for atomic scale defect characterization in uniformly thin, lanthanide-doped KLu₂F₇.¹⁵⁹ Owing to their careful consideration of particle geometry, dwell time, and spot size, Bian et al. succeeded in demonstrating that it is possible to correlate defects of a single LNP with their ensemble optical properties, even in a beam sensitive sample.¹⁵⁹ Furthermore, radial distributions of dopant ions can be imaged with STEM EDX and STEM EELS, providing quantitative insight on the nature and extent of anisotropic shell growth¹⁵² and cation diffusion across interfaces^152,166,167 in single LNPs. We believe that by the end of the decade, these three methods could become routine for generating statistics on heterogeneities across single LNPs.

Localizing every atom and defect feature in a molecule requires 3D imaging techniques such as electron tomography.¹⁸¹ Electron tomography has facilitated detailed atomic level structural analysis for a host of other non-LNP single particles, both dry^155,156,182 and solvated,^183,184 and has even been demonstrated on lanthanide-based nanotubes¹⁸⁵ with the help of direct electron detectors and rapid imaging. Migunov et al. collected a tilt series over the course of only 3.5 s containing over 3000 images of a (LaCeS)_1.2CrS₂ nanotube with sub-nanometer resolution and a dosage 10 times lower than what is normally achieved with cryo-electron tomography.¹⁸⁵ Electron tomography deserves attention due to its ability to map individual defects and atoms in 3D space.^{155,156,182,184} This data can then be used to directly quantify strain components^155,184 and the interatomic distances relevant for RET. If correlated with single particle optical measurements or cathodoluminescence, these techniques could potentially provide the LNP community with unprecedented insight into the effects of cross relaxation, energy transfer upconversion, and phonon assisted resonant energy transfer. A simple metric toward this end could be the average nearest neighbor distance, which has already proven itself useful in the analysis of tomographic data from plasmonic nanoparticles.¹⁸⁶ A more complicated but powerful metric we recommend is the Ripley’s K function¹⁸⁷ which quantitatively captures the degree of clustering or dispersion of dopant ions within optically active layers (see Supporting Information for more information). It has proven useful in statistically characterizing nanoparticle distributions on substrates imaged via SEM.^188,189 We believe this metric could similarly be applied to atomic resolution TEM data to help reflect the extent of coupling at various length scales: scales at which exchange, multipolar Coulombic, and Förster mechanisms are respectively operative. This analysis could potentially help disentangle the complicated mechanistic origins of RET.

Importantly, each of these EM techniques can be combined with advances in situ cathodoluminescence (CL) and photo-luminescence (PL) spectroscopy to correlate atomic structure with optical emission. These methods have been applied at the ensemble level, and single-particle spectroscopic studies are emerging;^190–192 with probe-corrected EM, atomic-scale optical studies are possible. Indeed, correlated optical and electron microscopy has helped reveal the relationship between the local strain environment and emission properties of individual defects in other color-center materials, like hexagonal boron nitride.¹⁹⁰ And beyond EM techniques, single particle inductively coupled plasma mass spectrometry is a potentially viable method to extract global particle composition.¹⁹³ Though it has the potential to be incredibly high-throughput,¹⁹⁴ more studies are necessary to confirm its reliability. From the standpoint of making single particle sensors as reliable and consistent as possible for translation to widespread use, these methods can help us understand sources of variance in their optical and structural properties using quantitative, practically generated, and reliable statistics. Moreover, the data generated in the process would help elucidate structure–property relationships with much finer detail, enabling a feedback loop for synthesis (Figure 4).

Figure 4.

Path toward improving the sensitivity, precision, and specificity of lanthanide nanoparticles for use as nanoscale sensors over the course of the decade. A combination of optical characterization (including analyses of sensitivity and responsiveness to competing external conditions) and structural characterization (including quantifying interparticle heterogeneities in size, dopant and defect concentration and distribution with various electron microscopy techniques) can be used to inform synthetic strategies. This is an iterative process that feeds back into itself, eventually leading to control over single particle structure and optical response for sensing.

ENGINEERING SINGLE PARTICLE NANOSCALE SENSORS

To realize single LNP sensing with the highest possible signal, response, selectivity, and compatibility, we recommend characterizing: (1) optical properties at the single particle level, (2) single particle structure, and (3) the effects of competing external conditions. Ultimately, the resolution of single LNP based measurements will be limited by a combination of measurement noise, interparticle heterogeneities, and competing external conditions, so synthetic strategies and experimental setups should be tailored to minimize their impact. This process is iterative and begins with a thorough characterization of structural and optical properties.

Optical properties and their response to stimuli need to be characterized at the single particle level. It is critical that researchers confirm with a high resolution technique such as AFM or EM that the measurements are done on single particles. When reporting the sample brightness, we recommend measuring at least 300 particles and being careful about the randomness of the selection.¹⁹⁵ We additionally recommend reporting the optical spectra or lifetime of single particles. Ideally, reporting brightness, spectra, and lifetime is beneficial to understanding interparticle optical variances within a synthetic batch.

Next, to improve the materials and their syntheses, we recommend careful structural studies to understand how differences in particle syntheses correspond to differences in response.^{34,80,140,153,163,170,171} Size and distributions should be reported for nanoparticles and, if core–shell or multilayer structures are synthesized, the size and distribution of each layer should be reported. Where possible, EELS or EDX should be reported to provide insight into intraparticle chemical composition, and HAADF should be reported to provide insight into the prevalence and distribution of particular defects. With appropriate imaging and sample preparation techniques, electron tomography of lanthanide particles could provide insight into dopant distributions and strain states, which are critical parameters for understanding how RET couples to external conditions.

Finally, when measuring the optical response of the particles to the stimulus of interest, it is necessary to report how competing external parameters such as laser power, temperature, chemical changes, and mechanical signals affect the response of the sensor. Note that if a particle needs to be functionalized to selectively respond to an external stimulus then all optical characterizations will ideally be done on functionalized particles.

There are many outstanding questions that would benefit from a robust nanoscale optical sensor. We project that lanthanide nanoparticle sensors can achieve signal resolution on par with ensemble sensors while drastically improving on the spatial resolution. In order to calculate the resolution of sensors, one needs to incorporate the error on the response from NES, differences in starting photon count rate, and other parameters such as lifetime or starting ratio of the wavelengths in question (details found in the Supporting Information). Consider pressure sensors with a lifetime readout in biological systems as an example; if we assume the excitation wavelength is 808 nm (such that cells will remain viable at 6 W/cm² intensity for extended excitation¹⁹⁶) and we engineer particles with a brightness average photon count rate (I₀) of 20 ± 0.2 kcps, a response (R) of 2 ± 0.02 τ₀/GPa, and a duty cycle of 1, then a measurement could detect a 50 MPa change in a one second integration with a starting pressure of 50 MPa. This response is competitive with ensemble measurements, which often use close to a billion nanoparticles in a diamond anvil cell measurement,¹²² but it improves the spatial resolution to that of a single nanoparticle. As another example, we calculate the detection limit of chemical sensing via a ratiometric response. Again assuming 6 W/cm² excitation power and a total brightness (I₀) of 20 ± 2 kcps, as well as the initial ratio of the two wavelengths being probed (α₀) of 1 ± 0.02, and a response (R) of 1.6 ± 0.16 ratio/μM, the limit of detection is 41 nM. The detection limit is three times the standard deviation of the measurement. For comparison, gold nanoparticles employed in cells for protein detection have shown nanomolar detection limits in a confocal microscope.¹⁹⁷ With advantages such as photostability, long-lived excited states, and near-infrared excitation at low powers and multiple readout mechanisms, i.e., lifetime, ratiometric, λ-shift, and intensity, LNPs are extremely promising in vitro and in vivo sensors. While these parameters are ambitious, given the trends in brightness achieved in single LNPs over the past decade, we are confident that they are achievable.

These sensing capabilities are useful for a range of diverse applications, from diagnostics and cellular physiology^62,143,198 to electronics and industrial catalysis.^76,199 Single LNP sensors could be used to detect analytes in solution, such as proteins for pathogen recognition, with high sensitivity,^62,198,200 or be deployed in biological systems to detect nanonewton scale mechanotransduction between cells.⁵ Small ensembles of LNPs have already helped elucidate temperature-dependent catalytic behavior at the microscale in micro-electromechanical reactors⁷⁶ and ruthenium decorated microstructures.¹⁹⁹ Transitioning to the single particle regime would only further improve our understanding of catalysis and energy efficient chemical synthesis. LNPs may also have potential applications in small scale devices to detect changes in chemical composition or pressure, both of which are signals of device failure.^201,202

CONCLUSION AND OUTLOOK

Because of the advantageous and unique optical properties of LNPs, it is not surprising that there are many studies identifying and quantifying their sensing properties at the ensemble level. While these ensemble measurements have generated valuable insights into fields from biology to physics, many questions remain that require much more granular sensing capabilities. Single LNP sensors promise us access to this new, high spatial resolution regime, but only with thoughtful attention to issues of precision.

With the advent of many recent nanoparticle synthetic strategies and designs, as well as the desire to fully realize high spatial resolution, we propose efforts toward precision and reproducibility for single LNP sensing applications. These efforts will be aided by a diligent consideration of the various noise sources described in Sources of Imprecision in Single Particle Sensing. Specifically, we believe that a careful consideration of the NES of a particular nanoparticle sensor and extensive structural and optical characterization of individual nanoparticles within a batch will help to elucidate these potential sources of imprecision. This extensive characterization is the first in a series of steps that ultimately culminates in a robust single particle optical sensor, offering a new lens into nanoscale dynamics.