Resonance Energy Transfer to Track the Motion of Lanthanide Ions—What Drives the Intermixing in Core-Shell Upconverting Nanoparticles?

The imagination of clearly separated core-shell structures is already outdated by the fact, that the nanoparticle core-shell structures remain in terms of efficiency behind their respective bulk material due to intermixing between core and shell dopant ions. In order to optimize the photoluminescence of core-shell UCNP the intermixing should be as small as possible and therefore, key parameters of this process need to be identified. In the present work the Ln(III) ion migration in the host lattices NaYF4 and NaGdF4 was monitored. These investigations have been performed by laser spectroscopy with help of lanthanide resonance energy transfer (LRET) between Eu(III) as donor and Pr(III) or Nd(III) as acceptor. The LRET is evaluated based on the Förster theory. The findings corroborate the literature and point out the migration of ions in the host lattices. Based on the introduced LRET model, the acceptor concentration in the surrounding of one donor depends clearly on the design of the applied core-shell-shell nanoparticles. In general, thinner intermediate insulating shells lead to higher acceptor concentration, stronger quenching of the Eu(III) donor and subsequently stronger sensitization of the Pr(III) or the Nd(III) acceptors. The choice of the host lattice as well as of the synthesis temperature are parameters to be considered for the intermixing process.


Introduction
Upconversion nanoparticles (UCNP) are potential optical probes for many applications in the environmental and life science context. In order to bring UCNPs into a broad practical application, further improvements in the synthesis design, host lattices, stability in water, and surface functionalization are needed to meet the specific challenges of real-world applications. UCNPs are competing with established optical probes such as organic dyes or quantum dots. Here, a major issue is the low brightness of UCNPs which limits their use in practical applications [1][2][3][4][5][6], e.g., for imaging, diagnostics and therapy (theranostics) [5][6][7][8][9]. UCNPs with at least one (protective) shell around the nanoparticle core, which contains the sensitizer and activator ion, is a very frequently used strategy to improve the UCNP emission efficiency. Here, the basic idea is that the outer shell protects the doped UCNP core from unwanted quenching by the environment (e.g., quenching by OH-vibrations of water molecules). However, it has been shown that the shielding effect by this outer layer is smaller than expected. One of the limitations found is the intermixing of dopant ions from the different layers. This intermixing process has been demonstrated, e.g., by TEM investigations. Examples are given by Hudry et al. revealing an intermixing layer formed during the synthesis of core-shell The percentages are mol% referring to the trivalent ions in the nanocrystal. The first shell is referred to as insulation shell/layer and its thickness has been varied in order to have different distances between the core and the outer shell. The composition, nanoparticle size, and insulation shell thickness for each set is summarized in Table 1. Each set has its respective reference sample without the acceptor ions in the core (pure host lattice) and without an insulation shell, indicated as Ref CS. The Ref CS samples have only Eu(III) ions doped in the outer shell. The L0 CS samples have been synthesized the same way as the Ref CS sample except for the acceptor doping being 20 mol% in the core (and only 80 mol% of Y(III) or Gd(III)). L1 CSS, L2 CSS and L3 CSS are as L0 CS but with an additional intermediate shell (see Figure 1, inner purple shell), that has been grown prior to the donor doped outer shell. The additional intermediate shell increases in thickness, which is indicated by increasing numbers in the sample declaration. The insulation shell separates the donor and the acceptor spatially from each other. The sample L1 CSS is based on the sample L1 CS, which is derived from the core of L0 C. An overview of two main sets is given in Table 1. In Table 1, only the diameters of the nanoparticles with the first shell (so, with the insulation shell, except for L0 CS) is given, as this is the important information with respect to the distance between donor and acceptor for the application of the LRET model described below (Equations (1)-(3)). The notation for the samples L1 CS, L2 CS and L3 CS corresponds to the nanoparticles prior to the growth of the outer shell, which is doped with Eu(III). The described nanoparticle design is illustrated in Figure 1, in which the respective energy levels of the applied Ln(III) ions are shown as well [32][33][34][35][36][37]. In addition to the main sets, two subsets were synthesized in order to clarify certain effects (vide infra and Appendix A, Table A1). Briefly, the Y300_UCNP and the Gd200 subsets were synthesized according to the same protocol used in the other respective sets. The Y300-UCNP set is the same set as Y300 except for the core doping, which has been changed to the upconversion pair of Yb(III) with 18 mol% and Pr(III) with 2 mol%. With this set, the upconversion luminescence of Yb-(upconversion sensitizer) and Pr-ions (upconversion activator and LRET-acceptor) and the LRET of Eu-to-Pr was investigated. The Gd200 set differs from the Gd300 set only by the synthesis temperature used which was reduced by 100 • C. Table 1. Overview of the sets and their sample composition with the corresponding particle sizes and their insulation shell thickness. Each set has its respective reference samples in which the LRET-acceptor is absent. The diameters are derived from the TEM images. Only the important nanoparticles for the determination of the insulation shell thickness have been examined. TEM images are shown in Figure 2 and in the Appendix A, Figure A1. Acceptor and donor doping are 20 mol% and 5 mol%, respectively, in percentage to the total amount of trivalent cations in the nanocrystal.

Insulation Shell Thickness/nm
Gd300 Ref CS NaGdF 4 @ NaGdF 4 :Eu -/--/-Gd300 L0 CS 2 NaGdF 4 :Nd @ NaGdF 4 :Eu 8.9 ± 1.5 0 Gd300 L1 CSS 2 NaGdF 4 :Nd @ NaGdF 4 @ NaGdF 4 :Eu 7.1 ± 0.4 0.7 ± 0.5 Gd300 L2 CSS 3 vide supra 10.8 ± 1.5 1.0 ± 1.0 Gd300 L3 CSS 3 vide supra 14.4 ± 1.  ( 1 I6) state and Nd(III) in the 4 G11/2 ( 2 D3/2 or 4 G9/2) [38]. Downward arrows indicate the respective Ln(III) luminescent transitions. Vide infra for corresponding emission spectra. Gd(III) on the right indicates its large energy gap and its indifference on the LRET for Eu(III) quenching. Table 1. Overview of the sets and their sample composition with the corresponding particle sizes and their insulation shell thickness. Each set has its respective reference samples in which the LRET-acceptor is absent. The diameters are derived from the TEM images. Only the important nanoparticles for the determination of the insulation shell thickness have been examined. TEM images are shown in Figure 2 and in the Appendix A, Figure A1. Acceptor and donor doping are 20 mol% and 5 mol%, respectively, in percentage to the total amount of trivalent cations in the nanocrystal.  Figure 2. Set Y300: TEM images of (a) L0 CS, (b) L3 CS and (c) XRD data of NaYF4:Pr20% @ NaYF4 @ NaYF4:Eu5%. TEM images show the desired nanoparticle size increase upon shell growth. The common core L0 C is not shown for this set. An overview of all recorded TEM images is given in the Appendix A, Figure A1. The XRD data reveals the nanoparticles' hexagonal phase. The top XRD trace shows the reference diffraction patterns of cubic NaYF4 (red, ICDD PDF #77-2042), hexagonal-NaYF4 (green, ICDD PDF #16-334), and hexagonal Gagarinite-(Y) (blue, ICSD #39696). The sharp diffraction peaks at 39° and 56° of L0 C are attributed to cubic NaF (ICSD #43611, reference not shown). Scale bar = 10 nm.

Nanoparticle Synthesis
All syntheses were performed as previously described [19,39], whereas the amounts of the RE trivalent cations (here: Pr(III) and Y(III) or Nd(III) and Gd(III)) had been adjusted.
Depending on the sample (compare composition in Table 1) the RE chlorides (YCl3·6 H2O; GdCl3·6 H2O, respectively 1 mmol) were used for the reference cores or in combination with the optical active RE chlorides for the core samples (0.8 mmol of Y(III) or Gd(III) Figure 2. Set Y300: TEM images of (a) L0 CS, (b) L3 CS and (c) XRD data of NaYF 4 :Pr 20% @ NaYF 4 @ NaYF 4 :Eu 5% . TEM images show the desired nanoparticle size increase upon shell growth. The common core L0 C is not shown for this set. An overview of all recorded TEM images is given in the Appendix A, Figure A1. The XRD data reveals the nanoparticles' hexagonal phase. The top XRD trace shows the reference diffraction patterns of cubic NaYF 4 (red, ICDD PDF #77-2042), hexagonal-NaYF 4 (green, ICDD PDF #16-334), and hexagonal Gagarinite-(Y) (blue, ICSD #39696). The sharp diffraction peaks at 39 • and 56 • of L0 C are attributed to cubic NaF (ICSD #43611, reference not shown). Scale bar = 10 nm.

Nanoparticle Synthesis
All syntheses were performed as previously described [19,39], whereas the amounts of the RE trivalent cations (here: Pr(III) and Y(III) or Nd(III) and Gd(III)) had been adjusted. Depending on the sample (compare composition in Table 1) the RE chlorides (YCl 3 ·6H 2 O; GdCl 3 ·6H 2 O, respectively 1 mmol) were used for the reference cores or in combination with the optical active RE chlorides for the core samples (0.8 mmol of Y(III) or Gd(III) and 0.2 mmol of Nd(III) or Pr(III) or as UC pair: 0.02 mmol Pr(III) and 0.18 mmol of Yb(III)). The RE chlorides, OA (25.2 mmol, 8 mL, 7.12 g) and the solvent Therminol ® 66 (12 mL) were transferred into a 50-mL-three-necked-flask. The reaction mixture was evacuated for 10 min at room temperature with subsequent heating to 140 • C under vacuum (<10 mbar) and vigorous stirring. 140 • C were maintained for at least 45 min, so that a clear solution was obtained. The reaction flask was vented with argon to add NaOA (2.5 mmol) and NH 4 F (4 mmol). After re-evacuation the temperature was set to 80 • C and kept for 30 min until all salts had dissolved. The reaction flask was re-vented with argon and heated up to 320 • C (heat rate: 25 • C/min) and kept for 15 min. Finally, the temperature was decreased to 250 • C by air and then to approx. 60 • C by a water bath. The nanoparticles were precipitated by ethanol and centrifuged at 3100 g for 8 min. Further purification was performed by washing with ethanol and re-centrifugation for three times. The final precipitate was dispersed in cyclohexane (15 mL).
With respect to the nanoparticle synthesis and the changing dopants, the host lattice change from NaYF 4 to NaGdF 4 is expected to work as before, since NaGdF 4 crystallizes in P6 space group [40] as well as NaYF 4 and NaNdF 4 [21,[41][42][43][44][45]. A more detailed discussion can be found in Ref. [19]. It should be kept in mind, that even if the synthesis conditions are constant, it cannot be guaranteed that all the lattices crystallize in the same space group which can lead to lattice variations [46]. The trivalent ion migration within the crystal host lattice becomes possible based on those variations and on lattice vacancies, elevated temperatures, dopant concentration, as well as the synthesis approach and the design of the core-shell(-shell) systems.

Shell-Precursor Synthesis of NaREF 4 and NaREF4:Eu
The NaREF 4 insulation shell (first shell) was prepared either with YCl 3 ·6H 2 O or with GdCl 3 ·6H 2 O (2 mmol, respectively). The outer NaREF 4 :Eu shell doped with 5 mol% Eu(III) was prepared with the same RE chlorides as before (but: 1.9 mmol of the Y/Gd chlorides; 0.1 mmol EuCl 3 ·6H 2 O). The respective RE chlorides were transferred together with OA (4 mL, 3.56 g) and Therminol ® 66 (8 mL) into a 50-mL-three-necked-flask. The flask was evacuated for 10 min, subsequently heated up to 140 • C and kept at this temperature for 45 min until a clear solution had formed. The reaction mixture was cooled down to 50 • C to add under an argon counter stream NaOA (2.5 mmol) and NH 4 F (4 mmol). After re-evacuation, the system was kept for at least 30 min at 80 • C until the salts had dissolved. The flask was vented with argon and the precursor was stored with an argon atmosphere.

Core-Shell and Core-Shell-Shell Synthesis
The respective nanoparticle cores (60 mg) were transferred into a 50-mL-three-neckedflask and OA (8 mL, 7.12 g) and Therminol ® 66 (8 mL) were added. This mixture was evacuated for 30 min at 75 • C and then vented with argon. The temperature was increased to 305 • C as fast as possible and the precursor solution was added at a rate of 2 mL/h. The volume addition of the insulation shell precursor relates to the increasing shell thickness and sample number: L1 = 0.5 mL; L2 = 1 mL; L3 = 4 mL (for set Y300) and L1 = 0.4 mL; L2 = 2 mL; L3 = 4 mL (for set Gd300)-the volume of the Eu(III) doped shell precursors was 1 mL-these declarations apply for all sets. After the precursor addition was completed, the precursor addition temperature (305 • C) was maintained for 5 min. The reaction mixture was cooled down and purified as described for the core nanoparticles. The final precipitate was dispersed in cyclohexane (8 mL).

Luminescence Emission Spectroscopy
The PL spectra and decay curves were recorded using a wavelength tunable pulsed Nd:YAG/OPO laser system (10 Hz, 26 mJ per pulse/130 mW). A Quanta Ray laser from Spectra Physics (Mountain View, CA, USA) was used for the excitation of the OPO (optical parametric oscillator) from GWU-Lasertechnik Vertriebsges. mbH (Erftstadt, Germany). The experimental setup was in a 90 • angle of excitation and emission light. The emitted photons were recorded with a Shamrock SR303i spectrograph from Andor Technology (Belfast, Great Britain). The spectrograph has a grating with 600 L/mm blazed at 500 nm and an iStar DH720-18V-73 intensified CCD-camera from Andor Technology. Luminescence decay curves were recorded using a stroboscopic technique [47]. The initial delays were set to 500 ns for static luminescence emission spectra and to 200 ns for recording luminescence decay curves. The delay was gradually increased by a linear time base function, so that smaller time steps in the beginning and larger time steps in the end of the decays were realized. The data analysis was made with MATLAB 2020b (The MathWorks, Inc., Natick, MA, USA) and with OriginPro 2020b (OriginLab Corporation, Northampton, MA, USA).

Size (TEM) and Structural (XRD) Characterization
Transmission electron microscopy (TEM) images were recorded with a Tecnai G2 F20 X-Twin TEM from FEI/Thermo Fisher Scientific being operated at 200 kV acceleration voltage. The images were evaluated and the nanoparticles sizes determined with help of the software ImageSP Viewer/Image Sys Prog (version 1.2.5.16 × 64).
The powder X-ray diffraction (XRD) patterns of the nanoparticles were investigated with a PANalytical Empyrean powder X-ray diffractometer in Bragg-Brentano geometry equipped with a PIXcel1D detector. The Cu Kα radiation (λ(Kα) = 1.5419 Å) was used with a voltage and current of 40 kV and 40 mA. The detector sensitivity level (PHD level) was adjusted to 45-80 to reduce fluorescence. The active length was set to 3.0061 • . The theta-theta scans were performed over a 2θ range of 4-70 • with a step size of 0.0131 • and over 190 min.

Theory
The obtained PL time-resolved emission spectra are analyzed with a stretched exponential model, Equation (1) [48], and an equation derived from the Förster theory, that expresses the number of acceptors around one theoretical donor, Equations (2) and (3) [47]. This model is denoted as LRET model. The stretched exponential model has been chosen to account for the slight differences in the microenvironment of Eu(III). The stretched exponential model is a robust and simple approach to describe the spatial distribution of the Eu(III) in the host lattice with a small number of fitting parameters.
The Index D stands for the donor in absence of the acceptor. I D (t) is the donor PL emission intensity to the given time t. Hence, I D (0) is the initial PL emission intensity and the amplitude for the model. τ D is the donor luminescence decay time and β D is a heterogeneity parameter describing the donor's microenvironment and its tiny variations, in absence of acceptors, respectively. If β D > 1, the model will be a stretched exponential function which can be interpreted as a continuous distribution of PL decay times [48]. If β D = 1, the model will be a mono-exponential function indicating a homogeneous microenvironment for the emitting donors in the host lattice. y 0 accounts for the background signal.
The index DA indicates the donor in presence of the acceptor, D as above the donor only. I DA (t) is the donor PL emission intensity to the given time t. Hence, I DA (0) is the initial luminescence emission intensity and amplitude of the mode. y 0 accounts for the background signal. τ D and β D are adopted from the donor PL decay model of the respective reference sample with the absence of the acceptors. The additional heterogeneity α parameter has been introduced to account for the acceptor distribution and its related microenvironments. The parameter γ scales with the number of acceptors in a threedimensional sphere, having a donor as center. The sphere has the radius of the Förster radius R 0 of the respective donor-acceptor pair. Here, the acceptor concentration c A is given in ions per Å 3 . The term c A 4 3 πR 3 0 expresses the average acceptor number (number of ions) in this 3D sphere with radius equal to R 0 around the donor.
The LRET efficiency E LRET is calculated with Equation (4) based on the donor PL decay time in presence (τ DA ) and in absence of the acceptor (τ D ). The parameter τ D had been calculated before with Equation (1). The parameter τ DA had been calculated with Equation (1) as well, but here τ D (and β D ) was replaced by τ DA (and β DA ), which parameters are also listed in Tables 2 and 3 and in the Appendix A, Tables A2-A4. Equation (1) would then look like:    (2): average acceptor concentration within a 3D sphere (radius of (Eu/Pr) = 8.2 Å) and parameters α, in dependence on the insulation shell thickness, respectively. With increasing insulation shell thickness, the average acceptor numbers decrease. Parameters α are not affected by the thickness of the insulation shell. Detailed regression parameters are shown the Appendix A, Table  A2. (d) Enhancement factors (τ(CSS)/τ(CS)) of the Pr(III) PL decay times at 524 nm and at 540 nm (potentially resulting from direct excitation as well as sensitization by Eu(III) re-populating the 3 P1 and 3 P0 state, as in (a)). Inset of (d): PL emission with its respective transitions of Pr(III) in black and Eu(III) in red around 530 nm with λex = 465 nm. Detailed regression parameters of the Pr(III) PL decay curves are in the Appendix A, Table A3.

Structural Characterization
Two representative examples of TEM images of set Y300 (being the NaYF4:Pr20% @ NaYF4 @ NaYF4:Eu5% nanoparticles synthesized at 320/305 °C) are shown in Figure 2 (other TEM images are shown in the Appendix A, Figure A1). As expected, L3 CS has a larger . Set Y300 (NaYF 4 :Pr 20% @ NaYF 4 @ NaYF 4 :Eu 5% ): Spectroscopic investigation of the Eu(III) and the Pr(III) emission of CSS nanoparticles. (a) Eu(III) and Pr(III) PL emission spectra around 600 nm (red labels = Eu(III) transitions, black labels = Pr(III) transitions, λ ex = 465 nm). The Pr(III) transitions labeled in brackets may result from direct excitation as well as sensitization of the 3 P i ← 3 H 6 transition by the 5 D 0 state of Eu(III). Ref CS has no Pr(III) (no acceptor in the core, Eu(III) (donor) in the shell). L3 CS contains Pr(III) (acceptor) in the core and is equipped with the insulation shell, so no Eu(III) (donor) in the shell. L3 CSS contains both ions, Pr(III) (acceptor) in core, no doping in the insulation shell, and Eu(III) (donor) in the outer shell. The PARAFAC separated emission spectra (top part) were calculated from L3 CSS raw PL emission data. (b) Eu(III) luminescence decay kinetics recorded at λ em = 616 nm (corresponds to the 5 D 0 → 7 F 2 transition of Eu(III), λ ex = 465 nm). With decreasing insulation shell thickness, the Eu(III) PL decay times decrease. In addition, from a visual inspection, it can be seen that the kinetics are no longer following a monoexponential decay as shown by Ref CS. Inset of (b) are the Pr(III) PL decay curves for λ em = 608 nm ( 1 D 2 → 3 H 4 ) being separated by PARAFAC from the Eu(III) PL emission at 616 nm (λ ex = 465 nm). (c) Results of the evaluation of Eu(III) kinetics based on Equation (2): average acceptor concentration within a 3D sphere (radius of R 0 (Eu/Pr) = 8.2 Å) and parameters α, in dependence on the insulation shell thickness, respectively. With increasing insulation shell thickness, the average acceptor numbers decrease. Parameters α are not affected by the thickness of the insulation shell. Detailed regression parameters are shown the Appendix A, Table A2. (d) Enhancement factors (τ (CSS) /τ (CS) ) of the Pr(III) PL decay times at 524 nm and at 540 nm (potentially resulting from direct excitation as well as sensitization by Eu(III) re-populating the 3 P 1 and 3 P 0 state, as in (a)). Inset of (d): PL emission with its respective transitions of Pr(III) in black and Eu(III) in red around 530 nm with λ ex = 465 nm. Detailed regression parameters of the Pr(III) PL decay curves are in the Appendix A, Table A3. Table 3. Set Gd300: Comparison of the insulation shell thickness, the acceptor numbers (#acceptors), Eu(III) decay times τ and LRET efficiencies E LRET , evaluation with Equations (1)-(4) of the Eu(III) luminescence at 616 nm ( 5 D 0 → 7 F 2 ) for the core-shell-shell nanoparticles (NaGdF 4 :Nd 20% @ NaGdF 4 @ NaGdF 4 :Eu 5% nanoparticles), λ ex = 465 nm 1 .

Set Gd300
Ref Because of the Pr(III) PL decay time being shorter than the Eu(III) PL decay time [19,[49][50][51][52], the PL decay curves of Pr(III) and Eu(III) were obtained by deconvolution of the respective experimental decay kinetics using parallel factor analysis (PARAFAC algorithm of MATLAB [53]), where necessary. Constrains were set to avoid negative values in the time base, wavelength and intensity. The deconvoluted decays were fitted using Equations (1) and (2) (with OriginPro) for the donor PL decay times and the acceptor PL decay times listed in the results section.
The presented acceptor PL decay times (in absence of the donor, indicated as "A" for CS samples, and in presence of the donor, indicated as "AD" for CSS samples) were also calculated with a stretched exponential decay model which transforms Equation (1) into:

Structural Characterization
Two representative examples of TEM images of set Y300 (being the NaYF 4 :Pr 20% @ NaYF 4 @ NaYF 4 :Eu 5% nanoparticles synthesized at 320/305 • C) are shown in Figure 2 (other TEM images are shown in the Appendix A, Figure A1). As expected, L3 CS has a larger diameter than L0 CS, since L0 CS has been prepared with 1 mL of Eu-doped precursor solution and L3 CS with 4 mL of the insulation shell precursor solution leading to the larger shell thickness. The TEM images of set Gd300 (NaGdF 4 :Nd 20% @ NaGdF 4 @ NaGdF 4 :Eu 5% ) nanoparticles synthesized at 320/305 • C are shown in the Appendix A, Figure A1. In Table 1, the nanoparticle sizes of intermediate step, the CS samples, and their respective insulation shell thicknesses are summarized.
The XRD investigations reveal good agreement between the reference XRD patterns and the patterns of the synthesized NaYF 4 ( Figure 2c) and NaGdF 4 (Appendix A, Figure A2) nanoparticles. Some samples of the NaYF 4 samples (set Y300) show reflexes of the cubic NaYF 4 which vanish gradually after shell addition (see Figure 2c). Furthermore, the XRD patterns of the core nanoparticles (of set Y300) show sharp reflexes at 39 • and at 56 • corresponding to NaF.

Luminescence of Set Y300
Compared to our previously published work in the set Y300 the acceptor Nd(III) was exchanged for Pr(III), which is only slightly larger than the former but has the advantage to show luminescence in the visible spectral range. Since it can also serve as an acceptor in combination with Eu(III) as donor, its luminescence may also be used to gain complementary information with respect to the sensitization due to LRET.
In Figure 3a, examples for the luminescence spectra of the Y300 nanoparticle set are shown (bottom part). After excitation at λ ex = 465 nm, the recorded emission spectra contained contributions of Eu(III) as well as of Pr(III) luminescence. The observed Pr(III) luminescence is a result of sensitized and direct excitation. The direct sensitization occurs via the 1 D 2 ← 3 H 4 of Pr(III). The other Pr(III) luminescence bands (see Figure 1, transition in brackets, and inset of Figure 3d) observed may be a combination of direct excitation (into 3 P 1 ), relaxation (e.g., into 3 H 5 or 3 H 6 ) and a (possible) subsequent sensitization (to 3 P 0 and 3 P 1 ). That a sensitization occurs can be seen from the differences in the decay times found for the nanoparticles without and with Eu(III) (see Table A3 containing the PL decay and enhancement data for the transitions 3 P 1 → 3 H 5 and 3 P 0 → 3 H 5 at 524 nm and 540 nm, respectively). We used PARAFAC to calculate the pure Eu(III) and the pure Pr(III) luminescence spectra (see Figure 3a, top part). Because of the fact that the Eu(III) PL emission also contains a fairly high contribution of luminescence arising from the 5 D 1 → 7 F 3 transition (around λ em = 585 nm) the luminescence kinetics were evaluated for the 5 D 0 → 7 F 2 transition at λ em ≈ 616 nm. Although emission bands of Pr(III) are also spectrally close (Pr(III) also has transitions in that spectral range: 3 P 1 → 3 H 6 at 585 nm as well as 1 D 2 → 3 H 4 and 3 P 0 → 3 H 6 at 608 nm [38,54]), the Pr(III) PL decay kinetics are much faster (vide infra) and therefore, the Eu(III) emission decay kinetics can be evaluated selectively. The luminescence decay kinetics of Eu(III) and Pr(III) are shown in Figure 3b. It can be seen that upon decreasing the thickness of the insulation layer the Eu(III) luminescence decay kinetics became faster. The observed decrease can be attributed to the LRET process between Eu(III) and Pr(III). It is intriguing that a distinct change is also found in the L3 CSS PL decay kinetics (see Figure 3b), although the thickness of the insulation layer was more than 7-times the Förster distance (insulation layer thickness = (6.0 ± 0.5) nm compared to R 0 (Eu/Pr) = 0.82 nm) (also see Table 2). Hence, mixing of Pr(III) and Eu(III) ions during synthesis into the insulation layer occurred, subsequently the average distance between donor and acceptor ions became much smaller than the insulation shell thickness, which makes the LRET possible. The inset of Figure 3b shows the Pr(III) PL decay times, that result from the PARAFAC analyzed decay curves and spectra of the emission at 608 nm. In Figure 3c the dependence of the average acceptor number on the insulation layer thickness is shown. In addition, the parameter α is shown, which is not changing with the insulation layer thickness basically indicating that there is no insulation layer related heterogeneity of the acceptor distribution. The results found for the Eu(III)/Pr(III) pair in the NaYF 4 host lattice are in very good agreement with our results reported for Nd(III) as the acceptor ion.
In addition to the Eu(III) emission also the luminescence of Pr(III) was investigated. Since the decay kinetics of Pr(III) luminescence are much faster than that of Eu(III), we were expecting to find an increased acceptor luminescence decay time due to LRET. However, we observed the contrary: decreasing luminescence decay time with decreasing insulation layer thickness (see inset of Figure 3b and Table 2, detailed regression parameters in the Appendix A, Table A2). In order to find an explanation for the observed trend, the Lx CS (x = 1-3) samples were investigated, in which no outer Eu(III) containing shell was present. The Lx CS samples were used as a reference for "no LRET". Interestingly, when comparing the luminescence decay times of the Lx CS with its respective Lx CSS sample (x = 1-3, see Table 2), we found that the τ-values for the Lx CSS samples were always larger. The enhancements (ratio τ-value for Lx CSS/Lx CS) are given in Table 2. The largest enhancement was found for L1 CSS, which had the thinnest insulation layer. We interpret this observation as the result of two opposing effects. High concentration of Pr(III) in the core leads to self-quenching, but due to the intermixing with the shell, the concentration in the core and subsequently the self-quenching is reduced. The extent of concentration reduction in the core is dependent on the thickness of the shell (insulation layer). Therefore, it is smallest for L1 and largest for L3. On the other hand, the LRET should be largest for L0 and L1, but smallest for L3. From our data, it may be concluded that the dilution effect is dominating. But, by using the comparison with Lx CS samples, it is possible to show the LRET effect on the acceptor luminescence. The luminescence of Pr(III) was also investigated at additional emission wavelengths, for which the enhancement factors have been plotted (see Figure 3d). In the appendix the Pr(III) decay times τ of Peak 1 at 524 nm ( 3 P 1 → 3 H 5 ) and Peak 2 at 540 nm ( 3 P 0 → 3 H 5 ) are summarized (see Appendix A,  Table A3). Here, basically the same trends were found supporting our findings.

Luminescence of Set Gd300
The Eu(III) emission spectra of the set Gd300 being quenched by the Nd(III) (LRETacceptor) are shown in Figure 4 (λ ex = 465 nm). In Figure 4a, the Eu(III) PL emission spectra of set Gd300 are shown with the respective assignment of electronic state transitions. The spectra were normalized to the maximum of the 5 D 0 → 7 F 2 transition. In Figure 4b, the Eu(III) PL decay kinetics are shown indicating decreasing luminescence decay times (judged by the increasing slope of the decay curves, see Table 3) with decreasing insulation shell thickness. The reference sample (no Nd(III) in the core) has the longest decay time (see Table 3). Even for the sample L3 CSS having the largest insulation shell thickness of 2.8 nm (exceeding the Förster radius R 0 (Eu/Nd) = 0.853 nm by a factor >3) a distinct quenching is found. core leads to self-quenching, but due to the intermixing with the shell, the concentration in the core and subsequently the self-quenching is reduced. The extent of concentration reduction in the core is dependent on the thickness of the shell (insulation layer). Therefore, it is smallest for L1 and largest for L3. On the other hand, the LRET should be largest for L0 and L1, but smallest for L3. From our data, it may be concluded that the dilution effect is dominating. But, by using the comparison with Lx CS samples, it is possible to show the LRET effect on the acceptor luminescence. The luminescence of Pr(III) was also investigated at additional emission wavelengths, for which the enhancement factors have been plotted (see Figure 3d). In the appendix the Pr(III) decay times τ of Peak 1 at 524 nm ( 3 P1 → 3 H5) and Peak 2 at 540 nm ( 3 P0 → 3 H5) are summarized (see Appendix A, Table A3). Here, basically the same trends were found supporting our findings.

Luminescence of Set Gd300
The Eu(III) emission spectra of the set Gd300 being quenched by the Nd(III) (LRETacceptor) are shown in Figure 4 (λex = 465 nm). In Figure 4a, the Eu(III) PL emission spectra of set Gd300 are shown with the respective assignment of electronic state transitions. The spectra were normalized to the maximum of the 5 D0 → 7 F2 transition. In Figure 4b, the Eu(III) PL decay kinetics are shown indicating decreasing luminescence decay times (judged by the increasing slope of the decay curves, see Table 3) with decreasing insulation shell thickness. The reference sample (no Nd(III) in the core) has the longest decay time (see Table 3). Even for the sample L3 CSS having the largest insulation shell thickness of 2.8 nm (exceeding the Förster radius R0(Eu/Nd) = 0.853 nm by a factor >3) a distinct quenching is found.    (1) and (2)). With increasing insulation shell thickness, the acceptor numbers decrease, whereas the parameters α result constantly at the value one.
Based on the LRET-model, the decreasing Eu(III) PL decay times translate in increasing acceptor concentrations as the insulation shell thickness decreases. The Gd300 sample Ref CS has an initial decay time of 2814 µs (λ ex = 465 nm). The PL decay time decreases from L3 CSS to L0 CS from 1505 µs down to 233 µs. Therefore, the LRET efficiency and subsequently the calculated average acceptor concentrations increase from 0.4 acceptors in the 3D sphere (according to the LRET model) for L3 CSS up to 1.9 for L0 CS (see Table 3 and Figure 4c). Looking at the heterogeneity parameters α and β, no significant alterations in the microenvironments of the donor or the acceptor ions are indicated.
A striking difference between the two lattices investigated is the intensity of the 5 D 1 → 7 F 3 transition, which is visible in both NP sets. The strong contribution of this transition to the overall detected emission is unusual. Comparing the Y300 set with the Gd300 set, the 5 D 1 → 7 F 3 transition is (i) more intense (judged by a comparison with the intensity of the 5 D 0 → 7 F j transitions) and (ii) it seems to be more affected by the presence of Nd(III) (compare Figures 3a and 4a). Based on the latter observation, it is tempting to assume a participation of the Eu(III) 5 D 1 energy level in the LRET process.
Complementary to the investigation of the acceptor-related luminescence of the Y300 set doped with Pr(III), the Nd(III) luminescence around 800 nm was analyzed for the Gd300 set. In Figure 5 the luminescence decay kinetics of the respective CS and CSS samples for the smallest and largest insulation layer (L1, L3, respectively) are shown. Alike in the case of the Y300 set, the acceptor decay kinetics were influenced by the thickness of the insulation layer (see Figure 5a). An increasing insulation layer thickness yielded also a decrease in the luminescence rate constant. That is in line with our interpretation of a partly dilution effect due to the intermixing process leading to a reduced concentration quenching of the Nd(III) ions in the core. In Figure 5b the luminescence decay kinetics of the corresponding CSS samples are shown. Table 4. Set Gd300: Evaluation of the Nd(III) PL decay curves with Equation (1), for PL decays in Figure 5b resulting from the major Nd(III) PL emission peaks at 795 nm and 805 nm ( 2 H 9/2 & 4 F 5/2 → 4 I 9/2 ), (λ ex = 465 nm) 1 .

Core-Shell: no Eu(III)
Core The CSS samples are listed with two decay times due to the abrupt change in the slope, compare inset in Figure 5b. Due to the significant change of the slope, the CSS samples have been analyzed twice with Equation (1). The shorter decay times (below 100 µs) correspond to the dashed regression curves in Figure 5 and refer to the points before the slope change [Nd(III) PL decay curve, without the influence of Eu(III)]. The longer decay times (larger than 100 µs) correspond to the solid regression curves in Figure 5b and refer to the points behind the slope change [Nd(III) PL decay curve with the influence of Eu(III)].
centration within a 3D sphere with the radius of R0(Eu/Nd) = 8.53 Å and parameters α, in dependence on the insulation shell thickness, from the evaluation of Eu(III) kinetics with the LRET model equation (Equations (1) and (2)). With increasing insulation shell thickness, the acceptor numbers decrease, whereas the parameters α result constantly at the value one.
Based on the LRET-model, the decreasing Eu(III) PL decay times translate in increasing acceptor concentrations as the insulation shell thickness decreases. The Gd300 sample Ref CS has an initial decay time of 2814 µs (λex = 465 nm). The PL decay time decreases from L3 CSS to L0 CS from 1505 µs down to 233 µs. Therefore, the LRET efficiency and subsequently the calculated average acceptor concentrations increase from 0.4 acceptors in the 3D sphere (according to the LRET model) for L3 CSS up to 1.9 for L0 CS (see Table  3 and Figure 4c). Looking at the heterogeneity parameters α and β, no significant alterations in the microenvironments of the donor or the acceptor ions are indicated.
A striking difference between the two lattices investigated is the intensity of the 5 D1 → 7 F3 transition, which is visible in both NP sets. The strong contribution of this transition to the overall detected emission is unusual. Comparing the Y300 set with the Gd300 set, the 5 D1 → 7 F3 transition is (i) more intense (judged by a comparison with the intensity of the 5 D0 → 7 Fj transitions) and (ii) it seems to be more affected by the presence of Nd(III) (compare Figures 3a and 4a). Based on the latter observation, it is tempting to assume a participation of the Eu(III) 5 D1 energy level in the LRET process.
Complementary to the investigation of the acceptor-related luminescence of the Y300 set doped with Pr(III), the Nd(III) luminescence around 800 nm was analyzed for the Gd300 set. In Figure 5 the luminescence decay kinetics of the respective CS and CSS samples for the smallest and largest insulation layer (L1, L3, respectively) are shown. Alike in the case of the Y300 set, the acceptor decay kinetics were influenced by the thickness of the insulation layer (see Figure 5a). An increasing insulation layer thickness yielded also a decrease in the luminescence rate constant. That is in line with our interpretation of a partly dilution effect due to the intermixing process leading to a reduced concentration quenching of the Nd(III) ions in the core. In Figure 5b the luminescence decay kinetics of the corresponding CSS samples are shown.  Table 4.
The decrease of the luminescence decay rate due to the insulation layer related dilution of the Nd(III) ion in the core is observed. However, for the CSS samples a second  Table 4.
The decrease of the luminescence decay rate due to the insulation layer related dilution of the Nd(III) ion in the core is observed. However, for the CSS samples a second much slower luminescence decay process is found (see inset of Figure 5b). This can be attributed to the LRET process and the resulting decrease (increase) of the luminescence decay rate (time). However, it does not become stronger with decreasing insulation layer thickness, because the concentration related quenching seems to be larger than the Nd(III) sensitization by Eu(III)-LRET (compare inset Figure 5b and values in Table 4 in which L1 (thin insulation shell) decays faster than L3 (thick insulation shell)).

Structural Characterization
The XRD experiments reveal a hexagonal crystal phase for both sets (Y300 and Gd300), because of the good match between the samples XRD reflexes and the hexagonal reference XRD reflexes. For the set Y300, the detected reflexes of the cubic NaYF 4 phase vanish with longer reaction time. Especially, L0 C and Ref C indicate purely cubic phased NaYF 4 nanoparticles. Related to the findings of the TEM investigation two ideas came up: Firstly, the cubic phased nanoparticles could have either transformed into the desired hexagonal phased nanoparticles related to the respective precursor shell additions and the associated longer reaction times, or the precursor materials have grown themselves in a hexagonal phase on the cubic phased cores. Previous research by Voss [55][56][57]. However, the TEM investigations do not support the dissolution of the initially formed cubic phased nanoparticles. A later work by Rinkel et al. reveals a conversion of the cubic to hexagonal phase NaYF 4 particles [58], which could support the first idea. On the other hand, Dong et al. revealed by increasing the dosage of their Ca(II) precursors for growing the CaF 2 shell on hexagonal phased UCNPs, that the XRD reflexes changed from hexagonal NaGdF 4 towards CaF 2 [17], which might indicate in the case here, a certain dependency of the XRD signal on the thickness of the shell (and the associated longer reaction time). In the case for these presented experiments, with the insulation layer of the same host material but increasing shell thicknesses, it could point towards the second idea. Unfortunately, the TEM images (discussed in the following paragraph) do not reveal a difference of the cores and the shells due to the same host lattice. The dopant concentration does not seem large enough to reveal significant contrast differences in TEM. Nevertheless, it can be summarized, the samples L1 CS, L2 CS, L1 CSS, L2 CSS and Ref CS and L0 CS show a mixture of reflexes from cubic and hexagonal NaYF 4 . The samples L5 CS and L5 CSS show only hexagonal NaYF 4 reflexes. We attribute this to a cubic-to-hexagonal transition, which already indicates the migration of the ions within the nanocrystal. This migration is surely not only limited to the Ln(III) ions.
The observed NaF XRD reflexes in Figure 2 relate to NaF, from which already small amounts are sufficient to provoke sharp reflexes in the XRD patterns. The NaF vanishes after the shell growth synthesis, which indicates either its consumption and integration into the nanoparticle during the reaction or its removal by the washing and centrifugation steps after the reaction.
The TEM investigation confirms increasing particle size upon shell material addition and subsequently the successful variation of the insulation layer thickness, which is the basis for the LRET analysis. Whereas, the differentiation of the core and shell structures was not possible. Here, two sets with different host lattices were synthesized at T = 320 • C for the core and at T = 305 • C for the shell growth reactions, see Figures 2 and A1 (Appendix A) and Table 1. The synthesis approach, with its applied synthesis conditions, yields spherical shaped nanoparticles, which can be seen here in the TEM images (Figures 2 and A1) and in Ref. [19].
However, it has to be kept in mind, that the changing sizes affect the luminescence properties of upconversion nanoparticles. Hence, it is very likely the same case for the nanoparticles investigated here. Although, some samples share the same core (from the same synthesis batch), their luminescence properties differ slightly as their size and shell thicknesses (insulation layer as well as donor-doped outer shell) change. An important point to note is that the largest nanoparticle (L3 CSS) possesses the thinnest outer shell and the largest surface, which may lead to stronger Eu(III) luminescence quenching.

LRET
First, we analyzed the Eu(III) luminescence (donor) with respect to the LRET formalism, which was straight forward since any possible interferences from acceptor emission were discriminated by combining spectral and kinetic aspects in a PARAFAC analysis (vide supra, Figure 3). The analysis of the Eu(III) decay kinetics based on Equation (1) indicates, that the chemical environment does not change distinctly, since the heterogeneity parameter β decreases only slightly with decreasing insulation shell thickness (compare Table A2). This observation could be attributed to the comparable chemical behavior of the Ln(III) ions and the major presence of Y(III) ions in the NaYF 4 host lattice in the core as well as in the shells. The same can be observed in the NaGdF 4 host lattice with Gd(III) ions as a major lattice part. This is further supported by the heterogeneity parameter α, which represents the situation for the acceptor ions (vide infra). Based on Equation (2), also no change in α was found (compare Appendix A, Tables A2 and A4 for Pr(III) and Nd(III), respectively). Therefore, within the used model the observed changes in the Eu(III) luminescence decay kinetics for the different insulation layer thicknesses are attributed to an alteration of the LRET efficiency. The insulation layer thickness has a clear effect on the Eu(III) luminescence decay kinetics: the luminescence decay time increased with increasing thickness. This was found for both acceptor ions (Pr(III) as well as Nd(III)) in the respective host lattices. This distance-dependent luminescence quenching was analyzed based on the LRET formalism (see Equations (1)-(4)). The LRET from Eu(III) to Pr(III) (or Nd(III)) cannot be suppressed-even if the insulation shell thickness exceeds the Förster radius R 0 by a factor >7 (R 0 (Eu/Pr) = 8.2 Å and R 0 (Eu/Nd) = 8.53 Å, respectively). The average acceptor concentration (#acceptors) within the 3D sphere with the radius of R 0 (of the respective LRET-pair) increases with decreasing insulation shell thickness (see Figure 6).
Biosensors 2021, 11, x FOR PEER REVIEW 15 of 24 Figure 6. Comparison of the average acceptor number (#acceptor) in the respective R0 volume for the sets Y300 and Gd300. Shown are also data of Ref [19] (Y300:Nd-old). The analysis is based on the donor PL emission data.
In Figure 6 the #acceptor (number of acceptors) for the different host lattices and different acceptor ions are compared. Data, resulting of research from Ref [19], are shown as well. Although the data base is small (e.g, missing of reliable errors) some trends might be seen: (i) for the same host lattice (NaYF4) no difference in the intermixing of Pr(III) and Nd(III) are found and (ii) for the same acceptor ion (Nd(III)) a small influence of the host lattice is seen. It seems that in case of the NaGdF4 lattice the intermixing is less for the larger insulation thicknesses. For the latter observation, differences in the lattice constants as well as lattice phase in combination with specific acceptor ion properties (e.g., ionic radius) could be the reason. Here, small differences in the heterogeneity factors found for the NaYF4 and NaGdF4 lattices obtained from the LRET analysis might point in this direction (vide infra, Appendix Tables A2 and A4). Furthermore, the ionic radii of Y(III) (121.5 pm), Gd(III) (124.7 pm), Eu(III) (126 pm), Nd(III) (130.3 pm), and Pr(III) (131.9 pm) [59] are within a deviation range of 15%, which should be noted. According to Goldschmidt's theory these deviations are tolerable in terms of isomorphism for crystals [18,60]. However, the cationic radius of Y(III) deviates stronger from the Ln(III) cations. The apparent Figure 6. Comparison of the average acceptor number (#acceptor) in the respective R 0 volume for the sets Y300 and Gd300. Shown are also data of Ref. [19] (Y300:Nd-old). The analysis is based on the donor PL emission data.
In Figure 6 the #acceptor (number of acceptors) for the different host lattices and different acceptor ions are compared. Data, resulting of research from Ref. [19], are shown as well. Although the data base is small (e.g, missing of reliable errors) some trends might be seen: (i) for the same host lattice (NaYF 4 ) no difference in the intermixing of Pr(III) and Nd(III) are found and (ii) for the same acceptor ion (Nd(III)) a small influence of the host lattice is seen. It seems that in case of the NaGdF 4 lattice the intermixing is less for the larger insulation thicknesses. For the latter observation, differences in the lattice constants as well as lattice phase in combination with specific acceptor ion properties (e.g., ionic radius) could be the reason. Here, small differences in the heterogeneity factors found for the NaYF 4 and NaGdF 4 lattices obtained from the LRET analysis might point in this direction (vide infra, Tables A2 and A4). Furthermore, the ionic radii of Y(III) (121.5 pm), Gd(III) (124.7 pm), Eu(III) (126 pm), Nd(III) (130.3 pm), and Pr(III) (131.9 pm) [59] are within a deviation range of 15%, which should be noted. According to Goldschmidt's theory these deviations are tolerable in terms of isomorphism for crystals [18,60]. However, the cationic radius of Y(III) deviates stronger from the Ln(III) cations. The apparent reduced intermixing of dopant Ln(III) ions in the NaGdF 4 host lattice could correlate with a stronger migration competition between dopant Ln(III) ions and the host lattice Gd(III) ions, that reduces stronger the dopant Ln(III) ion migration than the Y(III) ions, being smaller, in the NaYF 4 host lattice.
In addition to the analysis of the Eu(III) luminescence, we also analyzed the emission of the acceptor ions (Pr(III) for set Y300 and Nd(III) for set Gd300) in order to collect acceptorbased LRET data complementary to the donor results. The two donor-acceptor pairs Eu(III)/Nd(III) and Eu(III)/Pr(III) have been used before in LRET experiments [30,31,38]. However, in contrast to the analysis of the donor emission related data, for the acceptor luminescence some limitations are found with respect to selectivity in excitation and due to self-quenching because of the high local concentration of the respective acceptor ions in the core. In principle, for both acceptor ions a sensitization of their luminescence is shown. In order to quantify the sensitization effect induced by LRET (and separate contributions of direct acceptor excitation as well as self-quenching), the comparison between the CS and CSS samples of each set was necessary. Based on the data of the CS sets, it could be shown that a concentration of 20 mol% of the respective acceptor ion in the core is already high enough to induce concentration related self-quenching. The growth of an insulation layer is reducing the extent of self-quenching because acceptor ions from the core are intermixing with the shell (which is also an indication for the intermixing between core and shell). Here, this dilution effect becomes larger with increasing insulation layer thickness. Contrary to the self-quenching is the LRET based sensitization, which is largest for the L1 CSS samples with a thin insulation layer (see Tables 2 and 4). Especially for the Nd(III) luminescence, the opposing trends (self-quenching vs. sensitization) are seen in its decay kinetics, in which two components were resolved (see Figure 5b). One was attributed to Nd(III) ion in the core, which suffer from self-quenching and the other to Nd(III) ions, which were mixed into the insulation layer. For the latter, the self-quenching was reduced and in case of an outer Eu(III) containing shell (CSS samples) the sensitization was effective. The LRET-based enhancement can be quantified by the comparison between the respective CS and CSS samples, (see Table 2, last row for Pr(III) as the acceptor ion and Table 4, last column for Nd(III), respectively).

Conclusions
The work presented is a sequel to our investigation of core-shell UCNPs and the intermixing of ions between core and shell during the synthesis. In continuation of our previous work, we have varied the host lattice composition as well as the Ln(III) ion used as acceptor in the core. For the chosen donor/acceptor pairs the donor (Eu(III)) luminescence can be detected without interference of the acceptor-related emission. Here, we also investigated the acceptor-related luminescence in order to monitor the intermixing between core and shell. In addition to the spectral discrimination between luminescence signals from donor and acceptor, in case of Pr(III) a time gating can be used additionally, since the respective luminescence decay time of Pr(III) is much smaller. In combination with chemometry (PARAFAC) the selective detection of the acceptor's luminescence signal can be achieved. However, despite the advantages on the selective detection of the acceptor emission, we encountered a couple of draw backs in using the luminescence of Pr(III) or Nd(III) directly in the LRET analysis. Since the acceptor concentration in the core was high, we found a self-quenching, which was reduced upon adding a shell. With increasing shell thickness, the self-quenching was reduced indicated by the reference measurements using CS nanoparticles (no outer shell with Eu(III)), for which an increase in the acceptor luminescence decay time was found. This trend is opposite to the sensitization, for which also an increase in the acceptor's luminescence decay time is expected (e.g., donor τ Eu >> acceptor τ Pr ), however here the largest sensitization is expected for the smallest insulation layer thickness. The effect of self-quenching is also of relevance for the standard composition of UCNP containing approx. 18 mol% of Yb(III) ions as sensitizer. Maybe by determining the luminescence kinetics of Yb(III) directly, the intermixing between core and shell can also be monitored, which then would be a potential "quick check" without synthesizing nanoparticles with tailored donor-acceptor pairs for LRET analysis. We will pursuit this idea in future experiments.
Based on the evaluation of the donor PL emission using the LRET concept an average number of acceptor ions in the Förster volume around the donor ions is determined and the dependence on the insulation layer thickness is found. For the first time, we also present luminescence data of the respective acceptor (Pr(III) or Nd(III)) and how it is influenced by the intermixing. Here, two trends of opposite directions are reported: (i) reduction of concentration related self-quenching due to mixing of the acceptor ions from the core into the insulation layer and (ii) sensitization due to LRET. In order to quantify the sensitization, it is necessary to differentiate between both effects and a reference sample set is needed. Therefore, the LRET data analysis of the donor emission is preferred because here no additional samples are needed.
For the purpose of building highly protective shell structures for UCNPs, the intermixing between protective shell(s) and the sublayers has to be minimized. Here, we tested a couple of synthesis and composition parameters with respect to their influence on the intermixing. Using Pr(III) or Nd(III) as acceptor ions in the core of NaYF 4 -based UCNP made no difference on the observed intermixing. Here, probably the difference in the ionic radii of Pr(III) and Nd(III) is too small to come into play. After all, the LRET approach is limited to certain donor acceptor pair combinations. On the other hand, the comparison of different host lattices from our data shows that the intermixing for the NaGdF 4 lattice is smaller for medium and large insulation layer thicknesses (see Figure 6). It is tempting to attribute the observed effect to the difference in the matching between lattice cations (either Y(III) or Gd(III)) and dopant Ln(III) ions.
Here, work is in progress to investigate this parameter further. This is important because in the composition of UCNPs the "heavier" Ln(III) ions are normally used as sensitizer and activator. We have tested NP with a regular composition for UCNP in the core using our LRET approach (core doping 2 mol% Pr(III) and 18 mol% Yb(III), these are an activator and sensitizer pair for upconversion, and outer shell doping with Eu(III) whereas the insulation layer has been applied as before). However, the 2 mol% Pr(III) (activator and LRET-acceptor) were too small to induce a significant quenching of the Eu(III) luminescence (located in the outer layer of the CSS NP) and the Yb(III) ion cannot act as LRET-acceptor due to a missing spectral overlap. We plan to look directly at the Yb(III) luminescence and monitor alterations in a (possible) self-quenching like in the case of Pr(III) or Nd(III) in order to shed light on this aspect (the required instrumentation for time-resolved NIR luminescence detection is being set up at the moment in our lab).
The host lattice in combination with the sensitizer as well as activator properties (lattice matching, lattice phase) are not the only possible parameters to be checked in the course of minimizing the intermixing between core and shell. As well, the synthesis condition or the chemical properties of the shell(s) need to be considered, e.g., using CaF 2 shells [17]. Another possible influence parameter could be the composition of the solvent mixture, e.g., the amount of oleic acid ("oleic acid etching"). For synthesis in octadecene the amount of oleic acid as well as the pH of the reaction solution had a distinct effect on the shape and growth of the nanoparticles. In addition, the reaction time will be of importance [55,61,62]. In the present work we have carried out the synthesis under constant conditions with respect to solvent/surfactant ratio and reaction time. Moreover, we used Therminol ® instead of octadecene. But in the future, these parameters may be tested. We have performed first experiments, in which we synthesized the shell(s) at lower temperatures (core synthesis at 320 • C and shell synthesis at 205 • C), but first results with respect to particle size increase or monodispersity of the nanoparticles were unsatisfactory, e.g., it seemed, that in the synthesis step of shell growth, the precursor materials formed competing seeds leading to a second generation of nanoparticles. Here, modifications in the synthesis, e.g., parameters like the addition rate of precursor materials, will be tested in future work. Additional work is in progress, in which different core and shell lattices are used (e.g., Sc(III) in the core and Y(III) or Gd(III) in the shells or Ca(II) in the outer shell). With an improved understanding of the intermixing process and how to minimize (or eliminate) it, UCNP with a higher brightness (and quantum yields) could be obtained and will make this class of optical probes even more attractive for applications in life sciences.  Figure A1. TEM images of the measured samples for the set (a) Y300 (NaYF4:Pr20% @ NaYF4 @ NaYF4:Eu5%, with Pr(III) doping in the core and the insulation layer thicknesses) and (b) Gd300 (NaGdF4:Nd20% @ NaGdF4 @ NaGdF4:Eu5%, with Nd(III) doping in the core and the insulation layer thicknesses). The step of the insulation shell growth synthesis results in increasing particles in comparison to the initial core particle diameter. The NaYF4 based nanoparticles show a larger size distribution of particles than the NaGdF4 nanoparticles. Figure A1. TEM images of the measured samples for the set (a) Y300 (NaYF 4 :Pr 20% @ NaYF 4 @ NaYF 4 :Eu 5% , with Pr(III) doping in the core and the insulation layer thicknesses) and (b) Gd300 (NaGdF 4 :Nd 20% @ NaGdF 4 @ NaGdF 4 :Eu 5% , with Nd(III) doping in the core and the insulation layer thicknesses). The step of the insulation shell growth synthesis results in increasing particles in comparison to the initial core particle diameter. The NaYF 4 based nanoparticles show a larger size distribution of particles than the NaGdF 4 nanoparticles.