Probing nearby molecular vibrations with lanthanide-doped nanocrystals

The photoluminescence (PL) of lanthanide-doped nanocrystals can be quenched by energy transfer to vibrations of molecules located within a few nanometers from the dopants. Such short-range electronic-to-vibrational energy transfer (EVET) is often undesired as it reduces the photoluminescence efficiency. On the other hand, EVET may be exploited to extract information about molecular vibrations in the local environment of the nanocrystals. Here, we investigate the influence of solvent and gas environments on the PL properties of NaYF4:Er3+,Yb3+ upconversion nanocrystals. We relate changes in the PL spectrum and excited-state lifetimes in different solvents and their deuterated analogues to quenching of specific lanthanide levels by EVET to molecular vibrations. Similar but weaker changes are induced when we expose a film of nanocrystals to a gas environment with different amounts of H2O or D2O vapor. Quenching of green- and red-emitting levels of Er3+ can be explained in terms of EVET-mediated quenching that involves molecular vibrations with energies resonant with the gap between the energy levels of the lanthanide. Quenching of the near-infrared-emitting level is more complex and may involve EVET to combination-vibrations or defect-mediated quenching. EVET-mediated quenching holds promise as a mechanism to probe the local chemical environment—both for nanocrystals dispersed in a liquid and for nanocrystals exposed to gaseous molecules that adsorb onto the nanocrystal surface.


Section S2: Oscillator strengths of electronic relaxations in lanthanides
Following Ref. S1, the oscillator strength of an electric dipole transition from an initial electronic state with quantum numbers S, L and J, ⟨4f, SLJ⟩, to a final state with quantum numbers S ′ , L ′ and J ′ , ⟨4f, S ′ L ′ J ′ ⟩, can be calculated using Judd-Ofelt theory: where C is a prefactor (1.1 × 10 11 cm −1 ), ξ * is the transition barycenter, χ is the local-field factor (see Section S3) and n is the refractive index of the medium.Ω λ are the three lattice-specific Judd-Ofelt parameters (4.97 × 10 −20 , 1.16 × 10 −20 , and 2.03 × 10 −20 cm −2 for Ω2, Ω2 and Ω2 in β-NaYF4; Ref. S1) and U (λ) are the electric dipole tensor operators.The matrix elements | ⟨4f, SLJ|U (λ) We used the absorption spectrum of bulk β-NaGdF4 powder (Figure S2a; Obtained from Ref. Freddy) to estimate the transition energies and widths.First, we determined the energies of the different levels ν * (see Figure S2b-c) and (ignoring crystal-field splitting of the 4 I 15/2 ground state of erbium) approximated spectra of the oscillator strength T of a transition from initial state i to final state j as where ξ is the energy difference from the transition barycenter.Theoretical spectra in Figure 1f (main text) are based on the shape Ti,j(ξ), combined with the calculated values of fED (see Table S1) as an amplitude.

Initial state
Final state

Section S3: Intrinsic decay dynamics of nanocrystals
For lanthanide dopants in NCs with dimensions smaller than the wavelength of light, the radiative decay rate differs depending on the photonic environment according to the NC-cavity model: S3 Γ rad (n) = Γ0nχ 2 . (3) Here, Γ0 is the decay rate of the emitter in vacuum, n is the solvent refractive index, and χ is the local-field factor, which accounts for the fact that the local electric field amplitude of photon states at the position of the emitter is different from that of the macroscopic electric field.For spherical NCs with refractive index nNC, there is an analytical expression for χ 2 : S3 In Figure 2 (main text), we used the NC-cavity model (Eq.4) and literature values of the radiative decay rates (Ref.S4) to calculate theoretical decay curves of NCs dispersed in different solvents, where the only decay pathway is radiative.
For the green-emitting levels of erbium, cross-relaxation plays an important role in the decay dynamics.S4 The rate of cross-relaxation from a central donor ion depends on its local environment in terms of the number of acceptor ions and the corresponding donor-acceptor distances (with an r −6 -dependence).Due to random occupation of rare-earth sites by lanthanide ions, an ensemble of Er-doped NCs features a distribution of cross-relaxation rates.Importantly, donor-acceptor distances are discrete and follow a shell-like structure with nearest neighbors, next-nearest neighbors, etc. S4-S7 The β-NaYF4 unit cell has two different rare-earth sites: the A-site that is 100% available for lanthanide ions, and the B-sites that is 50% occupied by Na ions.S8 For a statistical distribution of lanthanide ions, there is an analytical expression for the (multi-exponential) contribution of cross-relaxation X(t) to the total decay dynamics: S4 (5) The dynamics of cross-relaxation has contributions of erbium donors in A and B sites, with acceptors positioned in shells i, with ni rare-earth sites at distances ri and r * i .Cross-relaxation becomes faster at higher doping concentrations ϕ.Theoretical decay curves in Figure 2a-d (main text) contain contributions of radiative decay (Eqs.3-4), Er-Er cross-relaxation and Er-Yb cross-relaxation (Eq.5).We used values CEr,Er and C Er,Yb from Ref. S4.Note that the shell model for cross-relaxation does not account for energy migration among lanthanide ions and neglects finite-size effects.The theoretical curves in Figure 2a-d  Relative contributions of the green and red upconversion emissions from a film of oleic-acid-coated NaYF4:Er 3+ (2%),Yb 3+ (18%), as a function of power density.The green and red datapoints correspond to measurements under dry nitrogen flow, and the dashed lines correspond to the same measurements under a flow containing H2O vapor at p/p0 = 0.17.Note that the power dependence is approximately the same under these two different gas flows.(b) Same as a, but for a film of silica-coated NaYF4:Er 3+ (2%),Yb 3+ (18%) NCs.(d-e) PL decay curves of the green and red emissions excited at 980 nm under dry nitrogen flow and in the presence of water vapor.The laser was operated in block-pulsed mode, where it was on for the first 2 ms (unshaded area) and off for the last 2 ms (shaded area).(f-g) Same as b-c, but using only the photons emitted in the second half of the block pulses (at times when the laser was off; grey areas in d-e).

Section S7: Lifetimes of the upconversion green and red emissions under different gas flows
We describe upconversion luminescence using a simple three-level system.Excitation of a lanthanide ions in the near-infrared with rate kexc builds up a fractional population of ions in an intermediate, near-infraredemitting level nNIR: Upconversion proceeds by ET from these near-infrared-emitting level, with rate kET.Populations of the green-and red-emitting levels nG and nR are with kR,G the decay rates of the two levels.The assumption of weak excitation is valid as we estimate kexc ≈ 10 −4 ms −1 (using the absorption cross-section of ytterbium in NaGdF4 1.1 × 10 −21 cm 2 (Ref.S1) and an excitation power of 10 Wcm −2 )-much slower than even the bulk radiative decay rate of ytterbium (0.58 ms −1 ; Ref S4).Furthermore, we do not take into account the NaYF4 crystal structure and ignore the effects of cross-relaxation and energy transfer.In the limit of low excitation power (i.e.kexc ≪ kNIR), the steady-state intensity of the green and red emissions I SS RG scales as We fitted the decay curves in Figure 3d-e (main text) to the model (Eq.S6,S7), assuming the limit of weak excitation and assuming a steady-state population of the green and red-emitting levels after 2 ms of laser excitation.The resulting fit parameters are k of 15.7, 17.4, 7.0, 7.8, 2.5 and 2.6 ms −1 .
For silica-capped NCs (see Fig. S7c-d), the fit parameters are k

Figure S3 |Figure S4 |
Figure S3 | Quenching of holmium levels in different chemical environments.(a) Transmission electron microscopy images of the oleic-acid-coated NaYF4:Ho 3+ (5%) NCs, with a diameter of 31 ± 3 nm.A ligand-exchange procedure yielding BF4 − -capped NCs, described in Ref. S9, was performed prior to dispersing the NCs in polar solvents.(b) Normalized oscillator strengths and energies of important relaxation transitions in Ho 3+ , calculated using the procedure described in Section S2.S2 Oscillator strengths fED of relaxations from the blue-, green-and red-emitting levels are 3.4 × 10 −7 , 6.2 × 10 −7 and 4.9 × 10 −9 .(c) Infrared absorption spectra of solvents molecules, reproduced from Ref. S10. (d-e) PL decay curves of the blue-emitting levels in acetone, ethanol, cyclohexanol and cyclohexanone are shown in purple, blue, green and yellow.Theoretical predictions for radiative decay in the absence of EVET and cross-relaxation are shown as solid lines.S11 (f) Schematic of EVET quenching of the blue-emitting donor level.Cross-relaxation is indicated by dashed arrows.(g-i)Same as d-f, but for the green-emitting level.(j-l) Same as d-f, but for the red-emitting level.The blue, green and red decay curves were obtained by exciting the sample at 447, 535 and 638 nm, and collecting the luminescence at 487, 542 and 645 nm.The setup used was the same as described in the Methods section.

Figure S5 |
Figure S5 | Effect of time gating on the detection of water vapor.(a)A drop-casted layer of upconversion NCs is exposed to a constant flow of dry nitrogen carrier gas with controllable amounts of water vapor.(b) Normalized green and red emission intensities of oleic-acid-coated NaYF4:Er 3+ (2%),Yb 3+ (18%) NCs, measured under dry nitrogen flow (brown-shaded areas) or in the presence of water vapor (p/p0 = 0.17; blue-shaded areas).(c) Same as b, but for the contribution of green emission to the upconversion PL.(d-e) PL decay curves of the green and red emissions excited at 980 nm under dry nitrogen flow and in the presence of water vapor.The laser was operated in block-pulsed mode, where it was on for the first 2 ms (unshaded area) and off for the last 2 ms (shaded area).(f-g) Same as b-c, but using only the photons emitted in the second half of the block pulses (at times when the laser was off; grey areas in d-e).

Figure S7 |Figure S8 |Figure S9 |Figure S10 |
Figure S7 | Upconversion emission lifetimes under different gas glows.(a)Upconversion emission lifetimes of NaYF4:Er 3+ (2%),Yb 3+ (18%) oleic-acid-coated NCs, under changing flows of dry nitrogen and a flow containing water vapor (p/p0 = 0.17; blue shaded areas for H2O and purple for D2O).Lifetimes are obtained by fitting a single exponential to decay curves with an integration time of 10 s.(b) Same as a, but normalized to the lifetime under dry nitrogen flow.(c-d) Traces of the green and red photoluminescence of silica-coated NaYF4:Er 3+ (2%),Yb 3+ (18%) NCs excited at 980 nm under dry nitrogen flow (yellow) and in the presence of water vapor (blue).The laser was operated in block-pulsed mode, where it was on for the first 2 ms (unshaded area) and off for the last 2 ms (shaded area).Solid lines are fits to the rate-equation model(Eq.7-8).(e-f) Same as a-b, but for a film of silica-coated NaYF4:Er 3+ (2%),Yb 3+ (18%) NCs.

Table S1 | Relaxation transitions of the erbium excited state
. Matrix elements of U(λ), obtained from Ref. S2. Transition oscillator strengths are calculated based on Eq. 1. Transition barycenters ξ * and widths σ are determined based on the absorption spectrum of bulk β-NaGdF4 powder (FigureS2).