Energy Transfer Sensitization of Luminescent Gold Nanoclusters: More than Just the Classical Förster Mechanism

Luminescent gold nanocrystals (AuNCs) are a recently-developed material with potential optic, electronic and biological applications. They also demonstrate energy transfer (ET) acceptor/sensitization properties which have been ascribed to Förster resonance energy transfer (FRET) and, to a lesser extent, nanosurface energy transfer (NSET). Here, we investigate AuNC acceptor interactions with three structurally/functionally-distinct donor classes including organic dyes, metal chelates and semiconductor quantum dots (QDs). Donor quenching was observed for every donor-acceptor pair although AuNC sensitization was only observed from metal-chelates and QDs. FRET theory dramatically underestimated the observed energy transfer while NSET-based damping models provided better fits but could not reproduce the experimental data. We consider additional factors including AuNC magnetic dipoles, density of excited-states, dephasing time, and enhanced intersystem crossing that can also influence ET. Cumulatively, data suggests that AuNC sensitization is not by classical FRET or NSET and we provide a simplified distance-independent ET model to fit such experimental data.


Supplementary Materials and Methods S-3 Chemicals S-3 Quantum Dots S-3 Cap Exchange of Quantum Dots S-3 Gold Nanoclusters S-3 Conjugation of Donors to AuNC Acceptors S-4 Electron Microscopy S-5 Dynamic Light
. TEM, DLS, Zeta-Potential S- 21  Table S2. Summary of Donor and Acceptor Lifetimes S-24 Table S3. AuNC Acceptor and Donor Optical Properties S-26 Table S4. Experimental  Following addition of the reducing agent the color of the reaction mixture immediately changed from clear to light brown. This mixture was stirred for at least 3 h while the reaction gradually progressed to completion. For aging and ripening, the clusters were stored for an additional two days at room temperature without stirring. The dispersion was then purified by removal of the free ligands with three cycles of centrifugation using a membrane filtration device (10 K molecular weight cut-off, Millipore Corporation). AuNC dispersions were characterized using UV-Vis absorption spectroscopy and TEM as described below. interactions. This is driven by the low pKa of the alkyl carboxylic acids (~4.8) and the high pKa of the primary amine group (∼10), 6,7 which means both will be mostly ionized at around the neutral pH of water. Zeta potential was measured to confirm the ionization of carboxylated QD (~ -42 mV) and amine-terminated AuNC (~13 mV) before self-assembly, see Table S1 in Steady-State Optical Characterization: Electronic absorption spectra were recorded using an HP 8453 diode array spectrophotometer (Agilent Technologies, Santa Clara, CA). Fluorescence spectra were collected using a Spex Fluorolog-3 spectrophotometer (JobinYvon Inc, Edison, NJ) equipped with a red-sensitive R2658 Hamamatsu photomultiplier tube (PMT) for wavelengthscanned spectra, and a liquid nitrogen-cooled CCD array for collection of dispersed spectra.

Conjugation of Donors to AuNC Acceptors
Sample excitation was accomplished using a monochromatized xenon lamp. The fluorescence spectra were corrected using the spectral output of a NIST-certified calibrated light source. The Here, F0/ΦD 0 is proportional to the total number of photons absorbed by the donor and (A-A0)/ΦA 0 is proportional to the total quanta transferred from donor to acceptor via energy transfer while accounting for the acceptor Φ 15 .

S-9
Energy Transfer Analysis.

I. Förster Resonance Energy Transfer (FRET):
Förster points out in classical theory that the electrostatic interaction energy between two electric dipoles is directly related to the magnitude of the two interacting dipoles and inversely related to the cube of the distance, R, between the donor and acceptor. 14,[17][18][19] Thus, the dipole-dipole energy transfer rate, kFRET, is proportional to R -6 . The distance, at which the decay rate of the donor deactivation in the absence of an acceptor, kD0, equals the energy transfer rate from donor to acceptor, is R0, defined as the critical separation or Förster distance where energy transfer efficiency is 50%. 14,17-19 R0 can be calculated from the donor luminescence and acceptor absorption data using the following equation 14 : where n is the refractive index of the buffer medium, NAv is Avogadro's number (6.022 × 10 23 mol -1 ), ΦD 0 is the donor in the absence of acceptor,  2 is the dipole orientation factor, and J is the spectral overlap integral function between donor emission and acceptor absorption. We use a  2 of 2/3, which is appropriate for the random dipole orientations of donor and acceptor found within these self-assembled configurations. 14,20 J is determined by integrating the acceptor absorbance εA(λ) multiplied by the normalized donor luminescence fD(λ) over all wavelengths, λ.
J(λ) for each potential donor-AuNC pair can be found in Figure S3. where N is the number of AuNCs per donor and R is the center-center distance from donor to acceptor. R was estimated using the molecular size of the ligand, donors and the NC radius as estimated from TEM analysis, see SI for details. If donor quenching were entirely due to FRET, then EQ = EFRET =ESen. If EQ does not equal EFRET, then other quenching mechanisms associated with the donor-acceptor complex must be considered. for the molecule located at some small distance above a metal surface. De-excitation of the molecule proceeded via interaction between the electric field of the oscillating dipole and the metal surface which was modeled as an electron gas. This occurs simultaneously as an electron in the metal is excited to a state above the Fermi level. Persson suggested two different models to describe the damping rate (energy transfer rate), kET, of a dye molecule above the metal: (1) Surface Damping, following a ~ 1/R 4 dependence, involves the excitation of electron-hole pairs in the metal surface, and (2) Volume Damping, which follows a~ 1/R 3 l dependence (l = electron mean free path), where the energy is dissipated by conversion of electronic currents in the metal into heat through scattering from phonons, impurities, and other electrons. 21,22 The damping rates were numerically calculated as follows:

II. Surface/Volume Damping of Excited Molecules Above a Metal
(Eq. S11) In the case of metal NPs , however, volume damping may not be negligible because the electron and its mean free path will be confined to the physical size of the NP especially when the NP size is smaller than the traditional mean free path of the electron in bulk metal. Since the volume damping rate was derived by using the dielectric function of the bulk metal, 22 here we suggest that it be adjusted by considering a modified dielectric function with a reduced mean free electron path, lCor, to account for the nanoscale size of the AuNCs (see the next section). This approach has been repeatedly put forth in the literature, see for example refs. [29][30][31][32] Similar to R0, the separation distances corresponding to 50% energy transfer efficiency can be derived for both surface and volume damping processes. For surface damping, R0 corresponding to the separation distance at which energy transfer efficiency equals 50%, was calculated by using the Einstein Coefficient A21; 27 where X = 4 for surface damping, referred to as NSET hereafter, and X = 3 for Volume Damping, referred to as nanovolume energy transfer or NVET hereafter.

Volume Damping Theory Modification based on Reduced Mean Free Path of Electron
Persson derived the volume damping rate from the bulk metal based on the Drude dielectric function εbulk(ω). [22] In the case of metal NPs, the dielectric function of bulk metal, εbulk(ω) needs to be modified if the metal size is smaller than the mean free path of the free electron in the bulk metal. [29][30][31] ( ) = 1 − vF is the Fermi velocity. l0 and leff are the mean free path of free electron in the case of the bulk metal and the effective mean free path of the electron in a metal NP respectively. The bulk mean free path of electron of gold is 20~ 25 nm. 25 A is a dimensionless parameter which depends upon the geometry. In the context of simple Drude theory and isotropic scattering, A is usually assumed to be unity. 30,31 However, there is literature that reports A= 0.7 for gold. 34 Thus, we can derive the volume damping rate for metal NPs by using the reduced mean free path of electrons confined to the size of the NPs following; Thus we can derive the critical distance R0 from the modified volume damping rate by using the Einstein A21 coefficient. If we consider the spontaneous emission is in accordance with Coulomb's law, 1/4πɛ, A21 can be 0 /4πɛ. 27 Here, l0 and leff are the mean free path of electrons in bulk metal and the effective S-14 mean free path of electrons in NPs when the size of the NPs are smaller than l0, respectively. And lCor is the corrected mean free path of electrons in metal NPs. The electron mean free path in NPs was reported to be leff = 4V/S (V = volume, S = Surface area) for three-dimensional nanoparticles. 31 Also for the sphere, classical theory gives leff = r (r = radius of sphere) for isotropic scattering, or leff = 4/3r for diffusive scattering, while the quantum particle in a box model yields, leff = 2/3L (L = length) for the cube, leff = 1.4r for a cylinder and leff = 1.64r for the sphere, 31 . In our calculations that use l0 = 25 nm and leff = 1.64r ~ 1.23 nm, lCor is ~ 2.34 nm.

Decay Rate Constant Calculation.
The total decay rate of the donor, kD0 is the inverse of the donor lifetime (τD0). The radiative and non-radiative decay rates of the donor, in the absence of an acceptor, can be calculated by using The steady-state donor quenching efficiency can be written (ET, Eq. 3) by using the donor decay rates before and after quenching. kQ is the quenching rate and N is the number of AuNCs per donor. k follows a 1/R 6 dependence (for FRET), or 1/R X dependence (X = 4 for NSET and X = 3 for NVET). 27

Worm-Like-Chain Model (WLC)
We assumed the PEG as a random coil configuration to determine the size of PEG by solving the mean square end-to-end distance of polymer, <R 2 >, in worm-like chain (WLC) model (Eq. S24). 37 (Eq. S24) Here Rmax = Nb is the maximum end-to-end distance of the actual polymer or the length of a fully extended PEG 600 (MW 600 ± 30). N is the repetition number of ethylene glycol units and b is the size of ethylene glycol, 0.15 nm and lp is the persistence length (stiffness) of the PEG,0.43 nm in aqueous solution. 38 The calculated end-to-end distance of PEG 600 was 1.0 ± 0.15 nm. So we used the average number of Rmax and end-to-end distance of PEG 600 calculated by WLC model, ~ 1.4 ± 0.15 nm.
S-17  b Inorganic core size of each NP and the dried distance between QD and AuNCs measured by TEM.     0.00 ± 0.00 0.96 ± 0.01 0.98 ± 0.00 0.99 ± 0.00 0.99 ± 0.00 a Corrected for the cs124 chelate contribution. b, c The R and R0 is the separation and the critical separation between donor and acceptor calculated depending on model.

Increased Energy Transfer Probability From Tb(chelate) to a Single AuNC with Increased Donor /Acceptor Conjugation Ratios.
If the lifetime of the donor is long enough to efficiently transfer energy to the acceptor, the energy transfer probability per single acceptor may increase with increasing donor conjugation number. In multiple donor-acceptor conjugation system, the high chance of energy transfer from the donor to single acceptor will not affect the total energy transfer efficiency of the system (E, energy transfer rate per donor), which means that the total energy transfer rate will still decrease with the increased donor conjugation ratio, M (=inverse of acceptor conjugation number per donor = 1/N). However, it changes the probability of that a single acceptor accepts energy from the donor via single energy transfer, as multiple donors are assembled. Thus, single AuNC will become more sensitized and brighter via energy transfer when the number of donors are increased during assembly (as N decreases), which can be interpreted as an increase in the net sensitization signal per acceptor, (A-A0)/ A0 (Eq. S10). The following paragraph is a derivation of the relevant equation. Here, E is the total energy transfer efficiency from donor to acceptor in each complex system. C is the concentration of AuNP and thus MC is the concentration of donor. Thus the net sensitization signal will follow, 20 This equation implies that as the number of donors that surround the acceptor increases (larger M), the emission due to energy transfer from the donor to single acceptor increases and the net sensitization signal per AuNC also increases. Figure

Calculation of Spin Number per AuNC
We consider two different approaches to calculate the molecular weight (MW) of AuNC with 1.5 nm diameter. As common factors, we used the unit volume of Au atom (0.017 nm 3 ), MW of Au (196.97), MW of ligand (791.048), sample for SQUID measurement (6 mg), and the total spin number measured by SQUID (2 × 10 17 ). Figure S11. SQUID measurement from AuNC confirming the existence of paramagnetism due to AuNC unpaired spin.
The total number of gold atoms per nanoparticle, NAu and the number of surface gold per nanoparticle, NS-Au based on complete volume filling, can also be calculated using; (Eq. S27) Approach 1: Assuming 1.5 nm AuNC as perfect sphere and the thickness of Au shell is 0.238 nm.
(Eq. S28) where R is the radius of AuNC (0.75 nm) , VAu ≅ 1.7x10 -2 nm 3 (using an atomic radius of 0.16 nm for Au) and [AuNP] designates the nanoparticle concentration The calculated total number Au per AuNC was 104, Au number in core was 33, Au number in shell was 71, the number of ligands was ~ 35, and MW of AuNC-NH2 was 48485, which resulted in the calculated spin number per AuNC ~2.7.

S-31
(Approach 2) Assuming 1.5 nm AuNC as perfect sphere and Au 55 as the inner core.
The calculated total number Au per AuNC was 104, Au number in core was 55, Au number in shell was 49, the number of ligands was ~ 24, and MW of AuNC-NH2 was 39805, which resulted in the calculated spin number per AuNC ~2.2.
Based on crystallographic studies, Jadzinsky reported that similar 1.5 nm mercaptobenzoic acidfunctionalized AuNC's have ≈102 Au atoms in their structure with ≈44 predicted to be on their surface and available for ligand binding. 39 In our bidentate ligands will be 22, MW of AuNC-NH2 will be 37494, which resulted in the calculated spin number per AuNC ~ 2.1.