# Combined Confocal Dynamic Light Scattering and Fluorescence Correlation Spectroscopy as an Advanced Technique to Characterize Colloidal Quantum Dot-Gold Nanoparticle Hybrid Systems

Pierre Bauer, Ali Dabbous, Sébastien Pairis, Vincent Maurel, Fabien Dubois, A. Barbara

► To cite this version:

Pierre Bauer, Ali Dabbous, Sébastien Pairis, Vincent Maurel, Fabien Dubois, et al. Combined Confocal Dynamic Light Scattering and Fluorescence Correlation Spectroscopy as an Advanced Technique to Characterize Colloidal Quantum Dot-Gold Nanoparticle Hybrid Systems. Analytical Chemistry, 2026, 98 (3), pp.2328 - 2338. 10.1021/acs.analchem.5c06564. hal-05512622

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Submitted on 16 Feb 2026

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Combined confocal Dynamic Light Scattering
and Fluorescence Correlation Spectroscopy as
an advanced technique to characterize
colloidal quantum dot-gold nanoparticle
hybrid systems

Pierre Bauer,† Ali Dabbous,‡ Sébastien Pairis,† Vincent Maurel,‡ Fabien Dubois,†
and Aude Barbara*,†

†Université Grenoble Alpes, CNRS, Grenoble INP, Institut Néel, 38000 Grenoble, France
‡Université Grenoble Alpes, CEA, CNRS, Grenoble INP, IRIG-SyMMES, 38000 Grenoble, France

E-mail: aude.barbara@neel.cnrs.fr

Abstract

Combined confocal dynamic light scattering (DLS) and fluorescence correlation spectroscopy (FCS) experiments were developed to study covalently bound CdSe/ZnS core-shell quantum dot (QD)-Au nanoparticle (AuNP) hybrid systems formed via click chemistry. This experimental approach has the advantage of probing sequentially both AuNPs and QDs, despite their very different optical properties, and in the same experimental conditions. The dynamic properties of the AuNPs are probed through DLS measurement whereas those of the QDs are obtained through FCS. As a result, the in-situ formation of hybrid systems and their characterization can be accessed. Here,
we also show that such experiments enabled to distinguish the solutions of bound QD-AuNP systems from unbound ones (QDs and AuNPs mixture) and permitted to monitor the kinetics of the click reaction. Finally, using hydrodynamic bead models, the nature of the formed hybrid systems was identified, even in complex cases where various types of particle assemblies were present.

Keywords: Quantum dots, Au nanoparticles, hybrid systems, confocal dynamic light scattering, fluorescence correlation spectroscopy

Introduction

Covalently bound hybrid systems (c-HS) composed of metal nanoparticles (NPs) and quantum dots (QDs) are promising candidates for improving and better controlling photoelectronic and photochemical properties at the nanoscale level,¹ thereby opening ways to developments in quantum plasmonics,²,³ non-linear optics⁴,⁵ or catalysis.⁶,⁷ Such systems indeed sustain exciton-plasmon near-field interactions yielding possible charge and energy transfers that may redefine the optical and electronic properties of the individual components.⁸⁻¹¹ The use of colloids to form c-HS is appealing due to robust and readily accessible preparation routes for both metal NPs¹²⁻¹⁴ and QDs.¹⁵ Moreover, a great versatility in the physical properties can be achieved due to the size- and shape-dependent optical and electronic properties of the particles.¹⁵⁻¹⁹ Consequently, the nature of the HS plays a major role in their physical and chemical properties and a quantitative understanding of the latter relies on the accurate characterization of the systems.

Despite the availability of many experimental tools, characterizing the binding reaction of c-HS and the as-formed systems remains challenging. Such a study effectively requires ensemble and *in-situ* measurements, to have reliable statistical information and to follow the chemical reactions, while ensuring sensitivity to both metal NPs and QDs. Combined confocal DLS and FCS meet these criteria as they are *in-situ* approaches that enable to
determine the size of colloids in suspension through their dynamic properties, i.e without
removal of the liquid, unlike methods like SEM. Hybrid systems are expected to present
the same diffusion time in DLS and FCS, since bound AuNPs and QDs have the same mo-
tion. On the opposite, in unconnected systems, AuNPs and QDs of different sizes have
an independent motion and will present different diffusion times in DLS and FCS. In most
reported studies, the characterization of QD-metal NP hybrid systems (covalently or not
covalently bound) is done by electronic microscopies, which indeed give robust indications
on the morphology of the particles but only probe a limited number of objects. Moreover,
their colloidal state may have been altered during the drying process, due to concentration or
sedimentation effects. Photoluminescence and lifetime measurements were also reported to
monitor the *in-situ* binding of QDs to metal NPs in solution, as a non-radiative decay of the
exciton in the metal, accompanied by a fluorescence quenching, is expected in this case.²⁰,²¹
Such an approach is mainly qualitative and may also be misleading, as other parameters can
lead to fluorescence quenching due to the chemical complexity of the colloidal suspensions
studied.²²,²³ In this context, scattering techniques appear as valuable complementary tools,
providing, among other information, the averaged and *in-situ* sizing of the particles. The
most widely used technique for this purpose is DLS, which determines the hydrodynamic
diameter of particles assuming they are spherical in shape. However, when the probed ob-
jects deviate significantly from a spherical shape or exhibit high size heterogeneity, as can be
the case for c-HS solutions, this technique provides an average diameter value that poorly
reflects the actual nature of the objects in solution. Advanced elastic scattering techniques
including light, X- ray, and neutron scattering have been developed to characterize more
complex nanoparticle solutions²⁴ but have rarely been applied to hybrid systems. The limi-
tation of these scattering techniques in the context of HS is that QDs are very weak elastic
light scatterers, and their signal is overwhelmed by that of the metal NPs when both are
present in the same solution. On the other hand, *in-situ* sizing of QDs by Fluorescence
Correlation Spectroscopy (FCS)²⁵⁻²⁷ has been reported, but only for simple QD colloidal
solutions.

In the present study, we take advantage of both DLS and FCS spectroscopies and advance them further to more comprehensively characterize the formation of c-HS, here composed of gold nanoparticles (AuNPs) and CdSe/ZnS core-shell QDs. To this end, we have developed an experimental approach of combined confocal DLS and FCS (Fig. 1a). In such a confocal approach, only a very small volume of the sample is probed ($V_c \sim 1fL$ typically) and the dynamic of the colloids is accessed through the temporal fluctuations of the local concentration in the observation volume. DLS experiments probe the hydrodynamic motion of the AuNPs, that scatter most of the elastic light, while FCS experiments probe the hydrodynamic behavior of the QDs which emit the whole fluorescence signal. The confocal DLS and FCS setup enables to perform both types of experiment under the same conditions, probing the solution in an identical manner such that AuNP-QD hybrid systems will have the same diffusion times in DLS and in FCS, whereas isolated (or aggregates of) AuNPs or isolated (or aggregates of) QDs will present different DLS and FCS diffusion times (Fig. 1b). We point out that cross-correlation between scattered light and fluorescence in a confocal environment was previously reported in the case of life science investigations of molecule-NP interactions.²⁸

The studied c-HS are here AuNP-CdSe/ZnS QD hybrid systems and were synthesized by a Copper-Catalyzed Azide to Alkyne Cycloaddition (CuAAC) reaction,²⁹ commonly referred to as "click reaction". Click chemistry, particularly the azide-alkyne cycloaddition, is known for its high specificity and efficiency, leading to the formation of the desired c-HS with minimal side reactions and thereby reducing the probability of forming unintended colloidal assemblies.³⁰,³¹ In this study, the AuNPs and the QDs were assembled by a click reaction involving the formation of triazole groups through a Huisgen 1,3-dipolar cycloaddition of organic azides and alkynes.³² We first used a synthesis route of a so-called selective click reaction, dedicated to specifically form AuNP-QD bonds, thereby optimizing the formation of c-HS. The binding occurred between alkyne-tagged AuNPs and azide-tagged QDs via the
<figure><img src="image_2.png" /><figcaption>Figure 1: (a) Schematic representation of the home-built confocal DLS and FCS optical setup. The red and green lines represent the fluorescence signal and the Rayleigh scattering respectively. DLS and FCS measurements are done in the configuration (A) and (B), respectively. BS: beamsplitter, L: lens, LD: lens doublet, P: pinhole and M: mirror.

(b) Principle of the combined DLS and FCS measurements: prior to the click reaction DLS (green line) probes the dynamics of the AuNPs (yellow sphere), and FCS (red line) probes the dynamics of the QDs (orange sphere) in solution. As they are not connected, each type of particles diffuses independently with its own characteristic time (highlighted by the dotted lines). After the click process, both DLS and FCS probe the formed c-HB linked up with a triazole group, and present the same and increased diffusion time.</figcaption></figure>
<figure><img src="image_3.png" /><figcaption>Figure 2: Schematic representation of the click reaction principle. (Upper panel) Selective click where the azide-alkyne CuAAC click reaction is solely obtained between the alkyne-tagged AuNPs functionalized with a mixture of amino-PEG-alkyne (—≡—) and amino-PEG-COOH (COO—) and the azide-tagged QDs functionalized with 4-azido-benzyl-phosphonic acid (N3). In this case, only one triazole per bond is formed. (Lower panel) Non-selective click where the azide-alkyne CuAAC click reaction occurs at both alkyne (—≡—) extremities of the bridging 1,4-Diethynilbenzene (DEB) with the azide-terminated APA ligands (N3) of the AuNPs and the azide-terminated 4-azido-benzyl-phosphonic acid ligands (N3) of the QDs. As a result, AuNPs and QDs may connect with each other via the formation of two triazole groups separated by a benzene ring.</figcaption></figure>
azide-alkyne CuAAC reaction, as schemed in Fig.2a. A second route of a non-selective click
reaction was also studied. In this case, azide-tagged AuNPs and azide-tagged QDs were
assembled via a bridging bis-alkyne, here the 1,4-Diethynilbenzene (DEB). The azide-alkyne
CuAAC reaction could thus take place on both sides of the DEB, either with AuNPs or
with QDs, thereby leading to different possible bonds, namely AuNP-AuNP, or QD-QD or
AuNP-QD, as shown in Fig.2b. This click reaction offers the advantage of forming rigid co-
valent bonds and permitted here to use shorter ligands, which are more favorable for electron
delocalization within the c-HS. However, the colloidal state of the c-HS is more complex to
analyse since different types of objects are formed. In this paper, we show that combined
confocal DLS and FCS enabled the unambiguous validation of the occurrence of the click
process and enabled to clearly distinguish it from the case of a mixture of non-connected
particles. Moreover, the key stages of the binding kinetics were accessed by identifying dif-
ferent situations where (i) the NPs and the QDs remain unconnected, (ii) hybrid QD-NP
systems are formed and co-exist with remaining unconnected particles and (iii) hybrid sys-
tems are predominantly formed. The nature of the formed hybrid systems was identified
using hydrodynamic bead-models.

Confocal DLS and FCS Theoretical Background

Normalized Auto-Correlation Functions in DLS and FCS

DLS and FCS belong to the class of photon correlation spectroscopy experiments by which
the translational diffusion coefficients *D* of colloidal NPs can be measured. The general
underlying principle is that the measured intensities, Rayleigh scattering for DLS and flu-
orescence for FCS, present temporal fluctuations due to the motion of the particles, which
depends on their size through *D*. These fluctuations are statistically analyzed to characterize
the dynamics of the system, by deriving the normalized intensity auto-correlation function
(ACF):

$$G(\tau) = \frac{\langle I(t)I(t + \tau) \rangle}{\langle I(t) \rangle^2},$$

where $\langle ... \rangle = \lim_{T \to \infty} \frac{1}{T} \int_0^T ... dt$ is an integration over the acquisition time.

Considering freely diffusing spherical NPs, i.e non-interacting particles driven by a Brownian motion, and a confocal volume where the laser intensity distribution can be described by a 3D-Gaussian law $I(x, y, z) = I_0 e^{-2(x^2+y^2)/r_0^2-2z^2/z_0^2}$, the DLS ACF writes as:³³

$$G(\tau) - 1 = \beta e^{-2\tau/\tau_c} + \frac{c^2}{\langle N \rangle} \frac{1}{(1 + \tau/\tau_D)(1 + \tau/w^2\tau_D)^{1/2}} \quad (1)$$

The first term of Eq.(1) is due to the interferences of the electric fields scattered by the different NPs.³⁴ This term decays with a characteristic time $\tau_c = 1/2q^2D$, where $q = 4\pi n \sin(\theta/2)/\lambda$ is the scattering vector, $\theta$ being the scattering angle, $n$ the refractive index of the solvent, $\lambda$ the laser wavelength, and $D$ is the translational diffusion coefficient of the NPs. $\beta$ is an adjustable parameter³⁴ related to the experimental setup, with $0 \le \beta \le 1$. The second term of Eq.(1) is due to the variation of the local concentration in the observation volume.³⁵ It decays with a characteristic time $\tau_D = r_0^2/4D$ where $r_0$ is the waist of the focused laser. Finally, $\langle N \rangle$ is the average number of NPs in the observation volume, $c$ is the ratio of the signal from the NP to the total measured intensity³⁶ and $w = z_0/r_0$.

In standard DLS, the interference term dominates as the probing volume, typically a few mm³, samples a large number of NPs and the term $1/\langle N \rangle$ tends to zero. Only in rare situations of extremely diluted samples can the second term become significant,³³,³⁵,³⁷ however the signal to noise ratio is then noticeably deteriorated and the measurement times are long.

Regarding FCS experiments, only the variation of the local concentration gives rise to intensity fluctuations as fluorescence is not a coherent process. The expression of the ACF
is then given by Eq. (1) without the interference term i.e according to:

$$G(\tau) - 1 = \frac{c^2}{\langle N \rangle} \frac{1}{(1 + \tau/\tau_D)(1 + \tau/(w^2\tau_D)^{1/2})} \quad (2)$$

## Hydrodynamic diameter determination

In the present study, and as it is very often the case, the translational diffusion coefficient $D$ is experimentally determined from the measured characteristic times, to access the hydrodynamic diameter $d_H$ of the NPs. When the latter are spherical, this is easily realized by applying the Stokes-Einstein relationship:³⁸

$$d_H = \frac{k_B T}{3\pi\eta D},$$

where $T$ and $\eta$ are the temperature and the viscosity of the solvent respectively, and $k_B$ is the Boltzmann constant. The hydrodynamic diameter corresponds to a slightly increased value of the physical diameter, due to the molecules surrounding the particles in solution.

Hereafter, the assumption of sphericity will be perfectly justified when dealing with the primary AuNPs and QDs. However, the study of aggregates or hybrid objects requires the use of more realistic hydrodynamic models considering chain-like³⁹,⁴⁰ or fractal⁴¹ aggregates of spherical particles. In these models, the diffusion coefficient of an aggregate $D_A = \frac{k_B T}{3\pi\eta d_A}$, where $d_A$ is its apparent hydrodynamic diameter, is defined as:

$$D_A = \alpha D_{eq},$$

where $D_{eq} = \frac{k_B T}{3\pi\eta d_{eq}}$ is the diffusion coefficient of a sphere of a volume equivalent to that of the aggregate or the hybrid system under consideration, $d_{eq}$ being its equivalent diameter.

The value of $\alpha$ is accessed numerically and depends on the number of primary particles and on the fractal dimension of the aggregate.

In the present case, we used the $\alpha$ values of the chain-like (or bead) model of linear assemblies,
a model that was shown to be relevant in the context of chemical bonding between spherical particles. 42 Considering an aggregate containing $n_s$ identical bead, its equivalent diameter is $d_{eq}(n_s) = d_0\sqrt[3]{n_s}$, where $d_0$ is the diameter of the individual beads, and the apparent diameter writes as:

$$d_A = \frac{d_{eq}(n_s)}{\alpha(n_s)}, \qquad (3)$$

where the values of $\alpha(n_s)$ are taken from Ref. 39,40 Considering now an hybrid system still containing $n_s$ primary spheres, of which $n$ are of diameter $d_0$ and $(n_s - n)$ are of diameter $d_1$, Eq.3 is applied with an equivalent diameter $d_{eq}(n_s, n) = d_0\sqrt[3]{n + (n_s - n)\left(\frac{d_1}{d_0}\right)^3}$. It is worth noting that in reality, the values of $\alpha(n_s)$ depend on whether the assemblies contain only identical spheres or not. However, in the latter case, the values of $\alpha(n_s)$ were not found in the literature, except for asymmetric dimers. 40 Yet, the difference between symmetric and asymmetric dimers leads to differences in the determination of $d_A$ which are smaller than the accuracy of the experiments, thus justifying our approximation.

# Experimental section

## Confocal DLS and FCS optical set-up.

The confocal DLS and FCS experiments were carried out on a home-made optical setup shown in Fig.1a. The colloidal suspensions are illuminated with a tightly focused CW laser beam at $\lambda = 532$ nm, using a $\times$60 water immersion objective with a $NA = 1.2$. The light emitted by the NPs is detected in a backscattering configuration by the same objective as that used for the illumination. A 50 $\mu$m-diameter pinhole, placed in the image plane of the focused beam and formed by a $f = 150$ mm lens tube, ensures the spatial filtering of the laser and reduces the sampling volume. After filtering, a $f = 30$ mm lens focuses the signal at the entrance of the monochromator. For DLS measurements, the monochromator selects
the signal at $\lambda = 532$ nm whereas for FCS measurements it selects the signal at $\lambda = 615$ nm, where the fluorescence signal of the QDs is maximal (Fig. 7-SI). For FCS, a notch filter of optical density 6 at $\lambda=532$ nm is also added to reject any residual scattered light. Moreover, test experiments were made to make sure that no luminescence from the AuNPs influences the FCS ACFs (Fig.11-SI) since one-photon luminescence correlation spectroscopy was reported$^{43}$ in equivalent experimental configuration, although for larger AuNPs and spectrally integrating the signal. For both DLS and FCS, the light is focused by a lens doublet on a 180 µm-avalanche photodiode (APD). Each photon detected by the APD creates a TTL signal and the successive TTL are measured by the correlator, a National Instrument 6602 card, with sampling times ranging for 1 µs to 1ms, to access the rapid temporal fluctuations of the intensities. The ACF are then computed from the recorded intensities $I(t)$.

Typical measurements consist in acquiring sequentially, either the scattered intensities for DLS or the fluorescence intensities for FCS, during 10 s and to reproduce the measurement 5-10 times. The normalized ACFs are calculated through the inverse Fourier transform of the spectral density $S(f) = \lim_{T \to \infty} \frac{1}{T} |\mathcal{I}(f)|^2$, where $\mathcal{I}(f)$ is the Fourier transform of the signal $I(t)$. As the fitting of the ACFs and the calculation of the hydrodynamic diameters of the particles depend on the size of the confocal volume (Eq. 1), the latter was characterized by calibration measurements$^{44}$ (see SI) that gave $r_0=220 \pm 20$ nm, $z_0=3.8 \pm 0.5$ µm and $w \sim 17$. Uncertainties in the size of the confocal volume lead to errors of $\sim 20\%$ in the particle size determination. In contrast, errors due to the spreading of the diffusion vector are minimized in our geometry and do not exceed 2%.$^{45}$

## Synthesis of the Gold Nanoparticle-CdSe/ZnS quantum dot covalent hybrid systems.

As stated in the introduction, two syntheses were used to form c-HS: (i) a selective route where alkyne-tagged AuNPs were bound to azide-tagged QDs via an azide-alkyne CuAAC
reaction, and (ii) a non-selective route where azide-tagged AuNPs and azide-tagged QDs were linked via an alkyne-terminated bridging molecule. Primary AuNPs and QDs in aqueous solutions were first prepared independently one from the other. Both type of particles were then functionalized with the desired clickable ligands and then mixed together with the click reaction reagents. Details of the different syntheses steps and characterizations of the obtained primary AuNPs and QDs are detailed in the Supporting Information. The different primary and functionalized AuNPs were characterized by SEM and standard DLS (Figs. 1-SI and 3-SI), and by UV-visible spectroscopy (Figs. 2-SI and 4-SI). The QDs were characterized by TEM and UV-visible spectroscopy (Figs. 6-SI and 7-SI).

For both types of click reactions, blanks (called hereafter reference samples) were also made using the same synthesis protocols as for the samples (called hereafter clicked samples) but using QDs bare of clickable ligands for the selective click and without DEB for the non-selective click. In both cases, the reference samples were systematically characterized in parallel to the clicked samples to ensure that the observed clicking process is actually due to a CuAAC reaction and not to colloidal instabilities due to the chemical environment.

# Results and Discussion

## Qualitative confirmation of the click reaction.

Figs. 3a and 3c show that the DLS ACFs exhibit the two characteristic times $\tau_c$ and $\tau_D$, expected from Eq. 1, while the FCS ACFs (Figs. 3b and 3d) only decay with $\tau_D$. Upon clicking, anisotropic c-HS are formed such that a rotational time decay may also appear at short times and coexist with the scattering term. This is one of the reasons, the others being detailed in the quantitative analyses section, why it is more reliable to study the click reaction through the behavior of the diffusion time $\tau_D$. For both the selective and the non-selective click reactions, the formation of AuNP-QD c-HS was qualitatively confirmed by observing an increase in the diffusion times $\tau_D$, in both DLS and FCS measurements, that
<figure><img src="image_4.png" /><figcaption>Figure 3: Qualitative observation of the click reaction with clickable ligands (a,b) and of the absence of reaction with non-clickable ligands (c,d). Experimental (dots) and calculated (lines) ACFs were obtained (a) in DLS on the primary AuNPs (gray) and on the clicked sample (blue) and (b) in FCS on the primary QDs (gray) and on the clicked sample (red). The longer characteristic time-decay observed on the clicked sample highlights a particle assembly process. Conversely, no changes are observed (c) in the DLS characteristic time-decay between the reference sample (blue) and the primary AuNPs (gray) nor (d) in the FCS characteristic time-decay between the reference sample (red) and the primary QDs (gray). All ACFs were normalized to one for an easier comparison.</figcaption></figure>
signals the formation of larger objects, under clicking conditions, that contain both AuNPs
and QDs. Such a behavior is presented in Fig.3a and b, in the case of the selective click
reaction. Furthermore, the occurrence of the clicking process is supported by experiments
performed on the reference sample, in which both DLS and FCS ACFs remain unchanged
compared with those of the primary alkyne-functionalized AuNPs (Fig.3c) and the primary
QDs (Fig.3d). In this case, the AuNPs and the QDs stay unbound and we can thus con-
fidently conclude that the NP assemblies observed in the click sample are c-HS structures
resulting from the intended click reaction rather than from colloidal instabilities induced by
the reaction.

Accessing the binding kinetics of the selective click reaction.

In the case of the selective click reaction, the reaction is slow enough to monitor its progres-
sion. DLS and FCS experiments were performed at different time steps over a 24-hour period,
permitting to follow the binding kinetics and to identify three different key-stages of the re-
action. The latter are indeed characterized by specific DLS and FCS signatures presented
in Fig.4. Before the reaction starts (Fig.4a), DLS and FCS experiments differ significantly
and present characteristic times corresponding to the diffusion of primary AuNPs and QDs,
respectively. In this case, the solution is a mixture of unconnected AuNPs and QDs. As the
click reaction begins (Fig.4b), both DLS and FCS ACFs shift to longer characteristic times,
indicating the formation of larger objects involving both AuNPs and QDs. However, the
DLS and FCS ACFs remain distinct one from the other. This signals a partially completed
click reaction, where free AuNPs and free QDs coexist with newly formed hybrid systems,
resulting in different averaged behavior in DLS (probing AuNPs and hybrid systems) and
in FCS (probing QDs and hybrid systems). Finally, when the click reaction is completed
(Fig.4c), the objects in solution are hybrid systems. Both AuNPs and QDs have the same
motion and therefore the same diffusion coefficient. In combined DLS and FCS, this results
in the same diffusion time since the confocal volume is the same in both experiments, which
permits the confirmation of the success of the click reaction.

Quantitative sizing of the c-HS formed by selective click reaction.

The quantitative analysis of the different stages of the reaction requires to access and anal-
yse the values of the characteristic times of the ACFs. In FCS, the data analysis consists
in fitting the experimental ACFs according to Eq. 2, by adjusting the value of the charac-
teristic time τD from which the diffusion coefficient D, then the diameter of the particles,
can be calculated. Similarly, the DLS data analysis involves fitting the experimental ACFs
according to Eq. 1 by adjusting both τc and τD. If both characteristic times should, in
principle, lead to the same value of the diffusion coefficient D, only the value of τD is used
in our analyses. There are several reasons for that: (i) as previously mentioned, the value of
τc may be altered by a rotational time decay which is not accounted for in Eq. 1, (ii) at the
studied low concentrations, single objects may cross the confocal volume without creating
scattering fluctuations and are thus not taken into account in τc, and (iii) by using the value
of τD, comparison to FCS is straightforward as it is the same physical effect that is probed.

For the primary particles, for which the Stokes-Einstein formula is valid, the hydrody-
namic diameters of the particles are obtained from τD via the relationship dH = 4(kB/T/η)τD/3πr⁴₀.
When assemblies are concerned, the previous relationship is also used but to access the ap-
parent hydrodynamic diameter dA, from which the nature of the formed object will be
determined (see Theoretical Background Section).

The applied procedure is detailed in the case of Fig.4, where the experiments were con-
ducted at a room temperature T = 22°C for which η(22°C) = 0.95 mPa.s and therefore
dH,A/τD = 37 ± 7 nm/ms in FCS and in DLS. We point out that the quantitative analysis
presented here to identify the different stages of the reaction is general and can be applied
to characterize any colloidal state of any selective click reaction. The results obtained in the
present case are summarized in Table 1.

In Fig.4a, the DLS ACF was fitted with $\tau_D=0.74$ ms yielding $d_H=27\pm5$ nm for the AuNPs, in perfect agreement with the size of the primary AuNPs determined by standard DLS (Fig. 1-SI). The FCS ACF was fitted with $\tau_D=0.45$ ms giving $d_H=16.8\pm3$ nm, in a correct agreement with functionalized 10-nm QDs in solution (Fig. 6-SI). However, a slight colloidal instability of the QDs cannot be ruled out. Overall, these values confirm that before the click reaction starts, the AuNPs and the QDs are mixed together in the same solution, each maintaining its original colloidal state (Table 1).

<figure><img src="image_5.png" /><figcaption>Figure 4: Example of a selective click reaction observed by confocal DLS and FCS. (a) before the reaction starts, when AuNP and QDs are not bound, (b) at a partial clicking stage when small c-HS start to appear, and (c) when the reaction is completed and large c-HS are formed. The particles and formed c-HS are schematically represented by yellow and orange spheres representing the AuNPs and QDs respectively.</figcaption></figure>

In Fig.4b, both DLS and FCS ACFs present increased characteristic times as compared
with that of the primary particles, but the ACFs differ one from the other. This implies that c-HS have been formed but that DLS and FCS experiments do not sample exactly the same particles. The DLS ACF was fitted with $\tau_D=0.95$ ms yielding $d_A= 35 \pm 6$ nm. Since our primary AuNPs have a diameter $d_0=27$ nm, the ratio $d_A/d_0=1.3$ is small and indicates that the probed objects contain only a few particles (Table1-SI). In the case of dimers, $\alpha(2)=0.907$ (Table1-SI) and the hydrodynamic diameter of AuNP-QD dimers is $d_A = \sqrt[3]{d_0^3 + d_1^3}/0.907=32$ nm, with $d_1=16.8$ nm, the value of the primary QDs. If QD-AuNP-QD trimers are considered, $\alpha=0.83$ and $d_A=37$ nm. Hence, the experimental characteristic time measured in DLS is in favor of the formation of dimers and trimers c-HS. In parallel, the FCS ACF was fitted with $\tau_D=0.65$ ms yielding $d_A= 24 \pm 4$ nm which is an intermediate value between that of dimers and trimers c-HS and unbound QDs. We note that the existence of unbound QDs can be easily understood in the present case since the formation of small c-HS only implies the binding one or two QDs/AuNP which is much less than the initial QD:AuNP concentration ratio of 25:1 (SI). The combination of the DLS and FCS results thus permits to confidently state that the experiments shown in Fig.4b correspond to the very initial stage of the click reaction, where dimers and trimers c-HS have successfully been formed and coexist with unbound particles (Table 1).

In Fig.4c, both DLS and FCS ACFs were fitted with $\tau_D=2$ ms yielding $d_A=75 \pm 15$ nm. The equality of the diffusion times in both experiments implies that the latter probe the same sample i.e. that the colloidal solution is essentially made of c-HS. However, the determination of the nature of the formed c-HS from the value of $d_A$ is not straightforward since $d_A$ depends on two unknown variables, $n_s$ the total number of particles in the c-HS and $n$ the number of AuNPs (see Theoretical section). A fair estimation of the nature of the formed c-HS can however be accessed by defining a range of possible values of $n_s$ considering the two limit cases (though impossible) of pure AuNP assemblies or pure QD assemblies. To this end, the ratio $d_A/d_{0,1}$ is calculated and $n_s$ is given by the values $\sqrt[3]{n_s}/\alpha(n_s)$ found in the literature. The latter values are reported in Table1-SI. For a hypothetic AuNP assemblies,
$d_A/d_0=2.8$ and corresponds to a chain of $n_s \sim 6-7$ AuNPs. For QD assemblies, $d_A/d_1=4.4$, corresponding to a chain of $n_s \sim 14$ QDs. The c-HS is thus formed of 6 to 14 particles. Within this range, $\alpha(n_s)$ varies slowly and is worth $\sim 0.6 \pm 0.1$. These values yield an equivalent diameter $d_{eq} = \alpha(n_s)d_A = 45 \pm 15$ nm, which is consistent with c-HS containing 2-4 AuNPs and 6-10 QDs (Table 1).

We highlight that the mean $\tau_D=2$ ms of the ACF comes from a series of several ACFs. Each of these can also be fitted individually to estimate the spreading of the diffusion time and thus the size heterogeneity of the formed objects. In the present cases, $\tau_D$ ranging from 1 to 3.5 ms (i.e. $d_A = 38$ to 110 nm) were obtained. This indicated an important heterogeneity in the size of the formed objects. SEM images were realized to validate our approach and such types of c-HS were indeed observed (Fig. 8-SI). We also note that the number of QDs per AuNP in the formed c-HS stays smaller than the initial concentration ratio of 25:1 QDs:AuNP. Therefore, unconnected QDs are still in solution. However, here, their presence is not detected anymore by the FCS measurement, and this occurs despite the possible quenching of the connected QDs. This is due to the fact that, in correlation spectroscopy, the amplitude and frequency of the temporal fluctuations are more relevant than the absolute value of the intensity of the signal. Hence the large and diluted c-HS generate important fluctuations in the measured fluorescence that overshadow the fluctuations caused by smaller and more concentrated QDs. One can also observe that some ACFs exhibit additional time-decays at short characteristic times (5-50 µs). Such an effect is usually attributed to the rotation, within the observation volume, of anisotropic shaped particles and can also be quantified through hydrodynamic models$^{40,42}$. Such analyses could not however be conducted in the present paper due to the possible blinking of the QDs that may also create time-decays within this time range.$^{46}$
<table><caption>Table 1: Summary of the measured hydrodynamic diameters for the selective click reaction</caption><thead><tr><th>Sample</th><th>DLS d<sub>H</sub><br>(nm)</th><th>FCS d<sub>H</sub><br>(nm)</th><th>c-HS</th></tr></thead><tbody><tr><td>No Click</td><td>27 ± 5</td><td>17 ± 3</td><td>-</td></tr><tr><td>Partial Click</td><td>35 ± 6</td><td>24 ± 4</td><td>dimers-trimers</td></tr><tr><td>Complete Click</td><td>75 ± 15</td><td>75 ± 15</td><td>2-4 AuNPs and 6-10 QDs</td></tr></tbody></table>

## Case of the non-selective click reaction.

In the case of the non-selective click reaction, DLS and FCS ACFs are necessarily different, even if the reaction is completed, since DLS will average both Au-QD c-HS and Au-Au clicked objects, whereas FCS averages Au-QD c-HS and QD-QD clicked objects.

The data analysis described above in the case of the selective reaction remains valid; however, all possible types of assemblies must be taken into consideration. The results obtained in the present case are summarized in Table 2. Fig. 5 shows DLS and FCS ACFs measured on a reference sample and on a clicked sample. These experiments were conducted at room temperature ($T = 28^{\circ}C$) for which $\eta(T) = 0.83$ mP.s and in a solvent of water:ethanol at 50:50 in volume. Such a solvent has a significantly higher viscosity than pure water or pure ethanol.⁴⁷ In the present case, the viscosity was determined by performing confocal DLS experiments on size-calibrated polystyrene beads in such a mixture (Fig. 12-SI) and was found to be 2.7±0.1 times larger than that of water, in good agreement with Ref. ⁴⁷ This leads to the relationship $d_H/\tau_D = 16.3$ nm/ms.

For the reference sample, the DLS and FCS ACFs were fitted with $\tau_D = 2$ms and $\tau_D = 0.75$ ms, respectively, yielding $d_H = 32 \pm 6$nm for the AuNPs and $d_H = 12 \pm 2$ nm for the QDs. The value of the hydrodynamic diameter of the AuNPs is in agreement with the size of the primary citrate-capped AuNPs obtained by standard DLS (Fig. 3-SI), slightly increased due to the clickable ligands. In the same way, the determined value of the hydrodynamic diameter of the QDs corresponds to isolated object, which confirms the absence of a click reaction. The values of the hydrodynamic diameter of the AuNPs and of the QDs
will be used as those of the primary particles in the quantitative analysis of the clicked sample.
In the latter, the ACFs were fitted with $\tau_D = 2.5$ ms in DLS, yielding $d_A = 40 \pm 7$ nm and
$\tau_D = 1.8$ ms in FCS, yielding $d_A = 29 \pm 5$ nm. From the DLS experiments, and consider-
ing AuNP assemblies, we determine that for the formed c-HS containing AuNPs are small
since $d_A/d_0= 1.25$, which corresponds to $n_s \sim 2$. The calculated hydrodynamic diameters
of AuNP-AuNP and AuNP-QD dimers are $d_A = 43$ nm and $d_A = 32$ nm respectively and
we note that the experimental value is in perfect agreement with an averaged contribution
of both types of possible formed dimers (Table 2). Analogously, FCS measurements yield
a value $d_A = 29$ nm, which is consistent with the average contributions of the AuNP-QD
dimers ($d_A = 35$ nm) and of QD-QD dimers ($d_A = 15$ nm). Since the AuNPs are much larger
than the QDs, their motion slightly differs depending on whether they are bound to one or
two QDs. The formation of QD-AuNP-QD trimers can thus not be excluded. In this click
reaction, no larger objects were observed. The reason why this non-selective reaction yields
much smaller c-Hs compared to the selective reaction can be attributed to the fact that it
requires the formation of more azide-alkyne CuAAC reactions. Indeed, the total number
of these reactions can be assumed to be limited by the Au:CuSO₄/NaAsc concentration ra-
tio. Although this ratio is twice larger in the selective reaction, in the none-selective case,
three different types of bonding occur (Au-Au, QD-QD, and QD-Au), and two azide-alkyne
CuAAC reactions are needed per bond due to the bifunctional DEB bridging molecule. This
results in a sixfold increase in the number of triazole cycles between the two types of reactions
for the formation of a same Au-QD c-HS. Other factors, such as the size of the nanoparticles
or ligand coverage, likely also play a role. Finally, we note that the ACFs presented in Fig.5,
do not perfectly tend to zero at long lag times, due to the solvent viscosity which makes the
diffusion times quite large, despite small diffusing objects. It was shown that in such situa-
tions, the fitting of the ACFs could lead to underestimated values of the diffusion times.⁴⁸ In
the present case, however, the diffusion times determined for the unconnected AuNPs and
QDs in the reference sample, led to particles diameters in perfect agreement with their size
expected from standard DLS, SEM and TEM images, and that for both types of particles
(Figs. 3-SI and 6-SI). This permits to ensure that the diffusion times determined for the click
sample also give access to reliable sizes of the formed c-HS. Moreover, the results obtained
by combined confocal DLS and FCS are confirmed by SEM images (Fig. 8-SI) showing the
presence of particles assemblies with only a few particles in the clicked sample. The different
types of binding (between AuNP only, between QDs only, and c-HS) were also observed.
<figure><img src="image_6.png" /><figcaption>Figure 5: Experimental (dots) and calculated (lines) ACFs measured (a) by DLS and (b) by FCS on the sample clicked with the non-selective reaction, and (c) by DLS and (d) by FCS on the reference sample. In both DLS and FCS, an increase of the diffusion time $τ_D$ with respect to that of the primary AuNPs and QDs is observed in the clicked sample. In contrast, no click reaction occurred in the reference sample where the diffusion times are the same as that of the isolated primary AuNPs and of the QDs. The particles and formed dimers are schematically represented by yellow and orange spheres that represent the AuNPs and QDs respectively.</figcaption></figure>
<table><caption>Table 2: Summary of the measured hydrodynamic diameters for the non-selective click reaction</caption><thead><tr><th></th><th>Dimer</th><th>d<sub>A</sub> calc</th><th>d<sub>A</sub> exp</th></tr></thead><tbody><tr><td rowspan="2">DLS</td><td>AuNP-AuNP</td><td>45 nm</td><td rowspan="2">40 ± 7 nm</td></tr><tr><td>AuNP-QD</td><td>36 nm</td></tr><tr><td rowspan="2">FCS</td><td>QD-QD</td><td>17 nm</td><td rowspan="2">29 ± 5 nm</td></tr><tr><td>AuNP-QD</td><td>36 nm</td></tr></tbody></table>

Conclusion

Combined confocal DLS and FCS experiments were developed to perform ensemble and *in-situ*, both sensitive to AuNPs and to fluorescent species, whose Rayleigh scattering is very small compared to that of the metal particle. Hybrid systems consisting of colloidal CdSe-ZnS QDs connected to AuNPs were synthesized by CuAAC click reactions. Two different reactions were developed: a selective reaction, where only AuNP-QD bonds can form, and a non-selective reaction, where bonding can occur between any type of particles. Combined confocal DLS and FCS experiments were conducted to probe the hydrodynamic motion of the AuNPs (by DLS) and that of the QDs (by FCS). In such an approach, AuNP-QD hybrid systems exhibit the same DLS and FCS diffusion times, whereas unconnected AuNPs and QDs exhibit different DLS and FCS diffusion times. The success of the click reaction was clearly observed and distinguished from the case of colloidal solutions of unconnected AuNPs and QDs. Beyond the evidence of the click reaction, we demonstrated that this approach enabled the identification of key stages in the selective click reaction: (i) the non-connected stage, where AuNPs and QDs present different motions, (ii) the early stage of the clicking process, where AuNP-QD dimers and trimers are formed while most of the QDs remain free in solution, and (iii) the final stage of the reaction, where large, and heterogenous AuNP-QD aggregates are formed. We also show that the more complex scenario of the non-selective click reaction can also be characterized by such an approach, by accounting for the different
types of assemblies that can occur. We believe that combining confocal DLS and FCS to
obtain such quantitative information is highly relevant for a deeper understanding of the
physicochemical properties of hybrid systems and the characterization of click reactions.

Supporting Information. Syntheses of the different samples. Standard DLD and electronic microscopy characterization of the samples. Confocal volume calibration. Validation of the absence of one-photon luminescence of the Au NPs. Viscosity determination of the water:ethanol solvent. Table of the $\alpha(n_s)$ values.

Acknowledgement

This work was supported by the Agence Nationale de la Recherche (ANR) through the ANR-
18-CE93-0004 project and the Swiss National Science Foundation (project 200021L-182078).

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# Supporting Information Available

## Preparation and characterization of the gold nanoparticles (AuNPs) with clickable ligands

### Chemicals.

Sodium hydroxide (NaOH pellets, > 97%), ethanol, sodium citrate tribasic dihydrate (Na3Cit, ACS reagent > 99%), hydrogen tetrachloroaurate trihydrate (HAuCl4, 3H2O > 99%), sodium-L-ascorbate (> 98%), amino-PEG8-acid (> 90%), 3-Azido-1-propanamine (> 95%), 1,4-Diethynilbenzene (C10H6, > 96%), were purchased from Sigma-Aldrich. Copper sulfate pentahydrate (> 98%) was purchased from Alfa Aesar. Propargyl-PEG9-amine (> 95%) was purchased from BroadPharm. All reactants were used without any further purification.

**Filters.** Minisart NML syringe filters with surfactant-free cellulose acetate (SFCA) membranes and pore sizes of 0.45 µm were purchased from Sartorius. Vivaspin 2 concentrators with 100 kDa MWCO pore size polyethersulfone (PES) membranes were purchased from Sigma.

### Citrate-capped Gold Nanoparticles.

Spherical citrate-capped gold nanoparticles (AuNPs) were first prepared following the classical method of reduction of tetrachloroauric acid (HAuCl4) with trisodium citrate (Na3Cit) in 100 mL of water at 100° C.¹ The ratio of Na3Cit/HAuCl4 = 2.4 was kept constant while the initial quantity of HAuCl4 was 0.32 mmol for the AuNPs used in the non-selective click reaction and 0.160 mmol for the AuNPs used in the selective click reaction. After boiling during 10 min, the colloids were cooled down to room temperature and filtered with the 0.45 µm filter.

The concentration of the AuNPs was roughly estimated from the initial mass of Au used for the synthesis, and the averaged size of the formed AuNPs (Figs.1-SI and 3-SI). This yielded to an upper limit AuNP concentration of 4nM for the non-selective reaction and of 8 nM for
the selective reaction.

## Alkyne-tagged AuNPs.

The functionalization of the citrate-capped AuNPs with alkyne-terminated ligands was done accordingly to Marti el al.² The ligands solution consist in a 1:1 molar equivalent mixture of short amino-PEG-alkyne and amino-PEG-COOH chains, the presence of terminal carboxylic acids being intended to ensure the stabilization of the surface charge density of the metallic nanoparticles. In practice, 5 mL of citrate-capped AuNPs were mixed with a 15µL/15µL aqueous solution of propargyl-PEG₉-amine/amino-PEG₈-acid at 0.125 mM together with 10 µL of aqueous NaOH at 10 mM. The mixture was stirred overnight. The alkyne-tagged AuNPs suspensions obtained were used without any other purification steps, except for a filtering at 0.45 µm before use.

## Azide-tagged AuNPs.

Citrate-capped AuNPs were functionalized with 3-azido-1-propanamine (APA) using a process based on a ligand exchange developed by Hua et al.³ Two mL of AuNPs were mixed with 60 µL of a 2 mM APA solution prepared in a 2:1 in volume ethanol:water solution. The mixture was immediately sonicated during 2 minutes and the azide-tagged AuNPs were obtained after 1 hour of reaction. The as-obtained azide-tagged AuNP were used without any other purification steps, except for a filtering at 0.45 µm before use, in order to minimize the possible formation of spontaneous aggregates.

## Characterization of the AuNPs in the case of the selective click reaction.

Field Emission Scanning Electron Microscopy (FESEM) images of the initial citrate-capped AuNPs and of the functionalized AuNPs were recorded using a Zeiss ultra+ scanning electron microscope, using a 3kV voltage and a working distance of 3 mm. The observations were done on 20 µL of the colloidal suspensions dried on a doped silicon wafer. Prior to the
deposition, the suspensions were careful washed using Vivaspin 2 (100 kDa MWCO) concentrators to minimize the presence of salts or impurity (buffer, ascorbate, sulfate..) by three successive centrifugations at 3000 rpm during 3 min and re-dispersed in pure water. Finally, the final washed solution was diluted by a factor of 100 to reduce the issues of spontaneous aggregation of the particles during the drying process.

In parallel, standard Dynamic Light Scattering (DLS) measurements were carried out on a commercial Cordouan Nanokin instrument operating with a red laser at 635 nm and a scattering angle of 170°. Data fitting was performed with a cumulant approach and considering spherical nanoparticles.

The synthesis of the AuNPs lead to fairly mono-dispersed spherical NPs of mean hydrodynamic $d_H$= 18 nm (Figs.1-SI(A) and (B)). Upon functionalization, the mean hydrodynamic diameter increased to $d_H$= 27 nm, which is coherent with the use of long PEG chains ligands, while to NPs essentially remained isolated (Fig.1-SI(C) and (D)).
<figure><img src="image_7.png" /><figcaption>Figure 1-SI: FESEM images of the AuNPs used for the selective reaction (A) after their synthesis (citrate-capped) and (C) after their functionalization with PEG-Alkyne. (B) size distribution of the hydrodynamic diameters of the citrate-capped AuNPs and (D) of the functionalized AuNPs obtained by standard DLS on the imaged particles when they are in an aqueous solution.</figcaption></figure>

These results are supported by the UV-visible extinction spectra that exhibit the expected electrostatic plasmonic band of small AuNPs around $\lambda = 528$ nm. After functionalization, the colloidal stability is maintained (Fig.2-SI).
<figure><img src="image_8.png" /><figcaption>Figure 2-SI: UV-visible extinction spectra of the AuNPs used for the selective reaction after their synthesis (black line) and after their functionalization with PEG-Alkyne (red line).</figcaption></figure>

## Characterization of the AuNPs in the case of the non-selective click reaction.

The same experimental procedure as that described in the previous section was applied. After the synthesis of the NPs, spherical AuNPs are formed as shown on the SEM image, together with little aggregates formed here and there (Fig. 3-SI(A)). Their existence is supported by a rather large size distribution of the hydrodynamic diameter, centered at $d_H$= 28 nm (Fig. 3-SI(B)). Upon functionalization, the SEM images do not show much differences with that of the primary AuNPs (Fig. 3-SI(C)), while the mean diameter measured in DLS increases to $d_H$= 36 nm (Fig. 3-SI(D)). In the present situation, this increase may not be attributed to the length of the ligands but is interpreted in terms of a slight colloidal instability that produces larger objects in solution.
<figure><img src="image_9.png" /><figcaption>Figure 3-SI: FESEM images of the AuNPs used for the non-selective reaction (A) after their synthesis (citrate-capped) and (C) after their functionalization with APA. (B) Size distribution of the hydrodynamic diameters of the citrate-capped AuNPs and of the functionalized AuNPs (D) obtained by standard DLS on the imaged particles when they are in an aqueous solution.</figcaption></figure>

These results are here again supported by the extinction spectra shown in (Fig.4-SI) where the slight colloidal instability of the functionalized NPs suspension is attested the decrease of the plasmonic band of the isolated NPs and a signal around λ=650 nm.
<figure><img src="image_10.png" /><figcaption>Figure 4-SI: UV-visible extinction spectra of the AuNPs used for the non-selective reaction after their synthesis (black line) and after their functionalization with APA (red line).</figcaption></figure>

# Preparation and characterization of the CdSe/ZnS quantum dots (QDs) with clickable ligands

## Chemicals.

The core-shell CdSe/ZnS QDs, with a core of 4 nm and a total diameter of 10 nm, suspended in toluene and coated with octadecylamine ligands were purchased from NN-Labs Laboratories. D-histidine, sodium hydroxide, chloroform, methanol, ethanol, sodium tetraborate decahydrate (ACS reagent > 99%), were purchased from Sigma-Aldrich. 4-Azidobenzyl phosphonic acid was synthesized following the procedure reported by Schönweiz et al⁴.

## Filters.

30 kDa centrifugal filters (milipore Amicon) were purchased from Sigma.
Phase transfer of CdSe/ZnS QDs from toluene to water and functionalization.

To render the core-shell CdSe/ZnS QDs suitable for the CuAAC reactions, a phase transfer
from their native toluene solvent to an aqueous solution was required, prior to their func-
tionalization with clickable ligands. The procedure is schemed hereafter (Fig. 5-SI). Ligand
exchange from octadecylamine to histidine ligands was first performed following a slightly
modified procedure reported by Zylstra et al.⁵ First, 500 µL of core-shell CdSe/ZnS QDs
in toluene was dried using a vacuum pump, then redispersed in chloroform (CHCl₃) as an
intermediate solvent. Next, 500 µL of a solution 3:1 methanol:H₂O containing 0.1 M his-
tidine and 0.25 M NaOH was added to the QDs suspension. After mixing and shaking, a
phase separation was observed, with the QDs moving from the organic phase to the aqueous
phase. Following decantation of the clear organic phase, 300 µL of a 1mM histidine and 2.5
mM NaOH solution in Milli-Q water was added to the aqueous phase containing the QDs.
This aqueous solution was washed 4 times with chloroform. Excess histidine was removed
via filtration using a 30 kDa centrifugal filter (Millipore Amicon). Finally, the QDs were
resuspended in water.

<figure><img src="image_11.png" /><figcaption>Figure 5-SI: Phase transfer of the QDs from Toluene to water by ligand exchange using water soluble histidine ligands, and functionalization with clickable azide ligands to obtained azide-tagged QDs.</figcaption></figure>

In a second step, the CdSe/ZnS QDs were functionalized with 4-azidobenzyl phosphonic acid ligands (clickable azide ligand). With this end, the obtained water-suspended CdSe/ZnS
QDs were dispersed in a borax buffered solution at pH=10. Then, 500 µM of 4-Azido-benzyl phosphoric acid prepared in borax buffer (pH = 10) was added to obtained CdSe/ZnS QD, which were coated with a mixture of histidine and (4-Azido-benzyl)phosphoric acid ligands. The final product was concentrated using a 30 kDa centrifugal filter (Millipore Amicon) and redispersed in a borax buffer solution. At the end of the process, the concentration of QDs was estimated to 800 nM using the UV-visible spectrum and the molar extinction coefficients reported by Jasieniak et al.⁶

**Characterization of the CdSe/ZnS core-shell QDs by TEM.**

Transmission electron microscopy (TEM) images were recorded on a Philips CM300 microscope operating at 300 KV. Images were collected with a TeamCam F416 TVIPS. The TEM grids were prepared by depositing a dilute drop of the chosen colloid on a carbon-coated copper grid.
<figure><img src="image_12.png" /><figcaption>Figure 6-SI: TEM images and corresponding size distribution of the commercial CdSe/ZnS QDs, (A) dried from their native toluene solvent and (B) dried from their aqueous solvent after their phase transfer and functionalization with APA. The size distributions (right) were determined from these TEM images using Image J software.</figcaption></figure>

Characterization of the CdSe/ZnS core-shell QDs by optical spectroscopy

The UV-Vis extinction spectra recorded on the QD colloidal solutions were performed using Hewlett Packard (hp) HP 8H52 diode array spectrophotometer. The measurements were done using quartz cuvettes and recorded over a wavelength range of 190 nm to 820 nm with a 2 nm step. The photoluminescence spectra were recorded using a PerkinElmer LS 55 spectrometer having a wavelength range between 200 to 800 nm and a power of 120 V, 1.25 A, 50/60 Hz. The excitation wavelength, the range and the width of the slits were adapted for each sample.
<figure><img src="image_13.png" /><figcaption>Figure 7-SI: (A) UV-Vis extinction and (B) fluorescence spectra of ~1µM CdSe/ZnS core-shell QDs in toluene (red) and in water (black).</figcaption></figure>

Clicking reaction procedures

Chemicals.

Ethanol, sodium tetraborate decahydrate (ACS reagent, 99%), Sodium hydroxide (pellets, > 97%), sodium-L-ascorbate (98%), 1,4-Diethynilbenzene (DEB, C10H6, 96%), were purchased from Sigma-Aldrich. Copper sulfate pentahydrate (98%) was purchased from Alfa Aesar.

Selective Click Reaction Procedure.

First, 1280 µL of water, 500 µL of the alkyne-tagged AuNPs solution (at ~ 8 nM) and 1020 µL of borax buffer (pH =10) were mixed together. To this mixture, 120 µL of azide-tagged QDs (or histidine-tagged QD for the reference sample) of 800 nM were added. Argon was bubbled into the colloidal suspension for a few minutes to remove any traces of oxygen before the addition of 40 µL of a 0.1 mM sodium ascorbate aqueous solution and 40 µL of a 0.05 mM copper sulfate aqueous solution. The final mixture of 3 mL contained approximatively 25 eq. of QDs in comparison with AuNPs based on the concentration estimations. The final mixture was stirred minimum 24 h before analysis.
## Non-selective Click Reaction Procedure.

The non-selective click reaction was obtained by mixing 1000 µL of water with 500 µL of the azide-tagged AuNPs at ~ 4 nM, 1500 µL of ethanol and 15 µL of the azide-tagged QDs at 1.4 µM. The sample was left undisturbed during 1 hour. Finally, 50 µL of a 0.3 mM DEB ethanol solution, 40 µL of a 0.1 mM sodium ascorbate in 2:1 ethanol:water solution and 40 µL of a 0.05 mM copper sulfate water solution were added to induce the reaction. The final mixture contained approximately 10 eq. of QDs in comparison with AuNPs based on the concentration estimations.

## Reference samples.

For both click reaction, reference sample are done in the same chemical environment but using non-functionalized QDs to prevent the click reaction.

## SEM images of the clicked and reference samples in the case of the selective click reaction.

<figure><img src="image_14.png" /><figcaption>Figure 8-SI: Selective click reaction: (Left) Image of the clicked sample where several c-HS are identified. The brighter and slightly larger particles are attributed to the AuNPs whereas, on the opposite, the duller and smaller particles are identified as QDs. In the reference sample, (Right) no such c-HS are observed and the AuNPs and QDs are well separated.</figcaption></figure>
SEM images of the clicked and reference samples in the case of the non-selective click reaction

<figure><img src="image_15.png" /><figcaption>Figure 9-SI: Non-selective click reaction: (Left) Image of the clicked sample where small c-HS are identified. The different types of possible c-HS, namely Au-Au, QD-QD or Au-QD are present. No large assemblies are detected. In the reference sample, (Right) no such c-HS are observed and the AuNPs and QDs are well separated.</figcaption></figure>

Calibration of the confocal volume.

The calibration of the in-plane waist $r_0$ of the confocal volume was realized by measuring DLS ACFs of commercial polystyrene NPs of diameter $d = 100$ nm, at a known room temperature $T_0$. In such conditions, the value of $r_0$ is given by the relationship:

$$r_0 = \sqrt{\frac{4k_B T_0 \tau_D}{3\pi\eta(T_0)d_H}},$$

where $\tau_D$ is experimentally determined.

In order to determine the value of the out of-plane waist $z_0$, a drop of water is used as a sample and its Raman signal is recorded as the focus point is scanned along the propagation direction of the laser (z-axis). The obtained signal is given by the cumulative distribution function:

$$I(z) = \frac{I_{max}}{2} \left( 1 + \operatorname{erf} \left( (z - z_c) \sqrt{2}/z_0 \right) \right) + I_B$$
where $I_B$ is the background signal, and $z_c$ is an arbitrary position of the center of the focus point. Figure 10-SI shows the Raman intensities measured with a pinhole of 50 µm in diameter. The best fit of $I(t)$ was obtained for $z_0=3.8$ µm

<figure><img src="image_16.png" /><figcaption>Figure 10-SI: Raman intensity of the water sample measured as a function of the position of the focus point along the z-direction (dot) and fitting with $z_0=3.8$ µm (line).</figcaption></figure>

The shape factor is thus $w = \frac{z_0}{r_0} \approx 17$.

## One-photon luminescence correlation spectroscopy test experiments.

In order to determine if the FCS measurements could possibly be polluted by one-photon luminescence at $\lambda=615$ nm, typical FCS experiments (i.e using a notch filter and at the same irradiance than for the studied samples) were conducted on the same AuNPs colloidal solutions than that used for the click reaction.

At $\lambda=615$ nm, the signal is very weak, ~350 cts/s and no ACFs is measured (Fig.11-SIa). To make sure that the absence of the ACF is due to a noise signal, i.e not to luminescence from the AuNPs, and is not due to the weakness of the signal, DLS experiments were also realized, at $\lambda=532$ nm, using OD filters to reduce the signal down to ~330 cts/s. Fig.11-SIb shows the DLS ACFs measured at different level of intensity. As expected, the ACFs become
very noisy at small lag time for very weak intensities, yet the ACFs do exist. We can thus
confidently state that one-photon luminescence of the AuNPs do not interfere in the FCS
ACFs.

<figure><img src="image_17.png" /><figcaption>Figure 11-SI: (A) ACF measured at $\lambda=615$ nm with a mean intensity $\langle I \rangle=340$ cps/s and (B) ACFs measured at $\lambda=532$ nm with mean intensities ranging from 6500 to 340 cps/s.</figcaption></figure>

Determination of the dynamic viscosity of a 1:1 (v:v) water:ethanol
mixture.

The experimental determination of the viscosity of the mixture $\eta_m$, at room temperature, was
determined by conducting confocal DLS measurements on a reference sample of polystyrene
beads of nominal diameter $d=100$ nm, in water and in a 1:1 (v:v) water:ethanol mixture
(Fig.12-SI).
<figure><img src="image_18.png" /><figcaption>Figure 12-SI: Normalized DLS ACFs measured on polystyrene beads (d=100 nm) in suspension in water (w) (blue dots) or in a 1:1 water:ethanol mixture (in volume) (green dots). In the presence of ethanol, the ACF presents an increased diffusion time, due to the change of viscosity of the solvent. The characteristic times were obtained from the adjustment of the experimental curves to Eq. (1) in the main text.</figcaption></figure>

To provide a value free of the experimental parameters, the diffusion coefficient of the beads in the mixture $\tau_{D,m}$, is normalized by that of the beads in water $\tau_{D,w}$, such that:

$$ \frac{\tau_{D,m}}{\tau_{D,w}} = \frac{3\pi\eta_m d_H r_0^2}{4k_B T} \cdot \frac{4k_B T}{3\pi\eta_w d_H r_0^2} = \frac{\eta_m}{\eta_w} $$

where $\eta_w$ is the viscosity of water at room temperature $T$, $k_B$ is the Boltzmann constant, $d_H$ the hydrodynamic diameter of the particles and $r_0^2$ the waist of the confocal volume.

At room temperature $T=20$ °C, $\eta_w=1$ mPa.s$^{-1}$ and $\eta_m = \frac{8}{3} = 2.7$ mPa.s$^{-1}$.
Table of the $\alpha=f(n_s)$ and $\sqrt[3]{n_s}/\alpha(n_s)$ values.

<table><caption>Table SI-1: Table of the values $\alpha$ as a function of the number $n_s$ of particles in a linear assembly of primary spherical particles. Corresponding values of $\sqrt[3]{n_s}/\alpha(n_s) = d_A/d_0$ where $d_A$ is the apparent hydrodynamic diameter of the NP assembly and $d_0$ is the diameter of the primary particles. The values were taken from Refs. 7,8</caption><thead><tr><th>n<sub>s</sub></th><th>α</th><th>√[n<sub>s</sub>]/α = d<sub>A</sub>/d<sub>0</sub></th></tr></thead><tbody><tr><td>2</td><td>0.906</td><td>1.39</td></tr><tr><td>3</td><td>0.834</td><td>1.73</td></tr><tr><td>4</td><td>0.78</td><td>2.037</td></tr><tr><td>5</td><td>0.74</td><td>2.32</td></tr><tr><td>6</td><td>0.7</td><td>2.6</td></tr><tr><td>7</td><td>0.67</td><td>2.86</td></tr><tr><td>8</td><td>0.64</td><td>3.12</td></tr><tr><td>9</td><td>0.62</td><td>3.37</td></tr><tr><td>10</td><td>0.6</td><td>3.6</td></tr><tr><td>12</td><td>0.56</td><td>4.07</td></tr><tr><td>14</td><td>0.53</td><td>4.52</td></tr><tr><td>16</td><td>0.51</td><td>4.95</td></tr><tr><td>18</td><td>0.48</td><td>5.4</td></tr><tr><td>20</td><td>0.46</td><td>5.8</td></tr></tbody></table>

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