Optical and mechanical properties of streptavidin-conjugated gold nanospheres through data mining techniques

The thermo-mechanical properties of streptavidin-conjugated gold nanospheres, adhered to a surface via complex molecular chains, are investigated by two-color infrared asynchronous optical sampling pump-probe spectroscopy. Nanospheres with different surface densities have been deposited and exposed to a plasma treatment to modify their polymer binding chains. The aim is to monitor their optical response in complex chemical environments that may be experienced in, e.g., photothermal therapy or drug delivery applications. By applying unsupervised learning techniques to the spectroscopic traces, we identify their thermo-mechanical response variation. This variation discriminates nanospheres in different chemical environments or different surface densities. Such discrimination is not evident based on a standard analysis of the spectroscopic traces. This kind of analysis is important, given the widespread application of conjugated gold nanospheres in medicine and biology.


Plasma treatment
The high density samples have been subject to an Oxygen plasma treatment using a low-pressure plasma system model PICO by Diener Electronic, 50 W for 90 s, to partially remove the polymer coating and expose the bare nanospheres.

Sample imaging
The sample imaging has been carried out with Atomic Force Microscopy (AFM) and Scanning Electron Microscopy (SEM). In the following, we briefly highlight the techniques and discuss the measurement results.
The topographic AFM measurements were performed employing a commercial Dimension Icon AFM (Bruker) operating in "peak force tapping mode" (PFT) 1 and using "ScanAsyst-air" probes (nominal elastic constant 0.4 N/m). PFT-mode imaging is performed by nanoindenting the sample pixel-by-pixel, controlling the force applied by the tip. This imaging mode allowed us to avoid any NPs scrubbing induced by the AFM probe. The results of a typical AFM topographical scanning on a sample without plasma treatment is shown in Fig. 1. The average height of the nanospheres is compatible, within errors, with the nominal diameter of 40 nm of the streptavidin-conjugated gold nanospheres declared by the vendor.
The SEM imaging exploited the charge compensator apparatus of our system (model Merlin, 30 keV FEG system, ZEISS) to perform direct imaging on NPs on sapphire, avoiding the need for any conductive coating layer on the sample surface. This methodology allowed high-resolution imaging on NPs, without topographic artifacts induced by the conductive film. The SEM images are shown in Fig. 1 b)-c) in the main text.

Surface density estimates
The surface density estimation of the samples on which the time-resolved optical measurements were taken has been carried out using AFM topographic images. This allowed the control of the height of the single nanosphere or cluster of nanospheres, to be sure we were imaging the nominal 40 nm diameter gold nanospheres. We found a height of 40 ± 7 nm (with background Figure 1. The topography of the gold nanospheres adhered to a sapphire surface by peak force tapping mode AFM. subtraction) on 11 random samples from high density and low-density samples. The count of the surface density of the nanoparticle clusters has been conducted on AFM image topography using ImageJ 2 (typical scanning area of 5-20 µm 2 , depending on the sample). On low-density samples, we found an average area of 3500 ± 900 nm 2 , corresponding to an average radius of 30 ± 4 nm. On the high-density samples, we found an average area of 9000 ± 6000 nm 2 , corresponding to an average radius of 55 ± 15 nm. We have to take into account that on the streptavidin-conjugated spheres a corona of polymer/antibody molecules contributes to a bigger AFM topographic cross-section and that the convolution with the tip radius of curvature (typically 20 nm) tends to increase the apparent dimensions of small particles in the images. Considering that the nominal core radius of the gold nanospheres is 20 nm, the results found for the low-density sample are compatible with clusters composed on average of a single nanosphere. Instead, the high-density sample the average cluster area is compatible with clusters formed on average by 3 ± 2 nanospheres. The SEM images have been used to verify the long-range uniformity of the surface distributions of nanoparticles. In the SEM images, a halo can be seen around each nanoparticle, that we attribute to a different electron scattering from the polymer around each particle (see Fig. 1 in the main text).

Absorption cross-section
The extinction cross-section for R= 20 nm radius gold spheres in a polymer matrix has been evaluated using the standard expression, keeping only the dipolar terms in Mie's theory 3,4 . In this approximation, the absorption cross-section is valid only for small particles (2R λ /10) and the extinction is dominated by absorption.
The composite material absorption cross section in this approximation is written: where ε m = n 2 m = 1.36 2 is the polymer dielectric constant where the sphere is supposed to be immersed and will be assumed frequency-independent and real. The polymer refraction index was obtained with an AnaLight refractometer. The Johnson and Christy refractive indexes for gold 5 have been used to retrieve the spectral dependence of ε 1 and ε 2 . In Fig. 2, the absorption cross-section as a function of wavelength is reported. Note that at the pump wavelength, marked by a red dot, the cross-section is three orders of magnitude less than in resonance.

Electron and lattice temperature estimations
The gold nanospheres have an average radius of R=20 nm. The refraction index of the hosting medium is n m = 1.36. The pump laser emits sub-ps pulses at a repetition rate of 100 MHz with an average power of 2 mW, resulting in an energy of 20 pJ/pulse. The pump wavelength is λ pu = 1560 nm, with a single particle pump absorption cross section σ pu = 2.7nm 2 (see the preceding section). The impinging pump beam is focalized through a lens to a spot size of area A pu in the focus of the lens. With an objective of numerical aperture NA=0.55 the spot radius in the focus is 0.61λ pu /NA = 1.77µm, the spot area is A pu = 9.4µm 2 .
We define I 0 pu as the pump intensity measured at a detector after the sample without the nanosphere in the focus of the impinging beam, I 1 pu is the intensity at the detector with the nanosphere in the focus of the impinging beam. Using the optical = ∆I pu /I 0 pu = σ pu /A pu . Since the time width of the pulse and spot area are the same, the relation is valid also for the variation in the energy of a single pulse, u 0 pu − u 1 pu = u pu = σ pu u 0 pu /A pu , where u 0 pu is the impinging pulse energy without the nanosphere, u 1 pu is the energy of the pulse after passing through the nanosphere, u pu is the absorbed energy in a single nanosphere. With the values shown above the absorbed energy per nanosphere is u pu = 45 hν pu . The maximum electronic temperature, neglecting thermal transport and energy exchange with the lattice, can be estimated from the energy balance between the rate of optical energy density input (P pu /V ), where P pu is the absorbed pump power by the nanoparticle electron gas and V the nanoparticle volume, and the energy needed to increase the electronic temperature (C e dT e dt ), where C e is the electronic thermal capacitance and T e is the electronic temperature. Taking into account that the electronic thermal capacitance is proportional to temperature C e = γT e , γ = 100 J/(m 3 K 2 ) for gold. Integrating on the pulse duration we obtain for the peak electronic temperature variation ∆T e (max) = T e (max) − T e (0) = T 2 e (0) + 2 u pu γV − T e (0) ≈ 6 K. The maximum lattice temperature could be estimated by supposing that the energy density stored in the electrons is finally released to the lattice with thermal capacity C l = 2.46 × 10 6 J/(m 3 K), resulting in a peak lattice temperature variation ∆T l (max) = u pu /(VC l ) ≈ 0.07 K.
The variation of the nanosphere radius due to the temperature increase is ∆R = R(1 − α∆T l (max)) ≈ 0.02 pm, where α = 14 × 10 −6 is the linear expansion coefficient for gold.

Probe transmission and pump induced cross-section variation
The probe laser emits sub-ps pulses at a repetition rate of 100 MHz with an average power of 0.25 mW, resulting in an energy per pulse of 2.5 pJ/pulse. The probe wavelength is λ pr = 780 nm, with a single particle probe absorption cross section σ pr = 25nm 2 (see the preceding section). With a lens of numerical aperture NA=0.55 the spot radius in the focus is 0.61λ pr /NA = 0.87µm, and the area is A pu = 2.35µm 2 . The presence of the nanosphere gives a probe transmission variation estimated as 6, 7 I 0 pr −I 1 pr I 0 pr = ∆I pr /I 0 pr = σ pr /A pr = 1 × 10 −5 . This would be the transmission variation measured in standard transmission microscopy measurements. However pump-probe experiments monitor the change in the probe beam intensity induced by the pump beam, i.e. ∆(∆I pr )/I 0 pr = ∆σ pr /A pr . From experiments we measure a peak relative transmission variation of the order of ∆T /T = −2/ − 5 × 10 −5 , which is of the same order of magnitude of the absolute transmission variation estimated above, taking into account the sign that comes from the definition of transient transmission (see main text). Using the measured average transmission variation in the pump-probe experiment and the above relation, the estimated peak variation in cross-section due to the pump excitation is ∆σ pr ≈ 80 nm 2 . The pump induces a cross-section peak variation much higher than the estimated particle cross-section for a static transmission experiment.

Clustering algorithm
The general workflow for a clustering algorithm is as follows. Given n experimental traces x i , consider initially n singleton clusters ω i = x i . Then, determine the two nearest clusters ω i and ω j using an appropriate distance (or linkage) d(ω i , ω j ).
Merge ω i and ω j : ω i j = {ω i , ω j }, therefore obtaining a solution with n − 1 clusters. Repeat the process until a single cluster is obtained. In the Ward's method implementation used in this work 8 , the squared distance d(ω i , ω j ) 2 is defined as the increase of the squared within-cluster distances (defined as the sum of the squares of the distances between all objects in the cluster and the centroid of the cluster) when the cluster merges and is computed as: where m is the centroid of the cluster. The metric ||...|| used to calculate the distance is the Euclidean distance between experimental traces. The factor of 2 is used so that the distance between two singleton clusters is the same as the Euclidean distance. At each step, the two clusters that merge are the ones that contribute to the smallest increase of the overall sum of the squared within-cluster distances.

Mechanical analysis
We show in Fig. 3 the full set of fitting parameters found in the mechanical analysis with relative errors. Refer to the corresponding section in the main text. Here we notice a few points that have values and associated errors considerably larger than the others, so that including them in the graph prevents a correct overall visualization. This is why only a subset of these points is reported in Fig. 5 b), c), d), e) in the main text. We stress that a large error associated with one parameter does not imply that the other parameters, associated with the same fit, are affected by large errors (see, e.g., points 9, 16). c) d) Figure 3. The complete set of fitting parameters for the mechanical analysis are shown. a) and b) reports the oscillation frequencies versus associated exponential damping times for the first ( f 1 vs τ 1 ) and second ( f 2 vs τ 2 ) oscillators. c) and d) reports the amplitude versus phase for the first (a 1 vs φ 1 ) and the second (a 2 vs φ 2 ) oscillators.