Robust Rules for Optimal Colorimetric Sensing Based on Gold Nanoparticle Aggregation

Spurred by outstanding optical properties, chemical stability, and facile bioconjugation, plasmonic metals have become the first-choice materials for optical signal transducers in biosensing. While the design rules for surface-based plasmonic sensors are well-established and commercialized, there is limited knowledge of the design of sensors based on nanoparticle aggregation. The reason is the lack of control over the interparticle distances, number of nanoparticles per cluster, or multiple mutual orientations during aggregation events, blurring the threshold between positive and negative readout. Here we identify the geometrical parameters (size, shape, and interparticle distance) that allow for maximizing the color difference upon nanoparticle clustering. Finding the optimal structural parameters will provide a fast and reliable means of readout, including unaided eye inspection or computer vision.


Synthesis and functionalization of gold nanoparticles
Gold nanospheres. 1 Gold nanoparticles were obtained through two-step overgrowth process. Typically, initial seeds were prepared by reduction of HAuCl 4 (5 mL, 0.25 mM) with a strong reducing agent, NaBH 4 (0.3 mL, 10 mM) in aqueous CTAB solution (100 mM). To ensure complete decomposition of the reducing agent, the mixture was left undisturbed at 27°C for 0.5 h. An aliquot of as-prepared seed (0.11 mL) was added to a growth solution containing CTAC (20 mL, 200 mM), HAuCl 4 (20 mL, 0.5 mM) and AA (15 mL, 100 mM).
The mixture was left undisturbed at 27°C for 30 min. To remove remaining reagents, the solution was centrifuged (1 h, 14000 rpm) and redispersed in water. The gold nanospheres (∼10 nm) of the resulting solution were used as seeds in the second overgrowth step to obtain 20 nm, 30 nm, 40 nm, and 50 nm nanoparticle sizes. In doing so, a solution of gold nanospheres (0.285 mL, 0.18 mL, 0.08 mL, and 0.01 mL at 3 mM for spheres of 20 nm, 30 nm, 40 nm, and 50 nm in diameter, respectively) was added to an aqueous growth solution of BDAC (50 mL, 100 mM), HAuCl 4 (0.25 mL, 50 mM) and AA (0.25 mL, 100 mM) at 40°C and vigorous stirring. The mixture was left undisturbed at 30°C for 30 min. To remove excess of reagents, the solution was centrifuged twice (6500 rpm, 30 min) and redispersed in water.
First, to prepare gold seeds, a freshly prepared NaBH 4 solution (0.25 mL, 25 mM) was added to a CTAC solution (10 mL, 50 mM) containing HAuCl 4 (0.25 mM) and citric acid (5 mM) under vigorous stirring at room temperature. After 2 minutes, the vial was closed and the seed solution was heated in an oil bath at 80°C for 90 minutes. Then, to prepare gold decahedra, a solution of gold seeds (4 mL, 0.65 mL, 0.2 mL, and 0.1 mL for decahedral nanoparticles of 20 nm, 30 nm, 40 nm, and 50 nm in edge length) was added under vigorous stirring to a growth solution containing BDAC (100 mL, 100 mM), HAuCl 4 (1 mL, 50 mM) and AA (0.75 mL, 100 mM) at 30°C. The mixture was left undisturbed at 30°C for 30 minutes.
Ligand exchange. 3 Prior to the functionalization of gold nanoparticles with DNA, the as-prepared nanoparticles were subjected to ligand exchange to replace native surfactant molecules with citrate ions.

Geometrical considerations
Upon analyte addition to the solution of nanoparticles, aggregation commences to produce clusters containing several nanoparticles accompanied by the change of color. [5][6][7][8] To study the effect of geometrical parameters (shape, size, and interparticle distance of nanoparticles) on color transition, we simulated the optical response of clusters comprising 6 and 10 nanoparticles. The following considerations were taken into account to set the upper and lower limits of the gap between nanoparticles in the aggregated state. The radially distributed DNA strands on the surface of the nanoparticles remain hydrated in a buffer solution to form a brush of approximately 11 nm. 9 Thus, to set the upper limit of a 12 nm gap, we assumed that DNA strands of adjacent nanoparticles intercalate, forming a double-stranded DNA bridge. The lower limit of 2 nm was set by estimating the mean interparticle distance (2.77    Figure S2). It should be stressed that TEM imaging imposes vacuum conditions where the organic shell is fully dehydrated and collapsed, making a 2 nm gap during aggregation in the liquid phase a less probable scenario in our experimental model. Nevertheless, such a small interparticle distance remains relevant for other molecular analytes (e.g., heavy metal ions), motivating us to keep a 2 nm of lower limit of the interparticle gap in our calculations. Finally, the cluster shape was considered as isotropic and of compact structure. Recent studies have shown that clustering of DNA-functionalized nanoparticles follows reaction-limited aggregation implying nearly spherical shape. 10,11

Extinction cross section calculation
Extinction cross-section spectra (σ ext ) of spherical, cubic, and decahedral single metal NPs and clusters were calculated using a 3D electromagnetic solver which applies the finite differential time domain (FDTD) method. 12 For all the calculations, the material for the nanoaprticles was considered to be gold with refractive index from CRC database 13 and the surrounding medium was considered to be water (n m = 1.333) to mimic a colloidal solution of Au NPs. First, the shape and dimensions of the simulated cubic and decahedral NPs were approximated to those of the experimental NPs, observed in TEM micrographs (Fig.   S1b, c), with the purpose of calculating σ ext of single Au NPs in good agreement with the corresponding experimental absorbance spectra and to estimate more precisely σ ext of NPs clusters; Blender software was used for NP design. 14 In the case of spherical NPs, Mie theory was applied, and the resulted spectra were also compared to the experimental ones 15 (the best calculated fits are showed in Fig. S3). Good agreement between experimental and theoretical spectra was reached.
Then, σ ext of the single NPs of different sizes and NPs clusters of different number of NPs and gaps were calculated. A typical simulation set up using FDTD consisted in the Au NP (or cluster) centered in a cubic simulation domain limited with perfect matched layers ensure good convergence. In order to guarantee numerical convergence of the calculations, the auto shutoff threshold was set to 1 × 10 −7 -if the fraction of the power remaining in the simulation is less than this value, it triggers the simulation to end -and the simulation time to 1000 fs. Each final σ ext spectrum resulted from averaging 25 individual spectra for various excitation light polarizations with the aim of simulating the unpolarized incoming light. More specificaly, a single NP was set with different randomized rotational angles (polar and azimuthal angles) in each simulation. In the case of the NPs clusters, the rotational angles and the positions of each nanoparticle were randomized, and the rotational angle of the whole cluster was also randomized for each of the 25 simulations that would conform the averaged spectra. The light wavelength range considered ranges from 400 nm to 750 nm (visible spectral range). The absorption (σ abs ) and scattering (σ sca ) cross sections (not shown here) were determined by using field monitors surrounding the objects under study, and σ ext was then calculated from the arithmetic addition of the scattering and the absorption cross-sections (σ ext = σ abs + σ sca ).

Conversion of optical spectra into RGB and HSV color models
It has been shown that the Hue (H) parameter, which originates from the HSV color model, exhibits superior sensitivity to the change of refractive index. 16 Analogically, we selected the Hue parameter to describe quantitatively the change of color of a solution during aggregation. To convert σ ext and the experimental absorbance spectra into RGB and HSV space colors, a methodology described previously in Refs. 16 and 17 was followed. First, the absorbance (for experimental results, Figure S7 Finally, HSV color model was calculated from the RGB values by using: G, B), and Calculated Hue values were rounded to the nearest hundredth in order to facilitate their interpretation.     These results indicate that the gap, rather than the number of particles per cluster, establishes color difference upon aggregation.
For the sake of simplicity, we proposed here a quantitative indicator based on the change of Hue (∆H), while the standardized measure to asses the difference between two colors, ∆E 76 , is defined as: where L, a, and b are the reference stimulus values of the CIE 1976 L*a*b* color space. 22,23 The perception of humans to distinguish between two colors follows the following classification: 23 • 0 < ∆E 76 < 1 : the difference is unnoticeable, • 1 < ∆E 76 < 2 : the difference is only noticed by an experienced observer, • 2 < ∆E 76 < 3.5 : the difference is also noticed by an unexperienced observer, • 3.5 < ∆E 76 < 5 : the difference is clearly noticeable, and • 5 < ∆E 76 : gives the impression that these are two different colors.
Therefore, to compare our indicator with the standardized measure we calculated ∆E 76 for numerical and experimental spectra of all cluster configurations (Table S2) (Figure 5a-c) and simulations ( Figure S11). However, it should be stated that the purpose of ∆E 76 is to determine the value of the lower threshold of differentiation between two colors, that is, the regime where such a difference can be difficult to assess objectively. The analysis of the values in Table S2 shows that virtually all nanoparticles shapes and cluster configurations studied here fall in the range of 3.5 < ∆E 76 < 5, that is, the aggregation of nanoparticles can be clearly differentiated and noticed. Therefore, we postulate that the ∆H indicator is a more convenient measure than ∆E 76 for our purpose, since we seek to compare the maxima of color transition rather than assessing qualitatively the lower limits of distinction between two colors. 22