Artificial neural networks modeling of the parameterized gold nanoparticles generation through photo-induced process

Tetrachloroauric(III) acid trihydrate 99.5% (AuCl₄H · 3H₂O) and tri-sodium citrate dehydrate (C₆H₅Na₃O₇ · 2H₂O) were purchased from Merck. Poly (4-styrenesulfonic acid, 18 wt% solution in water) (PSS) was purchased from Sigma-Aldrich. All chemicals were of purity grade and used as received. Double-distilled water, obtained in the laboratory, was used to prepare all solutions and for all-purpose cleaning.

Different amounts of tri-sodium citrate dihydrate (0.15 millimole and 1 millimole) were added to 1 ml PSS to obtain two stock solutions (denoted A1 and A2) with concentration of 0.15 mM and 1 mM, respectively. 1 mM stock solution of tetrachloroauric (III) acid trihydrate (denoted B) was prepared by adding 1 millimole of AuCl₄H · 3H₂O (denoted gold(III)) to 1 ml PSS.

Equal volumes of each stock solution A1 and A2 were mixed with an equal volume of stock solution B just before experiment to prepare two solutions (A1-B and A2-B) with molar ratios sodium citrate: gold(III) denoted c1 and c2, c2 being almost 7 times higher than c1.

Due to the high solubility of the precursors in PSS, the thick films were prepared by applying single 20 μl droplet of the prepared solutions A1-B and A2-B, respectively, onto the glass slide, followed by uniformly spread.

The above prepared thick films were then placed in a three-axis direct light writing (DLW) set-up, controlled by computer, allowing their translation relative to the focal point with a given scanning velocity from 2 to 80 μm s⁻¹ (12 velocities, denoted v2, v3, v5, v8, v10, v15, v20, v25, v30, v40, v60, v80) set by the appropriate macros, running in close-loop regime. DLW technique using piezoelectric controlled system [27–29] was used for its ease of conversion and spotting quality.

Direct light writing (DLW) set-up consists of an inverted microscope (BX71, Olympus, Japan), equipped with dry fluorite objectives (10X, 20X and 40X magnifications, 0.3 to 0.75 numerical apertures NA and 0.51 to 10 mm working distances WD), and an XYZ Piezo Stage System with 1 nm resolution (P-545, Physik Instrumente, Germany). First, a diode-pumped YbKGdW femtosecond laser amplifier (Pharos, Light Conversion, Lithuania) set at 380 nm, 170 fs (FWHM) pulse duration, 80 kHz repetition rate (75 μJ energy per pulse) and an average power of 20 mW was used to validate the process. Then, the radiation from a 100 W mercury lamp equipped with a longpass filter having the cut-on wavelength at 370 nm, coupled with a dichroic mirror at 410 nm and a barrier filter at 420 nm was directed into the inverted microscope to be focus within the sample and irradiate it. Because the lamp power is constant, it could be lowered to half only by using an absorbing neutral density filter (NDF) with 50% attenuation. The spot sizes of the light focused in the sample decreased with the increase of the objectives magnification as follows: 557 μm (10X), 281 μm (20X), and 139 μm (40X).

2.4.1. Optical microscopy and spectroscopy

2.4.2. Transmission electron microscopy

The artificial neural network model was developed using the Neural Network Toolbox from Matlab 2016b software.

In the ANN, each artificial neuron receives a signal from the neighboring neurons, processes these inputs and generates the neuron output. The received signal is the summation between the weighted output signals sent by the neurons located in the previous layers and the neuron bias.

Experiments revealed that AuNPs dimension is influenced by three input variables: citrate:gold(III) salt ratio, intensity and scanning velocity, and correlated with the gold local SPR absorption peak. In order to obtain appropriate observations, for each sample an absorption spectrum was recorded and the absorption maximum value was extracted. Consequently, the ANN data set consisted of three inputs (citrate:gold(III) salt ratio, intensity and scanning velocity) and one output (absorption maximum), with a total number of 118 experiments, was used for building the ANN model (figure 1).

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To improve the ANN performance, the experimental data set was divided into training, validation and testing data. Thereby, the testing data set was obtained by uniformly extracting every fifth sample from the initial data set sequence. From the remaining data the same method was used for extracting the validation data set. Finally, the remaining values represented the training data set. In these conditions, the training, validation and testing data consisted of 70, 24 and 24 data sets, respectively. For improving the accuracy of the model training, the input and output values were mapped to the range [−1, 1].

The ANN was trained for 2 hidden layers and with different number of neurons in each hidden layer.

A tangent sigmoid function (tansig) for the hidden layers and a linear transfer function (purelin) for the output layer were used to process the net inputs and generate the neuron output.

The multilayer feedforward network and the backpropagation Levenberg-Marquart learning algorithm were chosen for the ANN [26, 31]. The values of the weights and biases were adjusted in order to minimize the mean square error (MSE) objective function [17, 32]:

$$\begin{eqnarray}&&MSE=\displaystyle \frac{\displaystyle {\sum }_{i=1}^{n}{({x}_{i}-{y}_{i})}^{2}}{n},\end{eqnarray} \tag{ 1 }$$

where x_i is the experimental value, y_i is the model predicted value and n is the number of data points.

The number of neurons in each hidden layer was varied and chosen such that to maximize the artificial neural network performance. The performance of the model was studied with reference to the Pearson correlation coefficient (R) and the artificial neural network relative error (Rel_err), using the equation:

$$\begin{eqnarray}&&R=\displaystyle \frac{\displaystyle {\sum }_{i=1}^{n}({x}_{i}-\bar{x})({y}_{i}-\bar{y})}{\sqrt{\displaystyle {\sum }_{i=1}^{n}{({x}_{i}-\bar{x})}^{2}}\sqrt{\displaystyle {\sum }_{i=1}^{n}{({y}_{i}-\bar{y})}^{2}}},\end{eqnarray} \tag{ 2 }$$

where x_i is the experimental value, y_i is the model predicted value, $\bar{x}$ and $\bar{y}$ are the arithmetic mean of the experimental and model predicted values, respectively, and the equation:

$$\begin{eqnarray}&&{Re}{{l}}_{err}=100* \displaystyle \frac{{Pre}{{d}}_{out}-{\mathrm{Exp}}_{out}}{{\mathrm{Exp}}_{out}},\end{eqnarray} \tag{ 3 }$$

where Pred_out and Exp_out represent the predicted and the experimental outputs (maximum absorption wavelengths), respectively.

Thus, the best designed ANN architecture had the highest correlation factor and the lowest relative error.

The gold nanoparticles generation in the polymer thick films was accomplished by photochemical reduction [33, 34] of gold(III) salt, dispersed in a polymer matrix, using the DLW set-up described in the experimental section. The most important features of the process are that it occurs selectively in a limited volume/area in the focal plan of the sample, it takes place under ambient conditions, and follows the principles of green chemistry, respectively.

In nanoparticles, at the nanoscale, the color of the gold element is red to purple [35]. Therefore, the formation of gold nanoparticles in the transparent [36] yellowish colored polymer films can be observed in real time due to a change in color, since AuNPs are red. The photoreduction process has been validated first using a laser beam emitting in a single-photon regime at 380 nm and 20 mW power. Due to the multiple optical media the radiation is passing through before focusing into the sample, the power at the sample surface is almost 10 times lower than the output level. In this respect, the irradiation process efficiency is very low and we decided to use further a mercury lamp radiation, to deliver sufficient power into the sample.

Figure 2 presents two series of thread-like patterns generated in thick films prepared at the citrate:gold(III) ratio c2 by irradiation at a 6.3x magnification (10X objective) along a travel length of 180 μm under controlled conditions at tested powers P1 = 100 W (figure 2(a)) and P2 = 50 W (figure 2(b)). The identical set of the 12 scanning velocities tested (v2–v80 from right to left) represents default equivalent irradiation times decreasing from 94 s to 2 s.

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Figure 2 showed that working at the same scanning velocities set and citrate:gold(III) c2 ratio, the color [37] of the generated structures turned from Chili Red, when using the higher power P1 (figure 2(a)) to the darker shade Sangria, when the used power P2 was only half the P1 (figure 2(b)). The color is uniformly distributed inside of the pattern contour but the intensity tends to decrease at the end of the travel path, especially when the scanning velocity increased above 15 μm s⁻¹.

In addition, in both series the pattern size decreased with increasing the velocity, the effect being more evident when lowering the power. This behavior was clearly highlighted at scanning velocities larger than 15 μm s⁻¹, especially in the second serie at P2, where the appropriate patterns' color turned from darker to lighter red or even gray (figure 2(b)). These results emphasized that, in similar conditions of magnification and citrate:gold(III) ratio, the main factor which made the difference was the radiation power and only secondarily the scanning velocity.

In this respect, we chose to refer further to radiation intensity instead of the power itself because intensity is more relevant as a process parameter directly related to the objective magnification.

The intensity I represents the power incident on a surface and it is described by the equation:

$$\begin{eqnarray}&&I=\displaystyle \frac{P}{{A}_{spot}}\,[{\rm{W}}/{{\rm{cm}}}^{2}],\end{eqnarray} \tag{ 4 }$$

where P is the radiation power [W] and A_spot is the spot area [cm²].

Taking into consideration that the light was focused within the sample through different objectives with increasing magnifications, the appropriate spot sizes generated different intensities reported to the used powers, which changed significantly the photochemical response. The corresponding intensity delivered into the sample increased for both higher (P1) and lower (P2) used powers, respectively, as the spot size diameter decreased—parameter modification that is correlated with the magnification increase. Therefore, at the same spot sizes/magnifications above mentioned, the calculated intensities are presented in table 1 as follows:

Assuming that the radiation intensity can be controlled and the scanning velocity is automatically set during the macro running, we decided to choose them as input parameters in the development of the artificial neural network [38].

In order to control the sample reactivity in the given conditions, the color of the generated patterns have been observed and compared. The uniformly distributed color indicated that the structures are remarkably homogeneous in composition but there was necessary to consider a measurable output parameter instead of a qualitative one to monitor the system response. In this view, optical microscopy and spectroscopy correlated investigations have been done in case of the red colored patterns 'written' at the interface, after the 'writing' process, providing the most indicative proofs to monitor the changes inside of irradiated areas.

In figure 3 are presented UV–vis absorption spectra recorded in 450–700 nm range for both series of the gold structures generated in films at similar scanning velocities and citrate:gold(III) ratio c2 but decreasing intensities (same magnification 6.3x but different powers P1 and P2).

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All spectra displayed a well-defined peak specific to gold nanoparticles localized SPR, their maxima increasing in 540–552 nm range for a 4.11e4 W/cm² intensity (figure 3(a)) and 546–579 nm in case of 2.055e4 W/cm² intensity (figure 3(b)), respectively. Because the obtained localized SPR absorption maxima could be related to the nanoparticle size [9, 39], they could be ascribed to a broad distribution of AuNPs size which exceeds the 100 nm limit, but this is only if the recordings should be done in solution [13].

As time as the spectra have been collected from films, the real size of AuNPs could not be directly estimated from the absorption spectra because the particles stick together within a solid matrix and the additional interactions bring about a significant red-shift of 12 nm and 33 nm, respectively.

In this respect, the spectroscopic data showed that the generated thread-like DLW red structures were made up of gold nanoparticles instead of being continuous structures. The lack of continuity in the DLW gold structures does not result in failure, but can represent the starting point for the design of different types of materials with interesting properties dependent on the gold nanoparticle size.

As presented in table 2, in case of the same citrate:gold(III) ratio c2 and increasing magnifications (12.6x and 25.2x), the absorption maxima increased from 531 to 544 nm for 1.611e5 W/cm² intensity and from 540 to 559 nm for 8.055e4 W/cm² intensity. Also, the absorption maxima increased from 531 to 544 nm for a 6.6e5 W/cm² intensity and from 541 to 562 nm for an intensity of 3.3e5 W/cm².

It can be observed that the absorption maxima decreased with the increase of the intensity when working at c2 citrate:gold(III) ratio and the same magnification.

The absorption recordings have been done, also, in case of the patterns obtained at the lower citrate:gold(III) ratio c1 and increasing the magnifications (6.3x, 12.6x and 25.2x). Therefore, the absorption maxima increased from 547 to 589 nm for an intensity of 4.11e4 W/cm² and from 554 to 604 nm in case of 2.055e4 W/cm² intensity. Regarding 1.611e5 W/cm² and 8.055e4 W/cm² intensities, the absorption maxima increased in the range of 547–550 nm and 538–550 nm, respectively. Also, for 6.6e5 W/cm² intensity the absorption maxima increased from 544 to 548 nm, whereas for an intensity of 3.3e5 W/cm² the maxima are situated between 536 and 551 nm.

Plotting the patterns absorption maxima wavelength function on scanning velocity, it can be observed that the higher velocities the higher absorption maximum (figure 4). Particularly, the wavelengths have encountered a dramatical diminishing of their value when increasing the citrate:gold(III) ratio from c1 to c2 but maintaining the same intensity (4.11e4 W/cm²/6.3x magnification) (figure 4(a)).

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This behavior clearly substantiated the importance of the citrate anion's presence as a stabilizer agent against the AuNPs agglomeration. In case of c1 ratio, the maximum showed a spectacular increase of 25 nm firstly above the scanning velocity of 10 μm s⁻¹, followed by a 'terrace' between 20–30 μm s⁻¹ and a lower increase of 15 nm above 30 μm s⁻¹. In case of c2 ratio, the absorption maxima were situated around the value of 540 nm at a scanning velocity of 2–5 μm/s as well as around 550 nm when the scanning velocity increased above 20 μm s⁻¹ (figure 4(a)). The decreasing effect of larger citrate concentration (c2 ratio) among the absorption maxima was evaluated then at similar velocities but considering also half of the already used intensity (figure 4(b)). Therefore, the decrease of the intensity brought an almost exponential increase of absorption maxima at scanning velocities higher than 10 μm s⁻¹, emphasizing the critical effect of the intensity among the maxima values and default on the particle size evolution.

The particle size evolution was significantly influenced by the citrate:gold(III) ratio, particularly by adjusting the citrate amount as well as by using the PSS polymer matrix as environment for AuNPs generation process. Thus, in our experiment citrate played a double role: on a hand, as photosensitizer which induced the gold(III) cation photoreduction, on the other hand, as protective anion placed at the gold particles surface that protected them against forming larger particles [40–42]. The considerable length of the water-soluble PSS ion-exchange polymer chain as well as the presence of electron withdrawing sulfonyl hydroxide para-substituted styrene units overcome the tendency of agglomeration or aggregation of the already formed AuNPs [43].

For determining the AuNP diameter six samples that had absorption maxima values well distributed in the studied range were analyzed by TEM.

Figures 5(a)–(f) presents the typical TEM images of AuNPs prepared by DLW in PSS thick films at six power/citrate:gold(III) ratio/magnification/scanning velocity conditions P1c2-6.3x-v2, P1c2-25.2x-v15, P2c1-12.6x-v5, P2c2-6.3x-v2, P2c2-6.3x-v15 and P2c1-6.3x-v30, respectively. The AuNPs morphology showed mainly a nearly spherical-like shape and relative homogeneous distribution of size in a broad range of about 5–80 nm (figures 5(a)–(e)). Particularly, the photosynthesis resulted in flake-like shape particles in 5–450 nm range when playing in P2c1-6.3x-V30 conditions (figure 5(f)). Figures 5(a')–(f') shows the AuNPs number population (count) resulted in the six above-mentioned conditions as a function of the average particle diameter. The average particle size was determined at 13.65, 19.41, 23.82, 28.57, 38.61 and 85.49 nm, respectively (figure 5).

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From these data (table 3) it can be noticed that the particle size was increased with decreasing the intensity (figures 5(a) versus (d)) and citrate:gold(III) ratio (figures 5(b) versus (f)) as well as with increasing the scanning velocity (figures 5(d) versus (e)).

In order to determine the AuNPs real diameter, a correlation between the TEM measured mean diameters (table 3) from six samples and their absorption maxima that had well distributed values in the studied range (table 2) has been done. A similar study in which the localized SPR peak positions are accurately fitted by a simple exponential function is performed by Haiss [13]. The difference is that in Haiss work the localized SPR absorption maxima are measured for AuNPs dispersed in water, whereas in this study the SPR absorption maxima are measured in thick film.

Therefore, in this work an exponential function is used to fit the localized SPR absorption maxima as a function of the AuNP size (figure 6).

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Consequently, based on the localized SPR absorption maxima values, the AuNP diameter (d_AuNP) can be calculated with the equation:

$$\begin{eqnarray}&&{d}_{AuNP}=D* \,\mathrm{ln}\left(\displaystyle \frac{\lambda -{\lambda }_{0}}{{\lambda }_{1}}\right),\end{eqnarray} \tag{ 5 }$$

where λ₁(31.55), D (52.14) and λ₀ (491.36) are the fitting parameters for a correlation factor of 0.999.

Subsequently to performing the training of the designed artificial neural network, the trained ANN model was used to predict the gold nanoparticle dimension. The prediction aptitude was tested considering the testing set of data (not yet seen by the artificial neural network during the training step).

In order to demonstrate that ANN model was well fitted to the experimental results, the correlation factors between the ANN model predictions (Output) and the experimentally measured values of SPR absorption maxima (Target) were calculated for the training, validation, testing and overall data sets (figure 7). The correlation results are presented in figure 7, where the dotted line represents the perfect correlation (R = 1) and the circle points represent the real correlation between target and output values, while the solid line indicates the best linear fit of the points. They reveal the reduced deviance of the ANN model predictions from the experimental values.

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Figure 8 shows the ANN predicted versus experimentally measured values for the testing set of data, presented as relative errors.

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The best designed and trained ANN architecture showed to have in its two hidden layers a number of 3 and 7 neurons, respectively. As presented in figure 8, the performance of this ANN for the 25-testing data set demonstrated low relative errors, i.e. all relative errors (in absolute value) less than 2.6% are associated to a correlation factor of 0.959. In this respect, the mean value of the determined relative errors was of 0.5386%, emphasizing the high performance of the ANN model. High values were obtained for the correlation factors of the training and validation data sets, i.e. 0.992 and 0.980 respectively, while the correlation factor of 0.978 for the overall data set was also very good. These values proved that ANN predicted absorption maxima, directly connected with AuNPs diameter, are in good correlation with the experimentally measured value.

As a consequence of the successful training results, the developed ANN model was further used to make predictions on AuNP size in case of new values of its input parameters, values that were different with respect to the training, validation and testing data values. Specifically, the effects of different values of the radiation intensity, scanning velocity or citrate:gold(III) ratio on the AuNP dimension were investigated. These new predictions of the trained ANN are presented in figure 9.

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Figure 9 shows that the AuNPs size increases as the scanning velocity is elevated from 2 to 80 μm/s for the same intensity value of 3.419e5 W/cm² (figure 9(a)) or as the intensity is decreased to half of the maximum value for the same scanning velocity of 40 μm/s (figure 9(b)), both sets of predictions using the same citrate:gold(III) ratio c2. From these data it can be noticed that the effect was clearer at higher velocities. Both trends revealed by the ANN predictions are in good correlation with the observed process of AuNPs growth (figure 5). In addition, the particle size increases with decreasing the citrate:gold(III) ratio, while preserving the afore-mentioned dependence on the intensity and scanning velocity (figure 9(c)).

ANN predictions presented in figure 9(b) show that AuNP size decreases with the increase of the intensity at the same scanning velocity and citrate:gold(III) ratio. A higher irradiation power may lead to increasing the nucleation centers and thus reducing the AuNP size. Also, this result may be explained considering that already formed AuNPs are excited and further subjected to an ablation process [44].

The ANN predictions shown in figure 9(c) revealed the trend in AuNP size when citrate:gold(III) ratio changes. The predictions illustrated that an increase in the citrate:gold(III) ratio leads to a decrease of the AuNP size. This phenomenon can be explained by an increase of the colloidal stability due to the distribution of the stabilizer around the gold nanoparticle which overcomes their agglomeration [12].

In addition to the ANN predictions, the interpolation capability of the trained ANN is demonstrated in figure 10. The ANN predicted values of the AuNP size are situated between the experimentally measured data of the AuNP size, credibly corresponding to the new input intensity value of 4.9e5 W/cm², which is situated between the experimental input values of 3.3e5 W/cm² and 6.6e5 W/cm².

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The ordering of input variables according to their importance was also examined. A feature selection algorithm was used to find the subsets of features that optimally predict the measured data, revealing the features that are most influential. First, a generalized linear regression full model of the AuNP size output variable was built considering all three input feature variables and the full matrix of measurements. Then, an objective function was defined for assessing generalized regression reduced models fitted for subsets of the full set of features. Finally, a sequential search algorithm was used for selecting features in the decreasing order of their importance by evaluating the reduced model for each of the feature candidate subset. The deviance of fit for the reduced model is higher compared to the one for the full model and consequently, it was used to order and assess the importance of each feature subsets.

As a result of this assessment approach for the input variables importance, the built model showed that radiation intensity is the input that has the highest influence on the AuNP size, followed by the scanning velocity and the citrate:gold(III) ratio.