Optical Limiting of Carbon Nanohorn-Based Aqueous Nanofluids: A Systematic Study

Nowadays, the use of lasers has become commonplace in everyday life, and laser protection has become an important field of scientific investigation, as well as a security issue. In this context, optical limiters are receiving increasing attention. This work focuses on the identification of the significant parameters affecting optical limiting properties of aqueous suspensions of pristine single-wall carbon nanohorns. The study is carried out on the spectral range, spanning from ultraviolet to near-infrared (355, 532 and 1064 nm). Optical nonlinear properties are systematically investigated as a function of nanohorn morphology, concentration, dimensions of aggregates, sample preparation procedure, nanostructure oxidation and the presence and concentration of surfactants to identify the role of each parameter in the nonlinear optical behavior of colloids. The size and morphology of individual nanoparticles were identified to primarily determine optical limiting. A cluster size effect was also demonstrated, showing more effective optical limiting in larger aggregates. Most importantly, we describe an original approach to identify the dominant nonlinear mechanism. This method requires simple transmittance measurements and a fitting procedure. In our suspensions, nonlinearity was identified to be of electronic origin at a 532 nm wavelength, while at 355 nm, it was found in the generation of bubbles.


Introduction
Optical limiting systems are extremely important to protect human eyes or instrumentation in all applications where high-power laser beams are involved. Optical limiting (OL) is referred to as the phenomenon shown by some materials where the energy transmitted through the sample follows two well distinct regimes; at weak input intensities, the light transmitted through the material linearly depends on the intensity of incident radiation. In these conditions, the value of optical transmittance is constant and independent of the input light intensity. However, when the intensity of input light becomes higher than the threshold value characteristic of the material, the intensity of transmitted light becomes less dependent than linear on the input light, becoming also, in ideal cases, constant and independent of the incident intensity. In this regime, the transmittance suddenly decreases with respect to its initial low-intensity value, reaching, for high input intensities above the threshold, values even near to zero. In these conditions, the material becomes opaque or near-opaque to the incident high-intensity radiation. An extremely wide range of OL materials has been described in the literature, including organic molecules like porphyrins and Table 1. Investigated samples. All nanofluids, except oxidation (OX) ones, are prepared with not-functionalized (pristine) single-walled carbon nanohorns (SWCNHs). * Same protocol as NH2, prepared again for comparison with the OX sample at equal sample ages.

Sample Label Morphology
Individual Nanoparticle (Dry) Size (nm) bud-like and D80nm: dahlia-like), were prepared mechanically dispersing pristine SWCNHs in a water solution of SDS. An ultrasonic processor (VCX 130, Sonics & Materials) (Newtown, CT, USA) operating at 20 kHz and 70 W for 30 min was employed to obtain stable suspensions.

Concentration g/L Notes on Preparation
Particle size and zeta potential were measured using a Zetasizer Nano ZS (Malvern Panalytical, Malvern, UK) based on dynamic light scattering (DLS).
Spectral optical transmittance in the linearity regime was measured for diagnostic purposes using a double-beam UV-VIS spectrophotometer (Lambda900, PerkinElmer, Waltham, MA, USA) using a variable length cell [23,24]. High intensity light irradiation experiments were carried out using a pulsed nanosecond Nd:YAG laser as light source (Q-smart 850, Quantel lasers, Les Ulis, France, delivering 6 ns pulses at 1064, 532 and 355 nm wavelengths with a 10 Hz repetition rate). The three laser emission wavelengths were spatially separated by proper optical elements and focused on the sample by a lens. The sample was held in a quartz cuvette with a 10 mm path length. The beam exiting the sample was collected by a couple of lenses and focused on a pyroelectric detector (PE25C, Ophir Optronics, Jerusalem, Israel). The energy incident on the cuvette could be varied by means of proper polarizer beam splitters and measured using a pyroelectric detector (PE50BF, Ophir Optronics, Jerusalem, Israel) ( Figure 1). As a common protocol, all the samples were sonicated in an ultrasonic bath (ProsKit SS803F) (Prokit's Industries Co., Ltd., New Taipei City, Taiwan) for 10 min before the measurements.

Results and Discussion
All the investigated samples are listed in Table 1. Several subgroups can be identified among them, and they can be discriminated by different parameters: preparation technique (groups NH-OX-D80nm), aggregate morphology (dahlias with an 80 nm dry size: sample D80nm; dahlias with a 60 nm dry size: NH series samples and OX; buds with an 80 nm dry size: sample B80nm), dimensions of aggregates (NH series, see Table 2 below), etc. Moreover, each sample was prepared in different concentrations depending on the overall linear absorption at the investigated wavelengths. Table 1. Investigated samples. All nanofluids, except oxidation (OX) ones, are prepared with notfunctionalized (pristine) single-walled carbon nanohorns (SWCNHs). * Same protocol as NH2, prepared again for comparison with the OX sample at equal sample ages.

Sample Label
Morphology Individual Nanoparticle (Dry) Size (nm)

Results and Discussion
All the investigated samples are listed in Table 1. Several subgroups can be identified among them, and they can be discriminated by different parameters: preparation technique (groups NH-OX-D80nm), aggregate morphology (dahlias with an 80 nm dry size: sample D80nm; dahlias with a 60 nm dry size: NH series samples and OX; buds with an 80 nm dry size: sample B80nm), dimensions of aggregates (NH series, see Table 2 below), etc. Moreover, each sample was prepared in different concentrations depending on the overall linear absorption at the investigated wavelengths.
Mean dimensions of aggregates in fluid (DLS hydrodynamic sizes, measured by the relationship between the size of particles and their speed due to Brownian motion through the Stokes-Einstein equation), and ζ potential were measured to evaluate the aggregation and the stability of the suspensions. The absolute value of the ζ potential indicates the degree of electrostatic repulsion between adjacent, similarly charged particles in dispersion. A colloid is usually considered stable if the absolute value of zeta-potential is higher than 30 mV. The results are summarized in Table 2. In the NH1-NH5, series it is clear that the homogenization process decreases the aggregate dimension and improves the colloid stability up to an optimized homogenization time, as all homogenized samples have ζ-potential close Nanomaterials 2020, 10, 2160 5 of 22 to or higher than 30 mV in the absolute value. In fact, these samples in static conditions were stable for months; the pristine NH6 and the functionalized OX samples even showed higher ζ-potential values, indicating a very high stability. From the transmittance spectra, we obtained the extinction coefficient of samples in the linear regime, i.e., at low input light intensity. Figure 2 shows an example of the typical shape of the spectral curve for the B80nm and NH3 samples at 0.05 g/L concentration. The UV plasmonic peak at around 260 nm is characteristic of SWCNHs and extends towards infrared with an extremely smoothly decreasing tail. Spectral features at around 1000 and 1200 nm and, especially, the high peak at around 1445 nm can be ascribed to water. It is worth to mention that, even if the nominal concentrations of nanoparticles in the majority of investigated samples were the same, the specimens showed differences in the actual value of the extinction coefficient. This is connected to the intrinsic stability of each sample, which critically depends on the preparation technique, and on the connected occurrence of clustering and settling phenomena. In fact, if the nanofluid experiences clustering/settling, a part of the value of the extinction coefficient, that arising from nanoparticles, decreases.

Broadband Optical Limiting
Almost all investigated nanofluids showed a typical optical limiting at all three laser wavelengths (confirming the desirable broadband behavior) similar to what is reported in Figure 3, where we can see an example for sample NH4. Figure 3 shows the normalized transmittance, defined as the ratio between the output and input energies Eout/Ein, normalized to its value at low incident intensities, e.g., in the linearity regime, as a function of the input fluence.

Broadband Optical Limiting
Almost all investigated nanofluids showed a typical optical limiting at all three laser wavelengths (confirming the desirable broadband behavior) similar to what is reported in Figure 3, where we can see an example for sample NH 4 . Figure 3 shows the normalized transmittance, defined as the ratio between the output and input energies E out /E in , normalized to its value at low incident intensities, e.g., in the linearity regime, as a function of the input fluence.
Almost all investigated nanofluids showed a typical optical limiting at all three laser wavelengths (confirming the desirable broadband behavior) similar to what is reported in Figure 3, where we can see an example for sample NH4. Figure 3 shows the normalized transmittance, defined as the ratio between the output and input energies Eout/Ein, normalized to its value at low incident intensities, e.g., in the linearity regime, as a function of the input fluence. In Figure 3 we can clearly distinguish three different regimes: at very low incident fluence, the behavior of the sample is linear (Eout/Ein ≈ 1); after a certain input fluence value, the sample shows a decrease in the normalized transmittance-this is the optical limiting regime; and at higher incident energy densities, damage to the nanofluid can occur, and the normalized transmittance rises up again, as shown in Figure 3, for the 1064 nm wavelength, above 0.26 J/cm 2 . The damage to the nanofluids, when occurring, strongly depends on nanoparticle concentration and incident wavelength. Typically, the infrared radiation tends to damage the samples at lower energy compared to ultraviolet and visible wavelengths.
Nearly all the SWCNH samples we analyzed show broadband optical limiting qualitatively similar to that represented in Figure 3, except in the case of a few samples at the 1064 nm wavelength, where the quick damage at high input energies prevented acquiring enough experimental points to quantitatively characterize the nonlinear behavior. Table 3 shows the minimum obtained transmittances relative to the initial (low-energy) linear values. We can see that OL is more effective (i.e., a lower relative transmittance can be obtained) at shorter wavelengths due to the higher linear extinction coefficient. In Figure 3 we can clearly distinguish three different regimes: at very low incident fluence, the behavior of the sample is linear (E out /E in ≈ 1); after a certain input fluence value, the sample shows a decrease in the normalized transmittance-this is the optical limiting regime; and at higher incident energy densities, damage to the nanofluid can occur, and the normalized transmittance rises up again, as shown in Figure 3, for the 1064 nm wavelength, above 0.26 J/cm 2 . The damage to the nanofluids, when occurring, strongly depends on nanoparticle concentration and incident wavelength. Typically, the infrared radiation tends to damage the samples at lower energy compared to ultraviolet and visible wavelengths.
Nearly all the SWCNH samples we analyzed show broadband optical limiting qualitatively similar to that represented in Figure 3, except in the case of a few samples at the 1064 nm wavelength, where the quick damage at high input energies prevented acquiring enough experimental points to quantitatively characterize the nonlinear behavior. Table 3 shows the minimum obtained transmittances relative to the initial (low-energy) linear values. We can see that OL is more effective (i.e., a lower relative transmittance can be obtained) at shorter wavelengths due to the higher linear extinction coefficient.

Effect of Surfactant Concentration
For all nanofluids, with the only exception of OX, the SDS surfactant was added during the preparation (Table 1). Therefore, initially, we checked that the observed OL in nanofluids would not be directly ascribed to the surfactant itself. The experiments carried out on the base fluid with the surfactant, but with no nanoparticles, are reported in the Appendix A and did not show a nonlinear effect in the absence of nanoparticles. It could it be possible that the surfactant has a role in modifying the nonlinear properties of nanofluids as it changes the van der Waals interaction between nanoparticles and the surface tension of the base fluid. To check this, we investigated a series of samples with the same nanoparticle type and concentration and different SDS concentrations. Figure 4 shows the optical limiting properties of the NH6 nanofluid (0.0125 g/L SWCNH concentration) changing the concentration of the surfactant from 0 to 0.50 g/L under UV and visible radiation.
For neither for the 355 nor 532 nm wavelength was it possible to identify an effect of SDS concentration on the optical limiting properties of SWCNH-nanofluids, and a similar result was found for incident radiation at 1064 nm. The effect of the surfactant was only detectable, as expected, when the damage threshold of the samples was concerned. For the 355 nm wavelength, the lowest stability sample was that without the surfactant, while at 532 and 1064 nm wavelengths, the most stable were those with intermediate 0.25 g/L SDS content. This result suggests that, for each wavelength, an optimal concentration of the surfactant exists that maximizes the nanofluid stability under high-intensity optical radiation at that wavelength, which is an interesting result in view of future applications. Table 3. Obtained minimum transmittances at different wavelengths. The symbol "-" refers to the cases where the sample damage prevented quantitative measurements, and the symbol x to the cases of no optical limiting. For the 355 nm wavelength, due to the high linear absorption, which consistently reduced the amount of transmitted radiation below the detection limit of our apparatus, even in the linear regime, the characterization was possible only at the lowest concentration.

Effect of Surfactant Concentration
For all nanofluids, with the only exception of OX, the SDS surfactant was added during the preparation (Table 1). Therefore, initially, we checked that the observed OL in nanofluids would not be directly ascribed to the surfactant itself. The experiments carried out on the base fluid with the surfactant, but with no nanoparticles, are reported in the Appendix A and did not show a nonlinear effect in the absence of nanoparticles. It could it be possible that the surfactant has a role in modifying the nonlinear properties of nanofluids as it changes the van der Waals interaction between nanoparticles and the surface tension of the base fluid. To check this, we investigated a series of samples with the same nanoparticle type and concentration and different SDS concentrations. Figure  4 shows the optical limiting properties of the NH6 nanofluid (0.0125 g/L SWCNH concentration) changing the concentration of the surfactant from 0 to 0.50 g/L under UV and visible radiation.

Effect of Nanoparticle Concentration
The optical limiting properties of nanofluids also depend on the concentration of nanoparticles. All sample types, except NH6, were studied at two different nanoparticle concentrations. Due to the high linear extinction coefficient, for the characterization at 355 nm, it was needed in some cases (B80nm, D80nm, OX) to prepare an additional specimen with a reduced concentration (0.0125 g/L). At 532 nm incident wavelength, optical limiting is more effective (i.e., it occurs with a higher slope as a function of the input energy) at a low nanoparticle concentration, as reported in Figure 5 for the samples NH4 and NH5. The same result holds true for the 1064 nm wavelength. This behavior suggests that OL in these cases could be due to a saturation effect of the first excited state (excited state absorption-ESA, see below), because if a larger number of nanoparticles exists in the light-pumped volume, more energy is required to saturate their excited level; thus, the optical limiting at high concentrations needs a higher incident energy to reveal itself. Differently, at 355 nm, better optical limiting properties were observed for higher nanoparticle concentrations, as shown in Figure 6. This behavior agrees with that reported in the literature for carbon nanotubes [25], graphite/nanodiamond mixtures [26], functionalized graphene nanoplatelets [27,28] and gold nanoparticles [29] and can be explained in terms of the light-induced creation of bubbles within the fluid. In fact, under the effect of light irradiation, nanoparticles become localized heat sources within the fluid, ultimately producing vaporization of the surrounding fluid layers and/or ionization and expansion of nanostructures themselves. Therefore, as the number of nanoparticles in the light-pumped fluid volume increases, more bubbles will be created by the laser, resulting in a larger decrease in the sample transmittance.
At 532 nm incident wavelength, optical limiting is more effective (i.e., it occurs with a higher slope as a function of the input energy) at a low nanoparticle concentration, as reported in Figure 5 for the samples NH4 and NH5. The same result holds true for the 1064 nm wavelength. This behavior suggests that OL in these cases could be due to a saturation effect of the first excited state (excited state absorption-ESA, see below), because if a larger number of nanoparticles exists in the lightpumped volume, more energy is required to saturate their excited level; thus, the optical limiting at high concentrations needs a higher incident energy to reveal itself. Differently, at 355 nm, better optical limiting properties were observed for higher nanoparticle concentrations, as shown in Figure  6. This behavior agrees with that reported in the literature for carbon nanotubes [25], graphite/nanodiamond mixtures [26], functionalized graphene nanoplatelets [27,28] and gold nanoparticles [29] and can be explained in terms of the light-induced creation of bubbles within the fluid. In fact, under the effect of light irradiation, nanoparticles become localized heat sources within the fluid, ultimately producing vaporization of the surrounding fluid layers and/or ionization and expansion of nanostructures themselves. Therefore, as the number of nanoparticles in the lightpumped fluid volume increases, more bubbles will be created by the laser, resulting in a larger decrease in the sample transmittance.

Effect of Nanoparticle Morphology
Depending on the synthesis conditions of nanopowders, it is possible to obtain some typical morphologies of their aggregates. In particular, if SWCNHs are produced by laser ablation, aggregates assume a typical appearance called "dahlia". Otherwise if they are produced by arch discharge, their aggregation form tends to be a different shape called "bud-like" [30,31]. In the case of production by induction heating, as in the process used in our case, depending on the production parameters, either dahlia or bud morphologies ca be obtained. Figure 7 shows SEM images of our nanohorn powders. More details including TEM images, Raman and XRD investigations can be found in [32]. a b

Effect of Nanoparticle Morphology
Depending on the synthesis conditions of nanopowders, it is possible to obtain some typical morphologies of their aggregates. In particular, if SWCNHs are produced by laser ablation, aggregates assume a typical appearance called "dahlia". Otherwise if they are produced by arch discharge, their aggregation form tends to be a different shape called "bud-like" [30,31]. In the case of production by induction heating, as in the process used in our case, depending on the production parameters, either dahlia or bud morphologies ca be obtained. Figure 7 shows SEM images of our nanohorn powders. More details including TEM images, Raman and XRD investigations can be found in [32]. morphologies of their aggregates. In particular, if SWCNHs are produced by laser ablation, aggregates assume a typical appearance called "dahlia". Otherwise if they are produced by arch discharge, their aggregation form tends to be a different shape called "bud-like" [30,31]. In the case of production by induction heating, as in the process used in our case, depending on the production parameters, either dahlia or bud morphologies ca be obtained. Figure 7 shows SEM images of our nanohorn powders. More details including TEM images, Raman and XRD investigations can be found in [32]. We investigated several samples belonging to the family of dahlias and a sample of bud morphology. Figures 8 and 9 compare OL performances for samples belonging to dahlia and bud families. In particular, Figure 8 compares, at the same concentration and linear extinction coefficient values, dahlia and bud morphologies with similar mean dimensions of the starting dry nanoparticles (80 nm, labelled as samples D80nm and B80nm, respectively, in Table 1). It should be noted that these sizes are referred to as dry nanoparticles immediately after the synthesis and depend on the process parameters. When suspended in the fluid, individual nanoparticles can aggregate, producing clusters with the dimensions given in Table 2 (that include also the surfactant size), which, for these two samples, are 197 nm (buds) and 241 nm (dahlias), respectively. We investigated several samples belonging to the family of dahlias and a sample of bud morphology. Figures 8 and 9 compare OL performances for samples belonging to dahlia and bud families. In particular, Figure 8 compares, at the same concentration and linear extinction coefficient values, dahlia and bud morphologies with similar mean dimensions of the starting dry nanoparticles (80 nm, labelled as samples D80nm and B80nm, respectively, in Table 1). It should be noted that these sizes are referred to as dry nanoparticles immediately after the synthesis and depend on the process parameters. When suspended in the fluid, individual nanoparticles can aggregate, producing clusters with the dimensions given in Table 2 (that include also the surfactant size), which, for these two samples, are 197 nm (buds) and 241 nm (dahlias), respectively.  From Figure 8, we can see that the properties of the two samples are quite similar, with dahlias slightly better performing than buds, especially at the 532 nm laser wavelength and at the highest From Figure 8, we can see that the properties of the two samples are quite similar, with dahlias slightly better performing than buds, especially at the 532 nm laser wavelength and at the highest concentration. However, the samples also showed different cluster dimensions, thus, this comparison is not sufficient to assess whether the observed differences could be a morphology or a cluster size effect.
For this reason, we also compared two dahlia/bud samples with similar cluster sizes ( Figure 9): NH1 (dahlia with a cluster size of 202 nm) and B80nm (bud with a cluster size of 197 nm, see Table 2). The comparison was carried out considering two different situations. In the first case (Figure 9a), we considered different concentrations of the two samples in order to have similar values of linear extinction coefficients, and we found that the dahlia sample performed better at both 355 and 532 nm, and the same holds true for the 1064 nm wavelength. Numerical fitting (see the paragraph below) also confirmed the lowest energy threshold values shown by the sample (NH1, 0.025 g/L) with respect to B80nm (0.0125 g/L). In the second case (Figure 9b), we compared the two samples at the same concentration of 0.025 g/L. Again, the dahlia morphology showed stronger nonlinearity than buds, in particular for the green wavelength.  From Figure 8, we can see that the properties of the two samples are quite similar, with dahlias slightly better performing than buds, especially at the 532 nm laser wavelength and at the highest concentration. However, the samples also showed different cluster dimensions, thus, this comparison is not sufficient to assess whether the observed differences could be a morphology or a cluster size effect.
For this reason, we also compared two dahlia/bud samples with similar cluster sizes ( Figure 9): NH1 (dahlia with a cluster size of 202 nm) and B80nm (bud with a cluster size of 197 nm, see Table  2). The comparison was carried out considering two different situations. In the first case (Figure 9a), we considered different concentrations of the two samples in order to have similar values of linear extinction coefficients, and we found that the dahlia sample performed better at both 355 and 532 nm, and the same holds true for the 1064 nm wavelength. Numerical fitting (see the paragraph below) also confirmed the lowest energy threshold values shown by the sample (NH1, 0.025 g/L) with respect to B80nm (0.0125 g/L). In the second case (Figure 9b), we compared the two samples at the same concentration of 0.025 g/L. Again, the dahlia morphology showed stronger nonlinearity than buds, in particular for the green wavelength.
To complete the study of the dependence of optical limiting properties on nanoparticle morphology, a further comparison could be made between dahlia-like samples with different sizes of individual dry particles. Figure 10 compares the OL curves at 355 and 532 nm wavelengths of dahlias with individual average size of 80 nm (D80nm sample) and 60 nm (NH1 sample). Similarly to the previous case shown in Figure 9, a comparison was carried out either for similar values of To complete the study of the dependence of optical limiting properties on nanoparticle morphology, a further comparison could be made between dahlia-like samples with different sizes of individual dry particles. Figure 10 compares the OL curves at 355 and 532 nm wavelengths of dahlias with individual average size of 80 nm (D80nm sample) and 60 nm (NH1 sample). Similarly to the previous case shown in Figure 9, a comparison was carried out either for similar values of extinction coefficients (Figure 10a) or with equal nanoparticle concentrations (Figure 10b). It is clear that OL is always more pronounced for dahlias with an average size of 60 nm (NH1), despite the fact that the cluster size is larger for the other D80nm sample (241 versus 202 nm, see Table 2). Interestingly, the largest differences in OL performances among samples are shown again at the 532 nm laser wavelength. As a final comment, we should note that the D80nm nanofluid shows better stability against damage, especially at 355 nm, in agreement with the measured values of the ζ-potential. Nanomaterials 2020, 10, x FOR PEER REVIEW 11 of 21 extinction coefficients (Figure 10a) or with equal nanoparticle concentrations (Figure 10b). It is clear that OL is always more pronounced for dahlias with an average size of 60 nm (NH1), despite the fact that the cluster size is larger for the other D80nm sample (241 versus 202 nm, see Table 2). Interestingly, the largest differences in OL performances among samples are shown again at the 532 nm laser wavelength. As a final comment, we should note that the D80nm nanofluid shows better stability against damage, especially at 355 nm, in agreement with the measured values of the ζpotential. The analysis carried out in the previous paragraphs (see  allows us to infer that the main parameters affecting OL properties are primarily the size of individual nanoparticles and, secondly, the nanoparticle morphology. The role of cluster dimensions seems of secondary importance when compared to the two previous parameters, but it can be identified when the other parameters are kept unchanged (see Section 3.5 below).
It is worth noting that it is known that size and morphology are strictly connected to fundamental properties of nanoparticles, as they affect their energy level structure. Therefore, the largest impact of these parameters can be expected on the phenomena whose main origin arises from the properties of the energy level structure itself, such as the excited state absorption (ESA) mentioned in Section 3.3. In this framework, we recall that the largest differences among samples, as a function of individual nanoparticle size and morphology, were detected for the 532 nm laser The analysis carried out in the previous paragraphs (see  allows us to infer that the main parameters affecting OL properties are primarily the size of individual nanoparticles and, secondly, the nanoparticle morphology. The role of cluster dimensions seems of secondary importance when compared to the two previous parameters, but it can be identified when the other parameters are kept unchanged (see Section 3.5 below).
It is worth noting that it is known that size and morphology are strictly connected to fundamental properties of nanoparticles, as they affect their energy level structure. Therefore, the largest impact of these parameters can be expected on the phenomena whose main origin arises from the properties of the energy level structure itself, such as the excited state absorption (ESA) mentioned in Section 3.3. In this framework, we recall that the largest differences among samples, as a function of individual nanoparticle size and morphology, were detected for the 532 nm laser wavelength, while at 355 nm, the properties appear less differentiated. This further confirms that the dominant mechanisms producing OL in these two spectral ranges are different. Moreover, it also confirms that, at 532 nm, the dominant mechanism involves the fundamental electronic properties of nanoparticles to a greater extent, which is in agreement with the ESA hypothesis in Section 3.3 on the basis of the concentration-dependent trend.
Finally, it was also possible to compare the effect of functionalization of SWCNHs by oxidation. The oxidation process makes the nanofluids more stable over time, but it changes physical and chemical properties of nanoparticles and, consequently, it could change the interaction among them and with the base fluid. Figure 11 compares oxidized and pristine dahlia morphologies. When the comparison was carried out at the same 0.0125 g/L concentration (where, however, linear extinction coefficients of the OX sample are lower than those of NH6), at 532 nm, OX did not show optical limiting at all. If, however, we compare the NH6 sample at 0.0125 g/L with the OX sample at 0.025 g/L (thus, in this case, allowing a slightly higher extinction coefficient of OX than NH6), we are able to detect OL at 532 nm by the oxidized sample as well. It should be noted that OX (oxidized) and NH6 (pristine) samples are characterized by identical preparation methods and age. The different behavior at varying concentrations shows that some differences exist in the OL properties of the samples. The fact that these differences more clearly appear at 532 nm confirms their electronic origin. They can be due to a reduction in the oxidized sample of the interband π plasmon peak (π-π* transition), which is typical of SWCNH and other graphene-based nanostructures. This reduction of the plasmonic peak is probably ascribed to the presence of functional groups that are induced on the surface of the material and/or to partially damaged material due to oxidation process, as already observed in [33]. As for the 1064 nm wavelength, both samples are quickly damaged by the radiation, and the characterization was not possible. Nanomaterials 2020, 10, x FOR PEER REVIEW 12 of 21 transition), which is typical of SWCNH and other graphene-based nanostructures. This reduction of the plasmonic peak is probably ascribed to the presence of functional groups that are induced on the surface of the material and/or to partially damaged material due to oxidation process, as already observed in [33]. As for the 1064 nm wavelength, both samples are quickly damaged by the radiation, and the characterization was not possible.

Effect of Sizes of Aggregates
A comparison of OL performances of samples with different sizes of aggregates, but with every other parameter (morphology and individual nanoparticle size) fixed, for the same 0.05 g/L concentration, and at a 532 nm wavelength is shown in Figure 12.

Effect of Sizes of Aggregates
A comparison of OL performances of samples with different sizes of aggregates, but with every other parameter (morphology and individual nanoparticle size) fixed, for the same 0.05 g/L concentration, and at a 532 nm wavelength is shown in Figure 12

Effect of Sizes of Aggregates
A comparison of OL performances of samples with different sizes of aggregates, but with every other parameter (morphology and individual nanoparticle size) fixed, for the same 0.05 g/L concentration, and at a 532 nm wavelength is shown in Figure 12.  Table 2 for cluster dimensions).
The observed behavior is fairly correlated with the dimensions of aggregates: OL occurs at lower input energy density and with a higher slope as the dimensions of aggregates increase (see measured sizes in Table 2), similarly to what is reported in the literature for nanodiamond clusters [34]. The only exception to this trend is represented by sample NH5, which is characterized by partial damage of the nanohorn structure because of the prolonged homogenization process.
It is worth comparing here our results with the literature considering the NH4 sample, which is characterized by a similar hydrodynamic size with respect to the only available report (97 nm, see Table 2 vs. 95 nm as in [19]). For sample NH4 at the 532 nm wavelength, we observe that transmittance decreases to 90% of its linear value for input fluences of 0.1 J/cm 2 for the lowest and 0.3 J/cm 2 for the highest concentrations (Figure 5a), while in [19], the same transmittance value was obtained for input fluence of around 0.7 J/cm 2 . Considering the differences in the samples examined  Table 2 for cluster dimensions).
The observed behavior is fairly correlated with the dimensions of aggregates: OL occurs at lower input energy density and with a higher slope as the dimensions of aggregates increase (see measured sizes in Table 2), similarly to what is reported in the literature for nanodiamond clusters [34]. The only exception to this trend is represented by sample NH5, which is characterized by partial damage of the nanohorn structure because of the prolonged homogenization process.
It is worth comparing here our results with the literature considering the NH4 sample, which is characterized by a similar hydrodynamic size with respect to the only available report (97 nm, see Table 2 vs. 95 nm as in [19]). For sample NH4 at the 532 nm wavelength, we observe that transmittance decreases to 90% of its linear value for input fluences of 0.1 J/cm 2 for the lowest and 0.3 J/cm 2 for the highest concentrations (Figure 5a), while in [19], the same transmittance value was obtained for input fluence of around 0.7 J/cm 2 . Considering the differences in the samples examined in the two works and the fact that in the cited reference several sample details are not given, the obtention of the same order of magnitude can be accepted as a fair agreement.

Modelling the Optical Limiting Curve
The appearance of OL in nanosuspensions can basically be explained by two mechanisms: nonlinear absorption and nonlinear refraction [35], depending on the nature of nanoparticles and on the properties of suspending fluids [6]. The effect that actually occurs can be identified by applying semi-empirical models. Nonlinear absorption can be due to different effects, such as reverse saturable absorption, two-photon absorption etc [6]. It can be modeled by introducing a nonlinear term in the Lambert-Beer law [7]: where F(z) is the energy fluence at the z position in the sample, α is the linear extinction coefficient and, σ 1 is the excited state absorption (ESA) cross-section. If we solve this equation following the method described in [36,37], we can link the output energy from the nanofluid E out to incident energy E in , obtaining the following relationship: where T 2 s is a coefficient describing the reflection losses on the walls of the cuvette, and L is the thickness of the sample. The term e −αL describes the linear extinction, and E t is the threshold energy defined as the energy where the transmittance decreases to 90% of its original value [7]. In the following, we label this model as nonlinear Lambert-Beer (NL-LB).
On the other hand, a model where OL is only due to nonlinear refraction was developed in [38]. In the cited reference, nonlinear properties are ascribed to the scattering between laser photons and vapor bubbles yielded by the vaporization of the base fluid surrounding the nanoparticle and/or by ionization and vaporization of the nanoparticles: where α e is the nonlinear extinction coefficient, and E t is the energy threshold for bubble formation, both obtained from a fitting procedure of experimental data. This model will be labelled as McEwan-Milsom-James (MMJ) in the following paragraph.
In order to verify whether theoretical models are compatible with our experimental data and, in the positive case, to estimate the values of the model parameters, we carried out a series of numerical tests. The procedure consisted of a standard least-squares approach, where the objective function is the sum S of the squared differences between the observed E out values and the corresponding computed values for each E in . The best fit model is that for which S is the minimum. In other terms, we look for the values of the model's free parameters (E t and T s in the case of the NL-LB model, or E t , T s and α e in the case of the MMJ model) that cause S to be the minimum value (if they exist). The minimum value S min is a measure of the distance between the fittest theoretical model and the data set. Due to the fact that both E in and E out are affected by random errors, a χ 2 standard approach cannot be straightforwardly followed for the evaluation of the statistical goodness of fit, expressed in terms of the probability P that, just by chance, we could have found a larger value of S min . In order to determine the correct statistics of S min , we followed a fully numerical Monte-Carlo approach consisting of randomly generating a number of simulated experimental sets based on the same theoretical model from our best fit, perturbing the values of E in and E out each time. For each simulated data set, we repeated the fit, counting the number of times we obtained a larger S min . If the probability P was less than 5%, we rejected the fit, declaring the model not compatible with experimental data. A similar Monte-Carlo approach was used to estimate the formal errors on the fitted model parameters. Both in the computation of the formal errors and of the goodness of fit, we assumed Gaussian random errors in E in and E out experimental values.
As reported in Figure 13 for sample D80nm at 532 nm, when the optical limiting is not strong, both models are able to reconstruct the experimental data. For a fair comparison with both the data shown in the previous paragraphs and those reported in the literature, in the following, the fit results will be given in terms of fluence (energy density). Therefore, the obtained fluence threshold values in Figure 13 are (66 ± 4) ×10 −3 J/cm 2 for NL-LB and (44 ± 1) ×10 −3 J/cm 2 for MMJ models. On the other hand, if optical limiting is stronger, typically, the NL-LB model well reproduces the first experimental points deviating from linearity, while the MMJ model is more suited to reconstructing the final part of data points, as showed in Figure 14, depicting the NH1 sample for the 532 nm incident wavelength and 0.0025 g/L concentration. The plot on the right of Figure 14 is an enlargement of the first experimental points, showing that the NL-LB model better reproduces the experimental trend at lower input energy values, while the MMJ model is more appropriate for higher input ranges (Figure 14, left plot). For this specific case, the poor data reconstruction at low input energies prevents the MMJ model from being statistically acceptable (Table 4).
of data points, as showed in Figure 14, depicting the NH1 sample for the 532 nm incident wavelength and 0.0025 g/L concentration. The plot on the right of Figure 14 is an enlargement of the first experimental points, showing that the NL-LB model better reproduces the experimental trend at lower input energy values, while the MMJ model is more appropriate for higher input ranges ( Figure  14, left plot). For this specific case, the poor data reconstruction at low input energies prevents the MMJ model from being statistically acceptable (Table 4).  For all available data, both models were checked for fitting. The values of the obtained parameters for the different sample/concentration/wavelength combinations with a fixed statistical confidence level of 5% are listed in Table 4 for threshold fluence values Ft = Et/A, with the laser spot area A and Et given by Equations (2) and (3) and in Table 5 for the α e /α ratio (Equation (3)). As previously mentioned, in some cases, both models are valid, while in other cases, only one of them is a b and 0.0025 g/L concentration. The plot on the right of Figure 14 is an enlargement of the first experimental points, showing that the NL-LB model better reproduces the experimental trend at lower input energy values, while the MMJ model is more appropriate for higher input ranges ( Figure  14, left plot). For this specific case, the poor data reconstruction at low input energies prevents the MMJ model from being statistically acceptable (Table 4).  For all available data, both models were checked for fitting. The values of the obtained parameters for the different sample/concentration/wavelength combinations with a fixed statistical confidence level of 5% are listed in Table 4 for threshold fluence values Ft = Et/A, with the laser spot area A and Et given by Equations (2) and (3) and in Table 5 for the α e /α ratio (Equation (3)). As previously mentioned, in some cases, both models are valid, while in other cases, only one of them is a b For all available data, both models were checked for fitting. The values of the obtained parameters for the different sample/concentration/wavelength combinations with a fixed statistical confidence level of 5% are listed in Table 4 for threshold fluence values F t = E t /A, with the laser spot area A and E t given by Equations (2) and (3) and in Table 5 for the α e /α ratio (Equation (3)). As previously mentioned, in some cases, both models are valid, while in other cases, only one of them is acceptable. Energy threshold fluence values are between 10 −3 and 10 −1 J/cm 2 . Typically, for a fixed sample and concentration, the fluence threshold increases with wavelength in agreement with the decrease in the linear extinction coefficient. Modelling OL data for the 1064 nm wavelength is a difficult task because of sample damage, and this is the reason why fitting results in the infrared are less represented in Table 4. In the majority of cases when fitting with both models is possible, MMJ thresholds are lower than those of NL-LB, suggesting the quicker onset of bubbles with respect to saturation phenomena. Further cases are found when none of the models give a reliable result. This happens, for instance, when a particularly strong OL is detected. These cases are characterized by a nearly constant output energy, irrespective of the input one, for input ranges above certain values, like the data shown in Figure 15. This strong OL behavior, also observed at the 355 nm wavelength for D80nm(0.025 g/L) and NH1(0.025 g/L) samples, is similar to that observed for glycol suspensions of graphite/nanodiamond mixtures [26] and is likely the result of a strong optical scattering due to a massive bubble production, stronger than that described for the MMJ model. In some other cases, the unsuccessful fitting of our models can be also due to the strong mixing between the two effects, which on the other hand, within each one of the considered semi-empirical models, are taken into account separately. These facts display the need to develop a comprehensive model that is able to include both nonlinear absorption and nonlinear refraction, which, however, is beyond the scope of the present work and will be the subject of further studies.  acceptable. Energy threshold fluence values are between 10 −3 and 10 −1 J/cm 2 . Typically, for a fixed sample and concentration, the fluence threshold increases with wavelength in agreement with the decrease in the linear extinction coefficient. Modelling OL data for the 1064 nm wavelength is a difficult task because of sample damage, and this is the reason why fitting results in the infrared are less represented in Table 4. In the majority of cases when fitting with both models is possible, MMJ thresholds are lower than those of NL-LB, suggesting the quicker onset of bubbles with respect to saturation phenomena. Further cases are found when none of the models give a reliable result. This happens, for instance, when a particularly strong OL is detected. These cases are characterized by a nearly constant output energy, irrespective of the input one, for input ranges above certain values, like the data shown in Figure 15. This strong OL behavior, also observed at the 355 nm wavelength for D80nm(0.025 g/L) and NH1(0.025 g/L) samples, is similar to that observed for glycol suspensions of graphite/nanodiamond mixtures [26] and is likely the result of a strong optical scattering due to a massive bubble production, stronger than that described for the MMJ model. In some other cases, the unsuccessful fitting of our models can be also due to the strong mixing between the two effects, which on the other hand, within each one of the considered semi-empirical models, are taken into account separately. These facts display the need to develop a comprehensive model that is able to include both nonlinear absorption and nonlinear refraction, which, however, is beyond the scope of the present work and will be the subject of further studies.   In Figure 16, we show some examples of data with univocal fitting, while Figure 17 shows some cases that can be modelled by both NL-LB and MMJ. It is worth noting that these models are able to numerically reconstruct a wide range of experimental data sets, including weaker OL regimes identified by the higher thresholds in Table 4.
The ratio α e /α between the nonlinear and linear extinction coefficient obtained from MMJ data fitting is summarized in Table 5. Its value in the majority of cases decreases with increasing laser wavelength and nanoparticle concentration. The highest obtained values are around 2.8 and 2.5 and were shown by the lowest concentration samples (NH5 and NH2) under 355 nm radiation. The relative fitting curves are shown in Figure 18.
In Figure 16, we show some examples of data with univocal fitting, while Figure 17 shows some cases that can be modelled by both NL-LB and MMJ. It is worth noting that these models are able to numerically reconstruct a wide range of experimental data sets, including weaker OL regimes identified by the higher thresholds in Table 4. In Figure 16, we show some examples of data with univocal fitting, while Figure 17 shows some cases that can be modelled by both NL-LB and MMJ. It is worth noting that these models are able to numerically reconstruct a wide range of experimental data sets, including weaker OL regimes identified by the higher thresholds in Table 4. The ratio α e /α between the nonlinear and linear extinction coefficient obtained from MMJ data fitting is summarized in Table 5. Its value in the majority of cases decreases with increasing laser wavelength and nanoparticle concentration. The highest obtained values are around 2.8 and 2.5 and were shown by the lowest concentration samples (NH5 and NH2) under 355 nm radiation. The relative fitting curves are shown in Figure 18.

Production of Vapor Bubbles
Bubble production has often been theorized in the literature [21,22] for carbon nanoparticles, but it has never been documented to date, except for a recent case investigated by our group on graphite/nanodiamond nanofluids dispersed in ethylene glycol [26]. We report in Figure 19 a photo of bubble production of our aqueous nanohorn-based nanofluids under 355 nm incident radiation. The laser beam immediately creates nano-and micro-bubbles that increase in volume due to bubble dynamics and coalescence. We can clearly see over the white spot a contrail of vapor rising up to the nanofluid surface. The video (Supplementary Material Video S1) recording of bubble formation is made available as additional material. To the best of our knowledge, it constitutes the first evidence of light irradiation-induced bubble generation in a water-based nanofluid. In fact, it is worth recalling that bubble formation critically depends on the system, being strongly related to thermophysical a b

Production of Vapor Bubbles
Bubble production has often been theorized in the literature [21,22] for carbon nanoparticles, but it has never been documented to date, except for a recent case investigated by our group on graphite/nanodiamond nanofluids dispersed in ethylene glycol [26]. We report in Figure 19 a photo of bubble production of our aqueous nanohorn-based nanofluids under 355 nm incident radiation. The laser beam immediately creates nano-and micro-bubbles that increase in volume due to bubble dynamics and coalescence. We can clearly see over the white spot a contrail of vapor rising up to the nanofluid surface. The video (Supplementary Material Video S1) recording of bubble formation is made available as additional material. To the best of our knowledge, it constitutes the first evidence of light irradiation-induced bubble generation in a water-based nanofluid. In fact, it is worth recalling that bubble formation critically depends on the system, being strongly related to thermophysical properties of the dispersing fluid, as well as optical and thermal properties of nanoparticles. We saw a massive bubble production for the 355 nm wavelength, while at 532 nm, the amount of produced bubbles was lower due both to the lower extinction coefficient and to the mechanism of saturation, which likely is the dominant one. No bubble production was observed for the 1064 nm wavelength for any SWCNH sample probably because of the quick sample damage. Nanomaterials 2020, 10, x FOR PEER REVIEW 18 of 21 properties of the dispersing fluid, as well as optical and thermal properties of nanoparticles. We saw a massive bubble production for the 355 nm wavelength, while at 532 nm, the amount of produced bubbles was lower due both to the lower extinction coefficient and to the mechanism of saturation, which likely is the dominant one. No bubble production was observed for the 1064 nm wavelength for any SWCNH sample probably because of the quick sample damage.

Conclusions
The present work, using an original approach consisting of simple transmittance measurements joined to semi-empirical fitting models, proves nonlinear optical properties of SWCNH-based aqueous nanofluids at three different wavelengths (355, 532 and 1064 nm) and systematically investigates the dependence of optical nonlinearity from several sample parameters: surfactant concentration, nanoparticle concentration and morphology, dimensions of individual nanoparticles and dimensions of aggregates. The surfactant seems to have no impact on optical limiting, while dahlia morphologies appear to perform better than the bud one. Moreover, the starting size of individual nanoparticles, within the same dahlia-like morphology, appears to affect optical properties. Differences in optical limiting among pristine and oxidized dahlias are likely connected to the oxidation-induced reduction of the plasmonic peak. A cluster size effect is demonstrated for fixed morphology and individual nanoparticle size, showing that OL is more effective for larger aggregates. As for the effect of nanoparticle concentration, it is likely connected to the dominant mechanism producing optical limiting; at a 355 nm wavelength, OL is more effective (lower threshold and higher slope) for higher concentrations, while at 532 and 1064 nm wavelengths, it is more effective for lower concentrations. This dependence, together with the analysis of the nanoparticle size and morphology dependence of observed optical limiting, allows us to infer that the dominant mechanism at 355 nm is the generation of bubbles in the fluid, while at the other wavelengths, OL is mainly produced by saturation of absorption, even if, in the majority of cases, both effects appear to coexist. This is finally validated fitting experimental data by two models taking into account bubble formation and saturation, respectively. We also visually documented for the first time the generation of vapor bubbles in SWCNH samples under 355 nm radiation and, to a lower extent, under 532 nm radiation as well. The formation of bubbles is a key factor for possible future use of this type of nanoparticle in green energy, in particular as direct solar medium for vapor production.

Conclusions
The present work, using an original approach consisting of simple transmittance measurements joined to semi-empirical fitting models, proves nonlinear optical properties of SWCNH-based aqueous nanofluids at three different wavelengths (355, 532 and 1064 nm) and systematically investigates the dependence of optical nonlinearity from several sample parameters: surfactant concentration, nanoparticle concentration and morphology, dimensions of individual nanoparticles and dimensions of aggregates. The surfactant seems to have no impact on optical limiting, while dahlia morphologies appear to perform better than the bud one. Moreover, the starting size of individual nanoparticles, within the same dahlia-like morphology, appears to affect optical properties. Differences in optical limiting among pristine and oxidized dahlias are likely connected to the oxidation-induced reduction of the plasmonic peak. A cluster size effect is demonstrated for fixed morphology and individual nanoparticle size, showing that OL is more effective for larger aggregates. As for the effect of nanoparticle concentration, it is likely connected to the dominant mechanism producing optical limiting; at a 355 nm wavelength, OL is more effective (lower threshold and higher slope) for higher concentrations, while at 532 and 1064 nm wavelengths, it is more effective for lower concentrations. This dependence, together with the analysis of the nanoparticle size and morphology dependence of observed optical limiting, allows us to infer that the dominant mechanism at 355 nm is the generation of bubbles in the fluid, while at the other wavelengths, OL is mainly produced by saturation of absorption, even if, in the majority of cases, both effects appear to coexist. This is finally validated fitting experimental data by two models taking into account bubble formation and saturation, respectively. We also visually documented for the first time the generation of vapor bubbles in SWCNH samples under 355 nm radiation and, to a lower extent, under 532 nm radiation as well. The formation of bubbles is a key factor for possible future use of this type of nanoparticle in green energy, in particular as direct solar medium for vapor production.

Conflicts of Interest:
The authors declare no conflict of interest.

Appendix A Linearity of the Base Fluid
To exclude the notion that the observed OL in SWCNH-based nanofluids could be due to SDS surfactant rather than to nanoparticles, we prepared a solution of water and SDS without nanoparticles to also be subjected to optical limiting experiments.
To detect even very small OL effects produced by SDS, the SDS concentration in the sample without nanoparticles was 0.5 g/L, much higher than in all the samples laden with SWCNHs (Table 1), and the investigation was carried out exploring, for the different wavelengths, the energy range where OL was previously obtained in the cases of nanofluids, before their damage. As shown in Figure A1, at all wavelengths, the base fluid had a completely linear behavior. This allowed us to conclude that the OL effects we obtained for SWCNH-nanofluids arose from nanoparticles.