# Enhanced Thermal Lens Effect in Gold Nanoparticle-Doped Lyotropic Liquid Crystal by Nanoparticle Clustering Probed by Z-Scan Technique

## Abstract

This work presents an experimental study of the thermal lens effect in Au nanoparticles-doped lyotropic liquid crystals under cw 532 nm optical excitation. Spherical Au nanoparticles of about 12 nm were prepared by Turkevich’s method, and the lyotropic liquid crystal was a ternary mixture of SDS, 1-DeOH, and water that exhibits an isotropic phase at room temperature. The lyotropic matrix induces aggregation of the nanoparticles, leading to a broad and a red-shifted surface plasmon resonance. The thermal nonlinear optical refraction coefficient *n*_{2} increases as a power of number density of nanoparticles, being possible to address this behavior to nanoparticle clustering.

### Keywords

Thermal lens Gold nanoparticles Clustering Lyotropic liquid crystal## 1 Introduction

In the last years, there has been an increasing interest in the thermal and optical properties of nanocomposite materials because of the new phenomena arising from the nanoscale and the envisaged technological applications. In this field stands out the nanofluids, stable suspensions of metallic nanoparticles whose optical properties arise from the surface plasmon resonance (SPR), a collective oscillation of the free electrons in the conduction band [1, 2]. An important feature of this band is its dependence on size [3] and shape [4, 5] of the nanoparticles and on the presence of clusters [6, 7]. Nanofluids also exhibit enhanced thermal transport properties [8, 9, 10]. Liquids with suspended nanoparticles display thermal conductivities significantly higher than that of the base fluids. Besides the numerous researches on the linear and nonlinear optical properties of noble metal nanoparticles, the photothermal properties of nanofluids have not deserved the same attention [11, 12, 13]. In addition to an interest in basic research, the study of the photothermal properties of nanofluids is relevant for technological and medical applications. In this sense, plasmonic photothermal therapy of tumors already is a promising new field in the nanomedicine [14, 15]. An important issue in nanofluids, envisaging practical applications, is the clustering [16, 17]. It was shown that the aggregation of Au nanoparticles leads to an enhancement in the heating effect under optical excitation [18] but a complete model about the generation and transport of heat taking into account the complex structure of the aggregates is lacking.

The aim of this paper is to give an insight into the role of nanoparticle clustering in the thermal nonlinear optical response of a medium containing gold nanoparticles (AuNPs), proposing a phenomenological model of the thermal conductivity and of the thermal lens effect. To this end, we have explored the formation of a thermal lens by the Z-scan technique in two different media containing spherical citrated gold nanoparticles, water, and lyotropic liquid crystal, varying nanoparticle concentration, under cw optical excitation at 532 nm.

## 2 Experimental Details

_{4}) ⋅H

_{2}O (Vetec PA) as precursor and 2.0 ml of a 1 % solution of Na

_{3}C

_{6}H

_{5}O

_{7}⋅2H

_{2}O (Synth PA) as reductor and surfactant agent. These reagents were used without further purification. The temperature during the reaction was maintained close to 373 K. The half reactions for the synthesis of colloidal gold are given in (1) and (2).

The result was a ruby red colloid. Measurements of zeta potential reveal that the nanoparticles are highly stable and have an average surface charge of −33.4 ± 0.5 mV at pH 8.2, which remained stable, protected from the light, for at least 5 months.

The lyotropic liquid crystal used in this study is a mixture of sodium dodecyl sulfate (SDS) [23 wt%], 1-decanol (1-DeOH) [2 wt%], and water [75 wt%], which exhibits an isotropic phase at room temperature (24 °C). The basic units of these kind of liquid crystals are the micelles, anisotropic aggregates of amphiphilic molecules, whose average dimensions have a typical size of ∼100*Å* [20]. In the isotropic phase, the principal axes of the different anisotropic aggregates are oriented in space in a random way, i.e., the optical axis is not defined.

For both, colloidal gold and AuNP-doped lyotropic liquid crystal samples, named after colloid (*C*) and lyotropic (*L*), respectively, for shortness, we prepared seven dilutions of nanoparticles. The concentrations or number density (*N*) in particles/ml were *N*_{1}( 5.66×10^{11}), *N*_{2}( 8.49 × 10^{11}), *N*_{3}( 11.32 × 10^{11}), *N*_{4}( 14.15 × 10^{11}), *N*_{5}( 16.98×10^{11}), *N*_{6}(19.8×10^{11}), and *N*_{7}( 22.64 × 10^{11}). These concentrations correspond to a filling factor of ∼10^{−5}−10^{−4}*%*.

The following equipments were employed for characterizing the nanoparticles: Cary 50 from Varian (linear optical absorption), X-ray diffractometer Ultima IV from Rigaku (crystalline structure), Zetasizer Nano ZS90 from Malvern (zeta potential), TECNAI F30 (TEM), and Abbe refractometer RTA-100 (refraction index as a function of temperature).

### 2.1 The Z-scan Technique

*n*=

*n*

_{0}+(

*d*

*n*/

*d*

*T*)Δ

*T*, where

*n*

_{0}is the linear refraction index,

*d*

*n*/

*d*

*T*is the thermooptic coefficient, and Δ

*T*is the change in temperature [22]. Diffusion of heat leads to a spatial variation of the laser beam phase that does not match exactly its intensity spatial profile

*I*(

*r*). However, for media with low optical absorption

*α*and low thermal conductivity

*κ*, the Sheik-Bahae’s model [21], based in a purely local nonlinear optical effect, gives a good description of the transmittance in a Z-scan experiment for a thermal optical nonlinearity [23]. For a purely local nonlinear optical effect

*n*=

*n*

_{0}+

*n*

_{2}

*I*, where

*n*

_{2}is the nonliner refraction index. The magnitude and sign of the fitting parameter of the Sheik-Bahae’s model,

*n*

_{2}, can be obtained by means of the closed-aperture Z-scan configuration. In this implementation, whose details are found elsewhere [24], the transmitted intensity by the sample of the focused laser is measured behind an iris centered along the

*z*-axis at the far field as a function of the position of the sample around the focus. A medium characterized by

*n*

_{2}> 0 (<0) behaves like a positive (negative) lens. For a sufficiently thin sample, to first-order correction in the irradiance of a Gaussian laser beam, the normalized transmittance ( Γ

_{c}) is given by:

*z*

_{o}is the Rayleigh range of the beam, Φ =

*k*

*n*

_{2}

*I*

_{0}

*L*

_{ef},

*k*is the wave number,

*L*

_{ef}=[1− exp(−

*α*

*L*)]/

*α*is the effective thickness of the sample, and

*I*

_{0}is the irradiance at the beam waist (

*z*=0). For a thermal nonlinear optical response, it was shown [23] that:

The signal of *n*_{2} coincides with that of *d**n*/*d**T*. In this work, the samples were conditioned in 200 *μ*m-thick glass cells and it was used a Gaussian cw laser at *λ* = 532 nm (Ventus, Laser Quantum). The beam waist at focus was 26 *μ*m and data acquisition was made *via* oscilloscope (Tektronix, TDS1012B). The incident power on the sample was ∼18 mW. This value is the threshold for the appearance of a thermal lens effect, within the sensitivity of our experimental apparatus, without unwanted hydrodynamical effects. It is worth to mention also that the characteristic formation time of a thermal lens in the aqueous colloid, i.e., the time to develop a stable refraction index gradient, is about 5 ms. A concomitant process in colloidal systems, in which a thermal gradient is stablished, is a mass diffusion process, named thermophoretic effect, with time scale in the order of seconds and that leads to a lens of matter. Within the sensibility of our experimental setup, it was not observed the formation of a lens of matter, so the optical response comes just from a thermal lens effect.

## 3 Results and Discussions

*N*. This means that the average size of the clusters augments when

*N*increases. Gaikwad et al. [25] ascribed to aggregates the origin of a broad band in the linear optical absorption of an AuNP-doped sponge phase. A possible mechanism that leads to agglomeration is the shielding of the negative charges on the surface of the AuNPs by ions N

*a*

^{+}from the SDS, decreasing the electrostatic repulsion between the nanoparticles. Figure 3 shows a cryogenic scanning transmission electron microscopy in high angle annular dark field (CRYO-STEM-HAADF) image of a loosely packed aggregate with average radius 〈

*r*〉∼50 nm found in the lyotropics. Esteban et al. showed that the structure of the absorption spectrum of an 3D cluster, grown under typical diffusion-limited aggregation conditions, can be understood as the contribution of different length resonant chains [7]. So, the actual spectrum of the lyotropics should be the contribution of AuNPs clusters of different shape. Also, at the excitation wavelength (532 nm), the linear optical absorption of the AuNP-doped lyotropic increases linearly with

*N*(

*α*

_{L}∝

*N*) and for the same concentration of AuNPs,

*α*

_{C}≃1.3

*α*

_{L}(Fig. 4). This may be ascribed to the red shift of the plasmon resonance due to the clustering of the nanoparticles.

*z*position. Colloids and lyotropics display a self-defocusing effect (

*n*

_{2}<0). Within the sensibility of our experimental setup, and for the beam, powers used in this work were not observed in the formation of a thermal lens in the undoped lyotropic liquid crystal. Yet, the empty glass cells do not show any thermal lens effect. Figure 6 shows the value of

*n*

_{2}as a function of the number density of nanoparticles for the colloids and the lyotropics. It is worth to observe that the intensity of the thermal lens depends linearly on the intensity of the laser beam (graph does not shown). So, we have employed the same power in all the samples. At the lower concentration \({n_{2}^{L}}\sim 2\, {n_{2}^{C}}\), and a fitting of data show that \({n_{2}^{C}}\propto N\) and \({n_{2}^{L}}\propto N^{2.4}\) (solid lines in Fig. 6).

### 3.1 Dependence of *κ* and *n*_{2} on Clustering

*n*

_{2}∝

*N*[26]. Lyotropic liquid crystals doped with superparamagnetic magnetite nanoparticles and ferrofluids exhibit the same behavior [27]. The relative magnitude of

*n*

_{2}at lower concentration, i.e., for small aggregates, can be accounted for by the interplay between the thermo-optic coefficient, the effective thermal conductivity, and the optical absorption (see (4)) as follows: (1) for a similar ternary mixture of SDS, 1-DeOH, and water in the isotropic phase \(\frac {dn}{dT}\sim -2.7\times 10^{-4} \,{\circ }\textnormal {C}^{-1}\) [28] while for the colloids we obtained \(\tfrac {dn}{dT}^{C}\sim -1.5\times 10^{-4} \,\,\,^{\circ }\textnormal {C}^{-1}\) ; (2) the ratio between the linear optical coefficients of lyotropics and colloids is ∼0.7; 3) for low filling factors the effective thermal conductivity is approximately that of the liquid medium [29], so for the aqueous dispersion of AuNPs

*κ*

_{C}≃

*κ*

_{water}≃0.6 W

*m*

^{−1}

*K*

^{−1}[30] and for the AuNP-doped lyotropic liquid crystal

*κ*

_{L}≃

*κ*

_{lyotropic}≃0.3 W

*m*

^{−1}

*K*

^{−1}[31]. The dependence of

*n*

_{2}on the number density can be understood, at least qualitatively, by making the fundamental supposition that the average number of nanoparticles in the cluster (

*n*

^{o}) is proportional to

*N*. The transfer of heat is mainly a surface phenomenon. Kumar et al. showed that for nanoparticles of radius

*r*

_{p}immersed in a liquid medium, the effective thermal conductivity \(\kappa \propto \frac {1}{r_{p}}\) [29], i.e., \(\kappa \propto \frac {S}{V}\), where

*S*is the surface and

*V*the volume of the nanoparticle. With regard to thermal conductivity, the aggregates behave like particles with increased value of

*S/V*. To study the dependence of

*S/V*on

*N*, it was constructed an anisotropic aggregate of

*N*identical beads packed randomly. To each new bead added to the aggregate, it was determined the mean radius 〈

*r*〉 of the aggregate, averaging the linear dimension of the aggregate along three ortogonal directions (Fig. 7a). Figure 7b shows a log-log graph of the 〈

*r*〉 in units of the radius of the beads (

*r*

_{p}) as a function of

*N*. A linear fitting of data gives 〈

*r*〉∝

*N*

^{0.4}. Assuming for a cluster that \(S=N\,4\pi {r_{p}^{2}}\) and \(V=\frac {4}{3}\pi \left \langle r\right \rangle^{3}\),

*α*

_{L}∝

*N*, and assuming that \(\frac {dn}{dT}\propto N\), (4) gives

## 4 Conclusions

In this work, we have showed that lyotropic liquid crystals doped with AuNPs have an optical absorption spectrum characterized by a broad red-shifted surface plasmon resonance, which can be explained by the formation of nanoparticle aggregates. The induced thermal lens for both media, aqueous dispersions of AuNPs and AuNP-doped lyotropic liquid crystals, is negative ( *n*_{2}<0). It is found experimentally that *n*_{2}∝*N* for the aqueous dispersions of AuNPs and *n*_{2}∝*N*^{2.4} for the AuNP-doped lyotropic liquid crystals. The nonlinear dependence of *n*_{2} on *N* for the AuNP-doped lyotropic liquid crystals can be explained by a decrease of the surface to volume ratio of the loosely packed clusters when increase the number of particles in the aggregate. The theoretical value of the exponent, 2.2, is in good agreement to the experimental one.

## Notes

### Acknowledgments

This work had the financial support of the Brazilian agencies CAPES, CNPq, FINEP, and Fundação Araucária, and it is part of the research program of the Instituto Nacional de Ciência e Tecnologia de Fluidos Complexos (INCT-FCx). The authors also thanks to the Advanced Microscopy Laboratory (LMA) of the Institute of Nanoscience of Aragon.

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