# Photo-Aligned Nematic Liquid Crystals Enable the Modulation of Thermoplasmonic Heating
## 3 Results and Discussion
The thermo-optical setup used for the experiments is sketched in Figure 2c: A CW green laser (\(\lambda\) = 532 nm, spot size 2.25 \(\pm\) 0.22 mm), impinges perpendicularly onto the sample and excites simultaneously the plasmonic band of the irradiated AuNPs, with a consequent increase (\(\Delta T\)) of the macroscopic temperature of the sample with respect to the environment temperature (\(T_{0}\)). In general, to calculate the temperature variation at a point \(r\) from a single NP, it is necessary to solve the heat transfer equation [4], where the solution results are:  
\[\Delta T(r)=\frac{QR_{NP}^{3}}{3 rk_{H}} \tag{1}\]  
where \(Q\) is the heat production due to the Joule effect, \(R_{NP}\) is the NP radius and \(K_{H}\) is the thermal conductivity of the host medium. Thus, by illuminating a macroscopic surface region of the AuNPs layer with a laser spot \(w\) in radius, a considerable number of AuNPs are acted on by the light; in this case, as a matter of fact, the temperature increase has to be calculated by adding the contribution of all the irradiated AuNPs as specified in this formula [18]:  
Figure 1: **(a)** AFM image of the AuNPs monolayer on a glass substrate. In the inset, a photograph of the sample. Spectral response of the AuNPs monolayer surrounded by **(b)** air and **(c)** PAAD-27; In the inset, a photograph of the photo-aligning material. **(d)** Absorbance response of the AuNPs monolayer covered by the PAAD-27. \[\Delta T(r)=2\pi wn_{NP}\frac{V_{NP}Im(\chi_{NP})}{2\lambda k_{H}\sqrt{\varepsilon_ {H}}}|\frac{3\varepsilon_{H}}{2\varepsilon_{H}+\varepsilon_{NP}}|^{2}I \tag{2}\]  
where \(n_{NP}\) is the AuNPs surface density, \(V_{NP}\) is the average AuNP volume, \(K_{H}\) is the thermal conductivity of the host medium, \(\chi_{NP}\) is the AuNPs dielectric permeability, \(\varepsilon_{NP}\) and \(\varepsilon_{H}\) are the AuNPs and host medium dielectric permittivity, respectively. From Equation (2), it is evident that the temperature variation exhibits a strong enhancement under the Frolich condition, in which the quantity \(|2\varepsilon_{H}+\varepsilon_{NP}|\) assumes a minimum value, a condition that occurs if \(Re[\varepsilon_{NP}(\omega)]=-2\varepsilon_{H}\)[32]. Equation (2) shows also that the temperature variation \(\Delta T\) varies linearly with the intensity of the pump beam (\(I\)), used to excite the resonance of the AuNPs, and strongly depends on the optical and thermal characteristics of the medium that hosts the AuNPs, expressed by \(\varepsilon_{H}\) and \(k_{H}\), respectively. This behavior was experimentally demonstrated by illuminating the AuNPs with different pump beam intensities \(I\) and by monitoring the maximum induced \(\Delta T\) for each \(I\) value. By monitoring the temperature values \(T_{max}\) of the central pixel of each hot-spot of the thermographic images (Figure 2c), which corresponds to the warmest point, we plotted the temperature variation \(\Delta T=T_{max}-T_{0}\) versus the impinging intensity \(I\). Successively, we repeated the photo-thermal experiments (Figure 2d) by fixing the intensity range (\(I=0.05-1.2\) W/cm\({}^{2}\)) for the cases of AuNPs monolayer in air (red sphere) and covered by the PAAD-27 molecules before (green sphere) and after exposure to UV light of two different polarization directions (blue and magenta spheres). As predicted by Equation (2), the behavior of \(\Delta T\) as a function of \(I\) can be easily fitted with a linear curve. For the maximum \(I\) considered we acquire a \(\Delta T\) of about (3.2 \(\pm\) 0.3) \({}^{\circ}\)C for the AuNPs monolayer in air, (32.6 \(\pm\) 0.3) \({}^{\circ}\)C for the sample where AuNPs are covered by PAAD-27, and of about (49.0 \(\pm\) 0.3) \({}^{\circ}\)C and (38.0 \(\pm\) 0.3) \({}^{\circ}\)C for AuNPs-PAAD-27 samples acted on by UV light with two different polarization directions.