Gold nanorods have potential for photothermal cancer therapy. When exposed to laser light near their surface plasmon resonance wavelengths, gold nanorods efficiently absorb light and generate heat through electron oscillations. Smaller nanorods absorb shorter wavelengths. Nanorods have transverse and longitudinal surface plasmon resonances depending on their aspect ratio. Their strong light absorption and efficient conversion to heat makes them suitable for using mild hyperthermia to selectively destroy tumors through plasmonic photothermal therapy.

1. Gold nanorods for photothermal cancer therapy
Raquel Gavilán1, Ayla Pérez2, Sergio Pérez3
1,2,3 Degree in Materials Engineering students at Universidad Politécnica de Madrid
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Abstract
In this paper we review the optical properties of metal nanoparticles, focusing on Au behavior and the nanorod shape effect at nanoscale. The objective is to understand how Plasmonic Photothermal Therapy (PPT) works in tumors damage. The first part of the paper – larger and necessary to understand the second one –is a review of how gold nanorods (GNRs) interact with photons of lasers, an overview of Surface Plasmon Resonance (SPR) phenomena, and an explanation of the size and shape effects of those particles in our application. The second part of the paper explains the behavior mechanisms of photothermal cancer therapy, and the relevance of this PPT in society.
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Introduction
In photonics, metals haven’t been traditionally used, except perhaps as mirrors. This is because, in most cases, metals are strong reflectors of light, a consequence of their large free-electron density [1]. Light consists of electromagnetic waves, which induce the oscillation of electrons in the substance when it’s hit by the light. In an insulator such as glass, the electrons are firmly bound and can only oscillate around their normal position. This movement influences the propagation of light so that its wave velocity is reduced, while there is only a small loss of energy. In a metal, electrons are free to move over large distances in a kind of “electron gas” called plasma. The electron motion is damped so that energy is dissipated, and the wave amplitude decays very quickly in the metal. Associated with that decay there’s a loss of energy in the wave and some heating of the metal.
In the miniaturization to nanoscale of photonic circuits, it is now being realized that metallic structures can provide unique ways of manipulating light at length scales smaller than the wavelength, as the spatial length scale of the electronic motion is reduced with decreasing size, which have been traduced in a new research area: metallic nanoparticles, as nanospheres or nanorods.
Gold is an element specially attractive for this research lines, as we will see in this paper. It absorbs light orders of magnitudes stronger than other materials. The physical origin of the strong light absorption by noble metal nanoparticles is the coherent oscillation of the conduction band electrons (surface plasmon oscillation) induced by interaction with an electromagnetic field.
In the other hand, the use of lasers over the past few decades, has emerged to be highly promising for cancer therapy, for example for the photothermal therapy method,

2. which employs light absorbing nanoparticles for achieving the photothermal damage of tumors.
Because of all of these reasons, gold nanorods (GNR’s) are attractive new nanomaterials which have found a wide range of applications in the biomedical field, as the mentioned photothermal therapy. The nanorod structure is especially appealing due to its unique optical properties and wavelength tunability within the optical therapeutic window.
Overview of optical properties in Au nanoparticles
With metals, free electrons are treated collectively, as a plasma. A plasmon is the quantum of the classical plasma oscillation. The frequency at which this plasma oscillates determines what frequency of radiation will be absorbed, reflected, and scattered. This happens because permittivity, which measures the degree to which a material enables the propagation of photons, is determined by the Free Electron Plasma [2], the relation is given by:
Where fp is the oscillation frequency of the plasma, f is the frequency of the photon and ϒ is the damping energy.
Photons of frequency f < fp are reflected, because the high-energy (quicker) electrons serve to screen the lower-energy electric field of light; photons with frequency f > fp are transmitted because they are quick enough [3]. So, for low permittivity light is transmitted, and for big permittivity it is reflected. In most metals, fp is in the ultraviolet range, making them shiny (reflective) in the visible range; but in gold and some noble metals, it is in the visible range, so they tend to absorb light.
When the volume of the particle is in nanoscale, electrons will collide more often with the surface. The damping increases as size decreases, due to the increase of interactions of the plasma with the particle surface. The damping frequency for the free electrons is:
Where ϒ is the damping frequency of the bulk, vF is the electron velocity at the Fermi energy, and Ʌ is the adjusted mean free path (adjusted because of the small size of the particle):

3. Particles measuring just a few nanometers, as nanorods, tend to absorb and scatter the most photons at a particular frequency. As we need a low permittivity in our nanoparticle to transmit light, and permittivity is inverse proportional to damping frequency, a big damping frequency is needed. So, as we can observe, in size terms, this frequency is inversely proportional to particle size, so we can “tune” the photonic properties of a nanomaterial, such as the colors it absorbs or emits, by altering the size, and the light is less reflected in small particles, as nanoparticles. Smaller metal nanoparticles absorb smaller wavelengths.
Nanorods, because of their shape, have both a transverse and longitudinal plasma frequency, perpendicular and along the axis of the rod, as shown in the Figure 1.
Figure 1: transverse and longitudinal plasma oscillation in nanorods. Image from http://chem.skku.ac.kr/~skkim/research/plasmon-e.htm
Surface Plasmon Resonance (SPR)
As we have seen in the previous pages, when photons interact with nanoscale metal particles, physical phenomena occur which are not present in their corresponding bulk materials. The key to understand the unique optical properties of noble element nanoparticles is based on their Surface Plasmon Resonance (SPR).
Maxwell’s equations [4] tell us that an interface between a dielectric and a metal can support a surface plasmon (SP). A SP is a coherent electron oscillation that propagates along the interface together with an electromagnetic wave, as shown in Figure 2. These unique interface waves result from the special dispersion characteristics (dependence of dielectric constant on frequency) of metals. What distinguishes SPs from ‘regular’ photons is that they have smaller wavelength at the same frequency.
So, surface plasmons are those plasmons that are confined to surfaces and that interact strongly with light. They occur at the interface of a vacuum and material with a small positive imaginary and large negative real dielectric constant (usually a metal or doped dielectric) [5]. The electromagnetic field interacts with the conduction band electrons and induces a coherent oscillation of the free electrons in the metal.

4. Figure 2: Schematic showing the two SPRs of nanorods. Image from www.nanohybrids.net
The SPR is the extinction band that arises when the collective oscillation of the surface electrons are resonant with the incident photon frequency. Thus, a strong extinction band appears in a specific part of the electromagnetic spectrum which is dependent on the size and geometrical nature of the nanoparticle. At this resonant frequency two processes may occur:
1) First, several of the photons are released with the same frequency in all directions, known as scattering
2) Second, other photons are converted into phonons or vibrations of the lattice via absorption.
Figure 3: nanorods extinction curve has two curves because of their two axis oscillations
The surface plasmon resonance properties of GNRs split into two distinct bands which correspond to the oscillation of the free electrons along and perpendicular to the long axis of the rod [6], as shown in Figure 3. The transverse surface plasmon peak, TSP, in gold nanorods typically demonstrates a resonance peak close to 520 nm. The resonance of the longitudinal surface plasmon, LSP, is commonly found between the visible and NIR part of the electromagnetic spectrum. The position of the LSP is dependent on the ratio between the length and width of the nanorod, commonly referred to as the Aspect Ratio, which is given by:

5. R=L/W
Influence of the size and shape
The rod is more easily polarized longitudinally, meaning the SPR occurs at a lower energy, and thus higher wavelength (Figure 4). As the aspect ratio (ratio of length to width) of a nanorod is increased for a fixed diameter, the longitudinal and transverse plasmon resonances are both affected; however, the longitudinal axis is much more polarizable and therefore more sensitive to aspect ratio changes [7].
Unlike spherical nanoparticles, the absorption spectrum of the gold nanorods is very sensitive to the aspect ratio (length/width). For GNRs the influence of the diameter of the short axis and length of the long axis has been researched where it has been demonstrated that for short axis diameters of less than 30 nm and long axis lengths of less than 80 nm, the absorption of light is dominant.
In the other hand, we find that the extinction coefficient is the sum of the scattering coefficient and the absorption coefficient, so if absorption and extinction coefficients are equals, scattering is zero, so there’s only absorption [8]. In the Figure 4 we can appreciate that this happens for the lower rod length: if the rod is shorter, the absorption is higher.
Figure 4: the absorption is higher if the length is lower, because absorption and extinction coefficients are equals and scattering is null
This is interesting because this strong absorption can be tuned to the NIR (infrared radiation) region, a region where light penetration is optimal due to minimal absorption from tissue chromospheres and water. This makes NIR-resonant gold nanostructures (those who are sintonized to NIR region) very useful for clinical therapy applications involving tumors located deep within bodily tissue.
Conversion of photon energy into thermal energy
The principle of the plasmonic photothermal therapy is heating and so killing cancer cells. This is possible because gold nanoparticles can absorb big amounts of light, and after that, to transform the absorbed light into heat.

6. The process of energy transformation begins with a rapid loss of phase of the excited electrons (they are excited when they reach the laser light) through collisions electron -electron leading to the origin of " hot electrons " with temperatures up to 1000 K (collisions electron -electron and then these electrons are excited by the laser light and collide again with other electrons). This process lasts few femtoseconds.
Subsequently the electron passes the energy to phonon through interactions electron- phonon (a phonon is a quasiparticle that is in the crystal lattice as the atomic lattice of a solid, play a very important role in many physical properties, including thermal conductivities and electrical) having a duration of approximately 0.5- 1ps. This second process results in a “hot lattice” with temperatures that can reach the order of a few tens of degrees (usually between 40 and 50 ºC). The electron-phonon relaxation is a process independent of the size and shape [9].
Depending on the heat energy of the lattice, three different processes may occur:
1) If the power is not enough to cause melting of the nanparticle, a cooling process occurs due to the passage of heat to the environment through a phonon - phonon relaxation rate which occurs in approximately 100ps.
2) If the energy is sufficient to cause melting of the nanoparticle, it’s produced a cooling process, causing at the same time a competitive process between the heating of the network and the heat transmission to environment. If heating is much higher than cooling, heat energy is accumulated in the lattice, which can produce structural changes in the nanoparticle.
3) If the energy is enough to result in the total destruction of the nanoparticle, the mechanical effects of this process can be used to destruct many groups of localized cancer cells.
So, if the objective is generating heat to treat a tumor, it is necessary the first process (phonon -phonon relaxation), which takes place when we’re using continuous wave laser, allowing the heat dissipation from nanoparticles to environment. With a pulsed laser of high energy, it may occur normally ablation processes (destruction of the nanoparticle) very localized.
Plasmonic Photothermal Therapy (PPTT)
In recent years, the continuous and fast development of nanotechnology has provided a variety of nanostructures with unique optical properties that could be very useful in biology and biomedical applications.
From the point of view of cancer therapy, and according to the properties explained before, noble metal nanoparticles become very useful as agents because of their enhanced absorption cross sections [10], which are four to five orders of magnitude larger than those offered by conventional photoabsorbing dyes. This strong

7. absorption ensures effective laser therapy at relatively lower energies rendering the therapy method minimally invasive.
Additionally, metal nanostructures have higher photostability, and an effective light to heat energy conversion. Currently, gold nanorods are ones of the chief nanostructures that have been chosen for photothermal therapeutics due to their strongly enhanced absorption in the visible and NIR regions on account of their surface plasmon resonance (SPR) oscillations.
Hyperthermia is commonly defined as heating tissue to a temperature in the range 41–47°C for tens of minutes [11]. Tumors are selectively destroyed in this temperature range because of their reduced heat tolerance compared to normal tissue, which is due to their poor blood supply.
Conclusions
 Metal nanoparticles exposed to incident laser irradiation at wavelengths close to the surface plasmon resonance, efficiently couple the optical energy and generate heat
 Smaller metal nanoparticles absorb smaller wavelengths
 Nanorods extinction curve has two curves because of their two axis oscillations: transverse and longitudinal, being the longitudinal axis peak higher than the transverse axis one
 For PPTT, it is necessary the phonon -phonon relaxation process of energy conversion, which takes place when we’re using continuous wave laser, allowing the heat dissipation from nanoparticles to environment
References
[1] Polman, Albert; Harry A. Atwater (2005); Plasmonics: optics at the nanoscale
[2] Rogers, Pennathur, Adams; Nanotechnology, understanding small systems, Nanophototnics chapter
[3] S.Zeng et al. (2011). A review on functionalized gold nanoparticles for biosensing applications. Plasmonics
[4] J M Pitarke, V M Silkin, E V Chulkov and P M Echenique; Theory of surface plasmons and surface-plasmon polaritons
[5] S.Zeng et al. (2012). Size dependence of Au NP-enhanced surface plasmon resonance based on differential phase measurement
[6] Mitsuhiro Honda, Yuika Saito et al.Nanoscale heating of laser irradiated single gold nanoparticles in liquid
[7] Xiaohua Huang, Prashant K Jain, Plasmonic photothermal therapy using gold nanoparticles

8. [8] V K Pustovalov, A S Smetannikov, V P Zharov, Photothermal and accompained phenomena of selective nanophotothermolysis with gold nanoparticles and laser pulses
[9] B.N. Khlebtsov et al. Fabrication, stabilization and optical properties of gold nanorods with silver shells
[10] Fu, Ying (2011). Optical properties of nanostructures. Pan Stanford
[11] Xiaohua Huang, Svetlana Neretina, and Mostafa A. El-Sayed. Gold Nanorods: From Synthesis and Properties to Biological and Biomedical Applications