LASER-ASSISTED HEATING OF A PLASMONIC NANOFLUID IN A MICROCHANNEL

The work presented in this study analyses the theoretical modeling and experimentation of laser-assisted heating of plasmonic nanofluids (PNFs) in a microchannel for accurate, efficient, and ultra-fast heating of a microdroplet. Suspended plasmonic nanoparticles exhibit strong light absorption and scattering upon the excitation of localized surface plasmons (LSPs), resulting in intense and rapid photothermal heating. Several multiple stepped computational models were utilized to theoretically characterize and verify the laser-assisted heating behavior of gold nanoshells (GNS) and gold nanorod (GNR) plasmonic nanofluid droplets in a microchannel. From the experimental investigation, a full range of controllable steadystate temperatures, room temperature to 100°C, are confirmed to be achievable for the 780nm-tuned plasmonic nanofluid. Droplet fluid heating is verified to occur as a result of LSP excitation, in time scales of a second, and to be repeatable over many cycles. Additionally, the significance and effects of parameters in the process, such as nanoparticle structure, volumetric concentration, microchannel depth, and laser power density are established. The obtained results in this research may be integrated into other existing microfluidic technologies and biological techniques, such as the polymerase chain reaction, where accurate and ultra-fast heating of microdroplets in a microchannel can greatly improve efficiency.

Lab-on-a-chip (LOC) technology has led to pivotal progress over the decades in the down-scaling of mechanical fluid handling devices. These microfluidic technologies have been widely utilized across many fields of study in the development of both common and unorthodox applications. Often, many of these same applications require additional heating and cooling processes to be carried out that have been, historically, relatively inefficient and inaccurate [1]. These inefficiencies have existed as a bottleneck in the numerous biological applications specifically catered to by microfluidics. However, the advent of nanotechnology has brought about a surge of new, novel, and ground-breaking improvements on countless hurdles in past technology. One such improvement, where great potential exists for enhanced thermal performance in microfluidic technology, can be easily realized with suspended plasmonic nanoparticles, or plasmonic nanofluids (PNFs) [2].
Plasmonic nanoparticles exhibit strong light absorption upon the excitation of localized surface plasmons (LSP), resulting in efficient, intense, and rapid heating of the PNFs [2, 3,4]. LSPs result from the confinement of the surface plasmon phenomena in a particle that is on the order of, or smaller than, its own LSP excitation wavelength.
Upon LSP excitation, the loosely-bound outer electron charge cloud within the particle enters an oscillating state, or resonance, resulting from the balancing of the incoming photon energy and the restoring force of the atomic nucleus. The wavelength at which this LSP phenomenon occurs is very highly dependent on several factors such as: material, geometry, and local electric fields. For these reasons, plasmonic nanoparticles can be selectively tailored to specific wavelengths of light and thus possess the capacity to be used in a very wide range of applications. [3,4] One of the microfluidic applications where this enhanced thermal performance from plasmonic heating can be easily outlined, is in the Polymerase Chain Reaction [5]. PCR is a highly utilized biochemical technology to amplify segments of DNA across several orders of magnitude in a relatively short period of time. It has birthed a multi-billion dollar industry and is widely used in many fields of study and applications, such as: virus detection, diseases diagnosis, forensics, vaccine development, etc. [5] The process, itself, involves multiple steps of quick and precise heating and cooling to very specific temperatures over many repeated cycles. Current conventional systems used for PCR can achieve this, albeit through a generally complex and expensive design [1]. These conventional systems typically are equipped with thermoelectric heaters and coolers which generate relatively low heating/cooling rates and non-uniform temperature distributions; resulting in great inefficiencies and thus longer processing times.
It is in applications such as PCR, where the benefits of enhanced thermal performance by optical methods become very clear. Integration of photothermal processes here is highly favorable, as these methods only target the PCR droplets and do not collaterally waste energy and time heating/cooling the LOC device, like the conventional thermoelectric devices. Furthermore, these new photothermal designs possess potential for even faster heating/cooling rates and can improve efficiency still yet [1,4,6,7]. While some other optical heating methods have found success in improving LOC technology used for PCR [8][9][10][11][12], plasmonic heating still offers equal or greater potential. This work specifically aims to demonstrate, both computationally and experimentally, the laser-assisted heating of a plasmonic nanofluid microdroplet in a microchannel for controllable, accurate, rapid, and effective heating of the medium.
From this investigation, we anticipate to find a full range of controllable temperatures, room temperature to boiling, to be achievable for a 780-nm-tuned PNF. We expect to effectively verify that this fluid heating truly occurs as a result of LSP excitation, in time scales of milliseconds, and to be fully repeatable over time. Additionally, we will verify the importance and effects of parameters in the process, such as volumetric concentration, microchannel depth, and laser power density. The obtained results in this research will be evaluated for their viability of integration into other existing microfluidic technologies and biological techniques, such as the Polymerase Chain Reaction, where quick and accurate heating may greatly improve efficiency.

REVIEW OF LITERATURE
Accurately heating the fluids within microfluidic devices in a controllable manner is an extremely important topic in many LOC-based applications. These processes may require temperature homogeneity or gradients for their specific purposes, however both cases aim for the highest accuracy and repeatability as  14,25]. Furthermore, the common practice of using PDMS substrates tends to cause heating/cooling inefficiencies as its thermal conductivity rests relatively low.
Conversely, there are a number of studied and utilized optical methods in microfluidic heating and cooling as well. These noncontact-based techniques are often considered preferable as they generally aim to heat only the fluid inside rather than an external device and dissipate heat outward into the medium. This is highly advantageous, because resources are used more efficiently in these processes by using less energy and time that would otherwise, conventionally, be wasted in heating/cooling the microfluidic device as well. It has been found that when compared to conventional techniques, enhanced thermal cycling and faster reaction rates can be The first of these methods is microwave dielectric heating with time-varying electric fields (from 3-20 GHz) [10][11][12]. It can be designed to be spatially selective thanks to miniaturized elements and waveguide configurations and has been shown to be successful in PCR [10] and heating of biological cells [12]. Microwave heating methods have so far found best use in PCR applications when compared to conventional techniques when working with volumes of 2.5-15mL. It is at this scale, with reduced surface area to volume ratios, that conventional techniques greatly lose their efficiency.
A second optical method that has been utilized is infrared laser heating using aqueous solutions [8,9]. This method has gained interest because of the cheap cost and reliability of the modern laser diode; its the extremely small spatial resolution and highly precise control as a heat source is very well suited to even the smallest droplet sizes employed in microfluidic devices. Kim et al. [8] found that a de-focused 1.46μm wavelength laser diode could be utilized to heat nanoliter-sized liquid water droplets with sub-1°C accuracy in order to successfully perform a real-time PCR. This wavelength was chosen ad hoc as water absorbs extremely strongly in this specific infrared spectrum.
The third optical method that has been pursued for use in microfluidics is the utilization of the specialized nanoparticles to enhance optical heat generation. This method can further be divided into two sub-categories: non-plasmonic and plasmonic heating. Non-plasmonic heating is very simply achieved through broad absorption of incident light from a highly energetic source (i.e. laser); carbon nanoparticle structure mixtures are most exemplary in this sub-category. Many [4,31]. While many nanoparticle materials (i.e. noble metals) and geometries exhibit LSPs, silver and gold nanoparticle structures have been found particularly favorable in biological LOC-based applications because of their good biocompatibility, chemical stability, and easily tunable excitation wavelengths within the visible spectrum.  Figure 1a shows that it was found that the range from 500-1000nm is the most promising optical window for experimentation, as virtually no light absorption is expected for any of these materials. Therefore, the QD fluorescence excitation and emission, as well as the LSPR wavelength should fall within this spectrum without significant overlapping ( Figure   1b).  where is the size parameter of particle outer radius and index of refraction of water , m is the index of refraction of the particle medium, and and are related to spherical Bessel functions.
From these equations, the scattering and absorption cross-sections, and the asymmetry parameter, respectively, can be expressed in terms of and . (3.7) Commonly, these cross-section values are divided by the geometric cross-sectional area to give dimensionless scattering/absorption efficiency parameters, . However, when dispersed nanoparticles are taken into consideration rather than single nanoparticles, a more meaningful parameter is realized in the scattering and absorption coefficients, and , where is the absorption coefficient of water and is the volume fraction of the mixed nanoparticles. The coefficients can be generally expressed as summations in order to account for a case of multiple different nanoparticle structures in the mixture.
During this calculation process, consideration was given to the peak absorption wavelength and practicality of particle size in order to effectively optimize the ~1000nm limited spectrum window available for the LSPR excitation, QD excitation, and QD emission without significant overlaps. From this process and with these restrictions, the best suited spherical nanoparticles in this study were determined to be silica-core gold nanoshells.

Rod Nanoparticle Case: BEM Solution
Since the Mie scattering theory is only valid for spherical and elliptical , From the discretization of these equations, the resulting surface charges and currents at the inside and outside of the particle boundaries are finally computed.
On the user end, the program requires several initial parameters for successful computation including: generic geometric shape, particle dimensions, indices of refraction for all media, light spectrum, and light vector and polarization values. In the case of the GNR structures, the initial parameters were specified as: symmetric cylinder with hemispherical caps, 10nm X 38nm, refractive indices for gold and water, 785±10nm, and circularly polarized light both parallel and perpendicular to the particle axis. Ultimately, the boundary element method utilized here is able to compute the effective particle absorption and scattering cross-sections of the individual GNR. However, because the GNR is not symmetric in all spatial dimensions, it exhibits different absorption and scattering behavior in various orientations relative to the incident light. For this reason, two BEM computations were done for the GNR case: first oriented perpendicular to the light vector and second oriented parallel with. The scattering cross-sections for these GNR structures were found to be significantly smaller (greater than 1 order of magnitude) in comparison to their absorption cross-sections; thusly, the effects of light scattering were assumed negligible in subsequent calculations.

Monte Carlo Simulation
In the case of the GNS-suspended plasmonic nanofluids, the light scattering In the Monte Carlo simulation, the "drift" process (during which the photon bundle propagates) is treated independently from the scattering process (during which the photon bundle changes its propagation direction). It is assumed that the drift process is followed by the scattering process based on the scattering probability where is the propagation length of phonon bundle calculated by , is the scattering coefficient of the GNS, and is the combined absorption coefficient of the GNS and water. A uniform random number is generated to satisfy by a quasi-random sequence. It should be noted that the estimated L stochastically represents the mean-free-path (i.e., averaged propagation length) of . In determining whether to accept or reject the scattering event, an addiontional uniform random number is generated and compared with ; if the value of , then the ray will be scattered at the next nanoparticle encounter. Upon the scattering process, the post-scattering direction of the photon bundle is expressed by the polar angle and the azimuth angle with respect to the pre-scattering direction vector. For the greater simplicity, the polar angle is also stochastically determined by transforming the Henyey-Greenstein (H-G) scattering phase function. The azimuthal angle is determined by assuming that the scattering is isotropic in the azimuthal direction. It should be noted that the H-G scattering phase function is an approximation and cannot be regarded as the rigorous phase function for the light scattering from the GNS.
Despite this, the H-G scattering phase function provides the probability density of light scattering that can be seamlessly integrated with the Monte Carlo simulation.
Although the absorption of the GNS-based PNF is mainly due to the plasmonic absorption by the nanoparticles, the Monte Carlo simulation treats the whole of the PNF as an effective medium in which the energy of the photon bundle uniformly reduces by a factor of due to volumetric absorption while traveling a distance .
In the event that the photon bundle reaches the bottom surface of the glass, there is no consideration for reflection back into the effective medium. The drift and scattering processes described are repeated until the photon bundle leaves the microchannel or 99.9% of its energy is absorbed inside the PNF medium. where is the incident spectral intensity flux, is the light transmittance of the upper medium in the microchannel, is laser peak wavelength, and is the standard deviation with respect to the laser FWHM spectrum. Next, was multiplied through with the spectral absorptance depth distribution and integrated over the full laser spectrum; giving way to the volumetric laser energy absorption rate, at each where is the spectral absorptance depth distribution, and . The results of this calculation were exported as a single data file for the volumetric heat generation across the predefined increments of the total droplet depth.

GNR Heating
Determining the amount of heat generated by the GNR-based nanofluid was approached differently, because use of the Monte Carlo algorithm was restricted to spatially symmetric particles. A Matlab script was used to approximately convert the axial and lateral spectral absorption cross-sections to the averaged effective spectral absorption coefficient. By considering random particle orientation in 3 dimensions, the effective absorption cross-section at each wavelength increment can be written as, where and are the axial and lateral absorption cross-sections, respectively. The function was integrated only up to as further rotation beyond this angle would be redundant due to particle symmetry. The, effective spectral absorption cross-section values were multiplied by the number density ( ) of the GNR mixture to obtain the effective spectral absorption coefficients, Using the obtain spectral absorption coefficient, the Beer-Lambert Law was employed to acquire the spectral penetration depth from, where is the incident laser power and is the droplet depth. It should be noted that the spectral penetration depth can be expressed as or by defining the depth at which the spectral light intensity has decayed to of its incident value.
Since the GNR scattering effects are negligible, the spectral penetration depth values, can be considered to be a reasonable approximation of the spectral absorptance ( across the total droplet depth. To this end, the volumetric laser energy absorption rate, could then be calculated the same way as that of the GNS case.

FEA Microchannel Modeling
To compute the thermal behavior of the microchannel systen upon

Temperature-Fluorescence Calibration
All PNF solutions in these series of experiments were prepared from one of three different commercially available gold nanoparticle aqueous suspensions: an 60-11nm silica core GNS solution (Nanospectra), a 10-38nm GNR solution (Nanopartz), and a 10-102nm GNR solution (Nanopartz). Each gold nanoparticle solution was additionally prepared with an aqueous buffered solution of CdSe, ZnS coated quantum dots (Invitrogen, Qdot655) with 655nm emission (Figure 3.1b). The spectra in   In order to prepare well-dispersed nanoparticle suspensions, they were first sonicated (Elma, Elmasonic P) for 30minutes at 37kHz and 120W power. Solutions were then placed in a beaker and mixed in several concentrations with a magnetic stirrer; borosilicate was also added as buffer to make a pH of 9 after the nanoparticle solutions were mixed with quantum dot solutions. All PNF+QD solutions were sonicated for 30 minutes at 37kHz and 120W power prior to experiments.

Droplet Laser Heating
The same PNF+QD solution preparation procedure was utilized in the laser  After a full range of laser output power images were obtained, each image was post-processed with imaging software (ImageJ) by measuring the average pixel brightness within the boundaries of the droplet. Next, these values were normalized relative to the room temperature fluorescence emission. The normalized data was compared with the data of the previously calibrated temperature-dependant fluorescence emission intensity versus temperature for each corresponding PNF+QD mixture, as well as with the laser manufacturer's measured data for power output (mW) versus the controllable input current (mA). By linking all three of these different relations, the temperature of the PNF droplet could then be correlated with the excitation laser output power density, simply calculated by, .
Here, is the effective laser power output after transmission loses and is the area spot of the incident laser beam. It should be noted, that this is equation assumes a uniform distribution of intensity in the case of an de-focused incident beam as utilized in this work.

Simulation
The results of the FEA simulation of the PNF droplet heating in the microchannel are shown in     Conversely, it is clear that the penetration depth for the maximum GNR concentration used in the experiment (~20ppm) is estimated at ~150µm; nearly matching the total microchannel depth. This means that the predominant portion of available incident light is effectively absorbed by the GNR mixture microdroplet at this concentration.

Experiment
In order to ascertain accurate microdroplet temperature measurement, the temperature dependence of the fluorescence intensity change was calibrated.   Right-hand axis correlates relative intensity to inferred temperature.
It was found that the highest available concentration (~0.53ppm) of the GNSbased mixture was only able to reach ~26°C in droplet in the microchannel, or an approximate 5°C increase. Three GNR-based mixtures (0.59, 11.8, and 17.8) were capable of reaching ~40, 52, and 75°C, while the highest concentration (22.6ppm) is capable of reaching a temperature of ~100°C within droplet. It should be noted that the 22.6ppm GNR mixture is capable of heating the droplet further Although the lowest concentration GNR mixture is nearly the same as that of the GNS mixture, its heating capability is 225% more effective, able to achieve a ~10°C higher temperature increase. This was to be expected, as the utilized GNS solution had a maximum optical density of ~4AU and the GNR solution had ~100AU at 780nm wavelengths.. This strongly suggests that GNR structures would serve optimally for smaller microdroplets that have far fewer nanoparticles due to its superior absorption efficiency.
In order to clearly verify that the effects of this droplet heating is predominantly attributable to plasmonic heating, Figure 4.5 depicts two dissimilar GNR structures with different LSP absorption peaks. Accurately determining the transient effects of the PNF droplet heating serves an imperative role in weighing its effectiveness in time-sensitive applications. As mentioned, PCR offers as a direct example of the very wide range of applications which could decidedly benefit from plasmonic heating integrated microfluidics. In order to achieve a full plasmonic photothermal PCR, a fast, precise, and repeatable thermal cycling behavior is desired to achieve shorter processing times.  This is significant improvement compared to many of the best conventional PCR heating systems commercially available with a maximum rate of ~10°C/sec. It should be noted that only the first step in PCR would require full thermal response on the PNF droplet; the other intermittent steps require lower temperatures and thus could be reached much faster. Additionally, it should be noted that the transient response times of this process could be potentially further improved by increasing the PNF concentration still higher.