Optofluidic control using plasmonic TiN bowtie nanoantenna

The performance of plasmonic titanium nitride (TiN) nanoantennas for the manipulation of fluidic flow and suspended particles in an optofluidic chip is studied. A unified theoretical framework is utilized to model the multidisciplinary problem that comprises optics, thermodynamics, and hydrodynamics. Using multiphysics finite element analysis, we simulate the temperature rise resulting from the photothermal heating of a plasmonic TiN bowtie nanoantenna (BNA) and the accompanying hydrodynamic flow generated in a microfluidic channel. We show that the TiN BNA enables over three times higher electrothermoplasmonic flow velocity in comparison to a gold BNA under similar signal conditions. Our analysis shows that TiN BNAs at near-IR biological transparency wavelengths can be utilized to initiate strong microfluidic flow for directed transport and trapping of target nanoscale objects. This makes TiN an excellent plasmonic material choice for optically controlling heat, fluidic dynamics and heat-induced forces in microfluidic devices. © 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement


Introduction
Plasmonic nanoantennas provide unprecedented capability to confine light to deeply subwavelength scales and to enhance the local light field intensity [1][2][3].This local electromagnetic field enhancement and confinement is enabled by the coupling of the delocalized electron cloud in metals with the incident photons to generate surface plasmons.The surface plasmon wave provides the possibility to enhance light-matter interaction for myriad applications in sensing [4], imaging [5], quantum photonics [6,7] and information processing.A key emerging application of resonant plasmonic nanoantennas in optofluidics is for enhanced optical trapping of nanometric objects.Optical tweezer technology has emerged as a powerful technique to manipulate microscale objects such as bacteria, colloidal particles and cells [8][9][10], and was recently recognized with a Nobel Prize in physics awarded to Arthur Ashkin for pioneering the development of optical tweezers.In the conventional optical tweezers, the diffraction limit precludes the low power trapping of nanoscale objects [11].Since plasmonic nanoantennas can confine light to nanoscale volumes, they have generated significant interest as a platform for generating the tight trapping potential wells needed to trap nanoscale objects [11,12].Different kinds of nanoantenna geometries have been explored including nanopillar [13,14], coaxial aperture [15][16][17], double-nanoholes [18][19][20], bowtie aperture [21], dimers [22], and circular nanoholes supporting self-induced back-action [23].Furthermore, in addition to an enhanced local light field, the plasmonic nanoantennas also efficiently absorb light and dissipate heat, thereby providing the means to engineer the thermal landscape at the nanoscale [24][25][26].This heating may be leveraged to induce thermophoretic forces [27][28][29][30][31] and microfluidic flows [32,33] to enable the manipulation of suspended objects.The introduction of electrothermoplasmonic tweezers [34][35][36] resulted in plasmonic tweezers with a large radius of action, to overcome the diffusion-limited transport of objects while permitting the high-resolution trapping of nanoscale objects.This finding is now being employed for applications in biological sensing and directed assembly [37,38].
Traditionally, gold has been used as the material of choice for designing and experimentally demonstrating plasmonic optical tweezers in an optofluidic system due to its good optical properties and chemical stability.Advances in plasmonic materials research have ushered in alternative materials with optical properties across a broad range of the electromagnetic spectrum from UV to NIR such as aluminum [39][40][41][42][43] and transition metal nitrides [44][45][46][47][48]. Transition metal nitrides, particularly titanium nitride (TiN) has attracted significant attention because of their good plasmonic properties and photothermal response in the near-infrared biological transparency window.The interaction of the plasmonic nanostructures with light in a fluidic media is a complex process that involves several physical mechanisms including the interplay between resonant light absorption, heat generation and transport, perturbation of the thermophysical and electrical properties of the fluid, and the generation of fluidic motion.Furthermore, the application of an AC electric field to a fluidic medium with inhomogeneous dielectric properties resulting from a temperature gradient gives rise to additional volumetric body forces namely electrothermal forces to induce electrothermoplasmonic (ETP) flow in the fluid.The interplay of the multiphysical mechanisms described above can be understood via a Multiphysics modeling of the respective differential equations describing those physical effects.
In this article, we present theoretical results characterizing the performance of TiN as a plasmonic material for application in plasmon-enhanced optofluidic control.By using Multiphysics modeling, we investigate the electromagnetic, photothermal and accompanying fluid dynamics induced by TiN BNA and Au BNA submerged in a microfluidic chip.The coupled electromagnetic, heat transfer and fluid dynamics problem is solved numerically using COMSOL Multiphysics (v 5.3a) simulation software, and this analysis builds on our previous work reported in [34].In contrast to earlier models of electrothermal flow that have considered only joule heating in the fluid induced by an applied AC electric field, our approach models the optically-induced heating of fluid by an illuminated plasmonic nanoantenna.As such, our model comprises of solving the electromagnetic wave equation derived from Maxwell's equations, the heat transport equation and the Navier-Stokes equation.We simulated the electrothermoplasmonic flow generated via optically-induced heating of a single TiN BNA in the presence of an applied AC electric field.We find that the TiN BNA provides micrometer scale ETP flow velocities with velocities at least three times higher than those of a single Au BNA.

Multiphysics modeling
The photothermal heating of the fluid by the illuminated plasmonic nanoantenna results in a temperature gradient in the fluid.This temperature gradient in turn establishes a gradient in the temperature-dependent properties of the fluid namely: the density, permittivity and electrical conductivity.A gradient in the density of the fluid induces buoyancy-driven thermoplasmonic convection.On the other hand, if an AC electric field is applied in the presence of a gradient in the permittivity and electrical conductivity, ETP flow is induced.
The simulation begins by solving the time-independent electromagnetic wave equation given by 2 0 ( ) 0, where E is the total electric field in the vicinity of the BNA, k 0 is the free-space wavenumber with wavelength λ, and ε(r) is the complex, position-dependent (r) permittivity.The solution of Eq. ( 1) is used to obtain the heat dissipation power density q(r) = Re[J•E*]/2 [26], where J is the induced-current density in the BNA and in the underlying metallic film, Re stands for the real part and * is the complex conjugate.The optical properties of TiN and gold were taken from [47].The relatively low temperatures considered in this work (below 473 K) are not significant enough to cause an appreciable modulation of the optical properties of TiN and Au as described in [49,50].Hence, the temperature-independent dielectric properties for TiN and Au at a given wavelength were used in the simulations.The dielectric constant for glass and sapphire substrates were set as 2.10 and 3.06, respectively.The heat source density serves as a source term for the coupled, steady-state heat transfer and fluid mechanics (HT-FM) problem , where T(r), u(r) and p(r) are the spatial temperature, fluid-velocity and pressure distributions, respectively, and the material parameters are κ, ρ, c p and η (thermal conductivity, density, heat capacity, and kinematic viscosity, respectively).For TiN, ρ = 5400 kg/m 3 , c p = 533.3J/(kg•K) and κ = 60 W/(m•K), while for Au, ρ = 19300 kg/m 3 , c p = 126 J/(kg•K) and κ = 317 W/(m•K).For the water medium, ρ = 998 kg/m 3 , c p = 4200 J/(kg•K) and κ = 0.6 W/(m•K).For the glass substrate, ρ = 2700 kg/m 3 , c p = 840 J/(kg•K) and κ = 1.38 W/(m•K), while for sapphire, ρ = 3980 kg/m 3 , c p = 756 J/(kg•K) and κ = 25.8W/(m•K).The buoyancy-driven natural convection that occurs when only the laser illumination of the BNA is present is described via a volume force given by the Boussinesq approximation, buoy 0 ( , where g is the acceleration due to gravity, ρ = 998 kg/m 3 and T 0 = 293.15K are the reference density of water and temperature, respectively, and β(T) is the temperature-dependent thermal expansion coefficient of water.The assumption in the Boussinesq approximation is that the variations in the density of the fluid have no effect on the flow field, except that they give rise to buoyancy forces.The ETP flow is triggered by applying an AC electric field in addition to the optical illumination.It arises because the AC electric field acts on the heat-induced gradient in the permittivity and conductivity of the fluid element.The additional volume force resulting from the ETP flow F etp is added to the buoyancy-driven convection volume force density F buoy given by the Boussinesq approximation described above so that the total force becomes F = F etp + F buoy .The volume force resulting from ETP flow is given by [51] ( ) where τ = ε/σ is the charge relaxation time of the fluid, which is taken as water, and ε and σ are the permittivity and electrical conductivity of the fluid, respectively.The temperature dependence of the permittivity of water is represented as , while the temperature dependence of the conductivity of water is represented as . The electrical permittivity of the water medium at the reference temperature of T 0 = 293.15K was set as ε 0 = 80ε 0 F/m, where ε 0 is the permittivity of free space.The electrical conductivity of the water medium at the reference temperature was set as σ 0 = 50 μS/m.The expressions α = (1/ε)(∂ε/∂T) and γ = (1/σ)(∂σ/∂T) are linear approximations of the temperature dependence of the permittivity and electrical conductivity, respectively and are given as −0.004K −1 and 0.02 K −1 , respectively [52].E ac is the AC electric field in the fluid, which depends on the applied voltage v across the fluid.The voltage v used to generate the AC electric field across the water medium varies from 2 V to 6 V, with a frequency of 50 KHz.ection depicted m.We also sh ons have been gap spacing the enhancement i wave.We quantified substrates ma longitudinal d film system substrate was temperature f that the in-pla than the sapph of the water m dissipated hea hand, the ther there is more the axial (alon BNA on Au film on glass and sapphire substrates.The maximum temperature rise for all cases occurs on the surface of the BNA.As expected, the TiN BNA on glass substrate generated a high temperature rise of 56 K, while the peak temperature rise on the Au BNA system is only 9 K.This difference is because the TiN BNA on TiN film system absorbs more light than the Au BNA on Au film system.Furthermore, TiN film has a lower thermal conductivity (60 W/mK) than gold (317 W/mK), and hence there is less thermal spreading in the TiN film compared to the Au film.When the substrate was switched to sapphire, the maximum temperature rise on the surface of the TiN BNA reduces to 34 K, while the maximum temperature rise on the Au BNA reduces to 4 K. Furthermore, the use of a high thermal conductivity substrate like sapphire also resulted in a lower temperature rise inside the water medium.Thus, the use of high thermal conductivity substrates represents an elegant approach to manage the temperature rise in integrated nanoplasmonic systems [13].The use of sapphire as high thermal conductivity substrate has been recently used to prevent the elevation of the temperature of super-heated water as the optical power of the heating laser is increased [54].

Enhanced electrothermoplasmonic flow with plasmonic TiN nanoantenna
The heat transferred to the adjoining fluid medium by the hot BNA can generate thermoplasmonic convection flow in the fluid due to the gradient in the density of the fluid.If an AC electric field is applied to the fluid, a much stronger ETP flow is also induced in the fluid.A horizontal 2D slice of the ETP flow velocity profile for the TiN BNA with longitudinal polarization is shown in Fig. 4(a).We see that the flow is radially symmetric.The flow will act to transport suspended objects towards the thermal hotspot, which corresponds to the position of the TiN BNA.A vertical 2D slice of the ETP flow velocity profile for the TiN BNA with longitudinal polarization is shown in Fig. 4(b).In the axial direction, this flow moves in a direction away from the TiN BNA.This implies that in the axial direction, the flow would act to transport suspended objects away from the BNA. Figure 4(c) shows the in-plane radial velocity of the microfluidic flow induced in the fluid at a height of 10 μm from the surface of the BNA.For the case when only the laser illumination of the TiN BNA or Au BNA is applied, the velocity of the induced buoyancy-driven thermoplasmonic convection is extremely weak with a peak of 52.5 nm/s for the TiN BNA and 15.1 nm/s for the Au BNA.Such weak velocities cannot induce a net motion of suspended particles that are constantly undergoing Brownian motion.When an AC voltage of 2 V is applied to induce an electric field within the water medium, the velocity of the resulting ETP flow is enhanced significantly to 0.84 μm/s for TiN BNA and 0.28 μm/s for the Au BNA on glass substrates, respectively.We also find that increasing the voltage by a factor of 3, i.e. from 2 V to 6 V increases the velocity by a factor of approximately 8.5.A closer look at Eq. ( 4) shows that the volumetric body force for the ETP flow is proportional to not only the temperature gradient, but also to the square of the AC electric field magnitude |E ac | 2 , and hence it is proportional to the square of the AC voltage v 2 .Thus, the velocity of the ETP flow will be proportional to the product of the temperature gradient and the square of the applied voltage.Figure 5(d) shows that a plot of the maximum radial velocity versus the product of the maximum of the temperature gradient along the x-direction, and the square of the applied voltage v 2 is a straight line for both the glass and sapphire substrates.

Conclusion
Using Multiphysics thermodynamics modeling, we have investigated the potential of plasmonic TiN BNA illuminated at near-infrared biological transparency window for plasmon-enhanced optofluidic control in lab-on-a-chip devices.The TiN BNA provides efficient absorption of incident light and generates strong electrothermoplasmonic (ETP) microfluidic flow for on-demand capture and rapid transport of target particles towards the plasmonic hotspots.The TiN BNA generates an ETP flow with a peak velocity that is about three times higher than that of the Au BNA.This makes TiN-based nanoantenna attractive for engineering fluidic flow for directed assembly of analytes, promoting mixing and for enhanced biosensing.We show that for high thermal conductivity substrates where the temperature rise in the fluid is reduced, the ETP flow velocity can be increased by increasing the voltage.This follows from the fact that the ETP flow velocity scales as the square of the applied voltage and can be readily amplified by raising the applied voltage.Thus, for temperature sensitive applications, a high thermal conductivity substrate may be used to limit both the temperature rise and the local temperature gradient in the fluid, while the ETP flow is amplified on-demand by raising the applied voltage.Additionally, for applications requiring high optical intensities, the judicious choice of the substrate material can be used to control the thermal heating, while the ETP flow velocity is increased by raising the AC electric field or voltage.Finally, we note that the efficient heat generation enabled by the TiN BNA system also makes it a good candidate material for generating heat-induced forces such as thermophoresis that can be remotely triggered by optical illumination.The theoretical prediction of enhanced ETP flow enabled by plasmonic TiN nanoantennas will be useful for the growing range of lab-on-a-chip devices that utilize plasmonic nanostructures and would open new opportunities for controlling fluid flow on the micro-and nanoscale.
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