Open Access Article

This Open Access Article is licensed under a Creative Commons Attribution-Non Commercial 3.0 Unported Licence

Anh D. Phan*^{ab},
Vu D. Lam^{c} and
Katsunori Wakabayashi^{b}
^{a}Phenikaa Institute for Advanced Study, Artificial Intelligence Laboratory, Faculty of Computer Science, Materials Science and Engineering, Phenikaa University, Hanoi 12116, Vietnam. E-mail: anh.phanduc@phenikaa-uni.edu.vn
^{b}Department of Nanotechnology for Sustainable Energy, School of Science and Technology, Kwansei Gakuin University, Sanda, Hyogo 669-1337, Japan
^{c}Graduate University of Science and Technology, Vietnam Academy of Science and Technology, 18 Hoang Quoc Viet, Hanoi, Vietnam. E-mail: lamvd@ims.vast.ac.vn

Received
27th August 2020
, Accepted 11th November 2020

First published on 17th November 2020

We theoretically investigate equilibrium behaviors and photothermal effects of a flexible plasmonic metamaterial composed of aramid nanofibers and gold nanoparticles. The fiber matrix is considered as an external field to reconfigure a nanoparticle assembly. We find that the heating process tunes particle–particle and fiber–particle interactions, which alter adsorption of nanoparticles on fiber surfaces or clustering in pore spaces. Thus, it is possible to control the nanoparticle self-assembly by laser illumination. Gold nanoparticles strongly absorb radiations and efficiently dissipate absorbed energy into heat. By solving the heat transfer equation associated with an effective medium approximation, we calculate the spatial temperature rise. Remarkably, our theoretical results quantitatively agree with prior experiments. This indicates that we can ignore plasmonic coupling effects induced by particle clustering. Effects of the laser spot size and intensity on the photothermal heating are also discussed.

Recently, an ultra-flexible plasmonic metamaterial film was fabricated by mixing gold nanoparticles (AuNPs) and aramid nanofibers^{5} to generate broadband optical absorbers with durable mechanical strength. In this metamaterial, the aramid nanofibers have strong mechanical strength with a high flexibility. Localized surface plasmon resonances of gold nanoparticles enhance electromagnetic fields around the nanostructures, absorb light energy and effectively dissipate it into heat when illuminated. Thus, these flexible metamaterials become multifunctional materials for a wide range of applications. However, the photothermal heating increases the temperature of the metamaterials, and possibly affects the clustering of nanoparticles and structurally rearranges them. Here, several questions arise: does the nanoparticle assembly have a significant effect on the photothermal heating? Does the plasmonic coupling matter?

Can existing theoretical approaches describe photothermal responses without introducing new physics? The mechanisms have not been comprehensively reported so for. Theoretical insights into microstructures of fiber–nanoparticle composites would pave the way for applications in various areas, such as drug delivery,^{6} neuromorphic transistors,^{7} direct ink writing,^{8} and hyper-stretchable nanocomposites.^{9}

The light-induced temperature increase has been theoretically investigated in various systems. Neumann and her coworkers have simplified the heat diffusion equation to describe qualitatively the heating process and explain how air bubbles around photothermal agents are formed in water.^{10} Sousa-Castillo et al. have determined thermal gradients of a gold nanocapsule deposited on a glass substrate under simulated solar irradiation^{11} by finite element analysis. Recently, we have proposed new models^{12,13} to calculate time-dependent temperature distributions of aqueous solutions of plasmonic nanostructure solutions under solar irradiation. We treat this system as a homogeneous single layer system and capture the collective heating of the nanoparticles for a wide range of particle densities. In the year of 2020, these approaches have been developed to study the thermal gradients of multilayered systems such as graphene metamaterials^{14} and floating/hanging PANi fabrics.^{15} Numerical results in ref. 12–15 are in quantitative accordance with experiments. However, photothermal effects in nanoparticle–fiber composites have not been studied yet. The presence of fiber network introduces confinement effects on nanoparticles and possibly shortens the separation distance among them. Thus, strong plasmonic coupling between plasmonic nanoparticles can occur. In addition, while the distribution of nanoparticles in dilute solutions remains unchanged during the heating process, the thermal-induced reorganization of particles in nanoparticle–fiber composites is complicated.

In this work, we use the statistical mechanics theory to study the equilibrium structure and collective light heating of gold nanoparticles dispersed in a disorder nanofiber network using the polymer reference interaction site model (PRISM) integral equation theory. This composite is fabricated as an ultra-flexible plasmonic metamaterial in ref. 5. We determine contribution of particle–particle and fiber–particle interactions, and their length scales to the equilibrium isotropic structure. Our approach is useful for explaining other similar experimental systems such as nanoparticle–protein superlattice wires.^{16} These interactions can be tuned by laser heating under laser illumination. By using effective medium approximation, we can calculate spatial temperature increase. Our calculations are quantitatively close to experimental results in ref. 5. We discuss effects of the nanoparticle density, laser spot, and laser intensity on the heating process.

According to the fabrication in ref. 5, the diameter of AuNPs is D = 0.75d = 58 nm, the pore (mesh) size is ξ ≈ 3.23D, and N = 20, and the particle packing fraction Φ_{p} = 10^{−3} corresponds to the 5.7 wt% Au content. The pore size is smaller than the length of fiber to construct network. The pore size of the network is theoretically estimated by^{20}

(1) |

We compute site–site pair correlation functions for objects using the PRISM theory,^{21} or solving numerically Ornstein–Zernike (OZ) equations.^{21,22} In Fourier space, the matrix site–site generalized Ornstein–Zernike equations is given by

(2) |

For gold particles, ω_{p}(k) = 1. Meanwhile, the molecule structure factor of FJC polymer is^{18}

(3) |

To solve eqn (2), we apply the Percus–Yevick (PY) closure^{21,22} to the standard fiber–fiber and fiber–nanoparticle real space correlations. The site–site PY approximation for correlations inside species is zero. For outside species, this is

(4) |

(5) |

Now, one can employ the Picard or a Newton–Raphson algorithm^{22} to numerically solve eqn (2)–(5) to obtain the radial distribution functions and structure factors.

Under broadband laser irradiation, the spatial temperature gradient is analytically obtained by solving a heat energy balance equation of a slab. The temperature rise at coordinate (x, y, z)^{12,23} is

(6) |

According to effective medium approximations,^{24,25} an effective dielectric function of the metamaterials is ε_{eff} = ε_{f} + Φ_{p}ε_{p}, here ε_{f} and ε_{f} being the dielectric function of the aramid fiber^{5} and gold nanoparticles,^{26} respectively. We assume that the presence of nanoparticles does not change the packing fraction and macroscopic structure of the aramid fiber. Gold nanoparticles simply fill in the pore space. From this, one can determine the absorption coefficient by

(7) |

The thermal conductivity, mass density, and specific heat of the metamaterial can be approximately calculated using effective medium approximations^{24,25,27}

(8) |

The particle localization is strongly driven by a spatial range of interfacial forces. As seen in Fig. 1a, g_{pp}(r) increases with a growth of δ. One observes a tighter localization with the increase of the range of repulsion. This interacting length scale is tunable by varying a salt concentration. According to the Debye–Hückel theory,^{31} one has

(9) |

Eqn (9) indicates that the increase of salt screens particle–fiber repulsive interactions. In the absence of fiber network or in the large pore-size system, the state of hard-sphere fluids becomes localized as Φ_{p} ≥ 0.432.^{22} However, our results exhibit an emergence of the localized state at Φ_{p} = 10^{−3} in the presence of a small pore size network. The behavior reveals effects of geometrical constraints on forming the glass-like structure. The localization of particles are stronger at low salt concentrations and weaker (particles start delocalized) at large salt concentrations. These calculations are completely consistent with experiments in ref. 16. Although the prior work^{16} investigates the assembly of gold nanoparticles and anionic tobacco mosaic virus nanorods, parameters for interactions, density, and sizes for PRISM calculations are relatively similar.

Interestingly, the spatial fiber–particle correlation is very insensitive to ε_{pp}. The radial distribution function g_{fp}(r) is shown in the inset of Fig. 2. It implies that interfacial adsorption is unaffected by the interparticle interaction but gold nanoparticles are reorganized to favor either clustering in the pore or sequential multilayer adsorption.

Clearly, arrangement of particles can be controlled by heating. Under laser illumination, gold nanoparticles absorb electromagnetic fields or optical energy of incident light via plasmonic properties. The absorbed optical energy is effectively converted into heat and increases the temperature. The nanoparticle assembly can be continuously changed with turning on and off laser light as a reversible process.

Fig. 3a shows the temperature profile of the steady state under laser illumination with the intensity I = 30.4 mW mm^{−2}. The packing fraction is Φ_{p} = 2.3 × 10^{−3} to mimic photothermal experiments in ref. 5. The temperature rise at the surface center is ΔT(x = 0, y = 0) = 128 °C. In addition, the diameter of the hot area defined by ΔT(x, y) ≥ 96 °C is about 5 mm. These results and our spatial contour plot are very close to the prior study.^{5} This agreement between the calculations and experiments validates an effective medium approximation used in eqn (7) and (8). It means that the distribution of gold nanoparticles can be considered as a random dispersion. Although effects of interparticle plasmon coupling are expected to appear when gold nanoparticles are thermally reorganized, the collective heating is insensitive to this coupling enhancement. A possible reason for this behavior is the plasmonic coupling is very weak at wavelength of laser excitation. Another reason may be ε_{pp} and ε_{fp} ≪ k_{B}T. Consequently, the nanoparticle assembly remains unchanged during a heating process. This explains why multiple-switching light source does not change optical and thermal response of the metamaterial in ref. 5.

According to eqn (6), the temperature rise ΔT is linearly grows with the laser intensity. This clearly explains data in prior works.^{5,14,34,35} Our linear relation is ΔT(x = 0, y = 0) ≈ 4.28I, here I is in the unit of mW mm^{−2}. This calculation also quantitatively agrees with experimental results in ref. 5.

Fig. 3b and c show the density plots of ΔT for higher concentrations of nanoparticles (Φ_{p} = 4.6 × 10^{−3} and 6.9 × 10^{−3}) illuminated by laser light. An increase of the volume fraction of gold particles significantly localizes the absorbed optical energy at the interface. However, since the thermal conductivity of the metamaterial grows with increasing Φ_{p}, the light-to-heat conversion is efficiently conducted. As a result, the laser-induced temperature rise is decreased with densifying nanoparticles. This finding indicates that at the same packing fraction, replacing gold nanoparticles with TiN nanoparticles leads to a higher temperature rise since optical properties of TiN nanoparticles are similar to those of Au counterparts^{12} but K^{bulk}_{TiN} ≈ 29 W m^{−1} K^{−1} ≪ K_{p}.^{36}

Based on eqn (6), we determine the dependence of ΔT(x = y = z = 0) on the light spot size. Fig. 4 shows a linear relation between the steady temperature of center point on the surface and the diameter of illuminated laser spot at Φ_{p} = 2.3 × 10^{−3}, 4.6 × 10^{−3}, and 6.9 × 10^{−3}. A decrease of the incident laser spot area linearly reduces the temperature increase. Thus, except for the intensity I, one can tune ΔT by varying the diameter of incident light.

There are many other designs for broadband near-perfect absorbers or anti-reflectors. In prior works, the structures are composed of a periodic array of dielectric micro-spheres on a metal film,^{37} a periodic array of truncated metal/dielectric cones on a metal substrate,^{38} and a three-layer metallo–dielectric–metallo stack.^{39} These metamaterials anti-reflect almost all of incident electromagnetic fields and these are similar to our studied metamaterial. However, they are rigid and not flexible. In addition, the thermal conductivity of metal is much larger than that of fiber or even fiber mixed with plasmonic nanoparticles. Thus, under the same laser irradiation, the temperature rise of the rigid plasmonic metamaterials is smaller since heating the system of larger thermal conductivity needs more thermal energy.

To understand thermal-induced reassembly and plasmonic interactions of gold nanoparticles in this ultra-flexible plasmonic metamaterial, we have theoretically calculated the temperature gradient of the metamaterial under laser illumination. Our approach uses the analytical solution of the heat transfer differential equation associated with an effective medium approximation. This treatment means we ignore enhancement of electromagnetic fields at nanogaps among plasmonic nanostructures. Theoretical temperature rise agrees quantitatively well with prior photothermal characterization.^{5} This agreement indicates the plasmonic coupling effect is possibly small to be ignored even when the assembly of gold nanoparticles can be thermally reconfigured. Another possibility is that the fiber–particle and particle–particle interactions are much smaller than k_{B}T and the structure of nanocomposites is nearly independent of temperature. Our work also suggests it is possible to use a random distribution model to effectively describe the dispersion of nanoparticles in fiber matrix in the same manner as nanoparticles dispersed in aqueous solution. This theoretical approach can be exploited for the rational design of materials with tailored functions.

- Y. Liua and X. Zhang, Metamaterials: a new frontier of science and technology, Chem. Soc. Rev., 2011, 40, 2494–2507 RSC.
- S. Walia, C. M. Shah, P. Gutruf, H. Nili, D. R. Chowdhury, W. Withayachumnankul, M. Bhaskaran and S. Sriram, Flexible metasurfaces and metamaterials: a review of materials and fabrication processes at micro- and nano-scales, Appl. Phys. Rev., 2015, 2, 011303 Search PubMed.
- I. M. Pryce, K. Aydin, Y. A. Kelaita, R. M. Briggs and H. A. Atwater, Highly Strained Compliant Optical Metamaterials with Large Frequency Tunability, Nano Lett., 2010, 10, 4222 CrossRef CAS.
- Z. Xu and Y.-S. Lin, A Stretchable Terahertz Parabolic-Shaped Metamaterial, Adv. Opt. Mater., 2019, 7, 1900379 CrossRef CAS.
- H. Zhang, L. Feng, Y. Liang and T. Xu, An ultra-flexible plasmonic metamaterial film for efficient omnidirectional and broadband optical absorption, Nanoscale, 2019, 11, 437–443 RSC.
- J. Shi, C. Du, J. Shi, Y. Wang and S. Cao, Hollow multilayer microcapsules for pH-/thermally responsive drug delivery using aliphatic poly(urethane-amine) as smart component, Macromol. Biosci., 2013, 13, 494–502 CrossRef CAS.
- N. Liu, L. Q. Zhu, P. Feng, C. J. Wan, Y. H. Liu, Y. Shi and Q. Wan, Flexible Sensory Platform Based on Oxide-based Neuromorphic Transistors, Sci. Rep., 2015, 5, 18082 CrossRef CAS.
- J. A. Lewis, Direct Ink Writing of 3D Functional Materials, Adv. Funct. Mater., 2006, 16, 2193–2204 CrossRef CAS.
- C. K. Jeong, J. Lee, S. Han, J. Ryu, G.-T. Hwang, D. Y. Park, J. H. Park, S. S. Lee, M. Byun, S. H. Ko and K. J. Lee, A hyper-stretchable elastic-composite energy harvester, Adv. Mater., 2015, 27, 2866 CrossRef CAS.
- O. Neumann, A. S. Urban, J. Day, S. Lal, P. Nordlander and N. J. Halas, Solar vapor generation enabled by nanoparticles, ACS Nano, 2013, 7, 42–49 CrossRef CAS.
- A. Sousa-Castillo, O. Ameneiro-Prieto, M. Comesana-Hermoa, R. Yu, J. M. Vila-Fungueirino, M. Perez-Lorenzo, F. Rivadulla, F. J. G. de Abajo and M. A. Correa-Duarte, Hybrid plasmonic nanoresonators as efficient solar heat shields, Nano Energy, 2017, 37, 118–125 CrossRef CAS.
- A. D. Phan, N. B. Le, T. H. Lien Nghiem, L. M. Woods, S. Ishii and K. Wakabayashi, Confinement effects on the solar thermal heating process of TiN nanoparticle solutions, Phys. Chem. Chem. Phys., 2019, 21, 19915 RSC.
- A. D. Phan, N. B. Le, N. T. H. Lien and K. Wakabayashi, Multilayered Plasmonic Nanostructures for Solar Energy Harvesting, J. Phys. Chem. C, 2018, 122, 19801–19806 CrossRef CAS.
- A. D. Phan, D. T. Nga, D. C. Nghia, V. D. Lam and K. Wakabayashi, Effects of Mid-Infrared Graphene Plasmons on Photothermal Heating, Phys. Status Solidi RRL, 2020, 14, 1900656 CrossRef CAS.
- D. T. Nga, A. D. Phan, V. D. Lam, L. M. Woods and K. Wakabayashi, Enhanced solar photothermal effect of PANi fabrics with plasmonic nanostructures, RSC Adv., 2020, 10, 28447 RSC.
- V. Liljeström, A. Ora, J. Hassinen, H. T. Rekola, Nonappa, M. Heilala, V. Hynninen, J. J. Joensuu, R. H. A. Ras, P. Torma, O. Ikkala and M. A. Kostiainen, Cooperative colloidal self-assembly of metal-protein superlattice wires, Nat. Commun., 2017, 8, 671 CrossRef.
- M. Doi, and S. F. Edwards, Theory of Polymer Dynamics, Oxford University Press, New York, 1986 Search PubMed.
- J. B. Hooper and K. S. Schweizer, Contact Aggregation, Bridging, and Steric Stabilization in Dense Polymer Particle Mixtures, Macromolecules, 2005, 38, 8858–8869 CrossRef CAS.
- G. Brugger, L. S. Froufe-Perez, F. Scheffold and J. Jose Saenz, Controlling dispersion forces between small particles with artificially created random light fields, Nat. Commun., 2015, 6, 7460 CrossRef CAS.
- C. F. Schmidt, M. Barmann, G. Isenberg and E. Sackmann, Chain dynamics, mesh size, and diffusive transport in networks of polymerized actin: a quasielastic light scattering and microfluorescence study, Macromolecules, 1989, 22, 3638–3649 CrossRef CAS.
- K. S. Schweizer and J. G. Curro, Integral-equation theory of the structure of polymer melts, Phys. Rev. Lett., 1987, 58, 246 CrossRef CAS.
- J. P. Hansen and I. R. McDonald, Theory of Simple Liquids, Academic Press, London, 2nd edn, 1986 Search PubMed.
- B. J. Bartholomeusz, Thermal response of a laser-irradiated metal slab, J. Appl. Phys., 1988, 64, 3815 CrossRef CAS.
- L. D. Landau and E. M. Lifshitz, Electrodynamics of Continuous Media, Pergamon, Oxford, 1960 Search PubMed.
- C. F. Bohren and D. R. Huffman, Absorption and Scattering of Light by Small Particles, Wiley, Weinheim, Germany, 1998 Search PubMed.
- A. D. Phan, T. X. Hoang, T. H. L. Nghiem and L. M. Woods, Surface plasmon resonances of protein-conjugated gold nanoparticles on graphitic substrates, Appl. Phys. Lett., 2013, 103, 163702 CrossRef.
- P. Warrier and A. Teja, Effect of particle size on the thermal conductivity of nanofluids containing metallic nanoparticles, Nanoscale Res. Lett., 2011, 6, 247 CrossRef.
- http://www.matweb.com/search/datasheet.aspx?MatGUID=77b5205f0dcc43bb8cbe6fee7d36cbb5%26ckck=1.
- J. Callaway, Model for Lattice Thermal Conductivity at Low Temperatures, Phys. Rev., 1959, 113, 1046 CrossRef CAS.
- J. M. Ziman, Electrons and Phonons: The Theory of Transport Phenomena in Solids, Oxford University Press, Oxford, UK, 2001 Search PubMed.
- H. Ohshima, Biophysical Chemistry of Biointerfaces, John Wiley & Sons, Hoboken, NJ, 2010 Search PubMed.
- N. Hooshmanda and M. A. El-Sayed, Collective multipole oscillations direct the plasmonic coupling at the nanojunction interfaces, Proc. Natl. Acad. Sci. U. S. A., 2019, 116, 19299–19304 CrossRef.
- P. K. Jain and M. A. El-Sayed, Plasmonic coupling in noble metal nanostructures, Chem. Phys. Lett., 2010, 487, 153–164 CrossRef CAS.
- C. Faugeras, B. Faugeras, M. Orlita, M. Potemski, R. R. Nair and A. K. Geim, Thermal Conductivity of Graphene in Corbino Membrane Geometry, ACS Nano, 2010, 4, 1889 CrossRef CAS.
- V. T. T. Duong, A. D. Phan, N. T. H. Lien, D. T. Hue, D. Q. Hoa, D. T. Nga, T. H. Nhung and N. A. Viet, Near-Infrared Photothermal Response of Plasmonic Gold-Coated Nanoparticles in Tissues, Phys. Status Solidi A, 2018, 215, 1700564 CrossRef.
- https://www.memsnet.org/material/titaniumnitridetinbulk/.
- G. Liu, Y. Liu, X. Liu, J. Chen, G. Fu and Z. Liu, Sol. Energy Mater. Sol. Cells, 2018, 186, 142–148 CrossRef CAS.
- Z. Liu, P. Tang, X. Liu, Z. Yi, G. Liu, Y. Wang and M. Liu, Nanotechnology, 2019, 30, 305203 CrossRef CAS.
- Z. Liu, X. Liu, S. Huang, P. Pan, J. Chen, G. Liu and G. Gu, ACS Appl. Mater. Interfaces, 2015, 7, 4962–4968 CrossRef CAS.

This journal is © The Royal Society of Chemistry 2020 |