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Shape-mediated light absorption by spherical microcapsule with gold-nanoparticles-dope
Journal of Quantitative Spectroscopy & Radiative Transfer 236 (2019) 106595
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Shape-mediated light absorption by spherical microcapsule with gold-nanoparticles-dope Yury E. Geints∗, Ekaterina K. Panina, Alexander A. Zemlyanov V.E. Zuev Institute of Atmospheric Optics SB RAS, 1 Zuev square, 634021 Tomsk, Russia
a r t i c l e
i n f o
Article history: Received 3 June 2019 Revised 26 July 2019 Accepted 27 July 2019 Available online 2 August 2019 Keywords: Light absorption Microcapsule Nanoparticle Plasmon resonance Effective medium
a b s t r a c t The study of the light absorption efficiency of a hollow spherical microparticle (microcapsule) doped with strongly absorbing gold nanoparticles of spherical and cylindrical spatial shapes is presented. By means of the FDTD numerical simulations, the absorption spectra of a microcapsule doped with nanoparticles in the visible and near-IR spectral regions are calculated. We show the absorption efficiency of the capsule depends on the morphology of nano-inclusions. In particular, there is a noticeable absorption enhancement of the microcapsule in the regions of the resonant excitation of the localized surface plasmon modes of doping nanoparticles. The chromatic dispersion of capsule absorptivity decreases with an increase in the volume content of nanoparticles, as well as when simultaneously mixing nano-inclusions of various shapes (spheres + rods). In this case, it becomes possible to obtain a near-uniform absorption spectrum of the capsule in the considered wavelength range, which can be well fitted within the framework of effective homogeneous medium using, e.g., the Bruggeman mixing rule. © 2019 Elsevier Ltd. All rights reserved.
1. Introduction Polymeric hollow micro- and nanoparticles, which hereafter are referred to as the microcapsules, are in the last decades actively studied in various fields of science and technology ranging from nanomedicine, pharmaceuticals and nanocosmetology to nanophotonics, nanochemistry and biotechnology [1–6]. A typical and most relevant example of microcapsules employment is the so-called drug delivery system, which maximizes therapeutic efficacy while minimizing side effects through ultra-precise control over the space-time behavior of drugs nanodoses inside the patient’s body. The controlled release of therapeutic molecules from microcapsules at the right places and at the right times is becoming increasingly important for advanced treatment techniques, including gene therapy, antibody therapy and vaccine therapy [7,8]. The technology of microcapsules manufacturing is an independent engineering task and to-date can be implemented in various ways, e.g., by monomers polymerization on the emulsified micronuclei, or by poly-ion layer-by-layer assembly (LbL) on the solid-phase templates [9]. Inside such microcapsules the necessary cargo can be deposited in the form of individual molecules or other active contents. Then, the microcapsule as a transport container can deliver this cargo to the required consignee where it can be activated or opened by any type of external stimuli.
∗
Corresponding author. E-mail address: [email protected] (Y.E. Geints).
https://doi.org/10.1016/j.jqsrt.2019.106595 0022-4073/© 2019 Elsevier Ltd. All rights reserved.
Modern trends of microencapsulation technology of active substances are shifting towards the creation of multifunctional cargo carriers that would be susceptible to various physical and chemical stimuli for the controlled release of the contents. As a rule, to acquire the multi-functionality, such capsules are fabricated in the form of quasi spherical particles having a multilayer shell. The shell can be composed of several dissimilar organic/inorganic layers that respond to various external factors [10]. The most common way to impart the optical activity to the microcapsule in the desired spectral range is adding in capsule shell the dispersed inclusions usually of nanometer size, which are susceptible to optical radiation. As a rule, these are noble metals and their salts [9,11]. Metal nanoparticles distributed over the shell convert the absorbed light into Joule heat, which then is released into the polycomposite matrix material of the microcapsule leading to a non-uniform distribution of its temperature [12]. This in turn, can initiate or influence the rate of physical and chemical reactions in the capsule shell and lead to its degradation and cargo release. A striking example of multi-functional transport container is the microcapsule built of several layers containing polysaccharides and polypeptides along with titanium dioxide (TiO2 ) and silica (SiO2 ) [13,14]. Such capsules are biocompatible, cheap in manufacturing, possess improved strength properties, reduced permeability of their shell and are susceptible to the ultrasound and ultraviolet (UV) radiation. Being exposed to UV laser (in the range from 300 to 400 nm) the capsules experience the photocatalytic destruction of their shells.
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In the visible and near IR spectral regions, usually the photothermal activation of microcontainers is used by adding to their shells optically absorbing nanoparticles of noble metals (gold, silver) [15,16], liquid laser dyes [17], or metal oxides [14]. In particular, a technology has recently been proposed for creating a bifunctional microcontainer with a polysaccharide shell decorated with inclusions of iron oxide nanoparticles (Fe3 O4 ) and graphene, which ensures the susceptibility of the microcapsule to both a variable magnetic field in the microwave frequency range (magnetothermal effect) and optical radiation [18,19] as well. As known, the optical properties of metals being dispersed to nanometer scales change dramatically and demonstrate a pronounced resonance behavior at certain frequencies of the incident light. This is due to the excitation of localized plasmon resonances (LPR) of metallic nanoparticles when the collective behavior of free electrons in a metal is manifested, leading to consistent oscillations of the entire electron cloud under the action of an alternating electric field of an optical wave [20]. Thus, in gold nanospheres (with the radius a = 10–40 nm) deposited in air, the resonance wavelength of the lowest-frequency (dipole) plasmon oscillation, which is called the Fröhlich mode [21,22], is about 520 nm, and for silver nanoparticles it amounts to about 412 nm. In the case of relatively large metal spheres, for which the Mie parameter xa = 2π a/λ becomes of the order of unity, in addition to the Fröhlich mode the modes of higher orders (quadrupole and octupole) are excited [23]. LPR excitation in a nanoparticle leads to the appearance of pronounced peaks in the absorption and scattering spectra at the frequencies of plasmon resonances in comparison with the extinction spectrum of a bulk metal sample. Meanwhile, an important feature of the plasmon resonances is the intensity enhancement of the optical field near the nanoparticle that can achieve several orders of magnitude. The frequency and amplitude of plasmon resonance are influenced not only by the type of metal but also by a number of other factors such as the optical properties of the surrounding medium, the degree of particles aggregation, and their spatial shape. It is known that the plasmonic absorption spectrum, e.g., of metallic nanorods [24] is split into two subranges shifted to the red and blue spectral wings relative to the dipole LPR of a spherical nanoparticle. Bilayer nanospheres with a non-conducting core (silicon oxide) also exhibit a red shift of the LPR, which increases with the decreasing in the metal shell thickness [25]. Aggregation of nanoparticles leading to their integration into one-dimensional or multidimensional clusters is also of considerable importance when calculating the optical properties of metallic nano-inclusions. As reported in [26], the absorption cross-section of a spherules cluster may increase or decrease depending on the degree of electric fields coupling of neighboring particles and the magnitude of their mutual field screening, which in turn is determined by the size of the aggregate and its constituent nanoparticles. Obviously, if the shape of the particles differs from the sphere then the orientation anisotropy of light absorption by the cluster is also of importance. In this paper, the absorption of laser radiation by a micronsized capsule with embedded gold nanoparticles is considered. By numerical solving of Maxwell’s equations by means of finitedifference time-domain calculations we show that the situation is quite possible when an initially optically transparent microcapsule being doped with gold nanoparticles acquires the optical absorption with different spectral characteristics than that of isolated dope nanoparticles. In particular, for the microcapsule doped with spherical inclusions the broadening of the dipole LPR is realized, whereas in the case of gold nanorods the lateral plasmon mode of nanocylinder is suppressed. These features become more pronounced if the volume fraction of doping inclusions increases.
Fig. 1. (a, b) 2D-section of sample microcapsules doped with (a) spherical and (b) cylindrical nanoparticles.
2. Nanoparticles-doped microcapsule light absorption simulations details To solve the electrodynamic problem of scattering and absorption of optical radiation at a multilayer spherical particle containing nano-inclusions, we used the finite-difference timedomain (FDTD) method based on direct numerical integration of the Maxwell’s equations for the components of the electromagnetic field of an optical wave. A specific implementation of FDTD algorithms was provided by the Lumerical FDTD Solutions software package (ver. 2016a for Linux [27]). The numerical simulations ran on Intel® CoreTM i7-3930K (3.2 GHz) computer with 48GB RAM. The 3D geometry of the computational domain was used; on the boundaries the conditions for perfect field matching (PML) were set. The accuracy of the numerical solution of the equations was guaranteed by an adaptive mesh refinement algorithm when the nodes of the computational grid are condensed in regions of sharp gradients of the dielectric constant of the medium (over-meshing at the boundaries of nanoparticles). The total number of “Yee cells” was several millions with a minimum spatial mesh size of 2 nm and a time step of 0.01 fs. This is sufficient for accurate reproducing the scattering and absorption characteristics of individual metal nanoparticles (see Fig. 2(b)). To be more specific, we construct a sample microcapsule (Fig. 1(a, b)) in the form of a hollow ball with outer radius Rc = 500 nm loaded with a water core simulating cargo, and a polycomposite (PE-SiO2 ) hard shell with the thickness h = 50 nm containing a nano-dispersed component in the form of gold spheres or cylindrical rods. In the calculations, the refractive index of the core and the shell was fixed and equaled to nc = 1.33 and nl = 1.45, respectively. Optical wavelength λ, total number of metallic nano-inclusions N, their dimensions (a,L) and shape may vary. The environment surrounding the microcapsule is considered as water with refractive index n0 = nc . Worth noting, gold nanoparticles because of their better biocompatibility than other metal nano-inclusions (Ag, Al, Fe) are the most common absorbing dope to various transport biocontainers. This is why we considered only gold in this work. We emphasize that only the microcapsule shell is filled with metal nanoparticles while its core remains nonabsorbing. The particle-filling procedure consists in programmatic generation of N particles with corresponding shapes randomly distributed inside a spherical layer Rc − h ≤ r ≤ Rc . Particles have randomly distributed set of geometric parameters with the standard deviation SD = 0.2 f, where f is any of the dimensional parameters of the particle. This defines sufficiently broad range of data distribution:
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Fig. 2. (a) Dispersive parameters of refraction index n, absorption index κ and volume absorption α = 4π nκ /λ of bulk gold [28]; (b) Absorption efficiency Qabs of gold nanospheres and nanorods with different sizes. Symbols depict Lorenz–Mie theory Qabs calculations for 14 nm gold sphere.
fmax /fmin ≈ 2. Note this value of SD is chosen quite arbitrary and only reflects the randomness of target capsule seeding with absorbing nanoparticles. During the nanoparticles deposition procedure, the condition of their mutual independence is checked, i.e. individual particles do not allowed overlapping in space. Four types of nanoparticles are considered as the examples of typical absorbing dope: sphere ensembles with the average radii a = 14 and 20 nm, as well as the arrays of cylindrical rods with the size parameters (a × L) = 10 × 40 and 10 × 60 nm2 . In the case of gold nanorods, additionally the spatial orientation of cylinder principal axis varies randomly that simulates natural nanoparticle deposition during absorbing layers assembling process. At the lower boundary of simulation domain, a plane linearly polarized wave is injected with a unit amplitude E0 and wave vector directed along the vertical (z) axis (shown by arrows in Fig. 1). The spatial distribution of the electromagnetic field E(r) inside and near a sample microcapsule is calculated by the FDTD updating scheme. Next, the absorption efficiency factor of microcapsule Qabs = Pabs /(π R2c I0 ) is obtained based on the volume integrating of time-averaged optical field, where the total absorbed optical power Pabs in the microparticle volume Vc is expressed as:
Pabs =
π c ε0 λ
Vc
dr ε (r )|E(r )|2
(1)
Here, ε 0 is vacuum permittivity, ε is the imaginary part of microparticle permittivity, c is the speed of light, and I0 = (cn0 ε0 /2 )E02 denotes the optical intensity. As seen, the value Qabs is influenced not only by the optical field distribution in a capsule but also by the spatial configuration of absorbing inclusions (nanoparticles) which contribute to the ε -profile. Pure gold was used as the material of the nanoparticles, the optical parameters of which are taken from [28] and are shown in Fig. 2(a) for the reference. Notice that we imply the optical wave phasor as a positive exponent E(z)∝exp {ik(n + iκ )z} which leads to positive values of the absorption coefficient κ .
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The scaling of a bulk solid metal down to a nanometer-sized particle drastically changes its optical characteristics mainly due to the excitation of collective free-electrons oscillations. As can be seen in Fig. 2(b) in the absorption spectra of isolated nanoparticles, the pronounced maxima appear corresponding to different surface plasmon modes. Gold nanospheres in the considered spectral range have only one resonant absorption maximum at the wavelength of the dipole LPR around the value λ ∼ 520 nm when the dispersion condition for the so-called Fröhlich mode [21] is satisfied: [n(λ )]2 − [κ (λ )]2 = −2[n0 (λ )]2 . Metal cylindrical nanoparticles (nanorods) support two types of LPR, which are excited when the electric field polarization vector is directed along one of the rod axes. The shortest-wavelength plasmon mode corresponds to the wave polarization across the rod (lateral mode), and its resonance wavelength is almost constant for the selected particles (λ ∼ 510 nm). The frequency position of the second (longitudinal) plasmon resonance depends on the rod length L and varies significantly from λ ∼ 700 nm when L = 40 nm to λ ∼ 785 nm at L = 60 nm. Obviously, in the real situations when a microcapsule is doped with cylindrical nanoparticles, their spatial orientation relative to the polarization of the incident optical radiation can be arbitrary, which will lead in general to an equally probable excitation of both plasmon resonances in an assembly of cylindrical nanorods. Thus, for practical calculations it is important to have the absorption spectrum of an isolated nanocylinder averaged over possible spatial orientations of light wave polarization. Such spectra are shown in Fig. 2(b) for both considered types of particles and demonstrate two absorption maxima centered in the visible and IR spectral regions that corresponds to two excited plasmon modes. Noticeable, LPR for the longitudinal wave polarization is several times more intensive than the transverse polarization mode. 3. Results and discussion Consider the results of our numerical simulations. In Fig. 3(a, c) are shown the spectral profiles of the absorption efficiency Qabs of microcapsules doped with the spherical and cylindrical nanoparticles. The volume fraction δ = Vd /Vsh of the absorbing dope in capsule shell could vary and defines a wide range of effective absorption from an almost transparent capsule with a total number of nano-inclusions N of the order of 250, to a closely packed assembly of nanoparticles with N ≈ 2200 (δ = 18%) and high optical absorption. Here, Vd = Nj=1 V j is the total volume of all nanoparti-
cles in capsule, and Vsh = ξ −3 Vc [1 + 3ξ (1 − ξ )] is the volume of the capsule shell (ξ = h/Rc ). As expected, with the increase of nanoparticle fraction, the absorption efficiency of microcapsule increases in the entire spectral range. Meanwhile, like in isolated particles (Fig. 2(b)) the plasmon resonances also appear in the absorption spectra of nanoparticledoped microcapsules. Thus, a microcapsule with spherical inclusions demonstrates a pronounced absorption selectivity near the wavelength of a dipole LPR with a week red-shifting of the absorption maximum from λ = 537 nm at δ = 2% to λ = 566 nm atδ = 18%. Note that similar tendency in the optical absorption spectra was reported earlier in [29] for a cluster of nanometersized gold spherules and was associated with the increased coupling of the optical fields of neighboring nanoparticles. A microcapsule doped with nanorods also exhibits a resonant behavior of the absorption efficiency. Here, the resonance of the longitudinal plasmon mode of a cylindrical nanoparticle at λ = 676 nm (δ = 2%) is clearly pronounced, while the optical excitation of the transverse LPR is effectively suppressed especially for high dope concentration. As for spherical nano-inclusions, there is a noticeable spectral shift of collective LPR mode relative to that of isolated particle. However, this spectral shift is reversed and di-
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Fig. 3. (a,c) Absorption efficiency Qabs and (b,d) normalized absorption qabs of microcapsule doped with 14 nm nanospheres (a,b) and nanorods with L = 40 nm (c,d). Magenta dash-dot-dot curves are for isolated nanoparticles.
rected to the blue wing achieving about 24 nm for maximum gold filling of the capsule. This behavior of absorption efficiency can be attributed to the orientation dispersion of absorption of nanorods, which are randomly distributed inside the capsule shell. In this case depending on the direction of optical wave polarization, there would be a predominant excitation of one of the plasmon resonance modes in the visible or IR spectral regions. The superposition of the contributions of two absorption channels on LPRs with different intensities leads to an effect similar to the generation of Fano resonance in an asymmetric photonic metastructure [30], when a distorted Lorenz absorption spectrum is formed with the maximum shifted toward the short wavelength region. When the dope-filling factor δ increases, the broadening of LPR absorption contour and the decrease of its relative amplitude take place. This is clearly seen if we normalize all the curves for abmax , which are sorption efficiency Qabs to their maximal values Qabs realized at δ = 18%. The normalized capsule absorption qabs = max depending on the laser wavelength is presented in Qabs /Qabs Fig. 3(c, d). One of the possible reasons of the spectral broadening of the absorption curve in a capsule, especially in the case of nanorodfilled particle, is the size-dispersion of the nanoparticles [24,31], which was artificially introduced during our programmatic particle generation. Besides, with the increase in particle radius the fields coupling of neighboring nanoparticles becomes more prominent when they are randomly clusterized into the “macromolecules” what can also lead to a significant rise or fall in the total absorption cross-section at certain optical frequencies [29,32,33]. Additionally, in the conditions of high doping of the capsule shell, the partial field-screening effect is possible when absorbing particles located in the lower hemisphere of the capsule (along optical wave incidence) act as an opaque shield against the nanoparticles inside
Fig. 4. Spectral dependence of capsule absorption efficiency doped with nanoparticles of various shapes. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
capsule upper part. This effect is maximal at LPR frequencies and can ultimately reduce the resonant contribution to the spectral absorption contour. The change in the size parameters of nanoparticles even within the same spatial shape (sphere, cylinder) also affects the spectral dependence of the absorption of the microcapsule. Fig. 4 summarizes the spectral dispersion of the absorption efficiency Qabs for all types of gold-dope-nanoparticles used in simulations. As seen, a change in the size of nanospheres from 14 to 20 nm has almost no effect on the capsule absorption in LPR excitation band; however it becomes noticeable in the long wavelength range, especially at
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Fig. 5. Effective medium model for a polycomposite capsule with 18% gold nanoparticles.
high concentrations of nanoparticles. Here, the particle screening effect is clearly manifested: the larger gold spheres more strongly perturb the optical field inside the capsule shell causing increased light scattering in illuminated hemisphere and early light departure from the microcapsule. As a result, the optical radiation simply does not reach the shadow part of the microparticle that reduces net capsule absorption. In the microcapsule with cylindrical nanoparticles, the effect of field-screening is less prominent due to the elongated shape of rods. The microcapsule doped with nanorods shows plasmon resonances at the corresponding LPR wavelengths as for isolated cylinders (Fig. 2(b)). Meanwhile, only the longitudinal LPR mode survives. With a high concentration of nanorods (δ = 18%), the spectral dependence of capsule absorption becomes weak and the variation of Qabs - factor does not exceed 10%. Various absorption spectral dispersion acquired by the microcapsule when doped with gold nanoparticles of spherical or cylindrical shape make it possible to design a spherical cargo micro-container with close to neutral spectral absorption in the considered wavelength range. Indeed, as follows from Fig. 4 (blue dash-dot-dot curves), using a specific doping mixture of nanospheres (a = 14 nm, 20%) and different-sized nanorods (80%) it is possible to significantly reduce the spectral absorption variations of the whole microcapsule. For practical calculations of the microcapsules absorption, the applicability of a homogeneous effective medium model to the mixture of absorbing and non-absorbing components in the spatial configuration of a layered sphere is important. Our analysis shows that among the well-known models of effective medium characteristics [34] the closest results to the calculated absorption characteristics is provided by the Bruggeman phase mixing rule, when the matrix and inclusions are considered equally leading to a symmetric mixing formula for the effective permittivity of a twocomponent mixture:
δ
εe − εm εe − εi + (1 − δ ) =0 2εe + εi 2εe + εm
(2)
Here, ε m and ε i are the dielectric permittivity of the matrix (polycomposite) and inclusions (gold), respectively. The real and imaginary parts of the complex refractive index of √ effective medium me = εe = ne + iκe consisting of a polycompos2 ite with εm = nl and metallic gold inclusions with ε i = (n + iκ )2 (see Fig. 2(a)) are shown in Fig. 5 for 18%-dope volume fraction. The calculations are carried out according to Eq. (2) taking into account the considerations of Ref. [35] regarding the selection of a single-valued analytical branch of the square root of a complex-
Fig. 6. (a) Absorption efficiency of microcapsule doped with gold spherules and nanorods as well as calculated via Bruggeman mixing rule (2); (b, c) Relative error γ of the effective medium model approximation versus dope volume fraction δ for nanospheres (b) and nanorods (c).
valued function. Here, we does not account for the geometrical shape of the inclusion phase and treat it as a bulk absorber while some considerations concerning the size-effect of nanoparticles in the effective medium approximation can be found elsewhere [21,22]. As seen from this figure, artificial effective medium is characterized by the increased absorption index κ e when increasing laser wavelength; this is similar to Au dispersion law. The effective medium refraction index ne to the contrary demonstrates the opposite spectral dependence concerning that of gold providing for smooth volume absorption fall in the longer wavelength limit. Based on ε e dispersion we calculated the absorption efficiency of a water-containing microcapsule with a shell made of artificial material with the effective refractive index me (λ). Spectral dependences of Qabs are depicted in Fig. 6(a) for two nanoparticle-dope volume content. From this figure, it follows that the best approximation to the real data is obtained in the case of cylindrical nanoparticles and relatively high dope content (δ > 10%). As mentioned above, due to the averaging over spatial orientations the nanorods-doped capsule demonstrates smooth absorption within the spectral region considered that resembles the absorption characteristic of regular homogeneous or layered spherical particle. The relative approximation e )/Q error γ = (Qabs − Qabs abs of the effective medium model, where e Qabs stands for the absorption efficiency calculated with the help of Eq. (2), does not exceed 12% in this situation (see, Fig. 6(c)). When the dope fraction in the capsule shell decreases, the effective medium approximation exhibits fundamental discrepancies with the simulation data especially in the spectral region of collective LPR excitation. In the case of spherical absorbing nano-inclusions and high doping, the mixing rule (2) in general works also well resulting
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in no more than 20% approximation errors (Fig. 6(b)). Interestingly, the effective medium model can both underestimate and overestimate Qabs -values depending on the light wavelength. The latter (overestimating) is observed in IR absorption band where a decrease in the absorption efficiency of doped spherical capsule as a whole is observed according to the Lorenz-Mie theory [36]. Worth noting, our calculations show (not included in the text) that the Maxwell–Garnett mixing for the effective medium as applied to the microcapsule leads to the similar results as the Bruggeman rule at low dope volume fractions and to the stronger underestimation of the absorption efficiency at high δ -values. 4. Conclusions Based on the research results we can draw the several conclusions which are presented below. First, the absorption efficiency of initially transparent spherical microcapsule is effectively controlled by doping the necessary amount of strongly absorbing nanometersized metal (gold) particles. Meanwhile, with a rather low volume fraction of nano-inclusions in the capsule shell (∼18%), it is possible to rise its absorption cross-section to the value of an absolutely absorbing sphere (Qabs ≈ 1). Next, the spectral absorption of a microcapsule turns out to be quite non-uniform in the considered wavelength range of incident radiation (from 0.5 to 0.9 μm) and depends on the morphology of nano-inclusions. In some spectral regions, substantial capsule absorption enhancement is realized due to the resonant excitation of surface plasmon modes of nanoparticles (from 540 to 570 nm for spheres, from 670 to 770 nm for rods of various form factors). In the long-wavelength wing of the spectrum, the efficiency of absorption of a nanoparticle-doped capsule as a rule decreases due to its Mie-parameter decrease and a drop in the absorption coefficient of bulk gold (see, Fig. 2(a)). The chromatic dispersion of microcapsule absorption decreases with the increasing of volume content of nanoparticles. By simultaneous combining gold nanoparticles of various shapes (spheres and rods), it is possible to obtain a quasi-neutral absorption of composite capsule in the considered wavelength range. Finally, the absorptivity of a nanoparticle-doped microcapsule can be calculated using the effective homogenized medium formulae mainly in the conditions of weak chromatic dispersion of capsule absorption. This situation is usually realized with cylindershaped nano-inclusions or at high levels of total shell absorption. Besides, the Bruggeman mixing rule does not capture the surface plasmon resonances of nanoparticle-dope. Funding This work was partially supported by the Russian Foundation for Basic Research (Grant no. 19-47-70 0 0 01 р_а). References [1] Langer R, Tirrell DA. Designing materials for biology and medicine. Nature 2004;428:487–92. [2] Rosenberg M, Lee S-J. Water-insoluble, whey protein-based microspheres prepared by an all-aqueous process. J Food Sci 2004;69:FEP50–8. doi:10.1111/j. 1365-2621.2004.tb17867.x. [3] Miyazawa K, Yajima I, Kaneda I, Yanaki T. Preparation of a new soft capsule for cosmetic. J Cosmet Sci 20 0 0;51:239–52. [4] Pavlov AM, Gabriel SA, Sukhorukov GB, Gould DJ. Improved and targeted delivery of bioactive molecules to cells with magnetic layer-by-layer assembled microcapsules. Nanoscale 2015;7:9686–93. [5] E.I. Galanzha, R. Weingold, D.A. Nedosekin, M. Sarimollaoglu, A.S. Kuchyanov, R.G. Parkhomenko, A.I. Plekhanov, M.I. Stockman, V.P. Zharov, Spaser as novel versatile biomedical tool, arXiv:1501.00342 (2015). [6] Wang W, Duan W, Ahmed S, Mallouk TE, Sen A. Small power: autonomous nano- and micromotors propelled by self-generated gradients. Nano Today 2013;8:531–54.
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Shape-mediated light absorption by spherical microcapsule with gold-nanoparticles-dope Yury E. Geints∗, Ekaterina K. Panina, Alexander A. Zemlyanov V.E. Zuev Institute of Atmospheric Optics SB RAS, 1 Zuev square, 634021 Tomsk, Russia
a r t i c l e
i n f o
Article history: Received 3 June 2019 Revised 26 July 2019 Accepted 27 July 2019 Available online 2 August 2019 Keywords: Light absorption Microcapsule Nanoparticle Plasmon resonance Effective medium
a b s t r a c t The study of the light absorption efficiency of a hollow spherical microparticle (microcapsule) doped with strongly absorbing gold nanoparticles of spherical and cylindrical spatial shapes is presented. By means of the FDTD numerical simulations, the absorption spectra of a microcapsule doped with nanoparticles in the visible and near-IR spectral regions are calculated. We show the absorption efficiency of the capsule depends on the morphology of nano-inclusions. In particular, there is a noticeable absorption enhancement of the microcapsule in the regions of the resonant excitation of the localized surface plasmon modes of doping nanoparticles. The chromatic dispersion of capsule absorptivity decreases with an increase in the volume content of nanoparticles, as well as when simultaneously mixing nano-inclusions of various shapes (spheres + rods). In this case, it becomes possible to obtain a near-uniform absorption spectrum of the capsule in the considered wavelength range, which can be well fitted within the framework of effective homogeneous medium using, e.g., the Bruggeman mixing rule. © 2019 Elsevier Ltd. All rights reserved.
1. Introduction Polymeric hollow micro- and nanoparticles, which hereafter are referred to as the microcapsules, are in the last decades actively studied in various fields of science and technology ranging from nanomedicine, pharmaceuticals and nanocosmetology to nanophotonics, nanochemistry and biotechnology [1–6]. A typical and most relevant example of microcapsules employment is the so-called drug delivery system, which maximizes therapeutic efficacy while minimizing side effects through ultra-precise control over the space-time behavior of drugs nanodoses inside the patient’s body. The controlled release of therapeutic molecules from microcapsules at the right places and at the right times is becoming increasingly important for advanced treatment techniques, including gene therapy, antibody therapy and vaccine therapy [7,8]. The technology of microcapsules manufacturing is an independent engineering task and to-date can be implemented in various ways, e.g., by monomers polymerization on the emulsified micronuclei, or by poly-ion layer-by-layer assembly (LbL) on the solid-phase templates [9]. Inside such microcapsules the necessary cargo can be deposited in the form of individual molecules or other active contents. Then, the microcapsule as a transport container can deliver this cargo to the required consignee where it can be activated or opened by any type of external stimuli.
∗
Corresponding author. E-mail address: [email protected] (Y.E. Geints).
https://doi.org/10.1016/j.jqsrt.2019.106595 0022-4073/© 2019 Elsevier Ltd. All rights reserved.
Modern trends of microencapsulation technology of active substances are shifting towards the creation of multifunctional cargo carriers that would be susceptible to various physical and chemical stimuli for the controlled release of the contents. As a rule, to acquire the multi-functionality, such capsules are fabricated in the form of quasi spherical particles having a multilayer shell. The shell can be composed of several dissimilar organic/inorganic layers that respond to various external factors [10]. The most common way to impart the optical activity to the microcapsule in the desired spectral range is adding in capsule shell the dispersed inclusions usually of nanometer size, which are susceptible to optical radiation. As a rule, these are noble metals and their salts [9,11]. Metal nanoparticles distributed over the shell convert the absorbed light into Joule heat, which then is released into the polycomposite matrix material of the microcapsule leading to a non-uniform distribution of its temperature [12]. This in turn, can initiate or influence the rate of physical and chemical reactions in the capsule shell and lead to its degradation and cargo release. A striking example of multi-functional transport container is the microcapsule built of several layers containing polysaccharides and polypeptides along with titanium dioxide (TiO2 ) and silica (SiO2 ) [13,14]. Such capsules are biocompatible, cheap in manufacturing, possess improved strength properties, reduced permeability of their shell and are susceptible to the ultrasound and ultraviolet (UV) radiation. Being exposed to UV laser (in the range from 300 to 400 nm) the capsules experience the photocatalytic destruction of their shells.
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In the visible and near IR spectral regions, usually the photothermal activation of microcontainers is used by adding to their shells optically absorbing nanoparticles of noble metals (gold, silver) [15,16], liquid laser dyes [17], or metal oxides [14]. In particular, a technology has recently been proposed for creating a bifunctional microcontainer with a polysaccharide shell decorated with inclusions of iron oxide nanoparticles (Fe3 O4 ) and graphene, which ensures the susceptibility of the microcapsule to both a variable magnetic field in the microwave frequency range (magnetothermal effect) and optical radiation [18,19] as well. As known, the optical properties of metals being dispersed to nanometer scales change dramatically and demonstrate a pronounced resonance behavior at certain frequencies of the incident light. This is due to the excitation of localized plasmon resonances (LPR) of metallic nanoparticles when the collective behavior of free electrons in a metal is manifested, leading to consistent oscillations of the entire electron cloud under the action of an alternating electric field of an optical wave [20]. Thus, in gold nanospheres (with the radius a = 10–40 nm) deposited in air, the resonance wavelength of the lowest-frequency (dipole) plasmon oscillation, which is called the Fröhlich mode [21,22], is about 520 nm, and for silver nanoparticles it amounts to about 412 nm. In the case of relatively large metal spheres, for which the Mie parameter xa = 2π a/λ becomes of the order of unity, in addition to the Fröhlich mode the modes of higher orders (quadrupole and octupole) are excited [23]. LPR excitation in a nanoparticle leads to the appearance of pronounced peaks in the absorption and scattering spectra at the frequencies of plasmon resonances in comparison with the extinction spectrum of a bulk metal sample. Meanwhile, an important feature of the plasmon resonances is the intensity enhancement of the optical field near the nanoparticle that can achieve several orders of magnitude. The frequency and amplitude of plasmon resonance are influenced not only by the type of metal but also by a number of other factors such as the optical properties of the surrounding medium, the degree of particles aggregation, and their spatial shape. It is known that the plasmonic absorption spectrum, e.g., of metallic nanorods [24] is split into two subranges shifted to the red and blue spectral wings relative to the dipole LPR of a spherical nanoparticle. Bilayer nanospheres with a non-conducting core (silicon oxide) also exhibit a red shift of the LPR, which increases with the decreasing in the metal shell thickness [25]. Aggregation of nanoparticles leading to their integration into one-dimensional or multidimensional clusters is also of considerable importance when calculating the optical properties of metallic nano-inclusions. As reported in [26], the absorption cross-section of a spherules cluster may increase or decrease depending on the degree of electric fields coupling of neighboring particles and the magnitude of their mutual field screening, which in turn is determined by the size of the aggregate and its constituent nanoparticles. Obviously, if the shape of the particles differs from the sphere then the orientation anisotropy of light absorption by the cluster is also of importance. In this paper, the absorption of laser radiation by a micronsized capsule with embedded gold nanoparticles is considered. By numerical solving of Maxwell’s equations by means of finitedifference time-domain calculations we show that the situation is quite possible when an initially optically transparent microcapsule being doped with gold nanoparticles acquires the optical absorption with different spectral characteristics than that of isolated dope nanoparticles. In particular, for the microcapsule doped with spherical inclusions the broadening of the dipole LPR is realized, whereas in the case of gold nanorods the lateral plasmon mode of nanocylinder is suppressed. These features become more pronounced if the volume fraction of doping inclusions increases.
Fig. 1. (a, b) 2D-section of sample microcapsules doped with (a) spherical and (b) cylindrical nanoparticles.
2. Nanoparticles-doped microcapsule light absorption simulations details To solve the electrodynamic problem of scattering and absorption of optical radiation at a multilayer spherical particle containing nano-inclusions, we used the finite-difference timedomain (FDTD) method based on direct numerical integration of the Maxwell’s equations for the components of the electromagnetic field of an optical wave. A specific implementation of FDTD algorithms was provided by the Lumerical FDTD Solutions software package (ver. 2016a for Linux [27]). The numerical simulations ran on Intel® CoreTM i7-3930K (3.2 GHz) computer with 48GB RAM. The 3D geometry of the computational domain was used; on the boundaries the conditions for perfect field matching (PML) were set. The accuracy of the numerical solution of the equations was guaranteed by an adaptive mesh refinement algorithm when the nodes of the computational grid are condensed in regions of sharp gradients of the dielectric constant of the medium (over-meshing at the boundaries of nanoparticles). The total number of “Yee cells” was several millions with a minimum spatial mesh size of 2 nm and a time step of 0.01 fs. This is sufficient for accurate reproducing the scattering and absorption characteristics of individual metal nanoparticles (see Fig. 2(b)). To be more specific, we construct a sample microcapsule (Fig. 1(a, b)) in the form of a hollow ball with outer radius Rc = 500 nm loaded with a water core simulating cargo, and a polycomposite (PE-SiO2 ) hard shell with the thickness h = 50 nm containing a nano-dispersed component in the form of gold spheres or cylindrical rods. In the calculations, the refractive index of the core and the shell was fixed and equaled to nc = 1.33 and nl = 1.45, respectively. Optical wavelength λ, total number of metallic nano-inclusions N, their dimensions (a,L) and shape may vary. The environment surrounding the microcapsule is considered as water with refractive index n0 = nc . Worth noting, gold nanoparticles because of their better biocompatibility than other metal nano-inclusions (Ag, Al, Fe) are the most common absorbing dope to various transport biocontainers. This is why we considered only gold in this work. We emphasize that only the microcapsule shell is filled with metal nanoparticles while its core remains nonabsorbing. The particle-filling procedure consists in programmatic generation of N particles with corresponding shapes randomly distributed inside a spherical layer Rc − h ≤ r ≤ Rc . Particles have randomly distributed set of geometric parameters with the standard deviation SD = 0.2 f, where f is any of the dimensional parameters of the particle. This defines sufficiently broad range of data distribution:
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Fig. 2. (a) Dispersive parameters of refraction index n, absorption index κ and volume absorption α = 4π nκ /λ of bulk gold [28]; (b) Absorption efficiency Qabs of gold nanospheres and nanorods with different sizes. Symbols depict Lorenz–Mie theory Qabs calculations for 14 nm gold sphere.
fmax /fmin ≈ 2. Note this value of SD is chosen quite arbitrary and only reflects the randomness of target capsule seeding with absorbing nanoparticles. During the nanoparticles deposition procedure, the condition of their mutual independence is checked, i.e. individual particles do not allowed overlapping in space. Four types of nanoparticles are considered as the examples of typical absorbing dope: sphere ensembles with the average radii a = 14 and 20 nm, as well as the arrays of cylindrical rods with the size parameters (a × L) = 10 × 40 and 10 × 60 nm2 . In the case of gold nanorods, additionally the spatial orientation of cylinder principal axis varies randomly that simulates natural nanoparticle deposition during absorbing layers assembling process. At the lower boundary of simulation domain, a plane linearly polarized wave is injected with a unit amplitude E0 and wave vector directed along the vertical (z) axis (shown by arrows in Fig. 1). The spatial distribution of the electromagnetic field E(r) inside and near a sample microcapsule is calculated by the FDTD updating scheme. Next, the absorption efficiency factor of microcapsule Qabs = Pabs /(π R2c I0 ) is obtained based on the volume integrating of time-averaged optical field, where the total absorbed optical power Pabs in the microparticle volume Vc is expressed as:
Pabs =
π c ε0 λ
Vc
dr ε (r )|E(r )|2
(1)
Here, ε 0 is vacuum permittivity, ε is the imaginary part of microparticle permittivity, c is the speed of light, and I0 = (cn0 ε0 /2 )E02 denotes the optical intensity. As seen, the value Qabs is influenced not only by the optical field distribution in a capsule but also by the spatial configuration of absorbing inclusions (nanoparticles) which contribute to the ε -profile. Pure gold was used as the material of the nanoparticles, the optical parameters of which are taken from [28] and are shown in Fig. 2(a) for the reference. Notice that we imply the optical wave phasor as a positive exponent E(z)∝exp {ik(n + iκ )z} which leads to positive values of the absorption coefficient κ .
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The scaling of a bulk solid metal down to a nanometer-sized particle drastically changes its optical characteristics mainly due to the excitation of collective free-electrons oscillations. As can be seen in Fig. 2(b) in the absorption spectra of isolated nanoparticles, the pronounced maxima appear corresponding to different surface plasmon modes. Gold nanospheres in the considered spectral range have only one resonant absorption maximum at the wavelength of the dipole LPR around the value λ ∼ 520 nm when the dispersion condition for the so-called Fröhlich mode [21] is satisfied: [n(λ )]2 − [κ (λ )]2 = −2[n0 (λ )]2 . Metal cylindrical nanoparticles (nanorods) support two types of LPR, which are excited when the electric field polarization vector is directed along one of the rod axes. The shortest-wavelength plasmon mode corresponds to the wave polarization across the rod (lateral mode), and its resonance wavelength is almost constant for the selected particles (λ ∼ 510 nm). The frequency position of the second (longitudinal) plasmon resonance depends on the rod length L and varies significantly from λ ∼ 700 nm when L = 40 nm to λ ∼ 785 nm at L = 60 nm. Obviously, in the real situations when a microcapsule is doped with cylindrical nanoparticles, their spatial orientation relative to the polarization of the incident optical radiation can be arbitrary, which will lead in general to an equally probable excitation of both plasmon resonances in an assembly of cylindrical nanorods. Thus, for practical calculations it is important to have the absorption spectrum of an isolated nanocylinder averaged over possible spatial orientations of light wave polarization. Such spectra are shown in Fig. 2(b) for both considered types of particles and demonstrate two absorption maxima centered in the visible and IR spectral regions that corresponds to two excited plasmon modes. Noticeable, LPR for the longitudinal wave polarization is several times more intensive than the transverse polarization mode. 3. Results and discussion Consider the results of our numerical simulations. In Fig. 3(a, c) are shown the spectral profiles of the absorption efficiency Qabs of microcapsules doped with the spherical and cylindrical nanoparticles. The volume fraction δ = Vd /Vsh of the absorbing dope in capsule shell could vary and defines a wide range of effective absorption from an almost transparent capsule with a total number of nano-inclusions N of the order of 250, to a closely packed assembly of nanoparticles with N ≈ 2200 (δ = 18%) and high optical absorption. Here, Vd = Nj=1 V j is the total volume of all nanoparti-
cles in capsule, and Vsh = ξ −3 Vc [1 + 3ξ (1 − ξ )] is the volume of the capsule shell (ξ = h/Rc ). As expected, with the increase of nanoparticle fraction, the absorption efficiency of microcapsule increases in the entire spectral range. Meanwhile, like in isolated particles (Fig. 2(b)) the plasmon resonances also appear in the absorption spectra of nanoparticledoped microcapsules. Thus, a microcapsule with spherical inclusions demonstrates a pronounced absorption selectivity near the wavelength of a dipole LPR with a week red-shifting of the absorption maximum from λ = 537 nm at δ = 2% to λ = 566 nm atδ = 18%. Note that similar tendency in the optical absorption spectra was reported earlier in [29] for a cluster of nanometersized gold spherules and was associated with the increased coupling of the optical fields of neighboring nanoparticles. A microcapsule doped with nanorods also exhibits a resonant behavior of the absorption efficiency. Here, the resonance of the longitudinal plasmon mode of a cylindrical nanoparticle at λ = 676 nm (δ = 2%) is clearly pronounced, while the optical excitation of the transverse LPR is effectively suppressed especially for high dope concentration. As for spherical nano-inclusions, there is a noticeable spectral shift of collective LPR mode relative to that of isolated particle. However, this spectral shift is reversed and di-
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Fig. 3. (a,c) Absorption efficiency Qabs and (b,d) normalized absorption qabs of microcapsule doped with 14 nm nanospheres (a,b) and nanorods with L = 40 nm (c,d). Magenta dash-dot-dot curves are for isolated nanoparticles.
rected to the blue wing achieving about 24 nm for maximum gold filling of the capsule. This behavior of absorption efficiency can be attributed to the orientation dispersion of absorption of nanorods, which are randomly distributed inside the capsule shell. In this case depending on the direction of optical wave polarization, there would be a predominant excitation of one of the plasmon resonance modes in the visible or IR spectral regions. The superposition of the contributions of two absorption channels on LPRs with different intensities leads to an effect similar to the generation of Fano resonance in an asymmetric photonic metastructure [30], when a distorted Lorenz absorption spectrum is formed with the maximum shifted toward the short wavelength region. When the dope-filling factor δ increases, the broadening of LPR absorption contour and the decrease of its relative amplitude take place. This is clearly seen if we normalize all the curves for abmax , which are sorption efficiency Qabs to their maximal values Qabs realized at δ = 18%. The normalized capsule absorption qabs = max depending on the laser wavelength is presented in Qabs /Qabs Fig. 3(c, d). One of the possible reasons of the spectral broadening of the absorption curve in a capsule, especially in the case of nanorodfilled particle, is the size-dispersion of the nanoparticles [24,31], which was artificially introduced during our programmatic particle generation. Besides, with the increase in particle radius the fields coupling of neighboring nanoparticles becomes more prominent when they are randomly clusterized into the “macromolecules” what can also lead to a significant rise or fall in the total absorption cross-section at certain optical frequencies [29,32,33]. Additionally, in the conditions of high doping of the capsule shell, the partial field-screening effect is possible when absorbing particles located in the lower hemisphere of the capsule (along optical wave incidence) act as an opaque shield against the nanoparticles inside
Fig. 4. Spectral dependence of capsule absorption efficiency doped with nanoparticles of various shapes. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
capsule upper part. This effect is maximal at LPR frequencies and can ultimately reduce the resonant contribution to the spectral absorption contour. The change in the size parameters of nanoparticles even within the same spatial shape (sphere, cylinder) also affects the spectral dependence of the absorption of the microcapsule. Fig. 4 summarizes the spectral dispersion of the absorption efficiency Qabs for all types of gold-dope-nanoparticles used in simulations. As seen, a change in the size of nanospheres from 14 to 20 nm has almost no effect on the capsule absorption in LPR excitation band; however it becomes noticeable in the long wavelength range, especially at
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Fig. 5. Effective medium model for a polycomposite capsule with 18% gold nanoparticles.
high concentrations of nanoparticles. Here, the particle screening effect is clearly manifested: the larger gold spheres more strongly perturb the optical field inside the capsule shell causing increased light scattering in illuminated hemisphere and early light departure from the microcapsule. As a result, the optical radiation simply does not reach the shadow part of the microparticle that reduces net capsule absorption. In the microcapsule with cylindrical nanoparticles, the effect of field-screening is less prominent due to the elongated shape of rods. The microcapsule doped with nanorods shows plasmon resonances at the corresponding LPR wavelengths as for isolated cylinders (Fig. 2(b)). Meanwhile, only the longitudinal LPR mode survives. With a high concentration of nanorods (δ = 18%), the spectral dependence of capsule absorption becomes weak and the variation of Qabs - factor does not exceed 10%. Various absorption spectral dispersion acquired by the microcapsule when doped with gold nanoparticles of spherical or cylindrical shape make it possible to design a spherical cargo micro-container with close to neutral spectral absorption in the considered wavelength range. Indeed, as follows from Fig. 4 (blue dash-dot-dot curves), using a specific doping mixture of nanospheres (a = 14 nm, 20%) and different-sized nanorods (80%) it is possible to significantly reduce the spectral absorption variations of the whole microcapsule. For practical calculations of the microcapsules absorption, the applicability of a homogeneous effective medium model to the mixture of absorbing and non-absorbing components in the spatial configuration of a layered sphere is important. Our analysis shows that among the well-known models of effective medium characteristics [34] the closest results to the calculated absorption characteristics is provided by the Bruggeman phase mixing rule, when the matrix and inclusions are considered equally leading to a symmetric mixing formula for the effective permittivity of a twocomponent mixture:
δ
εe − εm εe − εi + (1 − δ ) =0 2εe + εi 2εe + εm
(2)
Here, ε m and ε i are the dielectric permittivity of the matrix (polycomposite) and inclusions (gold), respectively. The real and imaginary parts of the complex refractive index of √ effective medium me = εe = ne + iκe consisting of a polycompos2 ite with εm = nl and metallic gold inclusions with ε i = (n + iκ )2 (see Fig. 2(a)) are shown in Fig. 5 for 18%-dope volume fraction. The calculations are carried out according to Eq. (2) taking into account the considerations of Ref. [35] regarding the selection of a single-valued analytical branch of the square root of a complex-
Fig. 6. (a) Absorption efficiency of microcapsule doped with gold spherules and nanorods as well as calculated via Bruggeman mixing rule (2); (b, c) Relative error γ of the effective medium model approximation versus dope volume fraction δ for nanospheres (b) and nanorods (c).
valued function. Here, we does not account for the geometrical shape of the inclusion phase and treat it as a bulk absorber while some considerations concerning the size-effect of nanoparticles in the effective medium approximation can be found elsewhere [21,22]. As seen from this figure, artificial effective medium is characterized by the increased absorption index κ e when increasing laser wavelength; this is similar to Au dispersion law. The effective medium refraction index ne to the contrary demonstrates the opposite spectral dependence concerning that of gold providing for smooth volume absorption fall in the longer wavelength limit. Based on ε e dispersion we calculated the absorption efficiency of a water-containing microcapsule with a shell made of artificial material with the effective refractive index me (λ). Spectral dependences of Qabs are depicted in Fig. 6(a) for two nanoparticle-dope volume content. From this figure, it follows that the best approximation to the real data is obtained in the case of cylindrical nanoparticles and relatively high dope content (δ > 10%). As mentioned above, due to the averaging over spatial orientations the nanorods-doped capsule demonstrates smooth absorption within the spectral region considered that resembles the absorption characteristic of regular homogeneous or layered spherical particle. The relative approximation e )/Q error γ = (Qabs − Qabs abs of the effective medium model, where e Qabs stands for the absorption efficiency calculated with the help of Eq. (2), does not exceed 12% in this situation (see, Fig. 6(c)). When the dope fraction in the capsule shell decreases, the effective medium approximation exhibits fundamental discrepancies with the simulation data especially in the spectral region of collective LPR excitation. In the case of spherical absorbing nano-inclusions and high doping, the mixing rule (2) in general works also well resulting
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in no more than 20% approximation errors (Fig. 6(b)). Interestingly, the effective medium model can both underestimate and overestimate Qabs -values depending on the light wavelength. The latter (overestimating) is observed in IR absorption band where a decrease in the absorption efficiency of doped spherical capsule as a whole is observed according to the Lorenz-Mie theory [36]. Worth noting, our calculations show (not included in the text) that the Maxwell–Garnett mixing for the effective medium as applied to the microcapsule leads to the similar results as the Bruggeman rule at low dope volume fractions and to the stronger underestimation of the absorption efficiency at high δ -values. 4. Conclusions Based on the research results we can draw the several conclusions which are presented below. First, the absorption efficiency of initially transparent spherical microcapsule is effectively controlled by doping the necessary amount of strongly absorbing nanometersized metal (gold) particles. Meanwhile, with a rather low volume fraction of nano-inclusions in the capsule shell (∼18%), it is possible to rise its absorption cross-section to the value of an absolutely absorbing sphere (Qabs ≈ 1). Next, the spectral absorption of a microcapsule turns out to be quite non-uniform in the considered wavelength range of incident radiation (from 0.5 to 0.9 μm) and depends on the morphology of nano-inclusions. In some spectral regions, substantial capsule absorption enhancement is realized due to the resonant excitation of surface plasmon modes of nanoparticles (from 540 to 570 nm for spheres, from 670 to 770 nm for rods of various form factors). In the long-wavelength wing of the spectrum, the efficiency of absorption of a nanoparticle-doped capsule as a rule decreases due to its Mie-parameter decrease and a drop in the absorption coefficient of bulk gold (see, Fig. 2(a)). The chromatic dispersion of microcapsule absorption decreases with the increasing of volume content of nanoparticles. By simultaneous combining gold nanoparticles of various shapes (spheres and rods), it is possible to obtain a quasi-neutral absorption of composite capsule in the considered wavelength range. Finally, the absorptivity of a nanoparticle-doped microcapsule can be calculated using the effective homogenized medium formulae mainly in the conditions of weak chromatic dispersion of capsule absorption. This situation is usually realized with cylindershaped nano-inclusions or at high levels of total shell absorption. Besides, the Bruggeman mixing rule does not capture the surface plasmon resonances of nanoparticle-dope. Funding This work was partially supported by the Russian Foundation for Basic Research (Grant no. 19-47-70 0 0 01 р_а). References [1] Langer R, Tirrell DA. Designing materials for biology and medicine. Nature 2004;428:487–92. [2] Rosenberg M, Lee S-J. Water-insoluble, whey protein-based microspheres prepared by an all-aqueous process. J Food Sci 2004;69:FEP50–8. doi:10.1111/j. 1365-2621.2004.tb17867.x. [3] Miyazawa K, Yajima I, Kaneda I, Yanaki T. Preparation of a new soft capsule for cosmetic. J Cosmet Sci 20 0 0;51:239–52. [4] Pavlov AM, Gabriel SA, Sukhorukov GB, Gould DJ. Improved and targeted delivery of bioactive molecules to cells with magnetic layer-by-layer assembled microcapsules. Nanoscale 2015;7:9686–93. [5] E.I. Galanzha, R. Weingold, D.A. Nedosekin, M. Sarimollaoglu, A.S. Kuchyanov, R.G. Parkhomenko, A.I. Plekhanov, M.I. Stockman, V.P. Zharov, Spaser as novel versatile biomedical tool, arXiv:1501.00342 (2015). [6] Wang W, Duan W, Ahmed S, Mallouk TE, Sen A. Small power: autonomous nano- and micromotors propelled by self-generated gradients. Nano Today 2013;8:531–54.
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