ARTICLE pubs.acs.org/JPCC
Design of Photosensitive Gold Nanoparticles for Biomedical Applications Based on Self-Consistent Optical Response Theory Chie Kojima,† Yasutaka Watanabe,†,‡ Hironori Hattori,†,‡ and Takuya Iida†,§,* †
Nanoscience and Nanotechnology Research Center, Research Organization for the 21st Century, Osaka Prefecture University, 1-2, Gakuen-cho, Naka-ku, Sakai, Osaka 599-8570, Japan ‡ Department of Physics and Electronics, Graduate School of Engineering, Osaka Prefecture University, 1-1, Gakuen-cho, Naka-ku, Sakai, Osaka 599-8531, Japan § PRESTO, Japan Science and Technology Agency, 4-1-8 Honcho, Kawaguchi, Saitama 332-0012, Japan ABSTRACT: Gold nanoparticles (Au NPs) have been studied for both photothermal therapy and imaging. Efficient photothermogenic response to near-infrared light is necessary for in vivo applications. In this study, the photosensitive properties of Au NPs were theoretically analyzed by self-consistent treatment of Maxwell’s equation. With the Au concentration held constant, a single Au NP with a diameter of 60 nm had the most efficient photothermogenic properties by 532 nm laser irradiation. Particularly, due to the multiple interactions of mirror images of localized surface plasmons, closely spaced multiple Au NPs exhibited enhanced photothermogenic properties in the longer wavelength region even when the Au NPs were small. A comparison of the theoretical and experimental results suggests that the multiple Au NPs are created by the seeding growth of Au NPs in the PEGylated dendrimer. These results provide the guiding principles for design of Au NPs suitable for photorelated biomedical applications.
’ INTRODUCTION Gold nanoparticles (Au NPs) are photosensitive nanoparticles with a strong optical response induced by surface plasmon resonance (SPR), which makes them attractive for applications in the biological and medical fields. It has been reported that Au NPs are not only potential biosensors but also potential imaging probes for tumor cells.13 Recently, Au NPs have also been shown to be capable of converting strongly absorbed radiation into heat.4 This behavior is beneficial for both photothermal therapy and acoustic diagnosis with optical support.35 The photochemical properties of Au NPs are largely affected by their size and shape. Since visible light barely permeates into the body, near-infrared light-responding Au NPs such as Au nanorods and Au shells are useful for in vivo applications.611 However, the reproducibility of these Au nanostructures is not good because the preparation conditions are generally complicated. Therefore, design of a novel type of Au nanomaterial responding to nearinfrared light is necessary. Dendrimers are unique synthetic macromolecules that have well-defined structures and inner spaces ideal for encapsulating small molecules.1216 They can act as a template for metal NPs with a narrow size distribution. Research on dendrimer nanotemplating to control the size and stabilize the dispersion of the metal NPs has been reported.1,17,18 We studied PAMAM dendrimers attached to poly(ethylene glycol) (PEG) chains at every chain.19 These dendrimers are useful for biomedical applications such as drug delivery and imaging because of their biocompatibility.2022 Previously, Au NPs were prepared by r 2011 American Chemical Society
Figure 1. Schematic image of seeding growth in the PEG-attached dendrimer.
reduction of Au(III) ions in the PEG-attached PAMAM dendrimers using NaBH4. Even though the Au NPs had a narrow size distribution and were much more stably dispersed,23 their size was too small (2 nm). Additionally, the photoresponsive properties of the Au NPs remain to be improved. We next attempted seeding growth of Au NPs in the PEG-attached dendrimers.21,24 The reduction conditions are important for seeding growth because nucleation and seeding growth are dependent on the reduction potential.1,25 Therefore, it is possible that a larger Au NP and/or small multiple Au NPs could be produced by seeding growth depending on the growth conditions (Figure 1). Even though the relationship between size and photoabsorption properties has already been identified theoretically and Received: July 9, 2011 Revised: August 19, 2011 Published: August 23, 2011 19091
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experimentally,26 the influence of closely packed multiple Au NPs on the photothermogenic properties is still unclear. In this study, we performed a theoretical analysis to design Au NPs suitable for biomedical applications. Heat energy generated from the Au NPs by photoirradiation was analyzed based on the self-consistent treatment of Maxwell’s equations with Green’s function method. The effect of size on the photothermogenic properties was investigated while maintaining the same Au concentration. The photothermal properties of multiple Au NPs at different distances were also investigated. Kojima et al. already reported that seeding growth using NaBH4 was performed in the PEGylated dendrimer; the size and photosensitivity of the grown Au NPs changed depending on the repeat time.24 The experimental and theoretical results were compared in order to identify the best procedure for the Au NPs.
’ THEORETICAL AND EXPERIMENTAL PROCEDURES Model and Theoretical Method. To evaluate the photoinduced heat generated in the entire solvent, the model shown in Figure 2 is considered. It was assumed that the sample cell was divided into small cubic boxes with equally spaced intervals whose box contains single or coupled Au NPs. We calculated the local heat, Qi(ω), (absorption energy) of the ith Au NP induced by the monochromatic light field using the following equation
Q i ðωÞ ¼ Vi ÆiωPi 3 Ei æðωÞ
ð1Þ 3
where < > indicates the time average, Vi = (4π/3)(di/2) is the volume of each NP, di is the diameter of the ith NP, and Pi and Ei are the light-induced polarization and response electric field in the time harmonic form, respectively. This can be obtained from previously reported equations27 by using the continuity equation of charge and current.28 E and P are self-consistently determined by solving the discrete integral form of Maxwell’s equation29 as linear simultaneous equations of Pj assuming that the respective NPs are modeled using spherical meshes as follows ð0Þ
Ei ¼ Ei
þ
N
Gmed ðrij ÞPj Vj þ Si Pi ∑ j6¼ i
ð2Þ
P j ¼ χj E j
ð3Þ
where N is the number of NPs in each cubic box (Figure 2), E(0) i is the electric field of the incident light on the ith NP, Gmed is Green’s function in a homogeneous medium, rij = ri rj is the relative coordinate of the ith and jth NPs, and χj is the electric susceptibility in the optical frequency range. The integral for i = j, R i.e., the self-term Si = Vi dr0 Gmed(ri r0 ) as a function of the size and shape of the NP in eq 2, was analytically calculated under the assumption that the spatial variation of the internal field is negligible since the diameters of these NPs are much smaller than the light wavelength. Specifically, Drude-type electric susceptibility was used for each NP in the UVvis wavelength region as follows 2 χjAu ðωÞ ¼ ðεAu bulk ðωÞ nenv Þ
ðpΩpl Þ2 ðpωÞ þ ipωðΓbulk þ 2vf =dj Þ 2
ð4Þ 2 2 Au where εAu bulk(ω) = εexp(ω) + (pΩpl) /{(pω) + ipωΓbulk} is the background dielectric functions of bulk gold, εAu exp(ω) is the experimentally estimated complex dielectric function,30 nenv is
Figure 2. Schematic image of the model of the photothermal effect. The model for the calculation is also shown (inset).
the environmental refractive index, Ωpl is the bulk plasmon resonance frequency, Γbulk is the bulk nonradiative width (nonradiative decay rate), vf is the electron velocity at the Fermi level. Additionally, 2vf/dj represents the nonradiative decay rate of free electrons due to surface scattering, which corresponds to the inverse of effective time for free electrons at the Fermi level to move from the center of Au NP to the surface.31 εAu exp(ω) is phenomenologically determined from the experimental value including the interband effect in the UV region30 and corrected by subtraction of 1 to take into account the modification effects by the surface-protecting agent surrounding the Au NP. Finally, the total heat arising from the Au NPs can be described using the following equation H ¼
N
∑
i¼1
N
∑ ðRSV Ntot =NÞQ i ðωÞLS i¼1
ð5Þ
Q i ðωÞ=VN
where Ntot = MW/{(2π/3)(d/aL)3} V1 is the total number of NPs32 assuming the same diameter di = d and Vi = V for all the NPs, M is the concentration of Au atoms (110 μM), W is the volume of solvent in the sample cell (3 mL), aL is the edge length of a unit cell of Au crystal (4.0786 Å for Au),32 RSV is the rate of laser spot volume to sample cell volume (2.36 102), and LS is the laser irradiation time (300 s). Other parameters are pΩbulk = 8.958 eV, Γbulk= 72.3 meV, Vf = 0.922 nm eV,30,33 and nenv = 1.33. RSVNtot/N indicates the number of cubic boxes in the laser spot, and ∑N i = 1Q i(ω)LS indicates the total heat in each cubic box. A laser intensity, I0, of 12 W/cm2 is assumed here, as shown in Figure 2 1/2 ; c is the light velocity). By substituting (|E(0) i | = (2I0/(cnenv)) eqs 2 and 3 into eq 1, we can obtain the simple form as follows Q i ðωÞ=V ¼ ðω=2ÞIm½χi 3 jEi j2
ð6Þ
From eq 6, |Ei|2 has peak structure at the eigenenergy of the lowest collective mode of localized surface plasmon in Au NPs ~pl(d,rij) and that the peak width is interacting with each other pΩ the sum of the nonradiative width Γbulk + 2vf/dj and radiative ~pl(d,rij) and Γ ~pl(d,rij) can be numerically ~pl(d,rij). pΩ width Γ estimated from a real part and an imaginary part of solution of N 0 equation det[X] = 0, Ej = χ-1 j ∑i = 1Xj,iEi , of eqs 2 and 3, where Xj,i is the component of the inverse matrix X of the simultaneous ~pl(d,rij) are functions of ~pl(d,rij) and Γ equations of E and P. pΩ the diameter, d, and interparticle distance, |rij|, through Si and Gmed(rij). 19092
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Preparation of Gold Nanoparticles and Measurement of Absorption Spectra. The seeding growth of Au NPs was
performed according to previous reports.24 In summary, 55 equiv of HAuCl4 and 275 equiv of NaBH4 to 1 equiv of dendrimer were added to the seed and reacted for 30 min. This reduction was repeated 1, 3, 5, and 10 times. The absorption spectra of the obtained Au NPs were analyzed by UVvis spectrometry (JASCO, V-630). Transmission electron microscopy (TEM) analysis was performed using a JEOL2000 with carbon-coated copper grids according to our previous report.24
’ RESULTS AND DISCUSSION It was assumed that the photoinduced heat arises only from Au NPs in the laser spot in the constructed calculation model shown in Figure 2. The relationship between the heat energy and the wavelength of irradiated light was estimated by changing the diameter of a single Au NP (2, 5, 10, 20, 40, 60, and 70 nm) in eq 5 indicating Drude-type electric susceptibility for χ in eq 4. Taking |rij| f ∞, Gmed(rij) f 0 was obtained for i 6¼ j in eq 2; therefore, Au NPs can be considered as a single NP (N = 1) without interparticle interactions. The length of the sides of each cubic box is larger than 400 nm for NPs with a 2 nm diameter, which indicates that the interactions between NPs in the nearest neighbor boxes can be neglected. By increasing the diameter of the Au NPs, the maximum wavelength of the Au NPs was blue shifted for Au NPs smaller than 10 nm but red shifted for Au NPs larger than 20 nm (Figure 3). There are two factors to determine the peak position of a localized surface plasmon in a single Au NP. One is the self-term Si = Si(di)I in eq 2 (I = unit tensor), and the other is the size-dependent damping 2vf/dj in eq 4. The eigenenergy of a localized surface plasmon (proportional to the inverse of resonant wavelength) in a single NP can be approximately obtained as ~ pl ðd, ∞Þ ¼ pΩ
"
pΩpl ð̅Si ðdi ÞÞ1=2 ð1 þ ΔεAu ̅ i ðdi ÞÞ b S
1=2
1
# ðΓbulk þ 2vf =di Þ2 ð1 þ ΔεAu ̅ i ðdi ÞÞ b S 2 S̅ i ðdi Þ 8ðpΩpl Þ
ð7Þ by solving eqs 2 and 3 for small size limit with kenvdi , 1, where Au 2 2 the relations ΔεAu b = εbulk(ω) nenv, Si(di) = (1 (kenvdi/2) )/ 2 (3nenv) with kenv = nenvω/c are used. From eq 7, it can be 1/2 decreases (red confirmed that pΩpl(Si)1/2/(1 + ΔεAu b Si) shift) due to the effect of Si with an increase of the diameter di of Au NP and the term in square bracket increases (blue shift) due to 2vf/di with an increase of di. In the small size region less than 20 nm, the second factor, 2vf/di , is dominant and results in the blue shift. These tendencies are similar to those indicated by the absorption spectra of Au NPs obtained in a previous report.26 The photothermogenic effect at 532 nm was focused, since the wavelength is that of general purpose laser for spherical Au NPs (Figure 3). The photothermogenic effect was largely improved by increasing the size of the Au NPs to 60 nm, above which it decreased. The Au NP with a 60 nm diameter exhibited the highest photothermogenic properties by 532 nm laser irradiation according to our investigations. Thus, there is an optimum size for the most efficient photothermogenic properties. Since H in eq 5 is proportional to the absorption per volume, Qi(ω)/V, when the concentration of Au atoms is constant, the increase of ~pl(d,∞) is the peak arises from the decrease of 2vf/dj in eq 4; Γ negligible for NPs smaller than 10 nm. On the other hand, ~pl(d,∞) becomes greater and comparable to Γbulk + 2vf/dj as Γ ~pl(d,∞) d increases for larger NPs, as shown in eq 6, where Γ
Figure 3. Theoretical results for the photoinduced heat from single Au NPs with different diameters. (a) Photoinduced heat of Au NPs for a wide range of sizes. Vertical dashed line indicates 532 nm. (b) Relationship of size with maximum wavelength and heat induced by photoirradiation.
indicates the decay rate of an excited plasmon into the radiation field around the NPs. Therefore, the Au NPs with diameters of 60 nm maintained a good balance between the decrease of the nonradiative width, Γbulk + 2vf/dj, and the increase of the ~pl(d,∞), depending on the size of the NP. radiative width, Γ ~pl(d,∞) ~pl(d,∞) and Γ Further, it was also confirmed that both pΩ Au also depend on εbulk even in the same environment. Therefore, we can prepare Au NPs with an optimum diameter by regulating the synthetic procedure in order to design suitable Au NPs for biomedical applications. Next, the photothermogenic effect from multiple Au NPs was theoretically investigated at different distances by considering Green’s function in eq 2 for a small value of |rij| (Figures 4 and 5). Given that there are two neighboring Au NPs with diameters of 2 nm at different distances (here, we set the distance between the nearest neighbor NPs to be |ri,i+1| = s), the photothermogenic properties were affected by the distance (Figure 4b). The red shift and peak value in heat spectra increase with a decrease of the ~pl(d,s) interparticle distance s, and such a red shift arises from pΩ including an energy shift due to the interaction via Gmed(s) among the induced polarizations of localized surface plasmon in multiple Au NPs. In addition, spectral broadening arises from ~pl(d,s) has a large value 2vf/d with a large value for small d, and Γ for small s in eq 6. On the other hand, it was numerically confirmed that the peak value in a heat spectrum did not depend 2 on the interparticle distance in the case that εAu bulk(ω) = nenv is assumed in eq 4. Although such an assumption seems to be unrealistic, it gives important physical insight as follows. This indicates that the enhancement of heat in the near-infrared region, with a decrease of interparticle distance, arises from the finite value of ΔεAu b , providing multiple interactions of localized surface plasmons between Au NPs due to the effect of mirror images at the surface of Au NPs. As discussed in the part of a single Au NPs, since the generated heat depends on εAu bulk even for multiple Au NPs, the heat effect can be controlled by the design of a surface protecting agent or an environmental refractive index. Furthermore, considering the model in Figure 5a, the photoinduced heat generation of multiple contacting Au NPs with diameters of 2 nm for different number of Au NPs 19093
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Figure 4. (a) Model for a pair of Au NPs. (b) Theoretical results for photoinduced heat from pairs of Au NPs for different interparticle distances. Vertical dashed lines indicate 532 nm.
Figure 5. (a) Model for multiple Au NPs. (b) Theoretical results for the photoinduced heat from multinucleated Au NPs for different particle numbers. Vertical dashed lines indicate 532 nm.
was investigated. A very large red shift and enhancement of the photoinduced heating effect were obtained by increasing the number of Au NPs in each cubic box since the interaction of mirror images of the localized surface plasmon is greatly enhanced (Figure 5b). These results indicate that multiple closely spaced small Au NPs are more useful than single large Au NPs since the enhancement of the heat effect in the near-infrared region is indispensable for in vivo applications. As mentioned above, closely packed multiple Au NPs theoretically exhibited different photoresponsive properties from single large Au NPs. Finally, a comparison of the theoretical and experimental results was performed. The seeding growth of Au NPs in the PEGylated dendrimer was already performed by a step-by-step method using NaBH4.24 Figure 6a shows the experimental absorption spectra of Au NPs obtained by seeding growth. The maximum wavelength of the Au NPs is red shifted, and the spectral width became slightly broad. The average diameters of the grown Au NPs were estimated to be 2.0, 2.2, 2.9, and 3.9 nm, as observed by TEM (Figure 6bf). This behavior contradicts the theoretical result of a single enlarged Au NP, for which the absorption spectra were blue shifted and became sharp when the diameter was less than 10 nm (Figure 3).
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Figure 6. Experimental results of Au NPs grown in the PEGylated dendrimer via seeding growth. (a) Absorption spectra. Vertical dashed line indicates 532 nm. (bf) TEM images of the seed and grown Au NPs (b) seed, (c) 1-time, (d) 3-times, (e) 5-times, and (f ) 10-times..
Rather, this could be adopted as an estimation of the photothermogenic properties of multiple Au NPs as shown in Figures 4 and 5. The photothermal properties at 532 nm of two contacting Au NPs were 1.7 times greater than that of a single Au NP (Figure 4b). This tendency corresponds to previous experiments.24 Therefore, multiple small Au NPs were determined to be prepared in the PEGylated dendrimer by the step-by-step method. It is possible that multiple Au NPs were produced in the dendrimer because sodium borohydride is a strong reductant for nucleation and seeding growth. Considering the delivery system of Au NPs, the carrier is indispensable. In previous work, a PEGylated dendrimer, which is composed of PEG (molecular weight 2 k) and a polyamidoamine dendrimer of generation 4, with a diameter of 15 nm was used.19,34 This is because the PEGylated dendrimer is a potential nanocontainer with long blood circulation.20 Even though the photoinduced heat generation can be improved by increasing the size of single Au NPs within the PEGylated dendrimer, the size of the grown Au NPs is limited to the diameter of the nanocontainer. From our theory, it is suggested that the dendrimer played a role in preparing multiple Au NPs via seeding growth using NaBH4. As described above, closely packed multiple Au NPs are more useful than large single Au NPs for in vivo applications because the photoinduced heat generation is enhanced for nearinfrared light. Therefore, this preparation method is useful for production of Au NPs with near-infrared absorption that can penetrate into the body. We can synthesize various types of PEGylated dendrimers by changing the dendrimer generation and PEG chain length. Design of a suitable dendrimer and modification of the preparation procedure can lead to a novel type of Au NP nanoconstruction for photothermal therapy.
’ CONCLUSIONS Our theoretical estimation suggests that efficient Au NPs for photothermal therapy could be obtained by enlargement of the Au NPs and multinucleation of Au NPs at a very close distance. The latter method may be more useful because multiple Au NPs respond to red-shifted light and generate high heat originated from mirror images of localized surface plasmons. The theory also suggests that the previously prepared Au NPs grown in the PEGylated dendrimer were multiple particles. This work provides important guidelines for the design of suitable Au NPs for photothermal therapy in addition to various types of biomedical applications. 19094
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’ AUTHOR INFORMATION Corresponding Author
*Phone: +81 72 254 8132. Fax: +81 72 254 8132. E-mail: t-iida@ 21c.osakafu-u.ac.jp.
’ ACKNOWLEDGMENT We thank Yasuhito Umeda, Yasuhiro Haba, and Noriko Tano for their experimental support and support in layout editing. This work was supported by the Special Coordination Funds for Promoting Science and Technology from the Ministry of Education, Culture, Sports, Science and Technology of Japan (Improvement of Research Environment for Young Researchers (FY 2008-2012)), the PRESTO of JST, and the Grant-in-Aid for Scientific Research (B) No. 23310079 from JSPS. ’ REFERENCES (1) Daniel, M.-C.; Astruc, D. Gold nanoparticles: Assembly, supramolecular chemistry, quantum-size-related properties, and applications toward biology, catalysis, and nanotechnology. Chem. Rev. 2004, 104, 293–346. (2) Sonvico, F.; Dubernet, C.; Colombo, P.; Couvreur, P. Metallic colloid nanotechnology, applications in diagnosis and therapeutics. Curr. Pharm. Des. 2005, 11, 2095–2105. (3) Jain, P. K.; El-Sayed, I. H.; El-Sayed, M. A. Au nanoparticles target cancer. Nano Today 2007, 2, 18–29. (4) Govorov, A. O.; Richardson, H. H. Generating heat with metal nanoparticles. Nano Today 2007, 2, 30–38. (5) Pissuwan, D.; Valenzuela, S. M.; Cortie, M. B. Therapeutic possibilities of plasmonically heated gold nanoparticles. Trends Biotechnol. 2006, 24, 62–67. (6) Takahashi, H.; Niidome, Y.; Niidome, T.; Kaneko, K.; Kawasaki, H.; Yamada, S. Modification of gold nanorods using phosphatidylcholine to reduce cytotoxicity. Langmuir 2006, 22, 2–5. (7) Niidome, T.; Yamagata, M.; Okamoto, Y.; Akiyama, Y.; Takahashi, H.; Kawano, T.; Katayama, Y.; Niidome, Y. PEG-Modified gold nanorods with a stealth character for in vivo applications. J. Controlled Release 2006, 114, 343–347. (8) Murphy, C. J.; Gole, A. M.; Stone, J. W.; Sisco, P. N.; Alkilany, A. M.; Goldsmith, E. C.; Baxter, S. C. Gold nanoparticles in biology: Beyond toxicity to cellular imaging. Acc. Chem. Res. 2008, 12, 1721–1730. (9) Oldenburg, S. J.; Averitt, R. D.; Westcott, S. L.; Halas, N. J. Nanoengineering of optical resonances. Chem. Phys. Lett. 1998, 288, 243–247. (10) Kim, J.; Park, S.; Lee, J. E.; Jin, S. M.; Lee, J. H.; Lee, I. S.; Yang, I.; Kim, J. S.; Kim, S. K.; Cho, M. H.; Hyeon, T. Designed fabrication of multifunctional magnetic gold nanoshells and their application to magnetic resonance imaging and photothermal therapy. Angew. Chem., Int. Ed. 2006, 45, 7754–7758. (11) Wu, G.; Mikhailovsky, A.; Khant, H. A.; Fu, C.; Chiu, W.; Zasadzinski, J. A. Remotely triggered liposome release by near-infrared light absorption via hollow gold nanoshells. J. Am. Chem. Soc. 2008, 130, 8175–8177. (12) Medina, S. H.; El-Sayed, M. E. H. Dendrimers as carriers for delivery of chemotherapeutic agents. Chem. Rev. 2009, 109, 3141–3157. (13) Wolinsky, J. B.; Grinstaff, M. W. Therapeutic and diagnostic applications of dendrimers for cancer treatment. Adv. Drug Delivery Rev. 2008, 60, 1037–1055. (14) Tekade, R. K.; Kumar, P. V.; Jain, N. K. Dendrimers in oncology: An expanding horizon. Chem. Rev. 2009, 109, 49–87. (15) Lee, C. C.; MacKay, J. A.; Frechet, J. M.; Szoka, F. C. Designing dendrimers for biological applications. Nat. Biotechnol. 2005, 23, 1517–1526.
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