Hybrid Microgels with Reversibly Changeable Multiple Brilliant Color

Their Synthesis: An Introduction. Robert Pelton , Todd Hoare .... Au nanodisk arrays. Yue Bing Zheng , Vincent K. S. Hsiao , Tony Jun Huang. 2008,...
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Hybrid Microgels with Reversibly Changeable Multiple Brilliant Color Daisuke Suzuki and Haruma Kawaguchi* Faculty of Science & Technology, Keio UniVersity, 3-14-1 Hiyoshi, Kohoku-ku, Yokohama 223-8522, Japan ReceiVed NoVember 8, 2005. In Final Form: February 14, 2006 We report reversibly color changeable hybrid microgels that tune multiple brilliant colors due to interparticle interactions of SPR using several structured nanoparticles. The interparticle interactions were brought out using the thermosensitive swelling/deswelling property of microgel. We employ N-isopropylacrylamide (NIPAM) and glycidyl methacrylate (GMA) copolymerized microgels (NG microgels) as templates for in situ synthesis of Au nanoparticles. The seed Au nanoparticles could be stably grown by successive reduction of Au and Ag in the microgels. Interestingly, the hybrid microgels were able to exhibit multiple brilliant colors by attaching Au/Ag multiple core/shell bimetallic nanoparticles in the microgels, and the color change reversibility of each hybrid microgel was accomplished by adjusting the nanoparticles’ sizes. Obtained microgels shown in this study will find important applications such as in biomedical and electronic devices.

Introduction Over the past decade, inorganic nanoparticles have attracted much attention due to their potential use in optical, electronic, and magnetic devices. The nanoparticles have been assembled into one-, two-, and three-dimensional structures1 as well as colloidal aggregates2 to tune their fascinating properties. For Cu, Ag, and Au nanoparticles, surface plasmon resonance (SPR) is the most attractive property, which depends on several factors such as their size, surface functionality, refractive index of medium, and interparticle interactions.3 In addition, specifically designed structures such as core-shell, rod, and prism well determine the property.3,4 For example, the color of the dispersion changes dramatically when Au or Ag layers are subsequently deposited on the seed particles, because the outermost layer interacts dominantly with incoming light.4c In general, these nanoparticles are synthesized with the aid of stabilizer such as surfactant to suppress aggregation. Recently, without surfactant, Zhang and co-workers first reported on a comprehensive study of synthesizing inorganic nanoparticles (CdS, fluorescent and nonfluorescent Ag, and Fe3O4) in polymer microgels.5 This methodology has several advantages: simple and easy synthesis, and addition of microgel properties such as stimuli responsiveness to nanoparticles. We have reported the synthesis of hybrid core/ shell microgels that attached Au nanoparticles (AuNPs) in the gel matrix and exhibited a little color change due to the * Corresponding author. Phone: +81-45-566-1563. Fax: +81-45-5645095. E-mail: [email protected]. (1) (a) Musick, M. D.; Keating, C. D.; Keefe, M. H.; Natan, M. J. Chem. Mater. 1997, 9, 1499. (b) Gittins, D. I.; Bethell, D.; Nichols, R. J.; Schiffrin, D. J. AdV. Mater. 1999, 11, 737. (c) Wang, Z. L. AdV. Mater. 1998, 10, 13. (d) Kiely, C. J.; Fink, J.; Brust, M.; Bethell, D.; Schiffrin, D. J. Nature 1998, 396, 444. (2) (a) Mirkin, C. A.; Letsinger, R. L.; Mucic, R. C.; Storhoff, J. J. Nature 1996, 382, 607. (b) Shenton, W.; Davis, S. A.; Mann, S. AdV. Mater. 1999, 11, 449. (c) Boal, A. K.; Llhan, F.; Derouchey, J. E.; Thurn-Albrecht, T.; Russell, T. P.; Rotello, V. M. Nature 2000, 404, 746. (d) Maye, M. M.; Chun, S. C.; Han, L.; Rabinovich, D.; Zhong, C.-J. J. Am. Chem. Soc. 2002, 124, 4958. (3) (a) Shipway, A. N.; Katz, E.; Willner, I. ChemPhysChem 2000, 1, 18. (b) Daniel, M.-C.; Astruc, D. Chem. ReV. 2004, 104, 293. (c) Liz-Marza´n, L. M. Langmuir 2006, 22, 32. (4) (a) Lu, L.; Wang, H.; Zhou, Y.; Xi, Y.; Zhang, H.; Hu, J.; Zhao, B. Chem. Commun. 2002, 144. (b) Ung, T.; Liz-Marza´n, L. M.; Mulvaney, P. Langmuir 1998, 14, 3740. (c) Rodriguez-Gonzalez, B.; Burrows, A.; Watanabe, M.; Kiely, C. J.; Liz-Marza´n, L. M. J. Mater. Chem. 2005, 15, 1755. (5) (a) Zhang, J.; Xu, S.; Kumacheva, E. J. Am. Chem. Soc. 2004, 126, 7908. (b) Zhang, J.; Xu, S.; Kumacheva, E. AdV. Mater. 2005, 17, 2336.

thermosensitive property of the microgels,6 and the microgels in which Au nanoshells were in situ formed at the rigid core surface stably.7 Temperature-induced color change of a CdTe nanocrystal loaded PNIPAM microsphere has been also reported by another group.8 In this study, we present reversibly color changeable hybrid microgels that tune multiple brilliant colors due to interparticle interactions of SPR using several structured Au/Ag nanoparticles. The interparticle interactions were brought out using the thermosensitive swelling/deswelling property of microgel as shown in Scheme 1, bottom. As mentioned above, we have already reported this kind of hybrid microgel using AuNPs.6 Although the microgels could change their colors reversibly, the change was not clear, and the dispersion was opaque in this case. It was due to the existence of a rigid core of template core/shell microgels. Herein, we employ N-isopropylacrylamide (NIPAM) and glycidyl methacrlate (GMA) copolymerized microgels (NG microgels) with a lower feed ratio of GMA than those described previously.6 The obtained NG microgels in this study were much more transparent than those reported previously6 due to an decrease in the microgel scattering section. These transparent microgels overcame one weak point. In addition, seed AuNPs could be stably grown by successive reduction of Au and Ag in the microgels (Scheme 1, top), resulting in overcoming another weak point of ambiguous color change. Interestingly, the hybrid microgels were able to exhibit multiple brilliant colors by attaching Au/Ag multiple core/shell bimetallic nanoparticles in the microgels, and the color change reversibility of each hybrid microgel was accomplished by adjusting the nanoparticles’ sizes. Obtained microgels shown in this study will find important applications such as in biomedical and electronic devices. Experimental Section Materials. Unless stated otherwise, all materials were purchased from Wako Pure Chemical Industries, Ltd. NIPAM was kindly given by Kojin Co. and recrystallized from hexane-toluene (1:1 on a volume basis). GMA was purified by distillation under reduced pressure to remove inhibitors. N,N′-Methylenebisacrylamide (MBAAm) was used without further purification. Azobis-amidino(6) Suzuki, D.; Kawaguchi, H. Langmuir 2005, 21, 8175. (7) Suzuki, D.; Kawaguchi, H. Langmuir 2005, 21, 12016. (8) Gong, Y.; Gao, M.; Wang, D.; Mo¨hwald, H. Chem. Mater. 2005, 17, 2648.

10.1021/la052999f CCC: $33.50 © 2006 American Chemical Society Published on Web 03/14/2006

Hybrid Microgels with ReVersibly Changeable Color

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Scheme 1. Thermosensitive Color Change by Interparticle Interactions of SPR Using Several Structured Nanoparticles

Table 1. Average Sizes of Inorganic Nanoparticles in the Microgels code

seed microgel

1 wt % HAuCl4 (µL)

40 mM NH2OH‚HCl (µL)

average diameter of AuNp (nm)

NG-NH2-Au/Au1 NG-NH2-Au/Au2 NG-NH2-Au/Au3

NG-NH2-Aua NG-NH2-Au NG-NH2-Au

125 200 600

625 1000 3000

18.3 ( 4.0 22.7 ( 4.9 33.7 ( 7.3

code

seed microgel

100 mM AgNO3 (µL)

100 mM ascorbic acid (µL)

average diameter of Au/AgNp (nm)

NG-NH2-Au/Ag1 NG-NH2-Au/Ag2 NG-NH2-Au/Ag3 NG-NH2-Au/Ag4 NG-NH2-Au/Au/Au/Ag1 NG-NH2-Au/Au/Au/Ag2 NG-NH2-Au/Au/Au/Ag3 NG-NH2-Au/Au/Au/Ag4

NG-NH2-Au NG-NH2-Au NG-NH2-Au NG-NH2-Au NG-NH2-Au/Au1 NG-NH2-Au/Au1 NG-NH2-Au/Au1 NG-NH2-Au/Au1

100 300 500 1000 100 300 500 750

200 600 1000 2000 200 600 1000 1500

18.6 ( 2.8 23.5 ( 3.0 27.3 ( 5.4 44.3 ( 6.0 27.1 ( 4.1 34.4 ( 5.6 43.0 ( 9.1 51.8 ( 9.7

a

AuNp size of NG-NH2-Au: 13.9 ( 2.4 nm.

propane dihydrochloride (V-50) was used without further purification. 2-Aminoethanethiol (2-AET) was purchased from Tokyo Kasei Kogyo Co., Ltd. and was used without further purification. Chloroauric acid tetrahydrate (HAuCl4‚4H2O) and silver nitrate (AgNO3) were used as received. Sodium borohydrate (NaBH4), L-ascorbic acid, and hydroxylamine hydrochloride (NH2OH‚HCl; Junsei Chemical Co., Ltd.) were used as received. The water used in all experiments was from a Milli-Q reagent water system (Millipore). Amino-Functionalized Microgel Synthesis. The aminofunctionalized microgels were prepared by soap-free emulsion copolymerization of NIPAM, GMA, and MBAAm using V-50 as an initiator, subsequently modified with 2-AET as follows. A mixture of NIPAM (2.5 g), GMA (0.5 g), MBAAm (0.04 g), and water (90 g) was poured into a 200-mL three-neck, round-bottom flask equipped with a stirrer, a nitrogen gas inlet, and a condenser. Nitrogen gas was bubbled into the mixture to purge oxygen. The mixture was kept at 70 °C in an oil bath. V-50 initiator (0.06 g) was dissolved in water (10 g) and added to the flask for initiation of polymerization, which then continued for 6 h. The obtained NIPAM and GMA copolymerized microgels (NG microgels) were purified by centrifugation, decantation, and then washed with water. This purification cycle was carried out four times. The epoxy groups in NG microgels were then allowed to react with thiol groups of 2-AET to introduce the amino groups to the microgels. A mixture of NG microgel (1.0 g), 2-AET (1.5 g), and water (90 g) was poured into a 100-mL glass vial with stirring under room temperature, and the pH was adjusted to 11.0 with 6 N NaOH. The reaction was continued for 24 h. The obtained amino-functionalized NG microgels (NG-NH2 microgels) were purified by the same method as described above, and by 1 week of dialysis, in addition. In Situ Synthesis of AuNPs in NG-NH2 Microgels. The in situ synthesis of AuNPs in NG microgels was carried out as in our previous report.7 A mixture of NG-NH2 microgel (50 mg) and

HAuCl4 (4 mg) was stirred in 10 mL of aqueous medium (pH 2) at 4 °C for 4 h. After that, excess HAuCl4 was removed by centrifugation, decantation, and then washed with aqueous medium (pH 2) for generating no AuNPs except in the microgel. A total of 15 mL of water (pH 2) containing the microgels was poured into a 30-mL glass vial at 4 °C. NaBH4 (1.0 mg) was dissolved in water (1 mL) and added dropwise to the vial. After the addition of NaBH4, the mixture was stirred for 30 min. The AuNPs incorporated NGNH2 microgels (NG-NH2-Au microgels) were then purified by centrifugation, decantation, and a washing process (four times with water). Seed-Mediated Growth of AuNPs and Multishell Au/Ag Bimetallic Nanoparticles in NG-NH2 Microgels. AuNP growth from AuNP seed in NG-NH2 microgel was prepared using the procedure described previously.7,9 A mixture of NG-NH2-Au microgels (2.5 mg) and water (20 mL) was put into a 30-mL glass vial while being stirred at 4 °C. After 10 min of stirring, a mixture of HauCl4 (1 wt %, 125-600 µL) and NH2OH‚HCl (40 mM, 6003000 µL) was poured into the vial. The reaction was continued for 15 min, after which the microgels were purified by centrifugation, decantation, and then washed four times with water. The obtained hybrid microgels were coded as NG-NH2-Au/Au (see Table 1). Au/Ag Core-shell nanoparticles in the microgels were prepared using the modified procedure described previously.4c A mixture of NG-NH2-Au or AuNP-grown (NG-NH2-Au/Au1) microgels (2.5 mg), AgNO3 (10 mM, 100-750 µL), and water (20 mL) was put into a 30-mL glass vial while being stirred at 4 °C. After 10 min of stirring, a solution of L-ascorbic acid (100 mM, 200-1500 µL) was added dropwise to the vial. The reaction was continued for 15 min, after which the microgels were purified by centrifugation, decantation, and then washed four times with water. The obtained hybrid microgels were coded as NG-NH2-Au/Ag (see Table 1). (9) Liang, Z.; Susha, A.; Caruso, F. Chem. Mater. 2003, 15, 3176.

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Figure 1. (A) Temperature dependence of the hydrodynamic weight-averaged diameter of NG ([) and NG-NH2 (]) microgels in aqueous dispersions measured by DLS (temperature-raising process). (B) SEM views of NG (a) and NG-NH2 (b) microgels. Insets are close-up views of each microgel, and the scale bars are 300 nm. Multishell Au/Ag/Au bimetallic nanoparticles in the microgels were prepared using L-ascorbic acid as described previously.4c A mixture of NG-NH2-Au/Ag2 microgels (2.5 mg), HAuCl4 (1 wt %, 400 µL), and water (20 mL) was put into a 30-mL glass vial while being stirred at 4 °C. After 10 min of stirring, a solution of L-ascorbic acid (100 mM, 800 µL) was added dropwise to the vial. The reaction was continued for 15 min, after which the microgels were purified by centrifugation, decantation, and then washed four times with water. The obtained hybrid microgel was coded as NG-NH2-Au/ Ag/Au. Characterization. Approximately 2 µL of the diluted microgel suspension was dried on a carbon-coated copper grid and observed by field emission transmission electron microscopy (TEM, TECNAI F20, Philips Electron Optics Co.) operated at 200 kV. Also, approximately 5 µL of the diluted microgel suspension was dried on a polystyrene substrate and observed by field emission scanning electron microscopy (SEM, S-4700, Hitachi Ltd.). The SEM samples were sputter-coated with platinum/palladium before examination. Hydrodynamic diameters of microgels were determined by dynamic light scattering (DLS) using a laser particle analyzer system (PAR3, Otsuka Electronics Co.). The incident wavelength was 632 nm of a He-Ne laser, and the measurement angle was 90°. UV-visible absorption data were recorded on a Hitachi U-2001 spectrophotometer. The samples for DLS and UV-visible absorption experiments were allowed to equilibrate at each temperature for 10 min before measurement. An elemental analysis of dried microgels for carbon, hydrogen, nitrogen, oxygen, and sulfur was conducted using Vario EL (Elementar Analyzensysteme GmbH).

Results and Discussion Preparation and Characterization of the Template Microgels. NG microgels were prepared by soap-free emulsion polymerization of NIPAM and GMA using MBAAm as a crosslinker. Because of the different reactivity ratios of NIPAM and GMA (0.39 and 2.69, respectively),10 GMA tends to be consumed faster than NIPAM. Therefore, as each polymer’s hydrophilicity might not be very different during polymerization at 70 °C, the most outer layer of the NG microgel was supposed to be rich in PNIPAM. Next, amino groups were introduced to NG microgels (10) Virtanen, J.; Tenhu, H. J. Polym. Sci., Part A: Polym. Chem. 2001, 39, 3716.

(NG-NH2 microgel) using 2-AET.6,7 According to the elemental analysis result, 3.1 mol % of epoxy groups of GMA was converted to amino groups, corresponding to 4.2 × 105 amino groups/ microgel. The temperature dependence of the hydrodynamic diameter of NG and NG-NH2 microgels in aqueous medium (pH 6) was investigated by DLS. As shown in Figure 1A, the diameter of NG microgels depended on temperature in the range of 20-40 °C and reflected the transition of PNIPAM. After amino group introduction, the diameters of NG-NH2 microgels became larger than those before introduction, at any temperature in this range. This phenomenon was studied by some researchers and was attributed mainly to osmotic pressure or the Donnan potential due to counterions.11 It is worthwhile mentioning that NG-NH2 microgel at 40 °C did not reach the most deswollen state. It means that the dispersion is relatively transparent as the microgel still has water inside. This is important for accomplishing the purpose of this study (brilliant color change and its reversibility). The SEM views of NG (a) and NG-NH2 (b) microgels are shown in Figure 1B. Each microgel spontaneously arranged with spaces on the polystyrene substrate due to the unique property of PNIPAM-covered microgels.12 The structures of NG and NG-NH2 microgels dried on the substrate were different from each other because NG-NH2 microgels are more swollen than NG ones at room temperature (dried diameters: NG microgel, 496 nm; NG-NH2 microgel, 531 nm). Seed-Mediated Growth of AuNPs and Multishell Au/Ag Bimetallic Nanoparticles in NG-NH2 Microgels. In situ synthesis of AuNPs was carried out as described previously.7 TEM views of obtained microgels revealed that the hybrid microgels (NG-NH2-Au microgels) also arranged as did the parent microgels, and AuNPs’ size in the microgels was 13.9 ( 2.4 nm (Figure 2A and B(a)). Different from the case of the previous report,13 the nanoparticles were not released from the (11) Ferna´ndez-Nieves, A.; Ferna´ndez-Barbero, A.; Vincent, B.; de las Nieves, F. J. Macromolecules 2000, 33, 2114. (12) (a) Tsuji, S.; Kawaguchi, H. Langmuir 2004, 20, 2449. (b) Tsuji, S.; Kawaguchi, H. Langmuir 2005, 21, 2434. (c) Tsuji, S.; Kawaguchi, H. Langmuir 2005, 21, 8439. (13) Kuang, M.; Wang, D.; Bao, H.; Gao, M.; Mo¨hwald, H.; Jiang, M. AdV. Mater. 2005, 17, 267.

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Figure 2. TEM views of thermosensitive hybrid microgels deposited on carbon-coated copper grid dried at 25 °C. (A) The microgel array of NG-NH2-Au. (B) AuNPs in NG-NH2-Au microgel (a), AuNPs in NG-NH2-Au/Au2 microgel (b), Au/AgNPs in NG-NH2-Au/Ag2 microgel (c), Au/AgNPs in NG-NH2-Au/Au/Ag2 microgel (d), and Au/Ag/AuNps in NG-NH2-Au/Ag/Au microgel (e). Inset images are each hybrid microgel, and the scale bars are 200 nm.

Figure 3. UV-vis spectra of NG-NH2-Au/Au2 (a), NG-NH2-Au/Ag2 (b), and NG-NH2-Au/Ag/Au microgels (c) measured at 25 °C ([), 40 °C (gray square), and 25 °C after 10 heating-cooling cycles treatment (]). All spectra presented here were normalized by taking the temperature effects into account. Insets are the dispersion of each hybrid microgel at both 25 °C (left) and 40 °C (right).

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microgel even at the most swollen state (4 °C) due to the larger size of the nanoparticles, different preparation methods of hybrid microgels, and strong interaction between AuNPs and amino groups even at 4 °C. Using NG-NH2-Au microgels as templates, successive seed-mediated growth of bimetallic nanoparticles was carried out. The seed microgel, reagents and their amount, and obtained NPs’ size are listed in Table 1. For synthesizing sizegrown AuNPs (Au/AuNPs), HAuCl4 and NH2OH‚HCl were used.7,9 On the other hand, for synthesizing Au/Ag core/shell nanoparticles (Au/AgNPs), AgNO3 and L-ascorbic acid were used as reported previously.4 The size of each nanoparticle was easily controllable by selecting the amount of reagents. The absorption spectrum at 25 °C became stronger and a little redshifted as the size increased. In all cases, polydispersities became higher than that of AuNPs in the template microgel. The microgels including relatively large nanoparticles (>35 nm) were likely to be sedimented in a few days at 4 °C due to their heavy weight. So the hybrid microgels attaching smaller nanoparticles than that value (35 nm) were used in further investigations. Figure 2 shows TEM views of some characteristic hybrid microgels. Different from AuNps (parts (a) and (b) of Figure 2B), core/shell structures of Au/AgNPs can be distinguished due to the difference of the contrast between Au and Ag (parts (c) and (d) of Figure 2B). Yet in the case of Au/Ag/Au multiple core/shell nanoparticles in the microgels (NG-NH2-Au/Ag/Au microgels, Figure 2B(e)), these structures were no more spherical, and the size was distributed from 10 to 60 nm. This is because of galvanic replacement4b and, probably, lack of cetyltrimethylammonium bromide. Although these were not spherical nanoparticles, different from the previous report, and uncertainty remained, the color of dispersion was in agreement with the sample reported previously (shown in Figure 3c).4c Optical Properties of the Hybrid Microgels. To demonstrate the tuning colors by temperature change as shown in Scheme 1, three characteristic dispersions (code: NG-NH2-Au/Au2, NGNH2-Au/Ag3, and NG-NH2-Au/Ag/Au) were selected for UV-visible spectroscopy experiments measured repetitively at both 25 and 40 °C. For confirming the reversibility of color change, the dispersions have been employed for 10 heatingcooling cycles of measurement. Figure 3 shows UV-vis spectra of NG-NH2-Au/Au2 (a), NG-NH2-Au/Ag3 (b), and NGNH2-Au/Ag/Au (c) microgels in aqueous medium. As shown in Figure 3a, the absorption spectrum (peak at 537 nm) of the AuNps at 25 °C where the microgel was swollen became sharper than those of our previous report6 due to the larger size of AuNPs and less scattering from template microgels. The spectrum (peak at 545 nm) at 40 °C where the microgel was deswollen became broader than those at 25 °C. The broaden spectrum made the color of dispersion purple while red at 25 °C (Figure 3a, inset). Note that these dispersions are transparent, and the difference of colors can be distinguished even at lower concentration (4.28 pM of the hybrid microgels). This color change is attributed to interparticle interactions among neighboring AuNPs3,6 at different

Suzuki and Kawaguchi

swelling states of the microgels, which causes absorption change in the long-wavelength region. Even after 10 heating-cooling cycles treatment, the spectrum coincided with that of the nontreated microgel. In other words, the color of dispersion can be distinguished by naked eyes even after 10 heating-cooling cycles treatment. This indicates that irreversible aggregations of AuNPs attached inside the microgel were suppressed by the intermediate polymer matrix among neighboring nanoparticles. In the case of the hybrid microgels attaching Au/Ag core/shell nanoparticles (Figure 3b), the blue-shifted peak appeared at 424 nm at 25 °C. Similar to AuNPs attached microgels, the spectrum curve at 40 °C where microgel was deswollen became broader (peak at 442 nm), and the color change from yellow to orange (Figure 3b, inset, 2.14 pM of the hybrid microgels) was completely reversible even after 10 heating-cooling cycles treatment. In the case of Au/Ag/Au multiple core/shell nanoparticle attached microgels (Figure 3c), although the same tendency (the redshifted peak at 40 °C (784 nm) as compared to that at 25 °C (712 nm)) appeared, the spectrum after 10 heating-cooling cycles treatment did not necessarily coincide with that of nontreated hybrid microgels at 25 °C. This indicates that a part of the nanoparticles was aggregated irreversibly due to the lack of intermediate polymer matrix among neighboring nanoparticles. This case also happened when nanoparticle sizes were relatively larger (>35 nm). In addition, although the spectra changed dramatically between 25 and 40 °C, color change is little, and it might be attributable that the red-shifted peak measured at 40 °C is no longer in the visible region. Yet this switching microgel would find biomedical applications such as drug delivery carriers.14

Conclusions We have synthesized brilliant color changeable hybrid microgels using thermosensitive microgels as templates. AuNPs attached inside the microgel could serve as seeds for further growth such as Au/Ag core/shell nanoparticles. The color changes of the hybrid microgels originated from interparticle interactions of nanoparticles were brought out using the swelling/deswelling property of the thermosensitive microgel and were reversible when suitable nanoparticles were used. These hybrid microgels shown here have potential applications such as in biomedical and electronic devices. Acknowledgment. D.S. thanks the research fellowships of the Japan Society for the Promotion of Science for Young Scientists. This work was supported by a Grant-in-Aid for the 21st Century COE program “KEIO Life-Conjugated Chemistry” from the Ministry of Education, Culture, Sports, Science, and Technology, Japan. LA052999F (14) Simpson, C. R.; Kohl, M.; Essenpreis, M.; Cope, M. Phys. Med. Biol. 1998, 43, 2465.