Polymer-Modulated Optical Properties of Gold Sols - The Journal of

Article pubs.acs.org/JPCC

Polymer-Modulated Optical Properties of Gold Sols Cynthia Said-Mohamed,† Jukka Niskanen,‡ Didier Lairez,† Heikki Tenhu,‡ Paolo Maioli,§ Natalia Del Fatti,§ Fabrice Vallée,§ and Lay-Theng Lee*,† †

Laboratoire Léon Brillouin, CEA-Saclay, 91191 Gif-sur-Yvette Cedex, France Department of Chemistry, University of Helsinki, PB 55, FIN-00014 HY Helsinki, Finland § LASIM, Université Lyon 1, 43 Boulevard du 11 Novembre, 69622 Villeurbanne, France ‡

ABSTRACT: The optical properties of a series of gold nanoparticles (D ≈ 2.3−8 nm) grafted with a stabilizing polymer with a wide range of chain lengths (Mw ≈ 6.5K−29.5K) have been studied quantitatively in different dielectric solvents. Mie−Drude dipolar theory was applied to model the localized surface plasmon resonance (SPR) peak position, as well as the peak width of the absorption spectra, using the dielectric function of gold. The modeled spectra yielded information on the dielectric function of the polymer shell, ϵs, from which the average polymer concentration in the shell was deduced. Combining information from optical modeling and structural properties obtained from small-angle neutron scattering (SANS) on the polymer shell thickness and from transmission electron microscopy (TEM) on the gold core size, the SPR peak shifts and their attenuated sensitivity to solvent refractive index were characterized. The SPR behaviors for all of the gold colloids with different core sizes and graft chain lengths were thus expressed as a function of the effective polymer volume fraction, p, of the composite nanoparticle. It was found that sensitivity to the solvent dielectric property decreased until, for p > 0.9 (corresponding to an effective shell thickness on the order of the core radius), the SPR mode was “frozen” in by the polymer shell and lost sensitivity to the solvent.

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INTRODUCTION The most interesting optical characteristic of gold nanoparticles is the localized surface plasmon resonance (SPR) effect that gives them the particularity of exhibiting intense colors. This phenomenon is due to collective oscillations of electrons induced by an electromagnetic field that results in a resonance band in the UV−visible region of the absorption spectra.1,2 Based on this spectral signature, gold and other noble-metal nanoparticles have been widely exploited for potential applications in decorations and coatings,3 optical and electronic devices,4−6 biomedical and delivery systems,7−12 and environmental monitoring.13 The factors that govern the SPR of individual nano-objects are particle size14−20 and shape;18,19,21 charge density of the metal core;22,23 and dielectric environment,21,23−26 which includes the embedding medium and stabilizing ligands or coatings. For a homogeneous spherical metal particle embedded in a homogeneous matrix, the optical absorption and scattering were quantitatively described by Mie27 in terms of the metal complex dielectric function, ϵ = ϵ1 + iϵ2, and the matrix dielectric constant, ϵm. For particle size D much smaller than the optical wavelength λ (i.e., kD ≪ 1, k = 2π/λ), the absorption cross section is dominated by the lowest-order dipole term and the theory is reduced to1,2 σa(ω) = 9ϵm 3/2V

ϵ2(ω) ω c [ϵ1(ω) + 2ϵm]2 + ϵ2 2(ω)

and imaginary parts, respectively, of the frequency-dependent dielectric constant of the metal particle. The scattering cross section, σs(ω) ≈ 1/λ4, but for nanoparticles up to about 20 nm in the frequency range of interest, the absorption cross section is much greater than the scattering cross section [i.e., σa(ω) ≫ σs(ω)], and the extinction cross section (absorption + scattering) is dominated by σa(ω). From eq 1, it follows that resonance enhancement occurs when the denominator tends toward zero. For a small value of ϵ2(ω), this leads to the approximate resonance condition1,2 ϵ1(ω) + 2ϵm = 0

The resulting absorption peak, ϵ1(ωpeak) = −2ϵm, in the visible frequency range is the origin of the intense colors displayed by gold sols. Mie theory thus predicts the plasmon peak position to be determined mostly by ϵ1(ω) and the peak height and shape to be governed by ϵ2(ω).14 In practice, gold nanoparticles are colloidally unstable and susceptible to irreversible aggregation. To stabilize them, gold nanoparticles are usually coated with small organic molecules such as citrates28 and surfactants29 or functional ligands30 to provide an additional tool to design surface architecture and to modulate physicochemical properties for compatibility and detection. A large body of work therefore exists on stabilized gold colloids. Surface modifications alter the local dielectric

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Received: March 27, 2012 Revised: May 16, 2012 Published: May 22, 2012

where V is the particle volume; ω = 2πc/λ is the optical frequency; c is the speed of light; and ϵ1(ω) and ϵ2(ω) the real © 2012 American Chemical Society

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dx.doi.org/10.1021/jp3029209 | J. Phys. Chem. C 2012, 116, 12660−12669

The Journal of Physical Chemistry C

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60 °C for 24 h. The polymers were then precipitated in excess diethyl ether, purified by repeated precipitations, and dried under vacuum. Finally, the polymers were further purified by dialysis against water to remove oligomers. Samples of different molecular weights were prepared by varying the monomer/Cpa concentration ratio and the reaction time. Size-exclusion chromatography (SEC) was used to determine the molar mass of the polymer. Poly(methyl methacrylate) (PMMA) standards from PSS Polymer Standards Service GmbH were used for calibration using dimethylformamide (DMF)/LiBr (1 mg/mL) as the eluent. Synthesis and Characterization of Au-PNIPAM Nanoparticles. Au-PNIPAM nanoparticles were prepared by the grafting-to technique, where grafting of the PNIPAM chains occurred simultaneously with growth of the gold cores. The “one-step” method was employed in which the RAFT polymer was used directly without prehydrolysis.34 Cpa-PNIPAM (0.01 or 0.005 mmol) and HAuCl4·xH2O (0.01 mmol) were dissolved in THF (20 mL) and stirred at room temperature for 2 h. Then, 1.0 mL of a 1.0 M THF solution of LiB(C2H5)3H was added dropwise to the vigorously stirred solution (giving a final molar ratio of LiB(C2H5)3H/HAuCl4·xH2O = 10:1). The solution immediately turned purple with a little gas evolution and was further stirred for 2 h. The resulting dispersion was centrifuged at 5000 rpm for 30 min to remove large aggregates; only a small amount of precipitate was observed on the bottom of the centrifuge tube, and the supernatant was collected. Gold nanoparticles from the supernatant were then precipitated in a mixture of ether/hexane (2:1) and centrifuged at 5000 rpm at 6 °C for 30 min (three times at 10 min each). Finally, the nanoparticles were redissolved in THF and dialyzed against water for 48 h to ensure removal of free polymer and then dried under vacuum. To obtain different gold-core sizes, two molar ratios of HAuCl4 to polymer were used, 10:1 (0.1 mmol/0.01 mmol) to obtain small particles and 20:1 (0.1 mmol/0.005 mmol) to obtain larger particles; for samples grafted with the same polymer chains, the smaller-size particle is denoted s1, and the larger-size particle is denoted s2. The mean gold-core size was characterized by transmission electron microscopy (TEM). Figure 1 shows some Au-PNIPAM nanoparticles grafted with different polymer chain lengths and dispersed in various

environment, so the surface plasmon band rarely falls exactly where Mie theory predicts for bare particles. The resulting energy shift in the surface plasmon band depends on the ligandinduced changes to the metal-core charge density and on the relative dielectric function of the coating with respect to that of the embedding medium. In this respect, most of the past studies concentrated on small-molecule ligands and on qualitative shifts in the plasmon peak. Relatively few studies exist on polymeric systems, and to our knowledge, no detailed and quantitative study relating the polymer structure to the optical properties of gold nanoparticles has been reported. In this article, we present the optical properties of gold nanoparticles grafted with a layer of the protective hydrosoluble polymer poly(N-isopropylacrylamide) (PNIPAM). The objective was to correlate the polymer shell structure with the optical response of the embedded gold core (gold core with polymer shell) and to quantify the polymer-induced plasmon peak shifts and their subsequent attenuated sensitivity to the dielectric properties of the external solvent. The graft polymer layer thus serves a dual function as a colloidal stabilizer as well as a local stimulus to modulate the optical response of the gold nanoparticle. PNIPAM is a classic thermosensitive polymer that can provide a convenient thermal stimulus for this purpose. This thermal aspect, however, will be addressed in a later article. In this work, we concentrate on the effects of polymer chain length and solvent dielectric properties. A wide range of polymer chain lengths was used to generate polymer shells of varying thicknesses. Relatively monodisperse PNIPAM polymers were synthesized using reversible addition−fragmentation chain transfer (RAFT) polymerization and grafted onto gold nanoparticles by the “grafting-to” technique. The structural properties of the grafted polymer shells were characterized by small-angle neutron scattering (SANS). The optical responses (peak positions and widths) of these composite particles were modeled using Mie−Drude theory. Based on a combination of the optical data and the structural properties, we describe quantitatively the role of the protective polymer layers in modulating the optical properties, their effects on the sensitivity of the gold core to the external dielectric constant, and an eventual “freezing” of the SPR mode.

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EXPERIMENTAL SECTION Materials. N-Isopropylacrylamide (NIPAM) (Polyscience) was dissolved in tetrahydrofuran (THF) and recrystallized twice from hexane; 2,2-azobis(isobutyronitrile) (AIBN) (Fluka) was used as received. Dioxane (Lab-Scan) for the synthesis of polymers was distilled before use, and 4cyanopentanoic acid dithiobenzoate (Cpa RAFT agent) was synthesized in the laboratory.31 For the synthesis of gold nanoparticles, gold(III) chloride trihydrate (HAuCl4·3H2O, Aldrich), lithium triethylborohydride (1.0 M solution in THF), and THF (Aldrich) were used as received. Synthesis and Characterization of Cpa-PNIPAM Polymers. Cpa-PNIPAM polymer was synthesized by reversible addition−fragmentation chain transfer (RAFT) polymerization32 using 4-cyanopentanoic acid dithiobenzoate (Cpa) as the RAFT agent and 2,2′-azobis(isobutyronitrile) (AIBN) as the initiator.33 Recrystallized NIPAM monomer, Cpa, and AIBN were dissolved in distilled dioxane in a roundbottom flask equipped with a magnetic stirrer. The mixture was degassed by either a N2 flow for 45 min or three freeze− pump−thaw cycles to optimize the oxygen elimination, sealed under vacuum, and polymerized in a thermostatted oil bath at

Figure 1. (Left) Au-PNIPAM nanoparticles grafted with varying polymer chain lengths and dispersed in different solvents. (Right) TEM image of Au-PNIPAM265 prepared by grafting-to in a one-step method with HAuCl4/polymer = 20:1.

solvents and a TEM image of Au-PNIPAM265 particles (the subscript 265 denotes the degree of polymerization or the number of monomer repeat units). The characteristics of the samples are given in Table 1. Two populations of gold core sizes were obtained: D ≈ 2.3−3 nm synthesized using a 12661



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HAuCl4/polymer molar ratio 10:1 and D ≈ 4.5−8 nm synthesized using a molar ratio of 20:1.

and detailed study of the relationship between the polymer shell structure and the optical properties. To quantify these effects, we first characterized the thickness of the graft polymer layer by SANS. Structural Properties of Graft Polymer Layer on Gold Nanoparticles. Small-angle neutron scattering is an efficient and nondestructive technique for studying the conformation of polymer layers because of the possibility to enhance the contrast in the neutron refractive indices of the components through isotopic substitution; the same principle is also applied to solvent-match constituents in a multicomponent system to facilitate the study of each component separately. In the current work, we decided to maximize the signal from the protonated polymer layer (ρpolymer = 0.9 × 10−6 Å−2) in pure D2O (ρD2O = 6.37 × 10−6 Å−2) without contrast matching of the gold core (ρcore = 4.5 × 10−6 Å−2), where ρ is the neutron scattering length density. Nanoparticles grafted with polymers have in the past been modeled successfully with a core−shell or hairysphere model, for silica nanoparticles grafted with polystyrene chains36 and PNIPAM-based copolymers/silica system,37 respectively. In this work, we applied both of these models to fit the SANS spectra of Au-PNIPAM nanoparticles in aqueous solutions. Core−Shell Model. This model is a combination of form factors of homogeneous hard spheres:38 a small sphere of radius Rcore with a scattering length density of ρcore (the gold core) embedded in a larger sphere of radius Rshell (with a hollow center of radius Rcore) with a scattering length density of ρshell (the polymer shell). The form factor of a homogeneous sphere is P(q) = [A(q)]2, where A(q) is the amplitude of the form factor39

Table 1. Au-PNIPAMxxa Nanoparticles Synthesized with Different HAuCl4/Polymer Molar Ratios by the Grafting-to Technique in a One-Step Method graft polymer Mw

sample name

(g/mol) (PIb) 6500 (1.2) 17500 (1.2) 28600 (1.3) 14600 (1.2) 17500 (1.2) 28600 (1.3)

Au-PNIPAM57 Au-PNIPAM154 Au-PNIPAM265 Au-PNIPAM127 Au-PNIPAM154 Au-PNIPAM265

(s1) (s1) (s2) (s2)

HAuCl4/polymer

D

(molar ratio)

(±0.5 nm)

10:1 10:1 10:1 20:1 20:1 20:1

2.7 3.0 2.3 8.0 5.0 4.5

a Subscript xx denotes the degree of polymerization. bPI is the polymer polydispersity index.

Characterization of the Structural Properties of the Polymer Shell. Small-angle neutron scattering (SANS) was used to characterize the structural properties of the polymer chains grafted onto the gold nanoparticles. SANS experiments were carried out on the PACE spectrometer at the ORPHEE reactor (CEA-Saclay). Two different configurations were employed: neutron wavelength λ = 13 Å and sample−detector distance of 5 m (low-q) and λ = 6 Å and sample−detector distance of 1.5 m (medium-q). The resulting range of scattering wave vectors, q = 4π(sin θ)/λ, covered by these configurations was about 0.003−0.15 Å−1. Data treatment was carried out by the standard correction procedure using the expression35 Is(f , T , t ) − Iinc(f , T , t ) −C I(q) = IH2O(f , T , t ) − Iec(f , T , t ) (3)

A (q , R ) = 3

where Is(f,T,t) and Iinc( f,T,t) are the scattered intensities of the sample and of the solvent (D2O), respectively, and IH2O( f,T,t) and Iec(f,T,t) are the scattered intensities of H2O and the empty cell, respectively. These intensities were normalized by the incident neutron flux ( f), sample transmission (T), and thickness (t). C is a constant electronic background measured using a cadmium block. The spectra acquisition times were 2 h for the low-q configuration and 30 min for the high-q configuration. All measurements were carried out in D2O to optimize the signal of the polymer shell. The nanoparticle concentrations were around 0.5 mg/mL, and the experiments were performed at T ≈ 20 °C. Optical Measurements. Solutions of the Au-PNIPAM nanoparticles were prepared in Millipore water (n = 1.333), chloroform (n = 1.353), tetrahydrofuran (THF) (n = 1.408), and pyridine (n = 1.509). The concentrations of the nanoparticles varied from 0.3 to 0.5 mg/mL. UV−vis spectra of the gold nanoparticle dispersions were recorded on a Varian Cary100 spectrometer at T = 20 °C.

sin(qR ) − qR cos(qR ) (qR )3

(4)

For a composite sphere consisting of a core and a shell, the form factor is then Pcore−shell(q) = [Δρshell VshellA(q , R shell) − (Δρshell − Δρcore ) VcoreA(q , R core)]2

(5)

where Δρshell = ρshell − ρsolvent, Δρcore = ρcore − ρsolvent, and Vshell and Vcore are the volumes of the overall particle and of the core, respectively. The total scattering intensity is I(q) = nP(q) S(q), where n is the number density of the particles and S(q) is the structure factor that characterizes interparticle interactions. However, because the dispersions used in this work were very dilute (C ≈ 0.5 mg/mL), S(q) = 1, and only the form factor contributes to the scattering. The variable parameters in this model are Rcore and Rshell, with their respective polydispersities, and ρshell. The polymer shell thickness in this case is e = Rshell − Rcore. Furthermore, if the polymer shell is hydrated, then its scattering length density depends on the polymer volume fraction in the shell, ϕp, such that ρshell = ϕpρpolymer + (1 − ϕp)ρsolvent. Pedersen Hairy-Sphere Model. This model was originally developed to describe block copolymer micelles.40 For a spherical nanoparticle of radius Rcore grafted with polymer chains with a radius of gyration of Rg, this model takes into account self-correlation of the spherical core, self-correlation of the polymer chains, a cross term between the core and the chains, and a cross term between different chains. The first term is Psphere(q, Rcore) = [Asphere(q, Rcore)]2, as defined in the

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RESULTS AND DISCUSSION Stable colloidal gold nanoparticles protected with PNIPAM polymers with a wide range of molecular masses ranging from about 7K to 29K were synthesized by the grafting-to technique in a one-step procedure. Through control of the HAuCl4/ polymer molar ratio during the synthesis, nanoparticles ranging from about 2.3 to 8 nm were obtained. Using these AuPNIPAM nanoparticles with different core sizes grafted with polymers of varying chain lengths, we conducted a systematic 12662



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Figure 2. SANS intensity in D2O at T ≈ 20 °C. (a) Au-PNIPAM154 (s2) (D = 5.0 nm): core−shell fit with e = 3.2 nm (dashed line), hairy-sphere fit with Rg = 4.0 nm (solid line). (b) Au-PNIPAM265 (s2) (D = 4.5 nm): core−shell fit with e = 4.2 nm (dashed line), hairy-sphere fit with Rg = 5.8 nm (solid line). Inset: Plot of Iq2 versus q after background subtraction.

polymer chain is considered to represent the polymer shell thickness. The core−shell and hairy-sphere models therefore require at least five fitting parameters each. In our data fitting, we decided to reduce the number of fitting parameters by keeping Rcore constant using the value obtained from TEM and to impose a constant polydispersity of ±10%, a typical value for chain length dispersion. Only two free parameters, both describing the polymer shell, were therefore extracted from the fits: thickness e and scattering length density ρshell for the core−shell model and thickness Rg and number of chains per particle N for the Pedersen (hairy-sphere) model. For the discussion that follows, N was converted to the number of chains per square nanometer, N′. Figure 2 compares the fits with the two models of the SANS spectra for Au-PNIPAM154 (s2) (Dcore = 2Rcore = 5.0 nm) and Au-PNIPAM265 (s2) (Dcore = 4.5 nm). For AuPNIPAM154 (s2), the core−shell model gives e = 3.2 nm and ρshell = 4.95 × 10−6 Å−2, and the hairy-sphere model gives Rg = 4.0 nm and N′ = 0.3 (number of chains per square nanometer); for Au-PNIPAM265 (s2), the corresponding values are e = 4.2 nm, ρshell = 4.35 × 10−6 Å−2 and Rg = 5.8 nm, N′ = 0.6. These results show that, for both samples, the two models give reasonably good fits in the low-q region. In the high-q region, however, the core−shell model deviates significantly and decreases in intensity much faster than the experimental data because of the q−4 behavior predicted for hard spheres with abrupt interfaces. The hairy-sphere model, on the other hand, gives a good fit over the entire q range of the spectra. Here, the Debye function in the hairy-sphere model describes a q−2 dependence that is characteristic of Gaussian chains, indicating a hydrated shell layer with a smooth interface. The approach of the scattering curve to q−2 behavior is better demonstrated in the plot of Iq2 versus q (after subtraction of the incoherent scattering background), showing a leveling out of the curve at high q (inset). Another revealing feature from these plots is the shallow minimum around q ≈ 0.03 Å−1, which may be attributed to the cross term Score−chain and the large difference in scattering length density between the gold core and the polymer chain (Δρcore−chain ≈ 3.6 × 10−6 Å−2). This small oscillating feature becomes more marked with increasing grafting density N′ and Rg, as can be seen in the case of AuPNIPAM265 (s2) (inset, Figure 2b). Clearly, the hairy-sphere model is better able to describe polymer-coated gold nanoparticles dispersed in a good solvent.

previous section, and the self-correlation term for chains with Gaussian statistics is given by the Debye function40 Pchain(q , R g) =

2[exp(−q2R g 2) − 1 + q2R g 2] (q2R g 2)2

(6)

The cross term between the spherical core and the chain starting at the core surface is given by Score−chain(q , R core , R g) = A sphere(q , R core)Achain (q , R g)

sin[q(R core + R g)] q(R core + R g)

(7)

where Achain(q, Rg) is the amplitude of the form factor of the attached chain41 Achain (q , R g) =

1 − exp( −q2R g 2) q 2R g 2

(8)

The cross term between different attached chains is defined by Schain − chain(q , R core , R g) 2 ⎧ sin[q(R core + R g)] ⎫ ⎪ ⎪ ⎬ A (q , R g ) =⎨ ⎪ chain ⎪ q(R core + R g) ⎭ ⎩

(9)

For a nanoparticle grafted with N noninteracting Gaussian chains, the general expression of the form factor of this hairy sphere is given by40 Phairy sphere(q , R core , R g) = Vcore 2Δρcore 2 Psphere(q , R core) + NVchain 2Δρchain 2 Pchain(q , R g) + 2NVcoreVchainΔρcore Δρchain Score−chain (q , R core , R g) + N (N − 1)Vchain 2Δρchain 2 Schain − chain (q , R core , R g)

(10)

where Vcore and Vchain are the volumes of the core and the polymer chain, respectively, and Δρcore and Δρchain are the differences in scattering length densities between the core and the solvent and between the chain and the solvent, respectively. The variable parameters are Rcore and Rg, with their respective polydispersities, and N. In this model, Rg for the attached 12663



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Figure 3. (a) SANS spectra of Au-PNIPAM in D2O at T ≈ 20 °C: (△) Au-PNIPAM57 (D = 2.7 nm, Rg = 2.5 nm, N′ ≈ 0.2), (◊) Au-PNIPAM265 (s1) (D = 2.3 nm, Rg = 5.2 nm, N′ ≈ 0.5), (○) Au-PNIPAM265 (s2) (D = 4.5 nm, Rg = 5.8 nm, N′ ≈ 0.6). Comparison of Au-PNIPAM57 and AuPNIPAM265 (s1) underlines the effects of different Rg and N′ values at comparable core sizes (D = 2.3−2.7 nm); comparison of Au-PNIPAM265 (s1) and Au-PNIPAM265 (s2) shows the dependence on different core sizes at comparable Rg and N′ values. (b) SANS spectra of (□) Au-PNIPAM154 (s2) (D = 5.0 nm, Rg = 4.0 nm, N′ ≈ 0.3) and (○) Au-PNIPAM265 (s2) (D = 4.5 nm, Rg = 5.8 nm, N′ ≈ 0.6), showing the effects of different Rg and N′ values at larger core sizes (D = 4.5−5.0 nm).

≈ 2.3−8.0 nm, their plasmon peak positions are insensitive to this size effect. However, the amplitude and width of the absorption peak are directly influenced by particle size. In this classical picture, this effect is due to confinement of the free electrons in low dimension: When the particle radius is smaller than the mean free path of the conduction electrons (∼25 nm for bulk gold1,14), the electrons are additionally scattered by the particle surface. Because of this excess scattering, modeling the optical properties of very small particles requires a modification of the bulk gold dielectric function. This was carried out by decomposing the metal dielectric function into two terms: an interband (IB) contribution accounting for the response of the 5d electrons and a free-electron contribution (D), where15,42 ϵ1(ω) = ϵ1IB(ω) + ϵ1D(ω) and ϵ2(ω) = ϵ2IB(ω) + ϵ2D(ω). The free-electron behavior is given by the Drude model, which expresses the real and imaginary parts as1,2,43

The scattering spectra for other Au-PNIPAM samples fitted with the hairy-sphere model are shown in Figures 3a and b. In Figure 3a, the effect of gold-core size at comparable Rg (5.2−5.8 nm) and N′ (∼0.5−0.6 chains/nm2) values can be seen from Au-PNIPAM265 (s1) (Dcore = 2.3 nm) and Au-PNIPAM265 (s2) (Dcore = 4.5 nm), whereas the influence of polymer chain length and grafting density at comparable core size (Dcore = 2.3−2.7 nm) can be seen from Au-PNIPAM57 (Rg = 2.5 nm, N′ = 0.2 chains/nm2) and Au-PNIPAM265 (s1) (Rg = 5.2 nm, N′ ≈ 0.5 chains/nm2). These comparisons show qualitatively the effects of the graft polymer layer: Increasing the chain length increases the object size and the scattering intensity at low q, whereas increasing the grafting density induces a steeper slope in the medium-q range; these effects are also shown for larger particles in Figure 3b. The fitted parameters obtained for all of the samples using the hairy-sphere model are given in Table 2. Table 2. Hairy-Sphere Model Fit Parameters for AuPNIPAM Nanoparticles in Water at T ≈ 20°C sample Au-PNIPAM57 Au-PNIPAM127 Au-PNIPAM154 Au-PNIPAM154 Au-PNIPAM265 Au-PNIPAM265

(s1) (s2) (s1) (s2)

ϵ1D(ω) = 1 −

D (nm)

Rg

grafting density, N′

(TEM)

(nm)

(chains/nm2)

2.7 8.0 3.0 5.0 2.3 4.5

± ± ± ± ± ±

0.2 0.5 0.3 0.5 0.2 0.4

2.5 5.0 4.5 4.0 5.2 5.8

± ± ± ± ± ±

0.2 0.5 0.4 0.4 0.5 0.5

0.2 0.7 0.4 0.3 0.5 0.6

± ± ± ± ± ±

ϵ2D(ω) =

0.05 0.05 0.05 0.05 0.05 0.05

ωp2 ω 2 + ω0 2

and

ωp2ω0 ω(ω 2 + ω0 2)

(11)

In eqs 11, ωp is the bulk plasma frequency, which is related to the metal properties by ωp2 = Ne2/ϵ0m, where N and e are the electron density and charge, respectively, m is the effective mass, and ϵ0 is the vacuum permittivity. ω0 is the bulk scattering rate due to inelastic scattering within the metal and is related to the mean free path of the conduction electrons, Rmfp, and the Fermi velocity, vF, by ω0 = vF/Rmfp. It is thus a constant that characterizes the bulk relaxation or damping frequency for the metal. To introduce size dependence into the metal dielectric function, an extra surface scattering term was introduced1,42

Optical Properties of Gold Nanoparticles Grafted with Polymer Layer. For gold nanoparticles in the size range D ≈ 2−20 nm,1,2 the dipolar approximation of Mie theory predicts the plasmon peak position to be insensitive to particle size, which instead should contribute only to the absorption intensity in the term V. Within this size range, the plasmon band tends to the Fröhlich frequency1,2 (∼520 nm for gold); beyond the upper limit, the condition kD ≪ 1 is not fulfilled, the electric field in the particle can no longer be considered as constant, and higher multipole terms are required in Mie theory. In addition, the contribution from scattering will also become increasingly important in the extinction spectra. In the present study, because the nanoparticles fall in the size range D

ωs =

2gvF D

(12) −1

where D is the particle diameter, vF = 1.4 × 10 cm s is the Fermi velocity for gold,14 and g is a proportionality factor. The value of g is on the order of unity, although a wide range of values has been reported,15 the most reliable measurements being obtained from experiments on single nano-objects to avoid particle-to-particle fluctuations in size.44 The total 8

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Figure 4. (a) Absorption spectra of Au-PNIPAM nanoparticles coated with different molecular chain lengths in water at T = 20 °C; for reference, the dotted line was calculated for bare particles. (b) Corresponding peak positions versus molecular weight of the graft polymer.

Figure 5. Theoretical fits of absorption spectra of Au-PNIPAM nanoparticles in different solvents: (a) Au-PNIPAM57 (D = 2.7 nm; solvent from bottom to top = chloroform, THF, pyridine), (b) Au-PNIPAM154 (s1) (D = 3.0 nm; solvent from bottom to top = water, THF, pyridine), (c) AuPNIPAM154 (s2) (D = 5.0 nm; solvent from bottom to top = water, pyridine), (d) Au-PNIPAM127 (D = 8.0 nm; solvent from bottom to top = chloroform, THF, pyridine). Solid lines represent experimental curves; dashed lines represent theoretical curves. The spectra are vertically separated for better reading.

scattering rate, ω0 + ωs, is then the damping factor that controls the width of the plasmon peak. The term ω0 is very small ( ϵm is the effective dielectric constant that incorporates the polymer layer. A further consequence of the presence of a protective shell layer is the attenuation of the optical sensitivity of the nanoparticle cores to the embedding medium. This effect was studied for alkanethiolate-coated gold nanoparticles by Templeton et al.,23 who observed a decreased sensitivity to solvent with increasing shell thickness. Using an approximate approach, they also provided a convenient expression relating the plasmon peak position to the shell volume fraction, p = [(D/2 + e)3 − (D/2)3]/(D/2 + e)3, provided that the dielectric constant of the shell, ϵs, is constant throughout. This method, however, is more applicable to solid shell coatings, where the shell volume fraction is directly related to its thickness. For solvated polymer layers, this approach cannot be applied directly. Rather, to quantify the SPR peak shifts induced by the polymer shell, more detailed structural information on the shell layer is necessary. The objective here was thus to model the absorption spectra using Mie dipolar theory and, in combination with structural properties such as polymer shell thickness revealed by SANS and core dimension measured by TEM, to gain detailed information on the structure−property relationship and the influence of these properties on solvent sensitivity. Modeling of Absorption Spectra. Our model employs a core−shell configuration, consisting of a gold core and a homogeneous polymer shell, in which the pure-solvent dielectric function, ϵm, is replaced by an effective dielectric function, ϵeff, defined as45 ϵeff =

ϵs(1 − αβ) (1 + 2αβ)

(13)

In this expression, α is the gold-core volume fraction, given by α = (D/2)3/(D/2 + e)3, where D and e are the gold-core diameter and the shell thickness, respectively, and β = (ϵs − ϵm)/(ϵs + 2ϵm), where ϵs and ϵm are the dielectric functions of the shell and bulk solvent, respectively. The new resonance condition is thus ϵ1(ωpeak) + 2ϵeff = 0. Combining this condition with the Drude electron behavior gives ωp2 ωpeak 2 + (ω0 + ωs)2

= ϵ1IB(ω) + 2ϵeff (14) 12666



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brushes46 and confirms the presence of a dense protective layer for the gold core. The fitted parameters for all samples are presented in Table 3.

function of the dielectric constant of the solvent. First, consider the small-size particles dispersed in different solvents, represented by solid symbols: Au-PNIPAM57 (D = 2.7 nm, e = 2.5 nm) (solid squares), Au-PNIPAM154 (s1) (D = 3 nm, e = 4.5 nm) (solid triangles), and Au-PNIPAM265 (s1) (D = 2.3 nm, e = 5.2 nm) (solid circles). As expected, λpeak increases with ϵm, but with a lower slope, depending on the value of p, compared to that predicted for bare particle. The polymer shell thus reduces the sensitivity of the SPR to the solvent dielectric properties, and this effect increases with polymer chain length until the solvent dependence becomes negligible in the case of Au-PNIPAM265 (s1). The solid lines through these three data sets are the theoretical curves calculated using the average polymer concentration evaluated from the individual fits in different solvents. For this series of samples, therefore, for which e ≫ D/2, different chain lengths clearly affect the sensitivity of the SPR peak position to the solvent index. Next, consider the larger-size particles (open symbols): AuPNIPAM154 (s2) (D = 5.0 nm, e = 4.0 nm) (open squares), AuPNIPAM265 (s2) (D = 4.5 nm, e = 5.8 nm) (open inverted triangles), and Au-PNIPAM127, (D = 8.0 nm, e = 5.0 nm) (open triangles). In this case, where e is on the order of D/2, one has to take into account penetration of the solvent into the shell. One approach is to consider an effective “dry” shell thickness: eeff = eϕp, where e is the solvated shell thickness obtained from SANS and ϕp is the polymer concentration in the shell deduced from theoretical fits to the optical spectra. The corresponding shell volume fraction, p, for the composite particle is then replaced by p = [(D/2 + eeff)3 − (D/2)3]/(D/2 + eeff)3. The λpeak values for these larger particles can now be grouped together with λpeak for the smaller particles by their p values. The different samples with their various structural characteristics can now be seen to be consolidated into three populations: p ≈ 0.6 ± 0.1, p ≈ 0.8 ± 0.1, and p ≳ 0.9. With increase in p, the slope of λpeak versus ϵm decreases until it becomes negligible at p ≳ 0.9. In this case, the plasmon mode is considered to be “frozen” in by the polymer shell and completely loses sensitivity to the external medium. The polymer-induced modifications in the SPR behavior of the composite particle can thus be understood by considering the effective shell thickness. Under the new resonance condition ϵ1(ω) + 2ϵeff = 0, it can be further shown that the shell-thickness dependence of λpeak is given by45

Table 3. Fitted Parameters for Au-PNIPAM Nanoparticlesa Dispersed in Different Solvents at T = 20 °C solvent

λpeak (nm)

ϵs

ϕp

Au-PNIPAM57 (D = 2.7 nm, e = 2.5 nm) water 526 1.83 0.11 chloroform 528 1.90 0.17 THF 531 2.02 0.14 pyridine 537 2.25 − Au-PNIPAM127 (D = 8.0 nm, e = 5.0 nm) chloroform 532 2.03 0.48 THF 533 2.10 0.44 pyridine 536 2.22 − Au-PNIPAM154 (s1) (D = 3.0 nm, e = 4.5 nm) water 530 1.88 0.22 chloroform 532 1.92 0.21 THF 532 2.02 0.14 pyridine 537 2.22 − Au-PNIPAM154 (s2) (D = 5.0 nm, e = 4.0 nm) water 527 1.92 0.30 pyridine 537 2.25 − Au-PNIPAM265 (s1) (D = 2.3 nm, e = 5.2 nm) water 535 1.93 0.32 chloroform 536 1.95 0.28 THF 536 2.05 0.25 pyridine 536 2.23 − Au-PNIPAM256 (s2) (D = 4.5 nm, e = 5.8 nm) water 531 2.00 0.47 pyridine 536 2.22 −

g 1.3 1.3 1.3 1.2 2.5 2.4 2.7 1.4 1.4 1.4 1.2 0.9 1.2 1.3 1.4 1.3 1.2 1.4 1.4

a

D is the gold core diameter from TEM, and e is the thickness of the graft polymer layer from SANS.

From the ensemble of results obtained for different gold-core sizes, polymer chain lengths, and concentrations in the protective shell, the following observations can be made on the optical properties in relation to their physical structures: The plasmon peak position (λpeak) depends on ϵm and ϵs. Figure 6 shows λpeak for different Au-PNIPAM samples as a

Δλpeak (e) max Δλpeak

=

p 1 + 2(1 − p)(ϵs − ϵm)/(ϵs + 2ϵm)

(15)

where p is the shell volume fraction of the composite particle, Δλpeak(e) = λpeak(e) − λpeak(0), and Δλmax peak is the maximum peak shift for a particle ranging from ϵm to ϵs (corresponding to a change from a bare particle to a particle coated with an max infinitely thick shell). It follows that Δλ peak (e)/Δλ peak approaches unity as p increases. A plot of the normalized experimental peak shift, Δλpeak(eeff)/Δλmax peak, versus eeff/(D/2) for all of the samples studied in different solvents shows relatively good agreement with this theoretical prediction (Figure 7). From this figure, it can be seen that, for eeff ≈ D/2, max Δλpeak(eeff)/Δλpeak ≳ 0.8; this situation approaches the resonance condition ϵ1(ω) = −2ϵs (for a particle coated with an infinitely thick shell), so that the SPR mode is said to be frozen in by the shell dielectric function ϵs and the metal core loses sensitivity to the influence of the solvent. Thus, in this normalized plot, the relative SPR peak shifts are almost

Figure 6. SPR peak positions versus solvent dielectric constant: for p = 0.6 ± 0.1, (■) Au-PNIPAM57 and (□) Au-PNIPAM154 (s2); for p = 0.8 ± 0.1, (▲) Au-PNIPAM154 (s1), (△) Au-PNIPAM127, and (▽) Au-PNIPAM265 (s2); for p > 0.9, (●) Au-PNIPAM265 (s1). The solid lines are theoretical curves with corresponding average p values, and the dotted line is the theoretical curve for bare particles. 12667



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description of the composite nanoparticle. It is thus possible to express quantitatively the SPR peak shifts and their sensitivity to external solvents in a structure−property relationship. The optical behavior of all of the samples with different core sizes and different graft chain lengths can be consolidated and rationalized according to their effective shell volume fraction p. As p increases, sensitivity to the external solvent dielectric property decreases until, for p > 0.9 (corresponding to an effective shell thickness on the order of the core radius, D/2), the SPR mode is frozen in by the polymer shell; under such conditions, the particle is almost completely screened by the polymer layer and loses sensitivity to the solvent. The peak width of the SPR band is characterized by the proportionality parameter g, which is related to the intrinsic size-dependent surface scattering and inhomogeneous broadening arising from particle and environmental fluctuation effects.

Figure 7. Normalized SPR peak shift versus ratio of effective polymer shell thickness to core size, eeff/R (R = D/2) in (□) water, (○) chloroform, and (△) THF (triangles). Theoretical curves were calculated for water (solid line), chloroform (dashed line), and THF (dotted line).

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Tel.: (33)1 6908 9663. Fax: (33)1 6908 8261.

independent of particle and shell sizes and of the nature of the solvent, as demonstrated by the superposition of the theoretical curves calculated for different solvents. This universal behavior is analogous to the results of theoretical calculations by Jain and El-Sayed47 for silica core−metal nanoshell particles with varying shell thicknesses. It is related to the extension of field enhancement at the SPR in the proximity of a metal nanoparticle (over a distance on the order of its size) and thus serves as a useful guide for the sensing and detection of local environmental changes. The peak width of the SPR is affected by both homogeneous effects, namely, surface scattering due to reduced particle size,15 and inhomogeneous broadening related to particle-to-particle size, shape, and environment fluctuations in ensemble measurements. All of these effects contribute to the broadening of the resonance, and their individual contributions are not easy to separate. As a consequence, the parameter g is used in the analysis only as an adjustable parameter to reproduce the experimental peak width. The deduced values for g are affected by both intrinsic and inhomogeneous effects and cannot be considered as factors characterizing electron−surface scattering, as in single-particle studies.44 The g values obtained with smaller particles (see Table 3) are close to unity, whereas they increase for larger particle diameters; this is attributed to higher inhomogeneous broadening in the larger particles.

Notes

The authors declare no competing financial interest.

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REFERENCES

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CONCLUSIONS Colloidally stable gold nanoparticles (D ≈ 2.3−8 nm) protected with PNIPAM polymers with a wide range of chain lengths (Mw ≈ 6.5K−29.5K) were synthesized using the grafting-to technique in a one-step process. The optical properties of these Au-PNIPAM nanoparticles were studied in different solvents. The graft polymer shell was found to induce a red shift of the SPR peak up to a maximum shift of about 15 nm for the highest polymer-shell volume fraction in water. The absorption spectra were modeled with Mie−Drude dipolar theory taking into account corrections to the sizedependent dielectric function for gold; this allowed the peak position to be modeled in terms of the dielectric function of the polymer shell, ϵs. From ϵs, the concentration of polymer in the solvated shell was deduced. This valuable information, together with the thickness of the solvated layer measured by SANS and the core size measured by TEM, provides a complete structural 12668



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Polymer-Modulated Optical Properties of Gold Sols - The Journal of

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