Article pubs.acs.org/Macromolecules
Using Miscible Polymer Blends To Control Depletion−Attraction Forces between Au Nanorods in Nanocomposite Films Michael J. A. Hore and Russell J. Composto* Department of Materials Science and Engineering and the Laboratory for Research on the Structure of Matter, University of Pennsylvania, Philadelphia, Pennsylvania 19104, United States ABSTRACT: To fully utilize their optical absorption and polarizing abilities, the dispersion of Au nanorods (NRs) in a matrix, such as a polymer film, must be controlled. By functionalizing NRs with a polymer brush chemically similar to the matrix, NR dispersion and aggregation can be controlled by varying the ratio of brush (N) to matrix (P) chain length. For P/N > 2, aggregates containing mainly side-by-side arrangements of NRs are observed. Here, polystyrene (PS) functionalized Au NRs are incorporated into miscible thin film blends of PS and poly(2,6-dimethyl-p-phenylene oxide) (PPO) (P/N ≈ 30) and characterized using a combination of transmission electron microscopy (TEM) and UV−visible spectroscopy (UV−vis). As the volume fraction of PPO (ϕPPO) increases from 0.00 to 0.50, the NRs remain mainly aggregated; however, at ϕPPO = 0.75 they begin to disperse and finally completely disperse in a pure PPO matrix. Correspondingly, the longitudinal surface plasmon resonance peak undergoes a red shift, consistent with improved dispersion (i.e., individual NRs). A novel outcome of this work is to utilize UV−vis to detect nanometer-scale changes in Au nanorod dispersion. To understand the role of the PPO matrix chains, which favorably interact with the PS brush, self-consistent field theory (SCFT) calculations were performed to determine the brush and matrix density profiles. The brush profile is initially parabolic for ϕPPO < 0.25 and has a thickness that is nearly the radius of gyration of the brush. However, for ϕPPO = 0.50, the brush begins to stretch because of PPO matrix chain penetration. Finally, for ϕPPO = 0.75 and 1.00, the brush thickness increases by about 50%. These SCFT results help interpret the dispersion of nanorods determined from TEM and UV−vis. in the case where χ = 0, such as when the brush and matrix are chemically similar, the nanoparticle assembly depends on the relative values of N, P, and brush grafting density, σ. If P ≫ N, the brush on the nanoparticles rejects the relatively large matrix polymers; hence, this is referred to as the “dry brush” condition. Similarly, a “wet brush” condition corresponds to the case where the brush is interdigitated with the matrix polymer. As the brush evolves from “wet” to “dry”, nanoparticles have been observed to become increasingly aggregated due to depletion− attraction forces.5−14 Because the evolution from a “wet” to “dry” brush is not a thermodynamic phase transition, one objective of this paper is to correlate the brush density profile characteristics from SCFT with the experimentally observed nanorod dispersion. Experimental studies of nanoparticle dispersion in polymer composites have focused on particle dispersion as a function of α = P/N under the assumption that the particles aggregate due to depletion−attraction forces that result from dry brushes. For silica nanospheres, the transition from a dispersed to an aggregated morphology was observed to occur for α ≈ 0.7−1 at low to moderate σ.7,10 More recent experimental studies of Au nanospheres and nanorods have observed a dispersed-toaggregated transition for α = 311 and α = 2,3 respectively, at
1. INTRODUCTION Polymeric materials are attractive hosts for controlling the morphology of nanoparticles that impart these materials with tunable optical absorption, polarizibility, electrical conductivity, and enhanced mechanical properties. For optically active nanoparticles, such as noble metals including gold or silver that typically absorb light due to surface plasmon resonances (SPRs), both the nanoparticle dimensions and ensemble assembly are particularly important.1 For example, aggregated nanoparticles tend to have SPR wavelengths that are shifted compared to that of isolated particles. Furthermore, for anisotropic nanoparticles, the orientation of the nanoparticles with respect to each other is an important variable that impacts the optical absorption for large particle assembliessuch as those in polymer thin films. In particular, for Au nanorods, endto-end assemblies typically display red-shifted longitudinal SPRs (LSPRs), whereas side-by-side assemblies exhibit blueshifted LSPRs.2,3 To improve their miscibility and subsequent dispersion in polymer films, nanoparticles can be grafted with a polymer brush. If the brush/matrix interaction is favorable (i.e., Flory− Huggins parameter, χ < 0), nanoparticles can uniformly disperse throughout the polymer matrix independent of the brush (N) or matrix (P) degrees of polymerization.4 Under these conditions, the free energy of mixing is reduced due to favorable contacts between the miscible brush and matrix, and nanoparticles are effectively repelled from each other. However, © 2012 American Chemical Society
Received: May 16, 2012 Revised: June 25, 2012 Published: July 20, 2012 6078
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moderate to high σ. Furthermore, for Au nanorod/homopolymer composites, optical absorption can be utilized to determine whether Au NRs are dispersed or aggregated. For example, blue shifts in the LSPR wavelength are observed when nanorods align side-by-side in an aggregate.3 The approximate location of the wet-to-dry brush transition has been shown to depend on factors such as the geometry of the surface to which the brush is grafted,8,12 the grafting density σ,11,13 and the ratio α = P/N.3,8,11,13 For example, for planar surfaces, self-consistent field theory (SCFT) calculations have demonstrated that the transition occurs around α = 1. Taking into account the role of grafting density, recent SCFT calculations predict a transition at σ√N ≈ α−0.7 for α < 3.8 These SCFT calculations are in good agreement with experiments by Liu et al.5 and Reiter and Khanna.6 To date, SCFT calculations have consistently found that the wet-to-dry transition on curved surfaces will occur at higher values of α than for planar surfaces.12 Computational studies of nanorods in immiscible polymer blends have demonstrated that they can seed the formation of interesting needle-like morphologies15 or act as emulsifying agents to prevent phase separation of the two polymer components.16 Recent experiments investigating dispersion of CdSe nanorods within immiscible blends of poly(vinyl methyl ether) (PVME) and polystyrene17 have verified these computational studies. Despite the widespread interest in using polymer blends in devices, including organic photovoltaic devices18 and electrochemical cells,19 the dispersion of nanoparticles, in general, and nanorods, in particular, in miscible polymer blends (i.e., χ < 0) has received little attention. Blends of polystyrene and poly(2,6-dimethyl-p-phenylene oxide) (PPO) are a particularly attractive system because PS and PPO are completely miscible and their χ parameter is known.20 Moreover, the interfacial profile of PS brushes on planar surfaces in both a PS and PPO matrix have been previously studied by Char et al.21 We demonstrate here that depletion−attraction forces between polystyrene (PS) functionalized Au nanorods, PS− Au(N), in a PS matrix, PS(P), can be mediated by incorporating poly(2,6-dimethyl-p-phenylene oxide) (PPO) into the matrix. In this study, α ≫ 2. Upon increasing ϕPPO, the morphology evolves from aggregates containing tightly packed, side-by-side NRs to a uniform dispersion in PPO rich films (ϕPPO = 0.75 and 1.00). This evolution in nanorod morphology is accompanied by a red shift of the LSPR wavelength from λ ≈ 739 nm to λ ≈ 780 nm that can be attributed to a decrease in surface plasmon coupling; hence, polymer blends provide a versatile route to tune the morphology of nanorods and consequently optical properties. To interpret experimental results, SCFT calculations were performed to determine the brush and matrix density profiles as a function of ϕPPO. As a result of these calculations, we have obtained, to the best of our knowledge, the first visualization of polymer brush grafted nanoparticles in an attractive polymer blend matrix, i.e., χ < 0. At low ϕPPO, the brush density profiles are parabolic and have a height close to the unperturbed brush radius of gyration (i.e., dry brush). The brush density profile undergoes a significant broadening with increasing ϕPPO (i.e., wet brush). Correspondingly, the PPO matrix chains penetrate deeper into the brush as ϕPPO increases, consistent with our experimental results that show a transition from aggregated to dispersed nanorods over the same range of ϕPPO.
2. EXPERIMENTAL AND THEORETICAL SECTION 2.1. Synthesis of Au NR Nanocomposite Films. The Au NRs (12 × 42 nm) were synthesized using a seed-mediated growth method that has been described previously.3,22,23 Reagents were obtained from Sigma-Aldrich and used as received. Au NRs were then functionalized with thiolterminated polystyrene (thiol-PS) (5 kg/mol; PDI = 1.10; Polymer Source). The functionalization was performed by first centrifuging ∼45 mL of the as-synthesized Au NR solution for 60 min at 8000 rpm (Eppendorf Centrifuge 5804). The supernatant was discarded, and the preciptated Au NRs were redispersed in 250 μL of ultrapure H2O (Millipore). This solution was then pipetted into 8 mL of a 2 mM thiol-PS/ tetrahydrofuran (THF) solution and stirred for 24 h. The resulting solution was centrifuged for 30 min at 8000 rpm, and the precipitate redispersed in 10 mL of chloroform. A final centrifugation was performed before redispersing the Au NR precipitate in 1 mL of a 0.5 wt % PS/PPO/chloroform solution. Thin films (d ≈ 50 nm by ellipsometry) were spin-coated on clean glass substrates and dried in a fume hood overnight. Because nanorods reshape upon thermal annealing,25 and solvent annealing does not affect the nanorod morphology within the films,4 no further annealing was performed. However, on the basis of density functional theory calculations28 and Monte Carlo simulations3 using parameters representative of our experimental system at ϕPPO = 0.00, we believe the nanorod morphologies in our film are representative of equilibrium structures. Furthermore, on the basis of early forward recoil spectrometry (FRES) measurements of PS:PPO blends,20,24 the silicon substrate is assumed to interact similarly with PS and PPO and does not play a role in the formation of the nanocomposite. For the present study, PS having a molecular weight of 152 kg/mol (PDI < 1.05, Pressure Chemical) and PPO having a molecular weight of 42 kg/mol (PDI = 1.35, Polymer Source) were used. We define α = P/N in terms of the degree of polymerization of the PS matrix. Hence, α ≈ 30 for our composites. Transmission electron microscopy (TEM) specimens were prepared by scoring the film with a diamond scribe, floating off small portions in ultrapure H2O, and picking up the pieces on holey carboncoated TEM grids (mesh size 300, Structure Probe, Inc.). UV− vis absorption spectra were measured on an Agilent Cary 5000 spectrophotometer. 2.2. SCFT for a Polymer Tethered Nanorod in a Miscible Polymer Blend. To gain insight into the changes in the structure of the PS brush grafted to the Au NRs, SCFT was used to determine the brush density profile in the presence of a binary polymer blend. SCFT calculations have been successful in capturing the underlying physics in a variety of polymeric systems.8,12,26,27 To date, however, SCFT has not been employed to study polymer-grafted nanoparticles in miscible polymer blends. In the SCFT approach, polymers are modeled as Gaussian chains described by continuous space curves. For example, the configuration of the ith brush chain is described by Rb,i(s), where s varies between 0 at the grafted end and 1 at the free end of the chain. Our system contains a single polymer-grafted nanorod and an incompressible polymer matrix composed of chains with a statistical segment length a and a monomer volume 1/ρ0. The system has a volume V = 40 × 40Rg,b2, where Rg,b = a(N/6)1/2 is the unperturbed radius of gyration of a brush chain. The two components of the polymer matrix are 6079
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assumed to have the same length, αN. The nanorod is grafted with a brush of length N and a reduced grafting density σ* = σN/ρ0Rg,b. For our experimental system, σ* = 2.35 and the nanorod radius Rrod = 3.16Rg,b. For the present calculations, we chose the value of the interaction strength to be representative of a highly miscible system, i.e., χN = −10.00. With these definitions, the partition function of the system containing nb brush chains (i.e., PS), nm matrix chains (i.e., PS), and nPPO “compatibilizing” chains (i.e., PPO) is nb
A=
nm
ln Q PPO[iw+ + iw−]
1 V
Qm =
k=1
exp(−βU0[R b, i(s)] − βU0[R m, j(s)] − βU0[R PPO, k(s)] Q PPO =
− βU1[R b(s), R m(s), R PPO(s)])δ[1 − ϕb̂ − ϕm̂ ̂ ] − ϕPPO
nb
∑∫ i=1
1 V
∂qm(r, s)
∫ dr qPPO(r, s = αN )
(10)
(11)
∂qPPO(r, s)
ds δ(r − R b, i(s))
(9)
= ∇2 qm(r, s) − [iw+(r) − iw−(r)]qm(r, s)
∂s
N
0
∫ dr qm(r, s = αN )
where the propagators qm and qPPO obey Feynman−Kac equations
(1)
In eq 1, ϕ̂ b, ϕ̂ m, and ϕ̂ PPO are the dimensionless microscopic densities of the brush, matrix, and PPO, respectively, and are defined as 1 ϕb̂ (r) = ρ0
(8)
where C = ρ0V/N. Qb, Qm, and QPPO are the partition functions of a single chain of the brush, PS matrix, and PPO matrix, respectively. For the matrix chains, the partition functions are defined as
nPPO
j=1
⎤
∫ dr ⎢⎣ χ1N w−2 − iw+⎥⎦ − ϕb ln Q b[iw+ − iw−]
− ϕmα −1 ln Q m[iw+ − iw−] − ϕPPOα −1
∫ ∏ +R b,i(s) ∫ ∏ +R m,j(s) ∫ ∏ +RPPO,k(s) i=1
⎡
/ 1 = kBTC V
(2)
= ∇2 qPPO(r, s) − [iw+(r) + iw−(r)]qPPO(r, s)
∂s
(12)
ϕm̂ (r) =
1 ρ0
̂ (r) = ϕPPO
nm
∑∫ i=1
1 ρ0
with the initial condition qm(r,s = 0) = qPPO(r,s = 0) = 1. Equations 11 and 12 are solved using a pseudospectral operator splitting method on a spatial mesh (Mx = 512) having Δx = Δy = Lx/Mx = 0.08 and with a contour step size of Δs = 0.005 along the polymer chains. Because one end of the brush chain is grafted to the nanorod surface, the single chain partition function is defined as
αN
ds δ(r − R m, i(s))
0
nPPO
∑∫ i=1
(3)
αN
0
ds δ(r − R PPO, i(s))
(4)
where α = P/N. U0 corresponds to a harmonic potential between adjacent monomers in each polymer chain and for a continuous Gaussian chain of species l is commonly modeled as βU0[R l , i(s)] =
3 2a 2
∫0
Nl
ds
∂R l , i(s)
Qb =
(5)
ϕb(r) =
βU1[R b(s), R m(s), R PPO(s)] = v0χ
∫
(13)
where satisfies eq 11 subject to the same boundary conditions as qm(r,s), and qb(r,s) satisfies eq 11 with the initial condition qb(r,0) = δ(r − Rrod), which fixes the end of the brush chain to the surface of the nanorod. With these definitions, the polymer density profiles are calculated as
where a is the statistical segment length. Similarly, U1 describes interchain interactions and can be described by a Flory model
̂ (r) dr ([ϕb̂ (r) + ϕm̂ (r)]ϕPPO
∫ dr qb(r, s)qb†(r, N − s)
q†b(r,s)
2
∂s
1 V
ϕm(r) =
(6)
ϕb Qb
∫0
N
ds qb(r, s)qb†(r, N − s)
1 − ϕb − ϕPPO Q mα
∫0
(14)
αN
ds qm(r, s)qm(r, αN − s) (15)
The delta function in eq 1 enforces the incompressibility of the polymer system. Because the partition function in eq 1 is both numerically and analytically intractable, this function is transformed into a field theory using a combination of delta function and Hubbard−Stratonovich transformations, resulting in a partition function of the form A=
∫ +w+ ∫ +w− exp(−/[w+(r), w−(r)])
ϕPPO(r) =
ϕPPO
∫ α 0
Q PPO
αN
ds qPPO(r, s)qPPO(r, αN − s) (16)
At equilibrium a single configuration of w+ and w− (w*+ and w*_, respectively) is assumed to dominate the functional integral of eq 7, which is the commonly used self-consistent field theory approximation. Under this approximation, the functional derivatives of / with respect to the auxiliary fields are set to zero
(7)
where the Hamiltonian / is a functional of two auxiliary fields, w+ and w−. Under the condition that χ < 0, the Hamiltonian is given by
δ/ = 1 − ϕb(r) − ϕm(r) − ϕPPO(r) = 0 δw+ 6080
(17)
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Figure 1. (a) Polymer brush (solid lines) and matrix (dashed lines) density profiles as a function of distance from the nanorod surface for a similar brush/matrix system (χ = 0). Solid lines from botton to top at (h − Rrod)/Rg,b = 0 correspond to α = 1, 2, 3, and 6, respectively. The dashed lines from top to bottom correspond to the density profiles of the matrix polymer for α = 1, 2, 3, and 6, respectively. The dot-dashed lines are the density profiles calculated for a planar surface (α = 3). The inset defines the geometry of the calculation in terms of h and Rrod. (b) Density of the matrix polymer at the nanorod surface plotted as a function of α. The dashed line is a guide to the eye.
δ/ 2 * = ϕb(r) + ϕm(r) − ϕPPO(r) − w− = 0 δw− χN
In this section, SCFT calculations for the “chemically similar” brush/matix system show that subtle changes in the density profiles can lead to a wet to dry brush transition as α increases from 1 to 6. Then, starting with a PS brush/PS matrix that exhibits aggregated nanorods (α ≈ 30), NR morphology and UV−vis absorption studies are presented to show whether the addition of a matrix polymer that favorably interacts with the brush, while being miscible with PS, can induce the NRs to disperse. A related question is to determine the volume fraction of “compatibilizing” agent that must be added to produce a dispersion of NRs. Finally, in the discussion in section 4, the SCFT model is used to show how the density profiles of the brush and matrix polymers (i.e., similar and dissimilar to the brush) depend on the matrix composition. The brush height and excess of the compatibilizing polymer from SCFT provide new insight into the experimental conditions that produce well dispersed nanorods by controlling depletion−attractions in a polymer blend matrix. 3.1. SCFT Description of Au Nanorods in a Chemically Similar Polymer Matrix. We showed previously that PSfunctionalized Au NRs will aggregate in PS thin films for α = P/ N > 2 at grafting densities between 0.15 and 0.53 chains/nm2.3 This aggregation was attributed to a combination of depletion− attraction forces due to autophobic dewetting of the brush and matrix and van der Waals interactions between the nanorods. For σ* = 2.35 and Rrod = 3.16Rg,b, Figure 1a shows the results of SCFT calculations to determine the polymer brush density profiles as α increases from 1 to 6 (solid lines) on a curved nanorod surface as well as the profile on a planar surface for α = 3 (dot-dashed line). In all cases, the brush profiles are parabolic. The brush on the nanorod is wet by the polymer matrix as compared to the planar brush.8 As α increases, the density of the brush at the nanorod surface, ϕb(0), increases and the interface becomes correspondingly sharper. For all values of α, however, the density profiles remain parabolic. The matrix profiles reflect subtle changes in the brush density. While the demarcation between a “wet” and “dry” brush can be ambiguous,8,12 the effect of α on the polymer brush can be quantified by the brush density at the nanorod surface or, correspondingly, the density of the matrix at the nanorod surface, ϕm(0). As α increases, ϕm(0) decreases due to the entropic penalty for the polymer matrix to locate within the
(18)
w+* and w−* are determined using a Picard iterative scheme:12 w+*(r)new = w+*(r)old + λ+[1 − ϕb(r) − ϕm(r) − ϕPPO(r)] (19)
⎡ w−*(r)new = w−*(r)old + λ−⎢ϕb(r) + ϕm(r) − ϕPPO(r) ⎣ −
⎤ 2 * w− (r)old ⎥ ⎦ χN
(20)
For the present calculations, we set λ+ = λ− = 0.05. The fields are iterated until the mean-squared error in w+ and w− is less than 1 × 10−4.12
3. RESULTS Previously,3 we investigated the dispersion of Au NRs having a brush that is similar to the matrix polymer. These data were reduced to “dispersion map” which denotes combinations of brush (N) and matrix (P) degrees of polymerization that lead to aggregated (α = P/N > 2) and dispersed (α < 2) NRs. Here we present SCFT calculations that support these experimental findings and then in the Discussion section show that SCFT is a powerful method to model the density profiles in a more complex matrix, consisting of a binary mixture of athermal and attractive chains. One of the important outcomes of the SCFT approach is to provide a thermodynamic underpinning to understanding the interactions that lead to Au NR dispersion and aggregation. For all brush/matrix systems, excluded volume interactions and chain stretching that act to stretch and compress the brush, respectively, are balanced. For a binary matrix of two chemically distinct polymers, the thermodynamic contributions also include enthalpic interactions between the brush and each component of the matrix as well as interactions between the matrix polymer. If one matrix polymer interacts more favorably with the polymer brush, this matrix polymer will penetrate more deeply into the brush than the other matrix polymer, although this demixing in the interfacial region is limited by the loss of positional entropy. 6081
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Figure 2. Transmission electron micrographs of PS−AuNRs in PS/PPO films (thickness d ≈ 50 nm). The volume fraction of Au NRs is ϕrod ≈ 0.05. (a1) Corresponds to ϕPPO = 0.00 and shows high magnification images that highlight the side-by-side aggregation and uniform interrod spacing (∼7 nm). (a2) Shows a lower magnification image that captures the aggregate distribution. (b−e) correspond to ϕPPO = 0.25, 0.50, 0.75, and 1.00, respectively. The scale bars are 200 nm.
brush. Hence, the brush becomes increasingly dry as α increases. The largest change in the brush profile occurs between α = 1 and α = 2, where ϕm(0) decreases by 25%. This observation is consistent with experimental studies which show that the aggregation of nanoparticles is typically found near α ≈ 2. Note that for α > 3 ϕm(0) decreases very little as α increases and is almost constant. Although the changes in the brush profile shape appear small, subtle changes in the brush profile are found to have a large effect on the interrod attraction strength. The SCFT density profiles are in qualitative agreement with previous DFT calculations by Frischknecht,28 who demonstrated that small changes in the brush volume fraction can lead to depletion− attraction forces that are large enough to cause aggregation of nanorods. Similarly, calculations by Matsen and Gardiner8 on planar brushes observed that increasing α leads to an increasingly dry brush. The changes in the density profiles were subtle, yet can led to large depletion−attraction forces between planar surfaces. 3.2. Dispersion of Au Nanorods in Miscible Polymer Blends. Whereas in the chemically similar brush case, aggregation of nanorods is expected for α > 2;3 here we show that a polymer blend containing a favorable matrix polymer can be used to drive dispersion. For example, we previously observed that poly(ethylene glycol) (PEG) functionalized gold nanorods will disperse in poly(methyl methacrylate) (PMMA) matrices independent of α because of the favorable interaction between PEG and PMMA.4 Hence, by adding PPO to a PS matrix, favorable enthalpic interactions between the brush and PPO matrix can be utilized to drive dispersion.
Figure 2 contains TEM micrographs of polystyrene-functionalized Au NRs (PS−Au NRs, ϕrod ≈ 0.05) dispersed in blends of polystyrene (PS) and poly(2,6-dimethyl-p-phenylene oxide) (PPO), with which PS is miscible in all proportions. For these composites, α ≈ 30. In Figure 2a, the matrix is pure PS (ϕPPO = 0), and in agreement with previous work, the Au NRs are found in aggregates, containing mainly side-by-side aligned NRs. The alignment of NRs in the aggregates are highlighted in Figure 2a1, which contains higher magnification images of selected aggregates. Note that very few nanorods are observed to exist outside the aggregates as single, isolated nanorods (cf. Figure 2a2). Furthermore, the spacing between adjacent nanorods (≈ 7 nm) in these aggregates is very uniform. Upon adding 25% PPO, the nanorods remain mainly in aggregates, as shown in Figure 2b. For ϕPPO = 0.50 the morphology is similar to Figure 2b. However, the nanorod aggregates appear smaller and more isolated nanorods are observed for ϕPPO = 0.75 (cf. Figure 2d). For ϕPPO = 1.00 (Figure 2e), the nanorods are uniformly dispersed throughout the film, reminiscent of PEG-functionalized Au NRs in PMMA, where χ is favorable, or PSfunctionalized Au NRs in PS, where α < 2 and the brush is “wet”.3,4 3.3. Optical Absorption of Au Nanorods in Miscible Polymer Blends. The dispersion of Au NRs in a polymer matrix affects the wavelengths at which surface plasmons are excited. Relative to the position of individual particles, the longitudinal surface plasmon resonance wavelength (LSPR) will red-shift if pairs of Au NRs are aligned end-to-end and blue-shift if the Au NRs are arranged side-to-side. Furthermore, the magnitude of the shifts in LSPR wavelength depends on the 6082
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Figure 3. Spectroscopic analysis of PS−AuNR nanorods in PS/PPO thin film blends. (a) UV−vis spectra for ϕPPO = 0.25 (black), 0.50 (red), 0.75 (violet), and 1.00 (blue) (left to right). (b) The longitudinal surface plasmon resonance (LSPR) wavelength undergoes a red shift as ϕPPO increases, as noted by the arrow in (a). The largest shift corresponds to a transition from aggregated (ϕPPO = 0.50) to dispersed (ϕPPO = 0.75). λ0 = 739 nm. The dashed line is a guide to the eye.
distance separating the nanorods.2 These shifts have been observed in larger ensembles of Au NRs in films of PS and poly(2-vinylpyridine) (P2VP).3,29 The UV−vis spectra and the relative LSPR wavelength shift, Δλ/λ0, are shown in Figure 3. The LSPR wavelength position is representative of the dispersion and local orientation of the nanorods. Because nanorods aggregate side-by-side and exhibit a narrow (≈ 7 nm) uniform inter-rod spacing, substantial surface plasmon coupling between nanorods can occur, leading to a blue-shift the LSPR peak. No significant red-shift in the LSPR wavelength is observed for ϕPPO < 0.50, which supports TEM observations that the Au NRs remain aggregated at ϕrod = 0.25 and 0.50. However, for ϕPPO ≥ 0.50, the LSPR wavelength undergoes a red-shift from λ ≈ 739 nm to λ ≈ 780 nm, which reflects a reduction in Au NR aggregation and an increase in smaller aggregates and/or isolated nanorods. While the dotted line in Figure 3b serves only as a guide to the eye, the sigmoidal shape of Δλ/λ0 versus ϕPPO provides insight into the changes in nanorod dispersion. In particular, for ϕPPO < 0.50, the nanorods remain aggregated and, therefore, the optical absorption spectra are similar. As shown in Figure 2, for ϕPPO > 0.50, the dispersion of Au NRs increases, and as a result, the red-shift of the LSPR increases strongly, as shown in Figure 3b. If the matrix is PPO-rich (ϕPPO > 0.75), the Au NRs are mainly dispersed, as shown in Figure 2d,e. Correspondingly, the LSPR wavelength does not increase very much upon increasing ϕPPO from 0.70 to 1.00. The agreement between the TEM images of morphology and the UV−vis spectroscopy results provides a simple analytical tool to determine Au NR dispersion. Moreover, by controlling the relative proportions of polymers in a blend, nanoparticle dispersion and interparticle separation can be tuneda result that has implications for developing versitile platforms for single molecule assays.30
4a, the brush density profiles calculated from SCFT are plotted as a function of the dimensionless distance from the nanorod surface, (h − Rrod)/Rg,b for ϕPPO = 0.25, 0.50, 0.75, and 1.00. Note that the pure PS matrix case for α = 3 was already included in Figure 1. As the fraction of PPO in the matrix increases, the brush becomes increasingly wet, as evidenced by the increase in the stretching of the brush into the matrix. Correspondingly, the density of the brush at the nanorod surface decreases as the matrix chains increasingly wet the brush. The shapes of the polymer brush profiles for ϕPPO = 0.00 (dry brush) and ϕPPO = 1.00 (wet brush) are consistent with those calculated on planar surfaces8,26 and measured experimentally.21 The brush height (hb) can be used to quantify how the brush profile depends on ϕPPO and is defined here as the first moment of the brush density hb =
∫R
∞
dx xϕb(x)/ rod
∫R
∞
d x ϕ b( x ) rod
(21)
As shown in Figure 4b, the brush height increases from 1.12 to 1.60Rg,b as ϕPPO increases from 0 to 1.00, respectively. No substantial change in the brush height is observed for ϕPPO < 0.25. In turn, no substantial change in Au NR dispersion is observed, and therefore, no change in the optical absorption is measured. However, for ϕPPO > 0.25, hb begins to increase monotonically as ϕPPO increases. A priori, the Au NRs would be expected to start dispersing as the brush becomes increasingly wet by the matrix, a prediction in qualitative agreement with the TEM images in Figure 2. Corresondingly, because the dispersion is improving, the optical absorption properties are expected to also change. Namely, as ϕPPO increases from 0.25 to 0.75, the LSPR wavelength is expected to red-shift. Note that the largest increase in hb corresponds to the largest increase in Δλ/λ0, as shown by comparing Figures 4b and 3b. Finally, as ϕPPO approaches 1.00, the brush height and LSPR wavelength increase only weakly, as noted in Figures 4b and 3b, respectively. In addition to the brush density profiles, the PS and PPO matrix profiles can be determined by SCFT as a function of ϕPPO. The density profiles for the brush, PS, and PPO matrix polymers are shown for ϕPPO = 0.25 in Figure 4c. In comparison to Figure 1a (α = 3) and Figure 4a (top line),
4. DISCUSSION Depletion−attraction interactions between brush functionalized Au NRs in homopolymer thin films can be tuned by blending a miscible polymer into the matrix. Here, PPO was blended into a PS matrix to tune Au NR dispersion. To further understand how NR dispersion depends on ϕPPO, SCFT calculations were performed using the theory presented in section 2.2. In Figure 6083
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Figure 4. Polymer density profiles of the brush and matrix profiles for α = 3. (a) Polymer brush for ϕPPO = 0.00, 0.25, 0.50, 0.75, and 1.00 (top to bottom). (b) Brush height (hb) plotted as a function of ϕPPO. The profiles for the PS brush (black), PS matrix (red), and PPO matrix (blue) are shown for (c) ϕPPO = 0.25, (d) 0.50, (e) 0.75, and (f) 1.00.
clearly penetrates more deeply into the PS brush, whereas the PS matrix chains only penetrate into the tail region of the brush. At ϕPPO = 0.50, the aggregates with side-by-side nanorods just begin to break up (Figure 2c) and the degree of surface plasmon coupling weakensleading to a small redshift of the LSPR wavelength (Figure 3). When the matrix is PPO rich (i.e., ϕPPO > 0.50), the brush and matrix densities are significantly different compared to the ϕPPO ≈ 0.25. In Figure 4e, the PS brush/matrix interface for ϕPPO = 0.75 has moved farther away from the rod surface and is located at (h − Rrod)/Rg,b ≈ 3, a 50% increase compared to the ϕPPO = 0.50 case. As noted by comparing Figures 4e and 4f, only slight changes to the density profiles are observed upon increasing ϕPPO from 0.75 to 1.00. The increase in matrix PPO leads to a small reduction in the volume fraction of brush
the brush profile is not substantially different from that observed in the pure polystyrene case, ϕPPO = 0.00. In particular, the amount of PS matrix chains in the PS brush is ≈5% more than that for ϕPPO = 0.00. Although χPS/PPO < 0, the conformational entropic penalty caused by increased stretching of brush chains to accommodate the presence of PPO within the brush as well as the cost to demix PPO and PS may explain the small difference between the density profiles at ϕPPO = 0.00 and 0.25. The density profiles for ϕPPO = 0.50 are presented in Figure 4d. Notably, the position of the PS brush/matrix interface, defined at 1/2ϕm(∞), increases from approximately (h − Rrod)/Rg,b ≈ 1.5 to ≈2. Whereas the density profile for the PS matrix maintains a nearly parabolic shape, the PPO density profile decreases weakly from 0.5 in the bulk (ϕPPO(∞)) to ≈0.3 near the rod surface. Thus, at ϕPPO = 0.50, the PPO matrix 6084
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ϕPPO increases, an increasing amount of PPO, relative to the PS matrix, is located in the brush. The preferential segregation of PPO into the brush greatly alleviates the entropic penalty for contact between the PS matrix chains and the PS brush (recall, α = 3), and hence an improvement in dispersion of the Au NRs is observed. Finally in Figure 6, as a visual comparison, the density profile for a PS brush in the favorable PPO matrix (right) is compared to the same brush in a polystyrene matrix (left) that is shown in Figure 1. For both cases, α = 3 and σ* = 2.35. To our knowledge, this is the first calculation of the structure of a polymer brush on a highly curved nanoparticle surface where the brush and matrix have a favorable interaction (χ < 0).
polymer near the nanorod surface and a slight broadening of the brush density profile. The effect of the addition of PPO on the polymer density profiles and, hence, nanorod dispersion, can be further quantified by calculating the excess volume fraction of PPO in the brush ϕexcess =
∫R −
∞
⎧ ϕ [(h − R rod)/R g,b] PPO dh ⎨ ϕPPO(∞) ⎩ ⎪
⎪
rod
ϕm[(h − R rod)/R g,b] ⎫ ⎬ ϕm(∞) ⎭ ⎪
⎪
(22)
where ϕPPO(∞) and ϕm(∞) are the volume fractions of PPO and PS in the matrix far from the nanorod surface. With this definition, ϕexcess = 0 means that the PS and PPO chains in the brush are in equal proportions relative to their bulk values. If ϕexcess > 0, the PPO matrix chains are in excess in the brush, whereas if ϕexcess < 0, excess of PS is observed. The excess volume fraction is plotted in Figure 5 as a function of ϕPPO. For
5. CONCLUSIONS In summary, the dispersion of polystyrene-functionalized Au NRs in thin film polymer blends of polystyrene (PS) and poly(2,6-dimethyl-p-phenylene oxide) (PPO) has been studied using a combination of complementary experimental and theoretical tools to address the question of whether the addition of a compatibilizing agent (i.e., PPO) could drive dispersion of initially aggregated nanorods and, if so, how much of the agent was necessary. Previous studies demonstrated that for α = P/N > 2 PS-functionalized Au nanorods aggregated in a PS matrix due to depletion−attraction forces between the nanorods. The aggregated nanorods were observed to align side-by-side with a very uniform spacing.3 Starting with PSfunctionalized Au nanorods in a PS matrix (α ≈ 30), PPO was added and the nanorod morphology and optical absorption were determined. A surprising result is that a relatively large amount of PPO (ϕPPO > 0.50) is necessary to disperse the nanorods. A corresponding red-shift in the optical absorption is observed as the nanorod dispersion improves. The relative shift in the longitudinal surface plasmon resonance (LSPR) wavelength, Δλ/λ0, increases in a sigmoidal fashion (Figure 3b), which reflects the fact that nanorods remain aggregated for ϕPPO < 0.50, and their dispersion contintues to improve for ϕPPO > 0.50. Self-consistent field theory (SCFT) calculations find that the brush height, hb, follows similar sigmoidal behavior (Figure 4b). A unique outcome of this study is the similar sigmoidal behavior for the shifts in absorption from UV−vis spectroscopy and the increase in brush height calculated from SCFT density profiles. Because UV−vis absorption spectra from the nanorods are very sensitive to the interparticle spacing, and TEM has a relatively limited field of view, optical measurements are shown
Figure 5. Excess of PPO matrix chains relative to the PS matrix chains within the brush region plotted as a function of bulk PPO volume fraction, ϕPPO.
all blends, ϕexcess > 0, indicating an excess of PPO in the brush, despite an entropic penalty for demixing from the matrix. As
Figure 6. Left is a cartoon showing the geometry of the brush taken as a slice perpendicular to the nanorod. The middle and right plots correspond to χ = 0 and χ < 0, respectively, at fixed α = 3. The polymer brush is swollen and correspondingly more diffuse for χ < 0 due to favorable enthalpic interactions with the matrix. The scale on the right denotes brush volume fraction. 6085
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to be a powerful and sensitive tool for determing how the dispersion of Au nanorods improves as PPO is added to the PS matrix. While the TEM image for ϕPPO = 0.50 (Figure 2c) appears very similar to ϕPPO = 0.00 (Figure 2a2) and 0.25 (Figure 2b), the strongest evidence that nanorod dispersion begins to improve with the addition of PPO is provided by the UV−vis measurements, which have nanometer sensitivity to the Au nanorod spacing. SCFT results substantiate this observation and show that near ϕPPO = 0.50 the height of the brush increases, and the brush extends farther into the polymer matriximproving dispersion. Furthermore, SCFT has yielded new insight into understanding the dispersed case where PPO exists in excess in the PS brush. This partitioning of the matrix chains within the brush acts to reduce the entropic penalty for contact between the PS brush and PS matrix chains. Although these studies are fundamental in nature, they have applications for the creation of single molecule assays or nanoparticle-containing organic photovoltaic devices. In addition, the control achieved over the orientation and separation of Au nanorods can be applied to fabricate substrates for surface-enhanced Raman spectroscopy (SERS). This work demonstrates a new route to control the spatial distribution of nanoparticles in two-component, miscible blends, which is of large importance for energy applications. For example, incorporating Au nanoparticles into miscible blends of poly(3-hexylthiophene) and [6,6]-phenyl C61-butyric acid methyl ester (PCBM) has been shown to increase efficiencies in organic photovoltaic cells.31
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AUTHOR INFORMATION
Corresponding Author
*E-mail:
[email protected]. Notes
The authors declare no competing financial interest.
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ACKNOWLEDGMENTS This work was supported by the National Science Foundation with primary support from the Polymer (DMR09-07493), MRSEC (DMR11-20901), and IGERT (DGE02-21664) Programs. Secondary support was provided by NSF/NSEC (DMR08-32802). The authors acknowledge Prof. R. A. Riggleman (University of Pennsylvania) and Dr. A. L. Frischknecht (Sandia National Laboratories) for useful discussions regarding our self-consistent field theory calculations.
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REFERENCES
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