High-Transparency Polymer Nanocomposites Enabled by Polymer

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High Transparency Polymer Nanocomposites Enabled by Polymer Graft Modification of Particle Fillers Alei Dang, Satyajeet S Ojha, Chin Ming Hui, clare mahoney, Krzysztof Matyjaszewski, and Michael R. Bockstaller Langmuir, Just Accepted Manuscript • DOI: 10.1021/la5037037 • Publication Date (Web): 14 Nov 2014 Downloaded from http://pubs.acs.org on November 20, 2014

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High Transparency Polymer Nanocomposites Enabled by Polymer Graft Modification of Particle Fillers Alei Dang,1,2,‡ Satyajeet Ojha,1,#,‡ Chin Ming Hui,3 Clare Mahoney,1 Krzysztof Matyjaszewski,3 Michael R. Bockstaller*1 1

Department of Materials Science and Engineering, Carnegie Mellon University, 5000 Forbes Ave., Pittsburgh, PA 15213. 2

School of Materials Science and Engineering, Northwestern Polytechnical University, Xi'an 710072, People's Republic of China. 3

Department of Chemistry, Carnegie Mellon University, 4400 Fifth Ave., Pittsburgh, PA 15213.

#) current address: The Dow Chemical Company, 6600 La Porte Fwy., Houston, TX 77058 ‡) these authors contributed equally to the work

[email protected]; Phone: ++1 412 268 2709; Fax: ++1 412 268 7247

ACS Paragon Plus Environment

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ABSTRACT The role of polymeric ligands on the optical transparency of polymer-matrix composites is analyzed by evaluating the effect of surface-modification on the scattering cross-section of particle fillers in uniform particle dispersions. For the particular case of poly(styrene-racrylonitrile) (PSAN)-grafted silica particles embedded in poly(methyl methacrylate) (PMMA) it is shown that the tethering of polymeric chains with appropriate optical properties (such as to match the effective refractive index of the brush particle to the embedding matrix) facilitates the reduction of the particle scattering cross-section by several orders of magnitude as compared to pristine particle analogs. The conditions for minimizing the scattering cross-section of particle fillers by polymer-graft modification are established on the basis of effective medium as well as core-shell Mie theory and validated against experimental data on uniform liquid and solid particle dispersions. Effective medium theory is demonstrated to provide robust estimates of the ‘optimum polymer-graft composition’ to minimize the scattering cross section of particle fillers even in the limit of large particle dimensions (comparable to the wavelength of light). The application of polymer-graft modification to the design of large (500 nm diameter) silica particle composites with reduced scattering cross-section is demonstrated.

Keywords: Nanocomposite, Brush, ATRP, miscibility, transparency, scattering, effective medium

2


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INTRODUCTION The ability to augment the physical properties of polymer materials while maintaining their advantageous processibility characteristics has rendered polymer nanocomposites one of the most actively researched areas in the field of polymer materials [1-8]. One reason for the particular interest in nano-sized filler particles is the opportunity to achieve desired property enhancements without compromising auxiliary characteristics such as optical transparency [1, 5]. In the absence of optical absorption, the transparency of composite materials is determined by the scattering of light from dielectric (i.e. structural or compositional) heterogeneities. For the special case of nanocomposites based on transparent polymer host materials (e.g. amorphous thermoplastics or resins) the optical transparency is hence determined by the light scattering of particle inclusions [9]. The scattering strength of particle fillers is determined by the particles’ scattering crosssection that – for optically isotropic particles in the electrostatic limit – depends on the particle volume (Vp) and polarizability (α) as Csca ~ Vp2α2 [10, 11]. The dependence of the scattering cross-section on the square of the particle volume (i.e. the sixth power of particle size) renders nano-sized filler particles generally advantageous for the synthesis of

transparent

nanocomposite

materials.

Research

on

optically

transparent

nanocomposites has therefore mostly been focused on establishing the governing parameters that control the miscibility and dispersion of particle fillers in polymeric hosts [12-15]. Various methodologies have been developed to facilitate the formation of thermodynamically stable particle dispersions, either by grafting polymer chains of the same composition but higher molecular than the matrix or by modification of the particle surface such as to enable favorable particle/matrix interactions [16-26]. The reader is 3


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referred to references 16-18 for a comprehensive discussion of the conditions supporting the dispersion of particle fillers in polymeric media. However, while the attainment of uniform dispersion morphologies presents an important aspect in facilitating transparent composite materials, several factors can impede the realization of optical transparency. For example, the physical mechanisms associated with a desired property enhancement may dictate larger particle dimensions such as in the case of mechanical reinforcement that necessitates anisotropic particle fillers with one or two dimensions in the hundreds of nanometer range [5]. For some material compositions, nano-sized particles might not be economically viable or might not exhibit the physical properties that are desired for the particle filler. Furthermore, fundamental limitations in attaining dispersed particle morphologies (for example, particle aggregation induced by cross-linking of composite resins) might prevent the stabilization of uniform dispersed morphologies. In these instances the reduction of the polarizability of embedded particle fillers presents an alternative approach to reduce scattering losses in composite materials. This approach is motivated by the dependence of the polarizability on the dielectric contrast between the material constituents that – in the limit of the electrostatic approximation – may be written as α ~ |(εP – εm)/( εP + 2εm)|, where εP and εm denote the dielectric constant of the particle and matrix, respectively [11]. Note that for non-absorbing materials the dielectric constant is related to the refractive index via ε = n2 [5, 27]. If the dielectric contrast between particle fillers and embedding medium is reduced (for example, by means of suitable design of the microstructure of a multi-component particle) then scattering losses will accordingly decrease. In this context 4


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the application of ‘core-shell chemistries’ has attracted particular interest [28]. For a core-shell particle with linear dimensions less than the wavelength of light the effective dielectric constant can be estimated by homogenization theories that evaluate the physical properties of a composite particle using averaging functions depending on the composition and properties of the constituents [5, 29]. For example, Maxwell Garnett theory (a widely used effective medium model for composite materials with a discrete particulate morphology) yields the effective dielectric constant of a core-shell particle as εeff = εshell[1 + 3fx/(1 – fx)]

(1)

where x = 1/3 (εcore – εshell)/( εcore – 1/3 (εcore – εshell)), εshell and εcore represent the dielectric constant of shell and core, respectively, f = vcore/(vcore + vshell) is the relative core volume and vi = wi/ρi is the volume of component i (with ρi and wi denoting the density and mass of component i) [30, 31]. Hence, if a particle filler with refractive index greater (lesser) than the embedding medium is coated with a shell of lesser (greater) refractive index than the embedding matrix (i.e. ncore > nm > nshell or ncore < nm < nshell) then eq. 1 predicts scattering losses to vanish for core-shell architectures of particle fillers that satisfy neff = εeff1/2 = nm. Equation 1 has been widely applied to the fabrication of particle-filled optical glasses with suitable microstructures to reduce scattering losses [32, 33]. An extension of the indexmatch approach to polymer-matrix composites was presented by Li et al. who demonstrated that the coating of TiO2 particles with a silica shell significantly reduced the light scattering of particles in epoxy-based composites (since in this case nSiO2 < nepoxy < nTiO2) [34]. Bombalski et al. were the first to demonstrate the application of polymer graft modification to facilitate the index 5


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matching of nanoparticles dispersed in organic media [35]. For the particular case of polystyrene (PS)-grafted silica particles (diameter d ~ 15 nm) dispersed in toluene the authors demonstrated that the scattering cross-section of particles was reduced by about three orders of magnitude near to the index-match composition. Polymer-graft modification of particle fillers is a particularly interesting method to facilitate the reduction of optical scattering in polymer nanocomposite materials. This is because polymer grafting is ubiquitously being used to facilitate the compatibilization of particle fillers in polymeric media and hence only adjustments in the type of monomer, grafting density and degree of polymerization need to be made. Demir and coworkers were the first to apply the polymer-graft approach to polymer nanocomposites and demonstrated the increase of transparency of CeO2/PS composites upon grafting of poly(methyl methacrylate) (PMMA) to the surface of particle fillers (nPMMA < nPS < nCeO2) [36]. However, since PMMA and PS constitute an immiscible blend system, no stable particle dispersion could be achieved and hence the optical properties of this system are expected to be sensitive to processing conditions and sample history. The main purpose of the present contribution is to demonstrate the application of surfaceinitiated atom transfer radical polymerization (SI-ATRP) to facilitate the synthesis of indexmatched polymer-tethered particle fillers (in the following called ‘particle brush’ fillers) for the case of miscible graft/matrix compositions and to evaluate the applicability of effective medium theory to predict low-scattering particle brush compositions. The uniform particle dispersion morphology that is facilitated by miscible polymer graft and matrix systems enables the quantitative analysis of the scattering cross-section of embedded particle fillers as function of both particle size and composition. The evaluation of experimental and calculated scattering cross-sections reveals that effective medium theory (as exemplified by Maxwell Garnett theory, see eq. 1) provides reliable predictions of the ‘lowest possible scattering configuration’ up to the largest tested particle dimensions (here d = 500 nm). The results thus highlight the practical 6


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utility of effective medium theory to provide design guidelines for the synthesis of transparent polymer nanocomposite materials.

EXPERIMENTAL METHODS Particle-Brush Synthesis. Small and intermediate sized particle systems (R0 = 7.7 ± 2 nm, 56.6 ± 6 nm,) were obtained from Nissan Chemicals; the large silica particle system (R0 = 246 ± 8 nm) was obtained from Fiber Optic Center Inc. The refractive index of silica particles was provided by the manufacturer as nSiO2 ~ 1.46 – a typical value for fused silica. Methyl-methacrylate (MMA), styrene (S), and acrylonitrile (AN) monomers were obtained from Aldrich and purified by passing through an alumina-filled column. The synthesis of PMMA- and PS-grafted particle brush systems was performed using surface-initiated atom transfer radical polymerization (SI-ATRP) as described previously [37-40]. In a typical synthesis of poly(styrene-r-acrylonitrile) (PSAN)modified silica particles a Schlenk flask was charged with 0.40 g initiator-modified silica nanoparticles (0.477 mmol Br/g silica; 0.19 mmol ATRP initiator sites) and anisole (12.1 mL). The mixture was stirred until 24 h until a clear homogenous mixture was form. Styrene (4.5 mL, 39.7 mmol), AN (1.5 mL, 23.3 mmol) and PMDETA ligand (7.7 µL, 0.04 mmol) were added to the flask. The composition was chosen to result in a final molar composition of the random copolymer of S:AN = 3:1. Purification of product followed previously published methods on SIATRP [25]. Size Exclusion Chromatography (SEC). Molecular weight (MW) and molecular weight distribution (MWD) were determined by SEC, using a Waters 515 pump and Waters 2414 differential refractometer using PSS columns (Styrogel 105, 103, 102 Å) in THF as an eluent (35 °C, flow rate of 1 mL min–1), with toluene and diphenyl ether used as internal references. 7


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Poly(methyl methacrylate) (PMMA) standards were utilized for calibration. Prior to SEC analysis samples were etched with HF (to remove the silica core) in a polypropylene vial for 20 h, then neutralized with ammonium hydroxide, and subsequently dried with magnesium sulfate before SEC injection. It is noted that the neutralization process has to be conducted with caution under liquid nitrogen to dissipate heat. Differential Scanning Calorimetry (DSC). The glass transition temperatures (Tg) of nanocomposites films were determined using a TA Instruments DSC-Q-20. Each sample was heated from T = 60–180 oC at a rate of 10 oC/min. Tg was determined as the temperature corresponding to half the complete change in heat capacity, calculated as the peak maximum in the first derivative of heat flow. Thermogravimetric Analysis (TGA). The polymer weight fraction in particle brush was measured using a TA Instruments Q50 thermal analyzer operating in the temperature range of T = 20–800 °C, under nitrogen, with a heating rate of 10 °C/min. Chain grafting densities were calculated based on the polymer weight fraction and Mn measured by GPC. Fabrication of Nanocomposite Films and Solutions. Particle/polymer composite films of about 1 mm thickness were prepared by film casting from toluene solution after blending appropriate amounts of polymer and particle in toluene resulting in 5% (w/v) solutions of the respective target composition. Relative concentrations were chosen to result in a final number density of particle brushes of NP/V = 8 × 1010. Films were thermally annealed in vacuum for 7 days at T = 125 °C. For liquid systems, particle brush concentration was chosen such as to correspond to a number density of NP/V = 1.8 × 1011 cm-3. Morphological Analysis. Films of composite systems were sectioned using a Leica Ultracut microtome at T = -120°C. The morphology of particle distributions was subsequently determined 8


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by electron imaging of microsectioned films. Imaging was performed by transmission electron microscopy (TEM) using a JEOL EX2000 electron microscope operated at 200 kV. Particle size distributions and interparticle distances were analyzed by analysis of large area electron micrographs using ImageJ. UV-vis Analysis. Transmission of free-standing composite films was measured using a CARY-50 UV–vis Spectrometer (Varian, Palo Alto). Calculation of the Scattering Cross-Section of Embedded Core-Shell Particles. The scattering cross-section of PSAN-tethered particles embedded in PMMA was calculated using core-shell Mie theory assuming constant mass density of the polymer shell and bulk optical properties (corresponding to a reference wavelength of λ = 532 nm). Calculations were performed using Mathematica following a procedure described by Bohren and Huffman [11]. Specifically, the scattering cross section was calculated as sca =

∑ 2

+ 1 | | + | |

(2)

where the sum was truncated when higher order terms contributed less than 0.1% to the final result. In eq. 2 an and bn denote the Mie scattering coefficients for concentric core-shell systems that are defined as

(3)

=

− − − − − −

9


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− ! − − ! = − ! − − !

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(4)

with

" # " − # " # " = " # " − # " # "

(5)

(6) # " " − # " # " ! = " # " − # # " "

Here, m1 and m2 are the refractive index of core and shell relative to the embedding medium, i.e. mi = ni/nm; x = kR0, and y = kb are size parameters (with R0 denoting the core radius and b the overall radius of the core-shell particle calculated based on the assumption of uniform density), and k = 2πnm/λ denoting the modulus of the wave vector at wavelength λ; nm denotes the refractive index of the matrix. ψn(z) and ξn(z) are the Ricatti-Bessel functions (of order n) that are defined in terms of the spherical Bessel functions jn(z) and yn(z) as ψ (z) = zjn(z), χ (z) = zyn(z) and ξn(z) = zhn(z) where hn(z) = jn(z) +iyn(z) denotes the spherical Hankel function of order n. Where appropriate the ‘prime’ sign indicates derivatives.

RESULTS AND DISCUSSION 10


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The material system in our study consists of silica particles grafted with poly(methyl methacrylate) (PMMA), polystyrene (PS), and poly(styrene-r-acrylonitrile) (PS0.7AN0.3) random copolymer with a molar composition of S:AN = 3:1. PS0.7AN0.3 (abbreviated in the following as PSAN) was chosen as graft polymer because of its high refractive index nPSAN = 1.5731 that facilitates index matching of SiO2 to PMMA (since nSiO2 < nPMMA < nPSAN, where nSiO2 = 1.4584, nPMMA = 1.4893 and nPSAN = 1.5731; optical constants are cited for a wavelength λ = 532 nm) and the negative Flory-Huggins interaction parameter χPMMA/PSAN = -0.003 (Chi-value is cited for T = 298K) that enables the uniform dispersion of PSAN-grafted particles within PMMA [43, 44]. PMMA was chosen as graft polymer to support the dispersion of particles within the PMMA matrix without contributing to the total scattering cross-section (PMMA-grafted particles will thus be considered as a ‘reference’ for solid state systems). PS-grafts were chosen in accordance to reference 35 to facilitate index-matching of silica particles to toluene (for liquid state dispersions). Because of the more facile determination of the scattering cross-section of particles dispersed in liquids (using solution-based optical spectrophotometry), the ‘liquid state’ PSSiO2/toluene system will in the following serve as a model system to evaluate the role of polymer-tethering on the scattering properties of dispersed particles. The conclusions will subsequently be applied to evaluate the optical properties of solid polymer composites using a more narrow set of material compositions for the PSAN-SiO2/PMMA system. Three particle systems with radius R0 = 7.7 ± 2 nm, R0 = 56.6 ± 6 nm, and R0 = 246 ± 8 nm were evaluated to determine the role of particle size on the scattering of polymer-tethered particle systems. Tethering of PMMA, PS and PSAN was performed using surface-initiated atom transfer polymerization (SI-ATRP) according to previously published procedures (see also ‘Materials and Methods’ section). The characteristics of materials used in the present study as well as sample acronyms are as follows: PMMA-grafted small particle systems (R0 = 7.7 ± 2 nm)

11


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with grafting density σ ≅ 0.5-0.7 nm-2, and degree of polymerization of surface-tethered chains NG ≅ 40-4000 (sample ID: 8SiO2-MMANG); PMMA-grafted medium large particle systems (R0 = 246 ± 8 nm) with σ ≅ 0.5-0.8 nm-2, NG = 150 and 450 (sample ID: 250SiO2-MMANG). PS-grafted small particle systems (R0 = 7.7 ± 2 nm) with σ ≅ 0.5-0.8 nm-2 and NG = 10-1360 (sample ID: 8SiO2-SNG); PS-grafted medium-sized particle systems (R0 = 29.6 ± 6 nm) with σ ≅ 0.5-0.7 nm-2 and NG = 100-1800, (sample ID: 30SiO2-SNG); and PS-grafted large particle systems (R0 = 246 ± 8 nm) with σ ≅ 0.5-0.6 nm-2 and NG = 130-2100, (sample ID: 250SiO2-SNG). PSAN-grafted small particle systems (R0 = 7.7 ± 2 nm) with σ ≅ 0.6-0.7 nm-2, NG = 10-600 (sample ID: 8SiO2SANNG); and PSAN-grafted large particle systems (R0 = 56.6 ± 6 nm) with σ ≅ 0.5-0.7 nm-2 and NG = 190-450, (sample ID: 60SiO2-SANNG); as well as SAN-grafted large particle systems (R0 = 246 ± 8 nm) with σ ≅ 0.6 nm-2 as well as NG = 230 and 740, (sample ID: 250SiO2-SANNG). Note that all polymer-tethered particle systems are considered to be in the dense grafting regime (with the exception of 8SiO2-S140 and 8SiO2-S158) – this choice was made to reduce the effect of core-matrix interactions on the particle miscibility in liquid and solid embedding media. The characteristics of all particle brush systems are summarized in Table 1. Highlighted with ‘star’ symbols are particle brush compositions that approximately fulfill the index match condition (neff(PS-SiO2) = n(toluene) and neff(PSAN-SiO2) = n(PMMA)) that was estimated using Maxwell Garnett theory (see eq. 1) as φPS = 0.17 and φPSAN = 0.15 for the PS-SiO2/toluene and PSANSiO2/PMMA system (where φi denotes the weight fraction of polymer i), respectively.

Table 1. Characteristics of silica-brush systems with polystyrene (PS), poly(styrene-coacrylonitrile) (PSAN) and poly(methyl methacrylate)(PMMA) graft composition. Sample ID

R0/nm

Mn

Mw

NG

12


σ/nm-2

φ(wt %)

neff#

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*8SiO2-S10

7.7 ± 2

1050

1280

10

0.71

21.1

1.494

8SiO2-S13

7.7 ± 2

1400

1800

13

1.07

33.1

1.515

8SiO2-S80

7.7 ± 2

8400

10000

80

1.01

74.1

1.565

8SiO2-S140

7.7 ± 2

14600

18700

140

0.09

30.9

1.511

8SiO2-S150

7.7 ± 2

15800

18900

150

0.84

81.7

1.573

8SiO2-S158

7.7 ± 2

16500

20400

158

0.06

25.1

1.502

8SiO2-S770

7.7 ± 2

80300

100400

770

0.50

83.2

1.583

*60SiO2-S130

56.6 ± 6

13000

14040

130

0.61

26.5

1.504

60SiO2-S320

56.6 ± 6

33000

40000

320

0.63

47.8

1.535

60SiO2-S400

56.6 ± 6

41000

45920

400

0.61

52.6

1.541

60SiO2-S610

56.6 ± 6

63400

81800

610

0.55

60.4

1.550

60SiO2-S630

56.6 ± 6

65500

82000

630

0.52

59.6

1.549

60SiO2-S1100

56.6 ± 6

115000

146000

1100

0.5

71.4

1.562

60SiO2-S2100

56.6 ± 6

220000

280000

2100

0.47

81.4

1.572

*250SiO2-S360

246 ± 8

36400

44000

360

0.65

19.9

1.494

250SiO2-S520

246 ± 8

52000

59200

520

0.67

26.8

1.505

250SiO2-S1000

246 ± 8

104000

128000

1000

0.49

34.8

1.517

*8SiO2-SAN17

7.7 ± 2

1450

1725

17

0.63

23.7

1.498

8SiO2-SAN600

7.7 ± 2

52000

72500

600

0.67

92.1

1.568

8SiO2- MMA570

7.7 ± 2

570000

649800

570

0.56

91.6

1.488

*250SiO2-SAN230

246 ± 8

20000

25400

230

0.67

12.1

1.480

250SiO2-SAN740

246 ± 8

63000

81300

740

0.65

31.1

1.507

250SiO2-MMA450

246 ± 8

45000

57000

450

0.65

23.5

1.472

#) The effective refractive index of core-shell particles neff are caculated using M-G theory (eq. 1). The refractive index (at λ = 532nm) of the different constituent was assumed to be nSiO2 = 13


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1.4584, nPMMA = 1.4893, nPS =1.5917 and nPSAN = 1.5731 [44]. NG and φ(wt %) denote the degree of polymerization of grafted chains and the polymer weight fraction of the corresponding particle brushes, respectively. The star indicates samples compositions that are approximately indexmatched to the embedding medium (toluene or PMMA).

To quantitatively evaluate the effect of composition on the scattering cross-section of polymertethered particles embedded in organic media the scattering properties of SiO2–SNG particle dispersions in toluene were evaluated using optical spectrophotometry. Note that toluene is a good solvent for PS (as evidenced by the similar Hildebrandt solubility parameters δtol = 8.91 (cal/cm3)1/2 and δPS = 9.3 (cal/cm3)1/2) and hence uniform particle dispersions can readily be accomplished [43]. To avoid contributions of multiple scattering only dilute particle brush concentrations corresponding to a number density of NP/V = 1.8 × 1011 cm-3 were investigated (a system was considered ‘dilute’ if the average particle distance 〈D〉th ≈ (V/NP)1/3 is multiple times the particle diameter). The uniformity of particle brush dispersion was confirmed by dynamic light scattering (results not shown here). Figure 1 depicts the transmittance spectra of the 60SiO2– SNG particle brush series in toluene revealing an inverse relationship between scattering loss and wavelength that is a characteristic feature of scattering processes [45]. Note that the transmittance is drastically increased in case of the near index-matched 60SiO2–S130 brush system (for which the scattering was close to the detection limit) while scattering increases with index mismatch for other brush systems.

14


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Figure 1. Transmittance spectra of 60SiO2-SNG particle brush series dispersed in toluene. Near complete transparency across the visible range is observed for the near index-matched system, i.e. 60SiO2-S130. Green dotted line indicates the reference wavelength for evaluation of the scattering cross section.

The scattering cross-section of the different particle brush series was evaluated at a wavelength of λ = 532 nm from the experimental transmittance (T(λ) = I(λ)/I0(λ) where I and I0 represent the intensity of incident and transmitted light at a respective wavelength) as Csca = -(∆x NP/V)-1 lnT(λ = 532 nm), where ∆x = 10 mm denotes the optical pathlength. Figure 2 compares the calculated scattering cross-section for all SiO2-SNG/toluene systems along with the respective scattering cross section calculated using core-shell Mie theory. The figure reveals that – in agreement with expectation – total scattering increases with particle size; however, Csca sensitively depends on the composition of brush particles. For all particle systems a pronounced reduction of the scattering 15


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cross-section is observed in the vicinity of the ‘index-match’ composition – the reduction corresponds to about three and one order of magnitude for small (d = 15 nm) and large (d = 120 and 500 nm) particles, respectively.

Figure 2. Comparison of experimental (filled symbols) and calculated (open symbols) scattering cross section of 8SiO2-SNG (squares), 60SiO2-SNG (circles), and 250SiO2-SNG (triangles) particle brushes in toluene (NP/V = 1.8 × 1011 cm-3) at λ = 532 nm plotted as function of particle brush composition φPS (= wPS/wtotal). Samples at φPS = 0 correspond to pristine (initiator-functionalized) particle systems. The dotted line indicates the effective medium prediction for index-matched conditions.

Several observations should be highlighted in Figure 2: First, the general trend of the experimental Csca is consistent with the predicted values calculated using the core-shell Mie 16


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model; however, deviations occur for pristine particles (φPS = 0) as well as for high molecular polymer grafts. We attribute the increased scattering strength of pristine (i.e. initiator-grafted) particles to the reduced solubility in the absence of PS-grafts that has been reported before and that also was corroborated by dynamic light scattering [35]. Since Csca ~ Vp2, the total scattering of a number of particles increases upon aggregate formation. The increase of the deviation with particle size indicates that aggregation is more pronounced in the case of large particle systems. A further contribution to the deviation between the experimental and theoretical scattering crosssection for pristine particles could be the neglect of the effect of surface-grafted initiator on the particles’ net refractive index in the calculations of Csca (however, effective medium calculations suggest that the presence of initiator makes only a minor contribution to the particle refractive index in the present material systems) [46]. We rationalize the increased deviation of experimental and calculated scattering cross-section in the limit of high NG as a consequence of the more relaxed chain conformations of high-molecular grafted chains that promote the penetration of solvent into the brush thus rendering the refractive index profile more gradual then the step function profile assumed by the core-shell Mie model. Because steric crowding counteracts the penetration of solvent this effect should be most pronounced for the small (d = 15 nm) particle system as it is indeed observed in Figure 2 [20, 47]. It should be noted that nonuniformity of the particle brush could further amplify this effect [48]. A second observation in Figure 2 is that the variation of the grafting density in case of the 8SiO2-SNG system from dense to sparse (in the case of 8SiO2-S140 and 8SiO2-S158) does not significantly alter the trend of Csca thus suggesting that overall composition rather than the detailed brush architecture is the relevant parameter determining the scattering cross-section (although more data for larger particle systems would be required to draw affirmative conclusions). To further evaluate the scattering properties of embedded particle brushes and to demonstrate the application of the index-match concept to solid polymer-matrix composites the 17


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scattering properties of PSAN-grafted silica colloids dispersed in PMMA were evaluated. Nanocomposite films with a number density of particle fillers corresponding to NP/V = 8 × 1010 cm-3 were prepared by casting films with appropriate composition from toluene solution and subsequent thermal annealing in vacuum at T = 125 °C for 7 days. Composite microstructures were analyzed by transmission electron microscopy to confirm the dispersion of PSAN-grafted particles. Nanoparticle dispersions were considered miscible if no significant formation of particle aggregates was detected and if the average particle-particle distance was comparable to the estimated particle distance for a random particle distribution, i.e. 〈D〉th ≈ (V/NP)1/3. Figure 3 depicts a representative transmission electron micrograph revealing the microstructure of the 250SiO2-SAN230/PMMA for NP/V = 8 × 1010 cm-3. The absence of aggregate structures along with 〈D〉 = 824 nm ≈ 〈D〉th = 893 nm (where 〈D〉 is determined by evaluation of a sufficient number of micrographs such as Fig. 3 to facilitate meaningful sampling) supports the conclusion of a uniform particle dispersion. We note that the dispersion of d = 500 nm sized particles in a high molecular matrix (NPMMA = 9960) is remarkable and attributed to the favorable interactions between PSAN grafts and PMMA matrix that (over)compensate the significant loss in conformational entropy that is associated with the placement of large particle fillers within the polymer matrix [24].

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Figure 3. Representative bright-field transmission electron micrograph depicting the microstructure of 250SiO2-SAN230/PMMA (particle concentration is NP/V = 8 × 1010 cm-3). The absence of aggregate structures along with 〈D〉 = 824 nm ≈ 〈D〉th indicates uniform particle dispersion (see text for more details). Formation of small cavities is observed due to damage of the film during microsectioning (since the particle size approximately equals the section thickness). Scale bar is 5 µm. Inset depicts magnified image revealing dispersed 250SiO2SAN230 brush particles. Scale bar is 600 nm.

The scattering cross-section of 8SiO2-SANNG/PMMA and 250SiO2-SANNG/PMMA blend systems that was determined from transmittance measurements of nanocomposite films with NP/V = 8 × 1010 cm-3 along with the respective core-shell Mie prediction is shown in Figure 4a. The figure reveals excellent agreement between experimental and theoretical values for both particle brush systems. Consistent with the results of the liquid 250SiO2-SNG/toluene system the scattering cross-section of 250SiO2-SANNG is found to decrease by about an order-of-magnitude near the ‘index-match composition’ (indicated by the dotted line). Figure 4b and 4c depict pictures of the film samples for 250SiO2-MMA450/PMMA (Fig. 4b) and 250SiO2SAN230/PMMA (Fig. 4c), respectively, illustrating the increase in transmittance in case of the near index-matched 250SiO2-SAN230 particle brush system (film thickness is 0.5 mm).

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Figure 4. Panel a: Comparison of experimental (filled symbols) and calculated (open symbols) scattering cross-section of 8SiO2-SANNG (squares) and 250SiO2-SANNG (triangles) particle brushes dispersed within PMMA (NP/V = 8 × 1010 cm-3) at λ = 532 nm plotted as function of particle brush composition φPSAN (= wPSAN/wtotal). Samples at φPSAN = 0 correspond to PMMAgrafted particle systems. The dotted vertical line indicates the effective index match condition estimated using eq.1 (see text for more detail). Panel b and c: Pictures of nanocomposite films (film thickness is 0.5 mm) corresponding to 250SiO2-MMA450 (b) and 250SiO2-SAN230 (c).

Note that in case of the PSAN-SiO2/PMMA solid-state system the agreement between experimental and calculated scattering cross-section in the limit of large NG is improved (although for small particle fillers the scattering cross-section is still somewhat overestimated). We hypothesize that the reduced graft interpenetration in case of a high molecular embedding material (as compared to a low molecular liquid matrix in the case of PS-SiO2/toluene) renders 20


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Mie theory more appropriate to predict the scattering properties of solid state particle brush composites. The analysis of the scattering properties of embedded particle brush systems that is depicted in Figures 2 and 4 reveals important insights into the applicability of effective medium theory to predict low-scattering particle brush compositions. In particular, although the total scattering increases for nominally index-matched particle compositions with particle size, the lowest scattering composition predicted by Mie theory conforms well with the respective ‘indexmatch composition’ from effective medium theory. This is illustrated in Figure 5 that depicts the predicted scattering characteristics of PSAN-SiO2/PMMA composites at λ = 532 nm.

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Figure 5. Scattering characteristics of PSAN-SiO2/PMMA composites as function of particle core size calculated using core-shell Mie theory. Panel a: Calculated scattering cross-section (Csca) as function of particle core radius (R0) and composition (φPSAN) at λ = 532 nm. Compositions corresponding to minimum scattering cross-section are highlighted with star symbols. Panel b: Comparison of minimum scattering cross-section of PSAN-SiO2 brush particles (circles) along with corresponding value of Csca for pristine silica particles (squares) calculated as function of 22


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particle size. The relative reduction of the scattering cross-section by means of polymer graft modification increases with decreasing particle size. Panel c: Comparison of the actual minimum scattering composition (determined using Mie theory) for the PSAN-SiO2/PMMA system. The minimum scattering composition fluctuates within about 15% of the effective medium prediction. Panel d: Effect of ‘inversion’ of optical constants of SiO2-PSAN system on the scattering crosssection of particle brushes in PMMA (calculated for λ = 532 nm).

Several important conclusions can be drawn from Figure 5: First, although the composition corresponding to minimum scattering cross-section fluctuates with particle size, the optimum composition remains within about 15% of the effective medium prediction for index-matching up to particle diameters d = 500 nm (see Fig. 5a and 5c). Effective medium theory can thus be considered to provide a reliable guideline for the design of low-scattering particle brush compositions even in the limit of large particle fillers. Second, the efficiency of polymer graft modification to reduce the scattering cross-section decreases with increasing particle size (see Fig. 5b). For example, while a reduction by three orders-of-magnitude is expected in case of 10 nm silica particles, the relative reduction decreases to about one order-of-magnitude in case of d = 500 nm particle fillers. However, it should be noted that a reduction of the scattering crosssection by one order-of-magnitude (i.e. 90%) is still significant as it implies that filler concentrations can be raised ten-fold without incurring additional scattering losses. Systematic evaluation of the scattering cross-section of embedded particle brush systems upon variation of optical constants using Mie theory (not shown here) confirms that the trends derived from Figure 5 for the particular example of PSAN-SiO2/PMMA composites can be generalized to other polymer/particle-brush compositions (such as those shown in Table 2 below). Figure 5d 23


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exemplifies the effect of index variation by contrasting the calculated scattering cross-sections for ‘effective index-matched’ SiO2-PSAN/PMMA with those of a (hypothetical) ‘inverted’ PMMASiO2/PSAN’ composition. The figure reveals that the general trend of Csca is retained; however, overall scattering increases due to increased index contrast between core and matrix. The ability to predict low-scattering particle brush compositions renders effective medium theory a valuable asset for the design of nanocomposite formulations in which desired functionalities that are enabled by an increased inorganic fraction or larger particle dimensions are paired with increased levels of optical transparency. For example, Table 2 presents a compilation of the ‘effective index-match’ compositions for a range of technologically interesting particle fillers and miscible graft/matrix compositions.

Table 2. Calculated composition m(shell)/m(core) of various inorganics for selected compatible polymer graft/matrix compositions satisfying the index-matching condition. The calculation is based on eq. 1 assuming the density of the polymer shell to be equal to the bulk polymer density. 24


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Abbreviations are PMMA: poly(methyl methacrylate), PEO: poly(oxy ethylene), PSAN: poly(styrene-co-acrylonitrile), PLLA: poly(lactic acid), PS: polystyrene, PVA: poly(vinyl alcohol), PAA: poly(acrylic acid), PCS: (4-chlorostyrene), PPO: poly(3, 5-dimethyl-phenylene oxide). core

shell

matrix

m(shell)/m(core)*

BaTiO3

PMMA

PSAN

1.17

BaTiO3

PEO

PMMA

2.92

BaTiO3

PLLA

PMMA

3.93

Al2O3

PMMA

PSAN

0.76

Al2O3

PEO

PMMA

1.84

Al2O3

PLLA

PMMA

2.48

Al2O3

PVA

PAA

13.76

Al2O3

PS

PPO

0.69

ZnO

PMMA

PSAN

0.63

ZnO

PEO

PMMA

1.39

ZnO

PLLA

PMMA

1.88

ZnO

PVA

PAA

8.12

ZnO

PS

PPO

0.49

SiO2

PSAN

PMMA

0.16

SiO2

PAA

PVA

4.82

SiO2

PCS

PS

3.65

TiO2

PMMA

PSAN

3.01

TiO2

PEO

PMMA

5.31

TiO2

PLLA

PMMA

7.16

TiO2

PVA

PAA

61.14

TiO2

PS

PPO

4.90

25


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Diamond

PMMA

PSAN

2.03

Diamond

PEO

PMMA

5.05

Diamond

PLLA

PMMA

6.81

*) optical constants for the calculation were assumed to be n(BaTiO3) = 2.4, n(Al2O3) = 1.765, n(ZnO) = 1.79, n(SiO2) = 1.46, n(TiO2) = 2.95, n(Diamond) = 2.419, n(PMMA) = 1.4893, n(PSAN) = 1.5731, n(PEO) = 1.4539, n(PLLA) = 1.46, n(PVA) = 1.5214, n(PAA) = 1.524, n(PS) = 1.5894, n(PPO) = 1.643, n(PCS) = 1.6098 (adopted from reference 43). Values refer to wavelength λ = 532 nm.

CONCLUSIONS We have analyzed the effect of polymer-graft modification on the scattering cross-section of particle fillers in organic (liquid and polymeric) embedding media by evaluating the effect of polymer tethers on the uniformity of the particle dispersion (i.e. the size of scattering centers) as well as the particle’s net scattering cross-section. Favorable interactions between tethered and matrix chains (as realized in case of PSAN-grafted silica particles dispersed in PMMA) have been shown to be effective in facilitating uniform particle dispersion even in the case of large particle fillers (d = 500 nm) and high molecular polymeric hosts. For uniformly dispersed particle fillers the scattering cross-section can be further reduced by several orders of magnitude (depending on particle size) by strategic choice of the optical properties of the graft layer such that the refractive index of the matrix is within the range defined by the respective values of core and shell constituents (i.e. ncore < nmatrix < nshell or ncore > nmatrix > nshell). Effective medium theory (as exemplified by the Maxwell Garnett model) has been shown to reliably predict particle brush compositions with minimum scattering cross-section. Given the wide range of polymer chemistries that are enabled by recently developed surface-initiated controlled radical polymerization techniques these results should be relevant to the design of novel nanocomposite 26


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formulations that combine optical transparency with novel functionalities imparted by a higher inorganic fraction or larger particle size [47]. As there is no specific requirement for the ‘particle core’ to be inorganic in nature, the concept should be further applicable to the design of transparent polymer blends, for example, for the rubber-toughening of polymer glasses.

ACKNOWLEDGEMENT This work was supported by the National Science Foundation (via grants CMMI-1234263 and DMR-1410845), the Air Force Office for Scientific Research (via grant FA9550-09-1-0169) as well as the Department of Energy (via grant DE-EE0006702). AD also acknowledges support received from China Scholarship Council.

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[45] In the case of small molecular scattering centers Rayleigh’s law predicts Csca ~ λ-4 is expected. [46] Using effective medium models such as eq. 1 it can be shown that the effect of surface bound groups (in the present case propyl-2-bromoisobutyrate) on the particles’ net refractive index is negligible for the systems discussed here. However, it is noted that this conclusion is specific to the present system and a consequence of the small surface-to-volume ratio and particular composition. [47] Chui, C. M., Pietrasik, J.; Schmitt, M.; Mahoney, C.; Choi, J.; Bockstaller, M. R.; Matyjaszewski, K. Surface-Initiated Polymerization as an Enabling Tool for Multifunctional (Nano-)Engineered Hybrid Materials. Chem. Mater. 2014, 26, 745-762. [48] Hakem, I. F.; Leech, A. M.; Johnson, J. D.; Donahue, S. J.; Walker, J. P.; Bockstaller, M. R. Understanding Ligand Distributions in Modified Particle and Particlelike Systems. J. Am. Chem. Soc. 2010, (132), 16593-16598.

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TOC GRAPHICS

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High-Transparency Polymer Nanocomposites Enabled by Polymer

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