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Polymerization was carried out using the initiator-BPE-fixed chained nanoparticles following our previous report.160, 161 A Pyrex glass tube was charged with Cu(I)Cl (143 mg) as a catalyst (solid). A mixture of the initiator-fixed chained nanoparticle suspension in THF (6.3 wt%, 1.19 g) containing styrene (15 g), ethyl 2- bromoisobutyrate (9.4 mg) as a free initiator, and 4,4’-dinonyl-2,2’-bipyridine (1.18 g) as a ligand for complexation with copper was quickly added to the Pyrex glass tube. The tube was immediately degassed by three freeze–pump–thaw cycles and sealed off under vacuum. The polymerization was carried out in a shaking oil bath (TAITEC Corp., Saitama, Japan, Personal H-10) thermostated at 100 C for 48 h and quenched to room temperature. The reaction mixture was diluted by THF and centrifuged to collect the polymer-grafted chained nanoparticles. The cycle of centrifugation and redispersion in THF was repeated five times to obtain polymer-grafted chained nanoparticles that were perfectly free of unbound (free) polymer. To determine the molecular weight of the graft polymer, polystyrene chains were cleaved from the surface as follows: the polymer- grafted chained nanoparticles (50 mg) and tetraoctylammonium bromide (50 mg), as a phase transfer catalyst, were dissolved in toluene (5 mL), to which a 10% HF aqueous solution (5 mL) was added. The mixture was vigorously stirred for 3 h. The cleaved polymer in the organic layer was subjected to a GPC measurement. The polymerization gave a graft polymer with a Mn of 132 kg/mol and a Mw/Mn = 1.20; Mn and Mw are the

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polydispersity index. The grafting density is ~0.19 chians/nm2 determined by thermalgravimetric analysis (TGA). The final product of the PS-grafted chained nanoparticle (cNP) is shown in Figure 4.1a. To be clear, nanoparticles form aggregates before grafting the PS brush, and thus the brush is grafted around the periphery of the aggregate. There are ~5 individual Fe3O4 nanoparticles per cNP according to image

analysis (Figure 4.1b). A single batch of PS-grafted NPs was used for all the work reported here.

4.2.5 Preparation and characterization of polymer nanocomposites

In this work, a polymer nanocomposite is composed of PS and cNP. We aimed to well-disperse the cNPs in the PS matrix. PS and cNPs were dissolved in toluene separately by stirring for 24 hours. An appropriate amount of the cNP solution was mixed

L d 2 4 6 8 10 0 10 20 Number Percen t # of Single NP/cNP

(b)

(a)

Figure 4.1. (a) Chained nanoparticles (cNP) drop-cast on a TEM grid. The scale bar is 100 nm. (b) Distribution of spherical Fe3O4 nanoparticles per cNP. The solid line is a fit

using a log-normal distribution having an average of 5 nanoparticles per cNP. The inset shows a schematic illustration of a cNP grafted with PS brushes (blue) where the core dimensions are d = 5 nm and L = 25 nm.

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with the PS solution to produce the desired PNC composition, and the mixed solution was stirred for 24 hours. Films were prepared by doctor blading the mixed solution on a heated (100 ⁰C) glass substrate, which allows the solvent to evaporate rapidly. After doctor blading, the film was dried at 100 ⁰C in a hood for 10 minutes, and then was dried under vacuum at ambient temperature for 24 hours. The resulting thickness of the film was about 3 μm as determined by ellipsometry. The sample compositions are reported in volume fraction of iron oxide nanoparticle (ϕcNP) and vary from 0 to 0.024. Given the

grafting density and molecular weight of the PS brushes on the cNP, the sample with ϕcNP

= 0.024 corresponds to 100% PS-grafted cNP in the absence of PS matrix. The distribution of the nanoparticles was observed using transmission electron microscope (JEOL 2100) after cross-sectioning the nanocomposite thin film using a microtome.

4.2.6 Diffusion couple preparation and annealing

The diffusion couple consisted of a thick (~ 3 μm) nanocomposite film covered with a layer of thin dPS film. The nanocomposite film was floated from the glass substrate in water and picked up using a silicon wafer. The nanocomposite film on the wafer was aged at 150 ⁰C for three days in vacuo. The dPS tracer film was spin-coated on a silicon wafer and had a thickness ~25 nm as measured by ellipsometry. The tracer film was transferred from the silicon wafer to the top of the nanocomposite film, forming a diffusion couple. The diffusion couple was dried under ambient conditions overnight, and then annealed isothermally at 170 ± 1⁰C in a vacuum oven. The annealing time was chosen to allow sufficient penetration of the dPS into the matrix, typically ~300 nm. To

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ensure consistency of annealing condition, a control sample of dPS/PS was annealed adjacent to the sample.

4.2.7 Elastic Recoil Detection (ERD)

ERD was used to probe the dPS depth profile in the nanocomposite. Details of ERD have been reviewed elsewhere.138 The measurement was conducted under room temperature. The energy of the incident helium ion (He2+) beam was ~3.022 MeV, and the ion beam intersected the plane of the sample at 15⁰. The energy of the recoiled atom was detected by a solid-state detector. A 10 μm Mylar film was placed in front of the detector in order to filter forward scattered helium that masked the hydrogen and deuterium signal. A low beam current (< 2 nA) was used, and total 10 μC was collected. The ERD spectra of count versus channel were converted to dPS depth profile of dPS volume fraction versus depth. The diffusion coefficient of the tracer was obtained by fitting the depth profile using the one-dimensional (1-D) solution of Fick’s second law for a finite source in a semi-infinite medium.139 The instrumental resolution (σ), or half of the full width at half maximum (FWHM) was captured by the Gaussian function,𝑦 =

[1 𝝈⁄ (2𝜋)1 2⁄ _{] exp (−𝑥}2_⁄2𝝈2_{), where y is the dPS fraction and x is the depth. σ is 40 nm}

and the accessible depth was ~800 nm. The diffusion coefficients obtained in this work were from multiple measurements. Only the depth profiles having a sufficient diffusion length (> 300 nm) were used.

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