Synthesis of Mechanically Robust Very High Molecular Weight Polyisoprene Particle Brushes by Atom Transfer Radical Polymerization

Linear polyisoprene (PI) and SiO2-g-PI particle brushes were synthesized by both conventional and activators regenerated by electron transfer (ARGET) atom transfer radical polymerization (ATRP). The morphology and solution state study on the particle brushes by transmission electron microscopy (TEM) and dynamic light scattering (DLS) confirmed the successful grafting of PI ligands on the silica surface. The presence of nanoparticle clusters suggests low grafting density (associated with the limited initiation efficiency of ARGET for PI). Nevertheless, particle brushes with very high molecular weights, Mn > 300,000, were prepared, which significantly improved the dispersion of silica nanoparticles and also contributed to excellent mechanical performance. The reinforcing effects of SiO2 nanofillers and very high molecular weight PI ligands were investigated by dynamic mechanical analysis (DMA) as well as computational simulation for the cured linear PI homopolymer/SiO2-g-PI particle brush bulk films.

temperature and added to cold methanol to precipitate the product.The molecular weight of the polymer was measured by SEC.

Procedures for the synthesis of SiO2-g-PI particle brushes by ARGET ATRP.
Macroinitiator (SiO2-Br nanoparticles), solvents (anisole, DMF), CuBr2, and Me6TREN were mixed thoroughly in a sealed Ace Glass pressure tube.A stock solution of Sn(EH)2 in anisole and purified isoprene in a round flask were prepared, separately.Both mixtures and the isoprene monomers were degassed by nitrogen purging, then the isoprene monomer and the Sn(EH)2 solution were added into the Ace Glass pressure tube to activate the catalyst complex, and the tube was immediately sealed and put into an oil bath set at the desired temperature.The reaction mixture was cooled to room temperature and added to cold methanol to precipitate the product.The molecular weight of the polymer was measured by SEC.
Procedures for fabrication of linear PI homopolymer and SiO2-g-PI particle brush bulk films.
Linear PI homopolymers (L-1) and SiO2-g-PI particle brushes (PB-1, PB-2, PB-3) were dispersed in THF via sonication.5 wt% of dicumyl peroxide (DCP) as a crosslinking agent was added to the solution.After the solution was stirred for 0.5 h, the bulk dispersions were transferred into 15 mm × 5 mm rectangular Teflon molds.The solvent was slowly evaporated over 48 h at room temperature generating transparent nanocomposite films with a thickness of 0.15-0.2mm.The bulk films were transferred to the oven and cured under 160 °C in the N2 atmosphere for 20 minutes.The residual solvent was removed from the bulk films by transferring them to a vacuum oven and slowly increasing the temperature at the rate of 10 °C per 24 h to 120 °C.At least three specific bulk films of the same composition were investigated to systematically study the thermomechanical properties of the nanocomposite films.

Characterization.
Size Exclusion Chromatography (SEC).Number-average molecular weights (Mn) and molecular weight distributions (Mw/Mn) were determined by SEC.The SEC was conducted with a Waters 515 pump and a Waters 410 differential refractometer with PSS columns (Styrogel 105, 103, and 102 Å) in THF as an eluent at 35 °C and a flow rate of 1 mL min -1 .Linear PI and PS standards were used for calibration.

Nuclear Magnetic Resonance (NMR). Polymerization was monitored by 1 H NMR with a Bruker
Advance 500 MHz NMR spectroscopy in CDCl3 solvent.The tacticity of polyisoprene was studied by 13 C NMR with a Bruker Advance 500 MHz NMR spectroscopy in CDCl3 solvent.
Transmission Electron Microscopy (TEM).TEM was carried out using a JEOL 2000 EX electron microscope operated at 200 kV to characterize the morphology and structure of the SiO2g-PI particle brushes, samples were drop cast onto a carbon-coated copper grid.The spatial distribution, radius, and inter-particle distances of the SiO2 nanoparticles were determined from statistical analysis of the TEM micrographs using ImageJ software.TEM was carried out using a Tecnai G2 F30 electron microscope operated at an acceleration voltage of 300 kV to characterize the morphology and distribution of silica of the cured composite samples.Before characterization, an ultramicrotome (Leica EMUC7) was used to make a nanosheet and a freshly cut surface at -65 °C.
Dynamic Light Scattering (DLS).DLS using a Malvern Zetasizer Ultra was employed to determine the number-weighted average hydrodynamic radius and distribution.The SiO2-g-PI particle brushes were suspended in filtered THF (450 nm PTFE filter) at low concentrations (1 mg mL -1 ).
Thermogravimetric Analysis (TGA).TGA with TA Instruments 2950 was used to measure the fraction of SiO2 in the SiO2-g-PI particle brushes.The data were analyzed with TA Universal Analysis.The heating procedure involved four steps: (1) jump to 120 ºC; (2) hold at 120 ºC for 10 min; (3) ramp up at a rate of 20 ºC/min to 800 ºC; (4) hold for 2 min.The TGA plots were normalized to the total weight after holding at 120 ºC.
The grafting density was calculated using the formula (S1).
where fSiO2 is the SiO2 fraction measured by TGA, NAv is the Avogadro number, ρSiO2 is the density of SiO2 nanoparticles (2.2 g/cm 3 ), d is the average diameter of SiO2 nanoparticles (15.8 nm), Mn is the overall number-average MW of the cleaved polymer brushes.

Dynamic Mechanical Analysis (DMA).
Tensile test: the linear PI homopolymers (L-1) and SiO2-g-PI (PB-1, PB-2, PB-3) particle brush bulk films are tested in the tensile mode by using DMA (TA RSA-G2).The film thickness was between 150-200 μm.The samples were stretched at a constant tensile rate of 0.3 s -1 at room temperature.
Glass transition temperature measurement: The glass transition temperature was also measured through dynamic mechanical analysis (DMA, TA RSA-G2) at a constant frequency (1 Hz) in a temperature range of -80 ℃ to 80 ℃, with a heating rate of 3 ℃/min, and application of 0.1% strain.
Damping property measurement: The damping property was measured through dynamic mechanical analysis (DMA, TA RSA-G2) in a frequency range of 0.1-10 Hz at room temperature, with the application of 0.1% strain.All the samples were tested at least three times for consistency.nanoparticles (e.g. 100 mg).After purification, SEC and TGA were conducted to characterize the grafting density of the particle brushes.The particles used in the current study had grafting density ( 0 ) ~ 0.15 nm -2 , the -Br (initiating site) concentration on the surface was assumed the same.Based on the average radius of nanoparticles, 7.9 nm, and density of silica, 2.2 g/cm 3 , the average molar mass of SiO2-Br, is 23,270 g/mol.

Simulation Method.
In this study, the coarse-grain MD simulation was used to study the effect of the structure of the nanoparticles.In this simulation model, different numbers of grafted chains with various chain lengths (D = 1σ) are grafted on the core nanoparticle (D = 4σ).(Scheme S1).To correspond to the experimental section.The grafted amount (Ng) and length (L) of grafted chains are specific, which is shown in Table S1.To allow the modified nanoparticle to reach maximum grafted density, based on Thomson's theory, 4 a numerical method was adopted: a set of points with random velocity and coordinates are constrained on a spherical surface, and then the average distance of the adjacent particles are calculated until the system becomes stable.Iterating the process, the maximum number of points is achieved when the average distance is equal to the diameter of the surficial particles.The maximum number of grafted points is calculated by the following equation: where d is the average distance of the adjacent particles and ri/rj represents particle i and its neighbor j.H is the nearest neighbor function measured by Euclidean distance.
Scheme S1.The schematic diagram of PB-1, PB-2, and PB-3, where red spheres represented the nanoparticle, and gray spheres represented the grafted polymer chains with different lengths.The typical Lennard-Jones (LJ) potential was employed to model the interaction between different types of beads.The formula of the potential is: where rcutoff denotes the distance at which the interaction was truncated and shifted so that the energy and force were zero.Here the interaction range was offset by rEV to eliminate the excluded volume effect of different interaction sites.The interaction parameter (εnp) between nanoparticlematrix is set as 3.5 to endow a measure of the interaction between the nanoparticle and matrix to ensure the dispersion of nanoparticle is uniform, 5 while other ε is set as 1.0.
The bond energy between the connected beads in a polymer chain is represented by a stiff harmonic potential: the bond is set as 2 500( / ) k  = , r0 = 2.5, 1.12, and 1.0, corresponding to the 3 types of bonds: core nanoparticle-grafted chain bead, crosslinked bonds, and other bonds.This setting ensured a certain stiffness of the bonds and avoided high-frequency modes and chain crossing.The chemical cross-linking bonds are generated by a random bonding algorithm, ensuring that all cross-linking bonds will not be generated on the same molecular chain.The number of chemical crosslinking bonds is set as 400. 6 the grafted polymer is not specified, the reduced LJ units ε and σ are used and set to unity, which means that all calculated quantities are dimensionless.In this study, the reduced units of the temperature and the pressure are adopted and defined as follows: where kB is the Boltzmann constant which is equal to 1 for LJ potential.The simulations have been performed under the NPT ensemble where the temperature is fixed at T* = 1.0 and P* = 1.0 by using the Nose−Hoover temperature thermostat and barostat, respectively.Periodic boundary conditions are employed in all three directions.The velocity-Verlet algorithm is used to integrate the equations of motion, with a time step δt = 0.001, where the simulation time is represented by the reduced LJ time τ.All structures are equilibrated over a long time so that each chain has moved at least 2Rg, where Rg is the root mean square radius of gyration of polymer matrix chains.These fully equilibrated configurations are further used as starting structures for production runs during the structural and dynamic analysis.The Second Virial coefficient (B2) of the nanoparticles is also calculated, which is a good indicator of the tendency for NPs to aggregate or disperse, given by: where θ denotes the angle between a given element (two adjoining monomers in the chains) and the reference stretching direction.
The uniaxial tensile deformation has been performed using the protocol implemented in our previous work. 7The box length along the z direction is increased at a constant engineering strain rate, while the box lengths along the x and y directions are reduced simultaneously, to maintain the constant volume of the simulation box.The engineering strain rate is specified as  For the oscillatory shear deformation, the SLLOD equation of motion and the Lees-Edwards "sliding brick" boundary condition, were adopted.The upper XY plane of the simulation box was shifted along the x direction so that each point in the simulation box could be considered as having a ''streaming'' velocity.This position-dependent steaming velocity was subtracted from the actual velocity of each atom to yield a thermal velocity, which could be used for the temperature computation thermosetting.The shear strain was defined as / (0) All the MD simulations were carried out using the Largescale Atomic/Molecular Massively Parallel Simulator (distributed by Sandia National Laboratories). 8 SiO2-Br nanoparticles.The concentration of initiating sites on the surface of silica nanoparticles was determined by model reactions (i.e.polymerization of SiO2-g-PMMA, [MMA]0/[SiO2-Br]0/[CuBr2]0/[Me6TREN]0/[Sn(EH)2]0 = 2000:1:1:10:8 with 45 vol% anisoles, 5 vol% DMF at 60 ºC) with certain amount of SiO2-Br

.
The average stress s in the z direction was obtained from the deviated part of the stress tensor: 1 parameter m is Poisson's ratio, which is equal to 0.5 in the present simulations.
offset dX was the transverse displacement distance in the shear direction from the unstrained orientation, and LZ(0) was the box length perpendicular to the shear direction.The shear rate, n, was set as 0.01/τ, showing one cycle of constant-amplitude oscillation every 100t.The average shear stress was obtained from the deviatoric part of the stress tensor:

Figure S6 .
Figure S6.(a) DSC curves of SiO2-g-PI particle brushes before and after curing, (b)-(d) Plot of deriv.heat flow vs. temperature of SiO2-g-PI particle brushes before and after curing.

Figure S7 .
Figure S7.(a) DSC curves of linear PI homopolymers before and after curing, (b) Plot of deriv.heat flow vs. temperature of linear PI homopolymers before and after curing.

Figure S8 .
Figure S8.Strain-stress curves of SiO2-g-PI particle brush and linear PI homopolymer bulk films: (a) PB-1, (b) PB-2, (c) PB-3, (d) L-1.All samples were measured three times with different bulk films as shown in different color lines in the figures.

Table S1 .
The modeling details of grafted nanoparticles.

Table S2 .
The entanglement network analysis of polymer nanocomposites with various systems