Composition-Orientation Induced Mechanical Synergy in Nanoparticle Brushes with Grafted Gradient Copolymers

Gradient poly(methyl methacrylate/n-butyl acrylate) copolymers, P(MMA/BA), with various compositional ratios, were grafted from surface-modified silica nanoparticles (SiO2-g-PMMA-grad-PBA) via complete conversion surface-initiated activator regenerated by electron transfer (SI-ARGET) atom transfer radical polymerization (ATRP). Miniemulsion as the reaction medium effectively confined the interparticle brush coupling within micellar compartments, preventing macroscopic gelation and enabling complete conversion. Isolation of dispersed and gelled fractions revealed dispersed particle brushes to feature a higher Young’s modulus, toughness, and ultimate strain compared with those of the “gel” counterparts. Upon purification, brush nanoparticles from the dispersed phase formed uniform microstructures. Uniaxial tension testing revealed a “mechanical synergy” for copolymers with MMA/BA = 3:2 molar ratio to concurrently exhibit higher toughness and stiffness. When compared with linear analogues of similar composition, the brush nanoparticles with gradient copolymers had better mechanical properties, attributed to the synergistic effects of the combination of composition and propagation orientation, highlighting the significance of architectural design for tethered brush layers of such hybrid materials.

Analysis.Number-average molecular weight (Mn) and molecular-weight dispersity (Mw/Mn) were determined by gel permeation chromatography (GPC) equipped with Polymer Standards Services (PSS) columns (guard, 10 5 , 10 3 , and 10 2 Å) and a differential refractive index detector (Waters, 2410), with THF as eluent at a flow rate 1.00 mL/min (T = 35 °C).GPC traces were processed by WinGPC 8.0 software (PSS) using a calibration based on linear poly(methyl methacrylate) (PMMA) standards.All particle brush samples were etched with hydrofluoric acid (HF) for 12 h, neutralized with ammonia, and then processed through 1 mL neutral alumina column and a 450 nm PTFE filter before GPC measurement. 2Comonomer conversion was determined by proton nuclear magnetic resonance ( 1 H-NMR) measurement.Particle size distributions were determined by using a Zetasizer Ultra (from Malvern Instruments Ltd) at 25 °C with water (for miniemulsion) or THF (for particle brushes, ~10 mg/mL) as dispersant.
Samples were diluted prior to the measurement.Thermogravimetric analysis (TGA) was performed on a TA Instrument TGA 550 using air atmosphere, and the data was processed with TA Universal Analysis software.The heating procedure involved four steps: (1) ramp up at 20 °C/min to 120 °C; (2) hold at 120 °C for 10 min; (3) high-resolution ramp up at 20 °C/min to 800 °C; (4) hold at 800 °C for 5 min.The organic contents of the samples were normalized to the weight loss between 120 °C and 800 °C.The grafting densities were calculated using eq S1: The value of  SiO 2 in the equation is the silica fraction measured by TGA after exclusion of any residual solvent; NA is the Avogadro number;  SiO 2 is the density of silica NPs (2.2 g/cm 3 ); Dcore is the average diameter of silica NPs (15.8 nm); and Mn is the number-average molecular weight of untethered polymeric brushes.
Transmission electron microscopy (TEM) was performed using a Philips Tecnai F20 electron microscope.All samples were dissolved in THF with concentration around 5 mg/mL, and solvent casting on carbon film supported Cu grids.To confirm results obtained from TEM, dynamic light scattering (DLS) described above with THF as dispersant was employed to determine number-averaged hydrodynamic diameter and intensity-weighted distribution.
Surface modification of silica nanoparticles.Silica nanoparticles were modified similarly as described in previous reports. 2,3 pon anchoring the tetherable initiators, 3- standards after cleavage from silica using HF.The inorganic fractions of model particle brushes were determined by TGA.With the molecular weights and inorganic fractions, grafting densities were calculated by eq S1.The acquired average grafting density was assumed to be the accessible initiator densities (though the actual grafting densities may vary according to different monomer types).In this project, the molar concentration of tetherable initiator was determined to be 0.45 initiator molecules per nm 2 of silica nanoparticles (assuming a sphere with a diameter of 15.8 nm).were dissolved in 19.0 mL of ultrapure water.The organic and aqueous solutions were mixed (total volume ≈ 25.00 mL), placed in an ice bath, and homogenized by an ultrasonic probe sonicator, amplitude = 25 % for 1 min (application and rest time of 1 s each, 2 min in total).

General
Nitrogen was bubbled into the miniemulsion for 20 min.The flask was immersed in a 50 ℃ oil bath and then AsAc solution (0.027 g/mL in ultrapure water) was slowly injected by a syringe pump.Mola ratios were as follows: [MMA]0/[BA]0/[SiO2-Br, ≈0.45 Br/nm 2 ]0/[Cu II Br2(TPMA)]0 = 500/500/1/0.8.Samples were withdrawn periodically to follow the comonomer conversion by 1 H-NMR, while Mn and Mw/Mn of final products were determined by THF GPC (with PMMA standards).The final products were recovered by precipitation in methanol, redissolved in THF.
The dispersed samples as solutions in THF were kept, and further purified by ultrahigh speed centrifugation (Eppendorf 5418 Centrifuge, 16000×g for 1 h), dialysis in THF (with a 50kDa cutoff), and then dried in vacuum if necessary for further material characterizations.The average number of silica NPs allocated inside each monomer droplet was estimated from: ( SiO 2 = 7.9 nm).
where the total number of miniemulsion droplets in dispersed media was calculated from: , using total volume of organic phase (MMA, BA, and hexadecane) organic = 5.26 cm 3 from Table 1, and   = Using these values, eq S2 provided   2 / ≈ 11.Reaction conditions are listed as in Figure 1.

Degree of Polymerization Approximation of Particle Brush
Assume scaling of 0.98 and 0.58 based on "concentrated particle brush" (CPB) and "semidilute particle brush" (SDPB), respectively. 5e characteristics of our particle brush (PB) include a core diameter ( 0 ) of ~ 15 nm, particle size based on DLS (  ) of 144 nm, and the surface grafting density ( 0 ) of 0.66 chain/nm 2 .To distinguish the CPB and SDPB regime, we calculate the critical radius (  ) where the transition from CPB to SDPB occur based on Fukuda-Ohno model as follows, 6   =  0  0 * 1 2 ⁄  * −1 (eq S3) Here,  0 * is the reduced grafting density which can be determined from  0  2 , and  * is the reduced excluded volume parameter which is proportional to the excluded volume parameter =  √4 ⁄ (detailed derivation can be found in reference). 6Based on eq S3, the calculated   of our PB is 35.1 nm.This means that   is larger than the core radius ( 0 =  0 2 ⁄ ) and is smaller than the particle radius ( =   2 ⁄ ).Therefore, PB consists of both CPB and SDPB regimes.
To determine the degree of polymerization (N), this can be derived from the known size of the polymer shell, ℎ =  −  0 .Applying the previously obtained scaling from DLS of 0.98 and 0.58 in CPB and SDPB, respectively, gives: −  0 =   0.98 + ( −   ) 0.58 (eq S4) where the first term on the right-hand side corresponds to CPB and the second term to the SDPB.  is the critical degree of polymerization corresponding to   whereas  is the segmental length of the polymer shell.Since the length from particle core surface to CPB-SDPB transition can be determined from the known CPB scaling (i.e.,   −  0 =   0.98 ), we can rewrite eq S4 to then obtain the following: is approximated as 0.65 nm based on the known statistical segment length of PMMA. 7,8 h these known parameters, we can calculate  to be 1110.
BiBSiCl), the surface-modified silica nanoparticles dissolved in methyl ethyl ketone underwent four cycles of dialysis (3 times methanol, 1 time acetone in dialysis bag with a 10 kDa cutoff) to remove the untethered initiators and other impurities.After dialysis, small scale SI-ATRP model reactions were completed separately at least three times to roughly calculate the accessible initiator density.Reaction conditions: SiO2-Br 0.03g, MMA 3 mL, 50 vol% in anisole, CuBr2 catalyst (in DMF, 0.005 g/mL) 200 ppm compared to monomer, [CuBr2]:[Me6TREN]:[Tin II ] = 1:3:5, 50 ℃, 40 min reaction.The molecular weight of grafted brush layer was tested by THF GPC with PMMA Figure S1.Volume-based average hydrodynamic size distribution by dynamic light scattering

3 (
average radius of droplets was estimated as r  = 58 nm, according to the average hydrodynamic diameter measured by DLS).

Figure S2 .
Figure S2.Comonomer conversions as a function of copolymerization time (a, c, e, g, i), and

a
Figure S3.Digital photos of dried dispersed (the left 4 vials, mtotal = 3.0830 g) and residue

Figure S5 .
Figure S5.Young's modulus and toughness of dispersed and "gel" particle brush films

Figure S9 .
Figure S9.Thermal analysis by differential scanning calorimetry (DSC) on spontaneous gradient