Effect of Crosslink Homogeneity on the High Strain Behavior of Elastic Polymer Networks

Randomly crosslinked networks were synthesized by free-radical polymerization of

Randomly crosslinked networks were synthesized by free-radical polymerization of nbutyl acrylate (monomer) and hexanedioldiacrylate (crosslinker) in toluene.In a typical synthesis targeting a network with a molecular weight between crosslinks (M x ) of 5 kg/mol, butyl acrylate (10 mL, 8.9 g, 69 mmol, 80 eq) and hexanedioldiacrylate (199 µL, 197 mg, 0.87 mmol, 1 eq) were combined in an argon-purged vial.In parallel, 10 mL of a 0.07 M solution of benzoyl peroxide (0.8 eq) in toluene was sparged with argon for 10 minutes.This solution was then injected into the BA/HDD mixture, after which the mixture was vortexed and injected into a circular PTFE-lined mold (Fig. S1).The mold was sealed and placed into an oven at 100 • C for one hour to polymerize the reaction mixture.After polymerization, the samples were removed from the oven, released from the mold, and placed gently into a 3:1 methanol:acetone bath to allow unreacted monomer to diffuse out from the network.
The bath was changed daily for 5 days, after which the network was allowed to dry on the benchtop or in a warm (45 • C) oven under ambient pressure for two days.Once visible signs of residual solvent (e.g.opaque white spots in the sample) were no longer observed, the network was placed in a 50 • C oven under vacuum to make sure the network was completely dry, yielding the final network as a clear, colorless, rubbery material.Samples targeting other crosslinking densities were synthesized following the same general procedure, with the amount of crosslinker needed calculated using where M 0 is the molecular weight of the monomer, n BA is the moles of monomer, M x is the targeted molecular weight between crosslinks, and n HDD is the requisite moles of hexanediol diacrylate crosslinker.The reagent quantities used for all samples reported in this work are summarized Table S1.Tetrafunctional poly(n-butyl acrylate) star polymers used in the synthesis of regular networks were prepared by SET-LRP, as shown in Scheme S2.To activate the Cu(0) source for the catalyst, copper wire was first wrapped around a stir bar and placed in a side-arm round bottom flask under Ar(g).The flask was filled with enough degassed H 2 SO 4 to cover the stir bar.The solution was stirred vigorously under flow of Ar for 10-15 minutes, after which the copper turned a shiny, light orange color.The H 2 SO 4 was then removed from the flask and the flask and stir bar were rinsed with degassed MeOH at least three times to remove any remaining acid.The flask and stir bar were finally dried under flow of Ar(g) and stored under Ar prior to use.In a typical synthesis targeting a 15 kg/mol polymer, CuBr 2 (15.7 mg, 0.1 eq.) was added to the flask containing the Cu-wrapped stir bar under flow of argon.A degassed mixture of n-butyl acrylate monomer (13.7 g, 156 eq.), Me 6 TREN ligand (37.3 mg, 0.24 eq.), and anhydrous dimethyl sulfoxide (1:1 v:v relative to monomer) was cannulated into the flask, after which the tetra-BriB initiator (0.5 g, 1 eq.) was added under flow of Ar.The reaction mixture was stirred at high speed (600 rpm) at room temperature for 12 hours, during which time it changed from a transparent, low-viscosity blue/green solution to a green, cloudy, higher viscosity liquid as the polymers began to phase separate from the DMSO solvent.After 24 hours, the reaction was opened to air to terminate polymerization.

Synthesis of Regularly-Crosslinked Networks
Regularly-crosslinked networks were synthesized by crosslinking the tetrafunctional star polymers using a thiol-bromine click reaction.In a representative synthesis of the network with M x = 26 kg/mol, the precursor tetrafunctional star polymer (BA 52 , 4.25g, 0.08 mmol polymer, 1 eq.),DODT (0.0280g, 0.15 mmol, 2 eq.), MPDA (36.8 mg, 43.6 µL, 5.2 eq.) and anhydrous DMF (16.94 mL) were brought into a glovebox.The polymer and crosslinker were combined, dissolved in 70 % of the total DMF volume (approx.12 mL), and degassed in the glovebox antechamber to remove bubbles formed during mixing.The MPDA was dissolved in the remaining 30% of the DMF, after which both solutions were combined in a falcon tube and gently inverted to mix.The mixture was then poured into a teflon mold, covered with a petri dish to protect from dust, and left in the glovebox to react for for 24 hours.After 24 hours, the samples were removed from the glovebox, gently released from the molds, weighed, and measured.The DMF was then removed by soaking the samples in

Preparation of Double Networks
To synthesize double networks, the network of interest was submerged in a cold (2-4 • C) solution of monomer (1 eq.), hexanedioldiacrylate crosslinker (0.1 meq.), and benzoyl peroxide initiator (0.1 meq.) in an argon-flushed chamber.The networks were held at 2-4 • C and allowed to swell to equilibrium (minimum 2 hours), after which they were removed from the monomer/crosslinker solution under flow of Ar and gently blotted to remove excess monomer.Samples were then placed between two PTFE sheets with a silicone spacer and sandwiched between glass plates.The mold was sealed and placed in an oven at 100 • C for an hour to initiate polymerization of the second network.After one hour, the samples were removed from between the glass plates and placed back in the 100 • C oven overnight to evaporate unreacted monomer and crosslinker.Networks were dried under ambient pressure to avoid formation of bubbles, yielding the final double network as a clear and colorless rubbery material.

Uniaxial Extension Tests
Tensile samples were cut from the fully dried polymer networks using a custom micro dogbone die cutter, with dimensions shown in Fig. S5.The design of the die cutter is adapted from ASTM standard D638 type IV.S1 The resulting tensile samples were then loaded onto

Measurement Repeatability
Tensile tests were carried out on 2-5 dogbones cut from the same bulk sample of each network.While the strain-at-break varied somewhat from replicate to replicate, the shapes of the stress-strain curves were generally repeatable, with all replicates of the same sample having similar moduli and onsets of strain stiffening (Figs.S6-S9).We next assume that the number of chains per unit volume in the un-swollen network is N .After swelling, the number of chains per unit volume is N V 1 V 2 = N/(λ * ) 3 ; in tensile experiments conducted on double networks, this is the chain density in the "un-deformed" state of the double network.If the entropy of each chain with end-to-end distance r is s(r), then the total work of deformation is The stress at extension ratio λ is then For a Langevin chain with n links of length l, where k is the Boltzmann constant and L −1 is the inverse Langevin function (L(β) = coth(β) − 1 β ).Following the chain rule, for a chain pre-stretched to λ * and then subjected to uniaxial deformation to extension ratio λ, S-15 Combining Eqns.7 and 11 and substituting in r 0 = √ nl finally yields as given in the main text.Importantly, we note that this is not the same as replacing λ with λ * λ in the conventional expression for the 8-chain model; especially for networks with relatively short chains (low n) and/or high pre-swelling (large λ * ) it is necessary to include the isotropic pre-swelling in the functional form of the fit to obtain accurate values of n.
Representative fits to this model are shown in Figure S10.As seen in this figure, the model captures the low-strain behavior and the onset of strain stiffening with reasonable accuracy.
At the highest strains, the model predicts stronger strain-stiffening than is observed in the experimental samples; this deviation is likely due to the onset of bond-breakage in this regime.
Scheme S1: Synthesis of randomly crosslinked butyl acrylate networks

Figure S1 :
Figure S1: Schematic of the injection mold used in the synthesis of randomly crosslinked networks.Reaction mixtures were injected into the gap in the 1.3 mm thick silicone spacer, after which the molds were sealed using teflon tape, high temperature electrical tape, and binder clips around the perimeter of the mold.
either (1) an ADMET eXpert 5601-2C or (2) Material Testing Systems Insight Dual Transformer 820 XFMR-DUAL mechanical tester.The modulus of each sample was calculated using a linear fit to the stress-strain data at extension ratios below 1.2 and averaged over 3-5 samples.

Figure S5 :
Figure S5: Dimensions of micro dog-bone specimens used for uniaxial tensile tests.Dimensions are in mm.

Table S1 :
Reagents used in the synthesis of randomly crosslinked networks Sample Monomer a Crosslinker b Initiator c Solvent d