supplementary information · sergei s. sheiko. 1* 1. department of chemistry, university of north...

Mimicking biological stress-strain behavior with synthetic elastomers

Mohammad Vatankhah-Varnosfaderani,1 William F. M. Daniel,

1 Matthew H. Everhart,

1 Ashish

Pandya,1 Heyi Liang,

2 Krzysztof Matyjaszewski,

3 Andrey V. Dobrynin,

2* Sergei S. Sheiko

1*

1Department of Chemistry, University of North Carolina at Chapel Hill, North Carolina, 27599,

USA 2Department of Polymer Science, University of Akron, Akron, Ohio, 44325-3909, USA

3Department of Chemistry, Carnegie Mellon University, 4400 Fifth Avenue, Pittsburgh,

Pennsylvania, 15213, USA

S1 Synthesis and Characterization

S1.1 Materials. n-Butyl acrylate (nBA, 99%) and methyl methacrylate (MMA, 98%) were

obtained from Acros and purified using a basic alumina column to remove inhibitor. Potassium

tert-butoxide (KOtBu) was obtained from Fluka and used as received.

Monomethacryloxypropyl-terminated poly(dimethylsiloxane) (MCR-M11, average molar mass

1000 g/mol, PDI=1.15), monoaminopropyl-terminated poly(dimethylsiloxane) (MCR-A12,

average molar mass 2000 g/mol, PDI=1.15), and α,ω-methacryloxypropyl-terminated

poly(dimethylsiloxane) (DMS-R18, R22, with average molar masses 5000 and 10000 g/mol,

respectively, PDI=1.15) were obtained from Gelest and purified using basic alumina columns to

remove inhibitor. Methacryloyl chloride (MMACl,>97%), phenylbis(2,4,6-trimethyl-

benzoyl)phosphine oxide (BAPOs), triethylamine (TEA), copper(I) chloride (CuCl, ≥99.995%),

copper(I) bromide (CuBr, 99.999%), tris[2-(dimethylamino)ethyl]amine (Me6TREN),

N,N,N’,N”,N”-pentamethyldiethylenetriamine (PMDETA, 99%), ethyl α-bromoisobutyrate

(EBiB), α-bromoisobutyryl bromide (BIBB, 98%), ethylene bis(2-bromoisobutyrate) (2-BiB,

97%), dimethyl formaldehyde (DMF), dimethyl acetamide (DMA), tetrahydrofuran (THF), p-

xylene (PX), and acrylic acid (AA, 99%) were purchased from Aldrich and used as received, as

were all other reagents and solvents.

S1.2 Synthesis of poly(n-BA16) macromonomer. A 100 mL Schlenk flask equipped with a stir

bar was charged with EBiB (4.875 g, 25 mmol), nBA (64.0 g, 0.5 mol), PMDETA (0.87 g, 5

mmol), and DMF (16.0 mL). The solution was bubbled with dry nitrogen for 1 hr. Then, CuBr

(0.745 g, 5 mmol) was added to the reaction mixture under nitrogen atmosphere. The flask was

closed, purged for 5 m with nitrogen, and immersed in an oil bath thermostated at 65 °C. The

polymerization was stopped after 5 hrs when monomer conversion reached 80 mol% (determined

using 1H-NMR, Figure S1.1). The polymer solution was passed through a neutral aluminum

oxide column and the unreacted monomers were evaporated by bubbling with nitrogen gas. The

remaining polymer (50 g, 24.4 mmol) was dissolved in DMA (100 g) and transferred to a 250

mL flask. Potassium acrylate (8 g, 73.2 mmol) was synthesized by reaction of AA and KOtBu

and added to the solution, which was stirred for 72 hrs at room temperature. The solution was

filtered, diluted with methylene chloride (DCM, 100 mL), then washed with deionized (DI)

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water (3×100 mL). The macromonomer solution was dried by adding magnesium sulfate

(MgSO4) and then by overnight evaporation in air.

Figure S1.1: 1H-NMR of poly(n-BA16) reaction mixture at 80% conversion (400 MHz, CDCl3):

6.5-5.6 (CH2=CH-C=O, unreacted BA monomers, 3H), 4.2 (CO-OCH2, unreacted BA

monomers, t, 2H), 4.05 (CO-OCH2, reacted BA monomers m, 2H), 1.64-0.95 (CH2-CH2-CH3,

7H), conversion = area(a’)/area(a) = 80%, DP=16, PDI=1.11.

S1.3 Synthesis of poly(n-BA50) macro-crosslinker. A 25 mL Schlenk flask equipped with a stir

bar was charged with 2f-BiB (0.6 g, 1.7 mmol), nBA (12.8 g, 0.1 mol), PMDETA (0.115 g,

0.665 mmol), and DMF (5.0 mL). The solution was bubbled with dry nitrogen for 1 hr. Then,

CuBr (95 mg, 0.665 mmol) was added under nitrogen atmosphere. The flask was sealed, back-

filled with nitrogen, purged for 5 minutes, and immersed in an oil bath thermostated at 65 °C.

The polymerization was stopped after 2 hrs when the monomer conversion reached 83 mol%

(determined by 1H-NMR as in Section S1.2). The polymer solution was passed through a neutral

aluminum oxide column and the unreacted monomers were evaporated by bubbling with

nitrogen gas. The produced polymer (8 g, 1.25 mmol) was dissolved in 50 mL of DMA and

transferred to a 100 mL flask. Potassium acrylate (0.8 g, 7.3 mmol) was added and the solution


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was stirred for 72 hrs at room temperature. The solution was filtered, diluted with DCM (50 mL),

and then washed with DI water (3×100 mL). The macromonomer solution was dried by adding

MgSO4 and then by overnight evaporation in air.

S1.4 Synthesis of monomethacrylamidopropyl-terminated poly(dimethylsiloxane). MCR-

A12 (40 g, 20 mmol), anhydrous DCM (100 mL), and TEA (3.5 mL) were added to a 250 mL

round-bottom flask under nitrogen. The reaction mixture was cooled using an ice bath, then

injected with MMACl (2.3 g diluted with 3 mL DCM) over a 30 minute period. Next, the

reaction mixture was allowed to reach room temperature and stirred overnight. The filtrate was

washed with dilute sodium hydroxide solution (H2O2, 0.2 M, 3x150 mL) then by DI water

(3x150 mL). The mixture was dried by adding MgSO4, passed through a basic alumina column,

and stored in a freezer at -20 °C. The chemical structure and the 1H-NMR spectrum of the

macromonomer product are shown in Figure S1.2.

Figure S1.2: 1H-NMR of monomethacrylamidopropyl-terminated poly(dimethylsiloxane) (2000

g/mol) (400 MHz, CDCl3): δ 5.68-5.32 (CH2=C(CH3), 3H), 3.33 (CO-NH-CH2, 2H), 1.98 (t,

2H), 1.94 (CH2=C(CH3), 3H), 0.58 (CH2-Si(CH3)2.



S1.5 Synthesis of poly(dimethylsiloxane) bottlebrushes. A 25 mL Schlenk flask equipped with

a stir bar was charged with EBiB (2.4 mg, 12.5 µmol), MCR-M11 (15.0 g, 15.0 mmol),

Me6TREN (2.9 mg, 3.3 µL), and PX (12.0 mL). The solution was bubbled with dry nitrogen for

1 hr, then CuCl (1.2 mg, 0.012 mmol) was quickly added to the reaction mixture under nitrogen

atmosphere. The flask was sealed, back-filled with nitrogen, purged for 5 minutes, and then

immersed in an oil bath thermostated at 45 °C. The polymerization was stopped after 12 hrs at

75% monomer conversion (Figure S1.3), resulting in a bottlebrush PDMS polymer with degree

of polymerization (DP) of the backbone (𝑛𝑏𝑏) ~900. The polymer was precipitated three times

from DMF to purify, and dried under vacuum at room temperature until a constant mass was

reached. The AFM images, molecular weight, and PDI measurements of the product are shown

in Figure S1.4 and Table S1.

Figure S1.3: 1H-NMRs of S1.5 reaction mixture at 56-75% conversion (400 MHz, CDCl3): 6.19-

5.62 (CH2=C(CH3)-C=O, unreacted PDMS monomers, 2H), 4.19 (CO-OCH2, unreacted PDMS

monomers, t, 2H), 3,96 (CO-OCH2, reacted PDMS monomers m, 2H), 0.58 (CH2-Si(CH3)2,

conversion = area(a’)/area(a) = 75%. The last two NMRs showed complete removing of un-

reacted monomers after two times washing.



Figure S1.4: AFM height micrographs of different PDMS bottlebrush systems (a) single

bottlebrushes (𝑛𝑏𝑏 = 1200 and 𝑛𝑠𝑐 = 14) deposited by spin casting on a mica substrate. The

micrographs display individual worm-like molecules sparsely dispersed on the substrate. (b)

Dense monolayers of PDMS bottlebrushes (𝑛𝑏𝑏 = 1200 and 𝑛𝑠𝑐 = 14) prepared by the

Langmui-Blodget technique on a mica substrate. (c) Thick film of a PMMA-PDMS-PMMA

plastomer (nPMMA=180, 𝑛𝑏𝑏 = 900 and 𝑛𝑠𝑐 = 14) demonstrate microphase separation of

spherical PMMA domains (diameter 25 nm) surrounded by the PDMS bottlebrush matrix (inset).

The imaging was performed in PeakForce QNM mode using a multimode AFM (Brüker) with a

NanoScope V controller and silicon probes (resonance frequency of 50-90 Hz and spring

constant of ~0.4 N/m).

Table S1: Molecular characterization of PDMS bottlebrushes (𝑛𝑠𝑐 = 14)

Sample 𝑛𝑏𝑏 (NMR)a 𝑛𝑏𝑏 (AFM)

b Mn (g/mol) Mw (g/mol) Ð (AFM) b

PDMS-600 600 585±40 585000 680000 1.16

PDMS-900 900 902±70 902000 1061000 1.18

PDMS-1200 1200 1163±90 1163000 1267000 1.08

PDMS-1500 1500 1315±100 1315000 1494000 1.14 a)

Number average degree of polymerization of bottlebrush backbone (𝑛𝑏𝑏) determined by 1H-

NMR, b)

𝑛𝑏𝑏 and dispersity of bottlebrush backbone determined by AFM (Figure 1.4) as

𝑛𝑏𝑏 = 𝐿𝑛 𝑙0⁄ , where 𝐿𝑛 is number average contour length and 𝑙0 = 0.25 𝑛𝑚 is the length of the

monomeric unit. In-house software was used to measure the contour length. Typically, 300

molecule ensembles were analyzed to ensure standard deviation of the mean below 10%.

S1.6 Bottlebrush PDMS elastomer films. All bottlebrush elastomers were prepared by one-step

polymerization of MCR-M11 (1000 g/mol, and MCR-M12 (2000 g/mol) with different molar

ratios of cross-linker (DMS-R18 and DMS-R22 for M11 and M12, respectively) (Figure S1.5a).

The initial reaction mixtures contained: 56 wt% monomers (M11 or M12), 1.5 wt% BAPOs

photoinitiator, and 42.5 wt% PX as solvent. First, the mixtures were degassed by nitrogen

bubbling for 30 minutes. Then, to prepare films (Figure S1.5b), the mixtures were injected

between two glass plates with a 2.3 mm PDMS spacer and polymerized at room temperature for

12 hrs under N2 using a UV cross-linking chamber (365 nm UV lamp, 0.1 mW/cm-2

, 10 cm



distance). Films were washed with chloroform (2x with enough to immerse and fully swell the

films, each time for 8 hrs) in glass Petri dishes. The samples were then deswelled with ethanol

and dried in a 50 °C oven. The conversion of monomers to elastomers (gel fraction) was between

90 to 98 wt% in every case.

Figure S1.5: Synthesis of bottlebrush and comb-like PDMS and PBA elastomers by

photoinitiated radical polymerization of monofunctional macromonomers and diluent (nBA) in

the presence of difunctional crosslinker. (a) Chemical structure of macromonomers and cross-

linkers and diluent, (b) schematic of bottlebrush PDMS and PBA elastomers, and (c) schematic

of comb PDMS and PBA elastomers.

S1.7 Bottlebrush PBA elastomer films. All bottlebrush PBA elastomers were prepared by one-

step polymerization of monoacrylate-terminated poly(n-BA16) macromonomer (2000 g/mol,

DP=16) with different molar ratios of poly(n-BA50) macro cross-linker (6400 g/mol, DP=50)

(Figure S1.5a). The initial reaction mixtures contained: 56 wt% monomer, 1.5 wt% BAPOs

photoinitiator, and 42.5 wt% anisole as solvent. Exact amounts of poly(n-BA50) macro cross-

linker ([poly(n-BA50)-cross-linker]/[poly(n-BA16)-monomer] = 0.00125, 0.0025, 0.005, 0.0075,

0.01) were added to the mixtures and degassed by nitrogen bubbling for 30 minutes. The

mixtures were molded, cured, and washed in a manner similar to that described in Section S1.6

(Figure S1.5b).

S1.8 Comb-like elastomer films and melts. nBA and poly(n-BA16) with different molar ratios

(n-BA/poly(n-BA16) = 2, 4, 8, 16, 32, 64) were mixed in 20 mL flasks (Figure S1.5a). Anisole

solvent was added to the mixtures to give a solvent-to-monomer mass ratio of 0.75. BAPOs (2.5

wt% of monomer) photoinitiator and exact amounts of poly(n-BA50) macro cross-linker ([poly(n-



BA50) macro cross-linker]/[poly(n-BA16)-monomer] = 0.00125, 0.0025, 0.005, 0.0075, 0.01)

were added to the mixtures, which were then degassed by nitrogen bubbling for 30 minutes. The

mixtures were molded, cured, and washed in a manner similar to that described in S1.6 (Figure

S1.5c).

For synthesis comb polymer melt for determination of grafting distribution through polymer

strand in different conversion and final conversion, nBA and poly(n-BA16) with different molar

ratios (n-BA/poly(n-BA16) = 2, 4, 8, 16, 32, 64) were mixed in 20 mL air free flasks. Anisole

solvent was added to the mixtures to give a solvent-to-monomer mass ratio of 0.75. BAPOs (2.5

wt% of monomer) photoinitiator were added to the mixtures, which were then degassed by

nitrogen bubbling for 30 minutes in a dark chamber. The mixtures were moved and exposed to

the UV light and samples were taken every 15 minutes and conversion and the ratio of unreacted

monomers were measured by 1H-NMR (Figures S1.6 and S1.7). These experiments showed

that (i) the grafting density along the comb-like network strands is uniform (Figure S1.8), (ii)

conversion of monomers is >95%, and (iii) there is practically no unreacted monomers in final

product .

Figure S1.6: 1

H-NMRs of comb synthesis with nsc

=16, ng=8. The starting ng for synthesis of this

comb was 8 and 1

H-NMRs show that there is very homogenous grafting through the polymer

strands and the final 1

H-NMR show that the conversion is higher than 96.4% and there is a little

amount of un-reacted monomers in the system.



Figure S1.7: 1

H-NMRs of comb synthesis with nsc

=16, ng=16. The starting ng for synthesis of

this comb was 16 and 1

H-NMRs show that there is very homogenous grafting through the

polymer strands and the final 1

H-NMR show that the conversion is higher than 98.8% and there

is a little amount of un-reacted monomers in the system.

Figure S1.8: The accumulative grafting density of pBA combs during copolymerization of BA

monomers (spacer) and pBA macromonomer (side chain) as a function of monomer conversion.



S1.9 Linear-Bottlebrush-Linear (L-BB-L) plastomer film preparation. To prepare L-B-L

block copolymers, bottlebrush bifunctional macroinitiators with DP = 300, 600, 900, 1200, 1800

were synthesized in a manner similar to that described in Section S1.5, but with bifunctional

ATRP initiator (2f-BiB) instead. The products were washed to remove unreacted monomers and

passed through neutral aluminum oxide columns to remove residual catalyst. Then, the PDMS

bottlebrushes were used as bottlebrush ATRP initiators to grow side-blocks (e.g., PMMA) at

both ends. The compositions of L-BB-L copolymers in the reaction flasks were measured by 1H-

NMR and the samples were quenched when the mass ratio of linear-to-bottlebrush in the L-BB-L

copolymer reached 4, 8, 16, and 32%. The products were diluted with DCM, passed through

neutral aluminum oxide columns, and vacuumed overnight to remove unreacted monomers.

Finally, the degree of polymerization of MMA at the both side of PDMS bottlebrush and mass

ratio between bottle brush block and linear blocks were measured by 1H-NMR (CDCl3, Brüker

400 MHz spectrometer) experiment as shown in Figure S1.9 for pMMAL-PDMSB.B-pMMAL

(L180-B.B900-L180). The dried samples were dissolved in chloroform and poured into Teflon petri-

dishes (2 inches diameter). The dishes were placed in the hood overnight then in an oven at 50

°C for 2 hrs to dry. The samples were gently removed from the dishes and punched to prepare

dog bone samples for mechanical property measurements.

Figure S1.9: 1H-NMR of pMMAL-PDMSB.B-pMMAL (Linear-Bottlebrush-Linear (L180-

B.B900-L180)) (400 MHz, CDCl3): 3.9 (-CH2-O-C=O, br, 2H), 3.62 (CO-OCH3, s, 2H), 0.54 (CO-

OCH2-CH2-CH2-Si(CH3)2, t, 4H).



S1.10 Uniaxial tensile stress strain measurements

Dog bone-shaped samples with bridge dimensions of 12 mm × 2 mm × 1 mm were loaded into

an RSA-G2 DMA (TA Instruments) and subjected to uniaxial extension at a constant strain rate

of 0.003 s-1

and temperature of 20˚C. To measure elongation-at-break (Figure 2), the samples

were stretched until rupture occurred. To verify elasticity, the samples were subjected to repeated

loading-unloading cycles (Figure S1.10a). In each case, tests were conducted in triplicate to

ensure accuracy of the data. Measurement errors are calculated by taking the standard deviation

of the mean of values from three separate experiments. All figures in the main text show

dependence of the true stress on the elongation (deformation) ratio λ. The elongation ratio λ for

uniaxial network deformation is defined as the ratio of the sample’s instantaneous size L to its

initial size L0, λ=L/L0.

S1.11 Elasticity and viscoelasticity of bottlebrush elastomers. The highly elastic nature of

brush-like architectures is shown in Figure S1.10a: a bottlebrush (𝑛𝑠𝑐 = 14, 𝑛𝑥 = 200, 𝑛𝑔 = 1)

elastomer displays (i) fully reversible deformation and (ii) no sign of hysteresis after five cyclical

deformations to 100% strain. The strain rate of 0.003 s-1

corresponds to the elastic regime, which

is validated by measuring the frequency spectra of the storage modulus (Figure S1.10b). The

displayed experimental master curves for a PDMS bottlebrush elastomer with 𝑛𝑥 = 100 were

measured from 0.1 to 100 rad/s over temperatures ranging from 153 to 303 K and strains ranging

from 0.1 to 5% (ARES-G2 rheometer, TA Instruments). Multiple measurements at different

strains at a single temperature were performed to ensure a linear response. Using the Williams-

Landel-Ferry (WLF) equation, the time-temperature superposition principle was used to

construct the master curves with a reference temperature of 298 K and WLF shift factors given in

Figure S1.11. The samples display constant modulus in a wide range of frequencies, leading to

strain rate independent properties at effective strain rates up to 0.8 s-1

. Following the terminal

plateaus, the materials move through a series of relaxation transitions that were ascribed to a

crossover from Rouse-like relaxations of thick brush filaments to the relaxations of individual

linear chain segments [1,2].



Figure S1.10: a) Loading-unloading tensile cycles of a PDMS bottlebrush elastomer (𝑛𝑠𝑐 = 14,

𝑛𝑔 = 1, and 𝑛𝑥 = 200) taken at a strain rate of 0.003 s-1

. b) Shear storage modulus 𝐺0

′ as a

function of frequency for the PDMS bottlebrush elastomers with 𝑛𝑠𝑐 = 14, 𝑛𝑔 = 1, and 𝑛𝑥 =

100 [2].

Figure S1.11: Time−temperature superposition shift factors used to construct the master curve

in Figure S1.10b at reference of Tref = Tg + 150 K (298K) [2].

Dynamics of bottlebrush networks in relation to their static properties was discussed elsewhere

[2]. Here, it is important to point out that the value of the shear modulus in the low frequency

plateau regime in Figure S1.10b for 𝑛𝑥 = 100 is consistent with the value of the shear modulus

obtained in the linear deformation regime as shown in Table S6.4 below.

S2 Theoretical analysis

S2.1 Relationship between Young’s modulus, E, and elongation-at-break, max.

The Young’s modulus 𝐸 for incompressible polymeric networks of linear chains made of strands

with DP between crosslinks 𝑛𝑥, is defined as

𝐸 ≈𝑘𝐵𝑇𝜌

𝑛𝑥 (S1.1)

where is the monomer number density, 𝑘𝐵 is the Boltzmann constant, and T is the absolute

temperature. The elongation-at-break 𝜆𝑚𝑎𝑥, of a network chain is defined as the ratio of the

maximum strand end-to-end distance 𝑅𝑚𝑎𝑥, to the initial size of the strand, ⟨𝑅𝑖𝑛2 ⟩1/2. For flexible

network strands, we obtain the following scaling relation between 𝜆𝑚𝑎𝑥 and 𝑛𝑥

𝜆𝑚𝑎𝑥 =𝑅𝑚𝑎𝑥

⟨𝑅𝑖𝑛2 ⟩1/2

=𝑙𝑛𝑥

√𝑏𝑙𝑛𝑥

≈ 𝑛𝑥1 2⁄

(S1.2)

where l is monomer length and 𝑏 is Kuhn length of the network strand. Combining Eqs S1.1 and

S1.2, we can write

𝐸 ∝ 𝑛𝑥−1 ∝ 𝜆𝑚𝑎𝑥

−2 (S1.3)



Numerical coefficients in Eq. S1.3 depend on the chemical structure of polymer network strands.

S2.2 Conformation and mechanical properties of graft-polymer networks.

Mechanical properties. Consider a network composed by crosslinking of graft polymers (comb-

like or bottlebrush) with DP of the backbone strands between crosslinks 𝑛𝑥, DP of the side

chains 𝑛𝑠𝑐, and number of bonds between grafted side chains 𝑛𝑔. For such a network, the strand

extension ratio 𝛽, and 𝐸 are defined as [3]

𝛽 ≡⟨𝑅𝑖𝑛

2 ⟩

𝑅𝑚𝑎𝑥2

(S2.1)

𝐸 = 𝐶𝑘𝐵𝑇𝜌𝑠

⟨𝑅𝑖𝑛2 ⟩

𝑏𝑘𝑅𝑚𝑎𝑥 (S2.2)

where 𝐶 is a numerical constant that accounts for network topology and crosslink functionality.

𝜌𝑠 is the number density of stress-supporting network strands, while ⟨𝑅𝑖𝑛2 ⟩ and 𝑅𝑚𝑎𝑥 = 𝑛𝑥𝑙 are

the mean square end-to-end distance and contour length of the network strands. By considering a

graft polymer as a worm-like chain with effective Kuhn length 𝑏𝐾, ⟨𝑅𝑖𝑛2 ⟩ can be written as

⟨𝑅𝑖𝑛2 ⟩ = 𝑏𝐾𝑅𝑚𝑎𝑥 (1 −

𝑏𝐾

2𝑅𝑚𝑎𝑥(1 − 𝑒𝑥𝑝 (−

2𝑅𝑚𝑎𝑥

𝑏𝐾))) (S2.3)

From Eqs. S2.1 and S2.3, we can express as a function of the number of Kuhn segments per

strand, 𝛼−1 ≡ 𝑅𝑚𝑎𝑥 𝑏𝐾⁄ , as

𝛽 = 𝛼 (1 −𝛼

2(1 − 𝑒𝑥𝑝 (−

2

𝛼))) (S2.4)

In order to define 𝜌𝑠 (Eq. S2.1), the contribution of dangling network strand ends must be

established. We consider a network created by crosslinking graft polymers with backbone DP

𝑛𝑏𝑏. Each strand will produce two chain ends of varying length, which do not support network

stress upon deformation. For a melt of graft polymers with the density of monomers belonging to

precursor graft polymer backbones as 𝜌𝑚 = 𝜌𝜑, the density of the stress-supporting strands is

[4]

𝜌𝑠 = 𝜌𝜑 (1

𝑛𝑥−

2

𝑛𝑏𝑏) ( S2.5)

where 𝜌 is the total monomer density and 𝜑 corresponds to the molar fraction of backbone

monomers as

𝜑 =𝑛𝑔

𝑛𝑠𝑐 + 𝑛𝑔 (S2.6)

By substituting Eqs. S2.5 and S2.6 into Eq. S2.2, we obtain the following expression for E:

𝐸 = 𝐶𝑘𝐵𝑇𝜌𝛽𝛼−1𝜑(𝑛𝑥−1 − 2𝑛𝑏𝑏

−1) (S2.7)

State diagram. From the above equations, both E and depend on 𝑏𝐾. The Kuhn length bK, is

controlled by 𝑛𝑠𝑐 and 𝑛𝑔. Different brush regimes are thus described by distinct expressions for

bK depending on 𝑛𝑠𝑐 and 𝑛𝑔. Figure S2.1a summarizes the different regimes of the graft

polymers in a nsc and 𝜑−1plane, while Table S2 provides scaling expressions for bK in different



regimes. In Figures S2.1b, we use values for monomer excluded volume v, bond length l and

Kuhn length b of the backbone and side chains for PDMS given in caption of Table S2 to plot

diagram of states for PDMS brush-like elastomers.

Figure S2.1: (a) State diagram of graft polymers with monomer excluded volume v, bond length

l and Kuhn length b of the backbone and side chains in a melt [5]. The comb regime combines

loose comb (LC) and dense comb (DC) regimes from [1]). The SBB (stretched backbone) and

SSC (stretched side chain) regimes correspond to the loose bottlebrush regime (LB) and dense

bottlebrush (DB) regimes, respectively. RSC is the rod-like side chain regime. Logarithmic

scales. Crossover between Comb and Bottlebrush regimes is given by 𝜑−1 ≈ 𝜈−1(𝑏𝑙)3 2⁄ 𝑛𝑠𝑐1 2⁄

for

𝑛𝑠𝑐𝑙 𝑏⁄ > 1 and 𝜑−1 ≈ 𝜈−1𝑙3𝑛𝑠𝑐2 for 𝑛𝑠𝑐𝑙 𝑏⁄ < 1. Crossover between SBB and SSC regimes is

𝜑−1 ≈ 𝜈−1𝑏𝑙2𝑛𝑠𝑐 and crossover between SSC and RSC regimes is 𝜑−1 ≈ 𝜈−1𝑙3𝑛𝑠𝑐2 . (b) The

diagram of states of PDMS graft polymers in a melt. The crossover line from Comb to

Bottlebrush regime is calculated by setting 𝜑−1 ≈ 0.7 𝜈−1(𝑏𝑙)3 2⁄ 𝑛𝑠𝑐1 2⁄

for 𝑛𝑠𝑐𝑙 𝑏⁄ > 1 and

𝜑−1 ≈ 0.7 𝜈−1𝑙3𝑛𝑠𝑐2 for 𝑛𝑠𝑐𝑙 𝑏⁄ < 1. Logarithmic scales.

Table S2: Graft polymer’s Kuhn length in different regimes and regime boundaries.

Regime Regime boundaries Kuhn length, 𝑏𝐾

Combs

(LC&DC)*

2/12/31 )( scnblv , for 1/ blnsc

231

scnlv , for 1/ blnsc b

SBB (LB)* scsc nblvnbl 212/12/3)( 2/112/12/3

scnbvl

SSC (DB)* 2312

scsc nlvnbl 2/1/ lv

RSC 123 vnl sc scnl

l is monomer length (0.25 nm for PnBA and 0.3 nm for PDMS) and 𝑏 is Kuhn length of the

linear polymer strand (1.79±0.11 nm for linear nBA and 1.13±0.09 nm for linear PDMS) [6-8]

The monomer values of 𝑣 were taken from the known mass densities (0.195 nm3 for PnBA and

0.127 nm3 for PDMS). *LC, DC, LB, and DB are abbreviations of the loose comb, dense comb,

loose brush and dense brush regimes introduced in our earlier paper [1].



Combs. The loose grafting of side chains in the comb regime does not perturb the ideal polymer

chain conformation of either the side chain or backbone segments and leads to 𝑏𝑘 ≈ 𝑏. The side

chains result in dilution of the stress-supporting backbones, which in turn lowers 𝐸. For networks

with flexible strands (𝛽 ≪ 1), the mean square end-to-end distance of the network strands and

deformation ratio can be written as ⟨𝑅𝑖𝑛2 ⟩ ≈ 𝑏𝑅𝑚𝑎𝑥 and 𝛽 ≅ 𝛼, respectively. These give the

following expressions for 𝐸 (Eq. S2.7) and 𝛽 (Eq. S2.4):

𝐸 = 𝐶1𝜌𝑘𝐵𝑇𝜑(𝑛𝑥−1 − 2𝑛𝑏𝑏

−1) (S2.8a)

𝛽 = 𝐶2𝑛𝑥−1 (S2.8b)

where 𝐶1 and 𝐶2 are numerical constants.

Bottlebrushes: Stretched Backbone (SBB) Regime. In this regime, steric repulsion between

grafted sidechains causes extension of the backbone. The backbone extension results in larger

effective Kuhn segments (Table S2) and alters E as

𝐸 = 𝐶1𝜌𝑘𝐵𝑇𝛽𝛼−1𝜑(𝑛𝑥−1 − 2𝑛𝑏𝑏

−1) (S2.9a)

whereas 𝛽 is given by Eq. S2.4 with parameter 𝛼 as

𝛼 = 𝐶3𝑛𝑥−1𝜑−1𝑛𝑠𝑐

−1 2⁄ (S2.9b)

where 𝐶3 is a numerical constant.

At higher grafting density the steric repulsion causes extension of side chains and results in two

additional regimes of mechanical behavior. In the Stretched Side Chains (SSC) and Rod-like

Side Chains (RSC) regimes (Figure S2.1a), the expression for the Young’s modulus E remains

the same as in Eq S2.9a. However, a new equation for 𝛽 (Eq. S2.4) is obtained by substituting

the corresponding expressions for 𝑏𝐾 (Table S2) into Eq. S2.3.



S2.3 Verification of mapping procedure in computer simulations.

To confirm mapping procedure of stress-strain curves into the graft-polymer chemical structure

we have performed coarse grained molecular dynamics simulations of the graft-polymer network

deformations. Macromolecule backbones and side chains are modelled as bead-spring chains

composed of beads with diameter interacting through truncated shifted Lennard-Jones (LJ)

potential. The connectivity of monomers into graft polymers and crosslinking bonds are

modelled by the combination of the FENE and truncated shifted LJ potentials. We performed

simulations of macromolecules with FENE potential spring constants equal to 500 kBT/ 2

,

where kB is the Boltzmann constant and T is the absolute temperature. Graft polymers in a melt

state at monomer density 3=0.8 were randomly crosslinked with average number of backbone

monomers in network strands nx=16. The system parameters and simulation procedures are

described in details in [5,9]. Figure S2.2a shows simulation results for uniaxial deformation of

graft polymer networks at constant volume and Figure S2.2b tests relationships given by Eqs.

S2.8a and S2.9a.

S3. Library of graft polymers: calibration of numerical constants.

In order to test the above expressions and determine the numerical constants of Eqs. S2.7-S2.9,

multiple series of brush-like polymers were synthesized and subjected to tensile tests. Figure

S3.1 displays the corresponding stress-strain curves.

(a) (b)

Figure S2.2: (a) Uniaxial deformation of graft polymer networks. Dashed lines are the best

fit to equation 9/3/)/2(121)/1(222

Exx with E and as fitting

parameters. (b) Universal plot of the parameter /E as a function xn/ for graft polymer

networks. Values of the parameter used in this plot are solutions of the nonlinear equation

Eq. S2.4.

ng = 8 nsc = 2 4 8 16 32

1



Figure S3.1: a) Tensile true stress versus elongation 𝜆 = 𝐿/𝐿0 for PDMS bottlebrush elastomers

with the same (𝑛𝑠𝑐 = 14 and 𝑛𝑔 = 1) and different DPs of the backbone in the bottlebrush

network strand (as indicated). Dashed lines correspond to fitting with eq S3.1 b) Tensile true

stress versus elongation 𝜆 = 𝐿/𝐿0 for PDMS comb elastomers with the same (𝑛𝑥 = 600 and

𝑛𝑠𝑐 = 14) and different values of 𝑛𝑔 as indicated. Each curve was collected via uniaxial

extension of a 2212 mm dog bone sample 𝜀̇ =0.002 s-1

. Each curve was measured three times

according to the procedure in S1.10. Errors in values of the fitting parameters are presented in

Table S3 as the standard error of the mean.

The curves were fitted by Eq. S3.1 (dashed lines), with 𝐸 and 𝛽 as fitting parameters.

𝜎𝑡𝑟𝑢𝑒(𝜆) =𝐸

9(𝜆2 − 𝜆−1) [1 + 2 (1 −

𝛽(𝜆2 + 2𝜆−1)

3)

−2

] (S3.1)

At small deformations, Eq. S3.1 relates the apparent (𝐸0) and structural (𝐸) Young’s moduli as

𝐸0 ≡ lim𝜆→1

3𝜎𝑡𝑟𝑢𝑒(𝜆)

𝜆2 − 𝜆−1=

𝐸

3(1 + 2(1 − 𝛽)−2) (S3.2)

Note that 𝐸0 ≈ 𝐸 for networks with flexible strands (𝛽 ≪ 1). The resulting fitting parameters

are collected along with , obtained by solving Eq. S2.4, in Table S3.

Table S3: Mechanical properties of PDMS bottlebrush and comb-like networks.

ng nsc nx E [kPa]*

Ee [kPa]*

β α Regime#

bk[nm]

1 14 400 3.3±0.3 N/A 0.08±0.01 0.08 DB 2.52

1 14 200 8.4±0.3 N/A 0.11±0.01 0.12 DB 2.52

1 14 100 18.6±0.6 N/A 0.17±0.01 0.19 DB 2.52

1 14 67 30.0±1.2 N/A 0.23±0.01 0.27 DB 2.52

1 14 50 40.5±1.5 N/A 0.28±0.02 0.34 DB 2.52

1 14 600 2.6±0.1 N/A 0.055±0.001 0.056 DB 2.52

2 14 600 7.9±0.2 N/A 0.032±0.002 0.033 LB 1.55

4 14 600 24.6±0.8 1.2±0.5 0.027±0.001 0.027 DC 1.13

8 14 600 42.9±2.0 20.1±1.7 0.022±0.001 0.022 DC 1.13



16 14 600 60.3±2.1 45.0±2.5 0.017±0.002 0.017 LC 1.13

32 14 600 70.8±1.2 66.0±2.3 0.017±0.001 0.017 LC 1.13

64 14 600 79.5±1.1 84.0±5.1 0.015±0.006 0.015 LC 1.13 *𝐸 represents the structural Young’s modulus extracted by fitting 𝜎𝑡𝑟𝑢𝑒(𝜆) curves with Eq. S3.1.

𝐸𝑒 represents the modulus contribution from trapped entanglements by fitting with 𝜎𝑡𝑟𝑢𝑒(𝜆) =

𝐸

9(𝜆2 − 𝜆−1) [1 +

9𝐸𝑒

𝐸𝜆+ 2 (1 −

𝛽(𝜆2+2𝜆−1)

3)

−2

] as described elsewhere.1 The errors in the E, Ee,

and β values were taken from the average of values from several (at least three) stress-strain

curves as fit by equation S3.1 and its modified counterpart described above. Values of the

parameter are obtained by solving Eq. S2.4 for fitted values of the parameter . Note that these

values are larger than ones obtained by direct calculations using the equations in Table S2

because of the scaling nature of the direct calculation equations and the stoichiometric nature of

the nx in Eq. S2.4. For more accurate calculatons, numerical coefficients are extracted from the

calibration curves in Figure S3.2. # The regime names and boundaries are outlined in Table S2.

The data of the bottlebrush networks (𝑛𝑔 = 1, 2, 4) from Table S3 were fitted to a system of

transformed equations obtained from Eqs. S2.9a,b

𝛼𝐸

𝛽𝜑= 𝐶1𝑛𝑥

−1 − 𝐵 (S3.2a)

𝛼𝜑√𝑛𝑠𝑐 = 𝐶2𝑛𝑥−1 (S3.2b)

to determine the numerical coefficients 𝐶1 = 38.9 MPa, B = 0.60 MPa, and 𝐶2 = 3.6. Figure

S3.2 shows good agreement between the experimental data points and fitting line. In similar

fashion, the comb-like networks (𝑛𝑔= 8, 16, 32, and 64) were analyzed using

𝐸𝑛𝑥 = 𝐶3𝜑 − 𝐵 (S3.3)

to obtain 𝐶3 = 47 𝑀𝑃𝑎, 𝐵 = 9.48 𝑀𝑃𝑎.

Figure S3.2: Network data from Table S3 for obtaining numerical coefficients. Dashed lines

are the best fit: (a) y = 38922x + 60 (kPa), (b) y = 3.64x + 0.011, and (c) y = 47323x+9475



(kPa). Despite the relatively short side chains (~1 Kuhn length), the scaling arguments ensure

the good fit, because, in a melt state, 𝑛𝑠𝑐 is equivalent to linear mass density of bottlebrushes.

Combs have no 𝑛𝑔 dependence and so trend analysis was not applied to them. Errors in all

values are found to be less than ten percent, as derived from the values displayed in Table S3.

Note that elongation-at-break 𝜆𝑚𝑎𝑥 (Eq S1.2) and strand extension ratio 𝛽 (Eq S2.1) are related

as

𝜆𝑚𝑎𝑥 ≅ 𝑅𝑚𝑎𝑥 √⟨𝑅𝑖𝑛2 ⟩⁄ ≅ 𝛽−0.5 (S3.4)

where 𝛽 represents the pre-extension of the networks strands due to steric crowding of their side

chains. This relationship is verified in Figure S3.3, which shows close agreement between the

independently measured 𝜆𝑚𝑎𝑥 and 𝛽 and thus suggests uniform network structures of the

reported elastomers. This provides two independent methods for evaluation of the network

extensibility, whereby measurement of 𝛽 is more reliable because 𝜆𝑚𝑎𝑥 also depends on

specifics of fracture mechanics in macroscopic samples.

Figure S3.3: Verification of the linear relationship between elongation-at-break 𝜆𝑚𝑎𝑥 of the

PDMS bottlebrush () and comb-like () elastomers with 𝑛𝑠𝑐 = 14 and the strand elongation

√𝛽−1 (Eq. S3.4). Measurement error bars were calculated by taking the standard error of the

mean from three measurements of uniaxial stress strain curves.

S4. 𝑬(𝝀𝒎𝒂𝒙) correlations for graft polymers

The DP of polymer strand between entanglements, ne, is determined by the condition that there

are Pe chains within volume a3 occupied by a strand with DP=ne [1]. For a linear chain, the size

of the strand with ne monomers is equal to enbla . The excluded volume of a chain section

containing ne monomers with each monomer occupying volume v is equal to vne. Therefore, the

number of chains inside the volume, a3, is estimated as



e

e

e nv

bl

vn

aP

2/33

(S4.1)

Grafting side chains to a polymer backbone results in an increase of the effective Kuhn length bK

of the polymer backbone and in increase of the excluded volume of a section of a chain with gr

en

backbone monomers between entanglements to /vngr

e (where )/( gscg nnn is the molar

fraction of the backbone monomers between grafted side chains). Since the number of the chains

within volume a3 for those chains to entangle is a universal number, for graft polymers eq S4.1

transforms to

gr

eK

gr

e

e nv

lb

nv

aP

1

2/3

1

3

(S4.2)

By comparing eqs S4.1 and S4.2 the entanglement DP of the backbone of graft-polymers can be

expressed in terms of that of linear chains

e

K

gr

e

gr

eK

e nb

bnn

v

lbn

v

bl 2

32/32/3

(S4.3)

Using eq S4.3, the modulus of the entangled graft-polymer networks can be written as 3

,

3

,

b

bE

b

b

n

Tk

n

TkE K

lineK

e

B

gr

e

Bgre

(S4.4)

Maximum elongation of entangled linear strands with respect to unperturbed ideal chain state is

b

nl

nbl

nl e

e

eline , (S4.5)

For graft-polymers with backbone effective Kuhn length bK the maximum elongation is

controlled by the extension of the backbone. In this case we can obtain the following expression

for maximum backbone elongation

line

KK

gr

e

gr

eK

gr

egre

b

b

b

nl

nlb

nl,

1

2

,

(S4.6)

Eqs S4.4 and S4.6 are valid for all regimes of the comb and bottlebrush networks. The specifics

of the graft polymer structure enters through the graft polymer composition and dependence of

the Kuhn length bK on degree of polymerization of the side chains nsc and their grafting density 1

gn (see Table S2).

Boundaries of the different regimes in the mechanical phenotype map (Figure 3a):

The upper boundary of the map graph is given by the condition relating the Young’s modulus

with maximum strand elongation between crosslinks in linear chain elastomers (see eq S1.3).

This line ends at a point where degree of polymerization of network strand between crosslinks,

nx, becomes on the order of the degree of polymerization between entanglements, ne. For linear



chain networks, the lowest possible modulus is lineEE , , and maximum possible elongation is

line,max .

To further decrease modulus, this requires suppression of the entanglements, which is realized by

loose grafting of side chains (see Comb regime in Table S2). For combs the steric repulsion

between side chains is weak and the effective Kuhn length of a comb bK is on the order of the

Kuhn length of the linear chain b. Thus, in a comb regime suppression of the entanglements

takes place through dilution of the backbone by the side chain monomers. Substituting bK=b into

eqs S4.4 and S4.6 we obtain

linee ,

1

max,max (S4.7a)

3

max,

,

,

3

,,

e

line

linelinecombe EEE

(S4.7b)

Eq S4.7b determines the upper boundary of the comb triangle in Figure 3a. The λmax increase in

eqS4.7 is limited by the comb-bottlebrush crossover at 𝜑−1 ≅ √𝑛𝑠𝑐 (𝑏𝑙)3 2⁄ 𝑣⁄ (Table S2),

which results in 𝜆𝑚𝑎𝑥 ≅ √𝑛𝑠𝑐𝜆𝑒.𝑙𝑖𝑛.

In the networks of combs or bottlebrushes with the degree of polymerization between crosslinks

nx <ne the network Young’s modulus is

lin

x

B En

TkE (S4.8)

Thus, modulus of the graft polymer networks is times smaller than that of the networks of

linear chains with the same degree of polymerization of the network strands between crosslinks.

The maximum elongation of the graft polymer networks is obtained by substituting into eq S4.5

nx instead of ne

K

x

xK

x

b

nl

nlb

nlmax (S4.9)

The maximum elongation of the graft polymer networks in the unentangled network strand

regime decreases with increasing the effective Kuhn length of the graft polymer strands. Solving

eq S4.9 for nx as a function of the maximum elongation and substituting this expression into eq

S4.8 we can write down modulus of the graft polymer networks in terms of max

KK

B

x

B

b

l

b

lTk

n

TkE

2

max2

max

(S4.10)

It follows from this equation that for graft polymer networks the line in log-log plot for Young’s

modulus E as a function of max is shifted down from the corresponding line for the linear chain

networks by a factor )/log( Kbl since the value of the parameter, 1/ Kbl . In the case of the

graft polymer networks made of bottlebrush strands in the SSC regime for which 2/1/ lvbK



(see Table S2) the shift factor scales with the bottlebrush composition as 2/3 or with the side

chain degree of polymerization as 2/3

scn . This scaling relation was used to obtain the lower

boundary for Bottlebrushes and Combs regime in Figure 3a.

It is important to point out that bottlebrush networks with fully extended backbone (SCC regime

in Figure S2.1 and Table S2) cannot extend beyond the entanglement limit given by

𝜆𝑆𝑆𝐶 < 𝜆𝑆𝑆𝐶,𝑒 ≅𝑏2𝑙

𝑣𝜆𝑙𝑖𝑛,𝑒 ≈ 𝜆𝑙𝑖𝑛,𝑒 (S4.11)

This equation follows from eq S4.6 after substitution expression for 2/1/ lvbK from Table

S2. In other words, maximum extensibility of bottlebrush networks is nearly equal to that of

linear-chain networks measured at the onset of chain entanglements. In a 𝐸 𝑣𝑠. 𝜆𝑚𝑎𝑥 plot (see

Figure 3a in the main text), this condition gives the vertical line of the parallelogram.

S5: Brush-like triblock copolymers

Theory: Due to practical and theoretical limitations in the

possible 𝛽 values obtainable in brush-like materials (described

below), an additional parameter in the form of chemical

composition was added to the system. Specifically, ABA

triblock copolymers with phase separating linear A tails and

brush-like B blocks were designed. These molecules generate

physical networks composed of glassy multifunctional cross-

links formed by aggregates of A blocks bridged by brush-like

B block network strands (Figure S5.1). In order to estimate

the deformation of the middle block and obtain a scaling

relation for , we assume that the deformation of the middle

block is a leading factor in determining the spacing between

aggregates. The free energy of the brush-like middle block is a sum of the surface free energy of

the PDMS/PMMA interface with surface energy , surface area SAB, and elastic energy of the

graft polymer block deformation, having end-to-end distance RBB, as

xK

BB

B

AB

B

BB

nlb

R

Tk

S

Tk

F 2

(S5.1)

In Eq. S5.1 we have omitted all numerical prefactors. The packing condition of the graft polymer

block requires that the total number of monomers within volume BBAB RS equals the total number

of monomers in the brush-like block

/1/ xgscxBBAB nnnnRS (S5.2)

Substituting Eq. S5.2 into Eq. S5.1, we obtain free energy of the brush-like block as a function of

its end-to-end distance

Figure S5.1: Schematic plot of

the PDMS block connecting

two PMMA aggregates.

RBB



xK

BB

BBB

x

B

BB

nlb

R

RTk

n

Tk

F 2

(S5.3)

Minimization of Eq. S5.3 with respect to RBB results in an expression for the equilibrium size of

the graft polymer block connecting different aggregates

3/11223/1122

3/1

xKxK

B

BB nlbnlblTk

R (S5.4)

Thus, for networks prepared by association of the end blocks, the initial strand size Rin is equal to

RBB. Hense, the deformation ratio of the network strands can be written as follows 3/2

2

max

2

ln

bC

R

R

x

KBB (S5.5)

where 𝐶𝛽 is a constant whose value depends on the material properties (see Eq. S5.5). Note that

the particular expression for 𝑏𝐾 should be taken from Table S2 depending on 𝑛𝑔−1 and 𝑛𝑠𝑐.

Below, we consider an example of densely grafted side chains with ng = 1. For such graft

polymers 𝑏𝐾 can be approximated as 2/1Kb (see Table S2 for SSC regime). In this

approximation Eq. S5.5 transforms to 3/21 xnC (S5.6)

In writing the expression for the Young’s modulus 𝐸, we have to keep in mind that only a

fraction fBB of the network volume is occupied by deformable strands. The expression for the

modulus with this correction is

BBEBBxKBBBxB fCfnbRTkCfnTkCE 2/311

max

11 (S5.7)

where we substituted for 2/1Kb and absorbed a numerical coefficient into parameter CE. It is

important to point out that the fraction of graft polymer blocks that form loops is included in the

definition of CE. In the case of triblock copolymer networks, Eqs. S5.6 and S5.7 should be used

for mapping materials into graft copolymer mimics.

Experiments: A series of PMMA-PDMS-PMMA triblock copolymers with different DPs of the

PDMS bottlebrush backbone (𝑛𝑏𝑏 = 𝑛𝑥) and PMMA linear tails (N) were prepared as described

in S1.9. Figure S5.2 and Table S5 show results of the tensile tests.



Figure S5.2: True stress vs. uniaxial elongation of PMMA-PDMS-PMMA plastomers with the

same bottlebrush PDMS block (𝑛𝑠𝑐 = 14, 𝑛𝑏𝑏 = 1200) and different DPs of the linear PMMA

block (as indicated)

Table S5: Mechanical properties of PMMA-PDMS-PMMA plastomers from Figure S5.2

N a

MMA (%)

b

E (kPa) c

β d

λmax

e

2360 4.8 3.0 0.25 4.5

2480 6.3 4.2 0.26 3.7

2810 10.1 5.1 0.30 3.2

2930 11.4 5.7 0.36 2.9

a DP of the PMMA linear blocks,

b volume fraction of the PMMA blocks,

c structural Young’s

modulus obtained by fitting the stress-strain curves in Figure S5.2 with Eq. S3.1, d

strand

elongation ratio (Eq. S2.1) obtained by fitting the stress-strain curves in Figure S5.2 with Eq.

S3.1, e Average elongation-at-break. The central PDMS bottlebrush B block of the ABA

samples has 𝑛𝑔 = 1, 𝑛𝑠𝑐 = 14, 𝑛𝑏𝑏 = 1200.



Table S6.1: Inorganic materials

Material Comment E, GPa Strain () Ref

CNT, Graphene SW-CNT / MW-CNT 800-1050 0.05-0.3 2,4,14,

15,16, 17

Tungsten 400 0.03 2

Molybdenum TZM 330-360 0.1-0.2, 0.4-0.3 2,6,14

Steel ASTM-A36 207 0.1-0.2 1,19

Copper and alloys (2nd

number) 105 / 150 0.6 / 0.03 14

Aluminum and alloys (2nd

number) 69 / 79 0.12-0.17, 0.4 / 0.04 1,5, 14

Magnesium AZ31B 45 0.15 19

Lead and alloys (2nd

number) 14-16 0.5 / 0.09 11,14

Cast Iron grey / ductile 100 / 170 0.005 / 0.2 1,8

Titanium 110, 80-130 0.2-0.07 9, 14

Glass/porcelain depends on composition 50-90 2

Glass fiber 70-90 0.05 18

Table S6.2: Synthetic polymers

Material Comment E, GPa Strain () Ref

Polyimide 2.5 0.07 3

PC 2.6-3.5 1, 0.6-1.2 3,13,19

PET 2.7 1.2 3

PS below Tg 4-5, 3 0.07, 0.01-0.03 2,3,13,19

PMMA 3-5 0.02-0.1 13

PP 1.5-1.9 1-2.9, 0.1-7 3,12, 19

HDPE 0.8 5, 0.15-1 2,3,19

LDPE 0.1-0.9, 0.17 6, 0.9-8 2,19

PVC 3-6, 2.8 0.05-0.6, 0.02-0.3 13, 19

PTFE Teflon 0.6 1-3.5 13, 19

Nylon 6 1.8 0.9 3

Rubber 0.01-0.1 2-5 2

Table S6.3: Biological materials

Material Comment E, GPa Strain () 𝝀 − 𝝀−𝟐 Ref

Bone human cortical 14 (7-30) 0.01-0.02 2, 10,11

Tendon in vitro/ in vivo 1-2 / 0.3-1.4 0.04-0.1 11, 21

Ligament 1.2-1.8 0.13-0.18 27 (Ch2)

Collagen by AFM 1.2-12 0.3 0.7 28,29,32

Cartilage Hyaline 0.0004-0.02 0.1-1.2 27

Brain 0.2/2kPa 0.5 1.1

Lung 1/3kPa 1 1.8

Liver/Kidney Low strain foot /

high strain region 10

-6- 210

-4 /

0.001-0.01

0.8 30, 31

(table 2)

Blood vessel high strain

artery (E/E0)

vena (E/E0)

0.002-0.006

0.6/200kPa

3/600kPa

0.6-1.8 1.2-2.7 11, 22, 23

Skin high strain 0.015-0.15 0.3-1.2 1.1 24-27



low strain 600/6000k 0.5 Table 5.11

Wood/pulp along grain 11 0.03-0.1 1,20

References for the Tables S6.1-6.3:

1. http://www.eitexam.com/Search2/Mechanics/PropertiesEq.asp?SB=1

2. https://en.wikipedia.org/wiki/Young%27s_modulus

3. http://www.matweb.com/reference/tensilestrength.aspx

4. https://arxiv.org/ftp/arxiv/papers/0704/0704.0183.pdf

5. http://asm.matweb.com/search/SpecificMaterial.asp?bassnum=MA6061t6

6. http://www.dtic.mil/dtic/tr/fulltext/u2/606310.pdf

7. http://www.skpabi.com/MSEA-1%20reprint.pdf

8. http://www.makeitfrom.com/material-properties/Grey-Cast-Iron

9. http://asm.matweb.com/search/SpecificMaterial.asp?bassnum=MTU020

10. https://deepblue.lib.umich.edu/bitstream/handle/2027.42/49831/1091850102_ftp.pdf?sequence=1

11. http://web.mit.edu/8.01t/www/materials/modules/chapter26.pdf

12. http://classes.engr.oregonstate.edu/mime/winter2012/me453-001/Lab1%20-

%20Shear%20Strain%20on%20Polymer%20Beam/ASTM%20D638-02a.pdf

13. http://61.188.205.38:8081/hxgcx/polymer/UploadFiles/swf/%E8%B5%84%E6%96%99%E5%BA%9

3/Polymer%20Science%20and%20Technology/8939_CH13.pdf

14. https://www.pearsonhighered.com/samplechapter/0136081681.pdf

15. http://science.sciencemag.org/content/321/5887/385.full

16. http://www.sciencedirect.com/science/article/pii/S0022369799003765

17. http://journals.aps.org/prl/abstract/10.1103/PhysRevLett.84.5552

18. https://www3.nd.edu/~manufact/MPEM_pdf_files/Ch02.pdf

19. http://esminfo.prenhall.com/engineering/shackelford/closerlook/pdf/Shackelford_Ch6.pdf

20. Wood Pulp and Its Uses By Charles Frederick Cross, Edward John Bevan, R. W. Sindall, W. N.

Bacon

21. http://eknygos.lsmuni.lt/springer/503/17-24.pdf

22. http://www.ncbi.nlm.nih.gov/pmc/articles/PMC3317338/

23. http://www.ncbi.nlm.nih.gov/pubmed/12971612/

24. http://onlinelibrary.wiley.com/doi/10.1034/j.1600-0846.2001.007001018.x/pdf

25. http://courses.washington.edu/bioen327/Labs/Lit_BiomechPropsSkin.pdf


27. An Introduction to Materials Engineering and Science for Chemical and Materials Engineers by Brian

S. Mitchell. Source: Silver F.H., Christiansen, D.L. Biomaterials Science and Biocompatibility,

1999, Springer Verlag


29. http://scholarship.richmond.edu/cgi/viewcontent.cgi?article=1091&context=physics-faculty-

publications


31. Biomechanical Systems Technology: Computational methods By Cornelius T. Leondes

32. http://www.sciencedirect.com/science/article/pii/S0925443912002839



http://www.eitexam.com/Search2/Mechanics/PropertiesEq.asp?SB=1



https://en.wikipedia.org/wiki/Young's_modulus

https://en.wikipedia.org/wiki/Young's_modulus

http://www.matweb.com/reference/tensilestrength.aspx

http://www.matweb.com/reference/tensilestrength.aspx

https://arxiv.org/ftp/arxiv/papers/0704/0704.0183.pdf

https://arxiv.org/ftp/arxiv/papers/0704/0704.0183.pdf

http://asm.matweb.com/search/SpecificMaterial.asp?bassnum=MA6061t6

http://asm.matweb.com/search/SpecificMaterial.asp?bassnum=MA6061t6

http://www.dtic.mil/dtic/tr/fulltext/u2/606310.pdf

http://www.dtic.mil/dtic/tr/fulltext/u2/606310.pdf

http://www.skpabi.com/MSEA-1%20reprint.pdf

http://www.skpabi.com/MSEA-1%20reprint.pdf

http://www.makeitfrom.com/material-properties/Grey-Cast-Iron

http://www.makeitfrom.com/material-properties/Grey-Cast-Iron

http://asm.matweb.com/search/SpecificMaterial.asp?bassnum=MTU020

http://asm.matweb.com/search/SpecificMaterial.asp?bassnum=MTU020

https://deepblue.lib.umich.edu/bitstream/handle/2027.42/49831/1091850102_ftp.pdf?sequence=1

https://deepblue.lib.umich.edu/bitstream/handle/2027.42/49831/1091850102_ftp.pdf?sequence=1

http://web.mit.edu/8.01t/www/materials/modules/chapter26.pdf

http://web.mit.edu/8.01t/www/materials/modules/chapter26.pdf

http://classes.engr.oregonstate.edu/mime/winter2012/me453-001/Lab1%20-%20Shear%20Strain%20on%20Polymer%20Beam/ASTM%20D638-02a.pdf



http://61.188.205.38:8081/hxgcx/polymer/UploadFiles/swf/%E8%B5%84%E6%96%99%E5%BA%93/Polymer%20Science%20and%20Technology/8939_CH13.pdf




https://www.pearsonhighered.com/samplechapter/0136081681.pdf

https://www.pearsonhighered.com/samplechapter/0136081681.pdf

http://science.sciencemag.org/content/321/5887/385.full



http://www.sciencedirect.com/science/article/pii/S0022369799003765


http://journals.aps.org/prl/abstract/10.1103/PhysRevLett.84.5552

http://journals.aps.org/prl/abstract/10.1103/PhysRevLett.84.5552

https://www3.nd.edu/~manufact/MPEM_pdf_files/Ch02.pdf

https://www3.nd.edu/~manufact/MPEM_pdf_files/Ch02.pdf

http://esminfo.prenhall.com/engineering/shackelford/closerlook/pdf/Shackelford_Ch6.pdf

http://esminfo.prenhall.com/engineering/shackelford/closerlook/pdf/Shackelford_Ch6.pdf

http://eknygos.lsmuni.lt/springer/503/17-24.pdf

http://eknygos.lsmuni.lt/springer/503/17-24.pdf

http://www.ncbi.nlm.nih.gov/pmc/articles/PMC3317338/


http://www.ncbi.nlm.nih.gov/pubmed/12971612/

http://www.ncbi.nlm.nih.gov/pubmed/12971612/

http://onlinelibrary.wiley.com/doi/10.1034/j.1600-0846.2001.007001018.x/pdf

http://onlinelibrary.wiley.com/doi/10.1034/j.1600-0846.2001.007001018.x/pdf

http://courses.washington.edu/bioen327/Labs/Lit_BiomechPropsSkin.pdf

http://courses.washington.edu/bioen327/Labs/Lit_BiomechPropsSkin.pdf





http://scholarship.richmond.edu/cgi/viewcontent.cgi?article=1091&context=physics-faculty-publications






Table S6.4: Mechanical properties of all PDMS-based elastomers synthesized in this study

Sample nsca

nxb

ngc

E (kPa)d

e E0 (kPa)f λmax

gλmax,ex

h

Series 1 14 400 1 3.3±0.3 0.08±0.01 3.7 3.5±0.2 3.5±0.3

Bottlebrush 14 200 1 8.4±0.3 0.11±0.01 9.9 3.0±0.2 2.9±0.2

14 100 1 18.6±0.6 0.17±0.01 24.2 2.4±0.1 2.1±0.2

14 67 1 30.0±1.2 0.23±0.01 43.7 2.1±0.1 1.9±0.2

14 50 1 40.5±1.5 0.28±0.02 65.6 1.9±0.1 1.5±0.1

Series 2 28 400 1 2.4±0.2 0.14±0.04 3.0 2.7±0.1 2.6±0.5

Bottlebrush 28 200 1 3.8±0.2 0.17±0.04 4.9 2.4±0.1 2.5±0.5

28 100 1 8.6±0.3 0.31±0.01 14.9 1.8±0.1 1.6±0.2

28 50 1 21.3±1.5 0.44±0.02 52.4 1.5±0.1 1.4±0.1

Series 3 14 300 1 10.3±0.1 0.074±0.003 11.4 3.7±0.1 3.8±0.2

Comb 14 300 2 16.5±0.3 0.037±0.002 17.4 5.2±0.1 4.2±0.6

14 300 4 36.3±0.4 0.035±0.003 48.0 5.3±0.3 4.3±0.5

14 300 16 98.7±2.8 0.030±0.002 164.0 5.8±0.2 4.4±0.7

14 300 32 115.5±2.4 0.030±0.001 206.4 5.7±0.1 4.6±0.6

14 300 64 124.2±0.4 0.027±0.002 228.5 6.1±0.2 5.0±0.5

Series 4 14 600 1 2.7±0.1 0.066±0.004 3.0 3.9±0.1 4.5±0.2

Comb 14 600 2 7.9±0.2 0.032±0.002 8.3 5.6±0.2 5.5±0.4

14 600 4 24.6±0.8 0.027±0.001 26.7 6.1±0.1 5.5±0.3

14 600 8 42.9±2.0 0.022±0.001 64.3 6.8±0.1 6.4±0.1

14 600 16 60.3±2.1 0.017±0.002 106.7 7.7±0.2 6.6±0.5

14 600 32 70.8±1.1 0.017±0.001 138.5 7.6±0.1 8.0±0.1

14 600 64 79.5±1.0 0.015±0.004 165.1 8.2±0.9 7.7±0.4

Series 5 14 1200 1 1.4±0.2 0.039±0.001 1.5 5.1±0.1 5.9±0.1

Comb 14 1200 2 3.0±0.4 0.020±0.002 3.1 7.1±0.4 7.2±0.8

14 1200 4 10.7±0.3 0.014±0.001 15.4 8.4±0.3 7.8±0.4

14 1200 16 32.1±0.7 0.012±0.001 86.9 9.1±0.4 11.7±1.0

14 1200 32 37.2±0.4 0.011±0.001 126.6 9.5±0.4 7.6±0.7

14 1200 64 42.7±0.2 0.011±0.001 155.2 9.4±0.4 10.7±0.5

Series 6 14 1800-2 1 2.7±0.1 0.39±0.02 4.8 1.6±0.1 2.1±0.1

Plastomer 14 1200-2 1 4.2±0.1 0.26±0.02 4.5 2.0±0.1 3.7±0.3

𝜙𝑀𝑀𝐴 = 0.06 14 900-2 1 3.9±0.2 0.26±0.01 3.9 2.0±0.1 4.5±0.3

14 600-2 1 3.6±0.1 0.29±0.03 4.1 1.9±0.1 4.1±0.2

14 300-2 1 6.3±0.2 0.54±0.03 21.6 2.6±0.1 1.4±0.1

a-c) Degrees of polymerization of side chains, backbone of the network strand, and spacer

between side chains along the backbone, respectively. d,e)

Young’s modulus (E) and strand

extension ratio (β) obtained by fitting the experimental tensile stress-strain curves using Eq 1 in

the main text. f) Apparent Young’s modulus measured as a tangent to the corresponding stress-

strain curves at 𝜆 → 1. g,h)

Expected (𝜆𝑚𝑎𝑥 ≅ 𝛽−0.5) and measured elongation-at-break values.



S7 Biological tissues used for synthetic mimics

Figure S7.1 shows the original stress-strain curves of assorted biological tissues and synthetic

gels that were used for mimicking with PDMS brush-like elastomers. All curves were digitized

and converted to true tensile stress vs elongation, and then displayed in Figure 3c,d. In mapping

the networks’ elastic properties onto the strands’ chemical structures we did not use specific

values for the Kuhn length, bond length, or monomer excluded volume. These parameters always

enter the scaling equations in dimensionless combinations and are thus absorbed into numerical

constants. These constants define the correlations between modulus E, parameters α and β, and

the structural [𝑛𝑠𝑐, 𝑛𝑔, 𝑛𝑥] triplet for the particular (in terms of chemical structure) polymer

library (see discussion of mapping procedure in Section S3 of the SI).



Figure S7.1: Stress-strain curves of assorted biological tissues and gels were used for

preparation of synthetic mimics displayed in Figures 3b,c. The black arrows indicate which

particular curve was used for tissue or gel mimicking. (a) Five uniaxial tensile engineering

stress-strain curves of rectangular dog lung strips (solids lines) [10]. The tissues were prepped

via constant stress cycling to 5 kPa and back to resting in order to generate uniform stress

histories. The samples were exposed to a 0.5% of resting length per second uniaxial extension in

an oxygen rich aqueous media. (b) Figure 6d in ref [11] displays uniaxial tensile true stress–

stretch curves of different artery tissues taken from diseased human sources. All samples were

cut into rectangular strips and prepped by repetitive stress cycling to ensure consistent stress

histories. The samples were finally exposed to uniaxial extension at a rate of 1mm/s. Most

samples were measured in the axial direction including the sample chosen for analysis (V). (c)

Figure 3b in [12] displays uniaxial step by step engineering stress strain curve. The authors

progressively stretched a single human muscle finder from 76 to 140% of initial fiber length and

then released (hollow circles) again to 76% using a step duration of 3 min. Force, change of

passive force with respect to the value recorded at 76% of initial fiber length. The passive

tension values were calculated as the force recorded at the end of each step deformation divided

by fiber cross-sectional area and expressed as the change relative to the value at 76% of initial

fiber length. Fiber strain was defined as any given current fiber length divided by fiber length at

76% of initial length minus one. (d) Figure 2b in [13] displays uniaxial, compressive engineering

stress versus %strain curves of 20 mm diameter cylindrical jellyfish mesoglea tissue samples.

The samples were dried in air at ambient temperature for 72h followed by equilibrium swelling

in water (SW) and acetic acid aqueous solution (pH = 4.00) (SA). Compression testing was done

at a constant rate of 10 mm min-1

rate between flat parallel plates. The SW compression curve

was fitted by eq 1 (main text) and then replotted as a tensile curve in Figure 3b (main text). (e)

Figure 6 in ref [14] displays tensile engineering stress-strain curves of micelle cross-linked

acrylamide gels with differing concentrations of polyurethane macromonomer. The samples

were submitted to uniaxial extension at a constant deformation rate of 50 mm min-1

under a

constant crosshead velocity. (f) Figure 8a in ref [15] displays engineering uniaxial stress-strain

curves of alginate hydrogels. The samples were mold cast into cylindrical barbell shapes and

allowed to incubate in a standard tissue growth medium from 1 to 42 days. A uniaxial tension

was then applied at a deformation rate of 0.1 s-1

until sample rupture.

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superelastic bottlebrush melts and networks.” Nature Materials 15, 183-189 (2016).



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supplementary information · sergei s. sheiko. 1* 1. department of chemistry, university of north...

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