solvent-free, supersoft and superelastic solvent-free ... · 1 1 supplementary information...

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Supplementary Information

Solvent-free, supersoft and superelastic bottlebrushes melts and networksWilliam F. M. Daniel,1 Joanna Burdyńska,2 Mohammad Vatankhah-Varnosfaderani,1 Krzysztof Matyjaszewski,2 Jarosław Paturej, 1,4 Michael Rubinstein,1 Andrey V. Dobrynin,3 Sergei S. Sheiko1* 1Department of Chemistry, University of North Carolina at Chapel Hill, North Carolina, 27599, USA 2Department of Chemistry, Carnegie Mellon University, 4400 Fifth Avenue, Pittsburgh, Pennsylvania, 15213, USA 3Department of Polymer Science, University of Akron, Akron, OH 44325-3909, USA 4Current address: Institute of Physics, University of Szczecin, Wielkopolska 15, 70451 Szczecin, Poland

1. Synthesis and characterization

Materials. Butyl acrylate samples. n-Butyl acrylate (nBA, 99%, Acros) and (2-trimetylsiloxy)ethyl methacrylate (HEMA-TMS, Scientific Polymer Products) were purified by passing the monomer through a column filled with basic alumina to remove the inhibitor, 2,2′-azobis(2-methylpropionitrile) (AIBN, 98%, Aldrich) was recrystallized from methanol and dried under vacuum prior use. Sulfuric acid (20% fuming) was purchased from Alfa Aesar. All other reagents: 2-cyano-2-propyl 4-cyanobenzodithioate (98%), copper(I) bromide (CuIBr, 99.999%), copper(II) bromide (CuIIBr2, 99.999%), 4,4′-dinonyl-2,2′-dipyridyl (dNbpy, 97%), potassium fluoride (KF, 99%), tetrabutylammonium fluoride (TBAF, 1.0 M in THF), α-bromoisobutyryl bromide (98%), 2,5-di-tert-butylphenol (DTBP, 99%), triethylamine (TEA, ≤99%), 1-butanol (ACS reagent, ≥99.4%) and solvents were purchased from Aldrich and used as received without further purification.

Materials: Siloxane samples. Monomethacryloxypropyl terminated poly(dimethylsiloxane) (MCR-M07, M11, M17 with different average molecular mass 500, 1000, 5000 g/mol respectively) and methacryloxypropyl) terminated poly(dimethylsiloxane) (DMS-R11, R18 with different average molecular mass 1000, 3000 g/mol respectively) were purchased from Gelest company and purified by passing through a basic alumina column to remove the inhibitor. CuCl (98%), ligand N,N,N’,N’’,N’’-pentamethyldiethylenetriamine (PMDETA) and α-bromoisobutyryl bromide, triethylamine (TEA), tetrahydrofuran (THF), p-xylene (PX) were purchased from Aldrich and used as received. Difunctional initiator with two bromoisobutyrate groups (ethylene-1,2-bis(2-bromoisobutyrate)) was synthesized from ethylene glycol and2- bromoisobutyryl bromide. All other reagents and solvents were purchased from Aldrich and used as received without further purification.

Synthesis of 1 P(HEMA-TMS)2035 (2035-TMS). A 10 ml Schlenk flask was charged with 2-cyano-2-propyl 4-cyanobenzodithioate (0.0011 g, 0.0046 mmol), HEMA-TMS (10.0 mL, 45.9 mmol), AIBN (0.075 mg, 0.46 μmol, a stock solution) and toluene (0.5 mL). The solution was degassed by purging with nitrogen over 30 min. period. Afterwards, the sealed flask was immersed in an oil bath at 65 °C. Polymerization was terminated after 24 h and the polymer molecular weight was determined by THF GPC: Mn,GPC = 3.26·105, and Mw/Mn = 1.29 (Figure S1, gray). The degree of polymerization (DP) was calculated from the calibration curve (Mn,GPC=163.85·DP-7,000) and determined to be 2,035. The reaction mixture transferred to 100 mL pre-weighted, round-bottom flask, then the remaining monomer was removed by flushing air overnight and the polymer was used for the next step without further purification.

Synthesis of 2 (PBiBEM2035) (2035-Br). A 100 ml round-bottom flask was charged with 1 (4.40g, 21.8 mmol), KF (1.54 g, 26.1 mmol), DTBP (0.45 g, 2.18 mmol), and then dry THF (60 mL) was added under nitrogen. The reaction mixture was cooled down in an ice bath, followed by the injection of tetrabutylammonium fluoride (0.22

Solvent-free, supersoft and superelasticbottlebrush melts and networks

SUPPLEMENTARY INFORMATIONDOI: 10.1038/NMAT4508

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mL, 1.0 M in THF, 0.22 mmol) and subsequent dropwise addition of α-bromoisobutyryl bromide (6.01 g, 3.2 mL.

26.1 mmol) over the course of 20 min. Upon addition, the reaction mixture was allowed to reach room

temperature and was stirred for another 16 h.

Afterwards solids were filtered and the mixture was

precipitated into methanol/water (70/30), re-dissolved

in chloroform (50 mL) and passed through the column

filled with basic alumina. The product 2 was re-

precipitated three times in hexanes and dried overnight

under vacuum. Apparent molecular weight determined

by THF GPC: Mn,GPC = 6.94·105, and Mw/Mn = 1.76

(Figure S1, black).

Synthesis of 3 (PBiBEM2035-g-PnBA3/4)6 (BA-3/4). A

10 mL Schlenk flask equipped with a stir bar was

charged with macroinitiator 2 (0.1957 g, 0.7016 mmol

of BiBEM groups), nBA (5.0 mL, 35.08 mmol), dNbpy

(0.036 g, 0.088 mmol), CuIIBr2 (2.9 mg, 0.0130 mmol),

and anisole (0.5 mL). The solution was degassed by

three freeze-pump-thaw cycles. During the final cycle

CuIBr (4.4 mg, 0.0309 mmol) was quickly added to the

frozen reaction mixture under nitrogen atmosphere.

The flask was sealed, evacuated, back-filled with nitrogen five times, and then immersed in an oil bath

thermostated at 70 °C. The polymerization was stopped after 20 h, and the monomer conversion was determined

by 1H NMR (6.7%), resulting in the brush polymer 3 with DP~3-4 of side chains, assuming quantitative initiation

from all C-Br groups. The polymer was purified by three precipitations from cold methanol, and dried under

vacuum at room temperature, to a constant mass. Apparent molecular weight was determined using THF GPC:

Mn,GPC = 6.40·105, and Mw/Mn = 1.76 (Figure S1, red).

Synthesis of 4 (PBiBEM2035-g-PnBA10) (BA-17). The reaction was set up and analyzed in the same way as 3.

The amounts of reagents used for the polymerization: macroinitiator 2 (0.1957 g, 0.7016 mmol of BiBEM

groups), nBA (10.0 mL, 70.16 mmol), dNbpy (0.072 g, 0.175 mmol), CuIIBr2 (3.4 mg, 0.0153 mmol), anisole (1.0

mL) and CuIBr (10.4 mg, 0.0724 mmol). The polymerization was stopped after 24 h at 10.0 % conversion, giving

the brush polymer, 4, with DP=10 of side chains, assuming quantitative initiation from all C-Br groups. Apparent

molecular weight determined by THF GPC: Mn,GPC = 1.54·106, and Mw/Mn = 1.19 (Figure S1, orange).




mL) and CuIBr (11.3 mg, 0.0794 mmol). The polymerization was stopped after 18 h 30 min. at 8.0 % conversion,

giving the brush polymer, 5, with DP=16 of side chains, assuming quantitative initiation from all C-Br groups.

Apparent molecular weight determined by THF GPC: Mn,GPC = 1.87·106, and Mw/Mn = 1.19 (Figure S1, yellow).




mL) and CuIBr (11.9 mg, 0.0833 mmol). The polymerization was stopped after 19 h at 6.0 % conversion, giving

the brush polymer, 6, with DP=24 of side chains, assuming quantitative initiation from all C-Br groups. Apparent

molecular weight determined by THF GPC: Mn,GPC = 2.07·106, and Mw/Mn = 1.20 (Figure S1, pale green).

Figure S1. GPC traces of linear (gray) MI-TMS

and (black) MI-Br, and bottlebrushes (red) BA-3/4,

(orange) BA-17, (yellow), BA-23, (pale green), BA-

34, (dark green), BA-130, and (blue) BA-112.

104

105

106

107

Long Brushes, PnBA

2035-TMS

2035-Br

BA-3/4

BA-17

BA-23

BA-34

BA-130

BA-112

Molecular Weight


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Figure S2. LB isotherms of surface pressure versus

monomer area of linear and bottlebrush BA samples. The

𝐴𝐵𝑅 and 𝐴0 values were taken at identical surface

pressures (0.5 mN/m) to insure comparison of monolayers

at the same level of compression. Schematic displays

length L and width W of an adsorbed bottlebrush.



groups), nBA (10.0 mL, 70.16 mmol), dNbpy (0.048 g, 0.117 mmol), CuIIBr2 (0.69 mg, 0.0031 mmol), anisole

(1.1 mL) and CuIBr (12.5 mg, 0.0877 mmol). The polymerization was stopped after 20 h 15 min. at 8.1 %

conversion, giving the brush polymer, 7, with DP=48 of side chains, assuming quantitative initiation from all C-

Br groups. Apparent molecular weight determined by THF GPC: Mn,GPC = 3.38·106, and Mw/Mn = 1.13 (Figure S1,

dark green).

Typical procedure for side-chains cleavage. A 20 mL glass vial equipped with a stir bar was charged with a

bottlebrush (~50 mg) and dissolved in THF (~2 mL). Then 1-butanol (12 mL) was added followed by sulfuric

acid (5 drops). The vial was closed, sealed and placed in an oil bath at 100°C, for 7 days. Afterwards, the solvents

were removed on the residues were dissolved in THF (~3 ml) and passed through basic alumina.

Synthesis of PDMS bottlebrush elastomers. ,-Methacryloxypropyl terminated poly(dimethylsiloxane)

(DMS-R11) as cross-linker and monomethacryloxypropyl terminated poly(dimethylsiloxane) (5.0 mmol, 5.000

grams) (MCR-M11) as monomer with molar ratio of 0.005, 0.01, 0.02, 0.04 and ethylene bis(2-bromoisobutyrate)

(0.005 mmol, 1.80 mg), PMDETA (2 μL , 0.01 mmol) and p-xylene (4 mL) were added to an oxygen free flask.

CuCl (1.0 mg, 0.01 mmol) was added while the flask was purging with nitrogen and thermostated at 40C to start

the polymerization. The formed polymer networks were purified by swelling five times in fresh chloroform and

dried at atmospheric pressure and room temperature and then finally dried in vacuum at 60°C overnight. The

described polymerization process resulted in a gel fraction of 95% measured as mass ratio of the dried and as-

prepared networks.

Synthesis of poly(acrylamide) gels. A 20 ml glass vial was washed and dried the charged with deionized H2O

(18.37 g), monomer (1.60 g acrylamide, 22.5 mmol vinyl groups), crosslinker (43.1 mg N,N’-

methylenebis(acrylamide), 0.56 mmol vinyl groups), initiator (66.5 mg 2,2′-Azobis(2-methylpropionitrile) 0.36

mmol). The vial was vortexed at 2000 rpm for 2 min and a sample was drawn into a 3ml syringe. The syringe

was then sealed and placed into an 80° C oven to cure for 3 hrs.

2. Molecular weight analysis by LB-AFM

From the LB-AFM analysis, we determine the number

average mass per unit length of the backbone, which can

be directly translated to the side-chain degree of

polymerization per monomeric unit of the backbone as

𝑛𝑠𝑐

𝑛𝑔=

𝑟𝑡𝐴𝑏𝑟

𝑛𝑏𝑏𝐴0=

𝑟𝑡𝑙 (𝑊 +𝜋𝑟𝑡𝑊

2

4𝐿 )

𝐴0 (𝑆2.1)

where 𝑟𝑡- the LB transfer ratio, 𝐴𝑏𝑟- the area occupied a

bottlebrush macromolecule in AFM micrographs, and

𝐴0 = 𝑀0 (𝑚𝑁𝐴𝑣)⁄ is the area per BA monomer on a

Langmuir trough as calculated from the known mass of

material deposited per unit area of the trough (m) and

molar mass of the pBA monomer (𝑀0 = 128 𝑔/𝑚𝑜𝑙).

The molecular area 𝐴𝑏𝑟 was determined by two methods:

(i) counting the number of molecules () in AFM images


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per unit area, which gives 𝐴𝑏𝑟 = Ζ−1 and (ii) measuring contour length (L) and brush width (W) that give

𝐴𝑏𝑟 = 𝐿𝑊 + 𝜋𝑊2 4⁄ (assuming hemicircular end-caps of adsorbed bottlebrushes, (Fig. S2)). The results of the

LB-AFM analysis are summarized in Table S2. In eq S2.1, we assumed a fully extended backbone with a number

average contour length 𝐿 = 𝑛𝑏𝑏𝑙 = 510 𝑛𝑚 and a monomer length of 𝑙 = 0.25 𝑛𝑚. GPC measurement of the

macroinitiator DP displayed 𝑛𝑏𝑏 = 𝑀𝑀𝐼 𝑀0,𝑀𝐼⁄ = 2035 ± 100, in agreement with 𝑛𝑏𝑏 = 2040 ± 60 determined

by LB-AFM (Table 2). The full extension of the bottlebrush backbones is caused by steric repulsion of densely

grafted side chains resulting in a backbone tension of the order of 1 nN.1 The product of linear mass density

(equation S2.1) and bottlebrush contour length gives molecular weight distribution (MWD). Figure S3

demonstrates correlation between the MWD data obtained by the GPC and LB-AFM techniques. A slight shift

towards higher molecular weights seen in the LB-AFM is due to exclusion of small species analysis software.

Figure S3. Overlay of GPC traces of bottlebrush samples (red histograms) with LB-AFM molecular weight

distribution analysis (black lines). The green lines correspond to molecular weight distribution of the

macroinitiators (backbones without side chains).


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Table S1: Molecular characterization of PBA bottle brushes and their macroinitiators

Name Composition nsc,NMR 1

Mn,GPC2

Mw/Mn2

Mn,SC3

Mw/Mn,sc3

nsc4

Ieff5

MI-TMS P(HEMA-TMS)2035 - 326,000 1.29 - - - -

MI-Br PBiBEM2035 - 694,000 1.76 - - - -

BA-6 PBiBEM2035-g-PnBA3/4 3-4 640,000 1.76 - - - -

BA-17 PBiBEM2035-g-PnBA10 10 1,540,000 1.19 2,180 1.12 17 59

BA-23 PBiBEM2035-g-PnBA16 16 1,870,000 1.19 3,000 1.18 23 70

BA-34 PBiBEM2035-g-PnBA24 24 2,070,000 1.20 4,300 1.30 34 70

BA-130 PBiBEM2035-g-PnBA48 48 3,380,000 1.13 16,600 1.10 130 40 1Degree of polymerization of side-chains determined from the monomer conversion by

1H NMR, nSC,NMR =

ntargeted Mconversion. 2 Determined by THF GPC using PMMA standards. The GPC data are inaccurate due to the

large size and branched nature of the macromolecules. The more accurate AFM-LB data in Table 1 were used

for the data analysis. 3

Number average molecular weight and PDI of cleaved side chains determined by THF

GPC using PSt standards. 4

Degree of the polymerization of side chains determined from the equation: nSC =

Mn,SC / MBA, where MBA=128 – molecular weight of n-butyl acrylate 5

Initiation efficiency determined as Ieff =

(nSC,NMR / nSC)100%.

Table S2: LB-AFM analysis of the dimension and molecular weight of pBA bottlebrushes.

Sample 𝒓𝒕1 𝑨𝒃𝒓 (nm

-2)

2 W (nm) 3 𝒏𝒔𝒄 𝒏𝒈⁄ 4

Ln (nm) 5

Lw/Ln6

nbb7

BA-17 0.88 0.28 11 9 513 1.5 2052

BA-23 0.89 0.29 21 17 515 1.6 2060

BA-34 0.90 0.29 26 21 495 1.6 1980

BA-130 0.98 0.27 69 69 517 1.5 2068 1Transfer ratio defined as ratio of change in LB trough area over area of transfer substrate.

2Area per BA

monomer of the Langmuir monolayers on the water surface. 3Number average width of the PBA bottlebrush

samples from AFM. 4Number average DP of side-chains times grafting density as measured by LB-AFM (eq

S2.1). 5Number average contour length of PBA bottlebrush backbone measured using AFM.

6Dispersity of PBA

bottlebrush contour length, PDI=Lw/Ln, where Lw and Ln are weight and number average lengths.7Number

average DP of the backbone determined from the AFM contour length as nbb=L/l0, where l0=0.25 nm is the

monomer length.


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3. Theoretical description of bottlebrush and comb conformations

Molecular conformation and assembly of bottlebrush and comb-like polymers in melts depend on the degree of

polymerization (DP) of side chains (𝑛𝑠𝑐) and DP of the backbone spacer (𝑛𝑔) between grafting points of

neighboring side chains (Fig. S4), as well as on the monomeric volume 𝑣, the monomeric length 𝑙, and the

stiffness of polymer chains characterized by the Kuhn length b. For simplicity, we assume that parameters 𝑣, 𝑙,

and b are the same for both backbone and side chains. We introduce two dimensionless combinations of these

parameters as

𝑆 =𝑣

(𝑏𝑙)3/2 (𝑆3.1)

and

𝑠 =𝑣

𝑏𝑙2 (𝑆3.2)

Depending on the side-chain length and grafting density, we distinguish four conformational regimes with distinct

rheological behaviors (Fig. S4), however only the highest grafting density regime is considered in this

manuscript.

Figure S4: Diagrams of states of brush-like polymers in terms of degree of polymerization of side chains 𝑛𝑠𝑐

and backbone spacer between neighboring side chains 𝑛𝑔 (logarithmic scales). Comb regimes with almost

unperturbed Gaussian backbone and side chains: LC – loosely-grafted combs with strongly interpenetrating

neighboring combs, DC – dense combs with weak interpenetration. Bottlebrush regimes: LB – loosely-grafted

bottlebrushes with almost unperturbed Gaussian side chains and partially stretched backbone on length scale

of side chains, DB – dense bottlebrushes with extended side chains and stretched backbone on length scale of

side chains. Dashed lines at 𝑏/𝑙 correspond to boundaries of stiff side chains (vertical) for 𝑛𝑠𝑐 < 𝑏/𝑙, and stiff

spacer (horizontal) for 𝑛𝑔 < 𝑏/𝑙. Backbone is almost fully stretched up to length scale of side chain size

below the blue horizontal line 𝑛𝑔 ≅ 𝑛𝑔∗∗ ≅ 𝑠.


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3.1. Loosely-grafted comb regime (LC). At very low grafting density, the spacer between grafting points is

longer than side chains (𝑛𝑠𝑐 < 𝑛𝑔) and most of the molecular mass is in the polymer backbone. Both backbones

and side chains are in random Gaussian conformations. The entanglement degree of polymerization 𝑛𝑒 can be

estimated using the Kavassalis-Noolandi (K-N) conjecture2 that there is a fixed number 𝑃𝑒 ≅ 20 of sections of

different chains within the entanglement volume 𝑎3

𝑎3 ≈ (𝑏𝑙𝑛𝑒,𝑏𝑏)3 2⁄

(𝑆3.3)

The number of sections of different molecules within the entanglement volume 𝑎3 can be estimated as

𝑃𝑒 ≈𝑎3

𝑉𝑒≈

(𝑏𝑙𝑛𝑒,𝑏𝑏)3 2⁄

𝑣𝑛𝑒,𝑏𝑏(1 + 𝑛𝑠𝑐 𝑛𝑔⁄ ) (𝑆3.4)

where 𝑉𝑒 = 𝑣𝑛𝑒 - physical volume of the entanglement strand, 𝑛𝑒 = 𝑛𝑒,𝑏𝑏(1 + 𝑛𝑠𝑐 𝑛𝑔⁄ ) - total number of

monomeric units in the entanglement strand, and 1 + 𝑛𝑠𝑐 𝑛𝑔⁄ – reciprocal volume fraction of bottlebrush

backbones in the system. From eqs S3.1 and S3.4, we obtain the number of backbone monomers in the

entanglement strand of a comb-like macromolecule as

𝑛𝑒,𝑏𝑏 ≅ [𝑃𝑒𝑆 (𝑛𝑠𝑐

𝑛𝑔+ 1)]

2

(𝑆3.5)

Respectively, the number of monomeric units within a comb-like entanglement strand is

𝑛𝑒 ≅ 𝑃𝑒2𝑆2 (

𝑛𝑠𝑐

𝑛𝑔+ 1)

3

(𝑆3.6)

The plateau modulus of a melt of combs is equal to thermal energy kT per volume of an entanglement strand

𝑉𝑒 = 𝑣𝑛𝑒

𝐺𝑒 ≅𝑘𝑇

𝑉𝑒≅

𝑘𝑇

𝑣𝑃𝑒2𝑆2

(𝑛𝑔

𝑛𝑠𝑐 + 𝑛𝑔)

3

≅ 𝐺𝑒,𝑙𝑖𝑛 (𝑛𝑠𝑐

𝑛𝑔+ 1)

−3

(𝑛𝑠𝑐 < 𝑛𝑔) (𝑆3.7)

For loosely-grafted combs with very short side chains (very long spacers) 𝑛𝑠𝑐 ≪ 𝑛𝑔, the modulus is

approximately equal to that of linear polymer melt (see red horizontal LC lines in Figures S5a,b)

𝐺𝑒,𝑙𝑖𝑛 ≅𝑘𝑇

𝑃𝑒2

(𝑏𝑙)3

𝑣3≅

𝑘𝑇

𝑃𝑒2𝑣𝑆2

≅𝑘𝑇

𝑃𝑒2𝑑0

3 (𝑆3.8)

and the backbone DP of the entanglement strand (eq S3.5) is approximately equal to that of a linear polymer melt

𝑛𝑒,𝑙𝑖𝑛 ≅ (𝑃𝑒𝑆)2 ≅ 𝑃𝑒2

𝑣2

(𝑏𝑙)3 (𝑆3.9)

In eq S3.8, we introduce a characteristic length 𝑑0 ≅ (𝑣𝑆2)1 3⁄ , which corresponds to the average distance

between grafting points along the comb/bottlebrush contour (see Fig. S4) and will be defined in eq S3.17.


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3.2. Densely-grafted comb regime (DC). At intermediate grafting density with 𝑛𝑔∗ < 𝑛𝑔 < 𝑛𝑠𝑐, the

conformations of both side chains and backbone are almost unperturbed random Gaussian walks similar to the

loosely-grafted comb (LC) regime with end-to-end distance proportional to DP1/2

and “bare” Kuhn length b. Since

the grafting spacer is shorter than side chains (𝑛𝑔 < 𝑛𝑠𝑐), the pervaded volume of each side chain contains many

side chains from the same comb. With increasing grafting density 𝑛𝑔−1, this overlap of side chains from the same

comb increases, reducing interpenetration of side chains from the neighboring combs. To quantify this effect we

start from the overlap parameter of side chains 𝑃𝑠𝑐 equal to the ratio of their pervaded volume 𝑅𝑠𝑐3 ≈ (𝑏𝑙𝑛𝑠𝑐)

3 2⁄

and physical volume (𝑛𝑠𝑐𝑣)

𝑃𝑠𝑐 ≅ 𝑅𝑠𝑐3 (𝑛𝑠𝑐𝑣)⁄ ≅ 𝑛𝑠𝑐

1 2⁄𝑆⁄ (S3.10)

A section of a backbone passing through this volume 𝑅𝑠𝑐3 contains on average 𝑛𝑠𝑐 monomers because its

conformations are similar to the conformations of side chains. Therefore, there are groups of 𝑛𝑠𝑐 𝑛𝑔⁄ side chains

belonging to the same comb molecule and connected to each other through the backbone section containing 𝑛𝑠𝑐

monomers within the volume 𝑅𝑠𝑐3 . The number of such groups (branched sections) belonging to different comb

molecules overlapping with each other within the volume 𝑅𝑠𝑐3 is

𝑍 =𝑃𝑠𝑐𝑛𝑔

𝑛𝑠𝑐≅

𝑛𝑔

𝑆𝑛𝑠𝑐1 2⁄

≅𝑛𝑔

𝑛𝑔∗ ≥ 1 𝑓𝑜𝑟 𝑛𝑔

∗ < 𝑛𝑔 < 𝑛𝑠𝑐 (𝑆3.11)

where 𝑛𝑔∗ gives the lower boundary of spacer DP of the dense comb (DC) regime

𝑛𝑔∗ = 𝑛𝑠𝑐

1 2⁄𝑆 (𝑆3.12)

is provided by weak overlap (𝑍 ≅ 1) between side chains of neighboring molecules. In other words, the 𝑛𝑔 = 𝑛𝑔∗

boundary corresponds to transition from overlapping combs to segregated bottlebrushes with almost no overlap.

Figure S5: Different regimes of comb-like polymers as a function (a) degree of polymerization (DP) of the

spacer between neighboring side chains 𝑛𝑔 (at constant 𝑛𝑠𝑐) and (b) side chain DP 𝑛𝑠𝑐 (at constant 𝑛𝑔). (a)

Dependence of the plateau modulus 𝐺𝑒 of bottlebrush melt normalized by the plateau modulus of linear melt

𝐺𝑒,𝑙𝑖𝑛 (eq. S3.7 S3.25, S3.32) on the degree of polymerization 𝑛𝑔 of spacer between grafting points.

Logarithmic scales. (b) Dependence of the plateau modulus 𝐺𝑒 of bottlebrush melt normalized by the plateau

modulus of linear melt 𝐺𝑒,𝑙𝑖𝑛 (eq. S3.7 S3.25, S3.32) on the degree of polymerization 𝑛𝑠𝑐 of spacer.


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Since the conformation of a comb backbone remains ideal (𝑅𝑏𝑏~√𝑛𝑏𝑏), the expression for the plateau modulus

Ge in both loosely and densely grafted comb regimes is the same (eq S.7). For shorter spacers in the DC regime

(𝑛𝑔 < 𝑛𝑠𝑐), the plateau modulus decreases inversely proportional to cube of the degree of polymerization of side

chains (see red lines with slopes 3 and -3 in Figures 5a and 5b respectively)

𝐺𝑒 ≅ 𝐺𝑒,𝑙𝑖𝑛 (𝑛𝑔

𝑛𝑠𝑐)3

𝑓𝑜𝑟 𝑛𝑔∗ < 𝑛𝑔 < 𝑛𝑠𝑐 (𝑆3.13)

3.3 Loosely-grafted bottlebrush regime (LB). Increase of the grafting density reduces overlap of side chains

belonging to neighboring bottlebrushes which become nearly fully segregated (𝑍 < 1) at 𝑛𝑔 < 𝑛𝑔∗ (eq S3.11).

Further increase of the grafting density results in extension of the backbone followed by extension of the side

chains.1,3

Here we distinguish two bottlebrush regimes: (i) loosely-grafted and (ii) densely-grafted bottlebrushes.

The loose bottlebrushes (LB) are observed within an intermediate grafting density range

𝑛𝑔∗∗ < 𝑛𝑔 < 𝑛𝑔

∗ (𝑆3.14)

In this range, the side chains remain almost unperturbed with size

𝑅𝑠𝑐 ≅ 𝑅𝑠𝑐,0 ≅ (𝑏𝑙𝑛𝑠𝑐)1 2⁄ (𝑆3.15)

while the backbone of a loosely-grafted bottlebrush undergoes extension with increasing grafting density until it

reaches full extension at a grafting density of

𝑛𝑔∗∗ = 𝑑0 𝑙⁄ = 𝑣 𝑏𝑙2⁄ ≡ 𝑠 (𝑆3.16)

In the LB regime, the backbone is extended on length scale of side chains 𝑅𝑠𝑐 to avoid overcrowding and keep

the number of side chains 𝑃𝑠𝑐 (eq S3.10) within the volume 𝑅𝑠𝑐3 constant. As the backbone extends, it maintains

the constant average distance between grafting points along the contour of a bottlebrush is

𝑑0 =𝑅𝑠𝑐

𝑃𝑠𝑐≅ (𝑏𝑙)1 2⁄ 𝑆 ≅

𝑣

𝑏𝑙 (𝑆3.17)

The sections of the bottlebrush backbone in LB regime contain 𝑛𝑔𝑃𝑠𝑐 monomers stretched to length 𝑅𝑠𝑐 to avoid

overcrowding within volume 𝑅𝑠𝑐3 .

Another way to understand this is to estimate the smallest length scale 𝜉 (fig. S6a) on which this side chain

crowding effect near backbone occurs. Since there is no crowding problem up to length scale 𝜉, both side chain

and backbone sections of this size 𝜉 containing 𝑔 monomers each are in almost unperturbed Gaussian

conformations with

𝜉 ≅ (𝑏𝑙𝑔)1 2⁄ . (S3.18)

and there are 𝑔 𝑛𝑔⁄ side chains grafted to the backbone within length scale 𝜉. Sections of size 𝜉 of 𝑔 𝑛𝑔⁄ side

chains collectively contain 𝑔2 𝑛𝑔⁄ monomers with the total volume 𝑣 𝑔2 𝑛𝑔⁄ . The crowding problem occurs if

this total volume of side chain sections reaches their pervaded volume 𝜉3

𝜉3 ≅ (𝑏𝑙𝑔)3 2⁄ ≅ 𝑣 𝑔2 𝑛𝑔⁄ . (S3.19)

This condition gives the number of monomers 𝑔 ≅ (𝑛𝑔 𝑆⁄ )2 and the corresponding length scale

𝜉 ≈ 𝑛𝑔(𝑏𝑙)2 𝑣⁄ (S3.20)

The bottlebrush backbone has almost unperturbed Gaussian conformations with bare Kuhn length b up to this


10

length scale of tension blob 𝜉 (Eq. S3.21). On length scales larger than 𝜉, but smaller than side chain size 𝑅𝑠𝑐 it is

a stretched array of tension blobs to avoid crowding problem at these intermediate length scales. On length scales

larger than 𝑅𝑠𝑐 there is no crowding problem and backbone keeps its unperturbed Gaussian conformation. The

average distance between grafting points along the contour of bottlebrush in LB regime is (see eq S3.18)

𝜉

𝑔𝑛𝑔 ≅

𝑅𝑠𝑐

𝑃𝑠𝑐≅ 𝑣 𝑏𝑙⁄ ≅ 𝑑0 (𝑆3.21)

where the number of overlapping side chains Psc is given in Eq. S3.12.

Figure S6: (a) Conformation of a bottlebrush molecule in a melt in LB regime. The backbone is an almost

unperturbed Gaussian random walk on length scales smaller than tension blob size 𝜉, a stretched array of tension

blobs on length scales between 𝜉 and side chain size 𝑅𝑠𝑐 and a random walk on length scales larger than 𝑅𝑠𝑐. (b)

Dependence of bottlebrush backbone size 𝑅𝑏𝑏 and side chain size 𝑅𝑠𝑐 normalized by their Gaussian values

𝑅𝑏𝑏,0 ≅ (𝑏𝑙𝑛𝑏𝑏)1 2⁄ and 𝑅𝑠𝑐,0 ≅ (𝑏𝑙𝑛𝑠𝑐)

1 2⁄ on the degree of polymerization 𝑛𝑔 of spacer between grafting points.

In the bottlebrush regimes (LB and DB), the neighboring bottlebrush molecules only weakly interpenetrate and

can be thought as thick flexible cylindrically-shaped filaments with both thickness and effective persistence

length on the order of 𝑅𝑠𝑐 and with contour length

𝐿 ≅𝑛𝑏𝑏

𝑛𝑔𝑑0 (𝑆3.22)

By combining eqs S3.15, S3.17, S3.22, we can show that the mean square size of the molecule increases with

increasing DP (𝑛𝑠𝑐) and grafting density 𝑛𝑔−1 of the side chains as

𝑅𝑏𝑏2 ≅ 𝑅𝑠𝑐𝐿 ≅

𝑣

(𝑏𝑙)1 2⁄

𝑛𝑠𝑐1 2⁄

𝑛𝑏𝑏

𝑛𝑔≈ 𝑅𝑠𝑐

2 𝑆

𝑛𝑔𝑛𝑠𝑐1 2⁄

𝑛𝑏𝑏 𝑓𝑜𝑟 𝑛𝑔∗∗ < 𝑛𝑔 < 𝑛𝑔

∗ (𝑆3.23)

which is depicted by red solid lines with slope -1/2 in Figs. S6b.

Applying Kavassalis-Noolandi conjecture (eq S3.4) to the bottlebrush melt in LB regime using 𝑎 ≅ 𝑅𝑏𝑏,𝑒 with

𝑛𝑏𝑏 = 𝑛𝑏𝑏,𝑒 (eq S3.23), we obtain the DP of entanglement backbone strand

𝑛𝑏𝑏,𝑒 ≅𝑃𝑒

2𝑛𝑔𝑛𝑠𝑐1 2⁄

𝑆≅ 𝑛𝑒,𝑙𝑖𝑛

𝑛𝑔𝑛𝑠𝑐1 2⁄ (𝑏𝑙)9/2

𝑣3𝑓𝑜𝑟 𝑛𝑔

∗∗ < 𝑛𝑔 < 𝑛𝑔∗ (𝑆3.24)


11

and 𝑛𝑔-independent plateau modulus


𝑃𝑒2𝑅𝑠𝑐

3 ≅ 𝐺𝑒,𝑙𝑖𝑛

𝑣3

(𝑙𝑏)9 2⁄

1

𝑛𝑠𝑐3 2⁄

≅ 𝐺𝑒,𝑙𝑖𝑛

𝑆3

𝑛𝑠𝑐3 2⁄

𝑓𝑜𝑟 𝑛𝑔∗∗ < 𝑛𝑔 < 𝑛𝑔

∗ (𝑆3.25)

which is reciprocally proportional to the pervaded volume of side chains 𝐺𝑒~𝑅𝑠𝑐−3~𝑛𝑠𝑐

−3/2(see green line with

slope -3/2 in Figs.S5b). The modulus (𝐺𝑒,𝑙𝑖𝑛) and backbone DP of the entanglement strand of a linear polymer

melt (𝑛𝑒,𝑙𝑖𝑛) are given by eq S3.8 and eq S3.9, respectively. Eq S3.25 suggests that the plateau modulus of

loosely-grafted bottlebrushes is independent of grafting density, which is explained by extension of the backbone

within the cylindrical envelope of a bottlebrush at a constant density of entanglements.

3.4 Densely-grafted Bottlebrush Regime (DB) The boundary between the LB and DB regimes (𝑛𝑔 < 𝑛𝑔∗∗ = 𝑠)

corresponds to tension blob on the order of the Kuhn length 𝜉 ≈ 𝑏 and the DP of the spacer between grafting

points at this boundary is given by eq S3.16. At higher grafting density 1 ≤ 𝑛𝑔 < 𝑛𝑔∗∗ the backbone is almost

fully stretched as

𝐿 ≅ 𝑙𝑛𝑏𝑏 (𝑆3.26)

while maintaining random walk conformations on length scales larger than the side chain size 𝑅𝑠𝑐. The variation

of backbone stretching in this non-linear elastic regime is by the factor on the order of unity. The side chains

extend with increasing grafting density to assure that the side chain volume 𝑣𝑛𝑠𝑐 is equal to the bottlebrush

volume per backbone spacer 𝑛𝑔𝑙𝑅𝑠𝑐2 leading to side-chain size

𝑅𝑠𝑐 ≅ 𝑅𝑠𝑐,0 (𝑠

𝑛𝑔)

1 2⁄

𝑓𝑜𝑟 1 ≤ 𝑛𝑔 < 𝑛𝑔∗∗ (𝑆3.27)

where 𝑅𝑠𝑐,0 ≅ (𝑏𝑙𝑛𝑠𝑐)1 2⁄ – dimension of an unperturbed side chain. From eq S3.27, side-chain size (bottlebrush

diameter) increases as square root of grafting density 𝑛𝑔−1 (see the blue dashed line with slope -1/2 in Fig. S6b).

The thick flexible bottlebrush with both thickness and persistence length on the order of 𝑅𝑠𝑐 has mean square size

𝑅𝑏𝑏2 ≅ 𝑅𝑠𝑐𝐿 ≈ (

𝑣𝑙𝑛𝑠𝑐

𝑛𝑔)

1 2⁄

𝑛𝑏𝑏 (𝑆3.30)

increasing as one forth power of grafting density (𝑛𝑔−1) (see the red solid line with slope -1/4 in Fig. S6b). Note

that backbone size is proportional to one forth power of side chain DP.

From the Kavassalis-Noolandi conjecture one can estimate the DP of the entanglement backbone strand

𝑛𝑏𝑏,𝑒 ≅ 𝑃𝑒2 (

𝑣

𝑙3)1 2⁄

(𝑛𝑠𝑐

𝑛𝑔)

1 2⁄

≅ 𝑛𝑒,𝑙𝑖𝑛

𝑏3

𝑣3/2(𝑛𝑠𝑐

𝑛𝑔)

1 2⁄

𝑓𝑜𝑟 1 ≤ 𝑛𝑔 < 𝑛𝑔∗∗ (𝑆3.31)

and the corresponding to the plateau modulus


𝑃𝑒2 (

𝑙𝑛𝑔

𝑣0𝑛𝑠𝑐)

3 2⁄

≅𝑘𝑇

𝑃𝑒2𝑅𝑠𝑐

3 ≅ 𝐺𝑒,𝑙𝑖𝑛 (𝑣

𝑏2𝑙)3/2

(𝑛𝑔

𝑛𝑠𝑐)3/2

𝑓𝑜𝑟 1 ≤ 𝑛𝑔 < 𝑛𝑔∗∗ (𝑆3.32)

which is reciprocally proportional to the pervaded volume of side chains 𝐺𝑒~𝑅𝑠𝑐−3~𝑛𝑠𝑐

−3/2 (see blue line with slope

-3/2 in Fig.S5b). In this regime plateau modulus increases as 3/2 power of spacer chains DP (𝐺𝑒~𝑛𝑔3/2

), as shown

by the blue line with slope 3/2 in Fig. S5a. In eqs S3.31 and S3.32, the modulus (𝐺𝑒,𝑙𝑖𝑛) and backbone DP of the

entanglement strand of a linear polymer melt (𝑛𝑒,𝑙𝑖𝑛) are given by eq S3.8 and eq S3.9, respectively.


12

3.5 Extensibility of bottlebrush networks. The maximum extension ratio of a bottlebrush network is calculated

assuming that the number average degree of polymerization of the backbone of network stands (𝑛𝑥) is larger than

that of the entanglement strand (𝑛𝑏𝑏,𝑒 < 𝑛𝑏𝑏,𝑥) as

𝜆𝑚𝑎𝑥 ≅𝑅𝑒,𝑚𝑎𝑥

𝑅𝑒,0≅

𝑛𝑒,𝑏𝑏𝑙

𝑅𝑒,0 𝑆3.33

where 𝑅𝑒,0 and 𝑅𝑒,𝑚𝑎𝑥 are the end-to-end distances of the entanglement strand in the unperturbed state and after

full extension, respectively. While the contour length of a entanglement strand is straight forward (𝑅𝑒,𝑚𝑎𝑥 ≅

𝑛𝑒,𝑏𝑏𝑙), its Gaussian dimensions (𝑅𝑒,0) are controlled by bottlebrush rigidity depending on the DP of side chains

and grafting spacer as

𝑅𝑒,0 ≅ (𝑏𝐿𝑒)1 2⁄ ≅ √𝑏𝑙𝑛𝑒,𝑙𝑖𝑛 (𝑙𝑜𝑜𝑠𝑒 𝑐𝑜𝑚𝑏: 𝑛𝑠𝑐 < 𝑛𝑔) (𝑆3.34)

𝑅𝑒,0 ≅ (𝑏𝐿𝑒)1 2⁄ ≅ √𝑏𝑙𝑛𝑒,𝐷𝐶 (𝑑𝑒𝑛𝑠𝑒 𝑐𝑜𝑚𝑏: 𝑛𝑔

∗ < 𝑛𝑔 < 𝑛𝑠𝑐) (𝑆3.35)

𝑅𝑒,0 ≅ (𝑅𝑠𝑐𝐿𝑒)1 2⁄ ≅

𝑣1 2⁄

(𝑏𝑙)1 4⁄

𝑛𝑠𝑐1 4⁄

𝑛𝑔1 2⁄

𝑛𝑒,𝐿𝐵1 2⁄

(𝑙𝑜𝑜𝑠𝑒 𝑏𝑜𝑡𝑡𝑙𝑒𝑏𝑟𝑢𝑠ℎ: 𝑛𝑔∗∗ < 𝑛𝑔 < 𝑛𝑔

∗) (𝑆3.36)

𝑅𝑒,0 ≅ (𝑅𝑠𝑐𝐿𝑒)1 2⁄ ≅ (


𝑛𝑔)

1 4⁄

𝑛𝑒,𝐷𝐵1 2⁄

(𝑑𝑒𝑛𝑠𝑒 𝑏𝑜𝑡𝑡𝑙𝑒𝑏𝑟𝑢𝑠ℎ: 1 ≤ 𝑛𝑔 < 𝑛𝑔∗∗) (𝑆3.37)

where the degrees of polymerization of a backbone of the entanglement strand in the corresponding brush

regimes are defined by equations S3.5 (LC and DC), S3.24 (LB), and S3.31 (DB). From equation S3.35-S3.37,

we obtain the following relations for the maximum extension ratio:

𝜆𝐿𝐶 ≅ 𝜆𝑙𝑖𝑛 ≅ (𝑙

𝑏)1 2⁄

√𝑛𝑒,𝑙𝑖𝑛 (𝑙𝑜𝑜𝑠𝑒 𝑐𝑜𝑚𝑏: 𝑛𝑠𝑐 < 𝑛𝑔) (𝑆3.38)

𝜆𝐷𝐶

𝜆𝑙𝑖𝑛 ≅ √

𝑛𝑒,𝐷𝐶

𝑛𝑒,𝑙𝑖𝑛≅

𝑛𝑠𝑐

𝑛𝑔+ 1 ≅

𝑛𝑠𝑐

𝑛𝑔 (𝑑𝑒𝑛𝑠𝑒 𝑐𝑜𝑚𝑏: 𝑛𝑔

∗ < 𝑛𝑔 < 𝑛𝑠𝑐) (𝑆3.39)

𝜆𝐿𝐵

𝜆𝑙𝑖𝑛≅

𝑙3 4⁄ 𝑏3 4⁄

𝑣1 2⁄

𝑛𝑔1 2⁄

𝑛𝑠𝑐1 4⁄ √

𝑛𝑒,𝐿𝐵


𝑛𝑔(𝑏𝑙)3

𝑣2 (𝑙𝑜𝑜𝑠𝑒 𝑏𝑜𝑡𝑡𝑙𝑒𝑏𝑟𝑢𝑠ℎ: 𝑛𝑔∗∗ < 𝑛𝑔 < 𝑛𝑔

∗) (𝑆3.40)

𝜆𝐷𝐵

𝜆𝑙𝑖𝑛 ≅

𝑏1 2⁄ 𝑙1 4⁄

𝑣1 4⁄

𝑛𝑔1 4⁄

𝑛𝑠𝑐1 4⁄ √

𝑛𝑒,𝐷𝐵


𝑏2𝑙

𝑣(𝑑𝑒𝑛𝑠𝑒 𝑏𝑜𝑡𝑡𝑙𝑒𝑏𝑟𝑢𝑠ℎ: 1 ≤ 𝑛𝑔 < 𝑛𝑔

∗∗) (𝑆3.41)

3.6 Extensibility of polymeric gels

In undeformed as-prepared gel with polymer volume fraction 𝜙0 ≅ 𝑉𝑑𝑟𝑦 𝑉0⁄ , the polymeric strands between

crosslinks have a size on the order the square root of the mean square end-to-end distance of a chain in a

semidilute solution as

𝑅 ≅ 𝑅𝑜 (𝜙0

𝜙∗∗)−1 8⁄

≅ (𝑏𝑙𝑛)1 2⁄ (𝑣

(𝑏𝑙)3 2⁄)

1 4⁄

𝜙0−

18 (𝜙0 < 𝜙∗∗) (𝑆3.42)


13

where 𝑅0 ≅ (𝑏𝑙𝑛)1 2⁄ – root mean square end-to-end distance of an unperturbed strand, 𝜙0 – polymer

concentration in an as-prepared gel, 𝜙∗∗ ≅ 𝑣02 (𝑏𝑙)3⁄ - concentration at which thermal and correlation blobs are of

the same size, and 𝑣0 - excluded volume [Ch. 5, ref. 7].

The maximum elongation of the polymeric strand between crosslinks is on the order of the contour length of the

strand

𝑅𝑚𝑎𝑥 ≅ 𝑙 𝑛 (𝑆3.43)

From eqs 1 and 2 we estimate the maximum extensibility of a gel to be

𝜆𝑚𝑎𝑥𝑔𝑒𝑙

=𝑅𝑚𝑎𝑥

𝑅0≅ (

𝑙7

𝑏𝑣02)

1 8⁄

𝑛1 2⁄ 𝜙01/8

(𝑆3.44)

Shear modulus of an as-prepared gel depends on the polymer volume fraction as follows

𝐺 ≅𝜌𝑅𝑇

𝑛𝑀0𝜙0 (𝑆3.45)

From eqs 3 and 4, we obtain the maximum extensibility of a polymeric gel in an athermal solvent as


≅ (𝜌𝑅𝑇

𝑀0𝐺)1 2⁄

(𝑙7

𝑏𝑣02)

1 8⁄

𝜙05/8

(𝑆3.46)

For pMA gel (𝑀0 = 71 𝑔/𝑚𝑜𝑙, 𝜌 = 1.11 𝑔/𝑐𝑚3, 𝑏 = 2 𝑛𝑚, 𝑙 = 0.25 𝑛𝑚) in an athermal solvent (𝑣0 ≅ 10𝑣,

where 𝑣 = 𝑀0 𝜌⁄ = 0.11 𝑛𝑚3 - physical volume of the monomeric unit (Table 3.1 in ref 7)), eq 5 gives


≅ 7.8. This can be compared with the corresponding extensibility of a bottlebrush network (also expressed

as a function of its shear modulus) as

𝜆𝑚𝑎𝑥𝑏𝑏 ≅ (

𝜌𝑅𝑇

𝑀𝑜𝐺)1 2⁄

(𝑙3

𝑣)

1 4⁄

𝜙𝑏𝑏3 4⁄ (𝑆3.47)

where 𝜙𝑏𝑏 ≅ 𝑛𝑔 𝑛𝑠𝑐⁄ – volume fraction of bottlebrush backbones in the elastomer. For pBA bottlebrush

elastomer (𝑀𝑜 = 128 𝑔/𝑚𝑜𝑙, 𝜌 = 1.09 𝑔/𝑐𝑚3, 𝑏 = 1.8 𝑛𝑚, 𝑙 = 0.25 𝑛𝑚), eq 6 gives 𝜆𝑚𝑎𝑥𝑏𝑏 ≅ 9.2.

3.7 Summary


14

Figure S7: Diagrams of conformational and mechanical regimes. (a) Diagram of states of brush-like polymers

in terms of degree of polymerization of side chains 𝑛𝑠𝑐 and backbone spacer between neighboring side chains 𝑛𝑔

(logarithmic scales). Comb regimes are characterized by almost unperturbed Gaussian backbone and side chains:

LC – loosely-grafted combs strongly interpenetrate neighboring combs, DC – dense combs displaying weak

interpenetration. Bottlebrush regimes: LB – loosely-grafted bottlebrushes show unperturbed Gaussian side chains,

while the backbone is stretched on the length scale of the side chain, DB – dense bottlebrushes show extended

side chains and backbone. The solid lines indicate crossovers between the regimes that occur both upon

increasing grafting density and side-chain DP as (1) LC-DC at 𝑛𝑔 ≅ 𝑛𝑠𝑐, (2) DC-LB at 𝑛𝑔 ≅ 𝑛𝑔∗ = 𝑆𝑛𝑠𝑐

1 2⁄, and (3)

LB-DB at 𝑛𝑔 ≅ 𝑛𝑔∗∗ = 𝑠. Where 𝑠 = 𝑣 (𝑏𝑙2)⁄ and 𝑆 = 𝑣 (𝑏𝑙)3 2⁄⁄ are dimensionless parameters of the order of

unity depending on 𝑣-monomer volume, 𝑙-monomer length, and 𝑏-Kuhn length of the linear polymer. The dotted

vertical line at 𝑛𝑠𝑐 = 𝑏/𝑙 corresponds to the boundary between stiff and flexible side chains with a contour length

equal to the Kuhn monomer (𝑛𝑠𝑐𝑙 = 𝑏). The encircled numbers 1, 2, 3 indicates crossovers between the grafting

regimes along with the corresponding variations in the entanglement modulus b and extensibility c.

(b) The entanglement plateau modulus (𝐺𝑒,𝑏𝑟𝑢𝑠ℎ) of a melt of brush-like macromolecules decreases relatively to

the modulus of a linear-polymer melt (𝐺𝑒,𝑙𝑖𝑛𝑒𝑎𝑟) both with increasing 𝑛𝑠𝑐 and decreasing 𝑛𝑔 (vertical arrow).

Upper red line: The loosely grafted systems at a constant value of 𝑛𝑔 > 𝑛𝑔∗∗ = 𝑣 (𝑏𝑙2)⁄ transition through three

regimes as 𝑛𝑠𝑐 increases: (i) Loose combs (LC) display mechanical properties similar to linear polymer

(𝐺𝑒,𝑏𝑟𝑢𝑠ℎ ≅ 𝐺𝑒,𝑙𝑖𝑛𝑒𝑎𝑟). (ii) Dense combs (DC) repel neighboring combs due to steric repulsion leading to dilution

of molecular entanglements and modulus reduction as 𝐺𝑒,𝑏𝑟𝑢𝑠ℎ~𝑛𝑠𝑐−3. (iii) In loose bottlebrushes (LB), steric

repulsion between side chains stretches the backbone within the cylindrical envelope of a bottlebrush leading to

an increase of the persistence length as 𝑙𝑝~𝑛𝑠𝑐1 2⁄

(Fig. 1d), which slows down the modulus reduction as

𝐺𝑒~𝑛𝑠𝑐−3 2⁄

. Dashed red line: Upon decreasing 𝑛𝑔, the red line will shift displaying the LC-DC (1) and DC-LB (2)

crossovers at lower 𝑛𝑠𝑐 values. Lower blue line: At a higher grafting density (𝑛𝑔 < 𝑛𝑔∗∗), we deal with dense

bottlebrushes (DB) possessing both extended backbone and extended side chains. Dense brushes display the

𝐺𝑒~𝑛𝑠𝑐−3 2⁄

modulus reduction trend but at lower modulus (vertical dotted lines) values due to stretched side

chains. The loosely grafted systems (e.g. dense combs) may allow similarly low moduli, but only at longer side

chains (dash-doted line) potentially leading to temporary side chain entanglements.

(c) Maximum extensibility of brush-like elastomers 𝜆𝑏𝑟𝑢𝑠ℎ ≅ 𝑅𝑒,𝑚𝑎𝑥 𝑅𝑒,0⁄ relative to linear-chain networks is

calculated assuming the crosslinking density is lower than the entanglement density, where 𝑅𝑒,0 and 𝑅𝑒,𝑚𝑎𝑥 are

mean square end-to-end distances of the entanglement strand before and after extension, respectively. LC

elastomers display extensibility on similar to linear elastomers up until 𝑛𝑠𝑐 = 𝑛𝑔 (1) Extensibility of DC

elastomers increases as 𝜆𝐷𝐶 𝜆𝑙𝑖𝑛𝑒𝑎𝑟 ⁄ ≅ 𝑛𝑠𝑐 𝑛𝑔⁄ in the range of 𝑛𝑠𝑐 < 𝑛𝑔2 𝑆2⁄ (2) due to dilution of the network

with growing side chains. In the LB regime, 𝜆𝑏𝑟𝑢𝑠ℎ does not depend on 𝑛𝑠𝑐 leveling off at 𝜆𝐿𝐵 𝜆𝑙𝑖𝑛𝑒𝑎𝑟 ⁄ ≅ 𝑛𝑔 𝑆2⁄

(dotted horizontal line). This occurs due to dilution of entanglements with increasing bottlebrush diameter, which

is being counteracted by increase in entanglement density due to stiffening of bottlebrushes. For the same reason,

dense bottlebrushes (DB regime) also do not exhibit any dependence on 𝑛𝑠𝑐; yet, the maximum extensibility of

bottlebrush elastomers is higher than that of the linear-chain elastomers by a factor 𝑏2𝑙 𝑣⁄ . For pBA ( 𝑣 =0.2 𝑛𝑚3, 𝑙 = 0.25 𝑛𝑚, 𝑏 = 1.8 𝑛𝑚), we expect ca. 4 enhancement in extendibility. Even higher extensibility is

predicted for dense pBA combs depending on the spacer DP as 𝜆𝐿𝐵 𝜆𝑙𝑖𝑛𝑒𝑎𝑟 ⁄ ≅ 𝑛𝑔 𝑆2⁄ ≅ 2.3𝑛𝑔, where 𝑆 =

𝑣 (𝑏𝑙)3 2⁄⁄ ≅ 0.67. For dense combs with 𝑛𝑔 = 10, we expect a maximum extensibility of a comb elastomer 23

higher than that of an elastomer made of linear chains (3) (vertical dotted line).


15

Figure S8: Rheological master curve of storage

modulus (𝐺′), loss modulus (𝐺′′) and the tangent delta

(tan(δ)) as a function of angular frequency. The vertical

and horizontal dashed line mark the minimum of tangent

delta and the entanglement modulus, respectively.

Figure S9: Phase angle (δ) vs. complex modulus

(𝐺∗). The entanglement modulus is assigned

using the van Gurp Palmen method as the value of

the 𝐺∗ at the minimum value of the tan(δ) within

the entanglement regime.

4. Rheological master curves

Based on the time-temperature superposition principle, master curves of modulus versus frequency were

constructed using TRIOS software from TA instrument. A series of Williams–Landel–Ferry (WLF) parameters

was generated using eq S4.1 for each sample and used to shift the final master curves to 298 K

log(𝛼𝑡) =−𝐶1(𝑇−𝑇𝑟)

𝐶2+(𝑇−𝑇𝑟) (S4.1)

Where 𝛼𝑡-frequency shift factor for a desired reference temperature, 𝐶1and 𝐶2-

empirical fitting constants derived from manual shifts of data at multiple

temperatures, 𝑇 and 𝑇𝑟 - sample temperature and desired reference

temperature, respectively.4 Table S3 summarizes the corresponding WLF

parameters.

5. Characterizing the entanglement plateau

Two methods were used to analyze the entanglement plateau modulus of the polymer samples. Values of

entanglement moduli and relevant parameters for all methods are displayed in Table S4. Figure S11 shows trends

of entanglement moduli versus relative side-chain length. Both methods for assigning entanglement moduli give

excellent agreement with theory showing dependence on relative side-chains DP (𝐺𝑒~(𝑛𝑠𝑐 𝑛𝑔⁄ + 1)−3/2) as

shown in Figure S11 below.

5.1 Minimum method The value of the entanglement modulus is taken as the value of 𝐺′ at the frequency of the

minimum in the tangent delta as described in detail by Lomellini5 (Fig. S8). Entanglement modulus and tangent

delta data is represented in Table S4 and the trend in entanglement modulus versus relative sidechains DP is

displayed in black in Fig. S11.

5.2 van Gurp Palmen method. The van Gurp Palmen method assigns the entanglement modulus as the value of

the storage modulus at the minimum in phase angle within the entanglement regime of a VGP plot6 (Fig. S9).

Entanglement modulus and phase angle data are presented in Table S4, and entanglement moduli versus relative

sidechains size are displayed in red in Fig. S11.

Table S3: WLF parameters

sample C1 C2 (K)

BA-6 7.3 129.2

BA-17 3.9 153.9

BA-23 3.5 154.4

BA-34 3.8 161.8

BA-130 3.6 162.5


16

5.3 Double reptation model fitting. The value of the storage modulus determined by modeling experimental

data with a fitting equation described below. To evaluate the rheological data we model the storage modulus

𝐺′() and loss modulus 𝐺′′ () using the molar mass weight Me as a fitting parameter. The storage and loss

modulus can be presented as the sine and cosine transform of the time dependent modulus G(t)6,7

:

𝐺′(𝜔) = 𝜔 ∫ 𝐺(𝑡) sin(𝜔𝑡) 𝑑𝑡

∞

0

(𝑆5.1)

𝐺′′(𝜔) = 𝜔 ∫ 𝐺(𝑡) cos(𝜔𝑡) 𝑑𝑡

∞

0

(𝑆5.2)

A model for G(t) includes two distinct regions of rheological behavior seen in the bottlebrush sample. These are

Region 1: power law relaxation with exponent 0.6 representing transition zone of chain of effective Kuhn

monomers, where 𝐺1and 𝜏𝑡 are the modulus and relaxation time of the effective Kuhn monomer. Note 𝐺1and

𝜏𝑡serve to shift the date to allow overlap between the power law and experimental data. As their specific values

do not have physical meaning in the application of this theory

𝐺(𝑡)𝑝𝑜𝑤𝑒𝑟 = 𝐺1 (𝑡

𝜏1)−0.6

(𝑆5.3)

and Region 2: entanglement relaxation. For monodisperse melts, as the entanglement relaxation can be

approximated by a single exponential decay

𝐺(𝑡)𝑅𝑒𝑝𝑡 =𝜌𝑅𝑇

𝑀𝑒exp

[

−𝑡

𝜏𝑒 (𝑀𝑀𝑒

)3.4

]

(𝑆5.4)

where ρ,R,and T are the polymer melt density, the gas constant, and the absolute temperature respectively. τe and

Me are the entanglement onset time and entanglement molar mass, and M is the molar mass of the brush species.

To account for molar mass polydispersity, the double reptation model as the square of the integral of the

conventional reptation relaxation multiplied by the weight fraction of each respective species over all molar mass

species8

𝐺(𝑡)𝑅𝑒𝑝𝑡𝑎𝑡𝑖𝑜𝑛 =𝜌𝑅𝑇

𝑀𝑒(∫ 𝑤𝑖𝑒

−𝑡

𝜏𝑒(𝑚𝑖𝑀𝑒

)3.4⁄∞

0

)

2

(𝑆5.5)

Where wi and mi are the weight fraction and molar mass of a species. For discrete molar mass distribution data,

the final model was described as

𝐺(𝑡) = 𝐺1 (𝑡

𝜏1)

−0.6

+𝜌𝑅𝑇

𝑀𝑒(∑𝑤𝑖𝑒

−𝑡

𝜏𝑒(𝑚𝑖𝑀𝑒

)3.4⁄

𝑖=𝑘

𝑖=1

)

2

(𝑆5.6)

where G1/τ1-0.6

, Me, and τe are the fitting terms used to fit the model with the experimental data. Fitting parameters

are displayed in Table S4, and entanglement modulus versus the relative side chain DP are displayed in blue in

Fig. S11. Overlays of the model fitting and experimental data are shown in Fig. S10.


17

Figure S11. Comparison of entanglement modulus analysis methods yields excellent agreement with

theoretical trend of 𝐺𝑒~(𝑛𝑠𝑐 𝑛𝑔⁄ + 1)−3/2.

Figure S10. Overlay of theoretical model with experimental rheological master curves with corresponding

molecular weight distributions obtained from molecular imaging by AFM.


18

Table S4: PBA bottlebrush polymer melt plateau modulus characterization

Sample Ge1 Pa Min tan(δ)

2 Ge

3 Pa Min δ

4 Ge

5 Pa τe

6 s β

7Pa s

0.6 Me

8 g/mol

BA-6 11432 ± 331 0.49 ± 0.02 11506 28 7690±960 1.80E+05 1.20E+06 0.38

BA-17 2421 ± 75 0.71 ± 0.01 2383 34 1588±301 170 3.60E+03 1.7

BA-23 1310 ± 54 0.72 ± 0.01 1035 36 831±138 330 3.00E+03 3.25

BA-34 938 ± 28 0.79 ± 0.01 948 38 603±23 340 2.60E+03 4.48

BA-130 178 ± 7 0.86 ± 0.01 193 41 114±4 NA NA NA

1Plateau modulus determined as storage modulus at the frequency of the minimum in tan(δ) (Fig. S8).

2Mimimum value of the tangent delta used in the MIN method.

3Plateau modulus determined from value of

storage modulus at minimum in phase angle in VGP plot (Fig. S9). 4Mimimum value of the phase angle used

in the VGP method. 5Plateau modulus determined by fitting the experimental data with the double reptation

model (Fig. S9). 6Entanglement time fitting parameter used in the double reputation fit.

7 𝛽 = 𝑮 𝟏/𝝉𝟏−𝟎.𝟔 fitting

parameter representing the combined effective monomer modulus and relaxation time. 8Molar mass of the

entanglement strand used in the double reputation fit. Modulus error was calculated by taking the standard

error of the mean from three measurements of the master curve.

6. Packing length analysis

The packing length (𝑝) is an analysis parameter equivalent to the relative thickness of a polymer chain calculated

as9

𝑝 =𝑀

𝑅02𝜌𝑁𝐴

(𝑆6.1)

where 𝑀 = 𝑣𝑛𝑏𝑏𝑁𝐴𝜌(𝑛𝑠𝑐 𝑛𝑔⁄ + 1) - molar mass of a bottlebrush macromolecule, 𝜌-mass density, 𝑁𝐴-

Avogadro’s number, and 𝑅02- mean square chain end-to-end distance which is given by eqs 3.23 and 3.30 as

𝑅02 ≅ 𝐿𝑏 ≅ 𝑛𝑏𝑏𝑙𝑏 (𝑐𝑜𝑚𝑏𝑠 𝑎𝑛𝑑 𝑙𝑖𝑛𝑒𝑎𝑟 𝑝𝑜𝑙𝑦𝑚𝑒𝑟𝑠: 𝑛𝑔

∗ < 𝑛𝑔) (𝑆6.2)

𝑅02 ≅ 𝐿𝑅𝑠𝑐 ≅

𝑣

(𝑏𝑙)1 2⁄

𝑛𝑠𝑐1 2⁄

𝑛𝑏𝑏

𝑛𝑔(𝑙𝑜𝑜𝑠𝑒 𝑏𝑜𝑡𝑡𝑙𝑒𝑏𝑟𝑢𝑠ℎ: 𝑛𝑔

∗∗ < 𝑛𝑔 < 𝑛𝑔∗) (𝑆6.3)

𝑅02 ≅ 𝐿𝑅𝑠𝑐 ≈ (


𝑛𝑔)

1 2⁄

𝑛𝑏𝑏 (𝑑𝑒𝑛𝑠𝑒 𝑏𝑜𝑡𝑡𝑙𝑒𝑏𝑟𝑢𝑠ℎ: 1 ≤ 𝑛𝑔 < 𝑛𝑔∗∗) (𝑆6.4)

In the case of linear polymer the native pendent group is treated as a side chain with DP equal to the number of

carbons divided by two. Dividing the chain volume (𝑀 𝜌𝑁𝐴⁄ ) by the mean square end-to-end distance normalizes

for chemical differences and represents the relative thickness of a polymer species. As shown by Fetters et al10

,

the packing parameter is related to the mechanical properties of a polymer species as 𝐺𝑒~𝑝−3. Bellow Fig. S12

represents entanglement volumes versus the packing length three sample sets: In black PBA bottlebrushes

described above. Polyolefins including polyethylene, polypropylene (atactic, isotactic, and syndiotactic, and head

on), syndiotactic polypentene, polyhexene (iso and syndiotactic), syndiotactic polyoctene, polycyclohexyl

ethylene).10

And polystyrene combs of varying sidechain DP, backbone DP, and grafting densities.11

All three

sample sets display excellent agreement with 𝐺𝑒~𝑝−3.


19

Figure S12. Relation between packing length (derived from rheological measurement) and entanglement

volume of PBA bottlebrushes (black), polyolefins linear chains (red),10

and polystyrene combs (blue).11

All

samples show excellent agreement with packing length relation 𝐺𝑒~𝑝−3 or 𝑉𝑒~𝑝3.

References

1. Panyukov, S. et al. Tension amplification in molecular brushes in solutions and on substrates. J. Phys. Chem. B

113, 3750-3768 (2009).

2. Kavassalis, T. A. & Noolandi, J. Entanglement scaling in polymer melts and solutions. Macromolecules 22,

2709-2720 (1989).

3. Saariaho, M., Szleifer, I., Ikkala, O. & ten Brinke, G. Extended conformations of isolated molecular bottle-

brushes: Influence of side-chain topology. Macromolecular Theory and Simulations 7, 211-216, (1998).

4. Williams, M. L., Landel, R. F. & Ferry J. D. The time dependence of relaxation mechanisms in amorphous

polymers and other glass-forming liquids. J. Am. Chem. Soc. 77, 3701–3707 (1955).

5. Lomellini P. Effect of chain length on the network modulus and entanglement. Polymer 33,

1255-1259 (1992).

6. van Gurp, M. & Palmen, J. Time-temperature superposition for polymeric blends. Rheol. Bull. 67, 5-8 (1998).

7. Rubinstein, M. & Colby, R. H. Polymer Physics Ch.7 (Oxford Univ. Press, New York 2003).

8. des Cloizeaux, J. Double reptation vs. simple reptation in polymer melts. Europhys. Lett. 5, 437 (1988).

9. Witten, T. A., Milner, S. T. & Wang, Z. G. Multiphase Macromolecular Systems (Plenum Press, New York

1989).

10. Fetters, L. J., Lohse, D. J., Garcia-Franco, C. A., Brant, P. & Richter, D. Prediction of melt state Poly(R-

olefin) rheological properties: the unsuspected role of the average molecular weight per backbone bond.

Macromolecules 35, 10096-10101 (2002).

11. Kapnistos, M., Vlassopoulos, D., Roovers, J. & Leal, L.G. Linear rheology of architecturally complex

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