The microscopic origin of the rheology in

Supplementary Material

The microscopic origin of the rheology in supramolecular entangled polymer networks

1

S1. Characterization of the sample material

Sample: Base polyisoprene PI-84K-U0: Mw = 84.000 g/mol, PDI = 1.02

Agilent 1260 Infinity system containing 3 PolyPore columns Detector: - Light scattering: DAWN HELEOS 8+, Wyatt - Refractive index: Agilent 1260 Infinity Refractive Index Detector

Figure S1. Size exclusion chromatogram of the base polymer PI-84K-U0. Light scattering signal and corresponding distribution of the molecular weight Mw.

2

Sample: Polyisoprene with 2 mol% urazole groups PI-84K-U2

1H-NMR

(Varian), 600 MHz, (CDCL3, ppm):

𝛿 = 7.51 – 7.36 (C6H5), 5.13 (CH, 1,4-unit), 4.76 (=CH2, 3,4-unit), 4.68 (=CH2, 3,4unit), 2.04 (=CH2), 1.68 (=CH3, cis-1,4-unit), 1.60 (=CH3, trans-1,4-unit), 0.87 (=CH3, t-Bu).

ATR-FTIR: 𝜈 [𝑐𝑚−1 ] 3035, 2961, 2854, 2727, 1770, 1702, 1666, 1645, 1503, 1447, 1376, 1311, 1240, 1131, 1091, 1039.

3

S2. Fourier transform infrared (FTIR) spectroscopy

To determine the total concentration of urazole groups (Figure S2 and S3) the absorption peak height at 𝜈 = 1770 𝑐𝑚−1 with respect to its baseline was used, which corresponds to the temperature independent stretching vibration of the carbonyl groups1. Otherwise the absorption peak height of the temperature dependent stretching vibrations showing up at 𝜈 = 1702 𝑐𝑚−1 for the associated and 𝜈 = 1721 𝑐𝑚−1 for the dissociated state were used for the determination of the corresponding mol fractions of opened and closed groups (Figure S4 – S6).

Comparison of ATR-FTIR spectra for different functionalization degrees:

Figure S2: FTIR spectra of polyisoprene, functionalized with different amounts of urazole groups. As can be seen from the corresponding absorption peak heights, the functionalization degree with urazoles is precisely controllable.

1

R. Stadler and L. de Lucca Freitas. Thermoplastic Elastomers by Hydrogen Bonding 2. IR-Spectroscopic Characterization of the Hydrogen Bonding. Polymer Bulletin, 15(2):173-179, 1986.

4

The comparison of the absorbance peak height for different functionalization degrees, given in Figure S2, shows that the amount of urazole groups in the model system is precisely controllable.

Excluding retro-ene reaction due to covalent crosslinking process and inhibition of peroxidic crosslinking due to urazole groups:

To ensure that no retro-ene reaction due to the covalent crosslinking process as well as no inhibition of the peroxidic crosslinking due to the urazole groups occurred, the functionalized network chains were investigated before and after the covalent crosslinking procedure by FTIR spectroscopy. We exclude this unwanted secondary interactions, as the absorption peak height of the carbonyl groups resulting from the amount of urazole groups bonded covalently to the backbone of the polymer is not affected by the covalent crosslinking procedure within the accuracy of the method (Figure S3).

Figure S3: FTIR spectra of polyisoprene functionalized with 2.5 mol% urazole groups before and after the covalent crosslinking reaction. The corresponding absorption peaks show that the amount of functional urazole groups is not affected by the covalent crosslinking pprocedure within the accuracy of the method.

5

Figure S4. Absorbance spectra for PI-84K-U2, functionalized with 2 mol% urazole groups. The signal at 𝜈 = 1702 𝑐𝑚−1 corresponds to the associated, the signal at 𝜈 = 1702 𝑐𝑚−1 to the dissociated state. Additionally the isosbectic point is indicated.

Figure S5. Absorbance spectra for PI-84K-U4, functionalized with 4 mol% urazole groups. The signal at 𝜈 = 1702 𝑐𝑚−1 corresponds to the associated, the signal at 𝜈 = 1721 𝑐𝑚−1 to the dissociated state. Additionally the isosbectic point is indicated.

6

Figure S6. Fitting routine of the FTIR spectrum, exemplaric shown for PI-84K-U1 measured at 𝑇 = 373 𝐾. 6 GaussianLorentzian peaks were fitted per spectrum to obtain the envelope (green). The area marked blue is correlated to the absorption due to the associated state, while the area marked red corresponds to the dissociated urazole groups.

S3. Differential scanning calorimetry (DSC)

The procedures used for a quantitative analysis of the highlighted effects were taken from standard specifications2 and are depicted in Figure S7 for a better comprehension. To determine the glass transition temperature 𝑇𝑔 the midpoint determination method was used2. The effect of enthalpy recovery expressed by an endothermic peak slightly above 𝑇𝑔 , was quantified by its normalized peak area Δ𝐴𝑒𝑛𝑑𝑜 /𝑚𝑠𝑎𝑚𝑝𝑙𝑒

Δ𝐴𝑒𝑛𝑑𝑜 𝑚𝑠𝑎𝑚𝑝𝑙𝑒

2

=

1 𝑚𝑠𝑎𝑚𝑝𝑙𝑒

𝑇

𝑇

1

1

[∫𝑇 2 𝑠𝑡𝑟𝑎𝑖𝑔ℎ𝑡ℎ𝑖𝑔ℎ 𝑇 dT − ∫𝑇 2 ℎ𝑒𝑎𝑡 𝑓𝑙𝑜𝑤 dT]

(S1)

M. Abdel-Goad, W. Pyckhout-Hintzen, S. Kahle, J. Allgaier, D. Richter, and L. J. Fetters, Macromolecules 37, 8135 (2004).

7

Figure S7. Depicting the methods for determining the glass transition temperature 𝑇𝑔 (dark red) and the endothermic peak area related to the effect of enthalpy recovery (green).

8

S4. Frequency sweeps to detect the linear viscosity regime

To detect the linear viscosity regime, strain sweeps with an amplitude range of ɣ = 0.01 − 100% were carried out at 228 K, the lowest measurement temperature, for 𝜔 = 0.1 𝑟𝑎𝑑/𝑠 and 𝜔 = 100 𝑟𝑎𝑑/𝑠, the lowest and highest excitation frequency used for the frequency sweeps. The resulting strains sweep curves for PI-84K-U0 (linear reference) and the transient network with the highest amount of reassociating groups PI-84K-U4 are shown in Figure S8.

Figure S8. Strain sweeps for linear polyisoprene (PI-84K-U0) (left) and polyisoprene with a backbone modification of 4 mol% (PI-84K-U4) (right), carried out to detect the linear viscoelastic regime of the transient network samples.

A comparison of the strainsweeps for the 2 different systems shows a decrease of the linear viscolelastic regime as well as an increase of the storage and the loss modulus due to the functional groups.

9

S5.Havriliak-Negami (HN) functions:

The Havriliak-Negami model3 is often used for an analytical description of relaxation processes in polymeric systems as it allows a peak broadening as well as an asymmetric peak shape.

Fitting the loss part of the complex dielectric response:

In accordance to the generally accepted procedure, the spectra were fitted with a set of two HN fitting functions in order to extract the characteristic relaxation times of both relaxation processes from the dielectric loss curves.

𝐻𝑁𝑑𝑖𝑒𝑙−𝑑𝑜𝑢𝑏𝑙𝑒 = 𝐻𝑁1 (𝜏𝛼−𝑝𝑟𝑜𝑐𝑒𝑠𝑠 ) + 𝐻𝑁2 (𝜏𝛼∗−𝑝𝑟𝑜𝑐𝑒𝑠𝑠 )

S2

A schematic representation of the corresponding fitting function 𝐻𝑁𝑑𝑖𝑒𝑙−𝑑𝑜𝑢𝑏𝑙𝑒 is given in Figure S9, showing the underlying two single HN peaks as well as the fitting curve, resulting in accordance to Equation S2. The fitting range covered one decade to the low frequency flank with respect to 𝑓𝑝𝑒𝑎𝑘,𝛼∗−𝑝𝑟𝑜𝑐𝑒𝑠𝑠 and one decade to the high frequency flank with respect to 𝑓𝑝𝑒𝑎𝑘,𝛼−𝑝𝑟𝑜𝑐𝑒𝑠𝑠 for all data, thus providing comparability of the fitting output.

3

S. Havriliak and S. Negami. A complex plane representation of dielectric and mechanical processes in some polymers. Polymer, 8:161-210, 1967.

10

Figure S9. Schematic representation of the fitting function 𝐻𝑁𝑑𝑖𝑒𝑙−𝑑𝑜𝑢𝑏𝑙𝑒 shown on the basis of the relaxation spectra obtained for PI-84K-U2 at T = 243 K. The resulting fitting curves as well as the underlying two single HN peaks are presented.

The shape parameters 𝛼, related to a symmetric peak broadening and 𝛽, related to an asymmetric peak broadening of the relaxation time distribution amounted to 𝛽(𝛼 − 𝑝𝑟𝑜𝑐𝑒𝑠𝑠) = 𝛽(𝛼 ∗ − 𝑝𝑟𝑜𝑐𝑒𝑠𝑠) = 1, 𝛼(𝛼 − 𝑝𝑟𝑜𝑐𝑒𝑠𝑠) = 0.4 ± 0.1

and

𝛼(𝛼 ∗ −

𝑝𝑟𝑜𝑐𝑒𝑠𝑠) = 0.5 ± 0.1for all investigated samples and temperatures. This is in good agreement with literature values4 for similar systems and shows that both processes exhibit a Debye-like behavior. The within errors similar broadenings of the 𝛼- and 𝛼 ∗ process gain underline the intimate connection of both processes as proposed by Equation 2 and Equation 4 in the main text.

4

M. Müller, E. W. Fischer, F. Kremer, U. Seidel, and R. Stadler. The molecular dynamics of thermoreversible networks as studied by broadband dielectric spectroscopy. Colloid and Polymer Science, 273(1):38-46, 1995.

11

Fitting the loss part of the complex rheological response:

To provide comparability between the characteristic rheological relaxation times and the dielectric ones, the loss modulus 𝑏𝑇 𝐺 ′′ (𝜔) was fitted with a set of of two HN fitting functions, adding an additional contribution 𝐶 ∙ (𝑎 𝑇 𝜔)𝑚 to describe the Rouse flank.

𝐻𝑁𝑟ℎ𝑒𝑜−𝑑𝑜𝑢𝑏𝑙𝑒 = 𝐻𝑁1 (𝜏1 ) + 𝐻𝑁2 (𝜏𝑟ℎ𝑒𝑜 ) + 𝐶 ∙ (𝑎 𝑇 𝜔)𝑚

S2

A schematic representation of the corresponding fitting function 𝐻𝑁𝑟ℎ𝑒𝑜−𝑑𝑜𝑢𝑏𝑙𝑒 is given in Figure S10. The underlying two single HN peaks as well as the Rouse-regime, represented by a power law in a double-logarithmic representation are displayed separately. The fitting range for all data covered three decades to the low frequency flank with respect to 𝜔𝑝𝑒𝑎𝑘,1, while to the high frequency flank the fitting range was three decades with respect to the peak position 𝜔𝑝𝑒𝑎𝑘,𝑟ℎ𝑒𝑜 .

Figure S10. Schemtaic representation of the fitting function 𝐻𝑁𝑟ℎ𝑒𝑜−𝑑𝑜𝑢𝑏𝑙𝑒 shown on the basis of the mastercurved relaxation spectra obtained for PI-84K-U2 concerning a reference temperature of 𝑇𝑟𝑒𝑓 = 243 𝐾. The Rouse regime, represented by a power law in a double-logarithmic representation, as well as the underlying two single HN peaks are shown.

12

The asymmetry shape parameter 𝛽 for HN1(τ1) related to the terminal transition zone ranges between 0.11 and 0.18 for all temperatures and samples, showing no dependency on temperature or functionalization degree. The values of the peak broadening parameter 𝛼, which determines the slope of the flow frequency flank, results to 𝛼 = 1.00 for PI-84K-U0, 𝛼 = 0.77 for PI-84K-U1, 𝛼 = 0.50 for PI-84K-U2 and 𝛼 = 0.32 for PI-84K-U4, picturing increasing elastomeric properties due to group interactions. The peak shape for HN2(τrheo) related to the second rheological relaxation process introduced by the functional groups, yields an equal asymmetry as 𝛽 = 0.60 – 0.70 for all systems, while the peak broadening increases with an increasing amount of groups.

Mastercurves of the storage 𝒃𝑻 𝑮′ (𝝎) and the loss modulus 𝒃𝑻 𝑮′ ′(𝝎) for the transient sample system:

Figure S11. Mastercurves of the storage modulus 𝑏𝑇 𝐺 ′ (𝜔) and the loss modulus 𝑏𝑇 𝐺 ′′ (𝜔) for the transient sample system corresponding to a reference temperature of 𝑇𝑟𝑒𝑓 = 243 𝐾.

13