Dynamics and self-assembly in architecturally complex supramolecular polymers Golkaram, Milad
DOI:
10.33612/diss.126818904
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Chapter 5: Origin of the Linear Viscoelastic
Behavior in Supramolecular
Polymer Brushes: Effect of
Molecular Weight and
Crosslinking on Colloidal
Properties
This chapter is submitted in 2020.
5.1 ABSTRACT
Supramolecular bottlebrush polymers are a new class of dynamic materials that show unique melt dynamics such as an additional elastic response with a low plateau modulus value. In this study, we investigate the origin of this unique rheological response, using different polymer chemistries, topologies and molecular weights, combined with a recently developed sticker called ODIN. At low molecular weights of mono-functionalized polymers, the formed brushes show colloidal behavior, and therefore they do not flow even at highest experimentally studied temperatures (or at longest time scales). These polymers, that are not a transient network (they are not necessarily crosslinked) show an elastic plateau close to what has been seen in hyperstars and covalent bottlebrush polymers ( GN close to 10 kPa). Despite
similarities between covalent and transient bottlebrush polymers the elastic response in the later does not originate from the brush entanglements with large Me
(entanglement molecular weight), it rather stems from the impenetrable rigid backbone and caging effect similar to hyperstars. With increasing the molecular weight, a transition from colloidal to polymeric materials is observed whereby doubled-sized polymers as well as star-like aggregates are formed. With introducing crosslinking to the bottlebrush polymers, they show enhanced elasticity until they sacrifice their colloidal properties by network formation in tetra-functionalized polymers.
5.2 INTRODUCTION
Rheology of complex macromolecular architectures such as stars, combs and (bottle)brushes has been investigated extensively.1–17 In these types of polymers,
important features differ from the melt dynamics of their linear analogous. For instance, it is common for brush polymers to relax sequentially, therefore their stress relaxation mechanism consists of the segmental regime, arm regime and the terminal regime.3 On the other hand, in case of star polymers with low functionality (f < 8) and
long arms Ma, linear dynamics are well understood and described by the model of
Milner and McLeish based on arm retraction and contour length fluctuations (CLF) mechanisms;4,18 the stress relaxes by the free end of an arm retracting inward along its
primitive path and a new “tube” is formed. Since the retraction of the arm is entropically unfavorable, the arm relaxation is a slow process, which depends exponentially on the length of the arm Ma.19,20 Therefore, the outermost segments of
the arms (near the free ends) relax faster than inner segments close to the core region of the star.18,21 This difference between relaxation times leads to a hierarchy of length
scales and relaxation time scales that characterize the dynamics of star polymers. By increasing the number of arms and/or decreasing the size of the arms, a so-called hyperstar is formed.22–24 Hyperstars exhibit characteristics of both polymers and
colloids; displaying a high frequency relaxation of polymer segments, an intermediate frequency plateau of entangled star arms and then a two-step terminal relaxation characteristic of multi-arm star polymers.25 Within the later two-step process, first a
faster relaxation occurs due to arm retraction and then a structural rearrangement of star cores which is similar to the colloidal materials.25 In the extreme cases of more
than 800 short arms, a jamming phenomenon has been reported which prevents terminal relaxation in the accessible frequencies. Therefore, an additional plateau with low moduli values could be observed. Their low modulus makes them a good candidate for supersoft elastomers.25 The jamming character of these hyperstars is a
result of excluded volume effects which slows down their center-of-mass motion and makes them behave as hard spheres.25,26 Besides the star polymers, comb polymers
and supramolecular comb polymers with low grafting density are also characterized by a two steps relaxation. However, this is not due to jamming, it is rather attributed to the hierarchical relaxation of the branches of the comb polymer followed by the relaxation of its backbone.27–29 Microgels can also be categorized in the same category
as hyperstars since at high grafting density the terminal relaxation is arrested in the experimental frequency.30 On the other hand, polymer-grafted nanoparticles (PNP) can
behave similar to polymer (hyper)stars, showing viscoelastic liquid (for low grafting densities and long chains) or viscoelastic solid behavior (at higher grafting densities and short chains). Although, PNPs have similarities to hyperstars and microgels, they are composite materials and their core size is usually larger.31–33 Microphase-separated
block copolymers and telechelic supramolecular polymers able to create core-shell micelles can also be considered as soft colloids.34–39 However, their dynamics is
usually different than stable core-shell micelles, for instance they often show larger thermorheologically complex (TRC) behavior as their phase separation depends on temperature.40
We recently introduced a supramolecular system consisting of end-functionalized poly(tetrahydrofuran) (PTHF), which could mimic the melt rheological behavior of bottlebrush polymers.41,11 A novel sticker (ODIN)42 was used for
end-group functionalization which could undergo sextuple hydrogen bonding as well as stacking. Melt rheology showed that after relaxation of the arms, in longer time scales, additional relaxation corresponding to the entire supramolecular bottlebrush polymer appears. However, due to the impossibility to access the lower frequencies (longer time scales) by melt rheology, the origin of relaxation for the thick backbone of the polymer brush was not yet revealed. Therefore, two possibilities were proposed, i.e. either reptation of the entire supramolecular bottlebrush polymer similar to covalent bottlebrush polymers, or its relaxation through hopping mechanisms similar to hyperstars. In both scenarios the terminal relaxation is combined with the dissociation of the supramolecular backbone at higher temperatures (or longer time scales). In this manuscript, we describe a more accurate, yet broader view of the dynamics of these supramolecular polymers. In particular, the effect of different arm length in wider frequency ranges as well as chemistries and topologies is addressed to check whether the classical molecular pictures used for star and bottlebrush polymers is applicable to these novel transient analogues.
Therefore, three systems are discussed (Scheme 1):
1) linear poly(methyl acrylate) (PmA) (with Mn below, close and above Me)
containing one end-functionalization by stickers, thus able to create brush-like structures after stacking of the stickers,
2) 1, 2 and 4 arm star poly(ethylene glycol) (PEG) functionalized with stickers at the arm extremities to check the effect of crosslinking on association of the supramolecular backbone. In this case, the crosslinking point is the middle part of the PEGs and the brush backbone forms the arrays of stacked stickers.
3) one short poly(dimethyl siloxane) (PDMS) functionalized only at one end to represent a more generalized chemistry.
Scheme 1. Schematic representation of polymers PmA-i-ODIN, PEG-j-ODIN and PDMS-ODIN.
5.3 EXPERIMENTAL SECTION 5.3.1 Materials.
Methyl acrylate was purchased from Aldrich and passed through neutral alumina column before use. α,α’-Azobis-(isobutyronitrile) (AIBN, Fluka, 99%) was recrystallized from methanol. N,N-dimethylformamide (DMF, anhydrous) was purchased from Fisher Scientific and used as received. Chloroform (anhydrous), 4-cyano-4-[(dodecylsulfanylthiocarbonyl)sulfanyl]pentanol (CTA), dibutyltin dilaurate, poly(ethylene glycol)s (PEGs), malic acid, 2,6-diaminopyridine were purchased from Aldrich and used without further purification. Hexamethylene diisocyanate (HDI) was purchased from TCI.
5.3.2 Characterization.
1H NMR spectra were recorded at room temperature on a Varian VXR 400 MHz
(1H: 400 MHz) spectrometer using deuterated solvents. Chemical shifts (δ) are
reported in ppm, whereas the chemical shifts are calibrated to the solvent residual peaks. Tetramethylsilane (TMS) was used for calibration of chemical shifts. Gel permeation chromatography (GPC) measurements were performed in THF at 25 oC (1
mixed-C columns. Universal calibration was applied using a Viscotek H502 viscometer and a Shodex RI-71 refractive index detector. The GPC was calibrated using narrow disperse polystyrene standards (Polymer Laboratories).
Melt rheology was carried out via a TA Instruments, AR 1000 under nitrogen flow and 8 mm parallel plate geometries and interplate gap of 0.8-1 mm were used in all cases. Samples were vacuum dried overnight before use. All measurements were performed in the linear viscoelastic regime, determined via torque sweep measurements. Frequency sweeps 0.01-10 or 0.01-100 Hz (depending on the viscosity) were carried out in different temperatures between 20-160 oC for PmA based polymers
and 50-70 oC for PEGs. Mastercurves were constructed using TA rheology advantage
data analysis software. Temperature sweeps were carried out also within linear regimes in a temperature range between 20-170 oC depending on the sample stability and
viscosity. The temperature was kept constant for one minute at each temperature to ensure the equilibrium within the sample.
Differential scanning calorimetric (DSC) measurements were done on a TA-Instruments Q1000. For PEGs, the samples were heated from room temperature to 80 °C and kept there for 15 minutes to remove the thermal history. Then, they were cooled down to -50 °C with a rate of 2 °C min−1, equilibrated for 15 minutes and heated (10
°C min−1) to 80 °C. The data was obtained from the cooling and the second heating
scans. For PmAs the heating was up to 130 °C and cooling down to -40 °C.
5.3.3 Synthesis of poly(methyl acrylate)s (PmA).
A general procedure is as follows: to a Schlenk tube containing a magnetic stirrer, CTA, and AIBN ([CTA/AIBN]:10/1) in DMF (3 mL), methyl acrylate (2g, 23 mmol) was added followed by four times free-pump-thaw cycles. Then, the reaction mixture was inserted in a pre-heated oil bath of 75 oC and stirred for 6 hours.
Subsequently the reaction mixture was precipitated in a methanol water mixture and recovered via centrifugation. The polymers were dried under vacuum and yielded the desired product.
5.3.4 Synthesis of ((1-(6-Isocyanatohexyl)-3-(7-oxo-7,8-dihydro-1,8-naphthyridin-2-yl)urea) (ODIN)).
4g (0.025 mol) 7-amino-1,8-naphthyridin-2(1H)-one was added to a 100 mL three-necked round bottom flask equipped with an egg-shaped magnetic stirrer. The
solids were allowed to dry for one hour under vacuum. The flask was kept under nitrogen atmosphere by 3 consequent vacuum/nitrogen cycles. 60 mL HDI (0.37 mol) was added to the reaction flask. The reaction mixture was heated to 110 °C while stirring. After 19h the reaction mixture was cooled down to room temperature. Then, it was precipitated in 500 mL hexane. The precipitate was filtered off and the traces of HDI was removed by distillation under reduced pressure (0.01 mbar) at 130 °C. (84% yield) 1H NMR (400 MHz, DMSO-d 6) δ: 12.15 (s, 1H1), 9.63 (s, 1H2), 8.98 (t, 1H7), 7.88 (d, J = 8.5 Hz, 1H4), 7.75 (d, J = 9.4 Hz, 1H5), 6.83 (d, J = 8.5 Hz, 1H3), 6.31 (dd, J = 9.3, 1.9 Hz, 1H6), 3.0−3.3 (m, 4H8), 1.1−1.6 (m, 8H9). 1H NMR (400 MHz, chloroform-d) δ: 12.75 (s, 1H 1), 11.22 (s, 1H2), 8.19 (d, J = 8.8 Hz, 1H3), 7.80 (d, J = 8.8 Hz, 1H4), 7.70 (d, J = 9.3 Hz, 1H5), 6.45 (d, J = 9.3 Hz, 1H6), 5.93 (s, 1H7), 3.05−3.45 (m, 4H8), 1.25−1.75 (m, 8H9). 5.3.5 Synthesis of PmA-ODINs.
A 100 mL three necked round bottom flask was equipped with a reflux condenser and an egg-shaped magnetic stirrer and put under nitrogen atmosphere. 300 mg PmA and 3 equivalent of ODIN was added to the reaction flask under nitrogen atmosphere. Then, 10 mL of anhydrous chloroform and 2 droplets of DBTDL was added to the reaction mixture. The reaction mixture was refluxed overnight and then, hexane was added (3 mL) and the unreacted extra ODIN was isolated by centrifugation at 4500 rpm for 30 minutes. The solution was collected and the solvent was removed under reduced pressure. A yellow solid was obtained.
1H NMR (400 MHz, chloroform-d) δ: 12.89 (s, 1H
1), 11.25 (s, 1H2), 8.19 (d,
1H3), 7.83 (d, J = 8.6 Hz, 1H4), 7.72 (d, J = 9.4 Hz, 1H5), 6.54 (d, J = 9.5 Hz, 1H6),
5.99 (s, 1H7), 4.87 (s, 1H8), 1.10-4.10 (m, 320H9-12).
5.3.6 Synthesis of PEG-ODINs.
The same procedure as 5.3.5 was used for PEGs except that methanol as non-solvent for centrifugation was used instead of hexane.
5.3.7 Synthesis of PDMS-ODIN.
The same procedure as 5.3.5 was used for PDMS with hexane as non-solvent for ODIN.
5.4 RESULTS AND DISCUSSION 5.4.1 Polymer synthesis.
In order to investigate the dynamics of supramolecular polymer brushes within a wide range of frequencies an amorphous polymer with fairly low entanglement molecular weight was chosen so that the final polymer carries just a few entanglements. Also, the glass transition temperature of the polymer should not be very far from the dissociation temperature of the sticker so that the interplay between sticker and chain dynamics can be observed. Considering these points, PmA is a good candidate, especially its ease of synthesis and post polymerization modification with reversible addition-fragmentation chain transfer (RAFT) polymerization justifies its selection. Therefore, PmAs (PmA-i, i = 6k, 18k or 30k, check Table 1 or Scheme 2 for the sample names) with three different molecular weights were obtained (Figure 1).
Scheme 2. Synthesis of polymers PmA-i-ODIN, PEG-j-ODIN and PDMS-ODIN.
Table 1. Molecular characterization of the (co)polymers. Entry Sample Mn (kg mol-1) Đ Tg (oC) Z= Mn / Me * 1 PmA-6k 6 1.2 -9 <1 2 PmA-ODIN-6k 4 3 PmA-18k 18 1.3 -6 ̴ 2 4 PmA-ODIN-18k 12 5 PmA-30k 30 1.3 12 ̴ 4 6 PmA-ODIN-30k -12,18 Tc (oC) T(omC) Number arms** of 7 PEG-1 2 1.1 38 56 1 8 PEG-1-ODIN 33 53 9 PEG-2 4 1.1 45 59 2 10 PEG-2-ODIN 31 51 11 PEG-4 6.7 1.1 40 57 4 12 PEG-4-ODIN 29 50 Z= Mn / Me 13 PDMS-ODIN 4.6 1.1 - <1
*Z = number of entanglements for precursor polymer based on Me of 7 kg mol-1.** Mn per arm is ̴ 2
kg mol-1 for all samples.
The effect of topology and crosslinking was then tested, using commercially available star PEGs. Synthesis of supramolecular polymers was performed via coupling of the sticker to the hydroxyl end-groups of either PEG-j (j = 1, 2 or 4, Table 1 or Scheme 2) or PmAs. Figure 2 shows 1H NMR spectra of PmA-6k-ODIN and
PEG-1-ODIN (see Figures 3, 4, 5 for PEG-2-ODIN, PEG-4-ODIN and PDMS-ODIN, respectively). The presence of ODIN protons (assigned 1-7) and the appearance of peak corresponding to urethane bond formation (assigned 8) proves the coupling of ODIN to the chain ends.
Figure 3. 1H NMR spectrum of PEG-2-ODIN.
Figure 5. 1H NMR spectrum of PDMS-ODIN.
5.4.2 Rheology: effect of molecular weight.
The temperature dependent linear viscoelastic response of PmAs shows a transition from unentangled to entangled polymer dynamics (Figures 6-8). Using the equation 𝐺𝐺N = 4/5 𝜌𝜌𝜌𝜌𝜌𝜌
𝑀𝑀e, entanglement molecular weight is calculated to be around 7
kg mol-1. Figure 9, corresponds to the temperature sweep measurements (while
heating) for supramolecular polymers based on PmA. The viscoelastic response of the highest molecular weight polymer above Mc (red curve, PmA-30k-ODIN) displays a
first plateau at low temperatures (30 oC - 50 oC), which is also observed with the
unfunctionalized polymer and which can be attributed to the chain’s entanglements. This first plateau is absent with sample PmA-18k-ODIN since its molar mass is only slightly above Mc. While the storage modulus of both samples largely decreases at
around 80 oC, their terminal relaxation is slightly delayed, compared to the
unfunctionalized samples (Figures 7 and 8). This effect is further enhanced with the lowest molecular weight, PmA-6k-ODIN, for which a secondary plateau is clearly observed at high temperatures, with a storage modulus almost two decades larger than the storage modulus of the higher molecular weight samples. This plateau, which does not exist with the reference sample, extends until 160 oC, showing that this sample
Figure 6. Temperature sweep measurement (at ω = 1 Hz) for PmA-6k using small amplitude oscillatory shear (SAOS) technique.
Figure 7. Temperature sweep measurement (at ω = 1 Hz) for PmA-18k using small amplitude
Figure 8. Temperature sweep measurement (at ω = 1 Hz) for PmA-30k using small amplitude oscillatory shear (SAOS) technique.
Figure 9. Temperature sweep measurements (at ω = 1 Hz) for PmA-i-ODIN using small amplitude
In order to have a better understanding of the origin of this plateau, frequency sweep measurements were carried out in the linear regime for the precursors (Figures 11-13) and the supramolecular polymers and a mastercurve was constructed for PmA-6k-ODIN (Figure 10a). Samples were first left to equilibrate at room temperature and subsequently heated step by step. At each step/temperature first the sample was left to equilibrate between the plates and then the frequency sweep measurement was performed.
Figure 10. a) Constructed mastercurve of PmA-6k-ODIN at T ≃ Tg + 40 oC, b) shift factors of
PmA-6k-ODIN in comparison with PmA-6k. Shift factors where fitted using WLF equation to access a broader temperature range.
Figure 11. Frequency sweep measurements in the linear viscoelastic regime for PmA-6k at different
Figure 12. Frequency sweep measurements in the linear viscoelastic regime for PmA-18k at different
temperatures (20-75 oC).
Figure 13. Frequency sweep measurements in the linear viscoelastic regime for PmA-30k at different
A thermorheologicaly complex (TRC) behavior is observed for PmA-6k-ODIN, which is stronger at lower frequency side. This shows that the dynamics originates from two different origins, i.e. the sticker dissociation and the chain dynamics. Two minima are found in the tan (δ) curve, attributed to two relaxation processes. The low frequency plateau extends beyond the experimental frequency range. The high frequency plateau overlaps quite well with the entanglement plateau detected in Figure 9. In this high frequency regime (lower temperature), the TRC behavior is less tangible, which is supported by comparing the shift factors of PmA-6k-ODIN and its precursor PmA-6k (Figure 10b). These ones overlap at low temperatures, meaning that the viscoelastic response is dominated by the chain’s dynamics, similarly to a covalent brush. In this regime, the chain-end segments localized in the center of polymer brush are immobilized due to the stacking of their ODIN groups. Therefore, in the formed brush structure, the side chains can only relax similarly to the covalent bottlebrush polymers. It is important to note that the chain length of PmA-6k-ODIN is short in comparison to our previous study on highly entangled functionalized poly(tetrahydrofuran) (PTHF), which explains the relatively fast relaxation of the branches, compared to the slow decay of G’ and G” observed in our previous work.41
Although side chain molecular weight is less than Mc, an entanglement plateau is
observed. This phenomenon has also been seen in covalent bottlebrush polymers. We attribute it to both the fact that associated chains behave as linear chains with double molar mass and to the non-negligible polydispersity of the sample.
At higher temperatures close to the dissociation temperature of the stickers (where stacks start to lose their long-range order), shift factors diverge and show a different behavior, which manifests itself with a TRC in the low frequency regime in Figure 10a. At these longer times, on the scale of the correlation length ξ, the supramolecular backbones are correlated, which leads to a viscoelastic solid behavior, that we associate to a colloidal behavior of the sticker aggregates. In other words, each stacked supramolecular backbone is constrained within the cage formed by its neighbors which restricts its macroscopic motion and leads to a solid-like G’ > G” behavior. This caging effect is quite similar to the one observed with hyperstars which act like soft colloid due to their impenetrable center. It must be noted here that as discussed in ref. 41, in our design the stacked backbones are highly rigid and the chain segments nearby are also strongly stretched and impenetrable, as it was confirmed in
ref. 41 based on SAXS data, which suggested a lamellar organization of the ODIN groups. By increasing the temperature, the plateau modulus changes slightly but since the stacking is long-range ordered, the disruption of the stacks by temperature does not influence the viscoelastic response significantly. Therefore, for PmA-6k-ODIN a tentative scheme is drawn to include the proposed relaxation mechanism (scheme 3).
Scheme 3. Tentative representation of PmA-6k-ODIN colloidal behavior. The circles indicate the correlation length ξ.
Another possible scenario to explain the presence of a second, low frequency, plateau is considering that the supramolecular bottlebrush polymer is long enough to be entangled and show a rubbery plateau. In this case, instead of a caging effect as described in Scheme 3, reptation of the entangled backbone should be the mechanism of stress relaxation. This way of stress relaxation is similar to covalent bottlebrush polymers with very large backbone molecular weights.3 Using 𝐺𝐺
N~𝑀𝑀e-1 and the
apparent entanglement plateau modulus 𝐺𝐺𝑁𝑁𝑎𝑎𝑝𝑝𝑝𝑝 approximately 9 kPa for the diluted backbone, the entanglement molecular weight Me for the supramolecular bottlebrush
polymer backbone can be calculated to be around 2.6 × 105 g mol-1. Considering that
the terminal relaxation time is not visible, at least a few entanglements are expected, which means the molecular weight should go beyond Mn > 106 g mol-1 which is not
reasonable. This implies that the elastic response originates rather from the impenetrable core of the polymer brush (colloidal behavior) rather than the brush entanglement.
Figure 14 compares the built master curves for PmA-18k and PmA-18k-ODIN. A weak entanglement plateau can be seen at intermediate frequency from PmA-18k-ODIN with 𝐺𝐺N ≃ 0.3 MPa (measured at Tan (δ)min). The presence of entanglements can be assigned to the supramolecular associations leading to double-sized polymers above Mc. It is noteworthy that the precursor has Mn roughly close to Mc and yet no
pure Rouse-like relaxation (Figure 12). Thus, the presence of a plateau demonstrates the association of the stickers. On the other hand, at lower frequencies, a large fraction of the sample is able to relax. However, the terminal relaxation of the sample is not observed as the G’,G” slopes do not reach values of 2 and 1 respectively, as observed with the precursor PmA-18k. Shallowing of the slopes in PmA-18k-ODIN can be attributed to the presence of aggregates in addition to binary associations of the supramolecular groups, as has been seen in the literature.43
Figure 14. Built mastercurves of PmA-18k and PmA-18k-ODIN at T ≃ Tg + 40 oC using the shift factors
of PmA.
As in Figure 14, the mastercurve of PmA-18k-ODIN does not show significant TRC behavior despite the fact that it is built by using the shift factors of the reference sample, it can also be concluded that the chain relaxation is dominated by the CLF and reptation process, rather than by the dissociation of the stickers. This means that the stickers are dormant and stay associated in the experimental range of frequency and temperature, and τdisentanglement < τbreak.44 Therefore, for PmA-18k-ODIN a tentative
scheme is drawn to include the proposed relaxation mechanism (scheme 4): while most of the supramolecular polymers relax as double linear chains (in case of binary association) or star-like molecules (in case few stickers aggregate), there are also few larger aggregates which lead to broader relaxation times and shallow terminal slopes.
Scheme 4. Tentative representation of PmA-18k-ODIN and PmA-30k-ODIN dynamics below dissociation temperature of ODIN. The larger aggregates are shown with pink, smaller aggregates with green and binary associations with red color. The stress relaxation starts in (a) and ends in (d).
As shown in Figure 15, with increasing the size of the precursor polymer, the terminal relaxation time is becoming longer, as expected since reptation time of a linear polymer increases with τ ∼ η ∼ M 3.4.45 Figure 15 also shows the mastercurve of
PmA-30k-ODIN using the precursor shift factors. In this master curve, only the data obtained at low temperatures were used, to ensure thermo-rheological simplicity. Thus, in this range of temperatures, one can say that the sample relaxation is dominated by the reptation and CLF processes. As for PmA-18k-ODIN, it is expected that the supramolecular association of PmA-30k-ODIN leads to the creation of double-sized chains as well as star-like molecules formed from the aggregation of few stickers. Consequently, a longer plateau is observed in comparison to the precursor polymer PmA-30k. From the G’ and G” crossover for PmA-30k-ODIN, we see that τdisentanglement
≃ 16 s. However, using τ ∼ M 3.4, and τPmA-30k at crossover (T ≃ Tg + 40 oC) (see Figure
15), the terminal relaxation time for a linear polymer with twice the molecular weight as PmA-30k should be τ60k ≃ 1.4 s (ω60k ≃ 0.75 rad/s, vertical line in Figure 15) which
is shorter than what is experimentally obtained (τrel ≃ 16 s). On the other hand,
considering star-like assemblies are present, the relaxation of the star polymers can be predicted by equation 1:6
Figure 15. Mastercurve of PmA-30k-ODIN in comparison with PmA-30k at T ≃ Tg + 40 oC using the
shift factors of PmA. The vertical line showing the theoretical terminal relaxation time for linear PmA with 60 kg mol-1 at T = 55 oC.
leading to relaxation times which are longer than expected by linear binary associations, and which are in better agreement with the experimental data. We therefore conclude that a large fraction of the stickers associates into aggregates rather than into binary association. This also explains the broad relaxation time spectrum observed in the data. It must be noted that this effect is magnified for PmA-30k-ODIN in comparison with PmA-18k-ODIN as the terminal relaxation time in star polymers scales exponentially with the arm molecular weight (equation 1). As for sample PmA-18k-ODIN, we also expect the presence of few larger aggregates, characterized by longer relaxation time. This is confirmed by the frequency sweeps performed at higher temperatures (Figure 16), where it is observed that terminal regime of relaxation is not reached.
To conclude this first part, these results show that with increasing Mn, the sticker
concentration decreases and the samples display a colloid to polymer transition similar to the one observed with hyperstars, wherein long arms (high Ma) and low degree of
functionality (low f ) exhibits polymer like material in contrary to colloid-like behavior at high f and short Ma.
Figure 16. Frequency sweep measurements in the linear viscoelastic regime for PmA-30k-ODIN at
different temperatures (25-100 oC).
5.4.3 Rheology: effect of crosslinking.
Then we investigate the effect of crosslinking on the dynamics of supramolecular polymers. To this end, three samples, namely; 1-ODIN, 2-ODIN and PEG-4-ODIN were analyzed via rheology. Scheme 5a depicts the idealistic situation where stacking of the end-groups can co-exist with the crosslinking points. In this case, additional crosslinking should provide extra elasticity given that stacking (and colloidal effect) remains intact. In this view, bi-functional PEG (PEG-2-ODIN) should also have higher plateau modulus than PEG-1-ODIN but less than PEG-4-ODIN, as this last one is reinforced with covalent crosslinking in PEG-2-ODIN and PEG-4-ODIN.
Figure 17 shows the temperature sweep measurements in these samples. For 1 arm PEG end-capped with one sticker, expectedly after the melting point Tm (T = 53 oC) storage modulus drops significantly and ends by a plateau modulus around 6 kPa,
which is not observed with the reference sample PEG-1. This plateau modulus is similar to what was observed in PmA-6k-ODIN at lower frequencies and can be attributed to the stacking of the stickers. With increasing the temperature to 60 oC the
temperature. It must be pointed out here that PEG-1-ODIN and PmA-6k-ODIN both are short length polymers under Mc however, the fact that colloidal behavior persists
up to the highest experimental temperature (160 oC) for PmA-6k-ODIN but only up to
60 oC for PEG-1-ODIN implies that the stacking is significantly dependent on the
chemistry of the polymer.
Scheme 5. Representation of PEG-4-ODIN dynamics; a) idealistic case where the stickers are stacked and b) realistic picture where binary associations lead to percolation. Blue circles represent the crosslinking points.
Figure 17. Temperature sweep measurements of PEG-j-ODINs using small amplitude oscillatory shear
For PEG-2-ODIN, since this polymer has two stickers at both extremities, either long linear assemblies made of several precursors can be obtained (without stacking) or cross-linked supramolecular polymer brushes with the junction point being the center of PEG (similar to Scheme 5a with less crosslinking density). From Figure 17 it is clear that it is this last structure that is present in this sample. Indeed, the plateau modulus observed at intermediate temperature has significantly increased in comparison to PEG-1-ODIN, and this increase can be attributed to the formation of a network linking the supramolecular polymer brushes. However, for PEG-4-ODIN this is not the case anymore: no elastic plateau with G’ > G” could be even at low temperature. The sample rather behaves as a polymer near gel point, with G’ parallel to G”. This can be explained as follows: from the melt state, first the binary associations occur forming a percolated network. This strongly affects the motion of the star arms, which cannot easily move and diffuse to allow the stickers to stack into larger aggregates. Therefore, the stickers are kinetically trapped into binary or small aggregates. Considering that a tetravalent PEG-4-ODIN needs a significant chain stretching to contribute to all stacks, the formation of the stacks is not entropically favorable. Therefore, the image in Scheme 5b is more probable.
The frequency sweeps (Figures 18-20) also support this hypothesis. In PEG-1-ODIN at lower temperatures (at T = 50 oC) elastic behavior reminiscent of colloidal
caging appears. It has to be noted that PEG-1-ODIN cannot form a percolated network since each chain has only one functionalized extremity. At T = 60 oC the sample starts
to flow and terminal slopes characterized by 𝐺𝐺′, 𝐺𝐺"~𝜔𝜔2 and 𝜔𝜔1are reached (Figure
18). It is also noteworthy that at high temperature, with the other mono-functionalized samples PmA-18k-ODIN and PmA-30k-ODIN the presence of aggregates was still visible despite the absence of long range stacking while in sample PEG-1-ODIN, the flow regime is reached at high temperatures (60 °C) (Figure 18). This is probably due to the higher polarity of the PEG matrix, which reduces the probability of the ODIN groups to aggregate. On the other hand, sample PEG-2-ODIN does not flow at 60 °C (Figure 19), however it starts to relax at a higher temperature (80 °C), a temperature at which its terminal regime is not yet fully reached. This indicates that in PEG-2-ODIN, a larger fraction of chains can be trapped between two aggregates, preventing their relaxation. This makes sense considering that the chains are bifunctional and therefore
are able to create long linear assemblies of different chain lengths, which have a larger probability to be trapped between two aggregates. As already discussed, the behavior of PEG-4-ODIN is rather different, since it never shows G’> G” implying that no stacking occurs in this sample, regardless of the temperature and frequency (Figure 20).
Figure 18. Melt rheology (frequency sweeps) in the linear viscoelastic regime for PEG-1-ODIN at
different temperatures (>40 oC).
Figure 19. Melt rheology (frequency sweeps) in the linear viscoelastic regime for PEG-2-ODIN at
Figure 20. Melt rheology (frequency sweeps) in the linear viscoelastic regime for PEG-4-ODIN at
different temperatures (>40 oC).
The absence of large aggregates formed by the stacking of the stickers is further confirmed by looking at the effect of chain crystallization on the sticker stacking. Figures 21-23 show the heating and cooling curves for samples 1-ODIN, PEG-2-ODIN and PEG-4-ODIN, respectively. The samples were first heated step by step (ΔT = 1 oC) and equilibrated at each temperature for 30 seconds. At each temperature,
using a frequency of 1 Hz the modulus values were obtained. Subsequently, after the temperature sweep measurements, the sample was cooled down with a similar protocol (ΔT = -1 oC, 30 seconds equilibration time and frequency of 1 Hz) and the modulus
values were recorded upon cooling. In all temperature sweeps, there is a hysteresis between heating and cooling scans. This has been seen before for semi-crystalline poly(Ɛ-caprolactone)s end-capped with UPy and is expected for slower crystallization upon cooling.46 Such hysteresis induced by the sample crystallization is not observed
in PmAs samples (see Figure 24 for PmA-30k-ODIN). Moreover, heating and cooling the PEG-ODINs above Tm does not lead to a hysteresis either, which supports the reason behind the hysteresis; slow chain crystallization (Figure 25).
Figure 21. Temperature sweeps (at ω = 1 Hz) for PEG-1-ODIN during heating and cooling.
Figure 23. Temperature sweeps (at ω = 1 Hz) for PEG-4-ODIN during heating and cooling.
Figure 25. Temperature sweeps (at ω = 1 Hz) for PEG-2-ODIN during cooling and subsequent heating above Tm.
Furthermore, Figure 21 shows that in the heating curve, the plateau corresponding to the colloidal behavior of the chains is observed at high temperature (around T = 55 – 65 oC), after the melting of the sample, while it is absent in the cooling
curve at this range of temperatures and only appears at lower temperatures (40 – 50
oC), being almost one order of magnitude higher than in the heating curve. This shows
that while the sticker stacks resist high temperatures, lower temperatures are required to favor their formation (based on the protocol followed). It also shows that delaying crystallization of the chains may affect the sticker stacking. Moreover, to check whether the sample was in equilibrium and the plateau observed in the first heating is reproducible, the sample was heated again to 58 oC (above T
m) and the temperature
sweep was performed again, leading to similar results (Figure 21). Therefore, it can be concluded that for PEG-2-ODIN the time needed for the formation of stacks is longer than the time spent during cooling and the plateau does not appear upon cooling. This is not the case for PEG-1-ODIN and a plateau is visible in the cooling, probably because the motion of the polymer chains is faster in mono-functionalized polymer PEG-1-ODIN.
For PEG-4-ODIN no plateau is observed neither at heating nor cooling (Figure 23), confirming the hypothesis according to which no aggregates are formed due to restricted motion of the supramolecular star arms. Furthermore, in the heating curve, an increase in storage modulus is observed close to the Tm which is due to cold crystallization. This effect has been observed via dynamic mechanical analysis (DMA) in poly(lactic acid)s (PLA) and poly(ethylene terephthalate)s (PET) and can imply that in case of PEG-4-ODIN the dynamic of crystallization is slowed due to percolation.47,48 Although more experiments should be done to investigate the
crystallization of PEG-ODINs, it can be concluded that the polymer chain crystallization and crosslinking can affect the sticker stacking.
5.4.4 Rheology: effect of chemistry.
Finally, PDMS was end-capped at one side using the same sticker to generalize the dynamics to different chemistries. So far we showed the dynamics of transient polymer brushes in a range of polymer chemistries, namely; PTHF,41 PmA, and PEG.
Figure 26 shows the frequency sweeps for this new PDMS sample.
Figure 26. Frequency sweep measurements of PDMS-ODIN using small amplitude oscillatory shear
(SAOS) technique.
Similar behavior is observed. PDMS-ODIN which has a lower molecular weight than Mc shows elastic response below 100 oC after which the viscosity was too low for
the frequency sweep measurements. It is also observed that the level of the plateau significantly decreases with temperature, which shows the plateau must originate from stacking of the stickers and colloidal caging effects. Indeed, mono-functionalized PDMS is not able to associate into a polymer network. Therefore, PDMS-ODIN substantiates the image in Scheme 3, where the increase of temperature and decrease in correlation length ξ leads to liquid-like behavior. In other words, if the plateau would have been related to the brush entanglement, the plateau modulus should have been independent of the length of the brush (which is similar to the amount of stacking) as 𝐺𝐺N= 4/5
𝜌𝜌𝜌𝜌𝜌𝜌
𝑀𝑀e, which is not the case.
5.5 CONCLUSIONS
Using a variety of supramolecular polymers end-capped with a recently developed sticker, a wide range of dynamics could be observed depending on topology, chemistry and molecular weight. As a rule of thumb, in low molecular weights, colloidal behavior is more probable due to higher sticker concentration and stacking, leading to a plateau modulus in the order of 10 kPa. The colloidal behavior occurs as a result of excluded volume effects in densely grafted brush polymers and aromatic rings stacked to each other. With increasing the molecular weight, due to low sticker concentration, colloidal properties are not observed and only H-bonded stickers lead to double-sized polymers and star-like aggregates. Therefore, only a shallowing of the terminal slope occurs due to the distribution of relaxation times.
For polymers with 1 or 2 functionalities, the colloidal behavior occurs (at low molecular weights) and for the later case an additional crosslinking (the center of the polymers being the junction point) leads to an increase in the plateau modulus. For 4 arm star precursors forming a polymer with 4 functionality no stacking and no colloidal behavior could be observed due to steric hindrance and kinetically trapped topology, therefore only percolation occurs due to binary H-bonding. The stacking and presence of a plateau modulus was observed in different chemistries, proving a universal behavior in supramolecular polymers end-capped with ODIN as sticker. This study further rules out the possibility of entanglement on the backbone of the polymer brush and supports that caging effects are responsible for the rise of an elastic plateau. These polymers therefore show a transition from colloidal to polymeric material by increasing the chain length. Moreover, depending on the number of functionalities
in precursor polymers, they can show a transition from colloidal to crosslinked colloids to gel-like materials. By choosing the appropriate chemistry, functionality and molecular weight, one can isolate the dynamics in different time scales. Different dynamics in these materials can be used for different applications such as super soft elastomers and self-healing materials. On the other hand, by choosing two different polymer chemistries a dynamic (supramolecular) brush block copolymer can be obtained which has potential applications in photonic crystals.
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