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Article Category: Research Article
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Online Publication Date: 24 Dec 2024

DYNAMICS IN ELASTOMERS WITH HYDROGEN BOND INTERACTIONS

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Page Range: 568 – 581
DOI: 10.5254/rct.24.00036
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ABSTRACT

The dynamics of low molecular weight polybutadiene (PB) functionalized with side chains able to form hydrogen-bonded networks is investigated by a combination of calorimetry, rheology, and broadband dielectric spectroscopy (BDS). The modified PBs are found to have extremely different macroscopic viscosities with respect to the starting polymer; however, rather unexpectedly, when investigated using these three techniques, we find that the changes to the segmental motion responsible for the glass transition temperature remain unchanged. This is attributed to the high flexibility of the side chain, which does not restrict the motions of the highly flexible segments in the PB chain. In the presence of the hydrogen-bonded network we observe in both the rheological and dielectric spectra an additional relaxation, orders of magnitude slower than the segmental relaxation. We find that the temperature dependence and its dynamics are well explained in terms of the lifetime of the hydrogen bond, with a binding energy of about 100 kJ/mol.

INTRODUCTION

This manuscript is written as a tribute to C. Michael Roland. Mike joined the Chemistry Division at the U.S. Naval Research Laboratory (NRL) in Washington, DC, in 1986 and in his 34 years at NRL he was involved in countless applied and basic research programs, until his retirement due to ill health. NRL is where Mike met all of the authors on this article at different times in our careers while he was Section Head of the Polymer Physics Section, later renamed the Soft Matter Section to reflect the broader research area in which the section moved into during the later years. His dedication and passion for scientific inquiry was clear through his many journal articles, book chapters, and patents. This passion was both inspiring and stimulating to his collaborators and peers, and his deep intuition into the physics of materials undoubtedly saved lives in our recent national conflicts. It is clearly not possible to condense into a single paper our collaborations over many years and the numerous subjects we explored together, although many of the more significative results have already been collected and organized by Mike in his book.1 Instead we choose to present a paper on new results on a subject that had always been dear to Mike—elastomers and rubbers—the area in which he started his scientific research at Central Research Laboratories of Firestone Tire & Rubber Co. There are no doubts that with his contribution this paper would have been more insightful and more diligently written.

Polymers are an extremely diverse group of materials used for many applications, having nearly unlimited combinations of molecular structures that can be tailored to specific purposes. Rubbers and elastomers refer to polymers with glass transition temperature (Tg) below room temperature. Their physical properties are very similar to those of liquids, with viscosities that increase with molecular weight. Even those with very high molecular weights can still flow unless chemical bonds between the different chains (crosslinks) are formed by an additional chemical process. Their chemical structures allow them to withstand large mechanical strains, although generally there is a trade-off between strength and toughness that is dependent on the average distance between crosslinks. In some cases, chemical structure can be modified to allow nonpermanent bonds (i.e., ionic or hydrogen bonds) to be formed between the chains of low Tg polymers. In this class of materials, because bonds can be broken and reformed, the polymers can behave as both free chains or crosslinked networks, depending on specific conditions. In particular, the number of nonpermanent bonds depends on different conditions such as temperature, and the lifetime of the bonds becomes an additional parameter determining the conditions under which the flow of the material may be arrested.2–6

In this paper, we discuss the properties of a low molecular weight (unentangled) low Tg polymer functionalized with side chains that allows the formation of nonpermanent hydrogen bonds between the backbones. Thus, depending on the conditions of temperature (or time), the system transitions between a liquid state and a gel state. Using both dielectric and rheological measurements we show that the presence of the nonpermanent network gives rise to an additional relaxation process, slower than the other processes. In addition, we show how from the relaxation temperature dependence of this additional relaxation process we can determine the lifetime of the hydrogen bonds and their binding energy.

MATERIALS AND METHODOLOGIES

Low molecular weight polybutadiene (PB; Mw = 2800 g/mol) was functionalized with side chains able to form H bonds (PB-OH; Figure 1). The chemical reaction for the functionalization of PB was described in a previous publication.6 Varying the stoichiometry of the reagents, we were able to prepare PB-OH of a varying number of side chains. The number of hydroxyl groups per chain was quantified using standard proton nuclear magnetic resonance (NMR) spectroscopy. To obtain a well-resolved peak in the NMR spectra the alcohols on the polymer were capped with trimethylsilyl groups by reaction with hexamethyldisilazane.

Fig. 1.Fig. 1.Fig. 1.
Fig. 1. Modified PB with side chain able to form an interchain hydrogen bond.

Citation: Rubber Chemistry and Technology 97, 4; 10.5254/rct.24.00036

Differential scanning calorimetry (DSC) was performed using a liquid nitrogen Q100 calorimeter (TA Instruments, Delaware, USA) with a standard cooling rate of 10 K/min.

Dynamic mechanical measurement was carried out using an MCR 502 rheometer (Anton Paar, Graz, Austria), with a frequency range of 10−2 ≤ ω(rad/s) ≤ 102. Cone and plate geometries with different radii (8, 25, and 50 mm) and cone angles (1, 2, or 4°) were used for the characterization of different dynamical ranges (smaller radius close to Tg). Strain amplitude sweeps were measured for all samples to verify that the measurements were made in the linear response region, and a strain γ, 0.5% < γ <1.0%, was used. The rheological measurements are reported herein as master curves by using the standard method used in the literature. The horizontal shift necessary to superimposed the spectra is the shift factor, aT.

Dielectric relaxation spectroscopy was carried out using an Alpha analyzer (Novocontrol, Germany). The electrode diameter was 16 mm, with a Teflon spacer of 50 μm. During these measurements, the samples were held under vacuum in a closed-cycle helium cryostat.

RESULTS AND DISCUSSION

DSC

Figure 2 shows the DSC measurements of the neat low molecular weight PB and of two modified PBs with differing amounts of hydroxyl-bearing side chains. From the analysis of the DSC scan, we find that the glass transition of PB is Tg = 189 K, which is indicative of a larger amount of 1,4-PB repeat units. In fact, the glass transition of PB increases with vinyl content, with a Tg close to 273 K for 1,2-PB and 179 K for 1,4-PB.7 With the increasing number of sidechains, the Tg remains within 1 K of that of unfunctionalized PB. In the DSC data we observe that there is a decrease of the magnitude of the heat capacity change, ΔCp, at the glass transition for the PB-OH samples (Figure 2, inset). The decrease is roughly proportional to the percentage of the weight represented by the side chain; for example, for PB-OH with NOH = 10.3 the side chains are about 26% of the sample weight and we observed a reduction of about 30% of the heat capacity step at the glass transition. Therefore, the side chains appear not to be affected by the glass transition of the backbone. This is in contrast to the clear increase of the viscosity of the polymers with increasing numbers of side chains. Thus, although the functionalization with the side chains has a large effect on the overall diffusion of the chains, it has a small effect on the segmental motions of the highly flexible PB backbones and of the side chains.

Fig. 2.Fig. 2.Fig. 2.
Fig. 2. DSC of PB and PB-OH with varying amount of side chain. Inset: ΔCp at the glass transition vs the number of hydroxyl groups.

Citation: Rubber Chemistry and Technology 97, 4; 10.5254/rct.24.00036

RHEOLOGY

The effect on the chain diffusion is clearly evident in the rheology measurements. Figure 3 shows the storage modulus, G, for the neat PB and three PB-OH analogs (with OH functionality between 5.5 and 10.3). The glassy state, G, is on the order of 1 GPa, which is similar to a typical amorphous glass. The polymer then relaxes to a small rubbery plateau 1–10 MPa above the glass transition. The plateau is not very broad due to the low Mw of the polymer. At higher temperature, the terminal flow shows a Newtonian behavior. In the functionalized polymers, there is evidence of an additional process that alters the terminal flow of the polymer chain. This process can be ascribed to the presence of a hydrogen bond network, which becomes transient at high temperatures.

Fig. 3.Fig. 3.Fig. 3.
Fig. 3. Storage modulus master curve for PB and PB-OH with varying numbers of side chains.

Citation: Rubber Chemistry and Technology 97, 4; 10.5254/rct.24.00036

The loss peak master curve (Figure 4, right) of the PB reveals only one peak corresponding to the segmental relaxation (α), whereas the loss peak associated with the chain relaxation (estimated to be about 6 orders of magnitude slower) is hidden under the loss associated with the terminal flow (Newtonian viscosity). In the case of PB-OH with 10 side chains, in the loss master curve (Figure 4, right) all are well resolved three-loss processes. The faster process is associated with the segmental relaxation, the intermediate with the chain dynamics, and the slowest with the transient H-bonded network, with a timescale about 14 orders of magnitude slower than the segmental relaxation. Therefore, the functionalization with the side chains forming a hydrogen-bonded network gives rise to an additional relaxation process at lower frequency (higher temperature), which is timescale-dependent on the number of side chains per polymer chain.

Fig. 4.Fig. 4.Fig. 4.
Fig. 4. Tan δ master curves for PB (left) and PB-OH with NOH = 10.3 (right). Note the different scale on the y axis due to the much larger loss associated with the Newtonian flow in PB, which hides the α′ loss peak due to the chain relaxation.

Citation: Rubber Chemistry and Technology 97, 4; 10.5254/rct.24.00036

The shift factor, aT, was converted in the peak frequency, fmax, by adding a correction (i.e., a constant) determined from the peak frequency determined at a temperature where the peak maximum is within the measured frequency range. The temperature dependences for the peak frequencies of the three relaxations for PB and three PB-OH analogs are reported in Figure 5. Note that for PB only the α-process can be resolved, because the relaxation, α′ (chain mode), is hidden under the loss due to the viscosity, whereas the a-process is present only in the PB-OH.

Fig. 5.Fig. 5.Fig. 5.
Fig. 5. Peak frequency of the three mechanical relaxation peaks for PB and the three PB-OH analogs. The solid lines are the best fit to the VF equation, and the best fit parameters are reported in Table I.

Citation: Rubber Chemistry and Technology 97, 4; 10.5254/rct.24.00036

The temperature dependence of the peak frequency determined from the mechanical spectra is reported in Figure 5 for PB and the three PB-OH analogs. The solid line in Figure 5 is the best fit to the data using a Vogel Fulcher (VF) equation:1,8,9where B, f0, and T0, are constants. The VF equation describes the temperature behavior of the peak frequency, characterized by an increase of the activation energy with decreasing temperature and an apparent divergent temperature T0. The best fit parameters are reported in Table I.

Table I Best-Fit Parameters of VF Equation (Eq. 1) to Peak Frequency from Rheological Dataa
Table I

BROADBAND DIELECTRIC SPECTROSCOPY (BDS)

The dielectric loss spectra for PB (Figure 6) below the Tg show the presence of a secondary relaxation, β-process, very broad and weakly dependent on temperature. Above the glass transition, the segmental relaxation, α, is well evident and there is an extra contribution on the lower frequency flank of the α-process that we identify as the α-process. The presence of similar processes in dielectric spectra has been found before in other weakly polar polymers such as polyisobutylene (PIB).10 In many polymers or liquids, the lower flank of the α-process is masked by the presence of DC conductivity losses,11–14 which in this case is quite low. A reason for the lower DC conductivity losses is the low polarity of PB (and PIB) that results in a low dissociation constant for ionic impurities. Unlike polymers such as polypropylene glycol, which has a large dipole moment along the chain,15–21 the dipole moment along the chain for PB is very small and dependent on the different isomers. Thus, the relaxation likely does not represent the end-end dipole (i.e., chain mode), but rather the mode related to parts of the chain larger than single segments. This type of motion has been previously identified as a sub-Rouse mode.10,22

Fig. 6.Fig. 6.Fig. 6.
Fig. 6. Dielectric loss spectra of PB over a broad range of temperatures from well above to below the glass transition.

Citation: Rubber Chemistry and Technology 97, 4; 10.5254/rct.24.00036

The analysis of the dielectric spectra was done using a linear superposition of a Kohlrausch–Williams–Watts (KWW) function for the α and α relaxations and a Cole–Cole function for the β-process, plus a term due to DC conductivity loss:23where Liω indicates the Laplace transform, σDC is the DC conductivity, and αcc and n are constants. The peak frequencies for the α, α, and β-processes in PB are reported in Figure 7. The β-process shows the Arrhenius behavior typical of secondary relaxations below the glass transition, whereas the α and α behaviors are described by the VF equation (Eq. 1).

Fig. 7.Fig. 7.Fig. 7.
Fig. 7. Arrhenius plot for the dielectric relaxation peaks for PB and three PB-OH.

Citation: Rubber Chemistry and Technology 97, 4; 10.5254/rct.24.00036

The dielectric loss spectra of the PB-OH polymers show an additional process slower than the α-process, which can be observed only at temperatures much higher than the glass transition. This behavior is analogous to what is observed in the mechanical loss spectra where the a peak is observed (Figure 4, right).

The presence of an extra dielectric relaxation at lower frequency in the presence of a hydrogen bonds network is reminiscent to what is observed by dielectric spectroscopy in monoalcohols.24–26 In monoalcohols, the hydrogen-bonded network formed by the highly polar hydroxyl group gives rise to a dielectric relaxation, which intensity decreases with increasing temperature and pressure.27 In that case, however, this additional process (slower than the α-process), is well described by a nearly Debye relaxation function (i.e., with βKWW ∼ 1), and with a smaller timescale separation than observed herein. Some evidence has been reported of an additional relaxation process in polyalcohols,28,29 although there is still some controversy with respect to some of these data,30,31 and in very low molecular weight hydroxyl–terminated polydimethylsiloxane.32 Interestingly, the results obtained for the class of polymers presented herein supports the idea that these additional relaxation processes observed in polyalcohols are indeed linked to the hydrogen-bonding network and its lifetime.

To analyze the dielectric spectra of the PB-OH we used a superposition of relaxation function analogous to that used for PB, with an additional relaxation function to describe the a-process.

Notably, even if this fitting function has many free parameters (because it needs to describe many relaxation processes), not all relaxation processes are present in the same spectrum. For example, at high temperature (e.g., 369.2 K in Figure 8) the spectra are dominated by the conductivity losses and the a-process and the contributions from all the other processes are negligible. Similarly, at low temperatures (e.g. 155.1 K in Figure 8), only the β-process is observed.

Fig. 8.Fig. 8.Fig. 8.
Fig. 8. Dielectric spectra of PB-OH with NOH = 8.3. The spectra were measured at several temperatures, from well above to below the Tg.

Citation: Rubber Chemistry and Technology 97, 4; 10.5254/rct.24.00036

The peak frequencies of the four different relaxation processes in the PB-OH are reported in Figure 7. The temperature behavior for α, α, and β is very close to that of PB, which is indicative of the relatively small effect of the hydrogen bond network on the segmental motion, as observed by DSC and rheology.

The temperature dependence of the β-process is well described by an Arrhenius equation: where Eact is the activation energy and f0β is a constant.

For PB and PB-OH, the peak frequencies are independent of the chemical structures; this is not too surprising because the β-process is due to local motions of the segments having a smaller correlation length than the segmental motion, and they are generally of a noncooperative nature.33–35 From the best fit to the data (Figure 7) to Eq. 4 we obtain Eact= 0.37eV, which is in the range of the activation energy observed for secondary relaxations. The temperature dependence of the peak frequency for the processes a, α, and α shows an increase of the activation energy with decreasing temperature typically observed for the segmental and chain relaxation. Similar to the rheology data, this temperature behavior is well described by the VF equation (Eq. 1). The best-fit parameters obtained from the best fit of the VF equation to the data reported in Figure 7 are in turn reported in Table II.

Table II Best-Fit Parameters Obtained by Fitting VF Equation (Eq. 1) to Peak Frequency of Dielectric Relaxation Data Reported in Figure 7a
Table II

Notably, even if the relaxation scenario observed with rheology and BDS is very similar with the three processes α, α, and a, the timescales of the three relaxations are not equivalent. We find that the temperature dependence of the peak frequency determined using the two spectroscopies are very close. However, large differences were found for the peak frequencies of the other two processes. To show this, we reported both rheological and dielectric peak frequency data for the PB-OH, with NOH = 8.5, in Figure 9. As can be seen, both processes, α and a, are 3 orders of magnitude slower in rheological measurements than in dielectric measurements, whereas the difference between the α-process is well below 1 magnitude. A possible explanation for this difference is the fact that the α-process, measured by BDS, is a sub-Rouse relaxation involving only part of the chain, whereas the α-process, as measured from rheology, is due to the flow of all chain. Consequently, because the a-process is related to the chain motion hindered by the interchain hydrogen bonds, it is reasonable to assume that the difference between rheology and dielectric relaxation time is similar to that observed for the α-process.

Fig. 9.Fig. 9.Fig. 9.
Fig. 9. Peak frequency for PB-OH with NOH = 8.5 determined from rheology and dielectric spectra.

Citation: Rubber Chemistry and Technology 97, 4; 10.5254/rct.24.00036

CONCLUSIONS

The functionalization of a low molecular weight PB with side chains able to form hydrogen bonds (up to an average of 10.5 hydroxyl group per chains) has a profound effect on its macroscopic viscosity. By contrast with this macroscopic change, we found that functionalization had a negligible effect on the segmental relaxation (α-process) and therefore caused only small changes to the glass transition. This result was confirmed by calorimetry, rheology, and dielectric spectroscopy. The α-process is associated with the orientation of the polymer segments, and even if this motion is cooperative (i.e., involving multiple segments), it is minimally constrained because of the high flexibility of the side chains. Previously, large changes in the glass transition and temperature behavior of the α-process had been observed in crosslinked PB chains.36 In the case of hydroxyl-terminated polydimethylsiloxane, it has been reported that there is a large hydrogen-bonding effect on the fragility and glass transition.32 This difference seems to indicate that the highly flexible side chains, even when they form a hydrogen bond network, do not constrain the segmental motion. This behavior agrees with previous observations that, for polymers having the same backbone, a change in the segmental dynamics is observed when relatively more stiff side chains are present in the molecular structure.37 In PB-OH the added side chains are relatively more flexible than the backbone; for this reason, only a minimal effect on the temperature dependence of the segmental relaxation is observed, with the hydrogen bonds mainly affect the flow behavior at much longer times.

For the neat PB, we observed a relaxation slower than the α-process in dielectric measurements, indicated as α, which we identified as a sub-Rouse relaxation. This relaxation is not observed in the loss spectra from rheological measurements, presumably because it is hidden under the loss due the viscosity. The α-process is well resolved in the mechanical loss spectra of the PB-OH polymers, and it has a very similar relaxation time when varying the number of side chains. For these samples the viscosity is much higher, and so the α-process is not hidden by the viscosity as it is in the PB. The α-process was also resolved in the dielectric spectroscopy measurements, but the relaxation time of the α-process observed by dielectric spectroscopy is about 3 orders of magnitude faster than that determined from rheology measurements. A possible reason for this difference is attributed to the different number of segments involved in the α-process, as measured by the two types of spectroscopy. Because the dipole moment along the PB chain is very small and not uniform due to the presence of different isomers, the α-process is not related to the end-end motion of the chain, but rather to a smaller portion of the chain (i.e. sub-Rouse), whereas the chain flow observed in rheology is related to the motion involving all the segments of a chain.

In the functionalized polymers with hydrogen bonding side chains (PB-OH), we observed a third relaxation that is much slower than the α and α. This relaxation, indicated as a, is attributed to the transitory nature of the hydrogen bonded network between the polymer chains. In the case of the permanent polymer networks (i.e., with covalent bonds), an additional relaxation at low frequency (or high temperature) is not observed, but instead there is a constant G′ (or plateau) with negligible loss.1,38,39 In the case of the transitory network, the plateau is interrupted at low frequency (high temperature) when the network is disrupted and the chains are able to diffuse. The frequency at which the relaxation occurs is related to the hydrogen bond lifetime, τs. For times shorter than the lifetime (frequencies ≫ 1/τs), the system behaves like a permanent network, whereas for times longer than the lifetime (frequencies ≪ 1/τs), the system acts like free chains. In addition, the lifetime is expected to change with temperature depending on the strength of the bond. For H bonds, a binding energy, Ea, between 5 and 170 kJ/mol is generally observed and the temperature dependence of the lifetime is expected to be described by an Arrhenius-like dependence with τs=τ0exp(Ea/kT).

To estimate τs from our data we calculated the difference between τa and τα (where τ=1/2πfmax). The difference, τaτα, is a good approximation of τs  because it quantifies the delay between the free chain diffusion and the constrained chain diffusion. The difference, log(τaτα), vs the inverse temperature is shown in Figure 10. The temperature behavior of log(τaτα) is well described by an Arrhenius behavior (solid line in Figure 10) with a binding energy Ea=113 ± 4 kJ/mol, which is a reasonable value for hydrogen bonds binding energy. This result confirms the nature that we attributed the α-process.

Fig. 10.Fig. 10.Fig. 10.
Fig. 10. Difference of the relaxation times τa and τα for PB-OH with NOH = 8.5 determined from BDS measurements.

Citation: Rubber Chemistry and Technology 97, 4; 10.5254/rct.24.00036

Copyright: 2024
Fig. 1.
Fig. 1.

Modified PB with side chain able to form an interchain hydrogen bond.


Fig. 2.
Fig. 2.

DSC of PB and PB-OH with varying amount of side chain. Inset: ΔCp at the glass transition vs the number of hydroxyl groups.


Fig. 3.
Fig. 3.

Storage modulus master curve for PB and PB-OH with varying numbers of side chains.


Fig. 4.
Fig. 4.

Tan δ master curves for PB (left) and PB-OH with NOH = 10.3 (right). Note the different scale on the y axis due to the much larger loss associated with the Newtonian flow in PB, which hides the α′ loss peak due to the chain relaxation.


Fig. 5.
Fig. 5.

Peak frequency of the three mechanical relaxation peaks for PB and the three PB-OH analogs. The solid lines are the best fit to the VF equation, and the best fit parameters are reported in Table I.


Fig. 6.
Fig. 6.

Dielectric loss spectra of PB over a broad range of temperatures from well above to below the glass transition.


Fig. 7.
Fig. 7.

Arrhenius plot for the dielectric relaxation peaks for PB and three PB-OH.


Fig. 8.
Fig. 8.

Dielectric spectra of PB-OH with NOH = 8.3. The spectra were measured at several temperatures, from well above to below the Tg.


Fig. 9.
Fig. 9.

Peak frequency for PB-OH with NOH = 8.5 determined from rheology and dielectric spectra.


Fig. 10.
Fig. 10.

Difference of the relaxation times τa and τα for PB-OH with NOH = 8.5 determined from BDS measurements.


Contributor Notes

Corresponding author. Ph: 202-404-8042; email: riccardo.casalini@nrl.navy.mil
Received: 21 Jun 2024
Accepted: 21 Sept 2024
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