Article pubs.acs.org/Macromolecules
How Supramolecular Assemblies Control Dynamics of Associative Polymers: Toward a General Picture Hadi Goldansaz,† Charles-André Fustin,‡ Michael Wübbenhorst,*,§ and Evelyne van Ruymbeke*,† †
Bio and Soft Matter Division (BSMA), Institut de la Matière Condensée et des Nanosciences (IMCN), Université catholique de Louvain, Place Croix du Sud 1, 1348 Louvain-la-Neuve, Belgium ‡ Bio and Soft Matter Division (BSMA), Institut de la Matière Condensée et des Nanosciences (IMCN), Université catholique de Louvain, Place Pasteur 1, 1348 Louvain-la-Neuve, Belgium § Soft Matter and Biophysics, Department of Physics and Astronomy, KU Leuven, Celestijnenlaan 200d, 3001 Leuven, Belgium S Supporting Information *
ABSTRACT: The dynamics of supramolecular networks made up of partially hydrolyzed poly(n-butyl acrylate) [PnBA] is investigated. These linear entangled random copolymers [PnBA-AA] self-assemble via hydrogen bonding interactions between carboxylic acid groups. Two types of supramolecular assemblies are revealed, i.e., binary assembly of carboxylic acid dimers and collective assembly of dimers into distinct poly(acrylic acid) [PAA] domains. The latter is proved by emergence of new relaxation processes in broadband dielectric spectroscopy while the former is evident by an increase of the glass transition temperature as well as retardation of segmental mobility observed by rheology. Therefore, a “sea−island” morphology containing geometrically confined PAA nanodomains embedded in a PnBA-rich matrix is suggested for the supramolecular network. Thermodynamic theories are employed to rationalize the existence of an interlayer with restricted mobility between the two phases. A fraction of PnBA-AA segments that are trapped between more than one PAA domain are considered to describe the low-frequency plateau in storage modulus that is seen beyond the plateau modulus of PnBA as well as strain hardening in both shear and elongation fields. Finally, based on the observation in this work and wealth of literature on supramolecular networks, a general microstructure is proposed for associating polymers in which supramolecular moieties are situated along the contour length. This microstructure appropriately describes different dynamic observations made by rheology, calorimetry, and dielectric spectroscopy.
I. INTRODUCTION Supramolecular networks based on associating polymers are promising smart materials since they exhibit tunable properties achieved by the incorporation of stimuli-responsive supramolecular moieties to polymer backbones.1−10 The great advantage of self-assembling supramolecular networks is that their microstructures and consequently characteristic relaxation times depend on many tunable parameters such as the strength of the transient bonds,11−13 temperature,7,14 or the chemistry and architecture of the polymer precursor.15,16 Thanks to the possibility of tailoring their dynamics at large scale, supramolecular networks have been successfully employed in several high-tech applications in which a high degree of control over molecular dynamics is required, e.g., shock absorbers,17 polymer electrolytes,18 self-healing materials,19 and microswitches and sensors.20 Numerous investigations have been performed on dynamics in solution or unentangled melt of supramolecular polymers built from oligomers or small molecules. In such systems, viscoelastic properties are almost entirely dominated by the supramolecular bonds.21−23 Many of such supramolecular polymers have shown a single relaxation time which © XXXX American Chemical Society
corresponds to the lifetime of the supramolecular transient association.24 On the other hand, dynamics of supramolecular polymers with entangled polymer precursors have rarely been exploited. A big challenge is to successfully incorporate reversible supramolecular dynamics with disentanglement dynamics of macromolecules, so that the chains relax at the rhythm of association−dissociation of the supramolecular bonds.25 If the relaxation time of the supramolecular bonds is much larger than that of polymer chains, the supramolecular polymer will exhibit properties similar to a conventional elastomer.6,8,26,27 Vice versa, if polymer chains relax much slower than the dissociation of the supramolecular pairs, only a minor retardation of terminal relaxation is expected.12,28 Therefore, in order to achieve supramolecular systems in which both entanglements and transient associations contribute to viscoelasticity, the two time scales have to be in the same order of magnitude. Received: July 11, 2015 Revised: November 27, 2015
A
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Figure 1. Schematic representation of self-assembly of (a) telechelic building blocks, (b) binary associations lead to chain extension, and (c) collective and binary associations forming a supramolecular polymer network.
Table 1. Weight-Averaged Molar Mass (Mw), Dispersity (Mw/Mn), Acid Group Content, and Glass Transition of the Samples Used in This Study
a
name
Mw (kg/mol)
Mw/Mn
acrylic acid monomer content (mol %)
hydrolysis time (h) at 70 °C
PnBA PnBA-AA13% PnBA-AA38% PAA
210 198a 175a 15
1.38 1.38 1.38 1.1
3±2 13 ± 2 38 ± 2 100
4.5 7
glass transition temp (°C) at 10 °C/min −51 −49.5 −47 108
± ± ± ±
0.5 0.5 0.5 1.5
Calculated based on acrylic acid monomer content.28
backbone and supramolecular moieties43−46 or (ii) reduction of Gibbs free energy via formation of secondary bonds between supramolecular moieties, e.g., π−π interactions between aromatic rings in their architecture.47,48 Because of the high stability of collective assembly, the supramolecular systems usually exhibit higher solid−liquid transitions temperature and lower degree of stimuli responsiveness.14 Figure 1 schematically illustrates binary and collective assemblies of moieties in supramolecular polymers. In this work, we address dynamics of supramolecular networks based on partially hydrolyzed entangled poly(nbutyl acrylate) [PnBA]. These random copolymers [PnBA-AA] are self-associating via hydrogen bonds between carboxylic acid groups. We use rheology to characterize segmental and bulk dynamics of the polymer chains and broadband dielectric spectroscopy to independently investigate binary and collective dynamics of the supramolecular moieties. By combining the two techniques, we show that both segmental and bulk dynamics are affected by the transient frictions between supramolecular associations. Weak binary assemblies of AA groups affect the segmental dynamics at low temperatures, while collective assemblies dominate the bulk dynamics of supramolecular networks at every measured temperature. On the basis of the viscoelastic and dielectric data, we then propose a microstructure in which binary and collective assemblies of the supramolecular moieties are taken into account. We believe that this picture is applicable to any system in which associating side groups are distributed along the polymer backbone.
As a result of hierarchy of different relaxation modes, with different activation energies and time scales, contributing to the relaxation of entangled supramolecular networks, these systems are expected to show pronounced thermo-rheological complexity. Hence, a state of the art combination of several techniques is required to fully characterize segmental and bulk dynamics of the supramolecular polymers, since time−temperature superposition severely fails in these systems. In order to have an in-depth understanding of the whole relaxation mechanism in entangled supramolecular systems, it is essential to have independent measures of supramolecular dynamics at different time/length scales.9,13,29−37 Dealing with supramolecular associations, one has to consider the stimuli responsive nature of these interactions, meaning that small changes in compositions or conditions can largely change the equilibrium constant between associated and free moieties by several orders of magnitude.3,38−41 For instance, kinetic studies on terpyridine−Fe(II) bis-complexes demonstrated that the equilibrium constant varies up to 5 orders of magnitude by changing polarity of the medium. Also, attaching the complex to different organic or oligo(poly)meric groups was shown to largely alter the equilibrium constant.39 The sensitivity of supramolecular association phenomenon to different chemical or physical stimuli urges the need to investigate their dynamics in the system of interest and at the conditions of implementation, in order to correctly bridge polymer and supramolecular dynamics. In studying dynamics of supramolecular moieties attached to a polymer backbone, one has to consider different modes of assembly (for a comprehensive review see refs 42 and 43). In the first level of assembly, complementary moieties associate in often binary (sometimes higher orders) ensembles thanks to directional transient interactions, such as hydrogen bond or metal−ligand coordination. This is the most studied mode of assembly of supramolecular moieties, and we refer to it as “binary” associations. Depending on the architecture of the supramolecular polymer as well as chemistry and concentration of the associating motifs, they can spontaneously aggregate into dense rigid domains. The driving forces for “collective” association are (i) reduction of surface tension arising from large amphiphilicity or polarity difference between the polymer
II. MATERIALS AND METHODS Model linear monodisperse PnBA and poly(acrylic acid) [PAA] were purchased form Polymer Source (Montreal, Canada). The model well-entangled PnBA is then selectively hydrolyzed to convert a fraction of butyl acrylate side groups [BA] to acrylic acid [AA] side groups. A schematic representation of the syntheses of model PnBA and PAA samples as well as PnBA-AA supramolecular systems is shown in the Supporting Information (SI.I). In these supramolecular systems the carboxylic acid groups of different chains attract each other by weak hydrogen bonding and form transient networks. Note that the PnBA-AA copolymers have the same backbone length and polydispersity as the model PnBA. Table 1 summarizes properties of different systems used in this work. AA B
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Macromolecules monomer content is determined by 1H NMR spectroscopy. Details on the hydrolysis procedure and chemical characterization methods are reported in our earlier publications.28 The samples of these two studies are identical. DSC analysis was performed using a Mettler Toledo DSC821e calorimeter calibrated against indium. The sample weights were 7−12 mg. Heating ramps of 5−40 °C/min between −90 and 0 °C were used to determine glass transition temperatures. Viscoelastic properties of the PnBA-AA samples were investigated by small- and large-amplitude oscillatory shear rheology using a MCR 301 (Anton Paar, Germany) rheometer. Temperature was controlled using a convection oven operating under nitrogen. A parallel plate geometry (diameter 8, 15, or 20 mm) was used depending on the viscosity level of the system at the given temperature. Different geometries were used to ensure accounting for the setup compliance and inertia effects. No slip problem was observed due to good adhesion of the PnBA-based polymers to the surface of the steel geometries. It is worth noting that none of the samples were exposed to temperatures greater than 125 °C, since AA structure is reported to alter via dehydration and decarboxylation, which significantly affects its glass transition dynamics.49 Broadband dielectric relaxation spectroscopy (BDS) was performed using a high resolution Alpha analyzer (Novocontrol, Germany) over the frequency range of 0.1−107 Hz in combination with a cryostat operating under a nitrogen atmosphere. Materials were sandwiched between 20 and 10 mm gold-coated flat circular electrodes using 100 μm thick glass fiber spacers. Frequency sweep measurements were performed in heating and cooling ramps between 110 and −130 °C with 2.5 °C spacing. PnBA-AA polymers were then quenched from 110 °C using a liquid nitrogen bath, and the transition to the equilibrium state was monitored by a heating ramp from −130 to 110 °C. To correct for geometry discrepancies arising from variation of the spacer thickness or the quenching step, the BDS measurements were repeated for selected temperatures between 60 and −60 °C using a MCR 301 as the dielectric cell, in which the distance between electrodes can be controlled within ±1 μm precision. The imaginary part of permittivity (ε″(ω)) in dielectric relaxation spectra was decomposed using a set of empirical Havriliak−Negami equations to extract mean relaxation time, τ, and the shape factors describing broadness, a, and asymmetry, b, of the relaxation peaks:
ε″(ω) =
iσ Δε + 0 a b ωε (1 + (iωτ ) ) 0
Figure 2. 3D representation of ε″ (gray surface) and ε″KK (blue surface) against temperature and frequency for PnBA-AA13%. In PnBA-AA supramolecular networks a new set of processes, α*, is observed beyond the glass transition of reference PnBA.
unravel relaxation mechanisms which are masked by high dc conductivity. Four individual processes can be identified in the 3-D ε″KK(ω) spectra of PnBA-AA13%, shown in Figure 2. Besides α, β, and γ relaxations, which are present in pure PnBA, a set of dielectric relaxation occurs in the supramolecular networks beyond the α relaxation. These new emerging relaxation processes will be referred to as α*. The sharp rise of ε″KK(ω) at low frequencies is due to electrode polarization (EP), which is a consequence of partial accumulation of charge carriers at the interface between electrodes and sample. Electrode polarization leads to a drastic increase in the real part of permittivity and reduces the slope of imaginary part with respect to the frequency (d log ε″(ω)/d log ω < 1). We confidently assign the last rise to EP since it shows dependency on the geometrical aspect ratio of the dielectric sample.51 It is clear from Figure 3 that the α* process is composed of at least three different relaxation modes, hereafter referred to as α*1, α*2, and α*3. Looking at the low temperature data (50 and 70 °C) for both PBA-AA13% and 38%, it is clear that a small and extremely broad relaxation mode (α*1) is definitely needed to describe the plateau in ε″KK(ω) between 103 and 104 Hz. In a similar way, another contribution (α*3) is required to capture the extended plateau in the ε″KK(ω) which is clearly seen above 80 °C in the PBA-AA38% network. No information on the shape of this relaxation is available. Based on the discussion of this section, the α*3 relaxation shall exist in PnBAAA13%, though it is obscured under the strong Ep upturn. The low and high magnitude plateaus right before and after the main high-temperature relaxation (α*2) rationalize the choice of at least three relaxation processes to capture the dielectric spectra of PnBA-AAs above their glass transitions. To minimize the number of fitting parameters, we used Cole−Cole formalism for α*1 and Debye relaxations for α*2 and α*3. We also used a symmetric contribution to account for electrode polarization. Figure 3 demonstrates that the sum of these contributions properly describes the experimental data, although some minor deviations are also observed which might have been improved by considering more complex shapes for α*2 and α*3 relaxations. Nonetheless, the error bars and the degree of uncertainty will simultaneously increase by increasing the number of fitting parameters. Hence, we decided to work with the minimum number of free variables for the fit exercise to minimize the ill-posed property of the fit. The activation plots for the α, β, and γ relaxations are presented in Figure 4 for all samples. The error bars are
(1)
Δε and ε0 are the strength of relaxation and the permittivity of free space, respectively. ω and σ0 denote the angular frequency and frequency independent dc conductivity. The latter usually shows up above the glass transition and obscures dipolar relaxations at low frequencies. Based on the Kramers−Kronig relation, an accurate numerical approximation has been used to eliminate dc conductivity contribution from ε″(ω): 4
ε″KK (ω) =
∑ ak[ε′(ω/2k) − ε′(2k /ω)] k=1
(2)
where ak = 0.4453, 0.22726, −0.11, and 0.13458 (for more details see ref 50 and references therein). ε″KK(ω) and ε′(ω) are the conductivity free part of ε″(ω) and the real part of complex permittivity, respectively.
III. RESULTS AND DISCUSSION A. Broadband Dielectric Spectroscopy. Figure 2 shows a 3-D plot of ε″(ω) and ε″KK(ω) against temperature and frequency for PnBA-AA13%. The two surfaces perfectly overlay below the glass transition of the sample, where dc conductivity is low. Figure 2 clearly demonstrates that the numerical approximation of eq 2 does not introduce spurious effects on the dielectric spectra. On the contrary, this method enables to C
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Figure 4 demonstrates that the γ process is unaffected by modification of the butyl acrylate side groups to acrylic acid ones, while the relaxation time of the β process significantly increases from the reference PnBA sample to PnBA-AA38%. The systematic departure of the time scale of α relaxation upon increasing the AA monomers is in line with a minute increase of the glass transition temperature observed by differential scanning calorimetry (see Table 1). It can be seen in Figure 4 that at the dielectric glass transition temperature (TgD), i.e. temperature at which τα = 100 s, the apparent activation energy of the β process increases. The abrupt deviation from the Arrhenius behavior at TgD is a known feature of secondary relaxations such as the β process since these relaxations are not fully thermally activated. Similar behavior is reported for the β process in poly(methyl methacrylate) and is assigned to the large alteration of the free volume and its temperature dependency at the glass transition.54,55 Hayakawa and Adachi studied dielectric relaxation of PnBA and reported three characteristic α, β, and γ relaxation phenomena around 230, 190, and 140 K, respectively.56 They assigned the α relaxation to a cooperative process of rotation of the ester bonds (β relaxation) followed by segmental motion of polymer backbones. In a systematic study on poly(alkyl (meth)acrylates), Gaborieau et al.52 found that both α and β processes occur at lower frequencies with increasing side chain length while the γ process is independent of the side chain size. Gaborieau et al. reported that the β relaxation exhibits the highest sensitivity to any alteration in the side chain chemistry. Our data are in good agreement with these studies. The evolution of the relaxation times of the α* processes against reciprocal temperature is presented in Figure 5. It is worth noting that similar relaxation times are observed in heating and cooling ramps for all the relaxation processes in the supramolecular systems, i.e., γ, β, α, and α* relaxations, within experimental error. This observation suggests that the PnBAAAs are in equilibrium within the experimental conditions. On the other hand, once the supramolecular networks are quenched, the α* relaxations clearly accelerate compared to the equilibrium state (see Figure 5b). Though upon heating, the equilibrium behavior is again reached after a characteristic temperature (TC). Figure 5a shows the activation plot of the α* relaxation in a supramolecular network during a conventional heating ramp. The relaxation time of the α*2 process can be determined with great accuracy at temperatures greater than 30 °C (1000/T < 3.25). The error bars in this temperature range are smaller than the size of points. Given a symmetric shape for the α*3 process in PBA-AA38%, the relaxation time is determined with the same accuracy at 1000/T < 2.9. In the temperature ranges where the α*2 and α*3 processes are described quite accurately, both demonstrate Arrhenius temperature dependencies. Contrary to α*2 and α*3 processes, there are large uncertainties in determination of the α*1 relaxation time, which arises from the small relaxation strength of this peak in comparison with experimental and analytical errors. Naturally, the error bars are larger over the entire temperature range in which α*1 is determined. The change of slope at 1000/T ∼ 3.1, where relaxation time is smaller than 10−5 s, is clearly imposed by the fitting process. In this region α*1 relaxation is only partially captured in a range where experimental errors due to high-frequency noise are typically large. Considering the large
Figure 3. ε″KK(ω) of (left) PnBA-AA13% and (right) PnBA-AA38% supramolecular networks decomposed into different contributions, i.e., α*1, α*2, α*3, and Ep at various temperatures. In each data set the dashed and solid lines represent individual and sum of all contributions, respectively.
Figure 4. Activation plot of the α, β, and γ relaxations of the PnBA-AA supramolecular networks together with literature values of Gaborieau et al.52 (crossed circles) and Beiner and Huth53 (triangles).
indicated for every four points, allowing the reader to judge the accuracy of the fit process. Moreover, literature data of Gaborieau et al.52 and Beiner and Huth53 for PnBA are shown as crossed circles and triangles, respectively. A good agreement between our data and the literature values is observed. Discrepancies between the three data sets presented in Figure 4 possibly arise from different methods used to determine the relaxation times. In ref 52 relaxation times are reported based on the local maxima of the imaginary part of dielectric modulus, whereas, similar to our work, Beiner and Huth extracted the relaxation times by fitting ε″(ω) with Havriliak−Negami functions. D
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< T < 80 °C where α*3 can still be determined with good accuracy. The quantitative agreement between the α* relaxations in the PnBA-AA samples, particularly in the heating ramp after quenching, with the α and β relaxations of PAA suggests that there are distinct PAA domains embedded in a PnBA-rich matrix. These phases are formed via aggregation of AA monomers belonging to a single chain or several chains into individual domains. Based on this argument, the α*1 and α*3 relaxations are respectively assigned to β and accelerated α relaxation in the PAA-rich domains. The deviation of the α*3 process from the equilibrium behavior in pure PAA suggests confinementinduced accelerated dynamics, resulting in a substantial reduction of the glass transition temperature of nanometer sized PAA domains.58 Wübbenhorst and Napolitano recently proposed that the ultimate change in the temperature dependence of the relaxation time occurs in 3-dimensional confined systems where a complete transition from VFT to Arrhenius behavior is observed. Extensive explanations and examples are given in support of this argument.58 It seems perfectly reasonable that 3D confinement is the most probable confinement scenario in a random copolymer such as PnBAAA. A comprehensive discussion on the microstructure of PnBA-AA samples is given in section IV. Possible Origin of the α*2 Relaxation Process. Generally, there are two main possibilities for the origin of the α*2 relaxation: (i) a mesoscopic relaxation arises from polarization at the interface between the PAA- and PnBA-rich domains; (ii) a molecular relaxation of the associated supramolecular moieties. In the following we will discuss these two scenarios. Interfacial polarization (Ip) occurs due to the accumulation of charge carriers in the electric field at the interface of two phases with large differences in conductivity and permittivity. The hopping relaxation time of these charge carriers at the interface can give rise to an additional relaxation process. Ip strongly depends on the shape59,60 and size61 of the domains. In the “conventional” dielectric mixture theories, such as Maxwell− Wagner−Sillars (MWS), Looyenga, and Hanai−Bruggman, the size of the inclusions is not considered, and emphasis is put on the shape factor.59 There is a critical assumption in these conventional models that the free charges are accumulated at the boundaries. In reality, when an electric field is applied to a (partially) conductive heterogeneous dielectric material, the charges can move and accumulate near the boundaries. The diffusion of the charges away from the boundaries leads to a charged layer. The thickness of this layer is known as Debye’s screening length (1/κ). When the inclusion size (rp) is comparable to the Debye’s length, strong mismatch with the prediction of the conventional mixture models is observed because these models treat space charges as surface ones.61−63 Figure 6 shows the evolution of dc conductivity of the PnBAAA samples against temperature. In the equilibrium state, dc conductivity of the supramolecular samples is almost 1 order of magnitude lower than that of PnBA. However, upon quenching the conductivity level of PnBA can be retrieved in the supramolecular networks. Figure 6 proves that the presence of supramolecular moieties significantly decreases the diffusion coefficient of charge carriers in the PnBA-rich matrix, since AA groups interact with metallic cations, which are the major fraction of charged impurities in the system. As a matter of fact, a very low conductivity level is expected inside the PAA domains below 100 °C, since the conductivity
Figure 5. Activation plot of the α* relaxations for the PnBA-AA supramolecular networks (a) in equilibrium and (b) after quenching. Data captured in heating ramps for equilibrated and quenched samples are shown with open and half-filled symbols, respectively. Orange and brown dots in (a) are BDS experimental data of Okrasa et al.57 for PAA. Orange crosses are glass transition relaxation times of PAA based on DMA measurements, reported in ref 57.
error bars it is hard to justify temperature dependency of the α*1 relaxation. The black stars in Figure 5 corresponds to the α, β, and γ relaxation times of the model PAA (Mw = 15 kg/mol). The dielectric relaxation spectra of model PAA samples at various temperatures together with the corresponding fit functions are presented in Supporting Information SI.II. For comparison, PAA literature values reported by Okrasa et al.57 are also shown in Figure 5a. Orange and brown dots are respectively α and β relaxation times of PAA as determined by local maxima in dielectric modulus, and orange crosses are glass transition relaxation times measured by dynamic mechanical analysis (DMA).57 A good agreement between the two data sets is observed. Figure 5a shows that the β and γ processes of PAA both exhibit Arrhenius temperature dependency, while a Vogel−Fulcher−Tammann (VFT) behavior is envisaged for PAA’s α relaxation. In Figure 5, one can see a good agreement between the α*1 relaxation time in PnBA-AA networks and the β relaxation of PAA. A better agreement is observed for the α*1 in quenched supramolecular networks and PAA, although given the error bars, the α*1 relaxation times are not dramatically different in the equilibrium and nonequilibrium samples. In the case of the α*3 relaxation, there is some agreement in the absolute values with PAA α relaxation at T > 95 °C; however, the two processes exhibit different temperature dependency which causes the relaxation times to be distinctively different at 60 E
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In summary, in this section we provided compelling evidence that the PnBA-AA supramolecular networks are heterogeneous materials in which PAA domains are formed by aggregation of the supramolecular moieties (collective assembly). The PAA domains are expected to be geometrically confined in the PnBA-rich matrix. B. Rheology. In this section we investigate linear (LVE) and nonlinear viscoelastic (NLVE) response of PnBA-AA supramolecular networks. Our aim is to establish a direct relationship between segmental and bulk dynamics of supramolecular networks and the transient frictions imposed on the polymer chains by both binary supramolecular assemblies in PnBA-rich matrix and collective assemblies in the PAA domains. LVE responses of PnBA-AA copolymers and reference PnBA at 25 °C are compared in Figure 7. While
Figure 6. Evolution of the dc conductivity in the PnBA-AA supramolecular networks against temperature in the equilibrium state (solid lines) and after quenching (half-filled dots).
highly depends on the distance from Tg and also higher density of interaction between metallic cations and the supramolecular moieties are expected. Since the charge transport in the continuous PnBA-rich matrix is much faster than that in the isolated PAA domains, the system has to be treated as inclusions of insulating particles suspended in a partially conductive matrix. In addition, diffusion of ions away from the boundaries (i.e., space charges) has to be considered due to nonometric size of PAA domain. It is shown in Supporting Information SI.III that appropriate dielectric mixture models do not predict Ip relaxations in the frequency window relevant to that of α*2. Therefore, the α*2 relaxation cannot be attributed to Ip. The second possible scenario for rationalizing the α*2 relaxation is a molecular relaxation involving binary supramolecular associations. Müller et al.33 proposed that both dissociation of the supramolecular pairs or reorientation of the pairs with respect to the electric field can give rise to fluctuation of the polarization vector in time, which is manifested by the relaxations in the dielectric permittivity. These authors proved that the macroscopic dielectric relaxation is dominated by the relaxation process which occurs faster. When the dissociation occurs faster than the reorientation of the binary assembly, a Debye process, which is the main characteristic of chemical relaxations, is expected on macroscopic scale. On the other hand, if reorientation of the binary assemblies happens prior to dissociation, a broad asymmetric permittivity peak is expected since reorientation of the associated supramolecular moieties couples with the cooperative motion of the surrounding environment.33 As mentioned in the discussion of Figure 3, the α*2 is almost a Debye relaxation. Therefore, based on the arguments of Müller et al., the α*2 relaxation can be assigned to the dissociation dynamics of binary associations. The Arrhenius activation energy of the α*2 process is ∼29 kJ/mol, which matches with reported values for AA hydrogen bonding assemblies, i.e., 30 kJ/mol.64 However, given the complexity of the data, and a large number of relaxations beyond glass transition in PnBA-AA networks, as well as various hydrogenbonded forms of AA groups,65 a more detailed data set is required to draw decisive conclusions on the origin of the α*2. To provide some preliminary answers on the possible origin of α*2 relaxation, here we outline supramolecular dissociation dynamics as a possible scenario. We wish to leave this question open in this work and will try to address it in future publications.
Figure 7. linear viscoelastic response of PnBA-AA supramolecular networks at 25 °C. LVE of pristine PnBA is also shown for comparison.
PnBA is almost flowing at room temperature, the supramolecular samples show delayed terminal relaxation time. At low frequencies, a second plateau is emerging which becomes more pronounced by increasing the AA monomer content. It is obvious from Figure 7 that the friction imposed by the supramolecular moieties also causes departure from the plateau modulus of PnBA. Just like the second plateau, the classical plateau modulus also increases with increasing the density of supramolecular groups (also see Figure 9 and discussion there). The LVE response of the supramolecular networks is highly temperature dependent. Figure 8a shows that by increasing temperature, the second plateau decreases and shifts to lower frequencies. It is important to mention that the transition region between the first and the second plateau extends over several orders of magnitude by a slope of ∼1/2 against frequency axis (see Figure 8a). This slope manifests that a Rouse process is the dominating stress relaxation mechanism on this time scale. By increasing the temperature or decreasing the AA content, the second plateau eventually disappears and is replaced by nearly parallel dynamic moduli. This parallel region dominates the LVE behavior over >4 decades of frequency (see Figure 8b), a behavior that is indicative of hydrogen bonding systems,12 since the transient bonds are becoming weaker but do not vanish up to very high temperatures.29,66 Time evolution is another well-known feature of many supramolecular systems which arises from the competition between the equilibrium thermodynamics and hindered F
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Figure 9. Master curve of dynamic moduli for PnBA-AA supramolecular networks at iso-friction state (Tg + 36 °C). Segmental Rouse dynamics of the supramolecular polymer are systematically delayed due to friction imposed by the binary supramolecular assemblies. Different measurements are only horizontally shifted using shift factors of the reference PnBA.
superposition (tTs) can be successfully applied to construct master curves in this time/length scales. In other words, PnBAAA networks show thermo-rheological simplicity close to Tg. Similar behavior has been reported for other supramolecular networks.7,25,38 It is clear from Figure 9 that increasing AA monomer content results in delayed Rouse relaxation times as well as higher plateau modulus compared to PnBA. Nonetheless, it is expected that upon increasing temperature, which leads to lower density of assemblies in the supramolecular networks, the plateau modulus and the Rouse relaxation time of pristine PnBA are recovered in the PnBA-AA systems. Strain hardening is another important viscoelastic feature of the PnBA-AA networks. We previously reported that the PnBAAAs exhibit strong strain hardening in an uniaxial elongation field.28 Figure 10a shows the stress growth coefficient of PnBAAA38% and the reference PnBA for various strain rates at 21.5 °C. The data in Figure 10a are identical to those reported previously. The solid lines represent the corresponding LVE envelope determined from a multimode Maxwell fit to the LVE data. In the case of PnBA-AA38% strain rate ranges from 0.001 to 1 s−1. Almost at every strain rate, stress growth coefficient is 2 orders of magnitude greater than the calculated LVE envelope of PnBA-AA38%. At the lowest strain rate, stress growth coefficient of PnBA-AA38% reaches 4 orders of magnitude higher level than the zero shear rate viscosity of reference PnBA. In addition to strain rate, strain hardening magnitude also depends on temperature. Figure 10b demonstrates the evolution of dynamic moduli at 0.1 rad/s against shear amplitude. The vicinity of strain hardening is captured at 55 and 85 °C by the large-amplitude oscillatory shear flow, while at 115 °C the PnBA-AA38% network exhibits strain softening. Therefore, it can be concluded that just like LVE, NLVE behavior of the PnBA-AA supramolecular networks also shows thermo-rheological complexity. Summarizing the viscoelastic observations, we illustrated that both linear and nonlinear viscoelastic properties of the entangled PnBA-AAs are dominated by the supramolecular groups. The important dynamic features are emergence of a second plateau, strain hardening, and retardation of segmental
Figure 8. Temperature-dependent storage and loss moduli (open and solid symbols, respectively) for (a) PnBA-AA38% and (b) PnBAAA13% in the linear viscoelastic region.
molecular motion in these systems. Despite a highly retarded terminal relaxation, the PnBA-AA supramolecular networks, up to 38% AA content used in this work, exhibit equilibrium linear viscoelastic dynamics. In other words, the LVE data presented in Figures 7 and 8 are independent of the thermal history of the supramolecular polymers. To account for the possible role of slow relaxation mechanism during storage, the LVE of PnBAAA38% was remeasured at intervals of 3 and 9 months after the first measurement, and the original data was reproduced within the experimental errors. The equilibrium viscoelasticity indeed originates from the equilibrium dynamics of PAA aggregates in the conventional heating and cooling ramps (see discussion of Figure 5). In addition to bulk dynamics, segmental motion of the supramolecular networks is also altered with respect to that of pristine PnBA. Figure 9 shows the dynamic moduli master curves of PnBA-AA samples at the iso-friction state (Tg + 36 °C) constructed using frequency sweeps at six different temperatures between −45 and −15 °C. No vertical shift was used in constructing the master curves in Figure 9. For the supramolecular samples, different measurements are reduced to individual master curves using the shift factors of the reference PnBA in the corresponding temperature range. Apart from well-known systematic scattering in the transition region between glassy and Rouse dynamics,67 time temperature G
DOI: 10.1021/acs.macromol.5b01535 Macromolecules XXXX, XXX, XXX−XXX
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Macromolecules
domains from the one of bulk PAA suggests that the structural relaxations in the supramolecular aggregates are affected by chain connectivity. With respect to PAA phase there are three main observations: (i) acceleration of the structural relaxation dynamics (α*3) with respect to the that in the bulk (αPAA) and (ii) complete breakdown of VFT temperature dependency of structural relaxation dynamics to an Arrhenius one. These two observations are typical consequences of geometrical confinement in soft matter (see Chapter 7 in ref 58) and prove that PAA domains of a size of a few nanometers exist, being dispersed in the PnBA-rich matrix. According to Adams and Gibbs, who introduced the idea of cooperative glass transition dynamics by postulating cooperative rearranging regions (CRR), cooling a supercooled liquid increases the size of CRR (ξ), which is manifested by progressive increase of the structural relaxation time. The typical size of CCR has been found to be in the order of 2−3 nm for most glass formers at Tg and decreases accordingly for higher temperatures with increasing distance to Tg.68 Upon cooling a glass forming liquid, confinement effects are observed when ξ approaches the size of geometrical confinement. Although the present picture ignores the diversity in shape and heterogeneous nature of the dynamically correlated regions, it helps in acquiring information about the size of collective assemblies in PnBA-AAs. A second consideration concerns the impact of supramolecular association on the free energy of the system, which can be decomposed into four main contributions: (i) the supramolecular forces between moieties which are situated adjacent to each other; (ii) interfacial tension between matrix and collective assemblies; (iii) the entropic−elastic forces required to deform and stretch the polymer coil (see below); (iv) the hard core (steric) repulsion preventing the system from collapsing under influence of van der Waals and supramolecular interactions. Neglecting thermal expansion, steric repulsions lead to constant density (uniform packing) of the material.69 The decrease of thermal energy (kT) results in lower entropic− elastic forces and a larger equilibrium constant for binary supramolecular assemblies. The latter is the driving force toward collective assembly, and the former is the resistance against it.26 Hence, upon cooling, a larger number of AA groups can be accommodated inside the existing PAA domains, and new domains are expected to form.45 Minimization of the interfacial tension implies enlargement of existing PAA domains rather than formation of a large fraction of new ones. Hence, just like ξ, upon cooling, the PAA domains grow in size. According to the Adam Gibbs model, if ξ grows faster and eventually exceeds the size of the PAA domains (rPAA), a breakdown of the VFT-type dynamics due to geometrical confinement will be observed. Figure 5b illustrates that the confinement effect is observed below 100 °C, where a sizable deviation from the structural relaxation time of bulk PAA is observed. Hence, it can be suggested that rPAA∼ ξPAA at 100 °C. In other words, PAA domains are only a few nanometers in size (
