Dynamic Glass Transition and Electrical Conductivity Behavior

Article pubs.acs.org/Macromolecules

Dynamic Glass Transition and Electrical Conductivity Behavior Dominated by Proton Hopping Mechanism Studied in the Family of Hyperbranched Bis-MPA Polyesters K. Adrjanowicz,*,† K. Kaminski,∥,∇ M. Dulski,∥,∇ M. Jasiurkowska-Delaporte,† K. Kolodziejczyk,∥,∇ M. Jarek,† G. Bartkowiak,†,‡ L. Hawelek,⊥ S. Jurga,†,§ and M. Paluch∥,∇ †

NanoBioMedical Centre, and §Department of Macromolecular Physics, Adam Mickiewicz University, ul. Umultowska 85, 61-614 Poznan, Poland ‡ Faculty of Chemistry, Adam Mickiewicz University, Umultowska 89b, 61-614 Poznan, Poland ∥ Institute of Physics, University of Silesia, ul. Uniwersytecka 4, 40-007 Katowice, Poland ⊥ Institute of Non Ferrous Metals, ul. Sowinskiego 5, 44-100 Gliwice, Poland ∇ Silesian Center of Education and Interdisciplinary Research, University of Silesia, 75 Pulku Piechoty 1A, 41-500 Chorzow, Poland S Supporting Information *

ABSTRACT: Dielectric and infrared spectroscopies were employed to study inter- and intramolecular glass-transition dynamics in the series of hyperbranched polyesters of the second, third, and fourth generations. Our study shows that conductivity relaxation becomes increasingly faster than structural relaxation as the glass transition temperature Tg is approached, signifying decoupling between translational motions of charges and reorientation of molecules. Depending on the polymer’s generation conductivity relaxation times can be up to few orders of magnitude faster than structural dynamics. Because of extensive hydrogen bonding network, the most significant contribution to the total ionic conductivity comes from proton transfer along hydrogen bonds. Decoupling phenomenon was accompanied by narrowing the dispersion of the conductivity relaxation with decreasing temperature that reaches almost exponential decay in the glassy state. Finally, by analyzing the absorption spectra in terms of integral intensity, we have demonstrated significant role of H-bonded moieties in the course of vitrification of investigated materials.

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INTRODUCTION

them promising materials for variety of applications, such as drug delivery systems, biosensors, coatings, and so on.6−9 A large number of reported in the literature hyperbranched materials consist of 2,2-bis(hydroxymethyl)propionic acid (bisMPA) molecule used as a universal dendritic building block. Bis-MPA was successfully applied to synthesize a wide range of dendritic polymers such as dendritic−linear polymer hybrids and homo- and heterofunctional dendrimers.3 Today, dendrimers based on bis-MPA are constructed up to sixth generation, depending on the number of terminal groups.10 Because of the large number of hydroxyl end groups, hyperbranched bis-MPA polymers show inter- and intramolecular hydrogen-bonding interactions that influence in a significant way their physical properties. As demonstrated in the literature hyperbranched polyesters form complex hydrogen bonding, due to various proton donors (hydroxyl and carboxyl groups) and acceptors (ester, hydroxyl, and carboxyl groups)

Upon developing new types of polymeric materials for advanced and large volume applications, molecular architecture is the most important aspect that has to be taken into account. Depending on the backbone structure, number, and types of end groups, the intra- and intermolecular interactions might significantly change, resulting in different physicochemical properties that affects directly the range of potential usage of polymeric materials in medicine, pharmacy, or high technology. During the past decade nonlinear highly branched polymers (such as dendrimers, hyperbranched polyesters, or star polymers) have attracted a lot of attention because of several promising features, much different from those known for their linear counterparts. Highly branched polymers are generally built up from a great number of arms that come out from a central core. These polymers exhibit significant chain-end effects, higher solubility in various solvents, lower melt viscosity, entanglement degree and flexibility, scaffolding ability, and biocompatibility.1−5 It has been also reported that the above-mentioned features of hyperbranched polymers make © XXXX American Chemical Society

Received: March 26, 2014 Revised: July 27, 2014

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dx.doi.org/10.1021/ma5006155 | Macromolecules XXXX, XXX, XXX−XXX

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Figure 1. Chemical structure of hyperbranched bis-MPA polyesters of (a) second, (b) third, and (c) fourth generation.

available in that system.11 In such materials dynamic reorganization of hydroxyl groups via hydrogen bonds into an ordered microstructure was also reported.12 It is worth noting scientific research on the hyperbranched bis-MPA materials are devoted mainly to their various synthesis procedures, variety of architectures, and potential applications. Physicochemical properties of dendritic materials have been studied, however, to a much lesser extent. Most of these studies focused on the influence of various thermal groups or the number of polymer generation on the dynamics, glasstransition, thermal, or rheological properties.13−16 Because of complexity of the inter- and intramolecular interactions in hyperbranched polymeric systems, some of the physicochemical properties might not necessary follow molecular weight dependence as well as increasing polarity of end groups.17,18 Among various experimental techniques that can be used to study molecular dynamics of hyperbranched polyesters, dielectric spectroscopy has attracted considerable interests, as it enables to study relaxation processes in a broad range of time scales, temperatures, and even pressure.17,19−26 Irrespectively of molecular weight and type of terminal groups, for dendritic materials one should expect typical relaxations processes as that known for glass-forming liquids, i.e., α-relaxation related with dynamic glass transition and secondary relaxations originating from local motions. In the glassy state of hyperbranched bisMPA polyesters two secondary processes can be observed: β and γ, reflecting reorientation of hydroxyl units and ester groups, respectively.20,21 Unfortunately, in many hyperbranched polymers the α-relaxation cannot be observed directly because of conductivity effects that overlay entirely dielectric response collected above the glass transition temperature (e.g., refs 17−19 and 24). As a result, one cannot fully access the most important features related with their glass transition dynamics. It is also worth to note that the formation of an extended and complex hydrogen bonding networks creates various routes of proton transfer giving a rise to proton conductivity, not studied so far in such materials. Recent studies have shown that by combining dielectric spectroscopy with infrared spectroscopy it is possible to trace not only the intermolecular dynamics accompanying the glass formation but also intramolecular dynamics of specific molecular moieties.27−29 The temperature dependence of IR oscillators’ strengths and their positions show a specific “kink” on approaching Tg, with various sensitivity that depends on the analyzed vibration band. As a result, it is possible to probe the glass transition phenomenon at the molecular scale. In this work, using both spectroscopic techniques we focus on the dynamic properties and charge transfer of well-known

hyperbranched bis-MPA polyesters in vicinity of glass transition. Because of extensive and complex hydrogen bonding interactions, the proton moves herein along hydrogen bonds, giving rise to the total ionic conductivity that was probed dielectrically. We have noticed that as the glass transition temperature Tg is approached, conductivity relaxation becomes anomalously faster than structural relaxation, which indicates for a decoupling between translational motions of charges (mostly proton-like) and reorientation of molecules in the family of investigated hyperbranched polyesters. Despite the fact that relaxation dynamics of dentritic polyesters have been studied many times in the past, this contribution provides first experimental evidence of such phenomena. We have shown that proton hops along hydrogen bonds sense the glass transition, and depending on a polymer’s generation the time scale of translational motions of charges can be up to few orders of magnitude faster than reorientation of molecules. In order to follow the intramolecular effect accompanying the vitrification process, the analysis of temperature dependence of IR oscillators’ strength and their shifts were performed. As it turned out, the most significant changes were observed for hydroxyl group vibrations, indicating for a significant contribution of H-bonding networks in the glass transition dynamics that depends also on the molecular weight of investigated hyperbranched polyesters.

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EXPERIMENTAL SECTION

Hyperbranched bis-MPA (2,2-bis(hydroxymethyl)propionic acid) polyester-16-hydroxyl (generation 2, C75H128O45, Mw = 1749.79 g mol−1, average number of OH groups = 16), hyperbranched bis-MPA polyester-32-hydroxyl (generation 3, C155H256O93, Mw = 3607.64 g mol−1, average number of OH groups = 32), and hyperbranched bisMPA polyester-64-hydroxyl (generation 4, C315H512O189, Mw = 7323.32 g mol−1, average number of OH groups = 64) were purchased from Sigma-Aldrich with declared purity greater than 97%. The chemical structure of investigated materials in presented in Figure 1. Prior to studying dynamic properties accompanying the glasstransition event, each sample was heated up to 403 K and kept at that temperature for about 30 min to ensure complete melting and removal of absorbed water. Additional XRD and TGA measurements were performed to confirm that hyperbranched bis-MPA polyesters can be performed in the amorphous state by quenching without thermal decomposition. Results of those studies can be found together with description of XRD and thermogravimetric experiments in the Supporting Information. The dielectric measurements were performed by means of NovoControl Alpha dielectric spectrometer over frequency range from 1 × 10−2 to 3 × 106 Hz. Tested samples were placed between two stainless-steel electrodes separated by Teflon spacers (diameter: 10 B


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Figure 2. Real (a) and imaginary (b) part of complex dielectric permittivity, imaginary part of electric modulus (c) and real part of conductivity function (d) plotted versus frequency at various temperatures (in the range 333−261 K) as indicated for hyperbranched bis-MPA polyester of the third generation with approximately 32 hydroxyl terminal groups.

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mm; gap: 0.1 mm) and mounted in a cryostat. The temperature was controlled by a Quatro System using a nitrogen gas cryostat, with stability better than 0.1 K. Dielectric measurements were performed on cooling from the melting point down to the glassy state with the step of 4 K. Dielectric susceptibility and electric modulus formalisms were utilized. Fourier transform infrared (FTIR) absorption spectra were measured using a BRUKER IFS 66/s spectrometer in the wavenumber range of 700−4000 cm−1 with the resolution of 4 cm−1. The compound was placed between two KRS-5 windows. Prior to the measurements, the sample was annealed for about 30 min at 403 K. IR spectra were collected at each 2 K upon cooling in the range of temperatures Tg + 30 K to Tg − 30 K for each polymer generation. The temperature was controlled by Specac automatic temperature controller with an accuracy of 0.1 K. The bands in the OH region were fitted using a sum of Gaussian functions after subtraction of baseline. Their shifts were determined with respect to the peak position at Tg. The assignment of experimentally observed IR absorption peaks with characteristic vibrations was performed on the basis of literature data for hyperbranched polyester of the fourth generation. The geometries of the hyperbranched bis-MPA polyesters have been optimized using Becke’s hybrid exchange and correlated threeparameter with the Lee−Yang−Parr correlation functional (B3LYP)30−32 and standard Gaussian basis sets 6-31G(d,p).32 These calculations were carried out in the gas phase using density functional theory (DFT) calculations33−35 and the Gaussian09 software package.36 The optimized molecules with the labeling system used for the present calculations were visualized using GaussView 5.0.8 software. The optimized structures were used as input files for vibrational harmonic calculations. Based on these calculations, all conformers have positive harmonic vibrations indicating a true energy minimum.36 Viscosity measurements were performed by means of Ares rheometer (Rheometric Scientific). A plate−plate configuration (8 mm diameter) was used, and the gap between stainless still plates was set to be 1.0 mm.

RESULTS AND DISCUSSION

In Figure 2a,b we present representative dielectric plots of the real and imaginary part of complex permittivity ε*(f) (= ε′( f) − iε″(f)) as a function of temperature for hyperbranched bisMPA polyester of the third generation. As illustrated, dielectric

Figure 3. Temperature dependence of the conductivity relaxation times τσ plotted as a function of 1/T for hyperbranched polyesters of the second (circles), third (triangles), and fourth (stars) generations. Solid lines are VFT fits, while the dashed lines represent Arrhenius fits to the experimental data. The temperature at which the τσ dependence changes its character from VFT to Arrhenius-like indicates the glass transition event. The inset shows dependence of the decoupling index from the number of hydroxyl end groups of investigated bis-MPA hyperbranched polyesters. C


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relaxation dynamics associated with the glass-transition phenomenon. As mentioned in the Introduction, a similar problem with analyzing dielectric susceptibility data of dendritic materials was reported earlier by other researchers. Therefore, for mostly conductive materials it is very convenient to present dielectric spectra by using complex electric modulus M*(ω) or conductivity σ*(ω) functions that emphasize translational motion of charges and discriminate other unwanted effects. M*(ω), σ*(ω), and ε*(ω) are related to each other by the equation37−39 M *(ω) =

iε0ω 1 1 = = (ε′ − iε″) ε*(ω) σ *(ω)

(1)

where σ* = σ′ + iσ″ (σ′ = ε0ωε″ and σ″ = ε0ωε′). In the imaginary part of electric modulus the translation motions of charges are transformed into relaxation peak, as illustrated in Figure 2c. With decreasing temperature conductivity peak shifts toward lower frequencies which indicate that translational motions of charges slow down. Moreover, upon cooling the intensity of M″ peak increases, reaching almost a constant value once the glass transition is reached. In the studied by us range of temperatures except of conductivity relaxation secondary modes are visible, but their analysis is beyond the scope of this paper and can be found elsewhere. Figure 2d shows the temperature dependence of the real part of the complex conductivity σ′ for bis-MPA of the third generation. As illustrated, the characteristic plateau and critical frequency at which σ′ bends down decrease with decreasing temperature, which is rather typical behavior for materials with high conductivity. In the further part of this paper we have utilized electric modulus representation, as it enables to determine in very easy and convenient way the conductivity relaxation times. From analysis of imaginary part of complex electric modulus we have determined the conductivity relaxation time as the inverse of the frequency of M″ maximum peak position τσ = 1/ (2πf max). For studied generations of hyperbranched polyesters, we have observed that at certain temperature the dependence of τσ changes its character and becomes much weaker. This

Figure 4. Dielectric modulus spectra of hyperbranched bis-MPA polyesters of the (a) second, (b) third, and (c) fourth generations recorded in the supercooled liquid and glassy regions, as indicated. Solid lines represent the fit of the KWW function to the conductivity peak.

absorption and loss spectra collected in the liquid state are dominated by electrode polarization and conductivity effects, respectively. Analogical behavior was also observed for other generations. Since the charge transport masks up completely the structural relaxation peak, it is impossible to probe

Figure 5. Comparison of the behavior of the real part of conductivity function for hyperbranched bis MPA polyesters (a) in the supercooled liquid region at 305 K and (b) at the glass transition temperatures. D


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Figure 6. Temperature dependences of viscosity and conductivity relaxation times for (a) G2 and (b) G4. Symbols (red circle) and (green stars) refer to viscosity data, whereas (blue triangle) and (black square) conductivity relaxation times. Solid lines are Vogel−Fulcher−Tammann fits to the experimental data. Conductivity relaxation time shows a weaker temperature dependence below Tg (dashed line denotes Arrhenius fit). Insets show relation between viscosity and conductivity relaxation time with fractional DSE parameter s = 0.89 for G2 and s = 0.4 for G4.

transition temperature Tg is approached signifies decoupling phenomenon. With decreasing temperature, both types of motions slow down. When the system vitrifies, structural dynamics becomes frozen in, whereas the migration of charges is still possible and can be probed dielectrically. The mobility of charges preserve in the glassy state; however, its temperature dependence does not change in such significant manner as above Tg (Figure 3). The decoupling phenomenon was first observed for prototypic ionic supercooled liquid CKN.40,41 Recently, it was also reported for protic ionic liquids42,43 and polymerized ionic liquids.44 In order to characterize non-Arrhenius behavior of conductivity relaxation above the glass transition temperature, the Vogel−Fulcher−Tamman (VFT) equation was used ⎛ DT0 ⎞ τσ = τ0 exp⎜ ⎟ ⎝ T − T0 ⎠ Figure 7. Changes in M″ spectra of hyperbranched bis-MPA polyester at 267 K (Tg − 6 K) upon physical aging. The inset shows time evolution of conductivity relaxation time and amplitude of secondary relaxation at 267 K. Solid lines are fits to the stretched exponential functions.

(2)

where τ0, D, and T0 are constants. In contrast, the linear dependence of log τσ(1/T) in the glassy state was parametrized by using Arrhenius expression

⎛E ⎞ τσ = τ0 exp⎜ a ⎟ ⎝ RT ⎠

phenomenon is demonstrated in Figure 3 and indicates for vitrification process. Typically, the glass transition event occurs at temperature at which τα is equal to 100 s. At this temperature we observe that the temperature dependence of relaxation times changes behavior from VFT to Arrhenius-like. When conductivity remarkably decouples from structural dynamics, characteristic kink in the τσ(T) dependence occurs at much shorter relaxation times than 100 s. So, at the glass transition temperature structural relaxation time reaches 100 s whereas conductivity relaxation might be orders of magnitude faster. In the case of examined dendrimers, conductivity relaxation times at Tg equal ∼1.5, 0.27, and 0.15 s for second, third, and fourth generations, respectively. The fact that translational motions of charges become increasingly faster than structural relaxation as the glass

(3)

The temperature at which the characteristic change from VFTlike to Arrhenius-like behavior was observed signifies the glass transition event. As illustrated in Figure 3, the glass transition temperature of hyperbranched polyesters depends on molecular weight and increases with increasing polymer generation (Tg = 273 K for G2, Tg = 285 K for G3, and Tg = 295 K for G4). We have also observed that with increasing number of hydroxyl terminal groups of bis-MPA polyesters the characteristic kink in the τσ(T) dependence occurs at much shorter relaxation times. This indicates that the magnitude of the decoupling between charge transfer and structural dynamics depends on polymer’s generation. In order to quantify the degree of decoupling, we have employed decoupling index Rτ expressed as45,46 E


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Figure 8. (a) Integral intensity analysis of OH band components as a function of temperature for the hyperbranched bis-MPA generations. (b) Fitting procedure for OH stretching band in the 3050−3800 cm−1 range at Tg/T = 1 for G2, G3, and G4 hyperbranched bis-MPA with distinguished bands related to H-bond (B1 component) and free OH group (B5). Red arrows point to a band shift observed with increasing number of OH group. (c) The B1/B5 component ratio based on the FWHM and integral intensity analysis.

Rτ =

log(τα) log(τσ )

The glass transition event causes that the dependence of conductivity relaxation for studied hyperbranched polyesters becomes much weaker in the glassy state and can be parametrized by Arrhenius power law. In fact, the apparent activation energy of the proton conductivity below Tg was found out to vary with polymer’s generation. The following values were reported in the glassy state 123 kJ/mol for G2, 112 kJ/mol for G3, and Ea = 99 kJ/mol for G4, indicating a general trend of an ease of proton hopping along hydrogen bonds with increasing molecular weight and the number of hydroxyl end groups. In order to describe the nonexponential character of the conductivity relaxation in glassy ionic conductors, the Kohlrausch−Williams−Watts (KWW) function is typically employed

(4)

where τα and τσ are structural and conductivity relaxation times, respectively. By assuming that for typical glass-forming liquids the glass transition temperature is reached once structural relaxation time reaches 100 s, the charge transport in second, third, and fourth generations of bis-MPA polyesters was found out to be approximately 2, 2.5, and 3 orders of magnitude faster that structural relaxation, respectively. Large decoupling indicates that mobility of charges available in the system is much faster than structural dynamics. As the decoupling index turned out to be linearly correlated with the number of hydroxyl terminal groups (see the inset in Figure 3), it is evident that high conductivity of hyperbranched polyesters must originate in a significant manner from proton hopping along hydrogen bonding network. The similar mechanism of high conductivity was also suggested for other dendritic materials with amide and amines groups;24,47 however, there is still lack of qualitative studies on that matter.

ϕ(t ) = exp[−(t /τσ )β ]

(5)

where β is stretching parameter that measures the departure from the ideal exponential Debye response. We have used stretching parameter to describe the dispersion of conductivity relaxation for series of investigated polyesters in the temperF


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Figure 9. Different types of hydroxyl stretching vibrations for bis-MPA of the second generation. Various bands depends on the presence or lack of hydrogen bond (red dotted line).

charge carrier’s transport is called vehicle mechanism. For vehicle or mix vehicle- Grotthuss mechanisms the M″ dispersion conductivity spectra should be nonexponential, as composed not only from exponential conductivity relaxation due to intrinsic of extrinsic mobility charges, but also coupled dipole ion-pair or matrix relaxation that modifies the overall conductivity response (charge transfer accompanied by molecular diffusion). Figure 5 shows comparison of conductivity for studied hyperbranched bis-MPA polyesters in the supercooled liquid state (T = 305 K) and at the glass transition (Tg for respective generations). As illustrated, in studied range of temperature investigated materials are characterized by relatively low values of conductivity that depends also on the molecular weight. It is evident that at 305 K, i.e. above the glass transition of all investigated materials, conductivity is the highest for second generation, while the lowest for fourth generation. When isochronal condition is concerned, conductivity follows the same pattern as Tg (Figure 5b), i.e., increases with increasing molecular weight of hyperbranched polyester. The highest conductivity at glass-transition temperature was observed for the mostly decoupled hyperbranched polyester of the fourth generation. On the other hand, the most weakly decoupled bisMPa of the second generation has lowest conductivity from the investigated series. On the basis of all collected results, we can presume that the degree of decoupling should follow generation dependence. However, detailed studies should be performed on that matter, as in some cases the dynamics of dendritic materials was reported not to follow molecular weight trend.

Table 1. Position of the OH Band Components Observed on the Infrared Spectra at Tg B1 B2 B3 B4 B5

G2 νOH [cm−1]

G3 νOH [cm−1]

G4 νOH [cm−1]

dOH···O [Å]

3201 3290 3357 3429 3516

3198 3294 3368 3445 3536

3196 3298 3382 3460 3543

∼1.91, ∼1.94 ∼1.97 ∼2.00, ∼2.07

ature region covering the supercooled liquid and glassy states, as demonstrated in Figure 4. Similarly as for other highly conductive glass-formers, the narrowing of conductivity relaxation peak upon decreasing temperature was clearly observed.48 However, in contrast to most of ionic conductors, conductivity relaxation in hyperbranched polyester is generally narrower and more Debye-like (values of β parameter are close to 1). At the glass transition temperature the following values of stretched exponent β were reported 0.85, 0.825, and 0.88 for second, third, and fourth generation, respectively. Exponentiallike M″ relaxation spectra in vicinity of the glass transition are direct evidence that the overall conductivity in such systems is dominated mostly by proton hopping along highly efficient hydrogen-bonded networks. This type of charge transport in hydrogen bonding materials is termed in the literature as Grotthuss mechanism, and it is realized without structure diffusion. Therefore, electric conductivity in studied hyperbranched polyesters has been proven to be indeed due to proton conductivity. On the other hand, the conductivity mechanism that requires molecular diffusion to carry out the G


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dependencies of integrated intensity (Ia) of OH bands for hyperbranched bis-MPA polyesters are presented in Figure 8a. The Ia of four analyzed bands increases with decreasing temperature as an effect of inter- and/or intramolecular H-bond formation. The inverse trend exhibits only a band at around 3450 cm−1 which is related to decreased probability of intramolecular H-bond formation. The observed changes in H-bonding can be attributed to the macroscopic densification.29,53−56 All bands were found out to be sensitive to the glass transition, however Ia(Tg/T) shows the most pronounced kink at Tg. This proves that OH groups are strongly involved in the dynamic glass transition. It was also noted (similarly as from dielectric studies) that the glass transition temperature increases in high polyester generations. Values of glass transition temperatures determined from IR data (Tg = 273 K for G2, Tg = 285 K for G3, and Tg = 295 K for G4) coincide with those obtained from dielectric studies. It is worth noting that the total infrared band in the range corresponding to OH vibration (3050−3800 cm−1) is asymmetrically broadened due to the presence of different types of hydrogen bonds with varying binding energies. To better illustrate various types of Hbonds in hyperbranched bis-MPA polyesters as well as their impact on the infrared spectrum, we have performed theoretical calculations. They have indicated that in IR spectra of investigated materials there should be at least five components linked to the different, hydroxyl groups vibrations. Two of them are associated with free hydroxyl groups (B4, B5) while the other three originate from the hydroxyl vibration due to the presence of H-bond (B1, B2, B3) (see Figure 9). Moreover, the position of infrared bands strongly depends on the H-bond distance (see Table 1). Thus, the strong band component overlapping in the OH region should be deconvoluted using band fitting procedure which will allow determining the spectral parameters of intrinsic components, i.e., band position, integral intensity analysis, or full width at half-maximum (FWHM). Such analysis of the absorption band in the 3050−3800 cm−1 range with the deconvolved contributions is presented in Figure 8b. In further analysis, we have focused only on the bands designated as B1 and B5 which correspond to the strong Hbond with 1.94 Å bond distance and vibration of the free hydroxyl groups, respectively (see Figures 8b and 9).The ratio of the integral intensity and full width at half-maximum (FWHM) of peaks corresponding to H-bonded unites (B1) and free hydroxyl groups (B5) reveal the complexity of the hydrogen bonding network. The values of B1I/B5I and B1FWHM/B5FWHM ratios increase with an increasing generation number (see Figure 8c). This means that numerous chain-ends in high polymer generations facilitate formation of stronger hydrogen bonds. Consequently, as the polymer generation increases, the blue-shift of the band related to free hydroxyl groups and red-shift of peaks corresponding to H-bonded moieties are observed (Table1). These data have led to the conclusion that higher polymer generation is responsible for greater complexity of the structure due to higher number of the number of OH groups and intermolecular interaction.

In order to provide explicit confirmation of the decoupling phenomenon, we have performed additional viscosity measurements for G2 and G4 generations. The temperature dependence of conductivity relaxation time was then compared to that of η(T), as illustrated in Figure 6a,b. At the temperature referring to the glass transition temperature Tg viscosity of the system reaches 1012 Pa·s (or structural relaxation time ∼100 s), and a characteristic “kink” in the temperature dependence of the conductivity relaxation times occurs. This indicates that the motion of charge carriers senses macroscopic densification of the system. For glass-forming liquids and polymers the correlation between charge transport and reorientational motions of molecules is usually discussed in terms of Debye−Stokes− Einstein (DSE) relation, τση = constant. If in the supercooled liquid state decoupling between conductivity and structural relaxations takes place, DSE law is often rewritten as τσηs = constant, where s is fractional DSE exponent (s < 1). To quantify decoupling between charge transport and segmental dynamics of dendrimers at the same temperature, we have plotted conductivity relaxation time versus viscosity in doublelogarithmic scale, as shown in the inset of Figure 6a,b. In this case parameter s provides an estimate of the decoupling phenomenon and was found to be equaled to s = 0.89 and s = 0.4 for G2 and G4, respectively. Since both slopes at investigated range of temperatures are lower than 1, we can presume that decoupling between τα and η is a characteristic feature of bis-MPa dynamics on approaching Tg. In addition, fractional DSE exponent decreases with dendrimers generation which implies that indeed decoupling increase with increasing molecular weight and complexity of created hydrogen-bonded networks. Decoupling translational mobility of charges from the structural relaxation in hyperbranched polyesters makes possible to monitor the physical aging by following the timedependent changes in the M″ maximum spectra, as illustrated in Figure 7. Upon physical aging at given temperature each glassy system slowly relaxes toward equilibrium state. This is accompanied by increase of structural relaxation as well as conductivity relaxation times. The former cannot be measured directly because of exceedingly long time scale that is far outside experimentally accessible frequency window. However, by monitoring proton conductivity or secondary relaxations upon physical aging it is still possible to access structural changes in the glassy state. In Figure 7, we present timedependent changes upon physical aging of the second generation hyperbranched polyester. As illustrated, with increasing time there are two pronounced effects clearly visible; i.e., the shifts of proton conductivity peak toward lower frequencies and decrease of the amplitude of the secondary relaxation processes (the inset in Figure 7). Both can be utilized to determine the structural relaxation in the glassy state, as demonstrated recently for protic ionic liquids.49,50 To describe their time dependences, modified versions of stretched exponential functions, proposed by Casalini and Roland51 and Lunkenheimer et al.,52 were employed. Using both methods, we have obtained very similar values of structural relaxation time for second generation of polyester at temperature T = 267 K, i.e. 10 500 s (i.e., log τα= 4), which shows that both effect accompanying the glassy aging are somehow connected. In order to study intramolecular glass-transition dynamics of hyperbranched bis-MPA polyesters, the temperature-dependent infrared measurements were carried out. The temperature

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CONCLUSIONS The inter- and intramolecular glass-transition dynamics in the series of hyperbranched bis-MPA polyesters of the second, third, and fourth generations were studied by dielectric and infrared spectroscopies. A strong decoupling of conductivity from the structural relaxation was found. The magnitude of the decoupling index was found out to strongly depend on H


Macromolecules

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polymer’s generation. For studied generations, it increases almost linearly with the number of hydroxyl terminal groups. This is the first direct observation of such phenomenon in hyperbranched polyesters. The exponential-like behavior of the conductivity relaxation in vicinity of the glass transition suggests that translational motions in such systems should be dominated mostly by proton hopping along highly efficient hydrogen-bonded networks. Therefore, we expect that the charge transfer in hyperbranched polymers is realized mostly through Grotthuss mechanism. With increasing molecular weight, the lowering of the apparent activation energy of the proton conductivity in the glassy state was observed. This point out for an ease of proton hopping along hydrogen bonds as the structure of hyperbranched polymer becomes more complex. Finally, the infrared measurements have demonstrated significant role of hydrogen bonds in the course of vitrification and their increased complexity with increasing polymer’s generation.

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ASSOCIATED CONTENT

S Supporting Information *

Experimental procedures and results of thermogravimetric, calorimetric, and X-ray diffraction measurements. This material is available free of charge via the Internet at http://pubs.acs.org.

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected] (K.A.). Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS This work is primarily supported by the Polish National Science Centre (DEC-2012/05/D/ST4/00326). G.B. and S.J. appreciate financial assistance from Nation Centre for Research and Development (Nanomaterials and Their Potential Application in Nanobiomedicine). We thank the Laboratory of Structural Studies at the Faculty of Physics, Adam Mickiewicz University, for performing thermogravimetric experiments. K.A. acknowledges financial assistance from POKL (UAM) program. This research was also supported in part by PL-Grid Infrastructure.

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Dynamic Glass Transition and Electrical Conductivity Behavior

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