Relaxation response of polymers containing highly flexible side groups monitored by broadband dielectric spectroscopy

The relaxation behavior of poly(5-acryloxymethyl-5-methyl-1,3-dioxacyclohexane), a polymer containing highly flexible side groups, is studied by broadband dielectric spectroscopy in the frequency and temperature ranges 10(-1)-10(9) Hz and 123-473 K, respectively. Above the glass transition temperature T(g) the dielectric loss in the frequency domain exhibits a prominent alpha absorption, followed in increasing order of frequencies by two secondary absorptions called beta and gamma. At temperatures slightly higher than T(g), the a relaxation is well separated from the beta, but as temperature increases overlapping between both relaxations augments forming an alphabeta absorption in the vicinity of 420 K. This latter absorption displays a shoulder on its high-frequency side corresponding to the y relaxation. The strength of the a relaxation decreases with increasing temperature, eventually vanishing at the temperature at which the alphabeta absorption is formed. The time retardation spectra of the isotherms are calculated and further used to facilitate the deconvolution of the overlapping relaxations. The fact that the temperature dependence of the beta relaxation also describes that of the alphabeta absorption suggests that both relaxations have the same nature. It seems that as temperature increases, the a relaxation feeds on the beta absorption until its complete disappearance. The gamma relaxation, in turn, seems to increase at the expense of the alphabeta process at high temperature.     

Influence of structural chemical characteristics on polymer chain dynamics

A comparative study of the dielectric relaxation behavior of two structurally close polymers containing aliphatic-aromatic side groups was carried out in order to get a better understanding on how slight differences in chemical structure affect the molecular responses to perturbation fields. Specifically, chain dynamics of poly(2-acryloyloxyethyl-2-naphthalene-2-ylacetate) and poly(2-methacryloyloxyethyl-2-naphthalene-2-ylacetate) were studied by broadband dielectric spectroscopy in the frequency range of 10(-2)-10(8) Hz and temperature window of 298-403 K. Also, the relaxation behavior of (2-acetyloxyethyl-2-naphthalene-2-ylacetate), model compound of the polymer side groups, was analyzed. The isotherms representing the dielectric loss in the frequency domain show important conductive contributions, especially at high temperature, which hide the low frequency side of the alpha relaxation. Conductivity also increases the real component of the complex permittivity in the low frequencies region. Retardation spectra were obtained by minimizing the sum of the squares of the difference between the experimental values of the complex permittivity for each frequency and the analytical ones, predicted by the linear phenomenological theory, using a Tikhonov regularization technique. The spectra present an apparent alpha peak with an excess wing at short time side resulting from the overlapping of the true alpha relaxation and a beta process. Three absorptions, named in increasing order of time gamma, beta, and alpha relaxations, are separated by deconvolution methods. The activation energies associated with the gamma process are 70.0+/-1.8, 68.0+/-1.4, and 74.8+/-0.8 kJ mol(-1) for (2-acetyloxyethyl-2-naphthalene-2-yl acetate), poly(2-acryloyloxyethyl-2-naphthalene-2-yl acetate) and poly(2-methacryloyloxyethyl-2-naphthalene-2-yl acetate), respectively. The respective activation energies associated with the beta relaxation are 121.7+/-2.4, 135.3+/-1.4, and 141.6+/-1.3 kJ mol(-1). Values of the shape parameters and the strengths of the relaxation processes were obtained as a function of temperature. The dynamic fragility of the polymers and the model compound was studied and compared with that reported for macromolecular and monomeric systems. Also, the evolution of the size of the correlated domains associated with the alpha relaxation was estimated. Finally, the gamma relaxation rather than the beta absorption obeys the criteria apparently held by the Johari-Goldstein beta processes.     

Dielectric and shear mechanical alpha and beta relaxations in seven glass-forming liquids

We present shear mechanical and dielectric measurements taken on seven liquids: triphenylethylene, tetramethyltetra-phenyltrisiloxane (Dow Corning 704 diffusion pump fluid), polyphenyl ether (Santovac 5 vacuum pump fluid), perhydrosqualene, polybutadiene, decahydroisoquinoline (DHIQ), and tripropylene glycol. The shear mechanical and dielectric measurements are for each liquid performed under identical thermal conditions close to the glass transition temperature. The liquids span four orders of magnitude in dielectric relaxation strength and include liquids with and without Johari-Goldstein beta relaxation. The shear mechanical data are obtained by the piezoelectric shear modulus gauge method giving a large frequency span (10(-3)-10(4.5) Hz). This allows us to resolve the shear mechanical Johari-Goldstein beta peak in the equilibrium DHIQ liquid. We moreover report a signature (a pronounced rise in the shear mechanical loss at frequencies above the alpha relaxation) of a Johari-Goldstein beta relaxation in the shear mechanical spectra for all the liquids which show a beta relaxation in the dielectric spectrum. It is found that both the alpha and beta loss peaks are shifted to higher frequencies in the shear mechanical spectrum compared to the dielectric spectrum. It is in both the shear and dielectric responses found that liquids obeying time-temperature superposition also have a high-frequency power law with exponent close to -12. It is moreover seen that the less temperature dependent the spectral shape is, the closer it is to the universal -12 power-law behavior. The deviation from this universal power-law behavior and the temperature dependencies of the spectral shape are rationalized as coming from interactions between the alpha and beta relaxations.     

Dielectric relaxation processes in water mixtures of tripropylene glycol

Broadband dielectric measurements for anhydrous tripropylene glycol (3PG) and 96, 92, 84, 80, 74, 71, and 68 wt % 3PG-water mixtures are performed in the frequency range of 10(-2)-10(7) Hz and in the temperature range of 123-243 K. We examined the effect of adding water into anhydrous 3PG on relaxation dynamics. Apart from the two well-known relaxation processes, i.e., alpha and beta for anhydrous 3PG we observed new relaxation peak (beta') for all aqueous mixtures of 3PG. In addition we found the critical mole fraction of water x(w)=0.67 in which relaxation dynamics changes its behavior. According to the Sudo approach [S. Sudo et al., J. Non-Cryst. Solids 307-310, 356 (2002)], the behavior of relaxation processes was interpreted assuming the existence of three kinds of cooperative domains (CDs): containing only 3PG molecules, including only water molecules, and including both 3PG and water molecules, which molecules of each kind CD are bound by hydrogen bonds.     

Primary and secondary relaxations in bis-5-hydroxypentylphthalate

Broadband dielectric spectroscopy was used to study the relaxation dynamics in bis-5-hydroxypentylphthalate (BHPP) under both isobaric and isothermal conditions. The relaxation dynamics exhibit complex behavior, arising from hydrogen bonding in the BHPP. At ambient pressure above the glass transition temperature T(g), the dielectric spectrum shows a broad structural relaxation peak with a prominent excess wing toward higher frequencies. As temperature is decreased below T(g), the excess wing transforms into two distinct peaks, both having Arrhenius behavior with activation energies equal to 58.8 and 32.6 kJmol for slower (beta) and faster (gamma) processes, respectively. Furthermore, the relaxation times for the beta process increase with increasing pressure, whereas the faster gamma relaxation is practically insensitive to pressure changes. Analysis of the properties of these secondary relaxations suggests that the beta peak can be identified as an intermolecular Johari-Goldstein (JG) process. However, its separation in frequency from the alpha relaxation, and both its activation energy and activation volume, differ substantially from values calculated from the breadth of the structural relaxation peak. Thus, the dynamics of BHPP appear to be an exception to the usual correlation between the respective properties of the structural and the JG secondary relaxations.     

The glass transition and dielectric secondary relaxation of fructose-water mixtures

Broad-band dielectric measurements for fructose-water mixtures with fructose concentrations between 70.0 and 94.6 wt% were carried out in the frequency range of 2 mHz to 20 GHz in the temperature range of -70 to 45 degrees C. Two relaxation processes, the alpha process at lower frequency and the secondary beta process at higher frequency, were observed. The dielectric relaxation time of the alpha process was 100 s at the glass transition temperature, T(g), determined by differential scanning calorimetry (DSC). The relaxation time and strength of the beta process changed from weaker temperature dependences of below T(g) to a stronger one above T(g). These changes in behaviors of the beta process in fructose-water mixtures upon crossing the T(g) of the mixtures is the same as that found for the secondary process of water in various other aqueous mixtures with hydrogen-bonding molecular liquids, polymers, and nanoporous systems. These results lead to the conclusion that the primary alpha process of fructose-water mixtures results from the cooperative motion of water and fructose molecules, and the secondary beta process is the Johari-Goldstein process of water in the mixture. At temperatures near and above T(g) where both the alpha and the beta processes were observed and their relaxation times, tau(alpha) and tau(beta), were determined in some mixtures, the ratio tau(alpha)/tau(beta) is in accord with that predicted by the coupling model. Fixing tau(alpha) at 100 s, the ratio tau(alpha)/tau(beta) decreases with decreasing concentration of fructose in the mixtures. This trend is also consistent with that expected by the coupling model from the decrease of the intermolecular coupling parameter upon decreasing fructose concentration.     

Secondary and primary relaxations in hyperbranched polyglycerol: a comparative study in the frequency and time domains

The non-Debye relaxation behavior of hyperbranched polyglycerol was investigated by broadband dielectric spectroscopy. A thorough study of the relaxations was carried out paying special attention to truncation effects on deconvolutions of overlapping processes. Hyperbranched polyglycerol exhibits two relaxations in the glassy state named in increasing order of frequency beta and gamma processes. The study of the evolution of these two fast processes with temperature in the time retardation spectra shows that the beta absorption is swallowed by the alpha in the glass-liquid transition, the gamma absorption being the only relaxation that remains operative in the liquid state. In heating, a temperature is reached at which the alpha absorption vanishes appearing the alphagamma relaxation. Two characteristics of alpha absorptions, decrease of the dielectric strength with increasing temperature and rather high activation energy, are displayed by the alphagamma process. Williams' ansatz seems to hold for these topologically complex macromolecules.     

Dielectric study of the alpha and beta processes in supercooled ethylene glycol oligomer-water mixtures

Broadband dielectric measurements for 65 wt % ethylene glycol oligomer (EGO)-water mixtures with one to six repeat units of EGO molecules were performed in the frequency range of 10 microHz-10 GHz and the temperature range of 128-298 K. In the case of the water-EGO mixtures with one and two repeat units of the EGO molecule (small EGO), the shape of the dielectric loss peak of the primary process is asymmetrical about the logarithm of the frequency of maximum loss above the crossover temperature, T(C). The asymmetric process continues to the alpha process at a low frequency, and an additional beta process appears in the frequency range higher than that of the alpha process below T(C). In contrast, the water-EGO mixtures with three or more repeat units of the EGO molecule (large EGO) show a broad and symmetrical loss peak of the primary process above T(C). The symmetric process continues to the beta process, and an additional alpha process appears in the frequency range lower than that of the beta process below T(C). These different scenarios of the alpha-beta separation related to the shape of the loss peak above T(C) are a result of the difference in the cooperative motion of water and solute molecules. The solute and water molecules move cooperatively in the small EGO-water mixtures above T(C), and this cooperative motion leads to the asymmetric loss peak above T(C) and the alpha process below T(C). For the large EGO-water mixtures, the spatially restricted motion of water confined by solute molecules leads to the symmetric loss peak above T(C) and the beta process below T(C).     

Relation between solvent and protein dynamics as studied by dielectric spectroscopy

We present results obtained by dielectric spectroscopy in wide frequency (10(-2)-10(9) Hz) and temperature ranges on human hemoglobin in the three different solvents water, glycerol, and methanol, at a solvent level of 0.8 g of solvent/g of protein. In this broad frequency region, there are motions on several time-scales in the measured temperature range (110-370 K for water, 170-410 K for glycerol, and 110-310 K for methanol). For all samples, the dielectric data shows at least four relaxation processes, with frequency dependences that are well described by the Havriliak-Negami or Cole-Cole functions. The fastest and most pronounced process in the dielectric spectra of hemoglobin in glycerol and methanol solutions is similar to the alpha-relaxation of the corresponding bulk solvent (but shifted to slower dynamics due to surface interactions). For water solutions, however, this process corresponds to earlier results obtained for water confined in various systems and it is most likely due to a local beta-relaxation. The slowing down of the glycerol and methanol relaxations and the good agreement with earlier results on confined water show that this process is affected by the interaction with the protein surface. The second fastest process is attributed to motions of polar side groups on the protein, with a possible contribution from tightly bound solvent molecules. This process is shifted to slower dynamics with increasing solvent viscosity, and it shows a crossover in its temperature dependence from Arrhenius behavior at low temperatures to non-Arrhenius behavior at higher temperatures where there seems to be an onset of cooperativity effects. The origins of the two slowest relaxation processes (visible at high temperatures and low frequencies), which show saddlelike temperature dependences for the solvents water and methanol, are most likely due to motions of the polypeptide backbone and an even more global motion in the protein molecule.     

Broadband dielectric spectroscopic, calorimetric, and FTIR-ATR investigations of D-arabinose aqueous solutions

The dielectric relaxation behavior of D-arabinose aqueous solutions at different water concentrations is examined by broadband dielectric spectroscopy in the frequency range of 10(-2) -10(7) Hz and in the temperature range of 120-300 K. Differential scanning calorimetry is also performed to find the glass transition temperatures (T(g)). In addition, the same solutions are analyzed by Fourier transform infrared (FTIR) spectroscopy using the attenuated total reflectance (ATR) method at the same temperature interval and in the frequency range of 3800-2800 cm(-1). The temperature dependence of the relaxation times is examined for the different weight fractions (x(w)) of water along with the temperature dependence of dielectric strength. Two relaxation processes are observed in the aqueous solutions for all concentrations of water. The slower process, the so-called primary relaxation process (process-I), is responsible for the T(g) whereas the faster one (designated as process-II) is due to the reorientational motion of the water molecules. As for other hydrophilic water solutions, dielectric data for process-II indicate the existence of a critical water concentration above which water mobility is less restricted. Accordingly, FTIR-ATR measurements on aqueous solutions show an increment in the intensity (area) of the O-H stretching sub-band close to 3200 cm(-1) as the water concentration increases.     

Broadband dielectric study of the glass transition in poly(ethyleneglycol)-water mixture

We performed broadband dielectric measurements of a polyethyleneglycol-water mixture in the frequency range between 10 GHz and 1 microHz and the temperature range between 300 and 133 K. One relaxation process is observed throughout the whole temperature range. The temperature dependence of the relaxation time clearly obeys the Vogel-Fulcher law above 183 K, and the Arrhenius law below 183 K. This observed relaxation process is the secondary process, and the primary process related to the glass transition is masked by the low-frequency ionic contribution below 183 K. The glass transition concerned with the masked primary process leads to the Vogel-Fulcher to Arrhenius transition of the secondary process.     

Dynamics of glass-forming liquids. VIII. Dielectric signature of probe rotation and bulk dynamics in branched alkanes

We have measured the dielectric relaxation of several glass forming branched alkanes with very low dielectric loss in the frequency range 50 Hz-20 kHz. The molecular liquids of this study are 3-methylpentane, 3-methylheptane, 4-methylheptane, 2,3-dimethylpentane, and 2,4,6-trimethylheptane. All liquids display asymmetric loss peaks typical of supercooled liquids and slow beta relaxations of similar amplitudes. As an unusual feature, deliberate doping with 2-ethyl-1-hexanol, 5-methyl-2-hexanol, 2-methyl-1-butanol, 1-propanol, or 2-methyltetrahydrofuran at the 1 wt % level generates additional relaxation peaks at frequencies below those of the alpha relaxation. The relaxation times of these sub-alpha-peaks increase systematically with the size of the dopant molecules. Because these features are spectrally separate from the bulk dynamics, the rotational behavior and effective dipole moments of the probes can be studied in detail. For the alcohol guest molecules, the large relative rotational time scales and small effective dipole moments are indicative of hydrogen bonded clusters instead of individual molecules.     

Molecular motions in amorphous ibuprofen as studied by broadband dielectric spectroscopy

The molecular mobility of amorphous ibuprofen has been investigated by broadband dielectric relaxation spectroscopy (DRS) covering a temperature range of more than 200 K. Four different relaxation processes, labeled as alpha, beta, gamma, and D, were detected and characterized, and a complete relaxation map was given for the first time. The gamma-process has activation energy E a = 31 kJ.mol (-1), typical for local mobility. The weak beta-relaxation, observed in the glassy state as well as in the supercooled state was identified as the genuine Johari-Goldstein process. The temperature dependence of the relaxation time of the alpha-process (dynamic glass transition) does not obey a single VFTH law. Instead two VFTH regimes are observed separated by a crossover temperature, T B = 265 K. From the low temperature VFTH regime, a T g (diel) (tau =100 s) = 226 K was estimated, and a fragility or steepness index m = 93, was calculated showing that ibuprofen is a fragile glass former. The D-process has a Debye-like relaxation function but the temperature dependence of relaxation time also follows the VFTH behavior, with a Vogel temperature and a pre-exponential factor which seem to indicate that its dynamics is governed by the alpha-process. It has similar features as the Debye-type process observed in a variety of associating liquids, related to hydrogen bonding dynamics. The strong tendency of ibuprofen to form hydrogen bonded aggregates such as dimers and trimers either cyclic or linear which seems to control in particular the molecular mobility of ibuprofen was confirmed by IR spectroscopy, electrospray ionization mass spectrometry, and MD simulations.     

Aging of the Johari-Goldstein relaxation in the glass-forming liquids sorbitol and xylitol

Employing frequency-dependent dielectric susceptibility we characterize the aging in two supercooled liquids, sorbitol and xylitol, below their calorimetric glass transition temperatures. In addition to the alpha relaxation that tracks the structural dynamics, the susceptibility of both liquids possesses a secondary Johari-Goldstein relaxation at higher frequencies. Following a quench through the glass transition, the susceptibility slowly approaches the equilibrium behavior. For both liquids, the magnitude of the Johari-Goldstein relaxation displays a dependence on the time since the quench, or aging time, that is quantitatively very similar to the age dependence of the alpha peak frequency. The Johari-Goldstein relaxation time remains constant during aging for sorbitol while it decreases slightly with age for xylitol. Hence, one cannot sensibly assign a fictive temperature to the Johari-Goldstein relaxation. This behavior contrasts with that of liquids lacking distinct Johari-Goldstein peaks for which the excess wing of the alpha peak tracks the main part of the peak during aging, enabling the assignment of a single fictive temperature to the entire spectrum. The aging behavior of the Johari-Goldstein relaxation time further calls into question the possibility that the relaxation time possesses stronger temperature dependence in equilibrium than is observed in the out-of-equilibrium state below the glass transition.     

Molecular dissipation phenomena of nanoscopic friction in the heterogeneous relaxation regime of a glass former

Nanoscale sliding friction involving a polystyrene melt near its glass transition temperature Tg (373 K) exhibited dissipation phenomena that provide insight into the underlying molecular relaxation processes. A dissipative length scale that shows significant parallelism with the size of cooperatively rearranging regions (CRRs) could be experimentally deduced from friction-velocity isotherms, combined with dielectric loss analysis. Upon cooling to approximately 10 K above Tg, the dissipation length Xd grew from a segmental scale of approximately 3 A to 2.1 nm, following a power-law relationship with the reduced temperature Xd approximately TR-phi. The resulting phi=1.89+/-0.08 is consistent with growth predictions for the length scale of CRRs in the heterogeneous regime of fragile glass formers. Deviations from the power-law behavior closer to Tg suggest that long-range processes, e.g., the normal mode or ultraslow Fischer modes, may couple with the alpha relaxation, leading to energy dissipation in domains of tens of nanometers.     

Dielectric secondary relaxations in polypropylene glycols

Broadband dielectric measurements of polypropylene glycol of molecular weight M(w)=400 g / mol (PPG 400) were carried out at ambient pressure over the wide temperature range from 123 to 353 K. Three relaxation processes were observed. Besides the structural alpha relaxation, two secondary relaxations, beta and gamma, were found. The beta process was identified as the true Johari-Goldstein relaxation by using a criterion based on the coupling model prediction. The faster gamma relaxation, well separated from the primary process, undoubtedly exhibits the anomalous behavior near the glass transition temperature (T(g)) which is reflected in the presence of a minimum of the temperature dependence of the gamma-relaxation time. We successfully applied the minimal model [Dyre and Olsen, Phys. Rev. Lett. 91, 155703 (2003)] to describe the entire temperature dependence of the gamma-relaxation time. The asymmetric double-well potential parameters obtained by Dyre and Olsen for the secondary relaxation of tripropylene glycol at ambient pressure were modified by fitting to the minimal model at lower temperatures. Moreover, we showed that the effect of the molecular weight of polypropylene glycol on the minimal model parameters is significantly larger than that of the high pressure. Such results can be explained by the smaller degree of hydrogen bonds formed by longer chain molecules of PPG at ambient pressure than that created by shorter chains of PPG at high pressure.     

Dielectric and mechanical relaxation processes in methyl acrylate/tri-ethyleneglycol dimethacrylate copolymer networks

The dielectric properties of methylacrylate (MA)/tri-ethyleneglycol dimethacrylate (TrEGDMA) copolymers at different compositions, ranging from 0 to 100, were measured between −120 and 150 °C over the frequency range 0.1 Hz-1 MHz. In the given frequency range, three relaxation processes were detected by dielectric relaxation spectroscopy in homo poly-TrEGDMA and copolymers: the α process associated with the glass transition, and two secondary processes due to localized mobility. In PMA only one secondary process was observed besides the alpha relaxation process. The influence of copolymerization going from PMA, monofunctional softer component with a glass transition determined calorimetrically as 284 K, to poly-TrEGDMA, higher glass transition component, bifunctional, that also forms a dense network due to cross linking, reflects mainly in the alpha process that shifts to higher temperatures and becomes broader. The raise and broadening in the glass transition with TrEGDMA increase was also observed by dynamic mechanical thermal analysis and differential scanning calorimetry. The glass transition temperature of poly-TrEGDMA was not detected calorimetrically but a value of 429 K was estimated from the best fit of the Fox equation. In what concerns the secondary relaxation process detected in poly-TrEGDMA and copolymers at the lowest temperatures, it is related with local twisting motions of ethyleneglycol moieties, being designated as γ relaxation, while the process detected in the medium temperature range is associated with the rotation of the carboxylic groups as in poly(alkyl methacrylates), designated as β relaxation. This process is detected at much lower temperatures in homo PMA in the same temperature region than the above mentioned γ relaxation. The copolymerization influences mainly the α process while the γ process remains almost unaffected in copolymers relative to homo poly-TrEGDMA. The β process is largely determined by the presence o the tri-ethylene glycol dimethacrylate monomeric units even in copolymers with the lowest TrEGDMA content.     

Molecular dynamics of oligofluorenes: a dielectric spectroscopy investigation

The molecular dynamics were investigated in a series of "defect-free" oligofluorenes up to the polymer by dielectric spectroscopy (DS). The method is very sensitive to the presence of keto "defects" that when incorporated on the backbone give rise to poor optical and electronic properties. Two dielectrically active processes were found (beta and alpha process). The latter process (alpha) displays strongly temperature dependent relaxation times and temperature- and molecular weight-dependent spectral broadening associated with intramolecular correlations. The glass temperature (Tg) obeys the Fox-Flory equation and the polymer Tg is obtained by DS at 332 K. The effective dipole moment associated with the alpha process is 0.27 +/- 0.03 D.     

A study of absorption currents in polystyrene and polystyrene-chloranil complex

The absorption currents in polystyrene (PS) and its donor-acceptor complex with chloranil (PS-CA) have been analysed in the temperature range 323–413 K. Low frequency (10-s-10-3 Hz) dielectric loss has been computed utilizing Haman's Fourier conversion of the absorption currents. A relaxation peak has been observed in the isochronal current and dielectric loss thermograms and identified with the a relaxation process of these polymers. The activation energy of the relaxation process has been evaluated from the Arrhenius shift of the relaxation peak. The effects of complex formation on absorption currents and the relaxation process have been discussed.     

Dielectric study of the liquid crystalline dimer alpha, omega-bis(4'-cyanobiphenyl-4-yloxy)decane

The dielectric properties of a nematogenic dimer alpha,omega-bis(4-cyanobiphenyl-4-yloxy)decane in the nematic and isotropic phases have been investigated in the frequency range between 100 Hz and 13 MHz. It was found that the compound is characterized by a positive dielectric anisotropy. The dielectric constant in the nematic phase is lower than that in the isotropic phase, which suggests variation in the conformational distribution of the dimer after the phase transition. Only one relaxation process, both in the nematic and isotropic phases, has been observed in the frequency range used: the relaxation frequency has been found to take values between 2 and 4 MHz, depending on the temperature.