Effects of diluent on molecular motion and glass transitions in polymers. II. The system polyvinylchloride–tetrahydrofuran

Dielectric measurements, differential thermal analyses, and density measurements are reported on concentrated solutions of polyvinylchloride in tetrahydrofuran. The relaxation processes observed between 80 and 400°K have been classified into four types. From the analysis of experimental data, the primary process at the highest temperature and the process at the lowest temperature are assigned, respectively, to segmental motion of the polymer and motion of the solvent. Activation plots for the primary process conform to the Vogel–Tamman equation. The dielectric glass-transition temperature T'_g (defined as the temperature at which the dielectric relaxation time is 100 sec) determined with this equation agrees well with the glass-transition temperature T_g from thermal analysis. Therefore, T_g can be represented by an expression of the form The parameters of the Vogel–Tamman equation A and B are nearly independent of concentration, whereas T_o depends strongly on concentration. The dipole moment per monomeric unit calculated from the experimental data changes with concentration and exhibits steep increments around 30% and 90% by weight. The width of the distribution of the relaxation time also increases with the concentration. The results were compared with those for the system polystyrene–toluene studies in the same way.     

Effects of diluent on molecular motion and glass transitions in polymers. III. The system poly(vinyl acetate)–toluene

Dielectric measurements, differential thermal analyses (DTA), and broad-line proton magnetic resonance (NMR) measurements are reported on the system poly(vinyl acetate)–toluene. Four dielectric relaxations were observed between 80 and 400°K. From proton NMR measurements on solutions in toluene and in deuterated toluene, the relaxation processes can be assigned, respectively, to segmental motion of poly(vinyl acetate), α; motion of side group, β′ rotation of toluene, β; local motions of poly(vinyl acetate) and toluene, γ, in order of appearance with decreasing temperature. Two stepwise changes in DTA traces have been observed and can be assigned as glass transition points T_gI and T_gII. Comparison of these glass transition points with temperatures at which dielectric relaxation times for the α and β processes are 100 sec, indicate that segmental motion of poly(vinyl acetate) and rotation of toluene are frozen-in at T_gI and T_gII, respectively. Activation plots for the α process conform to the Vogel–Tamman equation. In terms of the parameters A, B, and T₀ of the equation, T_gI can be represented by an expression of the form T_gI ≈ T₀ + B/(A + 3). In the range of concentration above 50% by weight, A and B are almost independent of concentration but T₀ varies strongly. The nature of the secondary dispersions is also discussed.     

Dielectric relaxations in the liquid and glassy states of 47% polypropylene oxide in toluene as diluent

Molecular relaxations in 47-wt % polypropylene oxide of molecular weight 4000 in toluene as diluent have been studied by dielectric permittivity and loss measurements from 77 to 320 K, in the frequency range 1 Hz to 2 × 10⁵ Hz. One relaxation process (β process) is observed in the glassy state below T_g (= 148 K), and two processes are observed in the supercooled liquid at T > T_g. Relative to the amplitude of the fast relaxation process (i.e., the local segmental motions of the polymer chain), the amplitude of the slow process is increased and that of the β process decreased on dilution of the pure polymer. The β process has an Arrhenius energy of 17 kJ mol^?1. The rates of the two relaxations at T > T_g follow the Vogel–Fulcher–Tamman equation and seem to merge on cooling the liquid towards T_g. The relative temperatures at which the three relaxation processes occur at the rate of 1 kHz remain largely unaffected on dilution. The increase in static permittivity of the solution on cooling is more than anticipated from the temperature effects alone. It is suggested that the increase is due to the enhanced short-range orientational correlation of the dipoles, which may involve H bonding.     

Pressure dependence of dielectric properties of chlorinated polyethylene vulcanizate. I. α relaxation and shift factors

The complex dielectric constant was measured under elevated pressure for the α relaxation of vulcanized chlorinated polyethylene. Both temperature and pressure effects on the static dielectric constants, the activation enthalpy, and volume, and the pressure dependence of the glass-transition temperature were obtained. The dependence of shift factors on temperature was expressed by the Vogel–Fulcher–Tamman–Hesse (VFTH) equation: ?log a_T = A ? B/(T ? T₀). The parameters A, B, and T₀ for each pressure applied were calculated by minimizing the standard deviation between log a_T and experiments. The values of the parameters in the Williams–Landel–Ferry (WLF) equation: ?log a_T = C₁(T ? T_g)/[C₂ + (T ? T_g)], were also estimated from the resulting values of the VFTH parameters. All these parameters depended on pressure. The activation volume plotted against T ? T_g decreased with increasing pressure.     

Some evidence against the existence of the liquid-liquid transition. IV. The temperature dependence of shear viscosity

The viscosity data available for four anionically polymerized polystyrenes ranging in molecular weight from 1100 to 47,000 for the temperature range T_g to T_g + 100°C have been fitted by computer programs to both the Vogel, Fulcher, Tamman, and Hesse (VFTH) equation and to two optimum intersecting Arrhenius equations. The intersection point has been interpreted as a manifestation of a liquid-liquid transition. The fits to the VFTH equation were in every case found to be far superior. Systematic deviations of the residuals were observed for the best Arrhenius fits which indicate the lack of any validity for such a representation of the data.     

Evolution of morphology,segmental dynamics,and conductivity in ionic liquid swollen short side chain perfluorosulfonate ionomer membranes

We investigate the morphology, segmental dynamics, and conductivity of 1‐ethyl‐3‐methylimidazolium trifluoromethanesulfonate (EMI‐Tf) swollen short side chain perfluorosulfonate ionomer (Aquivion) over a broad uptake range using small angle X‐ray scattering (SAXS), dielectric relaxation spectroscopy, and transient current measurement. The SAXS data indicate that the absorbed EMI‐Tf is mainly bounded in the ionic region of Aquivion. At low uptakes, EMI‐Tf acts as an effective plasticizer lowering the cluster T_g and markedly shifting the segmental relaxation to a high frequency; however, at high uptakes, the additional EMI‐Tf acts like a filler instead. A time–domain model was employed to quantify the conductivity of these membranes containing two mobile ion species, that is, cations and anions. The conductivity of both neat EMI‐Tf and EMI‐Tf swollen membranes exhibits Vogel‐Fulcher‐Tamman relation, revealing different activation parameters for ionic conduction. Furthermore, membranes containing different EMI‐Tf uptakes have similar conductivity over the reduced T_g/T axis and also follow Debye‐Stokes‐Einstein relation. Therefore, despite the abrupt change in conductivity near the critical uptake (29 wt %), both cluster T_g and segmental motion remain the key factors for the ionic conduction in these EMI‐Tf swollen membranes. © 2015 Wiley Periodicals, Inc. J. Polym. Sci., Part B: Polym. Phys. 2015 , 53, 1273–1280     

Molecular relaxation of isotactic polystyrene: Real‐time dielectric spectroscopy and X‐ray scattering studies*

The molecular relaxation processes and structure of isotactic polystyrene (iPS) films were investigated with real‐time dielectric spectroscopy and simultaneous wide‐ and small‐angle X‐ray scattering. The purpose of this work was to explore the restrictions imposed on molecular mobility in the vicinity of the α relaxation (glass transition) for crystallized iPS. Isothermal cold crystallization at temperatures of T_c = 140 or 170 °C resulted in a sigmoidal increase of crystallinity with crystallization time. The glass‐transition temperature (T_g), determined calorimetrically, exhibited almost no increase during the first stage of crystal growth before impingement of spherulites. After impingement, the calorimetric T_g increased, suggesting that confinement effects occur in the latter stages of crystallization. For well‐crystallized samples, the radius of the cooperativity region decreased substantially as compared with the purely amorphous sample but was always smaller than the layer thickness of the mobile amorphous fraction. Dielectric experiments directly probed changes in the amorphous dipole mobility. The real‐time dielectric data were fitted to a Havriliak–Negami model, and the time dependence of the parameters describing the distribution of relaxation times and dielectric strength was obtained. The central dipolar relaxation time showed little variation before spherulite impingement but increased sharply during the second stage of crystal growth as confinement occurred. Vogel–Fulcher–Tammann analysis demonstrated that the dielectric reference temperature, corresponding to the onset of calorimetric T_g, did not vary for well‐crystallized samples. This observation agreed with a model in which constraints affect primarily the modes having longer relaxation times and thus broaden the glass‐transition relaxation process on the higher temperature side. © 2004 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 42: 777–789, 2004     

Pressure dependence of the β molecular relaxation process and dielectric properties of polyvinylidene fluoride

The effects of hydrostatic pressure to 20 kbar on the β molecular relaxation process of polyvinylidene fluoride (PVDF) and on the dielectric properties in the neighborhood of this relaxation have been investigated. This relaxation has a strong influence on the electrical and mechanical properties of PVDF. Pressure causes a large shift to higher temperatures (～ 10K/kbar) of the dielectric relaxation peak and a decrease in the width of the distribution of relaxation times. This slowing down of the relaxation process is discussed in terms of the Vogel–Fulcher equation and related models, and it results from an increase in both the energy barrier to dipolar motion and the reference temperature (T₀) for the kinetic relaxation process which represents the “static” dipolar freezing temperature for the process. The general applicability of the Vogel–Fulcher equation to relaxional processes in polymers and other systems is briefly discussed. The pressure dependence of the dielectric constant both above and below the relaxation peak temperature (T_max) is found to be dominated by the change in polarizability. The effect is larger above T_max because of the relatively large decrease in the dipolar orientational polarizability with pressure.     

Rebuttal to “comments on ‘some evidence against the existence of the liquid–liquid transition. IV. The temperature dependence of shear viscosity’”

Data on the temperature dependence of viscosity obtained on three different polystyrenes with narrow molecular weight distributions are fitted to the Vogel, Fulcher, Tamman, and Hesse (VTFH) equation as well as to two intersecting Arrhenius lines. Both fits are optimized by means of computer programs. The data were chosen to fit the requirements stated by Boyer. The results of the analyses support the earlier conclusions that temperature-dependent viscosity data do not indicate the presence of any liquid-liquid transition T_LL above the glass temperature T_g. In addition, evidence is presented which indicates that the viscosity at T_g of high-molecular-weight polystyrenes is proportional to the 3.4 power of the molecular weight. Hence T_g is not an isoviscous temperature.     

Pressure dependence of dielectric properties of chlorinated polyethylene vulcanizate. III. β relaxation

The effects of temperature and pressure on the shift factor and the dielectric increment of the β relaxation process were measured for vulcanized chlorinated polyethylene. The isobaric and isochoric activation enthalpies, H^*_P and H^*_V, the activation volume V^*, the pressure dependence of the glass–glass transition temperature, T_gβ/dP, and the apparent extinction temperature T_0β were obtained. The pressure dependences of both V^* and the dielectric increment would reach very small values near the liquid–glass transition temperature T_g, and the β process seems to be affected by the transition near T_g. The value of H^*v/H^*p for the β process is larger than that for the α process, and it is suggested that the molecular motions pertaining to the β process are more strongly restricted than those pertaining to the α process. The ratio T_0β/T₀, where T₀ is the characteristic temperature in the Vogel–Fulcher–Tammann–Hesse equation for the α process, follows the empirical relation of Matsuoka and Ishida, T_gβ/T_g ～0.75. The value of dT_gβ/dP estimated from T_g and T_0β/T₀ is consistent with the experimental value.     

Investigation of transitions and relaxation processes in polystyrene by using positron annihilation

The glass transition and relaxation processes in polystyrene resins with the number average molecular weight ranging from 7.0·10² to 9.8·10⁴ were studied with the positron annihilation technique. The pick-off annihilation lifetime of ortho-positronium (₃) and its intensity (I ₃) were measured in the temperature range from 20 to 430 K. The glass transition temperature (T _g) was determined as an onset temperature coefficient of ₃.T _g shows the molecular weight dependence in these samples. BelowT _g, local motions were detected by measurements ofI ₃. The local motions could be observed above 100 K in this experiment.I ₃ show the minimum at around 250 K and it does not show molecular weight dependence.     

Dependence of cooperative relaxation of amorphous polymers on diluent concentration

The Adam–Gibbs molecular theory, which describes the temperature dependence of relaxation phenomena in the main transition region in terms of the configurational entropy of a system, has been extended to include the effect of concentration of a low-molecular-weight compound on the viscoelastic behavior of concentrated polymer solutions. The concentration dependence of relaxation times in the polymer–diluent mixture leads to an expression of the concentration dependence both of the shift factor in the Williams–Landel–Ferry (WLF) equation and of the glass transition temperature T_g of the mixture. The constants of the WLF equation and the concentration dependence of T_g are given in terms of a difference between the specific heats of the liquid and glass ΔC_p of the equilibrium temperature T₂ of the second-order transition, and of the parameter Δμs/k, which includes the chemical potential Δμ and the configurational entropy s of the smallest cooperatively rearranging region. The resulting relationships also predict the temperature dependence of the constants of the concentration WLF equation. Good agreement was found between theory and the viscoelastic and T_g data on the systems poly(vinyl acetate) + diethyl phthalate, poly(methyl methacrylate) + diethyl phthalate and polystyrene + dibutyl phthalate. This finding indicates that the configurational entropy, at least in the first approximation, is responsible for the concentration dependence of relaxation phenomena in concentrated polymer solutions.     

Comments on “some evidence against the existence of the liquid-liquid transition. IV. The temperature dependence of shear viscosity”

A formal definition of T_LL as a function of M?ⁿ for polystyrene was prepared with literature T_LL values from torsional braid analysis (TBA), differential scanning calorimetry (DSC), and zero-shear melt viscosity η₀. Data from six authors using anionically prepared PS and blends thereof were involved. The resultant linear least-squares regression line, T_LL(°C) = 148.5 ? 11.487 × 10⁴M? [standard error in T_LL (calculated) 4.056 K, correlation coefficient R² = 0.9534] is considered valid from M?_n = 2000 to the entanglement molecular weight M_c = 35,000. The “best” T_LL values reported by Orbon and Plazek from double Arrhenius plots are well below this line for M?_v = 47,000, 16,400, 3400, and above it for M?_v = 1100. These best T_LL values are artifacts arising from no or insufficient data points above or below T_LL and/or too many data points near T_g. The associated high enthalpies of activation which they report confirm this diagnosis. The fact that these artificial T_LL values tend to disappear when checked by the three-parameter Vogel equation, logη = logA + B exp[(T ? T_∞)^?1], has no relevance to the controversy concerning the existence and meaning of T_LL. The claim by Orbon and Plazek that T_LL values obtained by TBA, DSC, and melt viscosity are all artifacts of the individual methods by which they were obtained is inconsistent with the excellent master plot which they generate. Alternative plotting devices which reveal T_LL > T_g from η₀ vs. T^?1 data, as developed by van Krevelen and Hoftyzer and by Utracki and Simha (not previously considered by either party), are reviewed. A statistical examination of the nature of the Vogel–Fulcher–Tammann–Hesse equation, based on synthetic data, is presented. Evidence for T_LL in atactic polypropylene is offered based on published data by Plazek and Plazek. T_LL is considered to possess both relaxational and quasiequilibrium attributes, just as T_g does.     

A dielectric study of chain motions in poly(vinyl methyl ether)

The dielectric permittivity and loss of poly(vinyl methyl ether) (mol. wt. 30,000) have been measured from 12 Hz to 100 kHz at temperatures from 77 K to 320 K. Two relaxation processes, γ and β, are observed at T < T_g (245 K), and one above T_g. The Arrhenius plots of the γ and β processes have activation energies of 20 and 41 kJ mole^?1 respectively. The relaxation rate of the α process is described by the Vogel-Fulcher-Tamman equation or the William-Landel-Ferry equation. The relaxation rates of γ and β processes evaluated from the isochrones differ from those evaluated from the isothermal spectrum. The features of chain motions observed are similar to those in other polymer and rigid molecular glasses.     

Pressure‐temperature study of dielectric relaxation of a polyurethane elastomer

The effect of hydrostatic pressure up to 1,361 atms on the dielectric properties of a segmented polyurethane elastomer (Dow 2103‐80AE) is studied at temperatures from 0°C to 80°C. The experimental results show that the relaxation time for both the I–process, associated with the molecular motions in the hard segments, and the α–process, associated with the glass transition, increases with pressure, and this shift is more pronounced for the I–process. Besides the glass transition, it is found that the I–process can be described by the Vogel–Fulcher (V–F) and Williams–Landel–Ferry (WLF) relations. At atmospheric pressure, T_g and T₀ for the I–process are 235.9 K and 4.2 × 10³ K, respectively. Based on the V–F and WLF relations and experimental results, it is found that a parameter, C₁, in the WLF relation is independent of the pressure. Thus, a method is introduced to determine the values of both the characteristic transition temperature (T_g) and activation energy (T₀) for the processes at different pressures. As the pressure increases from atmospheric to 1,361 atms, the increase of T_g for the I–process is about 30°C. The results also show that, for both the I– and the α–processes, T₀ decreases with increasing pressure. © 1999 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 37: 983–990, 1999     

Segmental and secondary dynamics in hydrogen‐bonded poly(4‐vinylphenol)/poly(methyl methacrylate) blends

Broadband dielectric spectroscopy was used to study the segmental (α) and secondary (β) relaxations in hydrogen‐bonded poly(4‐vinylphenol)/poly(methyl methacrylate) (PVPh/PMMA) blends with PVPh concentrations of 20–80% and at temperatures from ?30 to approximately glass‐transition temperature (T_g) + 80 °C. Miscible blends were obtained by solution casting from methyl ethyl ketone solution, as confirmed by single differential scanning calorimetry T_g and single segmental relaxation process for each blend. The β relaxation of PMMA maintains similar characteristics in blends with PVPh, compared with neat PMMA. Its relaxation time and activation energy are nearly the same in all blends. Furthermore, the dielectric relaxation strength of PMMA β process in the blends is proportional to the concentration of PMMA, suggesting that blending and intermolecular hydrogen bonding do not modify the local intramolecular motion. The α process, however, represents the segmental motions of both components and becomes slower with increasing PVPh concentration because of the higher T_g. This leads to well‐defined α and β relaxations in the blends above the corresponding T_g, which cannot be reliably resolved in neat PMMA without ambiguous curve deconvolution. The PMMA β process still follows an Arrhenius temperature dependence above T_g, but with an activation energy larger than that observed below T_g because of increased relaxation amplitude. © 2004 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 42: 3405–3415, 2004     

Glass transition in partially sulfonated polystyrene

The glass transition temperature T_g of partially sulfonated polystyrene has been measured dilatometrically as a function of degree of sulfonation. A semitheoretical relationship between T_g and degree of sulfonation has been derived by treating the strong-acid polymer as a highly polar copolymer of styrene and styrenesulfonic acid. The T_g of copolymer has been found to increase linearly up to 0.15 weight fraction of styrene-sulfonic acid w_A as given by: where T_gB is the glass transition temperature of loosely crosslined (1%) polystyrene matrix. Our experimental results agree well with theoretical relations developed on the basis of the iso-free-volume state of glass transition applied to sulfonated polystyrene. The marked linear increase in copolymer T_g with the styrenesulfonic acid is accounted for by the effect of progressively higher intermolecular forces due to the highly polar sulfonic acid substituents.     

Relaxations in thermosets. XIX. Dielectric effects during curing of diglycidyl ether of bisphenol-A with a catalyst and the properties of the thermoset

Changes in the dielectric permittivity ε′ and loss epsiv;″ during the curing of DGEBA catalyzed by 10 mole % dimethylbenzylamine have been studied from sol to gel to glass formation regions at different temperatures from 323 to 390 K. The ε′ monotonically decreases with time of cure, and ε″ initially decreases by several orders of magnitude and then increases to reach a peak value before finally decreasing to a low value characteristic of the glassy state. The features shift to shorter times and the peak vanishes as the curing temperature is increased. The decrease of ε″ at the initial stage of cure has been analyzed in terms of dc conductivity σ₀, which follows a power law, σ₀ ∝? (t_g–t)^x, as well as a new singularity equation, σ₀ ∝? exp[–B/(t₀–t)] where t_g, x, B, and t₀ are empirical constants that vary with the curing temperature; t_g is close to the time for gelation; and t₀ ≥ time for vitrification. The dielectric properties of the thermoset formed after different periods of cure have been studied from 77 to 325 K. Similar studies of the thermosets formed at different temperatures have been made. Increase in the curing period decreases the heights of both the γ-and α-relaxation peaks and increases their separation, while a β-relaxation peak emerges. Isothermal curing at high temperatures decreases the height of the γ peak to a vanishingly small value and increases that of the β peak from a vanishingly small value. In both the uncured and fully cured states, there is only one sub-T_g relaxation process named γ for the uncured and β for the cured state. These results are discussed in terms of our general physical concepts of local mode motions in an amorphous matrix. © 1993 John Wiley & Sons, Inc.     

Dielectric properties of sols of silver nanoparticles capped by alkyl carboxylate ligands

Sols of silver nanoparticles in toluene were studied by broadband dielectric spectroscopy (10⁻³–10⁵ Hz). The frequency dependences of the specific alternating current (ac) conductivity and the complex electric modulus were used to estimate the temperature/frequency intervals of long- and short-range charge transfer occurs, respectively. A considerable increase (by more than 30 °C) in the Vogel temperature T ₀ and the glass transition temperature T _g in sols compared with the pure solvent was found. It can be hypothesized that these cooperative effects reflect the initial stage of the superlattice formation. Although the dielectric characteristics of sols are generally controlled by the conductivity relaxation, the dielectric response was observed in the high-frequency range (1–10³ Hz) at low temperatures (from −50 to +10 °C). This response results from the presence of nanoparticles in solution. It is supposed that the relaxation is caused by the motion of ion impurities on the Ag nanoparticle surface within the carboxylate ligands shell. The dielectric properties of films strongly depend on both the characteristics of nanoparticles and the conditions of the film preparation. Like in sols, the direct current (dc) conductivity and the dielectric response of Ag nanoparticles in films are due to ion impurities.     

Dynamic mechanical and dielectric properties of epoxidized SBS triblock copolymer

The morphological and dynamic properties of epoxidized styrene–butadiene–styrene block copolymers were studied and compared with their parent styrene–butadiene–styrene block copolymer (SBS). Two peaks were observed in the mechanical loss (tan δ) curve which can be attributed to segmental motion of epoxidized polybutadiene (EPPB) and polystyrene. Analysis by DSC thermograms also showed the linear increase of glass transition temperature for EPPB domain with the epoxy group content. Phase separated structures of epoxidized SBS as observed by TEM suggests a considerable degree of mixing occurred between phases after 80 mol % of the double bonds in SBS were epoxidized. The interfacial region displays a third peak and causes much steeper drop in modulus at higher temperature than T_g of EPPB. Parallel dielectric relaxation measurements were also made in the frequency range of 30 Hz–1 KHz as a function of temperature. In each dielectric constant (?′) curve, there is a maximum near the T_g of EPPB determined from the dielectric loss tangent curve. The shift in T_g of EPPB versus epoxy group content was consistent with that measured by the thermal and dynamic mechanic analysis. These findings indicated an 8°C shift in glass transition temperature as the epoxy group content in EPPB increased 10%.