Measurements of the relaxation spectra of unplasticized poly(vinyl chloride) melts

We have measured the relaxation modulus in the temperature range 150–220°C of two samples of poly(vinyl chloride) resin with different molecular weights. The data were treated by the principle of reduced variables to yield composite curves. The shift factors (a_T) when plotted against reciprocal temperature gave good straight lines from which apparent activation energies were obtained. An apparent activation energy of 50 kcal/mole was obtained for both samples. A relaxation spectrum for each resin was calculated from the relaxation modulus data. These spectra showed a marked molecular weight dependence. The spectra were in the range characteristic of the terminal zone of the entanglement plateau. Zero-shear-rate viscosities were obtained from the integration of relaxation modulus plots. From extrapolation of capillary viscosity data it is shown that the viscosity of the higher molecular weight resin used in this study does not approach its zero-shear value until shear rates less than 10^?3 sec^?1 are reached. The effect of supermolecular flow units is briefly discussed.     

Diluent effects on molecular motions and glass transition in polymers. I. Polystyrene–toluene

The effects of diluent on molecular motions and glass transition in the polystyrene–toluene system was studied by means of dielectric, thermal, and NMR measurements. Three dielectric relaxations were observed between 80 and 400°K. On the basis of NMR measurements on solutions in toluene and in deuterated toluene, relaxation processes were assigned to segmental motions of polystyrene, rotations of toluene, and the local motions of polystyrene and toluene in order of appearance from the high-temperature side. The concentration dependence of the relaxation strength and of the activation energy for the primary relaxation (that at the highest temperature) show a step increment at about 50% by weight. The activation plots for the primary process were expressed by the Vogel–Tamman equation. With this equation, the temperatures at which the mean dielectric relaxation time becomes 100 sec is determined. This agrees well with the glass-transition temperature T_g and hence T_g in concentrated solution is expressed by in terms of the parameters A, B, and T₀ of the Vogel–Tamman equation. The values of A and B are, respectively, about 12 and 0.65 and independent of the concentration. The physical meaning of these parameters is discussed.     

Development of low field NMR technique for analyzing segmental mobility of crosslinked polymers

This low field NMR study established the correlation between the degree of crosslinking in rigid model systems to the proton spin lattice relaxation time (T₁) measured. For three model epoxy samples, our data have shown that as the number of crosslinks increases the T₁ minima shift toward higher temperatures. In addition, the magnitude of the T₁ minimum is also observed to shift to higher values as a function of crosslinks formed. These trends are consistent with the predictions of the Bloembergen, Purcell, and Pound analysis. For these highly crosslinked systems, it was necessary to incorporate the Fuoss Kirkwood distribution function for describing the coupled dynamics of the connected individual monomer units of each crosslink. By fitting the spin lattice relaxation data at different temperatures to the Fuoss Kirkwood modified BPP theory, the average activation energy for the molecular motion and the breadth of the relaxation spectrum were obtained. For these model systems, the increase in the activation energy to achieve mobility and the broadening of relaxation distribution have also been determined quantitatively. The results of this study provide the foundation for using T₁ to analyze the crosslinking process of polymeric systems. © 2018 Wiley Periodicals, Inc. J. Polym. Sci., Part B: Polym. Phys. 2018 , 56, 639–642     

Pulsed NMR study of molecular motion in the uncured diglycidyl ether of bisphenol-A

The diglycidyl ether of bisphenol-A, an uncured epoxy resin, has been studied by pulsed NMR. Values of the proton relaxation times T₁, T_1p, and T₂ have been measured over the temperature range from ?160 to 200°C. The resin was studied in its monomeric form and in two mixtures containing higher oligomers. The relaxation times are interpreted in terms of the molecular motion in the resins. The motion responsible for relaxation in the solid monomer form is thought to be methyl group reorientation at low temperatures and general molecular motion at high temperatures. The motions are characterized by activation energies of 5 kcal/mole and 33 kcal/mole, respectively. The solid mixtures exhibit similar effects to the monomer, but an additional relaxation mechanism is observed which is attributed to segmental motion. This motion is characterized by an activation energy of 12–15 kcal/mole. The self-diffusion coefficient was measured in the liquid monomer, and the activation energy for self-diffusion is found to be 11 kcal/mole.     

Tensile flow and stress–strain behavior over a wide temperature range for poly(butyl methacrylate) with a broad molecular weight distribution

The poly(butyl methacrylate) studied is a polymer with a normal molecular weight distribution and a relatively low molecular weight close to M_c, the critical molecular weight from the viscosity–molecular weight relation. The polymer was subjected to uniaxial extension and shear over a temperature range which included T_g. It was found that in the region of T_g an increase in applied stress is accompanied by a decrease both in the temperature shift factor a_T and in the activation energy for relaxation and rupture of polymer melts. Close attention is given to the long-term durability of the polymer. As is expected in the temperature range below T_g, its dependence on the stress is exponential, whereas at temperatures above T_g a power law fits the data. In the latter case a log-log plot of the long-term durability versus stress can be represented by two intersecting straight lines which can be replotted as a generalized straight line if the long-term durability values are normalized by the viscosity.     

Proton NMR study of molecular motion in polydimethylsiloxane

Proton spin–lattice relaxation times T₁ were measured for two samples of polydimethylsiloxane (PDMS), one with weight-average molecular weight M_w = 77,400 and the other with M_w = 609,000. Two T₁ minima and a T₁ discontinuity were observed for each compound. The high-temperature T₁ minima were attributed to a stretching and flexing motion of the PDMS chain. Quantitative comparison of the relaxation data with a theoretical model developed for this motion allowed the activation energy, 2.3 kcal/mole, and the maximum angular displacement of the methyl group symmetry axis to be determined. The latter was found to be 31°, independent of sample molecular weight. The low-temperature minima were ascribed to methyl reorientation with an activation energy of 1.6 kcal/mole. The T₁ discontinuities were attributed to melting and allowed the degree of crystallinity to be estimated.     

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.     

Diglycidyl ether of bisphenol-A with 4,4′-methylenedianiline: A pulsed NMR study of the curing process

The curing process, during which the monomeric diglycidyl ether of bisphenol-A is cured with 4,4′-methylenedianiline, has been studied by pulsed NMR. Values of the proton relaxation times T₁, T_1ρ, and T₂ have been measured as a function of time as the resin system cures at constant temperature. The relaxation times are interpreted in terms of the decrease in general molecular motion which results from the cure. Plots of correlation frequency versus time for the constant-temperature cure were constructed for three temperatures. It is shown that these three plots can be represented by a reduced curve. With certain simplifying assumptions, the shape of this reduced curve. With certain simplifying assumptions, the shape of this reduced curve can be accounted for in terms of the chemical rate constant and an exponent relating molecular weight to viscosity. The activation energy for the cure is estimated to be 11.7 kcal/mole.     

Pressure relaxation of polystyrene and its comparison to the shear response

Isothermal pressure relaxation as a function of temperature in two pressure ranges has been measured for polystyrene using a self-built pressurizable dilatometer. A master curve for pressure relaxation in each pressure regime is obtained based on the time–temperature superposition principle, and time–pressure superposition of the two master curves is found to be applicable when the master curves are referenced to their pressure-dependent T_g. The pressure relaxation master curves, the shift factors, and retardation spectra obtained from these curves are compared with those obtained from shear creep compliance measurements for the same material. The shift factors for the bulk and shear responses have the same temperature dependence, and the retardation spectra overlap at short times. Our results suggest that the bulk and shear response have similar molecular origin, but that long-time chain mechanisms available to shear are lost in the bulk response. © 2007 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 45: 3375–3385, 2007     

Dynamics of junction point motions in model network polymers

³¹P solid-state exchange 2D NMR and spin-lattice relaxation times (T₁^P) have been used to investigate the motion of a crosslink unit in model networks. The networks were formed from tris(4-isocyanatophenyl) thiophosphate with telechelic poly(propylene glycol) or poly(tetrahydrofuran). From the variation of the 2D NMR pattern with temperature and mix time, the motion of the crosslink is identified as Brownian reorientational diffusion. Good simulations of the spectra were obtained using the Williams-Watts distribution of correlation times. The temperature dependence of the crosslink motion follows the WLF equation. The parameters derived from the NMR data are sufficient to describe the temperature dependence and breadth of both the dielectric and mechanical loss associated with the glass transition. The T₁^P relaxation data fitted equally well to the Cole-Cole or the Williams-Watts relaxation functions. The motion of the crosslinks can be described quantitatively by the activation energies and the coupling parameters.     

Calorimetric relaxation and glass transition in poly(propylene glycols) and its monomer

The glass transition temperature T_g of propylene glycol (PG) and poly(propylene glycols) (PPGs) of molecular weight up to 4000 has been measured by differential scanning calorimetry, and the activation energy and change in heat capacity ΔC_p have been determined in the glass transition range. The activation energy increases with an increase in the molecular weight of the polymer, and ΔC_p measured at a fixed heating rate decreases. The increase in T_g with molecular weight is remarkably more rapid for poly(propylene glycols) than for other polymers, and a limiting value of T_g is reached for a chain containing 20 monomer units. These results are discussed in terms of the Fox-Flory and the entropy theories. The calorimetric relaxation times are comparable with the extrapolated dielectric relaxation times. The initial increase of ΔC_p from PG to PPG 200 is attributed to the decrease of H-bonding sites from 12 in 3 monomers to 4 on polymerization to PPG 200 and further decrease with increase in molecular weight to an increasingly large amplitude of the β-process at T < T_g.     

Effect of crosslink density on the pressure relaxation response of polycyanurate networks

The effect of crosslink density on the pressure-volume-temperature (PVT) behavior and on the pressure relaxation response for two polycyanurate networks is investigated using a custom-built pressurizable dilatometer. Isobaric cooling measurements were made to obtain the pressure-dependent glass transition temperature (T_g). The pressure relaxation studies were carried out as a function of time after volume jumps at temperatures in the vicinity of the pressure-dependent T_g, and the pressure relaxation curves obtained were shifted to construct master curves by time-temperature superposition. The reduced pressure relaxation curves are found to be identical in shape and placement, independent of crosslink density, when T_g is used as the reference temperature. The horizontal shift factors used to create the master curves are plotted as a function of the temperature departure from T_g (T − T_g), and they agree well with their counterparts obtained from the shear response. Moreover, the retardation spectra are derived from bulk compliance and compared to those from the shear. The results, similar to our previous work on polystyrene, indicate that at short times, the bulk and shear responses have similar underlying molecular mechanisms; however, the long-time mechanisms available to the shear response, which increase with decreasing crosslink density, are unavailable to the bulk response. © 2009 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 47: 2477–2486, 2009     

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.     

Dielectric relaxation phenomena in a series of polyhydroxyether copolymers of bisphenol-A—endcapped polyethylene glycol with epichlorohydrin

Dielectric relaxation spectra of a series of polyhydroxyether copolymers have been obtained. It has been shown that the systems exhibit very similar relaxation spectra with the α(T_g) process a function of molecular weight. All systems exhibit two secondary relaxations: β (ca. 240 K) and γ (ca. 180 K). These have been assigned as hydroxyl motion and main-chain motion, respectively. The peak positions are not functions of composition in the ranges studied. The effect of sorbed water on the relaxation spectra is discussed.     

Conductance and relaxations in the glassy and rubber states of aqueous poly( vinyl pyrrolidone): A cryofixation medium

The dielectric permittivity and loss of poly(vinyl pyrrolidone), molecular weight 40,000, containing 40% (by weight) water have been measured over the temperature range 77–325 K and frequency range 12 Hz to 0.1 MHz. A prominent relaxation due to rotational diffusion of water molecules in a hydrogen-bonded structure occurs at T < T_g (237 K). The half-width of the dipolar relaxation spectra is 2.27 decades and is temperature independent, which is strikingly different from the corresponding features of pure polymers. It is concluded that H-bonded amorphous solid water persists in the glassy polymer matrix and that the H-bonded structure contains the pyrrolidone side groups of the randomly oriented chain. The relaxation peak at T near T_g is masked by a large dc conductivity which, when expressed in terms of electric modulus, has a spectrum of half-width 1.37 instead of 1.14 decades expected for dc conductivity alone. The contribution from dipolar reorientation in the glass-rubber range of the PVP-H₂O solution is smaller than that in its sub-T_g relaxation.     

Thermoplastic elastomers by hydrogen bonding 1. Rheological properties of modified polybutadiene

Polybutadiene of narrow molecular weight distribution was modified using 4-phenyl-1, 2,4-triazoline-3,5-dione. The degree of modification was 1% and 2% with respect to the repeating units. Hydrogen bonding between the highly polar urazole groups thus incorporated into the polymer gives rise to the formation of a thermoreversible elastomeric network. Dynamic mechanical measurements in the temperature range between 220 and 330 K support the picture of the thermoreversible hydrogen bond interaction. The rubber elastic plateau is shifted to higher temperatures and lower frequencies. The increase in the plateau modulus cannot be attributed solely to the contribution of the network structure but is mainly a consequence of the broadening of the relaxation time spectrum in the modified samples. From the temperature dependence of the shift factors log(a _T ) it is concluded that the general WLF approach fails. The strong temperature dependence of the apparent activation energy of flow is a consequence of the temperature dependence of the hydrogen bond interaction.     

Temperature‐induced Molecular Chain Motions of Styrenic Triblock Copolymers Studied by Intrinsic Fluorescence Spectra

The temperature‐induced molecular chain motions of styrenic triblock copolymers (SBC), i.e. polystyrene‐block‐polybutadiene‐block‐polystyrene (SBS) and polystyrene‐block‐poly(ethylene‐co‐1‐butene)‐block‐polystyrene (SEBS), were studied by intrinsic fluorescence method. For SBS, the glass transition temperatures (T_gs) of B block and S block obtained by intrinsic fluorescence method were in good agreement with differential scanning calorimetry measurements (DSC). In the case of SEBS, an isoemission point was observed at about 310 nm at elevated temperatures, suggesting the slight conversion between the monomer and excimer emission. On this basis, the molecular chain motion of SEBS was monitored by both fluorescence intensity and excimer/monomer fluorescence ratio. Besides the T_gs of S block and EB blocks, a melting point (T_m) of weak crystalline in EB block was unambiguously determined by intrinsic fluorescence. Furthermore, it was found that the melting process directly led to the slight loosening of PS segments in interface and consequently the reduction of the amount of excimer. A reasonable mechanism was proposed to describe the molecular chain movements and phase transitions of SEBS upon heating. Moreover, the influence of temperature on the apparent activation energy of non‐radiative process (E_a^T) around T_g of S block was much stronger than that around T_g of B or EB blocks.     

Bulk and shear rheology of a symmetric three‐arm star polystyrene

The bulk and shear rheological properties of a symmetric three‐arm star polystyrene were measured using a self‐built pressurizable dilatometer and a commercial rheometer, respectively. The bulk properties investigated include the pressure–volume–temperature behavior, the pressure‐dependent glass transition temperature (T_g), and the viscoelastic bulk modulus and Poisson's ratio. Comparison with data for a linear polystyrene indicates that the star behaves similarly but with slightly higher T_gs at elevated pressures and slightly higher limiting bulk moduli in glass and rubbery states. The Poisson's ratio shows a minimum at short times similar to what is observed for the linear chain. The horizontal shift factors above T_g obtained from reducing the bulk and shear viscoelastic responses are found to have similar temperature dependence when plotted using T ? T_g scaling; in addition, the shift factors also exhibit a similar temperature dependence to linear polystyrene. The retardation spectra for the bulk and shear responses are compared and show that the long time molecular mechanisms available to the shear response are unavailable to the bulk. At short times, the two spectra have similar slopes, but the short‐time retardation spectrum for the shear response is significantly higher than that for the bulk, a finding that is, as yet, unexplained. © 2012 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys, 2012     

Dynamics of macromolecular chains. VI. Carbon 13 and proton nuclear magnetic relaxation of polystyrene in solution

Spin-lattice ¹H and ¹³C nuclear magnetic relaxation (NMR) times T₁ have been measured for solutions of polystyrene in hexachlorobutadiene at two different frequencies. Some nuclear Overhauser enhancements and linewidths have also been determined. At 15 and 25 MHz the relaxation times T₁ of the ortho and meta carbons show two different dependences on temperature. These measurements indicate internal motion of phenyl groups around the C_α—C_para axis. A single isotropic correlation time is inadequate to explain the relaxation data for the para carbon. Use of a diamond-lattice motional model reveals that segmental reorientation of the chain backbone of polystyrene can be described in terms of two correlation times, ρ characterizing the three-bond motion process, and θ reflecting either isotropic motions of subchains or departure from an ideal lattice. Data on low-molecular-weight polystyrene indicate the participation of overall rotatory diffusion in the relaxation process. This motion is no longer efficient in high-molecular-weight polymers, where relaxation is due to segmental reorientation.