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.     

Sub-TG relaxations in LiClO4-poly (propylene glycol)-2000 solutions

The dielectric permittivity and loss of LiClO₄ solutions in poly (propylene glycol (PPG)), molecular weight 2000, have been measured over a concentration range up to a ratio of Li⁺ to oxygen atoms in PPG of 33.3:100, between 77 and 350 K. The data have been analyzed in both the permittivity and electrical modulus formalisms. Addition of LiClO₄ to poly (propylene glycol) first increases the height of the β-relaxation peak, and ultimately a second sub-T_g relaxation peak at a higher temperature emerges. This is in addition to the β-relaxation peak due to the reorientation of PPG dipoles, whose strength decreases from that in pure PPG-2000. For a fixed temperature, the dc conductivity initially decreases with increasing Li⁺ concentration up to 20 Li⁺ per 100 O atoms and thereafter increases. This concentration corresponds to that at which the T_g of the solution reaches its limiting value of ca. 310 K. It is concluded that the formation of ion pairs causes a second and slower sub-T_g relaxation process and that the increase in the efficiency of chain packing reduces the strength of the β-relaxation of the polymer.     

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     

Investigation of molecular motions of crosslinked polyepichlorohydrin by nuclear magnetic resonance spectroscopy

The molecular motion of crosslinked polyepichlorohydrin (PECH) is studied qualitatively by NMR techniques. The results of temperature dependence of ¹H T₂ and T₁ indicate that the crosslinking (crosslink density < 3%) restricts molecular motions of the polymer even far above its T_g. The ¹H T₁ minimum, corresponding to the large-scale chain-motion of crosslinked PECH, shifts to higher temperatures with increasing crosslink density. ¹H T₂ data also show that the crosslinking hinders free chain motions of the polymer above its T_g. The ¹³C T₁ relaxation time is sensitive to such motional changes as well. ¹³C linewidths of crosslinked PECHs vary with the crosslink density in both the swollen state and the solid state. The mechanism of ¹³C linewidth broadening of crosslinked polymers is discussed in detail. In the case of PECH, the linewidth broadening is caused by changing molecular environment due to crosslinking (such as presence of various chemical shift structures and freezing effects in conformational environment as chain mobility decreases), rather than increasing correlation times, which shorten the relaxation time (T₂) of polymer chains. © 1994 John Wiley & Sons, Inc.     

Prediction of the glass transition temperature of cycloaliphatic amine–epoxy networks

Stoichiometric, completely cured binary or ternary mixtures of the diglycidylether of bisphenol A (DGEBA), isophorone diamine (IPD), and trimethylcyclohexylamine (TMCA) monomers were studied by differential scanning calorimetry. The relations between the glass transition temperature T_g and the structure of the copolymer networks were investigated. Good predictions of T_g can be obtained on the basis of the following hypothesis: (1) the molar contributions M_iT^?1_gi to the “copolymer effect” of difunctional groups are additive, (2) the crosslinking effect can be expressed by the DiMarzio relation in which the molar contribution of crosslink mers is an increasing function of the stiffness of linear segments. For the seven systems under study, the deviation between calculated and experimental T_g values is within experimental scatter.     

Dielectric relaxation of specially prepared polystyrene terminated with rigid polar groups

Two polystyrenes terminated withp-cyanobenzyl andp-cyanobiphenyl groups (=labels) were prepared and their complex dielectric constants were measured in the glass transition region in the frequency range 10^–2–10⁶ Hz. The glass temperaturesT _g (DSC) were considerably different, 92 and 97.5°C, resp., although their molecular weights were very similar (11 000 and 10 000 g/mol, resp.). Their relaxation behavior showed that the cyano groups relax cooperatively with the polymer segments. The cyanophenyl groups were found to relax with shorter relaxation times than the cyanobiphenyl groups. The measured relaxation strengths showed that there was no association between the dipoles. The relaxation mechanisms of the cyano groups in both labels seemed to be different although the only difference between them was an additional phenyl group in the case of the second label.     

The physical properties of bisphenol-a-based epoxy resins during and after curing. II. Creep behavior above and below the glass transition temperature

The creep behavior of a series of fully cured epoxy resins with different crosslink densities was determined from the glassy compliance level to the equilibrium compliance J_e at temperatures above T_g and at the glassy level below T_g during spontaneous densification at four aging temperatures, 4,4-diamino diphenyl sulfone DDS was used to crosslink the epoxy resins. The shear creep compliance curves J(t) obtained with materials at equilibrium densities near and above T_g were compared at their respective T_gs. T_gs from 101 to 205°C were observed for the epoxies which were based on the diglycidyl ether of bisphenol A. Creep rates were found to be the same at short times, and equilibrium compliances J_e were close to the predictions of the kinetic theory of rubberlike elasticity. Time scale shift factors determined during physical aging were reduced to T_g. At compliances below 2 × 10^?10 cm²/dyn, Andrade creep, where J(t) is a linear function of the cube root of creep time, was observed. The time to reach an equilibrium volume at T_g was found to be longer for the epoxy resin with lower crosslink densities. The increase of density during curing is illustrated for the epoxy resin with the highest crosslink density.     

Effects of the type of crosslink on viscoelastic properties of natural rubber

The viscoelastic properties of various crosslinked natural rubbers, NR, were investigated by mechanical spectroscopy. The glass transition temperature, T_g, was found to be dependent on both the crosslink density and the crosslink type. Higher values of T_g were obtained for sulfur-crosslinked NR than for peroxide-crosslinked NR at the same crosslink density. The greater influence of the sulfur content on T_g may be attributed to polysulfidic crosslinks and cyclic sulfide structures favored at high sulfur contents. Sulfur-vulcanized NRs with monosulfidic crosslinks, favored at relatively high accelerator/sulfur ratios, have properties more similar to the peroxide-cured NR with simple carbon(SINGLE BOND)carbon crosslinks covalent bonds, resulting in only small shifts in T_g. A qualitative analysis of monosulfidic crosslinks and polysulfidic structures was performed with ¹³C solid-state NMR spectroscopy. The storage modulus, E′, in the rubbery plateau region increased with increasing crosslink density. However, the crosslink type did not influence the moduli values as much as it influenced the T_g values. Different methods of detecting the crosslink density were also discussed. © 1996 John Wiley & Sons, Inc.     

Volume dependence of thermal conductivity and bulk modulus for poly(propylene glycol)

The thermal conductivity λ and heat capacity per unit volume of poly(propylene glycol) PPG (0.4 and 4.0 kg·mol⁻¹ in number-average molecular weight) have been measured in the temperature range 150–295 K at pressures up to 2 GPa using the transient hot-wire method. At 295 K and atmospheric pressure, λ = 0.147 W m⁻¹K⁻¹ for PPG (0.4 kg·mol⁻¹) and λ = 0.151 W m⁻¹K⁻¹ for PPG (4.0 kg·mol⁻¹). The temperature dependence of λ is less than 4 × 10⁻⁴ W m⁻¹K⁻² for both molecular weights. The bulk modulus has been measured in the temperature range 215–295 K up to 1.1 GPa. At atmospheric pressure, the room temperature bulk moduli are 1.97 GPa for PPG (0.4 kg·mol⁻¹) and 1.75 GPa for PPG (4.0 kg·mol⁻¹). These data were used to calculate the volume dependence of $ \lambda ,g\, = - \left( {\frac{{\partial \lambda /\lambda }}{{\partial V/V}}} \right)_T $. At room temperature and atmospheric pressure (liquid phase) we find g = 2.79 for PPG (0.4 kg·mol⁻¹) and g = 2.15 for PPG (4.0 kg·mol⁻¹). The volume dependence of g, (∂g/∂ log V)_T varies between −19 to −10 for both molecular weights. Under isochoric conditions, g is nearly independent of temperature. The difference in g between the glassy state and liquid phase is small and just outside the inaccuracy of g of about 8%. The theoretical model for λ by Horrocks and McLaughlin yields an overestimate of g by up to 120%. © 1998 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 36 : 345–355, 1998     

Viscoelastic characteristics of UV polymerized poly(ethylene glycol) diacrylate networks with varying extents of crosslinking

The viscoelastic relaxation characteristics of ultraviolet crosslinked networks based on poly(ethylene glycol) diacrylate [PEGDA] have been investigated by dynamic mechanical methods. Effective crosslink density in the networks was varied via the use of PEGDA prepolymers of different molecular weight, or by the introduction of controlled amounts of water in the reaction mixture. In all cases examined, fully amorphous networks were obtained. Time–temperature superposition was applied to obtain master curves of storage modulus versus frequency across the glass transition, and these could be satisfactorily described using the Kohlrausch–Williams–Watts relaxation function. The glass transition temperature (T_g), relaxation breadth, and fragility of the segmental relaxation were correlated with the effective crosslink density obtained in the networks. Gas permeation measurements on the PEGDA/water networks indicated only a very modest variation in gas transport properties, despite the sizeable variation in apparent crosslink density achieved in these materials. This result suggests that the controlling structural factor for gas transport in the networks is not simply crosslink density, and that attempts to correlate gas transport to network structure must necessarily consider the broader relationships between crosslink density, segmental mobility, and fractional free volume. © 2006 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 44: 2058–2070, 2006     

An NMR study of the electron beam-induced polymerization of trimethylolpropane triacrylate and trimethylolpropane trimethacrylate

Electron beam-induced polymerization of trimethylolpropane triacrylate (TMPTA) and its methacrylate analog (TMPTMA) was studied using nuclear magnetic resonance (NMR) relaxation time measurements. Free induction decays (FID) of partially polymerized samples consist of a short Gaussian component and a longer component comprised of a distribution of simple exponentials. The relative intensity of the Gaussian component increases with radiation dose. T₁ and T_1ρ values were measured as a function of temperature and radiation dose. The relaxation is due primarily to methyl group reorientation at low temperatures, ethyl group reorientation at intermediate temperatures, and whole-molecule reorientation at high temperatures. In both compounds, the T₁ and T_1ρ values at the high temperature minima increase with increasing dose, and the minima values can be used to estimate the degree of polymerization. The temperature at which the T_1ρ minimum occurs increases with dose, suggesting an increase in the glass transition temperature, T_g, with polymerization. The polymerization appears to have very little effect on the low temperature CH₃ reorientation in TMPTA. In TMPTMA the polymerization appears to reduce the mobility of the methacrylate methyl groups.     

NMR relaxation study of crosslinked cis-1,4-polybutadiene

Proton relaxation measurements have been used to investigate the effects of crosslinking on the segmental motion in cis-1,4-polybutadiene samples. The temperature dependence of proton spin–lattice relaxation time T₁ and spin–spin relaxation time T₂ at 60 and 24.3 MHz are reported in cis-1,4-polybutadiene (PB) samples with different crosslink density including uncrosslinked PB and samples with 140, 40, and 14 repeat units between crosslinks. In addition, spin-lattice relaxation times in rotating coordinate frame, T_1p, have also been determined. The relaxation data are interpreted in terms of the effects of crosslinks on segmental chain motions. Because of their sensitivity to low-frequency motion, T₂ data are of major interest. At temperatures well above the T₁ minimum the small T₂ temperature dependence resembles solidlike behavior reflecting the nonzero averaging of dipolar interactions due to anisotropic motion of the chain segments between crosslinks. The magnitude of T₂ at 60°C is found to be proportional to the average mass between crosslinks.     

Magic angle carbon-13 NMR study of solid poly(ethylene naphthalene-2,6-dicarboxylate)

Amorphous (1) and semicrystalline (2) samples of poly(ethylene naphthalene-2,6-dicarboxylate) (PEN) have been investigated by cross-polarization/magic angle spinning (CP/MAS) ¹³C NMR at 26°C (1 and 2), 100°C (1) and 120°C (2) in order to study the phase structure and the local motion of polymer chain segments at temperatures below and close to T_g (120°C). The lineshape of the ethylene unit ¹³C signal in sample 2 is consistent with the presence of two components which were assigned to trans and gauche conformations. The first component arises mainly from the crystalline regions and the second one from the amorphous part. Cross-polarization curves were traced by changing the contact time between carbon and proton reservoirs. T_CH (cross relaxation time) and proton T_1p (spin-lattice relaxation time in the rotating frame) values were obtained as best fit parameters by fitting calculated curves to the experimental data. All ¹³C NMR data are consistent with the presence of highly rigid ethylene units in both semicrystalline and amorphous samples within the temperature range (T) investigated. This result is in disagreement with the ¹H NMR wide line spectra which showed a noticeable narrowing of the linewidth with increasing temperature in the same range, hence indicating a great mobility of the chain segments. To account for this discrepancy a qualitative model based on the existence of two distinct dynamic regions, one where motion is highly restricted and the other one where large reorientations of ethylene group torsional angles take place, is suggested. The NMR results led to the conclusion that three structural phases are present in PEN: crystalline, very rigid amorphous, and very mobile amorphous. © 1995 John Wiley & Sons, Inc.     

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.     

Synergism and multiple mechanical relaxations observed in ternary systems based on benzoxazine,epoxy, and phenolic resins

The synergism in the glass‐transition temperature (T_g) of ternary systems based on benzoxazine (B), epoxy (E), and phenolic (P) resins is reported. The systems show the maximum T_g up to about 180 °C in BEP541 (B/E/P = 5/4/1). Adding a small fraction of phenolic resin enhances the crosslink density and, therefore, the T_g in the copolymers of benzoxazine and epoxy resins. To obtain the ultimate T_g in the ternary systems, 6–10 wt % phenolic resin is needed. The molecular rigidity from benzoxazine and the improved crosslink density from epoxy contribute to the synergistic behavior. The mechanical relaxation spectra of the fully cured ternary systems in a temperature range of −140 to 350 °C show four types of relaxation transitions: γ transition at −80 to −60 °C, β transition at 60–80 °C, α₁ transition at 135–190 °C, and α₂ transition at 290–300 °C. The partially cured specimens show an additional loss peak that is frequency‐independent as a result of the further curing process of the materials. The ternary systems have a potential use as electronic packaging molding compounds as well as other highly filled systems. © 2000 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 38: 1687–1698, 2000     

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     

23Na NMR in urethane cross-linked polyether solid polymer electrolytes

Sodium triflate/polyether urethane polymer electrolytes ranging in concentration from 0.05 molal to 1.75 molal have been investigated via ²³Na static solid-state NMR. Room temperature spectra and spin lattice relaxation times were consistent with a single narrow resonance indicating the presence of only mobile ionic species. The concentration and temperature dependence of relaxation times, chemical shifts, and linewidth have been investigated. The results suggest either a single species or rapid exchange between a number of species (even at temperatures below the glass transition temperature, T_g). The linewidth decreases with increasing concentration of ions and remains temperature independent below T_g. Below T_g a maximum quadrupolar interaction constant of 2 MHz is calculated. The addition of plasticizer to the polymer electrolyte causes significant chemical shift changes that depend on the solvent donicity of the plasticizer. The linewidth and T₁ relaxation times also depend on the T_g of the plasticized systems. Previous ²³Na NMR literature results are reviewed and qualitative models developed to account for the variation in results. © 1994 John Wiley & Sons, Inc.     

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.     

FOURIER TRANSFORM INFRARED STUDIES OF POLY (ETHYLENE TEREPHTHALATE) FILM IN THE GLASS TRANSITION REGION

Three specimens from a solution-cast poly (ethylene terephthalate) (PET) film, one being liquid-N_2 quenched from 92℃(Q), one being slowly cooled from 92℃(SC) and one being quenched and sub-T_g annealed at 67℃(AN), have been studied by specimen difference spectra Q-SC and AN-Q and temperature difference spectra T-70 and T_2-T_1 for every 2℃steps on heating to 90℃at 2℃/min. SC and AN showed more gauche conformers than Q. That means that the PET chain has more trans conformers at higher temperatures and some of these are frozen during quenching through T_g. A band at 1340 cm~(-1) has been found to be complex containing overlapping bands reflecting trans in crystalline regions and trans in amorphous regions. The temperature difference spectra on heating through T_g showed that the spectral changes in Q are gradual while a rather abrupt change occurs in AN at 80—82℃for the bands at 1340, 1042 and 1020 cm~(-1). No new conformational structure or new vibrational mode is involved. A kind of locking mechanism is suggested which hinders the molecular vibrational changes in AN below T_g until a sudden release occurs at T_g. These locking sites can be nothing else than sites of tighter local packing of chain segments. Consequently it is believed that inter-chain van der Waals attraction energy plays a dominating role in the volume relaxation and sub-T_g annealing of quenched amorphous polymers.     

The photo-isomerization of stilbene

The S₀ potential of stilbene has minima in the trans (t) and cis (c) configurations and a maximum in the perp (p) configuration. The S₁ potential has minima at t, p and c due to crossing of the ¹B_u and ¹A_g potentials, and it is proposed that the T₁ potential has similar minima due to crossing of the ³B_u and ³A_g potentials. Five alternative isomerization mechanisms are considered, the yields of which depend on competition between vertical radiative and radiationless transitions to lower states, and horizontal radiationless transitions between the t, p and c configurations of S₁ and T₁.