Interpretation of differences in temperature and pressure dependences of density and concentration fluctuations in amorphous poly(phenylmethyl siloxane)

Differences in the temperature and pressure dependences of the relaxation times of a slow diffusional process and the α structural relaxation pose an interesting problem. This feature, observed by dynamic light scattering in amorphous poly(phenylmethyl siloxane), is related to another basic feature of lack of thermorheological simplicity discovered by Plazek in polystyrene, poly(vinyl acetate), and amorphous polypropylene. A quantitative explanation based on the predictions of a general coupling theory of relaxations has been found. The coupling theory also predicts the Kohlrausch fractional exponential time correlation function exp[?(tτ^*)^1?n] at long times, as observed by photon correlation spectroscopy, and crossover to an exponential time dependence exp–(t/τ₀) at short times, as frequently assumed in Brillouin scattering. An additional relation between τ^* and τ₀ predicted by the theory is confirmed also by the experimental data.     

Molecular dynamics of poly(ATRIF) homopolymer and poly(AN-co-ATRIF) copolymer investigated by dielectric relaxation spectroscopy

Aiming to develop new dielectric polymers containing CN and F groups with strong dipole moments, a novel copolymer of acrylonitrile (AN) and 2,2,2-trifluoroethyl acrylate (ATRIF) was synthesized in acetonitrile by free radical process as well as the respective homopolymer (poly(ATRIF)). The copolymer’s composition and microstructure were analyzed by FTIR, ¹H and ¹³C NMR spectroscopy and SEC. The molar incorporation of AN determined in the copolymer by NMR was 58 mol%. Thermogravimetric analysis of poly(AN-co-ATRIF) copolymer showed good thermal stability comparatively to the fluorinated homopolymer.Both copolymer, poly(AN-co-ATRIF), and homopolymer, poly(ATRIF), were dielectrically characterized over a frequency range from 10⁻¹ to 10⁶ Hz, and in a temperature range from 223 to 393 K. The dominating relaxation process detected in both materials is the α-relaxation, associated with the dynamic glass transition. A VFTH temperature dependence of the relaxation times (τ) was found for both materials, as characteristic of cooperative processes, from which the respective glass transition temperatures (T_g(τ = 100 s)) were estimated, which differ ∼40 K, the one of the copolymer being higher (307 K) in accordance to the calorimetric analysis. This effect was attributed to a higher stiffness of the backbone in the copolymer originated by the inclusion of the acrylonitrile groups. Both relaxation functions have the same breath of relaxation times allowing constructing a single master curve, indicating similar non-exponential character. A less fragile behavior was found for the copolymer. This was rationalized in a more straightforward way by the free volume approach instead from a correlation between fragility and intermolecular coupling. It was found that in the copolymer the free volume increases at a lower rate with the temperature increase. It was inferred from the VFTH temperature dependence of the dc conductivity and low values of the decoupling index that ion motion is significantly influenced by the dynamics of the α-process.     

Dielectric relaxations and electrical conductivities of poly(alkyl methacrylates) under high pressure

Dielectric properties of four methacrylate polymers (methyl, ethyl, n-butyl and n-octyl) were studied in the frequency range 0.0001 cps–300 kcps at temperatures above and below the glass transition temperature and at various pressures up to 2500 atm. At temperatures well above T_g a single relaxation peak (α′ peak) was observed in the case of the higher n-alkyl methacrylates. However, this peak was split into two peaks, α and β, with decrease in temperature or increase in pressure. The molecular motions corresponding to the α and the β relaxation processes are the micro-Brownian motions of amorphous main chains and of flexible side chains, respectively. From the temperature and the pressure dependence of the average dielectric relaxation time of these polymers the single relaxation process (the α′ process) was attributed to the micro-Brownian motion of the main chain coupled with that of the side chain. The effects of temperature and pressure on the d.c. conductivity of these polymers were also studied.     

Temperature-dependent dielectric relaxation study of binary mixture using the time domain reflectometry method

Dielectric relaxation study of N,N-dimethylformamide (DMF) has been carried out with butylene glycol (BLG, i.e. 1,4-butanediol) at different temperatures. Time domain reflectometry in reflection mode has been used to measure the reflection coefficient in the frequency range from 10?MHz to 20?GHz. The dielectric parameters, static dielectric permittivity (ε ₀) and relaxation time (τ), have been obtained by Fourier transform and least squares fit methods. The experimental results show non-linear variation in dielectric permittivity, and relaxation time with volume fraction of BLG confirms the structural formation due to the intermolecular interaction between DMF and BLG. The variations in excess permittivity (ε^E ), excess inverse relaxation times (1/τ) ^E and Kirkwood correlation factors (g ^eff?;g?^f ) for the binary mixtures have also been reported in this article.     

Effect of curing on the broadband dielectric spectroscopy of powder coating

The effect of curing process of thermosetting powder coating consists of carboxylated polyester resin cured with triglycidyl isocyanurate has been investigated using broadband dielectric relaxation spectroscopy over a wide range of frequency (10⁻¹-10⁶ Hz) and temperature (70-105 °C) for different constant curing times. The molecular dynamics of the glass relaxation process (α-process) was investigated as a function of curing time, frequency, and temperature. It has been found that, only one common α-relaxation process has been observed for all measured samples of different degree of curing stages, its dynamics and broadness were found to be curing time dependent. In addition, the curing time dependence of the dielectric relaxation strength, Δε, has also been examined for the α and β-relaxation processes. The Δε for the two relaxation processes decreased strongly at the beginning of curing process and then became almost constant at longer curing times. This finding implied that the numbers of reoriented dipoles decrease with curing time as a result of the formation of three-dimensional polymer network. Furthermore, the dislocation energy, ε_s, calculated from the Meander model was found to be increased with increasing the curing time, i.e. the formation of a three-dimensional polymer network produces many structural defects or dislocation points. In addition, the activation energy of the curing process was calculated from the analysis of the calorimetric exothermic peaks of the curing process at different heating rates.     

Structural relaxation of glass-forming polymers based on an equation for configurational entropy, 4. Structural relaxation in styrene-acrylonitrile copolymer

The structural relaxation process in styrene-acrylonitrile copolymer has been characterized by means of differential scanning calorimetry (DSC) experiments. The results in the form of heat capacity, c_p(T), curves are analyzed using a model for the evolution of the configurational entropy during the process recently proposed by the authors.^11,12 The model simulation allows one to determine the enthalpy (or entropy) structural relaxation times and the β parameter of the Kohlrausch-Williams-Watts equation characterizing the width of the distribution of relaxation times. This material parameters are compared with their analogues determined from the dielectric and dynamic-mechanical relaxation processes. © 1997 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 35: 2201–2217, 1997     

A study of enthalpic relaxation of a liquid crystal

A liquid crystal, BL038, which was observed not to crystallize, has a glass transition at 215 K and a nematic to isotropic transition at 380 K. Samples aged below the glass transition at various temperatures T _a, exhibited an endotherm at the transition which developed with extent of ageing time, t _a. We attribute this endotherm to the relaxation of the glass towards the equilibrium liquid. The progress of the relaxation process was measured using differential scanning calorimetry. On subsequent reheating, the aged glass showed an apparent shift in the glass transition to higher temperatures. The endotherm was used to define the extent of enthalpic relaxation and the maximum value observed was found to increase initially then decrease, with the extent of undercooling from the glass transition temperature, Δ T, passing through a maximum for a Δ T = 15 K. From the temperature dependence of the relaxation times, an apparent activation enthalpy for the relaxation process of 85 ± 10 kJ mol^-1 was determined. The small value of the activation enthalpy compared with that found in the ageing of polymers reflects differences in the molecular species involved in relaxation processes.     

Photon correlation spectroscopy of bulk poly(n-hexyl methacrylate) near the glass transition

Slowly relaxing longitudinal density fluctuations in an optically perfect sample of bulk poly(n-hexyl methacrylate) (PHMA) have been studied by photon correlation spectroscopy in the temperature range 10–36°C. The glass transition temperature for this sample was measured to be T_g = −3°C by differential scanning calorimetry. The optical purity of the sample was verified by Rayleigh-Brillouin spectroscopy and the Landau-Placzek ratio was observed to be 2.3 at 25°C. Light-scattering relaxation functions were obtained over the time range 10⁻⁶-1 s. The shape of the relaxation functions broadened as the temperature was lowered towards the glass transition. Quantitative analysis of the results was carried out using the Kohlrausch-Williams-Watts (KWW) function to obtain average relaxation times, 〈τ〉, and width parameters, β. The width parameter decreased from 0.43 to 0.21 over the temperature interval, as suggested by visual inspection. Average relaxation times shifted with temperature in a manner consistent with previous mechanical studies of the primary glass-rubber relaxation in PHMA. The relaxation functions were also analyzed in terms of a distribution of relaxation rates, G(Γ). The calculated distributions were unimodal at all temperatures. The average relaxation times obtained from G(Γ) were in agreement with the KWW analysis, and the shape of the distribution broadened as the sample was cooled. The rate at which G(Γ) displayed a maximum correlated well with the corresponding frequency of maximum dielectric loss for PHMA. The temperature dependence of these two quantities could be reproduced with an Arrhenius activation energy of 21 Kcal/mol. A consistent picture of the molecular dynamics of PHMA near the glass transition requires a strong secondary relaxation process with a different temperature dependence from the primary glass-rubber relaxation. The present results suggest that the behavior of PHMA is similar to the other poly(alkyl methacrylates). © 1996 John Wiley & Sons, Inc.     

Frequency and molecular-mass-dependent nonexponential proton NMR relaxation in polymer melts

A theoretical treatment of the nonexponential relaxation behavior of the different proton nuclear magnetic resonance (NMR) relaxation processes in polymer melts is presented. Formulas are derived for a three-component model given by two versions and a homogeneous distribution of correlation times. The theoretical results were tested with measurements of T₁, T_2e, and T₂ as functions of frequency and molecular mass in linear fractionated polyethylene samples. While the T₁ relaxation always yields exponential magnetization decays, the T_2e and T₂ measurements show biexponential relaxation behavior. From the calculations it was found that the correlation time of the local motion is independent of the molecular mass, whereas the correlation time of the slowest motional process increases with M^2.8_w for the three-component model and with M^2.2_w for the distribution of correlation times, respectively. © 1992 John Wiley & Sons, Inc.     

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.     

High-Resolution Solid-State NMR Characterization of Morphology in Annealed Polylactic Acid

Single-pulse ¹³C NMR spectra and spin-lattice relaxation times T₁(¹H), detected indirectly via ¹³C carbons, and T₁(¹³C) were measured at 31°C for virgin pelletized and annealed polylactic acid (PLA) samples using the magic-angle spinning technique. The structural relaxation resulting in more regular crystals with narrower conformation distribution and increase in the lamellae thickness and crystallinity brought about by annealing at 100°C was deduced from the narrowing of the ¹³C NMR lines and proton spin-lattice relaxation times T₁(¹H). The spin-lattice relaxation times T₁(¹³C) related to the respective carbons of the α-polymorph of PLA are also discussed in the study.     

Molecular dynamics study of the ferroelectric liquid crystal CI IPNOC by proton spin-lattice relaxation

Abstract

Proton spin-lattice relaxation studies were carried out in the S_A and S*_C phases of the liquid crystal CI IPNOC using both conventional and fast field cycling NMR techniques. T ₁ dispersion curves were obtained at two different temperatures for each mesophase covering frequencies from 10² to 3 × 10⁸ Hz. In both mesophases the T ₁ data can be described assuming the presence of three different relaxation mechanisms, namely local molecular rotations, molecular self-diffusion and collective motions. The self-diffusion constant D ₁ was evaluated for several temperatures and the activation energy associated with the diffusion process was obtained. The expected contribution of the soft-mode for the spin-lattice relaxation could not be separated from the contribution of other collective motions. The correlation times associated with the rotations around the molecular long axis and with the fluctuations of this axis were evaluated for both the S_A and the S*_C phases.     

Evidence of two relaxation processes in the photon correlation spectra of poly(methyl methacrylate) above Tg

Photon correlation functions of a high-molecular-weight PMMA (M_w = 1.06 × 10⁷, M_n = 2.2 × 10⁶, T_g = 103°C) have been studied in the temperature range 98 ? 149°C. In contrast to previous results, two relaxation modes are observed in relaxation functions. The observed relaxation functions of PMMA are analyzed for the first time in terms of a continuous spectrum representing the distribution of retardation times. Using a modified computer program originally developed by Provencher, we have computed the spectrum of retardation times at various temperatures. The appearance of two distinct relaxation modes is clearly evident in the distribution of the retardation times and in the time correlation functions below 123°C.     

Some structural aspects in binary aqueous mixtures of simple amides from rotational molecular motions

Nuclear magnetic relaxation rates of²D and¹⁴N in binary aqueous mixtures of formamide,N-methylformamide (NMF), andN,N-dimethylformamide (DMF) are reported as a function of the mixture composition. From these intramolecular quadrupolar relaxation data separate rotational correlation times for the two components of the mixture can be determined. The relative variation of the single correlation time as a function of the composition is interpreted in terms of structural changes caused by hydrogen bonding and hydrophobic effects. The results also clearly reflect the expected characteristic variation of these effects on the rotational molecular motions in going from formamide to NMF and DMF. The maximum correlation time retardation of DMF in the aqueous mixture is compared with those of other hydrophobic solvents. A correlation between this maximum retardation and the excess enthalpy of mixing of hydrophobic solvents in aqueous solution can be established graphically.     

Correlation between Dynamic Heterogeneity and Local Structure in a Room‐Temperature Ionic Liquid: A Molecular Dynamics Study of [bmim][PF6]

The complex dynamics of a room‐temperature ionic liquid, 1‐n‐butyl‐3‐methylimidazolium hexafluorophosphate ([bmim][PF₆]), is studied using equilibrium classical molecular dynamics simulations in the temperature range of 250–450 K. The activation energies for the self‐diffusion of ions are around 30–34 kJ mol^?1, with that of the anion a little higher than that for the cation. The electrical conductivity of the liquid is calculated and good agreement with experiments is obtained. Structural relaxation is studied through the decay of coherent (total density–density correlation) and incoherent (self part of density–density correlation) intermediate scattering functions over a range of temperatures and wave vectors relevant to the system. The relaxation data are used to identify and characterize two processes, α and β. The dependence of the two relaxation times on temperature and wave vector is obtained. The dynamical heterogeneity of the ions determined through the non‐Gaussian parameter indicates the motion of the cation to be more heterogeneous than that of the anion. The faster ones among the cations are coordinated to faster anions, while slower cations are surrounded predominantly by slower anions. Thus, the dynamical heterogeneity in this ionic liquid is shown to have structural signatures.     

Photon correlation spectroscopy of poly(methyl methacrylate) near the glass transition

Poly(methyl methacrylate) (PMMA) has been studied by photon correlation spectroscopy in the temperature range 120–150°C. The relaxation functions for longitudinal density fluctuations were determined and analyzed using the empirical function ?(t) = exp[?(t/τ)^β]. The average relaxation times were calculated for each temperature and compared to mechanical and dielectric relaxation data. The agreement between the various techniques for the primary glass–rubber relaxation was good. The relaxation function observed by light scattering became increasingly broad as the temperature was lowered. This is similar to the results reported previously for poly(ethyl methacrylate) (PEMA). In fact, the light-scattering relaxation function is dominated by the secondary relaxations in these two polymers. Nevertheless, the average relaxation time 〈τ〉 is dominated by the longest relaxation times associated with the primary glass–rubber relaxation.     

Water effect in the thermal and molecular dynamics behavior of poly(<Emphasis Type="Italic">L</Emphasis>-lactic acid)

A detailed dielectric characterization of the relaxation modes found in a poly(L-lactic acid), PLLA, film containing 0.4 mass% of water is provided. The sub-glass relaxation process is a superposition of two processes, one highly influenced by water with activation energy of 50 kJ mol^–1, and another one, with longer relaxation times and lower intensity having activation energy of 38 kJ mol^–1. Dried PLLA exhibits an abnormally broad secondary β-relaxation that probably corresponds to the superposition of multiple processes. Upon water sorption the strength of the more mobile process significantly increases being shifted to lower temperatures which allows the detection of the underlying process. The glass transition relaxation process is deviated to higher frequencies almost one decade due to the water plasticizing effect. The reported results show that small quantities of water may have a profound impact in the relaxational features in PLLA, which should be taken in account when considering the properties and performance of this system.     

Evidence of dynamic heterogeneity as obtained from dielectric and brillouin light-scattering studies of poly(n-hexylmethacrylate)

We report dielectric relaxation and Rayleigh-Brillouin spectroscopic measurements on the side chain polymer poly(n-hexylmethacrylate), PHMA (T_g = 268 K), exhibiting a broad glass transition region. The dielectric loss curves can be represented by single Havriliak-Negami functions in the temperature range of 260–450 K. The width of the distribution relaxation function is a decreasing function of temperature up to T = 333 K ≊ 1.24 × T_g and remains virtually constant above that temperature. This is interpreted as marking the merging of the α-process with a slow β-relaxation in agreement with the value of the cooperativity length associated with the α-mode. Hence above that temperature, the relaxation times confirm well to an Arrhenius temperature dependence. The hypersonic dispersion deduced from the Brillouin spectra (210–550 K) surprisingly peaks at temperatures near T_g which bears no relation to the main α-relaxation. This structural relaxation is rather associated with the side hexyl group motion showing striking resemblance with the hypersonic dispersion in molecular liquids. It is conceivable that the observed damping in PHMA is dynamically related to the internal plasticization effect of the hexyl group. © 1996 John Wiley & Sons, Inc.     

Effect of high hydrostatic pressure on the dielectric relaxation in a non-crystallizable monohydroxy alcohol in its supercooled liquid and glassy states

The complex relative permittivity of a non-crystallizable secondary alcohol, 5-methyl-2-hexanol, is measured over a wide range of temperatures and pressures up to 1750 MPa (17.5 kbar). The data at atmospheric pressure (P = 0.101 MPa) are analyzed in terms of three processes, and the results are in complete agreement with that of O. E. Kalinovskaya and J. K. Vij [J. Chem. Phys. 112, 3262 (2000)]. Process I is of the Debye type and process II is of the Davidson-Cole type, whereas process III is identified as the Johari-Goldstein relaxation process. For pressures of ～500 MPa and higher, processes I and II are seen to merge into each other to form a single dominant process which unambiguously cannot be resolved into more than one process. The dielectric relaxation strength of process I decreases slightly initially with pressure and when the two processes have merged at elevated pressures, the total relaxation strength increases with increase in pressure. Process III is better resolvable at higher pressures especially above T(g) in the supercooled liquid state for the reason that the separation in the time scales between the dominant and the JG relaxation process increases at elevated pressures. Surprisingly we find a change in the slope in the plot of log τ(JG) vs. 1/T for P = 1750 MPa. The results for the relaxation time of alcohols are compared with the Kirkwood correlation factor, g, and it is found that higher is the g, lower is the relaxation time for process I, and it is more of the Debye type. On a reduction in g brought about by an increase in pressure at lower temperatures, the dominant process becomes non-Debye though extensive hydrogen bonding is still present. The dielectric strength of the merged processes increases with increase in pressure. The values of the steepness index, m = |d log τ/d(T(g)/T)|(T = Tg) for processes I and II are different for P = 0.1 MPa. However the value of m, for the composite process, which is a merger of processes I and II, for P = 1750 MPa is almost the same for process II at P = 0.1 MPa. From the results of the activation volume, activation enthalpy, and a comparison of the relaxation times with the g factor, we conclude that both processes I and II are significantly affected by hydrogen bonding and both contribute to the structural relaxation.     

Ionic thermal current study of the α′ process in poly(hexamethylene adipamide)

The ionic thermoconductivity (ITC) method has been used to study the α′ transition in the polyamide \documentclass{article}\pagestyle{empty}\begin{document}$ {\rm \hbox{--}\rlap{--} [NH(CH}_{\rm 2} )_6 {\rm NH}\hbox{---} \rm CO(CH_2 )_4 {\rm CO\hbox{--}\rlap{--} ]}_{{\rm x}} $\end{document} (nylon 66). Depending on the thermal history of the sample, the maximum of the thermocurrent peak attributed to the α′ relaxation is found somewhere between ca. 45°C and ca. 66°C; on one heating, it shifts to higher temperatures. The high sensitivity and resolving power of the ITC method permit resolution of this peak into four elementary “pure” activated processes, with constant activation energies in the relevant temperature range. Each of the four corresponding relaxation times follows an Arrhenius law, with a well-defined characteristic temperature T₀ = 83°C at which all these relaxation times are equal. When this last result is interpreted in the light of Eyring's or Bauer's theory, it gives a linear relation between “apparent” activation entropy and activation enthalpy of the elementary processes. The characteristic temperature T₀ is independent of the thermal history of the sample, and the temperature shift of the thermocurrent maximum can be interpreted by the observed variation of the relative intensities of the elementary processes, without modification of their other characteristic features.