The kinetics of the structural relaxation process in PHEMA-silica nanocomposites based on an equation for the configurational entropy

The enthalpy relaxation of polymer-silica nanocomposites prepared by simultaneous polymerization of poly(2-hydroxyethyl methacrylate) (PHEMA) and tetraethyloxysilane, TEOS, a silica precursor, is investigated. Both the glass transition temperature, T_g, and the temperature interval of the glass transition, ΔT _g , increase as the silica content in the sample does. Structural relaxation experiments show that the temperature interval in which conformational motions take place broadens as the silica content in the hybrid increases. A phenomenological model based on the evolution of the configurational entropy during the structural relaxation process, the SC model, has been used for determining the temperature dependence of the relaxation times during the process. The results show an increase of the fragility of the polymer as the silica content increases, a feature that can be related to the broadening of the distribution of relaxation times characterized by the β parameter of the stretched exponential distribution. On another hand the silica content increase produces a significant change of the relaxation times in the glassy state.     

dielectric relaxation in VDF<Subscript>60</Subscript>/Tr<Subscript>40</Subscript> and VDF<Subscript>88</Subscript>/Te<Subscript>12</Subscript> polar copolymers embedded in porous glass matrices

The dielectric properties of composite materials prepared by embedding P(VDF₆₀/Tr₄₀) and P(VDF₈₈/Te₁₂) polar copolymers in porous glass matrices with a mean flow-through pore diameter of around 320 nm were investigated in the temperature range 200–450 K. Strong dielectric relaxation, the characteristic time of which conformed to the Williams-Landel-Ferry law, was observed in the vicinity of glass transition point T _g of an amorphous fraction of polymer inclusions. An increase (≈10 K) in the T _g temperature of the amorphous fraction of incorporated polymeric materials was detected.     

Evidence for ordered regions in poly(n-butyl)methacrylate from light-scattering studies

From light-scattering studies on polybutylmethacrylate, a polymeric glass, the variation of the velocity and attenuation of thermally excited hypersonic phonons with temperature has been measured. Measurement of the temperature dependence of the ratio of the intensity of the Rayleigh line to the Brillouin lines is interpreted as due to a configurational rearrangement within the glass above the glass transition temperature, T_g . Only light scattered from longitudinal phonons was observed. The distinct change in the temperature dependence of the velocity, attenuation and intensity ratio identified the glass transition.

For samples annealed well above T_g, T_g was found to be about 0°C from the light-scattering studies, 12°C from differential scanning calorimetry (DSC), and 20°C from refractive index measurements. For an unannealed sample the behaviour of the above parameters with temperature was found to be different. T_g for the unannealed sample was 14°C from light-scattering, 18°C from DSC and 20°C from index of refraction measurements.     

Phenomenological theory of structural relaxation based on a thermorheologically complex relaxation time distribution

The aim of this work is to explore the consequences on the kinetics of structural relaxation of considering a glass-forming system to consist of a series of small but macroscopic relaxing regions that evolve independently from each other towards equilibrium in the glassy state. The result of this assumption is a thermorheologically complex model. In this approach each relaxing zone has been assumed to follow the Scherer-Hodge model for structural relaxation (with the small modification of taking a linear dependence of configurational heat capacity with temperature). The model thus developed contains four fitting parameters. A least-squares search routine has been used to find the set of model parameters that fit simultaneously four DSC thermograms in PVAc after different thermal histories. The computersimulated curves are compared with those obtained with Scherer-Hodge model and the model proposed by Gómez and Monleón. The evolution of the relaxation times during cooling or heating scans and also during isothermal annealing below the glass transition has been analysed. It has been shown that the relaxation times distribution narrows in the glassy state with respect to equilibrium. Isothermal annealing causes this distribution to broaden during the process to finally attain in equilibrium the shape defined at temperatures above T _g .     

Revisiting the Dielectric Relaxation of Ethylene-Vinylacetate Copolymers: Influence of Microstructure

The dielectric relaxation behavior of a series of ethylene-vinylacetate (EVA) copolymers was investigated by measuring the complex dielectric permittivity in a broad frequency and temperature range. Crystallinity of EVA copolymers was estimated by differential scanning calorimetry (DSC) and wide-angle X-ray scattering (WAXS). The shape of the higher temperature relaxation, appearing above the glass transition temperature T _g depends on the VA content. It was found that this relaxation was asymmetric for VA concentrations higher than 40 wt% and changed to a symmetric shape at lower VA values. Concurrently, as the VA content decreased, a major broadening of the relaxation over a wide frequency range was observed. It is found that the dielectric relaxation was preserved on going through the melting range of the semicrystalline samples, although it exhibited changes of its characteristic parameters that are typical for segmental relaxation appearing at T _g. This finding allows one to associate this relaxation to the segmental motions at T _g in the amorphous phase and not to the existence of interfacial regions.     

The Slow Molecular Mobility in Semicrystalline Poly(Ethylene Oxide)

The thermally stimulated depolarization current (TSDC) technique has been used to study the slow molecular mobility in the amorphous part of the semicrystalline polymer, poly(ethylene oxide) (PEO). Experiments were carried out in the temperature range that includes the glassy state, the glass transformation region and the rubber state. The dipole moments in the polymeric main chain originated a broad and low intensity secondary relaxation in the temperature region from ?130°C up to the glass transition region; the activation energy of the motional modes of this secondary relaxation was in the range between 35 and 100 kJ mol^?1. The glass transition temperature of the PEO, provided by the TSDC technique, was T_g = ?53°C, and the fragility index was found to be m = 43. A strong relaxation above T_g was observed, whose molecular origin was discussed. The thermal behavior of the PEO was also characterized by differential scanning calorimetry.     

Slow relaxation experiments in disordered charge and spin density waves: collective dynamics of randomly distributed solitons

We show that the dynamics of disordered charge density waves (CDWs) and spin density waves (SDWs) is a collective phenomenon. The very low temperature specific heat relaxation experiments are characterized by: (i) “interrupted” ageing (meaning that there is a maximal relaxation time); and (ii) a broad power-law spectrum of relaxation times which is the signature of a collective phenomenon. We propose a random energy model that can reproduce these two observations and from which it is possible to obtain an estimate of the glass cross-over temperature (typically T _g≃ 100-200 mK). The broad relaxation time spectrum can also be obtained from the solutions of two microscopic models involving randomly distributed solitons. The collective behavior is similar to domain growth dynamics in the presence of disorder and can be described by the dynamical renormalization group that was proposed recently for the one dimensional random field Ising model [D.S. Fisher, P. Le Doussal, C. Monthus, Phys. Rev. Lett. 80, 3539 (1998)]. The typical relaxation time scales like ∼τexp(T _g/T). The glass cross-over temperature T_g related to correlations among solitons is equal to the average energy barrier and scales like T _g∼ 2xξΔ. x is the concentration of defects, ξ the correlation length of the CDW or SDW and Δ the charge or spin gap. Received 12 December 2001     

Measuring surface and bulk relaxation in glassy polymers

We present a comprehensive study of gold nanoparticle embedding into polystyrene (PS) surfaces at temperatures ranging from T _g + 8 K to T _g − 83 K and times as long as 10⁵ minutes. This range in times and temperatures allows the first concurrent observation of and differentiation between surface and bulk behavior in the 20nm region nearest the free surface of the polymer film. Of particular importance is the temperature region near the bulk glass transition temperature where both surface and bulk processes can be measured. The results indicate that for the case of PS, enhanced surface mobility only exists at temperatures near or below the bulk T _g value. The surface relaxation times are only weakly temperature dependent and near T _g , the enhanced mobility extends less than 10nm into the bulk of the film. The results suggest that both the concept of a “surface glass transition” and the use of glass transition temperatures to measure local mobility near interfaces may not universally apply to all polymers. The results can also be used to make a quantitative connection to molecular dynamics simulations of polymer films and surfaces.     

Is the configurational entropic model able to predict the final equilibrium state reached by Se glasses after very long ageing durations?

This work compares the equilibrium states reached by glassy selenium (g-Se) after several ageing durations at temperatures lower than the glass transition temperature T _g, with the forecasts given by the configurational entropic model. The comparison is carried out through experimental data collected both on glassy samples after short-term ageing and on glassy samples older than 20?years, kept at room temperature. It is shown that the configurational entropic model is not able to describe the behaviour of g-Se, both at short- and long-ageing terms with the same set of fitting parameters. For short-term ageing, the forecasts given by the entropic model are in good agreement with the experimental data; the hypothesis that the heat capacities corresponding to the equilibrium state and to the state extrapolated from the liquid differ by an amount δ is therefore properly justified. For long-term ageing, the amount δ vanishes and the assumption does not hold any longer. Indeed, experimental results support the idea that at least two separate mechanisms of relaxation coexist in the physical ageing of g-Se, one with very fast kinetics and the other with much slower kinetics.     

Influence of stress and temperature on damping behavior of amorphous Pd77.5Cu6.0Si16.5 below Tg

In this work we analyzed the mechanical damping behavior of amorphous Pd_77.5Cu_6.0Si_16.5 below the glass transition temperature (T _g) with creep/recovery measurements. Here a correlation between temperature stimulation and external stress is found in an exponential, multiplicative way. This demonstrates that not only is the yield stress of the material influenced by temperature variation (mechanical melting) but also the secondary relaxation is modified under stress and temperature.     

Initial stage of physical ageing in network glasses

An atomistic view on Johari–Goldstein secondary β-relaxation processes responsible for structural relaxation far below the glass transition temperature (T_g ) in network glasses is developed for the archetypal chalcogenide glass, As₂₀Se₈₀, using positron annihilation lifetime, differential scanning calorimetry, Raman scattering and nuclear magnetic resonance techniques. Increased density fluctuations are shown to be responsible for the initial stage of physical ageing in these materials at the temperatures below T_g . They are correlated with changes in thermodynamic parameters of structural relaxation through the glass-to-supercooled liquid transition interval. General shrinkage, occurred during the next stage of physical ageing, is shown to be determined by the ability of system to release these redundant open volumes from the glass bulk through the densification process of glass network.     

Behaviour of ultrasonic velocities in amorphous Se90Ge10 and Se85Ge15 alloys near their glass transition

Precise measurements of 10 MHz frequency longitudinal and shear wave velocities are reported in amorphous SeGe alloys near their glass transition temperature T _g . There is a sharp decrease of the velocities near T _g , but the reduction in velocities appears smaller than expected.     

Configurational Entropy Relaxation of Silica Glass—Molecular Dynamics Simulations

Vitreous silica was modelled using molecular dynamics (MD). The glass structure was transferred into an undirected graph and decomposed into disjoint structural units that were ideally mixed to calculate the configurational entropy. The Debye relaxation model was suggested to simulate the evolution of entropy during the cooling of the system. It was found that the relaxation of the configurational entropy of MD corresponds to the effective cooling rate of 6.3 × 10⁶ Ks⁻¹ and its extrapolation to 0.33 Ks⁻¹ mimics the glass transition with T_g; close to the experimental value. Debye relaxation correctly describes the observed MD evolution of configurational entropy and explains the existence of freezing-in temperature and the shape of the curve in the transition region.     

Effect of structural relaxation on low energy excitations in amorphous Zr x Cu1−x

We report on an investigation of the liquid-quenched metallic glass Zr _x Cu_1?x (0.6≦x≦0.74) subjected to heat treatments below the glass transition temperatureT _g. Annealing temperatures up to 200°C (<0.8T _g) were chosen as to achieve topological relaxation only. The superconducting transition temperaturesT _c are lowered, as already observed for other metallic glasses. Low temperature measurements of the thermal conductivity (0.5 K≦T≦15 K) and of the specific heat (0.1 K≦T≦3 K) were carried out in order to determine the effect of structural relaxation on the low energy configurational excitations characteristic of the amorphous state. The annealed samples show no detectable (<20%) change in the specific heat forT?T _c, but an increase of the thermal conductivity by a factor of 2 forT?T _c is observed. Within the tunneling model of two level systems (TLS) for the low energy excitations, this behavior can be qualitatively understood in terms of a change of the TLS relaxation time distribution upon annealing. This distribution differs from that of the commonly used standard tunneling model. The change of the phonon scattering by TLS directly observed forT?T_c is largely responsible for the enhancement of the thermal conductivity found also aboveT _c.     

Segmental Dynamics in net -poly(methyl methacrylate)- co -poly(n-butyl acrylate) Copolymer Networks

Dynamic mechanical spectroscopy and differential scanning calorimetry investigations of segmental dynamics are reported for net-poly(methyl methacrylate)-co-poly(n-butyl acrylate) copolymer networks. Three characteristic temperatures, namely, Vogel (T_∞), glass transition (T _g ), and crossover (T _c ), were used to define cooperativity range and a new reduced temperature parameter (Solidness, S). The results showed that broadness of the α -dispersion (glass transition) and cooperativity length scale at the glass transition temperature decreased with increasing butyl acrylate content and T _g -scaled temperature dependence of the relaxation time (fragility). However, the cooperativity range (T _c –T_∞), decreased with increasing fragility index. Furthermore, the solidness at T _g (S(T _g )) was nearly independent of chemical structure of the samples. Finally, a correlation was found between two measures of cooperativity length scale in the glass transition region, namely, average volume of cooperatively rearranging regions, V _CRR , and the number of basic units in an act of rearrangement in the glass transition region, Z(T _g ), determined from two completely independent experimental techniques.     

The determination of the glass transition temperature by thermally stimulated depolarization currents. Comparison with the performance of other techniques

Several experimental techniques are currently used for the determination of the glass transition temperature, T_g. Thermally stimulated depolarization currents (TSDC) is a thermal analysis technique whose experimental results display a very clean glass transition signature and that, nevertheless, is seldom used as a technique for T_g determination. In the present work we explain how to get the glass transition temperature from TSDC data, and we compare the values obtained for a vast number of glass forming systems (with T_gs in a wide range between ?145 and +180 °C and fragilities between m = 15 and m = 100), with the values obtained by differential scanning calorimetry (DSC) and dielectric relaxation spectroscopy (DRS). We conclude that the T_g determination by TSDC is direct, accurate and reproducible and that the obtained values correlate very well with those obtained by DSC and DRS. This general survey thus suggests TSDC as a valuable alternative technique for determining T_g.     

Amorphous linear polyethylene: Annealing effects

The effect of annealing amorphous linear polyethylene films prepared by an improved ultraquenching technique at temperatures just below and above a dynamic mechanical relaxation peak (torsion braid) observed at ∽190K has been characterized by electron microscopy and torsion braid analysis. Based on the results described, this peak is believed related to the lower glass transition temperature T_g(L), the T_g of wholly amorphous linear polyethylene, whereas the β peak at 260K is T_g (upper). Annealing just below T_g (L) results in a growth in size of the nodules observed in the as-quenched samples, whereas annealing above T_g (L) can result in the growth of single crystal-like structures, spherulites, and shish-kebobs. Storage of the crystallized samples at room temperatures results in a decrease in size of the relaxation peak during subsequent torsion braid spectroscopy measurements. The results indicate significant amounts of molecular motion can occur during crystallization even at T_g.     

Molecular dynamics in thin films of isotactic poly(methyl methacrylate)

The molecular dynamics in thin films (18 nm-137 nm) of isotactic poly(methyl methacrylate) (i-PMMA) of two molecular weights embedded between aluminium electrodes are measured by means of dielectric spectroscopy in the frequency range from 50 mHz to 10 MHz at temperatures between 273 K and 392 K. The observed dynamics is characterized by two relaxation processes: the dynamic glass transition (α-relaxation) and a (local) secondary β-relaxation. While the latter does not depend on the dimensions of the sample, the dynamic glass transition becomes faster (≤2 decades) with decreasing film thickness. This results in a shift of the glass transition temperature T _g to lower values compared to the bulk. With decreasing film thickness a broadening of the relaxation time distribution and a decrease of the dielectric strength is observed for the α-relaxation. This enables to deduce a model based on immobilized boundary layers and on a region displaying a dynamics faster than in the bulk. Additionally, T _g was determined by temperature-dependent ellipsometric measurements of the thickness of films prepared on silica. These measurements yield a gradual increase of T _g with decreasing film thickness. The findings concerning the different thickness dependences of T _g are explained by changes of the interaction between the polymer and the substrates. A quantitative analysis of the T _g shifts incorporates recently developed models to describe the glass transition in thin polymer films. Received 12 August 2001 and Received in final form 16 November 2001     

Physical ageing in Se94Sn6 glass induced by gamma irradiation

A differential scanning calorimeter (DSC) has been used to monitor the influence of high-energy Co⁶⁰ gamma-irradiation on physical ageing in Se₉₆Sn₄ glass. It is observed that the relaxation process in the studied glass is slow after 1 and 3 years of natural storage, and can be highly accelerated by γ-irradiation. The glass transition temperature T_g and the endothermic peak area, which is directly related to the relaxation enthalpy Δh, were found to exhibit a remarkable change after irradiation and also during an additional natural storage for 6 months and 1 year of the irradiated Se₉₆Sn₄ glass. T_g value of γ-irradiated glass increases by 12 K; meanwhile, that of additional 6-months- and 1-year-stored glass T_g increases by 19 and 20 K in comparison to its counterpart of 1-year-aged non-irradiated sample. The same trend is also observed for Δh, which becomes 2.33, 3.61 and 3.65 times that of the 1-year-aged non-irradiated case, respectively, for γ-irradiated, additional 6-months- and 1-year-stored glass. These indications reveal that γ-irradiation activates the relaxation of the glass towards a state thermodynamically close to the equilibrium super-cooled liquid state.     

Effects of thermal and mechanical history on the viscoelastic properties of rigid poly(vinyl Chloride)

The effects of processing variables on the solid state properties of rigid PVC were studied by evaluating dynamic mechanical and tensile properties for thin film specimens of two different resins. The dynamic measurements were performed over the temperature range ?1]60 to 85°C, encompassing both the low temperature β transition and above ambient a transition (T_g). Engineering tensile strengths and energies to fracture were obtained at ambient conditions for several rates of elongation. Test specimens were prepared by solvent casting and compression molding techniques and subsequently were subjected to various thermal-mechanical histories. The results obtained were similar for both types of specimens and are described below. The various thermal histories considered include: (1) quick quenching from 225°C (samples referred to as “untreated”); (2) very slow (equilibrium) cooling after annealing at T_g; (3) quick quenching from T_g. In addition, the effects of frozen stresses were examined by systematically varying the stresses imposed on samples during the cooling processes 2 and 3. Increasing the load level imposed on specimens during equilibrium cooling resulted in enhancements of the β transition loss dispersion and tensile yield strength. Changes in loading during process 3, however, had little effect on the cooled specimens. But process 3 does alter the relaxation spectrum below T_g so that additional molecular relaxation is induced between T_β and T_α as much as 45°C below the a transition. The anomalous tan δ dispersions thus produced are accompanied by diminished tensile yield strengths and greatly increased energies to fracture. The most extreme case was encountered for the “untreated” specimens which were rapidly quenched from 225°C. The loss tangent data indicate remarkable differences in the region between T_β and T_α. When comparing the dynamic mechanical data with the fracture energy results for the same samples we note that increases in the intensity of the T < T_g anomalous dispersion correlate with increasing energies to fracture. On the other hand, the β transition intensity does not directly correlate. One molecular model which is consistent with these observations assumes that elongation induces a dilation of the polymer. Since most polymers possess Poisson ratios less than 0.5, the dilation will create extra internal volume (including free volume) in the polymer network. The increase in internal volume as elongation proceeds has the net effect of shifting the conditions of testing toward higher temperatures on a molecular relaxation scale permitting a higher level of molecular mobility at ambient conditions. As a sample continues to elongate one of two consequences is encountered: the imposed deformation cannot be accommodated by the available molecular mobility and the specimen fractures; or the deformation results in dilation to the extent that the response properties are shifted into a region of the relaxation spectrum where molecular mobility is sufficient for the specimen to accommodate the imposed deformation and yielding occurs. Yielding is expected if the effective temperature shifts as far as T_g before the sample fractures. In a case where there are additional molecular relaxation possibilities prior to the a transition, such as those in the anomalous dispersion region between T_β and T_α, sufficient dilation for yielding will be encountered before the normal T_g is reached. The anomalous T < T_g relaxation process thus tends to promote increased elongation and higher energies to fracture in PVC.