Calorimetric and Dielectric Investigations of Glass Transition in Intermediate Glass-forming Liquid

The calorimetric glass transition and dielectric dynamics of -relaxation in propylene glycol (PG) and its five oligomers (polypropylene glycol, PPG) have been investigated by the modulated differential scanning calorimetry (MDSC) and the broadband dielectric spectroscopy. From the temperature dependence of heat capacity of PPGs, it is clarified that the glass transition temperature (T_g) and the glass transition region are affected by the heating rate. The kinetic changes of PG and PPGs near T_g strongly depend on the underlying heating rate. With increasing the molecular mass of PPGs, the fragility derived from the relaxation time against temperature also increases. The PG monomer is stronger than its oligomers, PPGs, because of the larger number density of the —OH end group which tends to construct the intermolecular network structure. Adam-Gibbs (AG) theory could still hold for MDSC results due to the fact that the dielectric relaxation time can be related to the configurational entropy.This revised version was published online in November 2005 with corrections to the Cover Date.     

Simulation of the glass transition and physical ageing

A kinetic model simulating the glass transition and enthalpic relaxation in poly(3-hydroxybutyrate) is introduced. The model is based on the concept that enthalpic relaxation or physical ageing is a continuation of the glass forming process and uses the KWW function to describe the glass formation process and the subsequent ageing of the glass. Non-linearity is introduced by incorporating a dependence of the relaxation time on the fictive temperature. The effects of non-linearity on the distribution of relaxation times and the physical ageing process are investigated together with the development of the endothermic ageing peak at the glass transition with increasing extents of ageing.     

Broadband dielectric study of the glass transition in poly(ethyleneglycol)-water mixture

We performed broadband dielectric measurements of a polyethyleneglycol-water mixture in the frequency range between 10 GHz and 1 microHz and the temperature range between 300 and 133 K. One relaxation process is observed throughout the whole temperature range. The temperature dependence of the relaxation time clearly obeys the Vogel-Fulcher law above 183 K, and the Arrhenius law below 183 K. This observed relaxation process is the secondary process, and the primary process related to the glass transition is masked by the low-frequency ionic contribution below 183 K. The glass transition concerned with the masked primary process leads to the Vogel-Fulcher to Arrhenius transition of the secondary process.     

Slow dynamics of supercooled m-toluidine investigated by mechanical spectroscopy

Dynamics of supercooled m-toluidine close to the glass transition have been investigated by dynamic shear modulus measurements and stress relaxation experiments. The viscoelastic response of this material follows time-temperature-superposition in the temperature range investigated. Comparison with results at ultrasonic frequencies suggests the existence of a secondary relaxation. A change of the temperature dependent viscosity from a Vogel-Fulcher-Tammann behavior to another regime at low temperatures is also found. Compared to most inorganic glass formers, the viscosity of m-toluidine at the glass transition is approximately two orders of magnitude lower. The shear relaxation times are characterized by the same temperature dependence as the viscosity. They are in reasonable agreement with the results of previous ultrasonic measurements. The conclusions of the present work agree with recent results obtained by high resolution dielectric spectroscopy.     

Dielectric and mechanical relaxation processes in methyl acrylate/tri-ethyleneglycol dimethacrylate copolymer networks

The dielectric properties of methylacrylate (MA)/tri-ethyleneglycol dimethacrylate (TrEGDMA) copolymers at different compositions, ranging from 0 to 100, were measured between −120 and 150 °C over the frequency range 0.1 Hz-1 MHz. In the given frequency range, three relaxation processes were detected by dielectric relaxation spectroscopy in homo poly-TrEGDMA and copolymers: the α process associated with the glass transition, and two secondary processes due to localized mobility. In PMA only one secondary process was observed besides the alpha relaxation process. The influence of copolymerization going from PMA, monofunctional softer component with a glass transition determined calorimetrically as 284 K, to poly-TrEGDMA, higher glass transition component, bifunctional, that also forms a dense network due to cross linking, reflects mainly in the alpha process that shifts to higher temperatures and becomes broader. The raise and broadening in the glass transition with TrEGDMA increase was also observed by dynamic mechanical thermal analysis and differential scanning calorimetry. The glass transition temperature of poly-TrEGDMA was not detected calorimetrically but a value of 429 K was estimated from the best fit of the Fox equation. In what concerns the secondary relaxation process detected in poly-TrEGDMA and copolymers at the lowest temperatures, it is related with local twisting motions of ethyleneglycol moieties, being designated as γ relaxation, while the process detected in the medium temperature range is associated with the rotation of the carboxylic groups as in poly(alkyl methacrylates), designated as β relaxation. This process is detected at much lower temperatures in homo PMA in the same temperature region than the above mentioned γ relaxation. The copolymerization influences mainly the α process while the γ process remains almost unaffected in copolymers relative to homo poly-TrEGDMA. The β process is largely determined by the presence o the tri-ethylene glycol dimethacrylate monomeric units even in copolymers with the lowest TrEGDMA content.     

Molecular mobility of substituted poly(p-phenylenes) characterized by a range of polymer relaxation techniques

The free volume and related mobility properties of substituted poly(p-phenylene) polymers are examined. The techniques used range from positron annihilation, dielectric relaxation, and dynamic mechanical spectroscopy to thermally stimulated currents. Fractional free volume is determined for the samples with different substituted side groups and related to the glass transition temperature. Bulkier groups lead to a greater fractional free volume and lower glass transition temperatures. Comparison of molecular relaxation times using the different characterization techniques demonstrates that there is strong coupling between motion of the main chain and the side groups, on which the dipoles reside. Intermolecular coupling between the main chains at the primary relaxation is shown in this work to be related to the nature of the side chains and resultant free volume, as are the temperature locations of local, secondary relaxations. A qualitative model describing the effect of regiochemistry on the motions and packing of these materials is also proposed. © 1998 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 36: 1465–1481, 1998     

A simple model of entropy relaxation for explaining effective activation energy behavior below the glass transition temperature

Strong changes in relaxation rates observed at the glass transition region are frequently explained in terms of a physical singularity of the molecular motions. We show that the unexpected trends and values for activation energy and preexponential factor of the relaxation time tau, obtained at the glass transition from the analysis of the thermally stimulated current signal, result from the use of the Arrhenius law for treating the experimental data obtained in nonstationary experimental conditions. We then demonstrate that a simple model of structural relaxation based on a time dependent configurational entropy and Adam-Gibbs relaxation time is sufficient to explain the experimental behavior, without invoking a kinetic singularity at the glass transition region. The pronounced variation of the effective activation energy appears as a dynamic signature of entropy relaxation that governs the change of relaxation time in nonstationary conditions. A connection is demonstrated between the peak of apparent activation energy measured in nonequilibrium dielectric techniques, with the overshoot of the dynamic specific heat that is obtained in calorimetry techniques.     

The slow molecular mobility in amorphous trehalose.

The molecular mobility in amorphous trehalose is studied by thermally stimulated depolarisation currents (TSDC). The effect of aging on the sub-T(g) motional processes was analysed during annealing at a given aging temperature, some degrees below the calorimetric glass transition temperature T(g)=115 degrees C. The features of different motional components of the secondary relaxation are monitored as a function of time as the glass structurally relaxes on aging. The faster components of the secondary relaxation are negligibly dependent on aging and may be ascribed to intramolecular modes of motion, while the slower motional modes show a significant dependence on aging consisting of some kind of local motions with some intermolecular nature. The dielectric strength of this relaxation decreases with increasing aging time, and there is no evidence for any modification with aging of the relaxation time of this local mobility. The TSDC study of the molecular mobility of amorphous trehalose in the temperature region of the glass transformation provides the unexpected result that no glass transition signal is observable in this temperature region.     

Toward a constitutive model for cure-dependent modulus of a high temperature epoxy during the cure

A constitutive model, based on Kohlrausch-Williams-Watts (KWW) equations, was developed to simulate the evolution of the dynamic relaxation modulus during the cure of a ‘high temperature’ epoxy. The basic assumption of the modelling methodology proposed is the equivalence of the mechanisms underlying the evolution of the glass transition temperature and the relaxation time shift during the cure, leading to the use of a common potential function. This assumption is verified by the comparison of normalized glass transition data and principal relaxation times, which have been found to follow a single master curve. Results show satisfactory agreement between experimental data and model prediction over the range of chemical conversion considered.     

Viscoelastic properties of sulfonated styrene ionomers

The solid-state viscoelastic properties of polystyrene containing randomly distributed groups of styrene-p-sodium sulfonate are studied and compared with the corresponding properties of copolymers of styrene and sodium methacrylate (S-NaMA). The viscoelastic behavior in the primary transition region of these two ionomers is very similar. As for the S-NaMA copolymers, it is proposed that sulfonated polystyrene is composed of ion-rich regions (clusters) immersed in a matrix of low ion concentration. Two peaks are observed in the plot of mechanical loss tangent versus temperature for the sulfonated material. The lower peak is assigned to the glass transition of the ion-poor matrix and the upper to the glass transition of the clustered regions. As for some other ionomers, the presence of ions is found to slow down the stress relaxation rate, giving a broad distribution of relaxation times. Above a certain ion concentration, the sulfonated polystyrenes are thermorheologically complex owing to the onset of a secondary relaxation mechanism associated with the ion-rich regions.     

Glass transition cooperativity from broad band heat capacity spectroscopy

Molecular dynamics is often studied by broad band dielectric spectroscopy (BDS) because of the wide dynamic range available and the large number of processes resulting in electrical dipole fluctuations and with that in a dielectrically detectable relaxation process. Calorimetry on the other hand is an effective analytical tool to characterize phase and glass transitions by its signatures in heat capacity. In the linear response scheme, heat capacity is considered as entropy compliance. Consequently, only processes significantly contributing to entropy fluctuations appear in calorimetric curves. The glass relaxation is a prominent example for such a process. Here, we present complex heat capacity at the dynamic glass transition (segmental relaxation) of polystyrene (PS) and poly(methyl methacrylate) (PMMA) in a dynamic range of 11 orders of magnitude, which is comparable to BDS. As one of the results, we determined the characteristic length scale of the corresponding fluctuations. The dynamic glass transition measured by calorimetry is finally compared to the cooling rate dependence of fictive temperature and BDS data. For PS, dielectric and calorimetric data are similar but for PMMA with its very strong secondary relaxation process some peculiarities are observed.     

Aging of the Johari-Goldstein relaxation in the glass-forming liquids sorbitol and xylitol

Employing frequency-dependent dielectric susceptibility we characterize the aging in two supercooled liquids, sorbitol and xylitol, below their calorimetric glass transition temperatures. In addition to the alpha relaxation that tracks the structural dynamics, the susceptibility of both liquids possesses a secondary Johari-Goldstein relaxation at higher frequencies. Following a quench through the glass transition, the susceptibility slowly approaches the equilibrium behavior. For both liquids, the magnitude of the Johari-Goldstein relaxation displays a dependence on the time since the quench, or aging time, that is quantitatively very similar to the age dependence of the alpha peak frequency. The Johari-Goldstein relaxation time remains constant during aging for sorbitol while it decreases slightly with age for xylitol. Hence, one cannot sensibly assign a fictive temperature to the Johari-Goldstein relaxation. This behavior contrasts with that of liquids lacking distinct Johari-Goldstein peaks for which the excess wing of the alpha peak tracks the main part of the peak during aging, enabling the assignment of a single fictive temperature to the entire spectrum. The aging behavior of the Johari-Goldstein relaxation time further calls into question the possibility that the relaxation time possesses stronger temperature dependence in equilibrium than is observed in the out-of-equilibrium state below the glass transition.     

木糖醇玻璃焓松弛的量热分析

为了考察木糖醇的玻璃化转变和焓松弛行为,寻求碳链长度对线性多元醇玻璃化转变和焓松弛行为的影响,利用差示扫描量热(DSC)技术测定了不同降温速率下木糖醇在玻璃化转变温度(Tg)前后的比热容(Cp),通过曲线拟合获得了TNM(Tool-Narayanaswamy-Moynihan)模型参数,并和其他多元醇类已有研究结果进行对照.结果表明,尽管TNM模型可以很好地重现不同降温速率体系的实验比热容数据,但模型参数并不是材料常数,而是和热历史有关,不同的降温速率对应不同的模型参数.指前因子(A)、非线性参数(x)和非指数参数(β)均随着降温速率的增加而降低,松弛活化焓(△h*)的变化趋势刚好相反.几种线性多元醇玻璃化转变和TNM模型参数的对照表明,玻璃化转变温度,松弛活化焓和动力学脆度(m)都随着烷基碳链长度的增加而增加.虽然非线性参数、非指数参数随碳链长度的增加有降低的趋势,但木糖醇展现出反常变化的情形.     

Estimating the reversing and non‐reversing heat flow from standard DSC curves in the glass transition region

A mathematical model for the total heat flow obtained in differential scanning calorimetry (DSC) experiments from polymers with enthalpic relaxation is proposed. It is limited to the glass transition and enthalpic relaxation range of temperature and to the cases where the enthalpic relaxation is the only non‐reversing process taking place. The model consists of a mixture of functions representing the heat capacity heat flow of the glassy and non‐glassy fractions, the glass transition progress and the enthalpic relaxation heat flow. Optimal fittings of the model were performed on the experimental total heat flow data, obtained from two thermoplastics with different aging times. Considering which functions of the mixture represent reversing and non‐reversing processes, the reversing and non‐reversing heat flows were also estimated. The estimated reversing and non‐reversing signals were compared with the ones obtained by modulation. On the whole a good match was found, which was even better considering that the estimates are not affected by the frequency effect of the modulated temperature DSC (MTDSC) measurements. The model assumes linear trends for the heat capacity heat flow of the glassy and non‐glassy structures. The glass transition progress is represented by a generalized logistic function and the enthalpic relaxation heat flow by the first derivative of another generalized logistic. It brings about a new approach to these phenomena, where the parameters of these functions represent the temperature at which each event is centered, the change of heat capacity (C_p) at the glass transition and the energy involved in the enthalpic recovery. Copyright © 2011 John Wiley & Sons, Ltd.     

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.     

Dielectric relaxation in polymeric solids Part 1. A new model for the interpretation of the shape of the dielectric relaxation function

A model is proposed which explains the shape of the dielectric relaxation function at the glass transition of polymers. The model is based on the idea that the molecular mobility at the glass transition is controlled by intra- and intermolecular interaction. In addition, a specific model for the local chain dynamics in amorphous polymer systems is used. According to the scaling hypothesis of molecular dynamics the model relates the high frequency dependence of the dielectric loss curve to the local chain dynamics and the low frequency dependence to the intermolecular correlation.     

Photon correlation spectroscopy of polymers in the glassy state

Photon correlation spectroscopy has proven to be a very useful technique for studying slowly relaxing density and optical anisotropy fluctuations in bulk polymers near the glass transition. When some of the fluctuations achieve relaxation times much longer than the typical averaging time for the intensity autocorrelation function (10⁴ s), the result must be treated in the partially heterodyned limit. Also, when the sample is near the glass transition but not at equilibrium the correlation function is not stationary in time because the system is relaxing as a whole toward the equilibrium state. The above effects are discussed theoretically and demonstrated experimentally in polystyrene as a function of temperature and pressure. Light scattering with coherent excitation also fluctuates in space as well as in time (as shown in the accompanying paper). The consequences of this effect are discussed. When most of the intensity is associated with fluctuations whose relaxation times are very long in polystyrene, there is still a broad relaxation function evident. This is characteristic of a secondary relaxation process.     

On the relaxation theory of glass transition in liquids

A method for calculating the constant in the main equation of glass transition (which relates the relxation time and the cooling rate near the glass transition temperature) with consideration given to the temperature dependence of the activation energy in this region is proposed. A modification of the main glass transition equation is considered. Application of this equation to the relaxation spectrometry of amorphous polymers and inorganic glasses is discussed.     

A contribution to the theory of the structural glass transition

The equations characterizing the temperature dependence of the mobility of molecules in the glass transition region are compared and analysed. A relationship between the parameters of the relaxation theory of the glass transition and the concept of free volume is established. The Williams-Landel-Ferry equation is treated in terms of the relaxation theory of glass transition.