Enthalpy relaxation and fragility in polychlorinated biphenyls

We employ temperature modulated DSC (TMDSC) to determine the dependence of the fictive temperature on cooling rate for a series of polychlorinated biphenyls (PCB). From the slopes of semi-logarithmic plots of cooling rate vs. fictive temperature, the latter normalized by the fictive temperature for an arbitrary cooling rate, we determine the enthalpic fragilities. Despite significant differences in glass transition temperature and chemical structure (specifically chlorine content), the PCB have the same fragility. The value of the fragility determined using TMDSC is consistent with the fragility previously determined using dielectric relaxation spectroscopy.     

Influence of heating and cooling rates on the glass transition temperature and the fragility parameter of sorbitol and fructose as measured by DSC

The glass transition temperatures of sorbitol and fructose were characterized by four points determined on DSC heating thermograms (onset, mid-point, peak and end-point), plus the limit fictive temperature. The variations of these temperature values, observed as functions of cooling and heating rates, were used to determine the fragility parameter, as defined by Angell [1] to characterize the temperature dependence of the dynamic behavior of glass-forming liquids in the temperature range above the glass transition. The apparent activation energy values, determined for the different temperatures studied, were similar for fructose and sorbitol. These values were compared to data obtained from other techniques, such as mechanical spectroscopy. The variations of the apparent activation values, observed in experiments involving cooling and heating at the same rate, slow cooling followed by rate-heating, or rate-cooling followed by fast heating, were explained by aging effects occurring during the heating step.     

On some features of glass transition in amorphous substances

In Bartenev’s well-known approach to determining the dependence of glass-transition temperature on melt cooling rate, it was proposed to take into account the temperature dependence of the activation energy of the liquid-to-glass transition. The physical meaning of parameters of the obtained equation is discussed.     

Tuning polymer melt fragility with antiplasticizer additives

A polymer-diluent model exhibiting antiplasticization has been developed and characterized by molecular dynamics simulations. Antiplasticizer molecules are shown to decrease the glass transition temperature Tg but to increase the elastic moduli of the polymeric material in the low-temperature glass state. Moreover, the addition of antiplasticizing particles renders the polymer melt a stronger glass-forming material as determined by changes in the characteristic temperatures of glass formation, the fragility parameter D from fits to the Vogel-Folcher-Tamman-Hesse equation, and through the observation of the temperature dependence of the size of cooperatively rearranging regions (strings) in each system. The length of the strings exhibits a weaker temperature dependence in the antiplasticized glass-forming system than in the more fragile pure polymer, consistent with the Adam-Gibbs model of glass formation. Unexpectedly, the strings become increasingly concentrated in the antiplasticizer particles upon cooling. Finally, we discuss several structural indicators of cooperative dynamics, and find that the dynamic propensity (local Debye-Waller factor p) does seem to provide a strong correlation with local molecular displacements at long times. The authors also consider maps of the propensity, and find that the antiplasticized system exhibits larger fluctuations over smaller length scales compared to the pure polymer.     

Fragility of glass-forming polymer liquids

The fragility of polymeric glass-forming liquids is calculated as a function of molecular structural parameters from a generalized entropy theory of polymer glass-formation that combines the Adam-Gibbs (AG) model for the rate of structural relaxation with the lattice cluster theory (LCT) for polymer melt thermodynamics. Our generalized entropy theory predicts the existence of distinct high and low temperature regimes of glass-formation that are separated by a thermodynamically well-defined crossover temperature T(I) at which the product of the configurational entropy and the temperature has an inflection point. Since the predicted temperature dependence of the configurational entropy and structural relaxation time are quite different in these temperature regimes, we introduce separate definitions of fragility for each regime. Experimentally established trends in the fragility of polymer melts with respect to variations in polymer microstructure and pressure are interpreted within our theory in terms of the accompanying changes in the chain packing efficiency.     

Universal scaling, dynamic fragility, segmental relaxation, and vitrification in polymer melts

Our theory of dynamic barriers, slow relaxation, and the glass transition of polymers melts is numerically applied using parameters relevant to real materials. The numerical results are found to be in qualitative agreement with all the approximate analytic expressions previously derived with quantitative differences on the order of approximately 20-30% or much less. The analytic prediction of a universal temperature dependence of the alpha relaxation time, and its intimate connection with the idea of a nearly universal crossover time, is established. Inter-relations between the breadth of the deeply supercooled regime, two definitions of the dynamic fragility, and the magnitude of the fast local Arrhenius process at the glass transition temperature are demonstrated and system-specific limitations identified. A quantitative application to segmental relaxation over 16 orders of magnitude in a polyvinylacetate melt yields encouraging results regarding the accuracy of the theory. The theoretical relaxation time results are well fit by multiple empirical forms (generally containing an assumed singular aspect) using parameters consistent with experimental studies. No physical significance is ascribed to this finding, but it does provide additional support for the temperature dependence of the alpha relaxation process predicted by the theory.     

The effect of viscosity on the kinetics of redox reactions in highly viscous silicate liquids

The kinetics of the temperature dependent redox reaction between chromium and manganese (Cr(6+) + 3Mn(2+)?Cr(3+) + 3Mn(3+)) in highly viscous silicate melts were studied by UV-vis-NIR spectroscopy at temperatures in the range from 25 to 800 °C. At high temperatures, the reaction is in equilibrium. During cooling, it is continuously shifted to the right. During cooling from Tg+50 K to Tg (Tg = glass transition temperature), a further decrease in the Cr(6+) concentration was obtained which, however, was less pronounced if larger cooling rates were applied. In this temperature range, the kinetics plays an important part. Finally, at a certain temperatures below Tg, the equilibrium was frozen. The temperature, the equilibrium is frozen in decreases with decreasing cooling rate. It also decreases with the glass transition temperature of the respective composition. The activation energies increase with the activation energies of the viscosity of the respective melt. The redox reaction is controlled by the viscosity, i.e., the rearrangement of the glass network and not by diffusion. The reason is a drastic change in the coordination spheres during the reaction which leads to a high inner reorganization energy according to Marcus' Theory.     

Kinetics of structural relaxation of poly(ethylene terephthalate)

The results of an experimental study of the kinetics of structural relaxation of amorphous poly(ethylene terephthalate) are reported. Samples were prepared by ultraquenching the melt on rotating stainless-steel discs. Two types of measurements by differential scanning calorimetry were made: (1) the dependence of the “fictive” (or “structural”) temperature T_f(q^?) introduced by Tool, on the cooling rate q^? and (2) the dependence of the glass transition temperature T_g on the heating rate q⁺. In this way the value x = 0.47 was obtained for the dimensionless parameter proposed by Narayanaswamy.     

Coexistence of Immiscible Liquid Phases in the LaPO<Subscript>4</Subscript>–SiO<Subscript>2</Subscript>–NaF–Nb<Subscript>2</Subscript>O<Subscript>5</Subscript> System

It was determined that the system LaPO₄–SiO₂–NaF–Nb₂O₅ within the temperature range 850–1200°C has regions of immiscibility of liquid phases (silicate and phosphate–salt melts). The coexisting melts have contrast chemical and phase compositions and structural-textural features, because of which the methods for extracting rare-earth elements and niobium from these melts differ. The silicate melts form glass, whereas the phosphate–salt melts have high crystallization ability. The mutual solubility of the liquid phases does not exceed 5%. The components of the system are contrastively distributed between the silicate and phosphate–salt melts. A fraction of 95–97% of niobium is extracted into the silicate melt, and 93–95% of La and P is extracted into the phosphate–salt melt.     

The glass transition in polymer melts

This paper presents some results of a Monte Carlo simulation for the glass transition in two- and three-dimensional polymer melts. The melt was simulated by the bond-fluctuation model on a d-dimensional cubic lattice which was combined with a two-level hamiltonian favouring long bonds in order to generate a competition between the energetic and topological constraints in the system. This competition prevents crystallization and makes the melt freeze in an amorphous structure as soon as the internal relaxation times match the observation time of the simulation set by the cooling rate. The freezing point of the melt, i.e the glass transition temperature T_g, thus depends upon the cooling rate and additionally upon the chain length of the polymers. The dependence of the glass transition temperature on the cooling rate was closely analysed in three and that on the chain length in both two and three dimensions, resulting in a non-linear relationship between T_g and the logarithm of the cooling rate and a linear relationship between T_g and the inverse chain length, respectively. In addition to this behaviour of the melt during the cooling process an example for the relaxational properties of the three-dimensional model is provided by a quantitative analysis of the incoherent intermediate scattering function in the framework of the idealized mode coupling theory.     

Effect of the microphase separation on the electro-optical properties of isotropic melts of thermotropic liquid crystals

An analytical expression for the free energy of the isotropic melt of a mesogen under the conditions of the microphase separation is obtained on the basis of the Landau-de Gennes approach. The temperature dependence of the orientation and translational order parameters of the parameter characterizing microstructuring and the Kerr constant of a melt is calculated. The theoretical calculations are compared with the results from studying electric birefringence in isotropic melts of comb polymers. It is revealed that the break in the temperature dependence of the inverse Kerr constant can occur at the temperature of microphase separation for phase transitions of the first and second kind.     

Variable temperature 1H, 23Na,and 29Si MAS NMR studies on sodium silicate hydrates of composition Na2O · SiO2 · nH2O (n = 9, 6, 5): Local structure in crystals,melts, supercooled melts,and glasses

The local structure in crystals, melts, supercooled melts, and glasses of sodium silicate hydrates of composition Na₂O · SiO₂ · nH₂O (n = 9, 6, 5) is studied by variable temperature ¹H, ²³Na, and ²⁹Si MAS NMR spectroscopy. Detailed in situ investigations on the melting process of the crystalline materials reveal the importance of H₂O motion in the melting mechanism. Depending on the local coordination, crystallographically distinct Na sites show different behaviour during the melting process. Upon melting, the monomer silicate anions present in the crystalline hydrates undergo condensation reactions to oligomeric silicate anions. No recrystallization but glass formation occurs at low temperature if the melts were heated initially about 10 K above the melting point. In the glasses also oligomeric silicate anions are present with a preference for cyclotrimer species. In situ MAS NMR investigations and electric conductivity measurements of the melts, supercooled melts, and glasses suggest the distinction of three temperature ranges characterized by different local structure and dynamics of the sodium cations, water and silicate anions. These ranges comprise a glass and glass transition range A at low temperatures, an aggregation region B at intermediate temperatures, and a solution or electrolyte region C at high temperatures. In region B aggregation of sodium water complexes to hydrated polycation clusters is suggested, the dynamic behaviour of which is clearly different to that of the silicate anions, indicating that no long-lived contact ion pairs between sodium cations and silicate anions are formed.     

Structural relaxation of stacked ultrathin polystyrene films

The T_g depression and kinetic behavior of stacked polystyrene ultrathin films is investigated by differential scanning calorimetry (DSC) and compared with the behavior of bulk polystyrene. The fictive temperature (T_f) was measured as a function of cooling rate and as a function of aging time for aging temperatures below the nominal glass transition temperature (T_g). The stacked ultrathin films show enthalpy overshoots in DSC heating scans which are reduced in height but occur over a broader temperature range relative to the bulk response for a given change in fictive temperature. The cooling rate dependence of the limiting fictive temperature, T_f′, is also found to be higher for the stacked ultrathin film samples; the result is that the magnitude of the T_g depression between the ultrathin film sample and the bulk is inversely related to the cooling rate. We also find that the rate of physical aging of the stacked ultrathin films is comparable with the bulk when aging is performed at the same distance from T_g; however, when conducted at the same aging temperature, the ultrathin film samples show accelerated physical aging, that is, a shorter time is required to reach equilibrium for the thin films due to their depressed T_g values. The smaller distance from T_g also results in a reduced logarithmic aging rate for the thin films compared with the bulk, although this is not indicative of longer relaxation times. The DSC heating curves obtained as a function of cooling rate and aging history are modeled using the Tool-Narayanaswamy-Moynihan model of structural recovery; the stacked ultrathin film samples show lower β values than the bulk, consistent with a broader distribution of relaxation times. © 2008 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 46: 2741–2753, 2008     

基于位形熵模型的山梨醇玻璃焓松弛的量热分析

利用DSC技术考察了无定形山梨醇体系的焓松弛行为, 在10 K•min^－1的升温速率下测定了经历不同降温速率(0.5～20 K•min^－1)的山梨醇在玻璃化转变(T_g)前后的比热容[c_p(T)]. 利用基于位形熵演变的焓松弛现象学模型(GR模型)模拟了实验数据. 不论是否假设松弛过程存在一个亚稳极限态, 模型参数均能很好地重现经历不同热历史体系的升温c_p(T)曲线. 在物理意义明确的模型参数组中, 除了非指数参数随降温速率的增加而增加外, 其余均不随热历史的变化而变化. 拟合较低降温速率下c_p(T)曲线获得的GR模型参数的预测力明显好于在较大降温速率下获得的结果. 由于松弛时间对拟合过程中选择的“固定参数”的取值很敏感, 因此模型能否预测体系的比热容不能看成确定松弛时间的唯一依据. 在利用GR模型分析无定形山梨醇体系的脆度时, 如果选择极限假想温度作为T_g, 会导致计算结果明显小于文献值.     

Structure and diffusion in amorphous aluminum silicate: a molecular dynamics computer simulation

The amorphous aluminum silicate (Al2O3)2(SiO2) [AS2] is investigated by means of large scale molecular dynamics computer simulations. We consider fully equilibrated melts in the temperature range 6100 K> or =T> or =2300 K as well as glass configurations that were obtained from cooling runs from T=2300 to 300 K with a cooling rate of about 10(12) K/s. Already at temperatures as high as 4000 K, most of the Al and Si atoms are fourfold coordinated by oxygen atoms. Thus, the structure of AS2 is that of a disordered tetrahedral network. The packing of AlO4 tetrahedra is very different from that of SiO4 tetrahedra in that Al is involved with a relatively high probability in small-membered rings and in triclusters in which an O atom is surrounded by four cations. We find as typical configurations two-membered rings with two Al atoms in which the shared O atoms form a tricluster. On larger length scales, the system shows a microphase separation in which the Al-rich network structure percolates through the SiO2 network. The latter structure gives rise to a prepeak in the static structure factor at a wave number q=0.5 A(-1). A comparison of experimental x-ray data with the results from the simulation shows good agreement for the structure function. The diffusion dynamics in AS2 is found to be much faster than in SiO2. We show that the self-diffusion constants for O and Al are very similar and that they are by a factor of 2-3 larger than the one for Si.     

Crystallization of filled nylon 6 III. Non-isothermal crystallization

Summary DSC data on crystallization kinetics from the melt at different cooling rates of nylon 6 containing various amonts of untreated and surface-treated fillers, were analyzed in terms of a modified Kolmogorov-Avrami equation. It was established that mechanism of crystallinity development in molten nylon 6 does not change appreciably in presence of aminosilane-treated glass beads and small amounts of untreated glass beads, whereas time exponentn was found to decrease with increasing filler content in samples containing untreated glass beads and Aerosil. On the other hand, dependence of temperature of the onset of crystal nucleation on cooling rate obeyedm = 2 law for pure nylon 6 and samples containing surface-treated filler, whilem = 4 law seemed to hold for samples containing large amounts of untreated fillers at low cooling rates (m is the exponent at degree of supercooling). It was concluded that although isothermal conditions of crystallization should be preferred for further quantitative investigations of polymer-filler interactions in highly filled polymer melts, the above results qualitatively are consistent with trends discovered in isothermal crystallization experiments.     

The vitrification of alkali borate and alkali silicate melts

Glasses and crystals of compositions corresponding to the congruently melting compounds M₂O·2SiO₂ (M = Na. Rb, and Cs) and M₂O·4SiO₂ (M = K, Rb, and Cs) were studied by differential scanning calorimetry. The structure temperatures (T _f) and excess entropies at T _f of glasses were measured depending on the rate of cooling of the corresponding melts. The activation energies of glass formation (ΔE) and scale of cooperative motion in the transition region (ξ_a) were estimated. The totality of the data obtained were used to compare the thermodynamic (the ratio between the excess (with respect to the corresponding crystals) entropy of glass at T _f and the entropy of crystal melting), kinetic (fragility m = f(ΔE, T _f)), and microscopic (ξ_a) parameters of the vitrification of alkali silicate melts. The behaviors of alkali silicate and alkali borate melts were shown to be similar.     

Melt elongation flow behaviour of LDPE/LLDPE blends

The extensional rheological properties of low density polyethylene (LDPE)/linear low density polyethylene (LLDPE) blend melts were measured using a melt spinning technique under temperatures ranging from 160 to 200 °C and die extrusion velocities varying from 9 to 36 mm/s. The results showed that the melt elongation stress decreased with a rise of temperature while it increased with increasing extensional strain rate and the LDPE weight fraction. The dependence of the melt elongation viscosity on temperature roughly obeyed the Arrhenius equation, it increased with increasing extensional strain rate and the LDPE weight fraction when the extensional strain rate was lower than 0.5 s⁻¹, and it reached a maximum when the extensional strain rate was about 0.5 s⁻¹, which can be attributed to the stress hardening effect.     

X‐ray studies on the double melting behavior of poly(butylene terephthalate)

The double melting behavior of poly(butylene terephthalate) (PBT) was studied with differential scanning calorimetry (DSC) and wide‐angle X‐ray analysis. DSC melting curves of melt‐crystallized PBT samples, which we prepared by cooling from the melt (250 °C) at various cooling rates, showed two endothermic peaks and an exothermic peak located between these melting peaks. The cooling rate effect on these peaks was investigated. The melt‐crystallized PBT sample cooled at 24 K min^?1 was heated at a rate of 1 K min^?1, and its diffraction patterns were obtained successively at a rate of one pattern per minute with an X‐ray measurement system equipped with a position‐sensitive proportional counter. The diffraction pattern did not change in the melting process, except for the change in its peak height. This suggests that the double melting behavior does not originate from a change in the crystal structure. The temperature dependence of the diffraction intensity was obtained from the diffraction patterns. With increasing temperature, the intensity decreased gradually in the low‐temperature region and then increased distinctly before a steep decrease due to the final melting. In other words, the temperature‐dependence curve of the diffraction intensity showed a peak that is interpreted as proof of the recrystallization in the melting process. The peak temperature was 216 °C. The temperature‐dependence curve of the enthalpy change obtained by the integration of the DSC curve almost coincided with that of the diffraction intensity. The double melting behavior in the heating process of PBT is concluded to originate from the increase of crystallinity, that is, recrystallization. © 2001 John Wiley & Sons, Inc. J Polym Sci Part B: Polym Phys 39: 2005–2015, 2001     

Solubility of Al2O3 in some chloride-fluoride melts

Alumina solubility in chloride-fluoride melts of KCl-NaCl-NaF mixtures with ratios of 0.425:0.425:0.15 (I), 0.38:0.38:0.24 (II), and 0.35:0.35:0.30 (III) (molar fractions) was investigated in the 973-1123 K temperature range using the isothermal saturation method. Al2O3 solubility in the ionic melts studied was shown to be on the order of 0.06 g kg(-1) for system I, 0.12 g kg(-1) for system II, and 0.14 g kg(-1) for system III at 1073 K. All the "Al2O3 + melt" systems were found to demonstrate negative deviations from the ideal solutions. The solubility of Al2O3 in all the melts increases with the temperature increase; however, the dependences of -log N(Al2O3) versus T(-1) were characterized by the slopes (2.6 +/- 0.4) x 10(3) K (I and II) and (2.4 +/- 0.6) x 10(3) K (III), which were considerably less than the slope predicted by the Shreder-Le Chatelier equation (approximately 5.8 x 10(3)).