Crystallization time temperature dependence

As an example, we consider crystallization of polyethylene from a melt. As mentioned above, crystallization proceeds with the initial formation of isolated spherulites, which then grow until their mutual impingement with further slow crystallization. Time (t)-dependent measurements [26] of the density of the crystallizing melt at different temperatures are given in Figure 1.3 as a plot of degree of crystallinity versus logarithm of time. 

Crystallization of the polymer when the propellant formulation is subjected to low temperatures can be annoying (12). Formation of additional periodic attractions between molecules has the same effect as additional crosslinking. Upon crystallization, the propellant becomes hard and brittle with low strain capability. If the effect is caused by crystallization of the polymer, the original physical properties are obtained when the propellant is heated above the melting point of the polymer. These effects are time-temperature dependent and can have a significant effect on the selection of operating and storage temperatures... 

All the examples described above show that confinement in different cases may be responsible for nonmonotonic relaxation kinetics and can lead to a saddle-like dependence of relaxation time versus temperature. However, this is not the only possible reason for nonmonotonic kinetics. For instance, work [258] devoted to the dielectric study of an antiferromagnetic crystal discusses a model based on the idea of screening particles. Starting from the Arrhenius equation and implying that the Arrhenius activation energy has a linear dependence on the concentration of screening charge carriers, the authors of Ref. 258 also obtained an expression that can lead to nonmonotonic relaxation kinetics under certain conditions. However, the experimental data discussed in that work does not show clear saddle-like behavior of relaxation time temperature dependence. The authors of Ref. 258 do not even discuss such a possibility. 

Abstract Contribution of the Jahn-Teller system to the elastic moduli and ultrasonic wave attenuation of the diluted crystals is discussed in the frames of phenomenological approach and on the basis of quantum-mechanical theory. Both, resonant and relaxation processes are considered. The procedure of distinguishing the nature of the anomalies (either resonant or relaxation) in the elastic moduli and attenuation of ultrasound as well as generalized method for reconstruction of the relaxation time temperature dependence are described in detail. Particular attention is paid to the physical parameters of the Jahn-Teller complex that could be determined using the ultrasonic technique, namely, the potential barrier, the type of the vibronic modes and their frequency, the tunnelling splitting, the deformation potential and the energy of inevitable strain. The experimental results obtained in some zinc-blende crystals doped with 3d ions are presented. 

Now we will overview some experiments that reveal the specificities of the Jahn-Teller effect in diluted crystals. First of all, we will discuss a justification of their relaxation origin. We have mentioned before that the first experiments were done on the crystals of aluminum oxide (corundum), yttrium aluminum garnet, yttrium iron garnet, and lithium gallium spinel doped with a number of 3d ions [10,11]. The main result was the discovery of attenuation maximum which was considered to be observed at cot 1 and reconstruction of the relaxation time temperature dependence. In some experiments reported later both the velocity and attenuation of ultrasound were measured as functions of the temperature. They were done on ZnSe and ZnTe crystals doped with transition metals. These crystals have the zinc-blende structure with the Jahn-Teller ion in tetrahedral coordination. The following... 

The effect of stereosequence distribution on crystallization kinetics Is dramatic. We have previously reported our studies on the Important effects of stereosequence length on crystallization kinetics and morphology of propylene oxide polymers (22). Here we summarize the main conclusions of this study, so that results on the time-temperature dependence of mechanical response may be fully appreciated In the light of these conclusions. 

Chlorine, a member of the halogen family, is a greenish yellow gas having a pungent odor at ambient temperatures and pressures and a density 2.5 times that of air. In Hquid form it is clear amber SoHd chlorine forms pale yellow crystals. The principal properties of chlorine are presented in Table 15 additional details are available (77—79). The temperature dependence of the density of gaseous (Fig. 31) and Hquid (Fig. 32) chlorine, and vapor pressure (Fig. 33) are illustrated. Enthalpy pressure data can be found in ref. 78. The vapor pressure P can be calculated in the temperature (T) range of 172—417 K from the Martin-Shin-Kapoor equation (80) ... 

Sihca and aluminosihcate fibers that have been exposed to temperatures above 1100°C undergo partial conversion to mullite and cristobaUte (1). Cristobahte is a form of crystalline siUca that can cause siUcosis, a form of pneumoconiosis. lARC has deterrnined that cristobaUte should be classified as 2A, a probable carcinogen. The amount of cristobahte formed, the size of the crystals, and the nature of the vitreous matrix in which they are embedded are time- and temperature-dependent. Under normal use conditions, refractory ceramic fibers are exposed to a temperature gradient, thus only the hottest surfaces of the material may contain appreciable cristobahte. Manufacturers Material Safety Data Sheets (MSDS) should be consulted prior to handling RCF materials. 

Although not a heteroaromatic compound, the case of citrinin studied by Destro and Luz ([97JPC(A)5097] and references therein) is so significant that it deserves mention here. Citrinin exists in the crystal as a mixture of the p-quinone 5a and o-quinone 5b tautomers (Scheme 3). The equilibrium ii temperature dependent and by using CPMAS NMR (Section VI,F) and, more remarkably. X-ray crystallography, the authors were able to determine the AH and AS values (the rate is extremely fast on the NMR time scale, >10 s ). 

In the thermochromic liquid crystal (TLC) the dominant reflected wavelength is temperature-dependent and it has been employed for full-field mapping of temperature fields for over three decades. Although it is non-intrusive and cost effective, there are some problems in applying it to micro-scale measurements, because of size (typically tens of micrometers) and time response (from a few milliseconds to several hundred milliseconds depending on the material and the form). Examples of application are micro-fabricated systems (Chaudhari et al. 1998 Liu et al. 2002) and electronic components (Azar et al. 1991). 

The dramatic slowing down of molecular motions is seen explicitly in a vast area of different probes of liquid local structures. Slow motion is evident in viscosity, dielectric relaxation, frequency-dependent ionic conductance, and in the speed of crystallization itself. In all cases, the temperature dependence of the generic relaxation time obeys to a reasonable, but not perfect, approximation the empirical Vogel-Fulcher law ... 

Reid et al. [ 1.12] described the effect of 1 % addition certain polymers on the heterogeneous nucleation rate at-18 °C the rate was 30 times greater than in distilled, microfiltered water and at -15 °C, the factor was still 10 fold hogher. All added polymers (1 %) influenced the nucleation rate in a more or less temperature-dependent manner. However, the authors could not identify a connection between the polymer structure and nucleation rate. None the less it became clear that the growth of dendritic ice crystals depended on to factors (i) the concentration of the solution (5 % to 30 % sucrose) and (ii) the rate at which the phase boundary water - ice crystals moved. However, the growth was found to be independent of the freezing rate. (Note of the author the freezing rate influences the boundary rate). 

Characteristics and implementation of the treatments depend on the expected results and on the properties of the material considered a variety of processes are employed. In ferrous alloys, in steels, a eutectoid transformation plays a prominent role, and aspects described by time-temperature-transformation diagrams and martensite formation are of relevant interest. See a short presentation of these points in 5.10.4.5. Titanium alloys are an example of the formation of structures in which two phases may be present in comparable quantities. A few remarks about a and (3 Ti alloys and the relevant heat treatments have been made in 5.6.4.1.1. More generally, for the various metals, the existence of different crystal forms, their transformation temperatures, and the extension of solid-solution ranges with other metals are preliminary points in the definition of convenient heat treatments and of their effects. In the evaluation and planning of the treatments, due consideration must be given to the heating and/or cooling rate and to the diffusion processes (in pure metals and in alloys). 

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