Volume crystallization kinetics

Samples can be concentrated beyond tire glass transition. If tliis is done quickly enough to prevent crystallization, tliis ultimately leads to a random close-packed stmcture, witli a volume fraction (j) 0.64. Close-packed stmctures, such as fee, have a maximum packing density of (]) p = 0.74. The crystallization kinetics are strongly concentration dependent. The nucleation rate is fastest near tire melting concentration. On increasing concentration, tire nucleation process is arrested. This has been found to occur at tire glass transition [82]. 

Population balances and crystallization kinetics may be used to relate process variables to the crystal size distribution produced by the crystallizer. Such balances are coupled to the more familiar balances on mass and energy. It is assumed that the population distribution is a continuous function and that crystal size, surface area, and volume can be described by a characteristic dimension T. Area and volume shape factors are assumed to be constant, which is to say that the morphology of the crystal does not change with size. 

While in volumes 180 and 181 of this series several basic aspects of morphology, inter-phase structure and disorder were addressed, in the present volume, molecular interactions, modeling, phase transformation and crystallization kinetics are considered (see the subject index including keywords from volumes 180 and 181 at the end of the book). Needless to say, in spite of substantial success over 60 years or more we are still far from having a complete and unambiguous picture of polymer crystallization. We firmly believe that a fruitful approach to such a complex problem requires one to give way to many different and sometimes conflicting viewpoints, as we have attempted to do in these volumes. We do hope that they are not only a time-capsule left for... 

To truly control crystallization to give the desired crystalline microstructure requires an advanced knowledge of both the equilibrium phase behavior and the kinetics of nucleation and growth. The phase behavior of the particular mixture of TAG in a lipid system controls both the driving force for crystallization and the ultimate phase volume (solid fat content) of the solidified fat. The crystallization kinetics determines the number, size, polymorph, and shape of crystals that are formed as well as the network interactions among the various crystalline elements. There are numerous factors that influence both the phase behavior and the crystallization kinetics, and the effects of these parameters must be understood to control lipid crystallization. 

Stein, Gray and Guillet 82, 83) demonstrated the suitability of the GC method to study crystallization kinetics, through the variation of the retention volume with time. When the pcdymer stationary phase is cooled from the melt to a temperature below Tj, the retention volume decreases with time at the rate at which crystdline domains are being formed. The maximum possible crystallinity at a given temperature is obtained from the relation... 

So far the crystallization kinetics of HMFG have been less studied. Both continuous heating and isothermal experiments have been performed using DTA or DSC techniques. Bansal et al. (1983) studied the crystallization kinetics of a ZBL glass by means of isothermal and nonisothermal DSC heating above T. Under isothermal conditions, the volume fraction cc crystallized after a time t was found to follow the Avrami equation. 

Equations E23.2.8 and E23.2.9 can be solved using the appropriate initial and boundary conditions to compute the concentrations of A in the continuous and microphases as functions of time. However, these model equations depend on the average particle diameter, surface area, and volume of the microphase. Because they are constantly changing as more crystals nucleate and grow, complete knowledge of the crystallization kinetics of calcium sulfate is necessary to solve the equations. 

Link 5. Principle of Detailed Balance Connects Equilibrium to Kinetk Considerations Are our equilibrium results then unrelated to the kinetics of glasses It is easy to show that there is indeed an intimate connection between kinetic and equilibrium quantities. An experimental proof is in Kauzmann s paradox". If we did our experiments infinitely slowly we would, according to extrapolation of experimental curves for entropy and volume, reach negative entropies and volumes less than crystal volumes. Yet, kinetics always intervenes to save the day for thermodynamics. Since this always happens no matter what the experimental system we are forced to conclude on experimental grounds alone that there is a fundamental connection between viscosity and entropy such that whenever the entropy is approaching zero the viscosity is becoming very large. 

Fig. 10.2. Time sequences of SANS spectra showing crystallization kinetics in = 0.10 solution during the isothermal storage at 90° C. The inset shows the evolution of the volume fraction degree of crystallinity obtained from model fitting. It increases linearly with time. Note that the measurement of the rather small crystallinity quantity is not readily achievable by SAXS...

Fig. 2 Schematic phase diagram of a single flexible polymer chain in the thermodynamic limit (Af —> Qo) as a function of temperature T and range of attractive monomer-monomer interaction X. For 2 > At, there occurs a transition at T = 6 X) from the swollen coil to the collapsed fluid globule. At TcystCiV = < ) the globule crystalhzes. Due to slow crystallization kinetics, this transition may be undercooled and at FcystW the collapsed globule freezes into a glassy slate. Since it was assumed that the transition lines vary linearly with the interaction volume A, A rather than A has been chosen as an abscissa variable. Adapted from Binder et al. [4]...

Equation 4.31 is useful in simulations. Standard PVT data and the Tait equation can be used for calculation of at melt zone and at solid zone, while the specific volume at transition zone can be calculated using crystallization kinetics and a linear interpolation between 1/v and 1/v using Eq. 4.31. 

L. Capt,The pres sure-volume-temperature behavior and the effect of pressure on crystallization kinetics of polyethylene resins, M.Sc. thesis, McGill University, 1999. 

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