Kinetics of crystallization

Kinetics of crystallization. Trick (79) has reported a dilatometric study of the bulk crystallization of PTHF. The rates he observed for a polymer of Mw = 130,000 (Polymer A) are shown in Fig. 27. He also found that a lower molecular weight polymer (Polymer B, Mn = 6760) crystallized to a higher degree of crystallinity, whereas the introduction of comonomer units (Polymer C) decreased the degree of crystallinity (Fig. 28). From attempts to fit the Avrami Equation to the experimental data in the early stages of crystallization, a tentative value of n = 3 was 

Degradation in bulk. Davis and Golden (85) have studied the degradation of PTHF in bulk at various temperatures. The polymers that they studied were prepared using a THF/PF5 complex either in an open flask (polymer A) or in vacuum with exposure to air during the work up (polymer V). The intrinsic viscosity of polymer A. heated at fixed temperatures up to 150° C in a sealed system, fell rapidly to a constant value. Polymer V behaved similarly but the decrease was considerably smaller. When heated in air at a fixed temperature the viscosity of both polymers decreased continuously with eventual destruction of the polymer. Temperatures well in excess of 150° C were required for complete degradation of polymer A or V in vacuum. 

The rate of weight loss of polymer A was determined in vacuum and in air. The activation energy of degradation in vacuum calculated from this 

Kovarskaya, Levantovskaya, and Yazvikova 86) recently studied the kinetics of thermooxidative degradation of PTHF of low molecular weight (1130) at 90—120° C. Hydroperoxides were formed at all stages of the oxidation. The rate of accumulation of peroxides reached a maximum of 2—2.3 millimoles/g at all temperatures. Kinetic curves of the oxidation revealed an auto-acceleration according to the formula  

Degradation in solution. Davis and Golden (85) found that the viscosity of a benzene solution of PTHF heated in air dropped steadily in the absence of anti-oxidant with eventual complete destruction of the polymer. In the presence of anti-oxidant (e. g. 0.5% 2,6-di-t-butyl-4-methylphenol) the viscosity fell initially but thereafter became constant. As shown in Fig. 29, this initial drop was greater for polymer A 

Now As really expresses a state of equilibrium in which all thermodynamic forces balance, for the case in which one end of a PS sequence is fixed and the other end is free. Since one end of each chain is constrained, the neighboring chains must exhibit an excluded volume effect (proportional to 1/Z) in addition to the excluded volume otherwise characteristic of PS itself in the same solvent. As a result, the chains tend to undergo elongation in a direction at right angles to the plane of the lamella. At equilibrium, the tendency toward randomization will be compensated by an elastic retractive force due to the lower conformational entropy of the elongated PS sequences. 

in a quantitative manner, the dimensions and composition of crystals of block polymers can be related to the composition of the parent block copolymer and to the thermodynamic goodness of the solvent used as crystallization medium. 

As has been shown in previous sections, the presence of an uncrystallizable tail may hinder crystallization of an otherwise crystallizable sequence 

The homogeneity in size and form of the crystals produced by the techniques developed made it possible, for the first time, to relate microscopic observations under isothermal conditions to dilatometric measurements of the partial specific volume of the dissolved polymer Vi, of the precipitated polymer Vp, and of the partially crystallized polymer Vp. Thus the crystalline fraction z is given by 

Since the thickness of the PEO lamellae L is essentially constant (see Section 6.2.2), the isothermal contraction (v — Vp) is always proportional to the surface area of the crystals S (neglecting the lateral faces and assuming the crystals are two dimensional). Thus 

The crystalline content of a polymer has a profotmd effect on its properties, and it is important to know how the rate of crystallization will vary with the temperature, especially drrring the processing and manrrfacturing of polymeric articles. The chemical structure of the polymer is also an important featirre in the crystallization for example, polyethylene crystallizes readily and carmot be quenched rapidly enough to give a largely amorphous sample, whereas this is readily accomplished for isotactic polystyrene. However, this aspect will be discussed more fully later. 

FIGURE 11.8 Fully-developed spherulite grown from the melt, comprising chain-folded lamellae (magnified section) and branching points that help to impart a spherical shape to the structure. Most rapid growth occurs in the direction of the spherulite radius R. (Adapted from McCrum, N.B., Buckley, C.P., and Bucknall, C.B., Principles of Polymer Engineering, Oxford University Press, 1988. With permission.) 

During crystallization from the bulk, polymers form lamellae, which in turn are organized into spherulites or their predecessor structures, hedrites. This section is concerned with the rates of crystallization under various conditions of temperature, molecular weight, structure, and so on, and the theories that provide not only an insight into the molecular mechanisms but considerable predictive power. 

Temperature (°C) Radial Growth Rates (/mi/inm) for Various Compositions  

Section 6.4.2 described Keller s early preparations of single crystals from dilute solutions. Since the crystals were only about 100 A thick and the chains were oriented perpendicular to the flat faces, Keller postulated that the chains had to be folded back and forth. 

1 The A vrami Equation The original derivations by Avrami (73-75) have been simplified by Evans (81) and put into polymer context by Meares (82) and Hay (83). In the following, it is helpful to imagine raindrops falling in a puddle. These drops produce expanding circles of waves that intersect and cover the whole surface. The drops may fall sporadically or all at once. In either 

The probability that a point P is crossed by x fronts of growing spherulites is given by an equation originally derived by Poisson (84)  

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The kinetics of crystal growth has been much studied Refs. 98-102 are representative. Often there is a time lag before crystallization starts, whose parametric dependence may be indicative of the nucleation mechanism. The crystal growth that follows may be controlled by diffusion or by surface or solution chemistry (see also Section XVI-2C). 

We shall take up the kinetics of crystallization in detail in Secs. 4.5 and 4.6. For the present, our only interest is in examining what role kinetic factors play in complicating the crystal-liquid transition. In brief, the story goes like this. Polymers have a great propensity to supercool. If and when they do crystallize, it is an experimental fact that smaller crystal dimensions are obtained the lower the temperature at which the crystallization is carried out. The following considerations supply some additional details ... 

In order to carry out an experimental study of the kinetics of crystallization, it is first necessary to be able to measure the fraction d of polymer crystallized. While this is necessary, it is not sufficient we must also be able to follow changes in the fraction of crystallinity with time. So far in this chapter we have said nothing about the experimental aspects of determining 6. We shall now briefly rectify this situation by citing some of the methods for determining 6. It must be remembered that not all of these techniques will be suitable for kinetic studies. 

Nancollas, G.H. and Gardner, G.L., 1974. Kinetics of crystal growth of calcium oxalate monohydrate. Journal of Crystal Growth, 21, 267-276. 

Kinetics of Crystallization of Polypropylene Fractions and Polybutene-1-Part I", ONR Tech Rept 43, Contract Nonr 3357(00), Univ of Mass, Amherst (1962) 4) A. Opschoor,... 

KNUDSEN J c, ANTANUSE H s, RisBO j and SKIBSTED L H (2002) Induction time and kinetics of crystallization of amorphous lactose, infant formula and whole milk powder as studied by isothermal differential scanning calorimetry, Milchwissenschaft, 57, 543-546. 

Nielsen, A.E. (1958) The kinetics of crystal growth in barium sulphate precipitation. Acta Chem. Scand., 12, 951-958. 

Before discussing the effect of short-chain branching on the kinetics of crystallization process, it is necessary to revisit the theory of secondary nucleation and the concept of regimes as given by Lauritzen and Hoffmann... 

Mechanisms of dissolution kinetics of crystals have been intensively studied in the pharmaceutical domain, because the rate of dissolution affects the bioavailability of drug crystals. Many efforts have been made to describe the crystal dissolution behavior. A variety of empirical or semi-empirical models have been used to describe drug dissolution or release from formulations [1-6]. Noyes and Whitney published the first quantitative study of the dissolution process in 1897 [7]. They found that the dissolution process is diffusion controlled and involves no chemical reaction. The Noyes-Whitney equation simply states that the dissolution rate is directly proportional to the difference between the solubility and the solution concentration ... 

G. Shan, K. Igarashi, H. Ooshima. Dissolution kinetics of crystal in suspension and its application to L-aspartic acid crystals. Chem. Eng. 

The overall kinetics of crystal precipitation has to consider that the process consists of a series of consecutive processes in simple cases, the slowest is the rate determining step. Assuming the volume diffusion is not the rate determining step, we still have at least the following reaction sequences ... 

Buchner, S., Wiswe, D. and Zachman, H. G., Kinetics of crystallization and melting behaviour of poly(ethylene naphthalene-2,6-dicarboxylate),... 

In this study, D-SCMC seed crystals were put in a racemic SCMC supersaturated solution in a batchwise agitated vessel and growth rates in longitudinal and lateral directions and the optical purity of D-SCMC crystals were measured. The growth rates and optical purity were discussed considering surface states of grown crystal observed by a microscope. The kinetics of crystal growth were measured and a model of inclusion of impurity was proposed. 

The level of impurity uptake can be considered to depend on the thermodynamics of the system as well as on the kinetics of crystal growth and incorporation of units in the growing crystal. The kinetics are mainly affected by the residence time which determines the supersaturation, by the stoichiometry (calcium over sulfate concentration ratio) and by growth retarding impurities. The thermodynamics are related to activity coefficients in the solution and the solid phase, complexation constants, solubility products and dimensions of the foreign ions compared to those of the ions of the host lattice [2,3,4]. 

Even when the principles of interface reaction and diffusion are thought to be understood, the integrated results may still require major new work. For example, the growth rate of an individual crystal in an infinite melt can be predicted if parameters are known, but the growth rates of many crystals (and different minerals), i.e., the kinetics of crystallization of a magma, is not quantitatively understood. 

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