Secondary nucleation theory

Crystallization can be divided into three processes the primary nucleation process, the growth process, and the overgrowth process. The growth process is mainly controlled by the secondary nucleation mechanism. The steady (stationary) primary and secondary nucleation mechanisms of atomic or low molecular weight systems have been well studied since the 1930s by applying the classical nucleation theory (CNT) presented by Becker and Doring, Zeldovich, Frenkel and Turnbull and Fisher and so on [1-4]. 

On closer scrutiny the crystal growth data for PEO fractions deviate somewhat from those expected from secondary nucleation theory there were... 

The growth rate minima cannot be explained by the secondary nucleation theory in its present form. The two major simplifications that the LH theory makes are (a) neglect of the segmental ( fine-grain ) nature of stem... 

Once primary nuclei are formed the ensuing spherulites grow radially at a constant rate. Primary crystallization, which occurs initially on the surface of the primary nucleus and then on the surface of the growing lamellar, also involves a nucleation step, secondary nucleation. It is this step that largely governs the ultimate crystal thickness and which forms the focus of most kinetic theories of polymer crystallization. 

According to the secondary nucleation theory, polymer crystals grow by deposition of layers of stems on the side surface of the lamella183 (see Figure 33). Each new layer needs to be nucleated ( secondary or surface nucleation), after which it spreads comparatively rapidly. The main barrier to secondary nucleation is the excess side surface free energy 2blo... 

On closer scrutiny the crystal growth data for PEO fractions deviated somewhat from those expected from secondary nucleation theory there were departures from linearity of Gvs AT near the Tcm transition temperatures,185 188 and the value of a derived from the kinetics was unrealistically low.187... 

It is desirable to classify the various mechanisms of nucleation as shown in Figure 2.19. Primary nucleation occurs in the absence of crystalline surfaces, whereas secondary nucleation involves the active participation of these surfaces. Homogeneous nucleation rarely occurs in practice, however, it forms the basis of several nucleation theories. Heterogeneous nucleation is usually induced by the presence of dissolved impurities. Secondary nucleation involves the presence of crystals and its interaction with the environment (crystallizer walls, impellers, etc.). 

Nucleation. There is relatively little information available on nucleation rates of biochemicals from solution, yet the control of nucleation rates controls the number of particles produced and has a direct bearing on crystal size for a given yield of crystallizing product. Uncontrolled nucleation either heterogeneously from contaminants or as secondary particles produced from existing crystals can greatly affect the desired size distributions. The general principles of nucleation theory as discussed in Chapter 2 apply to biochemical systems. 

It is common practice to replot ln(growth rate) against l/TAT, so as to linearize the data and to allow its analysis in the context of secondary nucleation theory (see section imder Secondary Nucleation Theory). A large body of data... 

Polymer crystallization theory is a mature area, and there are several review articles available that present and discuss the different theories in great detail (eg, 103,104). Having said that, over the last 5 years or so there has been a flurry of new interest becanse of the increase in computational power, which has the potential to decisively enter the debate in some areas. In the following the underlying themes of the two principle theories of polymer crystallization, secondary nucleation theory and rough-surface or entropic barrier theory, are outlined. The results of more recent simulations are then briefly discussed, in which the constraints of the above theories, introduced to provide analytical solutions, have been relaxed. Finally, some of the more fundamentally different ideas that have recently appeared are discussed. 

Although secondary nucleation theory was, for a period, widely accepted, it is now coming under increasing pressure, from experimental data, from computer simulation, and from new approaches to the fundamental process of crystalhzation. It is not clear at this stage whether all that is required is a few adjustments to the theory, or whether the idea of a nucleation barrier is flawed, or even if the idea that the crystal thickness seen is the fastest growing is correct. With the development of new theoretical tools, and the increased integration of theory with computer simulation, it is hoped that a more complete model for polymer crystallization can be developed. 

Figure 4 Schematics depicting the basics of the Lauritzen-Hoffman secondary nucleation theory. G indicates the lateral rate of grovrth accessible in the experiments, while stands for the propagation rate of the nucleus in the row direction until it reaches a dislocation defect or impinges on a neighboring nucleus /.stands for the so-called persistence length of the lamellar crystal while /c is the fold length of the lamella a and b are the lateral dimensions of a crystalline stem and a are the surface energies for the fold and lateral surface, respectively.

Assuming secondary nucleation of a single chain at the two-dimensional locally smooth growth front, the free energy change based on the classical nucleation theory is... 

The crystal growth kinetics of P(3HB-co-3HH) copolyesters was analysed by using the secondary nucleation theory , which is written as ... 

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