Flow-Enhanced Nucleation

A number of FIC models are discussed in Section 14.4.1. The aim is to give an overview of the most successful approaches, in terms of capturing the phenomena observed in laboratory FIC experiments, and to compare the physical ideas in these models. Flow-enhanced nucleation is the main subject of Section 14.4.1, but some of the models discussed there additionally describe shish growth. A model for shish growth that is in better agreement with detailed experimental observations, developed by Custddio et al. [74], is summarized in Section 14.4.2. Implementation in IM simulations is discussed in Section 14.4.3. Results of such simulations by Custodio et al. are shown as an example of the current state of the art. Their model captures the following phenomena and features of FIC  

With the advent of sophisticated simulation techniques, the physics of the flow-enhanced nucleation process at the molecular level are gradually being unraveled (see Chapter 6). The results of such investigations can serve to validate and/or improve continuum-level FIC models. Some of the most advanced of these are compared here in terms of the formulation of flow-enhanced nucleation kinetics. A description of flow-induced oriented structure formation and application to IM are discussed in Section 14.4.2 and Section 14.4.3, respectively. We focus on models that calculate the number density and dimensions of nuclei since this is necessary to predict morphological features beyond merely the degree of crystallization or the volume fraction of semicrystalline material. Therefore, approaches based on a (modified) Nakamura equation are left out of consideration. 

The models discussed here can be divided into two groups, based on the two main hypotheses concerning the origin of FIPs. The first, which is more widely used, is that precursors are created in the amorphous phase through a sporadic process, driven by thermal fluctuations. Flow presumably lowers the free energy barrier associated with this process and thus accelerates it. As we will see, the specific effect of flow on the creation rate varies among the models developed. The second hypothesis, put forward by Janeschitz-Kriegl and coworkers [146-148], is that the amorphous phase already contains so-called dormant precursors of different sizes. 

The effect of flow on nucleation is usually ascribed exclusively to the creation of new precursors or to the activation of preexisting dormant precursors. However, it is possible that both processes take place. Current experimental capabilities are insufficient to resolve this issue because, unlike shish,point-hke precursors cannot be detected. Hence, it is unknown whether FIPs originate from the pure amorphous phase, from preexisting dormant precursors, or from both. Typical continuum-level FlC models lack the level of detail to determine which interpretation is correct. Nevertheless, they can shed some fight on the role of molecular deformation and relaxation in flow-enhanced nucleation. The objective of the present work is to provide a theoretical framework, in which models based either on one of the two or on both hypotheses are contained. We depart from the idea that sporadic creation and athermal activation of FIPs take place side by side. Eventually one of the two may be switched off and additional assumptions may be introduced to obtain a range of different models. 

The distribution function of precursors per unit volume with the number of stems n and the length I is denoted by p n, /). We introduce n (T, /) as the critical number of stems. The number densities of active and dormant precursors are then  

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It is important to note that Equation (14.16), Equation (14.17), and Equation (14.18) do not constitute a closed set of equations the evolution of the size distribution, Equation (14.10), still has to be calculated. For efficient simulations of flow-enhanced nucleation in polymer processing, closure of Equation (14.16), Equation (14.17), and Equation (14.18) is necessary. This is possible by introducing some assumptions. The mathematical structure of many existing flow-enhanced nucleation models, which do not contain all the details considered here, can be reproduced in this way, as shown in Sections 14.4.1.2-14.4.1.4. The influence of flow, for example on the rate of creation of precursors, is subsequently specifled for a number of these models. A common assumption is that all FIPs are active, so that their size distribution need not be considered. Quiescent precursors are then treated as a separate species because it is known from experiments that they do have a distribution of sizes or, equivalently, of activation temperatures. This is discussed next. 

TABLE 14.1 Form of the Terms in Equation (14.27) for Different Flow-Enhanced Nucleation Models. Symbols Are Explained in the Text... 

Models without a Flow-Induced Precursor Phase Flow-enhanced nucleation is in most cases described by an expression of the form... 

Note that these FIC models have not been validated in terms of morphological features, such as the number density or size distribution of spherulites. One problem is that the classical nucleation theory predicts a sporadic nucleation rate even in quiescent melts, which is not observed experimentally. Zheng and Kennedy [73] calculated the flow-enhanced nucleation rate as // = (AG) - (AG ). The last term in this equation is... 

A parameter known to influence flow-enhanced nucleation is the strain rate. It is customary to define an effective shear rate in terms of the deformation rate tensor D,... 

J. R. Thome, Mechanisms of Enhanced Nucleate Pbol Boiling, in Pool and External Flow Boiling, V. K. Dhir and A. E. Bergles eds., pp. 337-343, ASME, New York, 1992. 

Correlations for Boiling Heat Transfer Nucleate boiling is a complex phenomenon. Several mechanisms have been proposed to explain the boiling process, such as latent heat transport, microconvection, vapor-liquid exchange, wake flow, enhanced convection, and microlayer evaporation, details of which can be found in Ginoux (1978). 

It is believed that, similar to inorganic filler-enhanced nucleation, the shear/ extensional flow in different regions of the die, as well as the expansion of nucleated bubbles near the nanoparticles, would generate a pressure fluctuation around the suspended nanoparticles. The schematic in Figure 3.4 illustrates the induced-extensional flow around the side surface of the nanoclay particle. In extreme situations, such a local pressure held may even be negative and significantly promote cell nucleation. More details about the cell nucleation mechanism of polymer/fillers foaming systems have been presented in our newly submitted journal paper (Zhai et al., 2012), and the readers may get more information from this review paper. 

Eder and coworkers also observed that y was approximately constant at the transition from the spher-ulitic core to the fine-grained layer. If this layer is the result of flow-enhanced point-like nucleation, then the (again sharp) transition is not explained by their model with N[ y which leads to a number density of nuclei N oc yl... 

A number of organic pigments cause distortion in certain types of polyolefins, especially in HDPE. Pigments act as nucleating agents in such partially crystalline plastics i.e., they promote crystallization, which creates stress within the plastic product (Sec. 1.6.4.3). These pigments also enhance the shrinkage of polyolefins, particularly in the direction of the flow. 

The objective is to reduce volatiles to below 50-100-ppm levels. In most devolatilization equipment, the solution is exposed to a vacuum, the level of which sets the thermodynamic upper limit of separation. The vacuum is generally high enough to superheat the solution and foam it. Foaming is essentially a boiling mechanism. In this case, the mechanism involves a series of steps creation of a vapor phase by nucleation, bubble growth, bubble coalescence and breakup, and bubble rupture. At a very low concentration of volatiles, foaming may not take place, and removal of volatiles would proceed via a diffusion-controlled mechanism to a liquid-vapor macroscopic interface enhanced by laminar flow-induced repeated surface renewals, which can also cause entrapment of vapor bubbles. 

The dimensions of the space available are in the nanometer range. At this length scale, water is supposed to behave as a constrained liquid, which follows rules of diffusion, flow and structuring more akin to those of gels than to those observed in free liquids [108]. Furthermore, if the silk is present as a gel phase, the structured nature of the water molecules is even more enhanced. This in turn affects the activities of the ions within this medium, especially where polyelectrolytes are also involved. This speculative scenario envisages that the chemical environment of nucleation is very different from a simple saturated solution, and that the thermodynamics and kinetics of nucleation are more akin to crystallization from hydrogels. The same situation exists also in collagen-mediated mineralization, where the tiny apatite crystals form inside the... 

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