Quiescent nucleation

Other authors, for example, Coppola et al. (2001) and Zheng and Kennedy (2004), considered the flow-induced change in free energy as a driving force. The starting point to construct a formulation is based on theories of Lauritzen and Hoffman (1960) and Ziabicki (1996) for the quiescent nucleation rate, which is then extended to include the flow-induced change of free energy. Coppola et al. 

Quiescent Nucleation Well below the nominal melting point, which is the temperature regime relevant for processing, the number density of spheru-lites in a quiescent melt is a unique function of the temperature [3]. This has been observed even in very pure melts, where the majority of nuclei are homogeneous, that is, made of the polymer itself rather than impurities [50, 153]. The number density versus temperature does not decrease in time, nor is it affected by annealing even above the equilibrium melting point. In our theoretical framework, this behavior is reproduced as follows ... 

Coppola et al. [142] calculated the dimensionless induction time, defined as the ratio of the quiescent nucleation rate over the total nucleation rate, as a function of the strain rate in continuous shear flow. They used AG according to different rheological models the Doi-Edwards model with the independent alignment assumption, DE-IAA [143], the linear elastic dumbbell model [154], and the finitely extensible nonlinear elastic dumbbell model with Peterlin s closure approximation, FENE-P [155]. The Doi-Edwards results showed the best agreement with experimental dimensionless induction times, defined as the time at which the viscosity suddenly starts to increase rapidly, normalized by the time at which this happens in quiescent crystallization [156-158]. 

A self-consistent approach to their model would be to include 7 (AG ) in the quiescent nucleation rate. It can then be checked if this is indeed negligible compared with the athermal part. 

Graham and Olmsted [166,167] used coarse-grained kinetic Monte Carlo simulations to simulate anisotropic nucleation based on the chain configurations obtained from a molecular flow model, the Graham-Likhtman and Milner-McLeish (GLaMM) model [168,169].These simulations confirm the power law with exponent 4 up to reasonably high shear rates (molecular stretch up to 3 to 4). They actually found an exponential dependence on the square of the molecular stretch. A practical problem of such an expression is that it contains an extra parameter besides the prefactor for the stretch, there is a prefactor for the exponential function as a whole, which gives the quiescent sporadic creation rate. Since quiescent nucleation is predominantly athermal, this parameter cannot be determined for common melts. 

A hydrate nucleating agent (precipitated amorphous silica) and a quiescent surface inhibitor (sodium dodecyl sulfate) were used in an attempt to initiate hydrates in the bulk phase. While the induction time (for detectable hydrate formation) was not predictable, in every case hydrate was initiated at a surface—usually at the vapor-water interface, but infrequently along the sides of the sapphire tube in the gas phase, and at the metal end-plate below the liquid phase. 

A rep < 1, Des < 1, the nucleation dynamics is stochastic in nature as a critical fluctuation in one, or more, order parameters is required for the development of a nucleus. For DeYep > 1, Des < 1 the chains become more uniformly oriented in the flow direction but the conformation remains unaffected. Hence a thermally activated fluctuation in the conformation can be sufficient for the development of a nucleus. For a number of polymers, for example PET and PEEK, the Kuhn length is larger than the distance between two entanglements. For this class of polymers, the nucleation dynamics is very similar to the phase transition observed in liquid crystalline polymers under quiescent [8], and flow conditions [21]. In fast flows, Derep > 1, Des > 1, A > A (T), one reaches the condition where the chains are fully oriented and the chain conformation becomes similar to that of the crystalline state. Critical fluctuations in the orientation and conformation of the chain are therefore no longer needed, as these requirements are fulfilled, in a more deterministic manner, by the applied flow field. Hence, an increase of the parameters Deiep, Des and A results into a shift of the nucleation dynamics from a stochastic to a more deterministic process, resulting into an increase of the nucleation rate. 

Hao, Z., Iqbal, A. and Herren, F. (1999c). l,4-Diketo-3,6-bis-4-chloro-phenyl-pyrrolopyrrole in /3 and y modification, prepd. by acid hydrolysis of soluble carbamate. Derivation and preparation by cooling. Ciba-Geigy Ltd. EP 690059 B1. [271 ] Harano, Y. and Oota, K. (1978). Measurement of crystallization of potassium bro-mate from its quiescent aqueous solution by differential scanning calorimeter. Homogeneous nucleation rate. /. Chem. Eng. J., 11, 159-61. [70]... 

In quiescent homogeneous melts, crystallization proceeds by the formation of isotropic quasi-spherical clusters known as spherulite. Figure 1 illustrates the final structure of a crystallized polymer (PHB), showing clearly the different spherulites originating from nucleation, whose growth competing to fill the space was stopped by impingement. 

The process of formation of the crystalline state is controlled by the kinetics of nucleation and this may arise in a number of ways. Primary nucleation in a quiescent state must be associated with foreign bodies such as deliberately added nucleating agents, such as fine talc particles, or residual impurities such as heterogeneous catalyst particles followed by spherulite growth. The plot of extent of crystallinity, (p, as a function of time is sigmoidal in nature and follows an Avrami equation of the form... 

A clear example of such quiescent secondary nucleation is provided by some natural fats, i.e., mixtures of several triglycerides. Consider Figure 14.6a. At 15°C, the number concentration of catalytic impurities observed was about 3 1016m-3, which means one impurity per 30 pm3. A droplet of... 

Agitation is frequently used to induce crystallization. Stirred water, for example, will allow only about 1°C of supercooling before spontaneous nucle-ation occurs, whereas undisturbed water will allow over 5 °C. Actually, very pure water, free from all extraneous matter, has been supereooled some 40 °C. Most agitated solutions nucleate spontaneously at lower degrees of supereool-ing than quiescent ones. In other words, the supersolubility curve Figure 3.9) tends to approach the solubility curve more closely in agitated solutions, i.e. the width of the metastable zone is reduced. 

The K value observed in fibres coloured with quinacridone pagment is comparable to the value obtained during crystallization of polypropylene melt in quiescent conditions in the presence of very effective p nucleating agents. 

Yu, Y. White, J.L. (2001). Comparison of structure development in quiescent crystallization, die extrusion and melt spanning of isotactic polypropylene and its compounds containing fillers and nucleating agents. Polym.Eng.Sci, Vol. 41, Issue 7, pp.1292-1298. 

Even at quiescent conditions the fundamental mechanisms of polymer crystallization, especially at an early stage, are still poorly understood [6-16]. For many years, nucleation and growth as a stepwise process has dominated the discussion [11,12]. In contrast to this view Strobl [13] proposed a multistage process to explain polymer crystallization, while others concluded on the basis of X-ray scattering data to a spinodal-assisted process [17-29]. Common to both views is that the crystallization is preceded by an ordered precursor (so-called pre-ordering). Clear structural information about such possible precursors - necessary to verify these hypotheses - is still scarce. As a resiJt, during recent years an important and still open debate has been going on about polymer crystallization. 

Figure 5.1. Crystallization half-time ofiPP vs. concentration of nucleating agent (sodium 2,2 -methylene bis-(4,6-di-tert-butylphenyl) phosphate) under quiescent conditions. [Adapted, by permission, from Patil, N Invigorito, C Gahleitner, M Rastogi, Polymer, 54,5883-91,2013.]...

Figure 5.18 shows that pure iPP is oriented in the flow direction. Under the quiescent conditions no anisotropy is observed in the scattering pattem. Apphcation of shear causes equatorial orientation of the peak in the flow directiom When iPP contains elongated nucleating agent, some orientation already appears at quiescent ciystalhzation (Fig-... 

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