Spherulites nucleation

Figure 12.19. Optical micrographs of (a) PPBS spherulites, (b) PPBC spherulites in the presence of EPDM and (c) PPBC spherulites nucleating from interface with EPDM.

Another cause for tennis racket type patterns is the incompleteness of development of spherulites. Spherulites nucleate from bundle-like crystals which evolve into sheaves and eventually into complete spheres. Such evolution has been idealised by a model of sectors of spherulites" " ... 

Z. Bartczak, E. Martuscelli, A. Galeski, Primary spherulite nucleation in polypropylene-based blends, in Polypropylene. Structure, Blends and Composites, ed. by J. Karger-Kocsis. Copolymers and Blends, vol. 2 (Chapman and Hall, London, 1995), pp. 25-49 Z. Bartczak, A.S. Argon, R.E. Cohen, T. Kowalewski, Polymer 40, 2367-2380 (1999a)... 

Bartczak Z. Galeski A. PraceUa M. Spherulite nucleation in blends of isotactic polypropylene with high density polyethylene. Polymer. 1986,27,537-543. 

To characterize the spherulitic nucleation during nonisothermal crystallization, the Ozawa equation is applied, which could be obtained by integrating twice by parts the Avrami equation and assuming cooling at the constant rate, a. The slope of the plot ln -ln[l - a(T)] versus In(fl) equals two or three for instantaneous nucleation, three or four for nucleation prolonged in time, in two- and three-dimensional crystallization, respectively. The values from three to four, depending on temperature range were obtained for iPP from DSC nonisothermal crystallization [4],... 

Nowacki R, Monasse B, Piorkowska E, Galeski A, Haudin JM (2004) Spherulite nucleation in isotactic polypropylene based nanocomposites with montmOTillonite under shear. Polymer... 

Structure. In polyacetals this has been termed transcrystallinity [159,146]. Transcrystalline growth is controlled by the heat flow to the mold wall and is initiated by the cold mold wall. The melt at the wall cools rapidly, and dense spheru-lite nucleation takes place adjacent to the wall. Spherulites nucleated close to the wall, in the thermal gradient, have parabolic interfaces... 

Figure 4.14 presents crystallization isotherms of polyethylene obtained in time dependent measurements of the density during a spherulite nucleation and growth process. Isotherms are given in terms of the crystallinity, de-... 

Fig. 4.14. Kinetics of crystallization associated with spherulite nucleation and growth, observed for PE (M = 2.85 10 ) in time dependent density measurements at the indicated temperatures. Dilatometric data of Ergoz et al.[38]...

Nowacki, R., Monasse, B., Piorkowska, E., Galeski, A., Haudin, J.M. Spherulite nucleation in isotactic polypropylene based nanocomposites with montmorillonite under shetir. Polymer 45, 4877-4892 (2004)... 

One form of spherulite nucleation is illustrated in Figure 3.61. The single lamella in the first image (a) contains an induced nucleus that appears as a barely visible dot slightly below the midpoint. From this grow two lamellae in panel (b). As these new lamellae are on the same side of the parent lamella, they do not correspond to a screw dislocation. Additional induced nuclei... 

At time t, a volume (or a surface) F of a single unimpinged spherulite nucleated at time t, equals the volume (or the area) of a sphere (or a circle) having the radius r(T, t) ... 

When neighboring spherulites impinge, the boundary is formed. It can be noticed that for any two spherulites nucleated at Ti and T2, a difference between their radii, expressed by Equation (7.1a), remains constant during the further growth ... 

General Equation (7.19a) and Equation (7.19b) describing nonisothermal crystallization can be derived based on the probabilistic approach in a simpler way [17,18]. It is obvious that the point A remains at time t outside of all growing spherulites nucleated instantaneously at zero time, if no nuclei appeared in a sphere around the point A, having a radius equal to r(0, t) and a volume of E(0, t). According to Equation (7.15), the probability of this event is ... 

In the case of spontaneous nucleation one has to consider nucleation events occurring in consecutive infinitely small time intervals (tj T + dr) until time t, where Ti = 0 and Ti = i dr. The probability that the point A remains at time t beyond the reach of spherulites nucleated during the time interval (t , T + dr) can be written in the following form ... 

The point A will be occluded at time t by one spherulite nucleated at time x = t, if a nucleation site of this... 

Figure 7.3 Scheme of the conical zone in space and time drawn for 2D crystallization. From two spherulites nucleated at time r, only one, with a center at point P, that is, at distance r(r,t) from A can reach A at time t. Modified from Piorkowska, E., et al. Critical assessment of overall crystallization kinetics theories and predictions. Prog. Polym. ScL 2006,57,549-575. Copyright 2006, with kind permission from Elsevier. 

Both the approaches just described are equivalent. In both cases the number of spherulites nucleated per unit volume around A increases with time ... 

Calculation of the probability for A to be occluded at time t by one spherulite nucleated either inside a polymer or on polymer boundaries leads to the equations describing the respective components of conversion rate. Integration over time allows derivation of the separate expressions for two contributions to cr. the contribution from spherulites nucleated in the bulk of a polymer, a , and the contribution from those nucleated on the sample boundaries, respectively ... 

At very low crystallization temperatures (Fc < 75°C), the growth of iPB crystals in the blends proceeds simultaneously with the crystallization of iPP. The presence of iPB crystals may induce additional nucleation of iPP at the interface between the two polymers thus, two populations of spherulites can appear in the blends small iPB spherulites nucleated inside the iPB-rich phase and iPP spherulites nucleated at the interfaces. As a consequence of the above phenomena, the size of iPP spherulites in blends decreases at large undercooling, while it increases at low undercoolings, as compared with plain iPP crystallized at the same Fc [60]. 

In particular, considerable changes have been found in the spherulite nucleation, growth rate, and overall kinetics of crystallization of the blends as compared to pure iPP [83]. 

Irrespective of the reasons, the strong nucleation on fibers results in structures consisting of columnar entities with transcrystalline morphology. The content of spherulites nucleated in polymer bulk depends on fiber content and nucleation density on fiber surfaces and also inside a polymer matrix. 

Moreover, Equation (13.8) with Po(0 given by Equation (13.7) can be derived based on the concept of extended volume in this case all spherulites nucleated on a fiber have to be treated as a single domain with volume determined by an external envelope calculations require accounting for randomness of positions of nuclei along a fiber. 

Figure 13.8 Consecutive stages of isothermal crystallization in thin film of nanocomposite iPP/PP-g-MA/o-MMT (87 10 3 by weight), between glass sUdes, at 128°C. Reprinted from Nowacki, R., et al. Spherulite nucleation in isotactic polypropylene based nanocomposites with montmoriUonite under shear. Polymer 2004,45,4877-4892, with kind permission from Elsevier, Copyright 2004.

Swaminarayan and Charbon presented two methods of simulating the growth of an isolated spherulite the arborescent method and the front-tracking method [44]. In a second article [45], the same authors coupled the front-tracking techniques with (1) a stochastic model for spherulite nucleation, (2) a cellular model for spherulite impingement and solid fraction evolution, and (3) a finite difference method for solving the energy equation. This multiscale approach predicts the final microstructure in a macroscopic part. 

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