Phase coarsening

S.P. Marsh and M.E. Glicksman Kinetics of Phase Coarsening in Dense Systems. Acta Mater. 44, 3761 (1996). 

Molten polyethylenes of different type chain stmctures usually are immiscible (see Chap. 2, Thermodynamics of Polymer Blends ). Upon crystallization the spher-ulites of one PE (having higher Tm) are encapsulated by those of the other PEs. Co-crystallization of two PEs into a single-type isomorphic cell is rare (Utracki 1989a). However, due to low interfacial tension coefficient, the phase coarsening is slow. 

Mirabella, F.M. (1994) Phase separation and the kinetics of phase coarsening in commercial impact polypropylene copolymers. /. Polymer Sci. Polymer Phys., 32,1205-1216. 

Ti2 is the shear stress, <7 is the interfacial tension, is the volume fraction of the dispersed phase, Epf is the bulk breaking energy, and P, is the probability that a collision between two close particles will result in coalescence leading to phase coarsening. It is clear from the expression that the particle size at equilibrium diminishes as the shear stress increases, the interfacial tension decreases, and the volume fraction of the dispersed phase decreases. This theory has been verified experimentally for several immiscible blends where a master curve of particle size as a function of composition was found to follow a + dependence [11]. Fortelny et al. [12] have propos an expression (Equation 1.5) that accounts for a drop breakup (the first term in Equation 1.5) and a coalescence process (the second term in Equation 1.5) ... 

SEM photomicrographs of cryofractured and THF-etched surfaces of 20/80 LDPE/PS added with 10 wt% triblock copolymer. (A) not aimealed (B) aimealed for 150 min at 180°C. In the absence of compatibilizers the LDPE phase exhibited a substantial phase coarsening via a coalescence process. (From C. Harrats, R. Fayt, R. Jerome, and S. Blacher, /. Polym. Sci. Part B Polym. Phys. 41,202-216,2003. With permission.)... 

In the PP/EVA blend system, the effect of mixing time (converted as residence time) on phase coarsening has revealed a substantial linear particle size increase as a function of the mean residence time. As illustrated in Figure 22.4, the phase morphology is set up very fast (within a minute) and starts evolving by a more dominant coalescence process as the residence time is increased. The particle size is doubled after 2 min 30 s of residence time in the extruder. The pronounced coarsening effect is ascribed to a decrease in the viscosity of the dispersed phase a low viscosity favors flow of particles, their subsequent collision, and merging. 

Recent advances in the development of TMF predictive models have included the incorporation of solder microstructure as a state variable in the constitutive equation [92,93]. A contour map (Fig. 30) shows the Pb-rich phase coarsening predicted in a leadless chip solder joint subjected to six thermal cycles having temperature limits of —50° and 80°C, ramp rates of 6°C/ sec, and dwell times of 10 min at both limits. The microstructure-based, viscoplastic constitutive equation for Pb-Sn solder improves the accuracy of solder fatigue strain predictions throughout the interconnection geometry. It provides a real-time adjustment of the local solder mechanical properties resulting from local changes in the solder microstructure (i.e., the Pb-rich phase). 

FIG. 30 Contour map of Pb-rich phase coarsening in a 37Pb-63Sn chip capacitor solder joint predicted by a computational model. The Pb-rich phase size (coarsening) is the metric of fatigue deformation in the solder. The cycling conditions were 6 cycles temperature limits of —50 C and 80°C ramp rates of 6°C/sec, and dwell times of 10 min. (Courtesy of Sandia National Laboratories.)... 

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