Droplet-Matrix Structures

Components As most polymers are highly viscous and have closely-matched densities, buoyancy, inertia and Brownian motion can generally be neglected. In that case, the dynamics of isolated Newtonian droplets in a Newtonian matrix is determined by two independent dimensionless groups the capillary number Ca and the viscosity ratio p [29]. The capillary number represents the ratio of the deforming hydrodynamic stresses over the restoring interfacial stresses  

It can be seen that the droplet deformation obtained from the Taylor model increases linearly with the Cfl-number. The orientation angle p of the droplet with respect to the 

When the droplet deformation further increases, it is not possible anymore to find analytical solutions for the complex fluid mechanics problem of a deforming droplet in flow. For those cases, models that employ a shape tensor S are often used to describe the droplet dynamics. In a first approach, an ellipsoidal droplet shape is assumed and the tensor S is set to evolve with time according to the following equation [20]  

In this evolution equation for the shape tensor, S, D, and Q are the dimensionless versions of the shape tensor, rate of deformation tensor and vorticity tensor respectively. The eigenvalues of S represent the square semi-axes of the ellipsoid. The factors/j and/2 depend on the viscosity ratio and Ca  

These factors were chosen as such that the small deformation model of Taylor is recovered for small deformations. The left-hand side of Equation 19.6 represents the change of S with time and its rotation with the overall flow field. The first term on the right-hand side represents the restoring action of the interfacial tension, where g(S) is introduced to preserve the droplet volume. The second term on the right-hand side captures the deformation of the droplet with the flow. This equation allows to accurately predict the droplet deformation in flows with an arbitrary but uniform velocity gradient. In case of shear flow, the following expression is obtained for the steady state deformation parameter [30]  

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Figure 19.1 Schematic representations of (a) temperature-composition diagram for a partially miscible blend with a lower critical solution temperature and most common blend morphologies including (b) droplet-matrix structure, (c) fibrillar morphology, (d) cocontinuous...

In the present chapter, the morphology development of immiscible binary polymer blends is discussed. First, morphology development in droplet-matrix structures is described. Subsequently, the dynamics of fibrillar structures is reviewed and finally cocontinuous structures are briefly discussed. Although the main aspects of polymer blending are well established and polymer blends are already widely used in commercial products, recent novel insights in the areas of miniaturization and particle stabilization have opened new research topics in the area of polymer blending. In the last part of this chapter, these recent advances in polymer blend systems are briefly discussed. 

Figure 19.14 Transition from droplet-matrix structure to cocontinuous structure (a) Neat 60/40 PPS/PA66 blend. Zou et al. [193], Reproduced with permission of Elsevier, (b) 60/40 PPS/PA66 blend with 0,3 phr multiwall carbon nanotubes. Zou et al. [193]. Reproduced with permission of Elsevier, (c) Schematic representation of percolated particle network in a cocontinuous structure.

A second class of models directly relates flow to blend structure without the assumption of an ellipsoidal droplet shape. This description was initiated by Doi and Ohta for an equiviscous blend with equal compositions of both components [34], Coupling this method with a constraint of constant volume of the inclusions, leads again to equations for microstructural dynamics in blends with a droplet-matrix morphology [35], An alternative way to develop these microstructural theories is the use of nonequilibrium thermodynamics. This way, Grmela et al. showed that the phenomenological Maffettone-Minale model can be retrieved for a specific choice of the free energy [36], An in-depth review of the different available models for droplet dynamics can be found in the work of Minale [20]. 

We decided to rank apart the phase morphology in ternary immiscible blends because it can be droplet-in-matrix, co-continuous, or a mixture of both and, in many situations, an encapsulated droplet-in-matrix structure. 

Wood Hill (1991b) induced phase-separation in the clear glasses by heating them at temperatures above their transition temperatures. They found evidence for amorphous phase-separation (APS) prior to the formation of crystallites. Below the first exotherm, APS appeared to take place by spinodal decomposition so that the glass had an intercoimected structure (Cahn, 1961). At higher temperatures the microstructure consisted of distinct droplets in a matrix phase. 

Barry, Clinton Wilson (1979) examined the structure of cements prepared from a glass powder from which very fine particles had been removed to improve resolution. The microstructure of the set cement is clearly revealed by Nomarski reflectance optical microscopy (Figure 5.14). Glass particles are distinguished from the matrix by the presence of etched circular areas at the site of the phase-separated droplets. The micrograph... 

As has already been emphasized in Fig. 1.1, there is the further problem of connecting the mesoscopic scale, where one considers length scales from the size of effective monomers to the scale of the whole coils, to still much larger scales, to describe structures formed by multichain heterophase systems. Examples of such problems are polymer blends, where droplets of the minority phase exist on the background of the majority matrix, etc. The treatment of... 

Changes in the natures of individual phases of or phase separation within a formulation are reasons to discontinue use of a product. Phase separation may result from emulsion breakage, clearly an acute instability. More often it appears more subtly as bleeding—the formation of visible droplets of an emulsion s internal phase in the continuum of the semisolid. This problem is the result of slow rearrangement and contraction of internal structure. Eventually, here and there, globules of what is often clear liquid internal phase are squeezed out of the matrix. Warm storage temperatures can induce or accelerate structural crenulation such as this thus,... 

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