POLYMER BLENDS & THEIR RHEOLOGICAL BEHAVIOR 

This literature review covers generalities about immiscible polymer blends, the compatibilization using block copolymers or nanoparticles and the use of shear and extensional rheology to characterize polymer blends behavior.

Polymer blends: Generalities

The final properties of blends depend on the composition, but also on the interfacial properties and morphology. Over the years, numerous works on simple blends of two Newtonian fluids allowed the understanding of the different microstructural changes. Depending on the concentration in dispersed phase, the blend can have different morphologies .

For example, dilute systems usually display a droplet like morphology whereas both phases can create domains of uncertain shape when the concentration of dispersed phases increases. Our study focuses on the dilute or semi-dilute blends that exhibit a droplet like morphology. In this case, the creation of the microstructure is mainly governed by droplet breakup and coalescence under flow and after cessation of flow which are all described below.

Droplet breakup
Taylor [2], [3] and Rumscheidt and Mason [4] studied the dispersion of a Newtonian fluid into another Newtonian fluid subjected to small deformation. In such field, the droplets are deformed into an elongated shape in the direction of the flow. Taylor suggested that at low stress in a steady uniform shear flow .

Applying a flow can lead to droplet breakup when the interfacial tension forces cannot balance the viscous forces. That is what happens above a critical value of the capillary number: Cac. Below this value the droplets will not break anymore. Grace [5] provided data about this phenomenon by plotting Cac as a function of p for both simple shear and extensional flow  . The critical capillary number is significantly higher in simple shear than in elongation. In fact, in an elongational flow, droplet breakup can occur at any p whereas for a simple shear flow and a p ≥ 4, it is not possible to break the droplets anymore. Also, the weaker p, the higher Cac will be, which means that it will be more difficult to break the droplets of low viscosity in a highly viscous matrix. The lowest Cac, in other words the range where breakup is the easiest, is found for 0.1 ≤ p ≤ 1.0.

Coalescence
Coalescence is a process in which two or more droplets merge into one, resulting in a bigger droplet. Two types of coalescence can be distinguished:
• Flow driven coalescence where droplets are brought close by the flow .
• Static coalescence which involves only Brownian motion.

When two droplets collide, they develop a flat interface over which they are separated by a thin film of matrix fluid. If its thickness falls below a critical value hc (usually around 10 nm) then the film ruptures and the droplets coalesce [6]. Sundaraj and Macosko [7] showed that coalescence decreases if the matrix phase viscosity is above a critical value and the dispersed phase volume fraction under a critical value. The shear rate can also have an influence on the coalescence process: Van Puyvelde et al. [8] and Lyu et al. [9] both agreed that increasing the shear rate decreases coalescence which is in good agreement with the definition of the critical capillary number  .

Morphological hysteresis
In this figure, the coalescence limit under which coalescence occurs and the breakup limit above which breakup occurs can be visualized. The coalescence limit and breakup limit meet at a critical shear rate Ɣc . Above this value of shear rate, the steady state drop size is determined by a competition between coalescence and breakup  , here both can occur but the fastest one dominates. Below this critical number there exists a range of drops in the hysteresis region where the two phenomena cancel each other out  . In this region we observe neither coalescence nor breakup.

If we only want to observe coalescence, as Vinckier et al. [10] and many others did, it is possible to use the hysteresis present in these blends to do so. First, the blend undergoes a pre-shearing at high shear rate to generate a fine morphology and then the shear rate is lowered in step to below a critical value   allowing us to observe only coalescence.

Compatibilization of polymer blends

In order to obtain a fine and stable morphology, what is called compatibilizers can be added. They are expected to settle at the interface between the polymers and stabilize the morphology. Numerous papers focus on the use of block copolymer as compatibilizer. Recently, nanoparticles such as silica, clay or carbon nanotubes have been shown useful as well. Below the different types of compatibilizers that are commonly used in polymer blends are presented.

Block copolymers
The compatibilization effect of block copolymers is a subject that has been widely studied. It has become a usual way to stabilize polymer blends. They enhance the adhesion between the phases and allow to obtain finer dispersions by settling at the interface. There are two ways to compatibilize a blend: add a pre-synthesized block copolymer in the blend, or create it in-situ during the process the compatibilizer. The first option has the advantage of allowing a better control the molecular architecture of the compatibilizer. The second option is called reactive compatibilization. To directly generate the copolymer at the interface both polymers must have reactive groups. The main advantage of this option is that the compatibilizer is created directly at the interface so the problem of locate it there is no longer a concern. However, in this case, it is difficult to control the amount and the architecture of the compatibilizer [11], [12]. Most of the articles deal with the compatibilization with a pre-synthesized polymer, however, reactive compatibilization is often the solution chosen by the industry.

The presence of block copolymers at the interface can induce one or several of the following effects:
• reduction of the dispersed phase size
• decrease of interfacial tension
• inhibition of the droplet’s coalescence