Rheology models for miscible blends

Table 7.1. Rheological models for miscible and immiscible blends...

Rheology is a part of continuum mechanics that assumes continuity, homogeneity and isotropy. In multiphase systems, there is a discontinuity of material properties across the interface, a concentration gradient, and inter-dependence between the flow field and morphology. The flow behavior of blends is complex, caused by viscoelasticity of the phases, the viscosity ratio, A (that varies over a wide range), as well as diverse and variable morphology. To understand the flow behavior of polymer blends, it is beneficial to refer to simpler models — for miscible blends to solutions and mixtures of fractions, while for immiscible systems to emulsions, block copolymers, and suspensions [1,24]. 

Yu et al. (2011) studied rheology and phase separation of polymer blends with weak dynamic asymmetry ((poly(Me methacrylate)/poly(styrene-co-maleic anhydride)). They showed that the failure of methods, such as the time-temperature superposition principle in isothermal experiments or the deviation of the storage modulus from the apparent extrapolation of modulus in the miscible regime in non-isothermal tests, to predict the binodal temperature is not always applicable in systems with weak dynamic asymmetry. Therefore, they proposed a rheological model, which is an integration of the double reptation model and the selfconcentration model to describe the linear viscoelasticity of miscible blends. Then, the deviatirMi of experimental data from the model predictions for miscible... 

Information on the monomeric friction coefficients of the constituent components in a miscible polymer blend is therefore vital for a better understanding of the rheological behavior (the dynamics) of miscible blends. Efforts to obtain such information have been reported by some investigators (Composto et al. 1990, 1992 Kim et al. 1994), who employed forward recoil spectrometry to measure the reptation (tracer) diffusion coefficients of the constituent components in a miscible polymer blend. Specifically, measurements of tracer diffusion coefficient (D ) allowed them to calculate monomeric friction coefficients using the following expression, which is based on the tube model (Kim et al. 1994) 3... 

Fang et al. (2005) studied the thermal and rheological properties of two types of m-LLDPEs, two LDPEs, and their blends. The C2+6 m-LLDPE-1 was immiscible, whereas the C2+8 m-LLDPE-2 was miscible with the LDPEs, indicating that increasing the length of SCB in m-LLDPEs promoted miscibility with LDPE. The Palieme (1990, 1991) emulsion model provided good predictions of the linear viscoelastic behavior for both miscible and immiscible blends. The low-frequency data showed an influence of the interfacial tension on the elastic modulus of the blends for the immiscible blends. 

Another early work in this area is that of DeMeuse and Jaffe from Celanese who used several techniques such as rheology. X-ray diffraction, and calorimetry to demonstrate that a model system consisting of blends of two LCP polyesters of differing HBA/HNA ratios were in fact not miscible. This is in contrast to low molecular weight liquid crystals in which two liquid crystals which form the same type are expected to be miscible. This paper also demonstrated that transesterification did not occur at an appreciable rate under the conditions used for melt rheology measurements. They also discuss the concept that for copolymers in which the distribution of copolymer ratio is extremely wide, there could be phase separation within a nominally homogeneous copolymer. This is precisely the mechanism invoked to explain the anomalous temperature dependence of viscosity of HIQ LCP. ... 

---