Palieme model

Figure 9.17 Measured storage modulus of 11% polyisoprene (rjo = 60.9 Pa s) in poly-dimethylsiloxane (rjo = 73.7 Pa s) after preshearing at four different shear rates, along with predictions (lines) of the Palieme model, Eqs. (9-38) and (9-39). The interfacial tension, r = 3.2 dyn/cm, and the droplet radii were measured, so there are no fitting parameters. (From Kitade et al. 1997, with permission ftom the Journal of Rheology.)...

During the last few years the preparation of PNC with polymer blends as the matrix has expanded for two reasons (i) improved dispersion of the minor polymer phase and (ii) improvement of the blend performance. Several publications include experimental data on the flow properties in dynamic shear. As already discussed, the only fundamental approach involved the use of Palieme model, and thus has been limited to low clay content [371, 372, 377]. Table 2.4 lists the publications that detail the dynamic shear behavior of these systems. 

Figure 5.21 Comparison of experimental results with the models for the PS-Ox/EP-MA reactive blend at 30 wt.% rubber (A) PS-Ox matrix (O) Experimental results (+) Extended van der Poel model prediction (x) Palieme model prediction. T = 180°C...

Oldroy s model was extended by Palieme (1990) to emulsions with polydisperse spherical drops. The model considered viscoelastic liquids, the concentration range was extended up to that at which drop-drop interactions start complicating the flow field. However, the drops must be spherical, undergoing small deformation, and the interfacial tension coefficient was considered constant, independent of stress and the interfacial area. The following relation was derived for the complex modulus ... 

Paheme emulsion model failed to describe the dynamic modulus of the PP/EPDM blends after radiation, because the viscosity ratio increased significantly and the rubber phase changed from deformed droplets to hard domains after radiation (Cao et al. 2007). Intercoimections among inclusions of the dispersed phase (Shi et al. 2006) and the existence of multiple emulsion (emulsion-in-emulsion) structure exhibiting different relaxation domains in compatibilized systems are other factors contributing to the failure of Palieme s model (Friedrich and Antonov 2007 Pal 2007). 

The enhanced viscoelastic functions are attributable to additional relaxation processes that occur at low frequencies associated with deformation of the dispersed phase. Therefore, for cases such as mPE/LDPE, where partial miscibility at high LDPE content and the extremely different relaxatimi times of the phases in the blends rich in mPE are observed, a hybrid model including the double reptation approach for the matrix and the linear Palieme approach for the whole system could successfully explain the viscoelastic response of these blends (Peon et al. 2003). 

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. 

M. Bousmina, J.F. Palieme, L.A. Utracki, Modeling of polymer blends behavior during capillary flow. Polym. Eng. Sci. 39(6), 1049-1059 (1999)... 

J. Pe6n, C. Dominguez, J.F. Vega, M. Aroca, J. Martinez-Salazar, Viscoelastic behaviour of metallocene-catalysed polyethylene and low density polyethylene blends use of the double reptation and Palieme viscoelastic models. J. Matra-. Sci. 38,4757-4764 (2003)... 

The dynamic behavior of polymer blends under low strain has been theoretically treated from the perspective of microrheology. Table 2.3 lists a summary of this approach. These models well describe the experimental data within the range of stresses and concentrations where neither drop-breakup nor coalescence takes place. The two latter models yield similar predictions as that of Palierne. The last entry in the Table 2.3 is an empirical modification of Palieme s model by replacement of the volume fraction of dispersed phase by its efiective quantity (Eq. (2.24)), which extends the applicability of the relation up to 0 < 0.449. However, at these high concentrations the drop-drop interactions absent in the Palierne model must complicate the flow and coalescence is expected. The practical solution to the latter problem is compatibilization, but the presence of the third component in blends has not been treated theoretically. 

Structure and properties for binary blends of PLA and PBS are studied both in the solid and molten states. It is foimd that PLA and PBS are immiscible in the molten state and the blends exhibit phase-separated structure. The interfacial tension between PLA and PBS is estimated using a rheological emulsion model proposed by Palieme and foimd to be 3.5 mN/m as shown in Figs. 4.29,4.30 and 4.31. Basic theological parameters are also evaluated for PLA and PBS. It is suggested that the entanglement molecular weight of PLA is lower than that of PBS. 

The model due to Palieme accounts for the viscoelastic nature of the component phases and the particle size distribution in non-dilute emulsions [91]. The complex shear modulus of the blend can be expressed in terms of the complex moduli of each phase, the interfacial tension, and the radii of the dispersed droplets... 

The first point is described in Section 11.4 using the thermodynamics theory and in the present section with Palieme s model. The second point is also largely described in the present section, whereas the last point is hard to describe as there is a lack of investigations available in the literature because interfacial adhesion is difficult to evaluate directly. Mainly, an indirect method, such as the evaluation of the mechanical properties is used. 

For such blends containing the droplets embedded in matrices, linear viscoelastic moduli can be calculated from several models formulated on the basis of the local stress balance (or other phenomenological criteria). " Among these models, the emulsion model proposed by Palieme appears to be most frequently compared with the experimental data. The complex modulus G =G + iG" deduced from this model can be summarized as ... 

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