Interphase elasticity

Note The interphase elasticity is the capability of a deformed interphase to return to its original dimensions after the force causing the deformation has been removed. 

The modulus can be predicted by the elastic theory under the assumption of equal strain of the two phases (good adhesion), in the range of small strains. Adhesion is related to the radial pressure exerted on the beads due to the relative shrinkage of the polymer and the filler having different thermal expansion coefficients. Adhesion is therefore guaranteed in the case of small deformations and the influence of the chemical interaction on the interphase elastic modulus cannot be easily demonstrated. 

The Kerner-Nielsen equation (119) is a useful alternative to Eqs. (11.4) and (11.5) in the case when the elastic modulus of an interphase is substantially greater than that of the matrix. Most often, interphase elastic modulus is assumed to be equal to that of the filler resulting in a slightly overestimated elastic modulus of the compound. The effect of an interphase is then introduced in the Kerner-Nielsen equation substituting an effective filler volume fraction, Veff = (Vf + v,), for the filler volume fraction, Vt, (71) ... 

Kuznetsov et al. s methodological approach [72-75] provides another example of attempts to evalue the interphase thickness experimentally. Their approach was based on the hypothesis that the mesophase remains glassy while the bulk of the binder has already passed to the highly elastic state. Investigating the concentration... 

When a - 1 ( perfect adhesion) the elasticity modulus of the interphase decreases continuously from the fiber value to the matrix value, the interphase layer modulus being higher than that of the matrix. When a < 1, the interphase layer modulus assumes, some distance off the fiber surface, a minimum value smaller than the matrix value, and then increases tending asymptotically to the matrix modulus. 

Jayaraman, K.L.. Reifsnider, K.L. and Swain, R.E. (1993). Elastic and thermal effects in the interphase Part [[. Comments on modelling studies. J. Composite Technoi. Res. (JCTRERj 15, 14-22. 

As can be seen, the amorphous phase is not present in all samples and the mass fraction of the interphase decreases as the draw ratio increases. By drawing as many as 150 times, the mass fraction of the interphase becomes as low as 0.06. A sufficient effect of drawing is obtained and the elastic modulus becomes as high as 190 GPa. 

Naim [178] performed linear elastic stress analysis of residual stresses in unidirectional high-performance composites containing high-modulus fibers and an interphase region. Naim and Zoller [179] provided data for composites with thermoset and thermoplastic matrices, and showed by linear elastic stress analysis how the buildup of residual thermal stresses during fabrication is related to the disparate thermal expansion properties of the fibers and matrices. 

A different approach was used by Milner [326] in order to predict the phase diagram for asymmetric copolymer architectures (for example A2B, A3B etc. types of miktoarm stars). The free energy of the system can be calculated by summing the free energies of the polymer brushes existing on the two sides of the interphase. Milner described the effects of both chain architecture (i.e., number of arms) and elastic (conformational) asymmetry of the dissimilar chains, in the strong segregation limit, by the parameter... 

Owing to elasticity of the interphase, the first normal stress difference and the relaxation time could be calculated as [Schowalter et al., 1968] ... 

The experimental data of dynamic testing in the kHz region for ionic emulsions could be equally well described using either model. The emulsion elasticity was found to originate in droplet deformation. For non-ionic emulsions, only one relaxation time was observed. The data were interpreted in terms of the second Oldroyd s model, in which the interfacial tension is more important than the viscoelasticity of the interphase. 

Functionalized Polyolefins and Aliphatic Polyamide Blends Interphase Interactions, Rheology, and High Elastic Properties of Melts... 

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