Stiffness mismatch

We note that there are hints in Table I, and structural fluctuation quantities such as Ag(r) discussed elsewhere, that as N or stiffness mismatch increase the excess free energy of mixing also increases and the blend is less stable. Thus, the possibility of entropy-driven phase separation due to packing frustration of dissimilar flexibility chains as N increases beyond 200 remains open based on the simulation studies of Ref. 97. 

No phase separation is found for a stiffness asymmetry variable less than roughly 0.4, or for low values of N and any value of stiffness mismatch (consistent with simulation). Since experimentally one expects for hydrocarbon polymers that < 0 (since polyethylene has a high aspect ratio), this result suggests that a purely entropy-driven mechanism cannot account for the facile tendency of polyolefins to demix. Moreover, for chain parameter values typical of most semiflexible polymers of interest, the excess entropic effects appear small and much weaker than enthalpy related considerations associated with local packing differences between species (see Section V). 

Composites provide an atPactive alternative to the various metal-, polymer- and ceramic-based biomaterials, which all have some mismatch with natural bone properties. A comparison of modulus and fracture toughness values for natural bone provide a basis for the approximate mechanical compatibility required for arUficial bone in an exact structural replacement, or to stabilize a bone-implant interface. A precise matching requires a comparison of all the elastic stiffness coefficients (see the generalized Hooke s Law in Section 5.4.3.1). From Table 5.15 it can be seen that a possible approach to the development of a mechanically compatible artificial bone material... 

This similarity in reactivities probably derives from a fortuitous cancellation of substituent effects in 11. Fluorination increases chain stiffness and creates an unfavorable polarity mismatch between an electrophilic radical and an electron-poor double bond, but this is offset by the significant decrease of 7r-bond energy in 11. The vinyl ether 12 analog cyclizes about seven times faster than 11, which is consistent with the known lower 7r-bond energy and higher free-radical reactivity of perfluorovinyl ethers vs perfluoroalkenes [142]. 

To probe some of the possibilities for inadequate performance listed above additional low molecular weight, homo PB can be blended into the particles to coarsen the inner wave length at constant composition to preserve the average mechanical properties of the particles. Alternatively, additional PB or additional PS could be blended into the particles to increase the thickness or scale of only one of the components and simultaneously also either increase or decrease the stiffness and thermal expansion mismatch between the particles and the surrounding matrix. 

The SC solutions appear to run into difficulties when there is a large elastic mismatch between the constituent phases, for example, at high concentrations of a rigid phase in a compliant matrix or of a porous phase in a stiff matrix. The latter situation will be discussed in Section 3.6. One approach to this problem is known as the Generalized Self-Consistent Approach, the concept behind which is illustrated in Fig. 3.14. Instead of a single inclusion in an effective medium, a composite sphere is introduced into the medium. As in the composite sphere assemblage discussed in the last section, the relative size of the spheres reflects the volume fraction, i.e., V = a bf as before. Interestingly, this approach leads to the HS bounds for the bulk modulus. The solution for the shear modulus is complex but can be written in a closed form. 

This behaviour we reported yet in the past (Schneider, 2010), where we compared the mismatch between crystalline and global strain by a factor in the order of 10 indicating the different stiffness of the crystallites compared to that of the whole specimen due to the relatively soft amorphous regions. 

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