Free Energy of Flexible and Rigid Rod Polymer Blends

Free Energy of Flexible and Rigid Rod Polymer Blends 

We consider mixtures of a rod-like molecule of length I and diameter D and a flexible polymer chain of contour length attp, where a (a ) is the length (volume) of a unit segment on the polymer chain and rtp is the number of segments on the polymer. Let Np and Nr be the total number of the polymer and rod, respectively. We here assume that the polymer is sufficiently flexible and does not contribute to any nematic ordering. On the basis of the second virial theory, discussed in Section 2.2.2, we take into account here both the excluded volume interaction (Eq. (2.12)] and the orientation-dependent attractive interactions between rods [Eq. (2.37)]. Then the function Pi is given by 

Extending the second virial approximation ]Eq. (2.5)] to a solution consisting of a flexible polymer and a rod, the free energy is given by ]19, 55]  

The last term shows the attractive interaction energy, Eq. (2.37), between rods and the term sin p describes the excluded volume, Eq. (2.12), between rods. We define here the dimensionless anisotropic parameter Xa(= 0), where e shows the 

The free energy [Eq. (2.40)] contains compressible fluids, namely, it corresponds to a pseudo-temary system consisting of a polymer, a rod, and a solvent molecule. We here derive the free energy of mixing for binary mixtures of the flexible polymer and the rigid rod. The free energy of mixing for the blends can be calculated by  

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