Flory theory, determining chemical potentials

The change of chemical potential due to the elastic retractive forces of the polymer chains can be determined from the theory of rubber elasticity (Flory, 1953 Treloar, 1958). Upon equaling these two contributions an expression for determining the molecular weight between two adjacent crosslinks of a neutral hydrogel prepared in the absence of... 

This fact can be demonstrated as follows. Let us determine the value of the well-known Flory parameter x, which corresponds to the 6 point (i.e. to the point of inversion of the second virial coefficient of the solution of rods) in the Flory theory of Ref.9). This can be done by expanding the chemical potential of the solvent in the isotropic phase (Eq. (16) of Ref.9 ) into powers of the polymer volume fraction in the solution, and by equating the coefficient at the quadratic term of this expansion to zero this procedure gives Xe = 1/2 independently of p. On the other hand, it is well known26,27) that the value of x decreases with increasing p and that X < 1 at p > 1. The contradiction obtained shows that the expressions for the thermodynamic functions used in Ref.9) are not always correct... 

Phase separation occurs at temperatures satisfying x>Xc Equation [27] reveals that then the second derivative will be negative for a range of values. Because / is often inversely proportional to temperature (cf. solubility approach discussion), this implies that phase separation will occur at reduced temperatures. The calculation of the critical point and the spinodal within the Flory-Huggins theory is rather simple, but the determination of the coexistence curve is slightly more involved. For this, the chemical potential equations ) and A/U2 (p ) = Afi2 (p ) have to be... 

Harvey and Leonard were the first who analyzed the thermodynamics of copolymerization from the viewpoint of the Flory-Hu ins theory of intercomponent interactions in polymer solutions. Unfortunately, in deriving their equations, Harvey and Leonard assumed the same composition of copolymer chain ends as that of the whole copolymer. Mita provided an analogous solution without this assumption. He formulated the overall equilibrium as the equality of chemical potentials of comonomers and copolymer units fi = (9G/9N c)7-p N,(i c) where, i are comonomer (A, B,. ..) or comonomer unit, N,- is the number of moles of the system component i, G is the Gibbs energy of the system the partial derivative is determined for constant temperature, pressure. 

The chemical potential of the solvent in the solution can be determined using the Flory-Huggins theory and is given by combining Equations (3.39) and (3.43) as... 

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