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Question about the Gibbs free energy of mixing a polymer.

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We showed in lecture 16 that the Gibbs free energy of mixing a polymer of length X with a similar
solvent of length 1 can be approximated as: fl“Smile;M = kBTl¢s¢stp + CD5 In CPS + (EDP/X) In ¢pl For a long chain polymer with large X. the final term becomes negligible. Consider a long-chain
polymer in a monomer solvent, at an effective temperature of Xsp'i=fl.3. a] Plot the free energy of mixing {per site]+ flGmifo, as a function of clap. b} Determine the volume fraction of long chain polymer in the polymerurich phase of the equilibrium
two—phase system. [Hint: You will need the co—tangent construction usecl in worksheet 16.] c} If the oyerail sample has a polymer volume fraction of 0.5. at equilibrium, what volume fraction of
the mixture will he in the polymer—rich phase.

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