Consider a linear polymer chain with N = 400 Kuhn monomers, with a Kuhn length of b = 4 A, in a solvent with a -temperature of = 27 C. The mean field (i.e., Flory) approximation of the interaction portion of the free energy for a chain of size R is:

All temperatures are in Kelvin. The three-body term can be approximated as w b 6 . (i) Use Flory theory to estimate the size of the chain that is swollen at the -temperature due to three-body repulsion. (ii) For what values of T does the two-body repulsion dominate over the three-body repulsion? (iii) What is the number of Kuhn monomers in the largest chain that stays ideal at T = 60 C?

1. Consider a linear polymer chain with N=400 Kuhn monomers, with a Kuhn length of b=4A, in a solvent with a -temperature of =27C. The mean field (i.e., Flory) approximation of the interaction portion of the free energy for a chain of size R is: VFint=R3Fint=kBT[v(R3N)2+w(R3N)3+] where the excluded volume of a monomer can be approximated as: v(1T)b3 All temperatures are in Kelvin. The three-body term can be approximated as wb6. (i) Use Flory theory to estimate the size of the chain that is swollen at the -temperature due to three-body repulsion. (ii) For what values of T does the two-body repulsion dominate over the three-body repulsion? (iii) What is the number of Kuhn monomers in the largest chain that stays ideal at T=60C