Properties of Theta Solutions

2 Properties of Theta Solutions Solutions in the theta condition have A2 = 0. When A2 = 0, the second-order term in Il/Ilideai = 1 + A2MC + A Mc + (Eq. 2.20) is absent. The nonideality of the solution does not become apparent until the third-order term A Mc becomes sufficiently large. The osmotic pressure is 

In Section 1.4.2, we derived Rp = for an excluded-volume chain using Flory s method. Here, we use a similar method to derive Rp = for theta chains. The difference in the free energy A ,h of the chain is in the second term of Eq. 1.63. For the theta chains, binary interaction is effectively absent (A2 = 0) and therefore the leading term in the polymer-polymer interaction is b R (N/R y = b N /R, which is due to the ternary interactions. Then, Ajh is given as 

Ach minimizes when b A JksT)/bR n=R = 0, that is, Rp = bN , reproducing the experimental results. The relationship becomes questionable when N is large, however. See Problem 2.17. 

The nature of the theta solvent can be better understood in the lattice chain model. We choose the interaction with a solvent to be zero eps = epp = 0. Then X= -(Z/2)epp/T. The theta condition, 1 /2, is realized y epp/kpT = -1 /Z. 

This negative interaction in the monomer-monomer contact promotes association between monomers and contracts the polymer chain. The repulsive interaction due to the excluded volume is compensated by the attractive cpp. 

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