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At the theta point, a chain is expected to have a value of n = ½. If you look at the equation on Page 8 you will notice that the <s2> scales linearly with N: a straight-line graph is obtained.
There are still much controversies regarding the behavior (or indeed the location) of a theta chain. We will not discuss the controversies as this would lead to a lengthy discussion.
The value of ½ is interesting because this is also the value for an imaginary chain where the beads are allowed to freely overlap with one another. In other words, NO interaction exists between beads or solvent molecules. Such polymer obviously does not exist in reality.
Theorists called such chains as the non-excluded volume (NEV) chains. They are important in theoretical point of view as they are frequently used as starting steps to understand various chain properties of real polymers. In fact NEV chains can usually be handled
mathematically without resolving to computer simulations.
There is a great deal of interests in studying the behavior of coil-globule transitions. For example, the structure of a protein is compact and retains a globule shape. This corresponds to the biologically active site. When heated (temperature increases) the protein chain unfolds to give a looser coil shape and its
biological activity stops. Obviously, protein molecules are much more complex than most other polymeric materials and there are other factors influence the biological activities.
So far we have only discussed chains in 3-dimensions. In a 2-dimensional world coil-globule transitions can still be observed, but with different values of n. For 2-dimensional coil, theta and collapsed chains will have values of n
of 4/3, 4/7 and 1/2, respectively. Note that do not confuse the 2-dimensional collapsed chain with that of 3-dimensional theta chain which have similar value of n. The former is pretty compact and shows no ideal NEV bahavior!
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