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I am running on-lattice simulations of polymers. I am testing out different Hamiltonians and testing different regimes to test if they yield interesting behavior. My question is, how do I rigorously prove the existence of a coil-globule transition, in the event I see signatures of a collapse, or signatures of expansion in my polymer?

For example, I am running a simple Flory-Huggins-type simulation of a single chain on a lattice with solvent. The monomer units and solvent occupy the same volume. There is no solvent-solvent interaction, but there is monomer-monomer interaction $E_{mm}$ and a monomer-solvent interactino $E_{ms}$.

From FH theory, I see that for $E_{ms} > 2 E_{mm}$, it is considered a good solvent, and for $E_{ms} < 2 E_{mm}$, the solvent is considered a bad solvent.

If I run a simulation of a polymer in a bad solvent, I see that it starts of in a collapsed (small $R_g$) state and then expands. My question is, when can I say it went from a collaped (globule) to a expanded (coil) state?

What is the battery of tests that I perform on my simulation to prove that at in certain energetic regimes one can see this kind of behavior? I am following this paper, but what I do not get is how they obtained the theta condition. When I have $E_{ms} = 2 E_{mm}$, I see excluded volume like behavior $\nu = 0.58$, not $\nu = 0.5$.

I see kinks in $C_v$, I see drops in $R_g$ and an associated increase in monomer-monomer contacts, but is this sufficient to prove that a coil-globule transition is taking place?

I am following this paper: 10.1002/polb.21024.

My question is, how are the authors finding the theta-point? In Fig. 1, they plot radius of gyration. But my question is, at what temperature are these calculations being performed? How do I find the theta energy if the Radius of Gyration of the polymer is also dependent on temperature?

I would appreciate any advice or experience that you have with breaking down this phenomena!

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  • $\begingroup$ I gave my +1 long ago, but I wonder if there's been any progress with this over the last 6 months? $\endgroup$ Commented Dec 10, 2022 at 16:31

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