When it is uncoiled it can considered to be associating with the solvent i.e it is mixed. When it coils it associates with itself rather than the solvent and is demixed.

This type of system has an enthalpy of mixing term that is negative due to H-bonding between the two components of the mixture. However the H-bonding leads to a pairing up of the H-bonding sites on the water and the polymer chain in this case. This is more ordered than the de-mixed state. Thus the Entropy of mixing is negative. In the expression (deltas omitted) G = H -TS we can see that the curve of deltaHmix with composition will thus be a kind of parabola (OK not quite) that is always negative, but the -ve deltaSmix term in the expression is multiplied by -1 and T and hence it forms a similar (but not exactly the same shape) curve pointing in the positive direction. This makes the entorpy and enthalpy terms work in opposite directions to each other, with the entropy term being multiplied by T, but it it the enthalpy term and not the entropy term that causes the mixing here when you consider if deltaGmix is going to be overall negative. his occurs at lower T. Now as T increases the mixture becomes thermally agitated making it harder for the H-bonds to stay pointing in a straight line. This weakens them. Eventually they may break at some temperature around the critical point. Breaking H-bonds will be endothermic so that DeltaHmix gets less negative. At the same time entropy increases due to a bit more disorder - but it never switches sides to point the DeltaSmix with composition curve the other way and to counter ths T in the -TS term getting bigger. So the curve gets bigger and still points positive. Now a funny thin happens when the two curves have similar magnitue, slightly different shape and point in opposite directions. Whe you add then together to make the deltaGmix curve with composition then two minima form in the curve. These two minima are now at the stable compositions that will form on the binodal line on the phase diagram and the.

Actually in this temperature range there is a slightly different deltaGmix with composition curve for each of the temperatures in the lower T region the minima are closer together in composition and at highet T the minima are further appart in composition so the resulting phase diagram is a curve with a minimum at the lower T rather  one with a maximum at a higher T.

It is a common situation in mixtures where the entropy of mixing increases due to association typically when there are H-bonds and the dominating factor when they mix is enthalpy. This enthalpy can be overcome by raising T and the system breaks into twp components and readjusts the composition to a new pair of stable mixtures.

Now in the case of coiling and uncoiling the composition is probably best described by a new form of the polymer more or less coiled than previously, where the remaining water H-bonded to the chain has a ration with the NH residues that matched the equivalent of an new minimum in the deltaGmix with composition curve.  OR maybe there is actually a ratio of coiled to uncoiled curves in the mixture that similarly creates an over set of minima in the deltaGmix with composition curve. Actually that is an interesting point to try to assess. Somehow the latter seems more appealing, but it does mean rather a large degree of cooperation between residues to decide if o whole coil collapses whilst another remains uncoiled or if the entire systen forms tow different sets of chain that are partially coiled and with remaing wate but each with a different ratio. Both scenarios may occur depending on the volume fractions of each phase - I'll have to look into that!

When it is uncoiled it can considered to be associating with the solvent i.e it is mixed. When it coils it associates with itself rather than the solvent and is demixed.

This type of system has an enthalpy of mixing term that is negative due to H-bonding between the two components of the mixture. However the H-bonding leads to a pairing up of the H-bonding sites on the water and the polymer chain in this case. This is more ordered than the de-mixed state. Thus the Entropy of mixing is negative. In the expression (deltas omitted) G = H -TS we can see that the curve of deltaHmix with composition will thus be a kind of parabola (OK not quite) that is always negative, but the -ve deltaSmix term in the expression is multiplied by -1 and T and hence it forms a similar (but not exactly the same shape) curve pointing in the positive direction. This makes the entorpy and enthalpy terms work in opposite directions to each other, with the entropy term being multiplied by T, but it it the enthalpy term and not the entropy term that causes the mixing here when you consider if deltaGmix is going to be overall negative. his occurs at lower T. Now as T increases the mixture becomes thermally agitated making it harder for the H-bonds to stay pointing in a straight line. This weakens them. Eventually they may break at some temperature around the critical point. Breaking H-bonds will be endothermic so that DeltaHmix gets less negative. At the same time entropy increases due to a bit more disorder - but it never switches sides to point the DeltaSmix with composition curve the other way and to counter ths T in the -TS term getting bigger. So the curve gets bigger and still points positive. Now a funny thin happens when the two curves have similar magnitue, slightly different shape and point in opposite directions. Whe you add then together to make the deltaGmix curve with composition then two minima form in the curve. These two minima are now at the stable compositions that will form on the binodal line on the phase diagram and the.

Actually in this temperature range there is a slightly different deltaGmix with composition curve for each of the temperatures in the lower T region the minima are closer together in composition and at highet T the minima are further appart in composition so the resulting phase diagram is a curve with a minimum at the lower T rather  one with a maximum at a higher T.

It is a common situation in mixtures where the entropy of mixing increases due to association typically when there are H-bonds and the dominating factor when they mix is enthalpy. This enthalpy can be overcome by raising T and the system breaks into twp components and readjusts the composition to a new pair of stable mixtures.

Now in the case of coiling and uncoiling the composition is probably best described by a new form of the polymer more or less coiled than previously, where the remaining water H-bonded to the chain has a ration with the NH residues that matched the equivalent of an new minimum in the deltaGmix with composition curve.  OR maybe there is actually a ratio of coiled to uncoiled curves in the mixture that similarly creates an over set of minima in the deltaGmix with composition curve. Actually that is an interesting point to try to assess. Somehow the latter seems more appealing, but it does mean rather a large degree of cooperation between residues to decide if o whole coil collapses whilst another remains uncoiled or if the entire systen forms tow different sets of chain that are partially coiled and with remaing wate but each with a different ratio. Both scenarios may occur depending on the volume fractions of each phase - I'll have to look into that!

However - the  phase diagram is a bit less than classical as seen for binary mixtures. It seems to have a very extended minimum (see attachment) Yhey only show data up to 25wt% so perhaps it never mixes some way above this concentration. If this is the case then the deltaGmix with composition curve may not have a minimum on the PNIPAM side and it may just drift off to 100% demixed and become totally dehydrated just a little way above the critical point - ie it is a bat like a solid on the PNIPAM side? Yhat would probably explain the difference and simplify the description of composition of the demixed phases. One is like a solid globule and not really sovated any more and the other side of the composition curve .... well although they extrapolate differently it seems that it demixes to close to pure water just a little above the critical point..

Dear Dr. Jonathan Hobley, 

Thank you very much for very easy to understand explanation and your time. The answer bring me to think in a different aspect or view. Thank you again for sharing this knowledge.