Timeline for Why don’t ALL polymers collapse even when their compact state would clearly be favoured in terms of having a lower Helmholtz free energy?
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| Jun 10, 2019 at 11:54 | vote | accept | Confinement | ||
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| Jun 9, 2019 at 19:01 | vote | accept | Confinement | ||
| Jun 10, 2019 at 9:53 | |||||
| Jun 9, 2019 at 18:28 | answer | added | user197851 | timeline score: 0 | |
| Jun 9, 2019 at 17:50 | comment | added | Confinement | @LonelyProf. (To your first point: Ah yes, of course the collapse occurs below the theshold temperature and not above!) To your second point: But why exactly do the other 1/5 of the polymers at very high temperatures not also collapse if this would still lower the overall Helmholtz free energy? Even if their favoured only by a small margin, this shouldn't this eventually be the equilibrium configuration? | |
| Jun 9, 2019 at 17:44 | comment | added | user197851 | OK, I think I see two points of confusion. 1. The closed form has a lower Helmholtz function below a threshold temperature, not (as you just said) above. This is because the closed form has a lower energy, which dominates the entropy term at low $T$. This is the collapsed form. 2. Above the threshold temperature, you see predominantly the expanded form. At very high $T$, the different energies become almost unimportant, and the situation simply reflects the number of available states. This is dominated by entropy. | |
| Jun 9, 2019 at 17:35 | comment | added | Confinement | @LonelyProf. Thanks for pointing out my mistake! My question is: If the closed form of the polymers if favoured in terms of having a lower Helmholtz free energy above a certain threshold temperature, why do not ALL polymers collapse? When considering the Boltzmann distribution one finds that only 4/5 of the polymers seem to collapse. However, since the thermodynamic equilibrium under the conditions of constant temperature and volume corresponds to a minimum of F, I do not understand why this is the case. | |
| Jun 9, 2019 at 17:31 | history | edited | Confinement | CC BY-SA 4.0 |
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| Jun 9, 2019 at 17:29 | comment | added | user197851 | Your question contains some incorrect statements (you say the open configuration has lower entropy and the closed configuration has higher entropy, when the opposite is true) and does not make clear what the precise problem is. Polymer collapse (on lowering temperature or solvent quality) is a quite general phenomenon. Can you clarify exactly what you are not understanding? | |
| Jun 9, 2019 at 16:53 | history | edited | Confinement |
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| Jun 9, 2019 at 15:42 | comment | added | Confinement | @Jahan Claes. I do not understand why not ALL polymers would collapse, if the process of collapsing clearly lowers the Helmholtz free energy of the overall system. The two methods both predict that the open configuration is favoured at high temperatures, however in my mind they disagree on the exact distribution between open and closed states. | |
| Jun 9, 2019 at 15:39 | comment | added | Confinement | @Cort Ammon. Right cinematics certainly play a role when doing a real life experiment. However, here we make statements about the thermodynamic equilibrium. At no point are we concerned how fast this equilibrium will be achieved.. | |
| Jun 9, 2019 at 15:38 | comment | added | Jahan Claes | I'm not sure I understand the contradiction. The Helmholtz free energy predicts that you should have an open configuration above a critical temperature. The Boltzmann distribution predicts you should have an open configuration as $T$ gets large. Both say that open configurations should happen at high temperatures, no? Can you explain where you think the results disagree? | |
| Jun 9, 2019 at 15:36 | comment | added | Cort Ammon | You appear to have a pretty solid background on this, so forgive me if this is insultingly oversimplified, but could this just be a question of kinematics? Many things stay in a higher energy state for a very long time before their eventual collapse. | |
| Jun 9, 2019 at 15:29 | history | edited | Confinement | CC BY-SA 4.0 |
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| Jun 9, 2019 at 15:25 | review | First posts | |||
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| Jun 9, 2019 at 15:21 | history | asked | Confinement | CC BY-SA 4.0 |