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Entropy, Free Energy, and the Second Law of Thermodynamics
Published in Jeffrey Olafsen, Sturge’s Statistical and Thermal Physics, 2019
I recently was teaching my young son that every square is a special sort of rectangle, but not every rectangle is a square. We need to step back carefully from our macroscopic understanding of entropy that erroneously leads us to think of it synonymously as heat. Heat flow carries with it entropy, but not every entropy change involves heat. Recall our Carnot engine as a set of processes that allow us to extract work from (at least) two heat baths of different temperatures. We reverse the Carnot cycle and can instead just as well think of doing work to return ourselves to the same initial state of the system described by the state variables U,P,V,S,&T. Work must be done to change the entropy of the cycle back to its initial value. I walk into a room of temperature T with a box of argon atoms, also at temperature T. The box of argon atoms (gas) is already in thermal equilibrium with the room. I open the box and allow the argon atoms to mix with the air in the room. I close the box—the system (of the room plus the box) is not in its initial state. To restore the system to its initial state in phase space, I would have to walk through the room with molecular tweezers and capture every argon atom and air molecule and re-order the system with all the argon in the box and all the air in the room. Approximating both gases as ideal gases, the energy of the system never changed because the whole process occurred at temperature T. So the work I did of capturing and sorting the atoms didn’t go into changing the energy of the system, but to restoring the entropy of the system to its initial state value. There was never a flow of heat in the system, but there was a change in entropy.
Two-photon absorption in host-guest complexes
Published in Molecular Physics, 2020
Md. Mehboob Alam, Kenneth Ruud
Another well-known type of host molecules that can host aromatic guest molecules are molecular tweezers [20]. These were first synthesised in 1978 by Whitlock and Chen and are characterised by two more or less rigid and flat aromatic pincers separated from each other by a covalently bonded spacer [20]. Based on their study, Whitlock and Chen concluded that the binding of an aromatic guest molecule in molecular tweezers is enhanced if two rigid pincers in the latter are in syn conformation and separated from each other by a distance of 7 Å [20]. Based on this strategy, several other tweezer molecules have been synthesised and studied [21–23]. Such systems have also been studied and explored theoretically. Recently, in 2012, Jacquemin et al. [24] used dispersion-corrected density functionals to study the interaction of small organic molecules with a moleular tweezer. In another theoretical study, Grimme et al. [25,26] studied the geometries and binding energies of molecular tweezers and clips with six different aliphatic and aromatic substrates. In 2009, Chakrabarti and Ruud theoretically studied the two-photon absorption (TPA) process in the molecular tweezer-TNF host-guest system [27]. They found that tweezer-TNF display a very large TPA cross-section as compared to the constituents. In another work, the same authors theoretically studied the TPA process in yet another host-guest system – fullerene bound in a buckycatcher [28]. In this complex, they observed that one of the constituents (buckycatcher) has much larger TPA cross-section than the complex itself. Nevertheless, the complex showed fairly large TPA cross sections at desirable near-IR wavelengths. This was later confirmed experimentally [29]. Several other theoretical studies have also been conducted on systems having molecular tweezers as host and other organic molecules as guest [30–33]. All these works clearly indicate that molecular properties change when two systems combine together to form a host-guest system. However, questions such as how the nature of the host and guest molecules as electron donor and/or acceptor influences the overall molecular properties such as TPA has not yet been addressed. To fill this gap, in the present work we study the TPA process in a number of host-guest complexes. We will also study the role of the donor/acceptor nature of the host and guest molecules on the two-photon absorption (TPA) process in the resultant host-guest systems.