Free Energy Profile for the Complete Transport of Nonpolar Molecules through a Carbon Nanotube

Gas molecules or weakly interacting molecules are commonly observed to diffuse through and fill space. Therefore, when the molecules initially confined in one compartment are allowed to move through a channel into another empty compartment, we expect that some molecules will be transported into the initially empty compartment. In this work, we thermodynamically analyze this transport process using a simple model consisting of graphene plates, a carbon nanotube (CNT), and nonpolar molecules that are weakly interacting with each other. Specifically, we calculate the free energy change, or the potential of mean force (PMF), as the molecules are transported from one compartment to another compartment. The PMF profile clearly exhibits a global minimum, or a free energy well, at the state wherein the molecules are evenly distributed over the two compartments. To better understand the thermodynamic origin of the well, we calculate the energetic and entropic contributions to the formation of the well, and we show that the entropic change is responsible for it and is the driving force for transport. Our work not only enables a fundamental understanding of the thermodynamic nature of the transport of weakly interacting molecules with molecular details, but also provides a method for calculating the free energy change during transport between two separate spaces connected by a nanochannel.