Universal scaling law for polar and non-polar liquids in the bulk and nanotube confinement

It is hypothesized that the kinetics of liquid phases is controlled by the so called ‘cage effect’ i.e. each atom is curbed in a cage formed by immediate neighbors, endured with local density fluctuations. This line of... [ view full abstract ]

It is hypothesized that the kinetics of liquid phases is controlled by the so called ‘cage effect’ i.e. each atom is curbed in a cage formed by immediate neighbors, endured with local density fluctuations. This line of thinking has been successively reconnoitered to estimate the liquid state dynamics from the static structure, determined straight in the framework of renormalized kinematic schemes and through entropy like thermodynamic quantities. Most of the previous studies describe the diffusion mechanism based on Enskog theory. However, Enskog theory, in its existing form, is fully established only for the hard-sphere fluid and to utilize this for real systems, a hard sphere model is required, which is based on the approach that the diffusion in the systems are originated by binary collisions without consideration of long range interactions. Also, the structural diversity of liquid systems and their dependence specific to the minor details of intermolecular and intra-molecular interactions, impose a fundamental limitation to adequately describe real systems, therefore the implication of Enskog theory to the molecular systems has become a real challenge. Furthermore, if molecules are confined within nanoscale geometries, they do not follow continuum theory but form a cascade of anomalies. Since, nanotube confined fluids are known to show very peculiar properties, it would be very demanding to establish the scaling relation for these systems. Besides this, the scaling relation for nanotube confinement would be of great practical use as they relate to many biological channels such as aquaporins, proton pumps and protein cavities in lysozymes etc. Therefore, the pioneering work put forward in this direction by Dzugutov through a universal scaling law which connects the atomic diffusivity with the excess entropy. We formulate here a scaling law linking the diffusivity and excess entropy of molecular liquids and liquid mixtures both in bulk and under nano-confinement , which is shown to be universal and also reproduce the earlier scaling law for atomic diffusion. The excess entropy which is central to this universal scaling law has been estimated using robust and fast 2PT method, where density of states (DOS) has been employed. It is worth mentioning that the density of states may be obtained from power spectrum of diffusing liquids using scattering experiments and thus plays the similar role like radial distribution function. The transferability of the proposed scaling relation has been tested w.r.t. the molecular fluid as well as changed nanoscale geometries. Most importantly, the present work link the dynamic quantities like the self-diffusion coefficient which are very difficult to measure accurately by experiments, especially for CNT like one dimensional nano confinement with the experimentally more accessible thermodynamic quantities.  Hereby, this work attract a strong scientific and technological interest both w.r.t. theoretical as well as experimental implications.