Statistical thermodynamics in reversible clustering of gold nanoparticles. A first step towards nanocluster heat engines

Abstract

A statistical thermodynamics variational criterion is propounded to study thermal hysteresis in reversible clustering of gold (Au) nanoparticles. Experimentally, a transient equilibrium mapping analysis is employed to characterize it thermodynamically, further measurements being performed at the nanostructural and electrochemical levels (UV-Vis-NIR spectra, SLS/SAXS, zeta potential). Theoretically, it is successfully interpreted as a thermodynamic cycle, prompting that nanoclusters has potential to produce useful work from heat and paving the way to nanoclustering heat engines. By taking into account the virial expansion of hysteretic pressure, an entropy measure is deduced for a dilute system with given virial coefficients. This allows us to figure out the role of relevant interparticle potential parameters (i.e. surface potential, nanoparticle size, Debye's length, Hamaker energy) in both isothermal and isochoric variations at the onset of hysteresis. Application to spherical Au nanoparticles in watery salt solution (NaCl) is developed when an ad-hoc (DLVO) pairwise potential governs the second virial coefficient at the nanoscale. In particular, the variational criterion predicts a pressure drop between heating and cooling paths which is likely at the base of some energy redistribution (e.g. ordering/restructuring of electric double layers). We found an integrating factor that is able to numerically predict the existence of a critical value for the initial salt concentration maximizing the hysteretic area, and the effect of nanoparticle size on the cycle extent.