Density functional analysis of atomic force microscopy in a dense fluid

Abstract

We present a density functional (DF) analysis for the entropic force in Atomic Force Microscopy (AFM) across the layers of a dense fluid. Previous theoretical analysis, based on the ideal gas entropy, was apparently supported by the similarity in the oscillatory decay for the force and density profile. We point out that such similarity is a generic DF result, which carries no information on the interface, since the decaying mode is characteristic of the bulk fluid correlation. The truly interfacial information, from the layering measured by AFM, comes in its amplitude and not in the decay mode. With our rigorous study of a simple hard sphere model, we find semiempirical clues to disentangle the role of the tip radius and to relate the amplitude of the molecular layering to the oscillatory force on the AFM tip.

Noether's Theorem in Statistical Mechanics

“…DFT constitutes a powerful modern framework for the description of a broad range of interfacial, adsorption, solvation, and phase phenomenology in complex systems [9,[18][19][20]. Examples of recent pivotal applications include the treatments of hydrophobicity [21][22][23][24][25][26][27] and of drying [24][25][26], electrolytes near surfaces [28], dense fluid structuring as revealed in atomic force microscopy [29], thermal resistance of liquid-vapor interfaces [30], and layered freezing in confined colloids [31]. Xu and Rice [31] have used the sum rules of Refs.…”

Power functional theory for Newtonian many-body dynamics

“…These have addressed e.g. atomically resolved three-dimensional structures of electrolytes near a solid surface (Hernández-Muñoz et al, 2019;Martin-Jimenez et al, 2016), solvation phenomena in water 1 There are fascinating counterexamples, where the dynamics of a single particle already are exceedingly rich, such as in magnetically driven topological transport (Loehr et al, 2016(Loehr et al, , 2018 and in active (Maes, 2020) and viscoeslastic (Berner et al, 2018) solvents. 2 Accessible and compact descriptions of electronic DFT are given by, e.g., Kohn (1999), Jones and Gunnarsson (2015), and Jones (2015).…”

Fluctuation profiles in inhomogeneous fluids

“…Remarkably, χ T (x) also displays a very strong response near each wall; recall that this quantity is indicative of entropic correlation effects, cf. (6). Notably, the entropic fluctuations are much increased when the full temperature dependence is taken into account, cf.…”

“…Inhomogeneous fluids comprise a large class of relevant and fundamental physical systems, in which a broad range of phenomena and underlying mechanisms occur [1][2][3]. Examples include the behaviour of fluids in narrow confinement [4], electrolytes near surfaces [5], dense fluid structuring as revealed in atomic force microscopy [6], thermal resistance of liquid-vapor interfaces [7], nonequilibrium steady states in active [8,9], sheared [10] and driven [11] fluids, as well as the orientation-resolved ordering of water around complex solutes [12][13][14][15][16]. The average one-body density distribution, or short the density profile, is used as the standard tool for analyzing such inhomogeneous systems.…”

“…The form (5) has been given before in Refs. [18,20], while ( 7) is obtained by inserting the explicit Boltzmann form of Ψ into (6). Crucially (7) can be carried out via importance sampling in particlebased simulations (which is hampered in (6) due to the poor direct accessibility of ln Ψ).…”