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Friction in liquids arises from conservative forces between molecules and atoms. Although the hydrodynamics at the nanoscale is subject of intense research and despite the enormous interest in the non-Markovian dynamics of single molecules and solutes, the onset of friction from the atomistic scale so far could not be demonstrated. Here, we fill this gap based on frequency-resolved friction data from high-precision simulations of three prototypical liquids, including water. Combining with theory, we show that friction in liquids emerges abruptly at a characteristic frequency, beyond which viscous liquids appear as non-dissipative, elastic solids. Concomitantly, the molecules experience Brownian forces that display persistent correlations. A critical test of the generalised Stokes–Einstein relation, mapping the friction of single molecules to the visco-elastic response of the macroscopic sample, disproves the relation for Newtonian fluids, but substantiates it exemplarily for water and a moderately supercooled liquid. The employed approach is suitable to yield insights into vitrification mechanisms and the intriguing mechanical properties of soft materials.

The kinetics of bimolecular reactions in solution depends, among other factors, on intermolecular forces such as steric repulsion or electrostatic interaction. Microscopically, a pair of molecules first has to meet by diffusion before the reaction can take place. In this work, we establish an extension of Doi’s volume reaction model to molecules interacting via pair potentials, which is a key ingredient for interacting-particle-based reaction–diffusion (iPRD) simulations. As a central result, we relate model parameters and macroscopic reaction rate constants in this situation. We solve the corresponding reaction–diffusion equation in the steady state and derive semi- analytical expressions for the reaction rate constant and the local concentration profiles. Our results apply to the full spectrum from well-mixed to diffusion-limited kinetics. For limiting cases, we give explicit formulas, and we provide a computationally inexpensive numerical scheme for the general case, including the intermediate, diffusion-influenced regime. The obtained rate constants decompose uniquely into encounter and formation rates, and we discuss the effect of the potential on both subprocesses, exemplified for a soft harmonic repulsion and a Lennard-Jones potential. The analysis is complemented by extensive stochastic iPRD simulations, and we find excellent agreement with the theoretical predictions.

Finite-size corrections for the static structure factor of a liquid slab with open boundaries
(2020)

The presence of a confining boundary can modify the local structure of a liquid markedly. In addition, small samples of finite size are known to exhibit systematic deviations of thermodynamic quantities relative to their bulk values. Here, we consider the static structure factor of a liquid sample in slab geometry with open boundaries at the surfaces, which can be thought of as virtually cutting out the sample from a macroscopically large, homogeneous fluid. This situation is a relevant limit for the interpretation of grazing-incidence diffraction experiments at liquid interfaces and films. We derive an exact, closed expression for the slab structure factor, with the bulk structure factor as the only input. This shows that such free boundary conditions cause significant differences between the two structure factors, in particular, at small wavenumbers. An asymptotic analysis of this result yields the scaling exponent and an accurate, useful approximation of these finite-size corrections. Furthermore, the open boundaries permit the interpretation of the slab as an open system, supporting particle exchange with a reservoir. We relate the slab structure factor to the particle number fluctuations and discuss conditions under which the subvolume of the slab represents a grand canonical ensemble with chemical potential μ and temperature T. Thus, the open slab serves as a test-bed for the small-system thermodynamics in a μT reservoir. We provide a microscopically justified and exact result for the size dependence of the isothermal compressibility. Our findings are corroborated by simulation data for Lennard-Jones liquids at two representative temperatures.

We consider the theoretical model of Bergmann and Lebowitz for open systems out of equilibrium and translate its principles in the adaptive resolution simulation molecular dynamics technique. We simulate Lennard-Jones fluids with open boundaries in a thermal gradient and find excellent agreement of the stationary responses with the results obtained from the simulation of a larger locally forced closed system. The encouraging results pave the way for a computational treatment of open systems far from equilibrium framed in a well-established theoretical model that avoids possible numerical artifacts and physical misinterpretations.

The simulation of open molecular systems requires explicit or implicit reservoirs of energy and particles. Whereas full atomistic resolution is desired in the region of interest, there is some freedom in the implementation of the reservoirs. Here, a combined, explicit reservoir is constructed by interfacing the atomistic region with regions of point-like, non-interacting particles (tracers) embedded in a thermodynamic mean field. The tracer molecules acquire atomistic resolution upon entering the atomistic region and equilibrate with this environment, while atomistic molecules become tracers governed by an effective mean-field potential after crossing the atomistic boundary. The approach is extensively tested on thermodynamic, structural, and dynamic properties of liquid water. Conceptual and numerical advantages of the procedure as well as new perspectives are highlighted and discussed.

We study the formation of trails in populations of self-propelled agents that make oriented deposits of pheromones and also sense such deposits to which they then respond with gradual changes of their direction of motion. Based on extensive off-lattice computer simulations aiming at the scale of insects, e.g., ants, we identify a number of emerging stationary patterns and obtain qualitatively the non-equilibrium \add{state} diagram of the model, spanned by the strength of the agent--pheromone interaction and the number density of the population. In particular, we demonstrate the spontaneous formation of persistent, macroscopic trails, and highlight some behaviour that is consistent with a dynamic phase transition. This includes a characterisation of the mass of system-spanning trails as a potential order parameter. We also propose a dynamic model for a few macroscopic observables, including the sub-population size of trail-following agents, which captures the early phase of trail formation.