Molecular Origin of Driving-Dependent Friction in Fluids

Abstract

The friction coefficient of fluids may become a function of the velocity at increased external driving. This non-Newtonian behavior is of general theoretical interest and of great practical importance, for example, for the design of lubricants. Although the effect has been observed in large-scale atomistic simulations of bulk liquids, its theoretical formulation and microscopic origin are not well understood. Here, we use dissipation-corrected targeted molecular dynamics, which pulls apart two tagged liquid molecules in the presence of surrounding molecules, and analyze this nonequilibrium process via a generalized Langevin equation. The approach is based on a second-order cumulant expansion of Jarzynski’s identity, which is shown to be valid for fluids and therefore allows for an exact computation of the friction profile as well of the underlying memory kernel. We show that velocity-dependent friction in fluids results from an intricate interplay of near-order structural effects and the non-Markovian behavior of the friction memory kernel. For complex fluids such as the model lubricant C40H82, the memory kernel exhibits a stretched-exponential long-time decay, which reflects the multitude of timescales of the system.

Ligand Unbinding Pathway and Mechanism Analysis Assisted by Machine Learning and Graph Methods

“…For thermodynamic integration (TI), 71 we saved N = 21 structural snapshots at equidistant positions over the 2 nm pulling range and for each carried out 10 ns of constraint simulations with setting v c = 0 m/s. For the last 5 ns, we calculated the time average of constraint force ⟨f c (x i )⟩ and from them a free energy profile (16) with spacing Δx = 0.1 nm between the 21 snapshots.…”

“…The dcTMD method is based on a second-order cumulant expansion of the Jarzynski identity 21,22 and thus requires a normally distributed W. While this approximation holds for isotropic cases such as liquids, 16 we have found an imprudent application to biomolecular simulation data to result in a significant overestimation of friction and a subsequent underestimation of the potential of mean force. 17,18 Separating trajectories into ensembles that share similar characteristics in their dynamics during unbinding and calculating potentials of mean forces for each ensemble separately recovers a normally distributed W for each ensemble and removes the overestimation artifact.…”

“…13,14 In a similar vein, we have developed the dissipationcorrected targeted MD (dcTMD) method. 15,16 Enforcing a constant unbinding velocity by a constraint force, dcTMD allows the calculation of potentials of mean force (PMF) ΔG and friction profiles Γ for unbinding paths of protein−host complexes 17,18 from the resulting unbinding work W. Besides providing details on the unbinding mechanism, these fields can further serve as inputs for the numerical integration of a Markovian Langevin equation 19,20 to reach simulation time scales within a biomedically relevant range of minutes and more.…”

“…Protein–ligand complex formation and dissociation − are a current focus in the fields of biomolecular simulations and nonequilibrium statistical mechanics, as understanding their microscopic details is of considerable pharmaceutical interest. , Due to the time scales involved being several magnitudes outside of the capabilities of common all-atom molecular dynamics (MD) simulation methods, a range of biased simulation methods have been developed to enforce ligand unbinding such as infrequent metadynamics, , random acceleration MD, , scaled MD, − or weighted ensemble MD. , In a similar vein, we have developed the dissipation-corrected targeted MD (dcTMD) method. , Enforcing a constant unbinding velocity by a constraint force, dcTMD allows the calculation of potentials of mean force (PMF) Δ G and friction profiles Γ for unbinding paths of protein–host complexes , from the resulting unbinding work W . Besides providing details on the unbinding mechanism, these fields can further serve as inputs for the numerical integration of a Markovian Langevin equation , to reach simulation time scales within a biomedically relevant range of minutes and more.…”

Pair-Reaction Dynamics in Water: Competition of Memory, Potential Shape, and Inertial Effects

“…As simple model systems, we consider the dissociation and association kinetics of two different pair reactions in water, NaCl and methane, which exhibit drastically different hydration properties. Ions are favorably dissolved in water by the formation of a strongly ordered hydration shell, − whereas nonpolar small objects such as methane are repelled from water and induce strong water–water hydrogen bonding in their hydration shell. − In fact, NaCl ion-pair dissociation in water has been widely studied, − ,,,,,− and the failure of a Markovian kinetic model along a one-dimensional reaction coordinate, ,,, the relevance of inertial and memory effects, ,,, has been demonstrated. In contrast, the reaction dynamics of hydrophobic molecules has received less attention.…”