Nonempirical Free Volume Viscosity Model for Alkane Lubricants under Severe Pressures

Free volume theory explains the unusual behavior of viscosity in a non-confluent tissue during morphogenesis

A recent experiment on zebrafish blastoderm morphogenesis showed that the viscosity (η) of a non-confluent embryonic tissue grows sharply until a critical cell packing fraction (ϕS). The increase in η up to ϕS is similar to the behavior observed in several glass-forming materials, which suggests that the cell dynamics is sluggish or glass-like. Surprisingly, η is a constant above ϕS. To determine the mechanism of this unusual dependence of η on ϕ, we performed extensive simulations using an agent-based model of a dense non-confluent two-dimensional tissue. We show that polydispersity in the cell size, and the propensity of the cells to deform, results in the saturation of the available free area per cell beyond a critical packing fraction. Saturation in the free space not only explains the viscosity plateau above ϕS but also provides a relationship between equilibrium geometrical packing to the dramatic increase in the relaxation dynamics.

Combining Molecular Dynamics and Machine Learning to Analyze Shear Thinning for Alkane and Globular Lubricants in the Low Shear Regime

Lubricants with desirable frictional properties are important in achieving an energy-saving society. Lubricants at the interfaces of mechanical components are confined under high shear rates and pressures and behave quite differently from the bulk material. Computational approaches such as nonequilibrium molecular dynamics (NEMD) simulations have been performed to probe the molecular behavior of lubricants. However, the low-shear-velocity regions of the materials have rarely been simulated owing to the expensive calculations necessary to do so, and the molecular dynamics under shear velocities comparable with that in the experiments are not clearly understood. In this study, we performed NEMD simulations of extremely confined lubricants, i.e., two molecular layers for four types of lubricants confined in mica walls, under shear velocities from 0.001 to 1 m/s. While we confirmed shear thinning, the velocity profiles could not show the flow behavior when the shear velocity was much slower than thermal fluctuations. Therefore, we used an unsupervised machine learning approach to detect molecular movements that contribute to shear thinning. First, we extracted the simple features of molecular movements from large amounts of MD data, which were found to correlate with the effective viscosity. Subsequently, the extracted features were interpreted by examining the trajectories contributing to these features. The magnitude of diffusion corresponded to the viscosity, and the location of slips that varied depending on the spherical and chain lubricants was irrelevant. Finally, we attempted to apply a modified Stokes-Einstein relation at equilibrium to the nonequilibrium and confined systems. While systems with low shear rates obeyed the relation sufficiently, large deviations were observed under large shear rates.

Microscopic Origins of the Viscosity of a Lennard-Jones Liquid

Unlike crystalline solids or ideal gases, transport properties remain difficult to describe from a microscopic point of view in liquids, whose dynamics result from complex energetic and entropic contributions at the atomic scale. Two scenarios are generally proposed: one represents the dynamics in a fluid as a series of energy-barrier crossings, leading to Arrhenius-like laws, while the other assumes that atoms rearrange themselves by collisions, as exemplified by the free volume model. To assess the validity of these two views, we computed, using molecular dynamics simulations, the transport properties of the Lennard-Jones fluid and tested to what extent the Arrhenius equation and the free volume model describe the temperature dependence of the viscosity and of the diffusion coefficient at fixed pressure. Although both models reproduce the simulation results over a wide range of pressure and temperature covering the liquid and supercritical states of the Lennard-Jones fluid, we found that the parameters of the free volume model can be estimated directly from local structural parameters, also obtained in the simulations. This consistency of the results gives more credibility to the free volume description of transport properties in liquids.

Molecular Origin of Driving-Dependent Friction in Fluids

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.

How the Shape and Chemistry of Molecular Penetrants Control Responsive Hydrogel Permeability

The permeability of hydrogels for the selective transport of molecular penetrants (drugs, toxins, reactants, etc.) is a central property in the design of soft functional materials, for instance in biomedical, pharmaceutical, and nanocatalysis applications. However, the permeation of dense and hydrated polymer membranes is a complex multifaceted molecular-level phenomenon, and our understanding of the underlying physicochemical principles is still very limited. Here, we uncover the molecular principles of permeability and selectivity in hydrogel permeation. We combine the solution-diffusion model for permeability with comprehensive atomistic simulations of molecules of various shapes and polarities in a responsive hydrogel in different hydration states. We find in particular that dense collapsed states are extremely selective, owing to a delicate balance between the partitioning and diffusivity of the penetrants. These properties are sensitively tuned by the penetrant size, shape, and chemistry, leading to vast cancellation effects, which nontrivially contribute to the permeability. The gained insights enable us to formulate semiempirical rules to quantify and extrapolate the permeability categorized by classes of molecules. They can be used as approximate guiding ("rule-of-thumb") principles to optimize penetrant or membrane physicochemical properties for a desired permeability and membrane functionality.

Transport coefficients of model lubricants up to 400 MPa from molecular dynamics

In this paper, the predictive power of molecular dynamics methods is demonstrated for the cases of model paraffinic and aromatic lubricant liquids at pressures up to 400 MPa. The shear viscosity and self-diffusion coefficients are calculated for 2,2,4-trimethylpentane (C₈H₁₈) at 298 K and 1,1-diphenylethane (C₁₄H₁₄) at 333 K. Three force fields with different levels of accuracy are compared by the ability to predict the experimental data. The Stokes-Einstein correlation between viscosity and self-diffusion is demonstrated for both compounds.