D. M. Heyes

Pressure dependence of confined liquid behavior subjected to boundary-driven shear

Non-equilibrium molecular dynamics simulations of boundary-driven sheared Lennard-Jones liquids at variable pressure up to 5 GPa (for argon) reveal a rich out-of-equilibrium phase behavior with a strong degree of shear localization. At the lowest apparent shear rate considered (wall speed ~1 m s(-1)) the confined region is an homogeneously sheared solid (S) with no slip at the walls. This transforms at higher shear rates to a non-flowing plug with slip at the walls, referred to as the plug slip (PS) state. At higher shear rate a central localized (CL) state formed in which the shear gradient was localized in the center of the film, with the rest of the confined sample in a crystalline state commensurate with the wall lattice. The central zone liquidlike region increased in width with shear rate. A continuous rounded temperature profile across the whole system reflects strong dynamical coupling between the wall and confined region. The temperature rise in the confined film is consistent with the Brinkman number. The transition from the PS to CL states typically occurred at a wall speed near where the shear stress approached a critical value of ~3% of the shear modulus, and also near the peak in the traction coefficient, μ. The peak traction coefficient values computed, ~0.12-0.14 at 1000 MPa agree with those found for traction fluids and occur when the confined liquid is in the PS and CL states. At low wall speeds slip can occur at one wall and stick at the other. Poorly wetting liquids manifest long-lived asymmetries in the confined liquid properties across the system, and a shift in solid-liquid phase co-existence to higher shear rates. A non-equilibrium phase diagram based on these results is proposed. The good agreement of the tribological response of the Lennard-Jones fluid with that of more complicated molecular systems suggests that a corresponding states scaling of the tribological behavior could apply.

The equivalence between volume averaging and method of planes definitions of the pressure tensor at a plane.

It is shown analytically that the method of planes (MOP) [Todd, Evans, and Daivis, Phys. Rev. E 52, 1627 (1995)] and volume averaging (VA) [Cormier, Rickman, and Delph, J. Appl. Phys. 89, 99 (2001)] formulas for the local pressure tensor, P(α, y)(y), where α ≡ x, y, or z, are mathematically identical. In the case of VA, the sampling volume is taken to be an infinitely thin parallelepiped, with an infinite lateral extent. This limit is shown to yield the MOP expression. The treatment is extended to include the condition of mechanical equilibrium resulting from an imposed force field. This analytical development is followed by numerical simulations. The equivalence of these two methods is demonstrated in the context of non-equilibrium molecular dynamics (NEMD) simulations of boundary-driven shear flow. A wall of tethered atoms is constrained to impose a normal load and a velocity profile on the entrained central layer. The VA formula can be used to compute all components of P(αβ)(y), which offers an advantage in calculating, for example, P(xx)(y) for nano-scale pressure-driven flows in the x-direction, where deviations from the classical Poiseuille flow solution can occur.

Control-volume representation of molecular dynamics.

A molecular dynamics (MD) parallel to the control volume (CV) formulation of fluid mechanics is developed by integrating the formulas of Irving and Kirkwood [J. Chem. Phys. 18, 817 (1950)] over a finite cubic volume of molecular dimensions. The Lagrangian molecular system is expressed in terms of an Eulerian CV, which yields an equivalent to Reynolds transport theorem for the discrete system. This approach casts the dynamics of the molecular system into a form that can be readily compared to the continuum equations. The MD equations of motion are reinterpreted in terms of a Lagrangian-to-control-volume (LCV) conversion function ϑ(i) for each molecule i. The LCV function and its spatial derivatives are used to express fluxes and relevant forces across the control surfaces. The relationship between the local pressures computed using the volume average [Lutsko, J. Appl. Phys. 64, 1152 (1988)] techniques and the method of planes [Todd et al., Phys. Rev. E 52, 1627 (1995)] emerges naturally from the treatment. Numerical experiments using the MD CV method are reported for equilibrium and nonequilibrium (start-up Couette flow) model liquids, which demonstrate the advantages of the formulation. The CV formulation of the MD is shown to be exactly conservative and is, therefore, ideally suited to obtain macroscopic properties from a discrete system.

The method of planes pressure tensor for a spherical subvolume

Various formulas for the local pressure tensor based on a spherical subvolume of radius, R, are considered. An extension of the Method of Planes (MOP) formula of Todd et al. [Phys. Rev. E 52, 1627 (1995)] for a spherical geometry is derived using the recently proposed Control Volume formulation [E. R. Smith, D. M. Heyes, D. Dini, and T. A. Zaki, Phys. Rev. E 85, 056705 (2012)]. The MOP formula for the purely radial component of the pressure tensor is shown to be mathematically identical to the Radial Irving-Kirkwood formula. Novel offdiagonal elements which are important for momentum conservation emerge naturally from this treatment. The local pressure tensor formulas for a plane are shown to be the large radius limits of those for spherical surfaces. The radial-dependence of the pressure tensor computed by Molecular Dynamics simulation is reported for virtual spheres in a model bulk liquid where the sphere is positioned randomly or whose center is also that of a molecule in the liquid. The probability distributions of angles relating to pairs of atoms which cross the surface of the sphere, and the center of the sphere, are presented as a function of R. The variance in the shear stress calculated from the spherical Volume Averaging method is shown to converge slowly to the limiting values with increasing radius, and to be a strong function of the number of molecules in the simulation cell.

Rounded stretched exponential for time relaxation functions

A rounded stretched exponential function is introduced, C(t)=exp{(tau(0)/tau(E))(beta)[1-(1+(t/tau(0))(2))(beta/2)]}, where t is time, and tau(0) and tau(E) are two relaxation times. This expression can be used to represent the relaxation function of many real dynamical processes, as at long times, t>>tau(0), the function converges to a stretched exponential with normalizing relaxation time, tau(E), yet its expansion is even or symmetric in time, which is a statistical mechanical requirement. This expression fits well the shear stress relaxation function for model soft soft-sphere fluids near coexistence, with tau(E)<<tau(0). The function gives the correct limits at low and high frequency in Cole-Cole plots for dielectric and shear stress relaxation (both the modulus and viscosity forms). It is shown that both the dielectric spectra and dynamic shear modulus imaginary parts approach the real axis with a slope equal to 0 at high frequency, whereas the dynamic viscosity has an infinite slope in the same limit. This indicates that inertial effects at high frequency are best discerned in the modulus rather than the viscosity Cole-Cole plot. As a consequence of the even expansion in time of the shear stress relaxation function, the value of the storage modulus derived from it at very high frequency exceeds that in the infinite frequency limit (i.e., G(infinity)).

Non-equilibrium phase behavior and friction of confined molecular films under shear: a non-equilibrium molecular dynamics study

The phase behavior of a confined liquid at high pressure and shear rate, such as is found in elastohydrodynamic lubrication, can influence the traction characteristics in machine operation. Generic aspects of this behavior are investigated here using Non-equilibrium Molecular Dynamics (NEMD) simulations of confined Lennard-Jones (LJ) films under load with a recently proposed wall-driven shearing method without wall atom tethering [C. Gattinoni et al., Phys. Rev. E 90, 043302 (2014)]. The focus is on thick films in which the nonequilibrium phases formed in the confined region impact on the traction properties. The nonequilibrium phase and tribological diagrams are mapped out in detail as a function of load, wall sliding speed, and atomic scale surface roughness, which is shown can have a significant effect. The transition between these phases is typically not sharp as the external conditions are varied. The magnitude of the friction coefficient depends strongly on the nonequilibrium phase adopted by the confined region of molecules, and in general does not follow the classical friction relations between macroscopic bodies, e.g., the frictional force can decrease with increasing load in the Plug-Slip (PS) region of the phase diagram owing to structural changes induced in the confined film. The friction coefficient can be extremely low (∼0.01) in the PS region as a result of incommensurate alignment between a (100) face-centered cubic wall plane and reconstructed (111) layers of the confined region near the wall. It is possible to exploit hysteresis to retain low friction PS states well into the central localization high wall speed region of the phase diagram. Stick-slip behavior due to periodic in-plane melting of layers in the confined region and subsequent annealing is observed at low wall speeds and moderate external loads. At intermediate wall speeds and pressure values (at least) the friction coefficient decreases with increasing well depth of the LJ potential between the wall atoms, but increases when the attractive part of the potential between wall atoms and confined molecules is made larger.

Communication: Simple liquids' high-density viscosity.

This paper argues that the viscosity of simple fluids at densities above that of the triple point is a specific function of temperature relative to the freezing temperature at the density in question. The proposed viscosity expression, which is arrived at in part by reference to the isomorph theory of systems with hidden scale invariance, describes computer simulations of the Lennard-Jones system as well as argon and methane experimental data and simulation results for an effective-pair-potential model of liquid sodium.

A localized momentum constraint for non-equilibrium molecular dynamics simulations

A method which controls momentum evolution in a sub-region within a molecular dynamics simulation is derived from Gausss principle of least constraint. The technique for localization is founded on the equations by Irving and Kirkwood [J. Chem. Phys. 18, 817 (1950)] expressed in a weak form according to the control volume (CV) procedure derived by Smith et al. [Phys. Rev. E. 85, 056705 (2012)]. A term for the advection of molecules appears in the derived constraint and is shown to be essential in order to exactly control the time evolution of momentum in the subvolume. The numerical procedure converges the total momentum in the CV to the target value to within machine precision in an iterative manner. The localized momentum constraint can prescribe essentially arbitrary flow fields in non-equilibrium molecular dynamics simulations. The methodology also forms a rigorous mathematical framework for introducing coupling constraints at the boundary between continuum and discrete systems. This functionality is demonstrated with a boundary-driven flow test case.

Polyelectrolyte pKa from experiment and molecular dynamics simulation

The pKa of a polyelectrolyte has been determined experimentally by potentiometric titration and computed using Molecular Dynamics (MD) constant pH (CpH) methodology, which allows the pKa of each titratable site along the polymer backbone to be determined separately, a procedure which is not possible by current experimental techniques. By using experimental results within the CpHMD method, the simulations show that the protonation states of neighbouring residues are anti-correlated so that the charges are well-separated. As found with previous simulation studies on model polyelectrolytes, the end groups are predicted to be the most acidic. CpHMD is shown to result in distinct polymer conformations, brought about by the range of protonation states changes along the polymer; this can now be used in the design of pH-responsive polymers for, amongst other applications, additive formulation and drug delivery devices.

Molecular Dynamics Studies of Overbased Detergents on a Water Surface

Molecular dynamics (MD) simulations are reported of model overbased detergent nanoparticles on a model water surface which mimic their behavior on a Langmuir trough or large water droplet in engine oil. The simulations predict that the structure of the nanoparticle on a water surface is different to when it is immersed in a bulk hydrophobic solvent. The surfactant tails are partly directed out of the water, while the carbonate core maximizes its extent of contact with the water. Umbrella sampling calculations of the potential of mean force between two particles showed that they are associated with varying degrees with a maximum binding free energy of ca. 10 kBT for the salicylate stabilized particle, ca. 8 kBT for a sulfurized alkyl phenate stabilized particle, and ca. 5 kBT for a sulfonate stabilized particle. The differences in the strength of attraction depend on the proximity of nearest approach and the energy penalty associated with the disruption of the hydration shell of water molecules around the calcium carbonate core when the two particles approach. This is greatest for the sulfonate particle, which partially loses the surfactant ions to the solution, and least for the salicylate, which forms the weakest water cage. The particles are separated by a water hydration layer, even at the point of closest approach.